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commenting and documentation

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class-solution
Daniel Pozsar 2 months ago
parent 51fdb95eb9
commit 6563280eb7
5 changed files with 761 additions and 603 deletions
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140
src/grogupy/core.py
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@ -21,15 +21,57 @@
import numpy as np
from numpy.linalg import inv
from grogupy.utils import blow_up_orbindx, commutator, parse_magnetic_entity
from grogupy.magnetism import blow_up_orbindx, parse_magnetic_entity
from grogupy.utils import commutator
def parallel_Gk(HK, SK, eran, eset):
"""Calculates the Greens function by inversion.
It calculates the Greens function on all the energy levels at the same time.
Args:
HK : (NO, NO), np.array_like
Hamiltonian at a given k point
SK : (NO, NO), np.array_like
Overlap Matrix at a given k point
eran : (eset) np.array_like
Energy sample along the contour
eset : int
Number of energy samples along the contour
Returns:
Gk : (eset, NO, NO), np.array_like
Green's function at a given k point
"""
# Calculates the Greens function on all the energy levels
return inv(SK * eran.reshape(eset, 1, 1) - HK)
def sequential_GK(HK, SK, eran, eset):
"""Calculates the Greens function by inversion.
It calculates sequentially over the energy levels.
Args:
HK : (NO, NO), np.array_like
Hamiltonian at a given k point
SK : (NO, NO), np.array_like
Overlap Matrix at a given k point
eran : (eset) np.array_like
Energy sample along the contour
eset : int
Number of energy samples along the contour
Returns:
Gk : (eset, NO, NO), np.array_like
Green's function at a given k point
"""
# creates an empty holder
Gk = np.zeros(shape=(eset, HK.shape[0], HK.shape[1]), dtype="complex128")
# fills the holder sequentially by the Greens function on a given energy
for j in range(eset):
Gk[j] = inv(SK * eran[j] - HK)
@ -37,14 +79,19 @@ def sequential_GK(HK, SK, eran, eset):
def calc_Vu(H, Tu):
"""_summary_
"""Calculates the local perturbation in case of a spin rotation.
Args:
H (_type_): _description_
Tu (_type_): _description_
H : (NO, NO) np.array_like
Hamiltonian
Tu : (NO, NO) array_like
Rotation around u
Returns:
_type_: _description_
Vu1 : (NO, NO) np.array_like
First order perturbed matrix
Vu2 : (NO, NO) np.array_like
Second order perturbed matrix
"""
Vu1 = 1j / 2 * commutator(H, Tu) # equation 100
@ -54,15 +101,24 @@ def calc_Vu(H, Tu):
def remove_clutter_for_save(pairs, magnetic_entities):
"""_summary_
"""Removes unimportant data from the dictionaries.
It is used before saving to throw away data that
is not needed for post processing.
Args:
pairs (_type_): _description_
magnetic_entities (_type_): _description_
pairs : dict
Contains all the pair information
magnetic_entities : dict
Contains all the magnetic entity information
Returns:
_type_: _description_
pairs : dict
Contains all the reduced pair information
magnetic_entities : dict
Contains all the reduced magnetic entity information
"""
# remove clutter from magnetic entities and pair information
for pair in pairs:
del pair["Gij"]
@ -79,14 +135,22 @@ def remove_clutter_for_save(pairs, magnetic_entities):
def build_hh_ss(dh):
"""_summary_
"""It builds the Hamiltonian and Overlap matrix from the sisl.dh class.
It restructures the data in the SPIN BOX representation, where NS is
the number of supercells and NO is the number of orbitals.
Args:
dh (_type_): _description_
dh : sisl.physics.Hamiltonian
Hamiltonian read in by sisl
Returns:
_type_: _description_
hh : (NS, NO, NO) np.array_like
Hamiltonian in SPIN BOX representation
ss : (NS, NO, NO) np.array_like
Overlap matrix in SPIN BOX representation
"""
NO = dh.no # shorthand for number of orbitals in the unit cell
# preprocessing Hamiltonian and overlap matrix elements
@ -142,23 +206,35 @@ def build_hh_ss(dh):
]
)
return hh, ss, NO
return hh, ss
def setup_pairs_and_magnetic_entities(
magnetic_entities, pairs, dh, simulation_parameters
):
"""_summary_
"""It creates the complete structure of the dictionaries and fills some basic data.
