c09eyf extracts a selected set of discrete wavelet transform (DWT) coefficients from the full set of coefficients stored in compact form, as computed by c09ecf (two-dimensional DWT).

2 Specification

Fortran Interface

Subroutine c09eyf (

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

Integer, Intent (In)	::	ilev, cindex, lenc, ldd
Integer, Intent (Inout)	::	icomm(180), ifail
Real (Kind=nag_wp), Intent (In)	::	c(lenc)
Real (Kind=nag_wp), Intent (Inout)	::	d(ldd,*)

C Header Interface

#include <nag.h>

void	c09eyf_ (const Integer ilev, const Integer cindex, const Integer lenc, const double c[], double d[], const Integer ldd, Integer icomm[], Integer *ifail)

The routine may be called by the names c09eyf or nagf_wav_dim2_coeff_ext.

3 Description

c09eyf is intended to be used after a call to c09ecf (two-dimensional DWT), which in turn should be preceded by a call to c09abf (two-dimensional wavelet filter initialization). Given an initial two-dimensional data set

A

, a prior call to c09ecf computes the approximation coefficients (at the highest requested level) and three sets of detail coefficients at all levels and stores these in compact form in a one-dimensional array c. c09eyf can then extract either the approximation coefficients or one of the sets of detail coefficients at one of the levels into a matrix

D

. The dimensions of

D

depend on the level extracted and are available from the arrays dwtlvm and dwtlvn as returned by c09ecf which contain the first and second dimensions respectively. See Section 2.1 in the C09 Chapter Introduction for a discussion of the two-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, which, at level ilev, is equal to $dwtlvm (nwl - ilev + 1)$ as returned by a call to c09ecf transforming nwl levels.
$n_{cn}$ is the number of wavelet coefficients in the second dimension, which, at level ilev, is equal to $dwtlvn (nwl - ilev + 1)$ as returned by a call to c09ecf transforming nwl levels.

1: $ilev$ – Integer Input

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

Constraints:

$1 \leq ilev \leq nwl$ , where nwl is as used in a preceding call to c09ecf;
if $cindex = 0$ , $ilev = nwl$ .

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 and rows of the original matrix (LL). The approximation coefficients are available only for $ilev = nwl$ , where nwl is the value used in a preceding call to c09ecf.
$cindex = 1$: The vertical detail coefficients produced by applying the low pass filter over columns of the original matrix and the high pass filter over rows (LH).
$cindex = 2$: The horizontal detail coefficients produced by applying the high pass filter over columns of the original matrix and the low pass filter over rows (HL).
$cindex = 3$: The diagonal detail coefficients produced by applying the high pass filter over columns and rows of the original matrix (HH).

Constraint:

0 \leq cindex \leq 3

when

ilev = nwl

as used in c09ecf, otherwise

1 \leq cindex \leq 3

3: $lenc$ – Integer Input

On entry: the dimension of the array c as declared in the (sub)program from which c09eyf is called.

Constraint: lenc must be unchanged from the value used in the preceding call to c09ecf.

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

On entry: DWT coefficients, as computed by a preceding call to c09ecf.

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

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

n_{cn}

On exit: the requested coefficients.

ilev = nwl

(as used in c09ecf) and

cindex = 0

, the

n_{cm} \times n_{cn}

approximation coefficients

a_{i j}

are stored in

d (i, j)

, for

i = 1, 2, \dots, n_{cm}

and

j = 1, 2, \dots, n_{cn}

Otherwise the

n_{cm} \times n_{cn}

level ilev detail coefficients (of type specified by cindex)

d_{i j}

are stored in

d (i, j)

, for

i = 1, 2, \dots, n_{cm}

and

j = 1, 2, \dots, n_{cn}

6: $ldd$ – Integer Input

On entry: the first dimension of the array d as declared in the (sub)program from which c09eyf is called.

Constraint:

ldd \geq n_{cm}

7: $icomm (180)$ – 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.

8: $ifail$ – 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: $ilev \geq 1$ .

On entry, $ilev = ⟨ value ⟩$ and $nwl = ⟨ value ⟩$ .
Constraint: $ilev \leq nwl$ , where nwl is the number of levels used in the call to c09ecf.

$ifail = 2$: On entry, $cindex = ⟨ value ⟩$ .
Constraint: $cindex \leq 3$ .

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 a previous call to c09ecf.

$ifail = 4$: 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.

$ifail = 5$: On entry, $ilev = ⟨ value ⟩$ and $nwl = ⟨ value ⟩$ , but $cindex = 0$ .
Constraint: $cindex > 0$ when $ilev < nwl$ in the preceding call to c09ecf.

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

Either the initialization routine was called with $wtrans ='S'$ 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.