Model Decomposition#
- class sails.modal.MvarModalDecomposition[source]#
Object which calculates the modal decomposition of a fitted model derived from the AbstractLinearModel class. This is typically created using the
initialise()
classmethod which computes the decomposition and returns a populated object instance.- compute_modal_parameters()[source]#
Compute the order 1 or 2 autoregressive coefficients associated with each pole or conjugate pair.
Warning
This function is a work in progress and has not been fully validated.
- Returns:
Array containing the time-domain AR parameters for each mode
- Return type:
ndarray
- compute_residues()[source]#
Compute the residue matrix from the eigenvectors associated with each pole.
- Returns:
Array containing residue matrices for each pole.
- Return type:
ndarray
- excitation(resid_cov)[source]#
Compute the mode excitation as defined in [Neumaier2001]. This is a metric to quantify the dynamical importance of each mode in the decomposition.
Warning
This function is a work in progress and has not been fully validated.
- Parameters:
resid_cov (ndarray) – Residual covariance matrix for modelled system
- Returns:
Vector containing modal excitation values
- Return type:
ndarray
- get_mode_inds(fmin=0, fmax=None, mag_thresh=0, resid_thresh=0, index_mode='inclusive')[source]#
Helper function to identify mode indices based on given criteria.
- Parameters:
fmin (float) – Minimum frequency of modes to include (Default value = 0)
fmax (float) – Maximum frequency of modes to include (Default value = None)
mag_thresh (float ( 0 > mag_thresh > 1 )) – Minimum pole magnitude to include (Default value = 0)
resid_thresh (float) – Minimum value of mode residue norm to include (Default value = 0)
index_mode ({'inclusive','exclusive'}) – Flag indicating whether mode selection limits should be inclusive or exclusive (Default value = ‘inclusive’)
- Returns:
Array of integers indexing the included poles
- Return type:
ndarray
- classmethod initialise(model, sample_rate=None, normalise=False)[source]#
Compute the modal pole-residue decomposition of the A matrix from a fitted MVAR model.
Currently only implemented for a single realisation (A.ndim == 3)
- Parameters:
model (LinearModel) – Fitted model object. Must be derived from AbstractLinearModel.
sample_rate (float) – sample rate of system in Hz (Default value = None)
normalise (bool) – Whether to adjust the phase of the eigenvectors (Default value = False)
- Returns:
Modal decomposition object
- Return type:
type
- modal_timecourse(data)[source]#
Compute the modal time-course from a dataset and a fitted model. This is the transformation of a set of [nsignals x time] data observations into modal coordinates of shape [nmodes x time].
Warning
This function is a work in progress and has not been fully validated.
- Parameters:
data (ndarray) – Input data to convert into modal co-ordinates
- Returns:
Data transformed into modal time-series
- Return type:
ndarray
- modal_transfer_function(sample_rate, modes=None)[source]#
Compute a transfer function matrix based on the excitation period for each mode
- Parameters:
sample_rate (float) – sample rate of system in Hz
modes (list of int) – List of mode indices to evaluate over (optional) (Default value = None)
- Returns:
Transfer function computed for each mode
- Return type:
ndarray
- property mode_indices#
Returns a list of tuples of mode indices where each tuple contains the indices of either a pole-pair or an unpaired pole
- Returns:
list of tuples containing indices into the modes
- Return type:
List
- per_mode_transfer_function(sample_rate, freq_vect)[source]#
Extracts the transfer function for each mode by summing the transfer function across pole-pairs where necessary
The transfer function is computed for each pole using
transfer_function()
before summing individual modes (real valued poles or complex-conjugate pairs).- Parameters:
sample_rate – sample rate of system in Hz
freq_vect – Vector of frequencies at which to evaluate function
- Returns:
Array containing the transfer function for each individual mode
- Return type:
ndarray
- property period_hz#
This is an old and deprecated way of accessing peak_frequency
- pole_plot(ax=None, normscale=50, plottype='unitcircle')[source]#
Plot the poles of the current system.
- Parameters:
ax (matplotlib axes handle) – Optional axis on which to plot (Default value = None)
normscale (float) – Scaling factor for points on plot (Default value = 50)
plottype ({'unitcircle','eigenspectrum'}) – Flag indicating whether to plot results on a unit-circle or an eigenspectrum (Default value = ‘unitcircle’)
- Returns:
Reference to axes on which plot was drawn
- Return type:
matplotlib axes handle
- property residue_norm#
The matrix-norm of the residue matrix of each mode
- transfer_function(sample_rate, freq_vect, modes=None, sum_modes=True)[source]#
Compute the transfer function in pole-residue form, splitting the system into modes with separate transfer functions. The full system transfer function is then a linear sum of each modal transfer function.
When sum_modes is False, this function returns the transfer function for each individual pole (ie will return a transfer function for each pole in a conjugate pair). Please use per_mode_transfer_function to compute the transfer function for individual modes (ie one transfer function for each real pole or complex-conjugate pair)
- Parameters:
sample_rate (float) – sample rate of system in Hz
freq_vect (ndarray) – Vector of frequencies at which to evaluate function
modes (list of ints) – List of mode indices to evaluate over (optional) (Default value = None)
sum_modes (bool) – Boolean indicating whether to sum modes or return all (Default value = True)
- Returns:
Array containing the transfer function for each individual pole
- Return type:
ndarray