naginterfaces.library.matop.real_​gen_​trans_​inplace

naginterfaces.library.matop.real_gen_trans_inplace(a, m, n)

real_gen_trans_inplace transposes a rectangular matrix in-situ.

For full information please refer to the NAG Library document for f01cr

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f01/f01crf.html

Parameters

afloat, ndarray, shape $\left(\text{mn}\right)$, modified in place

On entry: the elements of the $m\times n$ matrix $A$, stored by columns.

On exit: the elements of the transpose matrix, also stored by columns.

mint

$m$, the number of rows of the matrix $A$.

nint

$n$, the number of columns of the matrix $A$.

Raises

NagValueError

(errno $i<0$)

A serious internal error has occurred in real_gen_trans_inplace.

(errno $1$)

On entry, $m=⟨value⟩$, $n=⟨value⟩$ and $\text{mn}=⟨value⟩$.

Constraint: $\text{mn}=m\times n$.

Notes

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

real_gen_trans_inplace requires that the elements of an $m\times n$ matrix $A$ are stored consecutively by columns in a one-dimensional array. It reorders the elements so that on exit the array holds the transpose of $A$ stored in the same way. For example, if $m=4$ and $n=3$, on entry the array must hold:

$$a_{11}{a}_{21}{a}_{31}{a}_{41}{a}_{12}{a}_{22}{a}_{32}{a}_{42}{a}_{13}{a}_{23}{a}_{33}{a}_{43}$$

and on exit it holds

$$a_{11}{a}_{12}{a}_{13}{a}_{21}{a}_{22}{a}_{23}{a}_{31}{a}_{32}{a}_{33}{a}_{41}{a}_{42}{a}_{43}\text{.}$$

References

Cate, E G and Twigg, D W, 1977, Algorithm 513: Analysis of in-situ transposition, ACM Trans. Math. Software (3), 104–110