NAG Library Function Document

nag_idwt_2d (c09ebc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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 function nag_wfilt_2d (c09abc).

2:     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 function nag_wfilt_2d (c09abc).

3:     ca[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array ca must be at least $\max \left(1,\mathbf{ldca}\times n_{\mathrm{cn}}\right)$ 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 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 function nag_dwt_2d (c09eac).

4:     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).

5:     ch[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array ch must be at least $\max \left(1,\mathbf{ldch}\times n_{\mathrm{cn}}\right)$ 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 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 function nag_dwt_2d (c09eac).

6:     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).

7:     cv[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array cv must be at least $\max \left(1,\mathbf{ldcv}\times n_{\mathrm{cn}}\right)$ 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 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 function nag_dwt_2d (c09eac).

8:     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).

9:     cd[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array cd must be at least $\max \left(1,\mathbf{ldcd}\times n_{\mathrm{cn}}\right)$ 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 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 function nag_dwt_2d (c09eac).

10:   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).

11:   b[$\mathbf{ldb}\times \mathbf{n}$] – doubleOutput

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

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 function nag_wfilt_2d (c09abc).

12:   ldb – IntegerInput

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

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

13:   icomm[$180$] – const 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:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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

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.

7  Accuracy

8  Further Comments

9  Example