def gen_strain_mode(CrystalType, Ord):
#function: generate the strain mode for given crystal type(CrystalType) and order(Ord)
StrainAll = gen_strain(1)
CijkInd = symdata.coef_ind(CrystalType, Ord)
CoefCoef = symdata.coef_crystal(CrystalType, Ord)
CijkUniq = np.array(symdata.get_unique(CijkInd))
n_uniq = len(CijkUniq)
Cijk = num2cijk(CijkUniq, Ord)
StrainMode = np.zeros((n_uniq, 3, 3), dtype=float)
#StrainModeCoef = np.zeros((n_uniq, n_uniq), dtype = float)
StrainModeCoef = CoefStr(Ord)
exec('StrainModeCoef.coef' + str(int(Ord)) +
' = np.zeros((n_uniq, n_uniq), dtype = float)')
for i in range(2, int(Ord)):
CijUniq = np.array(symdata.get_unique(symdata.coef_ind(CrystalType,
i)))
n_uniqi = len(CijUniq)
exec('StrainModeCoef.coef' + str(i) +
' = np.zeros((n_uniq, n_uniqi), dtype = float)')
count = 0
for i in range(0, len(StrainAll)):
Straini = vec2matrix(StrainAll[i])
StrainModei = gen_cijk_coef(CrystalType, Straini, Ord)
if i == 0:
StrainMode[count, :, :] = Straini
exec('StrainModeCoef.coef' + str(int(Ord)) +
'[count, :] = StrainModei')
for j in range(2, int(Ord)):
exec('StrainModeCoef.coef' + str(j) +
'[count, :] = gen_cijk_coef(CrystalType, Straini, j)')
count = count + 1
else:
StrainModetmp = np.zeros((count + 1, n_uniq), dtype=float)
#print StrainMode[0, :]
StrainModetmp[0:count, :] = eval('StrainModeCoef.coef' +
str(int(Ord)) + '[0:count, :]')
StrainModetmp[count, :] = StrainModei
SMRank = np.linalg.matrix_rank(StrainModetmp)
if SMRank == count + 1:
#print SMRank
exec('StrainModeCoef.coef' + str(int(Ord)) +
'[count, :] = StrainModei')
StrainMode[count, :, :] = Straini
for j in range(2, int(Ord)):
exec('StrainModeCoef.coef' + str(j) +
'[count, :] = gen_cijk_coef(CrystalType, Straini, j)')
#print StrainModei
count = count + 1
if count == n_uniq:
break
#print StrainModeCoef
#print StrainMode
return (StrainModeCoef, StrainMode)
def print_cijk(CrystalType, Ord):
#function: print the Cijk according to the crystal type and order
CijkInd = symdata.coef_ind(CrystalType, Ord)
CijkUniq = np.array(symdata.get_unique(CijkInd))
Cijk = num2cijk(CijkUniq, Ord)
print(Cijk)
return Cijk
def CoefForSingleMode(CrystalType, Ord, Strain):
#function: generate the coefficient for a specified strain and crystal type
#
#Cijk = print_cijk(CrystalType, Ord)
#print Cijk
m = Strain.shape
if len(m) == 1:
m = 1
else:
m = m[0]
StrainMode = np.zeros((m, 3, 3))
StrainModeCoef = CoefStr(Ord)
for i in range(2, int(Ord) + 1):
CijUniq = np.array(symdata.get_unique(symdata.coef_ind(CrystalType,
i)))
n_uniq = len(CijUniq)
exec('StrainModeCoef.coef' + str(i) +
' = np.zeros((m, n_uniq), dtype = float)')
#StrainModeCoef = CoefStr(Ord)
Cijk = CoefStr(Ord)
for i in range(2, int(Ord) + 1):
exec('Cijk.coef' + str(i) + ' = print_cijk(CrystalType, i)')
for j in range(0, m):
StrainM = vec2matrix(Strain[j, :])
StrainMode[j, :, :] = StrainM
#print StrainM
exec('StrainModeCoef.coef' + str(i) +
'[j, :] = gen_cijk_coef(CrystalType, StrainM, i)')
exec('print(StrainModeCoef.coef' + str(i) + ')')
return (Cijk, StrainModeCoef, StrainMode)
def gen_cijk_coef(CrystalType, Strain, Ord):
#function: generate the coefficients of independent elastic constant according to
# the crystal type(CrystalType) and the strain(Strain) and order(Ord)
(StrainOrd, StrainOrdCoef) = gen_strainord(Strain)
CijkInd = symdata.coef_ind(CrystalType, Ord)
CoefCoef = symdata.coef_crystal(CrystalType, Ord)
(Cijk, CijkCoef) = gen_strain_coef(StrainOrd, StrainOrdCoef, Ord)
CijkUniq = np.array(symdata.get_unique(CijkInd))
CoefStrain = np.zeros(len(CijkUniq))
CijkNum = cijk2num(Cijk, Ord)
for i in range(0, len(CijkNum)):
COrderi = CijkInd[CijkNum[i]]
#print COrderi
#print COrderi is list
if type(COrderi) is list:
for j in range(0, len(COrderi)):
#print CijkNum
#print CoefCoef[CijkNum[i]][j]
#print CijkCoef[i]
CoefOrderi = float(CoefCoef[CijkNum[i]][j]) * float(
CijkCoef[i])
Index_CoefStrain = np.argwhere(CijkUniq == COrderi[j])
Index_CoefStrain = Index_CoefStrain[0][0]
CoefStrain[Index_CoefStrain] = CoefStrain[
Index_CoefStrain] + CoefOrderi
else:
if COrderi != 0:
CoefOrderi = float(CoefCoef[CijkNum[i]]) * float(CijkCoef[i])
Index_CoefStrain = np.argwhere(CijkUniq == COrderi)
#print Index_CoefStrain
Index_CoefStrain = Index_CoefStrain[0][0]
CoefStrain[Index_CoefStrain] = CoefStrain[
Index_CoefStrain] + CoefOrderi
return CoefStrain
def gen_strain_mode(CrystalType, Ord):
#function: generate the strain mode for given crystal type(CrystalType) and order(Ord)
CijkInd = symdata.coef_ind(CrystalType, Ord)
CoefCoef = symdata.coef_crystal(CrystalType, Ord)
CijkUniq = np.array(symdata.get_unique(CijkInd))
n_uniq = len(CijkUniq)
#print(n_uniq)
if (Ord % 2.0 == 0) and (n_uniq > 5):
#n_uniq > 5 keep doubt? to do
n_row = int(math.ceil(n_uniq / 6.) * 6.) #+ 6
else:
n_row = int(math.ceil(n_uniq / 6.) * 6.)
