atan - 2-quadrant and 4-quadrant inverse tangent

Calling Sequence

phi=atan(x)

phi=atan(y,x)

Parameters

• x : real or complex scalar, vector or matrix
• phi : real or complex scalar, vector or matrix
• x, y : real scalars, vectors or matrices of the same size
• phi : 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 (-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)).

Examples

// examples with the second form
x=[1,%i,-1,%i]
phasex=atan(imag(x),real(x))
atan(0,-1)
atan(-%eps,-1)

// branch cuts
atan(-%eps + 2*%i)
atan(+%eps + 2*%i)
atan(-%eps - 2*%i)
atan(+%eps - 2*%i)

// values at the branching points
ieee(2)
atan(%i)
atan(-%i)
 

See Also

tan  ieee  

Authors

B.P. L.V.D. (authors of the complex atan function).