# NAG CL Interfacec09cbc (dim1_​sngl_​inv)

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## 1Purpose

c09cbc computes the inverse one-dimensional discrete wavelet transform (DWT) at a single level. The initialization function c09aac must be called first to set up the DWT options.

## 2Specification

 #include
 void c09cbc (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: c09cbc, nag_wav_dim1_sngl_inv or nag_idwt.

## 3Description

c09cbc performs the inverse operation of c09cac. That is, given sets of ${n}_{c}$ approximation coefficients and detail coefficients, computed by c09cac using a DWT as set up by the initialization function c09aac, on a real data array of length $n$, c09cbc will reconstruct the data array ${y}_{i}$, for $\mathit{i}=1,2,\dots ,n$, from which the coefficients were derived.

None.

## 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 c09cac.
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 c09cac.
4: $\mathbf{n}$Integer Input
On entry: $n$, the length of the original data array from which the wavelet coefficients were computed by c09cac 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
Either the initialization function has not been called first or array icomm has been corrupted.
Either the initialization function was called with ${\mathbf{wtrans}}=\mathrm{Nag_MultiLevel}$ or array icomm has been corrupted.
On entry, n is inconsistent with the value passed to the initialization function: ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$, n should be $⟨\mathit{\text{value}}⟩$.
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

c09cbc is not threaded in any implementation.