From 38a3be0558f770506e6ae0e7166e7462f3cefa22 Mon Sep 17 00:00:00 2001 From: Daniel Pozsar Date: Sat, 9 Nov 2024 13:31:32 +0100 Subject: [PATCH] working on documentation --- .readthedocs.yaml | 4 +- docs/_build/doctrees/environment.pickle | Bin 29369 -> 124354 bytes docs/_build/doctrees/grogupy.doctree | Bin 0 -> 134083 bytes .../doctrees/implementation/index.doctree | Bin 2496 -> 6981 bytes docs/_build/doctrees/index.doctree | Bin 9502 -> 11227 bytes docs/_build/doctrees/modules.doctree | Bin 0 -> 2783 bytes docs/_build/html/_modules/grogupy/core.html | 525 +++++++++++ docs/_build/html/_modules/grogupy/grogu.html | 587 +++++++++++++ docs/_build/html/_modules/grogupy/io.html | 456 ++++++++++ .../html/_modules/grogupy/magnetism.html | 348 ++++++++ .../html/_modules/grogupy/utilities.html | 457 ++++++++++ docs/_build/html/_modules/index.html | 127 +++ docs/_build/html/_sources/grogupy.rst.txt | 53 ++ .../_sources/implementation/index.rst.txt | 11 +- docs/_build/html/_sources/index.rst.txt | 10 +- docs/_build/html/_sources/modules.rst.txt | 7 + docs/_build/html/environment.html | 4 +- docs/_build/html/genindex.html | 236 ++++- docs/_build/html/grogupy.html | 822 ++++++++++++++++++ docs/_build/html/implementation/index.html | 28 +- docs/_build/html/index.html | 8 + docs/_build/html/modules.html | 179 ++++ docs/_build/html/objects.inv | Bin 592 -> 1171 bytes docs/_build/html/py-modindex.html | 70 +- docs/_build/html/searchindex.js | 2 +- docs/conf.py | 11 +- docs/grogupy.rst | 53 ++ docs/implementation/index.rst | 11 +- docs/index.rst | 10 +- docs/modules.rst | 7 + docs/requirements.txt | 1 + 31 files changed, 4004 insertions(+), 23 deletions(-) create mode 100644 docs/_build/doctrees/grogupy.doctree create mode 100644 docs/_build/doctrees/modules.doctree create mode 100644 docs/_build/html/_modules/grogupy/core.html create mode 100644 docs/_build/html/_modules/grogupy/grogu.html create mode 100644 docs/_build/html/_modules/grogupy/io.html create mode 100644 docs/_build/html/_modules/grogupy/magnetism.html create mode 100644 docs/_build/html/_modules/grogupy/utilities.html create mode 100644 docs/_build/html/_modules/index.html create mode 100644 docs/_build/html/_sources/grogupy.rst.txt create mode 100644 docs/_build/html/_sources/modules.rst.txt create mode 100644 docs/_build/html/grogupy.html create mode 100644 docs/_build/html/modules.html create mode 100644 docs/grogupy.rst create mode 100644 docs/modules.rst diff --git a/.readthedocs.yaml b/.readthedocs.yaml index 49c98f6..0f9c92a 100644 --- a/.readthedocs.yaml +++ b/.readthedocs.yaml @@ -24,8 +24,8 @@ sphinx: fail_on_warning: true # Optionally build your docs in additional formats such as PDF and ePub - formats: - - pdf +# formats: +# - pdf # - epub # Optional but recommended, declare the Python requirements required diff --git a/docs/_build/doctrees/environment.pickle b/docs/_build/doctrees/environment.pickle index 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+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for grogupy.core

+# Copyright (c) [2024] []
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import numpy as np
+from numpy.linalg import inv
+
+from grogupy.magnetism import blow_up_orbindx, parse_magnetic_entity
+from grogupy.utilities import commutator
+
+
+

+[docs]
+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)

+
+
+
+

+[docs]
+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)
+
+    return Gk

+
+
+
+

+[docs]
+def calc_Vu(H, Tu):
+    """Calculates the local perturbation in case of a spin rotation.
+
+    Args:
+        H : (NO, NO) np.array_like
+            Hamiltonian
+        Tu : (NO, NO) array_like
+            Rotation around u
+
+    Returns:
+        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
+    Vu2 = 1 / 8 * commutator(commutator(Tu, H), Tu)  # equation 100
+
+    return Vu1, Vu2

