naginterfaces.library.blas.droti

naginterfaces.library.blas.droti(x, indx, y, c, s)

droti applies a real plane rotation to a sparse real vector and a real vector.

For full information please refer to the NAG Library document for f06ex

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06exf.html

Parameters

xfloat, array-like, shape $\left(\text{nz}\right)$

The nonzero elements of the sparse vector $x$.

indxint, array-like, shape $\left(\text{nz}\right)$

$indx[\text{i}-1]$ must contain the index of $x[\text{i}-1]$ in the sparse vector $x$, for $\text{i}=1,2,\dots ,\text{nz}$.

yfloat, array-like, shape $(max\left(indx\right))$

The vector $y$. Only the elements corresponding to indices in $indx$ are referenced.

cfloat

The value $c$, the cosine of the rotation.

sfloat

The value $s$, the sine of the rotation.

Returns

xfloat, ndarray, shape $\left(\text{nz}\right)$

The transformed vector $x$.

yfloat, ndarray, shape $(max\left(indx\right))$

The transformed vector $y$. Only elements corresponding to indices in $indx$ are altered.

Notes

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

droti applies a real plane rotation to a sparse real vector $x$ stored in compressed form and a real vector $y$ in full storage form:

$$\begin{array}{c}\left(\begin{array}{c}{x}^T\\ y^T\end{array}\right)\leftarrow \left(\begin{array}{cc}c& s\\ -s& c\end{array}\right)\left(\begin{array}{c}{x}^T\\ y^T\end{array}\right)\text{.}\end{array}$$

The plane rotation has the form generated by drotg() or drotgc().

References

Dodson, D S, Grimes, R G and Lewis, J G, 1991, Sparse extensions to the Fortran basic linear algebra subprograms, ACM Trans. Math. Software (17), 253–263