def Hfun(x):
x_reshape = ctf.array(x)
x_reshape = ctf.reshape(x_reshape, (n1, n2, n3))
tmp = ctf.einsum('ijk,lmk->ijlm', F[i + 1], x_reshape)
tmp = ctf.einsum('njol,ijlm->noim', W[i], tmp)
res = ctf.einsum('pnm,noim->opi', F[i], tmp)
return -ctf.reshape(res, -1).to_nparray()
def test_sp_reshape(self):
a1 = ctf.tensor((2, 3), sp=True)
a1.fill_sp_random(0., 1., .5)
a0 = a1.to_nparray()
self.assertTrue(ctf.all(ctf.reshape(a1, (2, 3)) == a0.reshape(2, 3)))
a1 = ctf.tensor((2, 3, 4, 5), sp=True)
a1.fill_sp_random(0., 1., .5)
a0 = a1.to_nparray()
self.assertTrue(
ctf.all(ctf.reshape(a1, (2, 3, 4, 5)) == a0.reshape(2, 3, 4, 5)))
self.assertTrue(ctf.all(ctf.reshape(a1, (6, 20)) == a0.reshape(6, 20)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (6, 5, 4)) == a0.reshape(6, 5, 4)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (3, 10, 4)) == a0.reshape(3, 10, 4)))
self.assertTrue(ctf.all(ctf.reshape(a1, (6, -1)) == a0.reshape(6, -1)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (-1, 20)) == a0.reshape(-1, 20)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (6, -1, 4)) == a0.reshape(6, -1, 4)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (3, -1, 2)) == a0.reshape(3, -1, 2)))
self.assertTrue(ctf.all(a1.reshape(6, 20) == a0.reshape(6, 20)))
self.assertTrue(ctf.all(a1.reshape(6, 5, 4) == a0.reshape(6, 5, 4)))
self.assertTrue(
ctf.all(a1.reshape((3, 10, 4)) == a0.reshape(3, 10, 4)))
self.assertTrue(ctf.all(a1.reshape((6, -1)) == a0.reshape(6, -1)))
self.assertTrue(ctf.all(a1.reshape(-1, 20) == a0.reshape(-1, 20)))
self.assertTrue(ctf.all(a1.reshape(6, -1, 4) == a0.reshape(6, -1, 4)))
self.assertTrue(
ctf.all(a1.reshape((3, -1, 2)) == a0.reshape(3, -1, 2)))
with self.assertRaises(ValueError):
a1.reshape((1, 2))
def test_reshape(self):
a0 = numpy.arange(120).reshape(2, 3, 4, 5)
a1 = ctf.astensor(a0)
self.assertTrue(
ctf.all(ctf.reshape(a1, (2, 3, 4, 5)) == a0.reshape(2, 3, 4, 5)))
self.assertTrue(ctf.all(ctf.reshape(a1, (6, 20)) == a0.reshape(6, 20)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (6, 5, 4)) == a0.reshape(6, 5, 4)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (3, 10, 4)) == a0.reshape(3, 10, 4)))
self.assertTrue(ctf.all(ctf.reshape(a1, (6, -1)) == a0.reshape(6, -1)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (-1, 20)) == a0.reshape(-1, 20)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (6, -1, 4)) == a0.reshape(6, -1, 4)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (3, -1, 2)) == a0.reshape(3, -1, 2)))
self.assertTrue(ctf.all(a1.reshape(6, 20) == a0.reshape(6, 20)))
self.assertTrue(ctf.all(a1.reshape(6, 5, 4) == a0.reshape(6, 5, 4)))
self.assertTrue(
ctf.all(a1.reshape((3, 10, 4)) == a0.reshape(3, 10, 4)))
self.assertTrue(ctf.all(a1.reshape((6, -1)) == a0.reshape(6, -1)))
self.assertTrue(ctf.all(a1.reshape(-1, 20) == a0.reshape(-1, 20)))
self.assertTrue(ctf.all(a1.reshape(6, -1, 4) == a0.reshape(6, -1, 4)))
self.assertTrue(
ctf.all(a1.reshape((3, -1, 2)) == a0.reshape(3, -1, 2)))
with self.assertRaises(ValueError):
a1.reshape((1, 2))
def test_transpose_reshape(self):
a0 = numpy.arange(120).reshape(2, 3, 4, 5)
a1 = ctf.astensor(a0)
a0 = a0.transpose(3, 0, 2, 1)
a1 = a1.transpose(3, 0, 2, 1)
self.assertTrue(ctf.all(ctf.reshape(a1, (6, 20)) == a0.reshape(6, 20)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (6, 5, 4)) == a0.reshape(6, 5, 4)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (3, 10, 4)) == a0.reshape(3, 10, 4)))
self.assertTrue(ctf.all(ctf.reshape(a1, (6, -1)) == a0.reshape(6, -1)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (-1, 20)) == a0.reshape(-1, 20)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (6, -1, 4)) == a0.reshape(6, -1, 4)))
self.assertTrue(
ctf.all(ctf.reshape(a1, (3, -1, 2)) == a0.reshape(3, -1, 2)))
self.assertTrue(ctf.all(a1.reshape(6, 20) == a0.reshape(6, 20)))
self.assertTrue(ctf.all(a1.reshape(6, 5, 4) == a0.reshape(6, 5, 4)))
self.assertTrue(
ctf.all(a1.reshape((3, 10, 4)) == a0.reshape(3, 10, 4)))
self.assertTrue(ctf.all(a1.reshape((6, -1)) == a0.reshape(6, -1)))
self.assertTrue(ctf.all(a1.reshape(-1, 20) == a0.reshape(-1, 20)))
self.assertTrue(ctf.all(a1.reshape(6, -1, 4) == a0.reshape(6, -1, 4)))
self.assertTrue(
ctf.all(a1.reshape((3, -1, 2)) == a0.reshape(3, -1, 2)))
def test_transpose_reshape(self):
a0 = numpy.arange(120).reshape(2,3,4,5)
a1 = ctf.astensor(a0)
a0 = a0.transpose(3,0,2,1)
a1 = a1.transpose(3,0,2,1)
self.assertTrue(ctf.all(ctf.reshape(a1,(6,20)) ==a0.reshape(6,20)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,5,4)) ==a0.reshape(6,5,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,10,4))==a0.reshape(3,10,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,-1)) ==a0.reshape(6,-1)))
self.assertTrue(ctf.all(ctf.reshape(a1,(-1,20)) ==a0.reshape(-1,20)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,-1,4))==a0.reshape(6,-1,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,-1,2))==a0.reshape(3,-1,2)))
self.assertTrue(ctf.all(a1.reshape(6,20) ==a0.reshape(6,20)))
self.assertTrue(ctf.all(a1.reshape(6,5,4) ==a0.reshape(6,5,4)))
self.assertTrue(ctf.all(a1.reshape((3,10,4))==a0.reshape(3,10,4)))
self.assertTrue(ctf.all(a1.reshape((6,-1)) ==a0.reshape(6,-1)))
self.assertTrue(ctf.all(a1.reshape(-1,20) ==a0.reshape(-1,20)))
self.assertTrue(ctf.all(a1.reshape(6,-1,4) ==a0.reshape(6,-1,4)))
self.assertTrue(ctf.all(a1.reshape((3,-1,2))==a0.reshape(3,-1,2)))
def test_reshape(self):
a0 = numpy.arange(120).reshape(2,3,4,5)
a1 = ctf.astensor(a0)
self.assertTrue(ctf.all(ctf.reshape(a1,(6,20)) ==a0.reshape(6,20)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,5,4)) ==a0.reshape(6,5,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,10,4))==a0.reshape(3,10,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,-1)) ==a0.reshape(6,-1)))
