WigglyRivers.wavelet_tree package

Submodules

WigglyRivers.wavelet_tree.TreeScale module

Creation of tree scales class

class WigglyRivers.wavelet_tree.TreeScale.RiverTreeScales(trees=None, uid=0, logger=None)[source]

Bases: object

This class is the basic form of rivers.

Attribute	Description
uid	Unique identifier
trees	Dictionary of trees
tree_ids	List of tree ids
metrics	List of metrics
metrics_in_name	List of metrics in name

The following are the methods of the class.

Methods	Description
scale_coordinates	Scale coordinates by a given value

add_parameter_to_nodes(tree_ids=None, key=None, value=None)[source]: Add paramter to node

build_trees_from_tree_scales_dict(tree_scales)[source]: Build trees from tree scales dictionary

compile_database()[source]: Compile current trees databases to a single table

create_connectivity_matrix(tree_id)[source]: Create connectivity matrixrows and columns denote node IDs

filter_nodes(tree_ids=None, key=None, value=None)[source]: Filter nodes by key and value

load_tree(path_data)[source]: Load tree dictionary

load_trees_dict(trees_dict)[source]: Load data from a trees dictionary

prune(method='sinuosity', *args, **kwargs)[source]

save_tree(path_output='', file_name='tree.p')[source]: Save tree dictionary

save_tree_figure(tree_id, path_img='', file_name='tree.png')[source]: Save tree figure

select_node(tree_id, node_id)[source]: Select node with node_id

update_database()[source]: Update database

WigglyRivers.wavelet_tree.WaveletTreeFunctions module

These functions are based on Vermeulen et al. (2016) Meander tree generation

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

WigglyRivers.wavelet_tree.WaveletTreeFunctions.calculate_cwt(curvature, ds, pad=1, dj=0.05, s0=-1, j1=-1, mother='DOG', m=2)[source]

Description:

This function uses package created by Predybaylo (2014), modified by von Papen (2018), and is based on the MATLAB package created by Torrence and Compo (1998).

References:

Torrence, C., & Compo, G. P. (1998). A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, 79(1), 61–78. https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2

Args:

param curvature:: np.ndarray, Curvature of the river.
param ds:: float, Spatial resolution of the curvature.
param pad:: int, pad the time series with zeros, 1 or 0.
param dj:: float, spacing between discrete scales, 1/4 or 1/8.
param s0:: float, smallest scale of the wavelet, 2*dt or 1*dt.
param j1:: float, number of scales minus one, 7/4 or 3/2.
param mother:: str, mother wavelet function, can be ‘DOG’, ‘MORLET’, or ‘PAUL’.
param m:: int, order of the derivative of the Gaussian, 2 or 4.
return:: wave: real values of the wavelet transform. period: period of the wavelet. scales: scales of the wavelet. coi: cone of influence.

WigglyRivers.wavelet_tree.WaveletTreeFunctions.calculate_meander_shape(wave, wavelength, peak_row, peak_col, meander_id, bounds, scale, ds)[source]

Description:

Calculate the meander flatness and skewness using equation (7) and (8) from Vermulen et al. (2016).

This function is based on the matlab code by Vermulen et al. (2016)

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param wave:

np.ndarray, Waveform array.

param wavelength:

np.ndarray, Period array.

param peak_row:

np.ndarray, Peak row array.

param peak_col:

np.ndarray, Peak column array.

param meander_id:

np.ndarray, Meander id array.

param bounds:

np.ndarray, Bounds array.

param scale:

np.ndarray, Scale array.

param ds:

float, Sampling distance.

return:

sk_val, fl_val

WigglyRivers.wavelet_tree.WaveletTreeFunctions.check_conn(conn)[source]

Description:

Check if the connection matrix is valid.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
return:: conn
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.clean_tree(conn, meander_id)[source]

Description:

Remove all nodes from the tree with scales smaller than the meander scale.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
param meander_id:: np.ndarray, Meander indices
type meander_id:: np.ndarray
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.detect_meanders(wave, conn, peak_row, peak_col)[source]

Description:

