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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 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
import seaborn as sns
import matplotlib.colors as mcolors
# from matplotlib import rc
# rc('text', usetex=True) # Use LaTeX font
#
# import seaborn as sns
# sns.set(color_codes=True)
# set the colormap and centre the colorbar
class MidpointNormalize(mcolors.Normalize):
"""
Normalise the colorbar so that diverging bars work there way either side from a prescribed midpoint value)
e.g. im=ax1.imshow(array, norm=MidpointNormalize(midpoint=0.,vmin=-100, vmax=100))
"""
def __init__(self, vmin=None, vmax=None, midpoint=None, clip=False):
self.midpoint = midpoint
mcolors.Normalize.__init__(self, vmin, vmax, clip)
def __call__(self, value, clip=None):
# I'm ignoring masked values and all kinds of edge cases to make a
# simple example...
x, y = [self.vmin, self.midpoint, self.vmax], [0, 0.5, 1]
return np.ma.masked_array(np.interp(value, x, y), np.isnan(value))
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
def energy(a1,a2,q1,q2,q12,q3,b1,b2):
a = np.array([a1,a2])
b = np.array([b1,b2])
H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
tmp = H.dot(a)
# print('H',H)
# print('A',A)
# print('b',b)
# print('a',a)
# print('tmp',tmp)
tmp = (1/2)*a.dot(tmp)
# print('tmp',tmp)
tmp2 = A.dot(b)
# print('tmp2',tmp2)
tmp2 = 2*a.dot(tmp2)
# print('tmp2',tmp2)
energy = tmp - tmp2
# print('energy',energy)
# energy_axial1.append(energy_1)
return energy
# def energy(a1,a2,q1,q2,q12,q3,b1,b2):
#
#
# b = np.array([b1,b2])
# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
#
#
# tmp = H.dot(a)
#
# print('H',H)
# print('A',A)
# print('b',b)
# print('a',a)
# print('tmp',tmp)
#
# tmp = (1/2)*a.dot(tmp)
# print('tmp',tmp)
#
# tmp2 = A.dot(b)
# print('tmp2',tmp2)
# tmp2 = 2*a.dot(tmp2)
#
# print('tmp2',tmp2)
# energy = tmp - tmp2
# print('energy',energy)
#
#
# # energy_axial1.append(energy_1)
#
# return energy
#
################################################################################################################
################################################################################################################
################################################################################################################
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)
# -------------------------- Input Parameters --------------------
mu1 = 1.0
rho1 = 1.0
alpha = 5.0
theta = 1.0/2
# theta= 0.1
beta = 5.0
# mu1 = 1.0
# rho1 = 1.0
# alpha = 2.0
# theta = 1.0/2
# # theta= 0.1
# beta = 5.0
#Figure3:
# mu1 = 1.0
# rho1 = 1.0
# alpha = 2.0
# theta = 1.0/8
# # theta= 0.1
# beta = 2.0
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#set gamma either to 1. '0' 2. 'infinity' or 3. a numerical positive value
gamma = '0'
gamma = 'infinity'
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('----------------------------')
# ----------------------------------------------------------------
print('----------------------------')
# ----------------------------------------------------------------
q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta)
q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta)
q12 = 0.0
q3 = GetMuGamma(beta, theta,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
b1 = prestrain_b1(rho1,beta, alpha, theta )
b2 = prestrain_b2(rho1,beta, alpha, theta )
# 1-ParameterFamilyCase:
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)
b1=b[0]
b2=b[1]
print('q1 = ', q1)
print('q2 = ', q2)
print('q3 = ', q3)
print('q12 = ', q12)
print('b1 = ', b1)
print('b2 = ', b2)
num_Points = 400
