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