+
+
+
+

+[docs]
+def remove_clutter_for_save(pairs, magnetic_entities):
+    """Removes unimportant data from the dictionaries.
+
+    It is used before saving to throw away data that
+    is not needed for post processing.
+
+    Args:
+        pairs : dict
+            Contains all the pair information
+        magnetic_entities : dict
+            Contains all the magnetic entity information
+
+    Returns:
+        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"]
+        del pair["Gij_tmp"]
+        del pair["Gji"]
+        del pair["Gji_tmp"]
+    for mag_ent in magnetic_entities:
+        del mag_ent["Gii"]
+        del mag_ent["Gii_tmp"]
+        del mag_ent["Vu1"]
+        del mag_ent["Vu2"]
+
+    return pairs, magnetic_entities

+
+
+
+

+[docs]
+def build_hh_ss(dh):
+    """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 : sisl.physics.Hamiltonian
+            Hamiltonian read in by sisl
+
+    Returns:
+        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
+    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
+

+[docs]
+            @ 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())
+        ]
+    )
+
+    return hh, ss

+
+
+
+def setup_pairs_and_magnetic_entities(
+    magnetic_entities, pairs, dh, simulation_parameters
+):
+    """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:
+        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:
+        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
+        mag_ent["orbital_indices"] = parsed
+        mag_ent["spin_box_indices"] = blow_up_orbindx(
+            parsed
+        )  # calculate spin box indexes
+        # 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"] = []
+            # iterate over atoms
+            for atom_idx in mag_ent["atom"]:
+                mag_ent["tags"].append(
+                    f"[{atom_idx}]{dh.atoms[atom_idx].tag}({mag_ent['l']})"
+                )
+                mag_ent["xyz"].append(dh.xyz[atom_idx])
+
+        # calculate size for Greens function generation
+        spin_box_shape = len(mag_ent["spin_box_indices"])
+
+        # 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
+        mag_ent["Vu2"] = []
+
+        mag_ent["Gii"] = []  # Greens function
+        mag_ent["Gii_tmp"] = []  # Greens function for parallelization
+        for _ in simulation_parameters["ref_xcf_orientations"]:
+            # Rotations for every quantization axis
+            mag_ent["Vu1"].append([])
+            mag_ent["Vu2"].append([])
+            # Greens functions for every quantization axis
+            mag_ent["Gii"].append(
+                np.zeros(
+                    (simulation_parameters["eset"], spin_box_shape, spin_box_shape),
+                    dtype="complex128",
+                )
+            )
+            mag_ent["Gii_tmp"].append(
+                np.zeros(
+                    (simulation_parameters["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:
+        # calculate distance
+        xyz_ai = magnetic_entities[pair["ai"]]["xyz"]
+        xyz_aj = magnetic_entities[pair["aj"]]["xyz"]
+        xyz_aj = xyz_aj + pair["Ruc"] @ simulation_parameters["cell"]
+        pair["dist"] = np.linalg.norm(xyz_ai - xyz_aj)
+
+        # 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 = ""
+            # get atoms of magnetic entity
+            atoms_idx = mag_ent["atom"]
+            orbitals = mag_ent["l"]
+
+            # if magnetic entity contains one atoms
+            if isinstance(atoms_idx, int):
+                tag += f"[{atoms_idx}]{dh.atoms[atoms_idx].tag}({orbitals})"
+
+            # if magnetic entity contains more than one atoms
+            if isinstance(atoms_idx, list):
+                # iterate over atoms
+                atom_group = "{"
+                for atom_idx in atoms_idx:
+                    atom_group += f"[{atom_idx}]{dh.atoms[atom_idx].tag}({orbitals})--"
+                # end {} of the atoms in the magnetic entity
+                tag += atom_group[:-2] + "}"
+            pair["tags"].append(tag)
+        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"] = []
+        for _ in simulation_parameters["ref_xcf_orientations"]:
+            # Greens functions for every quantization axis
+            pair["Gij"].append(
+                np.zeros(
+                    (simulation_parameters["eset"], spin_box_shape_i, spin_box_shape_j),
+                    dtype="complex128",
+                )
+            )
+            pair["Gij_tmp"].append(
+                np.zeros(
+                    (simulation_parameters["eset"], spin_box_shape_i, spin_box_shape_j),
+                    dtype="complex128",
+                )
+            )
+            pair["Gji"].append(
+                np.zeros(
+                    (simulation_parameters["eset"], spin_box_shape_j, spin_box_shape_i),
+                    dtype="complex128",
+                )
+            )
+            pair["Gji_tmp"].append(
+                np.zeros(
+                    (simulation_parameters["eset"], spin_box_shape_j, spin_box_shape_i),
+                    dtype="complex128",
+                )
+            )
+
+    return pairs, magnetic_entities

