Matlab-Programs/symMinimization.m

+
+function [G, angle, Type, kappa] = symMinimization(print_Input,print_statPoint,print_Output,make_FunctionPlot, InputPath) %(Q_hom,B_eff)
+
+
+syms v1 v2 q1 q2 q3 q12 b1 b2 b3
+
+
+% -------- Options ----------
+% % print_Input = false;  %effective quantities
+% print_Input = true;
+% % print_statPoint = false;
+% print_statPoint = true;
+% print_Minimizer = true;
+% % make_FunctionPlot = false;
+% make_FunctionPlot = true;
+
+print_Uniqueness = false;         
+check_StationaryPoints = false;   % could be added to Input-Parameters..
+compare_with_Classification = false;  %maybe added later --- 
+
+
+%fprintf('Functions to be minimized:')
+f_plus(v1,v2,q1,q2,q3,q12,b1,b2,b3) = q1*v1^4 + q2*v2^4+2*q3*v1^2*v2^2-2*(q1*b1*v1^2+ q2*b2*v2^2+sqrt(2)*q3*b3*v1*v2)...
+                                        + q12*(v1^2*v2^2-b2*v1^2-b1*v2^2+b1*b2);
+f_minus(v1,v2,q1,q2,q3,q12,b1,b2,b3) = q1*v1^4 + q2*v2^4+2*q3*v1^2*v2^2+2*(q1*b1*v1^2+ q2*b2*v2^2+sqrt(2)*q3*b3*v1*v2)...
+                                        + q12*(v1^2*v2^2+b2*v1^2+b1*v2^2+b1*b2);
+
+
+% ---- Fix parameters
+
+
+% Epsilon used:
+epsilon = 1e-8;
+
+
+if ~exist('InputPath','var')
+     % third parameter does not exist, so default it to something
+      absPath = "/home/klaus/Desktop/DUNE/dune-microstructure/outputs";
+ end
+
+
+% 1. Import effective quantities from CellSolver-Code:
+%read as sparse Matrix...
+try %absolutePath
+    Qmat = spconvert(load(absPath + '' + "/QMatrix.txt"));
+    Bmat = spconvert(load(absPath + '' + "/BMatrix.txt"));
+%     fprintf('Use absolute Path')
+catch ME  % use relativePath
+    Qmat = spconvert(load('../outputs/QMatrix.txt'));
+    Bmat = spconvert(load('../outputs/BMatrix.txt'));
+%     fprintf('Use relative Path')
+end
+%convert to full matrix... 
+Qmat = full(Qmat);
+Bmat = full(Bmat);
+
+
+
+
+% --- TODO CHECK: assert if Q is orthotropic ???  check ifq13=q31=q23=q32= 0 ?
+
+
+if print_Input
+    fprintf('effective quadratic form:')
+    Qmat
+    fprintf('effective prestrain')
+    Bmat
+    
+    % check if Q is (close to..) symmetric
+    % könnte Anti-symmetric part berechnen und schauen dass dieser klein?
+    % Test: issymmetric(Qmat) does not work for float matrices?
+    % symmetric part 0.5*(Qmat+Qmat')
+    % anti-symmetric part 0.5*(Qmat-Qmat')
+    if norm(0.5*(Qmat-Qmat'),'fro') < 1e-8
+        fprintf('Qmat (close to) symmetric \n')
+        norm(0.5*(Qmat-Qmat'),'fro') % TEST
+    else
+        fprintf('Qmat not symmetric \n')
+    end
+    
+    
+    % Check if B_eff is diagonal this is equivalent to b3 == 0
+    if abs(Bmat(3)) < 1e-8
+        fprintf('B_eff is diagonal (b3 == 0) \n')
+    else
+        fprintf('B_eff is  NOT diagonal (b3 != 0)  \n')
+    end
+end
+
+
+
+
+% CAST VALUES TO SYM FIRST? This is done anyway..
+% % Substitute effective quantitites      
+f_plus = subs(f_plus,{q1, q2, q3, q12, b1, b2, b3}, {Qmat(1,1), Qmat(2,2), Qmat(3,3), Qmat(1,2), ...
+                                                     Bmat(1), Bmat(2), Bmat(3)});
+
+f_minus = subs(f_minus,{q1, q2, q3, q12, b1, b2, b3}, {Qmat(1,1), Qmat(2,2), Qmat(3,3), Qmat(1,2), ...
+                                                     Bmat(1), Bmat(2), Bmat(3)});
+
+
+% Compute the Gradients 
+df_plusx = diff(f_plus,v1);
+df_plusy = diff(f_plus,v2);
+df_minusx = diff(f_minus,v1);
+df_minusy = diff(f_minus,v2);
+
+% Setup Equations Grad(f) = 0 
+eq1 = df_plusx == 0;
+eq2 = df_plusy == 0;
+eqns_plus = [eq1, eq2];
+eq3 = df_minusx == 0;
+eq4 = df_minusy == 0;
+eqns_minus = [eq3, eq4];
+
+% -------  Symbolically Solve Equations: 
+% More robust (works even for values b_3 ~ 1e-08 ): 
+S_plus = solve(eqns_plus,v1,v2,'MaxDegree' , 5);  
+S_minus = solve(eqns_minus,v1,v2,'MaxDegree' , 5);
+
+A_plus = S_plus.v1;
+B_plus = S_plus.v2;
+A_minus = S_minus.v1;
+B_minus = S_minus.v2;
+
+if check_StationaryPoints
+    %---------- TEST if Grad(f) = 0 ---------------------
+    fprintf('Testing equation grad(f) = 0  with stationary points')
+    for i = 1:size(A_plus,1)
+        fprintf('Testing %d.point (f_plus): ',i )
+        [ double(subs(subs(df_plusx,v1,A_plus(i)),v2,B_plus(i))), double(subs(subs(df_plusy,v1,A_plus(i)),v2,B_plus(i))) ]
+    end
+    for i = 1:size(A_minus,1)
+        fprintf('Testing %d.point (f_minus): ',i )
+        [double(subs(subs(df_minusx,v1,A_minus(i)),v2,B_minus(i))), double(subs(subs(df_minusy,v1,A_minus(i)),v2,B_minus(i)))]
+    end
+    % ------------------------------------
+end
+
+% --- Extract only Real-Solutions
+% fprintf('real stationary points of f_plus:')
+tmp1 = A_plus(imag(double(A_plus))==0 & imag(double(B_plus)) == 0);
+tmp2 = B_plus(imag(double(A_plus))==0 & imag(double(B_plus)) == 0);
+A_plus = tmp1;
+B_plus = tmp2;
+SP_plus = [A_plus,B_plus];
+
+% fprintf('real stationary points of f_minus:')
+tmp1 = A_minus(imag(double(A_minus))==0 & imag(double(B_minus)) == 0);
+tmp2 = B_minus(imag(double(A_minus))==0 & imag(double(B_minus)) == 0);
+A_minus = tmp1;
+B_minus = tmp2;
+SP_minus = [A_minus,B_minus];
+
+% TODO one should use f_plus.subs(A_plus..) to compute function value symbolically?
+% in the end only the stationaryPoints are used.. should be ok to compare function values numerically
+
+% Determine global Minimizer from stationary points:
+% fprintf('function values at stationary points (f_plus):')
+T_plus = arrayfun(@(v1,v2) double(f_plus(v1,v2,q1,q2,q3,q12,b1,b2,b3)),A_plus,B_plus,'UniformOutput', false);
+T_plus = cell2mat(T_plus);
+
+%Test: use Substitution
+% subs(f_plus,{v1, v2}, {A_plus,B_plus})
+
+% fprintf('function values at stationary points (f_minus):')
+T_minus = arrayfun(@(v1,v2) double(f_minus(v1,v2,q1,q2,q3,q12,b1,b2,b3)),A_minus,B_minus,'UniformOutput', false);
+T_minus = cell2mat(T_minus);
+
+%Test: use Substitution
+% T_minus = subs(f_minus,{v1, v2}, {A_minus,B_minus})
+% double(T_minus)
+
+if print_statPoint
+    fprintf('real stationary points of f_plus: ')
+%     SP_Plus     %alternative: output as symbolic (can be unwieldy)
+    double(SP_plus)
+    fprintf('real stationary points of f_minus:')
+%     SP_Minus     %alternative: output as symbolic (can be unwieldy)
+    double(SP_minus)
+    fprintf('function values at stationary points (f_plus):')
+    T_plus
+    fprintf('function values at stationary points (f_minus):')
+    T_minus
+end
+
+% --- Find Stationary Point(s) with minimum Value 
+[Min_plus,MinIdx_plus] = min(T_plus, [], 'all', 'linear');    %find one min...
+[Min_minus,MinIdx_minus] = min(T_minus, [], 'all', 'linear');
+% [Min_minus,MinIdx_minus] = min(T_minus)                     % works with symbolic too
+
+% Compare Minimizers of f_plus & f_minus
+[globalMinimizerValue,GlobalIdx] = min([Min_plus,Min_minus]); 
+
+if GlobalIdx == 1     %Min_plus   % i.e. Global Minimizer is given by f_plus
+    GlobalMinimizer = SP_plus(MinIdx_plus,:);
+    sign = 1.0;
+elseif GlobalIdx == 2  %Min_minus % i.e. Global Minimizer is given by f_minus
+    GlobalMinimizer = SP_minus(MinIdx_minus,:);
+    sign = -1.0; 
+end
+
+% ------ Check if there are more SP with the same value...
+ MinIndices_minus = find(T_minus(:) == globalMinimizerValue);    % Find indices of All Minima
+ MinIndices_plus  = find(T_plus(:) == globalMinimizerValue);    % Find indices of All Minima                   
+ numMinSP_minus = size(MinIndices_minus,1);   % One of these is always >= 2 due to the structure of the roots..
+ numMinSP_plus  = size(MinIndices_plus,1);
+    
+%     AllMinSP_minus = SP_minus(MinIndices_minus,:)
+%     AllMinSP_minus = double(SP_minus(MinIndices_minus,:))
+%     AllMin = T_minus(MinIndices)  %bereits klar dass diese selben funktionswert haben..
+      
+    Minimizer = sign*(GlobalMinimizer'*GlobalMinimizer);  % global minimizing Matrix G*
+    MinimizerCount = 1;
+    % different Stationary Points might correspond to the same minimizing
+    % Matrix G*... check this: 
+    
+    % Compare only with other StationaryPoints/Minimizers
+    % remove Index of Minimizer
+    if GlobalIdx == 1     
+        MinIndices_plus = MinIndices_plus(MinIndices_plus~=MinIdx_plus);
+    elseif GlobalIdx == 2  
+        MinIndices_minus = MinIndices_minus(MinIndices_minus~=MinIdx_minus);
+    end
+    
+    MinIndices = cat(1,MinIndices_plus,MinIndices_minus);  %[Minimizers-Indices f_plus, Minimizer-Indices f_minus]
+    
+    for i = 1:(numMinSP_minus+numMinSP_plus-1)  % -1: dont count Minimizer itself.. 
+        idx = MinIndices(i);   
+        
+        if i > numMinSP_plus
+            SP = SP_minus(idx,:);
+        else
+            SP = SP_plus(idx,:); 
+        end
+        
+%         SP_value = T_minus(idx) % not needed? 
+        Matrix = sign*(SP'*SP);
+
+        if norm(double(Matrix-Minimizer),'fro') < 1e-8   %check is this sufficient here?
+%             fprintf('both StationaryPoints correspond to the same(Matrix-)Minimizer')
+        else
+%             fprintf('StationaryPoint corresponds to a different (Matrix-)Minimizer')
+            MinimizerCount = MinimizerCount + 1;
+        end
+    end
+% ----------------------------------------------------------------------------------------------------------------
+
+
+
+% Output Uniqueness of Minimizers:
+if print_Uniqueness
+    if MinimizerCount == 1
+        fprintf('Unique Minimzier')
+    elseif MinimizerCount == 2
+        fprintf('Two Minimziers')
+    else
+        fprintf('1-Parameter family of Minimziers')
+    end
+end
+
+
+
+
+
+% --- determine the angle of the Minimizer
+% a1 = Minimizer(1,1)
+% a2 = Minimizer(2,2)
+a1 = double(Minimizer(1,1));
+a2 = double(Minimizer(2,2));
+
+% compute the angle <(e,e_1) where Minimizer = kappa* (e (x) e)
+e = [sqrt((a1/(a1+a2))), sqrt((a2/(a1+a2)))];    % always positive under sqrt here .. basically takes absolute value here
+angle = atan2(e(2), e(1)); 
+
+% compute curvature kappa
+kappa = (a1 + a2);
+
+% % CHeck off diagonal entries:
+% sqrt(a1*a2);
+% double(Minimizer);
+
+G = double(Minimizer);
+
+
+
+% --- "Classification" / Determine the TYPE of Minimizer by using 
+% the number of solutions (Uniqueness?)
+% the angle (axial- or non-axial Minimizer)
+
+% (Alternative compute det[GlobalMinimizer' e1']  where e1 = [1 0] ?)
+
+% Check Uniqueness -- Options: unique/twoMinimizers/1-ParameterFamily
+if MinimizerCount == 1
+%     fprintf('Unique Minimzier')
+    % Check if Minimizer is axial or non-axial:
+    if (abs(angle-pi/2) < 1e-8 || abs(angle) < 1e-8) % axial Minimizer
+     Type = 3;
+    else % non-axial Minimizer   
+     Type = 1;
+    end
+elseif MinimizerCount == 2
+%     fprintf('Two Minimziers')
+    % Check if Minimizer is axial or non-axial:
+    if (abs(angle-pi/2) < 1e-8 || abs(angle) < 1e-8) % axial Minimizer
+        Type = 3;
+    else % non-axial Minimizer   
+        fprintf('ERROR: Two non-axial Minimizers cannot happen!')
+    end
+else
+%     fprintf('1-Parameter family of Minimziers')
+    % Check if Minimizer is axial or non-axial:
+    if (abs(angle-pi/2) < 1e-8 || abs(angle) < 1e-8) % axial Minimizer
+%         fprintf('ERROR: axial Minimizers cannot happen for 1-Parameter Family!')
+    else % non-axial Minimizer   
+        Type = 2;
+    end
+end
+% ------------------------------------------------------------------------------------------------------
+
+
+
+
+if print_Output
+    fprintf(' --------- Output symMinimization --------')
+    fprintf('Global Minimizer v: (%d,%d) \n', GlobalMinimizer(1),GlobalMinimizer(2) )
+    fprintf('Global Minimizer Value f(v): %d \n', sym(globalMinimizerValue) ) %cast to symbolic
+    %     fprintf('Global Minimizer Value : %d', globalMinimizerValue )
+    
+    fprintf('Global Minimizer G: \n' )
+    G 
+    fprintf("Angle = %d \n", angle)
+    fprintf("Curvature = %d \n", kappa)
+    fprintf("Type = %i \n", Type)
+    fprintf(' --------- -------------------- --------')
+end
+
+
+
+if make_FunctionPlot  
+    fsurf(@(x,y) f_plus(x,y,q1,q2,q3,q12,b1,b2,b3)) % Plot functions
+    hold on
+    plot3(double(A_plus),double(B_plus),T_plus,'g*')
+    %Plot GlobalMinimizer:
+    hold on
+    plot3(double(GlobalMinimizer(1)),double(GlobalMinimizer(2)),globalMinimizerValue, 'o', 'Color','c')
+    % view(90,0)
+    % view(2)
+
+    figure
+    fsurf(@(x,y) f_minus(x,y,q1,q2,q3,q12,b1,b2,b3))
+    hold on
+    plot3(double(A_minus),double(B_minus),T_minus,'g*')
+    hold on
+    plot3(double(GlobalMinimizer(1)), double(GlobalMinimizer(2)),globalMinimizerValue, 'o', 'Color','c')
+end
+
+
+return 
+
+
+% Write symbolic solution to txt-File in Latex format
+% fileID = fopen('txt.txt','w');
+% fprintf(fileID,'%s' , latex(S_plus.v1));
+% fclose(fileID);
+
+
+
+
+
+
+

Matlab-Programs/symSolveSystem.m

+
+
+syms q1 q2 q3 q12 b1 b2  a1 a2 
+
+% eqn1 = q1 * a1 + (q3 + (q12/2)) *a2 == -2*q1*b1 - q12*b2
+% 
+% eqn2 = (q3 + (q12/2)) * a1 + q2 *a2 == -2*q2*b2 - q12*b1
+
+
+eqn1 = q1 * a1 + (q3 + (q12/2)) *a2 == q1*b1 + (q12*b2/2)
+
+eqn2 = (q3 + (q12/2)) * a1 + q2 *a2 == q2*b2 + (q12*b1/2)
+
+
+
+[A,B] = equationsToMatrix([eqn1, eqn2], [a1,a2])
+
+X = linsolve(A,B)
+
+
+% check special case
+fprintf('special case q12 = 0 ') 
+subs(X,q12,0)
\ No newline at end of file

Paraview-Scripts/ParaViewSettings.txt

+
+Colormap: Cool-to-Warm
+
+Representation: Point-Gaussian
+Opacity: 0.01
+PointSize: 2
+Gaussian-radius: 0.0075
+Shader-Preset: Plain-Circle

Python-Scripts/1-ParameterFamily-Minimizers.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+from mpl_toolkits.mplot3d import Axes3D
+import pandas as pd
+import matplotlib.colors as mcolors
+from matplotlib import cm
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+# Extra packages :
+# from HelperFunctions import *
+# from ClassifyMin import *
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### Documentation #########################
+
+#..... add description here
+
+###########################################################
+
+
+def rot(v,alpha):
+
+#rotate about axis v with degree deg in radians:
+
+
+    tmp = np.array([ [v[0]**2*(1-np.cos(alpha))+np.cos(alpha), v[0]*v[1]*(1-np.cos(alpha))-v[2]*np.sin(alpha), v[0]*v[2]*(1-np.cos(alpha))+ v[1]*np.sin(alpha) ],
+         [v[0]*v[1]*(1-np.cos(alpha))+v[2]*np.sin(alpha), v[1]**2*(1-np.cos(alpha))+np.cos(alpha), v[1]*v[2]*(1-np.cos(alpha))+v[0]*np.sin(alpha) ],
+         [v[2]*v[0]*(1-np.cos(alpha))-v[1]*np.sin(alpha), v[2]*v[1]*(1-np.cos(alpha))+v[0]*np.sin(alpha) , v[2]**2*(1-np.cos(alpha))+np.cos(alpha) ] ])
+
+    return tmp
+
+
+
+def rotate_data(X, R):
+#rotate about axis v with degree deg in radians:
+# X : DataSet
+# R : RotationMatrix
+    print('ROTATE DATA FUNCTION ---------------')
+
+    rot_matrix = R
+    # print('rot_matrix:', rot_matrix)
+    # print('rot_matrix.shape:', rot_matrix.shape)
+    # print('X', X)
+    # print('shape of X[0]', X.shape[0])
+    B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+    # print('shape of B', B.shape)
+    # print('B',B)
+    # print('B[0,:]', B[0,:])
+    # print('B[0,:].shape', B[0,:].shape)
+    Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+    print('shape of Out', Out.shape)
+
+    return Out
+
+# def rotate_data(X, v,alpha): #(Old Version)
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#     rot_matrix = rot(v,alpha)
+#     # print('rot_matrix:', rot_matrix)
+#     # print('rot_matrix.shape:', rot_matrix.shape)
+#
+#     # print('X', X)
+#     # print('shape of X[0]', X.shape[0])
+#     B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+#
+#     # print('shape of B', B.shape)
+#     # print('B',B)
+#     # print('B[0,:]', B[0,:])
+#     # print('B[0,:].shape', B[0,:].shape)
+#     Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+#     print('shape of Out', Out.shape)
+#
+#     return Out
+
+
+# def translate_data(X, v):  ...
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#
+#     print('X', X)
+#     print('shape of X[0]', X.shape[0])
+#
+#     Out = X + v
+#     return Out
+
+
+def u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp for u',tmp)
+    if kappa == 0 :
+        tmp = np.array([0*x[0],  x[0]*e[0] + x[1]*e[1], x[1]*e[0] - x[0]*e[1] ])
+    else :
+        tmp = np.array([-(1/kappa)*np.cos(tmp)+(1/kappa),  (1/kappa)*np.sin(tmp), -x[0]*e[1]+x[1]*e[0] ])
+    return tmp
+
+
+
+
+def grad_u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp',tmp)
+
+    grad_u = np.array([ [np.sin(tmp)*e[0], np.sin(tmp)*e[1]], [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]] ])
+    # print('produkt', grad_u.dot(e) )
+    mapped_e = grad_u.dot(e)
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    # mapped_e = mapped_e.transpose()
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    return mapped_e
+
+def compute_normal(x,kappa,e):
+    tmp = (x.dot(e))*kappa
+    partial1_u = np.array([ np.sin(tmp)*e[0] ,np.cos(tmp)*e[0], -e[1] ])
+    partial2_u = np.array([ np.sin(tmp)*e[1], np.cos(tmp)*e[1], e[0]      ])
+    normal = np.cross(partial1_u,partial2_u)
+    # print('normal=',normal)
+    return normal
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+print('T:', T)
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+e_container = []
+
+
+for t in T :
+
+    abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+    abar_current[abar_current < 1e-10] = 0
+    # print('abar_current', abar_current)
+    # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    e_container.append(e)
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+    # print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+G_container = np.array(G_container)
+abar_container = np.array(abar_container)
+
+e_container = np.array(e_container)
+
+print('G_container', G_container)
+print('G_container.shape', G_container.shape)
+
+# idx_1 = np.where(alphas == np.pi/4)
+idx_1 = np.where(np.round(alphas,2) == round(np.pi/3,2))
+idx_2 = np.where(np.round(alphas,2) == 0.0)
+idx_3 = np.where(np.round(alphas,2) == round(np.pi/4,2))
+
+# idx_3 = np.where(alphas == 0)
+
+print('Index idx_1:', idx_1)
+print('Index idx_2:', idx_2)
+print('Index idx_3:', idx_3)
+print('Index idx_1[0][0]:', idx_1[0][0])
+print('Index idx_2[0][0]:', idx_2[0][0])
+print('Index idx_3[0][0]:', idx_3[0][0])
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+print('min alpha:', min(alphas))
+print('min kappa:', min(kappas))
+
+
+print('G_container[idx_1[0][0]]', G_container[idx_1[0][0]])
+print('G_container[idx_2[0][0]]', G_container[idx_2[0][0]])
+print('G_container[idx_3[0][0]]', G_container[idx_3[0][0]])
+
+
+print('e_container[idx_1[0][0]]', e_container[idx_1[0][0]])
+print('e_container[idx_2[0][0]]', e_container[idx_2[0][0]])
+print('e_container[idx_3[0][0]]', e_container[idx_3[0][0]])
+
+
+idx = 2
+
+e = e_container[idx_1[0][0]]
+e = e_container[idx_2[0][0]]
+# e = e_container[idx_3[0][0]]
+kappa = kappas[idx_1[0][0]]
+kappa = kappas[idx_2[0][0]]
+# kappa = kappas[idx_3[0][0]]
+
+angle = alphas[idx_1[0][0]]
+angle = alphas[idx_2[0][0]]
+# angle = alphas[idx_3[0][0]]
+
+
+# kappa = kappa*2
+
+print('kappa:',kappa)
+print('angle:',angle)
+
+#### TEST apply reflection
+#
+# G_tmp = G_container[idx_1[0][0]]
+#
+# print('G_tmp', G_tmp)
+#
+# # Basis:
+# G_1 = np.array([[1.0,0.0], [0.0,0.0]])
+# G_2 = np.array([[0.0,0.0], [0.0,1.0]])
+# G_3 = (1/np.sqrt(2))*np.array([[0.0,1.0], [1.0,0.0]])
+# print('G_1', G_1)
+# print('G_2', G_2)
+# print('G_3', G_3)
+#
+# G = G_tmp[0] * G_1 + G_tmp[1]*G_2 + G_tmp[2]*G_3
+# print('G:', G )
+#
+# T = np.array([[1.0 , -1.0] , [-1.0,1.0]])
+#
+# TG = np.multiply(T,G)
+# print('TG', TG)
+#
+#
+#
+# v = np.array([np.sqrt(TG[0][0]),np.sqrt(TG[1][1]) ])
+# print('v', v)
+# print('norm(v):', np.linalg.norm(v))
+# norm_v = np.linalg.norm(v)
+#
+# kappa = norm_v**2
+#
+# e = (1/norm_v)*v
+# print('e:', e)
+# print('kappa:', kappa)
+
+
+
+
+
+
+
+
+reflected_e = np.array([e[0], -1*e[1]])
+e = reflected_e                                         # Correct?! Reflect e on x-Axis ??!
+print('reflected_e:', reflected_e)
+
+
+############################################################################################################################################
+####################################################################### KAPPA NEGATIVE ####################################################
+############################################################################################################################################
+# kappa = -2
+num_Points = 200
+num_Points = 100
+
+
+# e = np.array([1,0])
+# e = np.array([0,1])
+# e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e = np.array([1/2,np.sqrt(3)/2])
+# e = np.array([np.sqrt(3)/2,1/2])
+# e = np.array([-1,0])
+# e = np.array([0,-1])
+
+###--- Creating dataset
+x = np.linspace(-2,2,num_Points)
+x = np.linspace(-3,3,num_Points)
+# x = np.linspace(-4,4,num_Points)
+
+# x = np.linspace(-1.5,1.5,num_Points)
+# x = np.linspace(-1,1,num_Points)
+y = np.linspace(-1/2,1/2,num_Points)
+y = np.linspace(-1/4,1/4,num_Points)
+
+print('type of x', type(x))
+print('max of x:', max(x))
+print('max of y:', max(y))
+# print('x:', x)
+
+x1, x2 = np.meshgrid(x,y)
+zero = 0*x1
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+
+# print('np.size(u1)',np.size(u1))
+# print('u1.shape',u1.shape)
+# colorfunction=(u1**2+u2**2)
+# print('colofunction',colorfunction)
+
+# print('u1.size:',np.size(u1))
+# tmp = np.ones(np.size(u1))*kappa
+# print('np.size(tmp)',np.size(tmp))
+B = np.full_like(u1, 1)
+# colorfunction=(u3)                                              # TODO Color by angle
+# colorfunction=(np.ones(np.size(u1))*kappa)
+colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+norm=mcolors.Normalize(colorfunction.min(),colorfunction.max())
+
+
+# -----------------------------------------------------
+# Display the mesh
+fig = plt.figure()
+
+
+width = 6.28 *0.5
+width = 6.28 * 0.333
+height = width / 1.618
+height = width / 2.5
+height = width
+
+
+
+ax = plt.axes(projection ='3d', adjustable='box')
+
+
+###---TEST MAP e-vectprs!
+# e1 = np.array([1,0])
+# e2 = np.array([0,1])
+# e3 = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e1 = np.array([0,1])
+# e2 = np.array([-1,0])
+# e3 = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# e1_mapped = u(e1,kappa,e1)
+# e2_mapped = u(e2,kappa,e2)
+# e3_mapped = u(e3,kappa,e3)
+# print('e1 mapped:',e1_mapped)
+# print('e2 mapped:',e2_mapped)
+# print('e3 mapped:',e3_mapped)
+### -----------------------------------
+
+#--e1 :
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([0,1,0])
+
+#--e2:
+Rotation_angle = np.pi/2
+Rotation_vector = np.array([1,0,0])
+
+###--e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([1,0,0])
+# #2te rotation :
+# Rotation_angle = np.pi/4
+# Rotation_vector = np.array([0,0,1])
+
+
+
+Rotation_angle = -np.pi/2
+Rotation_angle = 0
+# Rotation_angle = np.pi/2
+Rotation_vector = np.array([0,1,0])
+Rotation_vector = np.array([1,0,0])
+
+# rot(np.array([0,1,0]),np.pi/2)
+
+# ZERO ROTATION
+Rotation = rot(np.array([0,1,0]),0)
+
+
+
+# TEST :
+
+#DETERMINE ANGLE:
+angle = math.atan2(e[1], e[0])
+print('angle:', angle)
+
+## GENERAL TRANSFORMATION / ROTATION:
+Rotation = rot(np.array([0,0,1]),angle).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+
+
+### if e1:
+# Rotation = rot(np.array([0,0,1]),-np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+# Add another rotation around z-axis:
+# Rotation = rot(np.array([0,0,1]),+np.pi).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/8).dot(Rotation)
+
+#e3 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4)
+# Rotation = rot(np.array([1,0,0]),np.pi/4)
+#### if e1 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+#### if e2:
+# Rotation = rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2))
+# # #### if e3 :
+# zufall dass np.pi/4 genau dem Winkel angle alpha entspricht?:
+# (würde) bei e_2 keinen Unterschied machen um z achse zu rotieren?!
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+# Rotation = rot(np.array([0,0,1]),np.pi/2).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+
+# Rotation = rot(np.array([1,0,0]),np.pi/2)
+
+# Rotation_vector = e3_mapped  #TEST
+# Rotation_vector = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_vector = np.array([0,0,1])
+
+# v = np.array([1,0,0])
+# X = np.array([u1,u2,u3])
+
+
+
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 2, cstride = 2, facecolors=cm.brg(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.viridis(colorfunction), alpha=.4, zorder=4)
+
+
+###---- PLOT PARAMETER-PLANE:
+# ax.plot_surface(x1,x2,zero,color = 'w', rstride = 1, cstride = 1 )
+
+
+print('------------------ Kappa : ', kappa)
+
+#midpoint:
+midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+print('midpoint',midpoint)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+#
+# mapped_e = Rotation.dot(mapped_e)
+# normal = Rotation.dot(normal)
+
+
+# Plot Mapped_midPoint
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=4)          # line width
+
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [mapped_e[0]], [mapped_e[1]], [mapped_e[2]], color="red")
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [normal[0]], [normal[1]], [normal[2]], color="blue")
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 2,
+#            ec ='green',
+#            zorder=3)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 2,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 3)
+
+
+###-- TEST Rotation :
+# v = np.array([1,0,0])
+# t = np.array([0,1,0])
+#
+# ax.arrow3D(0,0,0,
+#            t[0],t[1],t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+#
+# # e_extend
+#
+# rotM = rot(v,np.pi/2)
+#
+# print('rotM:', rotM)
+#
+# rot_t = rotM.dot(t)
+#
+# print('rot_t:', rot_t)
+#
+# ax.arrow3D(0,0,0,
+#            rot_t[0],rot_t[1],rot_t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+### -------------------------------------------
+
+############################################################################################################################################
+####################################################################### KAPPA POSITIVE  ####################################################
+############################################################################################################################################
+
+# kappa = (-1)*kappa
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3, color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.3)  ##This one!
+
+
+# T = rotate_data(X,Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=False)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 2, cstride = 2, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, facecolors=cm.brg(colorfunction), alpha=.8, zorder=4)
+ax.plot_surface(T[0], T[1], T[2], rstride = 5, cstride = 5, color='orange', alpha=.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, color='blue', alpha=.8, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=0.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=1, zorde5r=5)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+# print('midpoint',midpoint)
+print('------------------ Kappa : ', kappa)
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+
+#
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+# Plot MIDPOINT:
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+
+
+
+# mapped_e = grad_u(midpoint,kappa,e)
+# normal = compute_normal(midpoint,kappa,e)
+
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+############################################################################################################################################
+####################################################################### KAPPA ZERO #########################################################
+############################################################################################################################################
+kappa = 0
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3,  rstride = 1, cstride = 1, color = 'white', alpha=0.85)
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride =1 , cstride = 1, color = 'white', alpha=0.55, zorder=3)
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.5, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 10, cstride = 10, color = 'white', alpha=0.55, zorder=2)
+ax.plot_surface(T[0], T[1], T[2],  rstride = 20, cstride = 20, color = 'gray', alpha=0.35, zorder=1, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'white', alpha=0.55, zorder=2)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+mapped_e = grad_u(midpoint,kappa,e)
+normal_zeroCurv = compute_normal(midpoint,kappa,e)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+##-----  PLOT MAPPED MIDPOINT :::
+
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# # linestyle='--',            # line style will be dash line
+# linewidth=1,
+# zorder=5)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='red',
+#            ec ='red')
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal_zeroCurv[0],normal_zeroCurv[1],normal_zeroCurv[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+
+##----------  PLOT MAPPED ORIGIN :::
+# origin = np.array([0,0])
+# origin_mapped = u(origin,kappa,e)
+# print('origin_mapped', origin_mapped)
+#
+# ax.plot(origin_mapped[0],origin_mapped[1],origin_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='green',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+#
+# # rotate mapped origin
+# # v = np.array([1,0,0])
+# # alpha  = Rotation_angle
+#
+# rotM = rot(Rotation_vector,Rotation_angle)
+# # origin_mRot = rotate_data(origin_mapped,v,alpha)
+# origin_mRot = rotM.dot(origin_mapped)
+# print('origin_mapped Rotated', origin_mRot)
+#
+# # --- Compute Distance to Origin 3D
+# origin_3D=np.array([0,0,0])
+# distance = origin_mapped-origin_3D
+# print('distance', distance)
+
+## --------------------------------------------------------
+
+# COMPUTE ANGLE WITH Z AXIS
+z = np.array([0,0,1])
+print('test', normal_zeroCurv*z)
+angle_z = np.arccos(normal_zeroCurv.dot(z) /( (np.linalg.norm(z)*np.linalg.norm(normal_zeroCurv) ) ))
+print('angle between normal and z-axis', angle_z)
+
+## unfinished...
+
+
+
+
+###-------------------------------------  PLOT :
+plt.axis('off')
+# plt.axis('tight')
+
+# ADD colorbar
+# scamap = plt.cm.ScalarMappable(cmap='inferno')
+# fig.colorbar(scamap)
+
+# ax.colorbar()
+# ax.axis('auto')
+# ax.set_title(r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e))
+# ax.set_title(r'Cylindrical minimizer' + '_$e$=' +  str(e))
+ax.set_xlabel(r"x-axis")
+ax.set_ylabel(r"y-axis")
+ax.set_zlabel(r"z-axis")
+
+# TEST :
+# ax.annotate3D('point 1', (0, 0, 0), xytext=(3, 3), textcoords='offset points')
+# ax.annotate3D('point 2', (0, 1, 0),
+#               xytext=(-30, -30),
+#               textcoords='offset points',
+#               arrowprops=dict(ec='black', fc='white', shrink=2.5))
+# ax.annotate3D('point 3', (0, 0, 1),
+#               xytext=(30, -30),
+#               textcoords='offset points',
+#               bbox=dict(boxstyle="round", fc="lightyellow"),
+#               arrowprops=dict(arrowstyle="-|>", ec='black', fc='white', lw=5))
+
+#######################################################################################################################
+
+u1 = T[0]
+u2 = T[1]
+u3 = T[2]
+
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /3
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /12
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /8
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /6
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /2
+mid_u1 = (u1.max()+u1.min()) * 0.5
+mid_u2 = (u2.max()+u2.min()) * 0.5
+mid_u3 = (u3.max()+u3.min()) * 0.5
+
+
+ax.set_xlim(mid_u1 - max_range, mid_u1 + max_range)
+ax.set_ylim(mid_u2 - max_range, mid_u2 + max_range)
+ax.set_zlim(mid_u3 - max_range, mid_u3 + max_range)
+
+ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+# ax.set_ylim((mid_u2 - max_range)-1.5, (mid_u2 + max_range)+1.5)
+# ax.autoscale(tight=True)
+
+
+
+
+##----- CHANGE CAMERA POSITION:
+# ax.view_init(elev=10., azim=0)
+# ax.view_init(elev=38, azim=90)
+# ax.view_init(elev=38, azim=120)
+# ax.view_init(elev=38)
+
+# if e1 ::
+# ax.view_init(elev=44)
+# ax.view_init(elev=38, azim=-90)
+# ax.view_init(elev=38, azim=0)
+ax.view_init(elev=25, azim=-30)
+
+# if e3 ::
+# ax.view_init(elev=25)
+
+# ax.set_xlim3d(-2, 2)
+# ax.set_ylim3d(-1.0,3.0)
+# ax.set_zlim3d(-1.5,2.5)
+
+# ax.set_ylim3d(-10,10)
+# ax.set_xlim(mid_u1 - max_range-0.2, mid_u1 + max_range+0.2)
+# ax.set_zlim(mid_u3 - max_range-0.2, mid_u3 + max_range+0.2)
+# ax.set_ylim(mid_u2 - max_range-0.2, mid_u2 + max_range+0.2)
+
+# width = 6.28 *0.5
+# height = width / 1.618
+# # height = width / 2.5
+# fig.set_size_inches(width, height)
+# fig.savefig('Test-Cylindrical.pdf')
+
+# Figurename = r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e)
+# Figurename = r'Cylindrical minimizer' + '_$e$=' +  str(e)
+Figurename = r'1-ParFamMinimizer_idx' + str(idx)
+# plt.savefig("test.png", bbox_inches='tight')
+# plt.figure().set_size_inches(width, height)
+# plt.set_size_inches(width, height)
+
+
+fig.set_size_inches(width, height)
+fig.savefig(Figurename+".pdf")
+
+plt.savefig(Figurename+".png", bbox_inches='tight')
+# plt.savefig(Figurename+".png")
+plt.show()
+
+
+
+# #---------------------------------------------------------------

