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How to use q3 method in pytest-benchmark

Best Python code snippet using pytest-benchmark

test_functions.py

Source:test_functions.py

1from sympy.vector.vector import Vector2from sympy.vector.coordsysrect import CoordSys3D3from sympy.vector.functions import express, matrix_to_vector, orthogonalize4from sympy import symbols, S, sqrt, sin, cos, ImmutableMatrix as Matrix, Rational5from sympy.testing.pytest import raises6N = CoordSys3D('N')7q1, q2, q3, q4, q5 = symbols('q1 q2 q3 q4 q5')8A = N.orient_new_axis('A', q1, N.k)  # type: ignore9B = A.orient_new_axis('B', q2, A.i)10C = B.orient_new_axis('C', q3, B.j)11def test_express():12    assert express(Vector.zero, N) == Vector.zero13    assert express(S.Zero, N) is S.Zero14    assert express(A.i, C) == cos(q3)*C.i + sin(q3)*C.k15    assert express(A.j, C) == sin(q2)*sin(q3)*C.i + cos(q2)*C.j - \16        sin(q2)*cos(q3)*C.k17    assert express(A.k, C) == -sin(q3)*cos(q2)*C.i + sin(q2)*C.j + \18        cos(q2)*cos(q3)*C.k19    assert express(A.i, N) == cos(q1)*N.i + sin(q1)*N.j20    assert express(A.j, N) == -sin(q1)*N.i + cos(q1)*N.j21    assert express(A.k, N) == N.k22    assert express(A.i, A) == A.i23    assert express(A.j, A) == A.j24    assert express(A.k, A) == A.k25    assert express(A.i, B) == B.i26    assert express(A.j, B) == cos(q2)*B.j - sin(q2)*B.k27    assert express(A.k, B) == sin(q2)*B.j + cos(q2)*B.k28    assert express(A.i, C) == cos(q3)*C.i + sin(q3)*C.k29    assert express(A.j, C) == sin(q2)*sin(q3)*C.i + cos(q2)*C.j - \30        sin(q2)*cos(q3)*C.k31    assert express(A.k, C) == -sin(q3)*cos(q2)*C.i + sin(q2)*C.j + \32        cos(q2)*cos(q3)*C.k33    # Check to make sure UnitVectors get converted properly34    assert express(N.i, N) == N.i35    assert express(N.j, N) == N.j36    assert express(N.k, N) == N.k37    assert express(N.i, A) == (cos(q1)*A.i - sin(q1)*A.j)38    assert express(N.j, A) == (sin(q1)*A.i + cos(q1)*A.j)39    assert express(N.k, A) == A.k40    assert express(N.i, B) == (cos(q1)*B.i - sin(q1)*cos(q2)*B.j +41            sin(q1)*sin(q2)*B.k)42    assert express(N.j, B) == (sin(q1)*B.i + cos(q1)*cos(q2)*B.j -43            sin(q2)*cos(q1)*B.k)44    assert express(N.k, B) == (sin(q2)*B.j + cos(q2)*B.k)45    assert express(N.i, C) == (46        (cos(q1)*cos(q3) - sin(q1)*sin(q2)*sin(q3))*C.i -47        sin(q1)*cos(q2)*C.j +48        (sin(q3)*cos(q1) + sin(q1)*sin(q2)*cos(q3))*C.k)49    assert express(N.j, C) == (50        (sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1))*C.i +51        cos(q1)*cos(q2)*C.j +52        (sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3))*C.k)53    assert express(N.k, C) == (-sin(q3)*cos(q2)*C.i + sin(q2)*C.j +54            cos(q2)*cos(q3)*C.k)55    assert express(A.i, N) == (cos(q1)*N.i + sin(q1)*N.j)56    assert express(A.j, N) == (-sin(q1)*N.i + cos(q1)*N.j)57    assert express(A.k, N) == N.k58    assert express(A.i, A) == A.i59    assert express(A.j, A) == A.j60    assert express(A.k, A) == A.k61    assert express(A.i, B) == B.i62    assert express(A.j, B) == (cos(q2)*B.j - sin(q2)*B.k)63    assert express(A.k, B) == (sin(q2)*B.j + cos(q2)*B.k)64    assert express(A.i, C) == (cos(q3)*C.i + sin(q3)*C.k)65    assert express(A.j, C) == (sin(q2)*sin(q3)*C.i + cos(q2)*C.j -66            sin(q2)*cos(q3)*C.k)67    assert express(A.k, C) == (-sin(q3)*cos(q2)*C.i + sin(q2)*C.j +68            cos(q2)*cos(q3)*C.k)69    assert express(B.i, N) == (cos(q1)*N.i + sin(q1)*N.j)70    assert express(B.j, N) == (-sin(q1)*cos(q2)*N.i +71            cos(q1)*cos(q2)*N.j + sin(q2)*N.k)72    assert express(B.k, N) == (sin(q1)*sin(q2)*N.i -73            sin(q2)*cos(q1)*N.j + cos(q2)*N.k)74    assert express(B.i, A) == A.i75    assert express(B.j, A) == (cos(q2)*A.j + sin(q2)*A.k)76    assert express(B.k, A) == (-sin(q2)*A.j + cos(q2)*A.k)77    assert express(B.i, B) == B.i78    assert express(B.j, B) == B.j79    assert express(B.k, B) == B.k80    assert express(B.i, C) == (cos(q3)*C.i + sin(q3)*C.k)81    assert express(B.j, C) == C.j82    assert express(B.k, C) == (-sin(q3)*C.i + cos(q3)*C.k)83    assert express(C.i, N) == (84        (cos(q1)*cos(q3) - sin(q1)*sin(q2)*sin(q3))*N.i +85        (sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1))*N.j -86        sin(q3)*cos(q2)*N.k)87    assert express(C.j, N) == (88        -sin(q1)*cos(q2)*N.i + cos(q1)*cos(q2)*N.j + sin(q2)*N.k)89    assert express(C.k, N) == (90        (sin(q3)*cos(q1) + sin(q1)*sin(q2)*cos(q3))*N.i +91        (sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3))*N.j +92        cos(q2)*cos(q3)*N.k)93    assert express(C.i, A) == (cos(q3)*A.i + sin(q2)*sin(q3)*A.j -94            sin(q3)*cos(q2)*A.k)95    assert express(C.j, A) == (cos(q2)*A.j + sin(q2)*A.k)96    assert express(C.k, A) == (sin(q3)*A.i - sin(q2)*cos(q3)*A.j +97            cos(q2)*cos(q3)*A.k)98    assert express(C.i, B) == (cos(q3)*B.i - sin(q3)*B.k)99    assert express(C.j, B) == B.j100    assert express(C.k, B) == (sin(q3)*B.i + cos(q3)*B.k)101    assert express(C.i, C) == C.i102    assert express(C.j, C) == C.j103    assert express(C.k, C) == C.k == (C.k)104    #  Check to make sure Vectors get converted back to UnitVectors105    assert N.i == express((cos(q1)*A.i - sin(q1)*A.j), N).simplify()106    assert N.j == express((sin(q1)*A.i + cos(q1)*A.j), N).simplify()107    assert N.i == express((cos(q1)*B.i - sin(q1)*cos(q2)*B.j +108            sin(q1)*sin(q2)*B.k), N).simplify()109    