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51 lines
1.9 KiB
51 lines
1.9 KiB
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 is the MatrixSolve equivalent of dxdq_lu
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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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