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Klaus Böhnlein
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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
import time
# from ClassifyMin import *
from ClassifyMin_New import *
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# from scipy.io import loadmat #not Needed anymore?
import codecs
import sys
def ReadEffectiveQuantities(QFilePath = os.path.dirname(os.getcwd()) + '/outputs/QMatrix.txt', BFilePath = os.path.dirname(os.getcwd())+ '/outputs/BMatrix.txt'):
# Read Output Matrices (effective quantities)
# From Cell-Problem output Files : ../outputs/Qmatrix.txt , ../outputs/Bmatrix.txt
# -- Read Matrix Qhom
X = []
# with codecs.open(path + '/outputs/QMatrix.txt', encoding='utf-8-sig') as f:
with codecs.open(QFilePath, encoding='utf-8-sig') as f:
for line in f:
s = line.split()
X.append([float(s[i]) for i in range(len(s))])
Q = np.array([[X[0][2], X[1][2], X[2][2]],
[X[3][2], X[4][2], X[5][2]],
[X[6][2], X[7][2], X[8][2]] ])
# -- Read Beff (as Vector)
X = []
# with codecs.open(path + '/outputs/BMatrix.txt', encoding='utf-8-sig') as f:
with codecs.open(BFilePath, encoding='utf-8-sig') as f:
for line in f:
s = line.split()
X.append([float(s[i]) for i in range(len(s))])
B = np.array([X[0][2], X[1][2], X[2][2]])
return Q, B
def SetParametersCellProblem(alpha,beta,theta,gamma,mu1,rho1,lambda1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset"):
with open(InputFilePath, 'r') as file:
filedata = file.read()
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)^gamma=.*','gamma='+str(gamma),filedata)
filedata = re.sub('(?m)^mu1=.*','mu1='+str(mu1),filedata)
filedata = re.sub('(?m)^rho1=.*','rho1='+str(rho1),filedata)
filedata = re.sub('(?m)^lambda1=.*','lambda1='+str(lambda1),filedata)
f = open(InputFilePath,'w')
f.write(filedata)
f.close()
#TODO combine these...
def SetParametersComputeMuGamma(beta,theta,gamma,mu1,rho1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset"):
with open(InputFilePath, 'r') as file:
filedata = file.read()
filedata = re.sub('(?m)^beta=.*','beta='+str(beta),filedata)
filedata = re.sub('(?m)^theta=.*','theta='+str(theta),filedata)
filedata = re.sub('(?m)^gamma=.*','gamma='+str(gamma),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()
def RunCellProblem(alpha,beta,theta,gamma,mu1,rho1,lambda1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset"):
# 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()
SetParametersCellProblem(alpha,beta,theta,gamma,mu1,rho1,lambda1, InputFilePath)
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# --- Run Cell-Problem
# Optional: Check Time
# t = time.time()
subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
capture_output=True, text=True)
# print('elapsed time:', time.time() - t)
# --------------------------------------------------------------------------------------
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def GetCellOutput(alpha,beta,theta,gamma,mu1,rho1,lambda1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset",
OutputFilePath = os.path.dirname(os.getcwd()) + "/outputs/outputMuGamma.txt" ):
RunCellProblem(alpha,beta,theta,gamma,mu1,rho1,lambda1, InputFilePath)
print('Read effective quantities...')
Q, B = ReadEffectiveQuantities()
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# print('Q:', Q)
# print('B:', B)
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':
mu_gamma = (1.0/6.0)*arithmeticMean(mu1, beta, theta) # = q2
# print('extreme regime: gamma = infinity')
mu_gamma = (1.0/6.0)*harmonicMean(mu1, beta, theta) # = q1
else:
# --- Scenario 1.2: compute mu_gamma with 'Compute_MuGamma' (much faster than running full Cell-Problem)
# print("Run computeMuGamma for Gamma = ", gamma)
SetParametersComputeMuGamma(beta,theta,gamma,mu1,rho1, InputFilePath)
# 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()
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# --- 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
def Compare_Classification(alpha,beta,theta,gamma,mu1,rho1,lambda1, InputFilePath = os.path.dirname(os.getcwd()) +"/inputs/computeMuGamma.parset"):
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# ---------------------------------------------------------------
# Comparison of the analytical Classification 'ClassifyMin'
# and the symbolic Minimizatio + Classification 'symMinimization'
# ----------------------------------------------------------------
comparison_successful = True
eps = 1e-8
# 1. Substitute Input-Parameters for the Cell-Problem
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)
filedata = re.sub('(?m)^lambda1=.*','lambda1='+str(lambda1),filedata)
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f = open(InputFilePath,'w')
f.write(filedata)
f.close()
# 2. --- Run Cell-Problem
print('Run Cell-Problem ...')
