c09fyf extracts a selected set of discrete wavelet transform (DWT) coefficients from the full set of coefficients stored in compact form, as computed by c09faf (single level three-dimensional DWT) or c09fcf (multi-level three-dimensional DWT).

2 Specification

Fortran Interface

Subroutine c09fyf (

ilev, cindex, lenc, c, d, ldd, sdd, icomm, ifail)

Integer, Intent (In)	::	ilev, cindex, lenc, ldd, sdd
Integer, Intent (Inout)	::	icomm(260), ifail
Real (Kind=nag_wp), Intent (In)	::	c(lenc)
Real (Kind=nag_wp), Intent (Inout)	::	d(ldd,sdd,*)

C Header Interface

#include <nag.h>

void	c09fyf_ (const Integer ilev, const Integer cindex, const Integer lenc, const double c[], double d[], const Integer ldd, const Integer sdd, Integer icomm[], Integer ifail)

The routine may be called by the names c09fyf or nagf_wav_dim3_coeff_ext.

3 Description

c09fyf is intended to be used after a call to either c09faf (single level three-dimensional DWT) or c09fcf (multi-level three-dimensional DWT), either of which must be preceded by a call to c09acf (three-dimensional wavelet filter initialization). Given an initial three-dimensional data set

A

, a prior call to c09faf or c09fcf computes the approximation coefficients (at the highest requested level in the case of c09fcf) and seven sets of detail coefficients (at all levels in the case of c09fcf) and stores these in compact form in a one-dimensional array c. c09fyf can then extract either the approximation coefficients or one of the sets of detail coefficients (at one of the levels following c09fcf) into a three-dimensional data set stored in d.

If a multi-level DWT was performed by a prior call to c09fcf then the dimensions of the three-dimensional data stored in d depend on the level extracted and are available from the arrays dwtlvm, dwtlvn and dwtlvfr as returned by c09fcf which contain the first, second and third dimensions respectively.

If a single level DWT was performed by a prior call to c09faf then the dimensions of the three-dimensional data stored in d can be determined from nwct, nwcn and nwcfr as returned by the setup routine c09acf.

See Section 2.1 in the C09 Chapter Introduction for a discussion of the three-dimensional DWT.

4 References

None.

5 Arguments

Note: the following notation is used in this section:

$n_{cm}$ is the number of wavelet coefficients in the first dimension. Following a call to c09faf (i.e., when $ilev = 0$ ) this is equal to $nwct / (8 \times nwcn \times nwcfr)$ as returned by c09acf. Following a call to c09fcf transforming nwl levels, and when extracting at level $ilev > 0$ , this is equal to $dwtlvm (nwl - ilev + 1)$ .
$n_{cn}$ is the number of wavelet coefficients in the second dimension. Following a call to c09faf (i.e., when $ilev = 0$ ) this is equal to nwcn as returned by c09acf. Following a call to c09fcf transforming nwl levels, and when extracting at level $ilev > 0$ , this is equal to $dwtlvn (nwl - ilev + 1)$ .
$n_{cfr}$ is the number of wavelet coefficients in the third dimension. Following a call to c09faf (i.e., when $ilev = 0$ ) this is equal to nwcfr as returned by c09acf. Following a call to c09fcf transforming nwl levels, and when extracting at level $ilev > 0$ , this is equal to $dwtlvfr (nwl - ilev + 1)$

1: $ilev$ – Integer Input

On entry: the level at which coefficients are to be extracted.

ilev = 0

, it is assumed that the coefficient array c was produced by a preceding call to the single level routine c09faf.

ilev > 0

, it is assumed that the coefficient array c was produced by a preceding call to the multi-level routine c09fcf.

Constraints:

$ilev = 0$ (following a call to c09faf);
$0 \leq ilev \leq nwl$ , where nwl is as used in a preceding call to c09fcf;
if $cindex = 0$ , $ilev = nwl$ (following a call to c09fcf).

2: $cindex$ – Integer Input

On entry: identifies which coefficients to extract. The coefficients are identified as follows:

$cindex = 0$: The approximation coefficients, produced by application of the low pass filter over columns, rows and frames of $A$ (LLL). After a call to the multi-level transform routine c09fcf (which implies that $ilev > 0$ ) the approximation coefficients are available only for $ilev = nwl$ , where nwl is the value used in a preceding call to c09fcf.
$cindex = 1$: The detail coefficients produced by applying the low pass filter over columns and rows of $A$ and the high pass filter over frames (LLH).
$cindex = 2$: The detail coefficients produced by applying the low pass filter over columns, high pass filter over rows and low pass filter over frames of $A$ (LHL).
$cindex = 3$: The detail coefficients produced by applying the low pass filter over columns of $A$ and high pass filter over rows and frames (LHH).
$cindex = 4$: The detail coefficients produced by applying the high pass filter over columns of $A$ and low pass filter over rows and frames (HLL).
$cindex = 5$: The detail coefficients produced by applying the high pass filter over columns, low pass filter over rows and high pass filter over frames of $A$ (HLH).
$cindex = 6$: The detail coefficients produced by applying the high pass filter over columns and rows of $A$ and the low pass filter over frames (HHL).
$cindex = 7$: The detail coefficients produced by applying the high pass filter over columns, rows and frames of $A$ (HHH).

