def test_doit_args(): A = ImmutableMatrix([[1, 2], [3, 4]]) B = ImmutableMatrix([[2, 3], [4, 5]]) assert MatAdd(A, MatPow(B, 2)).doit() == A + B**2 assert MatAdd(A, MatMul(A, B)).doit() == A + A*B assert (MatAdd(A, X, MatMul(A, B), Y, MatAdd(2*A, B)).doit() == MatAdd(3*A + A*B + B, X, Y))
def _eval_derivative_matrix_lines(self, x): from sympy.core.expr import ExprBuilder from sympy.codegen.array_utils import ( CodegenArrayContraction, CodegenArrayTensorProduct, ) from .matmul import MatMul from .inverse import Inverse exp = self.exp if self.base.shape == (1, 1) and not exp.has(x): lr = self.base._eval_derivative_matrix_lines(x) for i in lr: subexpr = ExprBuilder( CodegenArrayContraction, [ ExprBuilder( CodegenArrayTensorProduct, [ Identity(1), i._lines[0], exp * self.base**(exp - 1), i._lines[1], Identity(1), ], ), (0, 3, 4), (5, 7, 8), ], validator=CodegenArrayContraction._validate, ) i._first_pointer_parent = subexpr.args[0].args i._first_pointer_index = 0 i._second_pointer_parent = subexpr.args[0].args i._second_pointer_index = 4 i._lines = [subexpr] return lr if (exp > 0) == True: newexpr = MatMul.fromiter([self.base for i in range(exp)]) elif (exp == -1) == True: return Inverse(self.base)._eval_derivative_matrix_lines(x) elif (exp < 0) == True: newexpr = MatMul.fromiter( [Inverse(self.base) for i in range(-exp)]) elif (exp == 0) == True: return self.doit()._eval_derivative_matrix_lines(x) else: raise NotImplementedError("cannot evaluate %s derived by %s" % (self, x)) return newexpr._eval_derivative_matrix_lines(x)
def _eval_derivative_matrix_lines(self, x): from .matmul import MatMul exp = self.exp if (exp > 0) == True: newexpr = MatMul.fromiter([self.base for i in range(exp)]) elif (exp == -1) == True: return Inverse(self.base)._eval_derivative_matrix_lines(x) elif (exp < 0) == True: newexpr = MatMul.fromiter([Inverse(self.base) for i in range(-exp)]) elif (exp == 0) == True: return self.doit()._eval_derivative_matrix_lines(x) else: raise NotImplementedError("cannot evaluate %s derived by %s" % (self, x)) return newexpr._eval_derivative_matrix_lines(x)
def _entry(self, i, j, **kwargs): from sympy.matrices.expressions import MatMul A = self.doit() if isinstance(A, MatPow): # We still have a MatPow, make an explicit MatMul out of it. if A.exp.is_Integer and A.exp.is_positive: A = MatMul(*[A.base for k in range(A.exp)]) elif not self._is_shape_symbolic(): return A._get_explicit_matrix()[i, j] else: # Leave the expression unevaluated: from sympy.matrices.expressions.matexpr import MatrixElement return MatrixElement(self, i, j) return A[i, j]
def _eval_derivative_matrix_lines(self, x): from .matmul import MatMul from .inverse import Inverse exp = self.exp if (exp > 0) == True: newexpr = MatMul.fromiter([self.base for i in range(exp)]) elif (exp == -1) == True: return Inverse(self.base)._eval_derivative_matrix_lines(x) elif (exp < 0) == True: newexpr = MatMul.fromiter([Inverse(self.base) for i in range(-exp)]) elif (exp == 0) == True: return self.doit()._eval_derivative_matrix_lines(x) else: raise NotImplementedError("cannot evaluate %s derived by %s" % (self, x)) return newexpr._eval_derivative_matrix_lines(x)
def test_Trace_doit_deep_False(): X = Matrix([[1, 2], [3, 4]]) q = MatPow(X, 2) assert Trace(q).doit(deep=False).arg == q q = MatAdd(X, 2 * X) assert Trace(q).doit(deep=False).arg == q q = MatMul(X, 2 * X) assert Trace(q).doit(deep=False).arg == q
def _(expr, assumptions): factor, mmul = expr.as_coeff_mmul() if (all(ask(Q.positive_definite(arg), assumptions) for arg in mmul.args) and factor > 0): return True if (len(mmul.args) >= 2 and mmul.args[0] == mmul.args[-1].T and ask(Q.fullrank(mmul.args[0]), assumptions)): return ask(Q.positive_definite(MatMul(*mmul.args[1:-1])), assumptions)
