NAG CL Interface
c09ebc (dim2_​sngl_​inv)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{m}$ – Integer Input

On entry: number of rows, $m$, of data matrix $B$.

Constraint: this must be the same as the value m passed to the initialization function c09abc.

2: $\mathbf{n}$ – Integer Input

On entry: number of columns, $n$, of data matrix $B$.

Constraint: this must be the same as the value n passed to the initialization function c09abc.

3: $\mathbf{ca}\left[\mathit{dim}\right]$ – const double Input

Note: the dimension, dim, of the array ca must be at least $\mathbf{ldca}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function c09abc.

The $(i,j)$th element of the matrix is stored in $\mathbf{ca}\left[(j-1)\times \mathbf{ldca}+i-1\right]$.

On entry: contains the $n_{\mathrm{cm}}\times n_{\mathrm{cn}}$ matrix of approximation coefficients, $C_a$. This array will normally be the result of some transformation on the coefficients computed by function c09eac.

4: $\mathbf{ldca}$ – Integer Input

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

Constraint: $\mathbf{ldca}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function c09abc.

5: $\mathbf{ch}\left[\mathit{dim}\right]$ – const double Input

Note: the dimension, dim, of the array ch must be at least $\mathbf{ldch}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function c09abc.

The $(i,j)$th element of the matrix is stored in $\mathbf{ch}\left[(j-1)\times \mathbf{ldch}+i-1\right]$.

On entry: contains the $n_{\mathrm{cm}}\times n_{\mathrm{cn}}$ matrix of horizontal coefficients, $C_h$. This array will normally be the result of some transformation on the coefficients computed by function c09eac.

6: $\mathbf{ldch}$ – Integer Input

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

Constraint: $\mathbf{ldch}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function c09abc.

7: $\mathbf{cv}\left[\mathit{dim}\right]$ – const double Input

Note: the dimension, dim, of the array cv must be at least $\mathbf{ldcv}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function c09abc.

The $(i,j)$th element of the matrix is stored in $\mathbf{cv}\left[(j-1)\times \mathbf{ldcv}+i-1\right]$.

On entry: contains the $n_{\mathrm{cm}}\times n_{\mathrm{cn}}$ matrix of vertical coefficients, $C_v$. This array will normally be the result of some transformation on the coefficients computed by function c09eac.

8: $\mathbf{ldcv}$ – Integer Input

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

Constraint: $\mathbf{ldcv}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function c09abc.

9: $\mathbf{cd}\left[\mathit{dim}\right]$ – const double Input

Note: the dimension, dim, of the array cd must be at least $\mathbf{ldcd}\times n_{\mathrm{cn}}$ where $n_{\mathrm{cn}}$ is the argument nwcn returned by function c09abc.

The $(i,j)$th element of the matrix is stored in $\mathbf{cd}\left[(j-1)\times \mathbf{ldcd}+i-1\right]$.

On entry: contains the $n_{\mathrm{cm}}\times n_{\mathrm{cn}}$ matrix of diagonal coefficients, $C_d$. This array will normally be the result of some transformation on the coefficients computed by function c09eac.

10: $\mathbf{ldcd}$ – Integer Input

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

Constraint: $\mathbf{ldcd}\ge n_{\mathrm{cm}}$ where $n_{\mathrm{cm}}=n_{\mathrm{ct}}/\left(4n_{\mathrm{cn}}\right)$ and $n_{\mathrm{cn}}$, $n_{\mathrm{ct}}$ are returned by the initialization function c09abc.

11: $\mathbf{b}\left[\mathbf{ldb}\times \mathbf{n}\right]$ – double Output

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

On exit: the $m\times n$ reconstructed matrix, $B$, based on the input approximation, horizontal, vertical and diagonal coefficients and the transform options supplied to the initialization function c09abc.

12: $\mathbf{ldb}$ – Integer Input

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

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

13: $\mathbf{icomm}\left[180\right]$ – const 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 c09abc.

14: $\mathbf{fail}$ – 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 $⟨\mathit{\text{value}}⟩$ 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 $\mathbf{wtrans}=\mathrm{Nag\_MultiLevel}$ or icomm has been corrupted.

NE_INT

On entry, $\mathbf{ldca}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldca}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{ldcd}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldcd}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{ldch}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldch}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{ldcv}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ldcv}\ge ⟨\mathit{\text{value}}⟩$, the number of wavelet coefficients in the first dimension.

On entry, $\mathbf{m}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{m}=⟨\mathit{\text{value}}⟩$, the value of m on initialization (see c09abc).

On entry, $\mathbf{n}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{n}=⟨\mathit{\text{value}}⟩$, the value of n on initialization (see c09abc).

NE_INT_2

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

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.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example