grogu/test.py

import os
from sys import stdout
from tqdm import tqdm
from timeit import default_timer as timer

os.environ["OMP_NUM_THREADS"] = "1"  # export OMP_NUM_THREADS=4
os.environ["OPENBLAS_NUM_THREADS"] = "1"  # export OPENBLAS_NUM_THREADS=4
os.environ["MKL_NUM_THREADS"] = "1"  # export MKL_NUM_THREADS=6
os.environ["VECLIB_MAXIMUM_THREADS"] = "1"  # export VECLIB_MAXIMUM_THREADS=4
os.environ["NUMEXPR_NUM_THREADS"] = "1"  # export NUMEXPR_NUM_THREADS=6

import numpy as np
import sisl
from grogu.useful import *
from mpi4py import MPI
from numpy.linalg import inv
import warnings

start_time = timer()

# this cell mimicks an input file
fdf = sisl.get_sile(
    "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf"
)
# this information needs to be given at the input!!
scf_xcf_orientation = np.array([0, 0, 1])  # z
# list of reference directions for around which we calculate the derivatives
# o is the quantization axis, v and w are two axes perpendicular to it
# at this moment the user has to supply o,v,w on the input.
# we can have some default for this
ref_xcf_orientations = [
    dict(o=np.array([1, 0, 0]), vw=[np.array([0, 1, 0]), np.array([0, 0, 1])]),
    dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),
    dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),
]

# human readable definition of magnetic entities
magnetic_entities = [
    dict(atom=3, l=2),
    dict(atom=4, l=2),
    dict(atom=5, l=2),
#    dict(atom=[3, 4]),
]

# pair information
pairs = [
    dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),  # isotropic should be -82 meV
    dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),  # these should all be around -41.9 in the isotropic part
#    dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),
#    dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),
#    dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),
]

# Brilloun zone sampling and Green function contour integral
kset = 20
kdirs = "xy"
ebot = -30
eset = 100
esetp = 10000


# MPI parameters
comm = MPI.COMM_WORLD
size = comm.Get_size()
rank = comm.Get_rank()
root_node = 0
if rank == root_node:
    print("Number of nodes in the parallel cluster: ", size)

simulation_parameters = dict(path="Not yet specified.",
                             scf_xcf_orientation=scf_xcf_orientation, 
                             ref_xcf_orientations=ref_xcf_orientations,
                             kset=kset,
                             kdirs=kdirs, 
                             ebot=ebot,
                             eset=eset, 
                             esetp=esetp,
                             parallel_size=size)

# digestion of the input
# read in hamiltonian
dh = fdf.read_hamiltonian()
try:
    simulation_parameters["geom"] = fdf.read_geometry()
except:
    print("Error reading geometry.")

# unit cell index
uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])

setup_time = timer()

NO = dh.no  # shorthand for number of orbitals in the unit cell

# preprocessing Hamiltonian and overlap matrix elements
h11 = dh.tocsr(dh.M11r)
h11 += dh.tocsr(dh.M11i) * 1.0j
h11 = h11.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")

h22 = dh.tocsr(dh.M22r)
h22 += dh.tocsr(dh.M22i) * 1.0j
h22 = h22.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")

h12 = dh.tocsr(dh.M12r)
h12 += dh.tocsr(dh.M12i) * 1.0j
h12 = h12.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")

h21 = dh.tocsr(dh.M21r)
h21 += dh.tocsr(dh.M21i) * 1.0j
h21 = h21.toarray().reshape(NO, dh.n_s, NO).transpose(0, 2, 1).astype("complex128")

sov = (
    dh.tocsr(dh.S_idx)
    .toarray()
    .reshape(NO, dh.n_s, NO)
    .transpose(0, 2, 1)
    .astype("complex128")
)


# Reorganization of Hamiltonian and overlap matrix elements to SPIN BOX representation
U = np.vstack(
    [np.kron(np.eye(NO, dtype=int), [1, 0]), np.kron(np.eye(NO, dtype=int), [0, 1])]
)
# This is the permutation that transforms ud1ud2 to u12d12
# That is this transforms FROM SPIN BOX to ORBITAL BOX => U
# the inverse transformation is U.T u12d12 to ud1ud2
# That is FROM ORBITAL BOX to SPIN BOX => U.T

# From now on everything is in SPIN BOX!!
hh, ss = np.array(
    [
        U.T @ np.block([[h11[:, :, i], h12[:, :, i]], [h21[:, :, i], h22[:, :, i]]]) @ U
        for i in range(dh.lattice.nsc.prod())
    ]
), np.array(
    [
        U.T
        @ np.block([[sov[:, :, i], sov[:, :, i] * 0], [sov[:, :, i] * 0, sov[:, :, i]]])
        @ U
        for i in range(dh.lattice.nsc.prod())
    ]
)


