def __init__(self, *args, **kwargs):
super(TestMethods, self).__init__(*args, **kwargs)
if stat in ['F', 'B']:
self._b = irbasis.load(stat, Lambda)
elif stat == 'barB':
self._b = augmented_basis_b(irbasis.load('B', Lambda))
self._B = Basis(self._b, beta)
def test_sampling_point_y(self):
for stat in ['F', 'B']:
b = irbasis.load(stat, Lambda, "../irbasis.h5")
dim = b.dim()
whichl = dim - 1
sp = irbasis.sampling_points_y(b, whichl)
sp2 = b.sampling_points_y(whichl)
assert numpy.all(sp==sp2)
#print(len(sp), whichl)
#print(sp)
assert len(sp) == whichl+1
def test_sampling_point_x(self):
for stat in ['F', 'B']:
b = irbasis.load(stat, Lambda, "../irbasis.h5")
dim = b.dim()
whichl = dim - 1
sp = irbasis.sampling_points_x(b, whichl)
sp2 = b.sampling_points_x(whichl)
assert numpy.all(sp==sp2)
assert len(sp) == whichl+1
uxl = numpy.array([b.ulx(l, x) for l in range(dim) for x in sp]).reshape((dim, dim))
U, S, Vh = scipy.linalg.svd(uxl, full_matrices=False)
cond_num = S[0] / S[-1]
print("cond_num ", cond_num)
self.assertLessEqual(cond_num, 1E+4)
def test_sampling_point_tau(self):
for stat in ['F', 'B']:
if stat == 'barB':
b = Basis(augmented_basis_b(Lambda), beta)
else:
b = Basis(irbasis.load(stat, Lambda), beta)
dim = b.dim
whichl = dim - 1
sp = sampling_points_tau(b, whichl)
assert len(sp) == whichl+1
Utaul = numpy.array([b.Ultau(l, tau) for l in range(dim) for tau in sp]).reshape((dim, dim))
Utaul_real = from_complex_to_real_coeff_matrix(Utaul)
U, S, Vh = scipy.linalg.svd(Utaul_real, full_matrices=False)
cond_num = S[0] / S[-1]
print("cond_num ", cond_num)
self.assertLessEqual(cond_num, 1E+4)
def test_sampling_point_matsubara(self):
for stat in ['F', 'B']:
b = irbasis.load(stat, Lambda, "../irbasis.h5")
dim = b.dim()
whichl = dim - 1
sp = irbasis.sampling_points_matsubara(b, whichl)
sp2 = b.sampling_points_matsubara(whichl)
assert numpy.all(sp==sp2)
if stat == 'F':
assert numpy.all([-s-1 in sp for s in sp])
elif stat in ['B']:
assert numpy.all([-s in sp for s in sp])
assert len(sp) >= whichl + 1
Unl = b.compute_unl(sp)[:, :dim]
U, S, Vh = scipy.linalg.svd(Unl, full_matrices=False)
cond_num = S[0] / S[-1]
print("cond_num ", cond_num)
self.assertLessEqual(cond_num, 1E+4)
def test_sampling_point_matsubara(self):
for stat in ['F', 'B']:
if stat == 'barB':
b = Basis(augmented_basis_b(Lambda), beta)
else:
b = Basis(irbasis.load(stat, Lambda), beta)
dim = b.dim - 4
whichl = dim - 1
sp = sampling_points_matsubara(b, whichl)
if stat == 'F':
assert numpy.all([-s-1 in sp for s in sp])
elif stat in ['B', 'bB']:
assert numpy.all([-s in sp for s in sp])
assert len(sp) == whichl+1
Unl = b.compute_Unl(sp)[:, :dim]
Unl_real = from_complex_to_real_coeff_matrix(Unl)
U, S, Vh = scipy.linalg.svd(Unl_real, full_matrices=False)
cond_num = S[0] / S[-1]
print("cond_num ", cond_num)
self.assertLessEqual(cond_num, 1E+4)
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
matplotlib.rcParams['font.family'] = 'serif'
matplotlib.rcParams['mathtext.fontset'] = 'cm'
matplotlib.rcParams['mathtext.rm'] = 'serif'
import numpy
import irbasis
if __name__ == '__main__':
Lambda = 1000.0
statistics = 'F' # Fermion. use 'B' for bosons
basis = irbasis.load(statistics, Lambda)
linst = ['solid', 'dashed', 'dashdot', 'dotted']
mi = numpy.linspace(-1, 1, 10000)
#plt.figure(1, figsize=(8,6))
#plt.figure(2, figsize=(8,6))
idx = 0
for l in [0, 1, 2]:
plt.figure(1)
plt.plot(mi,
numpy.array([basis.ulx(l, x) for x in mi]),
linestyle=linst[idx],
label="$l = {}$".format(l))
return numpy.sqrt(self._beta / 2) * numpy.dot(
gtau_smpl[:, :], self._u_smpl[:, 0:nl]).reshape((nl))
if __name__ == '__main__':
stat = 'F' # 'F' for Fermionic or 'B' for Bosonic
wmax = 10.0
Lambda = 1000.0
beta = Lambda / wmax
pole = 2.0
assert numpy.abs(pole) <= wmax
basis = irbasis.load(stat, Lambda)
Nl = basis.dim()
# Initialize a transformer
trans = transformer(basis, beta)
# G(tau) generated by a pole at "pole = 2.0"
if stat == 'B':
gtau = lambda tau: -numpy.exp(-pole * tau) / (1 - numpy.exp(-beta *
pole))
elif stat == 'F':
gtau = lambda tau: -numpy.exp(-pole * tau) / (1 + numpy.exp(-beta *
pole))
#Compute expansion coefficients in IR by numerical integration
Gl = trans.compute_gl(gtau, Nl)
from __future__ import print_function
import numpy
import irbasis
# By default, Lambda = 10, 100, 1000, 10000 are available.
Lambda = 1000.0
# Fermionic
# If you has not installed the irbasis package via pip,
# you must specify the location of a data file as follows.
# irbasis.load('F', Lambda, './irbasis.h5')
basis = irbasis.load('F', Lambda)
l = 0
print("l =", l, ",Lambda =", Lambda)
x = 1
y = 1
# Dimensions of basis
print("Dim ", basis.dim())
# u_0(x = 1) and v_0(y = 1)
print("ulx ", basis.ulx(l, x))
print("vly ", basis.vly(l, y))
# Singular value s_0
print("sl ", basis.sl(l))
# The k-th derivative of u_l(x) and v_l(y) (k = 1,2,3)
for k in [1, 2, 3]: