def test_fft_kpq(nalpha):
# Create regular grid.
nmax = 2
mesh = [2 * nmax + 1] * 2
grid, eigs = generate_fft_grid(mesh)
qmax = 2 * nmax
qmesh = [2 * qmax + 1] * 2
qgrid, qeigs = generate_fft_grid(qmesh)
# Create wavefunction
nbasis = len(grid)
numpy.random.seed(7)
psi = get_random_wavefunction((nalpha, nalpha), nbasis)
I = get_random_wavefunction((nalpha, nalpha), nbasis)
trial = I[:, :nalpha].conj()
G, Gh = gab_mod(trial, psi[:, :nalpha])
nqgrid = numpy.prod(qmesh)
# Check by direct convolution f(q) = \sum_G Psi[G+Q] Gh[G].
fq_direct = numpy.zeros(nqgrid, dtype=numpy.complex128)
for i, q in enumerate(qgrid):
for j, k in enumerate(grid):
kpq = k + q
ikpq = lookup(kpq, grid)
if ikpq is not None:
fq_direct[i] += trial[ikpq, 0] * Gh[0, j]
trial_grid = numpy.flip(trial[:, 0]).reshape(mesh)
Gh_grid = Gh[0, :].reshape(mesh)
# Check by fft convolve
# Compare to fq
fq_conv = numpy.zeros(nqgrid, dtype=numpy.complex128)
fq_conv += nqgrid * convolve(Gh_grid, trial_grid, mesh)
fq_conv = numpy.flip(fq_conv)
import scipy.signal
fq_conv_sc = numpy.flip(
scipy.signal.fftconvolve(Gh_grid, trial_grid).ravel())
import matplotlib.pyplot as pl
pl.plot(fq_conv, label='fft')
pl.plot(fq_conv_sc, label='fft_scipy')
pl.plot(fq_direct, label='direct')
# pl.plot(fq, label='from_gf')
pl.legend()
pl.show()
def test_walker_energy():
numpy.random.seed(7)
nelec = (2, 2)
nmo = 5
h1e, chol, enuc, eri = generate_hamiltonian(nmo, nelec, cplx=False)
system = Generic(nelec=nelec,
h1e=h1e,
chol=chol,
ecore=enuc,
inputs={'integral_tensor': False})
(e0, ev), (d, oa, ob) = simple_fci(system, gen_dets=True)
na = system.nup
init = get_random_wavefunction(nelec, nmo)
init[:, :na], R = reortho(init[:, :na])
init[:, na:], R = reortho(init[:, na:])
trial = MultiSlater(system, (ev[:, 0], oa, ob), init=init)
trial.calculate_energy(system)
walker = MultiDetWalker({}, system, trial)
nume = 0
deno = 0
for i in range(trial.ndets):
psia = trial.psi[i, :, :na]
psib = trial.psi[i, :, na:]
oa = numpy.dot(psia.conj().T, init[:, :na])
ob = numpy.dot(psib.conj().T, init[:, na:])
isa = numpy.linalg.inv(oa)
isb = numpy.linalg.inv(ob)
ovlp = numpy.linalg.det(oa) * numpy.linalg.det(ob)
ga = numpy.dot(init[:, :system.nup], numpy.dot(isa, psia.conj().T)).T
gb = numpy.dot(init[:, system.nup:], numpy.dot(isb, psib.conj().T)).T
e = local_energy(system, numpy.array([ga, gb]), opt=False)[0]
nume += trial.coeffs[i].conj() * ovlp * e
deno += trial.coeffs[i].conj() * ovlp
print(nume / deno, nume, deno, e0[0])
def test_fft_kmq(nalpha):
# Create regular grid.
nmax = 1
mesh = [2 * nmax + 1] * 3
grid, eigs = generate_fft_grid(mesh)
qmax = 2 * nmax
qmesh = [2 * qmax + 1] * 3
qgrid, qeigs = generate_fft_grid(qmesh)
# Create wavefunction
nbasis = len(grid)
# numpy.random.seed(7)
psi = get_random_wavefunction((nalpha, nalpha), nbasis)
I = get_random_wavefunction((nalpha, nalpha), nbasis)
# Select lowest energy states for trial
trial = I[:, :nalpha].conj()
G, Gh = gab_mod(trial, psi[:, :nalpha])
nqgrid = numpy.prod(qmesh)
# # Check by direct convolution f(q) = \sum_G Psi[G-Q] Gh[G].
fq_direct = numpy.zeros(nqgrid, dtype=numpy.complex128)
for iq, q in enumerate(qgrid):
for i, g in enumerate(grid):
gmq = g - q
igmq = lookup(gmq, grid)
if igmq is not None:
fq_direct[iq] += trial[igmq, 0] * Gh[0, i]
trial_grid = trial[:, 0].reshape(mesh)
Gh_grid = numpy.flip(Gh[0, :]).reshape(mesh)
# Check by fft convolve
# Compare to fq
fq_conv = numpy.zeros(nqgrid, dtype=numpy.complex128)
fq_conv += nqgrid * convolve(trial_grid, Gh_grid, mesh)
fq_conv = numpy.flip(fq_conv)
import scipy.signal
fq_conv_sc = numpy.flip(
scipy.signal.fftconvolve(trial_grid, Gh_grid).ravel())
import matplotlib.pyplot as pl
pl.plot(fq_conv, label='fft')
pl.plot(fq_conv_sc, label='fft_scipy')
pl.plot(fq_direct, label='direct')
pl.legend()
pl.show()
def test_fft_kpq(nalpha):