assert N.j == express((sin(q1)*B.i + cos(q1)*cos(q2)*B.j -110        sin(q2)*cos(q1)*B.k), N).simplify()111    assert N.k == express((sin(q2)*B.j + cos(q2)*B.k), N).simplify()112    assert A.i == express((cos(q1)*N.i + sin(q1)*N.j), A).simplify()113    assert A.j == express((-sin(q1)*N.i + cos(q1)*N.j), A).simplify()114    assert A.j == express((cos(q2)*B.j - sin(q2)*B.k), A).simplify()115    assert A.k == express((sin(q2)*B.j + cos(q2)*B.k), A).simplify()116    assert A.i == express((cos(q3)*C.i + sin(q3)*C.k), A).simplify()117    assert A.j == express((sin(q2)*sin(q3)*C.i + cos(q2)*C.j -118            sin(q2)*cos(q3)*C.k), A).simplify()119    assert A.k == express((-sin(q3)*cos(q2)*C.i + sin(q2)*C.j +120            cos(q2)*cos(q3)*C.k), A).simplify()121    assert B.i == express((cos(q1)*N.i + sin(q1)*N.j), B).simplify()122    assert B.j == express((-sin(q1)*cos(q2)*N.i +123            cos(q1)*cos(q2)*N.j + sin(q2)*N.k), B).simplify()124    assert B.k == express((sin(q1)*sin(q2)*N.i -125            sin(q2)*cos(q1)*N.j + cos(q2)*N.k), B).simplify()126    assert B.j == express((cos(q2)*A.j + sin(q2)*A.k), B).simplify()127    assert B.k == express((-sin(q2)*A.j + cos(q2)*A.k), B).simplify()128    assert B.i == express((cos(q3)*C.i + sin(q3)*C.k), B).simplify()129    assert B.k == express((-sin(q3)*C.i + cos(q3)*C.k), B).simplify()130    assert C.i == express((cos(q3)*A.i + sin(q2)*sin(q3)*A.j -131            sin(q3)*cos(q2)*A.k), C).simplify()132    assert C.j == express((cos(q2)*A.j + sin(q2)*A.k), C).simplify()133    assert C.k == express((sin(q3)*A.i - sin(q2)*cos(q3)*A.j +134            cos(q2)*cos(q3)*A.k), C).simplify()135    assert C.i == express((cos(q3)*B.i - sin(q3)*B.k), C).simplify()136    assert C.k == express((sin(q3)*B.i + cos(q3)*B.k), C).simplify()137def test_matrix_to_vector():138    m = Matrix([[1], [2], [3]])139    assert matrix_to_vector(m, C) == C.i + 2*C.j + 3*C.k140    m = Matrix([[0], [0], [0]])141    assert matrix_to_vector(m, N) == matrix_to_vector(m, C) == \142           Vector.zero143    m = Matrix([[q1], [q2], [q3]])144    assert matrix_to_vector(m, N) == q1*N.i + q2*N.j + q3*N.k145def test_orthogonalize():146    C = CoordSys3D('C')147    a, b = symbols('a b', integer=True)148    i, j, k = C.base_vectors()149    v1 = i + 2*j150    v2 = 2*i + 3*j151    v3 = 3*i + 5*j152    v4 = 3*i + j153    v5 = 2*i + 2*j154    v6 = a*i + b*j155    v7 = 4*a*i + 4*b*j156    assert orthogonalize(v1, v2) == [C.i + 2*C.j, C.i*Rational(2, 5) + -C.j/5]157    # from wikipedia158    assert orthogonalize(v4, v5, orthonormal=True) == \159        [(3*sqrt(10))*C.i/10 + (sqrt(10))*C.j/10, (-sqrt(10))*C.i/10 + (3*sqrt(10))*C.j/10]160    raises(ValueError, lambda: orthogonalize(v1, v2, v3))...