+
+
+
+

+[docs]
+def onsite_projection(matrix, idx1, idx2):
+    """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 : (..., :, :) np.array_like
+            Some matrix
+        idx : np.array_like
+            The indexes of the orbitals
+
+    Returns:
+        np.array_like
+            Reduced matrix based on the projection
+    """
+
+    return matrix[..., idx1, :][..., idx2]

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_modules/grogupy/grogu.html b/docs/_build/html/_modules/grogupy/grogu.html new file mode 100644 index 0000000..bad6d5c --- /dev/null +++ b/docs/_build/html/_modules/grogupy/grogu.html @@ -0,0 +1,587 @@ + + + + + + + + grogupy.grogu — grogupy 1.0.0 documentation + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for grogupy.grogu

+# Copyright (c) [2024] []
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import warnings
+from sys import getsizeof
+from timeit import default_timer as timer
+
+# use numpy number of threads one
+try:
+    from threadpoolctl import threadpool_info, threadpool_limits
+
+    user_api = threadpool_info()["user_api"]
+    threadpool_limits(limits=1, user_api=user_api)
+except:
+    print("Warning: threadpoolctl could not make numpy use single thread!")
+
+import numpy as np
+import sisl
+from mpi4py import MPI
+
+try:
+    from tqdm import tqdm
+
+    tqdm_imported = True
+except:
+    print("Please install tqdm for nice progress bar.")
+    tqdm_imported = False
+
+from grogupy import *
+
+
+

+[docs]
+def main():
+    # runtime information
+    times = dict()
+    times["start_time"] = timer()
+
+    # input output stuff
+    ######################################################################
+    ######################################################################
+    ######################################################################
+
+    infile = "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf"
+    outfile = "./Fe3GeTe2_notebook"
+
+    magnetic_entities = [
+        dict(atom=3, l=2),
+        dict(atom=4, l=2),
+        dict(atom=5, l=2),
+    ]
+    pairs = [
+        dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),
+        dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),
+        dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),
+        dict(ai=0, aj=2, Ruc=np.array([-1, -1, 0])),
+        dict(ai=1, aj=2, Ruc=np.array([-1, -1, 0])),
+        dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),
+        dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),
+        dict(ai=1, aj=2, Ruc=np.array([-2, 0, 0])),
+        dict(ai=1, aj=2, Ruc=np.array([-3, 0, 0])),
+    ]
+    simulation_parameters = default_args
+    simulation_parameters["infile"] = infile
+    simulation_parameters["outfile"] = outfile
+    simulation_parameters["kset"] = 20
+    simulation_parameters["kdirs"] = "xy"
+    simulation_parameters["eset"] = 600
+    simulation_parameters["esetp"] = 10000
+
+    ######################################################################
+    ######################################################################
+    ######################################################################
+
+    # 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
+        try:
+            print("sisl version: ", sisl.__version__)
+        except:
+            print("sisl version unknown.")
+        try:
+            print("numpy version: ", np.__version__)
+        except:
+            print("numpy version unknown.")
+
+        # rename outfile
+        if not simulation_parameters["outfile"].endswith(".pickle"):
+            simulation_parameters["outfile"] += ".pickle"
+
+        # if ebot is not given put it 0.1 eV under the smallest energy
+        if simulation_parameters["ebot"] is None:
+            try:
+                eigfile = simulation_parameters["infile"][:-3] + "EIG"
+                simulation_parameters["ebot"] = read_siesta_emin(eigfile) - 0.1
+                simulation_parameters["automatic_ebot"] = True
+            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"])
+
+    # read in hamiltonian
+    dh = fdf.read_hamiltonian()
+
+    # read unit cell vectors
+    simulation_parameters["cell"] = fdf.read_geometry().cell
+
+    # unit cell index
+    uc_in_sc_idx = dh.lattice.sc_index([0, 0, 0])
+
+    if rank == root_node:
+        print("\n\n\n\n\n")
+        print(
+            "#################################################################### JOB INFORMATION ###########################################################################"
+        )
+        print_job_description(simulation_parameters)
+        print(
+            "################################################################################################################################################################"
+        )
+        print("\n\n\n\n\n")
+
+        times["setup_time"] = timer()
+        print(f"Setup done. Elapsed time: {times['setup_time']} s")
+        print(
+            "================================================================================================================================================================"
+        )
+
+    NO = dh.no  # shorthand for number of orbitals in the unit cell
+
+    # reformat Hamltonian and Overlap matrix for manipulations
+    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]):
+        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"] / 2 for f in traced]),
+            np.array([f["y"] / 2 for f in traced]),
+            np.array([f["z"] / 2 for f in traced]),
+        ]
+    )
+
+    # check if exchange field has scalar part
+    max_xcfs = abs(np.array(np.array([f["c"] / 2 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}"
+        )
+
+    if rank == root_node:
+        times["H_and_XCF_time"] = timer()
+        print(
+            f"Hamiltonian and exchange field rotated. Elapsed time: {times['H_and_XCF_time']} s"
+        )
+        print(
+            "================================================================================================================================================================"
+        )
+
+    # initialize pairs and magnetic entities based on input information
+    pairs, magnetic_entities = setup_pairs_and_magnetic_entities(
+        magnetic_entities, pairs, dh, simulation_parameters
+    )
+
+    if rank == root_node:
+        times["site_and_pair_dictionaries_time"] = timer()
+        print(
+            f"Site and pair dictionaries created. Elapsed time: {times['site_and_pair_dictionaries_time']} s"
+        )
+        print(
+            "================================================================================================================================================================"
+        )
+
+    # generate k space sampling
+    kset = make_kset(
+        dirs=simulation_parameters["kdirs"], NUMK=simulation_parameters["kset"]
+    )
+
+    # generate weights for k points
+    wkset = np.ones(len(kset)) / len(kset)
+
+    # split the k points based on MPI size
+    kpcs = np.array_split(kset, size)
+
+    # use progress bar if available
+    if rank == root_node and tqdm_imported:
+        kpcs[root_node] = tqdm(kpcs[root_node], desc="k loop")
+
+    if rank == root_node:
+        times["k_set_time"] = timer()
+        print(f"k set created. Elapsed time: {times['k_set_time']} s")
+        print(
+            "================================================================================================================================================================"
+        )
+
+    # this will contain the three Hamiltonian in the
+    # reference directions needed to calculate the energy
+    # variations upon rotation
+    hamiltonians = []
+
+    # iterate over the reference directions (quantization axes)
+    for i, orient in enumerate(simulation_parameters["ref_xcf_orientations"]):
+        # obtain rotated exchange field and Hamiltonian
+        R = RotMa2b(simulation_parameters["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
+
+        # store the relevant information of the Hamiltonian
+        hamiltonians.append(dict(orient=orient["o"], H=rot_H))
+
+        # these are the rotations (for now) perpendicular to the quantization axis
+        for u in orient["vw"]:
+            # section 2.H
+            Tu = np.kron(np.eye(NO, dtype=int), tau_u(u))
+            Vu1, Vu2 = calc_Vu(rot_H_XCF_uc, Tu)
+
+            for mag_ent in magnetic_entities:
+                idx = mag_ent["spin_box_indices"]
+                # fill up the perturbed potentials (for now) based on the on-site projections
