From 9f8437badfcd165586baad2b2c111b2da64badba Mon Sep 17 00:00:00 2001
From: Klaus <klaus.boehnlein@tu-dresden.de>
Date: Sun, 24 Oct 2021 09:30:43 +0200
Subject: [PATCH] Add plos for a_star
---
src/Plot_aStar_elliptic.py | 772 +++++++++++++++++++++++++++++++++++
src/Plot_aStar_hyperbolic.py | 770 ++++++++++++++++++++++++++++++++++
2 files changed, 1542 insertions(+)
create mode 100644 src/Plot_aStar_elliptic.py
create mode 100644 src/Plot_aStar_hyperbolic.py
diff --git a/src/Plot_aStar_elliptic.py b/src/Plot_aStar_elliptic.py
new file mode 100644
index 00000000..bab66f71
--- /dev/null
+++ b/src/Plot_aStar_elliptic.py
@@ -0,0 +1,772 @@
+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
+from HelperFunctions import *
+from ClassifyMin import *
+
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+# import tikzplotlib
+# # from pylab import *
+# from tikzplotlib import save as tikz_save
+
+
+# Needed ?
+mpl.use('pdf')
+
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+# Generalized Plot-Script giving the option to define
+# quantity of interest and the parameter it depends on
+# to create a plot
+#
+# Input: Define y & x for "x-y plot" as Strings
+# - Run the 'Cell-Problem' for the different Parameter-Points
+# (alternatively run 'Compute_MuGamma' if quantity of interest
+# is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+
+
+# figsize argument takes inputs in inches
+# and we have the width of our document in pts.
+# To set the figure size we construct a function
+# to convert from pts to inches and to determine
+# an aesthetic figure height using the golden ratio:
+# 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 == 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 == 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
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+# InputFile = "/inputs/cellsolver.parset"
+# OutputFile = "/outputs/output.txt"
+
+InputFile = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- 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: -----')
+mu1 = 10.0
+# lambda1 = 10.0
+rho1 = 1.0
+alpha = 5.0
+beta = 10.0
+theta = 1.0/4.0
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity' #Elliptic Setting
+# gamma = '0' #Hyperbolic Setting
+# gamma = 0.5
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+# yName = 'angle'
+# yName = 'curvature'
+yName = 'MinVec'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+
+
+# --- define Interval of x-va1ues:
+# xmin = 0.15
+xmin = 0.01
+xmax = 0.41
+
+# xmin = 0.18 #Achtung bei manchen werten von theta ist integration in ComputeMuGama/Cell_problem schlecht!
+# xmax = 0.41 # Materialfunktion muss von Gitter aufgelöst werden
+ # müssen vielfache von (1/2^i) sein wobei i integer
+
+
+# xmin = 0.18 #Achtung bei manchen werten von theta ist integration in ComputeMuGama/Cell_problem schlecht!
+# xmax = 0.23
+
+
+
+
+# xmin = 0.01
+# xmax = 3.0
+numPoints = 70
+# numPoints = 50
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+
+
+
+
+
+
+
+for theta in X_Values:
+
+ print('Situation of Lemma1.4')
+ q12 = 0.0
+ q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+ q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+ b1 = prestrain_b1(rho1, beta, alpha,theta)
+ b2 = prestrain_b2(rho1, beta, alpha,theta)
+ b3 = 0.0
+ # if gamma == '0':
+ # q3 = q2
+ # if gamma == 'infinity':
+ # q3 = q1
+ q3 = GetMuGamma(beta,theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
+
+
+ if yName == 'q1': # TODO: Better use dictionary?...
+ print('q1 used')
+ Y_Values.append(q1)
+ elif yName =='q2':
+ print('q2 used')
+ Y_Values.append(q2)
+ elif yName =='q3':
+ print('q3 used')
+ Y_Values.append(q3)
+ elif yName =='q12':
+ print('q12 used')
+ Y_Values.append(q12)
+ elif yName =='b1':
+ print('b1 used')
+ Y_Values.append(b1)
+ elif yName =='b2':
+ print('b2 used')
+ Y_Values.append(b2)
+ elif yName =='b3':
+ print('b3 used')
+ Y_Values.append(b3)
+ elif yName == 'angle' or yName =='type' or yName =='curvature' or yName =='MinVec':
+ G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3, mu1, rho1)
+ if yName =='angle':
+ print('angle used')
+ Y_Values.append(angle)
+ if yName =='type':
+ print('angle used')
+ Y_Values.append(type)
+ if yName =='curvature':
+ print('angle used')
+ Y_Values.append(curvature)
+ if yName =='MinVec':
+ print('MinVec used')
+ Y_Values.append(G)
+
+
+print("(Output) Values of " + yName + ": ", Y_Values)
+
+
+# idx = find_nearestIdx(Y_Values, 0)
+# print(' Idx of value closest to 0', idx)
+# ValueClose = Y_Values[idx]
+# print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+#
+#
+#
+# # Find Indices where the difference between the next one is larger than epsilon...