# symmetrizing Hamiltonian and overlap matrix to make them hermitian
for i in range(dh.lattice.sc_off.shape[0]):
    j = dh.lattice.sc_index(-dh.lattice.sc_off[i])
    h1, h1d = hh[i], hh[j]
    hh[i], hh[j] = (h1 + h1d.T.conj()) / 2, (h1d + h1.T.conj()) / 2
    s1, s1d = ss[i], ss[j]
    ss[i], ss[j] = (s1 + s1d.T.conj()) / 2, (s1d + s1.T.conj()) / 2

# identifying TRS and TRB parts of the Hamiltonian
TAUY = np.kron(np.eye(NO), tau_y)
hTR = np.array([TAUY @ hh[i].conj() @ TAUY for i in range(dh.lattice.nsc.prod())])
hTRS = (hh + hTR) / 2
hTRB = (hh - hTR) / 2

# extracting the exchange field
traced = [spin_tracer(hTRB[i]) for i in range(dh.lattice.nsc.prod())]  # equation 77
XCF = np.array(
    [
        np.array([f["x"] for f in traced]),
        np.array([f["y"] for f in traced]),
        np.array([f["z"] for f in traced]),
    ]
)  # equation 77

# Check if exchange field has scalar part
max_xcfs = abs(np.array(np.array([f["c"] for f in traced]))).max()
if max_xcfs > 1e-12:
    warnings.warn(
        f"Exchange field has non negligible scalar part. Largest value is {max_xcfs}"
    )

H_and_XCF_time = timer()

# for every site we have to store 3 Greens function (and the associated _tmp-s) in the 3 reference directions
for i, mag_ent in enumerate(magnetic_entities):
    parsed = parse_magnetic_entity(dh, **mag_ent)  # parse orbital indexes
    magnetic_entities[i]["orbital_indeces"] = parsed
    magnetic_entities[i]["spin_box_indeces"] = blow_up_orbindx(
        parsed
    )  # calculate spin box indexes
    spin_box_shape = len(
        mag_ent["spin_box_indeces"]
    )  # calculate size for Greens function generation

    mag_ent["energies"] = []  # we will store the second order energy derivations here

    mag_ent["Gii"] = []  # Greens function
    mag_ent["Gii_tmp"] = []  # Greens function for parallelization
    mag_ent["Vu1"] = [
        list([]) for _ in range(len(ref_xcf_orientations))
    ]  # These will be the perturbed potentials from eq. 100
    mag_ent["Vu2"] = [list([]) for _ in range(len(ref_xcf_orientations))]
    for i in ref_xcf_orientations:
        mag_ent["Gii"].append(
            np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
        )  # Greens functions for every quantization axis
        mag_ent["Gii_tmp"].append(
            np.zeros((eset, spin_box_shape, spin_box_shape), dtype="complex128")
        )

# for every site we have to store 2x3 Greens function (and the associated _tmp-s)
# in the 3 reference directions, because G_ij and G_ji are both needed
for pair in pairs:
    spin_box_shape_i, spin_box_shape_j = len(
        magnetic_entities[pair["ai"]]["spin_box_indeces"]
    ), len(
        magnetic_entities[pair["aj"]]["spin_box_indeces"]
    )  # calculate size for Greens function generation

    pair["energies"] = []  # we will store the second order energy derivations here

    pair["Gij"] = []  # Greens function
    pair["Gji"] = []
    pair["Gij_tmp"] = []  # Greens function for parallelization
    pair["Gji_tmp"] = []

    pair["Vij"] = [
        list([]) for _ in range(len(ref_xcf_orientations))
    ]  # These will be the perturbed potentials from eq. 100
    pair["Vji"] = [list([]) for _ in range(len(ref_xcf_orientations))]

    for i in ref_xcf_orientations:
        pair["Gij"].append(
            np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
        )
        pair["Gij_tmp"].append(
            np.zeros((eset, spin_box_shape_i, spin_box_shape_j), dtype="complex128")
        )  # Greens functions for every quantization axis
        pair["Gji"].append(
            np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
        )
        pair["Gji_tmp"].append(
            np.zeros((eset, spin_box_shape_j, spin_box_shape_i), dtype="complex128")
        )

site_and_pair_dictionaries_time = timer()

kset = make_kset(dirs=kdirs, NUMK=kset)  # generate k space sampling
wkset = np.ones(len(kset)) / len(kset)  # generate weights for k points
kpcs = np.array_split(kset, size)  # split the k points based on MPI size
kpcs[root_node] = tqdm(kpcs[root_node], desc='k loop', file=stdout)

k_set_time = timer()

