pdyna.analysis module

pdyna.analysis: The collection of analysis functions for outputs and figures.

pdyna.analysis.MO_correlation(cnsn, MDTimestep, SaveFigures, uniname)

Calculate the self-correlation of molecular vectors.

Parameters:

• cnsn (numpy.ndarray) – Molecular vectors.

• MDTimestep (float) – Molecular dynamics time step.

• SaveFigures (bool) – Whether to save the figure.

• uniname (str) – User-defined name for printing and figure saving.

Returns:

Time and correlation values.

Return type:

tuple

pdyna.analysis.Tilt_correlation(T, MDTimestep, smoother=0)

Compute time-correlation of tilting.

Parameters:

• T (numpy.ndarray) – Tilt data.

• MDTimestep (float) – Time step in picoseconds.

• smoother (int) – Smoothing window size.

Returns:

delta-t and self-correlation values of tilting.

Return type:

tuple

pdyna.analysis.abs_sqrt(m)

Calculate the sign-conversing square root of a number.

pdyna.analysis.compute_tilt_density(T, method='auto', plot_fitting=False, corr_vals=None)

Computes the tilt density from the given tilt angles.

Parameters:

• T (numpy.ndarray) – The tilt angle array.

• method (str) – The method for computing tilt density (‘auto’, ‘curve’, ‘kmean’, or ‘gaussian’).

• plot_fitting (bool) – Whether to plot the fitted peaks, only for the Gaussian mode.

• corr_vals (list) – NN1 Correlation values for the tilt angles.

Returns:

The fitted tilt angles for each axis.

Return type:

numpy.ndarray

pdyna.analysis.compute_tilt_domain(Corr, timestep, uniname, saveFigures, n_bins=42, tol=0, smoother=5)

Compute tilt domain lifetime.

Parameters:

• Corr (numpy.ndarray) – Correlation data.

• timestep (float) – Time step in picoseconds.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• tol (float) – Tolerance for zero crossing.

• smoother (int) – Smoothing window size.

Returns:

None

pdyna.analysis.defect_3D_scatter(peaks, uniname, deftype, saveFigures)

Draw a 3D scatter plot of defects.

Parameters:

• peaks (numpy.ndarray) – Peaks data.

• uniname (str) – User-defined name for printing and figure saving.

• deftype (str) – Type of defect.

• saveFigures (bool) – Whether to save the figure.

Returns:

None

pdyna.analysis.draw_MO_order_time(C, steps, uniname, saveFigures, smoother=0, n_bins=50)

Draw the evolution of molecular order over time.

Parameters:

• C (numpy.ndarray) – Correlation data.

• steps (numpy.ndarray) – Time steps.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – Smoothing window size.

• n_bins (int) – Number of bins for histogram.

Returns:

The time axis and the correlation data.

Return type:

tuple

pdyna.analysis.draw_MO_spatial_corr(C, uniname, saveFigures, n_bins=50)

Draw the spatial correlation of molecular orientations.

Parameters:

• C (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

Returns:

None

pdyna.analysis.draw_MO_spatial_corr_NN12(C, uniname, saveFigures, n_bins=100)

Draw the spatial correlation of molecular orientations for NN1 and NN2.

Parameters:

• C (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

Returns:

None

pdyna.analysis.draw_MO_spatial_corr_norm(C, uniname, saveFigures, n_bins=30)

Draw the normalized spatial correlation of molecular orientations.

Parameters:

• C (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

Returns:

The normalized spatial correlation data.

Return type:

numpy.ndarray

pdyna.analysis.draw_MO_spatial_corr_norm_var(C, uniname, saveFigures, n_bins=30)

Draw the normalized spatial correlation of molecular orientations.

Parameters:

• C (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

Returns:

The normalized spatial correlation data.

Return type:

numpy.ndarray

pdyna.analysis.draw_MO_spatial_corr_time(C, steps, uniname, saveFigures, smoother=0, n_bins=50)

Draw the evolution of spatial correlation of molecular orientations over time.

Parameters:

• C (numpy.ndarray) – Correlation data.

• steps (numpy.ndarray) – Time steps.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – Smoothing window size.

• n_bins (int) – Number of bins for histogram.

Returns:

The time axis and the correlation data.