Detect meanders in a wavelet transform from generated tree.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param wave:: np.ndarray, Wavelet transform
type wave:: np.ndarray
param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
param peak_row:: np.ndarray, Row indices of the peaks
type peak_row:: np.ndarray
param peak_col:: np.ndarray, Column indices of the peaks
type peak_col:: np.ndarray
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.find_peak_in_poly(poly, wave)[source]

Description:

Detect peaks of a 2D function within the given simple polygons

Args:

param poly:: np.ndarray, Polygons defining the regions of the cwt.
type poly:: np.ndarray
param wave:: np.ndarray, Wavelet transform
type wave:: np.ndarray
return:: (peak_pwr, peak_row, peak_col) - Peak power, row and column
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.find_wave_significance(curvature, ds, scales, sigtest=0, lag1=0, siglvl=0.95, dof=None, mother='DOG', param=None, gws=None)[source]

Description:

Calculate wave significiance.

This function uses package created by Predybaylo (2014), modified by von Papen (2018), and is based on the MATLAB package created by Torrence and Compo (1998).

References:

Torrence, C., & Compo, G. P. (1998). A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society, 79(1), 61–78. https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2

Args:

param curvature:

np.ndarray, Curvature of the river.

param ds:

float, Spatial resolution of the curvature.

param scales:

np.ndarray, Scales of the wavelet.

param sigtest:

int, perform significance test, 0, 1, or 2. Default is 0. If 0 (default), then just do a regulat chi-square test, i.e., Eqn (18) from Torrence and Compo (1998). If 1, then do a “time-average” test, i.e., Eqn (23). In this case, DOF should be set to np.nan, the number of local wavelet spectra that were averaged together. For the Global Wavelet Spectrum, this would be NA=N, where N is the number of points in the time series. If 2, then do a “scale-average” test, i.e., Eqn (25)-(28). In this case, DOF should be set to a two-element vector [S1,S2], which gives the scale range that were averaged together. For example, if the average between scales 2 and 8 was taken, then DOF=[2,8].

param lag1:

int, lag-1 autocorrelation, used for signif levels. Default is 0.

param siglvl:

float, significance level to use. Default is 0.95.

param dof:

int, degrees of freedom for significance test. If sigtest=0, then (automatically) set to 2 (or 1 for mother=’DOG’). If sigtest=1, then set to DOF=np.nan, the number if times averaged. If sigtest=2, then set to DOF=[S1,S2], the range of scales averaged.

param mother:

str, mother wavelet function, can be ‘DOG’, ‘MORLET’, or ‘PAUL’.

param param:

float, parameter for the mother wavelet.

param gws:

np.ndarray, global wavelet spectrum.

return:

signif: significance levels as a function of scale.
sig95: 95% significance level as a function of scale.

WigglyRivers.wavelet_tree.WaveletTreeFunctions.find_zc_lines(cwt_matrix)[source]

Description:

Find the zero-crossing lines pairs and the location of the singular points in the spectrum.

Based on Vermeulen et al. (2016) Meander tree generation

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param cwt_matrix:

np.ndarray, Wavelet transform of the curvature.

return:

conn: Vector in which each index corresponds to a tree node.: Roots nodes have a value of -1, while the other nodes have a value pointing to the row in conn of their parent node.
regions: Matrix that contains the same number of indices as conn.: for each index in conn the corresponding row in regions give the scale boundaries of the node and the spatial boundaries derived given the scale boundaries derived from where the zero crossing lines leave the scale space plane. The first column is the smallest bounding period, the second column is the largest bounding period, the third column is the spatial coordinate where the region starts and the last column is the spatial coordinate where the region ends.
poly: returns a vector of cells with the same size as conn containing: the coordinates of a polygon bounding the region of the corresponding node in conn. Unlike regions these coordinates follow the zero crossings lines bounding the region. The coordinates are given as [row, col].
zc_lines: return all zero corssing lines detected. Each element in: zc_lines contains a Nx2 matrix containing the coordinates of the zero crossing line given as [row, col].

zc_sign: returns the sign of each zero crossing line in zc_lines.