# this will contain all the data needed to calculate the energy variations upon rotation
hamiltonians = []

# iterate over the reference directions (quantization axes)
for i, orient in enumerate(ref_xcf_orientations):
    # obtain rotated exchange field
    R = RotMa2b(scf_xcf_orientation, orient["o"])
    rot_XCF = np.einsum("ij,jklm->iklm", R, XCF)
    rot_H_XCF = sum(
        [np.kron(rot_XCF[i], tau) for i, tau in enumerate([tau_x, tau_y, tau_z])]
    )
    rot_H_XCF_uc = rot_H_XCF[uc_in_sc_idx]

    # obtain total Hamiltonian with the rotated exchange field
    rot_H = hTRS + rot_H_XCF  # equation 76

    hamiltonians.append(
        dict(orient=orient["o"], H=rot_H, rotations=[])
    )  # store orientation and rotated Hamiltonian

    for u in orient[
        "vw"
    ]:  # these are the infinitezimal rotations (for now) perpendicular to the quantization axis
        Tu = np.kron(np.eye(NO, dtype=int), tau_u(u))  # section 2.H

        Vu1 = 1j / 2 * commutator(rot_H_XCF_uc, Tu)  # equation 100
        Vu2 = 1 / 8 * commutator(commutator(Tu, rot_H_XCF_uc), Tu)  # equation 100

        for mag_ent in magnetic_entities:
            mag_ent["Vu1"][i].append(
                Vu1[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
            )  # fill up the perturbed potentials (for now) based on the on-site projections
            mag_ent["Vu2"][i].append(
                Vu2[:, mag_ent["spin_box_indeces"]][mag_ent["spin_box_indeces"], :]
            )

        for pair in pairs:
            ai = magnetic_entities[pair["ai"]][
                "spin_box_indeces"
            ]  # get the pair orbital sizes from the magnetic entities
            aj = magnetic_entities[pair["aj"]]["spin_box_indeces"]
            pair["Vij"][i].append(
                Vu1[:, ai][aj, :]
            )  # fill up the perturbed potentials (for now) based on the on-site projections
            pair["Vji"][i].append(Vu1[:, aj][ai, :])

reference_rotations_time = timer()

if rank == root_node:
    print("Number of magnetic entities being calculated: ", len(magnetic_entities))
    print(
        "We have to calculate the Greens function for three reference direction and we are going to calculate 15 energy integrals per site."
    )
    print(f"The shape of the Hamiltonian and the Greens function is {NO}x{NO}.")
comm.Barrier()
# ----------------------------------------------------------------------

# make energy contour
# we are working in eV now  !
# and sisil shifts E_F to 0 !
cont = make_contour(emin=ebot, enum=eset, p=esetp)
eran = cont.ze

# ----------------------------------------------------------------------
# sampling the integrand on the contour and the BZ
for k in kpcs[rank]:
    wk = wkset[rank]  # weight of k point in BZ integral
    for i, hamiltonian_orientation in enumerate(
        hamiltonians
    ):  # iterate over reference directions
        # calculate Greens function
        H = hamiltonian_orientation["H"]
        HK, SK = hsk(H, ss, dh.sc_off, k)
        Gk = inv(SK * eran.reshape(eset, 1, 1) - HK)

        # store the Greens function slice of the magnetic entities (for now) based on the on-site projections
        for mag_ent in magnetic_entities:
            mag_ent["Gii_tmp"][i] += (
                Gk[:, mag_ent["spin_box_indeces"]][..., mag_ent["spin_box_indeces"]]
                * wk
            )

        for pair in pairs:
            # add phase shift based on the cell difference
            phase = np.exp(1j * 2 * np.pi * k @ pair["Ruc"].T)

            # get the pair orbital sizes from the magnetic entities
            ai = magnetic_entities[pair["ai"]]["spin_box_indeces"]
            aj = magnetic_entities[pair["aj"]]["spin_box_indeces"]

            # store the Greens function slice of the magnetic entities (for now) based on the on-site projections
            pair["Gij_tmp"][i] += Gk[:, ai][..., aj] * phase * wk
            pair["Gji_tmp"][i] += Gk[:, aj][..., ai] * phase * wk

