c09fbc computes the three-dimensional inverse discrete wavelet transform (IDWT) at a single level. The initialization function c09acc must be called first to set up the DWT options.

2 Specification

#include <nag.h>

void	c09fbc (Integer m, Integer n, Integer fr, Integer lenc, const double c[], double b[], Integer ldb, Integer sdb, const Integer icomm[], NagError *fail)

The function may be called by the names: c09fbc, nag_wav_dim3_sngl_inv or nag_idwt_3d.

3 Description

c09fbc performs the inverse operation of function c09fac. That is, given sets of wavelet coefficients computed by function c09fac using a DWT as set up by the initialization function c09acc, on a real data array,

B

, c09fbc 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 function c09acc.
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 function c09acc.
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 function c09acc.
4: $lenc$ – Integer Input: On entry: the dimension of the array c.

Constraint: $lenc \geq n_{ct}$ , where $n_{ct}$ is the total number of wavelet coefficients, as returned by c09acc.
5: $c [lenc]$ – const double Input: On entry: the coefficients of the discrete wavelet transform. This will normally be the result of some transformation on the coefficients computed by function c09fac.
Note that the coefficients in c may be extracted according to type into three-dimensional arrays using c09fyc, and inserted using c09fzc.
6: $b [\dim]$ – double Output: Note: the dimension, dim, of the array b must be at least $ldb \times sdb \times fr$ .

On exit: the $m \times n \times fr$ reconstructed array, $B$ , with $B_{i j k}$ stored in $b [(k - 1) \times ldb \times sdb + (j - 1) \times ldb + i - 1]$ . The reconstruction is based on the input wavelet coefficients and the transform options supplied to the initialization function c09acc.
7: $ldb$ – Integer Input: On entry: the stride separating row elements of each of the sets of frame coefficients in the three-dimensional data stored in b.

Constraint: $ldb \geq m$ .
8: $sdb$ – Integer Input: On entry: the stride separating corresponding coefficients of consecutive frames in the three-dimensional data stored in b.

Constraint: $sdb \geq n$ .
9: $icomm [260]$ – const Integer Communication Array: On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function c09acc.
10: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INITIALIZATION: Either the communication array icomm has been corrupted or there has not been a prior call to the initialization function c09acc.

The initialization function was called with $wtrans = Nag_MultiLevel$ .
NE_INT: On entry, $fr = ⟨ value ⟩$ .
Constraint: $fr = ⟨ value ⟩$ , the value of fr on initialization (see c09acc).

On entry, $m = ⟨ value ⟩$ .
Constraint: $m = ⟨ value ⟩$ , the value of m on initialization (see c09acc).

On entry, $n = ⟨ value ⟩$ .
Constraint: $n = ⟨ value ⟩$ , the value of n on initialization (see c09acc).
NE_INT_2: On entry, $ldb = ⟨ value ⟩$ and $m = ⟨ value ⟩$ .
Constraint: $ldb \geq m$ .

On entry, $lenc = ⟨ value ⟩$ and $n_{ct} = ⟨ value ⟩$ .
Constraint: $lenc \geq n_{ct}$ , where $n_{ct}$ is the number of DWT coefficients returned by c09acc in argument nwct.

On entry, $sdb = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $sdb \geq n$ .
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 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL 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.

c09fbc 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.