NAG Library Routine Document

C09ACF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     WAVNAM – CHARACTER(*)Input

On entry: the name of the mother wavelet. See the C09 Chapter Introduction for details.

$\mathbf{WAVNAM}=\text{'HAAR'}$

Haar wavelet.

$\mathbf{WAVNAM}=\text{'DB}\mathit{n}\text{'}$, where $\mathit{n}=2,3,\dots ,10$

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

$\mathbf{WAVNAM}=\text{'BIOR}\mathit{x}$.$\mathit{y}\text{'}$, where $\mathit{x}$.$\mathit{y}$ can be one of 1.1, 1.3, 1.5, 2.2, 2.4, 2.6, 2.8, 3.1, 3.3, 3.5 or 3.7

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

Constraint: $\mathbf{WAVNAM}=\text{'HAAR'}$, $\text{'DB2'}$, $\text{'DB3'}$, $\text{'DB4'}$, $\text{'DB5'}$, $\text{'DB6'}$, $\text{'DB7'}$, $\text{'DB8'}$, $\text{'DB9'}$, $\text{'DB10'}$, $\text{'BIOR1.1'}$, $\text{'BIOR1.3'}$, $\text{'BIOR1.5'}$, $\text{'BIOR2.2'}$, $\text{'BIOR2.4'}$, $\text{'BIOR2.6'}$, $\text{'BIOR2.8'}$, $\text{'BIOR3.1'}$, $\text{'BIOR3.3'}$, $\text{'BIOR3.5'}$ or $\text{'BIOR3.7'}$.

2:     WTRANS – CHARACTER(1)Input

On entry: the type of discrete wavelet transform that is to be applied.

$\mathbf{WTRANS}=\text{'S'}$

Single-level decomposition or reconstruction by discrete wavelet transform.

$\mathbf{WTRANS}=\text{'M'}$

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

Constraint: $\mathbf{WTRANS}=\text{'S'}$ or $\text{'M'}$.

3:     MODE – CHARACTER(1)Input

On entry: the end extension method.

$\mathbf{MODE}=\text{'P'}$

Periodic end extension.

$\mathbf{MODE}=\text{'H'}$

Half-point symmetric end extension.

$\mathbf{MODE}=\text{'W'}$

Whole-point symmetric end extension.

$\mathbf{MODE}=\text{'Z'}$

Zero end extension.

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

4:     M – INTEGERInput

On entry: the number of elements, $m$, in the first dimension (number of rows of each two-dimensional frame) of the input data, $A$.

Constraint: $\mathbf{M}\ge 2$.

5:     N – INTEGERInput

On entry: the number of elements, $n$, in the second dimension (number of columns of each two-dimensional frame) of the input data, $A$.

Constraint: $\mathbf{N}\ge 2$.

6:     FR – INTEGERInput

On entry: the number of elements, $\mathit{fr}$, in the third dimension (number of frames) of the input data, $A$.

Constraint: $\mathbf{FR}\ge 2$.

7:     NWL – INTEGEROutput

On exit: the maximum number of levels of resolution, $l_{\max }$, that can be computed if a multi-level discrete wavelet transform is applied ($\mathbf{WTRANS}=\text{'M'}$). It is such that $2^{l_{\max }}\le \min \left(m,n,\mathit{fr}\right)<2^{l_{\max }+1}$, for $l_{\max }$ an integer.

If $\mathbf{WTRANS}=\text{'S'}$, NWL is not set.

8:     NF – INTEGEROutput

On exit: 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.

9:     NWCT – INTEGEROutput

On exit: the total number of wavelet coefficients, $n_{\mathrm{ct}}$, that will be generated. When $\mathbf{WTRANS}=\text{'S'}$ the number of rows required (i.e., the first dimension of each two-dimensional frame) in each of the output coefficient arrays can be calculated as $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(8\times n_{\mathrm{cn}}\times n_{\mathrm{cfr}}\right)$. When $\mathbf{WTRANS}=\text{'M'}$ the length of the array used to store all of the coefficient matrices must be at least $n_{\mathrm{ct}}$.

10:   NWCN – INTEGEROutput

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

11:   NWCFR – INTEGEROutput

On exit: for a single-level transform ($\mathbf{WTRANS}=\text{'S'}$), the number of coefficients that would be generated in the third dimension, $n_{\mathrm{cfr}}$, for each coefficient type. For a multi-level transform ($\mathbf{WTRANS}=\text{'M'}$) this is set to $1$.

12:   ICOMM($260$) – INTEGER arrayCommunication Array

On exit: contains details of the wavelet transform and the problem dimension which is to be communicated to the two-dimensional discrete transform routines in this chapter.

13:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry, WAVNAM had an illegal value.

$\mathbf{IFAIL}=2$

On entry, WTRANS had an illegal value.

$\mathbf{IFAIL}=3$

On entry, MODE had an illegal value.

$\mathbf{IFAIL}=4$

On entry, $\mathbf{FR}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{FR}\ge 2$.

On entry, $\mathbf{M}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{M}\ge 2$.

On entry, $\mathbf{N}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{N}\ge 2$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (c09acfe.f90)

9.2  Program Data

Program Data (c09acfe.d)

9.3  Program Results

Program Results (c09acfe.r)