PhaseDiagram_backup.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
# print(sys.executable)

# --------------------------------------------------------------------
# START :
# INPUT (Parameters):   alpha, beta, theta, gamma, mu1, rho1
#
# -Option 1 : (Case lambda = 0 => q12 = 0)
#   compute q1,q2,b1,b2 from Formula
#       Option 1.1 :
#           set mu_gamma = 'q1' or 'q2' (extreme regimes: gamma \in {0,\infty})
#       Option 1.2 :
#           compute mu_gamma with 'Compute_MuGamma' (2D problem much faster then Cell-Problem)
# -Option 2 :
#   compute Q_hom & B_eff by running 'Cell-Problem'
#
# -> CLASSIFY ...
#
# OUTPUT: Minimizer G, angle , type, curvature
# -----------------------------------------------------------------------
#
#
# def GetMuGamma(beta,theta,gamma,mu1,rho1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset",
#                 OutputFilePath = os.path.dirname(os.getcwd()) + "/outputs/outputMuGamma.txt" ):
#     # ------------------------------------ get mu_gamma ------------------------------
#     # ---Scenario 1.1: extreme regimes
#     if gamma == '0':
#         print('extreme regime: gamma = 0')
#         mu_gamma = (1.0/6.0)*arithmeticMean(mu1, beta, theta) # = q2
#         print("mu_gamma:", mu_gamma)
#     elif gamma == 'infinity':
#         print('extreme regime: gamma = infinity')
#         mu_gamma = (1.0/6.0)*harmonicMean(mu1, beta, theta)   # = q1
#         print("mu_gamma:", mu_gamma)
#     else:
#         # --- Scenario 1.2:  compute mu_gamma with 'Compute_MuGamma' (much faster than running full Cell-Problem)
#         # print("Run computeMuGamma for Gamma = ", gamma)
#         with open(InputFilePath, 'r') as file:
#             filedata = file.read()
#         filedata = re.sub('(?m)^gamma=.*','gamma='+str(gamma),filedata)
#         # filedata = re.sub('(?m)^alpha=.*','alpha='+str(alpha),filedata)
#         filedata = re.sub('(?m)^beta=.*','beta='+str(beta),filedata)
#         filedata = re.sub('(?m)^theta=.*','theta='+str(theta),filedata)
#         filedata = re.sub('(?m)^mu1=.*','mu1='+str(mu1),filedata)
#         filedata = re.sub('(?m)^rho1=.*','rho1='+str(rho1),filedata)
#         f = open(InputFilePath,'w')
#         f.write(filedata)
#         f.close()
#         # --- Run Cell-Problem
#
#         # Check Time
#         # t = time.time()
#         # subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
#         #                                      capture_output=True, text=True)
#         # --- Run Cell-Problem_muGama   -> faster
#         # subprocess.run(['./build-cmake/src/Cell-Problem_muGamma', './inputs/cellsolver.parset'],
#         #                                              capture_output=True, text=True)
#         # --- Run Compute_muGamma (2D Problem much much faster)
#
#         subprocess.run(['./build-cmake/src/Compute_MuGamma', './inputs/computeMuGamma.parset'],
#                                                              capture_output=True, text=True)
#         # print('elapsed time:', time.time() - t)
#
#         #Extract mu_gamma from Output-File                                           TODO: GENERALIZED THIS FOR QUANTITIES OF INTEREST
#         with open(OutputFilePath, 'r') as file:
#             output = file.read()
#         tmp = re.search(r'(?m)^mu_gamma=.*',output).group()                           # Not necessary for Intention of Program t output Minimizer etc.....
#         s = re.findall(r"[-+]?\d*\.\d+|\d+", tmp)
#         mu_gamma = float(s[0])
#         # print("mu_gamma:", mu_gammaValue)
#     # --------------------------------------------------------------------------------------
#     return mu_gamma
#



# ----------- SETUP PATHS
# InputFile  = "/inputs/cellsolver.parset"
# OutputFile = "/outputs/output.txt"
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)


# -------------------------- Input Parameters --------------------
# mu1 = 10.0               # TODO : here must be the same values as in the Parset for computeMuGamma
mu1 = 1.0
rho1 = 1.0
alpha = 2.0
beta = 2.0
beta = 10.0
theta = 1.0/4.0
#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
gamma = '0'
gamma = 'infinity'
# gamma = 0.5
# gamma = 0.25
# gamma = 1.0

# gamma = 5.0

#added
# lambda1 = 10.0
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('----------------------------')
# ----------------------------------------------------------------

#
# gamma_min = 0.5
# gamma_max = 1.0
#
# # gamma_min = 1
# # gamma_max = 1
# Gamma_Values = np.linspace(gamma_min, gamma_max, num=3)
# # #
# # # Gamma_Values = np.linspace(gamma_min, gamma_max, num=13)    # TODO variable Input Parameters...alpha,beta...
# print('(Input) Gamma_Values:', Gamma_Values)
# # #
# for gamma in Gamma_Values:


    # muGamma = GetMuGamma(beta,theta,gamma,mu1,rho1,InputFilePath)
    # # muGamma = GetMuGamma(beta,theta,gamma,mu1,rho1)
    # print('Test MuGamma:', muGamma)

    # ------- Options --------
    # print_Cases = True
    # print_Output = True

                        #TODO
# generalCase = True #Read Output from Cell-Problem instead of using Lemma1.4 (special case)
generalCase = False

# make_3D_plot = True
make_3D_PhaseDiagram = True
make_2D_plot = False
make_2D_PhaseDiagram = False
make_3D_plot = False
# make_3D_PhaseDiagram = False
# make_2D_plot = True
# make_2D_PhaseDiagram = True
#

# --- Define effective quantities: q1, q2 , q3 = mu_gamma, q12 ---
# q1 = harmonicMean(mu1, beta, theta)
# q2 = arithmeticMean(mu1, beta, theta)
# --- Set q12
# q12 = 0.0  # (analytical example)              # TEST / TODO read from Cell-Output





# b1 = prestrain_b1(rho1, beta, alpha, theta)
# b2 = prestrain_b2(rho1, beta, alpha, theta)
#
# print('---- Input parameters: -----')
# print('mu1: ', mu1)
# print('rho1: ', rho1)
# print('alpha: ', alpha)
# print('beta: ', beta)
# print('theta: ', theta)
# print("q1: ", q1)
# print("q2: ", q2)
# print("mu_gamma: ", mu_gamma)
# print("q12: ", q12)
# print("b1: ", b1)
# print("b2: ", b2)
# print('----------------------------')
# print("machine epsilon", sys.float_info.epsilon)

# G, angle, type, kappa = classifyMin(q1, q2, mu_gamma, q12,  b1, b2, print_Cases, print_Output)
# Test = f(1,2 ,q1,q2,mu_gamma,q12,b1,b2)
# print("Test", Test)

# ---------------------- MAKE PLOT / Write to VTK------------------------------------------------------------------------------

# SamplePoints_3D = 10 # Number of sample points in each direction
# SamplePoints_2D = 10 # Number of sample points in each direction
SamplePoints_3D = 300 # Number of sample points in each direction
# SamplePoints_3D = 150 # Number of sample points in each direction
# SamplePoints_3D = 100 # Number of sample points in each direction
# SamplePoints_3D = 200 # Number of sample points in each direction
# SamplePoints_3D = 400 # Number of sample points in each direction
# SamplePoints_2D = 7500 # Number of sample points in each direction
SamplePoints_2D = 4000 # 4000 # Number of sample points in each direction


if make_3D_PhaseDiagram:
    alphas_ = np.linspace(-20, 20, SamplePoints_3D)
    # alphas_ = np.linspace(-10, 10, SamplePoints_3D)

    # betas_  = np.linspace(0.01,40.01,SamplePoints_3D) # Full Range
    # betas_  = np.linspace(0.01,20.01,SamplePoints_3D) # FULL Range



    # betas_  = np.linspace(0.01,1.0,SamplePoints_3D)  # weird part
    betas_  = np.linspace(1.01,40.01,SamplePoints_3D)     #TEST !!!!!  For Beta <1 weird tings happen...
    thetas_ = np.linspace(0.01,0.99,SamplePoints_3D)


    # TEST
    # alphas_ = np.linspace(-2, 2, SamplePoints_3D)
    # betas_  = np.linspace(1.01,10.01,SamplePoints_3D)
    # print('betas:', betas_)

    # TEST :
    # alphas_ = np.linspace(-40, 40, SamplePoints_3D)
    # betas_  = np.linspace(0.01,80.01,SamplePoints_3D) # Full Range

    # print('type of alphas', type(alphas_))
    # print('Test:', type(np.array([mu_gamma])) )
    alphas, betas, thetas = np.meshgrid(alphas_, betas_, thetas_, indexing='ij')
    classifyMin_anaVec = np.vectorize(classifyMin_ana)

    # Get MuGamma values ...
    GetMuGammaVec = np.vectorize(GetMuGamma)
    muGammas = GetMuGammaVec(betas, thetas, gamma, mu1, rho1)
    # Classify Minimizers....
    G, angles, Types, curvature = classifyMin_anaVec(alphas, betas, thetas, muGammas,  mu1, rho1)   # Sets q12 to zero!!!

