XMM-Newton Science Analysis System


selectlib (selectlib-4.77) [xmmsas_20230412_1735-21.0.0]

Vector operators and functions

A limited set of operators and functions to perform vector algebra in three-dimensional Eucledian space is available. The following table provides an overview over the available constructs:

description	symbol/name	type	comment
vector construction	vector(x, y, z)	vector	x/y/z can be arithmetic expressions
unit vector construction	unitvector(x, y, z)	vector	norm(unitvector(x, y, z))==1
construction sky vector in J2000 reference frame	skyvector(ra, dec)	vector	ra/dec Right Ascension/Declination in rad
unary minus	${\tt -}{\tt v}$	vector	v vector
vector addition	${\tt v1}{\tt +}{\tt v2}$	vector	v1/v2 vectors
vector subtraction	${\tt v1}{\tt -}{\tt v2}$	vector	v1/v2 vectors
multiplication with scalar	${\tt s}{\tt *}{\tt v}$	vector	v vector, s arithmetic expression
division by scalar	${\tt v}{\tt /}{\tt s}$	vector	v vector, s arithmetic expression $\neq0$
cross product	cross(v1, v2)	vector	v1/v2 vectors
vector component	v[i]	scalar	$0<={\tt i}<=2$
vector norm	norm(v)	scalar	equivalent to sqrt(v[0]**2+v[1]**2+v[2]**2)
scalar product	${\tt v1}{\tt *}{\tt v2}$	scalar	equivalent to v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2]

Example expressions involving vector algebra:

• norm(vector(1,2,3)-4*vector(8,9,10))
• cross(skyvector(0,0), skyvector(#PI/2, 0))
• norm(vector(3,4,5)*unitvector(-2,3,4))-1
• 5*vector(1,2,3)[0]