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# 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, )