NAG FL Interface
c09dbf (dim1_​mxolap_​inv)

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1 Purpose

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 nc 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 yi, for i=1,2,,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: lencnc, where nc 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 nc approximation coefficients, Ca. 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 nc detail coefficients, Cd. 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 Ca and Cd 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 or -1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, array dimension lenc not large enough: lenc=value but must be at least value.
On entry, n is inconsistent with the value passed to the initialization routine: n=value, n should be value.
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.
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.
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.
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

c09dbf is not threaded in any implementation.

9 Further Comments


10 Example

See c09daf.