c09dbf computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization routine c09aaf must be called first to set up the MODWT options.

2 Specification

Fortran Interface

Subroutine c09dbf (

lenc, ca, cd, n, y, icomm, ifail)

Integer, Intent (In)	::	lenc, n, icomm(100)
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	ca(lenc), cd(lenc)
Real (Kind=nag_wp), Intent (Out)	::	y(n)

C Header Interface

#include <nag.h>

void	c09dbf_ (const Integer lenc, const double ca[], const double cd[], const Integer n, double y[], const Integer icomm[], Integer *ifail)

The routine may be called by the names c09dbf or nagf_wav_dim1_mxolap_inv.

3 Description

c09dbf performs the inverse operation of c09daf. That is, given sets of

n_{c}

approximation coefficients and detail coefficients, computed by c09daf using a MODWT as set up by the initialization routine c09aaf, on a real data array of length

n

, c09dbf will reconstruct the data array

y_{i}

, for

i = 1, 2, \dots, n

, from which the coefficients were derived.

4 References

Percival D B and Walden A T (2000) Wavelet Methods for Time Series Analysis Cambridge University Press

5 Arguments

1: $lenc$ – Integer Input: On entry: the dimension of the arrays ca and cd as declared in the (sub)program from which c09dbf is called.

Constraint: $lenc \geq n_{c}$ , where $n_{c}$ is the value returned in nwc by the call to the initialization routine c09aaf.
2: $ca (lenc)$ – Real (Kind=nag_wp) array Input: On entry: the $n_{c}$ approximation coefficients, $C_{a}$ . These will normally be the result of some transformation on the coefficients computed by c09daf.
3: $cd (lenc)$ – Real (Kind=nag_wp) array Input: On entry: the $n_{c}$ detail coefficients, $C_{d}$ . These will normally be the result of some transformation on the coefficients computed by c09daf.
4: $n$ – Integer Input: On entry: $n$ , the length of the original data array from which the wavelet coefficients were computed by c09daf and the length of the data array y that is to be reconstructed by this routine.

Constraint: This must be the same as the value n passed to the initialization routine c09aaf.
5: $y (n)$ – Real (Kind=nag_wp) array Output: On exit: the reconstructed data based on approximation and detail coefficients $C_{a}$ and $C_{d}$ and the transform options supplied to the initialization routine c09aaf.
6: $icomm (100)$ – Integer array Communication Array: On entry: contains details of the discrete wavelet transform and the problem dimension and, possibly, additional information on the previously computed forward transform.
7: $ifail$ – 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, array dimension lenc not large enough: $lenc = ⟨ value ⟩$ but must be at least $⟨ value ⟩$ .

$ifail = 4$: On entry, n is inconsistent with the value passed to the initialization routine: $n = ⟨ value ⟩$ , n should be $⟨ value ⟩$ .

$ifail = 6$: On entry, the initialization routine c09aaf has not been called first or it has not been called with $wtrans ='T'$ , or the communication array icomm has become corrupted.

$ifail = - 99$: 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.