135 lines
4.8 KiB
Python
135 lines
4.8 KiB
Python
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from sympy.core.numbers import pi
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from sympy.core.symbol import symbols
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from sympy.functions.elementary.trigonometric import (cos, sin)
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from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
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from sympy.simplify.simplify import simplify
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from sympy.vector import (CoordSys3D, Vector, Dyadic,
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DyadicAdd, DyadicMul, DyadicZero,
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BaseDyadic, express)
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A = CoordSys3D('A')
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def test_dyadic():
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a, b = symbols('a, b')
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assert Dyadic.zero != 0
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assert isinstance(Dyadic.zero, DyadicZero)
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assert BaseDyadic(A.i, A.j) != BaseDyadic(A.j, A.i)
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assert (BaseDyadic(Vector.zero, A.i) ==
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BaseDyadic(A.i, Vector.zero) == Dyadic.zero)
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d1 = A.i | A.i
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d2 = A.j | A.j
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d3 = A.i | A.j
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assert isinstance(d1, BaseDyadic)
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d_mul = a*d1
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assert isinstance(d_mul, DyadicMul)
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assert d_mul.base_dyadic == d1
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assert d_mul.measure_number == a
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assert isinstance(a*d1 + b*d3, DyadicAdd)
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assert d1 == A.i.outer(A.i)
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assert d3 == A.i.outer(A.j)
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v1 = a*A.i - A.k
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v2 = A.i + b*A.j
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assert v1 | v2 == v1.outer(v2) == a * (A.i|A.i) + (a*b) * (A.i|A.j) +\
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- (A.k|A.i) - b * (A.k|A.j)
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assert d1 * 0 == Dyadic.zero
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assert d1 != Dyadic.zero
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assert d1 * 2 == 2 * (A.i | A.i)
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assert d1 / 2. == 0.5 * d1
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assert d1.dot(0 * d1) == Vector.zero
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assert d1 & d2 == Dyadic.zero
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assert d1.dot(A.i) == A.i == d1 & A.i
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assert d1.cross(Vector.zero) == Dyadic.zero
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assert d1.cross(A.i) == Dyadic.zero
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assert d1 ^ A.j == d1.cross(A.j)
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assert d1.cross(A.k) == - A.i | A.j
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assert d2.cross(A.i) == - A.j | A.k == d2 ^ A.i
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assert A.i ^ d1 == Dyadic.zero
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assert A.j.cross(d1) == - A.k | A.i == A.j ^ d1
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assert Vector.zero.cross(d1) == Dyadic.zero
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assert A.k ^ d1 == A.j | A.i
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assert A.i.dot(d1) == A.i & d1 == A.i
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assert A.j.dot(d1) == Vector.zero
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assert Vector.zero.dot(d1) == Vector.zero
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assert A.j & d2 == A.j
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assert d1.dot(d3) == d1 & d3 == A.i | A.j == d3
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assert d3 & d1 == Dyadic.zero
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q = symbols('q')
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B = A.orient_new_axis('B', q, A.k)
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assert express(d1, B) == express(d1, B, B)
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expr1 = ((cos(q)**2) * (B.i | B.i) + (-sin(q) * cos(q)) *
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(B.i | B.j) + (-sin(q) * cos(q)) * (B.j | B.i) + (sin(q)**2) *
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(B.j | B.j))
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assert (express(d1, B) - expr1).simplify() == Dyadic.zero
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expr2 = (cos(q)) * (B.i | A.i) + (-sin(q)) * (B.j | A.i)
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assert (express(d1, B, A) - expr2).simplify() == Dyadic.zero
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expr3 = (cos(q)) * (A.i | B.i) + (-sin(q)) * (A.i | B.j)
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assert (express(d1, A, B) - expr3).simplify() == Dyadic.zero
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assert d1.to_matrix(A) == Matrix([[1, 0, 0], [0, 0, 0], [0, 0, 0]])
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assert d1.to_matrix(A, B) == Matrix([[cos(q), -sin(q), 0],
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[0, 0, 0],
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[0, 0, 0]])
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assert d3.to_matrix(A) == Matrix([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
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a, b, c, d, e, f = symbols('a, b, c, d, e, f')
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v1 = a * A.i + b * A.j + c * A.k
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v2 = d * A.i + e * A.j + f * A.k
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d4 = v1.outer(v2)
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assert d4.to_matrix(A) == Matrix([[a * d, a * e, a * f],
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[b * d, b * e, b * f],
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[c * d, c * e, c * f]])
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d5 = v1.outer(v1)
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C = A.orient_new_axis('C', q, A.i)
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for expected, actual in zip(C.rotation_matrix(A) * d5.to_matrix(A) * \
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C.rotation_matrix(A).T, d5.to_matrix(C)):
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assert (expected - actual).simplify() == 0
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def test_dyadic_simplify():
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x, y, z, k, n, m, w, f, s, A = symbols('x, y, z, k, n, m, w, f, s, A')
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N = CoordSys3D('N')
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dy = N.i | N.i
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test1 = (1 / x + 1 / y) * dy
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assert (N.i & test1 & N.i) != (x + y) / (x * y)
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test1 = test1.simplify()
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assert test1.simplify() == simplify(test1)
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assert (N.i & test1 & N.i) == (x + y) / (x * y)
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test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * dy
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test2 = test2.simplify()
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assert (N.i & test2 & N.i) == (A**2 * s**4 / (4 * pi * k * m**3))
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test3 = ((4 + 4 * x - 2 * (2 + 2 * x)) / (2 + 2 * x)) * dy
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test3 = test3.simplify()
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assert (N.i & test3 & N.i) == 0
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test4 = ((-4 * x * y**2 - 2 * y**3 - 2 * x**2 * y) / (x + y)**2) * dy
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test4 = test4.simplify()
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assert (N.i & test4 & N.i) == -2 * y
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def test_dyadic_srepr():
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from sympy.printing.repr import srepr
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N = CoordSys3D('N')
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dy = N.i | N.j
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res = "BaseDyadic(CoordSys3D(Str('N'), Tuple(ImmutableDenseMatrix([["\
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"Integer(1), Integer(0), Integer(0)], [Integer(0), Integer(1), "\
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"Integer(0)], [Integer(0), Integer(0), Integer(1)]]), "\
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"VectorZero())).i, CoordSys3D(Str('N'), Tuple(ImmutableDenseMatrix("\
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"[[Integer(1), Integer(0), Integer(0)], [Integer(0), Integer(1), "\
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"Integer(0)], [Integer(0), Integer(0), Integer(1)]]), VectorZero())).j)"
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assert srepr(dy) == res
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