2-quadrant and 4-quadrant inverse tangent (original) (raw)

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atan

2-quadrant and 4-quadrant inverse tangent

Calling Sequence

phi=atan(x) phi=atan(y,x)

Arguments

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 complexx, 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 numberx+i*y. The range of atan(y,x) is (-pi, pi].

For real arguments, both forms yield identical values ifx>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)) orphi(i,j)=tan(y(i,j),x(i,j)).

Examples

x=[1,%i,-1,%i] phasex=atan(imag(x),real(x)) atan(0,-1) atan(-%eps,-1)

atan(-%eps + 2*%i) atan(+%eps + 2*%i) atan(-%eps - 2*%i) atan(+%eps - 2*%i)

ieee(2) atan(%i) atan(-%i)

See Also

Authors