switching to high quality piper tts and added label translations
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Matthias Hinrichs
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"""Utilities to deal with sympy.Matrix, numpy and scipy.sparse."""
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from sympy.core.expr import Expr
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from sympy.core.numbers import I
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from sympy.core.singleton import S
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from sympy.matrices.matrixbase import MatrixBase
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from sympy.matrices import eye, zeros
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from sympy.external import import_module
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__all__ = [
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'numpy_ndarray',
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'scipy_sparse_matrix',
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'sympy_to_numpy',
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'sympy_to_scipy_sparse',
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'numpy_to_sympy',
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'scipy_sparse_to_sympy',
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'flatten_scalar',
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'matrix_dagger',
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'to_sympy',
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'to_numpy',
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'to_scipy_sparse',
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'matrix_tensor_product',
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'matrix_zeros'
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]
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# Conditionally define the base classes for numpy and scipy.sparse arrays
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# for use in isinstance tests.
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np = import_module('numpy')
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if not np:
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class numpy_ndarray:
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pass
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else:
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numpy_ndarray = np.ndarray # type: ignore
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scipy = import_module('scipy', import_kwargs={'fromlist': ['sparse']})
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if not scipy:
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class scipy_sparse_matrix:
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pass
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sparse = None
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else:
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sparse = scipy.sparse
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scipy_sparse_matrix = sparse.spmatrix # type: ignore
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def sympy_to_numpy(m, **options):
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"""Convert a SymPy Matrix/complex number to a numpy matrix or scalar."""
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if not np:
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raise ImportError
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dtype = options.get('dtype', 'complex')
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if isinstance(m, MatrixBase):
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return np.array(m.tolist(), dtype=dtype)
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elif isinstance(m, Expr):
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if m.is_Number or m.is_NumberSymbol or m == I:
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return complex(m)
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raise TypeError('Expected MatrixBase or complex scalar, got: %r' % m)
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def sympy_to_scipy_sparse(m, **options):
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"""Convert a SymPy Matrix/complex number to a numpy matrix or scalar."""
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if not np or not sparse:
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raise ImportError
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dtype = options.get('dtype', 'complex')
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if isinstance(m, MatrixBase):
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return sparse.csr_matrix(np.array(m.tolist(), dtype=dtype))
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elif isinstance(m, Expr):
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if m.is_Number or m.is_NumberSymbol or m == I:
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return complex(m)
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raise TypeError('Expected MatrixBase or complex scalar, got: %r' % m)
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def scipy_sparse_to_sympy(m, **options):
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"""Convert a scipy.sparse matrix to a SymPy matrix."""
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return MatrixBase(m.todense())
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def numpy_to_sympy(m, **options):
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"""Convert a numpy matrix to a SymPy matrix."""
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return MatrixBase(m)
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def to_sympy(m, **options):
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"""Convert a numpy/scipy.sparse matrix to a SymPy matrix."""
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if isinstance(m, MatrixBase):
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return m
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elif isinstance(m, numpy_ndarray):
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return numpy_to_sympy(m)
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elif isinstance(m, scipy_sparse_matrix):
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return scipy_sparse_to_sympy(m)
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elif isinstance(m, Expr):
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return m
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raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)
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def to_numpy(m, **options):
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"""Convert a sympy/scipy.sparse matrix to a numpy matrix."""
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dtype = options.get('dtype', 'complex')
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if isinstance(m, (MatrixBase, Expr)):
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return sympy_to_numpy(m, dtype=dtype)
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elif isinstance(m, numpy_ndarray):
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return m
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elif isinstance(m, scipy_sparse_matrix):
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return m.todense()
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raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)
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def to_scipy_sparse(m, **options):
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"""Convert a sympy/numpy matrix to a scipy.sparse matrix."""
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dtype = options.get('dtype', 'complex')
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if isinstance(m, (MatrixBase, Expr)):
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return sympy_to_scipy_sparse(m, dtype=dtype)
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elif isinstance(m, numpy_ndarray):
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if not sparse:
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raise ImportError
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return sparse.csr_matrix(m)
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elif isinstance(m, scipy_sparse_matrix):
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return m
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raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % m)
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def flatten_scalar(e):
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"""Flatten a 1x1 matrix to a scalar, return larger matrices unchanged."""
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if isinstance(e, MatrixBase):
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if e.shape == (1, 1):
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e = e[0]
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if isinstance(e, (numpy_ndarray, scipy_sparse_matrix)):
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if e.shape == (1, 1):
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e = complex(e[0, 0])
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return e
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def matrix_dagger(e):
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"""Return the dagger of a sympy/numpy/scipy.sparse matrix."""
