C Library Functions  - atan (3)

NAME

ATAN(3) - [MATHEMATICS:TRIGONOMETRIC] Arctangent AKA inverse tangent function

SYNOPSIS

result = atan([x) | atan(y, x) 

         elemental TYPE(kind=KIND) function atan(y,x)


          TYPE(kind=KIND),intent(in) :: x
          TYPE(kind=**),intent(in),optional :: y

CHARACTERISTICS

o If Y is present X and Y must both be real. Otherwise, X may be complex.
o KIND can be any kind supported by the associated type.
o The returned value is of the same type and kind as X.

DESCRIPTION

ATAN(X)(3) returns the inverse tangent (ie. arctangent) of the elements of X in radians. The function accepts both real and complex inputs, specified as a scalar, vector, matrix. The atan operation is element-wise when X is nonscalar.
o For real values of X, atan(X) returns values in the interval [-PI/2, PI/2].
o For complex values of X, atan(X) returns complex values.
When Y is not supplied the inverse tangent is defined as 

    i=sqrt(-1)
    atan(z)=>(i/2)*log(i+z/i-z).
This definition of the atan function returns angles in radians within the interval [-PI/2, PI/2]. To find the four-quadrant inverse tangent, where the returned angles are in the interval [-PI, PI], use atan2.

OPTIONS

o X : The value to compute the arctangent of. if Y is present, X shall be real.
o Y : is of the same type and kind as X. If X is zero, Y must not be zero.

RESULT

The returned value is of the same type and kind as X. If Y is present, the result is identical to ATAN2(Y,X). Otherwise, it is the arc tangent of X, where the real part of the result is in radians and lies in the range -PI/2 <= ATAN(X) <= PI/2

EXAMPLES

Sample program: 

    program demo_atan
    use, intrinsic :: iso_fortran_env, only : real32, real64, real128
    implicit none
    character(len=*),parameter :: all=’(*(g0,1x))’
    real(kind=real64),parameter :: &
     Deg_Per_Rad = 57.2957795130823208767981548_real64
    real(kind=real64) :: x
        x=2.866_real64
        print all, atan(x)


        print all, atan( 2.0d0, 2.0d0),atan( 2.0d0, 2.0d0)*Deg_Per_Rad
        print all, atan( 2.0d0,-2.0d0),atan( 2.0d0,-2.0d0)*Deg_Per_Rad
        print all, atan(-2.0d0, 2.0d0),atan(-2.0d0, 2.0d0)*Deg_Per_Rad
        print all, atan(-2.0d0,-2.0d0),atan(-2.0d0,-2.0d0)*Deg_Per_Rad


    end program demo_atan
Results: 

     > 1.235085437457879
     > .7853981633974483 45.00000000000000
     > 2.356194490192345 135.0000000000000
     > -.7853981633974483 -45.00000000000000
     > -2.356194490192345 -135.0000000000000

STANDARD

FORTRAN 77 for a complex argument; and for two arguments Fortran 2008

SEE ALSO

ATAN2(3), TAN(3)

RESOURCES

o wikipedia: inverse trigonometric functions
Fortran intrinsic descriptions (license: MIT) @urbanjost

Nemo Release 3.1 atan (3) June 29, 2025
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