It creates orbital indexes, spin box indexes, coordinates and tags for magnetic entities.
Furthermore it creates the structures for the energies, the perturbed potentials and
the Greens function calculation. It dose the same for the pairs.
Args:
magnetic_entities (_type_): _description_
pairs (_type_): _description_
dh (_type_): _description_
simulation_parameters (_type_): _description_
pairs : dict
Contains the initial pair information
magnetic_entities : dict
Contains the initial magnetic entity information
dh : sisl.physics.Hamiltonian
Hamiltonian read in by sisl
simulation_parameters : dict
A set of parameters from the simulation
Returns:
_type_: _description_
pairs : dict
Contains the initial information and the complete structure
magnetic_entities : dict
Contains the initial information and the complete structure
"""
# for every site we have to store 3 Greens function (and the associated _tmp-s) in the 3 reference directions
for mag_ent in magnetic_entities:
parsed = parse_magnetic_entity(dh, **mag_ent) # parse orbital indexes
@ -169,11 +245,14 @@ def setup_pairs_and_magnetic_entities(
# if orbital is not set use all
if "l" not in mag_ent.keys():
mag_ent["l"] = "all"
# tag creation for one atom
if isinstance(mag_ent["atom"], int):
mag_ent["tags"] = [
f"[{mag_ent['atom']}]{dh.atoms[mag_ent['atom']].tag}({mag_ent['l']})"
]
mag_ent["xyz"] = [dh.xyz[mag_ent["atom"]]]
# tag creation for more atoms
if isinstance(mag_ent["atom"], list):
mag_ent["tags"] = []
mag_ent["xyz"] = []
@ -187,9 +266,8 @@ def setup_pairs_and_magnetic_entities(
# calculate size for Greens function generation
spin_box_shape = len(mag_ent["spin_box_indices"])
mag_ent["energies"] = (
[]
) # we will store the second order energy derivations here
# we will store the second order energy derivations here
mag_ent["energies"] = []
# These will be the perturbed potentials from eq. 100
mag_ent["Vu1"] = [] # so they are independent in memory
@ -197,7 +275,7 @@ def setup_pairs_and_magnetic_entities(
mag_ent["Gii"] = [] # Greens function
mag_ent["Gii_tmp"] = [] # Greens function for parallelization
for i in simulation_parameters["ref_xcf_orientations"]:
for _ in simulation_parameters["ref_xcf_orientations"]:
# Rotations for every quantization axis
mag_ent["Vu1"].append([])
mag_ent["Vu2"].append([])
@ -227,6 +305,7 @@ def setup_pairs_and_magnetic_entities(
# calculate size for Greens function generation
spin_box_shape_i = len(magnetic_entities[pair["ai"]]["spin_box_indices"])
spin_box_shape_j = len(magnetic_entities[pair["aj"]]["spin_box_indices"])
# tag generation
pair["tags"] = []
for mag_ent in [magnetic_entities[pair["ai"]], magnetic_entities[pair["aj"]]]:
tag = ""
@ -253,7 +332,7 @@ def setup_pairs_and_magnetic_entities(
pair["Gji"] = []
pair["Gij_tmp"] = [] # Greens function for parallelization
pair["Gji_tmp"] = []
for i in simulation_parameters["ref_xcf_orientations"]:
for _ in simulation_parameters["ref_xcf_orientations"]:
# Greens functions for every quantization axis
pair["Gij"].append(
np.zeros(
@ -284,14 +363,19 @@ def setup_pairs_and_magnetic_entities(
def onsite_projection(matrix, idx1, idx2):
"""_summary_
"""It produces the slices of a matrix for the on site projection.
The slicing is along the last two axes as these contains the orbital indexing.
