def compute_PIR(self, GR, Gsum, nF):
tau3GA = np.einsum('ab,...bc->...ac', Migdal.tau3, np.conj(GR))
tau3A = np.einsum('ab,...bc->...ac', Migdal.tau3, -1.0/np.pi * GR.imag)
return self.g0**2*self.dw/self.nk**2 * np.einsum('...aa->...', \
basic_conv(tau3A, Gsum, ['k+q,k','k+q,k','z,w-z'], [0,1,2], [True,True,False], op='...ab,...bc->...ac')[:,:,:self.nr] \
-basic_conv(tau3A, tau3GA*nF[None,None,:,None,None], ['k+q,k','k+q,k','w+z,z'], [0,1,2], [True,True,False], op='...ab,...bc->...ac')[:,:,:self.nr] \
+basic_conv(tau3A*nF[None,None,:,None,None], tau3GA, ['k+q,k','k+q,k','w+z,z'], [0,1,2], [True,True,False], op='...ab,...bc->...ac')[:,:,:self.nr])
def compute_SR(self, GR, Gsum, DR, nB, nF):
B = -1.0/np.pi * DR.imag
#tau3GRtau3 = np.einsum('ab,...bc,cd->...ad',Migdal.tau3,GR,Migdal.tau3)
return -self.g0**2*self.dw/self.nk*( \
basic_conv(B, Gsum, ['q,k-q','z,w-z'], [0,1], [True,False])[:,:self.nr] \
-basic_conv(B*(1+nB[None,:,None,None]), GR, ['q,k-q','z,w-z'], [0,1], [True,False])[:,:self.nr] \
+basic_conv(B, GR*nF[None,:,None,None], ['q,k-q','z,w-z'], [0,1], [True,False])[:,:self.nr])
def compute_PIR(self, GR, tau3Gsumtau3, nF):
tau3GAtau3 = np.einsum('ab,...bc,cd->...ad', Migdal.tau3, np.conj(GR),
Migdal.tau3)
A = -1.0 / np.pi * GR.imag
return self.g0**2*self.dw/self.nk * np.einsum('...aa->...', \
basic_conv(A, tau3Gsumtau3, ['k+q,k','z,w-z'], [0,1], [True,False], op='...ab,...bc->...ac')[:,:self.nr] \
-basic_conv(A, tau3GAtau3*nF[None,:,None,None], ['k+q,k','w+z,z'], [0,1], [True,False], op='...ab,...bc->...ac')[:,:self.nr] \
+basic_conv(A*nF[None,:,None,None], tau3GAtau3, ['k+q,k','w+z,z'], [0,1], [True,False], op='...ab,...bc->...ac')[:,:self.nr])
def compute_PIR(self, GR, Gsum, nF):
#tau3GA = np.einsum('ab,...bc->...ac', Migdal.tau3, conj(GR))
#tau3A = np.einsum('ab,...bc->...ac', Migdal.tau3, -1.0/np.pi * GR.imag)
GA = np.conj(GR)
A = -1.0/np.pi * GR.imag
return 2*self.g0**2*self.dw/self.nk * (
basic_conv(A, Gsum, ['k+q,k','z,w-z'], [0,1], [True,False], op='...ab,...bc->...ac')[:,:self.nr] \
-basic_conv(A, GA*nF[None,:,None,None], ['k+q,k','w+z,z'], [0,1], [True,False], op='...ab,...bc->...ac')[:,:self.nr] \
+basic_conv(A*nF[None,:,None,None], GA, ['k+q,k','w+z,z'], [0,1], [True,False], op='...ab,...bc->...ac')[:,:self.nr])
def compute_jjcorr(self, savedir, G, GR):
wn, vn, ek, w, nB, nF, DRbareinv = self.setup_realaxis()
# convert to imaginary frequency
G = fourier.t2w(G, self.beta, self.dim, 'fermion')[0]
# compute Gsum
Gsum = np.zeros([self.nk, self.nk, self.nr], dtype=complex)
for i in range(self.nr):
Gsum[:, :,
i] = np.sum(G / (
(w[i] + 1j * wn)[None, None, :]), axis=2) / self.beta
# handle sum over pos and negative freqs
Gsum += np.conj(Gsum)
print('finished Gsum')
del G
ks = np.arange(-np.pi, np.pi, 2 * np.pi / self.nk)
sin = np.sin(ks)
cos = np.cos(ks)
fk = (-2 * self.t * sin[:, None] -
4 * self.tp * sin[:, None] * cos[None, :])
GA = np.conj(GR)
A = -1.0 / np.pi * GR.imag
A *= (fk**2)[:, :, None]
