naginterfaces.library.wav.dim2_​init

naginterfaces.library.wav.dim2_init(wavnam, wtrans, mode, m, n)

dim2_init returns the details of the chosen two-dimensional discrete wavelet filter. For a chosen mother wavelet, discrete wavelet transform type (single-level or multi-level DWT) and end extension method, this function returns the maximum number of levels of resolution (appropriate to a multi-level transform), the filter length, the total number of approximation, horizontal, vertical and diagonal coefficients and the number of coefficients in the second dimension for the single-level case. This function must be called before any of the two-dimensional transform functions in this module.

For full information please refer to the NAG Library document for c09ab

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/c09/c09abf.html

Parameters

wavnamstr

The name of the mother wavelet. See the C09 Introduction for details.

$wavnam=\text{‘HAAR'}$

Haar wavelet, also known as $\text{‘DB1'}$ as a special case of the Daubechies wavelet.

$wavnam=\text{‘DBn'}$, where $n=2,3,\dots ,38$

Daubechies wavelet with $n$ vanishing moments ($2n$ coefficients). For example, $wavnam=\text{‘DB4'}$ is the name for the Daubechies wavelet with $4$ vanishing moments ($8$ coefficients).

$wavnam=\text{‘COIFn'}$, where $n=1,2,\dots ,17$

Coiflet wavelet of order $n$.

$wavnam=\text{‘BEYL'}$

Beylkin wavelet.

$wavnam=\text{‘VAID'}$

Vaidyanathan wavelet.

$wavnam=\text{‘SYMn'}$, where $n=2,3,\dots ,20$

Symlet wavelet of order $n$.

$wavnam=\text{‘BIORx.y'}$, where $x.y$ can be one of 1.1, 1.3, 1.5, 2.2, 2.4, 2.6, 2.8, 3.1, 3.3, 3.5, 3.7, 3.9, 4.4, 5.5 or 6.8

Biorthogonal wavelet of order $x.y$. For example $wavnam=\text{‘BIOR3.1'}$ is the name for the biorthogonal wavelet of order $3.1$.

$wavnam=\text{‘RBIOx.y'}$, where $x.y$ can be one of 1.1, 1.3, 1.5, 2.2, 2.4, 2.6, 2.8, 3.1, 3.3, 3.5, 3.7, 3.9, 4.4, 5.5 or 6.8

Reverse biorthogonal wavelet of order $x.y$. For example $wavnam=\text{‘RBIO3.1'}$ is the name for the reverse biorthogonal wavelet of order $3.1$.

wtransstr, length 1

The type of discrete wavelet transform that is to be applied.

$wtrans=\text{‘S'}$

Single-level decomposition or reconstruction by discrete wavelet transform.

$wtrans=\text{‘M'}$

Multiresolution, by a multi-level DWT or its inverse.

modestr, length 1

The end extension method.

$mode=\text{‘P'}$

Periodic end extension.

$mode=\text{‘H'}$

Half-point symmetric end extension.

$mode=\text{‘W'}$

Whole-point symmetric end extension.

$mode=\text{‘Z'}$

Zero end extension.

mint

The number of elements, $m$, in the first dimension (number of rows of data matrix $A$) of the input data.

nint

The number of elements, $n$, in the second dimension (number of columns of data matrix $A$) of the input data.

Returns

nwlmaxint

The maximum number of levels of resolution, $l_{max}$, that can be computed if a multi-level discrete wavelet transform is applied ($wtrans=\text{‘M'}$). It is such that $2^{l_{max}}\le min(m,n)<2^{l_{max}+1}$, for $l_{max}$ an integer.

If $wtrans=\text{‘S'}$, $nwlmax$ is not set.

nfint

The filter length, $n_f$, for the supplied mother wavelet. This is used to determine the number of coefficients to be generated by the chosen transform.

nwctint

The total number of wavelet coefficients, $n_{\text{ct}}$, that will be generated. When $wtrans=\text{‘S'}$ the number of rows required in each of the output coefficient matrices can be calculated as $n_{\text{cm}}=n_{\text{ct}}/\left(4n_{\text{cn}}\right)$. When $wtrans=\text{‘M'}$ the length of the array used to store all of the coefficient matrices must be at least $n_{\text{ct}}$.

nwcnint

For a single-level transform ($wtrans=\text{‘S'}$), the number of coefficients that would be generated in the second dimension, $n_{\text{cn}}$, for each coefficient type. For a multi-level transform ($wtrans=\text{‘M'}$) this is set to $1$.

commdict, communication object

Communication structure.

Raises

NagValueError

(errno $1$)

On entry, $wavnam$ not recognised: $wavnam=⟨value⟩$.

(errno $2$)

On entry, $wtrans=⟨value⟩$.

Constraint: $wtrans=\text{‘S'}\text{or}\text{‘M'}$.

(errno $3$)

On entry, $mode=⟨value⟩$.

Constraint: $mode=\text{‘P'},\text{‘H'},\text{‘W'}\text{or}\text{‘Z'}$.

(errno $4$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 2$.

(errno $4$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 2$.

Notes

Two-dimensional discrete wavelet transforms (DWT) are characterised by the mother wavelet, the end extension method and whether multiresolution analysis is to be performed. For the selected combination of choices for these three characteristics, and for given dimensions ($m\times n$) of data matrix $A$, dim2_init returns the dimension details for the transform determined by this combination. The dimension details are: $l_{max}$, the maximum number of levels of resolution that would be computed were a multi-level DWT applied; $n_f$, the filter length; $n_{\text{ct}}$ the total number of approximation, horizontal, vertical and diagonal coefficients (over all levels in the multi-level DWT case); and $n_{\text{cn}}$, the number of coefficients in the second dimension for a single-level DWT. These values are also stored in the communication array $comm$[‘icomm’], as are the input choices, so that they may be conveniently communicated to the two-dimensional transform functions in this module.