Args:
matrix (_type_): _description_
idx (_type_): _description_
matrix : (..., :, :) np.array_like
Some matrix
idx : np.array_like
The indexes of the orbitals
Returns:
_type_: _description_
np.array_like
Reduced matrix based on the projection
"""
return matrix[..., idx1, :][..., idx2]

74
src/grogupy/grogu.py
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@ -19,37 +19,36 @@
# SOFTWARE.
import os
import warnings
from sys import getsizeof
from timeit import default_timer as timer
import numpy as np
import sisl
from mpi4py import MPI
from grogupy import *
def main():
# constrain numpy in parallel run
os.environ["OMP_NUM_THREADS"] = "1" # export OMP_NUM_THREADS=1
os.environ["OPENBLAS_NUM_THREADS"] = "1" # export OPENBLAS_NUM_THREADS=1
os.environ["MKL_NUM_THREADS"] = "1" # export MKL_NUM_THREADS=1
os.environ["VECLIB_MAXIMUM_THREADS"] = "1" # export VECLIB_MAXIMUM_THREADS=1
os.environ["NUMEXPR_NUM_THREADS"] = "1" # export NUMEXPR_NUM_THREADS=1
from timeit import default_timer as timer
# runtime information
times = dict()
times["start_time"] = timer()
import warnings
from sys import getsizeof
import sisl
from mpi4py import MPI
from src.grogupy import *
# input output stuff
######################################################################
######################################################################
######################################################################
infile = (
"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf"
)
infile = "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf"
outfile = "./Fe3GeTe2_notebook"
magnetic_entities = [
@ -76,25 +75,21 @@ simulation_parameters["kdirs"] = "xy"
simulation_parameters["eset"] = 600
simulation_parameters["esetp"] = 10000
fdf = sisl.io.fdfSileSiesta("input.fdf")
fdf.get("XCF_Rotation")
######################################################################
######################################################################
######################################################################
# MPI parameters
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
root_node = 0
if rank == root_node:
# include parallel size in simulation parameters
simulation_parameters["parallel_size"] = size
# check versions for debugging
if rank == root_node:
try:
print("sisl version: ", sisl.__version__)
except:
@ -117,6 +112,8 @@ if simulation_parameters["ebot"] is None:
except:
print("Could not determine ebot.")
print("Parameter was not given and .EIG file was not found.")
else:
simulation_parameters["automatic_ebot"] = False
# read sile
fdf = sisl.get_sile(simulation_parameters["infile"])
@ -147,9 +144,10 @@ if rank == root_node:
"================================================================================================================================================================"
)
NO = dh.no # shorthand for number of orbitals in the unit cell
# reformat Hamltonian and Overlap matrix for manipulations
hh, ss, NO = build_hh_ss(dh)
hh, ss = build_hh_ss(dh)
# symmetrizing Hamiltonian and Overlap matrix to make them hermitian
for i in range(dh.lattice.sc_off.shape[0]):
@ -248,16 +246,6 @@ for i, orient in enumerate(simulation_parameters["ref_xcf_orientations"]):
# store the relevant information of the Hamiltonian
hamiltonians.append(dict(orient=orient["o"], H=rot_H))
if simulation_parameters["calculate_charge"]:
hamiltonians[-1]["GS"] = np.zeros(
(simulation_parameters["eset"], rot_H.shape[1], rot_H.shape[2]),
dtype="complex128",
)
hamiltonians[-1]["GS_tmp"] = np.zeros(
(simulation_parameters["eset"], rot_H.shape[1], rot_H.shape[2]),
dtype="complex128",
)
# these are the rotations (for now) perpendicular to the quantization axis
for u in orient["vw"]:
# section 2.H
@ -286,7 +274,9 @@ if rank == root_node:
if simulation_parameters["padawan_mode"]:
print("Padawan mode: ")
print(f"Total number of k points: {kset.shape[0]}")
print(f"Number of energy samples per k point: {simulation_parameters['eset']}")
print(
f"Number of energy samples per k point: {simulation_parameters['eset']}"
