WaveletMatrixPlot

WaveletMatrixPlot[dwd]

plots the basis tree of wavelet matrix coefficients in the DiscreteWaveletData dwd.

WaveletMatrixPlot[dwd,r]

plots coefficients up to refinement level r.

WaveletMatrixPlot[dwd,r,func]

applies func to coefficients before plotting.

Details and Options

WaveletMatrixPlot generates a single plot using a pyramid of matrix plots.
WaveletMatrixPlot[dwd] is equivalent to WaveletMatrixPlot[dwd,Automatic], corresponding to the basis of coefficients used in the InverseWaveletTransform.
The wavelet indices used in the Automatic setting are given by dwd["BasisIndex"].
The dwd should be generated from matrix data and produced by DiscreteWaveletTransform, DiscreteWaveletPacketTransform, or LiftingWaveletTransform.
WaveletMatrixPlot[dwd,r] plots basis coefficients up to refinement level r when dwd comes from DiscreteWaveletTransform or LiftingWaveletTransform.
WaveletMatrixPlot[dwd,r] plots all coefficients at refinement level r when dwd comes from DiscreteWaveletPacketTransform.
In WaveletMatrixPlot[dwd,r,func], each func[coef_i,wind_i] should yield an array with the same dimensions as coef_i.
WaveletMatrixPlot has the same options as MatrixPlot, with the following additions and changes: [List of all options]

Axes	True	whether to draw axes
Frame	None	whether to draw a frame
FrameTicks	Automatic	where to draw frame ticks
GridLines	Automatic	whether to draw grid lines
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLayout	Automatic	what layout to use for the plot

With the setting GridLines->Automatic, grid lines are drawn between adjacent coefficient matrices.
The Automatic setting for Ticks and FrameTicks draws ticks corresponding to refinement levels.
With the setting Method->"InverseTransform", the inverse transform of each coefficient array will be plotted.
WaveletMatrixPlot returns a Graphics object.

List of all options

AlignmentPoint	Center	the default point in the graphic to align with
AspectRatio	Automatic	ratio of height to width
Axes	True	whether to draw axes
AxesLabel	None	axes labels
AxesOrigin	Automatic	where axes should cross
AxesStyle	{}	style specifications for the axes
Background	None	background color for the plot
BaselinePosition	Automatic	how to align with a surrounding text baseline
BaseStyle	{}	base style specifications for the graphic
ClippingStyle	Automatic	how to show clipped values
ColorFunction	Automatic	how each cell should be colored
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
ColorRules	Automatic	rules for determining colors from values
ContentSelectable	Automatic	whether to allow contents to be selected
CoordinatesToolOptions	Automatic	detailed behavior of the coordinates tool
DataRange	All	the range of and values to assume
DataReversed	False	whether to reverse the order of rows
Epilog	{}	primitives rendered after the main plot
FormatType	TraditionalForm	the default format type for text
Frame	None	whether to draw a frame
FrameLabel	None	labels for rows and columns
FrameStyle	{}	style specifications for the frame
FrameTicks	Automatic	where to draw frame ticks
FrameTicksStyle	{}	style specifications for frame ticks
GridLines	Automatic	whether to draw grid lines
GridLinesStyle	{}	style specifications for grid lines
ImageMargins	0.	the margins to leave around the graphic
ImagePadding	All	what extra padding to allow for labels etc.
ImageSize	Automatic	the absolute size at which to render the graphic
LabelStyle	{}	style specifications for labels
MaxPlotPoints	Automatic	the maximum number of points to include
Mesh	False	whether to draw a mesh
MeshStyle	GrayLevel[GoldenRatio-1]	the style to use for a mesh
Method	Automatic	details of graphics methods to use
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotLabel	None	an overall label for the plot
PlotLayout	Automatic	what layout to use for the plot
PlotLegends	None	legends for datasets
PlotRange	All	the range of values to plot
PlotRangeClipping	False	whether to clip at the plot range
PlotRangePadding	Automatic	how much to pad the range of values
PlotRegion	Automatic	the final display region to be filled
PlotTheme	$PlotTheme	overall theme for the plot
PreserveImageOptions	Automatic	whether to preserve image options when displaying new versions of the same graphic
Prolog	{}	primitives rendered before the main plot
RotateLabel	True	whether to rotate y labels on the frame
TargetUnits	Automatic	units to display in the plot
Ticks	Automatic	axes ticks
TicksStyle	{}	style specifications for axes ticks

