F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06ERF (DDOTI)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06ERF (DDOTI) computes the scalar product of a sparse real vector, stored in compressed form, with a real vector.

## 2  Specification

 FUNCTION F06ERF ( NZ, X, INDX, Y)
 REAL (KIND=nag_wp) F06ERF
 INTEGER NZ, INDX(*) REAL (KIND=nag_wp) X(*), Y(*)
The routine may be called by its BLAS name ddoti.

## 3  Description

F06ERF (DDOTI) returns, via the function name, the value of the scalar product
 $xTy = x1 × yindx1 + x2 × yindy2 + ⋯ + xnz × yindxnz$
where $x$ is a sparse real vector, stored in compressed form and $y$ is a real vector in full storage format.

## 4  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

## 5  Parameters

1:     NZ – INTEGERInput
On entry: the number of nonzeros in the sparse vector $x$.
2:     X($*$) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array X must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{NZ}}\right)$.
On entry: the nonzero elements of the sparse vector $x$.
3:     INDX($*$) – INTEGER arrayInput
Note: the dimension of the array INDX must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{NZ}}\right)$.
On entry: ${\mathbf{INDX}}\left(\mathit{i}\right)$ must contain the index of ${\mathbf{X}}\left(\mathit{i}\right)$ in the sparse vector $x$, for $\mathit{i}=1,2,\dots ,{\mathbf{NZ}}$.
4:     Y($*$) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array Y must be at least $\underset{\mathit{k}}{\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left\{{\mathbf{INDX}}\left(\mathit{k}\right)\right\}$.
On entry: the vector $y$. Only elements corresponding to indices in INDX are accessed.

None.

Not applicable.

None.

None.