)
print(f"Total number of directions: {len(hamiltonians)}")
print(
f"Total number of matrix inversions: {kset.shape[0] * len(hamiltonians) * simulation_parameters['eset']}"
@ -339,10 +329,6 @@ for k in kpcs[rank]:
# solve Greens function sequentially for the energies, because of memory bound
Gk = sequential_GK(HK, SK, eran, simulation_parameters["eset"])
# saving this for total charge
if simulation_parameters["calculate_charge"]:
hamiltonian_orientation["GS_tmp"] += Gk @ SK * wk
# store the Greens function slice of the magnetic entities
for mag_ent in magnetic_entities:
idx = mag_ent["spin_box_indices"]
@ -362,10 +348,6 @@ for k in kpcs[rank]:
# summ reduce partial results of mpi nodes
for i in range(len(hamiltonians)):
# for total charge calculation
if simulation_parameters["calculate_charge"]:
comm.Reduce(hamiltonians[i]["GS_tmp"], hamiltonians[i]["GS"], root=root_node)
for mag_ent in magnetic_entities:
comm.Reduce(mag_ent["Gii_tmp"][i], mag_ent["Gii"][i], root=root_node)
@ -382,15 +364,7 @@ if rank == root_node:
"================================================================================================================================================================"
)
if rank == root_node:
# Calculate total charge
if simulation_parameters["calculate_charge"]:
for hamiltonian in hamiltonians:
GS = hamiltonian["GS"]
traced = np.trace((GS), axis1=1, axis2=2)
simulation_parameters["charges"].append(int_de_ke(traced, cont.we))
# iterate over the magnetic entities
for tracker, mag_ent in enumerate(magnetic_entities):
# iterate over the quantization axes
@ -473,3 +447,7 @@ if rank == root_node:
save_pickle(simulation_parameters["outfile"], results)
print("\n\n\n\n\n")
if __name__ == "__main__":
main()

53
src/grogupy/io.py
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@ -35,13 +35,9 @@ default_args = dict(
kset=2,
kdirs="xyz",
ebot=None,
automatic_ebot=False,
eset=42,
esetp=1000,
calculate_charge=False,
charges=[],
parallel_solver_for_Gk=False,
parallel_size=None,
padawan_mode=True,
)
@ -60,27 +56,33 @@ default_args = dict(
def save_pickle(outfile, data):
"""_summary_
"""Saves the data in the outfile with pickle.
Args:
outfile (_type_): _description_
data (_type_): _description_
outfile : str
Path to outfile
data : dict
Contains the data
"""
# save dictionary
with open(outfile, "wb") as output_file:
dump(data, output_file)
def load_pickle(infile, data):
"""_summary_
def load_pickle(infile):
"""Loads the data from the infile with pickle.
Args:
infile (_type_): _description_
data (_type_): _description_
infile : str
Path to infile
Returns:
_type_: _description_
data : dict
A dictionary of data
"""
# open and read file
with open(infile, "wb") as input_file:
data = load(data, input_file)
@ -88,11 +90,13 @@ def load_pickle(infile, data):
def print_parameters(simulation_parameters):
"""_summary_
"""It prints the simulation parameters for the grogu out.
Args:
simulation_parameters (_type_): _description_
simulation_parameters : dict
It contains the simulations parameters
"""
print(
"================================================================================================================================================================"
)
@ -138,12 +142,15 @@ def print_parameters(simulation_parameters):
def print_atoms_and_pairs(magnetic_entities, pairs):
"""_summary_
"""It prints the pair and magnetic entity information for the grogu out.
Args:
magnetic_entities (_type_): _description_
pairs (_type_): _description_
magnetic_entities : dict
It contains the data on the magnetic entities
pairs : dict
It contains the data on the pairs
"""
print("Atomic information: ")
print(
"----------------------------------------------------------------------------------------------------------------------------------------------------------------"
@ -223,11 +230,13 @@ def print_atoms_and_pairs(magnetic_entities, pairs):
def print_runtime_information(times):
"""_summary_
"""It prints the runtime information for the grogu out.