Python-Scripts/1-ParameterFamily-MinimizersTest.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+from mpl_toolkits.mplot3d import Axes3D
+import pandas as pd
+import matplotlib.colors as mcolors
+from matplotlib import cm
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+# Extra packages :
+# from HelperFunctions import *
+# from ClassifyMin import *
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### Documentation #########################
+
+#..... add description here
+
+###########################################################
+
+
+def rot(v,alpha):
+
+#rotate about axis v with degree deg in radians:
+
+
+    tmp = np.array([ [v[0]**2*(1-np.cos(alpha))+np.cos(alpha), v[0]*v[1]*(1-np.cos(alpha))-v[2]*np.sin(alpha), v[0]*v[2]*(1-np.cos(alpha))+ v[1]*np.sin(alpha) ],
+         [v[0]*v[1]*(1-np.cos(alpha))+v[2]*np.sin(alpha), v[1]**2*(1-np.cos(alpha))+np.cos(alpha), v[1]*v[2]*(1-np.cos(alpha))+v[0]*np.sin(alpha) ],
+         [v[2]*v[0]*(1-np.cos(alpha))-v[1]*np.sin(alpha), v[2]*v[1]*(1-np.cos(alpha))+v[0]*np.sin(alpha) , v[2]**2*(1-np.cos(alpha))+np.cos(alpha) ] ])
+
+    return tmp
+
+
+
+def rotate_data(X, R):
+#rotate about axis v with degree deg in radians:
+# X : DataSet
+# R : RotationMatrix
+    print('ROTATE DATA FUNCTION ---------------')
+
+    rot_matrix = R
+    # print('rot_matrix:', rot_matrix)
+    # print('rot_matrix.shape:', rot_matrix.shape)
+    # print('X', X)
+    # print('shape of X[0]', X.shape[0])
+    B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+    # print('shape of B', B.shape)
+    # print('B',B)
+    # print('B[0,:]', B[0,:])
+    # print('B[0,:].shape', B[0,:].shape)
+    Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+    print('shape of Out', Out.shape)
+
+    return Out
+
+# def rotate_data(X, v,alpha): #(Old Version)
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#     rot_matrix = rot(v,alpha)
+#     # print('rot_matrix:', rot_matrix)
+#     # print('rot_matrix.shape:', rot_matrix.shape)
+#
+#     # print('X', X)
+#     # print('shape of X[0]', X.shape[0])
+#     B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+#
+#     # print('shape of B', B.shape)
+#     # print('B',B)
+#     # print('B[0,:]', B[0,:])
+#     # print('B[0,:].shape', B[0,:].shape)
+#     Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+#     print('shape of Out', Out.shape)
+#
+#     return Out
+
+
+# def translate_data(X, v):  ...
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#
+#     print('X', X)
+#     print('shape of X[0]', X.shape[0])
+#
+#     Out = X + v
+#     return Out
+
+
+def u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp for u',tmp)
+    if kappa == 0 :
+        tmp = np.array([0*x[0],  x[0]*e[0] + x[1]*e[1], x[1]*e[0] - x[0]*e[1] ])
+    else :
+        tmp = np.array([-(1/kappa)*np.cos(tmp)+(1/kappa),  (1/kappa)*np.sin(tmp), -x[0]*e[1]+x[1]*e[0] ])
+    return tmp
+
+
+
+
+def grad_u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp',tmp)
+
+    grad_u = np.array([ [np.sin(tmp)*e[0], np.sin(tmp)*e[1]], [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]] ])
+    # print('produkt', grad_u.dot(e) )
+    mapped_e = grad_u.dot(e)
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    # mapped_e = mapped_e.transpose()
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    return mapped_e
+
+def compute_normal(x,kappa,e):
+    tmp = (x.dot(e))*kappa
+    partial1_u = np.array([ np.sin(tmp)*e[0] ,np.cos(tmp)*e[0], -e[1] ])
+    partial2_u = np.array([ np.sin(tmp)*e[1], np.cos(tmp)*e[1], e[0]      ])
+    normal = np.cross(partial1_u,partial2_u)
+    # print('normal=',normal)
+    return normal
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+print('T:', T)
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+e_container = []
+
+
+for t in T :
+
+    abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+    abar_current[abar_current < 1e-10] = 0
+    # print('abar_current', abar_current)
+    # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    e_container.append(e)
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+    # print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+G_container = np.array(G_container)
+abar_container = np.array(abar_container)
+
+e_container = np.array(e_container)
+
+print('G_container', G_container)
+print('G_container.shape', G_container.shape)
+
+# idx_1 = np.where(alphas == np.pi/4)
+idx_1 = np.where(np.round(alphas,2) == round(np.pi/3,2))
+idx_2 = np.where(np.round(alphas,2) == 0.0)
+idx_3 = np.where(np.round(alphas,2) == round(np.pi/4,2))
+
+# idx_3 = np.where(alphas == 0)
+
+print('Index idx_1:', idx_1)
+print('Index idx_2:', idx_2)
+print('Index idx_3:', idx_3)
+print('Index idx_1[0][0]:', idx_1[0][0])
+print('Index idx_2[0][0]:', idx_2[0][0])
+print('Index idx_3[0][0]:', idx_3[0][0])
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+print('min alpha:', min(alphas))
+print('min kappa:', min(kappas))
+
+
+print('G_container[idx_1[0][0]]', G_container[idx_1[0][0]])
+print('G_container[idx_2[0][0]]', G_container[idx_2[0][0]])
+print('G_container[idx_3[0][0]]', G_container[idx_3[0][0]])
+
+
+print('e_container[idx_1[0][0]]', e_container[idx_1[0][0]])
+print('e_container[idx_2[0][0]]', e_container[idx_2[0][0]])
+print('e_container[idx_3[0][0]]', e_container[idx_3[0][0]])
+
+
+idx = 2
+
+e = e_container[idx_1[0][0]]
+e = e_container[idx_2[0][0]]
+# e = e_container[idx_3[0][0]]
+kappa = kappas[idx_1[0][0]]
+kappa = kappas[idx_2[0][0]]
+# kappa = kappas[idx_3[0][0]]
+
+angle = alphas[idx_1[0][0]]
+angle = alphas[idx_2[0][0]]
+# angle = alphas[idx_3[0][0]]
+
+
+# kappa = kappa*2
+
+print('kappa:',kappa)
+print('angle:',angle)
+
+#### TEST apply reflection
+#
+# G_tmp = G_container[idx_1[0][0]]
+#
+# print('G_tmp', G_tmp)
+#
+# # Basis:
+# G_1 = np.array([[1.0,0.0], [0.0,0.0]])
+# G_2 = np.array([[0.0,0.0], [0.0,1.0]])
+# G_3 = (1/np.sqrt(2))*np.array([[0.0,1.0], [1.0,0.0]])
+# print('G_1', G_1)
+# print('G_2', G_2)
+# print('G_3', G_3)
+#
+# G = G_tmp[0] * G_1 + G_tmp[1]*G_2 + G_tmp[2]*G_3
+# print('G:', G )
+#
+# T = np.array([[1.0 , -1.0] , [-1.0,1.0]])
+#
+# TG = np.multiply(T,G)
+# print('TG', TG)
+#
+#
+#
+# v = np.array([np.sqrt(TG[0][0]),np.sqrt(TG[1][1]) ])
+# print('v', v)
+# print('norm(v):', np.linalg.norm(v))
+# norm_v = np.linalg.norm(v)
+#
+# kappa = norm_v**2
+#
+# e = (1/norm_v)*v
+# print('e:', e)
+# print('kappa:', kappa)
+
+
+
+
+
+
+
+
+reflected_e = np.array([e[0], -1*e[1]])
+e = reflected_e                                         # Correct?! Reflect e on x-Axis ??!
+print('reflected_e:', reflected_e)
+
+
+############################################################################################################################################
+####################################################################### KAPPA NEGATIVE ####################################################
+############################################################################################################################################
+# kappa = -2
+num_Points = 200
+num_Points = 100
+
+
+# e = np.array([1,0])
+# e = np.array([0,1])
+# e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e = np.array([1/2,np.sqrt(3)/2])
+# e = np.array([np.sqrt(3)/2,1/2])
+# e = np.array([-1,0])
+# e = np.array([0,-1])
+
+###--- Creating dataset
+x = np.linspace(-2,2,num_Points)
+x = np.linspace(-3,3,num_Points)
+# x = np.linspace(-4,4,num_Points)
+
+# x = np.linspace(-1.5,1.5,num_Points)
+# x = np.linspace(-1,1,num_Points)
+y = np.linspace(-1/2,1/2,num_Points)
+y = np.linspace(-1/4,1/4,num_Points)
+
+print('type of x', type(x))
+print('max of x:', max(x))
+print('max of y:', max(y))
+# print('x:', x)
+
+x1, x2 = np.meshgrid(x,y)
+zero = 0*x1
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+
+# print('np.size(u1)',np.size(u1))
+# print('u1.shape',u1.shape)
+# colorfunction=(u1**2+u2**2)
+# print('colofunction',colorfunction)
+
+# print('u1.size:',np.size(u1))
+# tmp = np.ones(np.size(u1))*kappa
+# print('np.size(tmp)',np.size(tmp))
+B = np.full_like(u1, 1)
+# colorfunction=(u3)                                              # TODO Color by angle
+# colorfunction=(np.ones(np.size(u1))*kappa)
+colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+norm=mcolors.Normalize(colorfunction.min(),colorfunction.max())
+
+
+# -----------------------------------------------------
+# Display the mesh
+fig = plt.figure()
+
+
+width = 6.28 *0.5
+width = 6.28 * 0.333
+height = width / 1.618
+height = width / 2.5
+height = width
+
+
+
+ax = plt.axes(projection ='3d', adjustable='box')
+
+
+###---TEST MAP e-vectprs!
+# e1 = np.array([1,0])
+# e2 = np.array([0,1])
+# e3 = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e1 = np.array([0,1])
+# e2 = np.array([-1,0])
+# e3 = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# e1_mapped = u(e1,kappa,e1)
+# e2_mapped = u(e2,kappa,e2)
+# e3_mapped = u(e3,kappa,e3)
+# print('e1 mapped:',e1_mapped)
+# print('e2 mapped:',e2_mapped)
+# print('e3 mapped:',e3_mapped)
+### -----------------------------------
+
+#--e1 :
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([0,1,0])
+
+#--e2:
+Rotation_angle = np.pi/2
+Rotation_vector = np.array([1,0,0])
+
+###--e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([1,0,0])
+# #2te rotation :
+# Rotation_angle = np.pi/4
+# Rotation_vector = np.array([0,0,1])
+
+
+
+Rotation_angle = -np.pi/2
+Rotation_angle = 0
+# Rotation_angle = np.pi/2
+Rotation_vector = np.array([0,1,0])
+Rotation_vector = np.array([1,0,0])
+
+# rot(np.array([0,1,0]),np.pi/2)
+
+# ZERO ROTATION
+Rotation = rot(np.array([0,1,0]),0)
+
+
+
+# TEST :
+
+#DETERMINE ANGLE:
+angle = math.atan2(e[1], e[0])
+print('angle:', angle)
+
+## GENERAL TRANSFORMATION / ROTATION:
+Rotation = rot(np.array([0,0,1]),angle).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+
+
+### if e1:
+# Rotation = rot(np.array([0,0,1]),-np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+# Add another rotation around z-axis:
+# Rotation = rot(np.array([0,0,1]),+np.pi).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/8).dot(Rotation)
+
+#e3 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4)
+# Rotation = rot(np.array([1,0,0]),np.pi/4)
+#### if e1 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+#### if e2:
+# Rotation = rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2))
+# # #### if e3 :
+# zufall dass np.pi/4 genau dem Winkel angle alpha entspricht?:
+# (würde) bei e_2 keinen Unterschied machen um z achse zu rotieren?!
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+# Rotation = rot(np.array([0,0,1]),np.pi/2).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+
+# Rotation = rot(np.array([1,0,0]),np.pi/2)
+
+# Rotation_vector = e3_mapped  #TEST
+# Rotation_vector = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_vector = np.array([0,0,1])
+
+# v = np.array([1,0,0])
+# X = np.array([u1,u2,u3])
+
+
+
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 2, cstride = 2, facecolors=cm.brg(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.viridis(colorfunction), alpha=.4, zorder=4)
+
+
+###---- PLOT PARAMETER-PLANE:
+# ax.plot_surface(x1,x2,zero,color = 'w', rstride = 1, cstride = 1 )
+
+
+print('------------------ Kappa : ', kappa)
+
+#midpoint:
+midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+print('midpoint',midpoint)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+#
+# mapped_e = Rotation.dot(mapped_e)
+# normal = Rotation.dot(normal)
+
+
+# Plot Mapped_midPoint
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=4)          # line width
+
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [mapped_e[0]], [mapped_e[1]], [mapped_e[2]], color="red")
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [normal[0]], [normal[1]], [normal[2]], color="blue")
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 2,
+#            ec ='green',
+#            zorder=3)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 2,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 3)
+
+
+###-- TEST Rotation :
+# v = np.array([1,0,0])
+# t = np.array([0,1,0])
+#
+# ax.arrow3D(0,0,0,
+#            t[0],t[1],t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+#
+# # e_extend
+#
+# rotM = rot(v,np.pi/2)
+#
+# print('rotM:', rotM)
+#
+# rot_t = rotM.dot(t)
+#
+# print('rot_t:', rot_t)
+#
+# ax.arrow3D(0,0,0,
+#            rot_t[0],rot_t[1],rot_t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+### -------------------------------------------
+
+############################################################################################################################################
+####################################################################### KAPPA POSITIVE  ####################################################
+############################################################################################################################################
+
+# kappa = (-1)*kappa
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3, color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.3)  ##This one!
+
+
+# T = rotate_data(X,Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=False)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 2, cstride = 2, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, facecolors=cm.brg(colorfunction), alpha=.8, zorder=4)
+ax.plot_surface(T[0], T[1], T[2], rstride = 5, cstride = 5, color='orange', alpha=.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, color='blue', alpha=.8, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=0.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=1, zorde5r=5)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+# print('midpoint',midpoint)
+print('------------------ Kappa : ', kappa)
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+
+#
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+# Plot MIDPOINT:
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+
+
+
+# mapped_e = grad_u(midpoint,kappa,e)
+# normal = compute_normal(midpoint,kappa,e)
+
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+############################################################################################################################################
+####################################################################### KAPPA ZERO #########################################################
+############################################################################################################################################
+kappa = 0
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3,  rstride = 1, cstride = 1, color = 'white', alpha=0.85)
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride =1 , cstride = 1, color = 'white', alpha=0.55, zorder=3)
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.5, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 10, cstride = 10, color = 'white', alpha=0.55, zorder=2)
+ax.plot_surface(T[0], T[1], T[2],  rstride = 20, cstride = 20, color = 'gray', alpha=0.35, zorder=1, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'white', alpha=0.55, zorder=2)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+mapped_e = grad_u(midpoint,kappa,e)
+normal_zeroCurv = compute_normal(midpoint,kappa,e)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+##-----  PLOT MAPPED MIDPOINT :::
+
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# # linestyle='--',            # line style will be dash line
+# linewidth=1,
+# zorder=5)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='red',
+#            ec ='red')
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal_zeroCurv[0],normal_zeroCurv[1],normal_zeroCurv[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+
+##----------  PLOT MAPPED ORIGIN :::
+# origin = np.array([0,0])
+# origin_mapped = u(origin,kappa,e)
+# print('origin_mapped', origin_mapped)
+#
+# ax.plot(origin_mapped[0],origin_mapped[1],origin_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='green',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+#
+# # rotate mapped origin
+# # v = np.array([1,0,0])
+# # alpha  = Rotation_angle
+#
+# rotM = rot(Rotation_vector,Rotation_angle)
+# # origin_mRot = rotate_data(origin_mapped,v,alpha)
+# origin_mRot = rotM.dot(origin_mapped)
+# print('origin_mapped Rotated', origin_mRot)
+#
+# # --- Compute Distance to Origin 3D
+# origin_3D=np.array([0,0,0])
+# distance = origin_mapped-origin_3D
+# print('distance', distance)
+
+## --------------------------------------------------------
+
+# COMPUTE ANGLE WITH Z AXIS
+z = np.array([0,0,1])
+print('test', normal_zeroCurv*z)
+angle_z = np.arccos(normal_zeroCurv.dot(z) /( (np.linalg.norm(z)*np.linalg.norm(normal_zeroCurv) ) ))
+print('angle between normal and z-axis', angle_z)
+
+## unfinished...
+
+
+
+
+###-------------------------------------  PLOT :
+plt.axis('off')
+# plt.axis('tight')
+
+# ADD colorbar
+# scamap = plt.cm.ScalarMappable(cmap='inferno')
+# fig.colorbar(scamap)
+
+# ax.colorbar()
+# ax.axis('auto')
+# ax.set_title(r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e))
+# ax.set_title(r'Cylindrical minimizer' + '_$e$=' +  str(e))
+ax.set_xlabel(r"x-axis")
+ax.set_ylabel(r"y-axis")
+ax.set_zlabel(r"z-axis")
+
+# TEST :
+# ax.annotate3D('point 1', (0, 0, 0), xytext=(3, 3), textcoords='offset points')
+# ax.annotate3D('point 2', (0, 1, 0),
+#               xytext=(-30, -30),
+#               textcoords='offset points',
+#               arrowprops=dict(ec='black', fc='white', shrink=2.5))
+# ax.annotate3D('point 3', (0, 0, 1),
+#               xytext=(30, -30),
+#               textcoords='offset points',
+#               bbox=dict(boxstyle="round", fc="lightyellow"),
+#               arrowprops=dict(arrowstyle="-|>", ec='black', fc='white', lw=5))
+
+#######################################################################################################################
+
+u1 = T[0]
+u2 = T[1]
+u3 = T[2]
+
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /3
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /12
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /8
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /6
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /2
+mid_u1 = (u1.max()+u1.min()) * 0.5
+mid_u2 = (u2.max()+u2.min()) * 0.5
+mid_u3 = (u3.max()+u3.min()) * 0.5
+
+
+ax.set_xlim(mid_u1 - max_range, mid_u1 + max_range)
+ax.set_ylim(mid_u2 - max_range, mid_u2 + max_range)
+ax.set_zlim(mid_u3 - max_range, mid_u3 + max_range)
+
+ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+# ax.set_ylim((mid_u2 - max_range)-1.5, (mid_u2 + max_range)+1.5)
+# ax.autoscale(tight=True)
+
+
+
+
+##----- CHANGE CAMERA POSITION:
+# ax.view_init(elev=10., azim=0)
+# ax.view_init(elev=38, azim=90)
+# ax.view_init(elev=38, azim=120)
+# ax.view_init(elev=38)
+
+# if e1 ::
+# ax.view_init(elev=44)
+# ax.view_init(elev=38, azim=-90)
+# ax.view_init(elev=38, azim=0)
+ax.view_init(elev=25, azim=-30)
+
+# if e3 ::
+# ax.view_init(elev=25)
+
+# ax.set_xlim3d(-2, 2)
+# ax.set_ylim3d(-1.0,3.0)
+# ax.set_zlim3d(-1.5,2.5)
+
+# ax.set_ylim3d(-10,10)
+# ax.set_xlim(mid_u1 - max_range-0.2, mid_u1 + max_range+0.2)
+# ax.set_zlim(mid_u3 - max_range-0.2, mid_u3 + max_range+0.2)
+# ax.set_ylim(mid_u2 - max_range-0.2, mid_u2 + max_range+0.2)
+
+# width = 6.28 *0.5
+# height = width / 1.618
+# # height = width / 2.5
+# fig.set_size_inches(width, height)
+# fig.savefig('Test-Cylindrical.pdf')
+
+# Figurename = r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e)
+# Figurename = r'Cylindrical minimizer' + '_$e$=' +  str(e)
+Figurename = r'1-ParFamMinimizer_idx' + str(idx)
+# plt.savefig("test.png", bbox_inches='tight')
+# plt.figure().set_size_inches(width, height)
+# plt.set_size_inches(width, height)
+
+
+fig.set_size_inches(width, height)
+fig.savefig(Figurename+".pdf")
+
+plt.savefig(Figurename+".png", bbox_inches='tight')
+# plt.savefig(Figurename+".png")
+plt.show()
+
+
+
+# #---------------------------------------------------------------

Python-Scripts/1-ParameterFamily-Minimizers_Test.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+from mpl_toolkits.mplot3d import Axes3D
+import pandas as pd
+import matplotlib.colors as mcolors
+from matplotlib import cm
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+# Extra packages :
+# from HelperFunctions import *
+# from ClassifyMin import *
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### Documentation #########################
+
+#..... add description here
+
+###########################################################
+
+
+def rot(v,alpha):
+
+#rotate about axis v with degree deg in radians:
+
+
+    tmp = np.array([ [v[0]**2*(1-np.cos(alpha))+np.cos(alpha), v[0]*v[1]*(1-np.cos(alpha))-v[2]*np.sin(alpha), v[0]*v[2]*(1-np.cos(alpha))+ v[1]*np.sin(alpha) ],
+         [v[0]*v[1]*(1-np.cos(alpha))+v[2]*np.sin(alpha), v[1]**2*(1-np.cos(alpha))+np.cos(alpha), v[1]*v[2]*(1-np.cos(alpha))+v[0]*np.sin(alpha) ],
+         [v[2]*v[0]*(1-np.cos(alpha))-v[1]*np.sin(alpha), v[2]*v[1]*(1-np.cos(alpha))+v[0]*np.sin(alpha) , v[2]**2*(1-np.cos(alpha))+np.cos(alpha) ] ])
+
+    return tmp
+
+
+
+def rotate_data(X, R):
+#rotate about axis v with degree deg in radians:
+# X : DataSet
+# R : RotationMatrix
+    print('ROTATE DATA FUNCTION ---------------')
+
+    rot_matrix = R
+    # print('rot_matrix:', rot_matrix)
+    # print('rot_matrix.shape:', rot_matrix.shape)
+    # print('X', X)
+    # print('shape of X[0]', X.shape[0])
+    B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+    # print('shape of B', B.shape)
+    # print('B',B)
+    # print('B[0,:]', B[0,:])
+    # print('B[0,:].shape', B[0,:].shape)
+    Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+    print('shape of Out', Out.shape)
+
+    return Out
+
+# def rotate_data(X, v,alpha): #(Old Version)
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#     rot_matrix = rot(v,alpha)
+#     # print('rot_matrix:', rot_matrix)
+#     # print('rot_matrix.shape:', rot_matrix.shape)
+#
+#     # print('X', X)
+#     # print('shape of X[0]', X.shape[0])
+#     B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+#
+#     # print('shape of B', B.shape)
+#     # print('B',B)
+#     # print('B[0,:]', B[0,:])
+#     # print('B[0,:].shape', B[0,:].shape)
+#     Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+#     print('shape of Out', Out.shape)
+#
+#     return Out
+
+
+# def translate_data(X, v):  ...
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#
+#     print('X', X)
+#     print('shape of X[0]', X.shape[0])
+#
+#     Out = X + v
+#     return Out
+
+#
+# def u(x,kappa,e):
+#
+#     tmp = (x.dot(e))*kappa
+#     # print('tmp for u',tmp)
+#     if kappa == 0 :
+#         tmp = np.array([0*x[0],  x[0]*e[0] + x[1]*e[1], x[1]*e[0] - x[0]*e[1] ])
+#     else :
+#         tmp = np.array([-(1/kappa)*np.cos(tmp)+(1/kappa),  (1/kappa)*np.sin(tmp), -x[0]*e[1]+x[1]*e[0] ])
+#     return tmp
+#
+#
+#
+#
+# def grad_u(x,kappa,e):
+#
+#     tmp = (x.dot(e))*kappa
+#     # print('tmp',tmp)
+#
+#     grad_u = np.array([ [np.sin(tmp)*e[0], np.sin(tmp)*e[1]], [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]] ])
+#     # print('produkt', grad_u.dot(e) )
+#     mapped_e = grad_u.dot(e)
+#     # print('mapped_e:', mapped_e)
+#     # print('siize of mapped_e', mapped_e.shape)
+#     # mapped_e = mapped_e.transpose()
+#     # print('mapped_e:', mapped_e)
+#     # print('siize of mapped_e', mapped_e.shape)
+#     return mapped_e
+#
+# def compute_normal(x,kappa,e):
+#     tmp = (x.dot(e))*kappa
+#     partial1_u = np.array([ np.sin(tmp)*e[0] ,np.cos(tmp)*e[0], -e[1] ])
+#     partial2_u = np.array([ np.sin(tmp)*e[1], np.cos(tmp)*e[1], e[0]      ])
+#     normal = np.cross(partial1_u,partial2_u)
+#     # print('normal=',normal)
+#     return normal
+
+
+
+def u(x,kappa,e):
+
+    tmp = (x.dot(e))*((-1)*kappa)
+    # print('tmp for u',tmp)
+    if kappa == 0 :
+        tmp = np.array([x[0]*e[0] + x[1]*e[1], x[1]*e[0] - x[0]*e[1], 0*x[0]  ])
+    else :
+        tmp = np.array([ -(1/kappa)*np.sin(tmp), -x[0]*e[1]+x[1]*e[0], (1/kappa)*np.cos(tmp)-(1/kappa)   ])
+    return tmp
+
+
+
+# def grad_u(x,kappa,e):
+#
+#     tmp = (x.dot(e))*kappa
+#     # print('tmp',tmp)
+#
+#     grad_u = np.array([ [np.sin(tmp)*e[0], np.sin(tmp)*e[1]], [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]] ])
+#     # print('produkt', grad_u.dot(e) )
+#     mapped_e = grad_u.dot(e)
+#     # print('mapped_e:', mapped_e)
+#     # print('siize of mapped_e', mapped_e.shape)
+#     # mapped_e = mapped_e.transpose()
+#     # print('mapped_e:', mapped_e)
+#     # print('siize of mapped_e', mapped_e.shape)
+#     return mapped_e
+#
+
+
+def grad_u(x,kappa,e):
+
+    tmp = (x.dot(e))*(-1)*kappa
+    # print('tmp',tmp)
+
+    grad_u = np.array([  [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]], [np.sin(tmp)*e[0], np.sin(tmp)*e[1]] ])
+    # print('produkt', grad_u.dot(e) )
+    mapped_e = grad_u.dot(e)
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    # mapped_e = mapped_e.transpose()
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    return mapped_e
+
+
+def compute_normal(x,kappa,e):
+    tmp = (x.dot(e))*(-1)*kappa
+    partial1_u = np.array([ np.cos(tmp)*e[0], -e[1],np.sin(tmp)*e[0]  ])
+    partial2_u = np.array([ np.cos(tmp)*e[1], e[0], np.sin(tmp)*e[1]  ])
+    normal = np.cross(partial1_u,partial2_u)
+    # print('normal=',normal)
+    return normal
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+print('T:', T)
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+e_container = []
+
+
+for t in T :
+
+    abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+    abar_current[abar_current < 1e-10] = 0
+    # print('abar_current', abar_current)
+    # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    e_container.append(e)
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+    # print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+G_container = np.array(G_container)
+abar_container = np.array(abar_container)
+
+e_container = np.array(e_container)
+
+print('G_container', G_container)
+print('G_container.shape', G_container.shape)
+
+# idx_1 = np.where(alphas == np.pi/4)
+idx_1 = np.where(np.round(alphas,2) == round(np.pi/3,2))
+idx_2 = np.where(np.round(alphas,2) == 0.0)
+idx_3 = np.where(np.round(alphas,2) == round(np.pi/4,2))
+
+# idx_3 = np.where(alphas == 0)
+
+print('Index idx_1:', idx_1)
+print('Index idx_2:', idx_2)
+print('Index idx_3:', idx_3)
+print('Index idx_1[0][0]:', idx_1[0][0])
+print('Index idx_2[0][0]:', idx_2[0][0])
+print('Index idx_3[0][0]:', idx_3[0][0])
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+print('min alpha:', min(alphas))
+print('min kappa:', min(kappas))
+
+
+print('G_container[idx_1[0][0]]', G_container[idx_1[0][0]])
+print('G_container[idx_2[0][0]]', G_container[idx_2[0][0]])
+print('G_container[idx_3[0][0]]', G_container[idx_3[0][0]])
+
+
+print('e_container[idx_1[0][0]]', e_container[idx_1[0][0]])
+print('e_container[idx_2[0][0]]', e_container[idx_2[0][0]])
+print('e_container[idx_3[0][0]]', e_container[idx_3[0][0]])
+
+
+
+###################################################
+
+reflect = False
+# reflect = True
+
+
+
+idx = 3
+
+if idx == 1 :
+    e = e_container[idx_1[0][0]]
+    kappa = kappas[idx_1[0][0]]
+    angle = alphas[idx_1[0][0]]
+    reflect = True
+
+if idx == 2 :
+    e = e_container[idx_2[0][0]]
+    kappa = kappas[idx_2[0][0]]
+    angle = alphas[idx_2[0][0]]
+
+
+if idx == 3 :
+    e = e_container[idx_3[0][0]]
+    kappa = kappas[idx_3[0][0]]
+    angle = alphas[idx_3[0][0]]
+
+### SCALE ?
+# kappa = kappa*2
+
+
+print('kappa:',kappa)
+print('angle:',angle)
+###################################################
+#### TEST apply reflection
+#
+# G_tmp = G_container[idx_1[0][0]]
+#
+# print('G_tmp', G_tmp)
+#
+# # Basis:
+# G_1 = np.array([[1.0,0.0], [0.0,0.0]])
+# G_2 = np.array([[0.0,0.0], [0.0,1.0]])
+# G_3 = (1/np.sqrt(2))*np.array([[0.0,1.0], [1.0,0.0]])
+# print('G_1', G_1)
+# print('G_2', G_2)
+# print('G_3', G_3)
+#
+# G = G_tmp[0] * G_1 + G_tmp[1]*G_2 + G_tmp[2]*G_3
+# print('G:', G )
+#
+# T = np.array([[1.0 , -1.0] , [-1.0,1.0]])
+#
+# TG = np.multiply(T,G)
+# print('TG', TG)
+#
+#
+#
+# v = np.array([np.sqrt(TG[0][0]),np.sqrt(TG[1][1]) ])
+# print('v', v)
+# print('norm(v):', np.linalg.norm(v))
+# norm_v = np.linalg.norm(v)
+#
+# kappa = norm_v**2
+#
+# e = (1/norm_v)*v
+# print('e:', e)
+# print('kappa:', kappa)
+
+
+
+
+
+
+if reflect == True:
+    reflected_e = np.array([e[0], -1*e[1]])
+    e = reflected_e                                         # Correct?! Reflect e on x-Axis ??!
+    print('reflected_e:', reflected_e)
+
+
+############################################################################################################################################
+####################################################################### KAPPA NEGATIVE ####################################################
+############################################################################################################################################
+# kappa = -2
+num_Points = 200
+# num_Points = 100
+
+
+# e = np.array([1,0])
+# e = np.array([0,1])
+# e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e = np.array([1/2,np.sqrt(3)/2])
+# e = np.array([np.sqrt(3)/2,1/2])
+# e = np.array([-1,0])
+# e = np.array([0,-1])
+
+###--- Creating dataset
+x = np.linspace(-2,2,num_Points)
+x = np.linspace(-2.5,2.5,num_Points)
+x = np.linspace(-3,3,num_Points)
+# x = np.linspace(-4,4,num_Points)
+
+# x = np.linspace(-1.5,1.5,num_Points)
+# x = np.linspace(-1,1,num_Points)
+y = np.linspace(-1/2,1/2,num_Points)
+y = np.linspace(-1/4,1/4,num_Points)
+
+print('type of x', type(x))
+print('max of x:', max(x))
+print('max of y:', max(y))
+# print('x:', x)
+
+x1, x2 = np.meshgrid(x,y)
+zero = 0*x1
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+
+# print('np.size(u1)',np.size(u1))
+# print('u1.shape',u1.shape)
+# colorfunction=(u1**2+u2**2)
+# print('colofunction',colorfunction)
+
+# print('u1.size:',np.size(u1))
+# tmp = np.ones(np.size(u1))*kappa
+# print('np.size(tmp)',np.size(tmp))
+B = np.full_like(u1, 1)
+# colorfunction=(u3)                                              # TODO Color by angle
+# colorfunction=(np.ones(np.size(u1))*kappa)
+colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+norm=mcolors.Normalize(colorfunction.min(),colorfunction.max())
+
+
+# -----------------------------------------------------
+# Display the mesh
+fig = plt.figure()
+
+
+width = 6.28 *0.5
+width = 6.28 * 0.333
+height = width / 1.618
+height = width / 2.5
+height = width
+
+
+
+ax = plt.axes(projection ='3d', adjustable='box')
+
+
+###---TEST MAP e-vectprs!
+# e1 = np.array([1,0])
+# e2 = np.array([0,1])
+# e3 = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e1 = np.array([0,1])
+# e2 = np.array([-1,0])
+# e3 = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# e1_mapped = u(e1,kappa,e1)
+# e2_mapped = u(e2,kappa,e2)
+# e3_mapped = u(e3,kappa,e3)
+# print('e1 mapped:',e1_mapped)
+# print('e2 mapped:',e2_mapped)
+# print('e3 mapped:',e3_mapped)
+### -----------------------------------
+
+#--e1 :
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([0,1,0])
+
+#--e2:
+Rotation_angle = np.pi/2
+Rotation_vector = np.array([1,0,0])
+
+###--e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([1,0,0])
+# #2te rotation :
+# Rotation_angle = np.pi/4
+# Rotation_vector = np.array([0,0,1])
+
+
+
+Rotation_angle = -np.pi/2
+Rotation_angle = 0
+# Rotation_angle = np.pi/2
+Rotation_vector = np.array([0,1,0])
+Rotation_vector = np.array([1,0,0])
+
+# rot(np.array([0,1,0]),np.pi/2)
+
+# ZERO ROTATION
+Rotation = rot(np.array([0,1,0]),0)
+
+# if idx == 1:
+# Rotation = rot(np.array([1,0,0]),np.pi)
+# Rotation = rot(np.array([1,0,0]),np.pi).dot(rot(np.array([0,0,1]),angle))
+
+Rotation = rot(np.array([1,0,0]),np.pi)
+
+# TEST :
+
+#DETERMINE ANGLE:
+angle = math.atan2(e[1], e[0])
+print('angle:', angle)
+
+## GENERAL TRANSFORMATION / ROTATION:
+# Rotation = rot(np.array([0,0,1]),angle).dot(Rotation)
+Rotation = rot(np.array([1,0,0]),np.pi).dot(rot(np.array([0,0,1]),angle))
+# Rotation = rot(np.array([0,0,1]),angle).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+
+# Rotation = rot(np.array([0,0,1]),np.pi/2).dot(Rotation)
+
+
+### if e1:
+# Rotation = rot(np.array([0,0,1]),-np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+# Add another rotation around z-axis:
+# Rotation = rot(np.array([0,0,1]),+np.pi).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/8).dot(Rotation)
+
+#e3 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4)
+# Rotation = rot(np.array([1,0,0]),np.pi/4)
+#### if e1 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+#### if e2:
+# Rotation = rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2))
+# # #### if e3 :
+# zufall dass np.pi/4 genau dem Winkel angle alpha entspricht?:
+# (würde) bei e_2 keinen Unterschied machen um z achse zu rotieren?!
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+# Rotation = rot(np.array([0,0,1]),np.pi/2).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+
+# Rotation = rot(np.array([1,0,0]),np.pi/2)
+
+# Rotation_vector = e3_mapped  #TEST
+# Rotation_vector = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_vector = np.array([0,0,1])
+
+# v = np.array([1,0,0])
+# X = np.array([u1,u2,u3])
+
+
+
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 2, cstride = 2, facecolors=cm.brg(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.viridis(colorfunction), alpha=.4, zorder=4)
+
+
+###---- PLOT PARAMETER-PLANE:
+# ax.plot_surface(x1,x2,zero,color = 'w', rstride = 1, cstride = 1 )
+
+
+print('------------------ Kappa : ', kappa)
+
+#midpoint:
+midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+print('midpoint',midpoint)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+#
+# mapped_e = Rotation.dot(mapped_e)
+# normal = Rotation.dot(normal)
+
+
+# Plot Mapped_midPoint
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=4)          # line width
+
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [mapped_e[0]], [mapped_e[1]], [mapped_e[2]], color="red")
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [normal[0]], [normal[1]], [normal[2]], color="blue")
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 2,
+#            ec ='green',
+#            zorder=3)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 2,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 3)
+
+
+###-- TEST Rotation :
+# v = np.array([1,0,0])
+# t = np.array([0,1,0])
+#
+# ax.arrow3D(0,0,0,
+#            t[0],t[1],t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+#
+# # e_extend
+#
+# rotM = rot(v,np.pi/2)
+#
+# print('rotM:', rotM)
+#
+# rot_t = rotM.dot(t)
+#
+# print('rot_t:', rot_t)
+#
+# ax.arrow3D(0,0,0,
+#            rot_t[0],rot_t[1],rot_t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+### -------------------------------------------
+
+############################################################################################################################################
+####################################################################### KAPPA POSITIVE  ####################################################
+############################################################################################################################################
+
+# kappa = (-1)*kappa
+
+# if kappa == 0 :
+#     u1 = 0*x1
+#     u2 = x1*e[0] + x2*e[1]
+#     u3 = x2*e[0] - x1*e[1]
+# else :
+#     u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+#     u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+#     u3 = x2*e[0] -x1*e[1]
+
+if kappa == 0 :
+    # u1 = 0*x1
+    # u2 = x1*e[0] + x2*e[1]
+    # u3 = x2*e[0] - x1*e[1]
+    u1 = x1*e[0] + x2*e[1]
+    u2 = x2*e[0] - x1*e[1]
+    u3 = 0*x1
+
+else :
+    # u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    # u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    # u3 = x2*e[0] -x1*e[1]
+    u1 = -(1/kappa)*np.sin((-1)*kappa*(x1*e[0]+x2*e[1]))
+    u2 =  x2*e[0] -x1*e[1]
+    u3 = (1/kappa)*np.cos((-1)*kappa*(x1*e[0]+x2*e[1]))-(1/kappa)
+
+
+
+# ax.plot_surface(u1, u2, u3, color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.3)  ##This one!
+
+
+# T = rotate_data(X,Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=False)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 2, cstride = 2, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, facecolors=cm.brg(colorfunction), alpha=.8, zorder=4)
+ax.plot_surface(T[0], T[1], T[2], rstride = 5, cstride = 5, color='orange', alpha=.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, color='blue', alpha=.8, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=0.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=1, zorde5r=5)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+# print('midpoint',midpoint)
+print('------------------ Kappa : ', kappa)
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+
+#
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+# Plot MIDPOINT:
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+
+
+#midpoint:
+endpoint = np.array([min(x),(max(y)+min(y))/2])
+print('endpoint',endpoint)
+
+# Map midpoint:
+endpoint_mapped = u(endpoint,kappa,e)
+print('mapped endpoint', endpoint_mapped)
+
+endpoint_mapped = Rotation.dot(endpoint_mapped)
+
+mapped_e = grad_u(endpoint,kappa,e)
+normal = compute_normal(endpoint,kappa,e)
+
+
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+
+reverse_normal = np.array([ (-1)*normal[0], (-1)*normal[1], (-1)*normal[2]])
+
+ax.plot(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],    # data
+marker='o',     # each marker will be rendered as a circle
+markersize=1,   # marker size
+markerfacecolor='black',   # marker facecolor
+markeredgecolor='black',  # marker edgecolor
+markeredgewidth=0.5,       # marker edge width
+linewidth=1,
+zorder=5)          # line width
+
+
+
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+           reverse_normal[0],reverse_normal[1],reverse_normal[2],
+           mutation_scale=10,
+            lw = 1.5,
+           arrowstyle="-|>",
+           linestyle='-',fc='purple', alpha=0.75,
+           ec ='purple',
+           zorder = 5)
+
+
+
+
+# second Endpoint
+endpoint = np.array([max(x),(max(y)+min(y))/2])
+print('endpoint',endpoint)
+
+# Map midpoint:
+endpoint_mapped = u(endpoint,kappa,e)
+print('mapped endpoint', endpoint_mapped)
+
+endpoint_mapped = Rotation.dot(endpoint_mapped)
+
+mapped_e = grad_u(endpoint,kappa,e)
+normal = compute_normal(endpoint,kappa,e)
+
+
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+
+reverse_normal = np.array([ (-1)*normal[0], (-1)*normal[1], (-1)*normal[2]])
+
+ax.plot(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],    # data
+marker='o',     # each marker will be rendered as a circle
+markersize=1,   # marker size
+markerfacecolor='black',   # marker facecolor
+markeredgecolor='black',  # marker edgecolor
+markeredgewidth=0.5,       # marker edge width
+linewidth=1,
+zorder=5)          # line width
+
+
+
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+           reverse_normal[0],reverse_normal[1],reverse_normal[2],
+           mutation_scale=10,
+            lw = 1.5,
+           arrowstyle="-|>",
+           linestyle='-',fc='purple', alpha=0.75,
+           ec ='purple',
+           zorder = 5)
+
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+############################################################################################################################################
+####################################################################### KAPPA ZERO #########################################################
+############################################################################################################################################
+kappa = 0
+
+# if kappa == 0 :
+#     u1 = 0*x1
+#     u2 = x1*e[0] + x2*e[1]
+#     u3 = x2*e[0] - x1*e[1]
+# else :
+#     u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+#     u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+#     u3 = x2*e[0] -x1*e[1]
+
+if kappa == 0 :
+    # u1 = 0*x1
+    # u2 = x1*e[0] + x2*e[1]
+    # u3 = x2*e[0] - x1*e[1]
+    u1 = x1*e[0] + x2*e[1]
+    u2 = x2*e[0] - x1*e[1]
+    u3 = 0*x1
+
+else :
+    # u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    # u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    # u3 = x2*e[0] -x1*e[1]
+    u1 = -(1/kappa)*np.sin((-1)*kappa*(x1*e[0]+x2*e[1]))
+    u2 =  x2*e[0] -x1*e[1]
+    u3 = (1/kappa)*np.cos((-1)*kappa*(x1*e[0]+x2*e[1]))-(1/kappa)
+# ax.plot_surface(u1, u2, u3,  rstride = 1, cstride = 1, color = 'white', alpha=0.85)
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride =1 , cstride = 1, color = 'white', alpha=0.55, zorder=3)
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.5, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 10, cstride = 10, color = 'white', alpha=0.55, zorder=2)
+ax.plot_surface(T[0], T[1], T[2],  rstride = 20, cstride = 20, color = 'gray', alpha=0.35, zorder=1, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'white', alpha=0.55, zorder=2)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+mapped_e = grad_u(midpoint,kappa,e)
+normal_zeroCurv = compute_normal(midpoint,kappa,e)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+##-----  PLOT MAPPED MIDPOINT :::
+
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# # linestyle='--',            # line style will be dash line
+# linewidth=1,
+# zorder=5)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='red',
+#            ec ='red')
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal_zeroCurv[0],normal_zeroCurv[1],normal_zeroCurv[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+
+##----------  PLOT MAPPED ORIGIN :::
+# origin = np.array([0,0])
+# origin_mapped = u(origin,kappa,e)
+# print('origin_mapped', origin_mapped)
+#
+# ax.plot(origin_mapped[0],origin_mapped[1],origin_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='green',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+#
+# # rotate mapped origin
+# # v = np.array([1,0,0])
+# # alpha  = Rotation_angle
+#
+# rotM = rot(Rotation_vector,Rotation_angle)
+# # origin_mRot = rotate_data(origin_mapped,v,alpha)
+# origin_mRot = rotM.dot(origin_mapped)
+# print('origin_mapped Rotated', origin_mRot)
+#
+# # --- Compute Distance to Origin 3D
+# origin_3D=np.array([0,0,0])
+# distance = origin_mapped-origin_3D
+# print('distance', distance)
+
+## --------------------------------------------------------
+
+# COMPUTE ANGLE WITH Z AXIS
+z = np.array([0,0,1])
+print('test', normal_zeroCurv*z)
+angle_z = np.arccos(normal_zeroCurv.dot(z) /( (np.linalg.norm(z)*np.linalg.norm(normal_zeroCurv) ) ))
+print('angle between normal and z-axis', angle_z)
+
+## unfinished...
+
+
+
+
+###-------------------------------------  PLOT :
+plt.axis('off')
+# plt.axis('tight')
+
+# ADD colorbar
+# scamap = plt.cm.ScalarMappable(cmap='inferno')
+# fig.colorbar(scamap)
+
+# ax.colorbar()
+# ax.axis('auto')
+# ax.set_title(r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e))
+# ax.set_title(r'Cylindrical minimizer' + '_$e$=' +  str(e))
+ax.set_xlabel(r"x-axis")
+ax.set_ylabel(r"y-axis")
+ax.set_zlabel(r"z-axis")
+
+# TEST :
+# ax.annotate3D('point 1', (0, 0, 0), xytext=(3, 3), textcoords='offset points')
+# ax.annotate3D('point 2', (0, 1, 0),
+#               xytext=(-30, -30),
+#               textcoords='offset points',
+#               arrowprops=dict(ec='black', fc='white', shrink=2.5))
+# ax.annotate3D('point 3', (0, 0, 1),
+#               xytext=(30, -30),
+#               textcoords='offset points',
+#               bbox=dict(boxstyle="round", fc="lightyellow"),
+#               arrowprops=dict(arrowstyle="-|>", ec='black', fc='white', lw=5))
+
+#######################################################################################################################
+
+u1 = T[0]
+u2 = T[1]
+u3 = T[2]
+
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /3
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /12
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /8
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /10
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /14
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /6
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /2
+mid_u1 = (u1.max()+u1.min()) * 0.5
+mid_u2 = (u2.max()+u2.min()) * 0.5
+mid_u3 = (u3.max()+u3.min()) * 0.5
+
+
+ax.set_xlim(mid_u1 - max_range, mid_u1 + max_range)
+ax.set_ylim(mid_u2 - max_range, mid_u2 + max_range)
+ax.set_zlim(mid_u3 - max_range, mid_u3 + max_range)
+
+ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+# ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+# ax.set_ylim((mid_u2 - max_range)-1.5, (mid_u2 + max_range)+1.5)
+# # ax.autoscale(tight=True)
+# ax.set_xlim((mid_u1 - max_range)-1, (mid_u1 + max_range)+1)
+# ax.set_xlim((mid_u1 - max_range)-0.5, (mid_u1 + max_range)+0.5)
+ax.set_xlim((mid_u1 - max_range)-2, (mid_u1 + max_range)+2)
+# ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+
+# ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+3)
+# ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+
+
+##----- CHANGE CAMERA POSITION:
+# ax.view_init(elev=10., azim=0)
+# ax.view_init(elev=38, azim=90)
+# ax.view_init(elev=38, azim=120)
+# ax.view_init(elev=38)
+
+# if e1 ::
+# ax.view_init(elev=44)
+# ax.view_init(elev=38, azim=-90)
+# ax.view_init(elev=38, azim=0)
+# ax.view_init(elev=25, azim=-30)
+# ax.view_init(elev=18, azim=-30)
+ax.view_init(elev=25, azim=-125)
+# ax.view_init(elev=25, azim=150)
+# ax.view_init(elev=25, azim=135)
+
+# ax.view_init(elev=25, azim=125)   #idx2
+
+
+
+# ax.view_init(elev=25, azim=145)
+
+
+# if e3 ::
+# ax.view_init(elev=25)
+
+# ax.set_xlim3d(-2, 2)
+# ax.set_ylim3d(-1.0,3.0)
+# ax.set_zlim3d(-1.5,2.5)
+
+# ax.set_ylim3d(-10,10)
+# ax.set_xlim(mid_u1 - max_range-0.2, mid_u1 + max_range+0.2)
+# ax.set_zlim(mid_u3 - max_range-0.2, mid_u3 + max_range+0.2)
+# ax.set_ylim(mid_u2 - max_range-0.2, mid_u2 + max_range+0.2)
+
+# width = 6.28 *0.5
+# height = width / 1.618
+# # height = width / 2.5
+# fig.set_size_inches(width, height)
+# fig.savefig('Test-Cylindrical.pdf')
+
+# Figurename = r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e)
+# Figurename = r'Cylindrical minimizer' + '_$e$=' +  str(e)
+Figurename = r'1-ParFamMinimizer_idx' + str(idx)
+# plt.savefig("test.png", bbox_inches='tight')
+# plt.figure().set_size_inches(width, height)
+# plt.set_size_inches(width, height)
+
+
+# fig.set_size_inches(width, height) !!!!!
+
+
+
+
+fig.savefig(Figurename+".pdf")
+
+plt.savefig(Figurename+".png", bbox_inches='tight', dpi=300)
+# plt.savefig(Figurename+".png")
+plt.show()
+
+
+
+# #---------------------------------------------------------------

