from sympy import (symbols, sin, cos, pi, zeros, eye, simplify, ImmutableMatrix as Matrix) from sympy.physics.vector import (ReferenceFrame, Vector, CoordinateSym, dynamicsymbols, time_derivative, express, dot) from sympy.physics.vector.frame import _check_frame from sympy.physics.vector.vector import VectorTypeError from sympy.testing.pytest import raises import warnings Vector.simp = True def test_dict_list(): A = ReferenceFrame('A') B = ReferenceFrame('B') C = ReferenceFrame('C') D = ReferenceFrame('D') E = ReferenceFrame('E') F = ReferenceFrame('F') B.orient_axis(A, A.x, 1.0) C.orient_axis(B, B.x, 1.0) D.orient_axis(C, C.x, 1.0) assert D._dict_list(A, 0) == [D, C, B, A] E.orient_axis(D, D.x, 1.0) assert C._dict_list(A, 0) == [C, B, A] assert C._dict_list(E, 0) == [C, D, E] # only 0, 1, 2 permitted for second argument raises(ValueError, lambda: C._dict_list(E, 5)) # no connecting path raises(ValueError, lambda: F._dict_list(A, 0)) def test_coordinate_vars(): """Tests the coordinate variables functionality""" A = ReferenceFrame('A') assert CoordinateSym('Ax', A, 0) == A[0] assert CoordinateSym('Ax', A, 1) == A[1] assert CoordinateSym('Ax', A, 2) == A[2] raises(ValueError, lambda: CoordinateSym('Ax', A, 3)) q = dynamicsymbols('q') qd = dynamicsymbols('q', 1) assert isinstance(A[0], CoordinateSym) and \ isinstance(A[0], CoordinateSym) and \ isinstance(A[0], CoordinateSym) assert A.variable_map(A) == {A[0]:A[0], A[1]:A[1], A[2]:A[2]} assert A[0].frame == A B = A.orientnew('B', 'Axis', [q, A.z]) assert B.variable_map(A) == {B[2]: A[2], B[1]: -A[0]*sin(q) + A[1]*cos(q), B[0]: A[0]*cos(q) + A[1]*sin(q)} assert A.variable_map(B) == {A[0]: B[0]*cos(q) - B[1]*sin(q), A[1]: B[0]*sin(q) + B[1]*cos(q), A[2]: B[2]} assert time_derivative(B[0], A) == -A[0]*sin(q)*qd + A[1]*cos(q)*qd assert time_derivative(B[1], A) == -A[0]*cos(q)*qd - A[1]*sin(q)*qd assert time_derivative(B[2], A) == 0 assert express(B[0], A, variables=True) == A[0]*cos(q) + A[1]*sin(q) assert express(B[1], A, variables=True) == -A[0]*sin(q) + A[1]*cos(q) assert express(B[2], A, variables=True) == A[2] assert time_derivative(A[0]*A.x + A[1]*A.y + A[2]*A.z, B) == A[1]*qd*A.x - A[0]*qd*A.y assert time_derivative(B[0]*B.x + B[1]*B.y + B[2]*B.z, A) == - B[1]*qd*B.x + B[0]*qd*B.y assert express(B[0]*B[1]*B[2], A, variables=True) == \ A[2]*(-A[0]*sin(q) + A[1]*cos(q))*(A[0]*cos(q) + A[1]*sin(q)) assert (time_derivative(B[0]*B[1]*B[2], A) - (A[2]*(-A[0]**2*cos(2*q) - 2*A[0]*A[1]*sin(2*q) + A[1]**2*cos(2*q))*qd)).trigsimp() == 0 assert express(B[0]*B.x + B[1]*B.y + B[2]*B.z, A) == \ (B[0]*cos(q) - B[1]*sin(q))*A.x + (B[0]*sin(q) + \ B[1]*cos(q))*A.y + B[2]*A.z assert express(B[0]*B.x + B[1]*B.y + B[2]*B.z, A, variables=True) == \ A[0]*A.x + A[1]*A.y + A[2]*A.z assert express(A[0]*A.x + A[1]*A.y + A[2]*A.z, B) == \ (A[0]*cos(q) + A[1]*sin(q))*B.x + \ (-A[0]*sin(q) + A[1]*cos(q))*B.y + A[2]*B.z assert express(A[0]*A.x + A[1]*A.y + A[2]*A.z, B, variables=True) == \ B[0]*B.x + B[1]*B.y + B[2]*B.z N = B.orientnew('N', 'Axis', [-q, B.z]) assert N.variable_map(A) == {N[0]: A[0], N[2]: A[2], N[1]: A[1]} C = A.orientnew('C', 'Axis', [q, A.x + A.y + A.z]) mapping = A.variable_map(C) assert