pymatgen.analysis.piezo_sensitivity — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.piezo_sensitivity

    """
    Piezo sensitivity analysis module.
    """

    from pymatgen.core.tensors import Tensor
    import pymatgen.io.phonopy

    import numpy as np
    import warnings
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer as sga
    from monty.dev import requires

    try:
        from phonopy import Phonopy
        from phonopy.harmonic import dynmat_to_fc as dyntofc
    except ImportError:
        Phonopy = None

    __author__ = "Handong Ling"
    __copyright__ = "Copyright 2019, The Materials Project"
    __version__ = "1.0"
    __maintainer__ = "Handong Ling"
    __email__ = "hling@lbl.gov"
    __status__ = "Development"
    __date__ = "Feb, 2019"

    class BornEffectiveCharge:
        """
        This class describes the Nx3x3 born effective charge tensor
        """

        def __init__(self, structure, bec, pointops, tol=1e-3):
            """
            Create an BornEffectiveChargeTensor object defined by a
            structure, point operations of the structure's atomic sites.
            Note that the constructor uses __new__ rather than __init__
            according to the standard method ofsubclassing numpy ndarrays.

            Args:
                input_matrix (Nx3x3 array-like): the Nx3x3 array-like
                    representing the born effective charge tensor
            """

            self.structure = structure
            self.bec = bec
            self.pointops = pointops
            self.BEC_operations = None
            if not np.sum(self.bec) < tol:
                warnings.warn(
                    "Input born effective charge tensor does "
                    "not satisfy charge neutrality"
                )

        def get_BEC_operations(self, eigtol=1e-05, opstol=1e-03):
            """
            Returns the symmetry operations which maps the tensors
            belonging to equivalent sites onto each other in the form
            [site index 1, site index 2, [Symmops mapping from site
            index 1 to site index 2]]

            Args:
                eigtol (float): tolerance for determining if two sites are
                related by symmetry
                opstol (float): tolerance for determining if a symmetry
                operation relates two sites

            Return:
                list of symmetry operations mapping equivalent sites and
                the indexes of those sites.
            """
            bec = self.bec
            struc = self.structure
            ops = sga(struc).get_symmetry_operations(cartesian=True)
            uniquepointops = []
            for op in ops:
                uniquepointops.append(op)

            for atom in range(len(self.pointops)):
                for op in self.pointops[atom]:
                    if op not in uniquepointops:
                        uniquepointops.append(op)

            passed = []
            relations = []
            for site in range(len(bec)):
                unique = 1
                eig1, vecs1 = np.linalg.eig(bec[site])
                index = np.argsort(eig1)
                neweig = np.real([eig1[index[0]], eig1[index[1]], eig1[index[2]]])
                for index in range(len(passed)):

                    if np.allclose(neweig, passed[index][1], atol=eigtol):
                        relations.append([site, index])
                        unique = 0
                        passed.append([site, passed[index][0], neweig])
                        break
                if unique == 1:
                    relations.append([site, site])
                    passed.append([site, neweig])
            BEC_operations = []
            for atom in range(len(relations)):
                BEC_operations.append(relations[atom])
                BEC_operations[atom].append([])

                for op in uniquepointops:
                    new = op.transform_tensor(self.bec[relations[atom][1]])

                    # Check the matrix it references
                    if np.allclose(new, self.bec[relations[atom][0]], atol=opstol):
                        BEC_operations[atom][2].append(op)

            self.BEC_operations = BEC_operations

        def get_rand_BEC(self, max_charge=1):
            """
            Generate a random born effective charge tensor which obeys a structure's
            symmetry and the acoustic sum rule

            Args:
                max_charge (float): maximum born effective charge value

            Return:
                np.array Born effective charge tensor
            """

            struc = self.structure
            symstruc = sga(struc)
            symstruc = symstruc.get_symmetrized_structure()

            l = len(struc)
            BEC = np.zeros((l, 3, 3))
            for atom in range(len(self.BEC_operations)):
                if self.BEC_operations[atom][0] == self.BEC_operations[atom][1]:
                    temp_tensor = Tensor(np.random.rand(3, 3) - 0.5)
                    temp_tensor = sum(
                        [temp_tensor.transform(symm_op) for symm_op in self.pointops[atom]]
                    ) / len(self.pointops[atom])
                    BEC[atom] = temp_tensor
                else:
                    tempfcm = np.zeros([3, 3])
                    for op in self.BEC_operations[atom][2]:

                        tempfcm += op.transform_tensor(BEC[self.BEC_operations[atom][1]])
                    BEC[self.BEC_operations[atom][0]] = tempfcm
                    if len(self.BEC_operations[atom][2]) != 0:
                        BEC[self.BEC_operations[atom][0]] = BEC[
                            self.BEC_operations[atom][0]
                        ] / len(self.BEC_operations[atom][2])

            #     Enforce Acoustic Sum
            disp_charge = np.einsum("ijk->jk", BEC) / l
            add = np.zeros([l, 3, 3])

            for atom in range(len(self.BEC_operations)):

                if self.BEC_operations[atom][0] == self.BEC_operations[atom][1]:
                    temp_tensor = Tensor(disp_charge)
                    temp_tensor = sum(
                        [temp_tensor.transform(symm_op) for symm_op in self.pointops[atom]]
                    ) / len(self.pointops[atom])
                    add[self.BEC_operations[atom][0]] = temp_tensor
                else:
                    temp_tensor = np.zeros([3, 3])
                    for op in self.BEC_operations[atom][2]:

                        temp_tensor += op.transform_tensor(
                            add[self.BEC_operations[atom][1]]
                        )

                    add[self.BEC_operations[atom][0]] = temp_tensor

                    if len(self.BEC_operations[atom]) != 0:
                        add[self.BEC_operations[atom][0]] = add[
                            self.BEC_operations[atom][0]
                        ] / len(self.BEC_operations[atom][2])

            BEC = BEC - add

            return BEC * max_charge

    class InternalStrainTensor:
        """
        This class describes the Nx3x3x3 internal tensor defined by a
        structure, point operations of the structure's atomic sites.
        """

        def __init__(self, structure, ist, pointops, tol=1e-3):
            """
            Create an InternalStrainTensor object.

            Args:
                input_matrix (Nx3x3x3 array-like): the Nx3x3x3 array-like
                    representing the internal strain tensor
            """

            self.structure = structure
            self.ist = ist
            self.pointops = pointops
            self.IST_operations = None

            obj = self.ist
            if not (obj - np.transpose(obj, (0, 1, 3, 2)) < tol).all():
                warnings.warn(
                    "Input internal strain tensor does " "not satisfy standard symmetries"
                )

        def get_IST_operations(self, opstol=1e-03):
            """
            Returns the symmetry operations which maps the tensors
            belonging to equivalent sites onto each other in the form
            [site index 1, site index 2, [Symmops mapping from site
            index 1 to site index 2]]

            Args:
                opstol (float): tolerance for determining if a symmetry
                operation relates two sites

            Return:
                list of symmetry operations mapping equivalent sites and
                the indexes of those sites.
            """

            struc = self.structure
            ops = sga(struc).get_symmetry_operations(cartesian=True)
            uniquepointops = []
            for op in ops:
                uniquepointops.append(op)

            for atom in range(len(self.pointops)):
                for op in self.pointops[atom]:
                    if op not in uniquepointops:
                        uniquepointops.append(op)

            IST_operations = []
            for atom in range(len(self.ist)):
                IST_operations.append([])
                for j in range(0, atom):
                    for op in uniquepointops:
                        new = op.transform_tensor(self.ist[j])

                        # Check the matrix it references
                        if np.allclose(new, self.ist[atom], atol=opstol):
                            IST_operations[atom].append([j, op])

            self.IST_operations = IST_operations

        def get_rand_IST(self, max_force=1):
            """
            Generate a random internal strain tensor which obeys a structure's
            symmetry and the acoustic sum rule

            Args:
                max_force(float): maximum born effective charge value

            Return:
                InternalStrainTensor object
            """

            l = len(self.structure)
            IST = np.zeros((l, 3, 3, 3))
            for atom in range(len(self.IST_operations)):
                temp_tensor = np.zeros([3, 3, 3])
                for op in self.IST_operations[atom]:
                    temp_tensor += op[1].transform_tensor(IST[op[0]])

                if len(self.IST_operations[atom]) == 0:
                    temp_tensor = Tensor(np.random.rand(3, 3, 3) - 0.5)
                    for dim in range(3):
                        temp_tensor[dim] = (temp_tensor[dim] + temp_tensor[dim].T) / 2
                    temp_tensor = sum(
                        [temp_tensor.transform(symm_op) for symm_op in self.pointops[atom]]
                    ) / len(self.pointops[atom])
                IST[atom] = temp_tensor
                if len(self.IST_operations[atom]) != 0:
                    IST[atom] = IST[atom] / len(self.IST_operations[atom])

            return IST * max_force

    class ForceConstantMatrix:
        """
        This class describes the NxNx3x3 force constant matrix defined by a
        structure, point operations of the structure's atomic sites, and the
        shared symmetry operations between pairs of atomic sites.
        """

        def __init__(self, structure, fcm, pointops, sharedops, tol=1e-3):
            """
            Create an ForceConstantMatrix object.