+# jump_idx = []
+# jump_xValues = []
+# jump_yValues = []
+# tmp = X_Values[0]
+# for idx, x in enumerate(X_Values):
+# print(idx, x)
+# if idx > 0:
+# if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+# print('jump candidate')
+# jump_idx.append(idx)
+# jump_xValues.append(x)
+# jump_yValues.append(Y_Values[idx])
+#
+#
+#
+
+
+#
+#
+# print("Jump Indices", jump_idx)
+# print("Jump X-values:", jump_xValues)
+# print("Jump Y-values:", jump_yValues)
+#
+# y_plotValues = [Y_Values[0]]
+# x_plotValues = [X_Values[0]]
+# # y_plotValues.extend(jump_yValues)
+# for i in jump_idx:
+# y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+# x_plotValues.extend([X_Values[i-1], X_Values[i]])
+#
+#
+# y_plotValues.append(Y_Values[-1])
+# # x_plotValues = [X_Values[0]]
+# # x_plotValues.extend(jump_xValues)
+# x_plotValues.append(X_Values[-1])
+#
+#
+# print("y_plotValues:", y_plotValues)
+# print("x_plotValues:", x_plotValues)
+# Y_Values[np.diff(y) >= 0.5] = np.nan
+
+
+#get values bigger than jump position
+# gamma = infty
+# x_rest = X_Values[X_Values>x_plotValues[1]]
+# Y_Values = np.array(Y_Values) #convert the np array
+# y_rest = Y_Values[X_Values>x_plotValues[1]]
+#
+#
+# # gamma = 0
+# x_rest = X_Values[X_Values>x_plotValues[3]]
+# Y_Values = np.array(Y_Values) #convert the np array
+# y_rest = Y_Values[X_Values>x_plotValues[3]]
+
+# gamma between
+# Y_Values = np.array(Y_Values) #convert the np array
+# X_Values = np.array(X_Values) #convert the np array
+#
+# x_one = X_Values[X_Values>x_plotValues[3]]
+# # ax.scatter(X_Values, Y_Values)
+# y_rest = Y_Values[X_Values>x_plotValues[3]]
+# ax.plot(X_Values[X_Values>0.135], Y_Values[X_Values<0.135])
+#
+#
+#
+
+
+# y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+# print('X_Values:', X_Values)
+# print('Y_Values:', Y_Values)
+# print('x_rest:', x_rest)
+# print('y_rest:', y_rest)
+# print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+
+
+
+
+# --- Convert to numpy array
+Y_Values = np.array(Y_Values)
+X_Values = np.array(X_Values)
+
+Y_arr = np.asarray(Y_Values, dtype=float)
+X_Values = np.asarray(X_Values, dtype=float)
+
+
+print('X_Values:', X_Values)
+print('Y_arr:', Y_arr)
+# ---------------- Create Plot -------------------
+
+#--- change plot style: SEABORN
+# plt.style.use("seaborn-paper")
+
+
+#--- Adjust gobal matplotlib variables
+# mpl.rcParams['pdf.fonttype'] = 42
+# mpl.rcParams['ps.fonttype'] = 42
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+
+# plt.rc('font', family='serif', serif='Times')
+# plt.rc('font', family='serif')
+# # plt.rc('text', usetex=True) #also works...
+# plt.rc('xtick', labelsize=8)
+# plt.rc('ytick', labelsize=8)
+# plt.rc('axes', labelsize=8)
+
+
+
+
+
+#---- Scale Figure apropriately to fit tex-File Width
+# width = 452.9679
+
+# width as measured in inkscape
+width = 6.28 *0.5
+height = width / 1.618
+
+#setup canvas first
+fig = plt.figure() #main
+# fig, ax = plt.subplots()
+# fig, (ax, ax2) = plt.subplots(ncols=2)
+# fig,axes = plt.subplots(nrows=1,ncols=2,figsize=(width,height)) # more than one plot
+
+
+# fig.subplots_adjust(left=.15, bottom=.16, right=.99, top=.97) #TEST
+
+
+# TEST
+# mpl.rcParams['figure.figsize'] = (width+0.1,height+0.1)
+# fig = plt.figure(figsize=(width+0.1,height+0.1))
+
+
+# mpl.rcParams['figure.figsize'] = (width,height)
+# fig = plt.figure(figsize=(10,6)) # default is [6.4,4.8] 6.4 is the width, 4.8 is the height
+# fig = plt.figure(figsize=(width,height)) # default is [6.4,4.8] 6.4 is the width, 4.8 is the height
+# fig = plt.figure(figsize=set_size(width))
+# fig = plt.subplots(1, 1, figsize=set_size(width))
+
+# --- To create a figure half the width of your document:#
+# fig = plt.figure(figsize=set_size(width, fraction=0.5))
+
+
+
+#--- You must select the correct size of the plot in advance
+# fig.set_size_inches(3.54,3.54)
+
+ax = plt.axes((0.1,0.1,0.8,0.8))
+# ax = plt.axes((0.1,0.1,0.5,0.8))
+# ax = plt.axes((0.1,0.1,1,1))
+# ax = plt.axes()
+
+# ax.spines['right'].set_visible(False)
+# ax.spines['left'].set_visible(False)
+# ax.spines['bottom'].set_visible(False)
+# ax.spines['top'].set_visible(False)
+# ax.tick_params(axis='x',which='major',direction='out',length=10,width=5,color='red',pad=15,labelsize=15,labelcolor='green',
+# labelrotation=15)
+# ax.tick_params(axis='x',which='major', direction='out',pad=5,labelsize=10)
+# ax.tick_params(axis='y',which='major', length=5, width=1, direction='out',pad=5,labelsize=10)
+
+
+# ax.tick_params(axis='x',which='major', direction='out',pad=3)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.05))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.025))
+
+
+#---- print data-types
+# print(ax.xaxis.get_major_locator())
+# print(ax.xaxis.get_minor_locator())
+# print(ax.xaxis.get_major_formatter())
+# print(ax.xaxis.get_minor_formatter())
+
+#---- Hide Ticks or Labels
+# ax.yaxis.set_major_locator(plt.NullLocator())
+# ax.xaxis.set_major_formatter(plt.NullFormatter())
+
+#---- Reducing or Increasing the Number of Ticks
+# ax.xaxis.set_major_locator(plt.MaxNLocator(3))
+# ax.yaxis.set_major_locator(plt.MaxNLocator(3))
+
+
+#----- Fancy Tick Formats
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 4))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+#