# Optional: Check Time
# t = time.time()
subprocess.run(['./build-cmake/src/Cell-Problem', './inputs/cellsolver.parset'],
capture_output=True, text=True)
# 3. --- Run Matlab symbolic minimization program: 'symMinimization'
eng = matlab.engine.start_matlab()
# s = eng.genpath(path + '/Matlab-Programs')
s = eng.genpath(os.path.dirname(os.getcwd()))
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eng.addpath(s, nargout=0)
# print('current Matlab folder:', eng.pwd(nargout=1))
eng.cd('Matlab-Programs', nargout=0) #switch to Matlab-Programs folder
# print('current Matlab folder:', eng.pwd(nargout=1))
Inp = False
print('Run symbolic Minimization...')
G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp, nargout=4) #Name of program:symMinimization
# G, angle, type, kappa = eng.symMinimization(Inp,Inp,Inp,Inp,path + "/outputs", nargout=4) #Optional: add Path
G = np.asarray(G) #cast Matlab Outout to numpy array
# --- print Output ---
print('Minimizer G:')
print(G)
print('angle:', angle)
print('type:', type )
print('curvature:', kappa)
# 4. --- Read the effective quantities (output values of the Cell-Problem)
# Read Output Matrices (effective quantities)
print('Read effective quantities...')
Q, B = ReadEffectiveQuantities()
print('Q:', Q)
print('B:', B)
q1 = Q[0][0]
q2 = Q[1][1]
q3 = Q[2][2]
q12 = Q[0][1]
b1 = B[0]
b2 = B[1]
b3 = B[2]
print("q1:", q1)
print("q2:", q2)
print("q3:", q3)
print("q12:", q12)
print("b1:", b1)
print("b2:", b2)
print("b3:", b3)
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# --- Check Assumptions:
# Assumption of Classification-Lemma1.6: [b3 == 0] & [Q orthotropic]
# Check if b3 is close to zero
assert (b3 < eps), "ClassifyMin only defined for b3 == 0 !"
# Check if Q is orthotropic i.e. q13 = q31 = q23 = q32 == 0
assert(Q[2][0] < eps and Q[0][2] < eps and Q[1][2] < eps and Q[2][1] < eps), "Q is not orthotropic !"
# 5. --- Get output from the analytical Classification 'ClassifyMin'
G_ana, angle_ana, type_ana, kappa_ana = classifyMin(q1, q2, q3, q12, b1, b2)
print('Minimizer G_ana:')
print(G_ana)
print('angle_ana:', angle_ana)
print('type_ana:', type_ana )
print('curvature_ana:', kappa_ana)
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# 6. Compare
# print('DifferenceMatrix:', G_ana - G )
# print('MinimizerError (FrobeniusNorm):', np.linalg.norm(G_ana - G , 'fro') )
if np.linalg.norm(G_ana - G , 'fro') > eps :
comparison_successful = False
print('Difference between Minimizers is too large !')
if type != type_ana :
comparison_successful = False
print('Difference in type !')
if abs(angle-angle_ana) > eps :
comparison_successful = False
print('Difference in angle is too large!')
if abs(kappa-kappa_ana) > eps :
comparison_successful = False
print('Difference in curvature is too large!')
if comparison_successful:
print('Comparison successful')
else:
print('Comparison unsuccessful')
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return comparison_successful
# ----------------------------------------------------------------------------------------------------------------------------