WigglyRivers.wavelet_tree.WaveletTreeFunctions.get_branch(cp, conn)[source]

Description:

Get the branch of a node in a tree from leafs to root.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param cp:: int, Node index
type cp:: int
param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.get_centers(conn, peak_row, peak_col, period, ds, x, y, extract_all=False, bound_to_poly=False, bounds=None)[source]

Description:

Computes the center of curving sections in the multiple loop tree

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
param peak_row:: np.ndarray, Row indices of the peaks
type peak_row:: np.ndarray
param peak_col:: np.ndarray, Column indices of the peaks
type peak_col:: np.ndarray
param period:: np.ndarray, Period of the wavelet transform
type period:: np.ndarray
param ds:: float, Delta of distance
type ds:: float
param x:: np.ndarray, X coordinates in the planimetry
type x:: np.ndarray
param y:: np.ndarray, Y coordinates in the planimetry
type y:: np.ndarray
return:: xc: np.ndarray, X coordinates of the center of curving sections yc: np.ndarray, Y coordinates of the center of curving sections
rtype:: np.ndarray

WigglyRivers.wavelet_tree.WaveletTreeFunctions.get_tree_scales_dict(conn, peak_row, peak_col, peak_pwr, wave, wavelength, scales, ds, x, y, s_curvature, poly, include_metrics=True, bound_to_poly=False)[source]

Description:

Computes the scales of the tree branches and collects all the information in a dictionary.

Args:

param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
param peak_row:: np.ndarray, Row indices of the peaks
type peak_row:: np.ndarray
param peak_col:: np.ndarray, Column indices of the peaks
type peak_col:: np.ndarray
param peak_pwr:: np.ndarray, Power of the peaks
type peak_pwr:: np.ndarray
param wavelength:: np.ndarray, Period of the peaks
type wavelength:: np.ndarray
param scales:: np.ndarray, Scales of the peaks
type scales:: np.ndarray
param ds:: float, Sampling distance
type ds:: float
param x:: np.ndarray, X coordinates of the river
type x:: np.ndarray
param y:: np.ndarray, Y coordinates of the river
type y:: np.ndarray
param poly:: np.ndarray, Polygon deliniating the scale tree
type poly:: np.ndarray

WigglyRivers.wavelet_tree.WaveletTreeFunctions.get_zcline(zcr, rw_start, col_start)[source]

Description:

Find zero crossing line given its starting position (singular point)

Based on Vermeulen et al. (2016) Meander tree generation

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param zcr:: np.ndarray, zcr lines.
type zcr:: np.ndarray
param rw_start:: int, Starting row
type rw_start:: int
param col_start:: int, Starting column
type col_start:: int
return:: (rw, col)
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.hexl(inmat)[source]

Description:

Constructs a hexagonal lattice for saddle points and extremes detection.

The size of the lattixe is [inmat.size(), 6], i.e. it has six elements in the third dimension each containing one of the dix surrounding elements in the lattice, in the following order: top left, top center, mid left, mid right, bottom center, bottom right.

This function was coded in MATLAB initially on Vermulen et al. (2016), and is based on Kuijper (2004).

References:

Kuijper, A. (2004), On detecting all saddle points in 2D images, Pattern
Recogn. Lett., 25 (15), 1665-1672, doi:10.1016/j.patrec.2004.06.017

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param inmat:: np.ndarray, Input matrix
type inmat:: np.ndarray
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.inpolygon(x, y, xv, yv)[source]

Description:

Check if points are inside a polygon

Based on Vermeulen et al. (2016) Meander tree generation

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param x:: np.ndarray, x coordinates of polygon vertices
type x:: np.ndarray
param y:: np.ndarray, y coordinates of polygon vertices
type y:: np.ndarray
param xv:: np.ndarray, x coordinates of points to check
type xv:: np.ndarray,
param yv:: np.ndarray, y coordinates of points to check
type yv:: np.ndarray
return:: is_inside: boolean vector with True if point is inside polygon
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.meander_bounds(poly, meander_id, peak_row, include_all=False)[source]

Description:

Computes the start and end-point of meander

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param poly:: np.ndarray, Polygon in the wavelet
param meander_id:: np.ndarray, Meander indices
param peak_row:: np.ndarray, Row indices of the peaks
return:: bounds: bounding indices for the meander

WigglyRivers.wavelet_tree.WaveletTreeFunctions.n_child(conn)[source]

Description:

Get the number of children for each node.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.plot_regions(regions, ax=None, **kwargs)[source]

Description:

Plot tree regions as done by Witkin 1984 based on the matlab code by Vermulen et al. (2016)

References:

Witkin, A. P. (1984), Scale-space filtering: A new approach to multi-scale description, in Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP ’84, vol. 9, pp. 150–153, IEEE, doi:10.1109/ICASSP.1984.1172729.

