# NAG CL Interfacec09dbc (dim1_​mxolap_​inv)

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## 1Purpose

c09dbc computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization function c09aac must be called first to set up the MODWT options.

## 2Specification

 #include
 void c09dbc (Integer lenc, const double ca[], const double cd[], Integer n, double y[], const Integer icomm[], NagError *fail)
The function may be called by the names: c09dbc, nag_wav_dim1_mxolap_inv or nag_imodwt.

## 3Description

c09dbc performs the inverse operation of c09dac. That is, given sets of ${n}_{c}$ approximation coefficients and detail coefficients, computed by c09dac using a MODWT as set up by the initialization function c09aac, on a real data array of length $n$, c09dbc will reconstruct the data array ${y}_{i}$, for $\mathit{i}=1,2,\dots ,n$, from which the coefficients were derived.

## 4References

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

## 5Arguments

1: $\mathbf{lenc}$Integer Input
On entry: the dimension of the arrays ca and cd.
Constraint: ${\mathbf{lenc}}\ge {n}_{c}$, where ${n}_{c}$ is the value returned in nwc by the call to the initialization function c09aac.
2: $\mathbf{ca}\left[{\mathbf{lenc}}\right]$const double Input
On entry: the ${n}_{c}$ approximation coefficients, ${C}_{a}$. These will normally be the result of some transformation on the coefficients computed by c09dac.
3: $\mathbf{cd}\left[{\mathbf{lenc}}\right]$const double Input
On entry: the ${n}_{c}$ detail coefficients, ${C}_{d}$. These will normally be the result of some transformation on the coefficients computed by c09dac.
4: $\mathbf{n}$Integer Input
On entry: $n$, the length of the original data array from which the wavelet coefficients were computed by c09dac and the length of the data array y that is to be reconstructed by this function.
Constraint: This must be the same as the value n passed to the initialization function c09aac.
5: $\mathbf{y}\left[{\mathbf{n}}\right]$double Output
On exit: the reconstructed data based on approximation and detail coefficients ${C}_{a}$ and ${C}_{d}$ and the transform options supplied to the initialization function c09aac.
6: $\mathbf{icomm}\left[100\right]$const Integer 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: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_ARRAY_DIM_LEN
On entry, array dimension lenc not large enough: ${\mathbf{lenc}}=⟨\mathit{\text{value}}⟩$ but must be at least $⟨\mathit{\text{value}}⟩$.
On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.
NE_INITIALIZATION
On entry, n is inconsistent with the value passed to the initialization function: ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$, n should be $⟨\mathit{\text{value}}⟩$.
On entry, the initialization function c09aac has not been called first or it has not been called with ${\mathbf{wtrans}}=\mathrm{Nag_MODWTSingle}$, or the communication array icomm has become corrupted.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

## 7Accuracy

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.