Return type:

tuple

pdyna.analysis.draw_RDF(da, rdftype, uniname, saveFigures, n_bins=200)

Draw the radial distribution function (RDF) histogram.

Parameters:

• da (numpy.ndarray) – Data for RDF.

• rdftype (str) – Type of RDF (‘CN’ or ‘BX’).

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

Returns:

None

pdyna.analysis.draw_conntype_tilt_density(T, oc, uniname, saveFigures, n_bins=100, symm_n_fold=4, title=None)

Isolate tilting pattern wrt. the connectivity type.

Parameters:

• T (numpy.ndarray) – The tilt angle array.

• oc (list) – The connectivity type list.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• symm_n_fold (int) – Symmetry fold for periodicity.

• title (str) – Title for the plot.

Returns:

None

pdyna.analysis.draw_dist_density(D, uniname, saveFigures, n_bins=100, xrange=[0, 0.5], gaus_fit=True, title=None)

Draws the density of distortion parameters.

Parameters:

• D (numpy.ndarray) – The distortion array.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• xrange (list) – Range for the x-axis.

• gaus_fit (bool) – Whether to fit a Gaussian to the plot.

• title (str) – Title for the plot.

Returns:

The mean and standard deviation of the fitted Gaussian if gaus_fit = True.

Return type:

tuple

pdyna.analysis.draw_dist_density_frame(D, uniname, saveFigures, n_bins=100, xrange=[0, 0.5])

Draws the density of distortion parameters for frames.

Parameters:

• D (numpy.ndarray) – The distortion array.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• xrange (list) – Range for the x-axis.

Returns:

The mean of the fitted Gaussian for each distortion parameter.

Return type:

list of float

pdyna.analysis.draw_dist_evolution(D, steps, Tgrad, uniname, saveFigures=False, xaxis_type='N', Ti=None, x_lims=None, y_lims=None, invert_x=False)

Draws the evolution of distortion parameters over time or temperature or MD steps.

Parameters:

• D (numpy.ndarray) – The distortion array.

• steps (numpy.ndarray) – The time or MD steps.

• Tgrad (float) – The temperature gradient.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• xaxis_type (str) – The type of x-axis (‘N’, ‘t’, or ‘T’).

• Ti (float) – Initial temperature.

• x_lims (list) – Limits for the x-axis.

• y_lims (list) – Limits for the y-axis.

• invert_x (bool) – Whether to invert the x-axis.

Returns:

The steps and the distortion parameters.

Return type:

tuple

pdyna.analysis.draw_dist_evolution_time(D, steps, uniname, saveFigures, smoother=0, y_lim=None)

Draws the evolution of distortion over time.

Parameters:

• D (numpy.ndarray) – The distortion array.

• steps (numpy.ndarray) – The time or MD steps.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – The smoothing factor.

• y_lim (list) – Limits for the y-axis.

Returns:

The steps and the smoothed distortion parameters.

Return type:

tuple

pdyna.analysis.draw_distortion_evolution_sca(D, steps, uniname, saveFigures, xaxis_type='N', scasize=2.5, y_lim=0.4)

Draws the evolution of distortion parameters over time or temperature or MD steps.

Parameters:

• D (numpy.ndarray) – The distortion array.

• steps (numpy.ndarray) – The time or MD steps.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• xaxis_type (str) – The type of x-axis (‘N’, ‘t’, or ‘T’).

• scasize (float) – Size of the scatter points.

• y_lim (float) – Limit for the y-axis.

Returns:

None

pdyna.analysis.draw_halideconc_dist_density(Dconc, concent, uniname, saveFigures, n_bins=100, xrange=[0, 0.5])

Isolate distortion mode wrt. the local halide concentration.

Parameters:

• Dconc (list) – The distortion data of each concentraion level.

• concent (list) – The halide concentrations.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• xrange (list) – The range for the histogram.

Returns:

The fitted distortion, distortion standard deviation.

Return type:

tuple

pdyna.analysis.draw_halideconc_lat_density(Lconc, concent, uniname, saveFigures, n_bins=100)

Isolate lattice parameter wrt. the local halide concentration.

Parameters:

• Lconc (list) – The lattice data of each concentraion level.

• concent (list) – The halide concentrations.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

The fitted lattice parameters, lattice parameter standard deviation.