    # G, angles, Types, curvature = classifyMin_anaVec(alphas, betas, thetas, muGammas,  mu1, rho1, True, True)
    # print('size of G:', G.shape)
    # print('G:', G)

    # Option to print angles
    # print('angles:', angles)


    # Out = classifyMin_anaVec(alphas,betas,thetas)
    # T = Out[2]
    # --- Write to VTK

    GammaString = str(gamma)
    VTKOutputName = "outputs/PhaseDiagram3D" + "Gamma" + GammaString
    gridToVTK(VTKOutputName , alphas, betas, thetas, pointData = {'Type': Types, 'angles': angles, 'curvature': curvature} )
    print('Written to VTK-File:', VTKOutputName )

if make_2D_PhaseDiagram:
    # alphas_ = np.linspace(-20, 20, SamplePoints_2D)
    # alphas_ = np.linspace(0, 1, SamplePoints_2D)
    thetas_ = np.linspace(0.01,0.99,SamplePoints_2D)
    alphas_ = np.linspace(-5, 5, SamplePoints_2D)
    # alphas_ = np.linspace(-5, 15, SamplePoints_2D)
    # thetas_ = np.linspace(0.05,0.25,SamplePoints_2D)


    # good range:
    # alphas_ = np.linspace(9, 10, SamplePoints_2D)
    # thetas_ = np.linspace(0.075,0.14,SamplePoints_2D)

    # range used:
    # alphas_ = np.linspace(8, 10, SamplePoints_2D)
    # thetas_ = np.linspace(0.05,0.16,SamplePoints_2D)

        # alphas_ = np.linspace(8, 12, SamplePoints_2D)
        # thetas_ = np.linspace(0.05,0.2,SamplePoints_2D)
    # betas_  = np.linspace(0.01,40.01,1)
    #fix to one value:
    # betas_ = 2.0;
    betas_ = 10.0;

    # TEST
    # alphas_ = np.linspace(-8, 8, SamplePoints_2D)
    # thetas_ = np.linspace(0.01,0.99,SamplePoints_2D)
    # betas_ = 1.0; #TEST Problem: disvison by zero if alpha = 9, theta = 0.1 !
    # betas_ = 0.9;
    # betas_ = 0.5;  #TEST!!!
    alphas, betas, thetas = np.meshgrid(alphas_, betas_, thetas_, indexing='ij')


    if generalCase:
        classifyMin_matVec = np.vectorize(classifyMin_mat)
        GetCellOutputVec = np.vectorize(GetCellOutput, otypes=[np.ndarray, np.ndarray])
        Q, B = GetCellOutputVec(alphas,betas,thetas,gamma,mu1,rho1,lambda1, InputFilePath ,OutputFilePath )


        # print('type of Q:', type(Q))
        # print('Q:', Q)
        G, angles, Types, curvature = classifyMin_matVec(Q,B)

    else:
        classifyMin_anaVec = np.vectorize(classifyMin_ana)
        GetMuGammaVec = np.vectorize(GetMuGamma)
        muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
        G, angles, Types, curvature = classifyMin_anaVec(alphas,betas,thetas, muGammas,  mu1, rho1)    # Sets q12 to zero!!!
        # print('size of G:', G.shape)
        # print('G:', G)
        # print('Types:', Types)
        # Out = classifyMin_anaVec(alphas,betas,thetas)
        # T = Out[2]
        # --- Write to VTK
        # VTKOutputName = + path + "./PhaseDiagram2DNEW"


    GammaString = str(gamma)
    VTKOutputName = "outputs/PhaseDiagram2D" + "Gamma_" + GammaString
    gridToVTK(VTKOutputName , alphas, betas, thetas, pointData = {'Type': Types, 'angles': angles, 'curvature': curvature} )
    print('Written to VTK-File:', VTKOutputName )


# --- Make 3D Scatter plot
if(make_3D_plot or make_2D_plot):
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    colors = cm.plasma(Types)
    # if make_2D_plot: pnt3d=ax.scatter(alphas,thetas,c=Types.flat)
    # if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=Types.flat)
    if make_2D_plot: pnt3d=ax.scatter(alphas,thetas,c=angles.flat)
    if make_3D_plot: pnt3d=ax.scatter(alphas,betas,thetas,c=angles.flat)
    # cbar=plt.colorbar(pnt3d)
    # cbar.set_label("Values (units)")
    plt.axvline(x = 8, color = 'b', linestyle = ':', label='$q_1$')
    plt.axhline(y = 0.083333333, color = 'b', linestyle = ':', label='$q_1$')

    ax.set_xlabel('alpha')
    ax.set_ylabel('beta')
    if make_3D_plot: ax.set_zlabel('theta')
    plt.show()
    # plt.savefig('common_labels.png', dpi=300)
    # print('T:', T)
    # print('Type 1 occured here:', np.where(T == 1))
    # print('Type 2 occured here:', np.where(T == 2))


    # print(alphas_)
    # print(betas_)





# ALTERNATIVE
# colors = ("red", "green", "blue")
# groups = ("Type 1", "Type2", "Type3")
#
# # Create plot
# fig = plt.figure()
# ax = fig.add_subplot(1, 1, 1)
#
# for data, color, group in zip(Types, colors, groups):
#     # x, y = data
#     ax.scatter(alphas, thetas, alpha=0.8, c=color, edgecolors='none', label=group)
#
# plt.title('Matplot scatter plot')
# plt.legend(loc=2)
# plt.show()