Source code for slothpy.core.compound_object

from os import path
from typing import Tuple, Union

from h5py import File, Group, Dataset
from numpy import (
    ndarray,
    array,
    float64,
    int64,
    complex128,
    linspace,
    arange,
    max,
)
from matplotlib.ticker import AutoMinorLocator, MultipleLocator
from matplotlib.gridspec import GridSpec
from matplotlib.animation import PillowWriter
from matplotlib.widgets import Slider
from matplotlib.ticker import FuncFormatter
from matplotlib.pyplot import (
    Normalize,
    plot,
    figure,
    subplots,
    rc,
    tight_layout,
    title,
    show,
    cla,
)

from slothpy.core._slothpy_exceptions import (
    SltFileError,
    SltCompError,
    SltSaveError,
    SltReadError,
    SltInputError,
    SltPlotError,
)
from slothpy._general_utilities._constants import (
    RED,
    GREEN,
    BLUE,
    PURPLE,
    RESET,
)
from slothpy._magnetism._g_tensor import _g_tensor_and_axes_doublet
from slothpy._magnetism._magnetisation import _mth, _mag_3d
from slothpy._magnetism._susceptibility import (
    _chitht,
    _chitht_tensor,
    _chit_3d,
)
from slothpy._magnetism._zeeman import (
    _zeeman_splitting,
    _get_zeeman_matrix,
    _helmholtz_energyth,
    _helmholtz_energy_3d,
)
from slothpy._general_utilities._grids_over_hemisphere import (
    lebedev_laikov_grid,
)
from slothpy._general_utilities._io import (
    _group_exists,
    _get_soc_energies_cm_1,
    _get_states_magnetic_momenta,
    _get_states_total_angular_momenta,
    _get_total_angular_momneta_matrix,
    _get_magnetic_momenta_matrix,
)
from slothpy._angular_momentum._pseudo_spin_ito import (
    _get_decomposition_in_z_pseudo_spin_basis,
    _ito_real_decomp_matrix,
    _ito_complex_decomp_matrix,
    _get_soc_matrix_in_z_pseudo_spin_basis,
    _get_zeeman_matrix_in_z_pseudo_spin_basis,
    _matrix_from_ito_complex,
    _matrix_from_ito_real,
)
from slothpy._general_utilities._math_expresions import (
    _normalize_grid_vectors,
    _normalize_orientations,
    _normalize_orientation,
)
from slothpy._general_utilities._auto_tune import _auto_tune
from slothpy._general_utilities._ploting_utilities import (
    colour_map,
    _custom_colour_cycler,
)


[docs] class Compound: """ The core object constituting the API and access to all the methods. """ @classmethod def _new(cls, filepath: str, filename: str): """ This is a private method for initializing the Compound object that should be only used by the creation_functions. Parameters ---------- filepath : str A path of the file that will be associated with the created instance of the Compound class. filename : str A name of the file that will be associated with the created instance of the Compound class. Returns ------- Compound An instance of the Compound class. """ filename += ".slt" hdf5_file = path.join(filepath, filename) obj = super().__new__(cls) obj._hdf5 = hdf5_file obj._get_hdf5_groups_datasets_and_attributes() return obj def __new__(cls, *args, **kwargs) -> None: """ The definition of this method prevents direct instantialization of the Compound class. Raises ------ TypeError Prevents Compound() from working. """ raise TypeError( "The Compound object should not be instantiated " "directly. Use a Compound creation function instead." ) def __repr__(self) -> str: """ Performs the operation __repr__. Creates a representation of the Compound object using names and attributes of the groups contained in the associated .slt file. Returns ------- str A representation in terms of the contents of the .slt file. """ representation = ( RED + "Compound " + RESET + "from " + GREEN + "File " + RESET + f'"{self._hdf5}" with the following ' + BLUE + "Groups " + RESET + "of data:\n" ) for group, attributes in self._groups.items(): representation += BLUE + f"{group}" + RESET + f": {attributes}\n" if self._datasets: representation += "and " + PURPLE + "Datasets" + RESET + ":\n" for dataset in self._datasets: representation += PURPLE + f"{dataset}\n" + RESET return representation # Set __str__ the same as an object representation using __repr__. __str__ = __repr__ def __setitem__( self, key: Union[ str, Tuple[str, str], Tuple[str, str, str], Tuple[str, str, str, str], ], value: ndarray, ) -> None: """ Performs the operation __setitem__. Provides a convenient method for setting groups and datasets in the .slt file associated with a Compund instance in an array-like manner. Parameters ---------- key : Union[str, Tuple[str, str], Tuple[str, str, str], Tuple[str, str, str]] A string or a 2/3/4-tuple of strings representing a dataset or group/dataset/dataset atribute/group atribute (Description), respectively, to be created or added (to the existing group). value : ndarray An ArrayLike structure (can be converted to ndarray) that will be stored in the dataset or group/dataset provided by the key. Raises ------ SltSaveError If setting the data set was unsuccessful. KeyError If the key is not a string or 2-tuple of strings. """ value = array(value) if isinstance(key, str): self._set_single_dataset(key, value) elif ( isinstance(key, tuple) and (len(key) in [2, 3, 4]) and all(isinstance(k, str) for k in key) ): self._set_group_and_dataset(key, value) else: raise KeyError( "Invalid key type. It has to be str or a 2/3/4-tuple of str." ) def __getitem__(self, key: Union[str, Tuple[str, str]]) -> ndarray: """ Performs the operation __getitem__. Provides a convenient method for getting datasets from the .slt file associated with a Compund instance in an array-like manner. Parameters ---------- key : Union[str, Tuple[str, str], Tuple[str, str, str]] A string or a 2-tuple of strings representing a dataset or group/dataset, respectively, to be read from the .slt file. Returns ------- ndarray An array contained in the dataset associated with the provided key. Raises ------ SltReadError If reading the data from dataset set was unsuccessful. KeyError If the key is not a string or 2-tuple of strings. """ if isinstance(key, str): return self._get_data_from_dataset(key) if ( isinstance(key, tuple) and len(key) >= 2 and all(isinstance(k, str) for k in key) ): return self._get_data_from_group_dataset(key) else: raise KeyError( "Invalid key type. It has to be str or 2-tuple of str." ) def _get_hdf5_groups_datasets_and_attributes(self): self._groups = {} self._datasets = [] def collect_objects(name, obj): if isinstance(obj, Group): self._groups[name] = dict(obj.attrs) elif isinstance(obj, Dataset): self._datasets.append(name) with File(self._hdf5, "r") as file: file.visititems(collect_objects) def _set_single_dataset(self, name: str, value: ndarray): try: with File(self._hdf5, "r+") as file: new_dataset = file.create_dataset( name, shape=value.shape, dtype=value.dtype ) new_dataset[:] = value[:] self._get_hdf5_groups_datasets_and_attributes() except Exception as exc: raise SltSaveError( self._hdf5, exc, message=f'Failed to set a Dataset: "{name}" in the .slt file', ) from None def _set_group_and_dataset( self, names: Union[ Tuple[str, str], Tuple[str, str, str], Tuple[str, str, str, str] ], value: ndarray, ): try: with File(self._hdf5, "r+") as file: if names[0] in file and isinstance(file[names[0]], Group): group = file[names[0]] else: group = file.create_group(names[0]) if len(names) == 4: group.attrs["Description"] = names[3] new_dataset = group.create_dataset( names[1], shape=value.shape, dtype=value.dtype ) new_dataset[:] = value[:] if len(names) >= 3: new_dataset.attrs["Description"] = names[2] self._get_hdf5_groups_datasets_and_attributes() except Exception as exc: raise SltSaveError( self._hdf5, exc, message=( f'Failed to set a Dataset: "{names[1]}" within the Group:' f' "{names[0]}" in the .slt file' ), ) from None def _get_data_from_dataset(self, name: str) -> ndarray: try: with File(self._hdf5, "r") as file: value = file[name][:] except Exception as exc: raise SltReadError( self._hdf5, exc, message=( f'Failed to get a Dataset: "{name}" from the .slt file' ), ) from None return value def _get_data_from_group_dataset(self, names: Tuple[str, str]) -> ndarray: try: with File(self._hdf5, "r") as file: value = file[names[0]][names[1]][:] except Exception as exc: raise SltReadError( self._hdf5, exc, message=( f'Failed to get a Dataset: "{names[0]}/{names[1]}" from' " the .slt file" ), ) from None return value
[docs] def delete_group_dataset(self, first: str, second: str = None) -> None: """ Deletes a group/dataset provided its full name/path from the .slt file. Parameters ---------- first : str A name of the gorup or dataset to be deleted. second : str, optional A name of the particular dataset inside the group from the first argument to be deleted. Raises ------ SltFileError If the deletion is unsuccessful. """ try: with File(self._hdf5, "r+") as file: if second is None: del file[first] else: del file[first][second] except Exception as exc: raise SltFileError( self._hdf5, exc, message=( f'Failed to delete "{first}"' + (f"/{second}" if second is not None else "") + " from the .slt file" ), ) from None self._get_hdf5_groups_datasets_and_attributes()
[docs] def calculate_g_tensor_and_axes_doublet( self, group: str, doublets: ndarray[int64], slt: str = None ) -> Tuple[ndarray[float64], ndarray[float64]]: """ Calculates pseudo-g-tensor components (for S = 1/2) and main magnetic axes for a given list of doublet states. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of g-tensors. doublets : ndarray[int64] ArrayLike structure (can be converted to numpy.NDArray) of integers corresponding to doublet labels (numbers). slt : str, optional If given, the results will be saved using this name to the .slt file with the suffix: _g_tensors_axes, by default None. Returns ------- Tuple[ndarray[float64], ndarray[float64]] The first array (g_tensor_list) contains a list g-tensors in a format [doublet_number, gx, gy, gz], the second one (magnetic_axes_list) contains respective rotation matrices. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If doublets are not one-diemsional array. SltCompError If the calculation of g-tensors is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ---- Magnetic axes are returned in the form of rotation matrices that diagonalise the Abragam-Bleaney tensor (G = gg.T). Coordinates of the main axes XYZ in the initial xzy frame are columns of such matrices (0-X, 1-Y, 2-Z). See Also -------- slothpy.exporting.table_energy_and_g, slothpy.exporting.axes_in_mol2, slothpy.exporting.axes_in_xyz """ if slt is not None: slt_group_name = f"{slt}_g_tensors_axes" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually", ) from None try: doublets = array(doublets, dtype=int64) except Exception as exc: raise SltInputError(exc) from None if doublets.ndim != 1: raise SltInputError( ValueError("The list of doublets has to be a 1D array.") ) from None try: ( g_tensor_list, magnetic_axes_list, ) = _g_tensor_and_axes_doublet(self._hdf5, group, doublets) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute g-tensors and main magnetic axes from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_g_tensors", "Dataset containing number of doublet and respective" f" g-tensors from Group {group}.", f"Group({slt}) containing g-tensors of doublets and" f" their magnetic axes calculated from Group: {group}.", ] = g_tensor_list[:, :] self[ slt_group_name, f"{slt}_axes", "Dataset containing rotation matrices from the initial" " coordinate system to the magnetic axes of respective" f" g-tensors from Group: {group}.", ] = magnetic_axes_list[:, :, :] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save g-tensors and magnetic axes to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return g_tensor_list, magnetic_axes_list
[docs] def calculate_mth( self, group: str, fields: ndarray[float64], grid: Union[int, ndarray[float64]], temperatures: ndarray[float64], states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates powder-averaged or directional molar magnetisation M(T,H) for a given list of temperature and field values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetisation. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which magnetisation will be computed. grid : Union[int, ndarray[float64]] If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over hemisphere will be used (see grids_over_hemisphere documentation), otherwise, user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],...] for powder-averaging. If one wants a calculation for a single, particular direction the list has to contain one entry like this: [[direction_x, direction_y, direction_z, 1.]]. Custom grids will be automatically normalized. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which magnetisation will be computed. states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _magnetisation., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting mth_array gives magnetisation in Bohr magnetons and is in the form [temperatures, fields] - the first dimension runs over temperature values, and the second over fields. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If fields are not a one-diemsional array. SltInputError If temperatures are not a one-diemsional array. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of magnetisation is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the provided field values. See Also -------- slothpy.Compound.plot_mth, slothpy.lebedev_laikov_grid : For the description of the prescribed Lebedev-Laikov grids. """ if slt is not None: slt_group_name = f"{slt}_magnetisation" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) temperatures = array(temperatures, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if isinstance(grid, int): grid = lebedev_laikov_grid(grid) else: grid = _normalize_grid_vectors(grid) if autotune: try: number_cpu, number_threads = _auto_tune( self._hdf5, group, fields.size, states_cutoff, grid.shape[0], temperatures.size, number_cpu, _autotune_size, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None try: mth_array = _mth( self._hdf5, group, fields, grid, temperatures, states_cutoff, number_cpu, number_threads, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute M(T,H) from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_mth", "Dataset containing M(T,H) magnetisation (T - rows, H" f" - columns) calculated from group: {group}.", f"Group({slt}) containing M(T,H) magnetisation" f" calculated from group: {group}.", ] = mth_array[:, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" f" simulation of M(T,H) from group: {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" f" simulation of M(T,H) from group: {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save M(T,H) to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return mth_array