Return type:

tuple

pdyna.analysis.draw_halideconc_tilt_density(Tconc, brconc, concent, uniname, saveFigures, corr_vals=None, n_bins=100, symm_n_fold=4)

Isolate tilting pattern wrt. the local halide concentration.

Parameters:

• Tconc (list) – The tilting data of each concentraion level.

• brconc (list) – The bromine concentration.

• concent (list) – The halide concentrations.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• corr_vals (list) – The correlation values.

• n_bins (int) – Number of bins for the histogram.

• symm_n_fold (int) – The symmetry fold.

Returns:

The fitted tilt angles

Return type:

tuple

pdyna.analysis.draw_halideconc_tilt_density_transient(Tconc, steps, concent, uniname, saveFigures, smoother=0)

Isolate tilting pattern wrt. the local halide concentration.

Parameters:

• Tconc (list) – The tilting data of each concentraion level.

• steps (list) – The x-axis steps.

• concent (list) – The halide concentrations.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – The smoothing window size.

Returns:

The halide concentrations, steps, and tilting data.

Return type:

tuple

pdyna.analysis.draw_hetero_dist_density(Dcls, uniname, saveFigures, n_bins=100, xrange=[0, 0.5])

Isolate distortion mode wrt. the local halide configuration.

Parameters:

• Dcls (list) – The distortion data of each configuration.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• xrange (list) – The range for the histogram.

Returns:

The fitted distortion, distortion standard deviation.

Return type:

tuple

pdyna.analysis.draw_hetero_lat_density(Lcls, uniname, saveFigures, n_bins=100)

Isolate distortion mode wrt. the local halide configuration.

Parameters:

• Lcls (list) – The lattice data of each configuration.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

The fitted lattice parameters, lattice parameter standard deviation.

Return type:

tuple

pdyna.analysis.draw_hetero_tilt_density(Tcls, TCNcls, typelib, uniname, saveFigures, corr_vals=None, n_bins=100, symm_n_fold=4)

Isolate tilting pattern wrt. the local halide configuration.

Parameters:

• Tcls (list) – The tilt data of each configuration.

• TCNcls (list) – The tilt data of each configuration.

• typelib (str) – The type of tilt.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• corr_vals (list) – The correlation values.

• n_bins (int) – Number of bins for the histogram.

• symm_n_fold (int) – The symmetry fold.

Returns:

The maximum tilt values.

Return type:

list of floats

pdyna.analysis.draw_lattice_density(Lat, uniname, saveFigures=False, n_bins=50, num_crop=0, screen=None, title=None)

Draws the lattice density distribution for a given lattice parameter array.

Parameters:

• Lat (numpy.ndarray) – The lattice parameter array.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – The number of bins for the histogram.

• num_crop (int) – The number of initial rows to crop from the array.

• screen (list) – The range of values to screen.

• title (str) – The title of the plot.

Returns:

Mean and standard deviation of the lattice parameters.

Return type:

tuple

pdyna.analysis.draw_lattice_evolution(dm, steps, Tgrad, uniname, saveFigures=False, xaxis_type='N', Ti=None, x_lims=None, y_lims=None, invert_x=False)

Draws the evolution of lattice parameters over time or temperature or MD steps.

Parameters:

• dm (numpy.ndarray) – The lattice parameter array.

• steps (numpy.ndarray) – The time or MD steps.

• Tgrad (float) – The temperature gradient.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• xaxis_type (str) – The type of x-axis (‘N’, ‘t’, or ‘T’).

• Ti (float) – Initial temperature.

• x_lims (list) – Limits for the x-axis.

• y_lims (list) – Limits for the y-axis.

• invert_x (bool) – Whether to invert the x-axis.

Returns:

None

pdyna.analysis.draw_lattice_evolution_time(dm, steps, Ti, uniname, saveFigures, smoother=0, x_lims=None, y_lims=None)

Draws the evolution of lattice parameters over time.

Parameters:

• dm (numpy.ndarray) – The lattice parameter array.

• steps (numpy.ndarray) – The time or MD steps.

• Ti (float) – Initial temperature.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – The smoothing factor.

• x_lims (list) – Limits for the x-axis.

• y_lims (list) – Limits for the y-axis.

