def add_random(self):
"""
Creates a new set of variables to reconstruct the dmatpawu
matrix_i (integers) is a matrix natpawu x ndim with entries are 0 or 1
matrix_d (deltas) is a matrix natpawu x ndim with entries are [0, 0.5)
P (matrices) is a set of matrices natpawu x ndim x ndim
Those three matrices allow to reconstruct the variable 'dmatpawu' used by ABINIT
:return:
"""
matrices_defined = []
matrix_i = self.num_indep_matrices*[None]
matrix_d = self.num_indep_matrices*[None]
euler = self.num_indep_matrices*[None]
for i in range(self.num_indep_matrices):
nelect = self.num_electrons_dftu[i]
val = [x for x in list(itertools.product(range(2), repeat=self.ndim)) if sum(x) == nelect]
ii = val[np.random.randint(len(val))]
dd = np.zeros(self.ndim)
matrix_i[i] = list(ii)
matrix_d[i] = list(dd)
matrices_defined.append(self.connections[i])
p = gram_smith_qr(self.ndim)
euler[i] = gea_all_angles(p)
data = {'E': euler, 'O': matrix_i, 'D': matrix_d}
return self.new_entry(data), None
def dmatpawu2params(dmatpawu, ndim):
"""
Takes the contents of the variable 'dmatpawu' and return their components as a set of 'occupations', 'deltas'
and 'euler_angles'
The Euler angles is a ordered list of angles that can rebuild a rotation matrix 'R'
The rotation matrix 'R' is ensured to be an element of SO(ndim), ie det(R)=1.
When the eigenvectors return a matrix with determinant -1 a mirror on the first dimension is applied.
Such condition has no effect on the physical result of the correlation matrix
:param dmatpawu: The contents of the variable 'dmatpawu'. A list of number representing N matrices ndim x ndim
:param ndim: ndim is 5 for 'd' orbitals and 7 for 'f' orbitals
:return:
"""
dm = np.array(dmatpawu).reshape((-1, ndim, ndim))
num_matrices = dm.shape[0]
eigval = np.array([np.linalg.eigh(x)[0] for x in dm])
occupations = np.array(np.round(eigval), dtype=int)
deltas = np.abs(eigval - occupations)
rotations = np.array([np.linalg.eigh(x)[1] for x in dm])
mirror = np.eye(ndim)
mirror[0, 0] = -1
for i in range(len(rotations)):
if np.linalg.det(rotations[i]) < 0:
rotations[i] = np.dot(rotations[i], mirror)
euler_angles = np.array([list(gea_all_angles(p)) for p in rotations])
return {'occupations': occupations, 'deltas': deltas, 'euler_angles': euler_angles, 'num_matrices': num_matrices}
def add_random(self):
"""
Creates a new set of variables to reconstruct the dmatpawu
matrix_i (integers) is a matrix natpawu x ndim with entries are 0 or 1
matrix_d (deltas) is a matrix natpawu x ndim with entries are [0, 0.5)
P (matrices) is a set of matrices natpawu x ndim x ndim
Those three matrices allow to reconstruct the variable 'dmatpawu' used by ABINIT
:return:
"""
matrices_defined = []
matrix_i = self.num_indep_matrices * [None]
matrix_d = self.num_indep_matrices * [None]
euler = self.num_indep_matrices * [None]
for i in range(self.num_indep_matrices):
nelect = self.num_electrons_dftu[i]
val = [
x for x in list(
itertools.product(list(range(2)), repeat=self.ndim))
if sum(x) == nelect
]
ii = val[np.random.randint(len(val))]
dd = np.zeros(self.ndim)
matrix_i[i] = list(ii)
matrix_d[i] = list(dd)
matrices_defined.append(self.connections[i])
p = gram_smith_qr(self.ndim)
euler[i] = gea_all_angles(p)
data = {
'euler_angles': euler,
'occupations': matrix_i,
'deltas': matrix_d,
'num_matrices': self.num_indep_matrices,
'ndim': self.ndim
}
return self.new_entry(data), None
def dmatpawu2params(dmatpawu, ndim):
"""
Takes the contents of the variable 'dmatpawu' and return their components as a set of 'occupations', 'deltas'
and 'euler_angles'
The Euler angles is a ordered list of angles that can rebuild a rotation matrix 'R'
The rotation matrix 'R' is ensured to be an element of SO(ndim), ie det(R)=1.
When the eigenvectors return a matrix with determinant -1 a mirror on the first dimension is applied.
Such condition has no effect on the physical result of the correlation matrix
:param dmatpawu: The contents of the variable 'dmatpawu'. A list of number representing N matrices ndim x ndim
:param ndim: ndim is 5 for 'd' orbitals and 7 for 'f' orbitals
:return:
"""
dm = np.array(dmatpawu).reshape((-1, ndim, ndim))
num_matrices = dm.shape[0]
eigval = np.array([np.linalg.eigh(x)[0] for x in dm])
occupations = np.array(np.round(eigval), dtype=int)
deltas = np.abs(eigval - occupations)
rotations = np.array([np.linalg.eigh(x)[1] for x in dm])
mirror = np.eye(ndim)
mirror[0, 0] = -1
for i in range(len(rotations)):
if np.linalg.det(rotations[i]) < 0:
rotations[i] = np.dot(rotations[i], mirror)
euler_angles = np.array([list(gea_all_angles(p)) for p in rotations])
return {
'occupations': occupations,
'deltas': deltas,
'euler_angles': euler_angles,
'num_matrices': num_matrices,
'ndim': ndim
}
