Add Plot-script for 1-parameterFamily

Matlab-Programs/Stefan_parabolic.m

+
+clc
+q1=1;
+q2=2;
+q12=1/2;
+q3=((4*q1*q2)^(1/2)-q12)/2;
+H=[2*q1,q12+2*q3;q12+2*q3,2*q2];
+A=[q1,1/2*q12;1/2*q12,q2];
+abar=[q12+2*q3;2*q2];
+abar=(abar(1)^2+abar(2)^2)^(-1/2).*abar
+b=1*A\abar
+sstar=1/(q1+q2)*abar'*(A*b)
+abarperp=[abar(2);-abar(1)]
+%
+N=10;
+T=linspace(-sstar*(q12+2*q3)/(2*q2),sstar*(2*q2)/(q12+2*q3),N)
+abars=sstar.*abar+T.*abarperp
+%
+G=[];
+e=[];
+alpha=[];
+kappa=[];
+K=[];
+for k=1:N
+    if abars(1,k)*abars(2,k)>=0
+        K=[K,k];
+        G=[G,[abars(1,k);abars(2,k);sqrt(2*abars(1,k)*abars(2,k))]];
+        g=[sqrt(abars(1,k)/(abars(1,k)+abars(2,k)));sqrt(abars(2,k)/(abars(1,k)+abars(2,k)))];
+        e=[e,g];
+        kappa=[kappa,abars(1,k)+abars(2,k)];
+%         alpha=[alpha,atan2(g(1),g(2))];                                                 %reversed here ???? 
+        alpha=[alpha,atan2(g(2),g(1))];    
+    end
+end
+% G1=[1,0;0,0];G2=[0,0;0,1];G3=[0,1/sqrt(2);1/sqrt(2),0];
+alpha
+kappa
+min(alpha)
+max(alpha)
+hold off;
+plot(alpha,kappa);
+hold;
+plot(-alpha,kappa);

src/Plot-1-ParameterFamily.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
+
+# from matplotlib import rc
+# rc('text', usetex=True) # Use LaTeX font
+#
+# import seaborn as sns
+# sns.set(color_codes=True)
+
+
+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
+
+
+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)
+
+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]))
+
+
+
+
+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, )
+
+
+
+ax.set_xlabel(r"angle $\alpha$")
+ax.set_ylabel(r"curvature  $\kappa$")
+
+
+
+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('Plot-1-ParameterFamily.pdf')
+
+plt.show()