112 lines
3.3 KiB
Python
112 lines
3.3 KiB
Python
#
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# test_linsolve.py
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#
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# Test the internal implementation of linsolve.
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#
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from sympy.testing.pytest import raises
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from sympy.core.numbers import I
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from sympy.core.relational import Eq
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from sympy.core.singleton import S
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from sympy.abc import x, y, z
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from sympy.polys.matrices.linsolve import _linsolve
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from sympy.polys.solvers import PolyNonlinearError
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def test__linsolve():
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assert _linsolve([], [x]) == {x:x}
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assert _linsolve([S.Zero], [x]) == {x:x}
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assert _linsolve([x-1,x-2], [x]) is None
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assert _linsolve([x-1], [x]) == {x:1}
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assert _linsolve([x-1, y], [x, y]) == {x:1, y:S.Zero}
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assert _linsolve([2*I], [x]) is None
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raises(PolyNonlinearError, lambda: _linsolve([x*(1 + x)], [x]))
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def test__linsolve_float():
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# This should give the exact answer:
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eqs = [
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y - x,
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y - 0.0216 * x
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]
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sol = {x:0.0, y:0.0}
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assert _linsolve(eqs, (x, y)) == sol
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# Other cases should be close to eps
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def all_close(sol1, sol2, eps=1e-15):
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close = lambda a, b: abs(a - b) < eps
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assert sol1.keys() == sol2.keys()
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return all(close(sol1[s], sol2[s]) for s in sol1)
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eqs = [
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0.8*x + 0.8*z + 0.2,
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0.9*x + 0.7*y + 0.2*z + 0.9,
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0.7*x + 0.2*y + 0.2*z + 0.5
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]
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sol_exact = {x:-29/42, y:-11/21, z:37/84}
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sol_linsolve = _linsolve(eqs, [x,y,z])
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assert all_close(sol_exact, sol_linsolve)
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eqs = [
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0.9*x + 0.3*y + 0.4*z + 0.6,
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0.6*x + 0.9*y + 0.1*z + 0.7,
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0.4*x + 0.6*y + 0.9*z + 0.5
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]
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sol_exact = {x:-88/175, y:-46/105, z:-1/25}
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sol_linsolve = _linsolve(eqs, [x,y,z])
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assert all_close(sol_exact, sol_linsolve)
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eqs = [
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0.4*x + 0.3*y + 0.6*z + 0.7,
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0.4*x + 0.3*y + 0.9*z + 0.9,
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0.7*x + 0.9*y,
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]
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sol_exact = {x:-9/5, y:7/5, z:-2/3}
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sol_linsolve = _linsolve(eqs, [x,y,z])
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assert all_close(sol_exact, sol_linsolve)
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eqs = [
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x*(0.7 + 0.6*I) + y*(0.4 + 0.7*I) + z*(0.9 + 0.1*I) + 0.5,
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0.2*I*x + 0.2*I*y + z*(0.9 + 0.2*I) + 0.1,
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x*(0.9 + 0.7*I) + y*(0.9 + 0.7*I) + z*(0.9 + 0.4*I) + 0.4,
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]
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sol_exact = {
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x:-6157/7995 - 411/5330*I,
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y:8519/15990 + 1784/7995*I,
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z:-34/533 + 107/1599*I,
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}
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sol_linsolve = _linsolve(eqs, [x,y,z])
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assert all_close(sol_exact, sol_linsolve)
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# XXX: This system for x and y over RR(z) is problematic.
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#
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# eqs = [
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# x*(0.2*z + 0.9) + y*(0.5*z + 0.8) + 0.6,
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# 0.1*x*z + y*(0.1*z + 0.6) + 0.9,
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# ]
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#
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# linsolve(eqs, [x, y])
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# The solution for x comes out as
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#
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# -3.9e-5*z**2 - 3.6e-5*z - 8.67361737988404e-20
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# x = ----------------------------------------------
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# 3.0e-6*z**3 - 1.3e-5*z**2 - 5.4e-5*z
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#
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# The 8e-20 in the numerator should be zero which would allow z to cancel
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# from top and bottom. It should be possible to avoid this somehow because
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# the inverse of the matrix only has a quadratic factor (the determinant)
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# in the denominator.
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def test__linsolve_deprecated():
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raises(PolyNonlinearError, lambda:
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_linsolve([Eq(x**2, x**2 + y)], [x, y]))
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raises(PolyNonlinearError, lambda:
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_linsolve([(x + y)**2 - x**2], [x]))
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raises(PolyNonlinearError, lambda:
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_linsolve([Eq((x + y)**2, x**2)], [x]))
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