Args:
times (_type_): _description_
times : dict
It contains the runtime data
"""
print("Runtime information: ")
print(f"Total runtime: {times['end_time'] - times['start_time']} s")
print(
@ -255,10 +264,12 @@ def print_runtime_information(times):
def print_job_description(simulation_parameters):
"""_summary_
"""It prints the parameters and the description of the job.
Args:
simulation_parameters (_type_): _description_
simulation_parameters : dict
It contains the simulations parameters
"""
print(

137
src/grogupy/magnetism.py
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@ -21,21 +21,119 @@
import numpy as np
def blow_up_orbindx(orb_indices):
"""Function to blow up orbital indices to make SPIN BOX indices.
Args:
orb_indices : np.array_like
These are the indices in ORBITAL BOX
Returns:
orb_indices : np.array_like
These are the indices in SPIN BOX
"""
orb_indices = np.array([[2 * o, 2 * o + 1] for o in orb_indices]).flatten()
return orb_indices
def spin_tracer(M):
"""Spin tracer utility.
This takes an operator with the orbital-spin sequence:
orbital 1 up,
orbital 1 down,
orbital 2 up,
orbital 2 down,
that is in the SPIN-BOX representation,
and extracts orbital dependent Pauli traces.
Args:
M : np.array_like
Traceable matrix
Returns:
dict
It contains the traced matrix with "x", "y", "z" and "c"
"""
M11 = M[0::2, 0::2]
M12 = M[0::2, 1::2]
M21 = M[1::2, 0::2]
M22 = M[1::2, 1::2]
M_o = dict()
M_o["x"] = M12 + M21
M_o["y"] = 1j * (M12 - M21)
M_o["z"] = M11 - M22
M_o["c"] = M11 + M22
return M_o
def parse_magnetic_entity(dh, atom=None, l=None, **kwargs):
"""Function to define orbital indexes of a given magnetic entity.
Args:
dh : sisl.physics.Hamiltonian
Hamiltonian from sisl
atom : integer or list of integers, optional
Defining atom (or atoms) in the unit cell forming the magnetic entity. Defaults to None
l : integer, optional
Defining the angular momentum channel. Defaults to None
Returns:
list
The orbital indexes of the given magnetic entity
"""
# case where we deal with more than one atom defining the magnetic entity
if type(atom) == list:
dat = []
for a in atom:
a_orb_idx = dh.geometry.a2o(a, all=True)
if (
type(l) == int
): # if specified we restrict to given l angular momentum channel inside each atom
a_orb_idx = a_orb_idx[[o.l == l for o in dh.geometry.atoms[a].orbitals]]
dat.append(a_orb_idx)
orbital_indeces = np.hstack(dat)
# case where we deal with a singel atom magnetic entity
elif type(atom) == int:
orbital_indeces = dh.geometry.a2o(atom, all=True)
if (
type(l) == int
): # if specified we restrict to given l angular momentum channel
orbital_indeces = orbital_indeces[
[o.l == l for o in dh.geometry.atoms[atom].orbitals]
]
return orbital_indeces # numpy array containing integers labeling orbitals associated to a magnetic entity.
def calculate_anisotropy_tensor(mag_ent):
"""_summary_
"""Calculates the renormalized anisotropy tensor from the energies.
It uses the grogu convention for output.
Args:
mag_ent (_type_): _description_
mag_ent : dict
An element from the magnetic entities
Returns:
_type_: _description_
K : np.array_like
elements of the anisotropy tensor
"""
# get the energies
energies = mag_ent["energies"]
# calculate the diagonal tensor elements
Kxx = energies[1, 1] - energies[1, 0]
Kyy = energies[0, 1] - energies[0, 0]
Kzz = 0
# perform consistency check
calculated_diff = Kyy - Kxx
expected_diff = energies[2, 0] - energies[2, 1]
consistency_check = abs(calculated_diff - expected_diff)
@ -44,14 +142,28 @@ def calculate_anisotropy_tensor(mag_ent):
def calculate_exchange_tensor(pair):
"""_summary_
"""Calculates the exchange tensor from the energies.
It produces the isotropic exchange, the relevant elements
from the Dzyaloshinskii-Morilla (Dm) tensor, the symmetric-anisotropy
and the complete exchange tensor.
