NAG Library Routine Document

c09ebf  (dim2_sngl_inv)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{m}$ – IntegerInput

On entry: number of rows, $m$, of data matrix $B$.

Constraint: this must be the same as the value m passed to the initialization routine c09abf.

2:     $\mathbf{n}$ – IntegerInput

On entry: number of columns, $n$, of data matrix $B$.

Constraint: this must be the same as the value n passed to the initialization routine c09abf.

3:     $\mathbf{ca}\left(\mathbf{ldca},*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the second dimension of the array ca must be at least $n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.

On entry: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of approximation coefficients, $C_a$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.

4:     $\mathbf{ldca}$ – IntegerInput

On entry: the first dimension of the array ca as declared in the (sub)program from which c09ebf is called.

Constraint: $\mathbf{ldca}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization routine c09abf.

5:     $\mathbf{ch}\left(\mathbf{ldch},*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the second dimension of the array ch must be at least $n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.

On entry: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of horizontal coefficients, $C_h$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.

6:     $\mathbf{ldch}$ – IntegerInput

On entry: the first dimension of the array ch as declared in the (sub)program from which c09ebf is called.

Constraint: $\mathbf{ldch}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization routine c09abf.

7:     $\mathbf{cv}\left(\mathbf{ldcv},*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the second dimension of the array cv must be at least $n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.

On entry: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of vertical coefficients, $C_v$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.

8:     $\mathbf{ldcv}$ – IntegerInput

On entry: the first dimension of the array cv as declared in the (sub)program from which c09ebf is called.

Constraint: $\mathbf{ldcv}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization routine c09abf.

9:     $\mathbf{cd}\left(\mathbf{ldcd},*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the second dimension of the array cd must be at least $n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.

On entry: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of diagonal coefficients, $C_d$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.

10:   $\mathbf{ldcd}$ – IntegerInput

On entry: the first dimension of the array cd as declared in the (sub)program from which c09ebf is called.

Constraint: $\mathbf{ldcd}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization routine c09abf.

11:   $\mathbf{b}\left(\mathbf{ldb},\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: the $m$ by $n$ reconstructed matrix, $B$, based on the input approximation, horizontal, vertical and diagonal coefficients and the transform options supplied to the initialization routine c09abf.

12:   $\mathbf{ldb}$ – IntegerInput

On entry: the first dimension of the array b as declared in the (sub)program from which c09ebf is called.

Constraint: $\mathbf{ldb}\ge \mathbf{m}$.

13:   $\mathbf{icomm}\left(180\right)$ – 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 c09abf.

14:   $\mathbf{ifail}$ – 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, $\mathbf{ldca}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldca}\ge 〈\mathit{\text{value}}〉$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{ldcd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldcd}\ge 〈\mathit{\text{value}}〉$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{ldch}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldch}\ge 〈\mathit{\text{value}}〉$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{ldcv}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldcv}\ge 〈\mathit{\text{value}}〉$, the number of wavelet coefficients in the first dimension.

$\mathbf{ifail}=2$

On entry, $\mathbf{ldb}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldb}\ge \mathbf{m}$.

$\mathbf{ifail}=4$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}=〈\mathit{\text{value}}〉$, the value of m on initialization (see c09abf).

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}=〈\mathit{\text{value}}〉$, the value of n on initialization (see c09abf).

$\mathbf{ifail}=6$

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

Either the initialization routine was called with $\mathbf{wtrans}=\text{'M'}$ or 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