# NAG CL Interfacec09fyc (dim3_​coeff_​ext)

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## 1Purpose

c09fyc extracts a selected set of discrete wavelet transform (DWT) coefficients from the full set of coefficients stored in compact form, as computed by c09fac (single level three-dimensional DWT) or c09fcc (multi-level three-dimensional DWT).

## 2Specification

 #include
 void c09fyc (Integer ilev, Integer cindex, Integer lenc, const double c[], double d[], Integer ldd, Integer sdd, Integer icomm[], NagError *fail)
The function may be called by the names: c09fyc, nag_wav_dim3_coeff_ext or nag_wav_3d_coeff_ext.

## 3Description

c09fyc is intended to be used after a call to either c09fac (single level three-dimensional DWT) or c09fcc (multi-level three-dimensional DWT), either of which must be preceded by a call to c09acc (three-dimensional wavelet filter initialization). Given an initial three-dimensional data set $A$, a prior call to c09fac or c09fcc computes the approximation coefficients (at the highest requested level in the case of c09fcc) and seven sets of detail coefficients (at all levels in the case of c09fcc) and stores these in compact form in a one-dimensional array c. c09fyc can then extract either the approximation coefficients or one of the sets of detail coefficients (at one of the levels following c09fcc) into a three-dimensional data set stored in d.
If a multi-level DWT was performed by a prior call to c09fcc then the dimensions of the three-dimensional data stored in d depend on the level extracted and are available from the arrays dwtlvm, dwtlvn and dwtlvfr as returned by c09fcc which contain the first, second and third dimensions respectively.
If a single level DWT was performed by a prior call to c09fac then the dimensions of the three-dimensional data stored in d can be determined from nwct, nwcn and nwcfr as returned by the setup function c09acc.
See Section 2.1 in the C09 Chapter Introduction for a discussion of the three-dimensional DWT.

None.