Python-Scripts/1-ParameterFamily-Minimizers_v2.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+from mpl_toolkits.mplot3d import Axes3D
+import pandas as pd
+import matplotlib.colors as mcolors
+from matplotlib import cm
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+# Extra packages :
+# from HelperFunctions import *
+# from ClassifyMin import *
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### Documentation #########################
+
+#..... add description here
+
+###########################################################
+
+
+def rot(v,alpha):
+
+#rotate about axis v with degree deg in radians:
+
+
+    tmp = np.array([ [v[0]**2*(1-np.cos(alpha))+np.cos(alpha), v[0]*v[1]*(1-np.cos(alpha))-v[2]*np.sin(alpha), v[0]*v[2]*(1-np.cos(alpha))+ v[1]*np.sin(alpha) ],
+         [v[0]*v[1]*(1-np.cos(alpha))+v[2]*np.sin(alpha), v[1]**2*(1-np.cos(alpha))+np.cos(alpha), v[1]*v[2]*(1-np.cos(alpha))+v[0]*np.sin(alpha) ],
+         [v[2]*v[0]*(1-np.cos(alpha))-v[1]*np.sin(alpha), v[2]*v[1]*(1-np.cos(alpha))+v[0]*np.sin(alpha) , v[2]**2*(1-np.cos(alpha))+np.cos(alpha) ] ])
+
+    return tmp
+
+
+
+def rotate_data(X, R):
+#rotate about axis v with degree deg in radians:
+# X : DataSet
+# R : RotationMatrix
+    print('ROTATE DATA FUNCTION ---------------')
+
+    rot_matrix = R
+    # print('rot_matrix:', rot_matrix)
+    # print('rot_matrix.shape:', rot_matrix.shape)
+    # print('X', X)
+    # print('shape of X[0]', X.shape[0])
+    B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+    # print('shape of B', B.shape)
+    # print('B',B)
+    # print('B[0,:]', B[0,:])
+    # print('B[0,:].shape', B[0,:].shape)
+    Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+    print('shape of Out', Out.shape)
+
+    return Out
+
+# def rotate_data(X, v,alpha): #(Old Version)
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#     rot_matrix = rot(v,alpha)
+#     # print('rot_matrix:', rot_matrix)
+#     # print('rot_matrix.shape:', rot_matrix.shape)
+#
+#     # print('X', X)
+#     # print('shape of X[0]', X.shape[0])
+#     B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+#
+#     # print('shape of B', B.shape)
+#     # print('B',B)
+#     # print('B[0,:]', B[0,:])
+#     # print('B[0,:].shape', B[0,:].shape)
+#     Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+#     print('shape of Out', Out.shape)
+#
+#     return Out
+
+
+# def translate_data(X, v):  ...
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#
+#     print('X', X)
+#     print('shape of X[0]', X.shape[0])
+#
+#     Out = X + v
+#     return Out
+
+
+def u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp for u',tmp)
+    if kappa == 0 :
+        tmp = np.array([0*x[0],  x[0]*e[0] + x[1]*e[1], x[1]*e[0] - x[0]*e[1] ])
+    else :
+        tmp = np.array([-(1/kappa)*np.cos(tmp)+(1/kappa),  (1/kappa)*np.sin(tmp), -x[0]*e[1]+x[1]*e[0] ])
+    return tmp
+
+
+
+
+def grad_u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp',tmp)
+
+    grad_u = np.array([ [np.sin(tmp)*e[0], np.sin(tmp)*e[1]], [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]] ])
+    # print('produkt', grad_u.dot(e) )
+    mapped_e = grad_u.dot(e)
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    # mapped_e = mapped_e.transpose()
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    return mapped_e
+
+def compute_normal(x,kappa,e):
+    tmp = (x.dot(e))*kappa
+    partial1_u = np.array([ np.sin(tmp)*e[0] ,np.cos(tmp)*e[0], -e[1] ])
+    partial2_u = np.array([ np.sin(tmp)*e[1], np.cos(tmp)*e[1], e[0]      ])
+    normal = np.cross(partial1_u,partial2_u)
+    # print('normal=',normal)
+    return normal
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+print('T:', T)
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+e_container = []
+
+
+for t in T :
+
+    abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+    abar_current[abar_current < 1e-10] = 0
+    # print('abar_current', abar_current)
+    # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    e_container.append(e)
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+    # print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+G_container = np.array(G_container)
+abar_container = np.array(abar_container)
+
+e_container = np.array(e_container)
+
+print('G_container', G_container)
+print('G_container.shape', G_container.shape)
+
+# idx_1 = np.where(alphas == np.pi/4)
+idx_1 = np.where(np.round(alphas,2) == round(np.pi/3,2))
+idx_2 = np.where(np.round(alphas,2) == 0.0)
+idx_3 = np.where(np.round(alphas,2) == round(np.pi/4,2))
+
+# idx_3 = np.where(alphas == 0)
+
+print('Index idx_1:', idx_1)
+print('Index idx_2:', idx_2)
+print('Index idx_3:', idx_3)
+print('Index idx_1[0][0]:', idx_1[0][0])
+print('Index idx_2[0][0]:', idx_2[0][0])
+print('Index idx_3[0][0]:', idx_3[0][0])
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+print('min alpha:', min(alphas))
+print('min kappa:', min(kappas))
+
+
+print('G_container[idx_1[0][0]]', G_container[idx_1[0][0]])
+print('G_container[idx_2[0][0]]', G_container[idx_2[0][0]])
+print('G_container[idx_3[0][0]]', G_container[idx_3[0][0]])
+
+
+print('e_container[idx_1[0][0]]', e_container[idx_1[0][0]])
+print('e_container[idx_2[0][0]]', e_container[idx_2[0][0]])
+print('e_container[idx_3[0][0]]', e_container[idx_3[0][0]])
+
+
+
+###################################################
+
+reflect = False
+# reflect = True
+
+
+
+idx = 1
+
+if idx == 1 :
+    e = e_container[idx_1[0][0]]
+    kappa = kappas[idx_1[0][0]]
+    angle = alphas[idx_1[0][0]]
+    reflect = True
+
+if idx == 2 :
+    e = e_container[idx_2[0][0]]
+    kappa = kappas[idx_2[0][0]]
+    angle = alphas[idx_2[0][0]]
+
+
+if idx == 3 :
+    e = e_container[idx_3[0][0]]
+    kappa = kappas[idx_3[0][0]]
+    angle = alphas[idx_3[0][0]]
+
+### SCALE ?
+# kappa = kappa*2
+
+
+print('kappa:',kappa)
+print('angle:',angle)
+###################################################
+#### TEST apply reflection
+#
+# G_tmp = G_container[idx_1[0][0]]
+#
+# print('G_tmp', G_tmp)
+#
+# # Basis:
+# G_1 = np.array([[1.0,0.0], [0.0,0.0]])
+# G_2 = np.array([[0.0,0.0], [0.0,1.0]])
+# G_3 = (1/np.sqrt(2))*np.array([[0.0,1.0], [1.0,0.0]])
+# print('G_1', G_1)
+# print('G_2', G_2)
+# print('G_3', G_3)
+#
+# G = G_tmp[0] * G_1 + G_tmp[1]*G_2 + G_tmp[2]*G_3
+# print('G:', G )
+#
+# T = np.array([[1.0 , -1.0] , [-1.0,1.0]])
+#
+# TG = np.multiply(T,G)
+# print('TG', TG)
+#
+#
+#
+# v = np.array([np.sqrt(TG[0][0]),np.sqrt(TG[1][1]) ])
+# print('v', v)
+# print('norm(v):', np.linalg.norm(v))
+# norm_v = np.linalg.norm(v)
+#
+# kappa = norm_v**2
+#
+# e = (1/norm_v)*v
+# print('e:', e)
+# print('kappa:', kappa)
+
+
+
+
+
+
+if reflect == True:
+    reflected_e = np.array([e[0], -1*e[1]])
+    e = reflected_e                                         # Correct?! Reflect e on x-Axis ??!
+    print('reflected_e:', reflected_e)
+
+
+############################################################################################################################################
+####################################################################### KAPPA NEGATIVE ####################################################
+############################################################################################################################################
+# kappa = -2
+num_Points = 200
+num_Points = 100
+
+
+# e = np.array([1,0])
+# e = np.array([0,1])
+# e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e = np.array([1/2,np.sqrt(3)/2])
+# e = np.array([np.sqrt(3)/2,1/2])
+# e = np.array([-1,0])
+# e = np.array([0,-1])
+
+###--- Creating dataset
+x = np.linspace(-2,2,num_Points)
+x = np.linspace(-3,3,num_Points)
+x = np.linspace(-4,4,num_Points)
+
+# x = np.linspace(-1.5,1.5,num_Points)
+# x = np.linspace(-1,1,num_Points)
+y = np.linspace(-1/2,1/2,num_Points)
+y = np.linspace(-1/4,1/4,num_Points)
+
+print('type of x', type(x))
+print('max of x:', max(x))
+print('max of y:', max(y))
+# print('x:', x)
+
+x1, x2 = np.meshgrid(x,y)
+zero = 0*x1
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+
+# print('np.size(u1)',np.size(u1))
+# print('u1.shape',u1.shape)
+# colorfunction=(u1**2+u2**2)
+# print('colofunction',colorfunction)
+
+# print('u1.size:',np.size(u1))
+# tmp = np.ones(np.size(u1))*kappa
+# print('np.size(tmp)',np.size(tmp))
+B = np.full_like(u1, 1)
+# colorfunction=(u3)                                              # TODO Color by angle
+# colorfunction=(np.ones(np.size(u1))*kappa)
+colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+norm=mcolors.Normalize(colorfunction.min(),colorfunction.max())
+
+
+# -----------------------------------------------------
+# Display the mesh
+fig = plt.figure()
+
+
+width = 6.28 *0.5
+width = 6.28 * 0.333
+height = width / 1.618
+height = width / 2.5
+height = width
+
+
+
+ax = plt.axes(projection ='3d', adjustable='box')
+
+
+###---TEST MAP e-vectprs!
+# e1 = np.array([1,0])
+# e2 = np.array([0,1])
+# e3 = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e1 = np.array([0,1])
+# e2 = np.array([-1,0])
+# e3 = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# e1_mapped = u(e1,kappa,e1)
+# e2_mapped = u(e2,kappa,e2)
+# e3_mapped = u(e3,kappa,e3)
+# print('e1 mapped:',e1_mapped)
+# print('e2 mapped:',e2_mapped)
+# print('e3 mapped:',e3_mapped)
+### -----------------------------------
+
+#--e1 :
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([0,1,0])
+
+#--e2:
+Rotation_angle = np.pi/2
+Rotation_vector = np.array([1,0,0])
+
+###--e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([1,0,0])
+# #2te rotation :
+# Rotation_angle = np.pi/4
+# Rotation_vector = np.array([0,0,1])
+
+
+
+Rotation_angle = -np.pi/2
+Rotation_angle = 0
+# Rotation_angle = np.pi/2
+Rotation_vector = np.array([0,1,0])
+Rotation_vector = np.array([1,0,0])
+
+# rot(np.array([0,1,0]),np.pi/2)
+
+# ZERO ROTATION
+Rotation = rot(np.array([0,1,0]),0)
+
+
+
+# TEST :
+
+#DETERMINE ANGLE:
+angle = math.atan2(e[1], e[0])
+print('angle:', angle)
+
+## GENERAL TRANSFORMATION / ROTATION:
+Rotation = rot(np.array([0,0,1]),angle).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+
+
+### if e1:
+# Rotation = rot(np.array([0,0,1]),-np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+# Add another rotation around z-axis:
+# Rotation = rot(np.array([0,0,1]),+np.pi).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/8).dot(Rotation)
+
+#e3 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4)
+# Rotation = rot(np.array([1,0,0]),np.pi/4)
+#### if e1 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+#### if e2:
+# Rotation = rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2))
+# # #### if e3 :
+# zufall dass np.pi/4 genau dem Winkel angle alpha entspricht?:
+# (würde) bei e_2 keinen Unterschied machen um z achse zu rotieren?!
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+# Rotation = rot(np.array([0,0,1]),np.pi/2).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+
+# Rotation = rot(np.array([1,0,0]),np.pi/2)
+
+# Rotation_vector = e3_mapped  #TEST
+# Rotation_vector = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_vector = np.array([0,0,1])
+
+# v = np.array([1,0,0])
+# X = np.array([u1,u2,u3])
+
+
+
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 2, cstride = 2, facecolors=cm.brg(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.viridis(colorfunction), alpha=.4, zorder=4)
+
+
+###---- PLOT PARAMETER-PLANE:
+# ax.plot_surface(x1,x2,zero,color = 'w', rstride = 1, cstride = 1 )
+
+
+print('------------------ Kappa : ', kappa)
+
+#midpoint:
+midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+print('midpoint',midpoint)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+#
+# mapped_e = Rotation.dot(mapped_e)
+# normal = Rotation.dot(normal)
+
+
+# Plot Mapped_midPoint
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=4)          # line width
+
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [mapped_e[0]], [mapped_e[1]], [mapped_e[2]], color="red")
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [normal[0]], [normal[1]], [normal[2]], color="blue")
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 2,
+#            ec ='green',
+#            zorder=3)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 2,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 3)
+
+
+###-- TEST Rotation :
+# v = np.array([1,0,0])
+# t = np.array([0,1,0])
+#
+# ax.arrow3D(0,0,0,
+#            t[0],t[1],t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+#
+# # e_extend
+#
+# rotM = rot(v,np.pi/2)
+#
+# print('rotM:', rotM)
+#
+# rot_t = rotM.dot(t)
+#
+# print('rot_t:', rot_t)
+#
+# ax.arrow3D(0,0,0,
+#            rot_t[0],rot_t[1],rot_t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+### -------------------------------------------
+
+############################################################################################################################################
+####################################################################### KAPPA POSITIVE  ####################################################
+############################################################################################################################################
+
+# kappa = (-1)*kappa
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3, color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.3)  ##This one!
+
+
+# T = rotate_data(X,Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=False)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 2, cstride = 2, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, facecolors=cm.brg(colorfunction), alpha=.8, zorder=4)
+ax.plot_surface(T[0], T[1], T[2], rstride = 5, cstride = 5, color='orange', alpha=.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, color='blue', alpha=.8, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=0.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=1, zorde5r=5)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+# print('midpoint',midpoint)
+print('------------------ Kappa : ', kappa)
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+
+#
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+# Plot MIDPOINT:
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+
+
+#midpoint:
+endpoint = np.array([min(x),(max(y)+min(y))/2])
+print('endpoint',endpoint)
+
+# Map midpoint:
+endpoint_mapped = u(endpoint,kappa,e)
+print('mapped endpoint', endpoint_mapped)
+
+endpoint_mapped = Rotation.dot(endpoint_mapped)
+
+mapped_e = grad_u(endpoint,kappa,e)
+normal = compute_normal(endpoint,kappa,e)
+
+
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+############################################################################################################################################
+####################################################################### KAPPA ZERO #########################################################
+############################################################################################################################################
+kappa = 0
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3,  rstride = 1, cstride = 1, color = 'white', alpha=0.85)
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride =1 , cstride = 1, color = 'white', alpha=0.55, zorder=3)
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.5, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 10, cstride = 10, color = 'white', alpha=0.55, zorder=2)
+ax.plot_surface(T[0], T[1], T[2],  rstride = 20, cstride = 20, color = 'gray', alpha=0.35, zorder=1, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'white', alpha=0.55, zorder=2)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+mapped_e = grad_u(midpoint,kappa,e)
+normal_zeroCurv = compute_normal(midpoint,kappa,e)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+##-----  PLOT MAPPED MIDPOINT :::
+
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# # linestyle='--',            # line style will be dash line
+# linewidth=1,
+# zorder=5)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='red',
+#            ec ='red')
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal_zeroCurv[0],normal_zeroCurv[1],normal_zeroCurv[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+
+##----------  PLOT MAPPED ORIGIN :::
+# origin = np.array([0,0])
+# origin_mapped = u(origin,kappa,e)
+# print('origin_mapped', origin_mapped)
+#
+# ax.plot(origin_mapped[0],origin_mapped[1],origin_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='green',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+#
+# # rotate mapped origin
+# # v = np.array([1,0,0])
+# # alpha  = Rotation_angle
+#
+# rotM = rot(Rotation_vector,Rotation_angle)
+# # origin_mRot = rotate_data(origin_mapped,v,alpha)
+# origin_mRot = rotM.dot(origin_mapped)
+# print('origin_mapped Rotated', origin_mRot)
+#
+# # --- Compute Distance to Origin 3D
+# origin_3D=np.array([0,0,0])
+# distance = origin_mapped-origin_3D
+# print('distance', distance)
+
+## --------------------------------------------------------
+
+# COMPUTE ANGLE WITH Z AXIS
+z = np.array([0,0,1])
+print('test', normal_zeroCurv*z)
+angle_z = np.arccos(normal_zeroCurv.dot(z) /( (np.linalg.norm(z)*np.linalg.norm(normal_zeroCurv) ) ))
+print('angle between normal and z-axis', angle_z)
+
+## unfinished...
+
+
+
+
+###-------------------------------------  PLOT :
+plt.axis('off')
+# plt.axis('tight')
+
+# ADD colorbar
+# scamap = plt.cm.ScalarMappable(cmap='inferno')
+# fig.colorbar(scamap)
+
+# ax.colorbar()
+# ax.axis('auto')
+# ax.set_title(r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e))
+# ax.set_title(r'Cylindrical minimizer' + '_$e$=' +  str(e))
+ax.set_xlabel(r"x-axis")
+ax.set_ylabel(r"y-axis")
+ax.set_zlabel(r"z-axis")
+
+# TEST :
+# ax.annotate3D('point 1', (0, 0, 0), xytext=(3, 3), textcoords='offset points')
+# ax.annotate3D('point 2', (0, 1, 0),
+#               xytext=(-30, -30),
+#               textcoords='offset points',
+#               arrowprops=dict(ec='black', fc='white', shrink=2.5))
+# ax.annotate3D('point 3', (0, 0, 1),
+#               xytext=(30, -30),
+#               textcoords='offset points',
+#               bbox=dict(boxstyle="round", fc="lightyellow"),
+#               arrowprops=dict(arrowstyle="-|>", ec='black', fc='white', lw=5))
+
+#######################################################################################################################
+
+u1 = T[0]
+u2 = T[1]
+u3 = T[2]
+
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /3
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /12
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /8
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /10
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /14
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /6
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /2
+mid_u1 = (u1.max()+u1.min()) * 0.5
+mid_u2 = (u2.max()+u2.min()) * 0.5
+mid_u3 = (u3.max()+u3.min()) * 0.5
+
+
+ax.set_xlim(mid_u1 - max_range, mid_u1 + max_range)
+ax.set_ylim(mid_u2 - max_range, mid_u2 + max_range)
+ax.set_zlim(mid_u3 - max_range, mid_u3 + max_range)
+
+ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+# ax.set_ylim((mid_u2 - max_range)-1.5, (mid_u2 + max_range)+1.5)
+# ax.autoscale(tight=True)
+ax.set_xlim((mid_u1 - max_range)-1, (mid_u1 + max_range)+1)
+ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+
+# ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+3)
+# ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+
+
+##----- CHANGE CAMERA POSITION:
+# ax.view_init(elev=10., azim=0)
+# ax.view_init(elev=38, azim=90)
+# ax.view_init(elev=38, azim=120)
+# ax.view_init(elev=38)
+
+# if e1 ::
+# ax.view_init(elev=44)
+# ax.view_init(elev=38, azim=-90)
+# ax.view_init(elev=38, azim=0)
+# ax.view_init(elev=25, azim=-30)
+ax.view_init(elev=18, azim=-30)
+
+# if e3 ::
+# ax.view_init(elev=25)
+
+# ax.set_xlim3d(-2, 2)
+# ax.set_ylim3d(-1.0,3.0)
+# ax.set_zlim3d(-1.5,2.5)
+
+# ax.set_ylim3d(-10,10)
+# ax.set_xlim(mid_u1 - max_range-0.2, mid_u1 + max_range+0.2)
+# ax.set_zlim(mid_u3 - max_range-0.2, mid_u3 + max_range+0.2)
+# ax.set_ylim(mid_u2 - max_range-0.2, mid_u2 + max_range+0.2)
+
+# width = 6.28 *0.5
+# height = width / 1.618
+# # height = width / 2.5
+# fig.set_size_inches(width, height)
+# fig.savefig('Test-Cylindrical.pdf')
+
+# Figurename = r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e)
+# Figurename = r'Cylindrical minimizer' + '_$e$=' +  str(e)
+Figurename = r'1-ParFamMinimizer_idx' + str(idx)
+# plt.savefig("test.png", bbox_inches='tight')
+# plt.figure().set_size_inches(width, height)
+# plt.set_size_inches(width, height)
+
+
+fig.set_size_inches(width, height)
+fig.savefig(Figurename+".pdf")
+
+plt.savefig(Figurename+".png", bbox_inches='tight')
+# plt.savefig(Figurename+".png")
+plt.show()
+
+
+
+# #---------------------------------------------------------------

Python-Scripts/1-ParameterFamily-Minimizers_v3.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+from mpl_toolkits.mplot3d import Axes3D
+import pandas as pd
+import matplotlib.colors as mcolors
+from matplotlib import cm
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+# Extra packages :
+# from HelperFunctions import *
+# from ClassifyMin import *
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### Documentation #########################
+
+#..... add description here
+
+###########################################################
+
+
+def rot(v,alpha):
+
+#rotate about axis v with degree deg in radians:
+
+
+    tmp = np.array([ [v[0]**2*(1-np.cos(alpha))+np.cos(alpha), v[0]*v[1]*(1-np.cos(alpha))-v[2]*np.sin(alpha), v[0]*v[2]*(1-np.cos(alpha))+ v[1]*np.sin(alpha) ],
+         [v[0]*v[1]*(1-np.cos(alpha))+v[2]*np.sin(alpha), v[1]**2*(1-np.cos(alpha))+np.cos(alpha), v[1]*v[2]*(1-np.cos(alpha))+v[0]*np.sin(alpha) ],
+         [v[2]*v[0]*(1-np.cos(alpha))-v[1]*np.sin(alpha), v[2]*v[1]*(1-np.cos(alpha))+v[0]*np.sin(alpha) , v[2]**2*(1-np.cos(alpha))+np.cos(alpha) ] ])
+
+    return tmp
+
+
+
+def rotate_data(X, R):
+#rotate about axis v with degree deg in radians:
+# X : DataSet
+# R : RotationMatrix
+    print('ROTATE DATA FUNCTION ---------------')
+
+    rot_matrix = R
+    # print('rot_matrix:', rot_matrix)
+    # print('rot_matrix.shape:', rot_matrix.shape)
+    # print('X', X)
+    # print('shape of X[0]', X.shape[0])
+    B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+    # print('shape of B', B.shape)
+    # print('B',B)
+    # print('B[0,:]', B[0,:])
+    # print('B[0,:].shape', B[0,:].shape)
+    Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+    print('shape of Out', Out.shape)
+
+    return Out
+
+# def rotate_data(X, v,alpha): #(Old Version)
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#     rot_matrix = rot(v,alpha)
+#     # print('rot_matrix:', rot_matrix)
+#     # print('rot_matrix.shape:', rot_matrix.shape)
+#
+#     # print('X', X)
+#     # print('shape of X[0]', X.shape[0])
+#     B = np.dot(rot_matrix, X.reshape(rot_matrix.shape[1],-1))
+#
+#     # print('shape of B', B.shape)
+#     # print('B',B)
+#     # print('B[0,:]', B[0,:])
+#     # print('B[0,:].shape', B[0,:].shape)
+#     Out = np.array([B[0,:].reshape(X.shape[1],X.shape[2]), B[1,:].reshape(X.shape[1],X.shape[2]), B[2,:].reshape(X.shape[1],X.shape[2])])
+#     print('shape of Out', Out.shape)
+#
+#     return Out
+
+
+# def translate_data(X, v):  ...
+# #rotate about axis v with degree deg in radians:
+# # X : DataSet
+#     print('ROTATE DATA FUNCTION ---------------')
+#     # v = np.array([1,0,0])
+#     # rotM = rot(v,np.pi/2)
+#     # print('rotM:', rotM)
+#
+#     print('X', X)
+#     print('shape of X[0]', X.shape[0])
+#
+#     Out = X + v
+#     return Out
+
+
+def u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp for u',tmp)
+    if kappa == 0 :
+        tmp = np.array([0*x[0],  x[0]*e[0] + x[1]*e[1], x[1]*e[0] - x[0]*e[1] ])
+    else :
+        tmp = np.array([-(1/kappa)*np.cos(tmp)+(1/kappa),  (1/kappa)*np.sin(tmp), -x[0]*e[1]+x[1]*e[0] ])
+    return tmp
+
+
+
+
+def grad_u(x,kappa,e):
+
+    tmp = (x.dot(e))*kappa
+    # print('tmp',tmp)
+
+    grad_u = np.array([ [np.sin(tmp)*e[0], np.sin(tmp)*e[1]], [np.cos(tmp)*e[0], np.cos(tmp)*e[1]], [-e[1], e[0]] ])
+    # print('produkt', grad_u.dot(e) )
+    mapped_e = grad_u.dot(e)
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    # mapped_e = mapped_e.transpose()
+    # print('mapped_e:', mapped_e)
+    # print('siize of mapped_e', mapped_e.shape)
+    return mapped_e
+
+def compute_normal(x,kappa,e):
+    tmp = (x.dot(e))*kappa
+    partial1_u = np.array([ np.sin(tmp)*e[0] ,np.cos(tmp)*e[0], -e[1] ])
+    partial2_u = np.array([ np.sin(tmp)*e[1], np.cos(tmp)*e[1], e[0]      ])
+    normal = np.cross(partial1_u,partial2_u)
+    # print('normal=',normal)
+    return normal
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+print('T:', T)
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+e_container = []
+
+
+for t in T :
+
+    abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+    abar_current[abar_current < 1e-10] = 0
+    # print('abar_current', abar_current)
+    # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    e_container.append(e)
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+    # print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+G_container = np.array(G_container)
+abar_container = np.array(abar_container)
+
+e_container = np.array(e_container)
+
+print('G_container', G_container)
+print('G_container.shape', G_container.shape)
+
+# idx_1 = np.where(alphas == np.pi/4)
+idx_1 = np.where(np.round(alphas,2) == round(np.pi/3,2))
+idx_2 = np.where(np.round(alphas,2) == 0.0)
+idx_3 = np.where(np.round(alphas,2) == round(np.pi/4,2))
+
+# idx_3 = np.where(alphas == 0)
+
+print('Index idx_1:', idx_1)
+print('Index idx_2:', idx_2)
+print('Index idx_3:', idx_3)
+print('Index idx_1[0][0]:', idx_1[0][0])
+print('Index idx_2[0][0]:', idx_2[0][0])
+print('Index idx_3[0][0]:', idx_3[0][0])
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+print('min alpha:', min(alphas))
+print('min kappa:', min(kappas))
+
+
+print('G_container[idx_1[0][0]]', G_container[idx_1[0][0]])
+print('G_container[idx_2[0][0]]', G_container[idx_2[0][0]])
+print('G_container[idx_3[0][0]]', G_container[idx_3[0][0]])
+
+
+print('e_container[idx_1[0][0]]', e_container[idx_1[0][0]])
+print('e_container[idx_2[0][0]]', e_container[idx_2[0][0]])
+print('e_container[idx_3[0][0]]', e_container[idx_3[0][0]])
+
+
+
+###################################################
+
+reflect = False
+# reflect = True
+
+
+
+idx = 1
+
+if idx == 1 :
+    e = e_container[idx_1[0][0]]
+    kappa = kappas[idx_1[0][0]]
+    angle = alphas[idx_1[0][0]]
+    reflect = True
+
+if idx == 2 :
+    e = e_container[idx_2[0][0]]
+    kappa = kappas[idx_2[0][0]]
+    angle = alphas[idx_2[0][0]]
+
+
+if idx == 3 :
+    e = e_container[idx_3[0][0]]
+    kappa = kappas[idx_3[0][0]]
+    angle = alphas[idx_3[0][0]]
+
+### SCALE ?
+# kappa = kappa*2
+
+
+print('kappa:',kappa)
+print('angle:',angle)
+###################################################
+#### TEST apply reflection
+#
+# G_tmp = G_container[idx_1[0][0]]
+#
+# print('G_tmp', G_tmp)
+#
+# # Basis:
+# G_1 = np.array([[1.0,0.0], [0.0,0.0]])
+# G_2 = np.array([[0.0,0.0], [0.0,1.0]])
+# G_3 = (1/np.sqrt(2))*np.array([[0.0,1.0], [1.0,0.0]])
+# print('G_1', G_1)
+# print('G_2', G_2)
+# print('G_3', G_3)
+#
+# G = G_tmp[0] * G_1 + G_tmp[1]*G_2 + G_tmp[2]*G_3
+# print('G:', G )
+#
+# T = np.array([[1.0 , -1.0] , [-1.0,1.0]])
+#
+# TG = np.multiply(T,G)
+# print('TG', TG)
+#
+#
+#
+# v = np.array([np.sqrt(TG[0][0]),np.sqrt(TG[1][1]) ])
+# print('v', v)
+# print('norm(v):', np.linalg.norm(v))
+# norm_v = np.linalg.norm(v)
+#
+# kappa = norm_v**2
+#
+# e = (1/norm_v)*v
+# print('e:', e)
+# print('kappa:', kappa)
+
+
+
+
+
+
+if reflect == True:
+    reflected_e = np.array([e[0], -1*e[1]])
+    e = reflected_e                                         # Correct?! Reflect e on x-Axis ??!
+    print('reflected_e:', reflected_e)
+
+
+############################################################################################################################################
+####################################################################### KAPPA NEGATIVE ####################################################
+############################################################################################################################################
+# kappa = -2
+num_Points = 200
+num_Points = 100
+
+
+# e = np.array([1,0])
+# e = np.array([0,1])
+# e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e = np.array([1/2,np.sqrt(3)/2])
+# e = np.array([np.sqrt(3)/2,1/2])
+# e = np.array([-1,0])
+# e = np.array([0,-1])
+
+###--- Creating dataset
+x = np.linspace(-2,2,num_Points)
+x = np.linspace(-3,3,num_Points)
+x = np.linspace(-4,4,num_Points)
+
+# x = np.linspace(-1.5,1.5,num_Points)
+# x = np.linspace(-1,1,num_Points)
+y = np.linspace(-1/2,1/2,num_Points)
+y = np.linspace(-1/4,1/4,num_Points)
+
+print('type of x', type(x))
+print('max of x:', max(x))
+print('max of y:', max(y))
+# print('x:', x)
+
+x1, x2 = np.meshgrid(x,y)
+zero = 0*x1
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+
+# print('np.size(u1)',np.size(u1))
+# print('u1.shape',u1.shape)
+# colorfunction=(u1**2+u2**2)
+# print('colofunction',colorfunction)
+
+# print('u1.size:',np.size(u1))
+# tmp = np.ones(np.size(u1))*kappa
+# print('np.size(tmp)',np.size(tmp))
+B = np.full_like(u1, 1)
+# colorfunction=(u3)                                              # TODO Color by angle
+# colorfunction=(np.ones(np.size(u1))*kappa)
+colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+norm=mcolors.Normalize(colorfunction.min(),colorfunction.max())
+
+
+# -----------------------------------------------------
+# Display the mesh
+fig = plt.figure()
+
+
+width = 6.28 *0.5
+width = 6.28 * 0.333
+height = width / 1.618
+height = width / 2.5
+height = width
+
+
+
+ax = plt.axes(projection ='3d', adjustable='box')
+
+
+###---TEST MAP e-vectprs!
+# e1 = np.array([1,0])
+# e2 = np.array([0,1])
+# e3 = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# e1 = np.array([0,1])
+# e2 = np.array([-1,0])
+# e3 = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# e1_mapped = u(e1,kappa,e1)
+# e2_mapped = u(e2,kappa,e2)
+# e3_mapped = u(e3,kappa,e3)
+# print('e1 mapped:',e1_mapped)
+# print('e2 mapped:',e2_mapped)
+# print('e3 mapped:',e3_mapped)
+### -----------------------------------
+
+#--e1 :
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([0,1,0])
+
+#--e2:
+Rotation_angle = np.pi/2
+Rotation_vector = np.array([1,0,0])
+
+###--e = np.array([1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_angle = -np.pi/2
+# Rotation_vector = np.array([1,0,0])
+# #2te rotation :
+# Rotation_angle = np.pi/4
+# Rotation_vector = np.array([0,0,1])
+
+
+
+Rotation_angle = -np.pi/2
+Rotation_angle = 0
+# Rotation_angle = np.pi/2
+Rotation_vector = np.array([0,1,0])
+Rotation_vector = np.array([1,0,0])
+
+# rot(np.array([0,1,0]),np.pi/2)
+
+# ZERO ROTATION
+Rotation = rot(np.array([0,1,0]),0)
+
+
+
+# TEST :
+
+#DETERMINE ANGLE:
+angle = math.atan2(e[1], e[0])
+print('angle:', angle)
+
+## GENERAL TRANSFORMATION / ROTATION:
+Rotation = rot(np.array([0,0,1]),angle).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+
+
+### if e1:
+# Rotation = rot(np.array([0,0,1]),-np.pi/4).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/16).dot(Rotation)
+
+# Add another rotation around z-axis:
+# Rotation = rot(np.array([0,0,1]),+np.pi).dot(Rotation)
+# Rotation = rot(np.array([0,0,1]),+np.pi/4).dot(Rotation)
+
+
+# Rotation = rot(np.array([0,0,1]),+np.pi/8).dot(Rotation)
+
+#e3 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2))
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4)
+# Rotation = rot(np.array([1,0,0]),np.pi/4)
+#### if e1 :
+# Rotation = rot(np.array([0,1,0]),-np.pi/2)
+#### if e2:
+# Rotation = rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2))
+# # #### if e3 :
+# zufall dass np.pi/4 genau dem Winkel angle alpha entspricht?:
+# (würde) bei e_2 keinen Unterschied machen um z achse zu rotieren?!
+
+# Rotation = rot(np.array([0,0,1]),np.pi/4).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+# Rotation = rot(np.array([0,0,1]),np.pi/2).dot(rot(np.array([0,1,0]),-np.pi/2).dot(rot(np.array([1,0,0]),-np.pi/2)))
+
+# Rotation = rot(np.array([1,0,0]),np.pi/2)
+
+# Rotation_vector = e3_mapped  #TEST
+# Rotation_vector = np.array([-1/np.sqrt(2),1/np.sqrt(2)])
+# Rotation_vector = np.array([0,0,1])
+
+# v = np.array([1,0,0])
+# X = np.array([u1,u2,u3])
+
+
+
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 2, cstride = 2, facecolors=cm.brg(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.viridis(colorfunction), alpha=.4, zorder=4)
+
+
+###---- PLOT PARAMETER-PLANE:
+# ax.plot_surface(x1,x2,zero,color = 'w', rstride = 1, cstride = 1 )
+
+
+print('------------------ Kappa : ', kappa)
+
+#midpoint:
+midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+print('midpoint',midpoint)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+#
+# mapped_e = Rotation.dot(mapped_e)
+# normal = Rotation.dot(normal)
+
+
+# Plot Mapped_midPoint
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=4)          # line width
+
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [mapped_e[0]], [mapped_e[1]], [mapped_e[2]], color="red")
+# ax.quiver([midpoint_mapped[0]], [midpoint_mapped[1]], [midpoint_mapped[2]], [normal[0]], [normal[1]], [normal[2]], color="blue")
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 2,
+#            ec ='green',
+#            zorder=3)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 2,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 3)
+
+
+###-- TEST Rotation :
+# v = np.array([1,0,0])
+# t = np.array([0,1,0])
+#
+# ax.arrow3D(0,0,0,
+#            t[0],t[1],t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+#
+# # e_extend
+#
+# rotM = rot(v,np.pi/2)
+#
+# print('rotM:', rotM)
+#
+# rot_t = rotM.dot(t)
+#
+# print('rot_t:', rot_t)
+#
+# ax.arrow3D(0,0,0,
+#            rot_t[0],rot_t[1],rot_t[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+### -------------------------------------------
+
+############################################################################################################################################
+####################################################################### KAPPA POSITIVE  ####################################################
+############################################################################################################################################
+
+# kappa = (-1)*kappa
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3, color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.3)  ##This one!
+
+
+# T = rotate_data(X,Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=False)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 2, cstride = 2, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, facecolors=cm.brg(colorfunction), alpha=.8, zorder=4)
+ax.plot_surface(T[0], T[1], T[2], rstride = 5, cstride = 5, color='orange', alpha=.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 10, cstride = 10, color='blue', alpha=.8, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=.4, zorder=4, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'w', rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=0.8, zorder=4)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, facecolors=cm.autumn(colorfunction), alpha=1, zorde5r=5)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+# print('midpoint',midpoint)
+print('------------------ Kappa : ', kappa)
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+#map origin
+origin = np.array([0,0])
+origin_mapped = u(origin,kappa,e)
+
+
+mapped_e = grad_u(midpoint,kappa,e)
+normal = compute_normal(midpoint,kappa,e)
+
+print('mapped_e', mapped_e)
+print('normal',normal )
+
+
+#
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+# Plot MIDPOINT:
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+
+
+#midpoint:
+endpoint = np.array([min(x),(max(y)+min(y))/2])
+print('endpoint',endpoint)
+
+# Map midpoint:
+endpoint_mapped = u(endpoint,kappa,e)
+print('mapped endpoint', endpoint_mapped)
+
+endpoint_mapped = Rotation.dot(endpoint_mapped)
+
+mapped_e = grad_u(endpoint,kappa,e)
+normal = compute_normal(endpoint,kappa,e)
+
+
+mapped_e = Rotation.dot(mapped_e)
+normal = Rotation.dot(normal)
+
+
+
+
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(endpoint_mapped[0],endpoint_mapped[1],endpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=15,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='green',
+#            lw = 1.5,
+#            ec ='green',
+#            zorder=5)
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+############################################################################################################################################
+####################################################################### KAPPA ZERO #########################################################
+############################################################################################################################################
+kappa = 0
+
+if kappa == 0 :
+    u1 = 0*x1
+    u2 = x1*e[0] + x2*e[1]
+    u3 = x2*e[0] - x1*e[1]
+else :
+    u1 = -(1/kappa)*np.cos(kappa*(x1*e[0]+x2*e[1])) + (1/kappa)
+    u2 = (1/kappa)*np.sin(kappa*(x1*e[0]+x2*e[1]))
+    u3 = x2*e[0] -x1*e[1]
+# ax.plot_surface(u1, u2, u3,  rstride = 1, cstride = 1, color = 'white', alpha=0.85)
+
+# T = rotate_data(np.array([u1,u2,u3]),Rotation_vector,Rotation_angle)
+
+T = rotate_data(np.array([u1,u2,u3]),Rotation)
+# T = rotate_data(T,np.array([0,1,0]),Rotation_angle)
+# T = rotate_data(T,np.array([0,0,1]),-1*Rotation_angle/2)
+
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride =1 , cstride = 1, color = 'white', alpha=0.55, zorder=3)
+
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.55, zorder=2)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 1, cstride = 1, color = 'white', alpha=0.5, zorder=2, antialiased=True)
+# ax.plot_surface(T[0], T[1], T[2],  rstride = 10, cstride = 10, color = 'white', alpha=0.55, zorder=2)
+ax.plot_surface(T[0], T[1], T[2],  rstride = 20, cstride = 20, color = 'gray', alpha=0.35, zorder=1, shade=True)
+# ax.plot_surface(T[0], T[1], T[2], color = 'white', alpha=0.55, zorder=2)
+
+# midpoint = np.array([(max(x)+min(x))/2,(max(y)+min(y))/2])
+mapped_e = grad_u(midpoint,kappa,e)
+normal_zeroCurv = compute_normal(midpoint,kappa,e)
+
+# Map midpoint:
+midpoint_mapped = u(midpoint,kappa,e)
+print('mapped midpoint', midpoint_mapped)
+
+##-----  PLOT MAPPED MIDPOINT :::
+
+# ax.plot(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='orange',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# # linestyle='--',            # line style will be dash line
+# linewidth=1,
+# zorder=5)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            mapped_e[0],mapped_e[1],mapped_e[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='red',
+#            ec ='red')
+#
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal_zeroCurv[0],normal_zeroCurv[1],normal_zeroCurv[2],
+#            mutation_scale=10,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue')
+
+
+##----------  PLOT MAPPED ORIGIN :::
+# origin = np.array([0,0])
+# origin_mapped = u(origin,kappa,e)
+# print('origin_mapped', origin_mapped)
+#
+# ax.plot(origin_mapped[0],origin_mapped[1],origin_mapped[2],    # data
+# marker='o',     # each marker will be rendered as a circle
+# markersize=4,   # marker size
+# markerfacecolor='green',   # marker facecolor
+# markeredgecolor='black',  # marker edgecolor
+# markeredgewidth=1,       # marker edge width
+# linewidth=1,
+# zorder=5)          # line width
+#
+# # rotate mapped origin
+# # v = np.array([1,0,0])
+# # alpha  = Rotation_angle
+#
+# rotM = rot(Rotation_vector,Rotation_angle)
+# # origin_mRot = rotate_data(origin_mapped,v,alpha)
+# origin_mRot = rotM.dot(origin_mapped)
+# print('origin_mapped Rotated', origin_mRot)
+#
+# # --- Compute Distance to Origin 3D
+# origin_3D=np.array([0,0,0])
+# distance = origin_mapped-origin_3D
+# print('distance', distance)
+
+## --------------------------------------------------------
+
+# COMPUTE ANGLE WITH Z AXIS
+z = np.array([0,0,1])
+print('test', normal_zeroCurv*z)
+angle_z = np.arccos(normal_zeroCurv.dot(z) /( (np.linalg.norm(z)*np.linalg.norm(normal_zeroCurv) ) ))
+print('angle between normal and z-axis', angle_z)
+
+## unfinished...
+
+
+
+
+###-------------------------------------  PLOT :
+plt.axis('off')
+# plt.axis('tight')
+
+# ADD colorbar
+# scamap = plt.cm.ScalarMappable(cmap='inferno')
+# fig.colorbar(scamap)
+
+# ax.colorbar()
+# ax.axis('auto')
+# ax.set_title(r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e))
+# ax.set_title(r'Cylindrical minimizer' + '_$e$=' +  str(e))
+ax.set_xlabel(r"x-axis")
+ax.set_ylabel(r"y-axis")
+ax.set_zlabel(r"z-axis")
+
+# TEST :
+# ax.annotate3D('point 1', (0, 0, 0), xytext=(3, 3), textcoords='offset points')
+# ax.annotate3D('point 2', (0, 1, 0),
+#               xytext=(-30, -30),
+#               textcoords='offset points',
+#               arrowprops=dict(ec='black', fc='white', shrink=2.5))
+# ax.annotate3D('point 3', (0, 0, 1),
+#               xytext=(30, -30),
+#               textcoords='offset points',
+#               bbox=dict(boxstyle="round", fc="lightyellow"),
+#               arrowprops=dict(arrowstyle="-|>", ec='black', fc='white', lw=5))
+
+#######################################################################################################################
+
+u1 = T[0]
+u2 = T[1]
+u3 = T[2]
+
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /3
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /12
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /8
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /10
+max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /14
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /6
+# max_range = np.array([u1.max()-u1.min(), u2.max()-u2.min(), u3.max()-u3.min()]).max() /2
+mid_u1 = (u1.max()+u1.min()) * 0.5
+mid_u2 = (u2.max()+u2.min()) * 0.5
+mid_u3 = (u3.max()+u3.min()) * 0.5
+
+
+ax.set_xlim(mid_u1 - max_range, mid_u1 + max_range)
+ax.set_ylim(mid_u2 - max_range, mid_u2 + max_range)
+ax.set_zlim(mid_u3 - max_range, mid_u3 + max_range)
+
+ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+# ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+# ax.set_ylim((mid_u2 - max_range)-1.5, (mid_u2 + max_range)+1.5)
+# # ax.autoscale(tight=True)
+ax.set_xlim((mid_u1 - max_range)-1, (mid_u1 + max_range)+1)
+ax.set_xlim((mid_u1 - max_range)-0.5, (mid_u1 + max_range)+0.5)
+# ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+2)
+ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+
+# ax.set_ylim((mid_u2 - max_range)-2, (mid_u2 + max_range)+3)
+# ax.set_zlim((mid_u2 - max_range), (mid_u2 + max_range)+2)
+
+
+##----- CHANGE CAMERA POSITION:
+# ax.view_init(elev=10., azim=0)
+# ax.view_init(elev=38, azim=90)
+# ax.view_init(elev=38, azim=120)
+# ax.view_init(elev=38)
+
+# if e1 ::
+# ax.view_init(elev=44)
+# ax.view_init(elev=38, azim=-90)
+# ax.view_init(elev=38, azim=0)
+ax.view_init(elev=25, azim=-30)
+# ax.view_init(elev=18, azim=-30)
+
+# if e3 ::
+# ax.view_init(elev=25)
+
+# ax.set_xlim3d(-2, 2)
+# ax.set_ylim3d(-1.0,3.0)
+# ax.set_zlim3d(-1.5,2.5)
+
+# ax.set_ylim3d(-10,10)
+# ax.set_xlim(mid_u1 - max_range-0.2, mid_u1 + max_range+0.2)
+# ax.set_zlim(mid_u3 - max_range-0.2, mid_u3 + max_range+0.2)
+# ax.set_ylim(mid_u2 - max_range-0.2, mid_u2 + max_range+0.2)
+
+# width = 6.28 *0.5
+# height = width / 1.618
+# # height = width / 2.5
+# fig.set_size_inches(width, height)
+# fig.savefig('Test-Cylindrical.pdf')
+
+# Figurename = r'Cylindrical minimizer_$\kappa$='+ str(kappa)+ '_$e$=' +  str(e)
+# Figurename = r'Cylindrical minimizer' + '_$e$=' +  str(e)
+Figurename = r'1-ParFamMinimizer_idx' + str(idx)
+# plt.savefig("test.png", bbox_inches='tight')
+# plt.figure().set_size_inches(width, height)
+# plt.set_size_inches(width, height)
+
+
+# fig.set_size_inches(width, height) !!!!!
+
+
+
+
+fig.savefig(Figurename+".pdf")
+
+plt.savefig(Figurename+".png", bbox_inches='tight')
+# plt.savefig(Figurename+".png")
+plt.show()
+
+
+
+# #---------------------------------------------------------------

