def gen_zero_energy_guess(H, rank):
"""
Generate psi such that <psi|H|psi> = 0
Parameters:
-----------
H: tt.matrix
hamiltonian in the TT-matrix format
rank: int
Rank of the guess
"""
v = 1.0
while v > 1e-12:
# Create two random TT vectors and normalize them
psi1 = tt.rand(H.n, r=rank)
psi2 = tt.rand(H.n, r=1)
psi1 = psi1 * (1.0 / psi1.norm())
psi2 = psi2 * (1.0 / psi2.norm())
# Calculate coefficients of the quadratic equation
h22 = tt.dot(tt.matvec(H, psi2), psi2)
h21 = tt.dot(tt.matvec(H, psi2), psi1)
h11 = tt.dot(tt.matvec(H, psi1), psi1)
# find vectors such that <psi|H|psi> = 0
rs = np.roots([h22, 2 * h21, h11])
v = np.linalg.norm(np.imag(rs))
psi = psi1 + rs[0] * psi2
psi = psi * (1.0 / psi.norm())
return psi
def add_to_final_mass_matrix(f, Ml, eps, d):
rhs = tt.ones(4, d)
# Впечатываем куда надо диагональные элементы
if f is None:
f = tt.matvec(Ml, rhs)
else:
f += tt.matvec(Ml, rhs)
return f.round(eps)
def full_matrix(A, Qs, t0, pt, dt):
support = -tt.delta(2, pt, center = 1) + tt.delta(2, pt, center = 0)
G_t = tt.Toeplitz(support,kind='L').T
G_t = G_t.round(1e-14)
support = tt.delta(2, pt, center = 1) + tt.delta(2, pt, center = 0)
M_t = tt.Toeplitz(support,kind='L').T
M_t = M_t.round(1e-14)
px = A.n.shape[0]
Id = tt.eye(2, px)
A_full = tt.kron(Id, G_t) - 0.5 * dt * tt.kron(A, M_t)
A_full = A_full.round(1e-14) # collected full matrix A
e1 = tt.delta(2, pt, center = 0)
left = t0 + 0.5* dt * tt.matvec(A, t0)
left = left.round(1e-14)
left = tt.kron(left, e1)
left = left.round(1e-14)
right = dt * Qs
Qs_full = left + right
Qs_full = Qs_full.round(1e-14)
return A_full, Qs_full
def windowed_mean_dimension(wst, mode='cross', eps=1e-6, verbose=False, **kwargs):
"""
Given a windowed Sobol TT, return a TT with the mean dimension of every window
:param wst:
:return:
"""
assert mode in ('matvec', 'cross')
N = wst.tt.d
if verbose:
print('Computing windowed mean dimension tensor...')
if mode == 'matvec':
return tt.matvec(wst, tr.core.hamming_weight(N))
else:
wst = wst.tt
cores = tt.vector.to_list(tr.core.hamming_weight(N))
for n in range(N):
cores[n] = cores[n][:, np.concatenate([np.zeros(wst.n[n]//2, dtype=np.int), np.ones(wst.n[n]//2, dtype=np.int)]), :]
h = tt.vector.from_list(cores)
wmd = tt.multifuncrs2([wst, h], lambda x: x[:, 0] * x[:, 1], eps=eps, verb=verbose, **kwargs)
wmd = tt.vector.from_list([core[:, :core.shape[1]//2, :] + core[:, core.shape[1]//2:, :] for core in tt.vector.to_list(wmd)])
return wmd
def apply_mask(A, f, mask, eps=1e-8):
"""
Apply boundary mask on tt-stiffness matrix and tt-force vector
:param A:
:param f:
:param mask:
:return:
"""
d = A.tt.d
return (mask * A + tt.eye(4, d) - mask).round(eps), tt.matvec(mask,
f).round(eps)
def matvec(self, other):
if not isinstance(other, Vector):
raise ValueError('Incorrect input.')
if self.isnone or other.isnone or self.mode != other.mode or self.d != other.d:
raise ValueError('Incorrect input.')
res = other.copy(copy_x=False)
if self.mode == MODE_NP or self.mode == MODE_SP:
res.x = self.x.dot(other.x)
if self.mode == MODE_TT:
res.x = tt.matvec(self.x, other.x)
res = res.round([self.tau, other.tau])
return res
def parallel_worker(task_id,
H,
operators,
guess_generator,
rank,
tau,
n_steps,
callbacks=[],
**kwargs):
"""
Parallel worker for the calculation of the expectation value
of an operator
Parameters:
-----------
H: tt.matrix
hamiltonain matrix in the TT format
operators: iterable of tt.matrix
matrix of the operator in the TT format
guess_generator: function
initial vector generator
rank: int
TT rank of the initial vector
tau: float
time step
n_steps:
number of steps of the dynamics
callbacks: list, default []
list of extra callbacks. The callback has to have a signature
(tt.vector) -> Scalar. The callback will receive the wavefunction,
and the result will be collected. The results of the
callbacks are stored in the matrix along with mean values of
the operators.
