naginterfaces.library.blas.ddoti

naginterfaces.library.blas.ddoti(x, indx, y)

ddoti computes the scalar product of a sparse real vector, stored in compressed form, with a real vector.

For full information please refer to the NAG Library document for f06er

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f06/f06erf.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 elements corresponding to indices in $indx$ are accessed.

Returns

dfloat

The scalar product of the sparse real vector, $x$, with the real vector $y$.

Notes

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

ddoti returns the value of the scalar product

$$x^{T}y=x\left(1\right)\times y\left(\text{indx}\left(1\right)\right)+x\left(2\right)\times y\left(\text{indy}\left(2\right)\right)+\cdots +x\left(nz\right)\times y\left(\text{indx}\left(nz\right)\right)$$

where $x$ is a sparse real vector, stored in compressed form and $y$ is a real vector in full storage format.

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