C09 Chapter Contents
C09 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentC09CBF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

C09CBF computes the inverse one-dimensional discrete wavelet transform (DWT) at a single level. The initialization routine C09AAF must be called first to set up the DWT options.

## 2  Specification

 SUBROUTINE C09CBF ( LENC, CA, CD, N, Y, ICOMM, IFAIL)
 INTEGER LENC, N, ICOMM(100), IFAIL REAL (KIND=nag_wp) CA(LENC), CD(LENC), Y(N)

## 3  Description

C09CBF performs the inverse operation of C09CAF. That is, given sets of ${n}_{c}$ approximation coefficients and detail coefficients, computed by C09CAF using a DWT as set up by the initialization routine C09AAF, on a real data array of length $n$, C09CBF will reconstruct the data array ${y}_{i}$, for $\mathit{i}=1,2,\dots ,n$, from which the coefficients were derived.

None.

## 5  Parameters

1:     LENC – INTEGERInput
On entry: the dimension of the arrays CA and CD as declared in the (sub)program from which C09CBF 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:     CA(LENC) – REAL (KIND=nag_wp) arrayInput
On entry: the ${n}_{c}$ approximation coefficients, ${C}_{a}$. These will normally be the result of some transformation on the coefficients computed by C09CAF.
3:     CD(LENC) – REAL (KIND=nag_wp) arrayInput
On entry: the ${n}_{c}$ detail coefficients, ${C}_{d}$. These will normally be the result of some transformation on the coefficients computed by C09CAF.
4:     N – INTEGERInput
On entry: $n$, the length of the original data array from which the wavelet coefficients were computed by C09CAF 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:     Y(N) – REAL (KIND=nag_wp) arrayOutput
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:     ICOMM($100$) – INTEGER arrayCommunication 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:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ 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).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, 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, ${\mathbf{LENC}}<{n}_{c}$, where ${n}_{c}$ is the value returned in NWC by the call to the initialization routine C09AAF.
${\mathbf{IFAIL}}=4$
On entry, N is inconsistent with the value passed to the initialization routine C09AAF.
${\mathbf{IFAIL}}=6$
On entry, the initialization routine C09AAF has not been called first or it has been called with ${\mathbf{WTRANS}}=\text{'M'}$, or the communication array ICOMM has become corrupted.

## 7  Accuracy

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.