#print(n_row)
Cijk = symmetry.num2cijk(CijkUniq, Ord)
StrainMode = np.zeros((int(math.ceil(n_row / 6.)), 3, 3), dtype=float)
#StrainModeCoef = np.zeros((n_row, n_uniq), dtype = float)
StrainModeCoef = symmetry.CoefStr(Ord)
exec('StrainModeCoef.coef' + str(int(Ord)) +
' = np.zeros((n_row, n_uniq), dtype = float)')
for i in range(2, int(Ord)):
CijUniq = np.array(symdata.get_unique(symdata.coef_ind(CrystalType,
i)))
n_uniqi = len(CijUniq)
exec('StrainModeCoef.coef' + str(i) +
' = np.zeros((n_row, n_uniqi), dtype = float)')
if n_uniq < 6:
#The ord must be 2
StrainAll = gen_strain(1)
for i in range(0, len(StrainAll)):
StrainModei = symmetry.vec2matrix(StrainAll[i])
StrainModeCoefi = gen_cijk_coef(CrystalType, StrainModei, Ord)
SMRank = np.linalg.matrix_rank(StrainModeCoefi)
if SMRank == n_uniq:
StrainMode[0, :, :] = StrainModei
StrainModeCoef = StrainModeCoefi
break
else:
print("Begin of generate the full-rank database.\n")
StrainAll = gen_fullrank_db(CrystalType, Ord)
print("The full-rank database were generated.\n")
#StrainAll = gen_alldiff_db()
#print StrainAll
n_strain = len(StrainAll)
#print(n_strain)
for j in range(0, n_strain):
count = 0
flag = 0
for i in range(j, n_strain):
Straini = StrainAll[i, :, :]
StrainModei = gen_cijk_coef(CrystalType, Straini, Ord)
if count == 0:
exec('StrainModeCoef.coef' + str(int(Ord)) +
'[0:6, :] = StrainModei')
#StrainModeCoef[0:6, :] = StrainModei
StrainMode[count, :, :] = Straini
for k in range(2, int(Ord)):
exec(
'StrainModeCoef.coef' + str(int(k)) +
'[0:6, :] = gen_cijk_coef(CrystalType, Straini, k)'
)
count = count + 1
#'''
if n_uniq == 6:
flag = 1
break
#'''
else:
StrainModetmp = np.zeros((6 * (count + 1), n_uniq),
dtype=float)
StrainModetmp[0:6 *
count, :] = eval('StrainModeCoef.coef' +
str(int(Ord)) +
'[0:6*count, :]')
StrainModetmp[6 * count:6 * (count + 1), :] = StrainModei
SMRank = np.linalg.matrix_rank(StrainModetmp)
#print(SMRank)
#print(n_uniq)
#print(count)
### NOTE: the default is SMRank == 6*(count + 1)
RnkLst = [
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84,
90, 96, 102, 108, 114, 120, 126
]
#if SMRank == 6*(count + 1) or SMRank == n_uniq:
if SMRank > (RnkLst[count] - 1) or SMRank == n_uniq:
#if SMRank > 5*(count + 1) or SMRank == n_uniq:
#exec('print(StrainModeCoef.coef' + str(int(Ord)) + ')')
#print(StrainModei)
exec('StrainModeCoef.coef' + str(int(Ord)) +
'[6*count:6*(count + 1), :] = StrainModei')
StrainMode[count, :, :] = Straini
for k in range(2, int(Ord)):
exec(
'StrainModeCoef.coef' + str(k) +
'[6*count:6*(count + 1), :] = gen_cijk_coef(CrystalType, Straini, k)'
)
count = count + 1
if SMRank == n_uniq:
print(SMRank)
flag = 1
break
if flag == 1:
break
return (StrainModeCoef, StrainMode)