atan — 2-quadrant and 4-quadrant inverse tangent
phi=atan(x) phi=atan(y,x)
real or complex scalar, vector or matrix
real or complex scalar, vector or matrix
real scalars, vectors or matrices of the same size
real scalar, vector or matrix
The first form computes the 2-quadrant inverse tangent, which is the
inverse of tan(phi)
. For real x
, phi
is in the
interval (-pi/2, pi/2). For complex x
, atan
has two
singular, branching points +%i
,-%i
and the chosen branch
cuts are the two imaginary half-straight lines [i, i*oo) and (-i*oo, -i].
The second form computes the 4-quadrant arctangent (atan2 in
Fortran), this is, it returns the argument (angle) of the complex
number x+i*y
. The range of atan(y,x)
is (-pi, pi].
For real arguments, both forms yield identical values if x>0
.
In case of vector or matrix arguments, the evaluation is done
element-wise, so that phi
is a vector or matrix of the same size
with phi(i,j)=atan(x(i,j))
or phi(i,j)=tan(y(i,j),x(i,j))
.