+#
+# # ax.set_yticks([0, np.pi/8, np.pi/4 ])
+#
+# ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+
+
+# --- manually change ticks&labels:
+# ax.set_xticks([0.2,1])
+# ax.set_xticklabels(['pos1','pos2'])
+
+# ax.set_yticks([0, np.pi/8, np.pi/4 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+# ax.set_yticklabels(labels)
+
+# a=ax.yaxis.get_major_locator()
+# b=ax.yaxis.get_major_formatter()
+# c = ax.get_xticks()
+# d = ax.get_xticklabels()
+# print('xticks:',c)
+# print('xticklabels:',d)
+#
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+
+# ax.plot(Y_arr[:,0], Y_arr[:,1] , 'royalblue')
+
+print('Y_arr[:,0]:', Y_arr[:,0])
+
+print('Y_arr[:,1]:', Y_arr[:,1])
+
+ax.plot(Y_arr[:,0], Y_arr[:,1] , 'royalblue', # data
+marker='o', # each marker will be rendered as a circle
+markersize=2, # marker size
+markerfacecolor='orange', # marker facecolor
+markeredgecolor='black', # marker edgecolor
+markeredgewidth=0.5, # marker edge width
+# linestyle='--', # line style will be dash line
+linewidth=1,
+zorder = 3) # line width
+# plt.figure()
+
+
+#--- Coordinate Axes:
+ax.spines.left.set_position('zero')
+ax.spines.right.set_color('none')
+ax.spines.bottom.set_position('zero')
+ax.spines.top.set_color('none')
+ax.xaxis.set_ticks_position('bottom')
+ax.yaxis.set_ticks_position('left')
+
+ax.set(xlim=(-25, 15), ylim=(-3, 3))
+
+#-- Decorate the spins
+arrow_length = 8 # In points
+# X-axis arrow
+ax.annotate('x', xy=(1, 0), xycoords=('axes fraction', 'data'),
+ xytext=(arrow_length, 0), textcoords='offset points',
+ ha='left', va='center',
+ arrowprops=dict(arrowstyle='<|-', fc='black'))
+
+# Y-axis arrow
+ax.annotate('y', xy=(0, 1), xycoords=('data', 'axes fraction'),
+ xytext=(0, arrow_length), textcoords='offset points',
+ ha='center', va='bottom',
+ arrowprops=dict(arrowstyle='<|-', fc='black'))
+
+
+
+# ax.scatter(Y_arr[21,0],Y_arr[21,1], s=6, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+# edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=5)
+
+# ax.text(Y_arr[21,0]-0.25 , Y_arr[21,1]+0.15, r"$1$", size=4, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5))
+# ax.text(Y_arr[21,0] , Y_arr[21,1], r"$1$", size=2, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5), zorder=5)
+
+ax.scatter(Y_arr[21,0] , Y_arr[21,1], s=4, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+ edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=0.5, zorder=5)
+
+ax.scatter(Y_arr[31,0] , Y_arr[31,1], s=4, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+ edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=0.5, zorder=5)
+
+ax.scatter(Y_arr[40,0] , Y_arr[40,1], s=4, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+ edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=0.5, zorder=5)
+
+ax.annotate( 1 , (Y_arr[21,0] , Y_arr[21,1]), xytext=(Y_arr[21,0]-0.35 , Y_arr[21,1]+1),
+ bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5),
+ arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1), fontsize=6)
+
+ax.annotate( 2 , (Y_arr[31,0] , Y_arr[31,1]), xytext=(Y_arr[31,0]+4 , Y_arr[31,1]-0.08),
+ bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5),
+ arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1), fontsize=6)
+
+ax.annotate( 3 , (Y_arr[40,0] , Y_arr[40,1]), xytext=(Y_arr[40,0]-0.35 , Y_arr[40,1]+1),
+ bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5),
+ arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1), fontsize=6)
+
+
+
+
+
+ # arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1, shrink=0.05), fontsize=4)
+# f,ax=plt.subplots(1)
+
+# plt.title(r''+ yName + '-Plot')
+# plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+
+# plt.plot(X_Values, Y_Values)
+
+# ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+
+
+
+# Gamma = '0'
+# ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+#
+# ax.plot([x_plotValues[1],x_plotValues[3]], [y_plotValues[2],y_plotValues[3]] , 'b')
+#
+# ax.plot(x_rest, y_rest, 'b')
+
+
+# Gamma between
+
+# x jump values (gamma 0): [0.13606060606060608, 0.21090909090909093]
+
+# ax.plot([[0,jump_xValues[0]], [0, 0]] , 'b')
+# ax.plot([jump_xValues[0],xmin], [y_plotValues[2],y_plotValues[2]] , 'b')
+
+# ax.plot([[0,0.13606060606060608], [0, 0]] , 'b')
+# ax.plot([[0.13606060606060608,xmin], [(math.pi/2),(math.pi/2)]], 'b')
+
+# jump_xValues[0]
+
+
+
+# --- leave out jumps:
+# ax.scatter(X_Values, Y_Values)
+
+
+
+
+# # --- leave out jumps:
+# if gamma == 'infinity':
+# ax.plot(X_Values[X_Values>=jump_xValues[0]], Y_Values[X_Values>=jump_xValues[0]] , 'royalblue')
+# ax.plot(X_Values[X_Values<jump_xValues[0]], Y_Values[X_Values<jump_xValues[0]], 'royalblue')
+# # ax.plot(X_Values[X_Values>=jump_xValues[0]], Y_Values[X_Values>=jump_xValues[0]])
+# # ax.plot(X_Values[X_Values<jump_xValues[0]], Y_Values[X_Values<jump_xValues[0]])
+
+
+
+
+# ax.plot(X_Values[X_Values>0.136], Y_Values[X_Values>0.136])
+# ax.plot(X_Values[X_Values<0.135], Y_Values[X_Values<0.135])
+# ax.scatter(X_Values, Y_Values)
+# ax.plot(X_Values, Y_Values)
+
+# plt.plot(x_plotValues, y_plotValues,'.')
+# plt.scatter(X_Values, Y_Values, alpha=0.3)
+# plt.scatter(X_Values, Y_Values)
+# plt.plot(X_Values, Y_Values,'.')
+# plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# plt.axis([0, 6, 0, 20])
+
+# ax.set_xlabel(r"volume fraction $\theta$", size=11)
+# ax.set_ylabel(r"angle $\angle$", size=11)
+# ax.set_xlabel(r"volume fraction $\theta$")
+# ax.set_ylabel(r"angle $\angle$")
+# ax.set_ylabel(r"$a^*$")
+# plt.ylabel('$\kappa$')
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+
+
+
+
+# Plot every other line.. not the jumps...
+
+# if gamma == '0':
+# tmp = 1
+# for idx, x in enumerate(x_plotValues):
+# if idx > 0 and tmp == 1:
+# # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+# ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]], 'royalblue' )
+# tmp = 0
+# else:
+# tmp = 1
+
+
+
+
+# for x in jump_xValues:
+# plt.axvline(x,ymin=0, ymax= 1, color = 'orange',alpha=0.5, linestyle = 'dashed', linewidth=1)
+
+
+
+ # plt.axvline(x,ymin=0, ymax= 1, color = 'orange',alpha=0.5, linestyle = 'dashed', label=r'$\theta_*$')
+
+# plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+
+
+# -- SETUP LEGEND
+# ax.legend(prop={'size': 11})
+# ax.legend()
+
+# ------------------ SAVE FIGURE
+# tikzplotlib.save("TesTout.tex")
+# plt.close()
+# mpl.rcParams.update(mpl.rcParamsDefault)
+
+# plt.savefig("graph.pdf",
+# #This is simple recomendation for publication plots
+# dpi=1000,
+# # Plot will be occupy a maximum of available space
+# bbox_inches='tight',
+# )
+# plt.savefig("graph.pdf")
+
+
+#
+# # Find transition point
+# lastIdx = len(Y_Values)-1
+#
+# for idx, y in enumerate(Y_Values):
+# if idx != lastIdx:
+# if abs(y-0) < 0.01 and abs(Y_Values[idx+1] - 0) > 0.05:
+# transition_point1 = X_Values[idx+1]
+# print('transition point1:', transition_point1 )
+# if abs(y-0.5*np.pi) < 0.01 and abs(Y_Values[idx+1] -0.5*np.pi)>0.01:
+# transition_point2 = X_Values[idx]
+# print('transition point2:', transition_point2 )
+# if abs(y-0) > 0.01 and abs(Y_Values[idx+1] - 0) < 0.01:
+# transition_point3 = X_Values[idx+1]
+# print('transition point3:', transition_point3 )
+#
+# # Add transition Points:
+# if gamma == '0':
+# ax.scatter([transition_point1, transition_point2],[np.pi/2,np.pi/2],s=6, marker='o', cmap=None, norm=None, facecolor = 'black',
+# edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
+#
+# ax.text(transition_point1-0.02 , np.pi/2-0.02, r"$1$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+#
+# ax.text(transition_point2+0.012 , np.pi/2-0.02, r"$2$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+# else:
+# ax.scatter([transition_point1, transition_point2, transition_point3 ],[np.pi/2,np.pi/2,0 ],s=6, marker='o', cmap=None, norm=None, facecolor = 'black',
+# edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
+#
+# ax.text(transition_point1-0.02 , np.pi/2-0.02, r"$1$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+#
+# ax.text(transition_point2 +0.015 , np.pi/2-0.02, r"$2$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+#
+# ax.text(transition_point3 +0.005 , 0+0.06, r"$3$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+
+
+fig.set_size_inches(width, height)
+fig.savefig('Plot-aStar_elliptic.pdf')
+
+
+
+
+# tikz_save('someplot.tex', figureheight='5cm', figurewidth='9cm')
+
+# tikz_save('fig.tikz',
+# figureheight = '\\figureheight',
+# figurewidth = '\\figurewidth')
+
+# ----------------------------------------
+
+
+plt.show()
+# #---------------------------------------------------------------
diff --git a/src/Plot_aStar_hyperbolic.py b/src/Plot_aStar_hyperbolic.py
new file mode 100644
index 00000000..23753fd8
--- /dev/null
+++ b/src/Plot_aStar_hyperbolic.py
@@ -0,0 +1,770 @@
+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
+from HelperFunctions import *
+from ClassifyMin import *
+
+import matplotlib.ticker as tickers
+import matplotlib as mpl
+from matplotlib.ticker import MultipleLocator,FormatStrFormatter,MaxNLocator
+import pandas as pd
+
+# import tikzplotlib
+# # from pylab import *
+# from tikzplotlib import save as tikz_save
+
+
+# Needed ?
+mpl.use('pdf')
+
+# from subprocess import Popen, PIPE
+#import sys
+
+###################### makePlot.py #########################
+# Generalized Plot-Script giving the option to define
+# quantity of interest and the parameter it depends on
+# to create a plot
+#
+# Input: Define y & x for "x-y plot" as Strings
+# - Run the 'Cell-Problem' for the different Parameter-Points
+# (alternatively run 'Compute_MuGamma' if quantity of interest
+# is q3=muGamma for a significant Speedup)
+
+###########################################################
+
+
+
+# figsize argument takes inputs in inches
+# and we have the width of our document in pts.
+# To set the figure size we construct a function
+# to convert from pts to inches and to determine
+# an aesthetic figure height using the golden ratio:
+# 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 == 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 == 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
+
+
+
+# TODO
+# - Fallunterscheidung (Speedup) falls gesuchter value mu_gamma = q3
+# - Also Add option to plot Minimization Output
+
+
+# ----- Setup Paths -----
+# InputFile = "/inputs/cellsolver.parset"
+# OutputFile = "/outputs/output.txt"
+
+InputFile = "/inputs/computeMuGamma.parset"
+OutputFile = "/outputs/outputMuGamma.txt"
+
+# path = os.getcwd()
+# InputFilePath = os.getcwd()+InputFile
+# OutputFilePath = os.getcwd()+OutputFile
+# --------- 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: -----')
+mu1 = 10.0
+# lambda1 = 10.0
+rho1 = 1.0
+alpha = 5.0
+beta = 10.0
+theta = 1.0/4.0
+
+lambda1 = 0.0
+gamma = 1.0/4.0
+
+gamma = 'infinity' #Elliptic Setting
+gamma = '0' #Hyperbolic Setting
+# gamma = 0.5
+
+
+print('mu1: ', mu1)
+print('rho1: ', rho1)
+print('alpha: ', alpha)
+print('beta: ', beta)
+print('theta: ', theta)
+print('gamma:', gamma)
+print('----------------------------')
+
+
+# TODO? : Ask User for Input ...
