def test_coordinate_vars(): """ Tests the coordinate variables functionality with respect to reorientation of coordinate systems. """ A = CoordSysCartesian('A') assert BaseScalar('Ax', 0, A, ' ', ' ') == A.x assert BaseScalar('Ay', 1, A, ' ', ' ') == A.y assert BaseScalar('Az', 2, A, ' ', ' ') == A.z assert BaseScalar('Ax', 0, A, ' ', ' ').__hash__() == A.x.__hash__() assert isinstance(A.x, BaseScalar) and \ isinstance(A.y, BaseScalar) and \ isinstance(A.z, BaseScalar) assert A.scalar_map(A) == {A.x: A.x, A.y: A.y, A.z: A.z} assert A.x.system == A B = A.orient_new_axis('B', q, A.k) assert B.scalar_map(A) == {B.z: A.z, B.y: -A.x*sin(q) + A.y*cos(q), B.x: A.x*cos(q) + A.y*sin(q)} assert A.scalar_map(B) == {A.x: B.x*cos(q) - B.y*sin(q), A.y: B.x*sin(q) + B.y*cos(q), A.z: B.z} assert express(B.x, A, variables=True) == A.x*cos(q) + A.y*sin(q) assert express(B.y, A, variables=True) == -A.x*sin(q) + A.y*cos(q) assert express(B.z, A, variables=True) == A.z assert express(B.x*B.y*B.z, A, variables=True) == \ A.z*(-A.x*sin(q) + A.y*cos(q))*(A.x*cos(q) + A.y*sin(q)) assert express(B.x*B.i + B.y*B.j + B.z*B.k, A) == \ (B.x*cos(q) - B.y*sin(q))*A.i + (B.x*sin(q) + \ B.y*cos(q))*A.j + B.z*A.k assert simplify(express(B.x*B.i + B.y*B.j + B.z*B.k, A, \ variables=True)) == \ A.x*A.i + A.y*A.j + A.z*A.k assert express(A.x*A.i + A.y*A.j + A.z*A.k, B) == \ (A.x*cos(q) + A.y*sin(q))*B.i + \ (-A.x*sin(q) + A.y*cos(q))*B.j + A.z*B.k assert simplify(express(A.x*A.i + A.y*A.j + A.z*A.k, B, \ variables=True)) == \ B.x*B.i + B.y*B.j + B.z*B.k N = B.orient_new_axis('N', -q, B.k) assert N.scalar_map(A) == \ {N.x: A.x, N.z: A.z, N.y: A.y} C = A.orient_new_axis('C', q, A.i + A.j + A.k) mapping = A.scalar_map(C) assert mapping[A.x] == 2*C.x*cos(q)/3 + C.x/3 - \ 2*C.y*sin(q + pi/6)/3 + C.y/3 - 2*C.z*cos(q + pi/3)/3 + C.z/3 assert mapping[A.y] == -2*C.x*cos(q + pi/3)/3 + \ C.x/3 + 2*C.y*cos(q)/3 + C.y/3 - 2*C.z*sin(q + pi/6)/3 + C.z/3 assert mapping[A.z] == -2*C.x*sin(q + pi/6)/3 + C.x/3 - \ 2*C.y*cos(q + pi/3)/3 + C.y/3 + 2*C.z*cos(q)/3 + C.z/3 D = A.locate_new('D', a*A.i + b*A.j + c*A.k) assert D.scalar_map(A) == {D.z: A.z - c, D.x: A.x - a, D.y: A.y - b} E = A.orient_new_axis('E', a, A.k, a*A.i + b*A.j + c*A.k) assert A.scalar_map(E) == {A.z: E.z + c, A.x: E.x*cos(a) - E.y*sin(a) + a, A.y: E.x*sin(a) + E.y*cos(a) + b} assert E.scalar_map(A) == {E.x: (A.x - a)*cos(a) + (A.y - b)*sin(a), E.y: (-A.x + a)*sin(a) + (A.y - b)*cos(a), E.z: A.z - c} F = A.locate_new('F', Vector.zero) assert A.scalar_map(F) == {A.z: F.z, A.x: F.x, A.y: F.y}
