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.

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)