Args:
pair (_type_): _description_
pair : dict
An element from the pairs
Returns:
_type_: _description_
J_iso : float
Isotropic exchange (Tr[J] / 3)
J_S : np.array_like
Symmetric-anisotropy (J_S = J - J_iso * I ––> Jxx, Jyy, Jxy, Jxz, Jyz)
D : np.array_like
DM elements (Dx, Dy, Dz)
J : np.array_like
Complete exchange tensor flattened (Jxx, Jxy, Jxz, Jyx, Jyy, Jyz, Jzx, Jzy, Jzz)
"""
# energies from rotations
energies = pair["energies"]
# Initialize output arrays
J = np.zeros((3, 3))
@ -96,16 +208,3 @@ def calculate_exchange_tensor(pair):
J_S = np.array([J[0, 0] - J_iso, J[1, 1] - J_iso, J[0, 1], J[0, 2], J[1, 2]])
return J_iso, J_S, D, J
def int_de_ke(traced, we):
"""_summary_
Args:
traced (_type_): _description_
we (_type_): _description_
Returns:
_type_: _description_
"""
return np.trapz(-1 / np.pi * np.imag(traced * we))

260
src/grogupy/utils.py
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@ -29,6 +29,25 @@ tau_z = np.array([[1, 0], [0, -1]])
tau_0 = np.array([[1, 0], [0, 1]])
def commutator(a, b):
"""Shorthand for commutator.
Commutator of two matrices in the mathematical sense.
Args:
a : np.array_like
The first matrix
b : np.array_like
The second matrix
Returns:
np.array_like
The commutator of a and b
"""
return a @ b - b @ a
# define some useful functions
def hsk(H, ss, sc_off, k=(0, 0, 0)):
"""Speed up Hk and Sk generation.
@ -36,14 +55,20 @@ def hsk(H, ss, sc_off, k=(0, 0, 0)):
Calculates the Hamiltonian and the Overlap matrix at a given k point. It is faster that the sisl version.
Args:
H (np.array_like): Hamiltonian in spin box form
ss (np.array_like): Overlap matrix in spin box form
sc_off (list): supercell indexes of the Hamiltonian
k (tuple, optional): The k point where the matrices are set up. Defaults to (0, 0, 0).
H : np.array_like
Hamiltonian in spin box form
ss : np.array_like
Overlap matrix in spin box form
sc_off : list
supercell indexes of the Hamiltonian
k : tuple, optional
The k point where the matrices are set up. Defaults to (0, 0, 0)
Returns:
np.array_like: Hamiltonian at the given k point
np.array_like: Overlap matrix at the given k point
np.array_like
Hamiltonian at the given k point
np.array_like
Overlap matrix at the given k point
"""
# this two conversion lines are from the sisl source
@ -60,46 +85,6 @@ def hsk(H, ss, sc_off, k=(0, 0, 0)):
return HK, SK
def make_contour(emin=-20, emax=0.0, enum=42, p=150):
"""A more sophisticated contour generator.
Calculates the parameters for the complex contour integral.
Args:
emin (int, optional): Energy minimum of the contour. Defaults to -20.
emax (float, optional): Energy maximum of the contour. Defaults to 0.0, so the Fermi level.
enum (int, optional): Number of sample points along the contour. Defaults to 42.
p (int, optional): Shape parameter that describes the distribution of the sample points. Defaults to 150.
Returns:
ccont: ccont
Contains all the information for the contour integral. Should clarify later...
"""
x, wl = roots_legendre(enum)
R = (emax - emin) / 2
z0 = (emax + emin) / 2
y1 = -np.log(1 + np.pi * p)
y2 = 0
y = (y2 - y1) / 2 * x + (y2 + y1) / 2
phi = (np.exp(-y) - 1) / p
ze = z0 + R * np.exp(1j * phi)
we = -(y2 - y1) / 2 * np.exp(-y) / p * 1j * (ze - z0) * wl
# just an empty container class
class ccont:
pass
cont = ccont()
cont.R = R
cont.z0 = z0
cont.ze = ze
cont.we = we
cont.enum = enum
return cont
def make_kset(dirs="xyz", NUMK=20):
"""Simple k-grid generator to sample the Brillouin zone.