mapping[A[0]] == 2*C[0]*cos(q)/3 + C[0]/3 - 2*C[1]*sin(q + pi/6)/3 +\ C[1]/3 - 2*C[2]*cos(q + pi/3)/3 + C[2]/3 assert mapping[A[1]] == -2*C[0]*cos(q + pi/3)/3 + \ C[0]/3 + 2*C[1]*cos(q)/3 + C[1]/3 - 2*C[2]*sin(q + pi/6)/3 + C[2]/3 assert mapping[A[2]] == -2*C[0]*sin(q + pi/6)/3 + C[0]/3 - \ 2*C[1]*cos(q + pi/3)/3 + C[1]/3 + 2*C[2]*cos(q)/3 + C[2]/3 def test_ang_vel(): q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4') q1d, q2d, q3d, q4d = dynamicsymbols('q1 q2 q3 q4', 1) N = ReferenceFrame('N') A = N.orientnew('A', 'Axis', [q1, N.z]) B = A.orientnew('B', 'Axis', [q2, A.x]) C = B.orientnew('C', 'Axis', [q3, B.y]) D = N.orientnew('D', 'Axis', [q4, N.y]) u1, u2, u3 = dynamicsymbols('u1 u2 u3') assert A.ang_vel_in(N) == (q1d)*A.z assert B.ang_vel_in(N) == (q2d)*B.x + (q1d)*A.z assert C.ang_vel_in(N) == (q3d)*C.y + (q2d)*B.x + (q1d)*A.z A2 = N.orientnew('A2', 'Axis', [q4, N.y]) assert N.ang_vel_in(N) == 0 assert N.ang_vel_in(A) == -q1d*N.z assert N.ang_vel_in(B) == -q1d*A.z - q2d*B.x assert N.ang_vel_in(C) == -q1d*A.z - q2d*B.x - q3d*B.y assert N.ang_vel_in(A2) == -q4d*N.y assert A.ang_vel_in(N) == q1d*N.z assert A.ang_vel_in(A) == 0 assert A.ang_vel_in(B) == - q2d*B.x assert A.ang_vel_in(C) == - q2d*B.x - q3d*B.y assert A.ang_vel_in(A2) == q1d*N.z - q4d*N.y assert B.ang_vel_in(N) == q1d*A.z + q2d*A.x assert B.ang_vel_in(A) == q2d*A.x assert B.ang_vel_in(B) == 0 assert B.ang_vel_in(C) == -q3d*B.y assert B.ang_vel_in(A2) == q1d*A.z + q2d*A.x - q4d*N.y assert C.ang_vel_in(N) == q1d*A.z + q2d*A.x + q3d*B.y assert C.ang_vel_in(A) == q2d*A.x + q3d*C.y assert C.ang_vel_in(B) == q3d*B.y assert C.ang_vel_in(C) == 0 assert C.ang_vel_in(A2) == q1d*A.z + q2d*A.x + q3d*B.y - q4d*N.y assert A2.ang_vel_in(N) == q4d*A2.y assert A2.ang_vel_in(A) == q4d*A2.y - q1d*N.z assert A2.ang_vel_in(B) == q4d*N.y - q1d*A.z - q2d*A.x assert A2.ang_vel_in(C) == q4d*N.y - q1d*A.z - q2d*A.x - q3d*B.y assert A2.ang_vel_in(A2) == 0 C.set_ang_vel(N, u1*C.x + u2*C.y + u3*C.z) assert C.ang_vel_in(N) == (u1)*C.x + (u2)*C.y + (u3)*C.z assert N.ang_vel_in(C) == (-u1)*C.x + (-u2)*C.y + (-u3)*C.z assert C.ang_vel_in(D) == (u1)*C.x + (u2)*C.y + (u3)*C.z + (-q4d)*D.y assert D.ang_vel_in(C) == (-u1)*C.x + (-u2)*C.y + (-u3)*C.z + (q4d)*D.y q0 = dynamicsymbols('q0') q0d = dynamicsymbols('q0', 1) E = N.orientnew('E', 'Quaternion', (q0, q1, q2, q3)) assert E.ang_vel_in(N) == ( 2 * (q1d * q0 + q2d * q3 - q3d * q2 - q0d * q1) * E.x + 2 * (q2d * q0 + q3d * q1 - q1d * q3 - q0d * q2) * E.y + 2 * (q3d * q0 + q1d * q2 - q2d * q1 - q0d * q3) * E.z) F = N.orientnew('F', 'Body', (q1, q2, q3), 313) assert F.ang_vel_in(N) == ((sin(q2)*sin(q3)*q1d + cos(q3)*q2d)*F.x + (sin(q2)*cos(q3)*q1d - sin(q3)*q2d)*F.y + (cos(q2)*q1d + q3d)*F.z) G = N.orientnew('G', 'Axis', (q1, N.x + N.y)) assert G.ang_vel_in(N) == q1d * (N.x + N.y).normalize() assert N.ang_vel_in(G) == -q1d * (N.x + N.y).normalize() def test_dcm(): q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4') N = ReferenceFrame('N') A = N.orientnew('A', 'Axis', [q1, N.z]) B = A.orientnew('B', 'Axis', [q2, A.x]) C = B.orientnew('C', 'Axis', [q3, B.y]) D = N.orientnew('D', 'Axis', [q4, N.y]) E = N.orientnew('E', 'Space', [q1, q2, q3], '123') assert