NAG FL Interface
c09faf (dim3_​sngl_​fwd)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

On entry: 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: $\mathbf{n}$ – Integer Input

On entry: 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: $\mathbf{fr}$ – Integer Input

On entry: the number of two-dimensional frames.

Constraint: this must be the same as the value fr passed to the initialization routine c09acf.

4: $\mathbf{a}(\mathbf{lda},\mathbf{sda},\mathbf{fr})$ – Real (Kind=nag_wp) array Input

On entry: the $m\times n\times \mathit{fr}$ three-dimensional input data $A$, where $A_{ijk}$ is stored in $\mathbf{a}(i,j,k)$.

5: $\mathbf{lda}$ – Integer Input

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: $\mathbf{sda}$ – Integer Input

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: $\mathbf{lenc}$ – Integer Input

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: $\mathbf{c}\left(\mathbf{lenc}\right)$ – Real (Kind=nag_wp) array Output

On exit: the coefficients of the discrete wavelet transform. If you need to access or modify the approximation coefficients or any specific set of detail coefficients then the use of c09fyf or c09fzf is recommended. For completeness the following description provides details of precisely how the coefficients are stored in c but this information should only be required in rare cases.

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 arguments nwcfr, nwct and nwcn in c09acf).

9: $\mathbf{icomm}\left(260\right)$ – 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 c09acf.

On exit: contains additional information on the computed transform.

10: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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 argument nwct.

$\mathbf{ifail}=6$

Either the communication array icomm has been corrupted or there has not been a prior call to the initialization routine c09acf.

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

$\mathbf{ifail}=-99$

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

10.1 Program Text

10.2 Program Data

10.3 Program Results