            Args:
                input_matrix (NxNx3x3 array-like): the NxNx3x3 array-like
                    representing the force constant matrix
            """

            self.structure = structure
            self.fcm = fcm
            self.pointops = pointops
            self.sharedops = sharedops
            self.FCM_operations = None

        def get_FCM_operations(self, eigtol=1e-05, opstol=1e-05):
            """
            Returns the symmetry operations which maps the tensors
            belonging to equivalent sites onto each other in the form
            [site index 1a, site index 1b, site index 2a, site index 2b,
            [Symmops mapping from site index 1a, 1b to site index 2a, 2b]]

            Args:
                eigtol (float): tolerance for determining if two sites are
                related by symmetry
                opstol (float): tolerance for determining if a symmetry
                operation relates two sites

            Return:
                list of symmetry operations mapping equivalent sites and
                the indexes of those sites.
            """
            struc = self.structure
            ops = sga(struc).get_symmetry_operations(cartesian=True)
            uniquepointops = []
            for op in ops:
                uniquepointops.append(op)

            for atom in range(len(self.pointops)):
                for op in self.pointops[atom]:
                    if op not in uniquepointops:
                        uniquepointops.append(op)

            passed = []
            relations = []
            for atom1 in range(len(self.fcm)):
                for atom2 in range(atom1, len(self.fcm)):
                    unique = 1
                    eig1, vecs1 = np.linalg.eig(self.fcm[atom1][atom2])
                    index = np.argsort(eig1)
                    neweig = np.real([eig1[index[0]], eig1[index[1]], eig1[index[2]]])

                    for entry in range(len(passed)):
                        if np.allclose(neweig, passed[entry][2], atol=eigtol):
                            relations.append(
                                [atom1, atom2, passed[entry][0], passed[entry][1]]
                            )
                            unique = 0
                            break
                    if unique == 1:
                        relations.append([atom1, atom2, atom2, atom1])
                        passed.append([atom1, atom2, np.real(neweig)])
            FCM_operations = []
            for entry in range(len(relations)):
                good = 0
                FCM_operations.append(relations[entry])
                FCM_operations[entry].append([])

                good = 0
                for op in uniquepointops:
                    new = op.transform_tensor(
                        self.fcm[relations[entry][2]][relations[entry][3]]
                    )

                    if np.allclose(
                        new, self.fcm[relations[entry][0]][relations[entry][1]], atol=opstol
                    ):
                        FCM_operations[entry][4].append(op)
                        good = 1
                if (
                    relations[entry][0] == relations[entry][3]
                    and relations[entry][1] == relations[entry][2]
                ):
                    good = 1
                if (
                    relations[entry][0] == relations[entry][2]
                    and relations[entry][1] == relations[entry][3]
                ):
                    good = 1
                if good == 0:
                    FCM_operations[entry] = [
                        relations[entry][0],
                        relations[entry][1],
                        relations[entry][3],
                        relations[entry][2],
                    ]
                    FCM_operations[entry].append([])
                    for op in uniquepointops:
                        new = op.transform_tensor(
                            self.fcm[relations[entry][2]][relations[entry][3]]
                        )
                        if np.allclose(
                            new.T,
                            self.fcm[relations[entry][0]][relations[entry][1]],
                            atol=opstol,
                        ):
                            FCM_operations[entry][4].append(op)

            self.FCM_operations = FCM_operations
            return FCM_operations

        def get_unstable_FCM(self, max_force=1):
            """
            Generate an unsymmeterized force constant matrix

            Args:
                max_charge (float): maximum born effective charge value

            Return:
                numpy array representing the force constant matrix
            """

            struc = self.structure
            operations = self.FCM_operations
            # set max force in reciprocal space
            numsites = len(struc.sites)
            D = (1 / max_force) * 2 * (np.ones([numsites * 3, numsites * 3]))
            for op in operations:
                same = 0
                transpose = 0
                if op[0] == op[1] and op[0] == op[2] and op[0] == op[3]:
                    same = 1
                if op[0] == op[3] and op[1] == op[2]:
                    transpose = 1
                if transpose == 0 and same == 0:
                    D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = np.zeros(
                        [3, 3]
                    )
                    D[3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3] = np.zeros(
                        [3, 3]
                    )

                    for symop in op[4]:

