Sources_For_Win/ParaView/Lib/site-packages/sympy/physics/quantum/matrixutils.py

"""Utilities to deal with sympy.Matrix, numpy and scipy.sparse."""

from sympy.core.expr import Expr
from sympy.core.numbers import I
from sympy.core.singleton import S
from sympy.matrices.matrices import MatrixBase
from sympy.matrices import eye, zeros
from sympy.external import import_module

__all__ = [
    'numpy_ndarray',
    'scipy_sparse_matrix',
    'sympy_to_numpy',
    'sympy_to_scipy_sparse',
    'numpy_to_sympy',
    'scipy_sparse_to_sympy',
    'flatten_scalar',
    'matrix_dagger',
    'to_sympy',
    'to_numpy',
    'to_scipy_sparse',
    'matrix_tensor_product',
    'matrix_zeros'
]

# Conditionally define the base classes for numpy and scipy.sparse arrays
# for use in isinstance tests.

np = import_module('numpy')
if not np:
    class numpy_ndarray:
        pass
else:
    numpy_ndarray = np.ndarray  # type: ignore

scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
if not scipy:
    class scipy_sparse_matrix:
        pass
    sparse = None
else:
    sparse = scipy.sparse
    scipy_sparse_matrix = sparse.spmatrix # type: ignore


def sympy_to_numpy(m, **options):
    """Convert a SymPy Matrix/complex number to a numpy matrix or scalar."""
    if not np:
        raise ImportError
    dtype = options.get('dtype', 'complex')
    if isinstance(m, MatrixBase):
        return np.matrix(m.tolist(), dtype=dtype)
    elif isinstance(m, Expr):
        if m.is_Number or m.is_NumberSymbol or m == I:
            return complex(m)
    raise TypeError('Expected MatrixBase or complex scalar, got: %r' % m)


def sympy_to_scipy_sparse(m, **options):
    """Convert a SymPy Matrix/complex number to a numpy matrix or scalar."""
    if not np or not sparse:
        raise ImportError
    dtype = options.get('dtype', 'complex')
    if isinstance(m, MatrixBase):
        return sparse.csr_matrix(np.matrix(m.tolist(), dtype=dtype))
    elif isinstance(m, Expr):
        if m.is_Number or m.is_NumberSymbol or m == I:
            return complex(m)
    raise TypeError('Expected MatrixBase or complex scalar, got: %r' % m)


def scipy_sparse_to_sympy(m, **options):
    """Convert a scipy.sparse matrix to a SymPy matrix."""
    return MatrixBase(m.todense())


def numpy_to_sympy(m, **options):
    """Convert a numpy matrix to a SymPy matrix."""
    return MatrixBase(m)


def to_sympy(m, **options):
    """Convert a numpy/scipy.sparse matrix to a SymPy matrix."""
    if isinstance(m, MatrixBase):
        return m
    elif isinstance(m, numpy_ndarray):
        return numpy_to_sympy(m)
    elif isinstance(m, scipy_sparse_matrix):
        return scipy_sparse_to_sympy(m)
    elif isinstance(m, Expr):
        return m
    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)


def to_numpy(m, **options):
    """Convert a sympy/scipy.sparse matrix to a numpy matrix."""
    dtype = options.get('dtype', 'complex')
    if isinstance(m, (MatrixBase, Expr)):
        return sympy_to_numpy(m, dtype=dtype)
    elif isinstance(m, numpy_ndarray):
        return m
    elif isinstance(m, scipy_sparse_matrix):
        return m.todense()
    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)


def to_scipy_sparse(m, **options):
    """Convert a sympy/numpy matrix to a scipy.sparse matrix."""
    dtype = options.get('dtype', 'complex')
    if isinstance(m, (MatrixBase, Expr)):
        return sympy_to_scipy_sparse(m, dtype=dtype)
    elif isinstance(m, numpy_ndarray):
        if not sparse:
            raise ImportError
        return sparse.csr_matrix(m)
    elif isinstance(m, scipy_sparse_matrix):
        return m
    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)


def flatten_scalar(e):
    """Flatten a 1x1 matrix to a scalar, return larger matrices unchanged."""
    if isinstance(e, MatrixBase):
        if e.shape == (1, 1):
            e = e[0]
    if isinstance(e, (numpy_ndarray, scipy_sparse_matrix)):
        if e.shape == (1, 1):
            e = complex(e[0, 0])
    return e


def matrix_dagger(e):
    """Return the dagger of a sympy/numpy/scipy.sparse matrix."""
    if isinstance(e, MatrixBase):
        return e.H
    elif isinstance(e, (numpy_ndarray, scipy_sparse_matrix)):
        return e.conjugate().transpose()
    raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % e)