Returns:

The steps and the smoothed lattice parameters.

Return type:

tuple

pdyna.analysis.draw_octatype_dist_density(Dtype, config_types, uniname, saveFigures, n_bins=100, xrange=[0, 0.5])

Isolate distortion mode wrt. the local halide configuration.

Parameters:

• Dtype (list) – The distortion array for each type.

• config_types (list) – The configuration types.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• xrange (list) – Range for the histogram.

Returns:

The distortion values, and distortion standard deviations.

Return type:

tuple

pdyna.analysis.draw_octatype_lat_density(Ltype, config_types, uniname, saveFigures, n_bins=100)

Isolate distortion mode wrt. the local halide configuration.

Parameters:

• Ltype (list) – The lattice parameter array for each type.

• config_types (list) – The configuration types.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

The lattice values, and lattice standard deviations.

Return type:

tuple

pdyna.analysis.draw_octatype_tilt_density(Ttype, typelib, config_types, uniname, saveFigures, corr_vals=None, n_bins=100, symm_n_fold=4)

Isolate tilting pattern wrt. the local halide configuration.

Parameters:

• Ttype (list) – The tilt angle array for each type.

• typelib (list) – The types.

• config_types (list) – The configuration types.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• corr_vals (list) – The correlation values.

• n_bins (int) – Number of bins for the histogram.

• symm_n_fold (int) – Symmetry fold for periodicity.

Returns:

The fitted tilt angles.

Return type:

list

pdyna.analysis.draw_octatype_tilt_density_transient(Ttype, steps, typelib, config_types, uniname, saveFigures, smoother=0)

Isolate tilting pattern wrt. the local halide configuration in transient mode.

Parameters:

• Ttype (list) – The tilt angle array for each type.

• steps (numpy.ndarray) – The time or MD steps.

• typelib (list) – The types.

• config_types (list) – The configuration types.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – Smoothing window size.

Returns:

The configuration types, steps, and tilt angles.

Return type:

tuple

pdyna.analysis.draw_tilt_and_corr_density_full(T, Cf, uniname, saveFigures, n_bins=100, title=None)

Generate the full 3-by-3 array of Glazer plots including the off-diagonal correlations.

Parameters:

• T (numpy.ndarray) – Tilt data.

• Cf (numpy.ndarray) – Full correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• title (str) – Title of the plot.

Returns:

tilt correlation polarity (TCP) values of each axis and direction.

Return type:

numpy.ndarray

pdyna.analysis.draw_tilt_and_corr_density_shade(T, Corr, uniname, saveFigures, n_bins=100, title=None)

Generate the Glazer plot.

Parameters:

• T (numpy.ndarray) – Tilt data.

• Corr (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• title (str) – Title of the plot.

Returns:

tilt correlation polarity (TCP) values of each axis.

Return type:

list of floats

pdyna.analysis.draw_tilt_and_corr_density_shade_frame(T, Corr, uniname, saveFigures, n_bins=100)

Generate the Glazer plot for a single frame.

Parameters:

• T (numpy.ndarray) – Tilt data.

• Corr (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

tilt correlation polarity (TCP) values of each axis.

Return type:

list of floats

pdyna.analysis.draw_tilt_and_corr_density_shade_longarray(T, Corr, uniname, saveFigures, n_bins=100, title=None)

Generate the Glazer plot for a reshaped array.

Parameters:

• T (numpy.ndarray) – Tilt data.

• Corr (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• title (str) – Title of the plot.

Returns:

tilt correlation polarity (TCP) values of each axis.

Return type:

list of floats

pdyna.analysis.draw_tilt_and_corr_density_shade_non3D(T, Corr, uniname, saveFigures, n_bins=100, title=None)

Generate the Glazer plot for non-3D structures.

Parameters:

• T (numpy.ndarray) – Tilt data.

• Corr (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• title (str) – Title of the plot.

Returns:

tilt correlation polarity (TCP) values of each axis.

Return type:

list of floats

pdyna.analysis.draw_tilt_coaxial(T, uniname, saveFigures, n_bins=171, title=None)

Draw the coaxial tilting correlation plots.

Parameters:

• T (numpy.ndarray) – Tilt data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• title (str) – Title of the plot.

