NAG FL Interface
c09ebf (dim2_​sngl_​inv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

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: $\mathbf{n}$ – Integer Input

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) array Input

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: $\mathbf{ldca}$ – Integer Input

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) array Input

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: $\mathbf{ldch}$ – Integer Input

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) array Input

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: $\mathbf{ldcv}$ – Integer Input

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) array Input

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: $\mathbf{ldcd}$ – Integer Input

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) array Output

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: $\mathbf{ldb}$ – Integer Input

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 array Communication 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: $\mathbf{ifail}$ – Integer Input/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 4 in the Introduction to the NAG Library FL Interface 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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example