def testOnes(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(A1)
y = kp.dot(x1)
self.assertSequenceEqual(list(y), list(y1))
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 inverseTest(A, x):
foo = time.time()
big_A = reduce(np.kron, A)
big_A = np.linalg.inv(big_A)
big_y1 = np.matmul(big_A, x)
time_full = time.time() - foo
foo = time.time()
newA = []
for i in range(len(A)):
newA.append(np.linalg.inv(A[i]))
big_A = reduce(np.kron, newA)
big_y2 = np.matmul(big_A, x)
time_kron = time.time() - foo
foo = time.time()
newA = []
for i in range(len(A)):
newA.append(np.linalg.inv(A[i]))
kp1 = KronProd(newA)
Y1 = kp1.dot(x)
time_kron_dyn = time.time() - foo
if (verifyCorrectness(big_y1, big_y2, Y1)):
print("Inverse Test Passed")
else:
print("Inverse Test Failed!")
return time_full, time_kron, time_kron_dyn
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(self):
n = 2 # number of factors
p = 100 # dimension of factor
r_As = [np.random.rand(p, p) for i in range(n)]
As = [m / m.sum(axis=1)[:, None] for m in r_As] # normalize each row
x = np.random.rand(p**n)
kp = KronProd(As)
Y = kp.dot(x)
print("efficient calc: ", Y)
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 _evalPolicyMatrix(self):
# Evaluate the value function of the policy using linear equations.
#
# Arguments
# ---------
# Let S = number of states, A = number of actions
# P(SxSxA) = transition matrix
# P could be an array with 3 dimensions or a cell array (1xA),
# each cell containing a matrix (SxS) possibly sparse
# R(SxSxA) or (SxA) = reward matrix
# R could be an array with 3 dimensions (SxSxA) or
# a cell array (1xA), each cell containing a sparse matrix (SxS)
# or a 2D array(SxA) possibly sparse
# discount = discount rate in ]0; 1[
# policy(S) = a policy
#
# Evaluation
# ----------
# Vpolicy(S) = value function of the policy
#
#Ppolicy, Rpolicy = self._computePpolicyPRpolicy()
# V = PR + gPV => (I-gP)V = PR => V = inv(I-gP)* PR
#self.V = _np.linalg.solve(
# (_sp.eye(self.S, self.S) - self.discount * Ppolicy), Rpolicy)
#Get appropiately size identity matrices
i_as = []
for i in self.P[0].n:
i_as.append(_np.eye(i))
kpI = KronProd(list(reversed(i_as)))
#Get max value vector
vectors = []
for aa in range(self.A):
#apply discount to a gP
gP = self.P[aa]
rP = self.R[aa]
Y1 = kpI.dot(rP)
Y2 = gP.dot(rP)
vectors.append(Y1-Y2)
newV = []
for i in range(len(vectors[0])):
local_max = float("-inf")
for j in range(len(vectors)):
if vectors[j][i] > local_max:
local_max = vectors[j][i]
newV.append(local_max)
self.V = _np.asarray(newV)
def testInts(self):
A1 = [
np.array([[1.0, 0.0], [0.0, 0.0]]),
np.array([[1., 1.], [0., 0.]])
]
x1 = np.array([1., 2., 3., 4.])
big_A = reduce(np.kron, A1)
print(big_A)
print(x1)
big_y = np.matmul(big_A, x1)
print("full calc: ", big_y)
kp = KronProd(A1)
Y = kp.dot(x1)
print("efficient calc: ", Y)
self.assertSequenceEqual(list(Y), list(big_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 testRandom(self):
n = 5 # number of factors
p = 5 # dimension of factor
r_As = [np.random.rand(p, p) for i in range(n)]
As = [m / m.sum(axis=1)[:, None] for m in r_As] # normalize each row
x = np.random.rand(p**n)
big_A = reduce(np.kron, As)
big_y = np.matmul(big_A, x)
print("full calc: ", big_y)
kp = KronProd(As)
Y = kp.dot(x)
print("efficient calc: ", Y)
np.testing.assert_almost_equal(big_y, Y, 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 dotTest(A, x):
foo = time.time()
big_A = reduce(np.kron, A)
big_y1 = np.matmul(big_A, x)
time_full = time.time() - foo
foo = time.time()
kp1 = KronProd(A)
Y1 = kp1.dot(x)
time_kron_dyn = time.time() - foo
if (verifyCorrectness(big_y1, big_y1, Y1)):
print("Dot Test Passed")
else:
print("Dot Test Failed!")
return time_full, time_kron_dyn
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)