ATAN2
This function extends FORTRAN’s generic function ATAN2 to evaluate the complex arc tangent of a ratio.
Function Return Value
ATAN2 — Complex function value in units of radians with the real part between -π and π. (Output)
Required Arguments
CSN — Complex numerator of the ratio for which the arc tangent is desired. (Input)
CCS — Complex denominator of the ratio. (Input)
FORTRAN 90 Interface
Generic: ATAN2 (CSN, CCS)
Specific: The specific interface names are CATAN2 and ZATAN2.
FORTRAN 77 Interface
Complex: CATAN2 (CSN, CCS)
Double complex: The double complex function name is ZATAN2.
Description
Let z1 = CSN and z2 = CCS. The ratio z = z1/z2 must not be ±i because tan‑1 (±i) is undefined. Likewise, z1 and z2 should not both be zero. Finally, z must not be so close to ±i that substantial accuracy loss occurs.
Comments
The result is returned in the correct quadrant (modulo 2 π).
Example
In this example,
is computed and printed.
USE ATAN2_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
COMPLEX VALUE, X, Y
! Compute
X = (2.0, 1.0)
Y = (0.5, 0.5)
VALUE = ATAN2(Y, X)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) Y, X, VALUE
99999 FORMAT (' ATAN2((', F6.3, ',', F6.3, '), (', F6.3, ',', F6.3,&
')) = (', F6.3, ',', F6.3, ')')
END
Output
ATAN2(( 0.500, 0.500), ( 2.000, 1.000)) = ( 0.294, 0.092)