def test_coordsyscartesian_equivalence(): A = CoordSysCartesian("A") A1 = CoordSysCartesian("A") assert A1 == A B = CoordSysCartesian("B") assert A != B assert A.locate_new("C1", A.i) == A.locate_new("C2", A.i) assert A.orient_new_axis("C1", a, A.i) == A.orient_new_axis("C2", a, A.i)
def test_coordsyscartesian_equivalence(): A = CoordSysCartesian('A') A1 = CoordSysCartesian('A') assert A1 == A B = CoordSysCartesian('B') assert A != B assert A.locate_new('C1', A.i) == A.locate_new('C2', A.i) assert A.orient_new_axis('C1', a, A.i) == \ A.orient_new_axis('C2', a, A.i)
def test_locatenew_point(): """ Tests Point class, and locate_new method in CoordSysCartesian. """ A = CoordSysCartesian('A') assert isinstance(A.origin, Point) v = a * A.i + b * A.j + c * A.k C = A.locate_new('C', v) assert C.origin.position_wrt(A) == \ C.position_wrt(A) == \ C.origin.position_wrt(A.origin) == v assert A.origin.position_wrt(C) == \ A.position_wrt(C) == \ A.origin.position_wrt(C.origin) == -v assert A.origin.express_coordinates(C) == (-a, -b, -c) p = A.origin.locate_new('p', -v) assert p.express_coordinates(A) == (-a, -b, -c) assert p.position_wrt(C.origin) == p.position_wrt(C) == \ -2 * v p1 = p.locate_new('p1', 2 * v) assert p1.position_wrt(C.origin) == Vector.zero assert p1.express_coordinates(C) == (0, 0, 0) p2 = p.locate_new('p2', A.i) assert p1.position_wrt(p2) == 2 * v - A.i assert p2.express_coordinates(C) == (-2 * a + 1, -2 * b, -2 * c)
def test_locatenew_point(): """ Tests Point class, and locate_new method in CoordSysCartesian. """ A = CoordSysCartesian('A') assert isinstance(A.origin, Point) v = a*A.i + b*A.j + c*A.k C = A.locate_new('C', v) assert C.origin.position_wrt(A) == \ C.position_wrt(A) == \ C.origin.position_wrt(A.origin) == v assert A.origin.position_wrt(C) == \ A.position_wrt(C) == \ A.origin.position_wrt(C.origin) == -v assert A.origin.express_coordinates(C) == (-a, -b, -c) p = A.origin.locate_new('p', -v) assert p.express_coordinates(A) == (-a, -b, -c) assert p.position_wrt(C.origin) == p.position_wrt(C) == \ -2 * v p1 = p.locate_new('p1', 2*v) assert p1.position_wrt(C.origin) == Vector.zero assert p1.express_coordinates(C) == (0, 0, 0) p2 = p.locate_new('p2', A.i) assert p1.position_wrt(p2) == 2*v - A.i assert p2.express_coordinates(C) == (-2*a + 1, -2*b, -2*c)
def test_coordinate_vars(): """ Tests the coordinate variables functionality with respect to reorientation of coordinate systems. """ A = CoordSysCartesian('A') assert BaseScalar('Ax', 0, A, ' ', ' ') == A.x assert BaseScalar('Ay', 1, A, ' ', ' ') == A.y assert BaseScalar('Az', 2, A, ' ', ' ') == A.z assert BaseScalar('Ax', 0, A, ' ', ' ').__hash__() == A.x.