self.assertTrue(ctf.all(ctf.reshape(a1,(-1,20)) ==a0.reshape(-1,20)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,-1,4))==a0.reshape(6,-1,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,-1,2))==a0.reshape(3,-1,2)))
self.assertTrue(ctf.all(a1.reshape(6,20) ==a0.reshape(6,20)))
self.assertTrue(ctf.all(a1.reshape(6,5,4) ==a0.reshape(6,5,4)))
self.assertTrue(ctf.all(a1.reshape((3,10,4))==a0.reshape(3,10,4)))
self.assertTrue(ctf.all(a1.reshape((6,-1)) ==a0.reshape(6,-1)))
self.assertTrue(ctf.all(a1.reshape(-1,20) ==a0.reshape(-1,20)))
self.assertTrue(ctf.all(a1.reshape(6,-1,4) ==a0.reshape(6,-1,4)))
self.assertTrue(ctf.all(a1.reshape((3,-1,2))==a0.reshape(3,-1,2)))
with self.assertRaises(ValueError):
a1.reshape((1,2))
tmp = ctf.einsum('eaf,cdf->eacd', M[i], F[i + 1])
tmp = ctf.einsum('ydbe,eacd->ybac', W[i], tmp)
F[i] = ctf.einsum('bxc,ybac->xya', ctf.conj(M[i]), tmp)
##############################################
# Optimization Sweeps ########################
converged = False
iterCnt = 0
E_prev = 0
while not converged:
# Right Sweep ----------------------------
print('Right Sweep {}'.format(iterCnt))
for i in range(N - 1):
H = ctf.einsum('jlp,lmin,kmq->ijknpq', F[i], W[i], F[i + 1])
(n1, n2, n3, n4, n5, n6) = H.shape
H = ctf.reshape(H, (n1 * n2 * n3, n4 * n5 * n6))
u, v = np.linalg.eig(ctf.to_nparray(H))
# Select max eigenvalue
max_ind = np.argsort(u)[-1]
E = u[max_ind]
v = ctf.from_nparray(v[:, max_ind])
print('\tEnergy at site {} = {}'.format(i, E))
M[i] = ctf.reshape(v, (n1, n2, n3))
# Right Normalize
M_reshape = ctf.reshape(M[i], (n1 * n2, n3))
(U, S, V) = ctf.svd(M_reshape)
M[i] = ctf.reshape(U, (n1, n2, n3))
M[i + 1] = ctf.einsum('i,ij,kjl->kil', S, V, M[i + 1])
# Update F
F[i + 1] = ctf.einsum('jlp,ijk,lmin,npq->kmq', F[i], ctf.conj(M[i]),
W[i], M[i])
def reshape(A, shape, order='F'):
return ctf.reshape(A, shape, order)
def main():
t0 = time.time()
######## Inputs ##############################
# SEP Model
N = 50
alpha = 0.35 # In at left
beta = 2. / 3. # Exit at right
s = -1. # Exponential weighting
gamma = 0. # Exit at left
delta = 0. # In at right
p = 1. # Jump right
q = 0. # Jump Left
# Optimization
tol = 1e-5
maxIter = 0
maxBondDim = 10
useCTF = True
##############################################
# Create MPS #################################
# PH - Make Isometries, Center Site
mpiprint('Generating MPS')
M = []
for i in range(int(N / 2)):
tmp = np.random.rand(2,
min(2**(i),maxBondDim),
min(2**(i+1),maxBondDim))\
+0.j
M.append(ctf.from_nparray(tmp))
for i in range(int(N / 2))[::-1]:
tmp = np.random.rand(2,
min(2**(i+1),maxBondDim),
min(2**i,maxBondDim))\
+0.j
M.append(ctf.from_nparray(tmp))
##############################################
# Create MPO #################################
mpiprint('Generating MPO')
# Simple Operators
Sp = np.array([[0., 1.], [0., 0.]])
Sm = np.array([[0., 0.], [1., 0.]])
n = np.array([[0., 0.], [0., 1.]])
v = np.array([[1., 0.], [0., 0.]])
I = np.array([[1., 0.], [0., 1.]])
z = np.array([[0., 0.], [0., 0.]])