+# function = input("Enter value you want to plot (y-value):\n")
+# print(f'You entered {function}')
+# parameter = input("Enter Parameter this value depends on (x-value) :\n")
+# print(f'You entered {parameter}')
+
+# Add Option to change NumberOfElements used for computation of Cell-Problem
+
+
+# --- Define Quantity of interest:
+# Options: 'q1', 'q2', 'q3', 'q12' ,'q21', 'q31', 'q13' , 'q23', 'q32' , 'b1', 'b2' ,'b3'
+# TODO: EXTRA (MInimization Output) 'Minimizer (norm?)' 'angle', 'type', 'curvature'
+# yName = 'q12'
+# # yName = 'b1'
+# yName = 'q3'
+# yName = 'angle'
+# yName = 'curvature'
+yName = 'MinVec'
+
+# --- Define Parameter this function/quantity depends on:
+# Options: mu1 ,lambda1, rho1 , alpha, beta, theta, gamma
+# xName = 'theta'
+# xName = 'gamma'
+# xName = 'lambda1'
+xName = 'theta'
+
+
+# --- define Interval of x-va1ues:
+# xmin = 0.15
+xmin = 0.01
+xmax = 0.41
+
+# xmin = 0.18 #Achtung bei manchen werten von theta ist integration in ComputeMuGama/Cell_problem schlecht!
+# xmax = 0.41 # Materialfunktion muss von Gitter aufgelöst werden
+ # müssen vielfache von (1/2^i) sein wobei i integer
+
+
+# xmin = 0.18 #Achtung bei manchen werten von theta ist integration in ComputeMuGama/Cell_problem schlecht!
+# xmax = 0.23
+
+
+
+
+# xmin = 0.01
+# xmax = 3.0
+numPoints = 70
+# numPoints = 50
+X_Values = np.linspace(xmin, xmax, num=numPoints)
+print(X_Values)
+
+
+Y_Values = []
+
+
+
+
+
+
+
+
+for theta in X_Values:
+
+ print('Situation of Lemma1.4')
+ q12 = 0.0
+ q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
+ q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
+ b1 = prestrain_b1(rho1, beta, alpha,theta)
+ b2 = prestrain_b2(rho1, beta, alpha,theta)
+ b3 = 0.0
+ # if gamma == '0':
+ # q3 = q2
+ # if gamma == 'infinity':
+ # q3 = q1
+ q3 = GetMuGamma(beta,theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
+
+
+ if yName == 'q1': # TODO: Better use dictionary?...
+ print('q1 used')
+ Y_Values.append(q1)
+ elif yName =='q2':
+ print('q2 used')
+ Y_Values.append(q2)
+ elif yName =='q3':
+ print('q3 used')
+ Y_Values.append(q3)
+ elif yName =='q12':
+ print('q12 used')
+ Y_Values.append(q12)
+ elif yName =='b1':
+ print('b1 used')
+ Y_Values.append(b1)
+ elif yName =='b2':
+ print('b2 used')
+ Y_Values.append(b2)
+ elif yName =='b3':
+ print('b3 used')
+ Y_Values.append(b3)
+ elif yName == 'angle' or yName =='type' or yName =='curvature' or yName =='MinVec':
+ G, angle, Type, curvature = classifyMin_ana(alpha,beta,theta, q3, mu1, rho1)
+ if yName =='angle':
+ print('angle used')
+ Y_Values.append(angle)
+ if yName =='type':
+ print('angle used')
+ Y_Values.append(type)
+ if yName =='curvature':
+ print('angle used')
+ Y_Values.append(curvature)
+ if yName =='MinVec':
+ print('MinVec used')
+ Y_Values.append(G)
+
+
+print("(Output) Values of " + yName + ": ", Y_Values)
+
+
+# idx = find_nearestIdx(Y_Values, 0)
+# print(' Idx of value closest to 0', idx)
+# ValueClose = Y_Values[idx]
+# print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+#
+#
+#
+# # Find Indices where the difference between the next one is larger than epsilon...