[docs] def calculate_mag_3d( self, group: str, fields: ndarray[float64], spherical_grid: int, temperatures: ndarray[float64], states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates 3D magnetisation over a spherical grid for a given list of temperature and field values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the 3D magnetisation. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which 3D magnetisation will be computed. spherical_grid : int Controls the density of the angular grid for the 3D magnetisation calculation. A grid of dimension (spherical_grid*2*spherical_grid) for spherical angles theta [0, pi], and phi [0, 2*pi] will be used. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temperature values (K) at which 3D magnetisation will be computed. states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _3d_magnetisation., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting mag_3d_array gives magnetisation in Bohr magnetons and is in the form [coordinates, fields, temperatures, mesh, mesh] - the first dimension runs over coordinates (0-x, 1-y, 2-z), the second over field values, and the third over temperatures. The last two dimensions are in a form of meshgrids over theta and phi, ready for 3D plots as xyz. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If fields are not a one-diemsional array. SltInputError If temperatures are not a one-diemsional array. SltInputError If spherical_grid is not a positive integer. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of 3D magnetisation is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over len(fields)*2*shperical_grid**2 tasks. Be aware that the resulting arrays and computations can quickly consume much memory (e.g. for a calculation with 100 field values 1-10 T, 300 temperatures 1-300 K, and spherical_grid = 60, the resulting array will take 3*100*300*2*60*60*8 bytes = 5.184 GB). See Also -------- slothpy.Compound.plot_3d, slothpy.Compound.interactive_plot_3d, slothpy.Compound.animate_3d """ if slt is not None: slt_group_name = f"{slt}_3d_magnetisation" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: temperatures = array(temperatures, dtype=float64) fields = array(fields, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if (not isinstance(spherical_grid, int)) or spherical_grid <= 0: raise SltInputError( ValueError("Spherical grid has to be a positive integer.") ) from None if autotune: try: number_cpu, number_threads = _auto_tune( self._hdf5, group, fields.size * 2 * spherical_grid**2, states_cutoff, 1, # Single grid point in the inner loop temperatures.size, number_cpu, _autotune_size, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None try: mag_3d_array = _mag_3d( self._hdf5, group, fields, spherical_grid, temperatures, states_cutoff, number_cpu, number_threads, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute 3D magnetisation from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_mag_3d", "Dataset containing 3D magnetisation as meshgird" " (0-x,1-y,2-z) arrays over sphere (xyz, field," " temperature, meshgrid, meshgrid) calculated from" f" group: {group}.", f"Group({slt}) containing 3D magnetisation calculated" f" from group: {group}.", ] = mag_3d_array[:, :, :, :, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" f" simulation of 3D magnetisation from group: {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" f" simulation of 3D magnetisation from group: {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save 3D magnetisation to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return mag_3d_array
[docs] def calculate_chitht( self, group: str, temperatures: ndarray[float64], fields: ndarray[float64], number_of_points: int = 1, delta_h: float = 0.0001, states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, exp: bool = False, T: bool = True, grid: Union[int, ndarray[float64]] = None, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates powder-averaged or directional molar magnetic susceptibility chi(T)(H,T) for a given list of field and temperatures values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetisation. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which magnetic susceptibility will be computed. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which magnetic susceptibility will be computed. number_of_points : int, optional Controls the number of points for numerical differentiation over the magnetic field values using the finite difference method with a symmetrical stencil. The total number of used points = (2 * num_of_opints + 1), therefore 1 is a minimum value to obtain the first derivative using 3 points - including the value at the point at which the derivative is taken. In this regard, the value 0 triggers the experimentalist model for susceptibility., by default 1 delta_h : float64, optional Value of field step used for numerical differentiation using finite difference method. 0.0001 (T) = 1 Oe is recommended as a starting point., by default 0.0001 states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 exp : bool, optional Turns on the experimentalist model for magnetic susceptibility., by default False T : bool, optional Results are returned as a product with temperature chiT(H,T)., by default True grid : Union[int, ndarray[float64]], optional If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over the hemisphere will be used (see grids_over_hemisphere documentation), otherwise, the user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],...] for powder-averaging. If one wants a calculation for a single, particular direction the list has to contain one entry like this: [[direction_x, direction_y, direction_z, 1.]]. If not given the average is taken over xyz directions, which is sufficient for a second rank tensor. Custom grids will be automatically normalized., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _susceptibility., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with a higher number of field values and number_of_points) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting chitht_array gives magnetic susceptibility (or product with temperature) in cm^3 (or * K) and is in the form [fields, temperatures] - the first dimension runs over field values, and the second over temperatures. Raises ------ SltSaveError If the name of the group already exists in the .slt file SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays SltInputError If temperatures are not a one-diemsional array. SltInputError If fields are not a one-diemsional array. SltInputError If the number of points for finite difference method is not a possitive integer. SltInputError If the field step for the finite difference method is not a possitive real number. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of magnetic susceptibility is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over fields.size*(2*number_of_points+1) tasks. See Also -------- slothpy.Compound.plot_chitht """ if slt is not None: slt_group_name = f"{slt}_susceptibility" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) temperatures = array(temperatures, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if (not isinstance(number_of_points, int)) or number_of_points < 0: raise SltInputError( ValueError( "The number of points for the finite difference method has" " to be a possitive integer." ) ) from None if (not isinstance(delta_h, float)) or delta_h <= 0: raise SltInputError( ValueError( "The field step for finite difference method has to be a" " possitive number." ) ) from None if isinstance(grid, int): grid = lebedev_laikov_grid(grid) elif grid is not None: grid = _normalize_grid_vectors(grid) if autotune: if exp: num_to_parallel = fields.size else: num_to_parallel = (2 * number_of_points + 1) * fields.size if grid is None: grid_shape = 3 # xyz grid in the inner loop else: grid_shape = grid.shape[0] try: number_cpu, number_threads = _auto_tune( self._hdf5, group, num_to_parallel, states_cutoff, grid_shape, temperatures.shape[0], number_cpu, _autotune_size, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if T: chi_name = "chiT(H,T)" chi_file = "chit" else: chi_name = "chi(H,T)" chi_file = "chi" try: chitht_array = _chitht( self._hdf5, group, temperatures, fields, number_of_points, delta_h, states_cutoff, number_cpu, number_threads, exp, T, grid, ) except Exception as exc: raise SltCompError( self._hdf5, exc, f"Failed to compute {chi_name} from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_{chi_file}ht", f"Dataset containing {chi_name} magnetic" " susceptibility (H - rows, T - columns) calculated" f" from group: {group}.", f"Group({slt}) containing {chi_name} magnetic" f" susceptibility calculated from group: {group}.", ] = chitht_array[:, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" " simulation of magnetic susceptibility from group:" f" {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" f" simulation of {chi_name} from group: {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, f"Failed to save {chi_name} to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return chitht_array
[docs] def calculate_chit_tensorht( self, group: str, temperatures: ndarray[float64], fields: ndarray[float64], number_of_points: int = 1, delta_h: float = 0.0001, states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, exp: bool = False, T: bool = True, rotation: ndarray[float64] = None, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates magnetic susceptibility chi(H,T) (Van Vleck) tensor for a given list of field and temperature values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetisation. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which magnetic susceptibility tensor will be computed. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which magnetic susceptibility tensor will be computed. number_of_points : int, optional Controls the number of points for numerical differentiation over the magnetic field values using the finite difference method with a symmetrical stencil. The total number of used points = (2 * num_of_opints + 1), therefore 1 is a minimum value to obtain the first derivative using 3 points - including the value at the point at which the derivative is taken. In this regard, the value 0 triggers the experimentalist model for susceptibility., by default 1 delta_h : float64, optional Value of field step used for numerical differentiation using finite difference method. 0.0001 (T) = 1 Oe is recommended as a starting point., by default 0.0001, states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 exp : bool, optional Turns on the experimentalist model for magnetic susceptibility., by default False T : bool, optional Results are returned as a product with temperature chiT(H,T)., by default True rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _susceptibility_tensor., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 500 with a higher number of field values and number_of_points) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting array gives magnetic susceptibility (Van Vleck) tensors (or products with temperature) in cm^3 (or * K) and is in the form [fields, temperatures, 3x3 tensor] - the first dimension runs over field values, the second over temperatures, and the last two accomodate 3x3 tensors. Raises ------ SltSaveError If the name of the group already exists in the .slt file SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays SltInputError If temperatures are not a one-diemsional array. SltInputError If fields are not a one-diemsional array. SltInputError If the number of points for finite difference method is not a possitive integer SltInputError If the field step for the finite difference method is not a possitive real number. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of magnetic susceptibility tensor is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over fields.size*(2*number_of_points+1) tasks. """ if slt is not None: slt_group_name = f"{slt}_susceptibility_tensor" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) temperatures = array(temperatures, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if (not isinstance(number_of_points, int)) or number_of_points < 0: raise SltInputError( ValueError( "The number of points for the finite difference method has" " to be a possitive integer." ) ) from None if (not isinstance(delta_h, float)) or delta_h <= 0: raise SltInputError( ValueError( "The field step for finite difference method has to be a" " possitive number." ) ) from None if autotune: if exp: num_to_parallel = fields.size else: num_to_parallel = (2 * number_of_points + 1) * fields.size try: number_cpu, number_threads = _auto_tune( self._hdf5, group, num_to_parallel, states_cutoff, 9, # Size of 3x3 tensor in the inner loop temperatures.shape[0], number_cpu, _autotune_size, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if T: chi_name = "chiT(H,T)" chi_file = "chit" else: chi_name = "chi(H,T)" chi_file = "chi" try: chitht_tensor_array = _chitht_tensor( self._hdf5, group, temperatures, fields, number_of_points, delta_h, states_cutoff, number_cpu, number_threads, exp, T, rotation, ) except Exception as exc: raise SltCompError( self._hdf5, exc, f"Failed to compute {chi_name} tensor from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_{chi_file}ht_tensor", f"Dataset containing {chi_name}_tensor Van Vleck" " susceptibility tensor (H, T, 3, 3) calculated from" f" group: {group}.", f"Group({slt}) containing {chi_name}_tensor Van Vleck" " susceptibility tensor calculated from group:" f" {group}.", ] = chitht_tensor_array[:, :, :, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" f" simulation of {chi_name}_tensor Van Vleck" f" susceptibility tensor from group: {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" f" simulation of {chi_name}_tensor Van Vleck" f" susceptibility tensor from group: {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, f"Failed to save {chi_name} tensor to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return chitht_tensor_array
[docs] def calculate_chit_3d( self, group: str, temperatures: ndarray[float64], fields: ndarray[float64], spherical_grid: int, number_of_points: int = 1, delta_h: float = 0.0001, states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, exp: bool = False, T: bool = True, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates 3D magnetic susceptibility over a spherical grid for a given list of temperature and field values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the 3D magnetic susceptibility. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temperature values (K) at which 3D magnetic susceptibility will be computed. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which 3D magnetic susceptibility will be computed. spherical_grid : int Controls the density of the angular grid for the 3D susceptibility calculation. A grid of dimension (spherical_grid*2*spherical_grid) for spherical angles theta [0, pi], and phi [0, 2*pi] will be used. number_of_points : int, optional Controls the number of points for numerical differentiation over the magnetic field values using the finite difference method with a symmetrical stencil. The total number of used points = (2 * num_of_opints + 1), therefore 1 is a minimum value to obtain the first derivative using 3 points - including the value at the point at which the derivative is taken. In this regard, the value 0 triggers the experimentalist model for susceptibility., by default 1 delta_h : float64, optional Value of field step used for numerical differentiation using finite difference method. 0.0001 (T) = 1 Oe is recommended as a starting point., by default 0.0001 states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 exp : bool, optional Turns on the experimentalist model for magnetic susceptibility., by default False T : bool, optional Results are returned as a product with temperature chiT(H,T)., by default True slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _3d_magnetisation., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting chi_3d_array gives magnetic susceptibility (or product with temperature) in cm^3 (or * K) and is in the form [coordinates, fields, temperatures, mesh, mesh] - the first dimension runs over coordinates (0-x, 1-y, 2-z), the second over field values, and the third over temperatures. The last two dimensions are in a form of meshgrids over theta and phi, ready for 3D plots as xyz. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If temperatures are not a one-diemsional array. SltInputError If fields are not a one-diemsional array. SltInputError If spherical_grid is not a positive integer. SltInputError If the number of points for finite difference method is not a possitive integer. SltInputError If the field step for the finite difference method is not a possitive real number. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of 3D magnetic susceptibility is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over len(fields)*(2*number_of_points + 1) *2*shperical_grid**2 tasks. Be aware that the resulting arrays and computations can quickly consume much memory (e.g. for calculation with 100 field values 1-10 T, 300 temperatures 1-300 K, number_of_points=3, and spherical_grid = 60, the intermediate array (before numerical differentiation) will take 7*100*300*2*60*60*8 bytes = 12.096 GB). See Also -------- slothpy.Compound.plot_3d, slothpy.Compound.interactive_plot_3d, slothpy.Compound.animate_3d """ temperatures = array(temperatures, dtype=float64) fields = array(fields, dtype=float64) if slt is not None: slt_group_name = f"{slt}_3d_susceptibility" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) temperatures = array(temperatures, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if (not isinstance(spherical_grid, int)) or spherical_grid <= 0: raise SltInputError( ValueError("Spherical grid has to be a positive integer.") ) from None if (not isinstance(number_of_points, int)) or number_of_points < 0: raise SltInputError( ValueError( "The number of points for the finite difference method has" " to be a possitive integer." ) ) from None if (not isinstance(delta_h, float)) or delta_h <= 0: raise SltInputError( ValueError( "The field step for finite difference method has to be a" " possitive number." ) ) from None if autotune: if exp: num_to_parallel = fields.size * 2 * spherical_grid**2 else: num_to_parallel = ( (2 * number_of_points + 1) * fields.size * 2 * spherical_grid**2 ) try: number_cpu, number_threads = _auto_tune( self._hdf5, group, num_to_parallel, states_cutoff, 1, # Single grid point in the inner loop temperatures.shape[0], number_cpu, _autotune_size, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if T: chi_name = "chiT(H,T)" chi_file = "chit" else: chi_name = "chi(H,T)" chi_file = "chi" try: chit_3d_array = _chit_3d( self._hdf5, group, temperatures, fields, spherical_grid, number_of_points, delta_h, states_cutoff, number_cpu, number_threads, exp, T, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute 3D magnetic susceptibility" f" {chi_name} from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_{chi_file}_3d", "Dataset containing 3D magnetic susceptibility" f" {chi_name} as meshgird (0-x,1-y,2-z) arrays over" " sphere ((xyz, field, temperature, meshgrid," f" meshgrid) calculated from group: {group}.", f"Group({slt}) containing 3D magnetic susceptibility" f" {chi_name} calculated from group: {group}.", ] = chit_3d_array[:, :, :, :, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" " simulation of 3D magnetic susceptibility" f" {chi_name} from group: {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" " simulation of 3D magnetic susceptibility" f" {chi_name} from group: {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, f"Failed to save 3D magnetic susceptibility {chi_name} to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return chit_3d_array
[docs] def calculate_helmholtz_energyth( self, group: str, fields: ndarray[float64], grid: ndarray[float64], temperatures: ndarray[float64], states_cutoff: int, number_cpu: int, number_threads: int, internal_energy: bool = False, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates powder-averaged or directional Helmholtz (or internal) energy for a given list of temperature and field values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the energy. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which energy will be computed. grid : ndarray[float64] If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over hemisphere will be used (see grids_over_hemisphere documentation), otherwise, user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],...] for powder-averaging. If one wants a calculation for a single, particular direction the list has to contain one entry like this: [[direction_x, direction_y, direction_z, 1.]]. Custom grids will be automatically normalized. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temeperature values (K) at which energy will be computed states_cutoff : int Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 internal_energy : bool, optional Turns on the calculation of internal energy., by default False slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _helmholtz_energy or _internal_energy., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting eth_array gives energy in cm-1 and is in the form [temperatures, fields] - the first dimension runs over temperature values, and the second over fields. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If fields are not a one-diemsional array SltInputError If temperatures are not a one-diemsional array SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of energy is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the provided field values. See Also -------- slothpy.Compound.plot_helmholtz_energyth slothpy.lebedev_laikov_grid : For the description of the prescribed Lebedev-Laikov grids. """ if internal_energy: group_suffix = "_internal_energy" name = "internal" else: group_suffix = "_helmholtz_energy" name = "Helmholtz" if slt is not None: slt_group_name = f"{slt}{group_suffix}" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) temperatures = array(temperatures, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if isinstance(grid, int): grid = lebedev_laikov_grid(grid) else: grid = _normalize_grid_vectors(grid) if autotune: try: number_cpu, number_threads = _auto_tune( self._hdf5, group, fields.size, states_cutoff, grid.shape[0], temperatures.size, number_cpu, _autotune_size, True, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None try: energyth_array = _helmholtz_energyth( self._hdf5, group, fields, grid, temperatures, states_cutoff, number_cpu, number_threads, internal_energy, ) except Exception as exc: raise SltCompError( self._hdf5, exc, f"Failed to compute {name} energy from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_eth", f"Dataset containing E(T,H) {name} energy (T - rows," f" H - columns) calculated from group: {group}.", f"Group({slt}) containing E(T,H) {name} energy" f" calculated from group: {group}.", ] = energyth_array[:, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" f" simulation of E(T,H) {name} energy from group:" f" {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" f" simulation of E(T,H) {name} energy from group:" f" {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, f"Failed to save {name} energy to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return energyth_array
[docs] def calculate_helmholtz_energy_3d( self, group: str, fields: ndarray[float64], spherical_grid: int, temperatures: ndarray[float64], states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, internal_energy: bool = False, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates 3D Helmholtz (or internal) energy over a spherical grid for a given list of temperature and field values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the 3D energy. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which 3D energy will be computed. spherical_grid : int Controls the density of the angular grid for the 3D magnetisation calculation. A grid of dimension (spherical_grid*2*spherical_grid) for spherical angles theta [0, pi], and phi [0, 2*pi] will be used. temperatures : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of temperature values (K) at which 3D energy will be computed. states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0, number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 internal_energy : bool, optional Turns on the calculation of internal energy., by default False slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _3d_helmholtz_energy or _3d_internal_energy., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default False Returns ------- ndarray[float64] The resulting energy_3d_array gives energy in cm-1 and is in the form [coordinates, fields, temperatures, mesh, mesh] - the first dimension runs over coordinates (0-x, 1-y, 2-z), the second over field values, and the third over temperatures. The last two dimensions are in a form of meshgrids over theta and phi, ready for 3D plots as xyz. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If fields are not a one-diemsional array. SltInputError If temperatures are not a one-diemsional array. SltInputError If spherical_grid is not a positive integer. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of 3D energy is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over len(fields)*2*shperical_grid**2 tasks. Be aware that the resulting arrays and computations can quickly consume much memory (e.g. for a calculation with 100 field values 1-10 T, 300 temperatures 1-300 K, and spherical_grid = 60, the resulting array will take 3*100*300*2*60*60*8 bytes = 5.184 GB). See Also -------- slothpy.Compound.plot_3d, slothpy.Compound.interactive_plot_3d, slothpy.Compound.animate_3d """ if internal_energy: group_suffix = "_3d_internal_energy" name = "internal" else: group_suffix = "_3d_helmholtz_energy" name = "Helmholtz" if slt is not None: slt_group_name = f"{slt}{group_suffix}" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: temperatures = array(temperatures, dtype=float64) fields = array(fields, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if temperatures.ndim != 1: raise SltInputError( ValueError("The list of temperatures has to be a 1D array.") ) from None if (not isinstance(spherical_grid, int)) or spherical_grid <= 0: raise SltInputError( ValueError("Spherical grid has to be a positive integer.") ) from None if autotune: try: number_cpu, number_threads = _auto_tune( self._hdf5, group, fields.size * 2 * spherical_grid**2, states_cutoff, 1, # Single grid point in the inner loop temperatures.size, number_cpu, _autotune_size, True, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None try: energy_3d_array = _helmholtz_energy_3d( self._hdf5, group, fields, spherical_grid, temperatures, states_cutoff, number_cpu, number_threads, internal_energy, ) except Exception as exc: raise SltCompError( self._hdf5, exc, f"Failed to compute 3D {name} energy from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_energy_3d", "Dataset containing 3D {name} energy as meshgird" " (0-x,1-y,2-z) arrays over sphere (xyz, field," " temperature, meshgrid, meshgrid) calculated from" f" group: {group}.", f"Group({slt}) containing 3D {name}_energy" f" calculated from group: {group}.", ] = energy_3d_array[:, :, :, :, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" f" simulation of 3D {name} energy from group:" f" {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_temperatures", "Dataset containing temperature T values used in" f" simulation of 3D {name} energy from group:" f" {group}.", ] = temperatures[:] except Exception as exc: raise SltFileError( self._hdf5, exc, f"Failed to save 3D {name} energy to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return energy_3d_array
[docs] def calculate_zeeman_splitting( self, group: str, number_of_states: int, fields: ndarray[float64], grid: ndarray[float64], states_cutoff: int = 0, number_cpu: int = 0, number_threads: int = 1, average: bool = False, slt: str = None, autotune: bool = False, _autotune_size: int = 2, ) -> ndarray[float64]: """ Calculates directional or powder-averaged Zeeman splitting for a given number of states and list of field values. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the Zeeman splitting. number_of_states : int Number of states whose energy splitting will be given in the result array. fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) at which Zeeman splitting will be computed. grid : ndarray[float64] If the grid is set to an integer from 0-11 then the prescribed Lebedev-Laikov grids over hemisphere will be used (see grids_over_hemisphere documentation) and powder-averaging will be turned on, otherwise, user can provide an ArrayLike structure (can be converted to numpy.NDArray) with the convention: [[direction_x, direction_y, direction_z, weight],...] with average = True for powder-averaging. If one wants a calculation for a list of particular directions the list has to follow the format: [[direction_x, direction_y, direction_z],...]. Custom grids will be automatically normalized. states_cutoff : int, optional Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 number_cpu : int, optional Number of logical CPUs to be assigned to perform the calculation. If set to zero, all available CPUs will be used., by default 0 number_threads : int, optional Number of threads used in a multithreaded implementation of linear algebra libraries used during the calculation. Higher values benefit from the increasing size of matrices (states_cutoff) over the parallelization over CPUs., by default 1 average : bool, optional Turns on powder-averaging using a list of directions and weights in the form of ArrayLike structure: [[direction_x, direction_y, direction_z, weight],...]. slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _zeeman_splitting., by default None autotune : bool, optional If True the program will automatically try to choose the best number of threads (and therefore parallel processes), for the given number of CPUs, to be used during the calculation. Note that this process can take a significant amount of time, so start to use it with medium-sized calculations (e.g. for states_cutoff > 300 with dense grids or a higher number of field values) where it becomes a necessity., by default Falsee Returns ------- ndarray[float64] The resulting array gives Zeeman splitting of number_of_states energy levels in cm-1 for each direction (or average) in the form [orientations, fields, energies] - the first dimension runs over different orientations, the second over field values, and the last gives energy of number_of_states states. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If fields are not a one-diemsional array. SltInputError If number of states is not a positive integer less or equal to the states cutoff. SltCompError If autotuning a number of processes and threads is unsuccessful. SltCompError If the calculation of Zeeman splitting is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. See Also -------- slothpy.Compound.plot_zeeman, slothpy.lebedev_laikov_grid : For the description of the prescribed Lebedev-Laikov grids. Note ----- Here, (number_cpu // number_threads) parallel processes are used to distribute the workload over the provided field values. """ if slt is not None: slt_group_name = f"{slt}_zeeman_splitting" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None if ( not isinstance(number_of_states, int) or number_of_states <= 0 or number_of_states > states_cutoff ): raise SltInputError( ValueError( "The number of states has to be an integer less or equal" " to the states cutoff." ) ) from None if isinstance(grid, int): grid = lebedev_laikov_grid(grid) average = True elif average: grid = _normalize_grid_vectors(grid) else: grid = _normalize_orientations(grid) if autotune: try: number_cpu, number_threads = _auto_tune( self._hdf5, group, fields.size, states_cutoff, grid.shape[0], 1, number_cpu, _autotune_size, True, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to autotune a number of processes and threads to" " the data within " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None try: zeeman_array = _zeeman_splitting( self._hdf5, group, number_of_states, fields, grid, states_cutoff, number_cpu, number_threads, average, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute Zeeman splitting from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if average: name = "average " else: name = "" if slt is not None: try: self[ slt_group_name, f"{slt}_zeeman", f"Dataset containing {name}Zeeman splitting over grid" " of directions with shape: (orientations, field," f" energy) calculated from group: {group}.", f"Group({slt}) containing {name}Zeeman splitting" f" calculated from group: {group}.", ] = zeeman_array[:, :, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" f" simulation of {name}Zeeman splitting from group:" f" {group}.", ] = fields[:] if average: self[ slt_group_name, f"{slt}_orientations", "Dataset containing magnetic field orientation" " grid with weights used in simulation of" f" {name}Zeeman splitting from group: {group}.", ] = grid[:, :] else: self[ slt_group_name, f"{slt}_orientations", "Dataset containing magnetic field orientations" " used in simulation of" f" {name}Zeeman splitting from group: {group}.", ] = grid[:, :3] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save Zeeman splitting to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return zeeman_array