__hash__() assert isinstance(A.x, BaseScalar) and \ isinstance(A.y, BaseScalar) and \ isinstance(A.z, BaseScalar) assert A.scalar_map(A) == {A.x: A.x, A.y: A.y, A.z: A.z} assert A.x.system == A B = A.orient_new_axis('B', q, A.k) assert B.scalar_map(A) == { B.z: A.z, B.y: -A.x * sin(q) + A.y * cos(q), B.x: A.x * cos(q) + A.y * sin(q) } assert A.scalar_map(B) == { A.x: B.x * cos(q) - B.y * sin(q), A.y: B.x * sin(q) + B.y * cos(q), A.z: B.z } assert express(B.x, A, variables=True) == A.x * cos(q) + A.y * sin(q) assert express(B.y, A, variables=True) == -A.x * sin(q) + A.y * cos(q) assert express(B.z, A, variables=True) == A.z assert express(B.x*B.y*B.z, A, variables=True) == \ A.z*(-A.x*sin(q) + A.y*cos(q))*(A.x*cos(q) + A.y*sin(q)) assert express(B.x*B.i + B.y*B.j + B.z*B.k, A) == \ (B.x*cos(q) - B.y*sin(q))*A.i + (B.x*sin(q) + \ B.y*cos(q))*A.j + B.z*A.k assert simplify(express(B.x*B.i + B.y*B.j + B.z*B.k, A, \ variables=True)) == \ A.x*A.i + A.y*A.j + A.z*A.k assert express(A.x*A.i + A.y*A.j + A.z*A.k, B) == \ (A.x*cos(q) + A.y*sin(q))*B.i + \ (-A.x*sin(q) + A.y*cos(q))*B.j + A.z*B.k assert simplify(express(A.x*A.i + A.y*A.j + A.z*A.k, B, \ variables=True)) == \ B.x*B.i + B.y*B.j + B.z*B.k N = B.orient_new_axis('N', -q, B.k) assert N.scalar_map(A) == \ {N.x: A.x, N.z: A.z, N.y: A.y} C = A.orient_new_axis('C', q, A.i + A.j + A.k) mapping = A.scalar_map(C) assert mapping[A.x] == 2*C.x*cos(q)/3 + C.x/3 - \ 2*C.y*sin(q + pi/6)/3 + C.y/3 - 2*C.z*cos(q + pi/3)/3 + C.z/3 assert mapping[A.y] == -2*C.x*cos(q + pi/3)/3 + \ C.x/3 + 2*C.y*cos(q)/3 + C.y/3 - 2*C.z*sin(q + pi/6)/3 + C.z/3 assert mapping[A.z] == -2*C.x*sin(q + pi/6)/3 + C.x/3 - \ 2*C.y*cos(q + pi/3)/3 + C.y/3 + 2*C.z*cos(q)/3 + C.z/3 D = A.locate_new('D', a * A.i + b * A.j + c * A.k) assert D.scalar_map(A) == {D.z: A.z - c, D.x: A.x - a, D.y: A.y - b} E = A.orient_new_axis('E', a, A.k, a * A.i + b * A.j + c * A.k) assert A.scalar_map(E) == { A.z: E.z + c, A.x: E.x * cos(a) - E.y * sin(a) + a, A.y: E.x * sin(a) + E.y * cos(a) + b } assert E.scalar_map(A) == { E.x: (A.x - a) * cos(a) + (A.y - b) * sin(a), E.y: (-A.x + a) * sin(a) + (A.y - b) * cos(a), E.z: A.z - c } F = A.locate_new('F', Vector.zero) assert A.scalar_map(F) == {A.z: F.z, A.x: F.x, A.y: F.y}
def test_coordinate_vars(): """ Tests the coordinate variables functionality with respect to reorientation of coordinate systems. """ A = CoordSysCartesian("A") assert BaseScalar("Ax", 0, A, " ", " ") == A.x assert BaseScalar("Ay", 1, A, " ", " ") == A.y assert BaseScalar("Az", 2, A, " ", " ") == A.z assert BaseScalar("Ax", 0, A, " ", " ").__hash__() == A.x.