NAG Library Function Document

nag_wfilt_3d (c09acc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     wavnam – Nag_WaveletInput

On entry: the name of the mother wavelet. See the c09 Chapter Introduction for details.

$\mathbf{wavnam}=\mathrm{Nag\_Haar}$

Haar wavelet.

$\mathbf{wavnam}=\mathrm{Nag\_Daubechies}\mathit{n}$, where $\mathit{n}=2,3,\dots ,10$

Daubechies wavelet with $\mathit{n}$ vanishing moments ($2\mathit{n}$ coefficients). For example, $\mathbf{wavnam}=\mathrm{Nag\_Daubechies4}$ is the name for the Daubechies wavelet with $4$ vanishing moments ($8$ coefficients).

$\mathbf{wavnam}=\mathrm{Nag\_Biorthogonal}\mathit{x}\_\mathit{y}$, where $\mathit{x}\_\mathit{y}$ can be one of 1_1, 1_3, 1_5, 2_2, 2_4, 2_6, 2_8, 3_1, 3_3, 3_5 or 3_7

Biorthogonal wavelet of order $\mathit{x}$.$\mathit{y}$. For example $\mathbf{wavnam}=\mathrm{Nag\_Biorthogonal1\_1}$ is the name for the Biorthogonal wavelet of order $1.1$.

Constraint: $\mathbf{wavnam}=\mathrm{Nag\_Haar}$, $\mathrm{Nag\_Daubechies2}$, $\mathrm{Nag\_Daubechies3}$, $\mathrm{Nag\_Daubechies4}$, $\mathrm{Nag\_Daubechies5}$, $\mathrm{Nag\_Daubechies6}$, $\mathrm{Nag\_Daubechies7}$, $\mathrm{Nag\_Daubechies8}$, $\mathrm{Nag\_Daubechies9}$, $\mathrm{Nag\_Daubechies10}$, $\mathrm{Nag\_Biorthogonal1\_1}$, $\mathrm{Nag\_Biorthogonal1\_3}$, $\mathrm{Nag\_Biorthogonal1\_5}$, $\mathrm{Nag\_Biorthogonal2\_2}$, $\mathrm{Nag\_Biorthogonal2\_4}$, $\mathrm{Nag\_Biorthogonal2\_6}$, $\mathrm{Nag\_Biorthogonal2\_8}$, $\mathrm{Nag\_Biorthogonal3\_1}$, $\mathrm{Nag\_Biorthogonal3\_3}$, $\mathrm{Nag\_Biorthogonal3\_5}$ or $\mathrm{Nag\_Biorthogonal3\_7}$.

2:     wtrans – Nag_WaveletTransformInput

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

$\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$

Single-level decomposition or reconstruction by discrete wavelet transform.

$\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$

Multiresolution, by a multi-level DWT or its inverse.

Constraint: $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$ or $\mathrm{Nag\_MultiLevel}$.

3:     mode – Nag_WaveletModeInput

On entry: the end extension method.

$\mathbf{mode}=\mathrm{Nag\_Periodic}$

Periodic end extension.

$\mathbf{mode}=\mathrm{Nag\_HalfPointSymmetric}$

Half-point symmetric end extension.

$\mathbf{mode}=\mathrm{Nag\_WholePointSymmetric}$

Whole-point symmetric end extension.

$\mathbf{mode}=\mathrm{Nag\_ZeroPadded}$

Zero end extension.

Constraint: $\mathbf{mode}=\mathrm{Nag\_Periodic}$, $\mathrm{Nag\_HalfPointSymmetric}$, $\mathrm{Nag\_WholePointSymmetric}$ or $\mathrm{Nag\_ZeroPadded}$.

4:     m – IntegerInput

On entry: the number of elements, $m$, in the first dimension (number of rows of each two-dimensional frame) of the input data, $A$.

Constraint: $\mathbf{m}\ge 2$.

5:     n – IntegerInput

On entry: the number of elements, $n$, in the second dimension (number of columns of each two-dimensional frame) of the input data, $A$.

Constraint: $\mathbf{n}\ge 2$.

6:     fr – IntegerInput

On entry: the number of elements, $\mathit{fr}$, in the third dimension (number of frames) of the input data, $A$.

Constraint: $\mathbf{fr}\ge 2$.

7:     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 ($\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$). It is such that $2^{l_{\max }}\le \min \left(m,n,\mathit{fr}\right)<2^{l_{\max }+1}$, for $l_{\max }$ an integer.

If $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$, nwlmax is not set.

8:     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.

9:     nwct – Integer *Output

On exit: the total number of wavelet coefficients, $n_{\mathrm{ct}}$, that will be generated. When $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$ the number of rows required (i.e., the first dimension of each two-dimensional frame) in each of the output coefficient arrays can be calculated as $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(8\times n_{\mathrm{cn}}\times n_{\mathrm{cfr}}\right)$. When $\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$ the length of the array used to store all of the coefficient matrices must be at least $n_{\mathrm{ct}}$.

10:   nwcn – Integer *Output

On exit: for a single-level transform ($\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$), the number of coefficients that would be generated in the second dimension, $n_{\mathrm{cn}}$, for each coefficient type. For a multi-level transform ($\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$) this is set to $1$.

11:   nwcfr – Integer *Output

On exit: for a single-level transform ($\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$), the number of coefficients that would be generated in the third dimension, $n_{\mathrm{cfr}}$, for each coefficient type. For a multi-level transform ($\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$) this is set to $1$.

12:   icomm[$260$] – 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.

13:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INT

On entry, $\mathbf{fr}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{fr}\ge 2$.

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}\ge 2$.

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge 2$.

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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (c09acce.c)

10.2  Program Data

Program Data (c09acce.d)

10.3  Program Results

Program Results (c09acce.r)