[docs] def zeeman_matrix( self, group: str, states_cutoff: int, fields: ndarray[float64], orientations: ndarray[float64], slt: str = None, ) -> ndarray[complex128]: """ Calculates Zeeman matrices for a given list of magnetic fields and their orientations. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the Zeeman matrices. states_cutoff : int Number of states that will be taken into account for construction of Zeeman Hamiltonian. If set to zero, all available states from the file will be used., by default 0 fields : ndarray[float64] ArrayLike structure (can be converted to numpy.NDArray) of field values (T) for which Zeeman matrices will be computed. orientations : ndarray[float64] List (ArrayLike structure) of particular magnetic field directions for which Zeeman matrices will be constructed. The list has to follow the format: [[direction_x, direction_y, direction_z],...]. The vectors will be automatically normalized. slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _zeeman_matrix., by default None Returns ------- ndarray[complex128] The resulting array gives Zeeman matrices for each field value and orientation in the form [fields, orientations, matrix, matrix] in atomic units a.u. (Hartree). Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltInputError If fields are not a one-diemsional array. SltCompError If the calculation of Zeeman matrices is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if slt is not None: slt_group_name = f"{slt}_zeeman_matrix" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: fields = array(fields, dtype=float64) except Exception as exc: raise SltInputError(exc) from None if fields.ndim != 1: raise SltInputError( ValueError("The list of fields has to be a 1D array.") ) from None orientations = _normalize_orientations(orientations) try: zeeman_matrix_array = _get_zeeman_matrix( self._hdf5, group, states_cutoff, fields, orientations ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to calculate Zeeman matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_matrix", "Dataset containing Zeeman matrices calculated from" f" group: {group} in the form [fields, orientations," " matrix, matrix].", f"Group({slt}) containing Zeeman matrices calculated" f" from group: {group}.", ] = zeeman_matrix_array[:, :, :, :] self[ slt_group_name, f"{slt}_fields", "Dataset containing magnetic field H values used in" " simulation of Zeeman matrices from group:" f" {group}.", ] = fields[:] self[ slt_group_name, f"{slt}_orientations", "Dataset containing magnetic field orientations" " used in simulation of" f" Zeeman matrices from group: {group}.", ] = orientations[:, :] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save Zeeman matrix to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return zeeman_matrix_array
[docs] def soc_energies_cm_1( self, group: str, number_of_states: int = 0, slt: str = None ) -> ndarray[float64]: """ Returns energies for the given number of first spin-orbit states in cm-1. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations. number_of_states : int, optional Number of states whose energy will be returned. If set to zero, all available states will be inculded., by default 0 slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _soc_energies., by default None Returns ------- ndarray[float64] The resulting array is one-dimensional and contains the energy of first number_of_states states in cm-1. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltReadError If the program is unable to get SOC energies from the .slt file. SltFileError If the program is unable to correctly save results to .slt file. See Also -------- slothpy.exporting.table_energy_and_g """ if slt is not None: slt_group_name = f"{slt}_soc_energies" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: soc_energies_array = _get_soc_energies_cm_1( self._hdf5, group, number_of_states ) except Exception as exc: raise SltReadError( self._hdf5, exc, "Failed to read SOC energies from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_energies", "Dataset containing SOC (Spin-Orbit Coupling) energies" f" calculated from group: {group}.", f"Group({slt}) containing SOC (Spin-Orbit Coupling)" f" energies calculated from group: {group}.", ] = soc_energies_array except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save SOC energies to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return soc_energies_array
[docs] def states_magnetic_momenta( self, group: str, states: Union[int, ndarray[int]] = 0, rotation: ndarray[float64] = None, slt: str = None, ) -> ndarray[float64]: """ Calculates magnetic momenta of a given list (or number) of SOC states. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetic momenta. states : Union[int, ndarray[int]], optional ArrayLike structure (can be converted to numpy.NDArray) of states indexes for which magnetic momenta will be calculated. If set to an integer it acts as a states cutoff (first n states will be given). For all available states set it to zero., by default 0 rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _states_magnetic_momenta., by default None Returns ------- ndarray[float64] The resulting array is one-dimensional and contains the magnetic momenta corresponding to the given states indexes in atomic units. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltCompError If the calculation of magnetic momenta is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if slt is not None: slt_group_name = f"{slt}_states_magnetic_momenta" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None if not isinstance(states, int): try: states = array(states, dtype=int64) except Exception as exc: raise SltInputError(exc) from None try: magnetic_momenta_array = _get_states_magnetic_momenta( self._hdf5, group, states, rotation ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute states magnetic momenta from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_magnetic_momenta", "Dataset containing states magnetic momenta" f" (0-x,1-y,2-z) calculated from group: {group}.", f"Group({slt}) containing states magnetic momenta" f" calculated from group: {group}.", ] = magnetic_momenta_array self[ slt_group_name, f"{slt}_states", "Dataset containing indexes of states (or states" " cutoff) used in simulation of magnetic momenta from" f" group: {group}.", ] = array(states) except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save states magnetic momenta to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return magnetic_momenta_array
[docs] def states_total_angular_momenta( self, group: str, states: Union[int, ndarray[int]] = 0, rotation: ndarray[float64] = None, slt: str = None, ) -> ndarray[float64]: """ Calculates total angular momenta of a given list (or number) of SOC states. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetic momenta. states : Union[int, ndarray[int]], optional ArrayLike structure (can be converted to numpy.NDArray) of states indexes for which total angular momenta will be calculated. If set to an integer it acts as a states cutoff (first n states will be given). For all available states set it to zero. , by default 0 rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _states_total_angular_momenta., by default None Returns ------- ndarray[float64] The resulting array is one-dimensional and contains the total angular momenta corresponding to the given states indexes in atomic units. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltInputError If input ArrayLike data cannot be converted to numpy.NDArrays. SltCompError If the calculation of total angular momenta is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if slt is not None: slt_group_name = f"{slt}_states_total_angular_momenta" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None if not isinstance(states, int): try: states = array(states, dtype=int64) except Exception as exc: raise SltInputError(exc) from None try: total_angular_momenta_array = _get_states_total_angular_momenta( self._hdf5, group, states, rotation ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute states total angular momenta from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_total_angular_momenta", "Dataset containing states total angular momenta" f" (0-x,1-y,2-z) calculated from group: {group}.", f"Group({slt}) containing states total angular momenta" f" calculated from group: {group}.", ] = total_angular_momenta_array self[ slt_group_name, f"{slt}_states", "Dataset containing indexes of states (or states" " cutoff) used in simulation of total angular momenta" f" from group: {group}.", ] = array(states) except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save states total angular momenta to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return total_angular_momenta_array
[docs] def magnetic_momenta_matrix( self, group: str, states_cutoff: ndarray = 0, rotation: ndarray[float64] = None, slt: str = None, ) -> ndarray[complex128]: """ Calculates magnetic momenta matrix for a given number of SOC states. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the magnetic momenta matrix. states_cutoff : ndarray, optional Number of states that will be taken into account for construction of the magnetic momenta matrix. If set to zero, all available states from the file will be included., by default 0 rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _magnetic_momenta_matrix., by default None Returns ------- ndarray[complex128] The resulting magnetic_momenta_matrix_array gives magnetic momenta in atomic units and is in the form [coordinates, matrix, matrix] - the first dimension runs over coordinates (0-x, 1-y, 2-z). Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltCompError If the calculation of magetic momenta matrix is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if slt is not None: slt_group_name = f"{slt}_magnetic_momenta_matrix" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: magnetic_momenta_matrix_array = _get_magnetic_momenta_matrix( self._hdf5, group, states_cutoff, rotation ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute magnetic momenta matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_magnetic_momenta_matrix", "Dataset containing magnetic momenta matrix" f" (0-x, 1-y, 2-z) calculated from group: {group}.", f"Group {group} containing magnetic momenta" f" matrix calculated from group: {group}.", ] = magnetic_momenta_matrix_array[:, :] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save states magnetic momenta to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return magnetic_momenta_matrix_array
[docs] def total_angular_momenta_matrix( self, group: str, states_cutoff: int = 0, rotation: ndarray[float64] = None, slt: str = None, ) -> ndarray[complex128]: """ Calculates total angular momenta matrix for a given number of SOC states. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the computation of the total angular momenta matrix. states_cutoff : ndarray, optional Number of states that will be taken into account for construction of the total angular momenta matrix. If set to zero, all available states from the file will be included., by default 0 rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _total angular_momenta_matrix., by default None Returns ------- ndarray[complex128] The resulting total_angular_momenta_matrix_array gives total angular momenta in atomic units and is in the form [coordinates, matrix, matrix] - the first dimension runs over coordinates (0-x, 1-y, 2-z). Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltCompError If the calculation of total angular momenta matrix is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if slt is not None: slt_group_name = f"{slt}_total_angular_momenta_matrix" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: total_angular_momenta_matrix_array = ( _get_total_angular_momneta_matrix( self._hdf5, group, states_cutoff, rotation ) ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute total angular momenta matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_total_angular_momenta_matrix", "Dataset containing total angular momenta matrix" f" (0-x, 1-y, 2-z) calculated from group: {group}.", f"Group {group} containing total angular momenta" f" matrix calculated from group: {group}.", ] = total_angular_momenta_matrix_array[:, :] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save states total angular momenta to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return total_angular_momenta_matrix_array
[docs] def matrix_decomposition_in_z_pseudo_spin_basis( self, group: str, matrix: Union["soc", "zeeman"], pseudo_kind: Union["magnetic", "total_angular"], start_state: int = 0, stop_state: int = 0, rotation: ndarray[float64] = None, field: float64 = None, orientation: ndarray[float64] = None, slt: str = None, ) -> ndarray[float64]: """ Calculates decomposition of a given matrix in "z" pseudo-spin basis. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for the construction of the matrix. matrix : Union["soc", "zeeman"] Type of a matrix to be decomposed. Two options available: "soc" or "zeeman". pseudo_kind : Union["magnetic", "total_angular"] Kind of a pseudo-spin basis. Two options available: "magnetic" or "total_angular" for the decomposition in a particular basis. start_state : int, optional Number of the first SOC state to be included., by default 0 stop_state : int, optional Number of the last SOC state to be included. If both start and stop are set to zero all available states from the file will be used. , by default 0 rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None field : float64, optional If matrix type = "zeeman" it controls a magnetic field value at which Zeeman matrix will be computed., by default None orientation : ndarray[float64], optional If matrix type = "zeeman" it controls the orientation of the magnetic field and has to be in the form [direction_x, direction_y, direction_z] and be an ArrayLike structure (can be converted to numpy.NDArray)., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _magnetic/total_angular_decomposition. , by default None Returns ------- ndarray[float64] The resulting array gives decomposition in % where rows are SOC/Zeeman states and columns are associated with pseudo spin basis (from -Sz to Sz). Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltCompError If the decomposition of the matrix is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if slt is not None: slt_group_name = f"{slt}_{pseudo_kind}_decomposition" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: if orientation is not None: orientation = _normalize_orientation(orientation) decomposition = _get_decomposition_in_z_pseudo_spin_basis( self._hdf5, group, matrix, pseudo_kind, start_state, stop_state, rotation, field, orientation, ) except Exception as exc: raise SltCompError( self._hdf5, exc, f"Failed to decompose {matrix} matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + f'". in {pseudo_kind} basis.', ) from None if slt is not None: dim = (decomposition.shape[1] - 1) / 2 try: self[ slt_group_name, f"{slt}_{pseudo_kind}_decomposition", "Dataset containing decomposition (rows - SO-states," f' columns - basis) in "z" {pseudo_kind} momentum' f" basis of {matrix} matrix from group: {group}.", f'Group({slt}) containing decomposition in "z"' f" {pseudo_kind} basis of {matrix} matrix calculated" f" from group: {group}.", ] = decomposition[:, :] self[ slt_group_name, f"{slt}_pseudo_spin_states", "Dataset containing Sz pseudo-spin states" " corresponding to the decomposition of" f" {matrix} matrix from group: {group}.", ] = arange(-dim, dim + 1, step=1, dtype=float64) except Exception as exc: raise SltFileError( self._hdf5, exc, f"Failed to save {pseudo_kind} decomposition of" f" {matrix} matrix " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return decomposition
