NAG FL Interface
c09caf (dim1_​sngl_​fwd)

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1 Purpose

c09caf computes the one-dimensional discrete wavelet transform (DWT) at a single level. The initialization routine c09aaf must be called first to set up the DWT options.

2 Specification

Fortran Interface
Subroutine c09caf ( n, x, lenc, ca, cd, icomm, ifail)
Integer, Intent (In) :: n, lenc
Integer, Intent (Inout) :: icomm(100), ifail
Real (Kind=nag_wp), Intent (In) :: x(n)
Real (Kind=nag_wp), Intent (Out) :: ca(lenc), cd(lenc)
C Header Interface
#include <nag.h>
void  c09caf_ (const Integer *n, const double x[], const Integer *lenc, double ca[], double cd[], Integer icomm[], Integer *ifail)
The routine may be called by the names c09caf or nagf_wav_dim1_sngl_fwd.

3 Description

c09caf computes the one-dimensional DWT of a given input data array, xi, for i=1,2,,n, at a single level. For a chosen wavelet filter pair, the output coefficients are obtained by applying convolution and downsampling by two to the input, x. The approximation (or smooth) coefficients, Ca, are produced by the low pass filter and the detail coefficients, Cd, by the high pass filter. To reduce distortion effects at the ends of the data array, several end extension methods are commonly used. Those provided are: periodic or circular convolution end extension, half-point symmetric end extension, whole-point symmetric end extension or zero end extension. The number nc, of coefficients Ca or Cd is returned by the initialization routine c09aaf.

4 References

Daubechies I (1992) Ten Lectures on Wavelets SIAM, Philadelphia

5 Arguments

1: n Integer Input
On entry: the number of elements, n, in the data array x.
Constraint: this must be the same as the value n passed to the initialization routine c09aaf.
2: x(n) Real (Kind=nag_wp) array Input
On entry: x contains the input dataset xi, for i=1,2,,n.
3: lenc Integer Input
On entry: the dimension of the arrays ca and cd as declared in the (sub)program from which c09caf is called. This must be at least the number, nc, of approximation coefficients, Ca, and detail coefficients, Cd, of the discrete wavelet transform as returned in nwc by the call to the initialization routine c09aaf.
Constraint: lencnc, where nc is the value returned in nwc by the call to the initialization routine c09aaf.
4: ca(lenc) Real (Kind=nag_wp) array Output
On exit: ca(i) contains the ith approximation coefficient, Ca(i), for i=1,2,,nc.
5: cd(lenc) Real (Kind=nag_wp) array Output
On exit: cd(i) contains the ith detail coefficient, Cd(i), for i=1,2,,nc.
6: icomm(100) 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 c09aaf.
On exit: contains additional information on the computed 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, n is inconsistent with the value passed to the initialization routine: n=value, n should be value.
On entry, array dimension lenc not large enough: lenc=value but must be at least value.
Either the initialization routine has not been called first or array icomm has been corrupted.
Either the initialization routine was called with wtrans='M' or array icomm has been 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

Background information to multithreading can be found in the Multithreading documentation.
c09caf is not threaded in any implementation.

9 Further Comments


10 Example

This example computes the one-dimensional discrete wavelet decomposition for 8 values using the Daubechies wavelet, wavnam='DB4', with zero end extension.

10.1 Program Text

Program Text (c09cafe.f90)

10.2 Program Data

Program Data (c09cafe.d)

10.3 Program Results

Program Results (c09cafe.r)