+# jump_idx = []
+# jump_xValues = []
+# jump_yValues = []
+# tmp = X_Values[0]
+# for idx, x in enumerate(X_Values):
+# print(idx, x)
+# if idx > 0:
+# if abs(Y_Values[idx]-Y_Values[idx-1]) > 1:
+# print('jump candidate')
+# jump_idx.append(idx)
+# jump_xValues.append(x)
+# jump_yValues.append(Y_Values[idx])
+#
+#
+#
+
+
+#
+#
+# print("Jump Indices", jump_idx)
+# print("Jump X-values:", jump_xValues)
+# print("Jump Y-values:", jump_yValues)
+#
+# y_plotValues = [Y_Values[0]]
+# x_plotValues = [X_Values[0]]
+# # y_plotValues.extend(jump_yValues)
+# for i in jump_idx:
+# y_plotValues.extend([Y_Values[i-1], Y_Values[i]])
+# x_plotValues.extend([X_Values[i-1], X_Values[i]])
+#
+#
+# y_plotValues.append(Y_Values[-1])
+# # x_plotValues = [X_Values[0]]
+# # x_plotValues.extend(jump_xValues)
+# x_plotValues.append(X_Values[-1])
+#
+#
+# print("y_plotValues:", y_plotValues)
+# print("x_plotValues:", x_plotValues)
+# Y_Values[np.diff(y) >= 0.5] = np.nan
+
+
+#get values bigger than jump position
+# gamma = infty
+# x_rest = X_Values[X_Values>x_plotValues[1]]
+# Y_Values = np.array(Y_Values) #convert the np array
+# y_rest = Y_Values[X_Values>x_plotValues[1]]
+#
+#
+# # gamma = 0
+# x_rest = X_Values[X_Values>x_plotValues[3]]
+# Y_Values = np.array(Y_Values) #convert the np array
+# y_rest = Y_Values[X_Values>x_plotValues[3]]
+
+# gamma between
+# Y_Values = np.array(Y_Values) #convert the np array
+# X_Values = np.array(X_Values) #convert the np array
+#
+# x_one = X_Values[X_Values>x_plotValues[3]]
+# # ax.scatter(X_Values, Y_Values)
+# y_rest = Y_Values[X_Values>x_plotValues[3]]
+# ax.plot(X_Values[X_Values>0.135], Y_Values[X_Values<0.135])
+#
+#
+#
+
+
+# y_rest = Y_Values[np.nonzero(X_Values>x_plotValues[1]]
+# print('X_Values:', X_Values)
+# print('Y_Values:', Y_Values)
+# print('x_rest:', x_rest)
+# print('y_rest:', y_rest)
+# print('np.nonzero(X_Values>x_plotValues[1]', np.nonzero(X_Values>x_plotValues[1]) )
+
+
+
+
+# --- Convert to numpy array
+Y_Values = np.array(Y_Values)
+X_Values = np.array(X_Values)
+
+Y_arr = np.asarray(Y_Values, dtype=float)
+X_Values = np.asarray(X_Values, dtype=float)
+
+
+print('X_Values:', X_Values)
+print('Y_arr:', Y_arr)
+# ---------------- Create Plot -------------------
+
+#--- change plot style: SEABORN
+# plt.style.use("seaborn-paper")
+
+
+#--- Adjust gobal matplotlib variables
+# mpl.rcParams['pdf.fonttype'] = 42
+# mpl.rcParams['ps.fonttype'] = 42
+mpl.rcParams['text.usetex'] = True
+mpl.rcParams["font.family"] = "serif"
+mpl.rcParams["font.size"] = "9"
+
+
+# plt.rc('font', family='serif', serif='Times')
+# plt.rc('font', family='serif')
+# # plt.rc('text', usetex=True) #also works...
+# plt.rc('xtick', labelsize=8)
+# plt.rc('ytick', labelsize=8)
+# plt.rc('axes', labelsize=8)
+
+
+
+
+
+#---- Scale Figure apropriately to fit tex-File Width
+# width = 452.9679
+
+# width as measured in inkscape
+width = 6.28 *0.5
+height = width / 1.618
+
+#setup canvas first
+fig = plt.figure() #main
+# fig, ax = plt.subplots()
+# fig, (ax, ax2) = plt.subplots(ncols=2)
+# fig,axes = plt.subplots(nrows=1,ncols=2,figsize=(width,height)) # more than one plot
+
+
+# fig.subplots_adjust(left=.15, bottom=.16, right=.99, top=.97) #TEST
+
+
+# TEST
+# mpl.rcParams['figure.figsize'] = (width+0.1,height+0.1)
+# fig = plt.figure(figsize=(width+0.1,height+0.1))
+
+
+# mpl.rcParams['figure.figsize'] = (width,height)
+# fig = plt.figure(figsize=(10,6)) # default is [6.4,4.8] 6.4 is the width, 4.8 is the height
+# fig = plt.figure(figsize=(width,height)) # default is [6.4,4.8] 6.4 is the width, 4.8 is the height
+# fig = plt.figure(figsize=set_size(width))
+# fig = plt.subplots(1, 1, figsize=set_size(width))
+
+# --- To create a figure half the width of your document:#
+# fig = plt.figure(figsize=set_size(width, fraction=0.5))
+
+
+
+#--- You must select the correct size of the plot in advance
+# fig.set_size_inches(3.54,3.54)
+
+# ax = plt.axes((0.1,0.1,0.8,0.8))
+ax = plt.axes((0,0.1,0.9,0.8))
+# ax = plt.axes((0.1,0.1,0.5,0.8))
+# ax = plt.axes((0.1,0.1,1,1))
+# ax = plt.axes()
+
+# ax.spines['right'].set_visible(False)
+# ax.spines['left'].set_visible(False)
+# ax.spines['bottom'].set_visible(False)
+# ax.spines['top'].set_visible(False)
+# ax.tick_params(axis='x',which='major',direction='out',length=10,width=5,color='red',pad=15,labelsize=15,labelcolor='green',
+# labelrotation=15)
+# ax.tick_params(axis='x',which='major', direction='out',pad=5,labelsize=10)
+# ax.tick_params(axis='y',which='major', length=5, width=1, direction='out',pad=5,labelsize=10)
+
+
+# ax.tick_params(axis='x',which='major', direction='out',pad=3)
+# ax.tick_params(axis='y',which='major', length=3, width=1, direction='out',pad=3)
+# ax.xaxis.set_major_locator(MultipleLocator(0.05))
+# ax.xaxis.set_minor_locator(MultipleLocator(0.025))
+
+
+#---- print data-types
+# print(ax.xaxis.get_major_locator())
+# print(ax.xaxis.get_minor_locator())
+# print(ax.xaxis.get_major_formatter())
+# print(ax.xaxis.get_minor_formatter())
+
+#---- Hide Ticks or Labels
+# ax.yaxis.set_major_locator(plt.NullLocator())
+# ax.xaxis.set_major_formatter(plt.NullFormatter())
+
+#---- Reducing or Increasing the Number of Ticks
+# ax.xaxis.set_major_locator(plt.MaxNLocator(3))
+# ax.yaxis.set_major_locator(plt.MaxNLocator(3))
+
+
+#----- Fancy Tick Formats