[docs] def soc_crystal_field_parameters( self, group: str, start_state: int, stop_state: int, order: int, pseudo_kind: Union["magnetic", "total_angular"], even_order: bool = True, complex: bool = False, rotation: ndarray[float64] = None, slt: str = None, ) -> list: """ Calculates ITO decomposition (CFPs) of SOC matrix. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for obtaining the SOC matrix. start_state : int Number of the first SOC state to be included. stop_state : int Number of the last SOC state to be included. If both start and stop are set to zero all available states from the file will be used. order : int Order of the highest ITO (CFP) to be included in the decomposition. pseudo_kind : Union["magnetic", "total_angular"] Kind of a pseudo-spin basis. Two options available: "magnetic" or "total_angular" for the decomposition in a particular basis. even_order : bool, optional If True, only even order ITOs (CFPs) will be included in the decomposition., by default True complex : bool, optional If True, instead of real ITOs (CFPs) complex ones will be given., by default False rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _soc_ito_decomposition., by default None Returns ------- list The resulting list gives CFP - B_k_q (ITO) in the form [k,q,B_k_q]. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltReadError If the program is unable to read SOC matrix from the file. SltInputError If the order exceeds 2S pseudo-spin value. SltCompError If the ITO decomposition of the matrix is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ---- The decomposition is obtained using a projection method described in [1] (eq. 41) employing ITOs defined in [2] (eq. 29) with a normalization factor from eq. 17. References ---------- .. [1] L. F. Chibotaru and L. Ungur "Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation" J. Chem. Phys. 137, 064112 (2012). .. [2] I. D. Ryabov "On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements" J. Magn. Reson. 140, 141–145 (1999). """ if slt is not None: slt_group_name = f"{slt}_soc_ito_decomposition" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: soc_matrix = _get_soc_matrix_in_z_pseudo_spin_basis( self._hdf5, group, start_state, stop_state, pseudo_kind, rotation, ) except Exception as exc: raise SltReadError( self._hdf5, exc, "Failed to read SOC matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + f'". in {pseudo_kind} basis.', ) from None dim = (soc_matrix.shape[1] - 1) / 2 if not isinstance(order, int) or order < 0 or order > 2 * dim: raise SltInputError( ValueError( "Order of ITO parameters has to be a positive integer or" " it exceeds 2S. Set it less or equal." ) ) try: if complex: cfp = _ito_complex_decomp_matrix(soc_matrix, order, even_order) else: cfp = _ito_real_decomp_matrix(soc_matrix, order, even_order) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to ITO decompose SOC matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + f'". in {pseudo_kind} basis.', ) from None cfp_return = cfp if slt is not None: cfp = array(cfp) try: self[ slt_group_name, f"{slt}_ito_parameters", 'Dataset containing ITO decomposition in "z"' " pseudo-spin basis of SOC matrix from group:" f" {group}.", f'Group({slt}) containing ITO decomposition in "z"' " pseudo-spin basis of SOC matrix calculated from" f" group: {group}.", ] = cfp[:, :] self[ slt_group_name, f"{slt}_pseudo_spin_states", "Dataset containing S pseudo-spin number" " corresponding to the decomposition of SOC matrix" f" from group: {group}.", ] = array([dim]) except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save ITO decomposition of SOC matrix to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return cfp_return
[docs] def zeeman_matrix_ito_decpomosition( self, group: str, start_state: int, stop_state: int, field: float64, orientation: ndarray[float64], order: int, pseudo_kind: Union["magnetic", "total_angular"], complex: bool = False, rotation: ndarray[float64] = None, slt: str = None, ) -> list: """ Calculates ITO decomposition of Zeeman matrix. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for obtaining the Zeeman matrix. start_state : int Number of the first Zeeman state to be included. stop_state : int Number of the last Zeeman state to be included. If both start and stop are set to zero all available states from the file will be used. field : float64 Magnetic field value at which Zeeman matrix will be computed. orientation : ndarray[float64] Orientation of the magnetic field in the form of an ArrayLike structure (can be converted to numpy.NDArray) [direction_x, direction_y, direction_z]. order : int Order of the highest ITO (CFP) to be included in the decomposition. pseudo_kind : Union["magnetic", "total_angular"] Kind of a pseudo-spin basis. Two options available: "magnetic" or "total_angular" for the decomposition in a particular basis. complex : bool, optional If True, instead of real ITOs (CFPs) complex ones will be given., by default False rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _zeeman_ito_decomposition., by default None Returns ------- list The resulting list gives ITOs - B_k_q in the form [k,q,B_k_q] Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltCompError If the program is unable to calculate Zeeman matrix from the file. SltInputError If the order exceeds 2S pseudo-spin value SltCompError If the ITO decomposition of the matrix is unsuccessful SltFileError If the program is unable to correctly save results to .slt file. Note ---- The decomposition is obtained using a projection method described in [1] (eq. 41) employing ITOs defined in [2] (eq. 29) with a normalization factor from eq. 17. References ---------- .. [1] L. F. Chibotaru and L. Ungur "Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation" J. Chem. Phys. 137, 064112 (2012). .. [2] I. D. Ryabov "On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements" J. Magn. Reson. 140, 141–145 (1999). """ if slt is not None: slt_group_name = f"{slt}_zeeman_ito_decomposition" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None orientation = _normalize_orientation(orientation) try: zeeman_matrix = _get_zeeman_matrix_in_z_pseudo_spin_basis( self._hdf5, group, field, orientation, start_state, stop_state, pseudo_kind, rotation, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to calculate Zeeman matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + f'". in {pseudo_kind} basis.', ) from None dim = (zeeman_matrix.shape[1] - 1) / 2 if not isinstance(order, int) or order < 0 or order > 2 * dim: raise SltInputError( ValueError( "Order of ITO parameters has to be a positive integer or" " it exceeds 2S. Set it less or equal." ) ) try: if complex: ito = _ito_complex_decomp_matrix(zeeman_matrix, order) else: ito = _ito_real_decomp_matrix(zeeman_matrix, order) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to ITO decompose Zeeman matrix from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + f'". in {pseudo_kind} basis.', ) from None ito_return = ito if slt is not None: ito = array(ito) try: self[ slt_group_name, f"{slt}_ito_parameters", 'Dataset containing ITO decomposition in "z"' " pseudo-spin basis of Zeeman matrix from group:" f" {group}.", f'Group({slt}) containing ITO decomposition in "z"' " pseudo-spin basis of Zeeman matrix calculated from" f" group: {group}.", ] = ito[:, :] self[ slt_group_name, f"{slt}_pseudo_spin_states", "Dataset containing S pseudo-spin number" " corresponding to the decomposition of Zeeman matrix" f" from group: {group}.", ] = array([dim]) except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save ITO decomposition of Zeeman matrix to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return ito_return
[docs] def matrix_from_ito( self, full_group_name: str, complex: bool, dataset_name: str = None, pseudo_spin: float64 = None, slt: str = None, ) -> ndarray[complex128]: """ Calculates matrix from a given ITO decomposition. Parameters ---------- full_group_name : str Full name of a group containing ITO decomposition. complex : bool Determines the type of ITOs in the dataset. If True, instead of real ITOs complex ones will be used., by default False dataset_name : str, optional A custom name for a user-created dataset within the group that contains list of B_k_q parameters in the form [k,q,B_k_q]., by default None pseudo_spin : float64, optional Pseudo spin S value for the user-defined dataset., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _matrix_from_ito., by default None Returns ------- ndarray[complex128] Matrix reconstructed from a given ITO list. Raises ------ SltSaveError If the name of the group already exists in the .slt file. SltCompError If the calculation of the matrix from ITOs is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. Note ---- ITOs defined in [2] (eq. 29) with a normalization factor from eq. 17 are used. References ---------- .. [1] I. D. Ryabov "On the Generation of Operator Equivalents and the Calculation of Their Matrix Elements" J. Magn. Reson. 140, 141–145 (1999). """ if slt is not None: slt_group_name = f"{slt}_matrix_from_ito" if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: if ( (dataset_name is not None) and (pseudo_spin is not None) and isinstance(pseudo_spin, int) and pseudo_spin > 0 ): J = pseudo_spin coefficients = self[f"{full_group_name}", f"{dataset_name}"] if complex: matrix = _matrix_from_ito_complex(J, coefficients) else: matrix = _matrix_from_ito_real(J, coefficients) else: if full_group_name.endswith("_zeeman_ito_decomposition"): dataset_name = full_group_name[ : -len("_zeeman_ito_decomposition") ] elif full_group_name.endswith("_soc_ito_decomposition"): dataset_name = full_group_name[ : -len("_soc_ito_decomposition") ] else: raise NameError( f"Invalid group name: {full_group_name}. It must end" " with _soc_ito_decomposition or" " _zeeman_ito_decomposition." ) J = self[ f"{full_group_name}", f"{dataset_name}_pseudo_spin_states", ] coefficients = self[ f"{full_group_name}", f"{dataset_name}_ito_parameters", ] if complex: matrix = _matrix_from_ito_complex(J[0], coefficients) else: matrix = _matrix_from_ito_real(J[0], coefficients) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute matrix from ITOs from " + BLUE + "Group " + RESET + '"' + BLUE + f"{full_group_name}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_matrix", "Dataset containing matrix from ITOs calculated from" f" group: {full_group_name}.", f"Group({slt}) containing matrix from ITO calculated" f" from group: {full_group_name}.", ] = matrix[:, :] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to save matrix from ITOs to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return matrix
[docs] def soc_zeem_in_z_angular_magnetic_momentum_basis( self, group: str, start_state: int, stop_state: int, matrix_type: Union["soc", "zeeman"], basis_kind: Union["magnetic", "total_angular"], rotation: ndarray[float64] = None, field: float64 = None, orientation: ndarray[float64] = None, slt: str = None, ) -> ndarray[complex128]: """ Calculates SOC or Zeeman matrix in "z" magnetic or total angular momentum basis. Parameters ---------- group : str Name of a group containing results of relativistic ab initio calculations used for obtaining the SOC or Zeeman matrix. start_state : int Number of the first SOC state to be included. stop_state : int Number of the last SOC state to be included. If both start and stop are set to zero all available states from the file will be used matrix_type : Union["soc", "zeeman"] Type of a matrix to be decomposed. Two options available: "soc" or "zeeman". basis_kind : Union["magnetic", "total_angular"] Kind of a basis. Two options available: "magnetic" or "total_angular" for the decomposition in a particular basis rotation : ndarray[float64], optional A (3,3) orthogonal rotation matrix used to rotate momenta matrices. Note that the inverse matrix has to be given to rotate the reference frame instead., by default None field : float64, optional _description_, by default None orientation : ndarray[float64], optional Orientation of the magnetic field in the form of an ArrayLike structure (can be converted to numpy.NDArray) [direction_x, direction_y, direction_z]., by default None slt : str, optional If given the results will be saved in a group of this name to .slt file with suffix: _{matrix_type}_matrix_in_{basis_kind}_basis., by default None Returns ------- ndarray[complex128] Matrix in a given kind of basis. Raises ------ SltInputError If an unsuported type of matrix or basis is provided. SltInputError If there is no field value or orientation provided for Zeeman matrix. SltSaveError If the name of the group already exists in the .slt file. SltCompError If the calculation of a matrix in "z" basis is unsuccessful. SltFileError If the program is unable to correctly save results to .slt file. """ if (matrix_type not in ["zeeman", "soc"]) or ( basis_kind not in ["total_angular", "magnetic"] ): raise SltInputError( NotImplementedError( "The only valid matrix types and pseudo spin kinds are" ' "soc" or "zeeman" and "magnetic" or "total_angular"' " respectively." ) ) if matrix_type == "zeeman" and ( (field is None) or (orientation is None) ): raise SltInputError( ValueError( "For Zeeman matrix provide field value and orientation." ) ) if slt is not None: slt_group_name = ( f"{slt}_{matrix_type}_matrix_in_{basis_kind}_basis" ) if _group_exists(self._hdf5, slt_group_name): raise SltSaveError( self._hdf5, NameError(""), message="Unable to save the results. " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '" ' + "already exists. Delete it manually.", ) from None try: if matrix_type == "zeeman": orientation = _normalize_orientation(orientation) matrix = _get_zeeman_matrix_in_z_pseudo_spin_basis( self._hdf5, group, field, orientation, start_state, stop_state, basis_kind, rotation, ) elif matrix_type == "soc": matrix = _get_soc_matrix_in_z_pseudo_spin_basis( self._hdf5, group, start_state, stop_state, basis_kind, rotation, ) except Exception as exc: raise SltCompError( self._hdf5, exc, "Failed to compute matrix from ITOs from " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if slt is not None: try: self[ slt_group_name, f"{slt}_matrix", f"Dataset containing {matrix_type} matrix in" f' {basis_kind} momentum "z" basis calculated from' f" group: {group}.", f"Group({slt}) containing {matrix_type} matrix in" f' {basis_kind} momentum "z" basis calculated from' f" group: {group}.", ] = matrix[:, :] except Exception as exc: raise SltFileError( self._hdf5, exc, f'Failed to save {matrix} matrix in "z"' f" {basis_kind} basis to " + BLUE + "Group " + RESET + '"' + BLUE + slt_group_name + RESET + '".', ) from None return matrix