Returns:
--------
(time, evs) : (np.array, np.array)
time array and array of expectation values
"""
# np.random.seed(seed)
psi = guess_generator(H, rank)
time = []
evs = []
t = 0
psi = ksl(A=-1j * H, y0=psi, tau=1e-10, **kwargs)
for i in range(n_steps):
ev = []
for operator in operators:
ev.append(tt.dot(tt.matvec(operator, psi), psi))
for func in callbacks:
ev.append(func(psi))
time.append(t)
evs.append(ev)
# update
psi = ksl(A=-1j * H, y0=psi, tau=tau, **kwargs)
t += tau
evs = np.array(evs).real
time = np.array(time)
return time, evs
def collect_ev_sequential(H,
operators,
guess_generator,
rank,
n_samples,
tau,
n_steps,
filename=None,
append_file=True,
dump_every=0,
callbacks=[],
**kwargs):
"""
Generate the expectation value of a provided operator
in the dynamical process generated by the hamiltonian H.
The dynamics starts from the initial vector, which is
generated by the guess_generator
Parameters:
-----------
H: tt.matrix
hamiltonain matrix in the TT format
operators: iterable of tt.matrix or tt.matrix
matrices of the operators in the TT format
guess_generator: function
initial vector generator
rank: int
TT rank of the initial vector
n_samples: int
number of sample trajectories
tau: float
time step
n_steps:
number of steps of the dynamics
filename: str, default None
filename to output results. The file is appended if exists
append_file: bool, default True
if we append to the existing file instead of replacing it
dump_every: int, default 0
dump current results every n parallel rounds. Default is 0.
callbacks: list, default []
list of extra callbacks. The callback has to have a signature
(tt.vector) -> Scalar. The callback will receive the wavefunction,
and the result will be collected. The results of the
callbacks are stored in the matrix along with mean values of
the operators.
Returns:
--------
(time, evs) : (np.array, np.array)
time array and array of expectation values
"""
# ensure that operators is iterable
if not isinstance(operators, Iterable):
operators = [operators]
evs_all_l = []
for s in tqdm(range(n_samples),
desc="guess={}, n_steps={}".format(guess_generator.__name__,
n_steps)):
# np.random.seed(s)
psi = guess_generator(H, rank)
time_l = []
evs = []
t = 0
psi = ksl(A=-1j * H, y0=psi, tau=1e-10, **kwargs)
for i in range(n_steps):
ev = []
for operator in operators:
ev.append(tt.dot(tt.matvec(operator, psi), psi))
for func in callbacks:
ev.append(func(psi))
time_l.append(t)
evs.append(ev)
# update
psi = ksl(A=-1j * H, y0=psi, tau=tau, **kwargs)
t += tau
evs_all_l.append(evs)
if ((dump_every > 0) and (s // dump_every == 0) and (s != 0)
and (filename is not None)):
# time to dump results
evs_all = np.array(evs_all_l).real
time = np.array(time_l)
if (s == dump_every) and (not os.path.isfile(filename)
or not append_file):
# rewrite old file with the first batch
np.savez(filename, t=time, evs=evs_all)
else:
time_old = np.load(filename)['t']
evs_old = np.load(filename)['evs']
assert (np.allclose(time_old, time))
evs_updated = np.vstack((evs_old, evs_all))
np.savez(filename, t=time, evs=evs_updated)
evs_all = np.array(evs_all_l).real
time = np.array(time_l)
if filename is not None:
if not os.path.isfile(filename) or not append_file:
np.savez(filename, t=time, evs=evs_all)
