NAG Library Function Document

nag_dwt_2d (c09eac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{m}$ – IntegerInput

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

Constraint: this must be the same as the value m passed to the initialization function nag_wfilt_2d (c09abc).

2:    $\mathbf{n}$ – IntegerInput

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

Constraint: this must be the same as the value n passed to the initialization function nag_wfilt_2d (c09abc).

3:    $\mathbf{a}\left[\mathbf{lda}\times \mathbf{n}\right]$ – const doubleInput

Note: the $\left(i,j\right)$th element of the matrix $A$ is stored in $\mathbf{a}\left[\left(j-1\right)\times \mathbf{lda}+i-1\right]$.

On entry: the $m$ by $n$ data matrix $A$.

4:    $\mathbf{lda}$ – IntegerInput

On entry: the stride separating matrix row elements in the array a.

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

5:    $\mathbf{ca}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array ca must be at least $\mathbf{ldca}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wfilt_2d (c09abc).

The $\left(i,j\right)$th element of the matrix is stored in $\mathbf{ca}\left[\left(j-1\right)\times \mathbf{ldca}+i-1\right]$.

On exit: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of approximation coefficients, $C_a$.

6:    $\mathbf{ldca}$ – IntegerInput

On entry: the stride separating matrix row elements in the array ca.

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 function nag_wfilt_2d (c09abc).

7:    $\mathbf{ch}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array ch must be at least $\mathbf{ldch}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wfilt_2d (c09abc).

The $\left(i,j\right)$th element of the matrix is stored in $\mathbf{ch}\left[\left(j-1\right)\times \mathbf{ldch}+i-1\right]$.

On exit: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of horizontal coefficients, $C_h$.

8:    $\mathbf{ldch}$ – IntegerInput

On entry: the stride separating matrix row elements in the array ch.

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 function nag_wfilt_2d (c09abc).

9:    $\mathbf{cv}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array cv must be at least $\mathbf{ldcv}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wfilt_2d (c09abc).

The $\left(i,j\right)$th element of the matrix is stored in $\mathbf{cv}\left[\left(j-1\right)\times \mathbf{ldcv}+i-1\right]$.

On exit: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of vertical coefficients, $C_v$.

10:  $\mathbf{ldcv}$ – IntegerInput

On entry: the stride separating matrix row elements in the array cv.

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 function nag_wfilt_2d (c09abc).

11:  $\mathbf{cd}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array cd must be at least $\mathbf{ldcd}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function nag_wfilt_2d (c09abc).

The $\left(i,j\right)$th element of the matrix is stored in $\mathbf{cd}\left[\left(j-1\right)\times \mathbf{ldcd}+i-1\right]$.

On exit: contains the $n_{\mathrm{cm}}$ by $n_{\mathrm{cn}}$ matrix of diagonal coefficients, $C_d$.

12:  $\mathbf{ldcd}$ – IntegerInput

On entry: the stride separating matrix row elements in the array cd.

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 function nag_wfilt_2d (c09abc).

13:  $\mathbf{icomm}\left[180\right]$ – IntegerCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function nag_wfilt_2d (c09abc).

14:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INITIALIZATION

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

Either the initialization function was called with $\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$ or icomm has been corrupted.

NE_INT

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.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}=〈\mathit{\text{value}}〉$, the value of m on initialization (see nag_wfilt_2d (c09abc)).

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}=〈\mathit{\text{value}}〉$, the value of n on initialization (see nag_wfilt_2d (c09abc)).

NE_INT_2

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 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 (c09eace.c)

10.2

Program Data

Program Data (c09eace.d)

10.3

Program Results

Program Results (c09eace.r)