# Create regular grid.
nmax = 2
mesh = [2*nmax+1]*1
grid, eigs = generate_fft_grid(mesh)
qmax = 2*nmax
qmesh = [2*qmax+1]*1
qgrid, qeigs = generate_fft_grid(qmesh)
# Create wavefunction
nbasis = len(grid)
numpy.random.seed(7)
psi = get_random_wavefunction((nalpha,nalpha), nbasis)
I = numpy.eye(nbasis, dtype=numpy.complex128)
# print(I.shape)
I = get_random_wavefunction((nalpha,nalpha), nbasis)
# print(I.shape)
# exit()
# Select lowest energy states for trial
trial = I[:,:nalpha].conj()
trial.imag[:] = 0
G, Gh = gab_mod(trial,psi[:,:nalpha])
nqgrid = numpy.prod(qmesh)
# # Check by direct convolution f(q) = \sum_G Psi[G+Q] Gh[G].
print(grid.shape)
fq_direct = numpy.zeros(nqgrid, dtype=numpy.complex128)
for iq, q in enumerate(qgrid):
Gtrace_direct = 0
# for a in range(nalpha):
# compute \sum_G f_G(q)
for i, k in enumerate(grid):
kpq = k+q
ikpq = lookup(kpq, grid)
if ikpq is not None:
Gtrace_direct += trial[ikpq,0] * Gh[0,i]
fq_direct[iq] = Gtrace_direct
# Check by fft convolve
# Compare to fq
fq_conv = numpy.zeros(nqgrid, dtype=numpy.complex128)
trial_pq = trial[:,0].copy()
Gh_pq = Gh[0,:].copy()
fq_conv += nqgrid*convolve(Gh_pq, numpy.flip(trial_pq), mesh)
fq_conv = numpy.flip(fq_conv)
import scipy.signal
fq_conv_sc = numpy.flip(scipy.signal.fftconvolve(
Gh_pq,numpy.flip(trial_pq)).ravel())
import matplotlib.pyplot as pl
pl.plot(fq_conv, label='fft')
pl.plot(fq_conv_sc, label='fft_scipy')
pl.plot(fq_direct, label='direct')
# pl.plot(fq, label='from_gf')
pl.legend()
pl.show()
def test_fft_kmq(nalpha):
# Create regular grid.
nmax = 2
mesh = [2*nmax+1]*1
grid, eigs = generate_fft_grid(mesh)
qmax = 2*nmax
qmesh = [2*qmax+1]*1
qgrid, qeigs = generate_fft_grid(qmesh)
# Create wavefunction
nbasis = len(grid)
numpy.random.seed(7)
psi = get_random_wavefunction((nalpha,nalpha), nbasis)
I = numpy.eye(nbasis, dtype=numpy.complex128)
# print(I.shape)
I = get_random_wavefunction((nalpha,nalpha), nbasis)
# print(I.shape)
# exit()
# Select lowest energy states for trial
trial = I[:,:nalpha].conj()
trial.imag[:] = 0
G, Gh = gab_mod(trial,psi[:,:nalpha])
nqgrid = numpy.prod(qmesh)
# # Check by direct convolution f(q) = \sum_G Psi[G+Q] Gh[G].
print(grid.shape)
fq_direct = numpy.zeros(nqgrid, dtype=numpy.complex128)
for iq, q in enumerate(qgrid):
Gtrace_direct = 0
# for a in range(nalpha):
# compute \sum_G f_G(q)
for i, k in enumerate(grid):
# kmq = q-k
kmq = k-q
ikmq = lookup(kmq, grid)
# idx = numpy.argwhere(basis == q-k)
# print(idx, ikmq)
if ikmq is not None:
Gtrace_direct += trial[i,0] * Gh[0,ikmq]
fq_direct[iq] = Gtrace_direct
print("trial[igmq,0] = {}".format(trial[:,0]))
print("Gh[0,i] = {}".format(Gh[0,:]))
# Check by fft convolve
# Compare to fq
fq_conv = numpy.zeros(nqgrid, dtype=numpy.complex128)
trial_pq = trial[:,0].copy()
Gh_pq = Gh[0,:].copy()
# \sum_G f(G-Q) g(G)
# -G-Q -> G'
# \sum_G g(-G-Q) f(-G) = \sum_G g(G) f(G+Q)
# trial_pq = numpy.conj(trial_pq)
fq_conv += nqgrid*convolve(Gh_pq, numpy.flip(trial_pq), mesh)
fq_conv = numpy.flip(fq_conv)
import scipy.signal
fq_conv_sc = numpy.flip(scipy.signal.fftconvolve(
Gh_pq,numpy.flip(trial_pq)).ravel())
# for i in range(qmesh[0]):
# target = fq_conv[i]
# print(numpy.abs(target))
# if (numpy.abs(target) > 1e-8):
# # print(target)
# idx = numpy.argwhere(numpy.abs(fq_direct - target) < 1e-8)
# # print(i, idx)
import matplotlib.pyplot as pl
pl.plot(fq_conv, label='fft')
pl.plot(fq_conv_sc, label='fft_scipy')
pl.plot(fq_direct, label='direct')
# pl.plot(fq, label='from_gf')
pl.legend()
pl.show()