__hash__() assert isinstance(A.x, BaseScalar) and isinstance(A.y, BaseScalar) and isinstance(A.z, BaseScalar) assert A.scalar_map(A) == {A.x: A.x, A.y: A.y, A.z: A.z} assert A.x.system == A B = A.orient_new_axis("B", q, A.k) assert B.scalar_map(A) == {B.z: A.z, B.y: -A.x * sin(q) + A.y * cos(q), B.x: A.x * cos(q) + A.y * sin(q)} assert A.scalar_map(B) == {A.x: B.x * cos(q) - B.y * sin(q), A.y: B.x * sin(q) + B.y * cos(q), A.z: B.z} assert express(B.x, A, variables=True) == A.x * cos(q) + A.y * sin(q) assert express(B.y, A, variables=True) == -A.x * sin(q) + A.y * cos(q) assert express(B.z, A, variables=True) == A.z assert express(B.x * B.y * B.z, A, variables=True) == A.z * (-A.x * sin(q) + A.y * cos(q)) * ( A.x * cos(q) + A.y * sin(q) ) assert ( express(B.x * B.i + B.y * B.j + B.z * B.k, A) == (B.x * cos(q) - B.y * sin(q)) * A.i + (B.x * sin(q) + B.y * cos(q)) * A.j + B.z * A.k ) assert simplify(express(B.x * B.i + B.y * B.j + B.z * B.k, A, variables=True)) == A.x * A.i + A.y * A.j + A.z * A.k assert ( express(A.x * A.i + A.y * A.j + A.z * A.k, B) == (A.x * cos(q) + A.y * sin(q)) * B.i + (-A.x * sin(q) + A.y * cos(q)) * B.j + A.z * B.k ) assert simplify(express(A.x * A.i + A.y * A.j + A.z * A.k, B, variables=True)) == B.x * B.i + B.y * B.j + B.z * B.k N = B.orient_new_axis("N", -q, B.k) assert N.scalar_map(A) == {N.x: A.x, N.z: A.z, N.y: A.y} C = A.orient_new_axis("C", q, A.i + A.j + A.k) mapping = A.scalar_map(C) assert ( mapping[A.x] == 2 * C.x * cos(q) / 3 + C.x / 3 - 2 * C.y * sin(q + pi / 6) / 3 + C.y / 3 - 2 * C.z * cos(q + pi / 3) / 3 + C.z / 3 ) assert ( mapping[A.y] == -2 * C.x * cos(q + pi / 3) / 3 + C.x / 3 + 2 * C.y * cos(q) / 3 + C.y / 3 - 2 * C.z * sin(q + pi / 6) / 3 + C.z / 3 ) assert ( mapping[A.z] == -2 * C.x * sin(q + pi / 6) / 3 + C.x / 3 - 2 * C.y * cos(q + pi / 3) / 3 + C.y / 3 + 2 * C.z * cos(q) / 3 + C.z / 3 ) D = A.locate_new("D", a * A.i + b * A.j + c * A.k) assert D.scalar_map(A) == {D.z: A.z - c, D.x: A.x - a, D.y: A.y - b} E = A.orient_new_axis("E", a, A.k, a * A.i + b * A.j + c * A.k) assert A.scalar_map(E) == {A.z: E.z + c, A.x: E.x * cos(a) - E.y * sin(a) + a, A.y: E.x * sin(a) + E.y * cos(a) + b} assert E.scalar_map(A) == { E.x: (A.x - a) * cos(a) + (A.y - b) * sin(a), E.y: (-A.x + a) * sin(a) + (A.y - b) * cos(a), E.z: A.z - c, } F = A.locate_new("F", Vector.zero) assert A.scalar_map(F) == {A.z: F.z, A.x: F.x, A.y: F.y}
