NAG Library Routine Document

C09AAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{WAVNAM}$ – 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:     $\mathrm{WTRANS}$ – 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.

$\mathbf{WTRANS}=\text{'T'}$

Single-level decomposition or reconstruction by maximal overlap discrete wavelet transform.

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

Multi-level resolution by a maximal overlap discrete wavelet transform or its inverse.

Constraint: $\mathbf{WTRANS}=\text{'S'}$, $\text{'M'}$, $\text{'T'}$ or $\text{'U'}$.

3:     $\mathrm{MODE}$ – CHARACTER(1)Input

On entry: the end extension method. Note that only periodic end extension is currently available for the MODWT.

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

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.

Constraints:

• $\mathbf{MODE}=\text{'P'}$, $\text{'H'}$, $\text{'W'}$ or $\text{'Z'}$ for DWT;
• $\mathbf{MODE}=\text{'P'}$ for MODWT.

4:     $\mathrm{N}$ – INTEGERInput

On entry: the number of elements, $n$, in the input data array, $x$.

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

5:     $\mathrm{NWLMAX}$ – INTEGEROutput

On exit: the maximum number of levels of resolution, $l_{\max }$, that can be computed when a multi-level discrete wavelet transform is applied. It is such that $2^{l_{\max }}\le n<2^{l_{\max }+1}$, for $l_{\max }$ an integer.

6:     $\mathrm{NF}$ – 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.

7:     $\mathrm{NWC}$ – INTEGEROutput

On exit: for a single-level transform ($\mathbf{WTRANS}=\text{'S'}$ or $\text{'T'}$), the number of approximation coefficients that would be generated for the given problem size, mother wavelet, extension method and type of transform; this is also the corresponding number of detail coefficients. For a multi-level transform ($\mathbf{WTRANS}=\text{'M'}$ or $\text{'U'}$) the total number of coefficients that would be generated over $l_{\max }$ levels and with $\mathbf{KEEPA}=\text{'A'}$ for MODWT.

8:     $\mathrm{ICOMM}\left(100\right)$ – INTEGER arrayCommunication Array

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

9:     $\mathrm{IFAIL}$ – 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, $\mathbf{WAVNAM}=〈\mathit{\text{value}}〉$ was an illegal value.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{WTRANS}=〈\mathit{\text{value}}〉$ was an illegal value.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{MODE}=〈\mathit{\text{value}}〉$ was an illegal value.

On entry, $\mathbf{WTRANS}=\text{'T'}$ or $\text{'U'}$ and $\mathbf{MODE}\ne \text{'P'}$.
Constraint: $\mathbf{MODE}=\text{'P'}$ when $\mathbf{WTRANS}=\text{'T'}$ or $\text{'U'}$.

$\mathbf{IFAIL}=4$

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

$\mathbf{IFAIL}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (c09aafe.f90)

10.2  Program Data

Program Data (c09aafe.d)

10.3  Program Results

Program Results (c09aafe.r)