def _eval_expand_basic(self, **hints): summand = self.function.expand(**hints) if summand.is_Add and summand.is_commutative: return Add(*[ self.func(i, *self.limits) for i in summand.args ]) elif summand.is_Matrix: return Matrix._new(summand.rows, summand.cols, [self.func(i, *self.limits) for i in summand._mat]) elif summand != self.function: return self.func(summand, *self.limits) return self
def _eval_expand_basic(self, **hints): summand = self.function.expand(**hints) if summand.is_Add and summand.is_commutative: return Add(*[self.func(i, *self.limits) for i in summand.args]) elif summand.is_Matrix: return Matrix._new(summand.rows, summand.cols, [self.func(i, *self.limits) for i in summand._mat]) elif summand != self.function: return self.func(summand, *self.limits) return self
def diag(*values, **kwargs): """Create a sparse, diagonal matrix from a list of diagonal values. Notes ===== When arguments are matrices they are fitted in resultant matrix. The returned matrix is a mutable, dense matrix. To make it a different type, send the desired class for keyword ``cls``. Examples ======== >>> from sympy.matrices import diag, Matrix, ones >>> diag(1, 2, 3) Matrix([ [1, 0, 0], [0, 2, 0], [0, 0, 3]]) >>> diag(*[1, 2, 3]) Matrix([ [1, 0, 0], [0, 2, 0], [0, 0, 3]]) The diagonal elements can be matrices; diagonal filling will continue on the diagonal from the last element of the matrix: >>> from sympy.abc import x, y, z >>> a = Matrix([x, y, z]) >>> b = Matrix([[1, 2], [3, 4]]) >>> c = Matrix([[5, 6]]) >>> diag(a, 7, b, c) Matrix([ [x, 0, 0, 0, 0, 0], [y, 0, 0, 0, 0, 0], [z, 0, 0, 0, 0, 0], [0, 7, 0, 0, 0, 0], [0, 0, 1, 2, 0, 0], [0, 0, 3, 4, 0, 0], [0, 0, 0, 0, 5, 6]]) When diagonal elements are lists, they will be treated as arguments to Matrix: >>> diag([1, 2, 3], 4) Matrix([ [1, 0], [2, 0], [3, 0], [0, 4]]) >>> diag([[1, 2, 3]], 4) Matrix([ [1, 2, 3, 0], [0, 0, 0, 4]]) A given band off the diagonal can be made by padding with a vertical or horizontal "kerning" vector: >>> hpad = ones(0, 2) >>> vpad = ones(2, 0) >>> diag(vpad, 1, 2, 3, hpad) + diag(hpad, 4, 5, 6, vpad) Matrix([ [0, 0, 4, 0, 0], [0, 0, 0, 5, 0], [1, 0, 0, 0, 6], [0, 2, 0, 0, 0], [0, 0, 3, 0, 0]]) The type is mutable by default but can be made immutable by setting the ``mutable`` flag to False: >>> type(diag(1)) <class 'sympy.matrices.dense.MutableDenseMatrix'> >>> from sympy.matrices import ImmutableMatrix >>> type(diag(1, cls=ImmutableMatrix)) <class 'sympy.matrices.immutable.ImmutableMatrix'> See Also ======== eye """ from .sparse import MutableSparseMatrix cls = kwargs.pop('cls', None) if cls is None: from .dense import Matrix as cls if kwargs: raise ValueError('unrecognized keyword%s: %s' % ( 's' if len(kwargs) > 1 else '', ', '.join(kwargs.keys()))) rows = 0 cols = 0 values = list(values) for i in range(len(values)): m = values[i] if isinstance(m, MatrixBase): rows += m.rows cols += m.cols elif is_sequence(m): m = values[i] = Matrix(m) rows += m.rows cols += m.cols else: rows += 1 cols += 1 res = MutableSparseMatrix.zeros(rows, cols) i_row = 0 i_col = 0 for m in values: if isinstance(m, MatrixBase): res[i_row:i_row + m.rows, i_col:i_col + m.cols] = m i_row += m.rows i_col += m.cols else: res[i_row, i_col] = m i_row += 1 i_col += 1 return cls._new(res)