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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))
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