Python-Scripts/1-ParameterFamily_G+.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+# from ClassifyMin import *
+from ClassifyMin_New import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+def evaluate(x,y):
+
+	# (abar[0,:]*abar[1,:])**0.5
+
+	return np.sqrt(x*y)
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+scale_domain = 5
+
+translate_startpoint = -5
+
+# T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+
+abar_tmp = abar
+
+for t in T :
+	abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+	abar_current[abar_current < 1e-10] = 0
+	# print('abar_current', abar_current)
+	# G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+	G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+	# print('type of G', type(G))
+	# print('G', G)
+	G_container.append(G)
+	abar_container.append(abar_current)
+	e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+	kappa = abar_current[0]+abar_current[1]
+	alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+	kappas.append(kappa)
+	alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+
+num_Points = 20
+num_Points = 50
+
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+range = 2
+
+x_1 = np.linspace(0,range,num_Points)
+y_1 = np.linspace(0,range,num_Points)
+x_2 = np.linspace(-range,0,num_Points)
+y_2 = np.linspace(-range,0,num_Points)
+
+
+X_1,Y_1 = np.meshgrid(x_1,y_1)
+X_2,Y_2 = np.meshgrid(x_2,y_2)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+# print('a1:', a1)
+# print('a2:',a2 )
+#
+# print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+tmp1 = a1[np.where(a1*a2 >= 0)]
+tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+# tmp1 = a1[np.where(a1>=0 and a2 >= 0)]
+# tmp2 = a2[np.where(a1>=0 and a2 >= 0)]
+
+
+# tmp1 = tmp1[np.where(a1 >= 0)]
+# tmp2 = tmp2[np.where(a1 >= 0)]
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0)]
+# tmp2_neg = a2[np.where(a1*a2 >= 0)]
+
+
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+
+
+tmp1 = tmp1.reshape(-1,int(tmp1.shape[0]/2))
+tmp2 = tmp2.reshape(-1,int(tmp2.shape[0]/2))
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+# Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+#
+# Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+# Z = (tmp2**2)/tmp1
+Z = np.sqrt(tmp1*tmp2)
+
+
+Z1 = np.sqrt(X_1*Y_1)
+Z2 = np.sqrt(X_2*Y_2)
+
+# Z_bar = np.sqrt(abar[0,:]*abar[1,:])
+Z_bar = (abar[0,:]*abar[1,:])**0.5*abar
+
+abar = abar.T
+
+
+
+v1 = abar[0,:]
+v2 = abar[1,:]
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+evaluateVec = np.vectorize(evaluate)
+Z_bar = evaluateVec(abar[0,:],abar[1,:])
+# Z = np.sqrt(np.multiply(tmp1,tmp2))
+# Z = np.sqrt(a1*a2)
+
+
+print('v1.shape', v1.shape)
+print('v1', v1)
+
+
+
+
+print('Z:', Z)
+print('Z_bar:', Z_bar)
+# print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+label_size = 8
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+# plt.style.use('seaborn')
+plt.style.use('seaborn-whitegrid')
+# sns.set()
+# plt.style.use('seaborn-whitegrid')
+
+label_size = 9
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+width = 6.28 *0.5
+width = 6.28
+height = width / 1.618
+fig = plt.figure()
+
+ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+ax.grid(True,which='major',axis='both',alpha=0.3)
+
+# colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+
+#translate Data
+# Z = Z - (Z.max()-Z.min())/2
+# Z = Z - 50
+# Z = Z - 500
+#
+# Z = Z.T
+
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+
+# print('Value of c:', c)
+
+
+
+# print('Z.min()', Z.min())
+# print('Z.max()', Z.max())
+# norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+# print('norm:', norm)
+# print('type of norm', type(norm))
+# print('norm(0):', norm(0))
+# print('norm(Z):', norm(Z))
+
+# ax.plot(theta_rho, theta_values, 'royalblue', zorder=3, )
+
+# ax.scatter(a1,a2, s=0.5)
+
+# ax.scatter(tmp1_pos,tmp2_pos, s=0.5)
+# ax.scatter(tmp1_neg,tmp2_neg, s=0.5)
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=100 )
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot,  levels=20 )
+
+
+# sns.kdeplot(np.array([a1, a2, Z]))
+# sns.kdeplot(tmp1_pos,tmp2_pos,Z_pos)
+
+# levels = [-5.0, -4, -3, 0.0, 1.5, 2.5, 3.5]
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, corner_mask=True,levels=levels)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot(norm(Z)), corner_mask=True)
+# CS = ax.contour(a1, a2, Z, cm.brg(norm(Z)), levels=20)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot, levels=20)
+# CS = ax.contour(a1, a2, Z, colors='k', levels=14,  linewidths=(0.5,))
+# CS = ax.contour(a1, a2, Z, colors='k', levels=18,  linewidths=(0.5,))
+
+# ax.contour(negZ_a1, negZ_a2, negativeValues, colors='k',  linewidths=(0.5,))
+# CS =  ax.contour(a1_in, a2_in, Z_in, colors='k',  linewidths=(0.5,))
+
+
+
+# df = pd.DataFrame(data=Z_in, columns=a1_in, index=a2_in)
+# df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+#                    columns=['a', 'b', 'c'])
+
+
+
+
+# sns.kdeplot(data=df2, x="waiting", y="duration")
+# sns.kdeplot(data=df2)
+
+# CS = ax.contour(a1, a2, Z, colors='k',   linewidths=(0.5,))
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k', extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k')
+#
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, levels=10 )
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, corner_mask=True)
+#
+# CS = ax.contour(a1, a2, Z,10,  colors = 'k')
+# ax.clabel(CS, inline=True, fontsize=4)
+
+
+# cmap = cm.brg(norm(Z))
+#
+# C_map = cm.inferno(norm(Z))
+
+# ax.imshow(Z, cmap=C_map, extent=[-20, 20, -20, 20], origin='lower', alpha=0.5)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20], origin='lower',
+#                   cmap='bwr', alpha=0.8)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', vmin=Z.min(), vmax=Z.max(),
+#                   cmap='bwr', alpha=0.6)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+
+cmap=mpl.cm.RdBu_r
+# cmap=mpl.cm.viridis_r
+cmap=mpl.cm.bwr
+# # cmap=mpl.cm.coolwarm
+# # cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.viridis
+# cmap=mpl.cm.inferno
+# # # cmap=mpl.cm.Blues
+# cmap=mpl.cm.magma
+cmap=mpl.cm.cividis
+# cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.gnuplot
+
+
+# cmap = cm.brg(Z)
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=8)
+
+
+
+
+# ##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+# epsilon = 0.1
+# # ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# # ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# # ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color='gray', zorder=5)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color='gray', zorder=5)#yellow
+
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.plot_surface(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.scatter(X_1,Y_1,Z1, s=0.2)
+# ax.scatter(X_2,Y_2,Z2, s=0.2)
+
+# ax.plot_surface(X_1,Y_1,Z1 ,cmap=cmap,
+#                        linewidth=0, antialiased=False,alpha=1, zorder=5)
+ax.plot_surface(X_1,Y_1,Z1 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=1, zorder=5)
+
+ax.plot_surface(X_2,Y_2,Z2 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=1, zorder=5)
+
+
+# ax.plot(G[0,:],G[1,:],G[2,:])
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='yellow', linestyle='--')
+# ax.scatter(abar[0,:],abar[1,:],Z_bar,  color='purple', zorder=5)
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='royalblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='dodgerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='cornflowerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='darkorange', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='yellow', linestyle='--')
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=1, color='coral', linestyle='--', zorder=3)
+line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=2)
+# CS = ax.contour(X_1,Y_1,Z1, colors='k', levels=18,  linewidths=(0.5,))
+
+start = np.array([abar[0,499],abar[1,499],Z_bar[499]])
+end = np.array([abar[0,500],abar[1,500],Z_bar[500]])
+
+# plot starting point:
+# ax.scatter(abar[0,0],abar[1,0],Z_bar[0], marker='^',  s=30, color='black', zorder=5)
+#
+#
+# ax.scatter(abar[0,500],abar[1,500],Z_bar[500], marker='^',  s=30, color='purple', zorder=5)
+
+# ax.scatter(start[0],start[1],start[2], marker='^',  s=30, color='purple', zorder=5)
+# ax.scatter(end[0],end[1],end[2], marker='^',  s=30, color='purple', zorder=5)
+
+print('start:', start)
+print('end:', end)
+
+
+dir = end-start
+# ax.arrow()
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=10,
+#            arrowstyle="->",
+#            linestyle='dashed',fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+# Check proof:
+# value at t = 0:
+abar_zero= sstar*abar_tmp
+# value_0 = [abar_zero[0], abar_zero[1] , (2*abar_zero[0]*abar_zero[1])**0.5 ]
+value_0 = evaluate(abar_zero[0], abar_zero[1])
+print('value_0', value_0)
+# ax.scatter(value_0[0],value_0[1],value_0[2], marker='x',  s=20, color='dodgerblue', zorder=5)
+# ax.scatter(abar_zero[0], abar_zero[1],value_0, marker='o',  s=30, color='dodgerblue', zorder=5)
+## -----------------------------
+
+
+
+
+
+
+
+
+
+
+# ax.scatter(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_surface(tmp1,Z, tmp2, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_trisurf(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+### PLot x and y- Axes
+# ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+# ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=1)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=1)
+
+
+
+ax.set_xlabel(r"$a_1$", fontsize=10 ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=10 ,labelpad=0)
+# ax.set_ylabel(r"energy")
+
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+
+
+
+
+# ax.legend(loc='upper right')
+
+
+
+fig.set_size_inches(width, height)
+fig.savefig('1-ParameterFamily_G+.pdf')
+
+plt.show()
+
+
+#
+#
+#
+# # Curve parametrised by \theta_rho = alpha in parameter space
+# N=100;
+# theta_rho = np.linspace(1, 3, num=N)
+# print('theta_rho:', theta_rho)
+#
+#
+# theta_values = []
+#
+#
+# for t in theta_rho:
+#
+#         s = (1.0/10.0)*t+0.1
+#         theta_values.append(s)
+#
+#
+#
+#
+#
+# theta_rho = np.array(theta_rho)
+# theta_values = np.array(theta_values)
+#
+# betas_ = 2.0
+#
+
+# alphas, betas, thetas = np.meshgrid(theta_rho, betas_, theta_values, indexing='ij')
+#
+#
+# harmonicMeanVec = np.vectorize(harmonicMean)
+# arithmeticMeanVec = np.vectorize(arithmeticMean)
+# prestrain_b1Vec = np.vectorize(prestrain_b1)
+# prestrain_b2Vec = np.vectorize(prestrain_b2)
+#
+# GetMuGammaVec = np.vectorize(GetMuGamma)
+# muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#
+# q1_vec = harmonicMeanVec(mu1, betas, thetas)
+# q2_vec = arithmeticMeanVec(mu1, betas, thetas)
+#
+# b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+# b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+
+# special case: q12 == 0!! .. braucht eigentlich nur b1 & b2 ...
+
+# print('type b1_values:', type(b1_values))
+
+
+
+# print('size(q1)',q1.shape)
+#
+#
+# energy_axial1 = []
+# energy_axial2 = []
+#
+# # for b1 in b1_values:
+# for i in range(len(theta_rho)):
+#     print('index i:', i)
+#
+#     print('theta_rho[i]',theta_rho[i])
+#     print('theta_values[i]',theta_values[i])
+#
+#     q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta_values[i])
+#     q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta_values[i])
+#     q12 = 0.0
+#     q3 = GetMuGamma(beta, theta_values[i],gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#     b1 = prestrain_b1(rho1,beta, theta_rho[i],theta_values[i] )
+#     b2 = prestrain_b2(rho1,beta, theta_rho[i],theta_values[i] )
+#
+#
+#     # q2_vec = arithmeticMean(mu1, betas, thetas)
+#     #
+#     # b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+#     # b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+#     print('q1[i]',q1)
+#     print('q2[i]',q2)
+#     print('q3[i]',q3)
+#     print('b1[i]',b1)
+#     print('b2[i]',b2)
+#     # print('q1[i]',q1[0][i])
+#     # print('q2[i]',q2[i])
+#     # print('b1[i]',b1[i])
+#     # print('b2[i]',b2[i])
+#     #compute axial energy #1 ...
+#
+#     a_axial1 = np.array([b1,0])
+#     a_axial2 = np.array([0,b2])
+#     b = np.array([b1,b2])
+#
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a_axial1)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial1',a_axial1)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial1.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial1.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_1 = tmp - tmp2
+#     print('energy_1',energy_1)
+#
+#
+#     energy_axial1.append(energy_1)
+#
+#
+#     tmp = H.dot(a_axial2)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial2',a_axial2)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial2.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial2.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_2 = tmp - tmp2
+#     print('energy_2',energy_2)
+#
+#
+#     energy_axial2.append(energy_2)
+#
+#
+#
+#
+#
+# print('theta_values', theta_values)
+#
+#
+#
+
+
+#
+#
+#
+#
+# kappas = []
+# alphas = []
+# # G.append(float(s[0]))
+#
+#
+#
+#
+# for t in T :
+#
+#     abar_current = sstar*abar+t*abarperp;
+#     # print('abar_current', abar_current)
+#     abar_current[abar_current < 1e-10] = 0
+#     # print('abar_current', abar_current)
+#
+#     # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+#
+#     e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+#     kappa = abar_current[0]+abar_current[1]
+#     alpha = math.atan2(e[1], e[0])
+#
+#     print('angle current:', alpha)
+#
+#     kappas.append(kappa)
+#     alphas.append(alpha)
+#
+#
+#
+# alphas = np.array(alphas)
+# kappas = np.array(kappas)
+#
+#
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+# print('min alpha:', min(alphas))
+# print('min kappa:', min(kappas))
+#
+# mpl.rcParams['text.usetex'] = True
+# mpl.rcParams["font.family"] = "serif"
+# mpl.rcParams["font.size"] = "9"
+# width = 6.28 *0.5
+# height = width / 1.618
+# fig = plt.figure()
+# # ax = plt.axes((0.15,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.21 ,0.8,0.75))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# # ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# # ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# # ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# # ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+#
+#
+#
+#
+# ax.plot(alphas, kappas, 'royalblue', zorder=3, )
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )

Python-Scripts/1-ParameterFamily_G+_Flat.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+from chart_studio import plotly
+import plotly.graph_objs as go
+import plotly.express as px
+import plotly.colors
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+
+def show(fig):
+    import io
+    import plotly.io as pio
+    from PIL import Image
+    buf = io.BytesIO()
+    pio.write_image(fig, buf)
+    img = Image.open(buf)
+    img.show()
+
+
+
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def set_size(width, fraction=1):
+    """Set figure dimensions to avoid scaling in LaTeX.
+
+    Parameters
+    ----------
+    width: float
+            Document textwidth or columnwidth in pts
+    fraction: float, optional
+            Fraction of the width which you wish the figure to occupy
+
+    Returns
+    -------
+    fig_dim: tuple
+            Dimensions of figure in inches
+    """
+    # Width of figure (in pts)
+    fig_width_pt = width * fraction
+
+    # Convert from pt to inches
+    inches_per_pt = 1 / 72.27
+
+    # Golden ratio to set aesthetic figure height
+    # https://disq.us/p/2940ij3
+    golden_ratio = (5**.5 - 1) / 2
+
+    # Figure width in inches
+    fig_width_in = fig_width_pt * inches_per_pt
+    # Figure height in inches
+    fig_height_in = fig_width_in * golden_ratio
+
+    fig_dim = (fig_width_in, fig_height_in)
+
+    return fig_dim
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+
+
+
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = -0.75
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+# gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+## ---- 1-ParameterFamilyCase:
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+# print('abar:',abar)
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+# b1=b[0]
+# b2=b[1]
+## ---------------
+
+
+
+
+
+########################################
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+##----------------------
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+##--------------
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('sstar*abar:', sstar*abar)
+# print('np.dot(sstar*abar):', np.dot(sstar*abar))
+print('----------------------------')
+
+
+N=1000;
+# N=10;
+scale_domain = 5
+
+translate_startpoint = -1.8
+
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+# T = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+test = sstar*abar
+
+
+abar_tmp = abar
+
+for t in T :
+    abar_current = sstar*abar+t*abarperp;
+    # abar_current[abar_current < 1e-10] = 0   # Projection onto x-y-axis!!
+    print('abar_current', abar_current)
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+
+
+
+
+
+######################################
+
+
+
+num_Points = 400
+num_Points = 200
+# num_Points = 20
+
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+
+x = np.linspace(-2,2,num_Points)
+y = np.linspace(-2,2,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+print('a1:', a1)
+print('a2:',a2 )
+
+print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+# tmp1 = a1[np.where(a1*a2 >= 0)]
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+#
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+tmp1 = a1[a1*a2 >= 0]
+tmp2 = a2[a1*a2 >= 0]
+tmp1 = tmp1.reshape(-1,5)
+tmp2 = tmp2.reshape(-1,5)
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+#
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+#
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+print('a1:', a1)
+print('a2:',a2 )
+print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+
+Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+print('Z:', Z)
+
+print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+label_size = 8
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+plt.style.use('seaborn')
+# plt.style.use('seaborn-whitegrid')
+# sns.set()
+# plt.style.use('seaborn-whitegrid')
+
+label_size = 9
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+width = 6.28 *0.5
+# width = 6.28 *0.33
+# width = 6.28
+height = width #/ 1.618
+
+# width = 452.9579/2
+# size= set_size(width, fraction=0.5)
+# print('set_size(width, fraction=0.5)', set_size(width, fraction=1))
+# print('size[0]',size[0])
+
+f_size = 10
+# fig= plt.figure()
+fig, ax = plt.subplots()
+# fig.set_size_inches(width, height)
+# fig.set_size_inches(set_size(width, fraction=0.5))
+# ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+
+# ax = plt.axes((0.17,0.23 ,0.7,0.7))
+# ax = plt.axes((0.17,0.23 ,1.0,1.0))
+# ax=plt.axes()
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+ax.grid(True,which='major',axis='both',alpha=0.3)
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+#
+# print('Value of c:', c)
+
+
+
+print('Z.min()', Z.min())
+print('Z.max()', Z.max())
+norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+
+
+cmap=mpl.cm.RdBu_r
+cmap=mpl.cm.viridis_r
+# cmap=mpl.cm.bwr
+cmap=mpl.cm.coolwarm
+# cmap=mpl.cm.gnuplot
+cmap=mpl.cm.magma_r
+# cmap=mpl.cm.inferno_r
+# cmap=mpl.cm.plasma
+# cmap=mpl.cm.plasma_r
+# cmap=mpl.cm.cividis_r
+# cmap = mpl.colors.LinearSegmentedColormap.from_list("", ["blue","violet","red"])
+# cmap = mpl.colors.LinearSegmentedColormap.from_list("", ["blue","orange"])
+
+# cmap = mpl.colors.LinearSegmentedColormap.from_list("", [(0,"red"), (.1,"violet"), (.5, "blue"), (1.0, "green")])
+# make a colormap that has land and ocean clearly delineated and of the
+# same length (256 + 256)
+#
+# colors_undersea = plt.cm.terrain(np.linspace(0, 0.17, 256))
+# colors_land = plt.cm.terrain(np.linspace(0.25, 1, 256))
+# all_colors = np.vstack((colors_undersea, colors_land))
+# # cmap = mcolors.LinearSegmentedColormap.from_list(
+# #     'terrain_map', all_colors)
+
+
+# cmap = px.colors.sequential.agsunset
+# cmap = plotly.colors.PLOTLY_SCALES["Viridis"]
+
+
+
+
+# cmap = cm.brg(Z)
+divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=(Z.max()+Z.min())/2, vmax=Z.max())
+# divnorm=mcolors.TwoSlopeNorm(vmin=-500, vcenter=0, vmax=Z.max())
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=-10, vcenter=0. ,vmax=10)
+# divnorm=mcolors.TwoSlopeNorm(vmin=-10, vcenter=0., vmax=Z.max())
+
+# divnorm=mcolors.LogNorm(vmin=Z.min(),  vmax=Z.max())  #Test LogNorm
+
+# cmap = cm.brg(divnorm(Z))
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# I = plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.9)
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+# I = plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+                  # cmap=cmap, alpha=0.6)
+
+
+# I = plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = mcolors.CenteredNorm(),
+#                   cmap=cmap, alpha=0.6)
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=f_size)
+# fig.colorbar(I)
+
+
+
+##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+epsilon = 0.001
+# ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+
+fillcolor = 'royalblue'
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color=fillcolor, zorder=4)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color=fillcolor, zorder=4)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=1.0, color=fillcolor, zorder=4)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=1.0, color=fillcolor, zorder=4)#yellow
+
+
+## FILL
+ax.fill_between([x.min(), 0-epsilon], y.min(), 0-epsilon, alpha=.25, color=fillcolor, zorder=4)#yellow
+ax.fill_between([0+epsilon, x.max()], 0+epsilon, y.max(), alpha=.25, color=fillcolor, zorder=4)#yellow
+
+
+ax.text(1,1, r"$\mathcal{G}^+_{\mathbf{R}^2}$", color='royalblue', size=15)
+
+# ax.text(0.25,0.25, r"$\mathcal{S}$", color='darkorange', size=15)
+
+# PLOT 1-PARAMETER FAMILY
+
+print('abar:', abar)
+print('abar[0,:]:', abar[0,:])
+print('abar[1,:]:', abar[1,:])
+
+line = ax.plot(abar[:,0],abar[:,1], linewidth=2, color='darkorange', linestyle='-', zorder=4)
+
+# plt.arrow(x=1, y=0, dx=0.5, dy=0, )
+# ax.arrow(1, 0, 0.5, 0, head_width=0.05, head_length=0.1, fc='k', ec='k', zorder=5)
+# plt.arrow(1, 0, 0.8, 0,  shape='full', lw=0, length_includes_head=True, head_width=.15, zorder=5, color='purple')
+
+
+## PLOT ARROW:
+# plt.arrow(1, 0, 0.5, 0,  shape='full', lw=0, length_includes_head=True, head_width=.20, zorder=5, color='darkorange')
+# plt.arrow(0, 1.8, 0, -0.8,  shape='full', lw=0, length_includes_head=True, head_width=.20, zorder=5, color='darkorange')
+
+
+# plt.arrow(0, 1.8, 0, -0.8, lw=0,  head_width=.12, zorder=5, color='darkorange')
+# plt.arrow(0, 2, 0, -0.5,  shape='full', lw=0, length_includes_head=True, head_width=.12, zorder=5, color='darkorange')
+# add_arrow(line, color='darkorange')
+
+
+
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+# print('test:',test)
+# ax.scatter(test[0],test[1])
+# ax.arrow(test[0],test[1],abarperp[0],abarperp[1])
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+### PLot x and y- Axes
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+
+
+
+ax.set_xlabel(r"$a_1$", fontsize=f_size ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=f_size ,labelpad=0)
+# ax.set_ylabel(r"energy")
+ax.tick_params(axis='both', which='major', labelsize=f_size)
+ax.tick_params(axis='both', which='minor', labelsize=f_size)
+
+
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+print('x.max()',x.max())
+print('y.max()',y.max())
+ax.set_xlim(x.min(),x.max())
+ax.set_xlim(y.min(),y.max())
+
+
+
+# ax.legend(loc='upper right')
+
+
+
+fig.set_size_inches(width, height)
+# fig.set_size_inches(set_size(width, fraction=0.33))
+fig.savefig('Energy_ContourG+_Flat.pdf')
+
+plt.show()
+
+
+#
+#
+#
+# # Curve parametrised by \theta_rho = alpha in parameter space
+# N=100;
+# theta_rho = np.linspace(1, 3, num=N)
+# print('theta_rho:', theta_rho)
+#
+#
+# theta_values = []
+#
+#
+# for t in theta_rho:
+#
+#         s = (1.0/10.0)*t+0.1
+#         theta_values.append(s)
+#
+#
+#
+#
+#
+# theta_rho = np.array(theta_rho)
+# theta_values = np.array(theta_values)
+#
+# betas_ = 2.0
+#
+
+# alphas, betas, thetas = np.meshgrid(theta_rho, betas_, theta_values, indexing='ij')
+#
+#
+# harmonicMeanVec = np.vectorize(harmonicMean)
+# arithmeticMeanVec = np.vectorize(arithmeticMean)
+# prestrain_b1Vec = np.vectorize(prestrain_b1)
+# prestrain_b2Vec = np.vectorize(prestrain_b2)
+#
+# GetMuGammaVec = np.vectorize(GetMuGamma)
+# muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#
+# q1_vec = harmonicMeanVec(mu1, betas, thetas)
+# q2_vec = arithmeticMeanVec(mu1, betas, thetas)
+#
+# b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+# b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+
+# special case: q12 == 0!! .. braucht eigentlich nur b1 & b2 ...
+
+# print('type b1_values:', type(b1_values))
+
+
+
+# print('size(q1)',q1.shape)
+#
+#
+# energy_axial1 = []
+# energy_axial2 = []
+#
+# # for b1 in b1_values:
+# for i in range(len(theta_rho)):
+#     print('index i:', i)
+#
+#     print('theta_rho[i]',theta_rho[i])
+#     print('theta_values[i]',theta_values[i])
+#
+#     q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta_values[i])
+#     q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta_values[i])
+#     q12 = 0.0
+#     q3 = GetMuGamma(beta, theta_values[i],gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#     b1 = prestrain_b1(rho1,beta, theta_rho[i],theta_values[i] )
+#     b2 = prestrain_b2(rho1,beta, theta_rho[i],theta_values[i] )
+#
+#
+#     # q2_vec = arithmeticMean(mu1, betas, thetas)
+#     #
+#     # b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+#     # b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+#     print('q1[i]',q1)
+#     print('q2[i]',q2)
+#     print('q3[i]',q3)
+#     print('b1[i]',b1)
+#     print('b2[i]',b2)
+#     # print('q1[i]',q1[0][i])
+#     # print('q2[i]',q2[i])
+#     # print('b1[i]',b1[i])
+#     # print('b2[i]',b2[i])
+#     #compute axial energy #1 ...
+#
+#     a_axial1 = np.array([b1,0])
+#     a_axial2 = np.array([0,b2])
+#     b = np.array([b1,b2])
+#
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a_axial1)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial1',a_axial1)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial1.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial1.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_1 = tmp - tmp2
+#     print('energy_1',energy_1)
+#
+#
+#     energy_axial1.append(energy_1)
+#
+#
+#     tmp = H.dot(a_axial2)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial2',a_axial2)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial2.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial2.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_2 = tmp - tmp2
+#     print('energy_2',energy_2)
+#
+#
+#     energy_axial2.append(energy_2)
+#
+#
+#
+#
+#
+# print('theta_values', theta_values)
+#
+#
+#
+
+
+#
+#
+#
+#
+# kappas = []
+# alphas = []
+# # G.append(float(s[0]))
+#
+#
+#
+#
+# for t in T :
+#
+#     abar_current = sstar*abar+t*abarperp;
+#     # print('abar_current', abar_current)
+#     abar_current[abar_current < 1e-10] = 0
+#     # print('abar_current', abar_current)
+#
+#     # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+#
+#     e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+#     kappa = abar_current[0]+abar_current[1]
+#     alpha = math.atan2(e[1], e[0])
+#
+#     print('angle current:', alpha)
+#
+#     kappas.append(kappa)
+#     alphas.append(alpha)
+#
+#
+#
+# alphas = np.array(alphas)
+# kappas = np.array(kappas)
+#
+#
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+# print('min alpha:', min(alphas))
+# print('min kappa:', min(kappas))
+#
+# mpl.rcParams['text.usetex'] = True
+# mpl.rcParams["font.family"] = "serif"
+# mpl.rcParams["font.size"] = "9"
+# width = 6.28 *0.5
+# height = width / 1.618
+# fig = plt.figure()
+# # ax = plt.axes((0.15,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.21 ,0.8,0.75))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# # ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# # ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# # ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# # ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+#
+#
+#
+#
+# ax.plot(alphas, kappas, 'royalblue', zorder=3, )
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )

Python-Scripts/1-ParameterFamily_G+_Flat_v2.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+from chart_studio import plotly
+import plotly.graph_objs as go
+import plotly.express as px
+import plotly.colors
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+
+def show(fig):
+    import io
+    import plotly.io as pio
+    from PIL import Image
+    buf = io.BytesIO()
+    pio.write_image(fig, buf)
+    img = Image.open(buf)
+    img.show()
+
+
+
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def set_size(width, fraction=1):
+    """Set figure dimensions to avoid scaling in LaTeX.
+
+    Parameters
+    ----------
+    width: float
+            Document textwidth or columnwidth in pts
+    fraction: float, optional
+            Fraction of the width which you wish the figure to occupy
+
+    Returns
+    -------
+    fig_dim: tuple
+            Dimensions of figure in inches
+    """
+    # Width of figure (in pts)
+    fig_width_pt = width * fraction
+
+    # Convert from pt to inches
+    inches_per_pt = 1 / 72.27
+
+    # Golden ratio to set aesthetic figure height
+    # https://disq.us/p/2940ij3
+    golden_ratio = (5**.5 - 1) / 2
+
+    # Figure width in inches
+    fig_width_in = fig_width_pt * inches_per_pt
+    # Figure height in inches
+    fig_height_in = fig_width_in * golden_ratio
+
+    fig_dim = (fig_width_in, fig_height_in)
+
+    return fig_dim
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+
+
+
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = -0.75
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+# gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+## ---- 1-ParameterFamilyCase:
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+# print('abar:',abar)
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+# b1=b[0]
+# b2=b[1]
+## ---------------
+
+
+
+
+
+########################################
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+##----------------------
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+##--------------
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('sstar*abar:', sstar*abar)
+# print('np.dot(sstar*abar):', np.dot(sstar*abar))
+print('----------------------------')
+
+
+N=1000;
+N=10;
+scale_domain = 5
+translate_startpoint = -1.8
+T_line = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+line_values = []
+for t in T_line :
+    print('sstar*abar+t*abarperp', sstar*abar+t*abarperp)
+    line_values.append(sstar*abar+t*abarperp)
+
+
+
+
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+test = sstar*abar
+
+
+abar_tmp = abar
+
+for t in T :
+    abar_current = sstar*abar+t*abarperp;
+    abar_current[abar_current < 1e-10] = 0   # Projection onto x-y-axis!!
+    print('abar_current', abar_current)
+    G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+    G_container.append(G)
+    abar_container.append(abar_current)
+    e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+    kappa = abar_current[0]+abar_current[1]
+    alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+    kappas.append(kappa)
+    alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+
+
+
+
+
+######################################
+
+
+
+num_Points = 400
+num_Points = 200
+# num_Points = 20
+
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+
+x = np.linspace(-2,2,num_Points)
+y = np.linspace(-2,2,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+print('a1:', a1)
+print('a2:',a2 )
+
+print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+# tmp1 = a1[np.where(a1*a2 >= 0)]
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+#
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+tmp1 = a1[a1*a2 >= 0]
+tmp2 = a2[a1*a2 >= 0]
+tmp1 = tmp1.reshape(-1,5)
+tmp2 = tmp2.reshape(-1,5)
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+#
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+#
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+print('a1:', a1)
+print('a2:',a2 )
+print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+
+Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+print('Z:', Z)
+
+print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+# mpl.rcParams['text.usetex'] = True
+# mpl.rcParams["font.family"] = "serif"
+# mpl.rcParams["font.size"] = "9"
+#
+# label_size = 8
+# mpl.rcParams['xtick.labelsize'] = label_size
+# mpl.rcParams['ytick.labelsize'] = label_size
+#
+# plt.style.use('seaborn')
+# # plt.style.use('seaborn-whitegrid')
+# # sns.set()
+# # plt.style.use('seaborn-whitegrid')
+#
+# label_size = 9
+# mpl.rcParams['xtick.labelsize'] = label_size
+# mpl.rcParams['ytick.labelsize'] = label_size
+
+# # plt.style.use("seaborn-darkgrid")
+# plt.style.use("seaborn-whitegrid")
+plt.style.use("seaborn")
+# plt.style.use("seaborn-paper")
+# plt.style.use('ggplot')
+# plt.rcParams["font.family"] = "Avenir"
+# plt.rcParams["font.size"] = 16
+
+# plt.style.use("seaborn-darkgrid")
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "10"
+# mpl.rcParams['xtick.labelsize'] = 16mpl.rcParams['xtick.major.size'] = 2.5
+# mpl.rcParams['xtick.bottom'] = True
+# mpl.rcParams['ticks'] = True
+mpl.rcParams['xtick.bottom'] = True
+mpl.rcParams['xtick.major.size'] = 3
+mpl.rcParams['xtick.minor.size'] = 1.5
+mpl.rcParams['xtick.major.width'] = 0.75
+mpl.rcParams['ytick.left'] = True
+mpl.rcParams['ytick.major.size'] = 3
+mpl.rcParams['ytick.minor.size'] = 1.5
+mpl.rcParams['ytick.major.width'] = 0.75
+
+mpl.rcParams.update({'font.size': 10})
+mpl.rcParams['axes.labelpad'] = 3.0
+
+width = 6.28 *0.5
+# width = 6.28 *0.33
+# width = 6.28
+height = width #/ 1.618
+
+# width = 452.9579/2
+# size= set_size(width, fraction=0.5)
+# print('set_size(width, fraction=0.5)', set_size(width, fraction=1))
+# print('size[0]',size[0])
+
+f_size = 10
+# fig= plt.figure()
+fig, ax = plt.subplots()
+# fig.set_size_inches(width, height)
+# fig.set_size_inches(set_size(width, fraction=0.5))
+# ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+
+# ax = plt.axes((0.17,0.23 ,0.7,0.7))
+# ax = plt.axes((0.17,0.23 ,1.0,1.0))
+# ax=plt.axes()
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+ax.grid(True,which='major',axis='both',alpha=0.3)
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+#
+# print('Value of c:', c)
+
+
+
+print('Z.min()', Z.min())
+print('Z.max()', Z.max())
+norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+
+
+cmap=mpl.cm.RdBu_r
+cmap=mpl.cm.viridis_r
+# cmap=mpl.cm.bwr
+cmap=mpl.cm.coolwarm
+# cmap=mpl.cm.gnuplot
+cmap=mpl.cm.magma_r
+# cmap=mpl.cm.inferno_r
+# cmap=mpl.cm.plasma
+# cmap=mpl.cm.plasma_r
+# cmap=mpl.cm.cividis_r
+# cmap = mpl.colors.LinearSegmentedColormap.from_list("", ["blue","violet","red"])
+# cmap = mpl.colors.LinearSegmentedColormap.from_list("", ["blue","orange"])
+
+# cmap = mpl.colors.LinearSegmentedColormap.from_list("", [(0,"red"), (.1,"violet"), (.5, "blue"), (1.0, "green")])
+# make a colormap that has land and ocean clearly delineated and of the
+# same length (256 + 256)
+#
+# colors_undersea = plt.cm.terrain(np.linspace(0, 0.17, 256))
+# colors_land = plt.cm.terrain(np.linspace(0.25, 1, 256))
+# all_colors = np.vstack((colors_undersea, colors_land))
+# # cmap = mcolors.LinearSegmentedColormap.from_list(
+# #     'terrain_map', all_colors)
+
+
+# cmap = px.colors.sequential.agsunset
+# cmap = plotly.colors.PLOTLY_SCALES["Viridis"]
+
+
+
+
+# cmap = cm.brg(Z)
+divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=(Z.max()+Z.min())/2, vmax=Z.max())
+# divnorm=mcolors.TwoSlopeNorm(vmin=-500, vcenter=0, vmax=Z.max())
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=-10, vcenter=0. ,vmax=10)
+# divnorm=mcolors.TwoSlopeNorm(vmin=-10, vcenter=0., vmax=Z.max())
+
+# divnorm=mcolors.LogNorm(vmin=Z.min(),  vmax=Z.max())  #Test LogNorm
+
+# cmap = cm.brg(divnorm(Z))
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# I = plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.9)
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+# I = plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+                  # cmap=cmap, alpha=0.6)
+
+
+# I = plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = mcolors.CenteredNorm(),
+#                   cmap=cmap, alpha=0.6)
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=f_size)
+# fig.colorbar(I)
+
+
+
+##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+epsilon = 0.001
+# ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+
+fillcolor = 'royalblue'
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color=fillcolor, zorder=4)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color=fillcolor, zorder=4)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=1.0, color=fillcolor, zorder=4)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=1.0, color=fillcolor, zorder=4)#yellow
+
+
+## FILL
+ax.fill_between([x.min(), 0-epsilon], y.min(), 0-epsilon, alpha=.25, color=fillcolor, zorder=4)#yellow
+ax.fill_between([0+epsilon, x.max()], 0+epsilon, y.max(), alpha=.25, color=fillcolor, zorder=4)#yellow
+
+
+ax.text(1,1, r"$\mathcal{G}^+_{\mathbf{R}^2}$", color='royalblue', size=15)
+
+# ax.text(0.25,0.25, r"$\mathcal{S}$", color='darkorange', size=15)
+
+# PLOT 1-PARAMETER FAMILY
+
+print('abar:', abar)
+print('abar[0,:]:', abar[0,:])
+print('abar[1,:]:', abar[1,:])
+
+line = ax.plot(abar[:,0],abar[:,1], linewidth=1.5, color='darkorange', linestyle='-', zorder=4)
+
+# plt.arrow(x=1, y=0, dx=0.5, dy=0, )
+# ax.arrow(1, 0, 0.5, 0, head_width=0.05, head_length=0.1, fc='k', ec='k', zorder=5)
+# plt.arrow(1, 0, 0.8, 0,  shape='full', lw=0, length_includes_head=True, head_width=.15, zorder=5, color='purple')
+
+
+## PLOT ARROW:
+# plt.arrow(1, 0, 0.5, 0,  shape='full', lw=0, length_includes_head=True, head_width=.20, zorder=5, color='darkorange')
+# plt.arrow(0, 1.8, 0, -0.8,  shape='full', lw=0, length_includes_head=True, head_width=.20, zorder=5, color='darkorange')
+
+
+# plt.arrow(0, 1.8, 0, -0.8, lw=0,  head_width=.12, zorder=5, color='darkorange')
+# plt.arrow(0, 2, 0, -0.5,  shape='full', lw=0, length_includes_head=True, head_width=.12, zorder=5, color='darkorange')
+# add_arrow(line, color='darkorange')
+
+
+
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+# print('test:',test)
+# ax.scatter(test[0],test[1])
+# ax.arrow(test[0],test[1],abarperp[0],abarperp[1])
+line_values= np.array(line_values)
+
+ax.plot(line_values[:,0],line_values[:,1],'k--', linewidth=1,color='orange',alpha=0.5)
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+### PLot x and y- Axes
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+
+
+
+ax.set_xlabel(r"$a_1$", fontsize=f_size ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=f_size ,labelpad=0, rotation=0)
+# ax.set_ylabel(r"energy")
+ax.tick_params(axis='both', which='major', labelsize=f_size)
+ax.tick_params(axis='both', which='minor', labelsize=f_size)
+
+
+
+ax.set_ylim(-2,2)
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+print('x.max()',x.max())
+print('y.max()',y.max())
+ax.set_xlim(x.min(),x.max())
+ax.set_xlim(y.min(),y.max())
+
+plt.subplots_adjust(bottom=0.15)
+plt.subplots_adjust(left=0.2)
+
+
+
+# ax.legend(loc='upper right')
+
+
+
+fig.set_size_inches(width, height)
+# fig.set_size_inches(set_size(width, fraction=0.33))
+fig.savefig('Energy_ContourG+_Flat.pdf')
+
+plt.show()
+
+
+#
+#
+#
+# # Curve parametrised by \theta_rho = alpha in parameter space
+# N=100;
+# theta_rho = np.linspace(1, 3, num=N)
+# print('theta_rho:', theta_rho)
+#
+#
+# theta_values = []
+#
+#
+# for t in theta_rho:
+#
+#         s = (1.0/10.0)*t+0.1
+#         theta_values.append(s)
+#
+#
+#
+#
+#
+# theta_rho = np.array(theta_rho)
+# theta_values = np.array(theta_values)
+#
+# betas_ = 2.0
+#
+
+# alphas, betas, thetas = np.meshgrid(theta_rho, betas_, theta_values, indexing='ij')
+#
+#
+# harmonicMeanVec = np.vectorize(harmonicMean)
+# arithmeticMeanVec = np.vectorize(arithmeticMean)
+# prestrain_b1Vec = np.vectorize(prestrain_b1)
+# prestrain_b2Vec = np.vectorize(prestrain_b2)
+#
+# GetMuGammaVec = np.vectorize(GetMuGamma)
+# muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#
+# q1_vec = harmonicMeanVec(mu1, betas, thetas)
+# q2_vec = arithmeticMeanVec(mu1, betas, thetas)
+#
+# b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+# b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+
+# special case: q12 == 0!! .. braucht eigentlich nur b1 & b2 ...
+
+# print('type b1_values:', type(b1_values))
+
+
+
+# print('size(q1)',q1.shape)
+#
+#
+# energy_axial1 = []
+# energy_axial2 = []
+#
+# # for b1 in b1_values:
+# for i in range(len(theta_rho)):
+#     print('index i:', i)
+#
+#     print('theta_rho[i]',theta_rho[i])
+#     print('theta_values[i]',theta_values[i])
+#
+#     q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta_values[i])
+#     q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta_values[i])
+#     q12 = 0.0
+#     q3 = GetMuGamma(beta, theta_values[i],gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#     b1 = prestrain_b1(rho1,beta, theta_rho[i],theta_values[i] )
+#     b2 = prestrain_b2(rho1,beta, theta_rho[i],theta_values[i] )
+#
+#
+#     # q2_vec = arithmeticMean(mu1, betas, thetas)
+#     #
+#     # b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+#     # b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+#     print('q1[i]',q1)
+#     print('q2[i]',q2)
+#     print('q3[i]',q3)
+#     print('b1[i]',b1)
+#     print('b2[i]',b2)
+#     # print('q1[i]',q1[0][i])
+#     # print('q2[i]',q2[i])
+#     # print('b1[i]',b1[i])
+#     # print('b2[i]',b2[i])
+#     #compute axial energy #1 ...
+#
+#     a_axial1 = np.array([b1,0])
+#     a_axial2 = np.array([0,b2])
+#     b = np.array([b1,b2])
+#
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a_axial1)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial1',a_axial1)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial1.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial1.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_1 = tmp - tmp2
+#     print('energy_1',energy_1)
+#
+#
+#     energy_axial1.append(energy_1)
+#
+#
+#     tmp = H.dot(a_axial2)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial2',a_axial2)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial2.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial2.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_2 = tmp - tmp2
+#     print('energy_2',energy_2)
+#
+#
+#     energy_axial2.append(energy_2)
+#
+#
+#
+#
+#
+# print('theta_values', theta_values)
+#
+#
+#
+
+
+#
+#
+#
+#
+# kappas = []
+# alphas = []
+# # G.append(float(s[0]))
+#
+#
+#
+#
+# for t in T :
+#
+#     abar_current = sstar*abar+t*abarperp;
+#     # print('abar_current', abar_current)
+#     abar_current[abar_current < 1e-10] = 0
+#     # print('abar_current', abar_current)
+#
+#     # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+#
+#     e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+#     kappa = abar_current[0]+abar_current[1]
+#     alpha = math.atan2(e[1], e[0])
+#
+#     print('angle current:', alpha)
+#
+#     kappas.append(kappa)
+#     alphas.append(alpha)
+#
+#
+#
+# alphas = np.array(alphas)
+# kappas = np.array(kappas)
+#
+#
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+# print('min alpha:', min(alphas))
+# print('min kappa:', min(kappas))
+#
+# mpl.rcParams['text.usetex'] = True
+# mpl.rcParams["font.family"] = "serif"
+# mpl.rcParams["font.size"] = "9"
+# width = 6.28 *0.5
+# height = width / 1.618
+# fig = plt.figure()
+# # ax = plt.axes((0.15,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.21 ,0.8,0.75))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# # ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# # ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# # ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# # ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+#
+#
+#
+#
+# ax.plot(alphas, kappas, 'royalblue', zorder=3, )
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )

Python-Scripts/1-ParameterFamily_G+_v2.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+def evaluate(x,y):
+
+	# (abar[0,:]*abar[1,:])**0.5
+
+	return np.sqrt(x*y)
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+class Arrow3D(FancyArrowPatch):
+
+    def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
+        super().__init__((0, 0), (0, 0), *args, **kwargs)
+        self._xyz = (x, y, z)
+        self._dxdydz = (dx, dy, dz)
+
+    def draw(self, renderer):
+        x1, y1, z1 = self._xyz
+        dx, dy, dz = self._dxdydz
+        x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
+
+        xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
+        self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
+        super().draw(renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+scale_domain = 5
+
+translate_startpoint = -5
+
+# T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+
+abar_tmp = abar
+
+for t in T :
+	abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+	abar_current[abar_current < 1e-10] = 0
+	# print('abar_current', abar_current)
+	# G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+	G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+	# print('type of G', type(G))
+	# print('G', G)
+	G_container.append(G)
+	abar_container.append(abar_current)
+	e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+	kappa = abar_current[0]+abar_current[1]
+	alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+	kappas.append(kappa)
+	alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+
+num_Points = 20
+num_Points = 50
+num_Points = 200
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+range = 2
+
+x_1 = np.linspace(0,range,num_Points)
+y_1 = np.linspace(0,range,num_Points)
+x_2 = np.linspace(-range,0,num_Points)
+y_2 = np.linspace(-range,0,num_Points)
+
+
+X_1,Y_1 = np.meshgrid(x_1,y_1)
+X_2,Y_2 = np.meshgrid(x_2,y_2)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+# print('a1:', a1)
+# print('a2:',a2 )
+#
+# print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+tmp1 = a1[np.where(a1*a2 >= 0)]
+tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+# tmp1 = a1[np.where(a1>=0 and a2 >= 0)]
+# tmp2 = a2[np.where(a1>=0 and a2 >= 0)]
+
+
+# tmp1 = tmp1[np.where(a1 >= 0)]
+# tmp2 = tmp2[np.where(a1 >= 0)]
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0)]
+# tmp2_neg = a2[np.where(a1*a2 >= 0)]
+
+
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+
+
+tmp1 = tmp1.reshape(-1,int(tmp1.shape[0]/2))
+tmp2 = tmp2.reshape(-1,int(tmp2.shape[0]/2))
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+# Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+#
+# Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+# Z = (tmp2**2)/tmp1
+Z = np.sqrt(tmp1*tmp2)
+
+
+Z1 = np.sqrt(X_1*Y_1)
+Z2 = np.sqrt(X_2*Y_2)
+
+# Z_bar = np.sqrt(abar[0,:]*abar[1,:])
+Z_bar = (abar[0,:]*abar[1,:])**0.5*abar
+
+abar = abar.T
+
+
+
+v1 = abar[0,:]
+v2 = abar[1,:]
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+evaluateVec = np.vectorize(evaluate)
+Z_bar = evaluateVec(abar[0,:],abar[1,:])
+# Z = np.sqrt(np.multiply(tmp1,tmp2))
+# Z = np.sqrt(a1*a2)
+
+
+print('v1.shape', v1.shape)
+print('v1', v1)
+
+
+
+
+print('Z:', Z)
+print('Z_bar:', Z_bar)
+# print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+label_size = 8
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+# plt.style.use('seaborn')
+plt.style.use('seaborn-whitegrid')
+# sns.set()
+# plt.style.use('seaborn-whitegrid')
+
+label_size = 9
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+width = 6.28 *0.5
+width = 6.28
+height = width / 1.618
+fig = plt.figure()
+
+ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+ax.grid(True,which='major',axis='both',alpha=0.3)
+
+# colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+
+#translate Data
+# Z = Z - (Z.max()-Z.min())/2
+# Z = Z - 50
+# Z = Z - 500
+#
+# Z = Z.T
+
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+
+# print('Value of c:', c)
+
+
+
+# print('Z.min()', Z.min())
+# print('Z.max()', Z.max())
+# norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+# print('norm:', norm)
+# print('type of norm', type(norm))
+# print('norm(0):', norm(0))
+# print('norm(Z):', norm(Z))
+
+# ax.plot(theta_rho, theta_values, 'royalblue', zorder=3, )
+
+# ax.scatter(a1,a2, s=0.5)
+
+# ax.scatter(tmp1_pos,tmp2_pos, s=0.5)
+# ax.scatter(tmp1_neg,tmp2_neg, s=0.5)
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=100 )
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot,  levels=20 )
+
+
+# sns.kdeplot(np.array([a1, a2, Z]))
+# sns.kdeplot(tmp1_pos,tmp2_pos,Z_pos)
+
+# levels = [-5.0, -4, -3, 0.0, 1.5, 2.5, 3.5]
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, corner_mask=True,levels=levels)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot(norm(Z)), corner_mask=True)
+# CS = ax.contour(a1, a2, Z, cm.brg(norm(Z)), levels=20)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot, levels=20)
+# CS = ax.contour(a1, a2, Z, colors='k', levels=14,  linewidths=(0.5,))
+# CS = ax.contour(a1, a2, Z, colors='k', levels=18,  linewidths=(0.5,))
+
+# ax.contour(negZ_a1, negZ_a2, negativeValues, colors='k',  linewidths=(0.5,))
+# CS =  ax.contour(a1_in, a2_in, Z_in, colors='k',  linewidths=(0.5,))
+
+
+
+# df = pd.DataFrame(data=Z_in, columns=a1_in, index=a2_in)
+# df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+#                    columns=['a', 'b', 'c'])
+
+
+
+
+# sns.kdeplot(data=df2, x="waiting", y="duration")
+# sns.kdeplot(data=df2)
+
+# CS = ax.contour(a1, a2, Z, colors='k',   linewidths=(0.5,))
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k', extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k')
+#
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, levels=10 )
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, corner_mask=True)
+#
+# CS = ax.contour(a1, a2, Z,10,  colors = 'k')
+# ax.clabel(CS, inline=True, fontsize=4)
+
+
+# cmap = cm.brg(norm(Z))
+#
+# C_map = cm.inferno(norm(Z))
+
+# ax.imshow(Z, cmap=C_map, extent=[-20, 20, -20, 20], origin='lower', alpha=0.5)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20], origin='lower',
+#                   cmap='bwr', alpha=0.8)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', vmin=Z.min(), vmax=Z.max(),
+#                   cmap='bwr', alpha=0.6)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+
+cmap=mpl.cm.RdBu_r
+# cmap=mpl.cm.viridis_r
+cmap=mpl.cm.bwr
+# # cmap=mpl.cm.coolwarm
+# # cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.viridis
+# cmap=mpl.cm.inferno
+cmap=mpl.cm.Blues
+# cmap=mpl.cm.magma
+# cmap=mpl.cm.cividis
+# cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.gnuplot
+cmap = mpl.colors.ListedColormap(["royalblue"], name='from_list', N=None)
+# m = cm.ScalarMappable(norm=norm, cmap=cmap)
+# m = cm.ScalarMappable(cmap=cmap)
+
+# cmap = cm.brg(Z)
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=8)
+
+
+
+
+# ##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+# epsilon = 0.1
+# # ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# # ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# # ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color='gray', zorder=5)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color='gray', zorder=5)#yellow
+
+
+
+line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=2)
+# CS = ax.contour(X_1,Y_1,Z1, colors='k', levels=18,  linewidths=(0.5,))
+
+start = np.array([abar[0,499],abar[1,499],Z_bar[499]])
+end = np.array([abar[0,500],abar[1,500],Z_bar[500]])
+
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.plot_surface(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.scatter(X_1,Y_1,Z1, s=0.2)
+# ax.scatter(X_2,Y_2,Z2, s=0.2)
+
+
+# X = np.concatenate((X_1, X_2), axis=0)
+# Y = np.concatenate((Y_1, Y_2), axis=0)
+# Z = np.concatenate((Z1, Z2), axis=0)
+# ax.plot_surface(X,Y,Z)
+
+
+ax.plot_surface(X_1,Y_1,Z1 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.75, zorder=5)
+ax.plot_surface(X_2,Y_2,Z2 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.75, zorder=5)
+# ax.plot_surface(X_1,Y_1,Z1 , facecolor = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , facecolor = 'lightblue', edgecolor='none',    #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+# ax.plot_surface(X_1,Y_1,Z1 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+
+
+# ax.plot_surface(X_2,Y_2,Z2 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0,  alpha=0.8, zorder=5, shade=True)
+# ax.plot_surface(X_2,Y_2,Z2)
+
+# X_2 = X_2.reshape(-1,1).flatten()
+# Y_2 = Y_2.reshape(-1,1).flatten()
+# Z2 = Z2.reshape(-1,1).flatten()
+# #
+# ax.plot_trisurf(X_2,Y_2,Z2, color='blue' )
+#
+#
+# X_1 = X_1.reshape(-1,1).flatten()
+# Y_1 = Y_1.reshape(-1,1).flatten()
+# Z1 = Z1.reshape(-1,1).flatten()
+# ax.plot_trisurf(X_1,Y_1,Z1 , color='blue')
+
+# ax.plot_surface(X_1,Y_1,Z1 , cmap=cmap,
+#                        linewidth=0, antialiased=False,alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , cmap=cmap,
+#                        linewidth=0, antialiased=True,alpha=1, zorder=5)
+
+# ax.plot_surface(X_2,Y_2,Z2 , color = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+# ax.plot(G[0,:],G[1,:],G[2,:])
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='yellow', linestyle='--')
+# ax.scatter(abar[0,:],abar[1,:],Z_bar,  color='purple', zorder=5)
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='royalblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='dodgerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='cornflowerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='darkorange', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='yellow', linestyle='--')
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=1, color='coral', linestyle='--', zorder=3)
+
+
+# plot starting point:
+# ax.scatter(abar[0,0],abar[1,0],Z_bar[0], marker='^',  s=30, color='black', zorder=5)
+#
+#
+# ax.scatter(abar[0,500],abar[1,500],Z_bar[500], marker='^',  s=30, color='purple', zorder=5)
+
+# ax.scatter(start[0],start[1],start[2], marker='^',  s=30, color='purple', zorder=5)
+# ax.scatter(end[0],end[1],end[2], marker='^',  s=30, color='purple', zorder=5)
+
+print('start:', start)
+print('end:', end)
+
+
+dir = end-start
+# ax.arrow()
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=10,
+#            arrowstyle="->",
+#            linestyle='dashed',fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+# Check proof:
+# value at t = 0:
+abar_zero= sstar*abar_tmp
+# value_0 = [abar_zero[0], abar_zero[1] , (2*abar_zero[0]*abar_zero[1])**0.5 ]
+value_0 = evaluate(abar_zero[0], abar_zero[1])
+print('value_0', value_0)
+# ax.scatter(value_0[0],value_0[1],value_0[2], marker='x',  s=20, color='dodgerblue', zorder=5)
+# ax.scatter(abar_zero[0], abar_zero[1],value_0, marker='o',  s=30, color='dodgerblue', zorder=5)
+## -----------------------------
+
+
+
+
+
+
+
+
+
+
+# ax.scatter(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_surface(tmp1,Z, tmp2, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_trisurf(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+### PLot x and y- Axes
+# ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+# ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=1)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=1)
+
+
+
+ax.set_xlabel(r"$a_1$", fontsize=10 ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=10 ,labelpad=0)
+# ax.set_ylabel(r"energy")
+
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+
+
+
+
+# ax.legend(loc='upper right')
+
+
+
+fig.set_size_inches(width, height)
+fig.savefig('1-ParameterFamily_G+.pdf')
+
+plt.show()
+
+
+#
+#
+#
+# # Curve parametrised by \theta_rho = alpha in parameter space
+# N=100;
+# theta_rho = np.linspace(1, 3, num=N)
+# print('theta_rho:', theta_rho)
+#
+#
+# theta_values = []
+#
+#
+# for t in theta_rho:
+#
+#         s = (1.0/10.0)*t+0.1
+#         theta_values.append(s)
+#
+#
+#
+#
+#
+# theta_rho = np.array(theta_rho)
+# theta_values = np.array(theta_values)
+#
+# betas_ = 2.0
+#
+
+# alphas, betas, thetas = np.meshgrid(theta_rho, betas_, theta_values, indexing='ij')
+#
+#
+# harmonicMeanVec = np.vectorize(harmonicMean)
+# arithmeticMeanVec = np.vectorize(arithmeticMean)
+# prestrain_b1Vec = np.vectorize(prestrain_b1)
+# prestrain_b2Vec = np.vectorize(prestrain_b2)
+#
+# GetMuGammaVec = np.vectorize(GetMuGamma)
+# muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#
+# q1_vec = harmonicMeanVec(mu1, betas, thetas)
+# q2_vec = arithmeticMeanVec(mu1, betas, thetas)
+#
+# b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+# b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+
+# special case: q12 == 0!! .. braucht eigentlich nur b1 & b2 ...
+
+# print('type b1_values:', type(b1_values))
+
+
+
+# print('size(q1)',q1.shape)
+#
+#
+# energy_axial1 = []
+# energy_axial2 = []
+#
+# # for b1 in b1_values:
+# for i in range(len(theta_rho)):
+#     print('index i:', i)
+#
+#     print('theta_rho[i]',theta_rho[i])
+#     print('theta_values[i]',theta_values[i])
+#
+#     q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta_values[i])
+#     q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta_values[i])
+#     q12 = 0.0
+#     q3 = GetMuGamma(beta, theta_values[i],gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+#     b1 = prestrain_b1(rho1,beta, theta_rho[i],theta_values[i] )
+#     b2 = prestrain_b2(rho1,beta, theta_rho[i],theta_values[i] )
+#
+#
+#     # q2_vec = arithmeticMean(mu1, betas, thetas)
+#     #
+#     # b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
+#     # b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
+#     print('q1[i]',q1)
+#     print('q2[i]',q2)
+#     print('q3[i]',q3)
+#     print('b1[i]',b1)
+#     print('b2[i]',b2)
+#     # print('q1[i]',q1[0][i])
+#     # print('q2[i]',q2[i])
+#     # print('b1[i]',b1[i])
+#     # print('b2[i]',b2[i])
+#     #compute axial energy #1 ...
+#
+#     a_axial1 = np.array([b1,0])
+#     a_axial2 = np.array([0,b2])
+#     b = np.array([b1,b2])
+#
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a_axial1)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial1',a_axial1)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial1.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial1.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_1 = tmp - tmp2
+#     print('energy_1',energy_1)
+#
+#
+#     energy_axial1.append(energy_1)
+#
+#
+#     tmp = H.dot(a_axial2)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a_axial2',a_axial2)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a_axial2.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a_axial2.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy_2 = tmp - tmp2
+#     print('energy_2',energy_2)
+#
+#
+#     energy_axial2.append(energy_2)
+#
+#
+#
+#
+#
+# print('theta_values', theta_values)
+#
+#
+#
+
+
+#
+#
+#
+#
+# kappas = []
+# alphas = []
+# # G.append(float(s[0]))
+#
+#
+#
+#
+# for t in T :
+#
+#     abar_current = sstar*abar+t*abarperp;
+#     # print('abar_current', abar_current)
+#     abar_current[abar_current < 1e-10] = 0
+#     # print('abar_current', abar_current)
+#
+#     # G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+#
+#     e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+#     kappa = abar_current[0]+abar_current[1]
+#     alpha = math.atan2(e[1], e[0])
+#
+#     print('angle current:', alpha)
+#
+#     kappas.append(kappa)
+#     alphas.append(alpha)
+#
+#
+#
+# alphas = np.array(alphas)
+# kappas = np.array(kappas)
+#
+#
+# print('kappas:',kappas)
+# print('alphas:',alphas)
+# print('min alpha:', min(alphas))
+# print('min kappa:', min(kappas))
+#
+# mpl.rcParams['text.usetex'] = True
+# mpl.rcParams["font.family"] = "serif"
+# mpl.rcParams["font.size"] = "9"
+# width = 6.28 *0.5
+# height = width / 1.618
+# fig = plt.figure()
+# # ax = plt.axes((0.15,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.21 ,0.8,0.75))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# # ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# # ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# # ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# # ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+#
+#
+#
+#
+# ax.plot(alphas, kappas, 'royalblue', zorder=3, )
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )

Python-Scripts/1-ParameterFamily_G+_v3.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+from mpl_toolkits.mplot3d import proj3d
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+
+import mayavi.mlab as mlab
+from mayavi.api import OffScreenEngine
+mlab.options.offscreen = True
+
+from chart_studio import plotly
+import plotly.graph_objs as go
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+def evaluate(x,y):
+
+	# (abar[0,:]*abar[1,:])**0.5
+
+	return np.sqrt(x*y)
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+
+
+class Arrow3D(FancyArrowPatch):
+    def __init__(self, xs, ys, zs, *args, **kwargs):
+        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
+        self._verts3d = xs, ys, zs
+
+    def draw(self, renderer):
+        xs3d, ys3d, zs3d = self._verts3d
+        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
+        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
+        FancyArrowPatch.draw(self, renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+# scale_domain = 5
+# translate_startpoint = -5
+
+scale_domain = 5
+translate_startpoint = -1.8
+
+
+# T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+
+abar_tmp = abar
+
+for t in T :
+	abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+	abar_current[abar_current < 1e-10] = 0
+	# print('abar_current', abar_current)
+	# G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+	G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+	# print('type of G', type(G))
+	# print('G', G)
+	G_container.append(G)
+	abar_container.append(abar_current)
+	e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+	kappa = abar_current[0]+abar_current[1]
+	alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+	kappas.append(kappa)
+	alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+
+num_Points = 20
+num_Points = 50
+num_Points = 200
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+range = 2
+
+x_1 = np.linspace(0,range,num_Points)
+y_1 = np.linspace(0,range,num_Points)
+x_2 = np.linspace(-range,0,num_Points)
+y_2 = np.linspace(-range,0,num_Points)
+
+
+X_1,Y_1 = np.meshgrid(x_1,y_1)
+X_2,Y_2 = np.meshgrid(x_2,y_2)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+# print('a1:', a1)
+# print('a2:',a2 )
+#
+# print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+tmp1 = a1[np.where(a1*a2 >= 0)]
+tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+# tmp1 = a1[np.where(a1>=0 and a2 >= 0)]
+# tmp2 = a2[np.where(a1>=0 and a2 >= 0)]
+
+
+# tmp1 = tmp1[np.where(a1 >= 0)]
+# tmp2 = tmp2[np.where(a1 >= 0)]
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0)]
+# tmp2_neg = a2[np.where(a1*a2 >= 0)]
+
+
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+
+
+tmp1 = tmp1.reshape(-1,int(tmp1.shape[0]/2))
+tmp2 = tmp2.reshape(-1,int(tmp2.shape[0]/2))
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+# Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+#
+# Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+# Z = (tmp2**2)/tmp1
+Z = np.sqrt(tmp1*tmp2)
+
+
+Z1 = np.sqrt(X_1*Y_1)
+Z2 = np.sqrt(X_2*Y_2)
+
+# Z_bar = np.sqrt(abar[0,:]*abar[1,:])
+Z_bar = (abar[0,:]*abar[1,:])**0.5*abar
+
+abar = abar.T
+
+
+
+v1 = abar[0,:]
+v2 = abar[1,:]
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+evaluateVec = np.vectorize(evaluate)
+Z_bar = evaluateVec(abar[0,:],abar[1,:])
+# Z = np.sqrt(np.multiply(tmp1,tmp2))
+# Z = np.sqrt(a1*a2)
+
+
+print('v1.shape', v1.shape)
+print('v1', v1)
+
+
+
+
+print('Z:', Z)
+print('Z_bar:', Z_bar)
+# print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+label_size = 8
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+# plt.style.use('seaborn')
+plt.style.use('seaborn-whitegrid')
+# sns.set()
+# plt.style.use('seaborn-whitegrid')
+
+label_size = 9
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+width = 6.28 *0.5
+# width = 6.28
+height = width / 1.618
+height = width
+fig = plt.figure()
+
+ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+ax.grid(True,which='major',axis='xy',alpha=0.3)
+# ax.grid(False,which='major',alpha=0.3)
+# Hide grid lines
+# ax.grid(False)
+
+
+
+# colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+
+#translate Data
+# Z = Z - (Z.max()-Z.min())/2
+# Z = Z - 50
+# Z = Z - 500
+#
+# Z = Z.T
+
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+
+# print('Value of c:', c)
+
+
+
+# print('Z.min()', Z.min())
+# print('Z.max()', Z.max())
+# norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+# print('norm:', norm)
+# print('type of norm', type(norm))
+# print('norm(0):', norm(0))
+# print('norm(Z):', norm(Z))
+
+# ax.plot(theta_rho, theta_values, 'royalblue', zorder=3, )
+
+# ax.scatter(a1,a2, s=0.5)
+
+# ax.scatter(tmp1_pos,tmp2_pos, s=0.5)
+# ax.scatter(tmp1_neg,tmp2_neg, s=0.5)
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=100 )
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot,  levels=20 )
+
+
+# sns.kdeplot(np.array([a1, a2, Z]))
+# sns.kdeplot(tmp1_pos,tmp2_pos,Z_pos)
+
+# levels = [-5.0, -4, -3, 0.0, 1.5, 2.5, 3.5]
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, corner_mask=True,levels=levels)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot(norm(Z)), corner_mask=True)
+# CS = ax.contour(a1, a2, Z, cm.brg(norm(Z)), levels=20)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot, levels=20)
+# CS = ax.contour(a1, a2, Z, colors='k', levels=14,  linewidths=(0.5,))
+# CS = ax.contour(a1, a2, Z, colors='k', levels=18,  linewidths=(0.5,))
+
+# ax.contour(negZ_a1, negZ_a2, negativeValues, colors='k',  linewidths=(0.5,))
+# CS =  ax.contour(a1_in, a2_in, Z_in, colors='k',  linewidths=(0.5,))
+
+
+
+# df = pd.DataFrame(data=Z_in, columns=a1_in, index=a2_in)
+# df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+#                    columns=['a', 'b', 'c'])
+
+
+
+
+# sns.kdeplot(data=df2, x="waiting", y="duration")
+# sns.kdeplot(data=df2)
+
+# CS = ax.contour(a1, a2, Z, colors='k',   linewidths=(0.5,))
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k', extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k')
+#
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, levels=10 )
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, corner_mask=True)
+#
+# CS = ax.contour(a1, a2, Z,10,  colors = 'k')
+# ax.clabel(CS, inline=True, fontsize=4)
+
+
+# cmap = cm.brg(norm(Z))
+#
+# C_map = cm.inferno(norm(Z))
+
+# ax.imshow(Z, cmap=C_map, extent=[-20, 20, -20, 20], origin='lower', alpha=0.5)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20], origin='lower',
+#                   cmap='bwr', alpha=0.8)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', vmin=Z.min(), vmax=Z.max(),
+#                   cmap='bwr', alpha=0.6)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+
+cmap=mpl.cm.RdBu_r
+# cmap=mpl.cm.viridis_r
+cmap=mpl.cm.bwr
+# # cmap=mpl.cm.coolwarm
+# # cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.viridis
+# cmap=mpl.cm.inferno
+cmap=mpl.cm.Blues
+# cmap=mpl.cm.magma
+# cmap=mpl.cm.cividis
+# cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.gnuplot
+cmap = mpl.colors.ListedColormap(["royalblue"], name='from_list', N=None)
+# m = cm.ScalarMappable(norm=norm, cmap=cmap)
+# m = cm.ScalarMappable(cmap=cmap)
+
+# cmap = cm.brg(Z)
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=8)
+
+
+
+
+# ##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+# epsilon = 0.1
+# # ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# # ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# # ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color='gray', zorder=5)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color='gray', zorder=5)#yellow
+
+
+
+
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=1)
+# CS = ax.contour(X_1,Y_1,Z1, colors='k', levels=18,  linewidths=(0.5,))
+
+start = np.array([abar[0,499],abar[1,499],Z_bar[499]])
+end = np.array([abar[0,500],abar[1,500],Z_bar[500]])
+
+
+
+
+
+# idx = np.where(np.round(Z_bar,3) == np.round( 0.03581463,3) )
+idx = np.where(np.round(Z_bar,3) == np.round( 0.02823972,3) )
+print('idx[0][0]', idx[0][0])
+
+# abar_1 = abar[0,0:idx[0][0]]
+# abar_2 = abar[1,0:idx[0][0]]
+line = ax.plot(abar[0,idx[0][0]:-1],abar[1,idx[0][0]:-1],Z_bar[idx[0][0]:-1], linewidth=2, color='coral', zorder=5)
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.plot_surface(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.scatter(X_1,Y_1,Z1, s=0.2)
+# ax.scatter(X_2,Y_2,Z2, s=0.2)
+
+
+# X = np.concatenate((X_1, X_2), axis=0)
+# Y = np.concatenate((Y_1, Y_2), axis=0)
+# Z = np.concatenate((Z1, Z2), axis=0)
+# ax.plot_surface(X,Y,Z)
+
+
+ax.plot_surface(X_1,Y_1,Z1 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.35, zorder=5)
+ax.plot_surface(X_2,Y_2,Z2 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.35, zorder=5)
+# ax.plot_surface(X_1,Y_1,Z1 , facecolor = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , facecolor = 'lightblue', edgecolor='none',    #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+# ax.plot_surface(X_1,Y_1,Z1 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+
+
+# ax.plot_surface(X_2,Y_2,Z2 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0,  alpha=0.8, zorder=5, shade=True)
+# ax.plot_surface(X_2,Y_2,Z2)
+
+# X_2 = X_2.reshape(-1,1).flatten()
+# Y_2 = Y_2.reshape(-1,1).flatten()
+# Z2 = Z2.reshape(-1,1).flatten()
+#
+# ax.plot_trisurf(X_2,Y_2,Z2, color='blue' )
+
+
+# X_1 = X_1.reshape(-1,1).flatten()
+# Y_1 = Y_1.reshape(-1,1).flatten()
+# Z1 = Z1.reshape(-1,1).flatten()
+# ax.plot_trisurf(X_1,Y_1,Z1 , color='blue')
+
+
+### MAYAVI TEST
+# mlab.figure(bgcolor=(1.0, 1.0, 1.0), size=(1000,1000))
+# mlab.view(azimuth=90, elevation=125)
+# mlab.view(azimuth=100, elevation=115)
+# axes = mlab.axes(color=(0, 0, 0), nb_labels=5)
+# mlab.orientation_axes()
+# mlab.mesh(X_1, Y_1,Z1, color=(0,0,1) ,  transparent=True )
+# mlab.plot3d(abar[0,:],abar[1,:],Z_bar, line_width=1)
+# mlab.mesh(X_2, Y_2,Z2)
+# mlab.savefig("./example.png")
+### --------------------------------------------
+
+
+
+# ax.plot_surface(X_1,Y_1,Z1 , cmap=cmap,
+#                        linewidth=0, antialiased=False,alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , cmap=cmap,
+#                        linewidth=0, antialiased=True,alpha=1, zorder=5)
+
+# ax.plot_surface(X_2,Y_2,Z2 , color = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+# ax.plot(G[0,:],G[1,:],G[2,:])
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='yellow', linestyle='--')
+# ax.scatter(abar[0,:],abar[1,:],Z_bar,  color='purple', zorder=5)
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='royalblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='dodgerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='cornflowerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='darkorange', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='yellow', linestyle='--')
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=1, color='coral', linestyle='--', zorder=3)
+
+
+# plot starting point:
+# ax.scatter(abar[0,0],abar[1,0],Z_bar[0], marker='^',  s=30, color='black', zorder=5)
+#
+#
+# ax.scatter(abar[0,500],abar[1,500],Z_bar[500], marker='^',  s=30, color='purple', zorder=5)
+
+# ax.scatter(start[0],start[1],start[2], marker='^',  s=30, color='purple', zorder=5)
+# ax.scatter(end[0],end[1],end[2], marker='^',  s=30, color='purple', zorder=5)
+
+
+# define origin
+o = np.array([0,0,0])
+
+start = np.array([1,0,0])
+end = np.array([2.5,0,0])
+
+
+print('start:', start)
+print('end:', end)
+
+
+dir = end-start
+print('dir:', dir)
+# ax.arrow()
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=10,
+#            arrowstyle="->",
+#            linestyle='dashed',fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=20,
+#            arrowstyle="->",
+#            fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=20,
+#            arrowstyle="->",
+#            fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+arrow_prop_dict = dict(mutation_scale=20, arrowstyle='-|>', color='k', shrinkA=0, shrinkB=0)
+# style = ArrowStyle('Fancy', head_length=1, head_width=1.5, tail_width=0.5)
+
+
+# ADD ARROW:
+# a = Arrow3D([start[0], end[0]], [start[1], end[1]], [start[2], end[2]], mutation_scale=15, arrowstyle='-|>', color='darkorange')
+# ax.add_artist(a)
+
+## ADD Annotation
+ax.text(0, 0, 1.5, r"$\mathcal G^+$", color='royalblue', size=12)
+# ax.text(0.5, 0.5, "Test")
+# ax.text(9, 0, 0, "red", color='red')
+
+### ---- Check proof:
+# value at t = 0:
+abar_zero= sstar*abar_tmp
+# value_0 = [abar_zero[0], abar_zero[1] , (2*abar_zero[0]*abar_zero[1])**0.5 ]
+value_0 = evaluate(abar_zero[0], abar_zero[1])
+print('value_0', value_0)
+# ax.scatter(value_0[0],value_0[1],value_0[2], marker='x',  s=20, color='dodgerblue', zorder=5)
+# ax.scatter(abar_zero[0], abar_zero[1],value_0, marker='o',  s=30, color='dodgerblue', zorder=5)
+## -----------------------------
+
+
+
+
+
+
+
+
+
+
+# ax.scatter(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_surface(tmp1,Z, tmp2, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_trisurf(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+
+### PLOT X AND Y AXIS:
+# ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+# ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=1 ,zorder=5)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=1)
+
+
+ax.set_xlabel(r"$a_1$", fontsize=10 ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=10 ,labelpad=0)
+
+
+# ax.get_xaxis().set_visible(False)
+# ax = plt.gca(projection="3d")
+# ax._axis3don = False
+ZL = ax.get_zgridlines()
+
+# ax.set_ylabel(r"energy")
+
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+
+
+
+
+# ax.legend(loc='upper right')
+
+
+
+fig.set_size_inches(width, height)
+fig.savefig('1-ParameterFamily_G+.pdf')
+
+plt.show()