                        tempfcm = D[3 * op[2]:3 * op[2] + 3, 3 * op[3]:3 * op[3] + 3]
                        tempfcm = symop.transform_tensor(tempfcm)
                        D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] += tempfcm

                    if len(op[4]) != 0:
                        D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = D[
                            3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                        ] / len(op[4])

                    D[3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3] = D[
                        3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                    ].T
                    continue
                else:
                    temp_tensor = Tensor(np.random.rand(3, 3) - 0.5) * max_force

                    temp_tensor_sum = sum(
                        [
                            temp_tensor.transform(symm_op)
                            for symm_op in self.sharedops[op[0]][op[1]]
                        ]
                    )
                    temp_tensor_sum = temp_tensor_sum / (len(self.sharedops[op[0]][op[1]]))
                    if op[0] != op[1]:
                        for pair in range(len(op[4])):

                            temp_tensor2 = temp_tensor_sum.T
                            temp_tensor2 = op[4][pair].transform_tensor(temp_tensor2)
                            temp_tensor_sum = (temp_tensor_sum + temp_tensor2) / 2

                    else:
                        temp_tensor_sum = (temp_tensor_sum + temp_tensor_sum.T) / 2

                    D[
                        3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                    ] = temp_tensor_sum
                    D[
                        3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3
                    ] = temp_tensor_sum.T

            return D

        def get_symmetrized_FCM(self, unsymmetrized_fcm, max_force=1):
            """
            Generate a symmeterized force constant matrix from an unsymmeterized matrix

            Args:
                unsymmetrized_fcm (numpy array): unsymmeterized force constant matrix
                max_charge (float): maximum born effective charge value

            Return:
                3Nx3N numpy array representing the force constant matrix
            """

            operations = self.FCM_operations
            D = unsymmetrized_fcm
            for op in operations:
                same = 0
                transpose = 0
                if op[0] == op[1] and op[0] == operations[2] and op[0] == op[3]:
                    same = 1
                if op[0] == op[3] and op[1] == op[2]:
                    transpose = 1
                if transpose == 0 and same == 0:
                    D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = np.zeros(
                        [3, 3]
                    )

                    for symop in op[4]:

                        tempfcm = D[3 * op[2]:3 * op[2] + 3, 3 * op[3]:3 * op[3] + 3]
                        tempfcm = symop.transform_tensor(tempfcm)

                        D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] += tempfcm

                    if len(op[4]) != 0:
                        D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = D[
                            3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                        ] / len(op[4])
                    D[3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3] = D[
                        3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                    ].T
                    continue
                else:

                    temp_tensor = Tensor(
                        D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3]
                    )
                    temp_tensor_sum = sum(
                        [
                            temp_tensor.transform(symm_op)
                            for symm_op in self.sharedops[op[0]][op[1]]
                        ]
                    )
                    if len(self.sharedops[op[0]][op[1]]) != 0:
                        temp_tensor_sum = temp_tensor_sum / (
                            len(self.sharedops[op[0]][op[1]])
                        )

                    # Apply the proper transformation if there is an equivalent already
                    if op[0] != op[1]:

                        for pair in range(len(op[4])):

                            temp_tensor2 = temp_tensor_sum.T
                            temp_tensor2 = op[4][pair].transform_tensor(temp_tensor2)
                            temp_tensor_sum = (temp_tensor_sum + temp_tensor2) / 2

                    else:
                        temp_tensor_sum = (temp_tensor_sum + temp_tensor_sum.T) / 2

                D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = temp_tensor_sum
                D[3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3] = temp_tensor_sum.T

            return D

        def get_stable_FCM(self, fcm, fcmasum=10):

            """
            Generate a symmeterized force constant matrix that obeys the objects symmetry
            constraints, has no unstable modes and also obeys the acoustic sum rule through an
            iterative procedure

            Args:
                fcm (numpy array): unsymmeterized force constant matrix
                fcmasum (int): number of iterations to attempt to obey the acoustic sum
                    rule

            Return:
                3Nx3N numpy array representing the force constant matrix
            """

            check = 0
            count = 0
            while check == 0:
                # if resymmetrizing brings back unstable modes 20 times, the method breaks
                if count > 20:
                    check = 1
                    break

                eigs, vecs = np.linalg.eig(fcm)

                maxeig = np.max(-1 * eigs)
                eigsort = np.argsort(np.abs(eigs))
                for i in range(3, len(eigs)):
                    if eigs[eigsort[i]] > 1e-06:
                        eigs[eigsort[i]] = -1 * maxeig * np.random.rand()
                diag = np.real(np.eye(len(fcm)) * eigs)

                fcm = np.real(np.matmul(np.matmul(vecs, diag), vecs.T))
                fcm = self.get_symmetrized_FCM(fcm)
                fcm = self.get_asum_FCM(fcm)
                eigs, vecs = np.linalg.eig(fcm)
                unstable_modes = 0
                eigsort = np.argsort(np.abs(eigs))
                for i in range(3, len(eigs)):
                    if eigs[eigsort[i]] > 1e-06:
                        unstable_modes = 1
                if unstable_modes == 1:
                    count = count + 1
                    continue
                else:
                    check = 1

            return fcm

        # acoustic sum

        def get_asum_FCM(self, fcm, numiter=15):
            """
            Generate a symmeterized force constant matrix that obeys the objects symmetry
            constraints and obeys the acoustic sum rule through an iterative procedure

            Args:
                fcm (numpy array): 3Nx3N unsymmeterized force constant matrix
                numiter (int): number of iterations to attempt to obey the acoustic sum
                    rule

            Return:
                numpy array representing the force constant matrix
            """

            # set max force in reciprocal space
            operations = self.FCM_operations
            numsites = len(self.structure)

            D = np.ones([numsites * 3, numsites * 3])
            for num in range(numiter):
                X = np.real(fcm)

                # symmetry operations
                pastrow = 0
                total = np.zeros([3, 3])
                for col in range(numsites):
                    total = total + X[0:3, col * 3:col * 3 + 3]

                total = total / (numsites)
                for op in operations:
                    same = 0
                    transpose = 0
                    if op[0] == op[1] and op[0] == op[2] and op[0] == op[3]:
                        same = 1
                    if op[0] == op[3] and op[1] == op[2]:
                        transpose = 1
                    if transpose == 0 and same == 0:
                        D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = np.zeros(
                            [3, 3]
                        )

                        for symop in op[4]:

                            tempfcm = D[
                                3 * op[2]:3 * op[2] + 3, 3 * op[3]:3 * op[3] + 3
                            ]
                            tempfcm = symop.transform_tensor(tempfcm)

                            D[
                                3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                            ] += tempfcm

                        if len(op[4]) != 0:
                            D[3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3] = D[
                                3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                            ] / len(op[4])
                        D[3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3] = D[
                            3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                        ].T
                        continue
                    else:
                        # Get the difference in the sum up to this point
                        currrow = op[0]
                        if currrow != pastrow:
                            total = np.zeros([3, 3])
                            for col in range(numsites):
                                total = (
                                    total
                                    + X[
                                        currrow * 3:currrow * 3 + 3, col * 3:col * 3 + 3
                                    ]
                                )
                            for col in range(currrow):
                                total = (
                                    total
                                    - D[
                                        currrow * 3:currrow * 3 + 3, col * 3:col * 3 + 3
                                    ]
                                )
                            total = total / (numsites - currrow)
                        pastrow = currrow

                        # Apply the point symmetry operations of the site
                        temp_tensor = Tensor(total)
                        temp_tensor_sum = sum(
                            [
                                temp_tensor.transform(symm_op)
                                for symm_op in self.sharedops[op[0]][op[1]]
                            ]
                        )

                        if len(self.sharedops[op[0]][op[1]]) != 0:
                            temp_tensor_sum = temp_tensor_sum / (
                                len(self.sharedops[op[0]][op[1]])
                            )

                        # Apply the proper transformation if there is an equivalent already
                        if op[0] != op[1]:

                            for pair in range(len(op[4])):

                                temp_tensor2 = temp_tensor_sum.T
                                temp_tensor2 = op[4][pair].transform_tensor(temp_tensor2)
                                temp_tensor_sum = (temp_tensor_sum + temp_tensor2) / 2

                        else:
                            temp_tensor_sum = (temp_tensor_sum + temp_tensor_sum.T) / 2

                        D[
                            3 * op[0]:3 * op[0] + 3, 3 * op[1]:3 * op[1] + 3
                        ] = temp_tensor_sum
                        D[
                            3 * op[1]:3 * op[1] + 3, 3 * op[0]:3 * op[0] + 3
                        ] = temp_tensor_sum.T
                fcm = fcm - D

            return fcm

        @requires(Phonopy, "phonopy not installed!")
        def get_rand_FCM(self, asum=15, force=10):
            """
            Generate a symmeterized force constant matrix from an unsymmeterized matrix
            that has no unstable modes and also obeys the acoustic sum rule through an
            iterative procedure

