def test_SortSomeVariables():
x = Variable("x")
y = Variable("y")
p = Variable("p")
assert VariableList([x, y]) == VariableList([y, x])
assert VariableList([x, p]) == VariableList([p, x])
assert VariableList([y, p]) == VariableList([p, y])
def test_KineticEnergy_Random():
Ntests = 1 # 10
x = Variable("x")
y = Variable("y")
for i in range(Ntests):
mass = np.random.rand()
vector3D = np.zeros(3, dtype="object")
vector3D += x.dt * np.random.rand(3)
vector3D += y.dt * np.random.rand(3)
E = KineticEnergy(mass, vector3D)
assert E == mass * np.dot(vector3D, vector3D) / 2
def test_SortAllVariables():
x = Variable("x")
y = Variable("y")
p = Variable("p")
listgood = VariableList([x, y, p])
assert VariableList([x, y, p]) == listgood
assert VariableList([x, p, y]) == listgood
assert VariableList([y, x, p]) == listgood
assert VariableList([y, p, x]) == listgood
assert VariableList([p, x, y]) == listgood
assert VariableList([p, y, x]) == listgood
def test_SetMatrixDim5_Random():
Ntests = 1 # 2
dim = 5
X = []
dX = []
for i in range(dim):
xi = Variable("x%d" % i)
X.append(xi)
dX.append(xi.dt)
X = np.array(X)
dX = np.array(dX)
for i in range(Ntests):
M = randomSymmetricMatrix(dim)
V = np.random.rand(dim, dim)
K = randomSymmetricMatrix(dim)
A = np.random.rand(dim)
B = np.random.rand(dim)
C = np.random.rand()
totalenergy = C
totalenergy += np.dot(dX, np.dot(M, dX)) / 2
totalenergy += np.dot(dX, np.dot(V, X))
totalenergy += np.dot(X, np.dot(K, X)) / 2
totalenergy += np.dot(A, dX)
totalenergy += np.dot(B, X)
E = Energy.frommatrix(X=X, M=M, V=V, K=K, A=A, B=B, C=C)
assert E == totalenergy
def test_QuadPosition():
Ntests = 1 # 10
x = Variable("x")
for i in range(Ntests):
a = np.random.rand()
E = Energy(a * x**2)
assert E == a * x**2
def test_VelocityPoint():
x = Variable("x")
R0 = FrameReference()
R1 = FrameReference(R0, translation=(x, 0, 0))
point = Object(R1)
np.testing.assert_almost_equal(point.get(R1, "v"), (0, 0, 0))
np.testing.assert_array_equal(point.get(R0, "v"), (x.dt, 0, 0))
def test_CompareWithMatrixDim5_Random():
Ntests = 1 # 2
dim = 5
X = []
dX = []
for i in range(dim):
xi = Variable("x%d" % i)
X.append(xi)
dX.append(xi.dt)
X = np.array(X)
dX = np.array(dX)
for i in range(Ntests):
M = randomSymmetricMatrix(dim)
V = np.random.rand(dim, dim)
K = randomSymmetricMatrix(dim)
A = np.random.rand(dim)
B = np.random.rand(dim)
C = np.random.rand()
totalenergy = C
totalenergy += np.dot(dX, np.dot(M, dX)) / 2
totalenergy += np.dot(dX, np.dot(V, X))
totalenergy += np.dot(X, np.dot(K, X)) / 2
totalenergy += np.dot(A, dX)
totalenergy += np.dot(B, X)
print("z")
E = Energy(totalenergy)
print("k")
assert E == totalenergy
def test_QuadSpeed():
Ntests = 1 # 10
x = Variable("x")
dx = x.dt
for i in range(Ntests):
a = np.random.rand()
E = Energy(a * dx**2)
assert E == a * dx**2
def test_KineticEnergy_Standard():
x = Variable("x")
dx = x.dt
mass = 1
vector3D = (dx, 0, 0)
E_good = mass * (dx**2) / 2
E_test = KineticEnergy(mass, vector3D)
E_good = Energy(E_good)
assert E_test == E_good
def test_Linear():
Ntests = 1 # 10
x = Variable("x")
dx = x.dt
for i in range(Ntests):
a, b, c = np.random.rand(3)
totalenergy = c
