# NAG CL Interfacec09dac (dim1_​mxolap_​fwd)

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## 1Purpose

c09dac computes the 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 c09dac (Integer n, const double x[], Integer lenc, double ca[], double cd[], Integer icomm[], NagError *fail)
The function may be called by the names: c09dac, nag_wav_dim1_mxolap_fwd or nag_modwt.

## 3Description

c09dac computes the one-dimensional MODWT of a given input data array, ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, at a single level. For a chosen wavelet filter pair, the output coefficients are obtained by applying convolution to the input, $x$. The approximation (or smooth) coefficients, ${C}_{a}$, are produced by the low pass filter and the detail coefficients, ${C}_{d}$, by the high pass filter. Periodic (circular) convolution is available as an end extension method for application to finite data sets. The number ${n}_{c}$, of coefficients ${C}_{a}$ or ${C}_{d}$ is returned by the initialization function c09aac.

## 4References

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

## 5Arguments

1: $\mathbf{n}$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 function c09aac.
2: $\mathbf{x}\left[{\mathbf{n}}\right]$const double Input
On entry: x contains the input dataset ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.
3: $\mathbf{lenc}$Integer Input
On entry: the dimension of the arrays ca and cd. This must be at least the number, ${n}_{c}$, of approximation coefficients, ${C}_{a}$, and detail coefficients, ${C}_{d}$, of the discrete wavelet transform as returned in nwc by the call to the initialization function c09aac.
Constraint: ${\mathbf{lenc}}\ge {n}_{c}$, where ${n}_{c}$ is the value returned in nwc by the call to the initialization function c09aac.
4: $\mathbf{ca}\left[{\mathbf{lenc}}\right]$double Output
On exit: ${\mathbf{ca}}\left[i-1\right]$ contains the $i$th approximation coefficient, ${C}_{a}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,{n}_{c}$.
5: $\mathbf{cd}\left[{\mathbf{lenc}}\right]$double Output
On exit: ${\mathbf{cd}}\left[\mathit{i}-1\right]$ contains the $\mathit{i}$th detail coefficient, ${C}_{d}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,{n}_{c}$.
6: $\mathbf{icomm}\left[100\right]$Integer Communication Array
On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function c09aac.
On exit: contains additional information on the computed 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.

## 8Parallelism and Performance

c09dac is not threaded in any implementation.

None.

## 10Example

This example computes the one-dimensional maximal overlap discrete wavelet decomposition for $8$ values using the Daubechies wavelet, ${\mathbf{wavnam}}=\mathrm{Nag_Daubechies4}$.

### 10.1Program Text

Program Text (c09dace.c)

### 10.2Program Data

Program Data (c09dace.d)

### 10.3Program Results

Program Results (c09dace.r)