3.2 Level 1 BLAS

The level 1 functions implement vector operations.

scal( alpha, x)

Scales a vector by a constant:

$\begin{displaymath} x := \alpha x. \end{displaymath}$

If x is a real matrix, the scalar argument alpha must be a Python integer or float. If x is complex, alpha can be an integer, float, or complex.

nrm2( x)

Euclidean norm of a vector: returns

$\begin{displaymath} \Vert x\Vert _2. \end{displaymath}$

asum( x)

L-1 norm of a vector: returns

$\begin{displaymath} \Vert x\Vert _1 \quad \mbox{($x$\ real)}, \qquad \Vert\Re x\Vert _1 + \Vert\Im x\Vert _1 \quad \mbox{($x$\ complex)}. \end{displaymath}$

iamax( x)

Returns

$\begin{displaymath} \mathop{\rm argmax}_{k=0,\ldots,n-1} \vert x_k\vert \quad \... ...e x_k\vert + \vert\Im x_k\vert \quad \mbox{($x$\ complex)}. \end{displaymath}$

If more than one coefficient achieves the maximum, the index of the first k is returned.

swap( x, y)

Interchanges two vectors:

$\begin{displaymath} x \leftrightarrow y. \end{displaymath}$

x and y are matrices of the same type ('d' or 'z').

copy( x, y)

Copies a vector to another vector:

$\begin{displaymath} y := x. \end{displaymath}$

x and y are matrices of the same type ('d' or 'z').

axpy( x, y[,alpha=1.0])

Constant times a vector plus a vector:

$\begin{displaymath} y := \alpha x + y. \end{displaymath}$

x and y are matrices of the same type ('d' or 'z'). If x is real, the scalar argument alpha must be a Python integer or float. If x is complex, alpha can be an integer, float, or complex.

dot( x, y)

Returns

$\begin{displaymath} x^Hy. \end{displaymath}$

x and y are matrices of the same type ('d' or 'z').

dotu( x, y)

Returns

$\begin{displaymath} x^Ty. \end{displaymath}$

x and y are matrices of the same type ('d' or 'z').