@ -110,12 +95,17 @@ def make_kset(dirs="xyz", NUMK=20):
Args:
dirs (str, optional): Directions of the k points in the Brillouin zone. They are the three lattice vectors. Defaults to "xyz".
NUMK (int, optional): The number of k points in a direction. Defaults to 20.
dirs : str, optional
Directions of the k points in the Brillouin zone. They are the three lattice vectors. Defaults to "xyz"
NUMK : int, optional
The number of k points in a direction. Defaults to 20
Returns:
np.array_like: An array of k points that uniformly sample the Brillouin zone in the given directions.
np.array_like
An array of k points that uniformly sample the Brillouin zone in the given directions
"""
# if there is no xyz in dirs return the Gamma point
if not (sum([d in dirs for d in "xyz"])):
return np.array([[0, 0, 0]])
@ -133,19 +123,50 @@ def make_kset(dirs="xyz", NUMK=20):
return kset
def commutator(a, b):
"""Shorthand for commutator.
def make_contour(emin=-20, emax=0.0, enum=42, p=150):
"""A more sophisticated contour generator.
Commutator of two matrices in the mathematical sense.
Calculates the parameters for the complex contour integral. It uses the
Legendre-Gauss quadrature method. It returns a class that contains
the information for the contour integral.
Args:
a (np.array_like): The first matrix.
b (np.array_like): The second matrix
emin : int, optional
Energy minimum of the contour. Defaults to -20
emax : float, optional
Energy maximum of the contour. Defaults to 0.0, so the Fermi level
enum : int, optional
Number of sample points along the contour. Defaults to 42
p : int, optional
Shape parameter that describes the distribution of the sample points. Defaults to 150
Returns:
np.array_like: The commutator of a and b.
ccont
Contains all the information for the contour integral
"""
return a @ b - b @ a
x, wl = roots_legendre(enum)
R = (emax - emin) / 2 # radius
z0 = (emax + emin) / 2 # center point
y1 = -np.log(1 + np.pi * p) # lower bound
y2 = 0 # upper bound
y = (y2 - y1) / 2 * x + (y2 + y1) / 2
phi = (np.exp(-y) - 1) / p # angle parameter
ze = z0 + R * np.exp(1j * phi) # complex points for path
we = -(y2 - y1) / 2 * np.exp(-y) / p * 1j * (ze - z0) * wl
# just an empty container class
class ccont:
pass
cont = ccont()
cont.R = R
cont.z0 = z0
cont.ze = ze
cont.we = we
cont.enum = enum
return cont
def tau_u(u):
@ -154,10 +175,12 @@ def tau_u(u):
Returns the vector u in the basis of the Pauli matrices.
Args:
u (list or np.array_like): The direction
u : list or np.array_like
The direction
Returns:
np.array_like: Arbitrary direction in the base of the Pauli matrices.
np.array_like
Arbitrary direction in the base of the Pauli matrices
"""
# u is force to be of unit length
@ -173,10 +196,12 @@ def crossM(u):
It acts as a cross product with vector u.
Args:
u (list or np.array_like): The second vector in the cross product
u : list or np.array_like
The second vector in the cross product
Returns:
np.array_like: The matrix that represents teh cross product with a vector.
np.array_like
The matrix that represents teh cross product with a vector
"""
return np.array([[0, -u[2], u[1]], [u[2], 0, -u[0]], [-u[1], u[0], 0]])
@ -186,12 +211,16 @@ def RotM(theta, u, eps=1e-10):
Args:
theta (float): The angle of rotation.
u (np.array_like): The rotation axis.
eps (float, optional): Cutoff for small elements in the resulting matrix. Defaults to 1e-10.
theta : float
The angle of rotation
u : np.array_like
The rotation axis
eps : float, optional
Cutoff for small elements in the resulting matrix. Defaults to 1e-10
Returns:
np.array_like: The rotation matrix.
np.array_like
The rotation matrix
"""
u = u / np.linalg.norm(u)
@ -213,12 +242,16 @@ def RotMa2b(a, b, eps=1e-10):
Function returns array R such that R @ a = b holds.
