NAG Library Routine Document

C09FAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

On entry: the first dimension of the input data: the number of rows of each two-dimensional frame.

Constraint: this must be the same as the value M passed to the initialization routine C09ACF.

2:     N – INTEGERInput

On entry: the second dimension of the input data: the number of columns of each two-dimensional frame.

Constraint: this must be the same as the value N passed to the initialization routine C09ACF.

3:     FR – INTEGERInput

On entry: the third dimension of the input data: the number of two-dimensional frames.

Constraint: this must be the same as the value FR passed to the initialization routine C09ACF.

4:     A(LDA,SDA,FR) – REAL (KIND=nag_wp) arrayInput

On entry: the $m$ by $n$ by $\mathit{fr}$ input three-dimensional array $A$.

5:     LDA – INTEGERInput

On entry: the first dimension of the array A as declared in the (sub)program from which C09FAF is called.

Constraint: $\mathbf{LDA}\ge \mathbf{M}$.

6:     SDA – INTEGERInput

On entry: the second dimension of the array A as declared in the (sub)program from which C09FAF is called.

Constraint: $\mathbf{SDA}\ge \mathbf{N}$.

7:     LENC – INTEGERInput

On entry: the dimension of the array C as declared in the (sub)program from which C09FAF is called.

Constraint: $\mathbf{LENC}\ge n_{\mathrm{ct}}$, where $n_{\mathrm{ct}}$ is the total number of wavelet coefficients, as returned by C09ACF.

8:     C(LENC) – REAL (KIND=nag_wp) arrayOutput

On exit: the coefficients of the discrete wavelet transform. The $8$ sets of coefficients are stored in the following order: approximation coefficients (LLL) first, followed by $7$ sets of detail coefficients: LLH, LHL, LHH, HLL, HLH, HHL, HHH, where L indicates the low pass filter, and H the high pass filter being applied to, respectively, the columns of length M, the rows of length N and then the frames of length FR. Note that for computational efficiency reasons each set of coefficients is stored in the order $n_{\mathrm{cfr}}\times n_{\mathrm{cm}}\times n_{\mathrm{cn}}$ (see output parameters NWCFR, NWCT and NWCN in C09ACF). See Section 9 for details of how to access each set of coefficients in order to perform extraction from C following a call to this routine, or insertion into C before a call to the three-dimensional inverse routine C09FBF.

9:     ICOMM($260$) – 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 C09ACF.

On exit: contains additional information on the computed transform.

10:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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, $\mathbf{FR}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{FR}=⟨\mathit{\text{value}}⟩$, the value of FR on initialization (see C09ACF).

On entry, $\mathbf{M}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{M}=⟨\mathit{\text{value}}⟩$, the value of M on initialization (see C09ACF).

On entry, $\mathbf{N}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{N}=⟨\mathit{\text{value}}⟩$, the value of N on initialization (see C09ACF).

$\mathbf{IFAIL}=2$

On entry, $\mathbf{LDA}=⟨\mathit{\text{value}}⟩$ and $\mathbf{M}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{LDA}\ge \mathbf{M}$.

On entry, $\mathbf{SDA}=⟨\mathit{\text{value}}⟩$ and $\mathbf{N}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{SDA}\ge \mathbf{N}$.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{LENC}=⟨\mathit{\text{value}}⟩$ and $n_{\mathrm{ct}}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{LENC}\ge n_{\mathrm{ct}}$, where $n_{\mathrm{ct}}$ is the number of DWT coefficients returned by C09ACF in parameter NWCT.

$\mathbf{IFAIL}=6$

Either the initialization routine C09ACF has not been called first or the communication array ICOMM has been corrupted.

The initialization routine was called with $\mathbf{WTRANS}=\text{'M'}$.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (c09fafe.f90)

9.2  Program Data

Program Data (c09fafe.d)

9.3  Program Results

Program Results (c09fafe.r)