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| from sympy.core.symbol import symbols | |
| from sympy.core.function import Function | |
| from sympy.matrices.dense import Matrix | |
| from sympy.matrices.dense import zeros | |
| from sympy.simplify.simplify import simplify | |
| from sympy.codegen.matrix_nodes import MatrixSolve | |
| from sympy.utilities.lambdify import lambdify | |
| from sympy.printing.numpy import NumPyPrinter | |
| from sympy.testing.pytest import skip | |
| from sympy.external import import_module | |
| def test_matrix_solve_issue_24862(): | |
| A = Matrix(3, 3, symbols('a:9')) | |
| b = Matrix(3, 1, symbols('b:3')) | |
| hash(MatrixSolve(A, b)) | |
| def test_matrix_solve_derivative_exact(): | |
| q = symbols('q') | |
| a11, a12, a21, a22, b1, b2 = ( | |
| f(q) for f in symbols('a11 a12 a21 a22 b1 b2', cls=Function)) | |
| A = Matrix([[a11, a12], [a21, a22]]) | |
| b = Matrix([b1, b2]) | |
| x_lu = A.LUsolve(b) | |
| dxdq_lu = A.LUsolve(b.diff(q) - A.diff(q) * A.LUsolve(b)) | |
| assert simplify(x_lu.diff(q) - dxdq_lu) == zeros(2, 1) | |
| # dxdq_ms is the MatrixSolve equivalent of dxdq_lu | |
| dxdq_ms = MatrixSolve(A, b.diff(q) - A.diff(q) * MatrixSolve(A, b)) | |
| assert MatrixSolve(A, b).diff(q) == dxdq_ms | |
| def test_matrix_solve_derivative_numpy(): | |
| np = import_module('numpy') | |
| if not np: | |
| skip("numpy not installed.") | |
| q = symbols('q') | |
| a11, a12, a21, a22, b1, b2 = ( | |
| f(q) for f in symbols('a11 a12 a21 a22 b1 b2', cls=Function)) | |
| A = Matrix([[a11, a12], [a21, a22]]) | |
| b = Matrix([b1, b2]) | |
| dx_lu = A.LUsolve(b).diff(q) | |
| subs = {a11.diff(q): 0.2, a12.diff(q): 0.3, a21.diff(q): 0.1, | |
| a22.diff(q): 0.5, b1.diff(q): 0.4, b2.diff(q): 0.9, | |
| a11: 1.3, a12: 0.5, a21: 1.2, a22: 4, b1: 6.2, b2: 3.5} | |
| p, p_vals = zip(*subs.items()) | |
| dx_sm = MatrixSolve(A, b).diff(q) | |
| np.testing.assert_allclose( | |
| lambdify(p, dx_sm, printer=NumPyPrinter)(*p_vals), | |
| lambdify(p, dx_lu, printer=NumPyPrinter)(*p_vals)) | |