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 __init__(self, E, IC, G, F, timesteps):
Validation_Solver.init(self, E, IC, G, F, timesteps)
if not isinstance(E, Energy):
E = Energy(E)
lagrange = Lagrangian(E)
self.X = E.X
self.timesteps = timesteps
self.n = len(self.X)
self.m = len(G)
self.__computeG(G)
self.__computeDG()
self.__computeDDG()
self.__computeM(lagrange)
self.__computeC(lagrange)
self.__computeK(lagrange)
self.__computeZ(lagrange)
self.__computeMvv(lagrange)
self.__computeMvp(lagrange)
self.__computeMpp(lagrange)
self.__resetAllMatrix()
self.__computeF(F)
self.__computet0()
self.__computeX0(IC)
self.__computedX0(IC)
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_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_X2():
x = Variable("x")
E = Energy(x**2)
L = Lagrangian(E)
Lvec = L.get()
assert Lvec.shape == (1, )
assert Lvec[0] == -2 * x
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_XdX():
x = Variable("x")
dx = x.dt
E = Energy(x * dx)
L = Lagrangian(E)
Lvec = L.get()
assert Lvec.shape == (1, )
assert Lvec[0] == 0
def test_dX2():
x = Variable("x")
dx = x.dt
ddx = x.ddt
E = Energy(dx**2)
L = Lagrangian(E)
Lvec = L.get()
assert Lvec.shape == (1, )
assert Lvec[0] == 2 * ddx
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_cosX():
x = Variable("x")
f = cos(x)
df = -1 * sin(x)
E = Energy(f)
L = Lagrangian(E)
Lvec = L.get()
assert Lvec.shape == (1, )
assert Lvec[0] == -1 * df
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_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_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_Constant():
E = Energy(1)
L = Lagrangian(E)
Lvec = L.get()
assert Lvec is None
def test_Constant():
Ntests = 1 # 10
for i in range(Ntests):
a = np.random.rand()
E = Energy(a)
assert E == a
def test_Build():
Energy(0)