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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 = 1.0 #10.0
# lambda1 = 10.0
rho1 = 1.0
# alpha = 5.0
# beta = 10.0
# alpha = 2.0
# beta = 2.0
# theta = 1.0/8.0 #1.0/4.0
lambda1 = 0.0
# gamma = 1.0/4.0
# TEST:
# alpha=3.0;
# # INTERESTING!:
# alpha = 3
beta = 2.0
# theta= 1/8
#TEST
# beta=2
gamma = 'infinity' #Elliptic Setting
gamma = '0' #Hyperbolic Setting
# gamma = 0.01
# # gamma= 3.0
gamma = 0.5
gamma = 0.75
# # gamma = 100.0
# gamma = 3.0
Gamma_Values = [0.5, 0.75, 1.5, 3.0]
# Gamma_Values = [ 1.5, 3.0]
Gamma_Values = [3.0]
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print('(Input) Gamma_Values:', Gamma_Values)
# #
for gamma in Gamma_Values:
print('mu1: ', mu1)
print('rho1: ', rho1)
# print('alpha: ', alpha)
print('beta: ', beta)
# print('theta: ', theta)
print('gamma:', gamma)
print('----------------------------')
# --- define Interval of x-va1ues:
xmin = -2.0
# xmax = 0.41
xmax = 3.0
xmin = -1.5
xmax = 2.0
xmin = -1.0
xmax = -0.5
Jumps = False
numPoints = 2000
numPoints = 300
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X_Values = np.linspace(xmin, xmax, num=numPoints)
print(X_Values)
Y_Values = []
Angle_Theta01 = []
Angle_Theta025 = []
Angle_Theta05 = []
Angle_Theta075 = []
Angle_Theta09 = []
for alpha 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
# q3_Theta01 = GetMuGamma(beta,0.1,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
# q3_Theta025 = GetMuGamma(beta,0.25,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
q3_Theta05 = GetMuGamma(beta,0.5,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
# q3_Theta075 = GetMuGamma(beta,0.75,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
# q3_Theta09 = GetMuGamma(beta,0.9,gamma,mu1,rho1,InputFilePath ,OutputFilePath)
# G, angle, Type, curvature = classifyMin_ana(alpha,beta,0.1, q3_Theta01, mu1, rho1)
# Angle_Theta01.append(angle)
#
# G, angle, Type, curvature = classifyMin_ana(alpha,beta,0.25, q3_Theta025, mu1, rho1)
# Angle_Theta025.append(angle)
G, angle, Type, curvature = classifyMin_ana(alpha,beta,0.5, q3_Theta05, mu1, rho1)
Angle_Theta05.append(angle)
# G, angle, Type, curvature = classifyMin_ana(alpha,beta,0.75, q3_Theta075, mu1, rho1)
# Angle_Theta075.append(angle)
#
# G, angle, Type, curvature = classifyMin_ana(alpha,beta,0.9, q3_Theta09, mu1, rho1)
# Angle_Theta09.append(angle)
#
# G, angle, Type, curvature = classifyMin_ana(-0.5,beta,theta, q3, mu1, rho1)
# Angle_alphaNeg05 .append(angle)
# G, angle, Type, curvature = classifyMin_ana(-0.25,beta,theta, q3, mu1, rho1)
# Angle_alphaNeg025.append(angle)
# G, angle, Type, curvature = classifyMin_ana(3.0,beta,theta, q3, mu1, rho1)
# Angle_alpha3.append(angle)
# G, angle, Type, curvature = classifyMin_ana(-1.0,beta,theta, q3, mu1, rho1)
# Angle_alphaNeg075.append(angle)
# G, angle, Type, curvature = classifyMin_ana(0,beta,theta, q3, mu1, rho1)
# Angle_alpha0.append(angle)
# # G, angle, Type, curvature = classifyMin_ana(-0.125,beta,theta, q3, mu1, rho1)
# # Angle_alphaNeg0125.append(angle)
# G, angle, Type, curvature = classifyMin_ana(-0.7,beta,theta, q3, mu1, rho1)
# Angle_alphaNeg0125.append(angle)
#
# G, angle, Type, curvature = classifyMin_ana(-0.625,beta,theta, q3, mu1, rho1)
# Angle_alphaNeg0625.append(angle)
# G, angle, Type, curvature = classifyMin_ana(-0.875,beta,theta, q3, mu1, rho1)
# Angle_alphaNeg0875.append(angle)
#
#
# print("(Output) Values of angle: ", 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)
Angle_Theta01 = np.array(Angle_Theta01)
Angle_Theta025 = np.array(Angle_Theta025)
Angle_Theta05 = np.array(Angle_Theta05)
Angle_Theta075 = np.array(Angle_Theta075)
Angle_Theta09 = np.array(Angle_Theta09)
# ---------------- 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
width = 6.28 *0.333
# width = 6.28
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((0.15,0.18,0.8,0.8))