[docs] def plot_mth( self, group: str, save: bool = False, colour_map_name: str or list[str] = "rainbow", xlim: tuple[int or float] = (), ylim: tuple[int or float] = (), xticks: int or float = 1, yticks: int or float = 0, field: Union["B", "H"] = "B", ): """ Creates graphs of M(H,T) given name of the group in HDF5 file, graphs can be optionally shown, saved, colour palettes can be changed. Parameters ---------- group: str Name of a group from HDF5 file for which a plot will be created. save: bool = False Determines if the plot is saved, name of the file will be in the following format: f"mgh_{group}.tiff". colour_map_name: str or list[str] = "rainbow" Input of the colour_map function. xlim: tuple(optional: float, optional: float) = () Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed. ylim: tuple(optional: float, optional: float) = () Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed. xticks: int or float = 1 Determines the frequency of x major ticks. yticks: int or float = 0 Determines the frequency of y major ticks. field: Union['B','H'] = 'B' Determines the field unit - B[T] or H[kOe]. Returns ------- Nothing Raises ------ SltFileError If unable to load the data file. Most likely encountered if the group name is incorrect. SltPlotError If unable to create the plot. SltSaveError If unable to save the plot as an image. See Also -------- slothpy.Compound.calculate_mth """ try: # Getting data from hdf5 or sloth file mth = self[f"{group}_magnetisation", f"{group}_mth"] fields = self[f"{group}_magnetisation", f"{group}_fields"] if field == "H": fields *= 10 xticks *= 10 temps = self[f"{group}_magnetisation", f"{group}_temperatures"] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load magnetisation file" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None try: # Plotting in matplotlib fig, ax = subplots() # Defining colour maps for graphs colour = iter( colour_map(colour_map_name)(linspace(0, 1, len(temps))) ) # Creating a plot for i, mh in enumerate(mth): c = next(colour) ax.plot(fields, mh, linewidth=2, c=c, label=f"{temps[i]} K") if yticks: ax.yaxis.set_major_locator(MultipleLocator(yticks)) ax.xaxis.set_major_locator(MultipleLocator(xticks)) ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.tick_params(which="major", length=7) ax.tick_params(which="minor", length=3.5) if field == "B": ax.set_xlabel(r"$B\ /\ \mathrm{T}$") elif field == "H": ax.set_xlabel(r"$H\ /\ \mathrm{kOe}$") ax.set_ylabel(r"$M\ /\ \mathrm{\mu_{B}}$") if xlim: if len(xlim) == 2: ax.set_ylim(xlim[0], xlim[1]) else: ax.set_ylim(xlim[0]) else: if len(temps) > 17: ax.set_xlim(0) ax.legend(loc="center left", bbox_to_anchor=(1, 0.5)) else: ax.set_xlim(0, fields[-1] + 0.3 * fields[-1]) ax.legend() if ylim: if len(ylim) == 2: ax.set_ylim(ylim[0], ylim[1]) else: ax.set_ylim(ylim[0]) else: ax.set_ylim(0) tight_layout() show() except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot magnetisation data" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if save: try: # Saving plot figure fig.savefig(f"mgh_{group}.tiff", dpi=300) except Exception as exc: raise SltSaveError( self._hdf5, exc, "Failed to save magnetisation data plot " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '", filename: ' + PURPLE + f"mgh_{group}.tiff", ) from None
[docs] def plot_chitht( self, group: str, save: bool = False, colour_map_name: str or list[str] = "funmat", xlim: tuple[int or float] = (), ylim: tuple[int or float] = (), xticks: int or float = 100, yticks: int or float = 0, field: Union["B", "H"] = "B", ): """ Creates graphs of chiT(H,T) or chi(H,T) depending on the content of .slt file, given a name of the group in .slt file, graphs can be optionally saved, colour palettes can be changed. Parameters ---------- group: str Name of a group from .slt file for which a plot will be created. save: bool = False Determines if the plot is saved, name of the file will be in the following format: f'chitht_{group}.tiff'. colour_map_name: str or list[str] = 'funmat' Input of colour_map function. xlim: tuple(optional: float, optional: float) = () Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed. ylim: tuple(optional: float, optional: float) = () Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed. xticks: int or float = 100 Determines the frequency of x major ticks. yticks: int or float = 0 Determines the frequency of y major ticks. field: Union['B','H'] = 'B' Determines the field unit - B[T] or H[kOe]. Returns ------- Nothing Raises ------ SltFileError If unable to load the data file. Most likely encountered if the group name is incorrect. SltPlotError If unable to create the plot. SltSaveError If unable to save the plot as an image. See Also -------- slothpy.Compound.calculate_chitht """ try: # Getting data from hdf5 or sloth file try: chi = self[f"{group}_susceptibility", f"{group}_chiht"] T = False except Exception as exc: chi = self[f"{group}_susceptibility", f"{group}_chitht"] T = True fields = self[f"{group}_susceptibility", f"{group}_fields"] if field == "H": fields *= 10 temps = self[f"{group}_susceptibility", f"{group}_temperatures"] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load susceptibility file" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None try: # Plotting in matplotlib fig, ax = subplots() # Defining colour maps for graphs colour = iter( colour_map(colour_map_name)(linspace(0, 1, len(fields))) ) # Creating a plot for i, ch in enumerate(chi): c = next(colour) ax.plot( temps, ch, linewidth=2, c=c, label=( f'{round(fields[i], 2)} {"kOe" if field == "H" else "T"}' ), ) ax.xaxis.set_major_locator(MultipleLocator(xticks)) if yticks: ax.yaxis.set_major_locator(MultipleLocator(yticks)) ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.tick_params(which="major", length=7) ax.tick_params(which="minor", length=3.5) ax.set_xlabel(r"$T\ /\ \mathrm{K}$") if T: ax.set_ylabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$" ) else: ax.set_ylabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$" ) if xlim: if len(xlim) == 2: ax.set_ylim(xlim[0], xlim[1]) else: ax.set_ylim(xlim[0]) else: ax.set_xlim(0, temps[-1]) if ylim: if len(ylim) == 2: ax.set_ylim(ylim[0], ylim[1]) else: ax.set_ylim(ylim[0]) else: ax.set_ylim(0) ax.legend() tight_layout() show() except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot susceptibility data" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if save: try: # Saving plot figure fig.savefig(f"chitht_{group}.tiff", dpi=300) except Exception as exc: raise SltSaveError( self._hdf5, exc, "Failed to save susceptibility data plot " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '", filename: ' + PURPLE + f"chitht_{group}.tiff", ) from None
[docs] def plot_helmholtz_energyth( self, group: str, internal_energy: bool = False, save: bool = False, colour_map_name: str or list[str] = "PrOr", xlim: tuple[int or float] = (), ylim: tuple[int or float] = (), xticks: int or float = 1, yticks: int or float = 0, field: Union["B", "H"] = "B", ): """ Creates graphs of Helmholtz energy(T,H) or internal energy(T,H) given a name of the group in .slt file, graphs can be optionally saved, colour palettes can be changed. Parameters ---------- group: str Name of a group from .slt file for which a plot will be created. internal_energy: bool = False Changes the plot from the Helmholtz to internal energy. save: bool = False Determines if the plot is saved, name of the file will be in the following format: f'energyth_{group}.tiff'. colour_map_name: str or list[str] = 'PrOr' Input of the colour_map function. xlim: tuple(optional: float, optional: float) = () Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed. ylim: tuple(optional: float, optional: float) = () Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed. xticks: int or float = 100 Determines the frequency of x major ticks. yticks: int = 0 Determines the freqency of y major ticks. field: Union['B','H'] = 'B' Determines the field unit - B[T] or H[kOe]. Returns ------- Nothing Raises ------ SltFileError If unable to load the data file. Most likely encountered if the group name is incorrect. SltPlotError If unable to create plot. SltSaveError If unable to save plot as image. See Also -------- slothpy.Compound.calculate_helmholtz_energyth """ if internal_energy: name = "internal" else: name = "helmholtz" try: # Getting data from hdf5 or sloth file eth = self[f"{group}_{name}_energy", f"{group}_eth"] fields = self[f"{group}_{name}_energy", f"{group}_fields"] if field == "H": fields *= 10 xticks *= 10 temps = self[f"{group}_{name}_energy", f"{group}_temperatures"] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load Helmholtz energy file" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None try: # Plotting in matplotlib fig, ax = subplots() # Defining colour maps for graphs colour = iter( colour_map(colour_map_name)(linspace(0, 1, len(temps))) ) # Creating a plot for i, eh in enumerate(eth): c = next(colour) ax.plot(fields, eh, linewidth=2, c=c, label=f"{temps[i]} K") if yticks: ax.yaxis.set_major_locator(MultipleLocator(yticks)) ax.xaxis.set_major_locator(MultipleLocator(xticks)) ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.tick_params(which="major", length=7) ax.tick_params(which="minor", length=3.5) if field == "B": ax.set_xlabel(r"$B\ /\ \mathrm{T}$") elif field == "H": ax.set_xlabel(r"$H\ /\ \mathrm{kOe}$") ax.set_ylabel(r"$E\ /\ \mathrm{cm^{-1}}$") if xlim: if len(xlim) == 2: ax.set_ylim(xlim[0], xlim[1]) else: ax.set_ylim(xlim[0]) else: if len(temps) > 17: ax.set_xlim(0, fields[-1]) ax.legend(loc="center left", bbox_to_anchor=(1, 0.5)) else: ax.set_xlim(0, fields[-1] + 0.3 * fields[-1]) ax.legend() if ylim: if len(ylim) == 2: ax.set_ylim(ylim[0], ylim[1]) else: ax.set_ylim(ylim[0]) tight_layout() show() except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot energy data" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if save: try: # Saving plot figure fig.savefig(f"energyth_{group}.tiff", dpi=300) except Exception as exc: raise SltSaveError( self._hdf5, exc, "Failed to save energy data plot " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '", filename: ' + PURPLE + f"energyth_{group}.tiff", ) from None
[docs] def plot_zeeman( self, group: str, save: bool = False, colour_map_name1: str or list[str] = "BuPi", colour_map_name2: str or list[str] = "BuPi_r", single: bool = False, xlim: tuple[int or float] = (), ylim: tuple[int or float] = (), xticks: int or float = 1, yticks: int or float = 0, field: Union["H", "B"] = "B", ): """ Function that creates graphs of E(H,orientation) given a name of the group in .slt file, graphs can be optionally saved, colour palettes can be changed. Parameters ---------- group: str Name of a group from .slt file for which a plot will be created. save: bool = False Determines if the plot is saved, name of the file will be in the following format: f'zeeman_{group}.tiff' or f'zeeman_{group} _Orientation {orientations[i]}.tiff'. colour_map_name1: str or list[str] = 'BuPi' Input of the colour_map function, determines a colour of the lower set of split lines. colour_map_name2: str or list[str] = 'BuPi_r' Input of the colour_map function, determines a colour of the higher set of split lines. single: bool = False Determines if all the orientations are plotted together. xlim: tuple of 1-2 floats = () Determines the lower and upper limit of the x-axis if two floats are passed, or just the upper limit if one is passed. ylim: tuple of 1-2 floats = () Determines the lower and upper limit of the y-axis if two floats are passed, or just the upper limit if one is passed. xticks: int or float = 1 Determines the frequency of x major ticks. yticks: int or float = 0 Determines the frequency of y major ticks. field: Union['B','H'] = 'B' Determines the field unit - B[T] or H[kOe]. Returns ------- Nothing Raises ------ SltFileError If unable to load the data file. Most likely encountered if the group name is incorrect. SltPlotError If unable to create the plot. SltSaveError If unable to save the plot as an image. See Also -------- slothpy.Compound.calculate_zeeman_splitting """ try: # Getting data from hdf5 or sloth file zeeman = self[f"{group}_zeeman_splitting", f"{group}_zeeman"] fields = self[f"{group}_zeeman_splitting", f"{group}_fields"] if field == "H": fields *= 10 xticks *= 10 orientations = self[ f"{group}_zeeman_splitting", f"{group}_orientations" ] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load Zeeman splitting file" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None try: # Plotting in matplotlib if not single: number_of_plots = len(orientations) if number_of_plots % 5 == 0: fig = figure(figsize=(16, 3.2 * (number_of_plots / 5))) gs = GridSpec(int(number_of_plots / 5), 5) divisor = 5 elif number_of_plots % 3 == 0: fig = figure(figsize=(9.6, 3.2 * (number_of_plots / 3))) gs = GridSpec(int(number_of_plots / 3), 3) divisor = 3 elif number_of_plots % 2 == 0: fig = figure(figsize=(6.4, 3.2 * (number_of_plots / 2))) gs = GridSpec(int(number_of_plots / 2), 2) divisor = 2 else: fig = figure(figsize=(6.4, 3.2 * number_of_plots)) gs = GridSpec(1, number_of_plots) divisor = 1 # Creating a plot for i, zee in enumerate(zeeman): if i % divisor != 0: rc( "axes", prop_cycle=_custom_colour_cycler( len(zeeman[0][0]), colour_map_name1, colour_map_name2, ), ) multiple_plots = fig.add_subplot( gs[i // divisor, i % divisor] ) plot(fields, zee, linewidth=0.75) multiple_plots.xaxis.set_major_locator( MultipleLocator(xticks * 2) ) if yticks: multiple_plots.yaxis.set_major_locator( MultipleLocator(yticks) ) multiple_plots.xaxis.set_minor_locator( AutoMinorLocator(2) ) multiple_plots.yaxis.set_minor_locator( AutoMinorLocator(2) ) multiple_plots.tick_params( which="major", left=False, labelleft=False, length=7, ) multiple_plots.tick_params( which="minor", left=False, length=3.5 ) if orientations.shape[1] != 3: title("Averaged Splitting") else: title( f"Orientation [{round(orientations[i][0], 3)}" + f"{round(orientations[i][1], 3)} {round(orientations[i][2], 3)}]" ) if xlim: if len(xlim) == 2: multiple_plots.set_xlim(xlim[0], xlim[1]) else: multiple_plots.set_xlim(xlim[0]) if ylim: if len(ylim) == 2: multiple_plots.set_ylim(ylim[0], ylim[1]) else: multiple_plots.set_ylim(ylim[0]) else: if (i // divisor) == 0: rc( "axes", prop_cycle=_custom_colour_cycler( len(zeeman[0][0]), colour_map_name1, colour_map_name2, ), ) multiple_plots = fig.add_subplot( gs[i // divisor, i % divisor] ) plot(fields, zee, linewidth=0.75) multiple_plots.xaxis.set_major_locator( MultipleLocator(xticks * 2) ) if yticks: multiple_plots.yaxis.set_major_locator( MultipleLocator(yticks) ) multiple_plots.xaxis.set_minor_locator( AutoMinorLocator(2) ) multiple_plots.tick_params(which="major", length=7) multiple_plots.tick_params( which="minor", length=3.5 ) multiple_plots.yaxis.set_minor_locator( AutoMinorLocator(2) ) if orientations.shape[1] != 3: title("Averaged Splitting") else: title( "Orientation" f" [{round(orientations[i][0], 3)} " f"{round(orientations[i][1], 3)} {round(orientations[i][2], 3)}]" ) if xlim: if len(xlim) == 2: multiple_plots.set_xlim(xlim[0], xlim[1]) else: multiple_plots.set_xlim(xlim[0]) if ylim: if len(ylim) == 2: multiple_plots.set_ylim(ylim[0], ylim[1]) else: multiple_plots.set_ylim(ylim[0]) else: rc( "axes", prop_cycle=_custom_colour_cycler( len(zeeman[0][0]), colour_map_name1, colour_map_name2, ), ) multiple_plots = fig.add_subplot( gs[i // divisor, i % divisor] ) plot(fields, zee, linewidth=0.75) multiple_plots.xaxis.set_major_locator( MultipleLocator(xticks * 2) ) if yticks: multiple_plots.yaxis.set_major_locator( MultipleLocator(yticks) ) multiple_plots.xaxis.set_minor_locator( AutoMinorLocator(2) ) multiple_plots.tick_params(which="major", length=7) multiple_plots.tick_params( which="minor", length=3.5 ) multiple_plots.yaxis.set_minor_locator( AutoMinorLocator(2) ) if orientations.shape[1] == 3: title("Averaged Splitting") else: title( "Orientation" f" [{round(orientations[i][0], 3)} " f"{round(orientations[i][1], 3)} {round(orientations[i][2], 3)}]" ) if xlim: if len(xlim) == 2: multiple_plots.set_xlim(xlim[0], xlim[1]) else: multiple_plots.set_xlim(xlim[0]) if ylim: if len(ylim) == 2: multiple_plots.set_ylim(ylim[0], ylim[1]) else: multiple_plots.set_ylim(ylim[0]) if field == "B": fig.supxlabel(r"$B\ /\ \mathrm{T}$") if field == "H": fig.supxlabel(r"$H\ /\ \mathrm{kOe}$") fig.supylabel(r"$\mathrm{Energy\ /\ cm^{-1}}$") tight_layout() show() elif single: for i, zee in enumerate(zeeman): rc( "axes", prop_cycle=_custom_colour_cycler( len(zeeman[0][0]), colour_map_name1, colour_map_name2, ), ) fig, ax = subplots() ax.plot(fields, zee, linewidth=0.75) if orientations.shape[1] != 3: title("Averaged Splitting") else: title( "Orientation" f" [{round(orientations[i][0], 3)} " f"{round(orientations[i][1], 3)} {round(orientations[i][2], 3)}]" ) if field == "B": ax.set_xlabel(r"$B\ /\ \mathrm{T}$") elif field == "H": ax.set_xlabel(r"$H\ /\ \mathrm{kOe}$") ax.set_ylabel(r"$\mathrm{Energy\ /\ cm^{-1}}$") ax.tick_params(which="major", length=7) ax.tick_params(which="minor", length=3.5) ax.xaxis.set_major_locator(MultipleLocator(xticks)) if yticks: ax.yaxis.set_major_locator(MultipleLocator(yticks)) ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) if xlim: if len(xlim) == 2: ax.set_xlim(xlim[0], xlim[1]) else: ax.set_xlim(xlim[0]) if ylim: if len(ylim) == 2: ax.set_ylim(ylim[0], ylim[1]) else: ax.set_ylim(ylim[0]) tight_layout() show() if save: try: # Saving plot figure fig.savefig( f"zeeman_{group}_Orientation" f" {orientations[i]}.tiff", dpi=300, ) except Exception as exc: raise SltSaveError( self._hdf5, exc, "Failed to save Zeeman splitting data plot" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '", filename: ' + PURPLE + f"zeeman_{group}_Orientation" + f" {orientations[i]}.tiff", ) from None except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot Zeeman splitting data" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if save and not single: try: # Saving plot figure fig.savefig(f"zeeman_{group}.tiff", dpi=300) except Exception as exc: raise SltSaveError( self._hdf5, exc, "Failed to save Zeeman splitting data plot " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '", filename: ' + PURPLE + f"zeeman_{group}.tiff", ) from None
