naginterfaces.library.blas.zgeapr

naginterfaces.library.blas.zgeapr(side, trans, perm, k, b)

zgeapr permutes the rows or columns of a complex rectangular matrix using a float array of permutations.

For full information please refer to the NAG Library document for f06vk

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/f06/f06vkf.html

Parameters

sidestr, length 1

Specifies the operation to be performed.

$side=\text{'L'}$ and $trans=\text{'T'}$

$B\leftarrow P^{T}B$.

$side=\text{'L'}$ and $trans=\text{'N'}$

$B\leftarrow PB$.

$side=\text{'R'}$ and $trans=\text{'T'}$

$B\leftarrow B{P}^T$.

$side=\text{'R'}$ and $trans=\text{'N'}$

$B\leftarrow BP$.

transstr, length 1

Specifies the operation to be performed.

$side=\text{'L'}$ and $trans=\text{'T'}$

$B\leftarrow P^{T}B$.

$side=\text{'L'}$ and $trans=\text{'N'}$

$B\leftarrow PB$.

$side=\text{'R'}$ and $trans=\text{'T'}$

$B\leftarrow B{P}^T$.

$side=\text{'R'}$ and $trans=\text{'N'}$

$B\leftarrow BP$.

permfloat, array-like, shape $\left(n\right)$

The $n$ indices $p_i$ which define the interchanges in the representation of $P$. It is usual to have $p_i\ge i$, but this is not necessary.

kint

$k$, the number of columns of $B$ if $side=\text{'L'}$, or the number of rows of $B$ if $side=\text{'R'}$.

bcomplex, array-like, shape $(:,:)$

Note: the required extent for this argument in dimension 1 is determined as follows: if $side=\text{'L'}$: $max(n,\text{m})$; if $side=\text{'R'}$: $k$; otherwise: $0$.

Note: the required extent for this argument in dimension 2 is determined as follows: if $side=\text{'L'}$: $k$; if $side=\text{'R'}$: $max(n,int(max\left(perm\right)))$; otherwise: $0$.

The original matrix $B$; $B$ is $\text{m}\times k$ if $side=\text{'L'}$, or $k\times \text{m}$ if $side=\text{'R'}$.

Returns

bcomplex, ndarray, shape $(:,:)$

The permuted matrix $B$.

Raises

NagValueError

(errno $2$)

On entry, error in parameter $trans$.

Constraint: $side=\text{'L'}$ or $\text{'R'}$.

(errno $2$)

On entry, error in parameter $trans$.

Constraint: $trans=\text{'N'}$ or $\text{'T'}$.

(errno $3$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $4$)

On entry, error in parameter $perm$.

Constraint: $1\le perm[i-1]\le \text{m}$.

(errno $5$)

On entry, error in parameter $k$.

Constraint: $k\ge 0$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

zgeapr performs one of the permutation operations

$$\begin{array}{c}\begin{array}{cc}B\leftarrow P^{T}B\text{,}& B\leftarrow PB\text{,}\\ B\leftarrow B{P}^T\text{or}& B\leftarrow BP\text{,}\end{array}\end{array}$$

where $B$ is a complex matrix, and $P$ is a permutation matrix.

$P$ is represented in the form

$$P=P_{1,p_1}{P}_{2,p_2}\cdots P_{n,p_n}\text{,}$$

where $P_{i,j}$ is the permutation matrix that interchanges items $i$ and $j$; that is, $P_{i,j}$ is the unit matrix with rows and columns $i$ and $j$ interchanged. If $i=j$, $P_{i,j}=I$.

Let $\text{m}$ denote the number of rows of $B$ if $side=\text{'L'}$, or the number of columns of $B$ if $side=\text{'R'}$: the function does not require $\text{m}$ to be passed as an argument, but assumes that $\text{m}\ge p_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

This function requires the indices $p_i$ to be supplied in a float array (the function takes the integer part of the array elements); zgeap() performs the same operation with the indices supplied in an int array.