def diagonalize(self,
istart=None,
jend=None,
energy_range=None,
TDA=False):
"""Evaluate Eigenvectors and Eigenvalues"""
ApB, AmB = self.map(istart, jend, energy_range)
nij = len(self.kss)
if TDA:
# Tamm-Dancoff approximation (B=0)
self.eigenvectors = 0.5 * (ApB + AmB)
eigenvalues = np.zeros((nij))
diagonalize(self.eigenvectors, eigenvalues)
self.eigenvalues = eigenvalues**2
else:
# the occupation matrix
C = np.empty((nij, ))
for ij in range(nij):
C[ij] = 1. / self.kss[ij].fij
S = C * inv(AmB) * C
S = sqrt_matrix(inv(S).copy())
# get Omega matrix
M = np.zeros(ApB.shape)
gemm(1.0, ApB, S, 0.0, M)
self.eigenvectors = np.zeros(ApB.shape)
gemm(1.0, S, M, 0.0, self.eigenvectors)
self.eigenvalues = np.zeros((nij))
diagonalize(self.eigenvectors, self.eigenvalues)
def diagonalize(self, istart=None, jend=None, energy_range=None, TDA=False):
"""Evaluate Eigenvectors and Eigenvalues"""
ApB, AmB = self.map(istart, jend, energy_range)
nij = len(self.kss)
if TDA:
# Tamm-Dancoff approximation (B=0)
self.eigenvectors = 0.5 * (ApB + AmB)
eigenvalues = np.zeros((nij))
diagonalize(self.eigenvectors, eigenvalues)
self.eigenvalues = eigenvalues ** 2
else:
# the occupation matrix
C = np.empty((nij,))
for ij in range(nij):
C[ij] = 1.0 / self.kss[ij].fij
S = C * inv(AmB) * C
S = sqrt_matrix(inv(S).copy())
# get Omega matrix
M = np.zeros(ApB.shape)
gemm(1.0, ApB, S, 0.0, M)
self.eigenvectors = np.zeros(ApB.shape)
gemm(1.0, S, M, 0.0, self.eigenvectors)
self.eigenvalues = np.zeros((nij))
diagonalize(self.eigenvectors, self.eigenvalues)
def diagonalize(self, istart=None, jend=None, energy_range=None):
"""Evaluate Eigenvectors and Eigenvalues:"""
map, kss = self.get_map(istart, jend, energy_range)
nij = len(kss)
if map is None:
ApB = self.ApB.copy()
AmB = self.AmB.copy()
nij = len(kss)
else:
ApB = np.empty((nij, nij))
AmB = np.empty((nij, nij))
for ij in range(nij):
for kq in range(nij):
ApB[ij,kq] = self.ApB[map[ij],map[kq]]
AmB[ij,kq] = self.AmB[map[ij],map[kq]]
# the occupation matrix
C = np.empty((nij,))
for ij in range(nij):
C[ij] = 1. / kss[ij].fij
S = C * inv(AmB) * C
S = sqrt_matrix(inv(S).copy())
# get Omega matrix
M = np.zeros(ApB.shape)
gemm(1.0, ApB, S, 0.0, M)
self.eigenvectors = np.zeros(ApB.shape)
gemm(1.0, S, M, 0.0, self.eigenvectors)
self.eigenvalues = np.zeros((len(kss)))
self.kss = kss
diagonalize(self.eigenvectors, self.eigenvalues)
import numpy as np from gpaw.test import equal from gpaw.utilities.lapack import sqrt_matrix # check sqrt of a matrix A = [[20, 4], [4, 1]] a = [[4.4, .8], [.8, .6]] A = np.array(A, float) print 'A=', A a = np.array(a) b = sqrt_matrix(A) print 'sqrt(A)=', b equal(((a - b)**2).sum(), 0, 1.e-12)
from __future__ import print_function
import numpy as np
from gpaw.test import equal
from gpaw.utilities.lapack import sqrt_matrix
# check sqrt of a matrix
A = [[20, 4], [4, 1]]
a = [[4.4, .8], [.8, .6]]
A = np.array(A, float)
print('A=', A)
a = np.array(a)
b = sqrt_matrix(A)
print('sqrt(A)=', b)
equal(((a-b)**2).sum(), 0, 1.e-12)