# List to hold MPOs
W = []
# First Site
site_0 = ctf.astensor(
[[alpha * (np.exp(-s) * Sm - v),
np.exp(-s) * Sp, -n, I]])
W.append(site_0)
# Central Sites
for i in range(N - 2):
site_i = ctf.astensor([[I, z, z, z], [Sm, z, z, z], [v, z, z, z],
[z, np.exp(-s) * Sp, -n, I]])
W.append(site_i)
# Last Site
site_N = ctf.astensor([[I], [Sm], [v], [beta * (np.exp(-s) * Sp - n)]])
W.append(site_N)
##############################################
# Canonicalize MPS ###########################
for i in range(int(N) - 1, 0, -1):
M_reshape = ctf.transpose(M[i], axes=[1, 0, 2])
(n1, n2, n3) = M_reshape.shape
M_reshape = M_reshape.reshape(n1, n2 * n3)
(U, S, V) = ctf.svd(M_reshape)
M_reshape = V.reshape(n1, n2, n3)
M[i] = ctf.transpose(M_reshape, axes=[1, 0, 2])
M[i - 1] = ctf.einsum('klj,ji,i->kli', M[i - 1], U, S)
##############################################
# Canonicalize MPS ###########################
def pick_eigs(w, v, nroots, x0):
idx = np.argsort(np.real(w))
w = w[idx]
v = v[:, idx]
return w, v, idx
##############################################
# Create Environment #########################
mpiprint('Generating Environment')
# Allocate empty environment
F = []
tmp = np.array([[[1.]]]) + 0.j
F.append(ctf.from_nparray(tmp))
for i in range(int(N / 2)):
tmp = np.zeros((min(2**(i + 1),
maxBondDim), 4, min(2**(i + 1), maxBondDim))) + 0.j
F.append(ctf.from_nparray(tmp))
for i in range(int(N / 2) - 1, 0, -1):
tmp = np.zeros(
(min(2**(i), maxBondDim), 4, min(2**i, maxBondDim))) + 0.j
F.append(ctf.from_nparray(tmp))
tmp = np.array([[[1.]]]) + 0.j
F.append(ctf.from_nparray(tmp))
# Calculate initial environment
for i in range(int(N) - 1, 0, -1):
tmp = ctf.einsum('eaf,cdf->eacd', M[i], F[i + 1])
tmp = ctf.einsum('ydbe,eacd->ybac', W[i], tmp)
F[i] = ctf.einsum('bxc,ybac->xya', ctf.conj(M[i]), tmp)
##############################################
# Optimization Sweeps ########################
converged = False
iterCnt = 0
E_prev = 0
while not converged:
# Right Sweep ----------------------------
tr = time.time()
mpiprint('Start Right Sweep {}'.format(iterCnt))
for i in range(N - 1):
(n1, n2, n3) = M[i].shape
# Make Hx Function
def Hfun(x):
x_reshape = ctf.array(x)
x_reshape = ctf.reshape(x_reshape, (n1, n2, n3))
tmp = ctf.einsum('ijk,lmk->ijlm', F[i + 1], x_reshape)
tmp = ctf.einsum('njol,ijlm->noim', W[i], tmp)
res = ctf.einsum('pnm,noim->opi', F[i], tmp)
return -ctf.reshape(res, -1).to_nparray()
def precond(dx, e, x0):
return dx
# Set up initial guess
guess = ctf.reshape(M[i], -1).to_nparray()
# Run eigenproblem
u, v = eig(Hfun, guess, precond, pick=pick_eigs)
E = -u
v = ctf.array(v)
M[i] = ctf.reshape(v, (n1, n2, n3))
# Print Results
mpiprint('\tEnergy at site {} = {}'.format(i, E))
# Right Normalize
M_reshape = ctf.reshape(M[i], (n1 * n2, n3))
(U, S, V) = ctf.svd(M_reshape)
M[i] = ctf.reshape(U, (n1, n2, n3))
M[i + 1] = ctf.einsum('i,ij,kjl->kil', S, V, M[i + 1])
# Update F
tmp = ctf.einsum('jlp,ijk->lpik', F[i], ctf.conj(M[i]))
tmp = ctf.einsum('lmin,lpik->mpnk', W[i], tmp)
F[i + 1] = ctf.einsum('npq,mpnk->kmq', M[i], tmp)
mpiprint('Complete Right Sweep {}, {} sec'.format(
iterCnt,
time.time() - tr))
# Left Sweep ------------------------------
tl = time.time()
mpiprint('Start Left Sweep {}'.format(iterCnt))