Python-Scripts/1-ParameterFamily_G+_v4.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+from ClassifyMin import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+from mpl_toolkits.mplot3d import proj3d
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+
+import mayavi.mlab as mlab
+from mayavi.api import OffScreenEngine
+mlab.options.offscreen = True
+
+from chart_studio import plotly
+import plotly.graph_objs as go
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+def evaluate(x,y):
+
+	# (abar[0,:]*abar[1,:])**0.5
+
+	return np.sqrt(x*y)
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+
+
+class Arrow3D(FancyArrowPatch):
+    def __init__(self, xs, ys, zs, *args, **kwargs):
+        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
+        self._verts3d = xs, ys, zs
+
+    def draw(self, renderer):
+        xs3d, ys3d, zs3d = self._verts3d
+        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
+        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
+        FancyArrowPatch.draw(self, renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+# scale_domain = 5
+# translate_startpoint = -5
+
+# scale_domain = 5
+# translate_startpoint = -1.8
+
+
+scale_domain = 5
+translate_startpoint = -1.8
+T_line = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+line_values = []
+for t in T_line :
+    print('sstar*abar+t*abarperp', sstar*abar+t*abarperp)
+    line_values.append(sstar*abar+t*abarperp)
+
+
+
+
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+# T = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+
+abar_tmp = abar
+
+for t in T :
+	abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+	abar_current[abar_current < 1e-10] = 0
+	# print('abar_current', abar_current)
+	# G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+	G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+	# print('type of G', type(G))
+	# print('G', G)
+	G_container.append(G)
+	abar_container.append(abar_current)
+	e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+	kappa = abar_current[0]+abar_current[1]
+	alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+	kappas.append(kappa)
+	alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+
+num_Points = 20
+num_Points = 50
+num_Points = 200
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+range = 2
+
+x_1 = np.linspace(0,range,num_Points)
+y_1 = np.linspace(0,range,num_Points)
+x_2 = np.linspace(-range,0,num_Points)
+y_2 = np.linspace(-range,0,num_Points)
+
+
+X_1,Y_1 = np.meshgrid(x_1,y_1)
+X_2,Y_2 = np.meshgrid(x_2,y_2)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+# print('a1:', a1)
+# print('a2:',a2 )
+#
+# print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+tmp1 = a1[np.where(a1*a2 >= 0)]
+tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+# tmp1 = a1[np.where(a1>=0 and a2 >= 0)]
+# tmp2 = a2[np.where(a1>=0 and a2 >= 0)]
+
+
+# tmp1 = tmp1[np.where(a1 >= 0)]
+# tmp2 = tmp2[np.where(a1 >= 0)]
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0)]
+# tmp2_neg = a2[np.where(a1*a2 >= 0)]
+
+
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+
+
+tmp1 = tmp1.reshape(-1,int(tmp1.shape[0]/2))
+tmp2 = tmp2.reshape(-1,int(tmp2.shape[0]/2))
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+# Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+#
+# Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+# Z = (tmp2**2)/tmp1
+Z = np.sqrt(tmp1*tmp2)
+
+
+Z1 = np.sqrt(X_1*Y_1)
+Z2 = np.sqrt(X_2*Y_2)
+
+# Z_bar = np.sqrt(abar[0,:]*abar[1,:])
+Z_bar = (abar[0,:]*abar[1,:])**0.5*abar
+
+abar = abar.T
+
+
+
+v1 = abar[0,:]
+v2 = abar[1,:]
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+evaluateVec = np.vectorize(evaluate)
+Z_bar = evaluateVec(abar[0,:],abar[1,:])
+# Z = np.sqrt(np.multiply(tmp1,tmp2))
+# Z = np.sqrt(a1*a2)
+
+
+print('v1.shape', v1.shape)
+print('v1', v1)
+
+
+
+
+print('Z:', Z)
+print('Z_bar:', Z_bar)
+# print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+label_size = 8
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+# plt.style.use('seaborn')
+plt.style.use('seaborn-whitegrid')
+# sns.set()
+# plt.style.use('seaborn-whitegrid')
+
+label_size = 9
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+width = 6.28 *0.5
+# width = 6.28
+height = width / 1.618
+height = width
+fig = plt.figure()
+
+ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+ax.grid(True,which='major',axis='xy',alpha=0.3)
+# ax.grid(False,which='major',alpha=0.3)
+# Hide grid lines
+# ax.grid(False)
+
+
+
+# colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+
+#translate Data
+# Z = Z - (Z.max()-Z.min())/2
+# Z = Z - 50
+# Z = Z - 500
+#
+# Z = Z.T
+
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+
+# print('Value of c:', c)
+
+
+
+# print('Z.min()', Z.min())
+# print('Z.max()', Z.max())
+# norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+# print('norm:', norm)
+# print('type of norm', type(norm))
+# print('norm(0):', norm(0))
+# print('norm(Z):', norm(Z))
+
+# ax.plot(theta_rho, theta_values, 'royalblue', zorder=3, )
+
+# ax.scatter(a1,a2, s=0.5)
+
+# ax.scatter(tmp1_pos,tmp2_pos, s=0.5)
+# ax.scatter(tmp1_neg,tmp2_neg, s=0.5)
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=100 )
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot,  levels=20 )
+
+
+# sns.kdeplot(np.array([a1, a2, Z]))
+# sns.kdeplot(tmp1_pos,tmp2_pos,Z_pos)
+
+# levels = [-5.0, -4, -3, 0.0, 1.5, 2.5, 3.5]
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, corner_mask=True,levels=levels)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot(norm(Z)), corner_mask=True)
+# CS = ax.contour(a1, a2, Z, cm.brg(norm(Z)), levels=20)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot, levels=20)
+# CS = ax.contour(a1, a2, Z, colors='k', levels=14,  linewidths=(0.5,))
+# CS = ax.contour(a1, a2, Z, colors='k', levels=18,  linewidths=(0.5,))
+
+# ax.contour(negZ_a1, negZ_a2, negativeValues, colors='k',  linewidths=(0.5,))
+# CS =  ax.contour(a1_in, a2_in, Z_in, colors='k',  linewidths=(0.5,))
+
+
+
+# df = pd.DataFrame(data=Z_in, columns=a1_in, index=a2_in)
+# df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+#                    columns=['a', 'b', 'c'])
+
+
+
+
+# sns.kdeplot(data=df2, x="waiting", y="duration")
+# sns.kdeplot(data=df2)
+
+# CS = ax.contour(a1, a2, Z, colors='k',   linewidths=(0.5,))
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k', extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k')
+#
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, levels=10 )
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, corner_mask=True)
+#
+# CS = ax.contour(a1, a2, Z,10,  colors = 'k')
+# ax.clabel(CS, inline=True, fontsize=4)
+
+
+# cmap = cm.brg(norm(Z))
+#
+# C_map = cm.inferno(norm(Z))
+
+# ax.imshow(Z, cmap=C_map, extent=[-20, 20, -20, 20], origin='lower', alpha=0.5)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20], origin='lower',
+#                   cmap='bwr', alpha=0.8)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', vmin=Z.min(), vmax=Z.max(),
+#                   cmap='bwr', alpha=0.6)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+
+cmap=mpl.cm.RdBu_r
+# cmap=mpl.cm.viridis_r
+cmap=mpl.cm.bwr
+# # cmap=mpl.cm.coolwarm
+# # cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.viridis
+# cmap=mpl.cm.inferno
+cmap=mpl.cm.Blues
+# cmap=mpl.cm.magma
+# cmap=mpl.cm.cividis
+# cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.gnuplot
+cmap = mpl.colors.ListedColormap(["royalblue"], name='from_list', N=None)
+# m = cm.ScalarMappable(norm=norm, cmap=cmap)
+# m = cm.ScalarMappable(cmap=cmap)
+
+# cmap = cm.brg(Z)
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=8)
+
+
+
+
+# ##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+# epsilon = 0.1
+# # ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# # ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# # ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color='gray', zorder=5)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color='gray', zorder=5)#yellow
+
+
+
+#### LINE SEGMENTS :
+line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=5)
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=1)
+# print('abar', abar)
+# print('abar.shape',abar.shape)
+# start = np.array([abar[0,499],abar[1,499],Z_bar[499]])
+# end = np.array([abar[0,500],abar[1,500],Z_bar[500]])
+# idx = np.where(np.round(Z_bar,3) == np.round( 0.02823972,3) )
+# print('idx[0][0]', idx[0][0])
+# line = ax.plot(abar[0,idx[0][0]:-1],abar[1,idx[0][0]:-1],Z_bar[idx[0][0]:-1], linewidth=2, color='coral', zorder=5)
+### -----------------------------------
+
+
+
+
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.plot_surface(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.scatter(X_1,Y_1,Z1, s=0.2)
+# ax.scatter(X_2,Y_2,Z2, s=0.2)
+
+
+# X = np.concatenate((X_1, X_2), axis=0)
+# Y = np.concatenate((Y_1, Y_2), axis=0)
+# Z = np.concatenate((Z1, Z2), axis=0)
+# ax.plot_surface(X,Y,Z)
+
+
+ax.plot_surface(X_1,Y_1,Z1 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.35, zorder=5)
+ax.plot_surface(X_2,Y_2,Z2 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.35, zorder=5)
+# ax.plot_surface(X_1,Y_1,Z1 , facecolor = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , facecolor = 'lightblue', edgecolor='none',    #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+# ax.plot_surface(X_1,Y_1,Z1 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+
+
+# ax.plot_surface(X_2,Y_2,Z2 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0,  alpha=0.8, zorder=5, shade=True)
+# ax.plot_surface(X_2,Y_2,Z2)
+
+# X_2 = X_2.reshape(-1,1).flatten()
+# Y_2 = Y_2.reshape(-1,1).flatten()
+# Z2 = Z2.reshape(-1,1).flatten()
+#
+# ax.plot_trisurf(X_2,Y_2,Z2, color='blue' )
+
+
+# X_1 = X_1.reshape(-1,1).flatten()
+# Y_1 = Y_1.reshape(-1,1).flatten()
+# Z1 = Z1.reshape(-1,1).flatten()
+# ax.plot_trisurf(X_1,Y_1,Z1 , color='blue')
+
+
+### MAYAVI TEST
+# mlab.figure(bgcolor=(1.0, 1.0, 1.0), size=(1000,1000))
+# mlab.view(azimuth=90, elevation=125)
+# mlab.view(azimuth=100, elevation=115)
+# axes = mlab.axes(color=(0, 0, 0), nb_labels=5)
+# mlab.orientation_axes()
+# mlab.mesh(X_1, Y_1,Z1, color=(0,0,1) ,  transparent=True )
+# mlab.plot3d(abar[0,:],abar[1,:],Z_bar, line_width=1)
+# mlab.mesh(X_2, Y_2,Z2)
+# mlab.savefig("./example.png")
+### --------------------------------------------
+
+
+
+# ax.plot_surface(X_1,Y_1,Z1 , cmap=cmap,
+#                        linewidth=0, antialiased=False,alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , cmap=cmap,
+#                        linewidth=0, antialiased=True,alpha=1, zorder=5)
+
+# ax.plot_surface(X_2,Y_2,Z2 , color = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+# ax.plot(G[0,:],G[1,:],G[2,:])
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='yellow', linestyle='--')
+# ax.scatter(abar[0,:],abar[1,:],Z_bar,  color='purple', zorder=5)
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='royalblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='dodgerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='cornflowerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='darkorange', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='yellow', linestyle='--')
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=1, color='coral', linestyle='--', zorder=3)
+
+
+# plot starting point:
+# ax.scatter(abar[0,0],abar[1,0],Z_bar[0], marker='^',  s=30, color='black', zorder=5)
+#
+#
+# ax.scatter(abar[0,500],abar[1,500],Z_bar[500], marker='^',  s=30, color='purple', zorder=5)
+
+# ax.scatter(start[0],start[1],start[2], marker='^',  s=30, color='purple', zorder=5)
+# ax.scatter(end[0],end[1],end[2], marker='^',  s=30, color='purple', zorder=5)
+
+
+# define origin
+o = np.array([0,0,0])
+
+start = np.array([1,0,0])
+end = np.array([2.5,0,0])
+
+
+print('start:', start)
+print('end:', end)
+
+
+dir = end-start
+print('dir:', dir)
+# ax.arrow()
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=10,
+#            arrowstyle="->",
+#            linestyle='dashed',fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=20,
+#            arrowstyle="->",
+#            fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=20,
+#            arrowstyle="->",
+#            fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+arrow_prop_dict = dict(mutation_scale=20, arrowstyle='-|>', color='k', shrinkA=0, shrinkB=0)
+# style = ArrowStyle('Fancy', head_length=1, head_width=1.5, tail_width=0.5)
+
+
+# ADD ARROW:
+# a = Arrow3D([start[0], end[0]], [start[1], end[1]], [start[2], end[2]], mutation_scale=15, arrowstyle='-|>', color='darkorange')
+# ax.add_artist(a)
+
+## ADD Annotation
+# ax.text(0, 0, 1.5, r"$\mathcal G^+$", color='royalblue', size=12)
+ax.text(0, 0, 1.5, r"$\mathcal G^+$", color='royalblue', size=15)
+# ax.text(0.5, 0.5, "Test")
+# ax.text(9, 0, 0, "red", color='red')
+
+### ---- Check proof:
+# value at t = 0:
+abar_zero= sstar*abar_tmp
+# value_0 = [abar_zero[0], abar_zero[1] , (2*abar_zero[0]*abar_zero[1])**0.5 ]
+value_0 = evaluate(abar_zero[0], abar_zero[1])
+print('value_0', value_0)
+# ax.scatter(value_0[0],value_0[1],value_0[2], marker='x',  s=20, color='dodgerblue', zorder=5)
+# ax.scatter(abar_zero[0], abar_zero[1],value_0, marker='o',  s=30, color='dodgerblue', zorder=5)
+## -----------------------------
+
+
+
+
+
+
+
+
+
+
+# ax.scatter(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_surface(tmp1,Z, tmp2, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_trisurf(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+
+### PLOT X AND Y AXIS:
+# ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+# ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=1 ,zorder=5)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=1)
+
+
+
+# Plot 1-Parameter Line
+line_values= np.array(line_values)
+ax.plot(line_values[:,0],line_values[:,1],'k--', linewidth=1,color='orange',alpha=0.8)
+
+
+ax.set_xlabel(r"$a_1$", fontsize=10 ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=10 ,labelpad=0)
+
+
+plt.subplots_adjust(left=0.0)
+plt.subplots_adjust(bottom=0.25)
+
+# ax.get_xaxis().set_visible(False)
+# ax = plt.gca(projection="3d")
+# ax._axis3don = False
+ZL = ax.get_zgridlines()
+
+# ax.set_ylabel(r"energy")
+
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+
+
+
+
+# ax.legend(loc='upper right')
+
+
+
+fig.set_size_inches(width, height)
+fig.savefig('1-ParameterFamily_G+.pdf')
+
+plt.show()

Python-Scripts/1-ParameterFamily_G+_v5.py

+import numpy as np
+import matplotlib.pyplot as plt
+import sympy as sym
+import math
+import os
+import subprocess
+import fileinput
+import re
+import matlab.engine
+import sys
+# from ClassifyMin import *
+from ClassifyMin_New import *
+from HelperFunctions import *
+# from CellScript import *
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.cm as cm
+from vtk.util import numpy_support
+from pyevtk.hl import gridToVTK
+import time
+import matplotlib.ticker as ticker
+
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+import seaborn as sns
+import matplotlib.colors as mcolors
+
+
+from mpl_toolkits.mplot3d.proj3d import proj_transform
+from mpl_toolkits.mplot3d import proj3d
+# from mpl_toolkits.mplot3d.axes3d import Axes3D
+from matplotlib.text import Annotation
+from matplotlib.patches import FancyArrowPatch
+
+
+import mayavi.mlab as mlab
+from mayavi.api import OffScreenEngine
+mlab.options.offscreen = True
+
+from chart_studio import plotly
+import plotly.graph_objs as go
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+# set the colormap and centre the colorbar
+class MidpointNormalize(mcolors.Normalize):
+	"""
+	Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
+
+	e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
+	"""
+	def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
+		self.midpoint = midpoint
+		mcolors.Normalize.__init__(self, vmin, vmax, clip)
+
+	def __call__(self, value, clip=None):
+		# I'm ignoring masked values and all kinds of edge cases to make a
+		# simple example...
+		x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
+		return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
+
+
+
+def format_func(value, tick_number):
+    # find number of multiples of pi/2
+    # N = int(np.round(2 * value / np.pi))
+    # if N == 0:
+    #     return "0"
+    # elif N == 1:
+    #     return r"$\pi/2$"
+    # elif N == -1:
+    #     return r"$-\pi/2$"
+    # elif N == 2:
+    #     return r"$\pi$"
+    # elif N % 2 > 0:
+    #     return r"${0}\pi/2$".format(N)
+    # else:
+    #     return r"${0}\pi$".format(N // 2)
+    ##find number of multiples of pi/2
+    N = int(np.round(4 * value / np.pi))
+    if N == 0:
+        return "0"
+    elif N == 1:
+        return r"$\pi/4$"
+    elif N == -1:
+        return r"$-\pi/4$"
+    elif N == 2:
+        return r"$\pi/2$"
+    elif N == -2:
+        return r"$-\pi/2$"
+    elif N % 2 > 0:
+        return r"${0}\pi/2$".format(N)
+    else:
+        return r"${0}\pi$".format(N // 2)
+
+
+
+def find_nearest(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return array[idx]
+
+
+def find_nearestIdx(array, value):
+    array = np.asarray(array)
+    idx = (np.abs(array - value)).argmin()
+    return idx
+
+
+
+def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+
+
+    a = np.array([a1,a2])
+    b = np.array([b1,b2])
+    H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+    A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+
+
+    tmp = H.dot(a)
+
+    # print('H',H)
+    # print('A',A)
+    # print('b',b)
+    # print('a',a)
+    # print('tmp',tmp)
+
+    tmp = (1/2)*a.dot(tmp)
+    # print('tmp',tmp)
+
+    tmp2 = A.dot(b)
+    # print('tmp2',tmp2)
+    tmp2 = 2*a.dot(tmp2)
+
+    # print('tmp2',tmp2)
+    energy = tmp - tmp2
+    # print('energy',energy)
+
+
+    # energy_axial1.append(energy_1)
+
+    return energy
+
+
+
+def evaluate(x,y):
+
+	# (abar[0,:]*abar[1,:])**0.5
+
+	return np.sqrt(x*y)
+
+
+# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
+#
+#
+#     b = np.array([b1,b2])
+#     H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+#     A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+#
+#
+#     tmp = H.dot(a)
+#
+#     print('H',H)
+#     print('A',A)
+#     print('b',b)
+#     print('a',a)
+#     print('tmp',tmp)
+#
+#     tmp = (1/2)*a.dot(tmp)
+#     print('tmp',tmp)
+#
+#     tmp2 = A.dot(b)
+#     print('tmp2',tmp2)
+#     tmp2 = 2*a.dot(tmp2)
+#
+#     print('tmp2',tmp2)
+#     energy = tmp - tmp2
+#     print('energy',energy)
+#
+#
+#     # energy_axial1.append(energy_1)
+#
+#     return energy
+#
+
+def add_arrow(line, position=None, direction='right', size=15, color=None):
+    """
+    add an arrow to a line.
+
+    line:       Line2D object
+    position:   x-position of the arrow. If None, mean of xdata is taken
+    direction:  'left' or 'right'
+    size:       size of the arrow in fontsize points
+    color:      if None, line color is taken.
+    """
+    if color is None:
+        color = line.get_color()
+
+    xdata = line.get_xdata()
+    ydata = line.get_ydata()
+
+    if position is None:
+        position = xdata.mean()
+    # find closest index
+    start_ind = np.argmin(np.absolute(xdata - position))
+    if direction == 'right':
+        end_ind = start_ind + 1
+    else:
+        end_ind = start_ind - 1
+
+    line.axes.annotate('',
+        xytext=(xdata[start_ind], ydata[start_ind]),
+        xy=(xdata[end_ind], ydata[end_ind]),
+        arrowprops=dict(arrowstyle="->", color=color),
+        size=size
+    )
+
+
+
+class Annotation3D(Annotation):
+    def __init__(self, text, xyz, *args, **kwargs):
+        super().__init__(text, xy=(0, 0), *args, **kwargs)
+        self._xyz = xyz
+
+    def draw(self, renderer):
+        x2, y2, z2 = proj_transform(*self._xyz, self.axes.M)
+        self.xy = (x2, y2)
+        super().draw(renderer)
+
+def _annotate3D(ax, text, xyz, *args, **kwargs):
+    '''Add anotation `text` to an `Axes3d` instance.'''
+
+    annotation = Annotation3D(text, xyz, *args, **kwargs)
+    ax.add_artist(annotation)
+
+setattr(Axes3D, 'annotate3D', _annotate3D)
+
+
+
+class Arrow3D(FancyArrowPatch):
+    def __init__(self, xs, ys, zs, *args, **kwargs):
+        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
+        self._verts3d = xs, ys, zs
+
+    def draw(self, renderer):
+        xs3d, ys3d, zs3d = self._verts3d
+        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
+        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
+        FancyArrowPatch.draw(self, renderer)
+
+
+def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
+    '''Add an 3d arrow to an `Axes3D` instance.'''
+
+    arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
+    ax.add_artist(arrow)
+
+setattr(Axes3D, 'arrow3D', _arrow3D)
+
+################################################################################################################
+################################################################################################################
+################################################################################################################
+
+InputFile  = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+# --------- Run  from src folder:
+path_parent = os.path.dirname(os.getcwd())
+os.chdir(path_parent)
+path = os.getcwd()
+print(path)
+InputFilePath = os.getcwd()+InputFile
+OutputFilePath = os.getcwd()+OutputFile
+print("InputFilepath: ", InputFilePath)
+print("OutputFilepath: ", OutputFilePath)
+print("Path: ", path)
+
+print('---- Input parameters: -----')
+
+# q1=1;
+# q2=2;
+# q12=1/2;
+# q3=((4*q1*q2)**0.5-q12)/2;
+# # H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+#
+# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+# abar = np.array([q12+2*q3, 2*q2])
+# abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+#
+# print('abar:',abar)
+#
+# b = np.linalg.lstsq(A, abar)[0]
+# print('b',b)
+#
+#
+# # print('abar:',np.shape(abar))
+# # print('np.transpose(abar):',np.shape(np.transpose(abar)))
+# sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# # sstar = (1/(q1+q2))*abar.dot(tmp)
+# print('sstar', sstar)
+# abarperp= np.array([abar[1],-abar[0]])
+# print('abarperp:',abarperp)
+
+
+# -------------------------- Input Parameters --------------------
+
+mu1 = 1.0
+rho1 = 1.0
+alpha = 5.0
+theta = 1.0/2
+# theta= 0.1
+beta = 5.0
+
+
+
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/2
+# # theta= 0.1
+# beta = 5.0
+
+
+#Figure3:
+# mu1 = 1.0
+# rho1 = 1.0
+# alpha = 2.0
+# theta = 1.0/8
+# # theta= 0.1
+# beta = 2.0
+
+
+# alpha= -5
+
+
+#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
+gamma = '0'
+gamma = 'infinity'
+
+
+lambda1 = 0.0
+
+
+print('---- Input parameters: -----')
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+# print('alpha: ', alpha)
+print('beta: ', beta)
+# print('theta: ', theta)
+print('gamma:', gamma)
+
+print('lambda1: ', lambda1)
+print('----------------------------')
+# ----------------------------------------------------------------
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+
+
+
+
+
+q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+q12 = 0.0
+q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
+b1 = prestrain_b1(rho1,beta, alpha, theta )
+b2 = prestrain_b2(rho1,beta, alpha, theta )
+
+
+# 1-ParameterFamilyCase:
+
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)**0.5-q12)/2;
+# H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+
+H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
+abar = np.array([q12+2*q3, 2*q2])
+abar = (1.0/math.sqrt((q12+2*q3)**2+(2*q2)**2))*abar
+
+print('abar:',abar)
+
+b = np.linalg.lstsq(A, abar)[0]
+print('b',b)
+
+b1=b[0]
+b2=b[1]
+
+
+# print('abar:',np.shape(abar))
+# print('np.transpose(abar):',np.shape(np.transpose(abar)))
+sstar = (1/(q1+q2))*abar.dot(A.dot(b))
+# sstar = (1/(q1+q2))*abar.dot(tmp)
+print('sstar', sstar)
+abarperp= np.array([abar[1],-abar[0]])
+print('abarperp:',abarperp)
+
+print('----------------------------')
+
+# ----------------------------------------------------------------
+
+N=1000;
+# scale_domain = 5
+# translate_startpoint = -5
+
+# scale_domain = 5
+# translate_startpoint = -1.8
+
+
+scale_domain = 5
+translate_startpoint = -1.8
+T_line = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+line_values = []
+for t in T_line :
+    print('sstar*abar+t*abarperp', sstar*abar+t*abarperp)
+    line_values.append(sstar*abar+t*abarperp)
+
+
+
+
+T = np.linspace(-sstar*(q12+2*q3)/(2*q2), sstar*(2*q2)/(q12+2*q3), num=N)
+# T = np.linspace(-sstar*(q12+2*q3)/(2*q2)*scale_domain + translate_startpoint, sstar*(2*q2)/(q12+2*q3)*scale_domain , num=N)
+# T = np.linspace(-2,2, num=N)
+# print('T:', T)
+
+print('T.min():', T.min())
+print('T.max():', T.max())
+
+kappas = []
+alphas = []
+# G.append(float(s[0]))
+
+G_container = []
+abar_container = []
+
+
+abar_tmp = abar
+
+for t in T :
+	abar_current = sstar*abar+t*abarperp;
+    # print('abar_current', abar_current)
+	abar_current[abar_current < 1e-10] = 0
+	# print('abar_current', abar_current)
+	# G = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
+	G = [abar_current[0], abar_current[1] , (2*abar_current[0]*abar_current[1])**0.5 ]
+	# print('type of G', type(G))
+	# print('G', G)
+	G_container.append(G)
+	abar_container.append(abar_current)
+	e = [(abar_current[0]/(abar_current[0]+abar_current[1]))**0.5, (abar_current[1]/(abar_current[0]+abar_current[1]))**0.5]
+	kappa = abar_current[0]+abar_current[1]
+	alpha = math.atan2(e[1], e[0])
+	# print('angle current:', alpha)
+	kappas.append(kappa)
+	alphas.append(alpha)
+
+
+alphas = np.array(alphas)
+kappas = np.array(kappas)
+
+# print('G_container', G_container)
+G = np.array(G_container)
+abar = np.array(abar_container)
+
+print('G', G)
+print('abar', abar)
+print('abar.shape',abar.shape)
+
+
+
+
+
+print('q1 = ', q1)
+print('q2 = ', q2)
+print('q3 = ', q3)
+print('q12 = ', q12)
+print('b1 = ', b1)
+print('b2 = ', b2)
+
+num_Points = 20
+num_Points = 50
+num_Points = 200
+
+# Creating dataset
+x = np.linspace(-5,5,num_Points)
+y = np.linspace(-5,5,num_Points)
+
+x = np.linspace(-20,20,num_Points)
+y = np.linspace(-20,20,num_Points)
+
+# x = np.linspace(-10,10,num_Points)
+# y = np.linspace(-10,10,num_Points)
+
+# x = np.linspace(-60,60,num_Points)
+# y = np.linspace(-60,60,num_Points)
+#
+#
+# x = np.linspace(-40,40,num_Points)
+# y = np.linspace(-40,40,num_Points)
+
+
+range = 2
+
+x_1 = np.linspace(0,range,num_Points)
+y_1 = np.linspace(0,range,num_Points)
+x_2 = np.linspace(-range,0,num_Points)
+y_2 = np.linspace(-range,0,num_Points)
+
+
+X_1,Y_1 = np.meshgrid(x_1,y_1)
+X_2,Y_2 = np.meshgrid(x_2,y_2)
+
+
+a1, a2 = np.meshgrid(x,y)
+
+# geyser = sns.load_dataset("geyser")
+# print('type of geyser:', type(geyser))
+# print('geyser:',geyser)
+
+ContourRange=20
+
+x_in = np.linspace(-ContourRange,ContourRange,num_Points)
+y_in = np.linspace(-ContourRange,ContourRange,num_Points)
+a1_in, a2_in = np.meshgrid(x_in,y_in)
+
+# print('a1:', a1)
+# print('a2:',a2 )
+#
+# print('a1.shape', a1.shape)
+
+#-- FILTER OUT VALUES for G+ :
+
+tmp1 = a1[np.where(a1*a2 >= 0)]
+tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+# tmp1 = a1[np.where(a1>=0 and a2 >= 0)]
+# tmp2 = a2[np.where(a1>=0 and a2 >= 0)]
+
+
+# tmp1 = tmp1[np.where(a1 >= 0)]
+# tmp2 = tmp2[np.where(a1 >= 0)]
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0)]
+# tmp2_neg = a2[np.where(a1*a2 >= 0)]
+
+
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+
+
+tmp1 = tmp1.reshape(-1,int(tmp1.shape[0]/2))
+tmp2 = tmp2.reshape(-1,int(tmp2.shape[0]/2))
+
+print('tmp1.shape',tmp1.shape)
+print('tmp1.shape[0]',tmp1.shape[0])
+print('tmp2.shape',tmp2.shape)
+print('tmp2.shape[0]',tmp2.shape[0])
+
+# np.take(a, np.where(a>100)[0], axis=0)
+# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
+# tmp2 = a2[np.where(a1*a2 >= 0)]
+
+# tmp1 = a1[a1*a2 >= 0]
+# tmp2 = a2[a1*a2 >= 0]
+
+
+# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
+# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
+# tmp1_pos = tmp1_pos[np.where(tmp1_pos  >= 0)]
+# tmp2_pos = tmp2_pos[np.where(tmp2_pos  >= 0)]
+
+# tmp1_neg = a1[a1*a2 >= 0 ]
+# tmp2_neg = a2[a1*a2 >= 0 ]
+# tmp1_neg = tmp1_neg[tmp1_neg  < 0]
+# tmp2_neg = tmp2_neg[tmp2_neg  < 0]
+# a1 = tmp1
+# a2 = tmp2
+#
+# a1 = a1.reshape(-1,5)
+# a2 = a2.reshape(-1,5)
+
+# tmp1_pos = tmp1_pos.reshape(-1,5)
+# tmp2_pos = tmp2_pos.reshape(-1,5)
+# tmp1_neg = tmp1_neg.reshape(-1,5)
+# tmp2_neg = tmp2_neg.reshape(-1,5)
+
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+
+
+
+energyVec = np.vectorize(energy)
+
+# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
+# Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
+#
+# Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
+
+
+
+
+# Z = (tmp2**2)/tmp1
+Z = np.sqrt(tmp1*tmp2)
+
+
+Z1 = np.sqrt(X_1*Y_1)
+Z2 = np.sqrt(X_2*Y_2)
+
+# Z_bar = np.sqrt(abar[0,:]*abar[1,:])
+Z_bar = (abar[0,:]*abar[1,:])**0.5*abar
+
+abar = abar.T
+
+
+
+v1 = abar[0,:]
+v2 = abar[1,:]
+
+# print('a1:', a1)
+# print('a2:',a2 )
+# print('a1.shape', a1.shape)
+
+
+evaluateVec = np.vectorize(evaluate)
+Z_bar = evaluateVec(abar[0,:],abar[1,:])
+# Z = np.sqrt(np.multiply(tmp1,tmp2))
+# Z = np.sqrt(a1*a2)
+
+
+print('v1.shape', v1.shape)
+print('v1', v1)
+
+
+
+
+print('Z:', Z)
+print('Z_bar:', Z_bar)
+# print('any', np.any(Z<0))
+
+#
+
+
+# negZ_a1 = a1[np.where(Z<0)]
+# negZ_a2 = a2[np.where(Z<0)]
+# negativeValues = Z[np.where(Z<0)]
+# print('negativeValues:',negativeValues)
+#
+# print('negZ_a1',negZ_a1)
+# print('negZ_a2',negZ_a2)
+#
+#
+# negZ_a1 = negZ_a1.reshape(-1,5)
+# negZ_a2 = negZ_a2.reshape(-1,5)
+# negativeValues = negativeValues.reshape(-1,5)
+#
+# Z_pos =  energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
+# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
+
+
+
+
+
+# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
+
+
+
+
+# print('Z_pos.shape', Z_pos.shape)
+
+
+
+
+
+
+
+## -- PLOT :
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+label_size = 8
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+# plt.style.use('seaborn')
+plt.style.use('seaborn-whitegrid')
+# sns.set()
+# plt.style.use('seaborn-whitegrid')
+
+label_size = 9
+mpl.rcParams['xtick.labelsize'] = label_size
+mpl.rcParams['ytick.labelsize'] = label_size
+
+mpl.rcParams["font.size"] =10
+
+width = 6.28 *0.5
+# width = 6.28
+height = width / 1.618
+height = width
+fig = plt.figure()
+
+ax = plt.axes(projection ='3d', adjustable='box')
+# ax = plt.axes((0.17,0.21 ,0.75,0.75))
+# ax = plt.axes((0.15,0.18,0.8,0.8))
+# ax.tick_params(axis='x',which='major', direction='out',pad=5)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.1))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 8))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 16))
+# ax.xaxis.set_major_locator(plt.MultipleLocator(np.pi / 2))
+# ax.xaxis.set_minor_locator(plt.MultipleLocator(np.pi / 4))
+# ax.xaxis.set_major_formatter(plt.FuncFormatter(format_func))
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+ax.grid(True,which='major',axis='xy',alpha=0.3)
+# ax.grid(False,which='major',alpha=0.3)
+# Hide grid lines
+# ax.grid(False)
+
+
+
+# colorfunction=(B*kappa)
+# print('colofunction',colorfunction)
+
+#translate Data
+# Z = Z - (Z.max()-Z.min())/2
+# Z = Z - 50
+# Z = Z - 500
+#
+# Z = Z.T
+
+
+# Substract constant:
+# c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
+# Z = Z-c
+
+# print('Value of c:', c)
+
+
+
+# print('Z.min()', Z.min())
+# print('Z.max()', Z.max())
+# norm=mcolors.Normalize(Z.min(),Z.max())
+# facecolors=cm.brg(norm)
+
+
+# print('norm:', norm)
+# print('type of norm', type(norm))
+# print('norm(0):', norm(0))
+# print('norm(Z):', norm(Z))
+
+# ax.plot(theta_rho, theta_values, 'royalblue', zorder=3, )
+
+# ax.scatter(a1,a2, s=0.5)
+
+# ax.scatter(tmp1_pos,tmp2_pos, s=0.5)
+# ax.scatter(tmp1_neg,tmp2_neg, s=0.5)
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=100 )
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot,  levels=20 )
+
+
+# sns.kdeplot(np.array([a1, a2, Z]))
+# sns.kdeplot(tmp1_pos,tmp2_pos,Z_pos)
+
+# levels = [-5.0, -4, -3, 0.0, 1.5, 2.5, 3.5]
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, corner_mask=True,levels=levels)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot(norm(Z)), corner_mask=True)
+# CS = ax.contour(a1, a2, Z, cm.brg(norm(Z)), levels=20)
+# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot, levels=20)
+# CS = ax.contour(a1, a2, Z, colors='k', levels=14,  linewidths=(0.5,))
+# CS = ax.contour(a1, a2, Z, colors='k', levels=18,  linewidths=(0.5,))
+
+# ax.contour(negZ_a1, negZ_a2, negativeValues, colors='k',  linewidths=(0.5,))
+# CS =  ax.contour(a1_in, a2_in, Z_in, colors='k',  linewidths=(0.5,))
+
+
+
+# df = pd.DataFrame(data=Z_in, columns=a1_in, index=a2_in)
+# df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
+#                    columns=['a', 'b', 'c'])
+
+
+
+
+# sns.kdeplot(data=df2, x="waiting", y="duration")
+# sns.kdeplot(data=df2)
+
+# CS = ax.contour(a1, a2, Z, colors='k',   linewidths=(0.5,))
+
+# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k', extend='both', levels=50)
+# CS = ax.contourf(a1, a2, Z,10, colors='k')
+#
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, levels=10 )
+# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, corner_mask=True)
+#
+# CS = ax.contour(a1, a2, Z,10,  colors = 'k')
+# ax.clabel(CS, inline=True, fontsize=4)
+
+
+# cmap = cm.brg(norm(Z))
+#
+# C_map = cm.inferno(norm(Z))
+
+# ax.imshow(Z, cmap=C_map, extent=[-20, 20, -20, 20], origin='lower', alpha=0.5)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20], origin='lower',
+#                   cmap='bwr', alpha=0.8)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', vmin=Z.min(), vmax=Z.max(),
+#                   cmap='bwr', alpha=0.6)
+
+# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+
+cmap=mpl.cm.RdBu_r
+# cmap=mpl.cm.viridis_r
+cmap=mpl.cm.bwr
+# # cmap=mpl.cm.coolwarm
+# # cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.viridis
+# cmap=mpl.cm.inferno
+cmap=mpl.cm.Blues
+# cmap=mpl.cm.magma
+# cmap=mpl.cm.cividis
+# cmap=mpl.cm.gnuplot
+# cmap=mpl.cm.gnuplot
+cmap = mpl.colors.ListedColormap(["royalblue"], name='from_list', N=None)
+# m = cm.ScalarMappable(norm=norm, cmap=cmap)
+# m = cm.ScalarMappable(cmap=cmap)
+
+# cmap = cm.brg(Z)
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
+#                   cmap='coolwarm', alpha=0.6)
+
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap='coolwarm', alpha=0.6)
+# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
+#                   cmap=cmap, alpha=0.6)
+
+# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
+#                   cmap=cmap, alpha=0.6)
+
+
+
+
+# COLORBAR :
+# cbar = plt.colorbar()
+# cbar.ax.tick_params(labelsize=8)
+
+
+
+
+# ##----- ADD RECTANGLE TO COVER QUADRANT :
+# epsilon = 0.4
+# epsilon = 0.1
+# # ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
+# # ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
+# # ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
+# ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color='gray', zorder=5)#yellow
+# ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color='gray', zorder=5)#yellow
+
+
+
+#### LINE SEGMENTS :
+line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=5)
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='coral', zorder=1)
+# print('abar', abar)
+# print('abar.shape',abar.shape)
+# start = np.array([abar[0,499],abar[1,499],Z_bar[499]])
+# end = np.array([abar[0,500],abar[1,500],Z_bar[500]])
+# idx = np.where(np.round(Z_bar,3) == np.round( 0.02823972,3) )
+# print('idx[0][0]', idx[0][0])
+# line = ax.plot(abar[0,idx[0][0]:-1],abar[1,idx[0][0]:-1],Z_bar[idx[0][0]:-1], linewidth=2, color='coral', zorder=5)
+### -----------------------------------
+
+
+
+
+
+# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.plot_surface(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+# ax.scatter(X_1,Y_1,Z1, s=0.2)
+# ax.scatter(X_2,Y_2,Z2, s=0.2)
+
+
+# X = np.concatenate((X_1, X_2), axis=0)
+# Y = np.concatenate((Y_1, Y_2), axis=0)
+# Z = np.concatenate((Z1, Z2), axis=0)
+# ax.plot_surface(X,Y,Z)
+
+
+ax.plot_surface(X_1,Y_1,Z1 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.35, zorder=5)
+ax.plot_surface(X_2,Y_2,Z2 ,cmap=cmap,
+                       linewidth=0, antialiased=True,alpha=.35, zorder=5)
+# ax.plot_surface(X_1,Y_1,Z1 , facecolor = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , facecolor = 'lightblue', edgecolor='none',    #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+# ax.plot_surface(X_1,Y_1,Z1 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+
+
+# ax.plot_surface(X_2,Y_2,Z2 , #color='C0',
+# 							rstride=1, cstride=1,linewidth=0,  alpha=0.8, zorder=5, shade=True)
+# ax.plot_surface(X_2,Y_2,Z2)
+
+# X_2 = X_2.reshape(-1,1).flatten()
+# Y_2 = Y_2.reshape(-1,1).flatten()
+# Z2 = Z2.reshape(-1,1).flatten()
+#
+# ax.plot_trisurf(X_2,Y_2,Z2, color='blue' )
+
+
+# X_1 = X_1.reshape(-1,1).flatten()
+# Y_1 = Y_1.reshape(-1,1).flatten()
+# Z1 = Z1.reshape(-1,1).flatten()
+# ax.plot_trisurf(X_1,Y_1,Z1 , color='blue')
+
+
+### MAYAVI TEST
+# mlab.figure(bgcolor=(1.0, 1.0, 1.0), size=(1000,1000))
+# mlab.view(azimuth=90, elevation=125)
+# mlab.view(azimuth=100, elevation=115)
+# axes = mlab.axes(color=(0, 0, 0), nb_labels=5)
+# mlab.orientation_axes()
+# mlab.mesh(X_1, Y_1,Z1, color=(0,0,1) ,  transparent=True )
+# mlab.plot3d(abar[0,:],abar[1,:],Z_bar, line_width=1)
+# mlab.mesh(X_2, Y_2,Z2)
+# mlab.savefig("./example.png")
+### --------------------------------------------
+
+
+
+# ax.plot_surface(X_1,Y_1,Z1 , cmap=cmap,
+#                        linewidth=0, antialiased=False,alpha=1, zorder=5)
+# ax.plot_surface(X_2,Y_2,Z2 , cmap=cmap,
+#                        linewidth=0, antialiased=True,alpha=1, zorder=5)
+
+# ax.plot_surface(X_2,Y_2,Z2 , color = 'lightblue',     #cmap=cmap,
+#                        linewidth=0, antialiased=True, alpha=1, zorder=5)
+
+
+# ax.plot(G[0,:],G[1,:],G[2,:])
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='yellow', linestyle='--')
+# ax.scatter(abar[0,:],abar[1,:],Z_bar,  color='purple', zorder=5)
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=2, color='royalblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='dodgerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='cornflowerblue', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='darkorange', linestyle='--')
+# ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=3, color='yellow', linestyle='--')
+# line = ax.plot(abar[0,:],abar[1,:],Z_bar, linewidth=1, color='coral', linestyle='--', zorder=3)
+
+
+# plot starting point:
+# ax.scatter(abar[0,0],abar[1,0],Z_bar[0], marker='^',  s=30, color='black', zorder=5)
+#
+#
+# ax.scatter(abar[0,500],abar[1,500],Z_bar[500], marker='^',  s=30, color='purple', zorder=5)
+
+# ax.scatter(start[0],start[1],start[2], marker='^',  s=30, color='purple', zorder=5)
+# ax.scatter(end[0],end[1],end[2], marker='^',  s=30, color='purple', zorder=5)
+
+
+# define origin
+o = np.array([0,0,0])
+
+start = np.array([1,0,0])
+end = np.array([2.5,0,0])
+
+
+print('start:', start)
+print('end:', end)
+
+
+dir = end-start
+print('dir:', dir)
+# ax.arrow()
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=10,
+#            arrowstyle="->",
+#            linestyle='dashed',fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+# ax.arrow3D(midpoint_mapped[0],midpoint_mapped[1],midpoint_mapped[2],
+#            normal[0],normal[1],normal[2],
+#            mutation_scale=15,
+#             lw = 1.5,
+#            arrowstyle="-|>",
+#            linestyle='dashed',fc='blue',
+#            ec ='blue',
+#            zorder = 5)
+
+
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=20,
+#            arrowstyle="->",
+#            fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+# ax.arrow3D(start[0],start[1],start[2],
+#            dir[0],dir[1],dir[2],
+#            mutation_scale=20,
+#            arrowstyle="->",
+#            fc='coral',
+#            lw = 1,
+#            ec ='coral',
+#            zorder=3)
+
+arrow_prop_dict = dict(mutation_scale=20, arrowstyle='-|>', color='k', shrinkA=0, shrinkB=0)
+# style = ArrowStyle('Fancy', head_length=1, head_width=1.5, tail_width=0.5)
+
+
+# ADD ARROW:
+# a = Arrow3D([start[0], end[0]], [start[1], end[1]], [start[2], end[2]], mutation_scale=15, arrowstyle='-|>', color='darkorange')
+# ax.add_artist(a)
+
+## ADD Annotation
+# ax.text(0, 0, 1.5, r"$\mathcal G^+$", color='royalblue', size=12)
+# ax.text(0, 0, 1.5, r"$\mathcal G^+$", color='royalblue', size=15)
+ax.text(0, 0, 1.5, r"$\mathcal G^+$", color='royalblue', size=13)
+# ax.text(0.5, 0.5, "Test")
+# ax.text(9, 0, 0, "red", color='red')
+
+### ---- Check proof:
+# value at t = 0:
+abar_zero= sstar*abar_tmp
+# value_0 = [abar_zero[0], abar_zero[1] , (2*abar_zero[0]*abar_zero[1])**0.5 ]
+value_0 = evaluate(abar_zero[0], abar_zero[1])
+print('value_0', value_0)
+# ax.scatter(value_0[0],value_0[1],value_0[2], marker='x',  s=20, color='dodgerblue', zorder=5)
+# ax.scatter(abar_zero[0], abar_zero[1],value_0, marker='o',  s=30, color='dodgerblue', zorder=5)
+## -----------------------------
+
+
+
+
+
+
+
+
+
+
+# ax.scatter(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_surface(tmp1,Z, tmp2, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+# ax.plot_trisurf(tmp1,tmp2, Z, cmap=cm.coolwarm,
+#                        linewidth=0, antialiased=False)
+
+
+# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
+# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
+# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
+
+
+
+
+# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
+
+
+
+
+### PLOT X AND Y AXIS:
+# ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
+# ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
+ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=1 ,zorder=5)
+ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=1)
+
+
+
+# Plot 1-Parameter Line
+line_values= np.array(line_values)
+ax.plot(line_values[:,0],line_values[:,1],'k--', linewidth=1,color='orange',alpha=0.8)
+
+
+ax.set_xlabel(r"$a_1$", fontsize=10 ,labelpad=0)
+ax.set_ylabel(r"$a_2$", fontsize=10 ,labelpad=0)
+
+
+
+# ax.margins(x=0.5, y=-0.25)   # Values in (-0.5, 0.0) zooms in to center
+# ax.margins(x=0.5, y=0)   # Values in (-0.5, 0.0) zooms in to center
+
+
+plt.subplots_adjust(left=0.0)
+plt.subplots_adjust(bottom=0.1)
+
+plt.rcParams["figure.autolayout"] = True
+
+# ax.get_xaxis().set_visible(False)
+# ax = plt.gca(projection="3d")
+# ax._axis3don = False
+ZL = ax.get_zgridlines()
+
+# ax.set_ylabel(r"energy")
+
+
+# ax.set_xticks([-np.pi/2, -np.pi/4  ,0,  np.pi/4,  np.pi/2 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$']
+# ax.set_yticklabels(labels)
+
+
+
+# ax.view_init(elev=30, azim=-65)
+
+# ax.legend(loc='upper right')
+
+# plt.tight_layout()
+# fig.tight_layout()
+
+fig.set_size_inches(width, height)
+fig.savefig('1-ParameterFamily_G+.pdf')
+
+plt.show()

