NAG Library Routine Document

c09dcf (dim1_mxolap_multi_fwd)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

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

Constraint: this must be the same as the value n passed to the initialization routine c09aaf.

2:     $\mathbf{x}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: x contains the input dataset $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

3:     $\mathbf{keepa}$ – Character(1)Input

On entry: determines whether the approximation coefficients are stored in array c for every level of the computed transform or else only for the final level. In both cases, the detail coefficients are stored in c for every level computed.

$\mathbf{keepa}=\text{'A'}$

Retain approximation coefficients for all levels computed.

$\mathbf{keepa}=\text{'F'}$

Retain approximation coefficients for only the final level computed.

Constraint: $\mathbf{keepa}=\text{'A'}$ or $\text{'F'}$.

4:     $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the array c as declared in the (sub)program from which c09dcf is called. c must be large enough to contain the number of wavelet coefficients.

If $\mathbf{keepa}=\text{'F'}$, the total number of coefficients, $n_c$, is returned in nwc by the call to the initialization routine c09aaf and corresponds to the MODWT being continued for the maximum number of levels possible for the given data set. When the number of levels, $n_l$, is chosen to be less than the maximum, then the number of stored coefficients is correspondingly smaller and lenc can be reduced by noting that $n_d$ detail coefficients are stored at each level, with the storage increased at the final level to contain the $n_a$ approximation coefficients.

If $\mathbf{keepa}=\text{'A'}$, $n_d$ detail coefficients and $n_a$ approximation coefficients are stored for each level computed, requiring $\mathbf{lenc}\ge n_l\times \left(n_a+n_d\right)=2\times n_l\times n_a$, since the numbers of stored approximation and detail coefficients are equal. The number of approximation (or detail) coefficients at each level, $n_a$, is returned in na.

Constraints:

• if $\mathbf{keepa}=\text{'F'}$, $\mathbf{lenc}\ge \left(n_l+1\right)\times n_a$;
• if $\mathbf{keepa}=\text{'A'}$, $\mathbf{lenc}\ge 2\times n_l\times n_a$.

5:     $\mathbf{c}\left(\mathbf{lenc}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the coefficients of a multi-level wavelet transform of the dataset.

The coefficients are stored in c as follows:

If $\mathbf{keepa}=\text{'F'}$,

$\mathbf{c}\left(1:n_a\right)$

Contains the level $n_l$ approximation coefficients;

$\mathbf{c}\left(n_a+\left(i-1\right)\times n_d+1:n_a+i\times n_d\right)$

Contains the level $\left(n_l-\mathit{i}+1\right)$ detail coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

If $\mathbf{keepa}=\text{'A'}$,

$\mathbf{c}\left(\left(i-1\right)\times n_a+1:i\times n_a\right)$

Contains the level $\left(n_l-\mathit{i}+1\right)$ approximation coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

$\mathbf{c}\left(n_l\times n_a+\left(i-1\right)\times n_d+1:n_l\times n_a+i\times n_d\right)$

Contains the level i detail coefficients, for $\mathit{i}=1,2,\dots ,n_l$;

The values $n_a$ and $n_d$ denote the numbers of approximation and detail coefficients respectively, which are equal and returned in na.

6:     $\mathbf{nwl}$ – IntegerInput

On entry: the number of levels, $n_l$, in the multi-level resolution to be performed.

Constraint: $1\le \mathbf{nwl}\le l_{\max }$, where $l_{\max }$ is the value returned in nwlmax (the maximum number of levels) by the call to the initialization routine c09aaf.

7:     $\mathbf{na}$ – IntegerOutput

On exit: na contains the number of approximation coefficients, $n_a$, at each level which is equal to the number of detail coefficients, $n_d$. With periodic end extension ($\mathbf{mode}=\text{'P'}$ in c09aaf) this is the same as the length, n, of the data array, x.

8:     $\mathbf{icomm}\left(100\right)$ – Integer arrayCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization routine c09aaf.

On exit: contains additional information on the computed transform.

9:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 argument, 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, n is inconsistent with the value passed to the initialization routine: $\mathbf{n}=〈\mathit{\text{value}}〉$, n should be $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=4$

On entry, lenc is set too small: $\mathbf{lenc}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lenc}\ge 〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=6$

On entry, $\mathbf{nwl}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nwl}\ge 1$.

On entry, nwl is larger than the maximum number of levels returned by the initialization function: $\mathbf{nwl}=〈\mathit{\text{value}}〉$, maximum = $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=8$

On entry, the initialization routine c09aaf has not been called first or it has not been called with $\mathbf{wtrans}=\text{'U'}$, or the communication array icomm has become corrupted.

$\mathbf{ifail}=-99$

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

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c09dcfe.f90)

10.2

Program Data

Program Data (c09dcfe.d)

10.3

Program Results

Program Results (c09dcfe.r)