c09fbf computes the three-dimensional inverse discrete wavelet transform (IDWT) at a single level. The initialization routine c09acf must be called first to set up the DWT options.

2 Specification

Fortran Interface

Subroutine c09fbf (

m, n, fr, lenc, c, b, ldb, sdb, icomm, ifail)

Integer, Intent (In)	::	m, n, fr, lenc, ldb, sdb, icomm(260)
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	c(lenc)
Real (Kind=nag_wp), Intent (Inout)	::	b(ldb,sdb,fr)

C Header Interface

#include <nag.h>

void	c09fbf_ (const Integer m, const Integer n, const Integer fr, const Integer lenc, const double c[], double b[], const Integer ldb, const Integer sdb, const Integer icomm[], Integer *ifail)

The routine may be called by the names c09fbf or nagf_wav_dim3_sngl_inv.

3 Description

c09fbf performs the inverse operation of routine c09faf. That is, given sets of wavelet coefficients computed by routine c09faf using a DWT as set up by the initialization routine c09acf, on a real data array,

B

, c09fbf will reconstruct

B

4 References

None.

5 Arguments

1: $m$ – 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: $n$ – 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: $fr$ – Integer Input: On entry: the number two-dimensional frames.

Constraint: this must be the same as the value fr passed to the initialization routine c09acf.
4: $lenc$ – Integer Input: On entry: the dimension of the array c as declared in the (sub)program from which c09fbf is called.

Constraint: $lenc \geq n_{ct}$ , where $n_{ct}$ is the total number of wavelet coefficients, as returned by c09acf.
5: $c (lenc)$ – Real (Kind=nag_wp) array Input: On entry: the coefficients of the discrete wavelet transform. This will normally be the result of some transformation on the coefficients computed by routine c09faf.
Note that the coefficients in c may be extracted according to type into three-dimensional arrays using c09fyf, and inserted using c09fzf.
6: $b (ldb, sdb, fr)$ – Real (Kind=nag_wp) array Output: On exit: the $m \times n \times fr$ reconstructed array, $B$ , with $B_{i j k}$ stored in $b (i, j, k)$ . The reconstruction is based on the input wavelet coefficients and the transform options supplied to the initialization routine c09acf.
7: $ldb$ – Integer Input: On entry: the first dimension of the array b as declared in the (sub)program from which c09fbf is called.

Constraint: $ldb \geq m$ .
8: $sdb$ – Integer Input: On entry: the second dimension of the array b as declared in the (sub)program from which c09fbf is called.

Constraint: $sdb \geq n$ .
9: $icomm (260)$ – 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.
10: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ 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 $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $fr = ⟨ value ⟩$ .
Constraint: $fr = ⟨ value ⟩$ , the value of fr on initialization (see c09acf).

On entry, $m = ⟨ value ⟩$ .
Constraint: $m = ⟨ value ⟩$ , the value of m on initialization (see c09acf).

On entry, $n = ⟨ value ⟩$ .
Constraint: $n = ⟨ value ⟩$ , the value of n on initialization (see c09acf).

$ifail = 2$: On entry, $ldb = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: $ldb \geq m$ .

On entry, $sdb = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $sdb \geq n$ .

$ifail = 3$: On entry, $lenc = ⟨ value ⟩$ and $n_{ct} = ⟨ value ⟩$ .
Constraint: $lenc \geq n_{ct}$ , where $n_{ct}$ is the number of DWT coefficients returned by c09acf in argument nwct.

$ifail = 6$: 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 $wtrans ='M'$ .

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The accuracy of the wavelet transform depends only on the floating-point operations used in the convolution and downsampling and should thus be close to machine precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

c09fbf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.