def MatMul(expr, assumptions): factor, mmul = expr.as_coeff_mmul() if all(ask(Q.symmetric(arg), assumptions) for arg in mmul.args): return True if len(mmul.args) >= 2 and mmul.args[0] == mmul.args[-1].T: if len(mmul.args) == 2: return True return ask(Q.symmetric(MatMul(*mmul.args[1:-1])), assumptions)
def _eval_derivative_matrix_lines(self, x): from sympy.core.expr import ExprBuilder from sympy.codegen.array_utils import CodegenArrayContraction, CodegenArrayTensorProduct from .matmul import MatMul from .inverse import Inverse exp = self.exp if self.base.shape == (1, 1) and not exp.has(x): lr = self.base._eval_derivative_matrix_lines(x) for i in lr: subexpr = ExprBuilder( CodegenArrayContraction, [ ExprBuilder( CodegenArrayTensorProduct, [ Identity(1), i._lines[0], exp*self.base**(exp-1), i._lines[1], Identity(1), ] ), (0, 3, 4), (5, 7, 8) ], validator=CodegenArrayContraction._validate ) i._first_pointer_parent = subexpr.args[0].args i._first_pointer_index = 0 i._second_pointer_parent = subexpr.args[0].args i._second_pointer_index = 4 i._lines = [subexpr] return lr if (exp > 0) == True: newexpr = MatMul.fromiter([self.base for i in range(exp)]) elif (exp == -1) == True: return Inverse(self.base)._eval_derivative_matrix_lines(x) elif (exp < 0) == True: newexpr = MatMul.fromiter([Inverse(self.base) for i in range(-exp)]) elif (exp == 0) == True: return self.doit()._eval_derivative_matrix_lines(x) else: raise NotImplementedError("cannot evaluate %s derived by %s" % (self, x)) return newexpr._eval_derivative_matrix_lines(x)
def _entry(self, i, j, **kwargs): from sympy.matrices.expressions import MatMul A = self.doit() if isinstance(A, MatPow): # We still have a MatPow, make an explicit MatMul out of it. if not A.base.is_square: raise ShapeError("Power of non-square matrix %s" % A.base) elif A.exp.is_Integer and A.exp.is_positive: A = MatMul(*[A.base for k in range(A.exp)]) #elif A.exp.is_Integer and self.exp.is_negative: # Note: possible future improvement: in principle we can take # positive powers of the inverse, but carefully avoid recursion, # perhaps by adding `_entry` to Inverse (as it is our subclass). # T = A.base.as_explicit().inverse() # A = MatMul(*[T for k in range(-A.exp)]) else: # Leave the expression unevaluated: from sympy.matrices.expressions.matexpr import MatrixElement return MatrixElement(self, i, j) return A._entry(i, j)
def MatMul(expr, assumptions): factor, mmul = expr.as_coeff_mmul() if all(ask(Q.symmetric(arg), assumptions) for arg in mmul.args): return True # TODO: implement sathandlers system for the matrices. # Now it duplicates the general fact: Implies(Q.diagonal, Q.symmetric). if ask(Q.diagonal(expr), assumptions): return True if len(mmul.args) >= 2 and mmul.args[0] == mmul.args[-1].T: if len(mmul.args) == 2: return True return ask(Q.symmetric(MatMul(*mmul.args[1:-1])), assumptions)
def test_doit_nested_MatrixExpr(): X = ImmutableMatrix([[1, 2], [3, 4]]) Y = ImmutableMatrix([[2, 3], [4, 5]]) assert MatPow(MatMul(X, Y), 2).doit() == (X*Y)**2 assert MatPow(MatAdd(X, Y), 2).doit() == (X + Y)**2
def test_trace_constant_factor(): # Issue 9052: gave 2*Trace(MatMul(A)) instead of 2*Trace(A) assert trace(2 * A) == 2 * Trace(A) X = ImmutableMatrix([[1, 2], [3, 4]]) assert trace(MatMul(2, X)) == 10
def test_bc_matpow(): A = MatrixSymbol('A', n, n) assert bc_matpow(A**2) == MatMul(A, A, evaluate=False) assert bc_matpow(A**n) == A**n
def test_trace_constant_factor(): # Issue 9052: LHS gives Trace(MatMul(A)) assert trace(2 * A) == 2 * Trace(A) X = ImmutableMatrix([[1, 2], [3, 4]]) assert trace(MatMul(2, X)) == 10