nag_wfilt_2d (c09abc) : NAG C Library, Mark 26

Purpose

nag_wfilt_2d (c09abc) returns the details of the chosen two-dimensional discrete wavelet filter. For a chosen mother wavelet, discrete wavelet transform type (single-level or multi-level DWT) and end extension method, this function returns the maximum number of levels of resolution (appropriate to a multi-level transform), the filter length, the total number of approximation, horizontal, vertical and diagonal coefficients and the number of coefficients in the second dimension for the single-level case. This function must be called before any of the two-dimensional transform functions in this chapter.

Description

Two-dimensional discrete wavelet transforms (DWT) 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 given dimensions (

m \times n

) of data matrix

A

, nag_wfilt_2d (c09abc) 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 would be computed were a multi-level DWT applied;

n_{f}

, the filter length;

n_{ct}

the total number of approximation, horizontal, vertical and diagonal coefficients (over all levels in the multi-level DWT case); and

n_{cn}

, the number of coefficients in the second dimension for a single-level DWT. These values are also stored in the communication array icomm, as are the input choices, so that they may be conveniently communicated to the two-dimensional transform functions in this chapter.

Arguments

wavnam

– Nag_WaveletInput

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_WaveletTransformInput

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.

Constraint:

wtrans = Nag_SingleLevel

Nag_MultiLevel

mode

– Nag_WaveletModeInput

On entry: the end extension method.

$mode = Nag_Periodic$: 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.

Constraint:

mode = Nag_Periodic

Nag_HalfPointSymmetric

Nag_WholePointSymmetric

Nag_ZeroPadded

m

– IntegerInput

On entry: the number of elements,

m

, in the first dimension (number of rows of data matrix

A

) of the input data.

Constraint:

m \geq 2

n

– IntegerInput

On entry: the number of elements,

n

, in the second dimension (number of columns of data matrix

A

) of the input data.

Constraint:

n \geq 2

nwlmax

– Integer *Output

On exit: the maximum number of levels of resolution,

l_{\max}

, that can be computed if a multi-level discrete wavelet transform is applied (

wtrans = Nag_MultiLevel

). It is such that

2^{l_{\max}} \leq \min (m, n) < 2^{l_{\max} + 1}

, for

l_{\max}

an integer.

wtrans = Nag_SingleLevel

, nwlmax is not set.

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.

nwct

– Integer *Output

On exit: the total number of wavelet coefficients,

n_{ct}

, that will be generated. When

wtrans = Nag_SingleLevel

the number of rows required in each of the output coefficient matrices can be calculated as

n_{cm} = n_{ct} / (4 n_{cn})

. When

wtrans = Nag_MultiLevel

the length of the array used to store all of the coefficient matrices must be at least

n_{ct}

nwcn

– Integer *Output

On exit: for a single-level transform (

wtrans = Nag_SingleLevel

), the number of coefficients that would be generated in the second dimension,

n_{cn}

, for each coefficient type. For a multi-level transform (

wtrans = Nag_MultiLevel

) this is set to

1

10:

icomm [180]

– IntegerCommunication Array

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

11:

fail

– NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument

〈value〉

had an illegal value.

NE_INT

On entry,

m = 〈value〉

.
Constraint:

m \geq 2

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

Example

This example computes the two-dimensional multi-level resolution for a

6 \times 6

matrix by a discrete wavelet transform using the Haar wavelet with whole-point symmetric end extensions. The number of levels of transformation actually performed is one less than the maximum possible. This number of levels, the length of the wavelet filter, the total number of coefficients and the number of coefficients in each dimension for each level are printed along with the vertical detail coefficients from the first level, before a reconstruction is performed.

10.1

Program Text

10.2

Program Data

10.3

Program Results

NAG C Library Function Document

nag_wfilt_2d (c09abc)

▸▿ 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 C Library Function Document

nag_wfilt_2d (c09abc)

▸▿ 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

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