for i in range(N - 1, 0, -1):
(n1, n2, n3) = M[i].shape
# Make Hx Function
def Hfun(x):
x_reshape = ctf.array(x)
x_reshape = ctf.reshape(x_reshape, (n1, n2, n3))
tmp = ctf.einsum('ijk,lmk->ijlm', F[i + 1], x_reshape)
tmp = ctf.einsum('njol,ijlm->noim', W[i], tmp)
res = ctf.einsum('pnm,noim->opi', F[i], tmp)
return -ctf.reshape(res, -1).to_nparray()
def precond(dx, e, x0):
return dx
# Set up initial guess
guess = ctf.reshape(M[i], -1).to_nparray()
# Run eigenproblem
u, v = eig(Hfun, guess, precond, pick=pick_eigs)
E = -u
v = ctf.array(v)
M[i] = ctf.reshape(v, (n1, n2, n3))
# Print Results
mpiprint('\tEnergy at site {}= {}'.format(i, E))
# Right Normalize
M_reshape = ctf.transpose(M[i], (1, 0, 2))
M_reshape = ctf.reshape(M_reshape, (n2, n1 * n3))
(U, S, V) = ctf.svd(M_reshape)
M_reshape = ctf.reshape(V, (n2, n1, n3))
M[i] = ctf.transpose(M_reshape, (1, 0, 2))
M[i - 1] = ctf.einsum('klj,ji,i->kli', M[i - 1], U, S)
# Update F
tmp = ctf.einsum('eaf,cdf->eacd', M[i], F[i + 1])
tmp = ctf.einsum('ydbe,eacd->ybac', W[i], tmp)
F[i] = ctf.einsum('bxc,ybac->xya', ctf.conj(M[i]), tmp)
mpiprint('Left Sweep {}, {} sec'.format(iterCnt, time.time() - tl))
# Convergence Test -----------------------
if np.abs(E - E_prev) < tol:
mpiprint('#' * 75 + '\nConverged at E = {}'.format(E) + '\n' +
'#' * 75)
converged = True
elif iterCnt > maxIter:
mpiprint('Convergence not acheived')
converged = True
else:
iterCnt += 1
E_prev = E
mpiprint('Total Time = {}'.format(time.time() - t0))
def test_reshape(self):
a = ctf.random.random((1,10,10,10))
self.assertTrue(ctf.all(a.reshape((10,100)) == a.to_nparray().reshape((10,100))))
base_shapes = [(2,3,4,5),(3,10,4),(1,3,10,4),(2,3,4,1,5)]
for shape in base_shapes:
a0 = numpy.arange(120).reshape(shape)
a1 = ctf.astensor(a0)
self.assertTrue(ctf.all(ctf.reshape(a1,(2,3,4,5)) ==a0.reshape(2,3,4,5)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,20)) ==a0.reshape(6,20)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,5,4)) ==a0.reshape(6,5,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,10,4))==a0.reshape(3,10,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(1,3,10,4))==a0.reshape(1,3,10,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(1,3,1,10,4))==a0.reshape(1,3,1,10,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(1,3,1,1,10,4))==a0.reshape(1,3,1,1,10,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,10,4,1))==a0.reshape(3,10,4,1)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,-1)) ==a0.reshape(6,-1)))
self.assertTrue(ctf.all(ctf.reshape(a1,(-1,20)) ==a0.reshape(-1,20)))
self.assertTrue(ctf.all(ctf.reshape(a1,(6,-1,4))==a0.reshape(6,-1,4)))
self.assertTrue(ctf.all(ctf.reshape(a1,(3,-1,2))==a0.reshape(3,-1,2)))
self.assertTrue(ctf.all(a1.reshape(6,20) ==a0.reshape(6,20)))
self.assertTrue(ctf.all(a1.reshape(6,5,4) ==a0.reshape(6,5,4)))
self.assertTrue(ctf.all(a1.reshape((3,10,4))==a0.reshape(3,10,4)))
self.assertTrue(ctf.all(a1.reshape((6,-1)) ==a0.reshape(6,-1)))
self.assertTrue(ctf.all(a1.reshape(-1,20) ==a0.reshape(-1,20)))
self.assertTrue(ctf.all(a1.reshape(6,-1,4) ==a0.reshape(6,-1,4)))
self.assertTrue(ctf.all(a1.reshape((3,-1,2))==a0.reshape(3,-1,2)))
with self.assertRaises(ValueError):
a1.reshape((1,2))
