4.1.1 Vector-by-Vector operations (BLAS1)

The following operations with vectors x, y and scalar $\alpha$ are included in BLAS1 :

1. For each component do

   Addition	$$	$x_i \;:=\; x_i + y_i$
   Subtraction	$$	$x_i \;:=\; x_i - y_i$
   Multiplication	$$	$x_i \;:=\; x_i \ast y_i \;;\; x_i \;:=\; \alpha \ast x_i$
   Division	$$	$x_i \;:=\; x_i / y_i$
   Copy	$$	$x_i \;\leftarrow\; y_i \;;\; x_i \;\leftrightarrow\; y_i$

2. Inner product SDOT, DDOT $\;\;\;\;\; s = \sum\limits_{i=1}^N x_i \ast y_i$.

3. Triades :		$x_i := x_i + \alpha \ast y_i$		SAXPY/DAXPY
   				Scalar Alpha times X Plus Y
   resp.		$x_i := x_i \ast ( \alpha + y_i )$

Parallel computer : Splitting of vectors into (disjoint) subvectors. The inner product requires at least one REDUCE operation Sect. 3.3.4).

Vector unit : Besides the inner product all operations are natural vector operation.