def test_coordinate_vars(): """ Tests the coordinate variables functionality with respect to reorientation of coordinate systems. """ A = CoordSysCartesian('A') # Note that the name given on the lhs is different from A.x._name assert BaseScalar('A.x', 0, A, 'A_x', r'\mathbf{{x}_{A}}') == A.x assert BaseScalar('A.y', 1, A, 'A_y', r'\mathbf{{y}_{A}}') == A.y assert BaseScalar('A.z', 2, A, 'A_z', r'\mathbf{{z}_{A}}') == A.z assert BaseScalar('A.x', 0, A, 'A_x', r'\mathbf{{x}_{A}}').__hash__() == A.x.__hash__() assert isinstance(A.x, BaseScalar) and \ isinstance(A.y, BaseScalar) and \ isinstance(A.z, BaseScalar) assert A.x*A.y == A.y*A.x assert A.scalar_map(A) == {A.x: A.x, A.y: A.y, A.z: A.z} assert A.x.system == A assert A.x.diff(A.x) == 1 B = A.orient_new_axis('B', q, A.k) assert B.scalar_map(A) == {B.z: A.z, B.y: -A.x*sin(q) + A.y*cos(q), B.x: A.x*cos(q) + A.y*sin(q)} assert A.scalar_map(B) == {A.x: B.x*cos(q) - B.y*sin(q), A.y: B.x*sin(q) + B.y*cos(q), A.z: B.z} assert express(B.x, A, variables=True) == A.x*cos(q) + A.y*sin(q) assert express(B.y, A, variables=True) == -A.x*sin(q) + A.y*cos(q) assert express(B.z, A, variables=True) == A.z assert expand(express(B.x*B.y*B.z, A, variables=True)) == \ expand(A.z*(-A.x*sin(q) + A.y*cos(q))*(A.x*cos(q) + A.y*sin(q))) assert express(B.x*B.i + B.y*B.j + B.z*B.k, A) == \ (B.x*cos(q) - B.y*sin(q))*A.i + (B.x*sin(q) + \ B.y*cos(q))*A.j + B.z*A.k assert simplify(express(B.x*B.i + B.y*B.j + B.z*B.k, A, \ variables=True)) == \ A.x*A.i + A.y*A.j + A.z*A.k assert express(A.x*A.i + A.y*A.j + A.z*A.k, B) == \ (A.x*cos(q) + A.y*sin(q))*B.i + \ (-A.x*sin(q) + A.y*cos(q))*B.j + A.z*B.k assert simplify(express(A.x*A.i + A.y*A.j + A.z*A.k, B, \ variables=True)) == \ B.x*B.i + B.y*B.j + B.z*B.k N = B.orient_new_axis('N', -q, B.k) assert N.scalar_map(A) == \ {N.x: A.x, N.z: A.z, N.y: A.y} C = A.orient_new_axis('C', q, A.i + A.j + A.k) mapping = A.scalar_map(C) assert mapping[A.x] == (C.x*(2*cos(q) + 1)/3 + C.y*(-2*sin(q + pi/6) + 1)/3 + C.z*(-2*cos(q + pi/3) + 1)/3) assert mapping[A.y] == (C.x*(-2*cos(q + pi/3) + 1)/3 + C.y*(2*cos(q) + 1)/3 + C.z*(-2*sin(q + pi/6) + 1)/3) assert mapping[A.z] == (C.x*(-2*sin(q + pi/6) + 1)/3 + C.y*(-2*cos(q + pi/3) + 1)/3 + C.z*(2*cos(q) + 1)/3) D = A.locate_new('D', a*A.i + b*A.j + c*A.k) assert D.scalar_map(A) == {D.z: A.z - c, D.x: A.x - a, D.y: A.y - b} E = A.orient_new_axis('E', a, A.k, a*A.i + b*A.j + c*A.k) assert A.scalar_map(E) == {A.z: E.z + c, A.x: E.x*cos(a) - E.y*sin(a) + a, A.y: E.x*sin(a) + E.y*cos(a) + b} assert E.scalar_map(A) == {E.x: (A.x - a)*cos(a) + (A.y - b)*sin(a), E.y: (-A.x + a)*sin(a) + (A.y - b)*cos(a), E.z: A.z - c} F = A.locate_new('F', Vector.zero) assert A.scalar_map(F) == {A.z: F.z, A.x: F.x, A.y: F.y}