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param regions:: np.ndarray, Regions array comming from the scale_space_tree function.
type regions:: np.ndarray
param ax:: axis handle, Axis handle to plot the regions.
type ax:: plt.axis
param kwargs:: dict, Keyword arguments to pass to the plot function.
type kwargs:: dict
return:: h
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.plot_tree(conn, x, y, ax=None, **kwargs)[source]

Description:

Plot a tree given its connection matrix and its node coordinates.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param conn:: np.ndarray, Connection matrix.
type conn:: np.ndarray
param x:: np.ndarray, x node coordinates.
type x:: np.ndarray
param y:: np.ndarray, y node coordinates.
type y:: np.ndarray
param ax:: axis handle, Axis handle to plot the tree.
type ax:: plt.axis
param kwargs:
type kwargs:
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.recursive_tree_structure(pair, i_node, singular_points, belongs_to, parent_node=None, pairs_taken=[])[source]

WigglyRivers.wavelet_tree.WaveletTreeFunctions.remove_nodes(conn, frm)[source]

Description:

Remove nodes from a tree (they become isolated root nodes).

This function was coded in MATLAB initially on Vermulen et al. (2016).

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param conn:: np.ndarray, Connection matrix
type conn:: np.ndarray
param frm:: np.ndarray, Vector with nodes to remove
type frm:: np.ndarray
return:: conn: Connection matrix
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.remove_peak_from_nodes(frm, peak_row, peak_col, peak_pwr)[source]

Description:

Remove a peak from the nodes.

This function was coded in MATLAB initially on Vermulen et al. (2016).

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param frm:: np.ndarray, Vector with nodes to remove
type frm:: np.ndarray
param peak_row:: np.ndarray, Row indices of the peaks
type peak_row:: np.ndarray
param peak_col:: np.ndarray, Column indices of the peaks
type peak_col:: np.ndarray
param peak_pwr:: np.ndarray, Power of the peaks
type peak_pwr:: np.ndarray
return:: peak_row, peak_col, peak_pwr: np.ndarray, Row and column indices and power of the peaks

WigglyRivers.wavelet_tree.WaveletTreeFunctions.sadext(inmat)[source]

Description:

Detect saddle points and extremes in a 2D matrix (Vermulen, 2016; Kuijper, 2004)

ID has the same size as inmat and contains an id which can have one of the following values:

0: The point is a local extreme 2: the point is a regular point 4: The point is a saddle point 6: The point is a degenerate saddle point

This function requires the hexl function to build the hexagonal lattice.

References:

Kuijper, A. (2004), On detecting all saddle points in 2D images, Pattern Recogn. Lett., 25 (15), 1665-1672, doi:10.1016/j.patrec.2004.06.017

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param inmat:
type inmat:
return:
rtype:

WigglyRivers.wavelet_tree.WaveletTreeFunctions.scale_space_tree(cwt_matrix)[source]

Description:

Construct a ternary scale space tree from the zero crossings of the wavelet transform of the curvature.

Based on Vermeulen et al. (2016) Meander tree generation

References:

Vermeulen, B., A. J. F. Hoitink, G. Zolezzi, J. D. Abad, and R. Aalto (2016), Multi-scale structure of meanders, Geophys. Res. Lett., 43, doi:10.1002/2016GL068238.