totalenergy += b * x
totalenergy += a * dx
E = Energy(totalenergy)
assert E == totalenergy
def test_CompareWithMatrixDim2_Random():
Ntests = 1 # 10
x = Variable("x")
y = Variable("y")
X = np.array([x, y])
dX = np.array([x.dt, y.dt])
for i in range(Ntests):
M = randomSymmetricMatrix(2)
V = np.random.rand(2, 2)
K = randomSymmetricMatrix(2)
A = np.random.rand(2)
B = np.random.rand(2)
C = np.random.rand()
totalenergy = C
totalenergy += np.dot(dX, np.dot(M, dX)) / 2
totalenergy += np.dot(dX, np.dot(V, X))
totalenergy += np.dot(X, np.dot(K, X)) / 2
totalenergy += np.dot(A, dX)
totalenergy += np.dot(B, X)
E = Energy(totalenergy)
assert E == totalenergy
def test_CompareWithMatrixDim2_Standard():
x = Variable("x")
y = Variable("y")
dx = x.dt
dy = y.dt
X = (x, y)
M = np.array([[14, 2], [2, 12]])
V = np.array([[4, 6], [3, 5]])
K = np.array([[-6, -3], [-3, -10]])
A = np.array([1, -7])
B = np.array([-5, 9])
C = 80
ener = 7*(dx**2) + 2*dx*dy + 6*(dy**2) + \
4*dx*x + 6*dx*y + 3*dy*x + 5*dy*y + \
(-3)*x**2 + (-3)*x*y + (-5)*y**2 + \
1*dx + (-7)*dy + (-5)*x + 9*y + 80
assert Energy(ener) == ener
def test_SetMatrixDim2_Random():
Ntests = 1 # 2
x = Variable("x")
y = Variable("y")
X = np.array([x, y])
dX = np.array([x.dt, y.dt])
for i in range(Ntests):
M = randomSymmetricMatrix(2)
V = np.random.rand(2, 2)
K = randomSymmetricMatrix(2)
A = np.random.rand(2)
B = np.random.rand(2)
C = np.random.rand()
totalenergy = C
totalenergy += np.dot(dX, np.dot(M, dX)) / 2
totalenergy += np.dot(dX, np.dot(V, X))
totalenergy += np.dot(X, np.dot(K, X)) / 2
totalenergy += np.dot(A, dX)
totalenergy += np.dot(B, X)
E = Energy.frommatrix(X=X, M=M, V=V, K=K, A=A, B=B, C=C)
assert E == totalenergy
def test_SetMatrixDim2_Standard():
x = Variable("x")
y = Variable("y")
dx = x.dt
dy = y.dt
X = (x, y)
M = np.array([[14, 2], [2, 12]])
V = np.array([[4, 6], [3, 5]])
K = np.array([[-6, -3], [-3, -10]])
A = np.array([1, -7])
B = np.array([-5, 9])
C = 80
ener = 7*(dx**2) + 2*dx*dy + 6*(dy**2) + \
4*dx*x + 6*dx*y + 3*dy*x + 5*dy*y + \
(-3)*x**2 + (-3)*x*y + (-5)*y**2 + \
1*dx + (-7)*dy + (-5)*x + 9*y + 80
E = Energy.frommatrix(X=X, M=M, V=V, K=K, A=A, B=B, C=C)
ener = Energy(ener)
assert E == ener
def test_AllQuantity():
Ntests = 1 # 10
x = Variable("x")
dx = x.dt
for i in range(Ntests):
m, v, k, a, b, c = np.random.rand(6)
totalenergy = c
totalenergy += a * dx
totalenergy += b * x
totalenergy += k * x**2 / 2
totalenergy += v * x * dx
totalenergy += m * dx**2 / 2
E = Energy(totalenergy)
assert E == totalenergy
def test_KineticEnergy():
m = 1
x = Variable("x")
R0 = FrameReference()
R1 = FrameReference(R0, translation=(x, 0, 0))
point = Object(R1)
point.mass = m
v = point.get(R1, "v")
E = point.KineticEnergy(R1)
assert E == m * np.dot(v, v) / 2
v = point.get(R0, "v")
E = point.KineticEnergy(R0)
assert E == m * np.dot(v, v) / 2
def test_Comparation():
x = Variable("x")
y = Variable("y")
assert x == x
assert x != y
def test_GetDerivative():
x = Variable("x")
dx = x.dt
def test_RebuildSameVariable():
x = Variable("x")
newx = Variable("x")
assert x is newx
def test_BuildTwoVariables():
x = Variable("x")
y = Variable("y")
def test_Build():
x = Variable("x")