def test_coordinate_vars(): """ Tests the coordinate variables functionality with respect to reorientation of coordinate systems. """ A = CoordSysCartesian('A') # Note that the name given on the lhs is different from A.x._name assert BaseScalar('A.x', 0, A, 'A_x', r'\mathbf{{x}_{A}}') == A.x assert BaseScalar('A.y', 1, A, 'A_y', r'\mathbf{{y}_{A}}') == A.y assert BaseScalar('A.z', 2, A, 'A_z', r'\mathbf{{z}_{A}}') == A.z assert BaseScalar('A.x', 0, A, 'A_x', r'\mathbf{{x}_{A}}').__hash__() == A.x.__hash__() assert isinstance(A.x, BaseScalar) and \ isinstance(A.y, BaseScalar) and \ isinstance(A.z, BaseScalar) assert A.x * A.y == A.y * A.x assert A.scalar_map(A) == {A.x: A.x, A.y: A.y, A.z: A.z} assert A.x.system == A assert A.x.diff(A.x) == 1 B = A.orient_new_axis('B', q, A.k) assert B.scalar_map(A) == { B.z: A.z, B.y: -A.x * sin(q) + A.y * cos(q), B.x: A.x * cos(q) + A.y * sin(q) } assert A.scalar_map(B) == { A.x: B.x * cos(q) - B.y * sin(q), A.y: B.x * sin(q) + B.y * cos(q), A.z: B.z } assert express(B.x, A, variables=True) == A.x * cos(q) + A.y * sin(q) assert express(B.y, A, variables=True) == -A.x * sin(q) + A.y * cos(q) assert express(B.z, A, variables=True) == A.z assert expand(express(B.x*B.y*B.z, A, variables=True)) == \ expand(A.z*(-A.x*sin(q) + A.y*cos(q))*(A.x*cos(q) + A.y*sin(q))) assert express(B.x*B.i + B.y*B.j + B.z*B.k, A) == \ (B.x*cos(q) - B.y*sin(q))*A.i + (B.x*sin(q) + \ B.y*cos(q))*A.j + B.z*A.k assert simplify(express(B.x*B.i + B.y*B.j + B.z*B.k, A, \ variables=True)) == \ A.x*A.i + A.y*A.j + A.z*A.k assert express(A.x*A.i + A.y*A.j + A.z*A.k, B) == \ (A.x*cos(q) + A.y*sin(q))*B.i + \ (-A.x*sin(q) + A.y*cos(q))*B.j + A.z*B.k assert simplify(express(A.x*A.i + A.y*A.j + A.z*A.k, B, \ variables=True)) == \ B.x*B.i + B.y*B.j + B.z*B.k N = B.orient_new_axis('N', -q, B.k) assert N.scalar_map(A) == \ {N.x: A.x, N.z: A.z, N.y: A.y} C = A.orient_new_axis('C', q, A.i + A.j + A.k) mapping = A.scalar_map(C) assert mapping[A.x].equals(C.x * (2 * cos(q) + 1) / 3 + C.y * (-2 * sin(q + pi / 6) + 1) / 3 + C.z * (-2 * cos(q + pi / 3) + 1) / 3) assert mapping[A.y].equals(C.x * (-2 * cos(q + pi / 3) + 1) / 3 + C.y * (2 * cos(q) + 1) / 3 + C.z * (-2 * sin(q + pi / 6) + 1) / 3) assert mapping[A.z].equals(C.x * (-2 * sin(q + pi / 6) + 1) / 3 + C.y * (-2 * cos(q + pi / 3) + 1) / 3 + C.z * (2 * cos(q) + 1) / 3) D = A.locate_new('D', a * A.i + b * A.j + c * A.k) assert D.scalar_map(A) == {D.z: A.z - c, D.x: A.x - a, D.y: A.y - b} E = A.orient_new_axis('E', a, A.k, a * A.i + b * A.j + c * A.k) assert A.scalar_map(E) == { A.z: E.z + c, A.x: E.x * cos(a) - E.y * sin(a) + a, A.y: E.x * sin(a) + E.y * cos(a) + b } assert E.scalar_map(A) == { E.x: (A.x - a) * cos(a) + (A.y - b) * sin(a), E.y: (-A.x + a) * sin(a) + (A.y - b) * cos(a), E.z: A.z - c } F = A.locate_new('F', Vector.zero) assert A.scalar_map(F) == {A.z: F.z, A.x: F.x, A.y: F.y}