## 5Arguments

Note: the following notation is used in this section:
• ${n}_{\mathrm{cm}}$ is the number of wavelet coefficients in the first dimension. Following a call to c09fac (i.e., when ${\mathbf{ilev}}=0$) this is equal to ${\mathbf{nwct}}/\left(8×{\mathbf{nwcn}}×{\mathbf{nwcfr}}\right)$ as returned by c09acc. Following a call to c09fcc transforming nwl levels, and when extracting at level ${\mathbf{ilev}}>0$, this is equal to ${\mathbf{dwtlvm}}\left[{\mathbf{nwl}}-{\mathbf{ilev}}\right]$.
• ${n}_{\mathrm{cn}}$ is the number of wavelet coefficients in the second dimension. Following a call to c09fac (i.e., when ${\mathbf{ilev}}=0$) this is equal to nwcn as returned by c09acc. Following a call to c09fcc transforming nwl levels, and when extracting at level ${\mathbf{ilev}}>0$, this is equal to ${\mathbf{dwtlvn}}\left[{\mathbf{nwl}}-{\mathbf{ilev}}\right]$.
• ${n}_{\mathrm{cfr}}$ is the number of wavelet coefficients in the third dimension. Following a call to c09fac (i.e., when ${\mathbf{ilev}}=0$) this is equal to nwcfr as returned by c09acc. Following a call to c09fcc transforming nwl levels, and when extracting at level ${\mathbf{ilev}}>0$, this is equal to ${\mathbf{dwtlvfr}}\left[{\mathbf{nwl}}-{\mathbf{ilev}}\right]$
1: $\mathbf{ilev}$Integer Input
On entry: the level at which coefficients are to be extracted.
If ${\mathbf{ilev}}=0$, it is assumed that the coefficient array c was produced by a preceding call to the single level function c09fac.
If ${\mathbf{ilev}}>0$, it is assumed that the coefficient array c was produced by a preceding call to the multi-level function c09fcc.
Constraints:
• ${\mathbf{ilev}}=0$ (following a call to c09fac);
• $0\le {\mathbf{ilev}}\le {\mathbf{nwl}}$, where nwl is as used in a preceding call to c09fcc;
• if ${\mathbf{cindex}}=0$, ${\mathbf{ilev}}={\mathbf{nwl}}$ (following a call to c09fcc).
2: $\mathbf{cindex}$Integer Input
On entry: identifies which coefficients to extract. The coefficients are identified as follows:
${\mathbf{cindex}}=0$
The approximation coefficients, produced by application of the low pass filter over columns, rows and frames of $A$ (LLL). After a call to the multi-level transform function c09fcc (which implies that ${\mathbf{ilev}}>0$) the approximation coefficients are available only for ${\mathbf{ilev}}={\mathbf{nwl}}$, where nwl is the value used in a preceding call to c09fcc.
${\mathbf{cindex}}=1$
The detail coefficients produced by applying the low pass filter over columns and rows of $A$ and the high pass filter over frames (LLH).
${\mathbf{cindex}}=2$
The detail coefficients produced by applying the low pass filter over columns, high pass filter over rows and low pass filter over frames of $A$ (LHL).
${\mathbf{cindex}}=3$
The detail coefficients produced by applying the low pass filter over columns of $A$ and high pass filter over rows and frames (LHH).
${\mathbf{cindex}}=4$
The detail coefficients produced by applying the high pass filter over columns of $A$ and low pass filter over rows and frames (HLL).
${\mathbf{cindex}}=5$
The detail coefficients produced by applying the high pass filter over columns, low pass filter over rows and high pass filter over frames of $A$ (HLH).
${\mathbf{cindex}}=6$
The detail coefficients produced by applying the high pass filter over columns and rows of $A$ and the low pass filter over frames (HHL).
${\mathbf{cindex}}=7$
The detail coefficients produced by applying the high pass filter over columns, rows and frames of $A$ (HHH).
Constraints:
• if ${\mathbf{ilev}}=0$, $0\le {\mathbf{cindex}}\le 7$;
• if ${\mathbf{ilev}}={\mathbf{nwl}}$, following a call to c09fcc transforming nwl levels, $0\le {\mathbf{cindex}}\le 7$;
• otherwise $1\le {\mathbf{cindex}}\le 7$.
3: $\mathbf{lenc}$Integer Input
On entry: the dimension of the array c.
Constraint: lenc must be unchanged from the value used in the preceding call to either c09fac or c09fcc.
4: $\mathbf{c}\left[{\mathbf{lenc}}\right]$const double Input
On entry: DWT coefficients, as computed by c09fac or c09fcc.
5: $\mathbf{d}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array d must be at least ${\mathbf{ldd}}×{\mathbf{sdd}}×{n}_{\mathrm{cfr}}$.
On exit: the requested coefficients.
If the DWT coefficients were computed by c09fac then
• if ${\mathbf{cindex}}=0$, the approximation coefficients are stored in ${\mathbf{d}}\left[\left(\mathit{k}-1\right)×{\mathbf{ldd}}×{\mathbf{sdd}}+\left(\mathit{j}-1\right)×{\mathbf{ldd}}+i-1\right]$, for $\mathit{i}=1,2,\dots ,{n}_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,{n}_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,{n}_{\mathrm{cfr}}$;