# ax = plt.axes((0.15,0.18,0.6,0.6))
# ax = plt.axes((0.15,0.2,0.75,0.75))
# ax = plt.axes((0.18,0.2,0.75,0.75))
# ax = plt.axes((0.28,0.3,0.65,0.65)) # This one!
ax = plt.axes((0.25,0.25,0.6,0.6))
# 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)
if gamma == '0':
Title = r'$0< \gamma \ll 1$'
ax.set_title(Title)
elif gamma == 'infinity':
print('THIS CASE')
Title = r'$\gamma \gg 1$'
ax.set_title(Title)
else:
Title = r'$ \gamma =$' + str(gamma)
ax.set_title(Title)
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# ax.xaxis.set_major_locator(MultipleLocator(0.05))
# ax.xaxis.set_minor_locator(MultipleLocator(0.025))
# ax.xaxis.set_major_locator(MultipleLocator(0.1))
# ax.xaxis.set_minor_locator(MultipleLocator(0.05))
ax.xaxis.set_major_locator(MultipleLocator(0.25))
ax.xaxis.set_minor_locator(MultipleLocator(0.125))
# ax.xaxis.set_major_locator(MultipleLocator(0.5))
# ax.xaxis.set_minor_locator(MultipleLocator(0.25))
#---- 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.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)
# plt.figure()
# 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)
# ax.set_xlabel(r"prestrain ratio $\theta_\rho$",labelpad=0)
ax.set_xlabel(r"$\theta_\rho$",labelpad=0)
ax.set_ylabel(r"$\alpha$")
# ax.set_ylabel(r"angle $\alpha$")
# ax.set_title(r"$\gamma = \ $"+str(gamma), fontsize=10)
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if Jumps:
# --- 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"angle $\alpha$")
# 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', zorder=2)
tmp = 0
else:
tmp = 1
# plt.plot([x_plotValues[0],x_plotValues[1]] ,[y_plotValues[0],y_plotValues[1]] )
# plt.plot([x_plotValues[2],x_plotValues[3]] ,[y_plotValues[2],y_plotValues[3]] )
# plt.plot([x_plotValues[4],x_plotValues[5]] ,[y_plotValues[4],y_plotValues[5]] )
# plt.plot([x_plotValues[6],x_plotValues[7]] ,[y_plotValues[6],y_plotValues[7]] )
for x in jump_xValues:
plt.axvline(x,ymin=0, ymax= 1, color = 'orange',alpha=0.5, linestyle = 'dashed', linewidth=1, zorder=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")
# ---- ADD additional scatter:
# ax.scatter(X_Values,Y_Values,s=1,c='black',zorder=4)
# 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 +0.011 , 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 +0.009 , 0+0.08, r"$3$", size=6, bbox=dict(boxstyle="circle",facecolor='white', alpha=1.0, pad=0.1, linewidth=0.5)
)
else:
# ax.scatter(X_Values,Y_Values,s=1, marker='o', cmap=None, norm=None, facecolor = 'blue',
# edgecolor = 'none', vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# ---------------------------------------------------------------
# l1 = ax.scatter(X_Values,Angle_alpha0,s=1, marker='o', edgecolor = 'black',cmap=None, norm=None, vmin=None, vmax=None, alpha=0.75, linewidths=None, zorder=4)
# l6 = ax.scatter(X_Values,Angle_alphaNeg1,s=2, marker='s', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=1, label=r"$\theta_\rho = -1.0$")
# l4 = ax.scatter(X_Values,Angle_alphaNeg05,s=1, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l3 = ax.scatter(X_Values,Angle_alphaNeg025,s=1, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l7 = ax.scatter(X_Values,Angle_alpha3,s=1, marker='o', facecolor = 'none',edgecolor = 'forestgreen', cmap=None, norm=None, vmin=None, vmax=None, alpha=1.0, linewidths=None, zorder=5)
# # l4 = ax.scatter(X_Values,Angle_alpha3,s=1, marker='o', markerfacecolor='red',markeredgecolor='black',markeredgewidth=2, cmap=None, norm=None, vmin=None, vmax=None, alpha=0.5, linewidths=None, zorder=3)
# l5 = ax.scatter(X_Values,Angle_alphaNeg075,s=1, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l2 = ax.scatter(X_Values,Angle_alphaNeg0125,s=1, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
#
# line_labels = [r"$\theta_\rho = -1.0$", r"$\theta_\rho = -0.5$", r"$\theta_\rho = -0.25$", r"$\theta_\rho = 3.0$"]
# ax.set_yticks([0, np.pi/8, np.pi/4, 3*np.pi/8 , np.pi/2, 5*np.pi/8 ])
# labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$',r'$5\pi/8$']
# ax.set_yticklabels(labels)
#
# ax.legend(handles=[l1,l2,l3,l4, l5, l6, l7],
# labels= [ r"$\theta_\rho = 0$", r"$\theta_\rho = -0.125$", r"$\theta_\rho = -0.25$", r"$\theta_\rho = -0.5$", r"$\theta_\rho = -0.75$", r"$\theta_\rho = -1.0$", r"$\theta_\rho = 3.0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
# ---------------------------------------------------------------
# l1 = ax.scatter(X_Values,Angle_alphaNeg1,s=2, marker='s', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=1)
# l2 = ax.scatter(X_Values,Angle_alphaNeg0875,s=2, marker='o',cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=4)
# l3 = ax.scatter(X_Values,Angle_alphaNeg075,s=2, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l4 = ax.scatter(X_Values,Angle_alphaNeg0625,s=2, marker='o',cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=4)
# l5 = ax.scatter(X_Values,Angle_alphaNeg05,s=2, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l6 = ax.scatter(X_Values,Angle_alphaNeg025,s=2, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l7 = ax.scatter(X_Values,Angle_alphaNeg0125,s=2, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# l8 = ax.scatter(X_Values,Angle_alpha0,s=2, marker='s', edgecolor = 'black', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=4)
# l1 = ax.plot(X_Values,Angle_alphaNeg05, color='blue', linewidth=1.5, zorder=3, label=r"$\theta_\rho=-0.5$")
# l2 = ax.plot(X_Values,Angle_alphaNeg055, linewidth=1.5, linestyle = '--', zorder=3,label=r"$\theta_\rho=-0.55$")
# l3 = ax.plot(X_Values,Angle_alphaNeg06,color='orangered', linewidth=1.5 ,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.6$")
# l4 = ax.plot(X_Values,Angle_alphaNeg065, linewidth=1.5 ,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.65$")
# l5 = ax.plot(X_Values,Angle_alphaNeg07,color='orange', linewidth=1.5 ,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.7$")
# l6 = ax.plot(X_Values,Angle_alphaNeg075, linewidth=1.5,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.75$")
# l7 = ax.plot(X_Values,Angle_alphaNeg08, linewidth=1.5,linestyle = '--' , zorder=3, label=r"$\theta_\rho=-0.8$")
# l8 = ax.plot(X_Values,Angle_alphaNeg085, linewidth=1.5,linestyle = '--' , zorder=3, label=r"$\theta_\rho=-0.85$")
# l9 = ax.plot(X_Values,Angle_alphaNeg09, color='teal',linestyle = '--', linewidth=1.5 , zorder=3, label=r"$\theta_\rho=-0.9$")
# l10 = ax.plot(X_Values,Angle_alphaNeg095, linewidth=1.5,linestyle = '--' , zorder=3, label=r"$\theta_\rho=-0.95$")
