def svd(a, full_matrices=False):
a = ctf.to_nparray(a)
u, s, v = np.linalg.svd(a, full_matrices=full_matrices)
u = ctf.from_nparray(u)
s = ctf.from_nparray(s)
v = ctf.from_nparray(v)
return u, s, v
def load_tensor_from_file(filename):
try:
T = np.load(filename)
print('Loaded tensor from file ', filename)
except FileNotFoundError:
raise FileNotFoundError('No tensor exist on: ', filename)
return ctf.from_nparray(T)
def sqrt(a):
if hasattr(a, 'shape'):
if (prod(a.shape) == 1) or (len(a.shape) == 0):
return npsqrt(ctf.to_nparray(a))
else:
return ctf.from_nparray(npsqrt(ctf.to_nparray(a)))
else:
return npsqrt(a)
def test_abs(self):
a0 = numpy.arange(2., 5.)
a1 = ctf.from_nparray(a0)
self.assertTrue(ctf.all(ctf.abs(a1) == ctf.abs(a0)))
self.assertTrue(ctf.all(ctf.abs(a1) == numpy.abs(a0)))
try:
a1 = a1 + 1j
self.assertAlmostEqual(ctf.abs(a1).sum(), numpy.abs(a1.to_nparray()).sum(), 14)
except AttributeError:
pass
def test_abs(self):
a0 = numpy.arange(2., 5.)
a1 = ctf.from_nparray(a0)
self.assertTrue(ctf.all(ctf.abs(a1) == ctf.abs(a0)))
self.assertTrue(ctf.all(ctf.abs(a1) == numpy.abs(a0)))
try:
a1 = a1 + 1j
self.assertAlmostEqual(ctf.abs(a1).sum(), numpy.abs(a1.to_nparray()).sum(), 14)
except AttributeError:
pass
def test_astensor(self):
# astensor converts python object to ctf tensor
a0 = ctf.astensor((1,2,3))
a0 = ctf.astensor([1,2.,3])
a0 = ctf.astensor([(1,2), (3,4)])
a0 = ctf.astensor(numpy.arange(3))
a0 = ctf.astensor([numpy.array((1,2)), numpy.array((3,4))+1j])
a1 = ctf.astensor(a0)
a1[:] = 0
self.assertTrue(ctf.all(a0==0))
self.assertTrue(ctf.all(a1==0))
a0 = numpy.asarray(a1)
# self.assertTrue(ctf.asarray(a0).__class__ == ctf.astensor(a0).__class__)
a0 = ctf.astensor([1,2.,3], dtype='D')
self.assertTrue(a0.dtype == numpy.complex128)
with self.assertRaises(TypeError):
ctf.astensor([1j,2j], dtype='d')
a0 = numpy.arange(4.).reshape(2,2)
a1 = ctf.to_nparray(ctf.from_nparray(a0))
self.assertTrue(ctf.all(a0==a1))
try:
a1 = ctf.from_nparray(a1).to_nparray()
self.assertTrue(ctf.all(a0==a1))
except AttributeError:
pass
a0 = ctf.from_nparray(numpy.arange(3))
a1 = ctf.from_nparray(a0)
a1[:] = 0
self.assertTrue(ctf.all(a0==0))
self.assertTrue(ctf.all(a1==0))
a0 = numpy.arange(6).reshape(2,3)
a1 = ctf.array(a0)
self.assertTrue(ctf.all(a0==a1))
self.assertTrue(ctf.all(a1==a0))
a1 = ctf.array(a0, copy=False)
self.assertTrue(ctf.all(a1==0))
def test_astensor(self):
# astensor converts python object to ctf tensor
a0 = ctf.astensor((1,2,3))
a0 = ctf.astensor([1,2.,3])
a0 = ctf.astensor([(1,2), (3,4)])
a0 = ctf.astensor(numpy.arange(3))
a0 = ctf.astensor([numpy.array((1,2)), numpy.array((3,4))+1j])
a1 = ctf.astensor(a0)
a1[:] = 0
self.assertTrue(ctf.all(a0==0))
self.assertTrue(ctf.all(a1==0))
a0 = numpy.asarray(a1)
# self.assertTrue(ctf.asarray(a0).__class__ == ctf.astensor(a0).__class__)
a0 = ctf.astensor([1,2.,3], dtype='D')
self.assertTrue(a0.dtype == numpy.complex128)
with self.assertRaises(TypeError):
ctf.astensor([1j,2j], dtype='d')
a0 = numpy.arange(4.).reshape(2,2)
a1 = ctf.to_nparray(ctf.from_nparray(a0))
self.assertTrue(ctf.all(a0==a1))
try:
a1 = ctf.from_nparray(a1).to_nparray()
self.assertTrue(ctf.all(a0==a1))
except AttributeError:
pass
a0 = ctf.from_nparray(numpy.arange(3))
a1 = ctf.from_nparray(a0)
a1[:] = 0
self.assertTrue(ctf.all(a0==0))
self.assertTrue(ctf.all(a1==0))
a0 = numpy.arange(6).reshape(2,3)
a1 = ctf.array(a0)
self.assertTrue(ctf.all(a0==a1))
self.assertTrue(ctf.all(a1==a0))