jj0w = 2.0 * self.dw / self.nk**2 * np.sum(
basic_conv(A, Gsum, ['z,w-z'], [2], [False], izero=self.izero)[:,:,:self.nr] \
-basic_conv(A, GA*nF[None,None,:], ['w+z,z'], [2], [False], izero=self.izero)[:,:,:self.nr] \
+basic_conv(A*nF[None,None,:], GA, ['w+z,z'], [2], [False], izero=self.izero)[:,:,:self.nr], axis=(0,1))
path = os.path.join(savedir, 'jj0w')
np.save(path, jj0w)
del GA
del A
del Gsum
print('done jj0w')
DR0 = 1 / DRbareinv
jjw = jj0w / (1 + self.g0**2 * DR0 * jj0w)
path = os.path.join(savedir, 'jjw')
np.save(path, jjw)
def compute_PIR(self, GR, Gsum, nF):
GA = np.conj(GR)
A = -1.0 / np.pi * GR.imag
return 2.0*self.g0**2*self.dw*(basic_conv(A, Gsum, ['z,w-z'], [0], [False])[:self.nr] \
-basic_conv(A, GA*nF, ['w+z,z'], [0], [False])[:self.nr] \
+basic_conv(A*nF, GA, ['w+z,z'], [0], [False])[:self.nr])
def compute_SR(self, GR, Gsum, DR, nB, nF):
B = -1.0 / np.pi * DR.imag
return -self.g0**2*self.dw*(basic_conv(B, Gsum, ['z,w-z'], [0], [False])[:self.nr] \
-basic_conv(B*(1+nB), GR, ['z,w-z'], [0], [False])[:self.nr] \
+basic_conv(B, GR*nF, ['z,w-z'], [0], [False])[:self.nr])
def conv(a, b, fc):
return basic_conv(a,
b, ['k+q,k', 'k+q,k', fc], [0, 1, 2],
[True, True, False],
izeros=izeros,
op='...ab,...bc->...ac')[:, :, :self.nr]
def conv(a, b):
return basic_conv(a,
b, ['q,k-q', 'q,k-q', 'z,w-z'], [0, 1, 2],
[True, True, False],
izeros=izeros)[:, :, :self.nr]
def compute_PIR(self, GR, Gsum, nF):
GA = np.conj(GR)
A = -1.0/np.pi * GR.imag
return 2.0*self.g0**2*self.gq2[:,None]*self.dw/self.nk*(basic_conv(A, Gsum, ['k+q,k','z,w-z'], [0,1], [True,False])[:,:self.nr] \
-basic_conv(A, GA*nF[None,:], ['k+q,k','w+z,z'], [0,1], [True,False])[:,:self.nr] \
+basic_conv(A*nF[None,:], GA, ['k+q,k','w+z,z'], [0,1], [True,False])[:,:self.nr])
def compute_SR(self, GR, Gsum, DR, nB, nF):
B = -1.0/np.pi * DR.imag
return -self.g0**2*self.dw/self.nk*(basic_conv(self.gq2[:,None]*B, Gsum, ['q,k-q','z,w-z'], [0,1], [True,False])[:,:self.nr] \
-basic_conv(self.gq2[:,None]*B*(1+nB)[None,:], GR, ['q,k-q','z,w-z'], [0,1], [True,False])[:,:self.nr] \
+basic_conv(self.gq2[:,None]*B, GR*nF[None,:], ['q,k-q','z,w-z'], [0,1], [True,False])[:,:self.nr])
def convfunc2(a, b):
return basic_conv(a,
b, ['k+q,k', 'k+q,k', 'w+z,z'], [0, 1, 2],
[True, True, False],
izeros=izeros)[:, :, :self.nr]
def convfunc(a, b, fc):
return basic_conv(a,
b, ['k+q,k', 'k+q,k', fc], [0, 1, 2],
[True, True, False],
izeros=izeros)[:, :, :self.nr]
@author: benno
"""
import numpy as np
import src
from convolution import basic_conv
n = 21
A = np.random.randn(n)
B = np.random.randn(n)
print('testing circular convolutions')
print('')
# convolve
C0 = basic_conv(A, B, ['x,y-x'], [0], [True], izeros=[n // 2])[:n]
# explicit convolve (assuming index 0 is at n//2)
C1 = np.zeros(n)
for iy in range(n):
for ix in range(n):
# when iy = n//2
# and ix = n//2
# C[iy] = A[ix] B[iy - ix + n//2]
C1[iy] += A[ix] * B[(iy - ix + n // 2) % n]
print(np.mean((C0 - C1)).real)
# convolve