            Args:
                force (float): maximum force constant
                asum (int): number of iterations to attempt to obey the acoustic sum
                    rule

            Return:
                NxNx3x3 np.array representing the force constant matrix

            """

            numsites = len(self.structure.sites)
            structure = pymatgen.io.phonopy.get_phonopy_structure(self.structure)
            pnstruc = Phonopy(structure, np.eye(3), np.eye(3))

            dyn = self.get_unstable_FCM(force)
            dyn = self.get_stable_FCM(dyn)

            dyn = np.reshape(dyn, (numsites, 3, numsites, 3)).swapaxes(1, 2)

            dynmass = np.zeros([len(self.structure), len(self.structure), 3, 3])
            masses = []
            for j in range(numsites):
                masses.append(self.structure.sites[j].specie.atomic_mass)
            dynmass = np.zeros([numsites, numsites, 3, 3])
            for m in range(numsites):
                for n in range(numsites):
                    dynmass[m][n] = dyn[m][n] * np.sqrt(masses[m]) * np.sqrt(masses[n])

            supercell = pnstruc.get_supercell()
            primitive = pnstruc.get_primitive()

            converter = dyntofc.DynmatToForceConstants(primitive, supercell)

            dyn = np.reshape(np.swapaxes(dynmass, 1, 2), (numsites * 3, numsites * 3))

            converter.set_dynamical_matrices(dynmat=[dyn])

            converter.run()
            fc = converter.get_force_constants()

            return fc

    def get_piezo(BEC, IST, FCM, rcond=0.0001):
        """
        Generate a random piezoelectric tensor based on a structure and corresponding
        symmetry

        Args:
            BEC (numpy array): Nx3x3 array representing the born effective charge tensor
            IST (numpy array): Nx3x3x3 array representing the internal strain tensor
            FCM (numpy array): NxNx3x3 array representing the born effective charge tensor
            rcondy (float): condition for excluding eigenvalues in the pseudoinverse

        Return:
            3x3x3 calculated Piezo tensor
        """

        numsites = len(BEC)
        temp_fcm = np.reshape(np.swapaxes(FCM, 1, 2), (numsites * 3, numsites * 3))

        eigs, vecs = np.linalg.eig(temp_fcm)
        K = np.linalg.pinv(
            -temp_fcm,
            rcond=np.abs(eigs[np.argsort(np.abs(eigs))[2]])
            / np.abs(eigs[np.argsort(np.abs(eigs))[-1]])
            + rcond,
        )

        K = np.reshape(K, (numsites, 3, numsites, 3)).swapaxes(1, 2)
        return np.einsum("ikl,ijlm,jmno->kno", BEC, K, IST) * 16.0216559424

    @requires(Phonopy, "phonopy not installed!")
    def rand_piezo(struc, pointops, sharedops, BEC, IST, FCM, anumiter=10):
        """
        Generate a random piezoelectric tensor based on a structure and corresponding
        symmetry

        Args:
            struc (pymatgen structure): structure whose symmetry operations the piezo tensor must obey
            pointops: list of point operations obeyed by a single atomic site
            sharedops: list of point operations shared by a pair of atomic sites
            BEC (numpy array): Nx3x3 array representing the born effective charge tensor
            IST (numpy array): Nx3x3x3 array representing the internal strain tensor
            FCM (numpy array): NxNx3x3 array representing the born effective charge tensor
            anumiter (int): number of iterations for acoustic sum rule convergence
        Return:
            list in the form of [Nx3x3 random born effective charge tenosr,
            Nx3x3x3 random internal strain tensor, NxNx3x3 random force constant matrix, 3x3x3 piezo tensor]
        """
        bec = BornEffectiveCharge(struc, BEC, pointops)
        bec.get_BEC_operations()
        rand_BEC = bec.get_rand_BEC()

        ist = InternalStrainTensor(struc, IST, pointops)
        ist.get_IST_operations()
        rand_IST = ist.get_rand_IST()

        fcm = ForceConstantMatrix(struc, FCM, pointops, sharedops)
        fcm.get_FCM_operations()
        rand_FCM = fcm.get_rand_FCM()

        P = get_piezo(rand_BEC, rand_IST, rand_FCM) * 16.0216559424 / struc.volume

        return (rand_BEC, rand_IST, rand_FCM, P)