def test_qr(self):
m = 8
n = 4
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n), ctf.dot(Q.T(), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex64)
rA = ctf.tensor((m,n),dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex64), ctf.dot(ctf.conj(Q.T()), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex128)
rA = ctf.tensor((m,n),dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex128), ctf.dot(ctf.conj(Q.T()), Q)))
def test_qr(self):
m = 8
n = 4
for dt in [numpy.float32, numpy.float64, numpy.complex64, numpy.complex128]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n), ctf.dot(Q.T(), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex64)
rA = ctf.tensor((m,n),dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex64), ctf.dot(ctf.conj(Q.T()), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex128)
rA = ctf.tensor((m,n),dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex128), ctf.dot(ctf.conj(Q.T()), Q)))
def test_conj(self):
a0 = ctf.zeros((2,3))
self.assertTrue(ctf.conj(a0).dtype == numpy.double)
self.assertTrue(a0.conj().dtype == numpy.double)
a0 = ctf.zeros((2,3), dtype=numpy.complex)
self.assertTrue(ctf.conj(a0).dtype == numpy.complex128)
self.assertTrue(a0.conj().dtype == numpy.complex128)
a0[:] = 1j
a0 = a0.conj()
self.assertTrue(ctf.all(a0 == -1j))
def test_conj(self):
a0 = ctf.zeros((2,3))
self.assertTrue(ctf.conj(a0).dtype == numpy.double)
self.assertTrue(a0.conj().dtype == numpy.double)
a0 = ctf.zeros((2,3), dtype=numpy.complex)
self.assertTrue(ctf.conj(a0).dtype == numpy.complex128)
self.assertTrue(a0.conj().dtype == numpy.complex128)
a0[:] = 1j
a0 = a0.conj()
self.assertTrue(ctf.all(a0 == -1j))
def test_qr(self):
for (m, n) in [(8, 4), (4, 7), (3, 3)]:
for dt in [np.float32, np.float64, np.complex64, np.complex128]:
A = ctf.random.random((m, n))
A = ctf.astensor(A, dtype=dt)
[Q, R] = ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q, R)))
if (m >= n):
self.assertTrue(allclose(ctf.eye(n), ctf.dot(Q.T(), Q)))
else:
self.assertTrue(allclose(ctf.eye(m), ctf.dot(Q, Q.T())))
A = ctf.tensor((m, n), dtype=np.complex64)
rA = ctf.tensor((m, n), dtype=np.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=np.float32)
iA.fill_random()
A.imag(iA)
[Q, R] = ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q, R)))
if (m >= n):
self.assertTrue(
allclose(ctf.eye(n, dtype=np.complex64),
ctf.dot(ctf.conj(Q.T()), Q)))
else:
self.assertTrue(
allclose(ctf.eye(m, dtype=np.complex64),
ctf.dot(Q, ctf.conj(Q.T()))))
A = ctf.tensor((m, n), dtype=np.complex128)
rA = ctf.tensor((m, n), dtype=np.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=np.float64)
iA.fill_random()
A.imag(iA)
[Q, R] = ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q, R)))
if (m >= n):
self.assertTrue(
allclose(ctf.eye(n, dtype=np.complex128),
ctf.dot(ctf.conj(Q.T()), Q)))
else:
self.assertTrue(
allclose(ctf.eye(m, dtype=np.complex128),
ctf.dot(Q, ctf.conj(Q.T()))))
def test_svd(self):
m = 9
n = 5
k = 5
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((m, n))
A = ctf.astensor(A, dtype=dt)
[U, S, VT] = ctf.svd(A, k)
[U1, S1, VT1] = la.svd(ctf.to_nparray(A), full_matrices=False)
self.assertTrue(allclose(A, ctf.dot(U, ctf.dot(ctf.diag(S), VT))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U.T(), U)))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT, VT.T())))
A = ctf.tensor((m, n), dtype=numpy.complex64)
rA = ctf.tensor((m, n), dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[U, S, VT] = ctf.svd(A, k)
self.assertTrue(allclose(A, ctf.dot(U, ctf.dot(ctf.diag(S), VT))))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex64),
ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex64),
ctf.dot(VT, ctf.conj(VT.T()))))
A = ctf.tensor((m, n), dtype=numpy.complex128)
rA = ctf.tensor((m, n), dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[U, S, VT] = ctf.svd(A, k)
self.assertTrue(allclose(A, ctf.dot(U, ctf.dot(ctf.diag(S), VT))))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex128),
ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex128),
ctf.dot(VT, ctf.conj(VT.T()))))
def test_svd(self):
m = 9
n = 5
k = 5
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[U,S,VT]=ctf.svd(A,k)
[U1,S1,VT1]=la.svd(ctf.to_nparray(A),full_matrices=False)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U.T(), U)))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT, VT.T())))
A = ctf.tensor((m,n),dtype=numpy.complex64)
rA = ctf.tensor((m,n),dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[U,S,VT]=ctf.svd(A,k)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex64), ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex64), ctf.dot(VT, ctf.conj(VT.T()))))
A = ctf.tensor((m,n),dtype=numpy.complex128)
rA = ctf.tensor((m,n),dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[U,S,VT]=ctf.svd(A,k)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex128), ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex128), ctf.dot(VT, ctf.conj(VT.T()))))
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 ----------------------------
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
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))
tmp = np.array([[[1.]]])
F.append(ctf.from_nparray(tmp))
print(F[0])
for i in range(int(N/2)):
tmp = np.zeros((min(2**(i+1),maxBondDim),4,min(2**(i+1),maxBondDim)))
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)))
F.append(ctf.from_nparray(tmp))
tmp = np.array([[[1.]]])
F.append(ctf.from_nparray(tmp))
# Calculate initial environment
for i in range(int(N)-1,0,-1):
tmp = np.einsum('eaf,cdf->eacd',M[i],F[i+1])
tmp = np.einsum('ydbe,eacd->ybac',W[i],tmp)
F[i] = np.einsum('bxc,ybac->xya',ctf.conj(M[i]),tmp)
##############################################
# Optimization Sweeps ########################
"""
# 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):