NAG FL Interfacec09ebf (dim2_​sngl_​inv)

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1Purpose

c09ebf computes the inverse two-dimensional discrete wavelet transform (DWT) at a single level. The initialization routine c09abf must be called first to set up the DWT options.

2Specification

Fortran Interface
 Subroutine c09ebf ( m, n, ca, ldca, ch, ldch, cv, ldcv, cd, ldcd, b, ldb,
 Integer, Intent (In) :: m, n, ldca, ldch, ldcv, ldcd, ldb, icomm(180) Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: ca(ldca,*), ch(ldch,*), cv(ldcv,*), cd(ldcd,*) Real (Kind=nag_wp), Intent (Inout) :: b(ldb,n)
#include <nag.h>
 void c09ebf_ (const Integer *m, const Integer *n, const double ca[], const Integer *ldca, const double ch[], const Integer *ldch, const double cv[], const Integer *ldcv, const double cd[], const Integer *ldcd, double b[], const Integer *ldb, const Integer icomm[], Integer *ifail)
The routine may be called by the names c09ebf or nagf_wav_dim2_sngl_inv.

3Description

c09ebf performs the inverse operation of routine c09eaf. That is, given sets of approximation, horizontal, vertical and diagonal coefficients computed by routine c09eaf using a DWT as set up by the initialization routine c09abf, on a real matrix, $B$, c09ebf will reconstruct $B$.

None.

5Arguments

1: $\mathbf{m}$Integer Input
On entry: number of rows, $m$, of data matrix $B$.
Constraint: this must be the same as the value m passed to the initialization routine c09abf.
2: $\mathbf{n}$Integer Input
On entry: number of columns, $n$, of data matrix $B$.
Constraint: this must be the same as the value n passed to the initialization routine c09abf.
3: $\mathbf{ca}\left({\mathbf{ldca}},*\right)$Real (Kind=nag_wp) array Input
Note: the second dimension of the array ca must be at least ${n}_{\mathrm{cn}}$ where ${n}_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.
On entry: contains the ${n}_{\mathrm{cm}}×{n}_{\mathrm{cn}}$ matrix of approximation coefficients, ${C}_{a}$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.
4: $\mathbf{ldca}$Integer Input
On entry: the first dimension of the array ca as declared in the (sub)program from which c09ebf is called.
Constraint: ${\mathbf{ldca}}\ge {n}_{\mathrm{cm}}$ where ${n}_{\mathrm{cm}}={n}_{\mathrm{ct}}/\left(4{n}_{\mathrm{cn}}\right)$ and ${n}_{\mathrm{cn}}$, ${n}_{\mathrm{ct}}$ are returned by the initialization routine c09abf.
5: $\mathbf{ch}\left({\mathbf{ldch}},*\right)$Real (Kind=nag_wp) array Input
Note: the second dimension of the array ch must be at least ${n}_{\mathrm{cn}}$ where ${n}_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.
On entry: contains the ${n}_{\mathrm{cm}}×{n}_{\mathrm{cn}}$ matrix of horizontal coefficients, ${C}_{h}$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.
6: $\mathbf{ldch}$Integer Input
On entry: the first dimension of the array ch as declared in the (sub)program from which c09ebf is called.
Constraint: ${\mathbf{ldch}}\ge {n}_{\mathrm{cm}}$ where ${n}_{\mathrm{cm}}={n}_{\mathrm{ct}}/\left(4{n}_{\mathrm{cn}}\right)$ and ${n}_{\mathrm{cn}}$, ${n}_{\mathrm{ct}}$ are returned by the initialization routine c09abf.
7: $\mathbf{cv}\left({\mathbf{ldcv}},*\right)$Real (Kind=nag_wp) array Input
Note: the second dimension of the array cv must be at least ${n}_{\mathrm{cn}}$ where ${n}_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.
On entry: contains the ${n}_{\mathrm{cm}}×{n}_{\mathrm{cn}}$ matrix of vertical coefficients, ${C}_{v}$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.
8: $\mathbf{ldcv}$Integer Input
On entry: the first dimension of the array cv as declared in the (sub)program from which c09ebf is called.
Constraint: ${\mathbf{ldcv}}\ge {n}_{\mathrm{cm}}$ where ${n}_{\mathrm{cm}}={n}_{\mathrm{ct}}/\left(4{n}_{\mathrm{cn}}\right)$ and ${n}_{\mathrm{cn}}$, ${n}_{\mathrm{ct}}$ are returned by the initialization routine c09abf.
9: $\mathbf{cd}\left({\mathbf{ldcd}},*\right)$Real (Kind=nag_wp) array Input
Note: the second dimension of the array cd must be at least ${n}_{\mathrm{cn}}$ where ${n}_{\mathrm{cn}}$ is the argument nwcn returned by routine c09abf.
On entry: contains the ${n}_{\mathrm{cm}}×{n}_{\mathrm{cn}}$ matrix of diagonal coefficients, ${C}_{d}$. This array will normally be the result of some transformation on the coefficients computed by routine c09eaf.
10: $\mathbf{ldcd}$Integer Input
On entry: the first dimension of the array cd as declared in the (sub)program from which c09ebf is called.
Constraint: ${\mathbf{ldcd}}\ge {n}_{\mathrm{cm}}$ where ${n}_{\mathrm{cm}}={n}_{\mathrm{ct}}/\left(4{n}_{\mathrm{cn}}\right)$ and ${n}_{\mathrm{cn}}$, ${n}_{\mathrm{ct}}$ are returned by the initialization routine c09abf.
11: $\mathbf{b}\left({\mathbf{ldb}},{\mathbf{n}}\right)$Real (Kind=nag_wp) array Output
On exit: the $m×n$ reconstructed matrix, $B$, based on the input approximation, horizontal, vertical and diagonal coefficients and the transform options supplied to the initialization routine c09abf.
12: $\mathbf{ldb}$Integer Input
On entry: the first dimension of the array b as declared in the (sub)program from which c09ebf is called.
Constraint: ${\mathbf{ldb}}\ge {\mathbf{m}}$.
13: $\mathbf{icomm}\left(180\right)$Integer array Communication Array
On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization routine c09abf.
14: $\mathbf{ifail}$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, ${\mathbf{ldca}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldca}}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.
On entry, ${\mathbf{ldcd}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldcd}}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.
On entry, ${\mathbf{ldch}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldch}}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.
On entry, ${\mathbf{ldcv}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldcv}}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{ldb}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldb}}\ge {\mathbf{m}}$.
${\mathbf{ifail}}=4$
On entry, ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m}}=⟨\mathit{\text{value}}⟩$, the value of m on initialization (see c09abf).
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$, the value of n on initialization (see c09abf).
${\mathbf{ifail}}=6$
Either the initialization routine has not been called first or icomm has been corrupted.
Either the initialization routine was called with ${\mathbf{wtrans}}=\text{'M'}$ or icomm has been 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.