# l11 = ax.plot(X_Values,Angle_alphaNeg1, color='red', linewidth=1.5 ,zorder=1, label=r"$\theta_\rho=-1.0$")
# l1 = ax.plot(X_Values,Angle_Theta01, color='blue', linewidth=1.5, zorder=3, label=r"$\theta=0.1$")
# # l2 = ax.plot(X_Values,Angle_alphaNeg055, linewidth=1.5, linestyle = '--', zorder=3,label=r"$\theta_\rho=-0.55$")
# l3 = ax.plot(X_Values,Angle_Theta025,color='orangered', linewidth=1.5 ,zorder=3, label=r"$\theta = 0.25$")
# # l4 = ax.plot(X_Values,Angle_alphaNeg065, linewidth=1.5 ,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.65$")
# l5 = ax.plot(X_Values,Angle_Theta05,color='orange', linewidth=1.5 ,zorder=3, label=r"$\theta = 0.5$")
# # l6 = ax.plot(X_Values,Angle_alphaNeg075, linewidth=1.5,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.75$")
# l7 = ax.plot(X_Values,Angle_Theta075, linewidth=1.5 , zorder=3, label=r"$\theta = 0.75$")
# # l8 = ax.plot(X_Values,Angle_alphaNeg085, linewidth=1.5,linestyle = '--' , zorder=3, label=r"$\theta_\rho=-0.85$")
# l9 = ax.plot(X_Values,Angle_Theta09, color='teal', linewidth=1.5 , zorder=3, label=r"$\theta =0.9$")
# # l10 = ax.plot(X_Values,Angle_alphaNeg095, linewidth=1.5,linestyle = '--' , zorder=3, label=r"$\theta_\rho=-0.95$")
# l1 = ax.scatter(X_Values,Angle_Theta01, color='blue', s=2, zorder=3, label=r"$\theta=0.1$")
# l2 = ax.plot(X_Values,Angle_alphaNeg055, linewidth=1.5, linestyle = '--', zorder=3,label=r"$\theta_\rho=-0.55$")
# l3 = ax.scatter(X_Values,Angle_Theta025,color='orangered', s=2 ,zorder=3, label=r"$\theta = 0.25$")
# l4 = ax.plot(X_Values,Angle_alphaNeg065, linewidth=1.5 ,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.65$")
l5 = ax.scatter(X_Values,Angle_Theta05, color='royalblue', s=0.15 ,zorder=3, label=r"$\theta = 0.5$")
# l5 = ax.scatter(X_Values,Angle_Theta05, color='royalblue' ,zorder=3, label=r"$\theta = 0.5$")
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# l6 = ax.plot(X_Values,Angle_alphaNeg075, linewidth=1.5,linestyle = '--' ,zorder=3, label=r"$\theta_\rho=-0.75$")
# l7 = ax.scatter(X_Values,Angle_Theta075, s=2, zorder=3, label=r"$\theta = 0.75$")
# l8 = ax.plot(X_Values,Angle_alphaNeg085, linewidth=1.5,linestyle = '--' , zorder=3, label=r"$\theta_\rho=-0.85$")
# l9 = ax.scatter(X_Values,Angle_Theta09, color='teal',s=2, zorder=3, alpha=1.0, label=r"$\theta =0.9$")
# ax.legend(handles=[l1[0],l2[0],l3[0],l4[0], l5[0], l6[0], l7[0], l8[0], l9[0], l10[0], l11[0]],
# # labels= [r"$\theta_\rho = -1.0$", r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = -\frac{3}{4}$" , r"$\theta_\rho = - \frac{5}{8}$", r"$\theta_\rho = - \frac{1}{2} $" , r"$\theta_\rho = - \frac{1}{4}$", r"$\theta_\rho = - \frac{1}{8}$" , r"$\theta_\rho = 0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
# ax.legend(handles=[l1[0],l3[0], l5[0], l7[0], l9[0]] ,
# # labels= [r"$\theta_\rho = -1.0$", r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = -\frac{3}{4}$" , r"$\theta_\rho = - \frac{5}{8}$", r"$\theta_\rho = - \frac{1}{2} $" , r"$\theta_\rho = - \frac{1}{4}$", r"$\theta_\rho = - \frac{1}{8}$" , r"$\theta_\rho = 0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
# ax.legend(handles=[l1,l3, l5, l7, l9] ,
# # labels= [r"$\theta_\rho = -1.0$", r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = -\frac{3}{4}$" , r"$\theta_\rho = - \frac{5}{8}$", r"$\theta_\rho = - \frac{1}{2} $" , r"$\theta_\rho = - \frac{1}{4}$", r"$\theta_\rho = - \frac{1}{8}$" , r"$\theta_\rho = 0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
# ax.legend(handles=[l5] ,
# # labels= [r"$\theta_\rho = -1.0$", r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = -\frac{3}{4}$" , r"$\theta_\rho = - \frac{5}{8}$", r"$\theta_\rho = - \frac{1}{2} $" , r"$\theta_\rho = - \frac{1}{4}$", r"$\theta_\rho = - \frac{1}{8}$" , r"$\theta_\rho = 0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
# ax.plot(X_Values, Y_Values, marker='o', markerfacecolor='orange', markeredgecolor='black', markeredgewidth=1, linewidth=1, zorder=3)
# l7 = ax.scatter(X_Values,Angle_alpha3,s=1, marker='o', facecolor = 'none',edgecolor = 'forestgreen', cmap=None, norm=None, vmin=None, vmax=None, alpha=1.0, linewidths=None, zorder=5)
# l4 = ax.scatter(X_Values,Angle_alpha3,s=1, marker='o', markerfacecolor='red',markeredgecolor='black',markeredgewidth=2, cmap=None, norm=None, vmin=None, vmax=None, alpha=0.5, linewidths=None, zorder=3)
# l5 = ax.scatter(X_Values,Angle_alphaNeg075,s=1, marker='o', cmap=None, norm=None, vmin=None, vmax=None, alpha=None, linewidths=None, zorder=3)
# line_labels = [r"$\theta_\rho = -1.0$",r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = - \frac{3}{4}$", r"$\theta_\rho = - \frac{5}{8}$",r"$\theta_\rho = - 0.5 $" ,r"$\theta_\rho = - 0.25", r"$\theta_\rho = - \frac{1}{8}" , r"$\theta_\rho = 0$"]
ax.set_yticks([0, np.pi/8, np.pi/4, 3*np.pi/8 , np.pi/2, 5*np.pi/8 ])
labels = ['$0$',r'$\pi/8$', r'$\pi/4$' ,r'$3\pi/8$' , r'$\pi/2$',r'$5\pi/8$']
ax.set_yticklabels(labels)
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# ax.legend(handles=[l1,l2,l3,l4, l5, l6, l7, l8],
# labels= [r"$\theta_\rho = -1.0$", r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = -\frac{3}{4}$" , r"$\theta_\rho = - \frac{5}{8}$", r"$\theta_\rho = - \frac{1}{2} $" , r"$\theta_\rho = - \frac{1}{4}$", r"$\theta_\rho = - \frac{1}{8}$" , r"$\theta_\rho = 0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
#
# ax.legend(handles=[l1,l3, l5, l7, l8],
# labels= [r"$\theta_\rho = -1.0$", r"$\theta_\rho = - \frac{7}{8}$", r"$\theta_\rho = -\frac{3}{4}$" , r"$\theta_\rho = - \frac{5}{8}$", r"$\theta_\rho = - \frac{1}{2} $" , r"$\theta_\rho = - \frac{1}{4}$", r"$\theta_\rho = - \frac{1}{8}$" , r"$\theta_\rho = 0$"],
# loc='upper left',
# bbox_to_anchor=(1,1))
#
# fig.legend([l1, l2, l3, l4], # The line objects
# labels=line_labels, # The labels for each line
# # loc="upper center", # Position of legend
# loc='upperleft', bbox_to_anchor=(1,1),
# borderaxespad=0.15 # Small spacing around legend box
# # title="Legend Title" # Title for the legend
# )
pdf_outputName = 'Plot-Angle-Alpha_Gamma'+ str(gamma)+ '_transition'+'.pdf'
fig.set_size_inches(width, height)
# fig.savefig('Plot-Angle-Theta.pdf')
fig.savefig(pdf_outputName)
# tikz_save('someplot.tex', figureheight='5cm', figurewidth='9cm')
# tikz_save('fig.tikz',
# figureheight = '\\figureheight',
# figurewidth = '\\figurewidth')
# ----------------------------------------
# plt.show()
# #---------------------------------------------------------------