NAG Library Routine Document

c09caf  (dim1_sngl_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:     $\mathbf{lenc}$ – IntegerInput

On entry: the dimension of the arrays ca and cd as declared in the (sub)program from which c09caf is called. This must be at least the number, $n_c$, of approximation coefficients, $C_a$, and detail coefficients, $C_d$, of the discrete wavelet transform as returned in nwc by the call to the initialization routine c09aaf.

Constraint: $\mathbf{lenc}\ge n_c$, where $n_c$ is the value returned in nwc by the call to the initialization routine c09aaf.

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

On exit: $\mathbf{ca}\left(i\right)$ contains the $i$th approximation coefficient, $C_a\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,n_c$.

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

On exit: $\mathbf{cd}\left(\mathit{i}\right)$ contains the $\mathit{i}$th detail coefficient, $C_d\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,n_c$.

6:     $\mathbf{icomm}\left(100\right)$ – 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.

7:     $\mathbf{ifail}$ – 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 $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=3$

On entry, array dimension lenc not large enough: $\mathbf{lenc}=〈\mathit{\text{value}}〉$ but must be at least $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=6$

Either the initialization routine has not been called first or array icomm has been corrupted.

Either the initialization routine was called with $\mathbf{wtrans}=\text{'M'}$ or array icomm has been 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 (c09cafe.f90)

10.2

Program Data

Program Data (c09cafe.d)

10.3

Program Results

Program Results (c09cafe.r)