# Creating dataset
x = np.linspace(-5,5,num_Points)
y = np.linspace(-5,5,num_Points)
x = np.linspace(-20,20,num_Points)
y = np.linspace(-20,20,num_Points)
# x = np.linspace(-10,10,num_Points)
# y = np.linspace(-10,10,num_Points)
# x = np.linspace(-60,60,num_Points)
# y = np.linspace(-60,60,num_Points)
#
#
# x = np.linspace(-40,40,num_Points)
# y = np.linspace(-40,40,num_Points)
geyser = sns.load_dataset("geyser")
print('type of geyser:', type(geyser))
print('geyser:',geyser)
ContourRange=20
x_in = np.linspace(-ContourRange,ContourRange,num_Points)
y_in = np.linspace(-ContourRange,ContourRange,num_Points)
a1_in, a2_in = np.meshgrid(x_in,y_in)
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print('a1:', a1)
print('a2:',a2 )
print('a1.shape', a1.shape)
#-- FILTER OUT VALUES for G+ :
# tmp1 = a1[np.where(a1*a2 >= 0)]
# tmp2 = a2[np.where(a1*a2 >= 0)]
# np.take(a, np.where(a>100)[0], axis=0)
# tmp1 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
# tmp2 = np.take(a1, np.where(a1*a2 >= 0)[0], axis=0)
# tmp2 = a2[np.where(a1*a2 >= 0)]
# tmp1 = a1[a1*a2 >= 0]
# tmp2 = a2[a1*a2 >= 0]
# tmp1_pos = a1[np.where(a1*a2 >= 0) ]
# tmp2_pos = a2[np.where(a1*a2 >= 0) ]
# tmp1_pos = tmp1_pos[np.where(tmp1_pos >= 0)]
# tmp2_pos = tmp2_pos[np.where(tmp2_pos >= 0)]
# tmp1_neg = a1[a1*a2 >= 0 ]
# tmp2_neg = a2[a1*a2 >= 0 ]
# tmp1_neg = tmp1_neg[tmp1_neg < 0]
# tmp2_neg = tmp2_neg[tmp2_neg < 0]
# a1 = tmp1
# a2 = tmp2
#
# a1 = a1.reshape(-1,5)
# a2 = a2.reshape(-1,5)
# tmp1_pos = tmp1_pos.reshape(-1,5)
# tmp2_pos = tmp2_pos.reshape(-1,5)
# tmp1_neg = tmp1_neg.reshape(-1,5)
# tmp2_neg = tmp2_neg.reshape(-1,5)
print('a1:', a1)
print('a2:',a2 )
print('a1.shape', a1.shape)
energyVec = np.vectorize(energy)
# Z = energyVec(np.array([a1,a2]),q1,q2,q12,q3,b1,b2)
Z = energyVec(a1,a2,q1,q2,q12,q3,b1,b2)
Z_in = energyVec(a1_in,a2_in,q1,q2,q12,q3,b1,b2)
print('Z:', Z)
print('any', np.any(Z<0))
#
# negZ_a1 = a1[np.where(Z<0)]
# negZ_a2 = a2[np.where(Z<0)]
# negativeValues = Z[np.where(Z<0)]
# print('negativeValues:',negativeValues)
#
# print('negZ_a1',negZ_a1)
# print('negZ_a2',negZ_a2)
#
#
# negZ_a1 = negZ_a1.reshape(-1,5)
# negZ_a2 = negZ_a2.reshape(-1,5)
# negativeValues = negativeValues.reshape(-1,5)
#
# Z_pos = energyVec(tmp1_pos,tmp2_pos,q1,q2,q12,q3,b1,b2)
# Z_neg = energyVec(tmp1_neg,tmp2_neg,q1,q2,q12,q3,b1,b2)
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# print('Test energy:' , energy(np.array([1,1]),q1,q2,q12,q3,b1,b2))
# print('Z_pos.shape', Z_pos.shape)
## -- PLOT :
mpl.rcParams['text.usetex'] = True
mpl.rcParams["font.family"] = "serif"
mpl.rcParams["font.size"] = "9"
label_size = 8
mpl.rcParams['xtick.labelsize'] = label_size
mpl.rcParams['ytick.labelsize'] = label_size
# plt.style.use('seaborn')
plt.style.use('seaborn-whitegrid')
# sns.set()
# plt.style.use('seaborn-whitegrid')
label_size = 9
mpl.rcParams['xtick.labelsize'] = label_size
mpl.rcParams['ytick.labelsize'] = label_size
width = 6.28 *0.5
# width = 6.28
height = width / 1.618
fig = plt.figure()
# ax = plt.axes(projection ='3d', adjustable='box')
ax = plt.axes((0.17,0.21 ,0.75,0.75))
# ax = plt.axes((0.15,0.18,0.8,0.8))
# 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)
# colorfunction=(B*kappa)
# print('colofunction',colorfunction)
#translate Data
# Z = Z - (Z.max()-Z.min())/2
# Z = Z - 50
# Z = Z - 500
#
# Z = Z.T
# Substract constant:
c = (b1**2)*q1+b1*b2*q12+(b2**2)*q2
Z = Z-c
print('Value of c:', c)
print('Z.min()', Z.min())
print('Z.max()', Z.max())
norm=mcolors.Normalize(Z.min(),Z.max())
# facecolors=cm.brg(norm)
print('norm:', norm)
print('type of norm', type(norm))
print('norm(0):', norm(0))
print('norm(Z):', norm(Z))