[docs] def plot_3d( self, group: str, data_type: Union[ "chit", "chi", "helmholtz_energy", "internal_energy", "magnetisation", ], field_i: int, temp_i: int, save: bool = False, colour_map_name: str or list[str] = "dark_rainbow_r_l", round_temp: int = 3, round_field: int = 3, lim_scalar: float = 1.0, ticks: float = 1.0, r_density: int = 0, c_density: int = 0, axis_off: bool = False, ): """ Creates 3d plots of data dependent on field B[T] and temperature T[K]. Parameters ---------- group: str Name of a group from .slt file for which a plot will be created. data_type: Union["chit", "chi", "helmholtz_energy", "internal_energy", "magnetisation"] Type of the data that will be used to create plot. field_i: int Index of the field from dataset that will be used for the plot. temp_i: int Index of the temperature from the dataset that will be used for the plot. save: bool = False Determines if the plot is saved, name of the file will be in the following format: f'{group}_3d_{data_type}.tiff'. colour_map_name: str or list[str] = 'dark_rainbow_r_l' Input of the colour_map function. round_temp: int = 3 Determines how many digits will be rounded in the graph's title for temperature. round_field: int = 3 Determines how many digits will be rounded in the graph's title for field. lim_scalar: float = 1. Scalar used to set limits of the axes, smaller values magnify the plotted figure. ticks: float = 1. Frequency of the ticks on all axes. r_density: int = 0 Determines the rcount of a 3D plot. c_density: int = 0 Determines the ccount of a 3D plot. axis_off: bool = False Determines if the axes are turned off. Returns ------- Nothing Raises ------ SltFileError If unable to load data file. Most likely encountered if group name is incorrect. SltPlotError If unable to create plot. SltSaveError If unable to save plot as image. See Also -------- slothpy.Compound.calculate_mag_3d, slothpy.Compound.calculate_chit_3d, slothpy.Compound.calculate_helmholtz_energy_3d """ try: T = False if data_type == "chit": x = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][ 0, field_i, temp_i, :, : ] y = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][ 1, field_i, temp_i, :, : ] z = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][ 2, field_i, temp_i, :, : ] description = ( "ChiT dependance on direction," f" B={round(self[f'{group}_3d_susceptibility', f'{group}_fields'][field_i], round_field)} T," f"T={round(self[f'{group}_3d_susceptibility', f'{group}_temperatures'][temp_i], round_temp)} K" ) T = True elif data_type == "chi": x = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][ 0, field_i, temp_i, :, : ] y = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][ 1, field_i, temp_i, :, : ] z = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][ 2, field_i, temp_i, :, : ] description = ( "Chi dependance on direction," f" B={round(self[f'{group}_3d_susceptibility', f'{group}_fields'][field_i], round_field)} T," f"T={round(self[f'{group}_3d_susceptibility', f'{group}_temperatures'][temp_i], round_temp)} K" ) elif data_type == "helmholtz_energy": x = self[f"{group}_3d_helmholtz_energy", f"{group}_energy_3d"][ 0, field_i, temp_i, :, : ] y = self[f"{group}_3d_helmholtz_energy", f"{group}_energy_3d"][ 1, field_i, temp_i, :, : ] z = self[f"{group}_3d_helmholtz_energy", f"{group}_energy_3d"][ 2, field_i, temp_i, :, : ] description = ( "Hemholtz energy dependence on direction," f" B={round(self[f'{group}_3d_helmholtz_energy', f'{group}_fields'][field_i], round_field)} T," f"T={round(self[f'{group}_3d_helmholtz_energy', f'{group}_temperatures'][temp_i], round_temp)} K" ) elif data_type == "internal_energy": x = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 0 ] y = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 1 ] z = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 2 ] description = ( "Internal energy dependence on distance," f" B={round(self[f'{group}_3d_internal_energy', f'{group}_fields'][field_i], round_field)} T," f"T={round(self[f'{group}_3d_internal_energy', f'{group}_temperatures'][temp_i], round_temp)} K" ) elif data_type == "magnetisation": x = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][ 0, field_i, temp_i, :, : ] y = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][ 1, field_i, temp_i, :, : ] z = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][ 2, field_i, temp_i, :, : ] description = ( "Magnetisation dependence on direction," f" B={round(self[f'{group}_3d_magnetisation', f'{group}_fields'][field_i], round_field)} T," f"T={round(self[f'{group}_3d_magnetisation', f'{group}_temperatures'][temp_i], round_temp)} K" ) else: raise ValueError except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load the 3D data file" + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None try: fig = figure() ax = fig.add_subplot(projection="3d") max_array = array([max(x), max(y), max(z)]) lim = max(max_array) norm = Normalize(z.min(), z.max()) colors = colour_map(colour_map_name)(norm(z)) rcount, ccount, _ = colors.shape if not r_density: r_density = rcount if not c_density: c_density = ccount surface = ax.plot_surface( x, y, z, rcount=r_density, ccount=c_density, facecolors=colors, shade=False, ) surface.set_facecolor((0, 0, 0, 0)) ax.set_xlim(-lim * lim_scalar, lim * lim_scalar) ax.set_ylim(-lim * lim_scalar, lim * lim_scalar) ax.set_zlim(-lim * lim_scalar, lim * lim_scalar) # Important order of operations! if data_type == "susceptibility": if T: ax.set_xlabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) else: ax.set_xlabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "helmholtz_energy": ax.set_xlabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "magnetisation": ax.set_xlabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) if ticks == 0: for axis_i in [ax.xaxis, ax.yaxis, ax.zaxis]: axis_i.set_ticklabels([]) axis_i._axinfo["axisline"]["linewidth"] = 1 axis_i._axinfo["axisline"]["color"] = (0, 0, 0) axis_i._axinfo["grid"]["linewidth"] = 0.5 axis_i._axinfo["grid"]["linestyle"] = "-" axis_i._axinfo["grid"]["color"] = (0, 0, 0) axis_i._axinfo["tick"]["inward_factor"] = 0.0 axis_i._axinfo["tick"]["outward_factor"] = 0.0 axis_i.set_pane_color((0.95, 0.95, 0.95)) else: ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.zaxis.set_minor_locator(AutoMinorLocator(2)) if not (not T and ticks == 1): ax.xaxis.set_major_locator(MultipleLocator(ticks)) ax.yaxis.set_major_locator(MultipleLocator(ticks)) ax.zaxis.set_major_locator(MultipleLocator(ticks)) ax.grid(False) ax.set_box_aspect([1, 1, 1]) title(description) if axis_off: ax.set_axis_off() show() except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot 3D data " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None if save: try: if axis_off: fig.savefig( f"{group}_3d_{data_type}.tiff", transparent=True, dpi=600, ) fig.savefig(f"{group}_3d_{data_type}.tiff", dpi=600) except Exception as exc: raise SltSaveError( self._hdf5, exc, "Failed to save the 3D data plot " + BLUE + "Group " + RESET + '"' + BLUE + f"{group}" + RESET + '", filename: ' + PURPLE + f"{group}_3d_{data_type}.tiff", ) from None
[docs] def animate_3d( self, group: str, data_type: Union[ "chit", "chi", "helmholtz_energy", "internal_energy" "magnetisation", ], animation_variable: Union["temperature", "field"], filename: str, i_start: int = 0, i_end: int = -1, i_constant: int = 0, colour_map_name: str or list[str] = "dark_rainbow_r_l", lim_scalar: float = 1.0, ticks: int or float = 1, r_density: int = 0, c_density: int = 0, axis_off: bool = False, fps: int = 15, dpi: int = 100, bar: bool = True, bar_scale: bool = False, bar_colour_map_name: str or list[str] = "dark_rainbow_r", temp_rounding: int = 0, field_rounding: int = 0, ): """ Creates animations of 3d plots of data dependent on field B[T] and temperature T[K]. Parameters ---------- group: str Name of a group from .slt file for which a plot will be created. data_type: Union["chit", "chi", "helmholtz_energy", "internal_energy", "magnetisation"] Type of the data that will be used to create the plot. animation_variable: Union["temperature", "field"] Variable changing during the animation, can take one of two values: temperature or field. filename: str Name of the output .gif file. i_start: int = 0 Index of the first frame's field/temperature. i_end: int = -1 Index of the last frame's field/temperature. i_constant: int Index of the constant temperature/field value. colour_map_name: str or list = 'dark_rainbow_r_l' Input of tje colour_map function, determines a colour of the main figure. lim_scalar: float = 1. Scalar used to set the limits of axes, smaller values magnify the plotted figure. ticks: float = 1 Determines the ticks spacing. r_density: int = 0 Determines the rcount of the 3D plot. c_density: int = 0 Determines the ccount of the 3D plot. axis_off: bool = False Determines if the axes are turned off. fps: int Number of frames per second in the animation. dpi: int Dots per inch resolution of the frames. bar: bool = True Determines if the bar representing animation variable is shown. bar_scale: bool = False Determines if a scale should be shown for bar. bar_colour_map_name: str or list = 'dark_rainbow_r_l' Input of the colour_map function, determines a colour of the bar. temp_rounding: int = 0 Determines how many decimal places are shown in the bar/plot labels for temperatures. field_rounding: int = 0 Determines how many decimal places are shown in the bar/plot labels for fields. Returns ------- Nothing Raises ------ SltFileError If unable to load the data file. Most likely encountered if the group name is incorrect. SltPlotError If unable to create the plot. See Also -------- slothpy.Compound.calculate_mag_3d, slothpy.Compound.calculate_chit_3d, slothpy.Compound.calculate_helmholtz_energy_3d """ try: T = False if data_type == "chit": x0 = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][0] y0 = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][1] z0 = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][2] fields = self[f"{group}_3d_susceptibility", f"{group}_fields"] temps = self[ f"{group}_3d_susceptibility", f"{group}_temperatures" ] T = True elif data_type == "chi": x0 = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][0] y0 = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][1] z0 = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][2] fields = self[f"{group}_3d_susceptibility", f"{group}_fields"] temps = self[ f"{group}_3d_susceptibility", f"{group}_temperatures" ] elif data_type == "helmholtz_energy": x0 = self[ f"{group}_3d_helmholtz_energy", f"{group}_energy_3d" ][0] y0 = self[ f"{group}_3d_helmholtz_energy", f"{group}_energy_3d" ][1] z0 = self[ f"{group}_3d_helmholtz_energy", f"{group}_energy_3d" ][2] fields = self[ f"{group}_3d_helmholtz_energy", f"{group}_fields" ] temps = self[ f"{group}_3d_helmholtz_energy", f"{group}_temperatures" ] elif data_type == "internal_energy": x0 = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 0 ] y0 = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 1 ] z0 = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 2 ] fields = self[f"{group}_3d_internal_energy", f"{group}_fields"] temps = self[ f"{group}_3d_internal_energy", f"{group}_temperatures" ] elif data_type == "magnetisation": x0 = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][0] y0 = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][1] z0 = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][2] fields = self[f"{group}_3d_magnetisation", f"{group}_fields"] temps = self[ f"{group}_3d_magnetisation", f"{group}_temperatures" ] else: raise ValueError( "Acceptable data types: chit, chi, helmholtz_energy and" " magnetisation" ) except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load 3D data file" + BLUE + " Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None if animation_variable == "temperature": description = ( f"f{data_type[0].upper() + data_type[1:].split('_')} dependence" f" on direction, B={fields[i_constant]:.4f} T" ) elif animation_variable == "field": description = ( f"f{data_type[0].upper() + data_type[1:].split('_')} dependence" f" on direction, T={temps[i_constant]:.4f} K" ) else: raise ValueError( "There exist only two animation variables: field and" " temperature" ) title = description try: fig = figure() ax = fig.add_subplot(projection="3d") if bar: colour = iter( colour_map(bar_colour_map_name)( linspace(0, 1, i_end - i_start) ) ) indicator = linspace(0, 1, i_end - i_start) if bar_scale: def my_ticks(x, pos): if animation_variable == "temperature": return f"{round(x * temps[-1], temp_rounding)} K" else: return f"{round(x * fields[-1], field_rounding)} T" writer = PillowWriter(fps=fps) with writer.saving(fig, f"{filename}.gif", dpi): if animation_variable == "temperature": for i_temp in range(i_start, i_end): x = x0[i_constant, i_temp, :, :] y = y0[i_constant, i_temp, :, :] z = z0[i_constant, i_temp, :, :] if data_type == "chit": ax.set_xlabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "chi": ax.set_xlabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) elif ( data_type == "helmholtz_energy" or "internal_energy" ): ax.set_xlabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "magnetisation": ax.set_xlabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) else: raise ValueError( "Acceptable data types: chit, chi," " helmholtz_energy and magnetisation" ) max_array = array([max(x), max(y), max(z)]) lim = max(max_array) norm = Normalize(z.min(), z.max()) colors = colour_map(colour_map_name)(norm(z)) rcount, ccount, _ = colors.shape if not r_density: r_density = rcount if not c_density: c_density = ccount surface = ax.plot_surface( x, y, z, rcount=r_density, ccount=c_density, facecolors=colors, shade=False, ) surface.set_facecolor((0, 0, 0, 0)) ax.set_xlim(-lim * lim_scalar, lim * lim_scalar) ax.set_ylim(-lim * lim_scalar, lim * lim_scalar) ax.set_zlim(-lim * lim_scalar, lim * lim_scalar) # Important order of operations! if ticks == 0: for axis_i in [ax.xaxis, ax.yaxis, ax.zaxis]: axis_i.set_ticklabels([]) axis_i._axinfo["axisline"]["linewidth"] = 1 axis_i._axinfo["axisline"]["color"] = (0, 0, 0) axis_i._axinfo["grid"]["linewidth"] = 0.5 axis_i._axinfo["grid"]["linestyle"] = "-" axis_i._axinfo["grid"]["color"] = (0, 0, 0) axis_i._axinfo["tick"]["inward_factor"] = 0.0 axis_i._axinfo["tick"]["outward_factor"] = 0.0 axis_i.set_pane_color((0.95, 0.95, 0.95)) else: ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.zaxis.set_minor_locator(AutoMinorLocator(2)) if