Returns:

None

pdyna.analysis.draw_tilt_corr_density_time(T, Corr, steps, uniname, saveFigures, smoother=0, n_bins=50)

Generate the time evolution of correlation density plots for tilting.

Parameters:

• T (numpy.ndarray) – Tilt data.

• Corr (numpy.ndarray) – Correlation data.

• steps (numpy.ndarray) – Time steps.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – Smoothing window size.

• n_bins (int) – Number of bins for the histogram.

Returns:

Time steps and correlation values for each axis.

Return type:

tuple

pdyna.analysis.draw_tilt_corr_evolution_sca(T, steps, uniname, saveFigures, xaxis_type='t', scasize=1.5, y_lim=[-1, 1])

Draw the tilt correlation evolution.

Parameters:

• T (numpy.ndarray) – Tilt data.

• steps (numpy.ndarray) – Steps data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• xaxis_type (str) – Type of x-axis (‘N’, ‘T’, or ‘t’).

• scasize (float) – Size of scatter points.

• y_lim (list) – Y-axis limits.

Returns:

None

pdyna.analysis.draw_tilt_density(T, uniname, saveFigures, n_bins=100, symm_n_fold=4, title=None)

Draws the density of tilt angles.

Parameters:

• T (numpy.ndarray) – The tilt angle array.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

• symm_n_fold (int) – Symmetry fold for periodicity.

• title (str) – Title for the plot.

Returns:

None

pdyna.analysis.draw_tilt_evolution(T, steps, Tgrad, uniname, saveFigures=False, xaxis_type='N', Ti=None, x_lims=None, y_lims=None, invert_x=False, use_gaussian=False)

Draws the evolution of tilt angles over time or temperature or MD steps.

Parameters:

• T (numpy.ndarray) – The tilt angle array.

• steps (numpy.ndarray) – The time or MD steps.

• Tgrad (float) – The temperature gradient.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• xaxis_type (str) – The type of x-axis (‘N’, ‘t’, or ‘T’).

• Ti (float) – Initial temperature.

• x_lims (list) – Limits for the x-axis.

• y_lims (list) – Limits for the y-axis.

• invert_x (bool) – Whether to invert the x-axis.

• use_gaussian (bool) – Whether to use Gaussian fitting (require a large enough data).

Returns:

The steps and the tilt angles.

Return type:

tuple

pdyna.analysis.draw_tilt_evolution_sca(T, steps, uniname, saveFigures, xaxis_type='t', scasize=2.5, y_lim=None)

Draws the evolution of tilt angles over time or temperature or MD steps.

Parameters:

• T (numpy.ndarray) – The tilt angle array.

• steps (numpy.ndarray) – The time or MD steps.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• xaxis_type (str) – The type of x-axis (‘N’, ‘t’, or ‘T’).

• scasize (float) – Size of the scatter points.

• y_lim (list) – Limits for the y-axis.

Returns:

None

pdyna.analysis.draw_tilt_evolution_time(T, steps, uniname, saveFigures, smoother=0, y_lim=None)

Draws the evolution of tilt angles over time.

Parameters:

• T (numpy.ndarray) – The tilt angle array.

• steps (numpy.ndarray) – The time or MD steps.

• uniname (str) – The user-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• smoother (int) – The smoothing factor.

• y_lim (list) – Limits for the y-axis.

Returns:

The steps and the smoothed tilt angles.

Return type:

tuple

pdyna.analysis.draw_tilt_prediction(c, pred, preds, yc, maxs, override=[False, False, False])

Draws the tilt prediction based on the computed density.

Parameters:

• c (numpy.ndarray) – The computed density.

• pred (list) – The total density.

• preds (list) – The individual peaks.

• yc (numpy.ndarray) – The y-coordinates for the density plot.

• maxs (list) – The maximum values for each tilt angle.

• override (list) – Flags to override the predictions.

Returns:

None

pdyna.analysis.draw_tilt_spatial_corr(C, uniname, saveFigures, n_bins=100)

Generate the spatial correlation plots for tilting.

Parameters:

• C (numpy.ndarray) – Correlation data.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

None

pdyna.analysis.draw_transient_properties(Lobj, Tobj, Cobj, Mobj, uniname, saveFigures)

Draw transient properties of the system.

Parameters:

• Lobj (list) – List containing lattice parameters.

