Vehicle-cpp/hkpc/software/sympy/vector/tests/test_dyadic.py

from sympy.core.numbers import pi
from sympy.core.symbol import symbols
from sympy.functions.elementary.trigonometric import (cos, sin)
from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
from sympy.simplify.simplify import simplify
from sympy.vector import (CoordSys3D, Vector, Dyadic,
                          DyadicAdd, DyadicMul, DyadicZero,
                          BaseDyadic, express)


A = CoordSys3D('A')


def test_dyadic():
    a, b = symbols('a, b')
    assert Dyadic.zero != 0
    assert isinstance(Dyadic.zero, DyadicZero)
    assert BaseDyadic(A.i, A.j) != BaseDyadic(A.j, A.i)
    assert (BaseDyadic(Vector.zero, A.i) ==
            BaseDyadic(A.i, Vector.zero) == Dyadic.zero)

    d1 = A.i | A.i
    d2 = A.j | A.j
    d3 = A.i | A.j

    assert isinstance(d1, BaseDyadic)
    d_mul = a*d1
    assert isinstance(d_mul, DyadicMul)
    assert d_mul.base_dyadic == d1
    assert d_mul.measure_number == a
    assert isinstance(a*d1 + b*d3, DyadicAdd)
    assert d1 == A.i.outer(A.i)
    assert d3 == A.i.outer(A.j)
    v1 = a*A.i - A.k
    v2 = A.i + b*A.j
    assert v1 | v2 == v1.outer(v2) == a * (A.i|A.i) + (a*b) * (A.i|A.j) +\
           - (A.k|A.i) - b * (A.k|A.j)
    assert d1 * 0 == Dyadic.zero
    assert d1 != Dyadic.zero
    assert d1 * 2 == 2 * (A.i | A.i)
    assert d1 / 2. == 0.5 * d1

    assert d1.dot(0 * d1) == Vector.zero
    assert d1 & d2 == Dyadic.zero
    assert d1.dot(A.i) == A.i == d1 & A.i

    assert d1.cross(Vector.zero) == Dyadic.zero
    assert d1.cross(A.i) == Dyadic.zero
    assert d1 ^ A.j == d1.cross(A.j)
    assert d1.cross(A.k) == - A.i | A.j
    assert d2.cross(A.i) == - A.j | A.k == d2 ^ A.i

    assert A.i ^ d1 == Dyadic.zero
    assert A.j.cross(d1) == - A.k | A.i == A.j ^ d1
    assert Vector.zero.cross(d1) == Dyadic.zero
    assert A.k ^ d1 == A.j | A.i
    assert A.i.dot(d1) == A.i & d1 == A.i
    assert A.j.dot(d1) == Vector.zero
    assert Vector.zero.dot(d1) == Vector.zero
    assert A.j & d2 == A.j

    assert d1.dot(d3) == d1 & d3 == A.i | A.j == d3
    assert d3 & d1 == Dyadic.zero

    q = symbols('q')
    B = A.orient_new_axis('B', q, A.k)
    assert express(d1, B) == express(d1, B, B)

    expr1 = ((cos(q)**2) * (B.i | B.i) + (-sin(q) * cos(q)) *
            (B.i | B.j) + (-sin(q) * cos(q)) * (B.j | B.i) + (sin(q)**2) *
            (B.j | B.j))
    assert (express(d1, B) - expr1).simplify() == Dyadic.zero

    expr2 = (cos(q)) * (B.i | A.i) + (-sin(q)) * (B.j | A.i)
    assert (express(d1, B, A) - expr2).simplify() == Dyadic.zero

    expr3 = (cos(q)) * (A.i | B.i) + (-sin(q)) * (A.i | B.j)
    assert (express(d1, A, B) - expr3).simplify() == Dyadic.zero

    assert d1.to_matrix(A) == Matrix([[1, 0, 0], [0, 0, 0], [0, 0, 0]])
    assert d1.to_matrix(A, B) == Matrix([[cos(q), -sin(q), 0],
                                         [0, 0, 0],
                                         [0, 0, 0]])
    assert d3.to_matrix(A) == Matrix([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
    a, b, c, d, e, f = symbols('a, b, c, d, e, f')
    v1 = a * A.i + b * A.j + c * A.k
    v2 = d * A.i + e * A.j + f * A.k
    d4 = v1.outer(v2)
    assert d4.to_matrix(A) == Matrix([[a * d, a * e, a * f],
                                      [b * d, b * e, b * f],
                                      [c * d, c * e, c * f]])
    d5 = v1.outer(v1)
    C = A.orient_new_axis('C', q, A.i)
    for expected, actual in zip(C.rotation_matrix(A) * d5.to_matrix(A) * \
                               C.rotation_matrix(A).T, d5.to_matrix(C)):
        assert (expected - actual).simplify() == 0


def test_dyadic_simplify():
    x, y, z, k, n, m, w, f, s, A = symbols('x, y, z, k, n, m, w, f, s, A')
    N = CoordSys3D('N')

    dy = N.i | N.i
    test1 = (1 / x + 1 / y) * dy
    assert (N.i & test1 & N.i) != (x + y) / (x * y)
    test1 = test1.simplify()
    assert test1.simplify() == simplify(test1)
    assert (N.i & test1 & N.i) == (x + y) / (x * y)

    test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * dy
    test2 = test2.simplify()
    assert (N.i & test2 & N.i) == (A**2 * s**4 / (4 * pi * k * m**3))

    test3 = ((4 + 4 * x - 2 * (2 + 2 * x)) / (2 + 2 * x)) * dy
    test3 = test3.simplify()
    assert (N.i & test3 & N.i) == 0

    test4 = ((-4 * x * y**2 - 2 * y**3 - 2 * x**2 * y) / (x + y)**2) * dy
    test4 = test4.simplify()
    assert (N.i & test4 & N.i) == -2 * y


def test_dyadic_srepr():
    from sympy.printing.repr import srepr
    N = CoordSys3D('N')

    dy = N.i | N.j
    res = "BaseDyadic(CoordSys3D(Str('N'), Tuple(ImmutableDenseMatrix([["\
        "Integer(1), Integer(0), Integer(0)], [Integer(0), Integer(1), "\
        "Integer(0)], [Integer(0), Integer(0), Integer(1)]]), "\
        "VectorZero())).i, CoordSys3D(Str('N'), Tuple(ImmutableDenseMatrix("\
        "[[Integer(1), Integer(0), Integer(0)], [Integer(0), Integer(1), "\
        "Integer(0)], [Integer(0), Integer(0), Integer(1)]]), VectorZero())).j)"
    assert srepr(dy) == res