N.dcm(C) == Matrix([ [- sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), - sin(q1) * cos(q2), sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)], [sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)], [- sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)]]) # This is a little touchy. Is it ok to use simplify in assert? test_mat = D.dcm(C) - Matrix( [[cos(q1) * cos(q3) * cos(q4) - sin(q3) * (- sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4)), - sin(q2) * sin(q4) - sin(q1) * cos(q2) * cos(q4), sin(q3) * cos(q1) * cos(q4) + cos(q3) * (- sin(q4) * cos(q2) + sin(q1) * sin(q2) * cos(q4))], [sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * cos(q2), sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)], [sin(q4) * cos(q1) * cos(q3) - sin(q3) * (cos(q2) * cos(q4) + sin(q1) * sin(q2) * sin(q4)), sin(q2) * cos(q4) - sin(q1) * sin(q4) * cos(q2), sin(q3) * sin(q4) * cos(q1) + cos(q3) * (cos(q2) * cos(q4) + sin(q1) * sin(q2) * sin(q4))]]) assert test_mat.expand() == zeros(3, 3) assert E.dcm(N) == Matrix( [[cos(q2)*cos(q3), sin(q3)*cos(q2), -sin(q2)], [sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1), sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q2)], [sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3), - sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1), cos(q1)*cos(q2)]]) def test_w_diff_dcm1(): # Ref: # Dynamics Theory and Applications, Kane 1985 # Sec. 2.1 ANGULAR VELOCITY A = ReferenceFrame('A') B = ReferenceFrame('B') c11, c12, c13 = dynamicsymbols('C11 C12 C13') c21, c22, c23 = dynamicsymbols('C21 C22 C23') c31, c32, c33 = dynamicsymbols('C31 C32 C33') c11d, c12d, c13d = dynamicsymbols('C11 C12 C13', level=1) c21d, c22d, c23d = dynamicsymbols('C21 C22 C23', level=1) c31d, c32d, c33d = dynamicsymbols('C31 C32 C33', level=1) DCM = Matrix([ [c11, c12, c13], [c21, c22, c23], [c31, c32, c33] ]) B.orient(A, 'DCM', DCM) b1a = (B.x).express(A) b2a = (B.y).express(A) b3a = (B.z).express(A) # Equation (2.1.1) B.set_ang_vel(A, B.x*(dot((b3a).dt(A), B.y)) + B.y*(dot((b1a).dt(A), B.z)) + B.z*(dot((b2a).dt(A), B.x))) # Equation (2.1.21) expr = ( (c12*c13d + c22*c23d + c32*c33d)*B.x + (c13*c11d + c23*c21d + c33*c31d)*B.y + (c11*c12d + c21*c22d + c31*c32d)*B.z) assert B.ang_vel_in(A) - expr == 0 def test_w_diff_dcm2(): q1, q2, q3 = dynamicsymbols('q1:4') N = ReferenceFrame('N') A = N.orientnew('A', 'axis', [q1, N.x]) B = A.orientnew('B', 'axis', [q2, A.y]) C = B.orientnew('C', 'axis', [q3, B.z]) DCM = C.dcm(N).T D = N.orientnew('D', 'DCM', DCM) # Frames D and C are the same ReferenceFrame, # since they have equal DCM respect to frame N. # Therefore, D and C should have same angle velocity in N. assert D.dcm(N) == C.dcm(N) == Matrix([ [cos(q2)*cos(q3), sin(q1)*sin(q2)*cos(q3) + sin(q3)*cos(q1), sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3)], [-sin(q3)*cos(q2), -sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)], [sin(q2), -sin(q1)*cos(q2), cos(q1)*cos(q2)]]) assert (D.ang_vel_in(N) - C.ang_vel_in(N)).express(N).simplify() == 0 def test_orientnew_respects_parent_class(): class MyReferenceFrame(ReferenceFrame): pass B = MyReferenceFrame('B') C = B.orientnew('C', 