• Tobj (list) – List containing tilting properties.

• Cobj (list) – List containing tilting correlation properties.

• Mobj (list) – List containing molecular properties.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

Returns:

None

pdyna.analysis.fit_3D_disp_atomwise(disp, readTimestep, uniname, moltype, saveFigures, n_bins=50, title=None)

A-site displacement calculation to extract vibration of atoms about their average position.

Parameters:

• disp (numpy.ndarray) – Displacement data.

• readTimestep (float) – Time step for reading data.

• uniname (str) – User-defined name for printing and figure saving.

• moltype (str) – Type of molecule.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

• title (str) – Title for the plot.

Returns:

The peaks of the displacement data.

Return type:

numpy.ndarray

pdyna.analysis.fit_3D_disp_total(dispt, uniname, moltype, saveFigures, n_bins=100, title=None)

A-site displacement calculation (total displacement for all given sites).

Parameters:

• dispt (numpy.ndarray) – Total displacement data.

• uniname (str) – User-defined name for printing and figure saving.

• moltype (str) – Type of molecule.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for histogram.

• title (str) – Title for the plot.

Returns:

None

pdyna.analysis.fit_damped_oscillator(x, y)

Fit a damped oscillator model to the given data.

Parameters:

• x (numpy.ndarray) – Independent variable data.

• y (numpy.ndarray) – Dependent variable data.

Returns:

The fitted frequency.

Return type:

float

pdyna.analysis.fit_exp_decay(x, y, allow_redo=True)

Fit an exponential decay to the given data.

Parameters:

• x (numpy.ndarray) – Independent variable data.

• y (numpy.ndarray) – Dependent variable data.

• allow_redo (bool) – Whether to allow a second fitting attempt.

Returns:

The fitted decay constant.

Return type:

float

pdyna.analysis.fit_exp_decay_both(x, y)

Fit a two-component exponential decay to the given data.

Parameters:

• x (numpy.ndarray) – Independent variable data.

• y (numpy.ndarray) – Dependent variable data.

Returns:

The fitted decay constants and coefficients.

Return type:

tuple

pdyna.analysis.fit_exp_decay_both_correct(x, y)

Fit a two-component exponential decay to the given data with correction term.

Parameters:

• x (numpy.ndarray) – Independent variable data.

• y (numpy.ndarray) – Dependent variable data.

Returns:

The fitted decay constants, coefficients, and correction term.

Return type:

tuple

pdyna.analysis.fit_exp_decay_fixed(x, y, aconst=0.9)

Fit a two-component exponential decay with a fixed coefficient to the given data.

Parameters:

• x (numpy.ndarray) – Independent variable data.

• y (numpy.ndarray) – Dependent variable data.

• aconst (float) – Fixed coefficient for the first exponential term.

Returns:

The fitted decay constant.

Return type:

float

pdyna.analysis.fit_exp_decay_single(x, y)

Fit a single exponential decay to the given data.

Parameters:

• x (numpy.ndarray) – Independent variable data.

• y (numpy.ndarray) – Dependent variable data.

Returns:

The fitted decay constant.

Return type:

float

pdyna.analysis.get_cube(limits=None)

Get the vertices, edges, and faces of a cuboid defined by its limits.

Parameters:

limits (numpy.ndarray) –

A 2D array of shape (3, 2) defining the limits of the cuboid. .. rubric:: Example

limits = np.array([[x_min, x_max],

[y_min, y_max], [z_min, z_max]])

Returns:

A tuple containing:

• vertices (numpy.ndarray): An array of the coordinates of the cuboid vertices.

• edges (numpy.ndarray): An array of paired indices for connecting vertices that form an edge.

• faces (numpy.ndarray): An array of groups of four indices that form a face.

Return type:

tuple

pdyna.analysis.get_norm_corr(TC, T)

Calculate normalized correlation from tensor components, converting 6 neighbours to three principle directions.

Parameters:

• TC (numpy.ndarray) – Tilting correlation components.

• T (numpy.ndarray) – Tilting magnitudes.

Returns:

Normalized correlation values.

Return type:

numpy.ndarray

pdyna.analysis.get_tcp_from_list(TC)

Calculate TCP from a list of tensor components.

