Spaces:
Sleeping
Sleeping
| from sympy.core.assumptions import check_assumptions | |
| from sympy.core.logic import fuzzy_and | |
| from sympy.core.sympify import _sympify | |
| from sympy.matrices.kind import MatrixKind | |
| from sympy.sets.sets import Set, SetKind | |
| from sympy.core.kind import NumberKind | |
| from .matexpr import MatrixExpr | |
| class MatrixSet(Set): | |
| """ | |
| MatrixSet represents the set of matrices with ``shape = (n, m)`` over the | |
| given set. | |
| Examples | |
| ======== | |
| >>> from sympy.matrices import MatrixSet | |
| >>> from sympy import S, I, Matrix | |
| >>> M = MatrixSet(2, 2, set=S.Reals) | |
| >>> X = Matrix([[1, 2], [3, 4]]) | |
| >>> X in M | |
| True | |
| >>> X = Matrix([[1, 2], [I, 4]]) | |
| >>> X in M | |
| False | |
| """ | |
| is_empty = False | |
| def __new__(cls, n, m, set): | |
| n, m, set = _sympify(n), _sympify(m), _sympify(set) | |
| cls._check_dim(n) | |
| cls._check_dim(m) | |
| if not isinstance(set, Set): | |
| raise TypeError("{} should be an instance of Set.".format(set)) | |
| return Set.__new__(cls, n, m, set) | |
| def shape(self): | |
| return self.args[:2] | |
| def set(self): | |
| return self.args[2] | |
| def _contains(self, other): | |
| if not isinstance(other, MatrixExpr): | |
| raise TypeError("{} should be an instance of MatrixExpr.".format(other)) | |
| if other.shape != self.shape: | |
| are_symbolic = any(_sympify(x).is_Symbol for x in other.shape + self.shape) | |
| if are_symbolic: | |
| return None | |
| return False | |
| return fuzzy_and(self.set.contains(x) for x in other) | |
| def _check_dim(cls, dim): | |
| """Helper function to check invalid matrix dimensions""" | |
| ok = not dim.is_Float and check_assumptions( | |
| dim, integer=True, nonnegative=True) | |
| if ok is False: | |
| raise ValueError( | |
| "The dimension specification {} should be " | |
| "a nonnegative integer.".format(dim)) | |
| def _kind(self): | |
| return SetKind(MatrixKind(NumberKind)) | |