The routine may be called by the names c09dbf or nagf_wav_dim1_mxolap_inv.
c09dbf performs the inverse operation of c09daf. That is, given sets of 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 , c09dbf will reconstruct the data array
, for ,
from which the coefficients were derived.
Percival D B and Walden A T (2000) Wavelet Methods for Time Series Analysis Cambridge University Press
1: – IntegerInput
On entry: the dimension of the arrays ca and cd as declared in the (sub)program from which c09dbf is called.
, where is the value returned in nwc by the call to the initialization routine c09aaf.
2: – Real (Kind=nag_wp) arrayInput
On entry: the approximation coefficients, . These will normally be the result of some transformation on the coefficients computed by c09daf.
3: – Real (Kind=nag_wp) arrayInput
On entry: the detail coefficients, . These will normally be the result of some transformation on the coefficients computed by c09daf.
4: – IntegerInput
On entry: , 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.
This must be the same as the value n passed to the initialization routine c09aaf.
5: – Real (Kind=nag_wp) arrayOutput
On exit: the reconstructed data based on approximation and detail coefficients and and the transform options supplied to the initialization routine c09aaf.
6: – Integer arrayCommunication 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: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , 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: but must be at least .
On entry, n is inconsistent with the value passed to the initialization routine: , n should be .
On entry, the initialization routine c09aaf has not been called first or it has not been called with , or the communication array icomm has become corrupted.
An unexpected error has been triggered by this routine. Please
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.
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.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.