# ax.plot(theta_rho, theta_values, 'royalblue', zorder=3, )
# ax.scatter(a1,a2, s=0.5)
# ax.scatter(tmp1_pos,tmp2_pos, s=0.5)
# ax.scatter(tmp1_neg,tmp2_neg, s=0.5)
# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=100 )
# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, levels=20 )
# sns.kdeplot(np.array([a1, a2, Z]))
# sns.kdeplot(tmp1_pos,tmp2_pos,Z_pos)
# levels = [-5.0, -4, -3, 0.0, 1.5, 2.5, 3.5]
# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, corner_mask=True,levels=levels)
# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot(norm(Z)), corner_mask=True)
# CS = ax.contour(a1, a2, Z, cm.brg(norm(Z)), levels=20)
# CS = ax.contour(a1, a2, Z, cmap=plt.cm.gnuplot, levels=20)
# CS = ax.contour(a1, a2, Z, colors='k', levels=14, linewidths=(0.5,))
# CS = ax.contour(a1, a2, Z, colors='k', levels=18, linewidths=(0.5,))
# ax.contour(negZ_a1, negZ_a2, negativeValues, colors='k', linewidths=(0.5,))
CS = ax.contour(a1_in, a2_in, Z_in, colors='k', linewidths=(0.5,))
# df = pd.DataFrame(data=Z_in, columns=a1_in, index=a2_in)
# df2 = pd.DataFrame(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]),
# columns=['a', 'b', 'c'])
# sns.kdeplot(data=df2, x="waiting", y="duration")
# sns.kdeplot(data=df2)
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# CS = ax.contour(a1, a2, Z, colors='k', linewidths=(0.5,))
# CS = ax.contour(a1, a2, Z,10, cmap=plt.cm.gnuplot, extend='both', levels=50)
# CS = ax.contourf(a1, a2, Z,10, colors='k', extend='both', levels=50)
# CS = ax.contourf(a1, a2, Z,10, colors='k')
#
# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, levels=10 )
# # CS = ax.contour(tmp1_pos,tmp2_pos, Z_pos,10, cmap=plt.cm.gnuplot, corner_mask=True)
#
# CS = ax.contour(a1, a2, Z,10, colors = 'k')
ax.clabel(CS, inline=True, fontsize=4)
# cmap = cm.brg(norm(Z))
#
# C_map = cm.inferno(norm(Z))
# ax.imshow(Z, cmap=C_map, extent=[-20, 20, -20, 20], origin='lower', alpha=0.5)
# ax.imshow(norm(Z), extent=[-20, 20, -20, 20], origin='lower',
# cmap='bwr', alpha=0.8)
# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', vmin=Z.min(), vmax=Z.max(),
# cmap='bwr', alpha=0.6)
# ax.imshow(norm(Z), extent=[-20, 20, -20, 20],origin='lower', norm = norm,
# cmap='coolwarm', alpha=0.6)
cmap=mpl.cm.RdBu_r
# cmap=mpl.cm.viridis_r
cmap=mpl.cm.bwr
# cmap=mpl.cm.coolwarm
cmap=mpl.cm.gnuplot
# cmap = cm.brg(Z)
divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower', norm = norm,
# cmap='coolwarm', alpha=0.6)
# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
# cmap='coolwarm', alpha=0.6)
# ax.imshow(Z, extent=[-20, 20, -20, 20],origin='lower',
# cmap=cmap, alpha=0.6)
# divnorm=mcolors.TwoSlopeNorm(vmin=Z.min(), vcenter=0., vmax=Z.max())
# plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower',
# cmap=cmap, alpha=0.6)
plt.imshow(Z, extent=[x.min(), x.max(), y.min(), y.max()],origin='lower', norm = divnorm,
cmap=cmap, alpha=0.6)
# COLORBAR :
# cbar = plt.colorbar()
# cbar.ax.tick_params(labelsize=8)
##----- ADD RECTANGLE TO COVER QUADRANT :
epsilon = 0.4
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# ax.axvspan(0, x.max(), y.min(), 0, alpha=1, color='yellow', zorder=5)#yellow
# ax.fill_between([0, x.max()], y.min(), 0, alpha=0.3, color='yellow', zorder=5)#yellow
# ax.fill_between([x.min(), 0], 0, y.max(), alpha=0.3, color='yellow', zorder=5)#yellow
ax.fill_between([0+epsilon, x.max()], y.min(), 0-epsilon, alpha=0.7, color='gray', zorder=5)#yellow
ax.fill_between([x.min(), 0-epsilon], 0+epsilon, y.max(), alpha=0.7, color='gray', zorder=5)#yellow