a1 = ctf.array(a0, copy=False)
self.assertTrue(ctf.all(a1==0))
def test_sum_axis(self):
a0 = numpy.ones((2, 3, 4))
a1 = ctf.from_nparray(a0)
self.assertEqual(a1.sum(axis=0).shape, (3, 4))
self.assertEqual(a1.sum(axis=1).shape, (2, 4))
self.assertEqual(a1.sum(axis=-1).shape, (2, 3))
self.assertEqual(ctf.sum(a1, axis=2).shape, (2, 3))
self.assertEqual(ctf.sum(a1.transpose(2, 1, 0), axis=2).shape, (4, 3))
self.assertEqual(ctf.sum(a1, axis=(1, 2)).shape, (2, ))
self.assertEqual(ctf.sum(a1, axis=(0, 2)).shape, (3, ))
self.assertEqual(ctf.sum(a1, axis=(2, 0)).shape, (3, ))
self.assertEqual(ctf.sum(a1, axis=(0, -1)).shape, (3, ))
self.assertEqual(ctf.sum(a1, axis=(-1, -2)).shape, (2, ))
def test_sum_axis(self):
a0 = numpy.ones((2,3,4))
a1 = ctf.from_nparray(a0)
self.assertEqual(a1.sum(axis=0).shape, (3,4))
self.assertEqual(a1.sum(axis=1).shape, (2,4))
self.assertEqual(a1.sum(axis=-1).shape, (2,3))
self.assertEqual(ctf.sum(a1, axis=2).shape, (2,3))
self.assertEqual(ctf.sum(a1.transpose(2,1,0), axis=2).shape, (4,3))
self.assertEqual(ctf.sum(a1, axis=(1,2)).shape, (2,))
self.assertEqual(ctf.sum(a1, axis=(0,2)).shape, (3,))
self.assertEqual(ctf.sum(a1, axis=(2,0)).shape, (3,))
self.assertEqual(ctf.sum(a1, axis=(0,-1)).shape, (3,))
self.assertEqual(ctf.sum(a1, axis=(-1,-2)).shape, (2,))
def sqrt(a):
return ctf.from_nparray(np.sqrt(ctf.to_nparray(a)))
def test_sum(self):
a0 = numpy.arange(4.)
a1 = ctf.from_nparray(a0)
self.assertAlmostEqual(ctf.sum(a1), a1.sum(), 9)
def qr(a):
a = ctf.to_nparray(a)
q, r = np.linalg.qr(a)
q = ctf.from_nparray(q)
r = ctf.from_nparray(r)
return q, r
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 min(a):
return ctf.from_nparray(np.min(ctf.to_nparray(a)))
def append(a, b):
return ctf.from_nparray(np.append(ctf.to_nparray(a), ctf.to_nparray(b)))
def inv(a):
return ctf.from_nparray(np.linalg.pinv(ctf.to_nparray(a)))
def max(a):
return ctf.from_nparray(np.max(ctf.to_nparray(a)))
def array(tens, dtype=None, copy=True, subok=False, ndimin=0):
ten = nparray(tens)
return ctf.from_nparray(ten)
def expm(a):
return ctf.from_nparray(sla.expm(ctf.to_nparray(a)))
def test_sum(self):
a0 = numpy.arange(4.)
a1 = ctf.from_nparray(a0)
self.assertAlmostEqual(ctf.sum(a1), a1.sum(), 9)
def eigh(a):
a = ctf.to_nparray(a)
u, v = np.linalg.eigh(a)
u = ctf.from_nparray(u)
v = ctf.from_nparray(v)
return u, v
def from_nparray(arr):
return ctf.from_nparray(arr)
def fill_diagonal(matrix, value):
return ctf.from_nparray(np.fill_diagonal(matrix, value))
tol = 1e-5
maxIter = 10
maxBondDim = 10
useCTF = True
##############################################
# Create MPS #################################
# PH - Make Isometries, Center Site
print('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 #################################
print('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.]])
def log2(a):
return ctf.from_nparray(np.log2(ctf.to_nparray(a)))
q = 0. # Jump Left
# Optimization
tol = 1e-5
maxIter = 10
maxBondDim = 20
##############################################
# Create MPS #################################
# PH - Make Isometries, Center Site
print('Generating MPS')
M = []
for i in range(int(N/2)):
tmp = np.random.rand(2,
min(2**(i),maxBondDim),
min(2**(i+1),maxBondDim))
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))
M.append(ctf.from_nparray(tmp))
##############################################
# Create MPO #################################
print('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.]])
