# NAG FL Interfacec09dbf (dim1_​mxolap_​inv)

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## 1Purpose

c09dbf computes the inverse one-dimensional maximal overlap discrete wavelet transform (MODWT) at a single level. The initialization routine c09aaf must be called first to set up the MODWT options.

## 2Specification

Fortran Interface
 Subroutine c09dbf ( lenc, ca, cd, n, y,
 Integer, Intent (In) :: lenc, n, icomm(100) Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: ca(lenc), cd(lenc) Real (Kind=nag_wp), Intent (Out) :: y(n)
#include <nag.h>
 void c09dbf_ (const Integer *lenc, const double ca[], const double cd[], const Integer *n, double y[], const Integer icomm[], Integer *ifail)
The routine may be called by the names c09dbf or nagf_wav_dim1_mxolap_inv.

## 3Description

c09dbf performs the inverse operation of c09daf. That is, given sets of ${n}_{c}$ approximation coefficients and detail coefficients, computed by c09daf using a MODWT as set up by the initialization routine c09aaf, on a real data array of length $n$, c09dbf 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 as declared in the (sub)program from which c09dbf is called.
Constraint: ${\mathbf{lenc}}\ge {n}_{c}$, where ${n}_{c}$ is the value returned in nwc by the call to the initialization routine c09aaf.
2: $\mathbf{ca}\left({\mathbf{lenc}}\right)$Real (Kind=nag_wp) array Input
On entry: the ${n}_{c}$ approximation coefficients, ${C}_{a}$. These will normally be the result of some transformation on the coefficients computed by c09daf.
3: $\mathbf{cd}\left({\mathbf{lenc}}\right)$Real (Kind=nag_wp) array Input
On entry: the ${n}_{c}$ detail coefficients, ${C}_{d}$. These will normally be the result of some transformation on the coefficients computed by c09daf.
4: $\mathbf{n}$Integer Input
On entry: $n$, the length of the original data array from which the wavelet coefficients were computed by c09daf and the length of the data array y that is to be reconstructed by this routine.
Constraint: This must be the same as the value n passed to the initialization routine c09aaf.
5: $\mathbf{y}\left({\mathbf{n}}\right)$Real (Kind=nag_wp) array 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 routine c09aaf.
6: $\mathbf{icomm}\left(100\right)$Integer array 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: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, array dimension lenc not large enough: ${\mathbf{lenc}}=⟨\mathit{\text{value}}⟩$ but must be at least $⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=4$
On entry, n is inconsistent with the value passed to the initialization routine: ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$, n should be $⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=6$
On entry, the initialization routine c09aaf has not been called first or it has not been called with ${\mathbf{wtrans}}=\text{'T'}$, or the communication array icomm has become corrupted.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL 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.