Python-Scripts/2DPhaseDiagram_PlotScript.py

+## trace generated using paraview version 5.7.0
+#
+# To ensure correct image size when batch processing, please search
+# for and uncomment the line `# renderView*.ViewSize = [*,*]`
+
+#### import the simple module from the paraview
+from paraview.simple import *
+#### disable automatic camera reset on 'Show'
+paraview.simple._DisableFirstRenderCameraReset()
+
+
+
+case = 1
+case = 2
+#
+
+# curvature = 1
+
+
+
+# create a new 'XML Structured Grid Reader'
+if case == 1:
+    phaseDiagram2DGamma_infinity55_4000spvts = XMLStructuredGridReader(FileName=['/home/klaus/Desktop/DUNE/dune-microstructure/outputs/PhaseDiagram2DGamma0-5+5_4000sp.vts'])
+    phaseDiagram2DGamma_infinity55_4000spvts = XMLStructuredGridReader(FileName=['/home/klaus/Desktop/DUNE/dune-microstructure/outputs/PhaseDiagram2DGamma0.vts'])
+if case == 2:
+    phaseDiagram2DGamma_infinity55_4000spvts = XMLStructuredGridReader(FileName=['/home/klaus/Desktop/DUNE/dune-microstructure/outputs/PhaseDiagram2DGamma_infinity-5+5_4000sp.vts'])
+    phaseDiagram2DGamma_infinity55_4000spvts = XMLStructuredGridReader(FileName=['/home/klaus/Desktop/DUNE/dune-microstructure/outputs/PhaseDiagram2DGamma_infinity.vts'])
+
+
+phaseDiagram2DGamma_infinity55_4000spvts.CellArrayStatus = []
+phaseDiagram2DGamma_infinity55_4000spvts.PointArrayStatus = ['Type', 'angles', 'curvature']
+
+# get active view
+renderView1 = GetActiveViewOrCreate('RenderView')
+# uncomment following to set a specific view size
+# renderView1.ViewSize = [1380, 547]
+
+# show data in view
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay = Show(phaseDiagram2DGamma_infinity55_4000spvts, renderView1)
+
+# get color transfer function/color map for 'Type'
+typeLUT = GetColorTransferFunction('Type')
+typeLUT.AutomaticRescaleRangeMode = "Grow and update on 'Apply'"
+typeLUT.InterpretValuesAsCategories = 0
+typeLUT.AnnotationsInitialized = 0
+typeLUT.ShowCategoricalColorsinDataRangeOnly = 0
+typeLUT.RescaleOnVisibilityChange = 0
+typeLUT.EnableOpacityMapping = 0
+typeLUT.RGBPoints = [1.0, 0.001462, 0.000466, 0.013866, 1.007844, 0.002258, 0.001295, 0.018331, 1.015686, 0.003279, 0.002305, 0.023708, 1.02353, 0.004512, 0.00349, 0.029965, 1.0313720000000002, 0.00595, 0.004843, 0.03713, 1.0392160000000001, 0.007588, 0.006356, 0.044973, 1.0470579999999998, 0.009426, 0.008022, 0.052844, 1.0549019999999998, 0.011465, 0.009828, 0.06075, 1.0627460000000002, 0.013708, 0.011771, 0.068667, 1.0705879999999999, 0.016156, 0.01384, 0.076603, 1.0784319999999998, 0.018815, 0.016026, 0.084584, 1.086274, 0.021692, 0.01832, 0.09261, 1.094118, 0.024792, 0.020715, 0.100676, 1.10196, 0.028123, 0.023201, 0.108787, 1.109804, 0.031696, 0.025765, 0.116965, 1.117648, 0.03552, 0.028397, 0.125209, 1.12549, 0.039608, 0.03109, 0.133515, 1.133334, 0.04383, 0.03383, 0.141886, 1.1411760000000002, 0.048062, 0.036607, 0.150327, 1.1490200000000002, 0.05232, 0.039407, 0.158841, 1.1568619999999998, 0.056615, 0.04216, 0.167446, 1.1647059999999998, 0.060949, 0.044794, 0.176129, 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0.42295, 2.6, 0.994738, 0.62435, 0.427397, 2.607844, 0.995122, 0.631696, 0.431951, 2.615686, 0.99548, 0.639027, 0.436607, 2.6235299999999997, 0.99581, 0.646344, 0.441361, 2.631372, 0.996096, 0.653659, 0.446213, 2.6392160000000002, 0.996341, 0.660969, 0.45116, 2.647058, 0.99658, 0.668256, 0.456192, 2.654902, 0.996775, 0.675541, 0.461314, 2.6627460000000003, 0.996925, 0.682828, 0.466526, 2.670588, 0.997077, 0.690088, 0.471811, 2.678432, 0.997186, 0.697349, 0.477182, 2.686274, 0.997254, 0.704611, 0.482635, 2.694118, 0.997325, 0.711848, 0.488154, 2.7019599999999997, 0.997351, 0.719089, 0.493755, 2.709804, 0.997351, 0.726324, 0.499428, 2.717648, 0.997341, 0.733545, 0.505167, 2.7254899999999997, 0.997285, 0.740772, 0.510983, 2.733334, 0.997228, 0.747981, 0.516859, 2.7411760000000003, 0.997138, 0.75519, 0.522806, 2.74902, 0.997019, 0.762398, 0.528821, 2.756862, 0.996898, 0.769591, 0.534892, 2.7647060000000003, 0.996727, 0.776795, 0.541039, 2.77255, 0.996571, 0.783977, 0.547233, 2.780392, 0.996369, 0.791167, 0.553499, 2.788236, 0.996162, 0.798348, 0.55982, 2.796078, 0.995932, 0.805527, 0.566202, 2.803922, 0.99568, 0.812706, 0.572645, 2.811764, 0.995424, 0.819875, 0.57914, 2.8196079999999997, 0.995131, 0.827052, 0.585701, 2.82745, 0.994851, 0.834213, 0.592307, 2.835294, 0.994524, 0.841387, 0.598983, 2.8431379999999997, 0.994222, 0.84854, 0.605696, 2.85098, 0.993866, 0.855711, 0.612482, 2.8588240000000003, 0.993545, 0.862859, 0.619299, 2.866666, 0.99317, 0.870024, 0.626189, 2.87451, 0.992831, 0.877168, 0.633109, 2.882352, 0.99244, 0.88433, 0.640099, 2.890196, 0.992089, 0.89147, 0.647116, 2.89804, 0.991688, 0.898627, 0.654202, 2.905882, 0.991332, 0.905763, 0.661309, 2.913726, 0.99093, 0.912915, 0.668481, 2.9215679999999997, 0.99057, 0.920049, 0.675675, 2.929412, 0.990175, 0.927196, 0.682926, 2.9372540000000003, 0.989815, 0.934329, 0.690198, 2.9450979999999998, 0.989434, 0.94147, 0.697519, 2.952942, 0.989077, 0.948604, 0.704863, 2.9607840000000003, 0.988717, 0.955742, 0.712242, 2.968628, 0.988367, 0.962878, 0.719649, 2.97647, 0.988033, 0.970012, 0.727077, 2.984314, 0.987691, 0.977154, 0.734536, 2.992156, 0.987387, 0.984288, 0.742002, 3.0, 0.987053, 0.991438, 0.749504]
+typeLUT.UseLogScale = 0
+typeLUT.ColorSpace = 'RGB'
+typeLUT.UseBelowRangeColor = 0
+typeLUT.BelowRangeColor = [0.0, 0.0, 0.0]
+typeLUT.UseAboveRangeColor = 0
+typeLUT.AboveRangeColor = [0.5, 0.5, 0.5]
+typeLUT.NanColor = [0.0, 1.0, 0.0]
+typeLUT.NanOpacity = 1.0
+typeLUT.Discretize = 1
+typeLUT.NumberOfTableValues = 256
+typeLUT.ScalarRangeInitialized = 1.0
+typeLUT.HSVWrap = 0
+typeLUT.VectorComponent = 0
+typeLUT.VectorMode = 'Magnitude'
+typeLUT.AllowDuplicateScalars = 1
+typeLUT.Annotations = []
+typeLUT.ActiveAnnotatedValues = []
+typeLUT.IndexedColors = []
+typeLUT.IndexedOpacities = []
+
+# get opacity transfer function/opacity map for 'Type'
+typePWF = GetOpacityTransferFunction('Type')
+typePWF.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.4276729533762702, 0.625, 0.5, 0.0, 1.7232704162597656, 0.6691176295280457, 0.5, 0.0, 2.3332666599993335, 0.8676470518112183, 0.5, 0.0, 2.471698045730591, 0.6911764740943909, 0.5, 0.0, 3.0, 0.8014705777168274, 0.5, 0.0]
+typePWF.AllowDuplicateScalars = 1
+typePWF.UseLogScale = 0
+typePWF.ScalarRangeInitialized = 1
+
+# trace defaults for the display properties.
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Representation = 'Surface'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.AmbientColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ColorArrayName = ['POINTS', 'Type']
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DiffuseColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.LookupTable = typeLUT
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.MapScalars = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.MultiComponentsMapping = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.InterpolateScalarsBeforeMapping = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Opacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PointSize = 2.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.LineWidth = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.RenderLinesAsTubes = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.RenderPointsAsSpheres = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Interpolation = 'Gouraud'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Specular = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SpecularColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SpecularPower = 100.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Luminosity = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Ambient = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Diffuse = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.EdgeColor = [0.0, 0.0, 0.5]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.BackfaceRepresentation = 'Follow Frontface'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.BackfaceAmbientColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.BackfaceDiffuseColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.BackfaceOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Position = [0.0, 0.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Scale = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Orientation = [0.0, 0.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Origin = [0.0, 0.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Pickable = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Texture = None
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Triangulate = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.UseShaderReplacements = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ShaderReplacements = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.NonlinearSubdivisionLevel = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.UseDataPartitions = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OSPRayUseScaleArray = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OSPRayScaleArray = 'Type'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OSPRayScaleFunction = 'PiecewiseFunction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OSPRayMaterial = 'None'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Orient = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OrientationMode = 'Direction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectOrientationVectors = 'None'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Scaling = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleMode = 'No Data Scaling Off'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleFactor = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectScaleArray = 'Type'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType = 'Arrow'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.UseGlyphTable = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphTableIndexArray = 'Type'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.UseCompositeGlyphTable = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.UseGlyphCullingAndLOD = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.LODValues = []
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ColorByLODIndex = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GaussianRadius = 0.05
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ShaderPreset = 'Sphere'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.CustomTriangleScale = 3
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.CustomShader = """ // This custom shader code define a gaussian blur
+ // Please take a look into vtkSMPointGaussianRepresentation.cxx
+ // for other custom shader examples
+ //VTK::Color::Impl
+   float dist2 = dot(offsetVCVSOutput.xy,offsetVCVSOutput.xy);
+   float gaussian = exp(-0.5*dist2);
+   opacity = opacity*gaussian;
+"""
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.Emissive = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleByArray = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SetScaleArray = ['POINTS', 'Type']
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleArrayComponent = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.UseScaleFunction = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleTransferFunction = 'PiecewiseFunction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OpacityByArray = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OpacityArray = ['POINTS', 'Type']
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OpacityArrayComponent = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OpacityTransferFunction = 'PiecewiseFunction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid = 'GridAxesRepresentation'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelColor = [0.0, 1.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelFontSize = 18
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelJustification = 'Left'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionCellLabelShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelColor = [1.0, 1.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelFontSize = 18
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelJustification = 'Left'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectionPointLabelShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes = 'PolarAxesRepresentation'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScalarOpacityFunction = typePWF
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScalarOpacityUnitDistance = 0.03988178566826777
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SelectMapper = 'Projected tetra'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SamplingDimensions = [128, 128, 128]
+
+# init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OSPRayScaleFunction.UseLogScale = 0
+
+# init the 'Arrow' selected for 'GlyphType'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType.TipResolution = 6
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType.TipRadius = 0.1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType.TipLength = 0.35
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType.ShaftResolution = 6
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType.ShaftRadius = 0.03
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.GlyphType.Invert = 0
+
+# init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleTransferFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.4276729533762702, 0.625, 0.5, 0.0, 1.7232704162597656, 0.6691176295280457, 0.5, 0.0, 2.3332666599993335, 0.8676470518112183, 0.5, 0.0, 2.471698045730591, 0.6911764740943909, 0.5, 0.0, 3.0, 0.8014705777168274, 0.5, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.ScaleTransferFunction.UseLogScale = 0
+
+# init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OpacityTransferFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.4276729533762702, 0.625, 0.5, 0.0, 1.7232704162597656, 0.6691176295280457, 0.5, 0.0, 2.3332666599993335, 0.8676470518112183, 0.5, 0.0, 2.471698045730591, 0.6911764740943909, 0.5, 0.0, 3.0, 0.8014705777168274, 0.5, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.OpacityTransferFunction.UseLogScale = 0
+
+# init the 'GridAxesRepresentation' selected for 'DataAxesGrid'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitle = 'X Axis'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitle = 'Y Axis'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitle = 'Z Axis'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XTitleOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YTitleOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZTitleOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.FacesToRender = 63
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.CullBackface = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.CullFrontface = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.GridColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ShowGrid = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ShowEdges = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ShowTicks = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.LabelUniqueEdgesOnly = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.AxesToLabel = 63
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XLabelOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YLabelOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZLabelOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XAxisNotation = 'Mixed'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XAxisPrecision = 2
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XAxisUseCustomLabels = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.XAxisLabels = []
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YAxisNotation = 'Mixed'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YAxisPrecision = 2
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YAxisUseCustomLabels = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.YAxisLabels = []
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZAxisNotation = 'Mixed'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZAxisPrecision = 2
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZAxisUseCustomLabels = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.ZAxisLabels = []
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.UseCustomBounds = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.DataAxesGrid.CustomBounds = [0.0, 1.0, 0.0, 1.0, 0.0, 1.0]
+
+# init the 'PolarAxesRepresentation' selected for 'PolarAxes'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.Visibility = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.Translation = [0.0, 0.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.Scale = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.Orientation = [0.0, 0.0, 0.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.EnableCustomBounds = [0, 0, 0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.CustomBounds = [0.0, 1.0, 0.0, 1.0, 0.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.EnableCustomRange = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.CustomRange = [0.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.RadialAxesVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.DrawRadialGridlines = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarArcsVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.DrawPolarArcsGridlines = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.NumberOfRadialAxes = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.AutoSubdividePolarAxis = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.NumberOfPolarAxis = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.MinimumRadius = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.MinimumAngle = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.MaximumAngle = 90.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.RadialAxesOriginToPolarAxis = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.Ratio = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarArcsColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryPolarArcsColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitle = 'Radial Distance'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleLocation = 'Bottom'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarLabelVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarLabelFormat = '%-#6.3g'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarLabelExponentLocation = 'Labels'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.RadialLabelVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.RadialLabelFormat = '%-#3.1f'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.RadialLabelLocation = 'Bottom'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.RadialUnitsVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ScreenSize = 10.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTitleFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisLabelFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTextFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextColor = [1.0, 1.0, 1.0]
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextOpacity = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextFontFamily = 'Arial'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextFontFile = ''
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextBold = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextItalic = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextShadow = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SecondaryRadialAxesTextFontSize = 12
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.EnableDistanceLOD = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.DistanceLODThreshold = 0.7
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.EnableViewAngleLOD = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ViewAngleLODThreshold = 0.7
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.SmallestVisiblePolarAngle = 0.5
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarTicksVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcTicksOriginToPolarAxis = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.TickLocation = 'Both'
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.AxisTickVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.AxisMinorTickVisibility = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcTickVisibility = 1
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcMinorTickVisibility = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.DeltaAngleMajor = 10.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.DeltaAngleMinor = 5.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisMajorTickSize = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTickRatioSize = 0.3
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisMajorTickThickness = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.PolarAxisTickRatioThickness = 0.5
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisMajorTickSize = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTickRatioSize = 0.3
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisMajorTickThickness = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.LastRadialAxisTickRatioThickness = 0.5
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcMajorTickSize = 0.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcTickRatioSize = 0.3
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcMajorTickThickness = 1.0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.ArcTickRatioThickness = 0.5
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.Use2DMode = 0
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.PolarAxes.UseLogAxis = 0
+
+# reset view to fit data
+renderView1.ResetCamera()
+
+#changing interaction mode based on data extents
+renderView1.InteractionMode = '2D'
+renderView1.CameraPosition = [0.0, 10010.0, 0.5]
+renderView1.CameraFocalPoint = [0.0, 10.0, 0.5]
+renderView1.CameraViewUp = [1.0, 0.0, 0.0]
+
+# show color bar/color legend
+phaseDiagram2DGamma_infinity55_4000spvtsDisplay.SetScalarBarVisibility(renderView1, True)
+
+# update the view to ensure updated data information
+renderView1.Update()
+
+# create a new 'Transform'
+transform1 = Transform(Input=phaseDiagram2DGamma_infinity55_4000spvts)
+transform1.Transform = 'Transform'
+transform1.TransformAllInputVectors = 1
+
+# init the 'Transform' selected for 'Transform'
+transform1.Transform.Translate = [0.0, 0.0, 0.0]
+transform1.Transform.Rotate = [0.0, 0.0, 0.0]
+transform1.Transform.Scale = [1.0, 1.0, 1.0]
+
+# Properties modified on transform1.Transform
+transform1.Transform.Scale = [0.1, 1.0, 1.0]
+
+# show data in view
+transform1Display = Show(transform1, renderView1)
+
+# trace defaults for the display properties.
+transform1Display.Representation = 'Surface'
+transform1Display.AmbientColor = [1.0, 1.0, 1.0]
+transform1Display.ColorArrayName = ['POINTS', 'Type']
+transform1Display.DiffuseColor = [1.0, 1.0, 1.0]
+transform1Display.LookupTable = typeLUT
+transform1Display.MapScalars = 1
+transform1Display.MultiComponentsMapping = 0
+transform1Display.InterpolateScalarsBeforeMapping = 1
+transform1Display.Opacity = 1.0
+transform1Display.PointSize = 2.0
+transform1Display.LineWidth = 1.0
+transform1Display.RenderLinesAsTubes = 0
+transform1Display.RenderPointsAsSpheres = 0
+transform1Display.Interpolation = 'Gouraud'
+transform1Display.Specular = 0.0
+transform1Display.SpecularColor = [1.0, 1.0, 1.0]
+transform1Display.SpecularPower = 100.0
+transform1Display.Luminosity = 0.0
+transform1Display.Ambient = 0.0
+transform1Display.Diffuse = 1.0
+transform1Display.EdgeColor = [0.0, 0.0, 0.5]
+transform1Display.BackfaceRepresentation = 'Follow Frontface'
+transform1Display.BackfaceAmbientColor = [1.0, 1.0, 1.0]
+transform1Display.BackfaceDiffuseColor = [1.0, 1.0, 1.0]
+transform1Display.BackfaceOpacity = 1.0
+transform1Display.Position = [0.0, 0.0, 0.0]
+transform1Display.Scale = [1.0, 1.0, 1.0]
+transform1Display.Orientation = [0.0, 0.0, 0.0]
+transform1Display.Origin = [0.0, 0.0, 0.0]
+transform1Display.Pickable = 1
+transform1Display.Texture = None
+transform1Display.Triangulate = 0
+transform1Display.UseShaderReplacements = 0
+transform1Display.ShaderReplacements = ''
+transform1Display.NonlinearSubdivisionLevel = 1
+transform1Display.UseDataPartitions = 0
+transform1Display.OSPRayUseScaleArray = 0
+transform1Display.OSPRayScaleArray = 'Type'
+transform1Display.OSPRayScaleFunction = 'PiecewiseFunction'
+transform1Display.OSPRayMaterial = 'None'
+transform1Display.Orient = 0
+transform1Display.OrientationMode = 'Direction'
+transform1Display.SelectOrientationVectors = 'None'
+transform1Display.Scaling = 0
+transform1Display.ScaleMode = 'No Data Scaling Off'
+transform1Display.ScaleFactor = 0.1
+transform1Display.SelectScaleArray = 'Type'
+transform1Display.GlyphType = 'Arrow'
+transform1Display.UseGlyphTable = 0
+transform1Display.GlyphTableIndexArray = 'Type'
+transform1Display.UseCompositeGlyphTable = 0
+transform1Display.UseGlyphCullingAndLOD = 0
+transform1Display.LODValues = []
+transform1Display.ColorByLODIndex = 0
+transform1Display.GaussianRadius = 0.005
+transform1Display.ShaderPreset = 'Sphere'
+transform1Display.CustomTriangleScale = 3
+transform1Display.CustomShader = """ // This custom shader code define a gaussian blur
+ // Please take a look into vtkSMPointGaussianRepresentation.cxx
+ // for other custom shader examples
+ //VTK::Color::Impl
+   float dist2 = dot(offsetVCVSOutput.xy,offsetVCVSOutput.xy);
+   float gaussian = exp(-0.5*dist2);
+   opacity = opacity*gaussian;
+"""
+transform1Display.Emissive = 0
+transform1Display.ScaleByArray = 0
+transform1Display.SetScaleArray = ['POINTS', 'Type']
+transform1Display.ScaleArrayComponent = ''
+transform1Display.UseScaleFunction = 1
+transform1Display.ScaleTransferFunction = 'PiecewiseFunction'
+transform1Display.OpacityByArray = 0
+transform1Display.OpacityArray = ['POINTS', 'Type']
+transform1Display.OpacityArrayComponent = ''
+transform1Display.OpacityTransferFunction = 'PiecewiseFunction'
+transform1Display.DataAxesGrid = 'GridAxesRepresentation'
+transform1Display.SelectionCellLabelBold = 0
+transform1Display.SelectionCellLabelColor = [0.0, 1.0, 0.0]
+transform1Display.SelectionCellLabelFontFamily = 'Arial'
+transform1Display.SelectionCellLabelFontFile = ''
+transform1Display.SelectionCellLabelFontSize = 18
+transform1Display.SelectionCellLabelItalic = 0
+transform1Display.SelectionCellLabelJustification = 'Left'
+transform1Display.SelectionCellLabelOpacity = 1.0
+transform1Display.SelectionCellLabelShadow = 0
+transform1Display.SelectionPointLabelBold = 0
+transform1Display.SelectionPointLabelColor = [1.0, 1.0, 0.0]
+transform1Display.SelectionPointLabelFontFamily = 'Arial'
+transform1Display.SelectionPointLabelFontFile = ''
+transform1Display.SelectionPointLabelFontSize = 18
+transform1Display.SelectionPointLabelItalic = 0
+transform1Display.SelectionPointLabelJustification = 'Left'
+transform1Display.SelectionPointLabelOpacity = 1.0
+transform1Display.SelectionPointLabelShadow = 0
+transform1Display.PolarAxes = 'PolarAxesRepresentation'
+transform1Display.ScalarOpacityFunction = typePWF
+transform1Display.ScalarOpacityUnitDistance = 0.005557396853320044
+transform1Display.SelectMapper = 'Projected tetra'
+transform1Display.SamplingDimensions = [128, 128, 128]
+
+# init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+transform1Display.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+transform1Display.OSPRayScaleFunction.UseLogScale = 0
+
+# init the 'Arrow' selected for 'GlyphType'
+transform1Display.GlyphType.TipResolution = 6
+transform1Display.GlyphType.TipRadius = 0.1
+transform1Display.GlyphType.TipLength = 0.35
+transform1Display.GlyphType.ShaftResolution = 6
+transform1Display.GlyphType.ShaftRadius = 0.03
+transform1Display.GlyphType.Invert = 0
+
+# init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+transform1Display.ScaleTransferFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.4276729533762702, 0.625, 0.5, 0.0, 1.7232704162597656, 0.6691176295280457, 0.5, 0.0, 2.3332666599993335, 0.8676470518112183, 0.5, 0.0, 2.471698045730591, 0.6911764740943909, 0.5, 0.0, 3.0, 0.8014705777168274, 0.5, 0.0]
+transform1Display.ScaleTransferFunction.UseLogScale = 0
+
+# init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+transform1Display.OpacityTransferFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.4276729533762702, 0.625, 0.5, 0.0, 1.7232704162597656, 0.6691176295280457, 0.5, 0.0, 2.3332666599993335, 0.8676470518112183, 0.5, 0.0, 2.471698045730591, 0.6911764740943909, 0.5, 0.0, 3.0, 0.8014705777168274, 0.5, 0.0]
+transform1Display.OpacityTransferFunction.UseLogScale = 0
+
+# init the 'GridAxesRepresentation' selected for 'DataAxesGrid'
+transform1Display.DataAxesGrid.XTitle = 'X Axis'
+transform1Display.DataAxesGrid.YTitle = 'Y Axis'
+transform1Display.DataAxesGrid.ZTitle = 'Z Axis'
+transform1Display.DataAxesGrid.XTitleColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.XTitleFontFamily = 'Arial'
+transform1Display.DataAxesGrid.XTitleFontFile = ''
+transform1Display.DataAxesGrid.XTitleBold = 0
+transform1Display.DataAxesGrid.XTitleItalic = 0
+transform1Display.DataAxesGrid.XTitleFontSize = 12
+transform1Display.DataAxesGrid.XTitleShadow = 0
+transform1Display.DataAxesGrid.XTitleOpacity = 1.0
+transform1Display.DataAxesGrid.YTitleColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.YTitleFontFamily = 'Arial'
+transform1Display.DataAxesGrid.YTitleFontFile = ''
+transform1Display.DataAxesGrid.YTitleBold = 0
+transform1Display.DataAxesGrid.YTitleItalic = 0
+transform1Display.DataAxesGrid.YTitleFontSize = 12
+transform1Display.DataAxesGrid.YTitleShadow = 0
+transform1Display.DataAxesGrid.YTitleOpacity = 1.0
+transform1Display.DataAxesGrid.ZTitleColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.ZTitleFontFamily = 'Arial'
+transform1Display.DataAxesGrid.ZTitleFontFile = ''
+transform1Display.DataAxesGrid.ZTitleBold = 0
+transform1Display.DataAxesGrid.ZTitleItalic = 0
+transform1Display.DataAxesGrid.ZTitleFontSize = 12
+transform1Display.DataAxesGrid.ZTitleShadow = 0
+transform1Display.DataAxesGrid.ZTitleOpacity = 1.0
+transform1Display.DataAxesGrid.FacesToRender = 63
+transform1Display.DataAxesGrid.CullBackface = 0
+transform1Display.DataAxesGrid.CullFrontface = 1
+transform1Display.DataAxesGrid.GridColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.ShowGrid = 0
+transform1Display.DataAxesGrid.ShowEdges = 1
+transform1Display.DataAxesGrid.ShowTicks = 1
+transform1Display.DataAxesGrid.LabelUniqueEdgesOnly = 1
+transform1Display.DataAxesGrid.AxesToLabel = 63
+transform1Display.DataAxesGrid.XLabelColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.XLabelFontFamily = 'Arial'
+transform1Display.DataAxesGrid.XLabelFontFile = ''
+transform1Display.DataAxesGrid.XLabelBold = 0
+transform1Display.DataAxesGrid.XLabelItalic = 0
+transform1Display.DataAxesGrid.XLabelFontSize = 12
+transform1Display.DataAxesGrid.XLabelShadow = 0
+transform1Display.DataAxesGrid.XLabelOpacity = 1.0
+transform1Display.DataAxesGrid.YLabelColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.YLabelFontFamily = 'Arial'
+transform1Display.DataAxesGrid.YLabelFontFile = ''
+transform1Display.DataAxesGrid.YLabelBold = 0
+transform1Display.DataAxesGrid.YLabelItalic = 0
+transform1Display.DataAxesGrid.YLabelFontSize = 12
+transform1Display.DataAxesGrid.YLabelShadow = 0
+transform1Display.DataAxesGrid.YLabelOpacity = 1.0
+transform1Display.DataAxesGrid.ZLabelColor = [1.0, 1.0, 1.0]
+transform1Display.DataAxesGrid.ZLabelFontFamily = 'Arial'
+transform1Display.DataAxesGrid.ZLabelFontFile = ''
+transform1Display.DataAxesGrid.ZLabelBold = 0
+transform1Display.DataAxesGrid.ZLabelItalic = 0
+transform1Display.DataAxesGrid.ZLabelFontSize = 12
+transform1Display.DataAxesGrid.ZLabelShadow = 0
+transform1Display.DataAxesGrid.ZLabelOpacity = 1.0
+transform1Display.DataAxesGrid.XAxisNotation = 'Mixed'
+transform1Display.DataAxesGrid.XAxisPrecision = 2
+transform1Display.DataAxesGrid.XAxisUseCustomLabels = 0
+transform1Display.DataAxesGrid.XAxisLabels = []
+transform1Display.DataAxesGrid.YAxisNotation = 'Mixed'
+transform1Display.DataAxesGrid.YAxisPrecision = 2
+transform1Display.DataAxesGrid.YAxisUseCustomLabels = 0
+transform1Display.DataAxesGrid.YAxisLabels = []
+transform1Display.DataAxesGrid.ZAxisNotation = 'Mixed'
+transform1Display.DataAxesGrid.ZAxisPrecision = 2
+transform1Display.DataAxesGrid.ZAxisUseCustomLabels = 0
+transform1Display.DataAxesGrid.ZAxisLabels = []
+transform1Display.DataAxesGrid.UseCustomBounds = 0
+transform1Display.DataAxesGrid.CustomBounds = [0.0, 1.0, 0.0, 1.0, 0.0, 1.0]
+
+# init the 'PolarAxesRepresentation' selected for 'PolarAxes'
+transform1Display.PolarAxes.Visibility = 0
+transform1Display.PolarAxes.Translation = [0.0, 0.0, 0.0]
+transform1Display.PolarAxes.Scale = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.Orientation = [0.0, 0.0, 0.0]
+transform1Display.PolarAxes.EnableCustomBounds = [0, 0, 0]
+transform1Display.PolarAxes.CustomBounds = [0.0, 1.0, 0.0, 1.0, 0.0, 1.0]
+transform1Display.PolarAxes.EnableCustomRange = 0
+transform1Display.PolarAxes.CustomRange = [0.0, 1.0]
+transform1Display.PolarAxes.PolarAxisVisibility = 1
+transform1Display.PolarAxes.RadialAxesVisibility = 1
+transform1Display.PolarAxes.DrawRadialGridlines = 1
+transform1Display.PolarAxes.PolarArcsVisibility = 1
+transform1Display.PolarAxes.DrawPolarArcsGridlines = 1
+transform1Display.PolarAxes.NumberOfRadialAxes = 0
+transform1Display.PolarAxes.AutoSubdividePolarAxis = 1
+transform1Display.PolarAxes.NumberOfPolarAxis = 0
+transform1Display.PolarAxes.MinimumRadius = 0.0
+transform1Display.PolarAxes.MinimumAngle = 0.0
+transform1Display.PolarAxes.MaximumAngle = 90.0
+transform1Display.PolarAxes.RadialAxesOriginToPolarAxis = 1
+transform1Display.PolarAxes.Ratio = 1.0
+transform1Display.PolarAxes.PolarAxisColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.PolarArcsColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.LastRadialAxisColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.SecondaryPolarArcsColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.SecondaryRadialAxesColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.PolarAxisTitleVisibility = 1
+transform1Display.PolarAxes.PolarAxisTitle = 'Radial Distance'
+transform1Display.PolarAxes.PolarAxisTitleLocation = 'Bottom'
+transform1Display.PolarAxes.PolarLabelVisibility = 1
+transform1Display.PolarAxes.PolarLabelFormat = '%-#6.3g'
+transform1Display.PolarAxes.PolarLabelExponentLocation = 'Labels'
+transform1Display.PolarAxes.RadialLabelVisibility = 1
+transform1Display.PolarAxes.RadialLabelFormat = '%-#3.1f'
+transform1Display.PolarAxes.RadialLabelLocation = 'Bottom'
+transform1Display.PolarAxes.RadialUnitsVisibility = 1
+transform1Display.PolarAxes.ScreenSize = 10.0
+transform1Display.PolarAxes.PolarAxisTitleColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.PolarAxisTitleOpacity = 1.0
+transform1Display.PolarAxes.PolarAxisTitleFontFamily = 'Arial'
+transform1Display.PolarAxes.PolarAxisTitleFontFile = ''
+transform1Display.PolarAxes.PolarAxisTitleBold = 0
+transform1Display.PolarAxes.PolarAxisTitleItalic = 0
+transform1Display.PolarAxes.PolarAxisTitleShadow = 0
+transform1Display.PolarAxes.PolarAxisTitleFontSize = 12
+transform1Display.PolarAxes.PolarAxisLabelColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.PolarAxisLabelOpacity = 1.0
+transform1Display.PolarAxes.PolarAxisLabelFontFamily = 'Arial'
+transform1Display.PolarAxes.PolarAxisLabelFontFile = ''
+transform1Display.PolarAxes.PolarAxisLabelBold = 0
+transform1Display.PolarAxes.PolarAxisLabelItalic = 0
+transform1Display.PolarAxes.PolarAxisLabelShadow = 0
+transform1Display.PolarAxes.PolarAxisLabelFontSize = 12
+transform1Display.PolarAxes.LastRadialAxisTextColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.LastRadialAxisTextOpacity = 1.0
+transform1Display.PolarAxes.LastRadialAxisTextFontFamily = 'Arial'
+transform1Display.PolarAxes.LastRadialAxisTextFontFile = ''
+transform1Display.PolarAxes.LastRadialAxisTextBold = 0
+transform1Display.PolarAxes.LastRadialAxisTextItalic = 0
+transform1Display.PolarAxes.LastRadialAxisTextShadow = 0
+transform1Display.PolarAxes.LastRadialAxisTextFontSize = 12
+transform1Display.PolarAxes.SecondaryRadialAxesTextColor = [1.0, 1.0, 1.0]
+transform1Display.PolarAxes.SecondaryRadialAxesTextOpacity = 1.0
+transform1Display.PolarAxes.SecondaryRadialAxesTextFontFamily = 'Arial'
+transform1Display.PolarAxes.SecondaryRadialAxesTextFontFile = ''
+transform1Display.PolarAxes.SecondaryRadialAxesTextBold = 0
+transform1Display.PolarAxes.SecondaryRadialAxesTextItalic = 0
+transform1Display.PolarAxes.SecondaryRadialAxesTextShadow = 0
+transform1Display.PolarAxes.SecondaryRadialAxesTextFontSize = 12
+transform1Display.PolarAxes.EnableDistanceLOD = 1
+transform1Display.PolarAxes.DistanceLODThreshold = 0.7
+transform1Display.PolarAxes.EnableViewAngleLOD = 1
+transform1Display.PolarAxes.ViewAngleLODThreshold = 0.7
+transform1Display.PolarAxes.SmallestVisiblePolarAngle = 0.5
+transform1Display.PolarAxes.PolarTicksVisibility = 1
+transform1Display.PolarAxes.ArcTicksOriginToPolarAxis = 1
+transform1Display.PolarAxes.TickLocation = 'Both'
+transform1Display.PolarAxes.AxisTickVisibility = 1
+transform1Display.PolarAxes.AxisMinorTickVisibility = 0
+transform1Display.PolarAxes.ArcTickVisibility = 1
+transform1Display.PolarAxes.ArcMinorTickVisibility = 0
+transform1Display.PolarAxes.DeltaAngleMajor = 10.0
+transform1Display.PolarAxes.DeltaAngleMinor = 5.0
+transform1Display.PolarAxes.PolarAxisMajorTickSize = 0.0
+transform1Display.PolarAxes.PolarAxisTickRatioSize = 0.3
+transform1Display.PolarAxes.PolarAxisMajorTickThickness = 1.0
+transform1Display.PolarAxes.PolarAxisTickRatioThickness = 0.5
+transform1Display.PolarAxes.LastRadialAxisMajorTickSize = 0.0
+transform1Display.PolarAxes.LastRadialAxisTickRatioSize = 0.3
+transform1Display.PolarAxes.LastRadialAxisMajorTickThickness = 1.0
+transform1Display.PolarAxes.LastRadialAxisTickRatioThickness = 0.5
+transform1Display.PolarAxes.ArcMajorTickSize = 0.0
+transform1Display.PolarAxes.ArcTickRatioSize = 0.3
+transform1Display.PolarAxes.ArcMajorTickThickness = 1.0
+transform1Display.PolarAxes.ArcTickRatioThickness = 0.5
+transform1Display.PolarAxes.Use2DMode = 0
+transform1Display.PolarAxes.UseLogAxis = 0
+
+# hide data in view
+Hide(phaseDiagram2DGamma_infinity55_4000spvts, renderView1)
+
+
+
+
+
+# ----------------- DRAW LINE -----------------
+
+# # create a new 'Line'
+# line1 = Line()
+#
+# # show data in view
+# line1Display = Show(line1, renderView1)
+# # set active source
+# SetActiveSource(line1)
+#
+# # Properties modified on line1
+# line1.Point1 = [0.3, 0.0, 0.0]
+# line1.Point2 = [0.3, 0.0, 1.0]
+#
+# # Properties modified on line1Display
+# # line1Display.LineWidth = 2.0
+# line1Display.LineWidth = 4.0
+#
+# # change solid color
+# line1Display.AmbientColor = [1.0, 1.0, 0.4980392156862745]
+# line1Display.DiffuseColor = [1.0, 1.0, 0.4980392156862745]
+#
+# # toggle 3D widget visibility (only when running from the GUI)
+# Show3DWidgets(proxy=line1)
+#
+# # update the view to ensure updated data information
+# renderView1.Update()
+
+
+
+
+
+
+
+
+
+# show color bar/color legend
+transform1Display.SetScalarBarVisibility(renderView1, True)
+
+# update the view to ensure updated data information
+renderView1.Update()
+
+# toggle 3D widget visibility (only when running from the GUI)
+Hide3DWidgets(proxy=transform1.Transform)
+
+# reset view to fit data
+renderView1.ResetCamera()
+
+# change representation type
