atan
2-quadrant and 4-quadrant inverse tangent
Syntax
phi = atan(x) phi = atan(y, x)
Arguments
- x
a real or complex scalar, vector or matrix.
- phi
a real or complex scalar, vector or matrix.
- x, y
a real scalars, vectors or matrices of the same size.
- phi
a real scalar, vector or matrix.
Description
The first form computes the 2-quadrant inverse tangent, which is the
inverse of tan(phi)
. For real x
,
phi
is in the interval (-π/2,π/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∞) and (-i∞,-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 (-π,π].
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) = atan(y(i, j), x(i, j))
.
Examples
See also
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