NAG Library Function Document

nag_imldwt_2d (c09edc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     nwlinv – IntegerInput

On entry: the number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{\mathrm{fwd}}$, which has the value of argument nwl as used in the computation of the wavelet coefficients using nag_mldwt_2d (c09ecc). The data will be reconstructed to level $\left(\mathbf{nwl}-\mathbf{nwlinv}\right)$, where level $0$ is the original input dataset provided to nag_mldwt_2d (c09ecc).

Constraint: $1\le \mathbf{nwlinv}\le \mathbf{nwl}$, where nwl is the value used in a preceding call to nag_mldwt_2d (c09ecc).

2:     lenc – IntegerInput

On entry: the dimension of the array c.

Constraint: $\mathbf{lenc}\ge n_{\mathrm{ct}}$, where $n_{\mathrm{ct}}$ is the total number of coefficients that correspond to a transform with nwlinv levels and is unchanged from the preceding call to nag_mldwt_2d (c09ecc).

3:     c[lenc] – const doubleInput

On entry: the coefficients of a multi-level wavelet transform of the original matrix, $A$, which may have been filtered or otherwise manipulated.

Let $q\left(\mathit{i}\right)$ be the number of coefficients (of each type) at level $\mathit{i}$, for $\mathit{i}=n_{\mathrm{fwd}},n_{\mathrm{fwd}}-1,\dots ,1$. Then, setting $k_1=q\left(n_{\mathrm{fwd}}\right)$ and $k_{j+1}=k_j+q\left(n_{\mathrm{fwd}}-⌈j/3⌉+1\right)$, for $j=1,2,\dots ,3n_{\mathrm{fwd}}$, the coefficients are stored in c as follows:

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,k_1$

Contains the level $n_{\mathrm{fwd}}$ approximation coefficients, $a_{n_{\mathrm{fwd}}}$.

$\mathbf{c}\left[\mathit{i}-1\right]$, for $\mathit{i}=k_j+1,\dots ,k_{j+1}$

Contains the level $n_{\mathrm{fwd}}-⌈j/3⌉+1$ vertical, horizontal and diagonal coefficients. These are:

• vertical coefficients if $j\mathrm{ mod }3=1$;
• horizontal coefficients if $j\mathrm{ mod }3=2$;
• diagonal coefficients if $j\mathrm{ mod }3=0$,

for $j=1,\dots ,3n_{\mathrm{fwd}}$.

Note that the coefficients in c may be extracted according to level and type into two-dimensional arrays using nag_wav_2d_coeff_ext (c09eyc), and inserted using nag_wav_2d_coeff_ins (c09ezc).

4:     m – IntegerInput

On entry: the number of elements, $m$, in the first dimension of the reconstructed matrix $B$. For a full reconstruction of nwl levels, where nwl is as supplied to nag_mldwt_2d (c09ecc), this must be the same as argument m used in the call to nag_mldwt_2d (c09ecc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$ levels, this must be equal to $\mathbf{dwtlvm}\left[\mathbf{nwlinv}\right]$, as returned from nag_mldwt_2d (c09ecc).

5:     n – IntegerInput

On entry: the number of elements, $n$, in the second dimension of the reconstructed matrix $B$. For a full reconstruction of nwl levels, where nwl is as supplied to nag_mldwt_3d (c09fcc), this must be the same as argument n used in the call to nag_mldwt_2d (c09ecc). For a partial reconstruction of $\mathbf{nwlinv}<\mathbf{nwl}$, this must be equal to $\mathbf{dwtlvn}\left[\mathbf{nwlinv}\right]$, as returned from nag_mldwt_2d (c09ecc).

6:     b[$\mathbf{ldb}\times \mathbf{n}$] – doubleOutput

Note: the $\left(i,j\right)$th element of the matrix $B$ is stored in $\mathbf{b}\left[\left(j-1\right)\times \mathbf{ldb}+i-1\right]$.

On exit: the $m$ by $n$ reconstructed matrix, $B$, based on the input multi-level wavelet transform coefficients and the transform options supplied to the initialization function nag_wfilt_2d (c09abc).

7:     ldb – IntegerInput

On entry: the stride separating matrix row elements in the array b.

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

8:     icomm[$180$] – const IntegerCommunication Array

On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function nag_wfilt_2d (c09abc).

9:     fail – NagError *Input/Output

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

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

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

NE_INITIALIZATION

Either the initialization function has not been called first or icomm has been corrupted.

Either the initialization function was called with $\mathbf{wtrans}=\mathrm{Nag\_SingleLevel}$ or icomm has been corrupted.

NE_INT

On entry, $\mathbf{lenc}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lenc}\ge ⟨\mathit{\text{value}}⟩$, the total number of coefficients generated by the preceding call to nag_mldwt_2d (c09ecc).

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}\ge ⟨\mathit{\text{value}}⟩$, the number of coefficients in the first dimension at the required level of reconstruction.

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}\ge ⟨\mathit{\text{value}}⟩$, the number of coefficients in the second dimension at the required level of reconstruction.

On entry, $\mathbf{nwlinv}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{nwlinv}\ge 1$.

NE_INT_2

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

On entry, $\mathbf{nwlinv}=⟨\mathit{\text{value}}⟩$ and $n_{\mathrm{fwd}}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{nwlinv}\le n_{\mathrm{fwd}}$.

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