'Axis', [0, B.x]) assert isinstance(C, MyReferenceFrame) def test_orientnew_respects_input_indices(): N = ReferenceFrame('N') q1 = dynamicsymbols('q1') A = N.orientnew('a', 'Axis', [q1, N.z]) #modify default indices: minds = [x+'1' for x in N.indices] B = N.orientnew('b', 'Axis', [q1, N.z], indices=minds) assert N.indices == A.indices assert B.indices == minds def test_orientnew_respects_input_latexs(): N = ReferenceFrame('N') q1 = dynamicsymbols('q1') A = N.orientnew('a', 'Axis', [q1, N.z]) #build default and alternate latex_vecs: def_latex_vecs = [(r"\mathbf{\hat{%s}_%s}" % (A.name.lower(), A.indices[0])), (r"\mathbf{\hat{%s}_%s}" % (A.name.lower(), A.indices[1])), (r"\mathbf{\hat{%s}_%s}" % (A.name.lower(), A.indices[2]))] name = 'b' indices = [x+'1' for x in N.indices] new_latex_vecs = [(r"\mathbf{\hat{%s}_{%s}}" % (name.lower(), indices[0])), (r"\mathbf{\hat{%s}_{%s}}" % (name.lower(), indices[1])), (r"\mathbf{\hat{%s}_{%s}}" % (name.lower(), indices[2]))] B = N.orientnew(name, 'Axis', [q1, N.z], latexs=new_latex_vecs) assert A.latex_vecs == def_latex_vecs assert B.latex_vecs == new_latex_vecs assert B.indices != indices def test_orientnew_respects_input_variables(): N = ReferenceFrame('N') q1 = dynamicsymbols('q1') A = N.orientnew('a', 'Axis', [q1, N.z]) #build non-standard variable names name = 'b' new_variables = ['notb_'+x+'1' for x in N.indices] B = N.orientnew(name, 'Axis', [q1, N.z], variables=new_variables) for j,var in enumerate(A.varlist): assert var.name == A.name + '_' + A.indices[j] for j,var in enumerate(B.varlist): assert var.name == new_variables[j] def test_issue_10348(): u = dynamicsymbols('u:3') I = ReferenceFrame('I') I.orientnew('A', 'space', u, 'XYZ') def test_issue_11503(): A = ReferenceFrame("A") A.orientnew("B", "Axis", [35, A.y]) C = ReferenceFrame("C") A.orient(C, "Axis", [70, C.z]) def test_partial_velocity(): N = ReferenceFrame('N') A = ReferenceFrame('A') u1, u2 = dynamicsymbols('u1, u2') A.set_ang_vel(N, u1 * A.x + u2 * N.y) assert N.partial_velocity(A, u1) == -A.x assert N.partial_velocity(A, u1, u2) == (-A.x, -N.y) assert A.partial_velocity(N, u1) == A.x assert A.partial_velocity(N, u1, u2) == (A.x, N.y) assert N.partial_velocity(N, u1) == 0 assert A.partial_velocity(A, u1) == 0 def test_issue_11498(): A = ReferenceFrame('A') B = ReferenceFrame('B') # Identity transformation A.orient(B, 'DCM', eye(3)) assert A.dcm(B) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) assert B.dcm(A) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) # x -> y # y -> -z # z -> -x A.orient(B, 'DCM', Matrix([[0, 1, 0], [0, 0, -1], [-1, 0, 0]])) assert B.dcm(A) == Matrix([[0, 1, 0], [0, 0, -1], [-1, 0, 0]]) assert A.dcm(B) == Matrix([[0, 0, -1], [1, 0, 0], [0, -1, 0]]) assert B.dcm(A).T == A.dcm(B) def test_reference_frame(): raises(TypeError, lambda: ReferenceFrame(0)) raises(TypeError, lambda: ReferenceFrame('N', 0)) raises(ValueError, lambda: ReferenceFrame('N', [0, 1])) raises(TypeError, lambda: ReferenceFrame('N', [0, 1, 2])) raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], 0)) raises(ValueError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], [0, 1])) raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], [0, 