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# atan

### 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 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)```

• tan — tangent
• ieee — set floating point exception mode

### Authors

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