naginterfaces.library.wav.dim1_​mxolap_​inv

naginterfaces.library.wav.dim1_mxolap_inv(ca, cd, n, comm)

dim1_mxolap_inv computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. 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 c09db

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/c09/c09dbf.html

Parameters

cafloat, array-like, shape $\left(\text{lenc}\right)$

The $n_c$ approximation coefficients, $C_a$. These will normally be the result of some transformation on the coefficients computed by dim1_mxolap_fwd().

cdfloat, array-like, shape $\left(\text{lenc}\right)$

The $n_c$ detail coefficients, $C_d$. These will normally be the result of some transformation on the coefficients computed by dim1_mxolap_fwd().

nint

$n$, the length of the original data array from which the wavelet coefficients were computed by dim1_mxolap_fwd() and the length of the data array $y$ that is to be reconstructed by this function.

commdict, communication object

Communication structure.

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

Returns

yfloat, ndarray, shape $\left(n\right)$

The reconstructed data based on approximation and detail coefficients $C_a$ and $C_d$ and the transform options supplied to the initialization function dim1_init().

Raises

NagValueError

(errno $1$)

On entry, array dimension $\text{lenc}$ not large enough: $\text{lenc}=⟨value⟩$ but must be at least $⟨value⟩$.

(errno $4$)

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

(errno $6$)

On entry, the initialization function dim1_init() has not been called first or it has not been called with $wtrans=\text{‘T'}$, or the communication array $comm$[‘icomm’] has become corrupted.

Notes

dim1_mxolap_inv performs the inverse operation of dim1_mxolap_fwd(). That is, given sets of $n_c$ approximation coefficients and detail coefficients, computed by dim1_mxolap_fwd() using a MODWT as set up by the initialization function dim1_init(), on a real data array of length $n$, dim1_mxolap_inv will reconstruct the data array $y_i$, for $\text{i}=1,2,\dots ,n$, from which the coefficients were derived.

References

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