1, 2])) raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], ['a', 'b', 'c'], 0)) raises(ValueError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], ['a', 'b', 'c'], [0, 1])) raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], ['a', 'b', 'c'], [0, 1, 2])) N = ReferenceFrame('N') assert N[0] == CoordinateSym('N_x', N, 0) assert N[1] == CoordinateSym('N_y', N, 1) assert N[2] == CoordinateSym('N_z', N, 2) raises(ValueError, lambda: N[3]) N = ReferenceFrame('N', ['a', 'b', 'c']) assert N['a'] == N.x assert N['b'] == N.y assert N['c'] == N.z raises(ValueError, lambda: N['d']) assert str(N) == 'N' A = ReferenceFrame('A') B = ReferenceFrame('B') q0, q1, q2, q3 = symbols('q0 q1 q2 q3') raises(TypeError, lambda: A.orient(B, 'DCM', 0)) raises(TypeError, lambda: B.orient(N, 'Space', [q1, q2, q3], '222')) raises(TypeError, lambda: B.orient(N, 'Axis', [q1, N.x + 2 * N.y], '222')) raises(TypeError, lambda: B.orient(N, 'Axis', q1)) raises(IndexError, lambda: B.orient(N, 'Axis', [q1])) raises(TypeError, lambda: B.orient(N, 'Quaternion', [q0, q1, q2, q3], '222')) raises(TypeError, lambda: B.orient(N, 'Quaternion', q0)) raises(TypeError, lambda: B.orient(N, 'Quaternion', [q0, q1, q2])) raises(NotImplementedError, lambda: B.orient(N, 'Foo', [q0, q1, q2])) raises(TypeError, lambda: B.orient(N, 'Body', [q1, q2], '232')) raises(TypeError, lambda: B.orient(N, 'Space', [q1, q2], '232')) N.set_ang_acc(B, 0) assert N.ang_acc_in(B) == Vector(0) N.set_ang_vel(B, 0) assert N.ang_vel_in(B) == Vector(0) def test_check_frame(): raises(VectorTypeError, lambda: _check_frame(0)) def test_dcm_diff_16824(): # NOTE : This is a regression test for the bug introduced in PR 14758, # identified in 16824, and solved by PR 16828. # This is the solution to Problem 2.2 on page 264 in Kane & Lenvinson's # 1985 book. q1, q2, q3 = dynamicsymbols('q1:4') s1 = sin(q1) c1 = cos(q1) s2 = sin(q2) c2 = cos(q2) s3 = sin(q3) c3 = cos(q3) dcm = Matrix([[c2*c3, s1*s2*c3 - s3*c1, c1*s2*c3 + s3*s1], [c2*s3, s1*s2*s3 + c3*c1, c1*s2*s3 - c3*s1], [-s2, s1*c2, c1*c2]]) A = ReferenceFrame('A') B = ReferenceFrame('B') B.orient(A, 'DCM', dcm) AwB = B.ang_vel_in(A) alpha2 = s3*c2*q1.diff() + c3*q2.diff() beta2 = s1*c2*q3.diff() + c1*q2.diff() assert simplify(AwB.dot(A.y) - alpha2) == 0 assert simplify(AwB.dot(B.y) - beta2) == 0 def test_orient_explicit(): A = ReferenceFrame('A') B = ReferenceFrame('B') A.orient_explicit(B, eye(3)) assert A.dcm(B) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) def test_orient_axis(): A = ReferenceFrame('A') B = ReferenceFrame('B') A.orient_axis(B,-B.x, 1) A1 = A.dcm(B) A.orient_axis(B, B.x, -1) A2 = A.dcm(B) A.orient_axis(B, 1, -B.x) A3 = A.dcm(B) assert A1 == A2 assert A2 == A3 raises(TypeError, lambda: A.orient_axis(B, 1, 1)) def test_orient_body(): A = ReferenceFrame('A') B = ReferenceFrame('B') B.orient_body_fixed(A, (1,1,0), 'XYX') assert B.dcm(A) == Matrix([[cos(1), sin(1)**2, -sin(1)*cos(1)], [0, cos(1), sin(1)], [sin(1), -sin(1)*cos(1), cos(1)**2]]) def test_orient_space(): A = ReferenceFrame('A') B = ReferenceFrame('B') B.orient_space_fixed(A, (0,0,0), '123') assert B.dcm(A) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) def