+# ax.yaxis.set_major_locator(plt.MultipleLocator(np.pi / 4))
+# ax.yaxis.set_minor_locator(plt.MultipleLocator(np.pi / 12))
+#
+#
+# # ax.set_yticks([0, np.pi/8, np.pi/4 ])
+#
+# ax.yaxis.set_major_formatter(plt.FuncFormatter(format_func))
+
+
+
+# --- manually change ticks&labels:
+# ax.set_xticks([0.2,1])
+# ax.set_xticklabels(['pos1','pos2'])
+
+# ax.set_yticks([0, np.pi/8, np.pi/4 ])
+# labels = ['$0$',r'$\pi/8$', r'$\pi/4$']
+# ax.set_yticklabels(labels)
+
+# a=ax.yaxis.get_major_locator()
+# b=ax.yaxis.get_major_formatter()
+# c = ax.get_xticks()
+# d = ax.get_xticklabels()
+# print('xticks:',c)
+# print('xticklabels:',d)
+#
+# ax.grid(True,which='major',axis='both',alpha=0.3)
+
+# ax.plot(Y_arr[:,0], Y_arr[:,1] , 'royalblue')
+
+print('Y_arr[:,0]:', Y_arr[:,0])
+
+print('Y_arr[:,1]:', Y_arr[:,1])
+
+ax.plot(Y_arr[:,0], Y_arr[:,1] , 'royalblue', # data
+marker='o', # each marker will be rendered as a circle
+markersize=2, # marker size
+markerfacecolor='orange', # marker facecolor
+markeredgecolor='black', # marker edgecolor
+markeredgewidth=0.5, # marker edge width
+# linestyle='--', # line style will be dash line
+linewidth=1,
+zorder = 3) # line width
+# plt.figure()
+
+
+#--- Coordinate Axes:
+ax.spines.left.set_position('zero')
+ax.spines.right.set_color('none')
+ax.spines.bottom.set_position('zero')
+ax.spines.top.set_color('none')
+ax.xaxis.set_ticks_position('bottom')
+ax.yaxis.set_ticks_position('left')
+
+ax.set(xlim=(-25, 15), ylim=(-3, 3))
+
+#-- Decorate the spins
+arrow_length = 8 # In points
+# X-axis arrow
+ax.annotate('x', xy=(1, 0), xycoords=('axes fraction', 'data'),
+ xytext=(arrow_length, 0), textcoords='offset points',
+ ha='left', va='center',
+ arrowprops=dict(arrowstyle='<|-', fc='black'))
+
+# Y-axis arrow
+ax.annotate('y', xy=(0, 1), xycoords=('data', 'axes fraction'),
+ xytext=(0, arrow_length), textcoords='offset points',
+ ha='center', va='bottom',
+ arrowprops=dict(arrowstyle='<|-', fc='black'))
+
+
+
+# ax.scatter(Y_arr[21,0],Y_arr[21,1], s=6, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+# edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=5)
+
+# ax.text(Y_arr[21,0]-0.25 , Y_arr[21,1]+0.15, r"$1$", size=4, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5))
+# ax.text(Y_arr[21,0] , Y_arr[21,1], r"$1$", size=2, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5), zorder=5)
+
+ax.scatter(Y_arr[21,0] , Y_arr[21,1], s=4, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+ edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=0.5, zorder=5)
+
+ax.scatter(Y_arr[34,0] , Y_arr[34,1], s=4, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+ edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=0.5, zorder=5)
+
+ax.scatter(Y_arr[35,0] , Y_arr[35,1], s=4, marker='o', cmap=None, norm=None, facecolor = 'forestgreen',
+ edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=0.5, zorder=5)
+
+ax.annotate( 1 , (Y_arr[21,0] , Y_arr[21,1]), xytext=(Y_arr[21,0]-0.35 , Y_arr[21,1]+1),
+ bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5),
+ arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1), fontsize=6)
+
+ax.annotate( 2 , (Y_arr[34,0] , Y_arr[34,1]), xytext=(Y_arr[34,0]+4 , Y_arr[34,1]-0.08),
+ bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5),
+ arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1), fontsize=6)
+
+ax.annotate( 3 , (Y_arr[35,0] , Y_arr[35,1]), xytext=(Y_arr[35,0]-0.35 , Y_arr[35,1]+1),
+ bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5),
+ arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1), fontsize=6)
+
+
+ # arrowprops = dict(arrowstyle="simple",color='blue', linewidth=0.1, shrink=0.05), fontsize=4)
+# f,ax=plt.subplots(1)
+
+# plt.title(r''+ yName + '-Plot')
+# plt.plot(X_Values, Y_Values,linewidth=2, '.k')
+# plt.plot(X_Values, Y_Values,'.k',markersize=1)
+# plt.plot(X_Values, Y_Values,'.',markersize=0.8)
+
+# plt.plot(X_Values, Y_Values)
+
+# ax.plot([[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+
+
+
+# Gamma = '0'
+# ax.plot([x_plotValues[0],x_plotValues[1]], [y_plotValues[0],y_plotValues[1]] , 'b')
+#
+# ax.plot([x_plotValues[1],x_plotValues[3]], [y_plotValues[2],y_plotValues[3]] , 'b')
+#
+# ax.plot(x_rest, y_rest, 'b')
+
+
+# Gamma between
+
+# x jump values (gamma 0): [0.13606060606060608, 0.21090909090909093]
+
+# ax.plot([[0,jump_xValues[0]], [0, 0]] , 'b')
+# ax.plot([jump_xValues[0],xmin], [y_plotValues[2],y_plotValues[2]] , 'b')
+
+# ax.plot([[0,0.13606060606060608], [0, 0]] , 'b')
+# ax.plot([[0.13606060606060608,xmin], [(math.pi/2),(math.pi/2)]], 'b')
+
+# jump_xValues[0]
+
+
+
+# --- leave out jumps:
+# ax.scatter(X_Values, Y_Values)
+
+
+
+
+# # --- leave out jumps:
+# if gamma == 'infinity':
+# ax.plot(X_Values[X_Values>=jump_xValues[0]], Y_Values[X_Values>=jump_xValues[0]] , 'royalblue')
+# ax.plot(X_Values[X_Values<jump_xValues[0]], Y_Values[X_Values<jump_xValues[0]], 'royalblue')
+# # ax.plot(X_Values[X_Values>=jump_xValues[0]], Y_Values[X_Values>=jump_xValues[0]])
+# # ax.plot(X_Values[X_Values<jump_xValues[0]], Y_Values[X_Values<jump_xValues[0]])
+
+
+
+
+# ax.plot(X_Values[X_Values>0.136], Y_Values[X_Values>0.136])
+# ax.plot(X_Values[X_Values<0.135], Y_Values[X_Values<0.135])
+# ax.scatter(X_Values, Y_Values)
+# ax.plot(X_Values, Y_Values)
+
+# plt.plot(x_plotValues, y_plotValues,'.')