# summ reduce partial results of mpi nodes
for i in range(len(hamiltonians)):
    for mag_ent in magnetic_entities:
        comm.Reduce(mag_ent["Gii_tmp"][i], mag_ent["Gii"][i], root=root_node)

    for pair in pairs:
        comm.Reduce(pair["Gij_tmp"][i], pair["Gij"][i], root=root_node)
        comm.Reduce(pair["Gji_tmp"][i], pair["Gji"][i], root=root_node)

green_function_inversion_time = timer()

if rank == root_node:
    # iterate over the magnetic entities
    for tracker, mag_ent in enumerate(magnetic_entities):
        # iterate over the quantization axes
        for i, Gii in enumerate(mag_ent["Gii"]):
            storage = []
            # iterate over the first and second order local perturbations
            for Vu1, Vu2 in zip(mag_ent["Vu1"][i], mag_ent["Vu2"][i]):
                # The Szunyogh-Lichtenstein formula
                traced = np.trace((Vu2 @ Gii + 0.5 * Gii @ Vu1 @ Gii), axis1=1, axis2=2)
                # evaluation of the contour integral
                storage.append(np.trapz(-1 / np.pi * np.imag(traced * cont.we)))

            # fill up the magnetic entities dictionary with the energies
            mag_ent["energies"].append(storage)

    # iterate over the pairs
    for tracker, pair in enumerate(pairs):
        # iterate over the quantization axes
        for i, (Gij, Gji) in enumerate(zip(pair["Gij"], pair["Gji"])):
            site_i = magnetic_entities[pair["ai"]]
            site_j = magnetic_entities[pair["aj"]]

            storage = []
            # iterate over the first order local perturbations in all possible orientations for the two sites
            for Vui in site_i["Vu1"][i]:
                for Vuj in site_j["Vu1"][i]:
                    # The Szunyogh-Lichtenstein formula
                    traced = np.trace((Vui @ Gij @ Vuj @ Gji), axis1=1, axis2=2)
                    # evaluation of the contour integral
                    storage.append(np.trapz(-1 / np.pi * np.imag(traced * cont.we)))

            # fill up the pairs dictionary with the energies
            pairs[tracker]["energies"].append(storage)

    end_time = timer()

    print("############################### GROGU OUTPUT ###################################")
    print("================================================================================")
    print("Input file: ")
    print(simulation_parameters["path"])
    print("Number of nodes in the parallel cluster: ", simulation_parameters["parallel_size"])
    print("================================================================================")
    try:
        print("Cell [Ang]: ")
        print(simulation_parameters["geom"].cell)
    except:
        print("Geometry could not be read.")
    print("================================================================================")
    print("DFT axis: ")
    print(simulation_parameters["scf_xcf_orientation"])
    print("Quantization axis and perpendicular rotation directions:")
    for ref in ref_xcf_orientations:
        print(ref["o"], " --» ", ref["vw"])
    print("================================================================================")
    print("number of k points: ", simulation_parameters["kset"])
    print("k point directions: ", simulation_parameters["kdirs"])
    print("================================================================================")
    print("Parameters for the contour integral:")
    print("Ebot: ", simulation_parameters["ebot"])
    print("Eset: ", simulation_parameters["eset"])
    print("Esetp: ", simulation_parameters["esetp"])
    print("================================================================================")
    print("Atomic informations: ")
    print("")
    print("")
    print("Not yet specified.")
    print("")
    print("")
    print("================================================================================")
    print("Exchange [meV]")
    print("--------------------------------------------------------------------------------")
    print("Atom1    Atom2   [i  j  k]   d [Ang]")
    print("--------------------------------------------------------------------------------")
    for pair in pairs:
        J_iso, J_S, D = calculate_exchange_tensor(pair)
        J_iso = J_iso * sisl.unit_convert("eV", "meV")
        J_S = J_S * sisl.unit_convert("eV", "meV")
        D = D * sisl.unit_convert("eV", "meV")
        
        print(pair["ai"], pair["aj"], pair["Ruc"], "distance")
        print("Isotropic: ", J_iso)
        print("DMI: ", D)
        print("Symmetric-anisotropy: ", J_S)
        print("")
    
    print("================================================================================")
    print("Runtime information: ")
    print("Total runtime: ", end_time - start_time)
    print("--------------------------------------------------------------------------------")
    print("Initial setup: ", setup_time - start_time)
    print(f"Hamiltonian conversion and XC field extraction: {H_and_XCF_time - setup_time:.3f} s")
    print(f"Pair and site datastructure creatrions: {site_and_pair_dictionaries_time - H_and_XCF_time:.3f} s")
    print(f"k set cration and distribution: {k_set_time - site_and_pair_dictionaries_time:.3f} s")
    print(f"Rotating XC potential: {reference_rotations_time - k_set_time:.3f} s")
    print(f"Greens function inversion: {green_function_inversion_time - reference_rotations_time:.3f} s")
    print(f"Calculate energies and magnetic components: {end_time - green_function_inversion_time:.3f} s")