else:
time_old = np.load(filename)['t']
evs_old = np.load(filename)['evs']
assert (np.allclose(time_old, time))
evs_updated = np.vstack((evs_old, evs_all))
np.savez(filename, t=time, evs=evs_updated)
return time, evs_all
import tt
from tt.amen import amen_solve
""" This program test two subroutines: matrix-by-vector multiplication
and linear system solution via AMR scheme"""
d = 12
A = tt.qlaplace_dd([d])
x = tt.ones(2,d)
y = amen_solve(A,x,x,1e-6)
#%%
c = tt.multifuncrs2([a, b], lambda x: np.sum(x, axis=1), eps=1E-6)
y = amen_solve(A,x,x,1e-6)
# %%
y
# %%
A
# %%
x
# %%
z=tt.matvec(A,x)
# %%
z
# %%
z.full().reshape(-1)
# %%
#------------------building 3d lf matrix in TT-format with TT-kronecker product
Lf_qtt = tt.kron(tt.kron(Lf_qtt,Identity_qtt),Identity_qtt)+tt.kron(tt.kron(Identity_qtt,Lf_qtt),Identity_qtt)+tt.kron(tt.kron(Identity_qtt,Identity_qtt),Lf_qtt)
#------------------building 3d laplacian matrix in TT-format with TT-kronecker product------------------
L_qtt = tt.kron(tt.kron(L_qtt,Identity_qtt),Identity_qtt)+tt.kron(tt.kron(Identity_qtt,L_qtt),Identity_qtt)+tt.kron(tt.kron(Identity_qtt,Identity_qtt),L_qtt)
# #adding boundary matrix to laplacian matrix
L_qtt = L_qtt+Lbd_qtt
# #matrix-vector multiplication to maintain f and g and sum both to get the complete righside b
b1_qtt = tt.matvec(Lf_qtt,f1_qtt) + tt.matvec(Lbd_qtt,g1_qtt)
b2_qtt = tt.matvec(Lf_qtt,f2_qtt) + tt.matvec(Lbd_qtt,g2_qtt)
#------------------solving higher order linear system in TT-format------------------
#defining initial guess vector
x_qtt= tt.ones(2,int(np.log2(n+1)*(d)))
#solving the higher order linear system with AMEN
print("")
print("Solving Problem 1 with AMEN")
print("")
u1_qtt=amen_solve(L_qtt,b1_qtt,x_qtt,1e-10,nswp=100)
time.sleep(0.01)
#consts
I0 = 1
rho = 1
tau = 1
r02 = 1
k_sc = 1
k_abs = 1
k_t = 1
Cv = 1
T0 = 1
#tensor dim
dx = 50
pt = 50
dt = 1e-10
#initialisation'
t1 = time.time()
A = matrix(dx, rho, Cv, k_t)
Qs = vector(dx, pt, tau, I0, r02, k_sc, k_abs, rho, Cv, T0)
t0 = initial_cond(T0, dx)
A, Qs = full_matrix(A, Qs, t0, pt, dt)
y = amen_solve(A, Qs, Qs, 1e-14)
t2 = time.time()
print('error:', (tt.matvec(A, y) - Qs).norm() / Qs.norm())
print('time:', (t2-t1))
y = _reshape(y, (ry1 * n * ry2, b))
return y
if __name__ == '__main__':
d = 12
n = 15
m = 15
ra = 30
rb = 10
eps = 1e-6
a = 0 * _tt.rand(n * m, d, r=ra)
a = a + _tt.ones(n * m, d)
#a = a.round(1e-12)
a = _tt.vector.to_list(a)
for i in xrange(d):
sa = a[i].shape
a[i] = _reshape(a[i], (sa[0], m, n, sa[-1]))
A = _tt.matrix.from_list(a)
b = _tt.rand(n, d, r=rb)
c = amen_mv(A, b, eps, y=None, z=None, nswp=20, kickrank=4,
kickrank2=0, verb=True, init_qr=True, renorm='gram', fkick=False)
d = _tt.matvec(A, b).round(eps)
print((c[0] - d).norm() / d.norm())
ra = 30
rb = 10
eps = 1e-6
a = 0 * _tt.rand(n * m, d, r=ra)
a = a + _tt.ones(n * m, d)
#a = a.round(1e-12)
a = _tt.vector.to_list(a)
for i in xrange(d):
sa = a[i].shape
a[i] = _reshape(a[i], (sa[0], m, n, sa[-1]))
A = _tt.matrix.from_list(a)
b = _tt.rand(n, d, r=rb)
c = amen_mv(A,
b,
eps,
y=None,
z=None,
nswp=20,
kickrank=4,
kickrank2=0,
verb=True,
init_qr=True,
renorm='gram',
fkick=False)
d = _tt.matvec(A, b).round(eps)
print(c[0] - d).norm() / d.norm()