test_orient_quaternion(): A = ReferenceFrame('A') B = ReferenceFrame('B') B.orient_quaternion(A, (0,0,0,0)) assert B.dcm(A) == Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]]) def test_looped_frame_warning(): A = ReferenceFrame('A') B = ReferenceFrame('B') C = ReferenceFrame('C') a, b, c = symbols('a b c') B.orient_axis(A, A.x, a) C.orient_axis(B, B.x, b) with warnings.catch_warnings(record = True) as w: warnings.simplefilter("always") A.orient_axis(C, C.x, c) assert issubclass(w[-1].category, UserWarning) assert 'Loops are defined among the orientation of frames. ' + \ 'This is likely not desired and may cause errors in your calculations.' in str(w[-1].message) def test_frame_dict(): A = ReferenceFrame('A') B = ReferenceFrame('B') C = ReferenceFrame('C') a, b, c = symbols('a b c') B.orient_axis(A, A.x, a) assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(a), -sin(a)],[0, sin(a), cos(a)]])} assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0, cos(a), sin(a)],[0, -sin(a), cos(a)]])} assert C._dcm_dict == {} B.orient_axis(C, C.x, b) # Previous relation is not wiped assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(a), -sin(a)],[0, sin(a), cos(a)]])} assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0, cos(a), sin(a)],[0, -sin(a), cos(a)]]), \ C: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]])} assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]])} A.orient_axis(B, B.x, c) # Previous relation is updated assert B._dcm_dict == {C: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]]),\ A: Matrix([[1, 0, 0],[0, cos(c), -sin(c)],[0, sin(c), cos(c)]])} assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(c), sin(c)],[0, -sin(c), cos(c)]])} assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]])} def test_dcm_cache_dict(): A = ReferenceFrame('A') B = ReferenceFrame('B') C = ReferenceFrame('C') D = ReferenceFrame('D') a, b, c = symbols('a b c') B.orient_axis(A, A.x, a) C.orient_axis(B, B.x, b) D.orient_axis(C, C.x, c) assert D._dcm_dict == {C: Matrix([[1, 0, 0],[0, cos(c), sin(c)],[0, -sin(c), cos(c)]])} assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]]), \ D: Matrix([[1, 0, 0],[0, cos(c), -sin(c)],[0, sin(c), cos(c)]])} assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0, cos(a), sin(a)],[0, -sin(a), cos(a)]]), \ C: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]])} assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(a), -sin(a)],[0, sin(a), cos(a)]])} assert D._dcm_dict == D._dcm_cache D.dcm(A) # Check calculated dcm relation is stored in _dcm_cache and not in _dcm_dict assert list(A._dcm_cache.keys()) == [A, B, D] assert list(D._dcm_cache.keys()) == [C, A] assert list(A._dcm_dict.keys()) == [B] assert list(D._dcm_dict.keys()) == [C] assert A._dcm_dict != A._dcm_cache A.orient_axis(B, B.x, b) # _dcm_cache of A is wiped out and new relation is stored. assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), sin(b)],[0, -sin(b), cos(b)]])} assert A._dcm_dict == A._dcm_cache assert B._dcm_dict == {C: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]]), \ A: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b), cos(b)]])}