test_vector.py

Source:test_vector.py

1from sympy import symbols, pi, sin, cos, ImmutableMatrix as Matrix2from sympy.physics.vector import ReferenceFrame, Vector, dynamicsymbols, dot3from sympy.abc import x, y, z4from sympy.testing.pytest import raises5Vector.simp = True6A = ReferenceFrame('A')7def test_Vector():8    assert A.x != A.y9    assert A.y != A.z10    assert A.z != A.x11    assert A.x + 0 == A.x12    v1 = x*A.x + y*A.y + z*A.z13    v2 = x**2*A.x + y**2*A.y + z**2*A.z14    v3 = v1 + v215    v4 = v1 - v216    assert isinstance(v1, Vector)17    assert dot(v1, A.x) == x18    assert dot(v1, A.y) == y19    assert dot(v1, A.z) == z20    assert isinstance(v2, Vector)21    assert dot(v2, A.x) == x**222    assert dot(v2, A.y) == y**223    assert dot(v2, A.z) == z**224    assert isinstance(v3, Vector)25    # We probably shouldn't be using simplify in dot...26    assert dot(v3, A.x) == x**2 + x27    assert dot(v3, A.y) == y**2 + y28    assert dot(v3, A.z) == z**2 + z29    assert isinstance(v4, Vector)30    # We probably shouldn't be using simplify in dot...31    assert dot(v4, A.x) == x - x**232    assert dot(v4, A.y) == y - y**233    assert dot(v4, A.z) == z - z**234    assert v1.to_matrix(A) == Matrix([[x], [y], [z]])35    q = symbols('q')36    B = A.orientnew('B', 'Axis', (q, A.x))37    assert v1.to_matrix(B) == Matrix([[x],38                                      [ y * cos(q) + z * sin(q)],39                                      [-y * sin(q) + z * cos(q)]])40    #Test the separate method41    B = ReferenceFrame('B')42    v5 = x*A.x + y*A.y + z*B.z43    assert Vector(0).separate() == {}44    assert v1.separate() == {A: v1}45    assert v5.separate() == {A: x*A.x + y*A.y, B: z*B.z}46    #Test the free_symbols property47    v6 = x*A.x + y*A.y + z*A.z48    assert v6.free_symbols(A) == {x,y,z}49    raises(TypeError, lambda: v3.applyfunc(v1))50def test_Vector_diffs():51    q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4')52    q1d, q2d, q3d, q4d = dynamicsymbols('q1 q2 q3 q4', 1)53    q1dd, q2dd, q3dd, q4dd = dynamicsymbols('q1 q2 q3 q4', 2)54    N = ReferenceFrame('N')55    A = N.orientnew('A', 'Axis', [q3, N.z])56    B = A.orientnew('B', 'Axis', [q2, A.x])57    v1 = q2 * A.x + q3 * N.y58    v2 = q3 * B.x + v159    v3 = v1.dt(B)60    v4 = v2.dt(B)61    v5 = q1*A.x + q2*A.y + q3*A.z62    assert v1.dt(N) == q2d * A.x + q2 * q3d * A.y + q3d * N.y63    assert v1.dt(A) == q2d * A.x + q3 * q3d * N.x + q3d * N.y64    assert v1.dt(B) == (q2d * A.x + q3 * q3d * N.x + q3d *\65                        N.y - q3 * cos(q3) * q2d * N.z)66    assert v2.dt(N) == (q2d * A.x + (q2 + q3) * q3d * A.y + q3d * B.x + q3d *67                        N.y)68    assert v2.dt(A) == q2d * A.x + q3d * B.x + q3 * q3d * N.x + q3d * N.y69    assert v2.dt(B) == (q2d * A.x + q3d * B.x + q3 * q3d * N.x + q3d * N.y -70                        q3 * cos(q3) * q2d * N.z)71    assert v3.dt(N) == (q2dd * A.x + q2d * q3d * A.y + (q3d**2 + q3 * q3dd) *72                        N.x + q3dd * N.y + (q3 * sin(q3) * q2d * q3d -73                        cos(q3) * q2d * q3d - q3 * cos(q3) * q2dd) * N.z)74    assert v3.dt(A) == (q2dd * A.x + (2 * q3d**2 + q3 * q3dd) * N.x + (q3dd -75                        q3 * q3d**2) * N.y + (q3 * sin(q3) * q2d * q3d -76                        cos(q3) * q2d * q3d - q3 * cos(q3) * q2dd) * N.z)77    assert v3.dt(B) == (q2dd * A.x - q3 * cos(q3) * q2d**2 * A.y + (2 *78                        