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 = crydef.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 = crydef.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 CoefForSingleMode(CrystalType='c1',
Ord=3,
Strain=np.array([[0.5, -2, -0.5, 1, 1, 0]])):
'''
Generate the coefficient for specified strain modes
Parameter
---------
CrystalType: str
The crystal type (symmetry), in Laue's group
Ord: int
The order of elastic constants
Strain: 2D np.ndarray
The strain modes, support multi-strain modes
Note: in Voigt's notation and the size is nx6
e.g. np.array([[1, 1, 0, 2, 0, 0]])
Return
------
Cijk: elastic3rd.symmetry.symmetry.CoefStr object
The independent elastic constants (in Ord order)
StrainModeCoef: elastic3rd.symmetry.symmetry.CoefStr object
The coefficients of independent elastic constants
StrainMode: 3D np.ndarray
The strain modes nx3x3
'''
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 = crydef.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='c1',
Strain=np.array([[1, 0, 0], [0, 1, 1], [0, 1, 0]]),
Ord=3):
'''
Generate the coefficients of independent elastic constants
according to symmetry and strain and elastic constants order
Parameter
---------
CrystalType: str
The crystal type, in Laue group
Strain: 2D np.ndarray
The strain in matrix/tensor format
Ord: int
The order of elasti constants
Return
------
CoefStrain: 1D np.ndarray
The coefficients of the independent elastic constants in current Strain
The sequence is in order of the index, e.g. for cubicI, [111, 112, 123, 144, 155, 456]
'''
(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]]
if type(COrderi) is list:
for j in range(0, len(COrderi)):
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 print_cijk(CrystalType='c1', Ord=3):
'''
Print independent Cijk according to the crystal type and order
Parameter
---------
CrystalType: str
The crystal type (symmetry), in Laue's group
Ord: int
The order of elastic constants
Return
------
Cijk: np.ndarray
The list of Cijk (order is determined by Ord)
'''
CijkInd = symdata.coef_ind(CrystalType, Ord)
CijkUniq = np.array(symdata.get_unique(CijkInd))
Cijk = num2cijk(CijkUniq, Ord)
print(Cijk)
return Cijk
def gen_strain_mode(CrystalType='c1', Ord=3):
'''
Generate the strain mode for give symmetry and order
Parameter
---------
CrystalType: str
The crystal type, in Laue group
Ord: int
The order of elastic constants
Return
------
StrainModeCoef: elastic3rd.symmetry.symmetry.CoefStr object
elastic3rd defined coefficients object
It contains several attributes.
e.g. CoefStr.coef2, CoefStr.coef3, ..., CoefStr.coefn, ...
Here n equal to Ord
In each attributes, it is a 2D np.ndarray
StrainMode: 3D np.ndarray
The strain mode in matrix/tesnsor format
size: nx3x3, here n is the number of strain modes
'''
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 = 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 = crydef.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)
StrainModetmp[0:count, :] = eval('StrainModeCoef.coef' +
str(int(Ord)) + '[0:count, :]')
StrainModetmp[count, :] = StrainModei
SMRank = np.linalg.matrix_rank(StrainModetmp)
if SMRank == count + 1:
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)')
count = count + 1
if count == n_uniq:
break
return (StrainModeCoef, StrainMode)