# TODO: Move this into sympy.matricies.
def _sympy_tensor_product(*matrices):
    """Compute the kronecker product of a sequence of SymPy Matrices.
    """
    from sympy.matrices.expressions.kronecker import matrix_kronecker_product

    return matrix_kronecker_product(*matrices)


def _numpy_tensor_product(*product):
    """numpy version of tensor product of multiple arguments."""
    if not np:
        raise ImportError
    answer = product[0]
    for item in product[1:]:
        answer = np.kron(answer, item)
    return answer


def _scipy_sparse_tensor_product(*product):
    """scipy.sparse version of tensor product of multiple arguments."""
    if not sparse:
        raise ImportError
    answer = product[0]
    for item in product[1:]:
        answer = sparse.kron(answer, item)
    # The final matrices will just be multiplied, so csr is a good final
    # sparse format.
    return sparse.csr_matrix(answer)


def matrix_tensor_product(*product):
    """Compute the matrix tensor product of sympy/numpy/scipy.sparse matrices."""
    if isinstance(product[0], MatrixBase):
        return _sympy_tensor_product(*product)
    elif isinstance(product[0], numpy_ndarray):
        return _numpy_tensor_product(*product)
    elif isinstance(product[0], scipy_sparse_matrix):
        return _scipy_sparse_tensor_product(*product)


def _numpy_eye(n):
    """numpy version of complex eye."""
    if not np:
        raise ImportError
    return np.matrix(np.eye(n, dtype='complex'))


def _scipy_sparse_eye(n):
    """scipy.sparse version of complex eye."""
    if not sparse:
        raise ImportError
    return sparse.eye(n, n, dtype='complex')


def matrix_eye(n, **options):
    """Get the version of eye and tensor_product for a given format."""
    format = options.get('format', 'sympy')
    if format == 'sympy':
        return eye(n)
    elif format == 'numpy':
        return _numpy_eye(n)
    elif format == 'scipy.sparse':
        return _scipy_sparse_eye(n)
    raise NotImplementedError('Invalid format: %r' % format)


def _numpy_zeros(m, n, **options):
    """numpy version of zeros."""
    dtype = options.get('dtype', 'float64')
    if not np:
        raise ImportError
    return np.zeros((m, n), dtype=dtype)


def _scipy_sparse_zeros(m, n, **options):
    """scipy.sparse version of zeros."""
    spmatrix = options.get('spmatrix', 'csr')
    dtype = options.get('dtype', 'float64')
    if not sparse:
        raise ImportError
    if spmatrix == 'lil':
        return sparse.lil_matrix((m, n), dtype=dtype)
    elif spmatrix == 'csr':
        return sparse.csr_matrix((m, n), dtype=dtype)


def matrix_zeros(m, n, **options):
    """"Get a zeros matrix for a given format."""
    format = options.get('format', 'sympy')
    if format == 'sympy':
        return zeros(m, n)
    elif format == 'numpy':
        return _numpy_zeros(m, n, **options)
    elif format == 'scipy.sparse':
        return _scipy_sparse_zeros(m, n, **options)
    raise NotImplementedError('Invaild format: %r' % format)


def _numpy_matrix_to_zero(e):
    """Convert a numpy zero matrix to the zero scalar."""
    if not np:
        raise ImportError
    test = np.zeros_like(e)
    if np.allclose(e, test):
        return 0.0
    else:
        return e


def _scipy_sparse_matrix_to_zero(e):
    """Convert a scipy.sparse zero matrix to the zero scalar."""
    if not np:
        raise ImportError
    edense = e.todense()
    test = np.zeros_like(edense)
    if np.allclose(edense, test):
        return 0.0
    else:
        return e


def matrix_to_zero(e):
    """Convert a zero matrix to the scalar zero."""
    if isinstance(e, MatrixBase):
        if zeros(*e.shape) == e:
            e = S.Zero
    elif isinstance(e, numpy_ndarray):
        e = _numpy_matrix_to_zero(e)
    elif isinstance(e, scipy_sparse_matrix):
        e = _scipy_sparse_matrix_to_zero(e)
    return e