+                mag_ent["Vu1"][i].append(onsite_projection(Vu1, idx, idx))
+                mag_ent["Vu2"][i].append(onsite_projection(Vu2, idx, idx))
+
+    if rank == root_node:
+        times["reference_rotations_time"] = timer()
+        print(
+            f"Rotations done perpendicular to quantization axis. Elapsed time: {times['reference_rotations_time']} s"
+        )
+        print(
+            "================================================================================================================================================================"
+        )
+
+    # provide helpful information to estimate the runtime and memory
+    # requirements of the Greens function calculations
+    if rank == root_node:
+        print("Starting matrix inversions.")
+        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"Total number of directions: {len(hamiltonians)}")
+            print(
+                f"Total number of matrix inversions: {kset.shape[0] * len(hamiltonians) * simulation_parameters['eset']}"
+            )
+            print(
+                f"The shape of the Hamiltonian and the Greens function is {NO}x{NO}={NO*NO}"
+            )
+            # https://stackoverflow.com/questions/70746660/how-to-predict-memory-requirement-for-np-linalg-inv
+            # memory is O(64 n**2) for complex matrices
+            memory_size = getsizeof(hamiltonians[0]["H"].base) / 1024
+            print(
+                f"Memory taken by a single Hamiltonian is: {getsizeof(hamiltonians[0]['H'].base) / 1024} KB"
+            )
+            print(f"Expected memory usage per matrix inversion: {memory_size * 32} KB")
+            print(
+                f"Expected memory usage per k point for parallel inversion: {memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32} KB"
+            )
+            print(
+                f"Expected memory usage on root node: {len(np.array_split(kset, size)[0]) * memory_size * len(hamiltonians) * simulation_parameters['eset'] * 32 / 1024} MB"
+            )
+        print(
+            "================================================================================================================================================================"
+        )
+
+    # MPI barrier
+    comm.Barrier()
+
+    # make energy contour
+    cont = make_contour(
+        emin=simulation_parameters["ebot"],
+        enum=simulation_parameters["eset"],
+        p=simulation_parameters["esetp"],
+    )
+    eran = cont.ze
+
+    # sampling the integrand on the contour and the BZ
+    for k in kpcs[rank]:
+        # weight of k point in BZ integral
+        wk = wkset[rank]
+
+        # iterate over reference directions
+        for i, hamiltonian_orientation in enumerate(hamiltonians):
+            # calculate Hamiltonian and Overlap matrix in a given k point
+            H = hamiltonian_orientation["H"]
+            HK, SK = hsk(H, ss, dh.sc_off, k)
+
+            if simulation_parameters["parallel_solver_for_Gk"]:
+                Gk = parallel_Gk(HK, SK, eran, simulation_parameters["eset"])
+            else:
+                # solve Greens function sequentially for the energies, because of memory bound
+                Gk = sequential_GK(HK, SK, eran, simulation_parameters["eset"])
+
+            # store the Greens function slice of the magnetic entities
+            for mag_ent in magnetic_entities:
+                idx = mag_ent["spin_box_indices"]
+                mag_ent["Gii_tmp"][i] += onsite_projection(Gk, idx, idx) * 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_indices"]
+                aj = magnetic_entities[pair["aj"]]["spin_box_indices"]
+
+                # store the Greens function slice of the magnetic entities
+                pair["Gij_tmp"][i] += onsite_projection(Gk, ai, aj) * phase * wk
+                pair["Gji_tmp"][i] += onsite_projection(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)
+
+    if rank == root_node:
+        times["green_function_inversion_time"] = timer()
+        print(
+            f"Calculated Greens functions. Elapsed time: {times['green_function_inversion_time']} s"
+        )
+        print(
+            "================================================================================================================================================================"
+        )
+
+    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
+                    )  # this is the on site projection
+                    # evaluation of the contour integral
+                    storage.append(int_de_ke(traced, cont.we))
+                # fill up the magnetic entities dictionary with the energies
+                magnetic_entities[tracker]["energies"].append(storage)
+            # convert to np array
+            magnetic_entities[tracker]["energies"] = np.array(
+                magnetic_entities[tracker]["energies"]
+            )
+
+        # 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
+                        )  # this is the on site projection
+                        # evaluation of the contour integral
+                        storage.append(int_de_ke(traced, cont.we))
+                # fill up the pairs dictionary with the energies
+                pairs[tracker]["energies"].append(storage)
+            # convert to np array
+            pairs[tracker]["energies"] = np.array(pairs[tracker]["energies"])
+
+        # calculate magnetic parameters
+        for mag_ent in magnetic_entities:
+            Kxx, Kyy, Kzz, consistency = calculate_anisotropy_tensor(mag_ent)
+            mag_ent["K"] = np.array([Kxx, Kyy, Kzz]) * sisl.unit_convert("eV", "meV")
+            mag_ent["K_consistency"] = consistency
+
+        for pair in pairs:
+            J_iso, J_S, D, J = calculate_exchange_tensor(pair)
+            pair["J_iso"] = J_iso * sisl.unit_convert("eV", "meV")
+            pair["J_S"] = J_S * sisl.unit_convert("eV", "meV")
+            pair["D"] = D * sisl.unit_convert("eV", "meV")
+            pair["J"] = J * sisl.unit_convert("eV", "meV")
+
+        times["end_time"] = timer()
+        print("\n\n\n\n\n")
+        print(
+            "##################################################################### GROGU OUTPUT #############################################################################"
+        )
+
+        print_parameters(simulation_parameters)
+        print_atoms_and_pairs(magnetic_entities, pairs)
+        print(
+            "################################################################################################################################################################"
+        )
+        print_runtime_information(times)
+        print("")
+
+        # remove unwanted stuff before saving
+        pairs, magnetic_entities = remove_clutter_for_save(pairs, magnetic_entities)
+        # create output dictionary with all the relevant data
+        results = dict(
+            parameters=simulation_parameters,
+            magnetic_entities=magnetic_entities,
+            pairs=pairs,
+            runtime=times,
+        )
+
+        # save results
+        save_pickle(simulation_parameters["outfile"], results)
+
+        print("\n\n\n\n\n")