Examples

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Basic Examples (2)

Plot wavelet matrix coefficients in a pyramid layout:

Plot wavelet matrix coefficients in a grid layout:

Plot a full tree of wavelet packet coefficients at different refinement levels:

Scope (11)

Data (6)

DiscreteWaveletTransform of matrix data:

Plot matrix wavelet coefficients in a hierarchical grid with wavelet index as a tooltip:

The plotted coefficients are the Automatic coefficients used in the inverse transform:

Use WaveletMatrixPlot[dwd,r] to plot coefficients only up to refinement level r:

The hierarchical layout corresponds to the tree structure of the wavelet coefficients:

DiscreteWaveletPacketTransform of matrix data:

The DiscreteWaveletData object contains a full tree of coefficients at each level:

Default Automatic coefficients for packet transform correspond to the highest refinement level:

WaveletBestBasis computes a different Automatic tree of coefficients:

Specify a function f to apply to wavelet coefficients before plotting:

"Grid" layout is used to plot coefficients from StationaryWaveletTransform:

Presentation (5)

Add labels:

Use a named color gradient:

Include a frame:

Place ticks indicating refinement level on all sides:

Specify an overall style for grid lines separating wavelet coefficients:

Generalizations & Extensions (3)

Data need not be square:

Plot rectangular coefficients in a hierarchical grid layout:

DiscreteWaveletTransform of complex data:

Specify a real-valued function to apply to complex data before plotting:

By default, Re is applied:

Use a theme with minimal styling:

Options (15)

Axes (1)

Plot with no axes:

ColorFunction (1)

Specify a function to determine the colors of coefficients:

Use a named color function:

Frame (1)

Include a frame:

FrameTicks (2)

Draw no frame ticks:

Draw frame ticks indicating refinement level on all sides:

Draw frame ticks only on the specified sides:

Draw tick marks at the specified positions:

Draw tick marks at the specified positions with the specified labels:

GridLines (1)

Plot without drawing grid lines separating coefficients:

Draw only horizontal grid lines:

GridLinesStyle (1)

Specify an overall style for grid lines separating wavelet coefficients:

Specify separate styles for horizontal and vertical grid lines:

Method (1)

Inverse transform each coefficient before plotting:

Inverse transform coefficients from stationary wavelet transform:

Inverse transform coefficients from lifting wavelet transform:

PlotLayout (1)

Show the plot in a pyramid layout:

Use a gridded layout instead:

PlotLegends (3)

Use legends for coefficient values:

Use BarLegend to add an overall legend label:

Use Placed to put legends above the plot:

PlotTheme (2)

Use a monochrome theme:

Change the grid lines style:

Ticks (1)

Draw ticks on the vertical axis only:

Properties & Relations (4)

WaveletMatrixPlot plots matrix wavelet coefficients in a hierarchical grid layout:

dwd[…,"MatrixPlot"] gives each coefficient as a separate matrix plot:

WaveletMatrixPlot plots the Automatic coefficients used in the inverse transform:

WaveletBestBasis selects a different default tree of coefficients:

WaveletImagePlot shows image wavelet coefficients in a hierarchical grid:

WaveletScalogram plots vector coefficients with numerical magnitude indicated by color:

WaveletListPlot plots vector coefficients with a common horizontal or vertical axis:

Possible Issues (2)

Wavelet coefficients from stationary wavelet transform cannot be plotted using pyramid layout:

Pyramid layout cannot be constructed for inverse transformed wavelet coefficients:

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