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if isinstance(e, MatrixBase):
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return e.H
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elif isinstance(e, (numpy_ndarray, scipy_sparse_matrix)):
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return e.conjugate().transpose()
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raise TypeError('Expected sympy/numpy/scipy.sparse matrix, got: %r' % e)
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# TODO: Move this into sympy.matrices.
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def _sympy_tensor_product(*matrices):
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"""Compute the kronecker product of a sequence of SymPy Matrices.
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"""
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from sympy.matrices.expressions.kronecker import matrix_kronecker_product
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return matrix_kronecker_product(*matrices)
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def _numpy_tensor_product(*product):
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"""numpy version of tensor product of multiple arguments."""
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if not np:
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raise ImportError
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answer = product[0]
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for item in product[1:]:
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answer = np.kron(answer, item)
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return answer
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def _scipy_sparse_tensor_product(*product):
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"""scipy.sparse version of tensor product of multiple arguments."""
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if not sparse:
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raise ImportError
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answer = product[0]
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for item in product[1:]:
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answer = sparse.kron(answer, item)
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# The final matrices will just be multiplied, so csr is a good final
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# sparse format.
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return sparse.csr_matrix(answer)
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def matrix_tensor_product(*product):
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"""Compute the matrix tensor product of sympy/numpy/scipy.sparse matrices."""
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if isinstance(product[0], MatrixBase):
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return _sympy_tensor_product(*product)
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elif isinstance(product[0], numpy_ndarray):
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return _numpy_tensor_product(*product)
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elif isinstance(product[0], scipy_sparse_matrix):
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return _scipy_sparse_tensor_product(*product)
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def _numpy_eye(n):
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"""numpy version of complex eye."""
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if not np:
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raise ImportError
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return np.array(np.eye(n, dtype='complex'))
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def _scipy_sparse_eye(n):
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"""scipy.sparse version of complex eye."""
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if not sparse:
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raise ImportError
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return sparse.eye(n, n, dtype='complex')
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def matrix_eye(n, **options):
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"""Get the version of eye and tensor_product for a given format."""
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format = options.get('format', 'sympy')
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if format == 'sympy':
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return eye(n)
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elif format == 'numpy':
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return _numpy_eye(n)
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elif format == 'scipy.sparse':
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return _scipy_sparse_eye(n)
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raise NotImplementedError('Invalid format: %r' % format)
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def _numpy_zeros(m, n, **options):
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"""numpy version of zeros."""
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dtype = options.get('dtype', 'float64')
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if not np:
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raise ImportError
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return np.zeros((m, n), dtype=dtype)
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def _scipy_sparse_zeros(m, n, **options):
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"""scipy.sparse version of zeros."""
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spmatrix = options.get('spmatrix', 'csr')
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dtype = options.get('dtype', 'float64')
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if not sparse:
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raise ImportError
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if spmatrix == 'lil':
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return sparse.lil_matrix((m, n), dtype=dtype)
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elif spmatrix == 'csr':
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return sparse.csr_matrix((m, n), dtype=dtype)
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def matrix_zeros(m, n, **options):
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""""Get a zeros matrix for a given format."""
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format = options.get('format', 'sympy')
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if format == 'sympy':
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return zeros(m, n)
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elif format == 'numpy':
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return _numpy_zeros(m, n, **options)
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elif format == 'scipy.sparse':
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return _scipy_sparse_zeros(m, n, **options)
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raise NotImplementedError('Invaild format: %r' % format)
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def _numpy_matrix_to_zero(e):
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"""Convert a numpy zero matrix to the zero scalar."""
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if not np:
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raise ImportError
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test = np.zeros_like(e)
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if np.allclose(e, test):
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return 0.0
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else:
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return e
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def _scipy_sparse_matrix_to_zero(e):
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"""Convert a scipy.sparse zero matrix to the zero scalar."""
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if not np:
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raise ImportError
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edense = e.todense()
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test = np.zeros_like(edense)
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if np.allclose(edense, test):
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return 0.0
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else:
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return e
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def matrix_to_zero(e):
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"""Convert a zero matrix to the scalar zero."""
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if isinstance(e, MatrixBase):
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if zeros(*e.shape) == e:
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e = S.Zero
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elif isinstance(e, numpy_ndarray):
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e = _numpy_matrix_to_zero(e)
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elif isinstance(e, scipy_sparse_matrix):
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e = _scipy_sparse_matrix_to_zero(e)
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return e
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