Args:
a (np.array_like): First vector.
b (np.array_like): Second vector.
eps (float, optional): Cutoff for small elements in the resulting matrix. Defaults to 1e-10.
a : np.array_like
First vector
b : np.array_like
Second vector
eps : float, optional
Cutoff for small elements in the resulting matrix. Defaults to 1e-10
Returns:
np.array_like: The rotation matrix with the above property.
np.array_like
The rotation matrix with the above property
"""
v = np.cross(a, b)
@ -230,89 +263,42 @@ def RotMa2b(a, b, eps=1e-10):
return M
def spin_tracer(M):
"""Spin tracer utility.
This takes an operator with the orbital-spin sequence:
orbital 1 up,
orbital 1 down,
orbital 2 up,
orbital 2 down,
that is in the SPIN-BOX representation,
and extracts orbital dependent Pauli traces.
def read_siesta_emin(eigfile):
"""It reads the lowest energy level from the siesta run.
It uses the .EIG file from siesta that contains the eigenvalues.
Args:
M (np.array_like): Traceble matrix.
eigfile : str
The path to the .EIG file
Returns:
dict: It contains the traced matrix with "x", "y", "z" and "c".
float
The energy minimum
"""
M11 = M[0::2, 0::2]
M12 = M[0::2, 1::2]
M21 = M[1::2, 0::2]
M22 = M[1::2, 1::2]
M_o = dict()
M_o["x"] = M12 + M21
M_o["y"] = 1j * (M12 - M21)
M_o["z"] = M11 - M22
M_o["c"] = M11 + M22
return M_o
# read the file
eigs = eigSileSiesta(eigfile).read_data()
def parse_magnetic_entity(dh, atom=None, l=None, **kwargs):
"""Function to define orbital indexes of a given magnetic entity.
Args:
dh (sisl.physics.Hamiltonian): Hamiltonian
atom (integer or list of integers, optional): Defining atom (or atoms) in the unit cell forming the magnetic entity. Defaults to None.
l (integer, optional): Defining the angular momentum channel. Defaults to None.
return eigs.min()
Returns:
list: The orbital indexes of the given magnetic entity.
"""
# case where we deal with more than one atom defining the magnetic entity
if type(atom) == list:
dat = []
for a in atom:
a_orb_idx = dh.geometry.a2o(a, all=True)
if (
type(l) == int
): # if specified we restrict to given l angular momentum channel inside each atom
a_orb_idx = a_orb_idx[[o.l == l for o in dh.geometry.atoms[a].orbitals]]
dat.append(a_orb_idx)
orbital_indeces = np.hstack(dat)
# case where we deal with a singel atom magnetic entity
elif type(atom) == int:
orbital_indeces = dh.geometry.a2o(atom, all=True)
if (
type(l) == int
): # if specified we restrict to given l angular momentum channel
orbital_indeces = orbital_indeces[
[o.l == l for o in dh.geometry.atoms[atom].orbitals]
]
return orbital_indeces # numpy array containing integers labeling orbitals associated to a magnetic entity.
def blow_up_orbindx(orb_indices):
"""
Function to blow up orbital indeces to make SPIN BOX indices.
"""
return np.array([[2 * o, 2 * o + 1] for o in orb_indices]).flatten()
def int_de_ke(traced, we):
"""It numerically integrates the traced matrix.
def read_siesta_emin(eigfile):
"""_summary_
It is a wrapper from numpy.trapz and it contains the
relevant constants to calculate the energy integral from
equation 93 or 96.
Args:
eigfile (_type_): _description_
traced : np.array_like
The trace of a matrix or a matrix product
we : float
The weight of a point on the contour
Returns:
_type_: _description_
float
The energy calculated from the integral formula
"""
eigs = eigSileSiesta(eigfile).read_data()
return eigs.min()
return np.trapz(-1 / np.pi * np.imag(traced * we))

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