Parameters:

TC (list of numpy.ndarray) – Tilting correlation components.

Returns:

TCP values.

Return type:

numpy.ndarray

pdyna.analysis.if_arrays_are_different(arr, tol=0.2)

Checks if the maximum and minimum values of an array are significantly different.

Parameters:

• arr (numpy.ndarray) – The input array.

• tol (float) – The tolerance value for comparison.

Returns:

A tuple indicating the category of difference.

Return type:

tuple

pdyna.analysis.orientation_density(cnsn, moltype, SaveFigures, uniname, title=None, miller_mask=False)

Visualize the orientation density of molecular vectors in 2D polar plot.

Parameters:

• cnsn (numpy.ndarray) – Molecular vectors.

• moltype (str) – Molecular type name.

• SaveFigures (bool) – Whether to save the figure.

• uniname (str) – User-defined name for printing and figure saving.

• title (str) – Title for the plot.

• miller_mask (bool) – Whether to apply Miller indices masking.

Returns:

None

pdyna.analysis.orientation_density_2pan(cnsn, nnsn, moltype, SaveFigures, uniname, title=None, miller_mask=True)

Visualize the orientation density of molecular vectors in 2D with two panels.

Parameters:

• cnsn (numpy.ndarray) – First molecular vectors.

• nnsn (numpy.ndarray) – Secondary molecular vectors.

• moltype (str) – Molecular type name.

• SaveFigures (bool) – Whether to save the figure.

• uniname (str) – User-defined name for printing and figure saving.

• title (str) – Title for the plot.

• miller_mask (bool) – Whether to apply Miller indices masking.

Returns:

None

pdyna.analysis.orientation_density_3D_dots(cnsn, moltype, SaveFigures, uniname, title=None)

Visualize the orientation density of molecular vectors in 3D.

Parameters:

• cnsn (numpy.ndarray) – Molecular vectors.

• moltype (str) – Molecular type name.

• SaveFigures (bool) – Whether to save the figure.

• uniname (str) – User-defined name for printing and figure saving.

• title (str) – Title for the plot.

Returns:

None

pdyna.analysis.orientation_density_3D_sphere(cnsn, moltype, SaveFigures, uniname, title=None)

Visualize the orientation density of molecular vectors in 3D using a sphere.

Parameters:

• cnsn (numpy.ndarray) – Molecular vectors.

• moltype (str) – Molecular type name.

• SaveFigures (bool) – Whether to save the figure.

• uniname (str) – User-defined name for printing and figure saving.

• title (str) – Title for the plot.

Returns:

Variance of the counts (spread metric).

Return type:

float

pdyna.analysis.peaks_3D_scatter(peaks, uniname, moltype, saveFigures)

Draw a 3D scatter plot of peaks.

Parameters:

• peaks (numpy.ndarray) – Peaks data.

• uniname (str) – User-defined name for printing and figure saving.

• moltype (str) – Type of molecule.

• saveFigures (bool) – Whether to save the figure.

Returns:

None

pdyna.analysis.print_partition(typelib, config_types, brconc, halcounts)

Print the partition of the halide configurations.

Parameters:

• typelib (list) – The list of halide configurations.

• config_types (list) – The configuration types.

• brconc (list) – The bromine concentration.

• halcounts (list) – The counts of halides.

Returns:

None

pdyna.analysis.properties_to_binned_grid(T, D, tcorr, bc, ss, bin_indices)

Assign tilting and distortion to 3D grids.

Parameters:

• T (numpy.ndarray) – Tilt data.

• D (numpy.ndarray) – Distortion data.

• tcorr (numpy.ndarray) – Time correlation data.

• bc (numpy.ndarray) – B-site displacement data.

• ss (int) – Supercell size of the grid.

• bin_indices (numpy.ndarray) – Binned indices of B-sites.

Returns:

Gridded tilt, distortion, time correlation, and B-site displacement values.

Return type:

tuple

pdyna.analysis.quantify_halideconc_tilt_domain(TCconc, concent, uniname, saveFigures, n_bins=100)

Isolate tilting pattern wrt. the local halide concentration.

Parameters:

• TCconc (numpy.ndarray) – Tilt correlation data.