+transform1Display.SetRepresentationType('Point Gaussian')
+
+# Properties modified on transform1Display
+transform1Display.ShaderPreset = 'Plain circle'
+
+# set scalar coloring
+ColorBy(transform1Display, ('POINTS', 'angles'))
+
+# Hide the scalar bar for this color map if no visible data is colored by it.
+HideScalarBarIfNotNeeded(typeLUT, renderView1)
+
+# rescale color and/or opacity maps used to include current data range
+transform1Display.RescaleTransferFunctionToDataRange(True, False)
+
+# show color bar/color legend
+transform1Display.SetScalarBarVisibility(renderView1, True)
+
+# get color transfer function/color map for 'angles'
+anglesLUT = GetColorTransferFunction('angles')
+anglesLUT.AutomaticRescaleRangeMode = "Grow and update on 'Apply'"
+anglesLUT.InterpretValuesAsCategories = 0
+anglesLUT.AnnotationsInitialized = 0
+anglesLUT.ShowCategoricalColorsinDataRangeOnly = 0
+anglesLUT.RescaleOnVisibilityChange = 0
+anglesLUT.EnableOpacityMapping = 0
+anglesLUT.RGBPoints = [0.0, 0.001462, 0.000466, 0.013866, 0.006160663193689554, 0.002258, 0.001295, 0.018331, 0.012319755591052443, 0.003279, 0.002305, 0.023708, 0.018480418784742, 0.004512, 0.00349, 0.029965, 0.024639511182104886, 0.00595, 0.004843, 0.03713, 0.03080017437579444, 0.007588, 0.006356, 0.044973, 0.03695926677315698, 0.009426, 0.008022, 0.052844, 0.043119929966846535, 0.011465, 0.009828, 0.06075, 0.04928059316053644, 0.013708, 0.011771, 0.068667, 0.05543968555789898, 0.016156, 0.01384, 0.076603, 0.061600348751588534, 0.018815, 0.016026, 0.084584, 0.06775944114895142, 0.021692, 0.01832, 0.09261, 0.07392010434264097, 0.024792, 0.020715, 0.100676, 0.08007919674000387, 0.028123, 0.023201, 0.108787, 0.08623985993369342, 0.031696, 0.025765, 0.116965, 0.09240052312738298, 0.03552, 0.028397, 0.125209, 0.09855961552474586, 0.039608, 0.03109, 0.133515, 0.10472027871843542, 0.04383, 0.03383, 0.141886, 0.1108793711157983, 0.048062, 0.036607, 0.150327, 0.11704003430948787, 0.05232, 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1.1026377603532722, 0.967671, 0.439703, 0.35981, 1.108796852750635, 0.96968, 0.446936, 0.360311, 1.114957515944325, 0.971582, 0.45421, 0.36103, 1.121116608341688, 0.973381, 0.46152, 0.361965, 1.127277271535377, 0.975082, 0.468861, 0.363111, 1.1334379347290668, 0.97669, 0.476226, 0.364466, 1.1395970271264295, 0.97821, 0.483612, 0.366025, 1.145757690320119, 0.979645, 0.491014, 0.367783, 1.1519167827174819, 0.981, 0.498428, 0.369734, 1.1580774459111713, 0.982279, 0.505851, 0.371874, 1.164236538308534, 0.983485, 0.51328, 0.374198, 1.170397201502224, 0.984622, 0.520713, 0.376698, 1.1765578646959134, 0.985693, 0.528148, 0.379371, 1.182716957093276, 0.9867, 0.535582, 0.38221, 1.188877620286966, 0.987646, 0.543015, 0.38521, 1.1950367126843289, 0.988533, 0.550446, 0.388365, 1.201197375878018, 0.989363, 0.557873, 0.391671, 1.2073564682753808, 0.990138, 0.565296, 0.395122, 1.2135171314690707, 0.990871, 0.572706, 0.398714, 1.21967779466276, 0.991558, 0.580107, 0.402441, 1.2258368870601228, 0.992196, 0.587502, 0.406299, 1.2319975502538125, 0.992785, 0.594891, 0.410283, 1.2381566426511754, 0.993326, 0.602275, 0.41439, 1.2443173058448649, 0.993834, 0.609644, 0.418613, 1.2504763982422278, 0.994309, 0.616999, 0.42295, 1.2566370614359172, 0.994738, 0.62435, 0.427397, 1.262797724629607, 0.995122, 0.631696, 0.431951, 1.2689568170269698, 0.99548, 0.639027, 0.436607, 1.275117480220659, 0.99581, 0.646344, 0.441361, 1.2812765726180217, 0.996096, 0.653659, 0.446213, 1.2874372358117117, 0.996341, 0.660969, 0.45116, 1.2935963282090743, 0.99658, 0.668256, 0.456192, 1.2997569914027638, 0.996775, 0.675541, 0.461314, 1.3059176545964537, 0.996925, 0.682828, 0.466526, 1.3120767469938164, 0.997077, 0.690088, 0.471811, 1.3182374101875058, 0.997186, 0.697349, 0.477182, 1.3243965025848687, 0.997254, 0.704611, 0.482635, 1.3305571657785582, 0.997325, 0.711848, 0.488154, 1.3367162581759209, 0.997351, 0.719089, 0.493755, 1.3428769213696108, 0.997351, 0.726324, 0.499428, 1.3490375845633003, 0.997341, 0.733545, 0.505167, 1.355196676960663, 0.997285, 0.740772, 0.510983, 1.3613573401543528, 0.997228, 0.747981, 0.516859, 1.3675164325517157, 0.997138, 0.75519, 0.522806, 1.3736770957454048, 0.997019, 0.762398, 0.528821, 1.3798361881427677, 0.996898, 0.769591, 0.534892, 1.3859968513364576, 0.996727, 0.776795, 0.541039, 1.3921575145301468, 0.996571, 0.783977, 0.547233, 1.3983166069275097, 0.996369, 0.791167, 0.553499, 1.4044772701211992, 0.996162, 0.798348, 0.55982, 1.410636362518562, 0.995932, 0.805527, 0.566202, 1.4167970257122517, 0.99568, 0.812706, 0.572645, 1.4229561181096146, 0.995424, 0.819875, 0.57914, 1.4291167813033039, 0.995131, 0.827052, 0.585701, 1.4352758737006668, 0.994851, 0.834213, 0.592307, 1.4414365368943567, 0.994524, 0.841387, 0.598983, 1.4475972000880457, 0.994222, 0.84854, 0.605696, 1.4537562924854086, 0.993866, 0.855711, 0.612482, 1.4599169556790985, 0.993545, 0.862859, 0.619299, 1.4660760480764612, 0.99317, 0.870024, 0.626189, 1.4722367112701507, 0.992831, 0.877168, 0.633109, 1.4783958036675136, 0.99244, 0.88433, 0.640099, 1.4845564668612032, 0.992089, 0.89147, 0.647116, 1.4907171300548927, 0.991688, 0.898627, 0.654202, 1.4968762224522556, 0.991332, 0.905763, 0.661309, 1.503036885645945, 0.99093, 0.912915, 0.668481, 1.5091959780433077, 0.99057, 0.920049, 0.675675, 1.5153566412369976, 0.990175, 0.927196, 0.682926, 1.5215157336343605, 0.989815, 0.934329, 0.690198, 1.5276763968280496, 0.989434, 0.94147, 0.697519, 1.5338370600217395, 0.989077, 0.948604, 0.704863, 1.5399961524191024, 0.988717, 0.955742, 0.712242, 1.5461568156127916, 0.988367, 0.962878, 0.719649, 1.5523159080101545, 0.988033, 0.970012, 0.727077, 1.5584765712038442, 0.987691, 0.977154, 0.734536, 1.564635663601207, 0.987387, 0.984288, 0.742002, 1.5707963267948966, 0.987053, 0.991438, 0.749504]
+anglesLUT.UseLogScale = 0
+anglesLUT.ColorSpace = 'RGB'
+anglesLUT.UseBelowRangeColor = 0
+anglesLUT.BelowRangeColor = [0.0, 0.0, 0.0]
+anglesLUT.UseAboveRangeColor = 0
+anglesLUT.AboveRangeColor = [0.5, 0.5, 0.5]
+anglesLUT.NanColor = [0.0, 1.0, 0.0]
+anglesLUT.NanOpacity = 1.0
+anglesLUT.Discretize = 1
+anglesLUT.NumberOfTableValues = 256
+anglesLUT.ScalarRangeInitialized = 1.0
+anglesLUT.HSVWrap = 0
+anglesLUT.VectorComponent = 0
+anglesLUT.VectorMode = 'Magnitude'
+anglesLUT.AllowDuplicateScalars = 1
+anglesLUT.Annotations = []
+anglesLUT.ActiveAnnotatedValues = []
+anglesLUT.IndexedColors = []
+anglesLUT.IndexedOpacities = []
+
+# get opacity transfer function/opacity map for 'angles'
+anglesPWF = GetOpacityTransferFunction('angles')
+anglesPWF.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.33589355211648514, 0.625, 0.5, 0.0, 0.5680552565701278, 0.6691176295280457, 0.5, 0.0, 1.0471451860825267, 0.8676470518112183, 0.5, 0.0, 1.15586894219242, 0.6911764740943909, 0.5, 0.0, 1.5707963267948966, 0.8014705777168274, 0.5, 0.0]
+anglesPWF.AllowDuplicateScalars = 1
+anglesPWF.UseLogScale = 0
+anglesPWF.ScalarRangeInitialized = 1
+
+# Apply a preset using its name. Note this may not work as expected when presets have duplicate names.
+anglesLUT.ApplyPreset('Cool to Warm', True)
+
+
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.XTitle = '  $\\theta_\\rho$  '
+renderView1.AxesGrid.ZTitle = '  $\\theta$   '
+renderView1.AxesGrid.XTitleFontSize = 20
+renderView1.AxesGrid.ZTitleFontSize = 20
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.ShowGrid = 1
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.FacesToRender = 2
+renderView1.AxesGrid.CullFrontface = 0
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.Visibility = 1
+renderView1.AxesGrid.DataScale = [0.1, 1.0, 1.0]
+
+
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.XTitleFontSize = 22
+renderView1.AxesGrid.ZTitleFontSize = 22
+renderView1.AxesGrid.ZAxisUseCustomLabels = 1
+renderView1.AxesGrid.ZAxisLabels = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.ShowEdges = 0
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.XAxisPrecision = 1
+renderView1.AxesGrid.XAxisLabels = [0.0]
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.ZAxisPrecision = 1
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.XAxisUseCustomLabels = 1
+renderView1.AxesGrid.XAxisLabels = [0.0, -5.0, -4.0, -3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.XLabelFontSize = 16
+renderView1.AxesGrid.ZLabelFontSize = 16
+
+
+renderView1.AxesGrid.XTitleFontSize = 65  #24
+renderView1.AxesGrid.ZTitleFontSize = 65
+renderView1.AxesGrid.XLabelFontSize = 45  #default:12
+renderView1.AxesGrid.ZLabelFontSize = 45
+
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['', '']
+anglesLUT.IndexedColors = [1.0, 1.0, 1.0]
+anglesLUT.IndexedOpacities = [1.0]
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '']
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '0', '', '']
+anglesLUT.IndexedColors = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0]
+anglesLUT.IndexedOpacities = [1.0, 1.0]
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '0', '1.5707963267948966', '']
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '0', '1.5707963267948966', '$\\pi/2$', '', '']
+anglesLUT.IndexedColors = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0]
+anglesLUT.IndexedOpacities = [1.0, 1.0, 1.0]
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '0', '1.5707963267948966', '$\\pi/2$', '0,785398163', '']
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '0', '1.5707963267948966', '$\\pi/2$', '0,785398163', '$\\pi/4$']
+
+# Properties modified on anglesLUT
+anglesLUT.Annotations = ['0', '0', '1.5707963267948966', '$\\pi/2$', '0.785398163', '$\\pi/4$']
+
+# get color legend/bar for anglesLUT in view renderView1
+anglesLUTColorBar = GetScalarBar(anglesLUT, renderView1)
+anglesLUTColorBar.AutoOrient = 1
+anglesLUTColorBar.Orientation = 'Vertical'
+anglesLUTColorBar.WindowLocation = 'LowerRightCorner'
+anglesLUTColorBar.Position = [0.89, 0.02]
+anglesLUTColorBar.Title = 'angles'
+anglesLUTColorBar.ComponentTitle = ''
+anglesLUTColorBar.TitleJustification = 'Centered'
+anglesLUTColorBar.HorizontalTitle = 0
+anglesLUTColorBar.TitleColor = [1.0, 1.0, 1.0]
+anglesLUTColorBar.TitleOpacity = 1.0
+anglesLUTColorBar.TitleFontFamily = 'Arial'
+anglesLUTColorBar.TitleFontFile = ''
+anglesLUTColorBar.TitleBold = 0
+anglesLUTColorBar.TitleItalic = 0
+anglesLUTColorBar.TitleShadow = 0
+anglesLUTColorBar.TitleFontSize = 16
+anglesLUTColorBar.LabelColor = [1.0, 1.0, 1.0]
+anglesLUTColorBar.LabelOpacity = 1.0
+anglesLUTColorBar.LabelFontFamily = 'Arial'
+anglesLUTColorBar.LabelFontFile = ''
+anglesLUTColorBar.LabelBold = 0
+anglesLUTColorBar.LabelItalic = 0
+anglesLUTColorBar.LabelShadow = 0
+anglesLUTColorBar.LabelFontSize = 16
+anglesLUTColorBar.AutomaticLabelFormat = 1
+anglesLUTColorBar.LabelFormat = '%-#6.3g'
+anglesLUTColorBar.DrawTickMarks = 1
+anglesLUTColorBar.DrawTickLabels = 1
+anglesLUTColorBar.UseCustomLabels = 0
+anglesLUTColorBar.CustomLabels = []
+anglesLUTColorBar.AddRangeLabels = 1
+anglesLUTColorBar.RangeLabelFormat = '%-#6.1e'
+anglesLUTColorBar.DrawAnnotations = 1
+anglesLUTColorBar.AddRangeAnnotations = 0
+anglesLUTColorBar.AutomaticAnnotations = 0
+anglesLUTColorBar.DrawNanAnnotation = 0
+anglesLUTColorBar.NanAnnotation = 'NaN'
+anglesLUTColorBar.TextPosition = 'Ticks right/top, annotations left/bottom'
+anglesLUTColorBar.ReverseLegend = 0
+anglesLUTColorBar.ScalarBarThickness = 16
+anglesLUTColorBar.ScalarBarLength = 0.33
+
+# Properties modified on anglesLUTColorBar
+anglesLUTColorBar.DrawTickLabels = 0
+anglesLUTColorBar.AddRangeLabels = 0
+
+# Properties modified on anglesLUTColorBar
+anglesLUTColorBar.Title = 'angle $\\alpha$'
+# anglesLUTColorBar.Title = 'angle $\\angle$'
+anglesLUTColorBar.HorizontalTitle = 1
+anglesLUTColorBar.TitleFontSize = 20
+# Properties modified on anglesLUTColorBar
+anglesLUTColorBar.LabelFontSize = 20
+
+anglesLUTColorBar.TitleFontSize = 24
+# Properties modified on anglesLUTColorBar
+anglesLUTColorBar.LabelFontSize = 20
+
+# Properties modified on anglesLUTColorBar
+anglesLUTColorBar.DrawTickMarks = 0
+
+
+
+
+# Properties modified on renderView1.AxesGrid
+renderView1.AxesGrid.GridColor = [0.1803921568627451, 0.20392156862745098, 0.21176470588235294]
+
+
+# only label 2 axes...
+renderView1.AxesGrid.AxesToLabel = 7
+
+renderView1.OrientationAxesVisibility = 0
+
+#### saving camera placements for all active views
+
+# current camera placement for renderView1
+renderView1.InteractionMode = '2D'
+renderView1.CameraPosition = [0.0, 7.295131721662212, 0.5]
+renderView1.CameraFocalPoint = [0.0, 10.0, 0.5]
+renderView1.CameraViewUp = [0.0, 0.0, 1.0]
+renderView1.CameraParallelScale = 0.7000714249274855
+
+
+# DRAW LINE
+
+#
+# # create a new 'Line'
+# line1 = Line()
+#
+# # find source
+# xMLStructuredGridReader1 = FindSource('XMLStructuredGridReader1')
+#
+# # Properties modified on line1
+# line1.Point1 = [0.3, 0.0, 0.0]
+# line1.Point2 = [0.3, 0.0, 1.0]
+# line1.Resolution = 500
+# # Properties modified on line1Display
+#
+#
+# # get active view
+# renderView1 = GetActiveViewOrCreate('RenderView')
+# # uncomment following to set a specific view size
+# # renderView1.ViewSize = [1380, 518]
+#
+# # show data in view
+# line1Display = Show(line1, renderView1)
+#
+# # trace defaults for the display properties.
+# line1Display.Representation = 'Surface'
+# line1Display.ColorArrayName = [None, '']
+# line1Display.OSPRayScaleArray = 'Texture Coordinates'
+# line1Display.OSPRayScaleFunction = 'PiecewiseFunction'
+# line1Display.SelectOrientationVectors = 'None'
+# line1Display.ScaleFactor = 0.1
+# line1Display.SelectScaleArray = 'None'
+# line1Display.GlyphType = 'Arrow'
+# line1Display.GlyphTableIndexArray = 'None'
+# line1Display.GaussianRadius = 0.005
+# line1Display.SetScaleArray = ['POINTS', 'Texture Coordinates']
+# line1Display.ScaleTransferFunction = 'PiecewiseFunction'
+# line1Display.OpacityArray = ['POINTS', 'Texture Coordinates']
+# line1Display.OpacityTransferFunction = 'PiecewiseFunction'
+# line1Display.DataAxesGrid = 'GridAxesRepresentation'
+# line1Display.PolarAxes = 'PolarAxesRepresentation'
+#
+# # init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+# line1Display.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+#
+# # init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+# line1Display.ScaleTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.2138364766881351, 0.625, 0.5, 0.0, 0.3616352081298828, 0.6691176295280457, 0.5, 0.0, 0.6666333299996667, 0.8676470518112183, 0.5, 0.0, 0.7358490228652954, 0.6911764740943909, 0.5, 0.0, 1.0, 0.8014705777168274, 0.5, 0.0]
+#
+# # init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+# line1Display.OpacityTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.2138364766881351, 0.625, 0.5, 0.0, 0.3616352081298828, 0.6691176295280457, 0.5, 0.0, 0.6666333299996667, 0.8676470518112183, 0.5, 0.0, 0.7358490228652954, 0.6911764740943909, 0.5, 0.0, 1.0, 0.8014705777168274, 0.5, 0.0]
+#
+# # find source
+# transform1 = FindSource('Transform1')
+#
+# # update the view to ensure updated data information
+# renderView1.Update()
+#
+# # change solid color
+# line1Display.AmbientColor = [1.0, 1.0, 0.4980392156862745]
+# line1Display.DiffuseColor = [1.0, 1.0, 0.4980392156862745]
+#
+# # change representation type
+# line1Display.SetRepresentationType('Points')
+#
+# line1Display.PointSize = 3.0
+# # reset view to fit data bounds
+# renderView1.ResetCamera(0.30000001192092896, 0.30000001192092896, 0.0, 0.0, 0.0, 1.0)
+#
+# # toggle 3D widget visibility (only when running from the GUI)
+# Hide3DWidgets(proxy=line1)
+#
+# #### saving camera placements for all active views
+#
+# # current camera placement for renderView1
+# renderView1.InteractionMode = '2D'
+# renderView1.CameraPosition = [0.30000001192092896, -1.9318516525781368, 0.5]
+# renderView1.CameraFocalPoint = [0.30000001192092896, 0.0, 0.5]
+# renderView1.CameraViewUp = [0.0, 0.0, 1.0]
+# renderView1.CameraParallelScale = 0.7320500000000002
+#
+
+
+# # reset view to fit data
+# renderView1.ResetCamera()
+
+
+# create a new 'Line'
+line1 = Line()
+
+# Properties modified on line1
+line1.Point1 = [0.3, 0.0, 0.0]
+line1.Point2 = [0.3, 0.0, 1.0]
+line1.Resolution = 400
+
+# get active view
+renderView1 = GetActiveViewOrCreate('RenderView')
+# uncomment following to set a specific view size
+# renderView1.ViewSize = [1046, 545]
+
+# show data in view
+line1Display = Show(line1, renderView1)
+
+# trace defaults for the display properties.
+line1Display.Representation = 'Surface'
+line1Display.ColorArrayName = [None, '']
+line1Display.OSPRayScaleArray = 'Texture Coordinates'
+line1Display.OSPRayScaleFunction = 'PiecewiseFunction'
+line1Display.SelectOrientationVectors = 'None'
+line1Display.ScaleFactor = 0.1
+line1Display.SelectScaleArray = 'None'
+line1Display.GlyphType = 'Arrow'
+line1Display.GlyphTableIndexArray = 'None'
+line1Display.GaussianRadius = 0.005
+line1Display.SetScaleArray = ['POINTS', 'Texture Coordinates']
+line1Display.ScaleTransferFunction = 'PiecewiseFunction'
+line1Display.OpacityArray = ['POINTS', 'Texture Coordinates']
+line1Display.OpacityTransferFunction = 'PiecewiseFunction'
+line1Display.DataAxesGrid = 'GridAxesRepresentation'
+line1Display.PolarAxes = 'PolarAxesRepresentation'
+
+# init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+line1Display.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+line1Display.ScaleTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.2138364766881351, 0.625, 0.5, 0.0, 0.3616352081298828, 0.6691176295280457, 0.5, 0.0, 0.6666333299996667, 0.8676470518112183, 0.5, 0.0, 0.7358490228652954, 0.6911764740943909, 0.5, 0.0, 1.0, 0.8014705777168274, 0.5, 0.0]
+
+# init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+line1Display.OpacityTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.2138364766881351, 0.625, 0.5, 0.0, 0.3616352081298828, 0.6691176295280457, 0.5, 0.0, 0.6666333299996667, 0.8676470518112183, 0.5, 0.0, 0.7358490228652954, 0.6911764740943909, 0.5, 0.0, 1.0, 0.8014705777168274, 0.5, 0.0]
+
+# find source
+xMLStructuredGridReader1 = FindSource('XMLStructuredGridReader1')
+
+# find source
+transform1 = FindSource('Transform1')
+
+# update the view to ensure updated data information
+renderView1.Update()
+
+# change representation type
+line1Display.SetRepresentationType('Points')
+
+# change solid color
+line1Display.AmbientColor = [1.0, 1.0, 0.4980392156862745]
+line1Display.DiffuseColor = [1.0, 1.0, 0.4980392156862745]
+
+# Properties modified on line1Display
+line1Display.PointSize = 3.0
+
+# toggle 3D widget visibility (only when running from the GUI)
+Hide3DWidgets(proxy=line1)
+
+# reset view to fit data
+renderView1.ResetCamera()
+
+# reset view to fit data
+renderView1.ResetCamera()
+
+#### saving camera placements for all active views
+
+# current camera placement for renderView1
+renderView1.InteractionMode = '2D'
+renderView1.CameraPosition = [0.0, -14.510745305395833, 0.5]
+renderView1.CameraFocalPoint = [0.0, 5.0, 0.5]
+renderView1.CameraViewUp = [0.0, 0.0, 1.0]
+renderView1.CameraParallelScale = 0.7506135276429463
+
+
+
+
+
+#
+if case == 1:
+
+    # get color transfer function/color map for 'angles'
+    anglesLUT = GetColorTransferFunction('angles')
+    anglesLUT.AutomaticRescaleRangeMode = "Grow and update on 'Apply'"
+    anglesLUT.InterpretValuesAsCategories = 0
+    anglesLUT.AnnotationsInitialized = 0
+    anglesLUT.ShowCategoricalColorsinDataRangeOnly = 0
+    anglesLUT.RescaleOnVisibilityChange = 0
+    anglesLUT.EnableOpacityMapping = 1
+    anglesLUT.RGBPoints = [0.0, 0.23137254902, 0.298039215686, 0.752941176471, 0.9632241725921631, 0.865, 0.865, 0.865, 1.5707963267948966, 0.705882352941, 0.0156862745098, 0.149019607843]
+    anglesLUT.UseLogScale = 0
+    anglesLUT.ColorSpace = 'Diverging'
+    anglesLUT.UseBelowRangeColor = 0
+    anglesLUT.BelowRangeColor = [0.0, 0.0, 0.0]
+    anglesLUT.UseAboveRangeColor = 0
+    anglesLUT.AboveRangeColor = [0.5, 0.5, 0.5]
+    anglesLUT.NanColor = [1.0, 1.0, 0.0]
+    anglesLUT.NanOpacity = 1.0
+    anglesLUT.Discretize = 1
+    anglesLUT.NumberOfTableValues = 256
+    anglesLUT.ScalarRangeInitialized = 1.0
+    anglesLUT.HSVWrap = 0
+    anglesLUT.VectorComponent = 0
+    anglesLUT.VectorMode = 'Magnitude'
+    anglesLUT.AllowDuplicateScalars = 1
+    anglesLUT.Annotations = ['1.57', '$\\pi / 2$', '0.78', '$\\pi/4$', '0', '0']
+    anglesLUT.ActiveAnnotatedValues = []
+    anglesLUT.IndexedColors = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0]
+    anglesLUT.IndexedOpacities = [1.0, 1.0, 1.0, 1.0]
+
+    # get opacity transfer function/opacity map for 'angles'
+    anglesPWF = GetOpacityTransferFunction('angles')
+    anglesPWF.Points = [0.0, 0.136764707416296, 0.5, 0.0, 0.705621357414266, 1.0, 0.5, 0.0, 0.82168139570297, 1.0, 0.5, 0.0, 0.9799451305746117, 1.0, 0.5, 0.0, 1.0960051688633157, 1.0, 0.5, 0.0, 1.5707963267948966, 1.0, 0.5, 0.0]
+    anglesPWF.AllowDuplicateScalars = 1
+    anglesPWF.UseLogScale = 0
+    anglesPWF.ScalarRangeInitialized = 1
+
+    # Properties modified on anglesLUT
+    anglesLUT.InterpretValuesAsCategories = 1
+    anglesLUT.AnnotationsInitialized = 1
+
+    # Properties modified on anglesLUT
+    anglesLUT.Annotations = ['1.57', '$\\pi / 2$', '0.78', '$\\pi/4$', '0', '0', '1.5707963267948966', '1.5708']
+
+    # Properties modified on anglesLUT
+    anglesLUT.Annotations = ['1.57', '$\\pi / 2$', '0.78', '$\\pi/4$', '0', '0']
+    anglesLUT.IndexedColors = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0]
+    anglesLUT.IndexedOpacities = [1.0, 1.0, 1.0]
+
+    # Properties modified on anglesLUT
+    anglesLUT.Annotations = ['1.57', '$\\pi / 2$', '0', '0']
+    anglesLUT.IndexedColors = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0]
+    anglesLUT.IndexedOpacities = [1.0, 1.0]
+
+    # Properties modified on anglesLUT
+    anglesLUT.Annotations = ['1.5707963267948966', '$\\pi / 2$', '0', '0']
+
+    # Properties modified on anglesLUT
+    anglesLUT.IndexedColors = [1.0, 0.0, 0.0, 1.0, 0.0, 0.0]
+
+    # Properties modified on anglesLUT
+    anglesLUT.IndexedColors = [1.0, 0.0, 0.0, 0.23137254901960785, 0.2980392156862745, 0.7529411764705882]
+    # Properties modified on anglesLUT
+    anglesLUT.IndexedColors = [0.7058823529411765, 0.01568627450980392, 0.14901960784313725, 0.23137254901960785, 0.2980392156862745, 0.7529411764705882]
+
+    # Properties modified on anglesLUT
+    anglesLUT.IndexedOpacities = [1.0, 0.02]
+
+    # Properties modified on anglesLUT
+    anglesLUT.IndexedOpacities = [1.0, 0.05]
+
+    # Properties modified on anglesLUT
+    anglesLUT.IndexedOpacities = [1.0, 0.1]
+
+    # #TEST: (only for 100SP..)
+    # anglesLUT.IndexedOpacities = [1.0, 0.03]
+    # transform1Display.Opacity = 0.1  #overall Opacity
+
+
+
+
+
+
+
+if curvature == 1 :
+
+    # find source
+    transform1 = FindSource('Transform1')
+
+    # set active source
+    SetActiveSource(transform1)
+
+    # get color transfer function/color map for 'angles'
+    anglesLUT = GetColorTransferFunction('angles')
+    anglesLUT.RGBPoints = [0.0, 0.23137254902, 0.298039215686, 0.752941176471, 0.7853981633974483, 0.865, 0.865, 0.865, 1.5707963267948966, 0.705882352941, 0.0156862745098, 0.149019607843]
+    anglesLUT.ScalarRangeInitialized = 1.0
+    anglesLUT.Annotations = ['0', '0', '1.5707963267948966', '$\\pi/2$', '0.785398163', '$\\pi/4$']
+    anglesLUT.IndexedColors = [1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0]
+    anglesLUT.IndexedOpacities = [1.0, 1.0, 1.0]
+
+    # get opacity transfer function/opacity map for 'angles'
+    anglesPWF = GetOpacityTransferFunction('angles')
+    anglesPWF.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 0.33589355211648514, 0.625, 0.5, 0.0, 0.5680552565701278, 0.6691176295280457, 0.5, 0.0, 1.0471451860825267, 0.8676470518112183, 0.5, 0.0, 1.15586894219242, 0.6911764740943909, 0.5, 0.0, 1.5707963267948966, 0.8014705777168274, 0.5, 0.0]
+    anglesPWF.ScalarRangeInitialized = 1
+
+    # get active view
+    renderView1 = GetActiveViewOrCreate('RenderView')
+    # uncomment following to set a specific view size
+    # renderView1.ViewSize = [1046, 545]
+
+    # get display properties
+    transform1Display = GetDisplayProperties(transform1, view=renderView1)
+
+    # set scalar coloring
+    ColorBy(transform1Display, ('POINTS', 'curvature'))
+
+    # Hide the scalar bar for this color map if no visible data is colored by it.
+    HideScalarBarIfNotNeeded(anglesLUT, renderView1)
+
+    # rescale color and/or opacity maps used to include current data range
+    transform1Display.RescaleTransferFunctionToDataRange(True, False)
+
+    # show color bar/color legend
+    transform1Display.SetScalarBarVisibility(renderView1, True)
+
+    # get color transfer function/color map for 'curvature'
+    curvatureLUT = GetColorTransferFunction('curvature')
+    curvatureLUT.RGBPoints = [-74.1, 0.001462, 0.000466, 0.013866, -73.517583, 0.002258, 0.001295, 0.018331, -72.93531449999999, 0.003279, 0.002305, 0.023708, -72.3528975, 0.004512, 0.00349, 0.029965, -71.77062899999999, 0.00595, 0.004843, 0.03713, -71.18821199999998, 0.007588, 0.006356, 0.044973, -70.60594350000001, 0.009426, 0.008022, 0.052844, -70.02352650000002, 0.011465, 0.009828, 0.06075, -69.44110949999998, 0.013708, 0.011771, 0.068667, -68.858841, 0.016156, 0.01384, 0.076603, -68.276424, 0.018815, 0.016026, 0.084584, -67.6941555, 0.021692, 0.01832, 0.09261, -67.1117385, 0.024792, 0.020715, 0.100676, -66.52946999999999, 0.028123, 0.023201, 0.108787, -65.947053, 0.031696, 0.025765, 0.116965, -65.36463599999999, 0.03552, 0.028397, 0.125209, -64.78236749999999, 0.039608, 0.03109, 0.133515, -64.19995049999999, 0.04383, 0.03383, 0.141886, -63.61768199999998, 0.048062, 0.036607, 0.150327, -63.03526499999998, 0.05232, 0.039407, 0.158841, -62.452996500000005, 0.056615, 0.04216, 0.167446, -61.870579500000005, 0.060949, 0.044794, 0.176129, -61.28816249999998, 0.06533, 0.047318, 0.184892, -60.705894, 0.069764, 0.049726, 0.193735, -60.12347700000001, 0.074257, 0.052017, 0.20266, -59.541208499999996, 0.078815, 0.054184, 0.211667, -58.9587915, 0.083446, 0.056225, 0.220755, -58.37652299999999, 0.088155, 0.058133, 0.229922, -57.79410599999999, 0.092949, 0.059904, 0.239164, -57.21183749999999, 0.097833, 0.061531, 0.248477, -56.62942049999998, 0.102815, 0.06301, 0.257854, -56.04700349999999, 0.107899, 0.064335, 0.267289, -55.464734999999976, 0.113094, 0.065492, 0.276784, -54.882317999999984, 0.118405, 0.066479, 0.286321, -54.30004950000001, 0.123833, 0.067295, 0.295879, -53.71763250000001, 0.12938, 0.067935, 0.305443, -53.135363999999996, 0.135053, 0.068391, 0.315, -52.552947, 0.140858, 0.068654, 0.324538, -51.970530000000004, 0.146785, 0.068738, 0.334011, -51.3882615, 0.152839, 0.068637, 0.343404, -50.8058445, 0.159018, 0.068354, 0.352688, -50.22357599999999, 0.165308, 0.067911, 0.361816, -49.64115899999999, 0.171713, 0.067305, 0.370771, -49.05889049999998, 0.178212, 0.066576, 0.379497, -48.47647349999998, 0.184801, 0.065732, 0.387973, -47.89405649999999, 0.19146, 0.064818, 0.396152, -47.31178800000001, 0.198177, 0.063862, 0.404009, -46.729370999999986, 0.204935, 0.062907, 0.411514, -46.1471025, 0.211718, 0.061992, 0.418647, -45.56468550000001, 0.218512, 0.061158, 0.425392, -44.982417, 0.225302, 0.060445, 0.431742, -44.400000000000006, 0.232077, 0.059889, 0.437695, -43.817583, 0.238826, 0.059517, 0.443256, -43.235314499999994, 0.245543, 0.059352, 0.448436, -42.652897499999995, 0.25222, 0.059415, 0.453248, -42.07062899999999, 0.258857, 0.059706, 0.45771, -41.48821199999999, 0.265447, 0.060237, 0.46184, -40.90594349999998, 0.271994, 0.060994, 0.46566, -40.323526499999986, 0.278493, 0.061978, 0.46919, -39.741109499999986, 0.284951, 0.063168, 0.472451, -39.158840999999974, 0.291366, 0.064553, 0.475462, -38.57642399999998, 0.29774, 0.066117, 0.478243, -37.994155500000005, 0.304081, 0.067835, 0.480812, -37.411738500000006, 0.310382, 0.069702, 0.483186, -36.82947, 0.316654, 0.07169, 0.48538, -36.247053, 0.322899, 0.073782, 0.487408, -35.664636, 0.329114, 0.075972, 0.489287, -35.0823675, 0.335308, 0.078236, 0.491024, -34.4999505, 0.341482, 0.080564, 0.492631, -33.917681999999985, 0.347636, 0.082946, 0.494121, -33.33526499999999, 0.353773, 0.085373, 0.495501, -32.752996500000016, 0.359898, 0.087831, 0.496778, -32.17057949999998, 0.366012, 0.090314, 0.49796, -31.58816249999999, 0.372116, 0.092816, 0.499053, -31.005894000000012, 0.378211, 0.095332, 0.500067, -30.423476999999977, 0.384299, 0.097855, 0.501002, -29.8412085, 0.390384, 0.100379, 0.501864, -29.258791500000008, 0.396467, 0.102902, 0.502658, -28.676522999999996, 0.402548, 0.10542, 0.503386, -28.094105999999996, 0.408629, 0.10793, 0.504052, -27.51183749999999, 0.414709, 0.110431, 0.504662, -26.929420499999992, 0.420791, 0.11292, 0.505215, -26.347003499999992, 0.426877, 0.115395, 0.505714, -25.764734999999988, 0.432967, 0.117855, 0.50616, -25.182317999999988, 0.439062, 0.120298, 0.506555, -24.600049499999976, 0.445163, 0.122724, 0.506901, -24.017632499999984, 0.451271, 0.125132, 0.507198, -23.435364000000007, 0.457386, 0.127522, 0.507448, -22.852946999999972, 0.463508, 0.129893, 0.507652, -22.270530000000008, 0.46964, 0.132245, 0.507809, -21.688261500000003, 0.47578, 0.134577, 0.507921, -21.105844500000003, 0.481929, 0.136891, 0.507989, -20.523576, 0.488088, 0.139186, 0.508011, -19.941159, 0.494258, 0.141462, 0.507988, -19.358890499999987, 0.500438, 0.143719, 0.50792, -18.776473499999994, 0.506629, 0.145958, 0.507806, -18.194056499999995, 0.512831, 0.148179, 0.507648, -17.611787999999983, 0.519045, 0.150383, 0.507443, -17.02937099999999, 0.52527, 0.152569, 0.507192, -16.447102500000014, 0.531507, 0.154739, 0.506895, -15.864685499999979, 0.537755, 0.156894, 0.506551, -15.282417000000002, 0.544015, 0.159033, 0.506159, -14.70000000000001, 0.550287, 0.161158, 0.505719, -14.117582999999975, 0.556571, 0.163269, 0.50523, -13.535314499999998, 0.562866, 0.165368, 0.504692, -12.952897500000006, 0.569172, 0.167454, 0.504105, -12.370628999999994, 0.57549, 0.16953, 0.503466, -11.788211999999994, 0.581819, 0.171596, 0.502777, -11.20594349999999, 0.588158, 0.173652, 0.502035, -10.62352649999999, 0.594508, 0.175701, 0.501241, -10.04110949999999, 0.600868, 0.177743, 0.500394, -9.458840999999978, 0.607238, 0.179779, 0.499492, -8.876423999999986, 0.613617, 0.181811, 0.498536, -8.294155499999974, 0.620005, 0.18384, 0.497524, -7.71173850000001, 0.626401, 0.185867, 0.496456, -7.129469999999998, 0.632805, 0.187893, 0.495332, -6.547053000000005, 0.639216, 0.189921, 0.49415, -5.964636000000013, 0.645633, 0.191952, 0.49291, -5.382367500000001, 0.652056, 0.193986, 0.491611, -4.7999505000000084, 0.658483, 0.196027, 0.490253, -4.217681999999996, 0.664915, 0.198075, 0.488836, -3.6352649999999898, 0.671349, 0.200133, 0.487358, -3.052996499999992, 0.677786, 0.202203, 0.485819, -2.4705794999999853, 0.684224, 0.204286, 0.484219, -1.8881624999999929, 0.690661, 0.206384, 0.482558, -1.3058939999999808, 0.697098, 0.208501, 0.480835, -0.7234769999999884, 0.703532, 0.210638, 0.479049, -0.14120850000000473, 0.709962, 0.212797, 0.477201, 0.4412085000000161, 0.716387, 0.214982, 0.47529, 1.0234770000000282, 0.722805, 0.217194, 0.473316, 1.6058939999999922, 0.729216, 0.219437, 0.471279, 2.1881625000000042, 0.735616, 0.221713, 0.46918, 2.7705794999999966, 0.742004, 0.224025, 0.467018, 3.3529965000000033, 0.748378, 0.226377, 0.464794, 3.935265000000001, 0.754737, 0.228772, 0.462509, 4.517682000000008, 0.761077, 0.231214, 0.460162, 5.099950499999977, 0.767398, 0.233705, 0.457755, 5.682367500000012, 0.773695, 0.236249, 0.455289, 6.264636000000024, 0.779968, 0.238851, 0.452765, 6.847052999999988, 0.786212, 0.241514, 0.450184, 7.429470000000009, 0.792427, 0.244242, 0.447543, 8.011738500000021, 0.798608, 0.24704, 0.444848, 8.594155499999985, 0.804752, 0.249911, 0.442102, 9.176423999999997, 0.810855, 0.252861, 0.439305, 9.758841000000032, 0.816914, 0.255895, 0.436461, 10.341109500000002, 0.822926, 0.259016, 0.433573, 10.923526500000008, 0.828886, 0.262229, 0.430644, 11.5059435, 0.834791, 0.26554, 0.427671, 12.088212000000013, 0.840636, 0.268953, 0.424666, 12.670629000000005, 0.846416, 0.272473, 0.421631, 13.252897500000017, 0.852126, 0.276106, 0.418573, 13.83531450000001, 0.857763, 0.279857, 0.415496, 14.417582999999993, 0.86332, 0.283729, 0.412403, 15.000000000000014, 0.868793, 0.287728, 0.409303, 15.582416999999978, 0.874176, 0.291859, 0.406205, 16.16468549999999, 0.879464, 0.296125, 0.403118, 16.747102500000025, 0.884651, 0.30053, 0.400047, 17.329370999999995, 0.889731, 0.305079, 0.397002, 17.911788, 0.8947, 0.309773, 0.393995, 18.4940565, 0.899552, 0.314616, 0.391037, 19.076473500000006, 0.904281, 0.31961, 0.388137, 19.6588905, 0.908884, 0.324755, 0.385308, 20.24115900000001, 0.913354, 0.330052, 0.382563, 20.823576000000003, 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+    curvatureLUT.ColorSpace = 'RGB'
+    curvatureLUT.NanColor = [0.0, 1.0, 0.0]
+    curvatureLUT.ScalarRangeInitialized = 1.0
+
+    # get opacity transfer function/opacity map for 'curvature'
+    curvaturePWF = GetOpacityTransferFunction('curvature')
+    curvaturePWF.Points = [-74.1, 0.8602941036224365, 0.5, 0.0, -42.34528321181193, 0.625, 0.5, 0.0, -20.397171592712397, 0.6691176295280457, 0.5, 0.0, 24.89504950495052, 0.8676470518112183, 0.5, 0.0, 35.173579895496374, 0.6911764740943909, 0.5, 0.0, 74.4, 0.8014705777168274, 0.5, 0.0]
+    curvaturePWF.ScalarRangeInitialized = 1
+
+    # create a new 'Contour'
+    contour1 = Contour(Input=transform1)
+    contour1.ContourBy = ['POINTS', 'Type']
+    contour1.Isosurfaces = [2.0]
+    contour1.PointMergeMethod = 'Uniform Binning'
+
+    # find source
+    line1 = FindSource('Line1')
+
+    # find source
+    xMLStructuredGridReader1 = FindSource('XMLStructuredGridReader1')
+
+    # Properties modified on contour1
+    contour1.ContourBy = ['POINTS', 'curvature']
+    contour1.Isosurfaces = [0.0]
+
+    # show data in view
+    contour1Display = Show(contour1, renderView1)
+
+    # trace defaults for the display properties.
+    contour1Display.Representation = 'Surface'
+    contour1Display.ColorArrayName = ['POINTS', 'curvature']
+    contour1Display.LookupTable = curvatureLUT
+    contour1Display.OSPRayScaleArray = 'curvature'
+    contour1Display.OSPRayScaleFunction = 'PiecewiseFunction'
+    contour1Display.SelectOrientationVectors = 'None'
+    contour1Display.ScaleFactor = 0.08543854954749906
+    contour1Display.SelectScaleArray = 'curvature'
+    contour1Display.GlyphType = 'Arrow'
+    contour1Display.GlyphTableIndexArray = 'curvature'
+    contour1Display.GaussianRadius = 0.004271927477374953
+    contour1Display.SetScaleArray = ['POINTS', 'curvature']
+    contour1Display.ScaleTransferFunction = 'PiecewiseFunction'
+    contour1Display.OpacityArray = ['POINTS', 'curvature']
+    contour1Display.OpacityTransferFunction = 'PiecewiseFunction'
+    contour1Display.DataAxesGrid = 'GridAxesRepresentation'
+    contour1Display.PolarAxes = 'PolarAxesRepresentation'
+
+    # init the 'PiecewiseFunction' selected for 'OSPRayScaleFunction'
+    contour1Display.OSPRayScaleFunction.Points = [1.0, 0.8602941036224365, 0.5, 0.0, 1.213836476688135, 0.625, 0.5, 0.0, 1.3616352081298828, 0.6691176295280457, 0.5, 0.0, 1.6666333299996667, 0.8676470518112183, 0.5, 0.0, 1.7358490228652954, 0.6911764740943909, 0.5, 0.0, 2.0, 0.8014705777168274, 0.5, 0.0]
+
+    # init the 'PiecewiseFunction' selected for 'ScaleTransferFunction'
+    contour1Display.ScaleTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 2.5142493840581125e-39, 0.625, 0.5, 0.0, 4.252039284300157e-39, 0.6691176295280457, 0.5, 0.0, 7.838150278676329e-39, 0.8676470518112183, 0.5, 0.0, 8.651975477491057e-39, 0.6911764740943909, 0.5, 0.0, 1.1757813367477812e-38, 0.8014705777168274, 0.5, 0.0]
+
+    # init the 'PiecewiseFunction' selected for 'OpacityTransferFunction'
+    contour1Display.OpacityTransferFunction.Points = [0.0, 0.8602941036224365, 0.5, 0.0, 2.5142493840581125e-39, 0.625, 0.5, 0.0, 4.252039284300157e-39, 0.6691176295280457, 0.5, 0.0, 7.838150278676329e-39, 0.8676470518112183, 0.5, 0.0, 8.651975477491057e-39, 0.6911764740943909, 0.5, 0.0, 1.1757813367477812e-38, 0.8014705777168274, 0.5, 0.0]
+
+    # show color bar/color legend
+    contour1Display.SetScalarBarVisibility(renderView1, True)
+
+    # update the view to ensure updated data information
+    renderView1.Update()
+
+    # turn off scalar coloring
+    ColorBy(contour1Display, None)
+
+    # Hide the scalar bar for this color map if no visible data is colored by it.
+    HideScalarBarIfNotNeeded(curvatureLUT, renderView1)
+
+    # change solid color
+    contour1Display.AmbientColor = [1.0, 1.0, 0.4980392156862745]
+    contour1Display.DiffuseColor = [1.0, 1.0, 0.4980392156862745]
+
+    # change solid color
+    contour1Display.AmbientColor = [0.0, 0.0, 0.0]
+    contour1Display.DiffuseColor = [0.0, 0.0, 0.0]
+
+    # set active source
+    SetActiveSource(transform1)
+
+    # Apply a preset using its name. Note this may not work as expected when presets have duplicate names.
+    curvatureLUT.ApplyPreset('Cold and Hot', True)
+
+    # set active source
+    SetActiveSource(contour1)
+
+    # change solid color
+    contour1Display.AmbientColor = [1.0, 1.0, 0.4980392156862745]
+    contour1Display.DiffuseColor = [1.0, 1.0, 0.4980392156862745]
+
+    # change solid color
+    contour1Display.AmbientColor = [1.0, 1.0, 1.0]
+    contour1Display.DiffuseColor = [1.0, 1.0, 1.0]
+
+    #### saving camera placements for all active views
+
+    # current camera placement for renderView1
+    renderView1.InteractionMode = '2D'
+    renderView1.CameraPosition = [0.0, -14.510745305395833, 0.5]
+    renderView1.CameraFocalPoint = [0.0, 5.0, 0.5]
+    renderView1.CameraViewUp = [0.0, 0.0, 1.0]
+    renderView1.CameraParallelScale = 0.7506135276429463
+
+    curvatureLUTColorBar = GetScalarBar(curvatureLUT, renderView1)
+    curvatureLUTColorBar.Title = 'curvature'
+    curvatureLUTColorBar.ComponentTitle = ''
+
+    # Properties modified on curvatureLUTColorBar
+    curvatureLUTColorBar.Title = '$ \\kappa $'
+    curvatureLUTColorBar.HorizontalTitle = 1
+    curvatureLUTColorBar.TitleFontSize = 24
+    curvatureLUTColorBar.LabelFontSize = 20
+
+
+    # get active source.
+    contour1 = GetActiveSource()
+
+    # get active view
+    renderView1 = GetActiveViewOrCreate('RenderView')
+    # uncomment following to set a specific view size
+    # renderView1.ViewSize = [1046, 545]
+
+    # get display properties
+    contour1Display = GetDisplayProperties(contour1, view=renderView1)
+
+    # change representation type
+    contour1Display.SetRepresentationType('Surface')
+
+    # change representation type
+    contour1Display.SetRepresentationType('Points')
+
+    # Properties modified on contour1Display
+    contour1Display.PointSize = 3.0
+
+    # Properties modified on contour1Display
+    contour1Display.PointSize = 2.0
+
+    # Properties modified on contour1Display
+    contour1Display.RenderPointsAsSpheres = 0
+
+    # Properties modified on contour1Display
+    contour1Display.RenderPointsAsSpheres = 1
+
+
+
+#### uncomment the following to render all views
+# RenderAllViews()
+# alternatively, if you want to write images, you can use SaveScreenshot(...).
+# ----------------- EXPORT -----------------
+# save screenshot
+# SaveScreenshot('/home/klaus/Desktop/PhaseDiagramPlot.png', renderView1, ImageResolution=[1257, 934])
+# SaveScreenshot('/home/klaus/Desktop/PhaseDiagramPlot.png', renderView1, ImageResolution=[2514, 1868])
+# SaveScreenshot('/home/klaus/Desktop/PhaseDiagramPlot.png', renderView1, ImageResolution=[1063, 657])
+
+
+SaveScreenshot('/home/klaus/Desktop/2DPhaseDiagram.png', renderView1, ImageResolution=[2126, 1314])
+# export view
+# ExportView('/home/klaus/Desktop/PhaseDiagramPlot.pdf', view=renderView1)