C09 Chapter Contents
C09 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentC09FBF

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

C09FBF computes the three-dimensional inverse discrete wavelet transform (IDWT) at a single level. The initialization routine C09ACF must be called first to set up the DWT options.

## 2  Specification

 SUBROUTINE C09FBF ( M, N, FR, LENC, C, B, LDB, SDB, ICOMM, IFAIL)
 INTEGER M, N, FR, LENC, LDB, SDB, ICOMM(260), IFAIL REAL (KIND=nag_wp) C(LENC), B(LDB,SDB,FR)

## 3  Description

C09FBF performs the inverse operation of routine C09FAF. That is, given sets of wavelet coefficients computed by routine C09FAF using a DWT as set up by the initialization routine C09ACF, on a real data array, $B$, C09FBF will reconstruct $B$.

None.

## 5  Parameters

1:     M – INTEGERInput
On entry: the first dimension of the output data: the number of rows of each two-dimensional frame.
Constraint: this must be the same as the value M passed to the initialization routine C09ACF.
2:     N – INTEGERInput
On entry: the second dimension of the output data: the number of columns of each two-dimensional frame.
Constraint: this must be the same as the value N passed to the initialization routine C09ACF.
3:     FR – INTEGERInput
On entry: the third dimension of the output data: the number two-dimensional frames.
Constraint: this must be the same as the value FR passed to the initialization routine C09ACF.
4:     LENC – INTEGERInput
On entry: the dimension of the array C as declared in the (sub)program from which C09FBF is called.
Constraint: ${\mathbf{LENC}}\ge {n}_{\mathrm{ct}}$, where ${n}_{\mathrm{ct}}$ is the total number of wavelet coefficients, as returned by C09ACF.
5:     C(LENC) – REAL (KIND=nag_wp) arrayInput
On entry: the coefficients of the discrete wavelet transform. This will normally be the result of some transformation on the coefficients computed by routine C09FAF.
6:     B(LDB,SDB,FR) – REAL (KIND=nag_wp) arrayOutput
On exit: the $m$ by $n$ by $\mathit{fr}$ reconstructed array, $B$, based on the input wavelet coefficients and the transform options supplied to the initialization routine C09ACF.
7:     LDB – INTEGERInput
On entry: the first dimension of the array B as declared in the (sub)program from which C09FBF is called.
Constraint: ${\mathbf{LDB}}\ge {\mathbf{M}}$.
8:     SDB – INTEGERInput
On entry: the second dimension of the array B as declared in the (sub)program from which C09FBF is called.
Constraint: ${\mathbf{SDB}}\ge {\mathbf{N}}$.
9:     ICOMM($260$) – INTEGER arrayCommunication Array
On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization routine C09ACF.
10:   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, ${\mathbf{FR}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{FR}}=⟨\mathit{\text{value}}⟩$, the value of FR on initialization (see C09ACF).
On entry, ${\mathbf{M}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{M}}=⟨\mathit{\text{value}}⟩$, the value of M on initialization (see C09ACF).
On entry, ${\mathbf{N}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{N}}=⟨\mathit{\text{value}}⟩$, the value of N on initialization (see C09ACF).
${\mathbf{IFAIL}}=2$
On entry, ${\mathbf{LDB}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{M}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{LDB}}\ge {\mathbf{M}}$.
On entry, ${\mathbf{SDB}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{N}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{SDB}}\ge {\mathbf{N}}$.
${\mathbf{IFAIL}}=3$
On entry, ${\mathbf{LENC}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{ct}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{LENC}}\ge {n}_{\mathrm{ct}}$, where ${n}_{\mathrm{ct}}$ is the number of DWT coefficients returned by C09ACF in parameter NWCT.
${\mathbf{IFAIL}}=6$
Either the initialization routine has not been called first or the communication array ICOMM has been corrupted.
The initialization routine was called with ${\mathbf{WTRANS}}=\text{'M'}$.
${\mathbf{IFAIL}}=-999$
Dynamic memory allocation failed.

## 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.

None.

## 9  Example

See Section 9 in C09FAF.