def testOnes_inv(self):
A1 = [np.array([[1., 1.], [1., 1.]]), np.array([[1., 1.], [1., 1.]])]
x1 = np.array([1., 1., 1., 1.])
y1 = np.array([4, 4, 4, 4])
kp = KronProd(invert(A1))
x = kp.dot(y1)
np.testing.assert_almost_equal(x, x1, decimal=7, verbose=True)
def testBig_inv(self):
n = 2 # number of factors
p = 100 # dimension of factor
r_As = [ortho_group.rvs(dim=p) for i in range(n)]
As = [m / m.sum(axis=1)[:, None] for m in r_As] # normalize each row
y = np.random.rand(p**n)
kp = KronProd(invert(As))
x = kp.dot(y)
print("efficient calc: ", x)
def testBig_pInv(self):
n = 2 # number of factors
p = 100 # dimension of factor
r_As = [np.random.rand(p, p) for i in range(n)]
#Make first and second row the same so that way it becomes a non-invertible matrix
for A in r_As:
A[1, :] = A[0, :]
As = [m / m.sum(axis=1)[:, None] for m in r_As] # normalize each row
x = np.random.rand(p**n)
kp = KronProd(invert(As))
Y = kp.dot(x)
print("efficient calc: ", Y)
def testRandom_inv(self):
n = 5 # number of factors
p = 5 # dimension of factor
r_As = [ortho_group.rvs(dim=p) for i in range(n)]
As = [m / m.sum(axis=1)[:, None] for m in r_As] # normalize each row
y = np.random.rand(p**n)
big_A = reduce(np.kron, As)
big_x = np.linalg.solve(big_A, y)
print("full calc: ", big_x)
kp = KronProd(invert(As))
x = kp.dot(y)
print("efficient calc: ", x)
np.testing.assert_almost_equal(x, big_x, decimal=7, verbose=True)
def testInts_pInv(self):
A1 = [ np.array([[1.0, 0.0], [0.0,0.0]]),
np.array([[1.,1.], [0.,0.]])]
y1 = np.array([1.,2.,3.,4.])
A1_inv = []
for a in A1:
A1_inv.append(np.linalg.pinv(a))
big_A = reduce(np.kron, A1_inv)
big_x = big_A.dot(y1)
print("FOO")
print("full calc: ",big_x)
kp = KronProd(invert(A1))
x = kp.dot(y1)
print("efficient calc: ", x)
print("BAR")
self.assertSequenceEqual(list(x), list(big_x))
def testFail(self):
#For some reason this breaks the property of kron product - (A_1 kron A_2)^+ = A_1^+ kron A_2^+
#The equivalent test for this is testRandom_pInv, but the reduce is performed after pinv. If it isn't then we get this error.
#This error didn't seem to happen for n=p=3 or 2 but does occur sometimes when n=p=4 and somewhat frequently when n=p=5.
n = 4
p = 4
As = As_fail
y = Y_fail
big_A = reduce(np.kron, As)
big_A_inv = np.linalg.pinv(big_A)
big_x = big_A_inv.dot(y)
kp = KronProd(invert(As))
x = kp.dot(y)
if (np.allclose(x, big_x) == False):
return
else:
self.fail("No equivalent!")
def testRandom_pInv(self):
n = 5 # number of factors
p = 5 # dimension of factor
r_As = [ortho_group.rvs(dim=p) for i in range(n)]
#Make first and second row the same so that way it becomes a non-invertible matrix
for A in r_As:
A[1, :] = A[0, :]
As = [m / m.sum(axis=1)[:, None] for m in r_As] # normalize each row
y = np.random.rand(p**n)
As_inv = []
for a in As:
As_inv.append(np.linalg.pinv(a))
big_A = reduce(np.kron, As_inv)
big_x = big_A.dot(y)
print("[test_kron_inv - testRandom_pInv] full calc: ", big_x)
kp = KronProd(invert(As))
x = kp.dot(y)
print("[test_kron_inv - testRandom_pInv] efficient calc: ", x)
np.testing.assert_almost_equal(big_x, x, decimal=7, verbose=True)