c09aac (dim1_init) : NAG Library CL Interface, Mark 28

1 Purpose

c09aac returns the details of the chosen one-dimensional discrete wavelet filter. For a chosen mother wavelet, discrete wavelet transform type (single-level or multi-level DWT or MODWT) and end extension method, this function returns the maximum number of levels of resolution (appropriate to a multi-level transform), the filter length, and the number of approximation coefficients (equal to the number of detail coefficients) for a single-level DWT or MODWT or the total number of coefficients for a multi-level DWT or MODWT. This function must be called before any of the one-dimensional discrete transform functions in this chapter.

2 Specification

#include <nag.h>

void	c09aac (Nag_Wavelet wavnam, Nag_WaveletTransform wtrans, Nag_WaveletMode mode, Integer n, Integer nwlmax, Integer nf, Integer nwc, Integer icomm[], NagError fail)

The function may be called by the names: c09aac, nag_wav_dim1_init or nag_wfilt.

3 Description

One-dimensional discrete wavelet transforms (DWT) or maximum overlap wavelet transforms (MODWT) are characterised by the mother wavelet, the end extension method and whether multiresolution analysis is to be performed. For the selected combination of choices for these three characteristics, and for a given length,

n

, of the input data array,

x

, c09aac returns the dimension details for the transform determined by this combination. The dimension details are:

l_{\max}

, the maximum number of levels of resolution that that could be computed were a multi-level DWT/MODWT applied;

n_{f}

, the filter length;

n_{c}

the number of approximation (or detail) coefficients for a single-level DWT/MODWT or the total number of coefficients generated by a multi-level DWT/MODWT over

l_{\max}

levels. These values are also stored in the communication array icomm, as are the input choices, so that they may be conveniently communicated to the one-dimensional transform functions in this chapter.

5 Arguments

wavnam

– Nag_Wavelet Input

On entry: the name of the mother wavelet. See the C09 Chapter Introduction for details.

$wavnam = Nag_Haar$: Haar wavelet.
$wavnam = Nag_Daubechies n$ , where $n = 2, 3, \dots, 38$: Daubechies wavelet with $n$ vanishing moments ( $2 n$ coefficients). For example, $wavnam = Nag_Daubechies4$ is the name for the Daubechies wavelet with $4$ vanishing moments ( $8$ coefficients).
$wavnam = Nag_Coiflet n$ , where $n = 1, 2, \dots, 17$: Coiflet wavelet of order $n$ .
$wavnam = Nag_Beylkin$: Beylkin wavelet.
$wavnam = Nag_Vaidyanathan$: Vaidyanathan wavelet.
$wavnam = Nag_Symlet n$ , where $n = 2, 3, \dots, 20$: Symlet wavelet of order $n$ .
$wavnam = Nag_Biorthogonal x_y$ , where $x_y$ can be one of 1_1, 1_3, 1_5, 2_2, 2_4, 2_6, 2_8, 3_1, 3_3, 3_5, 3_7, 3_9, 4_4, 5_5 or 6_8: Biorthogonal wavelet of order $x . y$ . For example $wavnam = Nag_Biorthogonal1_1$ is the name for the Biorthogonal wavelet of order $1.1$ .
$wavnam = Nag_Reverse_Biorthogonal x_y$ , where $x_y$ can be one of 1_1, 1_3, 1_5, 2_2, 2_4, 2_6, 2_8, 3_1, 3_3, 3_5, 3_7, 3_9, 4_4, 5_5 or 6_8: Reverse biorthogonal wavelet of order $x . y$ . For example $wavnam = Nag_Reverse_Biorthogonal1_1$ is the name for the reverse biorthogonal wavelet of order $1.1$ .

Constraint:

wavnam = Nag_Haar

Nag_Daubechies2

Nag_Daubechies3

Nag_Daubechies4

Nag_Daubechies5

Nag_Daubechies6

Nag_Daubechies7

Nag_Daubechies8

Nag_Daubechies9

Nag_Daubechies10

Nag_Daubechies11

Nag_Daubechies12

Nag_Daubechies13

Nag_Daubechies14

Nag_Daubechies15

Nag_Daubechies16

Nag_Daubechies17

Nag_Daubechies18

Nag_Daubechies19

Nag_Daubechies20

Nag_Daubechies21

Nag_Daubechies22

Nag_Daubechies23

Nag_Daubechies24

Nag_Daubechies25

Nag_Daubechies26

Nag_Daubechies27

Nag_Daubechies28

Nag_Daubechies29

Nag_Daubechies30

Nag_Daubechies31

Nag_Daubechies32

Nag_Daubechies33

Nag_Daubechies34

Nag_Daubechies35

Nag_Daubechies36

Nag_Daubechies37

Nag_Daubechies38

Nag_Coiflet1

Nag_Coiflet2

Nag_Coiflet3

Nag_Coiflet4

Nag_Coiflet5

Nag_Coiflet6

Nag_Coiflet7

Nag_Coiflet8

Nag_Coiflet9

Nag_Coiflet10

Nag_Coiflet11

Nag_Coiflet12

Nag_Coiflet13

Nag_Coiflet14

Nag_Coiflet15

Nag_Coiflet16

Nag_Coiflet17

Nag_Beylkin

Nag_Vaidyanathan

Nag_Symlet2

Nag_Symlet3

Nag_Symlet4

Nag_Symlet5

Nag_Symlet6

Nag_Symlet7

Nag_Symlet8

Nag_Symlet9

Nag_Symlet10

Nag_Symlet11

Nag_Symlet12

Nag_Symlet13

Nag_Symlet14

Nag_Symlet15

Nag_Symlet16

Nag_Symlet17

Nag_Symlet18

Nag_Symlet19

Nag_Symlet20

Nag_Biorthogonal1_1

Nag_Biorthogonal1_3

Nag_Biorthogonal1_5

Nag_Biorthogonal2_2

Nag_Biorthogonal2_4

Nag_Biorthogonal2_6

Nag_Biorthogonal2_8

Nag_Biorthogonal3_1

Nag_Biorthogonal3_3

Nag_Biorthogonal3_5

Nag_Biorthogonal3_7

Nag_Biorthogonal3_9

Nag_Biorthogonal4_4

Nag_Biorthogonal5_5

Nag_Biorthogonal6_8

Nag_Reverse_Biorthogonal1_1

Nag_Reverse_Biorthogonal1_3

Nag_Reverse_Biorthogonal1_5

Nag_Reverse_Biorthogonal2_2

Nag_Reverse_Biorthogonal2_4

Nag_Reverse_Biorthogonal2_6

Nag_Reverse_Biorthogonal2_8

Nag_Reverse_Biorthogonal3_1

Nag_Reverse_Biorthogonal3_3

Nag_Reverse_Biorthogonal3_5

Nag_Reverse_Biorthogonal3_7

Nag_Reverse_Biorthogonal3_9

Nag_Reverse_Biorthogonal4_4

Nag_Reverse_Biorthogonal5_5

Nag_Reverse_Biorthogonal6_8

wtrans

– Nag_WaveletTransform Input

On entry: the type of discrete wavelet transform that is to be applied.

$wtrans = Nag_SingleLevel$: Single-level decomposition or reconstruction by discrete wavelet transform.
$wtrans = Nag_MultiLevel$: Multiresolution, by a multi-level DWT or its inverse.
$wtrans = Nag_MODWTSingle$: Single-level decomposition or reconstruction by maximal overlap discrete wavelet transform.
$wtrans = Nag_MODWTMulti$: Multi-level resolution by a maximal overlap discrete wavelet transform or its inverse.

Constraint:

wtrans = Nag_SingleLevel

Nag_MultiLevel

Nag_MODWTSingle

Nag_MODWTMulti

mode

– Nag_WaveletMode Input

On entry: the end extension method. Note that only periodic end extension is currently available for the MODWT.

$mode = Nag_Periodic$: Periodic end extension.
$mode = Nag_HalfPointSymmetric$: Half-point symmetric end extension.
$mode = Nag_WholePointSymmetric$: Whole-point symmetric end extension.
$mode = Nag_ZeroPadded$: Zero end extension.

Constraints:

$mode = Nag_Periodic$ , $Nag_HalfPointSymmetric$ , $Nag_WholePointSymmetric$ or $Nag_ZeroPadded$ for DWT;
$mode = Nag_Periodic$ for MODWT.

n

– Integer Input

On entry: the number of elements,

n

, in the input data array,

x

Constraint:

n \geq 2

nwlmax

– Integer * Output

On exit: the maximum number of levels of resolution,

l_{\max}

, that can be computed when a multi-level discrete wavelet transform is applied. It is such that

2^{l_{\max}} \leq n < 2^{l_{\max} + 1}

, for

l_{\max}

an integer.

nf

– Integer * Output

On exit: the filter length,

n_{f}

, for the supplied mother wavelet. This is used to determine the number of coefficients to be generated by the chosen transform.

nwc

– Integer * Output

On exit: for a single-level transform (

wtrans = Nag_SingleLevel

Nag_MODWTSingle

), the number of approximation coefficients that would be generated for the given problem size, mother wavelet, extension method and type of transform; this is also the corresponding number of detail coefficients. For a multi-level transform (

wtrans = Nag_MultiLevel

Nag_MODWTMulti

) the total number of coefficients that would be generated over

l_{\max}

levels and with

keepa = Nag_StoreAll

for MODWT.

icomm [100]

– Integer Communication Array

On exit: contains details of the wavelet transform and the problem dimension which is to be communicated to the one-dimensional discrete transform functions in this chapter.

fail

– NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

On entry, argument

⟨ value ⟩

had an illegal value.

On entry,

wtrans = Nag_MODWTSingle

Nag_MODWTMulti

and

mode \neq Nag_Periodic

.
Constraint:

mode = Nag_Periodic

when

wtrans = Nag_MODWTSingle

Nag_MODWTMulti

NE_INT

On entry,

n = ⟨ value ⟩

.
Constraint:

n \geq 2

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

10 Example

This example computes the one-dimensional multi-level resolution for

8

values by a discrete wavelet transform using the Haar wavelet with zero end extensions. The length of the wavelet filter, the number of levels of resolution, the number of approximation coefficients at each level and the total number of wavelet coefficients are printed.

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
c09aac (dim1_init)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interfacec09aac (dim1_​init)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
c09aac (dim1_init)