# ax.plot_surface(a1,a2, Z, cmap=cm.coolwarm,
# linewidth=0, antialiased=False)
# ax.plot(theta_rho, energy_axial1, 'royalblue', zorder=3, label=r"axialMin1")
# ax.plot(theta_rho, energy_axial2, 'forestgreen', zorder=3, label=r"axialMin2")
# ax.plot(-1.0*alphas, kappas, 'red', zorder=3, )
# lg = ax.legend(bbox_to_anchor=(0.0, 0.75), loc='upper left')
### PLot x and y- Axes
ax.plot(ax.get_xlim(),[0,0],'k--', linewidth=0.5)
ax.plot([0,0],ax.get_ylim(), 'k--', linewidth=0.5)
ax.set_xlabel(r"$a_1$", fontsize=10 ,labelpad=0)
ax.set_ylabel(r"$a_2$", fontsize=10 ,labelpad=0)
# ax.set_ylabel(r"energy")
# 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('Energy_ContourG+.pdf')
plt.show()
#
#
#
# # Curve parametrised by \theta_rho = alpha in parameter space
# N=100;
# theta_rho = np.linspace(1, 3, num=N)
# print('theta_rho:', theta_rho)
#
#
# theta_values = []
#
#
# for t in theta_rho:
#
# s = (1.0/10.0)*t+0.1
# theta_values.append(s)
#
#
#
#
#
# theta_rho = np.array(theta_rho)
# theta_values = np.array(theta_values)
#
# betas_ = 2.0
#
# alphas, betas, thetas = np.meshgrid(theta_rho, betas_, theta_values, indexing='ij')
#
#
# harmonicMeanVec = np.vectorize(harmonicMean)
# arithmeticMeanVec = np.vectorize(arithmeticMean)
# prestrain_b1Vec = np.vectorize(prestrain_b1)
# prestrain_b2Vec = np.vectorize(prestrain_b2)
#
# GetMuGammaVec = np.vectorize(GetMuGamma)
# muGammas = GetMuGammaVec(betas,thetas,gamma,mu1,rho1,InputFilePath ,OutputFilePath )
#
# q1_vec = harmonicMeanVec(mu1, betas, thetas)
# q2_vec = arithmeticMeanVec(mu1, betas, thetas)
#
# b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
# b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
# special case: q12 == 0!! .. braucht eigentlich nur b1 & b2 ...
# print('type b1_values:', type(b1_values))
# print('size(q1)',q1.shape)
#
#
# energy_axial1 = []
# energy_axial2 = []
#
# # for b1 in b1_values:
# for i in range(len(theta_rho)):
# print('index i:', i)
#
# print('theta_rho[i]',theta_rho[i])
# print('theta_values[i]',theta_values[i])
#
# q1 = (1.0/6.0)*harmonicMean(mu1, beta, theta_values[i])
# q2 = (1.0/6.0)*arithmeticMean(mu1, beta, theta_values[i])
# q12 = 0.0
# q3 = GetMuGamma(beta, theta_values[i],gamma,mu1,rho1,InputFilePath ,OutputFilePath )
# b1 = prestrain_b1(rho1,beta, theta_rho[i],theta_values[i] )
# b2 = prestrain_b2(rho1,beta, theta_rho[i],theta_values[i] )
#
#
# # q2_vec = arithmeticMean(mu1, betas, thetas)
# #
# # b1_vec = prestrain_b1Vec(rho1, betas, alphas, thetas)
# # b2_vec = prestrain_b2Vec(rho1, betas, alphas, thetas)
# print('q1[i]',q1)
# print('q2[i]',q2)
# print('q3[i]',q3)
# print('b1[i]',b1)
# print('b2[i]',b2)
# # print('q1[i]',q1[0][i])
# # print('q2[i]',q2[i])
# # print('b1[i]',b1[i])
# # print('b2[i]',b2[i])
# #compute axial energy #1 ...
#
# a_axial1 = np.array([b1,0])
# a_axial2 = np.array([0,b2])
# b = np.array([b1,b2])
#
# H = np.array([[2*q1, q12+2*q3], [q12+2*q3,2*q2] ])
# A = np.array([[q1,1/2*q12], [1/2*q12,q2] ])
#
#
# tmp = H.dot(a_axial1)
#
# print('H',H)
# print('A',A)
# print('b',b)
# print('a_axial1',a_axial1)
# print('tmp',tmp)
#
# tmp = (1/2)*a_axial1.dot(tmp)
# print('tmp',tmp)
#
# tmp2 = A.dot(b)
# print('tmp2',tmp2)
# tmp2 = 2*a_axial1.dot(tmp2)
#
# print('tmp2',tmp2)
# energy_1 = tmp - tmp2
# print('energy_1',energy_1)
#
#
# energy_axial1.append(energy_1)
#
#
# tmp = H.dot(a_axial2)
#
# print('H',H)
# print('A',A)
# print('b',b)
# print('a_axial2',a_axial2)
# print('tmp',tmp)
#
# tmp = (1/2)*a_axial2.dot(tmp)
# print('tmp',tmp)
#
# tmp2 = A.dot(b)
# print('tmp2',tmp2)
# tmp2 = 2*a_axial2.dot(tmp2)
#
# print('tmp2',tmp2)
# energy_2 = tmp - tmp2
# print('energy_2',energy_2)
#
#
# energy_axial2.append(energy_2)
#
#
#
#
#
# print('theta_values', theta_values)
#
#
#
#
#
#
#
# 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, )