Constraints:

if $ilev = 0$ , $0 \leq cindex \leq 7$ ;
if $ilev = nwl$ , following a call to c09fcf transforming nwl levels, $0 \leq cindex \leq 7$ ;
otherwise $1 \leq cindex \leq 7$ .

3: $lenc$ – Integer Input

On entry: the dimension of the array c as declared in the (sub)program from which c09fyf is called.

Constraint: lenc must be unchanged from the value used in the preceding call to either c09faf or c09fcf.

4: $c (lenc)$ – Real (Kind=nag_wp) array Input

On entry: DWT coefficients, as computed by c09faf or c09fcf.

5: $d (ldd, sdd, *)$ – Real (Kind=nag_wp) array Output

Note: the last dimension of the array d must be at least

n_{cfr}

On exit: the requested coefficients.

If the DWT coefficients were computed by c09faf then

if $cindex = 0$ , the approximation coefficients are stored in $d (i, j, k)$ , for $i = 1, 2, \dots, n_{cm}$ , $j = 1, 2, \dots, n_{cn}$ and $k = 1, 2, \dots, n_{cfr}$ ;
if $1 \leq cindex \leq 7$ , the detail coefficients, as indicated by cindex, are stored in $d (i, j, k)$ , for $i = 1, 2, \dots, n_{cm}$ , $j = 1, 2, \dots, n_{cn}$ and $k = 1, 2, \dots, n_{cfr}$ .

If the DWT coefficients were computed by c09fcf then

if $cindex = 0$ and $ilev = nwl$ , the approximation coefficients are stored in $d (i, j, k)$ , for $i = 1, 2, \dots, n_{cm}$ , $j = 1, 2, \dots, n_{cn}$ and $k = 1, 2, \dots, n_{cfr}$ ;
if $1 \leq cindex \leq 7$ , the detail coefficients, as indicated by cindex, for level ilev are stored in $d (i, j, k)$ , for $i = 1, 2, \dots, n_{cm}$ , $j = 1, 2, \dots, n_{cn}$ and $k = 1, 2, \dots, n_{cfr}$ .

6: $ldd$ – Integer Input

On entry: the first dimension of the array d as declared in the (sub)program from which c09fyf is called.

Constraint:

ldd \geq n_{cm}

7: $sdd$ – Integer Input

On entry: the second dimension of the array d as declared in the (sub)program from which c09fyf is called.

Constraint:

sdd \geq n_{cn}

8: $icomm (260)$ – 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 c09acf.

9: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

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

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $ilev = ⟨ value ⟩$ .
Constraint: $ilev = 0$ following a call to the single level routine c09faf.

On entry, $ilev = ⟨ value ⟩$ .
Constraint: $ilev > 0$ following a call to the multi-level routine c09fcf.

On entry, $ilev = ⟨ value ⟩$ and $nwl = ⟨ value ⟩$ .
Constraint: $ilev \leq nwl$ , where nwl is the number of levels used in the call to c09fcf.

$ifail = 2$: On entry, $cindex = ⟨ value ⟩$ .
Constraint: $cindex \leq 7$ .

On entry, $cindex = ⟨ value ⟩$ .
Constraint: $cindex \geq 0$ .

$ifail = 3$: On entry, $lenc = ⟨ value ⟩$ and $n_{ct} = ⟨ value ⟩$ .
Constraint: $lenc \geq n_{ct}$ , where $n_{ct}$ is the number of DWT coefficients computed in the preceding call to c09faf.

$ifail = 4$: On entry, $ldd = ⟨ value ⟩$ and $n_{cm} = ⟨ value ⟩$ .
Constraint: $ldd \geq n_{cm}$ , where $n_{cm}$ is the number of DWT coefficients in the first dimension at the selected level ilev.

On entry, $ldd = ⟨ value ⟩$ and $n_{cm} = ⟨ value ⟩$ .
Constraint: $ldd \geq n_{cm}$ , where $n_{cm}$ is the number of DWT coefficients in the first dimension following the single level transform.

On entry, $sdd = ⟨ value ⟩$ and $n_{cn} = ⟨ value ⟩$ .
Constraint: $sdd \geq n_{cn}$ , where $n_{cn}$ is the number of DWT coefficients in the second dimension at the selected level ilev.

On entry, $sdd = ⟨ value ⟩$ and $n_{cn} = ⟨ value ⟩$ .
Constraint: $sdd \geq n_{cn}$ , where $n_{cn}$ is the number of DWT coefficients in the second dimension following the single level transform.

$ifail = 5$: On entry, $ilev = ⟨ value ⟩$ and $nwl = ⟨ value ⟩$ , but $cindex = 0$ .
Constraint: $cindex > 0$ when $ilev < nwl$ in the preceding call to c09fcf.

$ifail = 6$: Either the initialization routine has not been called first or icomm has been corrupted.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: 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.