• if $1\le {\mathbf{cindex}}\le 7$, the detail coefficients, as indicated by cindex, are stored in ${\mathbf{d}}\left[\left(\mathit{k}-1\right)×{\mathbf{ldd}}×{\mathbf{sdd}}+\left(\mathit{j}-1\right)×{\mathbf{ldd}}+i-1\right]$, for $\mathit{i}=1,2,\dots ,{n}_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,{n}_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,{n}_{\mathrm{cfr}}$.
If the DWT coefficients were computed by c09fcc then
• if ${\mathbf{cindex}}=0$ and ${\mathbf{ilev}}={\mathbf{nwl}}$, the approximation coefficients are stored in ${\mathbf{d}}\left[\left(\mathit{k}-1\right)×{\mathbf{ldd}}×{\mathbf{sdd}}+\left(\mathit{j}-1\right)×{\mathbf{ldd}}+i-1\right]$, for $\mathit{i}=1,2,\dots ,{n}_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,{n}_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,{n}_{\mathrm{cfr}}$;
• if $1\le {\mathbf{cindex}}\le 7$, the detail coefficients, as indicated by cindex, for level ilev are stored in ${\mathbf{d}}\left[\left(\mathit{k}-1\right)×{\mathbf{ldd}}×{\mathbf{sdd}}+\left(\mathit{j}-1\right)×{\mathbf{ldd}}+i-1\right]$, for $\mathit{i}=1,2,\dots ,{n}_{\mathrm{cm}}$, $\mathit{j}=1,2,\dots ,{n}_{\mathrm{cn}}$ and $\mathit{k}=1,2,\dots ,{n}_{\mathrm{cfr}}$.
6: $\mathbf{ldd}$Integer Input
On entry: the stride separating row elements of each of the sets of frame coefficients in the three-dimensional data stored in d.
Constraint: ${\mathbf{ldd}}\ge {n}_{\mathrm{cm}}$.
7: $\mathbf{sdd}$Integer Input
On entry: the stride separating corresponding coefficients of consecutive frames in the three-dimensional data stored in d.
Constraint: ${\mathbf{sdd}}\ge {n}_{\mathrm{cn}}$.
8: $\mathbf{icomm}\left[260\right]$Integer Communication Array
On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function c09acc.
9: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error 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.
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.
NE_INT
On entry, ${\mathbf{cindex}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{cindex}}\le 7$.
On entry, ${\mathbf{cindex}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{cindex}}\ge 0$.
On entry, ${\mathbf{ilev}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ilev}}=0$ following a call to the single level function c09fac.
On entry, ${\mathbf{ilev}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ilev}}>0$ following a call to the multi-level function c09fcc.
NE_INT_2
On entry, ${\mathbf{ilev}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{nwl}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ilev}}\le {\mathbf{nwl}}$, where nwl is the number of levels used in the call to c09fcc.
On entry, ${\mathbf{ldd}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{cm}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldd}}\ge {n}_{\mathrm{cm}}$, where ${n}_{\mathrm{cm}}$ is the number of DWT coefficients in the first dimension following the single level transform.
On entry, ${\mathbf{lenc}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{ct}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lenc}}\ge {n}_{\mathrm{ct}}$, where ${n}_{\mathrm{ct}}$ is the number of DWT coefficients computed in the preceding call to c09fac.
On entry, ${\mathbf{lenc}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{ct}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lenc}}\ge {n}_{\mathrm{ct}}$, where ${n}_{\mathrm{ct}}$ is the number of DWT coefficients computed in the preceding call to c09fcc.
On entry, ${\mathbf{sdd}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{cn}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{sdd}}\ge {n}_{\mathrm{cn}}$, where ${n}_{\mathrm{cn}}$ is the number of DWT coefficients in the second dimension following the single level transform.
NE_INT_3
On entry, ${\mathbf{ilev}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{nwl}}=⟨\mathit{\text{value}}⟩$, but ${\mathbf{cindex}}=0$.
Constraint: ${\mathbf{cindex}}>0$ when ${\mathbf{ilev}}<{\mathbf{nwl}}$ in the preceding call to c09fcc.
On entry, ${\mathbf{ldd}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{cm}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ldd}}\ge {n}_{\mathrm{cm}}$, where ${n}_{\mathrm{cm}}$ is the number of DWT coefficients in the first dimension at the selected level ilev.
On entry, ${\mathbf{sdd}}=⟨\mathit{\text{value}}⟩$ and ${n}_{\mathrm{cn}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{sdd}}\ge {n}_{\mathrm{cn}}$, where ${n}_{\mathrm{cn}}$ is the number of DWT coefficients in the second dimension at the selected level ilev.
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.

Not applicable.

## 8Parallelism and Performance

c09fyc is not threaded in any implementation.