not (not T and ticks == 1): ax.xaxis.set_major_locator( MultipleLocator(ticks) ) ax.yaxis.set_major_locator( MultipleLocator(ticks) ) ax.zaxis.set_major_locator( MultipleLocator(ticks) ) ax.grid(False) ax.set_box_aspect([1, 1, 1]) ax.set_title(title) if axis_off: ax.set_axis_off() if bar: c = next(colour) axins = ax.inset_axes([0, 0.6, 0.098, 0.2]) axins.bar( 1, indicator[i_temp - i_start], width=0.2, color=c, ) axins.set_ylim(0, 1) if not bar_scale: axins.text( 1, 1, s=( f"{round(temps[i_end], temp_rounding)} K" ), verticalalignment="bottom", horizontalalignment="center", ) axins.text( 1, -0.03, s=( f"{round(temps[i_start], temp_rounding)} K" ), verticalalignment="top", horizontalalignment="center", ) axins.axison = False if bar_scale: axins.get_xaxis().set_visible(False) axins.xaxis.set_tick_params(labelbottom=False) axins.yaxis.set_major_formatter( FuncFormatter(my_ticks) ) axins.yaxis.set_minor_locator( AutoMinorLocator(2) ) writer.grab_frame() cla() elif animation_variable == "field": for i_field in range(i_start, i_end): x = x0[i_field, i_constant, :, :] y = y0[i_field, i_constant, :, :] z = z0[i_field, i_constant, :, :] if data_type == "chit": ax.set_xlabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "chi": ax.set_xlabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "helmholtz_energy": ax.set_xlabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$E\ /\ \mathrm{cm^{-1}}$", labelpad=20 * len(str(ticks)) / 4, ) elif data_type == "magnetisation": ax.set_xlabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) ax.set_ylabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) ax.set_zlabel( r"$M\ /\ \mathrm{\mu_{B}}$", labelpad=10 * len(str(ticks)) / 4, ) else: raise ValueError( "Acceptable data types: chit, chi," " helmholtz_energy and magnetisation" ) max_array = array([max(x), max(y), max(z)]) lim = max(max_array) norm = Normalize(z.min(), z.max()) colors = colour_map(colour_map_name)(norm(z)) rcount, ccount, _ = colors.shape if not r_density: r_density = rcount if not c_density: c_density = ccount surface = ax.plot_surface( x, y, z, rcount=r_density, ccount=c_density, facecolors=colors, shade=False, ) surface.set_facecolor((0, 0, 0, 0)) ax.set_xlim(-lim * lim_scalar, lim * lim_scalar) ax.set_ylim(-lim * lim_scalar, lim * lim_scalar) ax.set_zlim(-lim * lim_scalar, lim * lim_scalar) # Important order of operations! if ticks == 0: for axis in [ax.xaxis, ax.yaxis, ax.zaxis]: axis.set_ticklabels([]) axis._axinfo["axisline"]["linewidth"] = 1 axis._axinfo["axisline"]["color"] = (0, 0, 0) axis._axinfo["grid"]["linewidth"] = 0.5 axis._axinfo["grid"]["linestyle"] = "-" axis._axinfo["grid"]["color"] = (0, 0, 0) axis._axinfo["tick"]["inward_factor"] = 0.0 axis._axinfo["tick"]["outward_factor"] = 0.0 axis.set_pane_color((0.95, 0.95, 0.95)) else: ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.zaxis.set_minor_locator(AutoMinorLocator(2)) if not (not T and ticks == 1): ax.xaxis.set_major_locator( MultipleLocator(ticks) ) ax.yaxis.set_major_locator( MultipleLocator(ticks) ) ax.zaxis.set_major_locator( MultipleLocator(ticks) ) ax.grid(False) ax.set_box_aspect([1, 1, 1]) if axis_off: axis("off") if bar: c = next(colour) axins = ax.inset_axes([0, 0.6, 0.098, 0.2]) axins.bar( 1, indicator[i_field - i_start], width=0.2, color=c, ) axins.set_ylim(0, 1) if not bar_scale: axins.text( 1, 1, s=( f"{round(fields[i_end], field_rounding)} T" ), verticalalignment="bottom", horizontalalignment="center", ) axins.text( 1, -0.03, s=( f"{round(fields[i_start], field_rounding)} T" ), verticalalignment="top", horizontalalignment="center", ) axins.axison = False if bar_scale: axins.get_xaxis().set_visible(False) axins.xaxis.set_tick_params(labelbottom=False) axins.yaxis.set_major_formatter( FuncFormatter(my_ticks) ) writer.grab_frame() cla() else: raise ValueError( "There exist only two animation variables: field and" " temperature" ) except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot and save 3D data" + BLUE + " Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None
[docs] def interactive_plot_3d( self, group: str, data_type: Union[ "chit", "chi", "helmholtz_energy", "internal_energy", "magnetisation", ], colour_map_name: str or list[str] = "dark_rainbow_r", T_slider_colour: str = "#77f285", B_slider_colour: str = "#794285", temp_bar_colour_map_name: str or list[str] = "BuRd", field_bar_colour_map_name: str or list[str] = "BuPi", lim_scalar: float = 1.0, ticks: int or float = 1, bar: bool = True, bar_scale: bool = False, temp_rounding: int = 2, field_rounding: int = 2, axis_off: int = False, ): """ Creates interactive widget plot dependent on field and temperature values. Parameters ---------- group: str Name of a group from HDF5 file for which plot will be created. data_type: Union["chit", "chi", "helmholtz_energy", "internal_energy", "magnetisation"] Type of the data that will be used to create the plot. colour_map_name: str or list = 'dark_rainbow_r_l' Input of the colour_map function, determines a colour of the main figure. T_slider_colour: str Determines a colour of the temperature slider. B_slider_colour: str Determines a colour of the field slider. temp_bar_colour_map_name: str or list[str] = 'BuRd' Input of the colour_map function, determines a colour map of the temperature bar. field_bar_colour_map_name: str or list[str] = 'BuPi' Input of the colour_map function, determines a colour map of the field bar. lim_scalar: float = 1. Scalar used to set limits of the axes, smaller values magnify the plotted figure. ticks: float = 1 Determines the ticks spacing. bar: bool = True Determines if the bar is shown. bar_scale: bool = False Determines if the bar scale is shown. temp_rounding: int = 2 Determines how many significant digits are shown relative to the int(value) for temperature. temp_rounding: int = 2 Determines how many significant digits are shown relative to the int(value) for field. axis_off: bool = False Determines if the axes are turned off. Returns ------- Nothing Raises ------ SltFileError If unable to load the data file. Most likely encountered if the group name is incorrect. SltPlotError If unable to create the plot. See Also -------- slothpy.Compound.calculate_mag_3d, slothpy.Compound.calculate_chit_3d, slothpy.Compound.calculate_helmholtz_energy_3d """ field_i, temp_i = 0, 0 try: T = False if data_type == "chit": x0 = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][0] y0 = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][1] z0 = self[f"{group}_3d_susceptibility", f"{group}_chit_3d"][2] fields = self[f"{group}_3d_susceptibility", f"{group}_fields"] temps = self[ f"{group}_3d_susceptibility", f"{group}_temperatures" ] T = True if data_type == "chi": x0 = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][0] y0 = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][1] z0 = self[f"{group}_3d_susceptibility", f"{group}_chi_3d"][2] fields = self[f"{group}_3d_susceptibility", f"{group}_fields"] temps = self[ f"{group}_3d_susceptibility", f"{group}_temperatures" ] elif data_type == "helmholtz_energy": x0 = self[ f"{group}_3d_helmholtz_energy", f"{group}_energy_3d" ][0] y0 = self[ f"{group}_3d_helmholtz_energy", f"{group}_energy_3d" ][1] z0 = self[ f"{group}_3d_helmholtz_energy", f"{group}_energy_3d" ][2] fields = self[ f"{group}_3d_helmholtz_energy", f"{group}_fields" ] temps = self[ f"{group}_3d_helmholtz_energy", f"{group}_temperatures" ] elif data_type == "internal_energy": x0 = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 0 ] y0 = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 1 ] z0 = self[f"{group}_3d_internal_energy", f"{group}_energy_3d"][ 2 ] fields = self[f"{group}_3d_internal_energy", f"{group}_fields"] temps = self[ f"{group}_3d_internal_energy", f"{group}_temperatures" ] elif data_type == "magnetisation": x0 = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][0] y0 = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][1] z0 = self[f"{group}_3d_magnetisation", f"{group}_mag_3d"][2] fields = self[f"{group}_3d_magnetisation", f"{group}_fields"] temps = self[ f"{group}_3d_magnetisation", f"{group}_temperatures" ] except Exception as exc: raise SltFileError( self._hdf5, exc, "Failed to load 3d data file" + BLUE + " Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".' + RED + "Check if the group exists.", ) from None try: fig = figure() global ax ax = fig.add_subplot(projection="3d") if bar: colour1 = colour_map(temp_bar_colour_map_name)( linspace(0, 1, len(temps)) ) colour2 = colour_map(field_bar_colour_map_name)( linspace(0, 1, len(fields)) ) indicator1 = linspace(0, 1, len(temps)) indicator2 = linspace(0, 1, len(fields)) if bar_scale: def my_ticks(x, pos): return f"{round(x * temps[-1], temp_rounding)} K" def my_ticks2(x, pos): return f"{round(x * fields[-1], field_rounding)} T" x = x0[field_i, temp_i, :, :] y = y0[field_i, temp_i, :, :] z = z0[field_i, temp_i, :, :] max_array = array([max(x), max(y), max(z)]) lim = max(max_array) norm = Normalize(z.min(), z.max()) colors = colour_map(colour_map_name)(norm(z)) rcount, ccount, _ = colors.shape r_density = rcount c_density = ccount surface = ax.plot_surface( x, y, z, rcount=r_density, ccount=c_density, facecolors=colors, shade=False, ) surface.set_facecolor((0, 0, 0, 0)) ax.set_xlim(-lim * lim_scalar, lim * lim_scalar) ax.set_ylim(-lim * lim_scalar, lim * lim_scalar) ax.set_zlim(-lim * lim_scalar, lim * lim_scalar) # Important order of operations! labelpad = 20 * len(str(ticks)) / 4 if data_type in "chit": if T: ax_label = ( r"$\chi_{\mathrm{M}}T\ /\ \mathrm{cm^{3}mol^{-1}K}$" ) else: ax_label = ( r"$\chi_{\mathrm{M}}\ /\ \mathrm{cm^{3}mol^{-1}}$" ) elif data_type == "helmholtz_energy" or "internal_energy": ax_label = r"$E\ /\ \mathrm{cm^{-1}}$" elif data_type == "magnetisation": ax_label = r"$M\ /\ \mathrm{\mu_{B}}$" ax.set_xlabel(ax_label, labelpad=labelpad) ax.set_ylabel(ax_label, labelpad=labelpad) ax.set_zlabel(ax_label, labelpad=labelpad) if ticks == 0: for axis_i in [ax.xaxis, ax.yaxis, ax.zaxis]: axis_i.set_ticklabels([]) axis_i._axinfo["axisline"]["linewidth"] = 1 axis_i._axinfo["axisline"]["color"] = (0, 0, 0) axis_i._axinfo["grid"]["linewidth"] = 0.5 axis_i._axinfo["grid"]["linestyle"] = "-" axis_i._axinfo["grid"]["color"] = (0, 0, 0) axis_i._axinfo["tick"]["inward_factor"] = 0.0 axis_i._axinfo["tick"]["outward_factor"] = 0.0 axis_i.set_pane_color((0.95, 0.95, 0.95)) else: ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.zaxis.set_minor_locator(AutoMinorLocator(2)) if not (not T and ticks == 1): ax.xaxis.set_major_locator(MultipleLocator(ticks)) ax.yaxis.set_major_locator(MultipleLocator(ticks)) ax.zaxis.set_major_locator(MultipleLocator(ticks)) ax.grid(False) ax.set_box_aspect([1, 1, 1]) fig.subplots_adjust(left=0.1) if bar: c = colour1[temp_i] axins = ax.inset_axes([-0.05, 0.7, 0.098, 0.2]) axins.bar(1, indicator1[temp_i], width=0.2, color=c) axins.set_ylim(0, 1) c = colour2[field_i] axins2 = ax.inset_axes([-0.05, 0.2, 0.098, 0.2]) axins2.bar(1, indicator2[field_i], width=0.2, color=c) axins2.set_ylim(0, 1) if not bar_scale: axins.text( 1, 1, s=f"{round(temps[-1], 1)} K", verticalalignment="bottom", horizontalalignment="center", ) axins.text( 1, -0.03, s=f"{round(temps[0], 1)} K", verticalalignment="top", horizontalalignment="center", ) axins.axison = False axins2.text( 1, 1, s=f"{round(fields[-1], 1)} T", verticalalignment="bottom", horizontalalignment="center", ) axins2.text( 1, -0.03, s=f"{round(fields[0], 1)} T", verticalalignment="top", horizontalalignment="center", ) axins2.axison = False if bar_scale: axins.get_xaxis().set_visible(False) axins.xaxis.set_tick_params(labelbottom=False) axins.yaxis.set_major_formatter(FuncFormatter(my_ticks)) axins.yaxis.set_minor_locator(AutoMinorLocator(2)) axins2.get_xaxis().set_visible(False) axins2.xaxis.set_tick_params(labelbottom=False) axins2.yaxis.set_major_formatter(FuncFormatter(my_ticks2)) axins2.yaxis.set_minor_locator(AutoMinorLocator(2)) if bar: c = colour1[temp_i] axins = ax.inset_axes([-0.05, 0.7, 0.098, 0.2]) axins.bar(1, indicator1[temp_i], width=0.2, color=c) axins.set_ylim(0, 1) axins.text( 1, 1, s=f"{round(temps[-1], 1)} K", verticalalignment="bottom", horizontalalignment="center", ) axins.text( 1, -0.03, s=f"{round(temps[0], 1)} K", verticalalignment="top", horizontalalignment="center", ) ax_temp = fig.add_axes([0.05, 0.6, 0.1, 0.2]) ax_temp.axison = False ax_field = fig.add_axes([0.05, 0.3, 0.1, 0.2]) ax_field.axison = False slider_temp = Slider( ax_temp, "T [index]", valmin=0, valmax=temps.size - 1, orientation="vertical", valstep=1, initcolor=None, color=T_slider_colour, ) slider_field = Slider( ax_field, "B [index]", valmin=0, valmax=fields.size - 1, orientation="vertical", initcolor=None, valstep=1, color=B_slider_colour, ) def slider_update(val): temp_i = slider_temp.val field_i = slider_field.val ax.cla() x = x0[field_i, temp_i, :, :] y = y0[field_i, temp_i, :, :] z = z0[field_i, temp_i, :, :] max_array = array([max(x), max(y), max(z)]) lim = max(max_array) norm = Normalize(z.min(), z.max()) colors = colour_map(colour_map_name)(norm(z)) rcount, ccount, _ = colors.shape r_density = rcount c_density = ccount surface = ax.plot_surface( x, y, z, rcount=r_density, ccount=c_density, facecolors=colors, shade=False, ) surface.set_facecolor((0, 0, 0, 0)) ax.set_xlim(-lim * lim_scalar, lim * lim_scalar) ax.set_ylim(-lim * lim_scalar, lim * lim_scalar) ax.set_zlim(-lim * lim_scalar, lim * lim_scalar) ax.set_title( f"B={fields[field_i]:.4f} T, T={temps[temp_i]:.4f} K" ) ax.set_xlabel(ax_label, labelpad=labelpad) ax.set_ylabel(ax_label, labelpad=labelpad) ax.set_zlabel(ax_label, labelpad=labelpad) if ticks == 0: for axis_i in [ax.xaxis, ax.yaxis, ax.zaxis]: axis_i.set_ticklabels([]) axis_i._axinfo["axisline"]["linewidth"] = 1 axis_i._axinfo["axisline"]["color"] = (0, 0, 0) axis_i._axinfo["grid"]["linewidth"] = 0.5 axis_i._axinfo["grid"]["linestyle"] = "-" axis_i._axinfo["grid"]["color"] = (0, 0, 0) axis_i._axinfo["tick"]["inward_factor"] = 0.0 axis_i._axinfo["tick"]["outward_factor"] = 0.0 axis_i.set_pane_color((0.95, 0.95, 0.95)) else: ax.xaxis.set_minor_locator(AutoMinorLocator(2)) ax.yaxis.set_minor_locator(AutoMinorLocator(2)) ax.zaxis.set_minor_locator(AutoMinorLocator(2)) if not (not T and ticks == 1): ax.xaxis.set_major_locator(MultipleLocator(ticks)) ax.yaxis.set_major_locator(MultipleLocator(ticks)) ax.zaxis.set_major_locator(MultipleLocator(ticks)) ax.grid(False) fig.subplots_adjust(left=0.1) if bar: c = colour1[temp_i] axins = ax.inset_axes([-0.05, 0.7, 0.098, 0.2]) axins.bar(1, indicator1[temp_i], width=0.2, color=c) axins.set_ylim(0, 1) c = colour2[field_i] axins2 = ax.inset_axes([-0.05, 0.2, 0.098, 0.2]) axins2.bar(1, indicator2[field_i], width=0.2, color=c) axins2.set_ylim(0, 1) if not bar_scale: axins.text( 1, 1, s=f"{round(temps[-1], 1)} K", verticalalignment="bottom", horizontalalignment="center", ) axins.text( 1, -0.03, s=f"{round(temps[0], 1)} K", verticalalignment="top", horizontalalignment="center", ) axins.axison = False axins2.text( 1, 1, s=f"{round(fields[-1], 1)} T", verticalalignment="bottom", horizontalalignment="center", ) axins2.text( 1, -0.03, s=f"{round(fields[0], 1)} T", verticalalignment="top", horizontalalignment="center", ) axins2.axison = False if bar_scale: axins.get_xaxis().set_visible(False) axins.xaxis.set_tick_params(labelbottom=False) axins.yaxis.set_major_formatter( FuncFormatter(my_ticks) ) axins.yaxis.set_minor_locator(AutoMinorLocator(2)) axins2.get_xaxis().set_visible(False) axins2.xaxis.set_tick_params(labelbottom=False) axins2.yaxis.set_major_formatter( FuncFormatter(my_ticks2) ) axins2.yaxis.set_minor_locator(AutoMinorLocator(2)) fig.canvas.draw() slider_temp.on_changed(slider_update) slider_field.on_changed(slider_update) if axis_off: ax.set_axis_off() show() except Exception as exc: raise SltPlotError( self._hdf5, exc, "Failed to plot 3D data" + BLUE + " Group " + RESET + '"' + BLUE + f"{group}" + RESET + '".', ) from None