+# plt.scatter(X_Values, Y_Values, alpha=0.3)
+# plt.scatter(X_Values, Y_Values)
+# plt.plot(X_Values, Y_Values,'.')
+# plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+# plt.axis([0, 6, 0, 20])
+
+# ax.set_xlabel(r"volume fraction $\theta$", size=11)
+# ax.set_ylabel(r"angle $\angle$", size=11)
+# ax.set_xlabel(r"volume fraction $\theta$")
+# ax.set_ylabel(r"angle $\angle$")
+# ax.set_ylabel(r"$a^*$")
+# plt.ylabel('$\kappa$')
+
+# ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%g $\pi$'))
+# ax.yaxis.set_major_locator(ticker.MultipleLocator(base=0.1))
+
+
+
+
+# Plot every other line.. not the jumps...
+
+# if gamma == '0':
+# tmp = 1
+# for idx, x in enumerate(x_plotValues):
+# if idx > 0 and tmp == 1:
+# # plt.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]] )
+# ax.plot([x_plotValues[idx-1],x_plotValues[idx]] ,[y_plotValues[idx-1],y_plotValues[idx]], 'royalblue' )
+# tmp = 0
+# else:
+# tmp = 1
+
+
+
+
+# for x in jump_xValues:
+# plt.axvline(x,ymin=0, ymax= 1, color = 'orange',alpha=0.5, linestyle = 'dashed', linewidth=1)
+
+
+
+ # plt.axvline(x,ymin=0, ymax= 1, color = 'orange',alpha=0.5, linestyle = 'dashed', label=r'$\theta_*$')
+
+# plt.axvline(x_plotValues[1],ymin=0, ymax= 1, color = 'g',alpha=0.5, linestyle = 'dashed')
+
+# plt.axhline(y = 1.90476, color = 'b', linestyle = ':', label='$q_1$')
+# plt.axhline(y = 2.08333, color = 'r', linestyle = 'dashed', label='$q_2$')
+# plt.legend()
+
+
+# -- SETUP LEGEND
+# ax.legend(prop={'size': 11})
+# ax.legend()
+
+# ------------------ SAVE FIGURE
+# tikzplotlib.save("TesTout.tex")
+# plt.close()
+# mpl.rcParams.update(mpl.rcParamsDefault)
+
+# plt.savefig("graph.pdf",
+# #This is simple recomendation for publication plots
+# dpi=1000,
+# # Plot will be occupy a maximum of available space
+# bbox_inches='tight',
+# )
+# plt.savefig("graph.pdf")
+
+
+#
+# # Find transition point
+# lastIdx = len(Y_Values)-1
+#
+# for idx, y in enumerate(Y_Values):
+# if idx != lastIdx:
+# if abs(y-0) < 0.01 and abs(Y_Values[idx+1] - 0) > 0.05:
+# transition_point1 = X_Values[idx+1]
+# print('transition point1:', transition_point1 )
+# if abs(y-0.5*np.pi) < 0.01 and abs(Y_Values[idx+1] -0.5*np.pi)>0.01:
+# transition_point2 = X_Values[idx]
+# print('transition point2:', transition_point2 )
+# if abs(y-0) > 0.01 and abs(Y_Values[idx+1] - 0) < 0.01:
+# transition_point3 = X_Values[idx+1]
+# print('transition point3:', transition_point3 )
+#
+# # Add transition Points:
+# if gamma == '0':
+# ax.scatter([transition_point1, transition_point2],[np.pi/2,np.pi/2],s=6, marker='o', cmap=None, norm=None, facecolor = 'black',
+# edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
+#
+# ax.text(transition_point1-0.02 , np.pi/2-0.02, r"$1$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+#
+# ax.text(transition_point2+0.012 , np.pi/2-0.02, r"$2$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+# else:
+# ax.scatter([transition_point1, transition_point2, transition_point3 ],[np.pi/2,np.pi/2,0 ],s=6, marker='o', cmap=None, norm=None, facecolor = 'black',
+# edgecolor = 'black', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
+#
+# ax.text(transition_point1-0.02 , np.pi/2-0.02, r"$1$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+#
+# ax.text(transition_point2 +0.015 , np.pi/2-0.02, r"$2$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+#
+# ax.text(transition_point3 +0.005 , 0+0.06, r"$3$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
+# )
+
+
+fig.set_size_inches(width, height)
+fig.savefig('Plot-aStar_hyperbolic.pdf')
+
+
+
+
+# tikz_save('someplot.tex', figureheight='5cm', figurewidth='9cm')
+
+# tikz_save('fig.tikz',
+# figureheight = '\\figureheight',
+# figurewidth = '\\figurewidth')
+
+# ----------------------------------------
+
+
+plt.show()
+# #---------------------------------------------------------------
--
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