q3d**2 + q3 * q3dd) * N.x + (q3dd - q3 * q3d**2) *79                        N.y + (2 * q3 * sin(q3) * q2d * q3d - 2 * cos(q3) *80                        q2d * q3d - q3 * cos(q3) * q2dd) * N.z)81    assert v4.dt(N) == (q2dd * A.x + q3d * (q2d + q3d) * A.y + q3dd * B.x +82                        (q3d**2 + q3 * q3dd) * N.x + q3dd * N.y + (q3 *83                        sin(q3) * q2d * q3d - cos(q3) * q2d * q3d - q3 *84                        cos(q3) * q2dd) * N.z)85    assert v4.dt(A) == (q2dd * A.x + q3dd * B.x + (2 * q3d**2 + q3 * q3dd) *86                        N.x + (q3dd - q3 * q3d**2) * N.y + (q3 * sin(q3) *87                        q2d * q3d - cos(q3) * q2d * q3d - q3 * cos(q3) *88                        q2dd) * N.z)89    assert v4.dt(B) == (q2dd * A.x - q3 * cos(q3) * q2d**2 * A.y + q3dd * B.x +90                        (2 * q3d**2 + q3 * q3dd) * N.x + (q3dd - q3 * q3d**2) *91                        N.y + (2 * q3 * sin(q3) * q2d * q3d - 2 * cos(q3) *92                        q2d * q3d - q3 * cos(q3) * q2dd) * N.z)93    assert v5.dt(B) == q1d*A.x + (q3*q2d + q2d)*A.y + (-q2*q2d + q3d)*A.z94    assert v5.dt(A) == q1d*A.x + q2d*A.y + q3d*A.z95    assert v5.dt(N) == (-q2*q3d + q1d)*A.x + (q1*q3d + q2d)*A.y + q3d*A.z96    assert v3.diff(q1d, N) == 097    assert v3.diff(q2d, N) == A.x - q3 * cos(q3) * N.z98    assert v3.diff(q3d, N) == q3 * N.x + N.y99    assert v3.diff(q1d, A) == 0100    assert v3.diff(q2d, A) == A.x - q3 * cos(q3) * N.z101    assert v3.diff(q3d, A) == q3 * N.x + N.y102    assert v3.diff(q1d, B) == 0103    assert v3.diff(q2d, B) == A.x - q3 * cos(q3) * N.z104    assert v3.diff(q3d, B) == q3 * N.x + N.y105    assert v4.diff(q1d, N) == 0106    assert v4.diff(q2d, N) == A.x - q3 * cos(q3) * N.z107    assert v4.diff(q3d, N) == B.x + q3 * N.x + N.y108    assert v4.diff(q1d, A) == 0109    assert v4.diff(q2d, A) == A.x - q3 * cos(q3) * N.z110    assert v4.diff(q3d, A) == B.x + q3 * N.x + N.y111    assert v4.diff(q1d, B) == 0112    assert v4.diff(q2d, B) == A.x - q3 * cos(q3) * N.z113    assert v4.diff(q3d, B) == B.x + q3 * N.x + N.y114def test_vector_var_in_dcm():115    N = ReferenceFrame('N')116    A = ReferenceFrame('A')117    B = ReferenceFrame('B')118    u1, u2, u3, u4 = dynamicsymbols('u1 u2 u3 u4')119    v = u1 * u2 * A.x + u3 * N.y + u4**2 * N.z120    assert v.diff(u1, N, var_in_dcm=False) == u2 * A.x121    assert v.diff(u1, A, var_in_dcm=False) == u2 * A.x122    assert v.diff(u3, N, var_in_dcm=False) == N.y123    assert v.diff(u3, A, var_in_dcm=False) == N.y124    assert v.diff(u3, B, var_in_dcm=False) == N.y125    assert v.diff(u4, N, var_in_dcm=False) == 2 * u4 * N.z126    raises(ValueError, lambda: v.diff(u1, N))127def test_vector_simplify():128    x, y, z, k, n, m, w, f, s, A = symbols('x, y, z, k, n, m, w, f, s, A')129    N = ReferenceFrame('N')130    test1 = (1 / x + 1 / y) * N.x131    assert (test1 & N.x) != (x + y) / (x * y)132    test1 = test1.simplify()133    assert (test1 & N.x) == (x + y) / (x * y)134    test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * N.x135    test2 = test2.simplify()136    assert (test2 & N.x) == (A**2 * s**4 / (4 * pi * k * m**3))137    test3 = ((4 + 4 * x - 2 * (2 + 2 * x)) / (2 + 2 * x)) * N.x138    test3 = test3.simplify()139    assert (test3 & N.x) == 0140    test4 = ((-4 * x * y**2 - 2 * y**3 - 2 * x**2 * y) / (x + y)**2) * N.x141    test4 = test4.simplify()...

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