Args:

param cwt_matrix:

np.ndarray, Wavelet transform of the curvature.

return:

conn: Vector in which each index corresponds to a tree node.: Roots nodes have a value of -1, while the other nodes have a value pointing to the row in conn of their parent node.
regions: Matrix that contains the same number of indices as conn.: for each index in conn the corresponding row in regions give the scale boundaries of the node and the spatial boundaries derived given the scale boundaries derived from where the zero crossing lines leave the scale space plane. The first column is the smallest bounding period, the second column is the largest bounding period, the third column is the spatial coordinate where the region starts and the last column is the spatial coordinate where the region ends.
poly: returns a vector of cells with the same size as conn containing: the coordinates of a polygon bounding the region of the corresponding node in conn. Unlike regions these coordinates follow the zero crossings lines bounding the region. The coordinates are given as [row, col].
zc_lines: return all zero corssing lines detected. Each element in: zc_lines contains a Nx2 matrix containing the coordinates of the zero crossing line given as [row, col].

zc_sign: returns the sign of each zero crossing line in zc_lines.

WigglyRivers.wavelet_tree.waveletFunctions module

WigglyRivers.wavelet_tree.waveletFunctions.calculate_global_wavelet_spectrum(wave)[source]

Description:

Calculates the global wavelet spectrum (GWS) from the wavelet transform using equation (22) in Torrence and Compo (1998). This function also finds the index for the peaks in the global wavelet spectrum.

Created by Daniel Gonzalez-Duque on 11/19/2023.

References:

Torrence, C., and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61–78, https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2

Args:

param wave:

np.ndarray, Wavelet transform.

return:

gws: np.ndarray, Global wavelet spectrum. peaks: np.ndarray, Indices for the peaks in the GWS.

WigglyRivers.wavelet_tree.waveletFunctions.calculate_scale_averaged_wavelet_power(wave, scales, ds, dj, c_delta)[source]

Description:

Calculates the scale-averaged wavelet power (SAWP) from the wavelet transform using equation (9) in Zolezzi and Güneralp (2016).

Created by Daniel Gonzalez-Duque on 11/19/2023.

References:

Zolezzi, G., & Güneralp, I. (2016). Continuous wavelet characterization of the wavelengths and regularity of meandering rivers. Geomorphology, 252, 98–111. https://doi.org/10.1016/j.geomorph.2015.07.029

Args:

param wave:

np.ndarray, Wavelet transform.

param scales:

np.ndarray, Vector of scales.

param dt:

float, Time or spatial resolution of the data.

param dj:

float, Scale increment.

param c_delta:

float, Reconstruction factor.

return:

Scale-averaged wavelet power.

WigglyRivers.wavelet_tree.waveletFunctions.chisquare_inv(P, V)[source]

WigglyRivers.wavelet_tree.waveletFunctions.chisquare_solve(XGUESS, P, V)[source]

WigglyRivers.wavelet_tree.waveletFunctions.iwavelet(Y, dt, scale, scale_indices=None, mother='MORLET', param=None)[source]

Description:

Inverse wavelet transform of Y, using [Eqn(11)] in Torrence and Compo (1998).

Created by Daniel Gonzalez-Duque on 07/02/2023

Args:

param Y:: np.ndarray, Wavelet transform of a time series.
param dt:: float, Time interval between samples.
param scale:: np.ndarray, Vector of scale indices.
param scale_indices:: np.ndarray, Vector of scale indices where the reconstruction will be applied.
param mother:: str, Wavelet type.
param param:: np.ndarray Wavelet parameters.
return:

WigglyRivers.wavelet_tree.waveletFunctions.wave_bases(mother, k, scale, param)[source]

WigglyRivers.wavelet_tree.waveletFunctions.wave_signif(Y, dt, scale, sigtest=0, lag1=0.0, siglvl=0.95, dof=None, mother='MORLET', param=None, gws=None)[source]

WigglyRivers.wavelet_tree.waveletFunctions.wavelet(Y, dt, pad=0, dj=-1, s0=-1, J1=-1, mother=-1, param=-1, freq=None)[source]

WigglyRivers.wavelet_tree package

Submodules

WigglyRivers.wavelet_tree.TreeScale module

WigglyRivers.wavelet_tree.WaveletTreeFunctions module

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

Description:

Args:

WigglyRivers.wavelet_tree.waveletFunctions module

Description:

Args:

Description:

Args:

Description:

Args:

Module contents