+
+
+
+if __name__ == "__main__":
+    main()
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_modules/grogupy/io.html b/docs/_build/html/_modules/grogupy/io.html new file mode 100644 index 0000000..5794a71 --- /dev/null +++ b/docs/_build/html/_modules/grogupy/io.html @@ -0,0 +1,456 @@ + + + + + + + + grogupy.io — grogupy 1.0.0 documentation + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for grogupy.io

+# Copyright (c) [2024] []
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+from argparse import ArgumentParser
+from pickle import dump, load
+
+import numpy as np
+
+default_args = dict(
+    infile=None,
+    outfile=None,
+    scf_xcf_orientation=np.array([0, 0, 1]),
+    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])]),
+    ],
+    kset=2,
+    kdirs="xyz",
+    ebot=None,
+    eset=42,
+    esetp=1000,
+    parallel_solver_for_Gk=False,
+    padawan_mode=True,
+)
+
+# parser = ArgumentParser()
+
+# parser.add_argument('--input'   , dest = 'infile' , default=None                       , help = 'Input file name')
+# parser.add_argument('--output'  , dest = 'outfile', default=None                       , help = 'Output file name')
+
+# parser.add_argument('--kset'    , dest = 'kset'   , default  = 2           , type=int  , help = 'k-space resolution of Jij calculation')
+# parser.add_argument('--kdirs'   , dest = 'kdirs'  , default  = 'xyz'                   , help = 'Definition of k-space dimensionality')
+# parser.add_argument('--ebot'    , dest = 'ebot'   , default  = None        , type=float, help = 'Bottom energy of the contour')
+# parser.add_argument('--eset'    , dest = 'eset'   , default  = 42          , type=int  , help = 'Number of energy points on the contour')
+# parser.add_argument('--eset-p'  , dest = 'esetp'  , default  = 1000        , type=int  , help = 'Parameter tuning the distribution on the contour')
+
+# cmd_line_args = parser.parse_args()
+
+
+

+[docs]
+def save_pickle(outfile, data):
+    """Saves the data in the outfile with pickle.
+
+    Args:
+        outfile : str
+            Path to outfile
+        data : dict
+            Contains the data
+    """
+
+    # save dictionary
+    with open(outfile, "wb") as output_file:
+        dump(data, output_file)

+
+
+
+

+[docs]
+def load_pickle(infile):
+    """Loads the data from the infile with pickle.
+
+    Args:
+        infile : str
+            Path to infile
+
+    Returns:
+        data : dict
+            A dictionary of data
+    """
+
+    # open and read file
+    with open(infile, "wb") as input_file:
+        data = load(data, input_file)
+
+    return data

+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_modules/grogupy/magnetism.html b/docs/_build/html/_modules/grogupy/magnetism.html new file mode 100644 index 0000000..bf2e92a --- /dev/null +++ b/docs/_build/html/_modules/grogupy/magnetism.html @@ -0,0 +1,348 @@ + + + + + + + + grogupy.magnetism — grogupy 1.0.0 documentation + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for grogupy.magnetism

+# Copyright (c) [2024] []
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import numpy as np
+
+
+

+[docs]
+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

+
+
+
+

+[docs]
+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

+
+
+
+

+[docs]
+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.

+
+
+
+

+[docs]
+def calculate_anisotropy_tensor(mag_ent):
+    """Calculates the renormalized anisotropy tensor from the energies.
+
+    It uses the grogu convention for output.
+
+    Args:
+        mag_ent : dict
+            An element from the magnetic entities
+
+    Returns:
+        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)
+
+    return Kxx, Kyy, Kzz, consistency_check

+
+
+
+

+[docs]
+def calculate_exchange_tensor(pair):
+    """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 : dict
+            An element from the pairs
+
+    Returns:
+        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))
+    D = np.zeros(3)
+
+    # J matrix calculations
+    # J(1,1) = mean([DEij(2,2,2), DEij(2,2,3)])
+    J[0, 0] = np.mean([energies[1, 3], energies[2, 3]])
+
+    # J(1,2) = -mean([DEij(1,2,3), DEij(2,1,3)])
+    J[0, 1] = -np.mean([energies[2, 1], energies[2, 2]])
+    J[1, 0] = J[0, 1]
+
+    # J(1,3) = -mean([DEij(1,2,2), DEij(2,1,2)])
+    J[0, 2] = -np.mean([energies[1, 1], energies[1, 2]])
+    J[2, 0] = J[0, 2]
+
+    # J(2,2) = mean([DEij(2,2,1), DEij(1,1,3)])
+    J[1, 1] = np.mean([energies[0, 3], energies[2, 0]])
+
+    # J(2,3) = -mean([DEij(1,2,1), DEij(2,1,1)])
+    J[1, 2] = -np.mean([energies[0, 1], energies[0, 2]])
+    J[2, 1] = J[1, 2]
+
+    # J(3,3) = mean([DEij(1,1,1), DEij(1,1,2)])
+    J[2, 2] = np.mean([energies[0, 0], energies[1, 0]])
+
+    # D vector calculations
+    # D(1) = mean([DEij(1,2,1), -DEij(2,1,1)])
+    D[0] = np.mean([energies[0, 1], -energies[0, 2]])
+
+    # D(2) = mean([DEij(2,1,2), -DEij(1,2,2)])
+    D[1] = np.mean([energies[1, 2], -energies[1, 1]])
+
+    # D(3) = mean([DEij(1,2,3), -DEij(2,1,3)])
+    D[2] = np.mean([energies[2, 1], -energies[2, 2]])
+
+    J_iso = np.trace(J) / 3
+    # based on the grogu output pdf
+    # traceless symmetric exchange matrix:
+    # Jxx, Jyy, Jxy, Jxz, Jyz
+    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

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_modules/grogupy/utilities.html b/docs/_build/html/_modules/grogupy/utilities.html new file mode 100644 index 0000000..c7f9775 --- /dev/null +++ b/docs/_build/html/_modules/grogupy/utilities.html @@ -0,0 +1,457 @@ + + + + + + + + grogupy.utilities — grogupy 1.0.0 documentation + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for grogupy.utilities

+# Copyright (c) [2024] []
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import numpy as np
+from scipy.special import roots_legendre
+from sisl.io.siesta import eigSileSiesta
+
+# Pauli matrices
+tau_x = np.array([[0, 1], [1, 0]])
+tau_y = np.array([[0, -1j], [1j, 0]])
+tau_z = np.array([[1, 0], [0, -1]])
+tau_0 = np.array([[1, 0], [0, 1]])
+
+
+

+[docs]
+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
+

+[docs]
+def hsk(H, ss, sc_off, k=(0, 0, 0)):
+    """Speed up Hk and Sk generation.
+
+    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)
+
+    Returns:
+        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
+    k = np.asarray(k, np.float64)
+    k.shape = (-1,)
+
+    # this generates the list of phases
+    phases = np.exp(-1j * 2 * np.pi * k @ sc_off.T)
+
+    # phases applied to the hamiltonian
+    HK = np.einsum("abc,a->bc", H, phases)
+    SK = np.einsum("abc,a->bc", ss, phases)
+
+    return HK, SK

+
+
+
+

+[docs]
+def make_kset(dirs="xyz", NUMK=20):
+    """Simple k-grid generator to sample the Brillouin zone.
+
+    Depending on the value of the dirs
+    argument k sampling in 1,2 or 3 dimensions is generated.
+    If dirs argument does not contain either of x, y or z
+    a kset of a single k-pont at the origin is returned. The total number of k points is the NUMK**(dimensions)
+
+
+    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
+
+    Returns:
+        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]])
+
+    kran = len(dirs) * [np.linspace(0, 1, NUMK, endpoint=False)]
+    mg = np.meshgrid(*kran)
+    dirsdict = dict()
+
+    for d in enumerate(dirs):
+        dirsdict[d[1]] = mg[d[0]].flatten()
+    for d in "xyz":
+        if not (d in dirs):
+            dirsdict[d] = 0 * dirsdict[dirs[0]]
+    kset = np.array([dirsdict[d] for d in "xyz"]).T
+
+    return kset

+
+
+
+

+[docs]
+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. It uses the
+    Legendre-Gauss quadrature method.   It returns a class that contains
+    the information for the 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
+            Contains all the information for the contour integral
+    """
+    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

+
+
+
+

+[docs]
+def tau_u(u):
+    """Pauli matrix in direction u.
+
+    Returns the vector u in the basis of the Pauli matrices.
+
+    Args:
+        u : list or np.array_like
+            The direction
+
+    Returns:
+        np.array_like
+            Arbitrary direction in the base of the Pauli matrices
+    """
+
+    # u is force to be of unit length
+    u = u / np.linalg.norm(u)
+
+    return u[0] * tau_x + u[1] * tau_y + u[2] * tau_z

