naginterfaces.library.wav.dim1_​mxolap_​multi_​inv

naginterfaces.library.wav.dim1_mxolap_multi_inv(nwlinv, keepa, c, n, comm)[source]

dim1_mxolap_multi_inv computes the inverse one-dimensional multi-level maximal overlap discrete wavelet transform (MODWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by dim1_mxolap_multi_fwd() from an original set of data. The initialization function dim1_init() must be called first to set up the MODWT options.

For full information please refer to the NAG Library document for c09dd

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/c09/c09ddf.html

Parameters
nwlinvint

The number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to , which has the value of argument as used in the computation of the wavelet coefficients using dim1_mxolap_multi_fwd(). The data will be reconstructed to level , where level is the original input dataset provided to dim1_mxolap_multi_fwd().

keepastr, length 1

Determines whether the approximation coefficients are stored in array for every level of the computed transform or else only for the final level. In both cases, the detail coefficients are stored in for every level computed.

Retain approximation coefficients for all levels computed.

Retain approximation coefficients for only the final level computed.

cfloat, array-like, shape

The coefficients of a multi-level wavelet transform of the dataset.

The coefficients are stored in as follows:

If ,

Contains the level approximation coefficients;

Contains the level detail coefficients, for ;

If ,

Contains the level approximation coefficients, for ;

Contains the level detail coefficients, for .

The values and denote the numbers of approximation and detail coefficients respectively, which are equal.

This number is returned as output in from a preceding call to dim1_mxolap_multi_fwd().

See dim1_mxolap_multi_fwd() for details.

nint

, the length of the data array, , to be reconstructed.

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to dim1_init().

Returns
yfloat, ndarray, shape

The dataset reconstructed from the multi-level wavelet transform coefficients and the transformation options supplied to the initialization function dim1_init().

Raises
NagValueError
(errno )

On entry, is larger than the number of levels computed by the preceding call to dim1_mxolap_multi_fwd(): , expected .

(errno )

On entry, .

Constraint: .

(errno )

On entry, is set too small: .

Constraint: .

(errno )

On entry, is inconsistent with the value passed to the initialization function: , should be .

(errno )

On entry, the initialization function dim1_init() has not been called first or it has not been called with , or the communication array [‘icomm’] has become corrupted.

(errno )

On entry, .

Constraint: .

Notes

dim1_mxolap_multi_inv performs the inverse operation of dim1_mxolap_multi_fwd(). That is, given a set of wavelet coefficients computed by dim1_mxolap_multi_fwd() using a MODWT as set up by the initialization function dim1_init() on a real array of length , dim1_mxolap_multi_inv will reconstruct the data array , for , from which the coefficients were derived.

References

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