• concent (list) – List of halide concentrations.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

Correlation lengths (diagonal and off-diagonal) for each concentration

Return type:

numpy.ndarray

pdyna.analysis.quantify_hetero_tilt_domain(TCcls, uniname, saveFigures, n_bins=100)

Isolate tilting pattern wrt. the local halide configuration in hetero-mode.

Parameters:

• TCcls (numpy.ndarray) – Tilt correlation data for each type.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

Correlation lengths (diagonal and off-diagonal) for each configuration type.

Return type:

numpy.ndarray

pdyna.analysis.quantify_octatype_tilt_domain(TCtype, config_types, uniname, saveFigures, n_bins=100)

Isolate tilting pattern wrt. the local halide configuration.

Parameters:

• TCtype (numpy.ndarray) – Tilt correlation data for each type.

• config_types (list) – List of halide configurations.

• uniname (str) – User-defined name for printing and figure saving.

• saveFigures (bool) – Whether to save the figure.

• n_bins (int) – Number of bins for the histogram.

Returns:

Correlation lengths (diagonal and off-diagonal) for each configuration type.

Return type:

numpy.ndarray

pdyna.analysis.quantify_tilt_domain(sc, scnorm, plot_label='tilt')

Compute spatial coorelation of tilting.

Parameters:

• sc (numpy.ndarray) – Spatial correlation data.

• scnorm (numpy.ndarray) – Normalized spatial correlation data.

• plot_label (str) – Label for plotting.

Returns:

Decay lengths for each tilt axis and spatial direction.

Return type:

numpy.ndarray

pdyna.analysis.savitzky_golay(y, window_size=51, order=3, deriv=0, rate=1)

Smooth (and optionally differentiate) data with a Savitzky-Golay filter.

References [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of

Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.

[2] Numerical Recipes 3rd Edition: The Art of Scientific Computing

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688

Parameters:

• y (numpy.ndarray) – the input signal

• window_size (int) – the length of the window (must be an odd integer)

• order (int) – the order of the polynomial used in the filtering

• deriv (int) – the order of the derivative to compute (default is 0 means only smoothing)

• rate (int) – rate of change of the x values (default is 1)

Returns:

the smoothed signal

Return type:

numpy.ndarray

pdyna.analysis.set_axes_equal(ax)

Set the aspect ratio of a 3D plot to be equal.

Parameters:

ax (matplotlib.axes._axes.Axes) – The axes object to set the aspect ratio for.

Returns:

None

pdyna.analysis.sphere_bin_count(cnsn)

Count the number of molecular vectors in spherical bins.

Parameters:

cnsn (numpy.ndarray) – Molecular vectors.

Returns:

Mesh coordinates (x, y, z), counts array, and variance (spread metric).

Return type:

tuple

pdyna.analysis.sphere_mesh(res=80)

Create a sphere mesh for visualization.

Parameters:

res (int) – Resolution of the sphere mesh.

Returns:

Mesh coordinates (x, y, z) and sampled points.

Return type:

tuple

pdyna.analysis.spherical_coordinates(cn)

Convert Cartesian coordinates to spherical coordinates.

Parameters:

cn (numpy.ndarray) – Cartesian coordinates (x, y, z).

Returns:

Spherical coordinates (theta, phi).

Return type:

tuple

pdyna.analysis.vis3D_domain_anime(cfeat, frs, tstep, ss, bin_indices, figname)

Visualise tilting in 3D animation. Better visual effects can be done with professional software.

Parameters:

• cfeat (numpy.ndarray) – Color feature data.

• frs (list) – Frame indices.

• tstep (float) – Time step.

• ss (int) – Supercell size of the grid.

• bin_indices (numpy.ndarray) – Binned indices of B-sites.

• figname (str) – Name of the figure file.

Returns:

None

pdyna.analysis.vis3D_domain_frame(cfeat, ss, bin_indices, cmap, clbedge, figname, saveFigures)

Visualise tilting in 3D for a single frame.

Parameters:

• cfeat (numpy.ndarray) – Color feature data.

• ss (int) – Supercell size of the grid.

• bin_indices (numpy.ndarray) – Binned indices of B-sites.

• cmap (str) – Color map.

• clbedge (float) – Color bar edge.

• figname (str) – Name of the figure file.

• saveFigures (bool) – Whether to save the figure.

Returns:

None