+
+
+
+#
+

+[docs]
+def crossM(u):
+    """Definition for the cross-product matrix.
+
+    It acts as a cross product with vector u.
+
+    Args:
+        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
+    """
+    return np.array([[0, -u[2], u[1]], [u[2], 0, -u[0]], [-u[1], u[0], 0]])

+
+
+
+

+[docs]
+def RotM(theta, u, eps=1e-10):
+    """Definition of rotation matrix with angle theta around direction u.
+
+
+    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
+
+    Returns:
+        np.array_like
+            The rotation matrix
+    """
+
+    u = u / np.linalg.norm(u)
+
+    M = (
+        np.cos(theta) * np.eye(3)
+        + np.sin(theta) * crossM(u)
+        + (1 - np.cos(theta)) * np.outer(u, u)
+    )
+
+    # kill off small numbers
+    M[abs(M) < eps] = 0.0
+    return M

+
+
+
+

+[docs]
+def RotMa2b(a, b, eps=1e-10):
+    """Definition of rotation matrix rotating unit vector a to unit vector b.
+
+    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
+
+    Returns:
+        np.array_like
+            The rotation matrix with the above property
+    """
+
+    v = np.cross(a, b)
+    c = a @ b
+    M = np.eye(3) + crossM(v) + crossM(v) @ crossM(v) / (1 + c)
+
+    # kill off small numbers
+    M[abs(M) < eps] = 0.0
+    return M

+
+
+
+

+[docs]
+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:
+        eigfile : str
+            The path to the .EIG file
+
+    Returns:
+        float
+            The energy minimum
+    """
+
+    # read the file
+    eigs = eigSileSiesta(eigfile).read_data()
+
+    return eigs.min()

+
+
+
+

+[docs]
+def int_de_ke(traced, we):
+    """It numerically integrates the traced matrix.
+
+    It is a wrapper from numpy.trapz and it contains the
+    relevant constants to calculate the energy integral from
+    equation 93 or 96.
+
+    Args:
+        traced : np.array_like
+            The trace of a matrix or a matrix product
+        we : float
+            The weight of a point on the contour
+
+    Returns:
+        float
+            The energy calculated from the integral formula
+    """
+
+    return np.trapz(-1 / np.pi * np.imag(traced * we))

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_modules/index.html b/docs/_build/html/_modules/index.html new file mode 100644 index 0000000..420bb05 --- /dev/null +++ b/docs/_build/html/_modules/index.html @@ -0,0 +1,127 @@ + + + + + + + + Overview: module code — grogupy 1.0.0 documentation + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Overview: module code
    • +
  • +
    • +
+
+
+
+
+ +

All modules for which code is available

+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/docs/_build/html/_sources/grogupy.rst.txt b/docs/_build/html/_sources/grogupy.rst.txt new file mode 100644 index 0000000..18af50d --- /dev/null +++ b/docs/_build/html/_sources/grogupy.rst.txt @@ -0,0 +1,53 @@ +grogupy package +=============== + +Submodules +---------- + +grogupy.core module +------------------- + +.. automodule:: grogupy.core + :members: + :undoc-members: + :show-inheritance: + +grogupy.grogu module +-------------------- + +.. automodule:: grogupy.grogu + :members: + :undoc-members: + :show-inheritance: + +grogupy.io module +----------------- + +.. automodule:: grogupy.io + :members: + :undoc-members: + :show-inheritance: + +grogupy.magnetism module +------------------------ + +.. automodule:: grogupy.magnetism + :members: + :undoc-members: + :show-inheritance: + +grogupy.utilities module +------------------------ + +.. automodule:: grogupy.utilities + :members: + :undoc-members: + :show-inheritance: + +Module contents +--------------- + +.. automodule:: grogupy + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/_build/html/_sources/implementation/index.rst.txt b/docs/_build/html/_sources/implementation/index.rst.txt index 2e4c4a7..cca03c6 100644 --- a/docs/_build/html/_sources/implementation/index.rst.txt +++ b/docs/_build/html/_sources/implementation/index.rst.txt @@ -1,2 +1,11 @@ Implementation -============== \ No newline at end of file +============== + +.. autosummary:: + :toctree: generated + :recursive: + + core + magnetism + utilities + io \ No newline at end of file diff --git a/docs/_build/html/_sources/index.rst.txt b/docs/_build/html/_sources/index.rst.txt index ada1368..e4aad29 100644 --- a/docs/_build/html/_sources/index.rst.txt +++ b/docs/_build/html/_sources/index.rst.txt @@ -71,4 +71,12 @@ More on the theoretical background can be seen `here - + @@ -101,7 +101,7 @@