using inverse trigonometric functions of complex argument in fortran?

[280286]

Hello, guys. im writing my current program in fortran 90 and i've come across this problem: how to calculate arccos(z) if z is a complex number, z=x+i*y.is it possible in fortran to calculate it at all. And if it isnt then are there any alternatives?
thank you, i woould be very thankful for your help.

 

[mikrom]

I don't know about library available for calculating it,
but IMHO to calculate Arccos(z) for complex z, |z| <= 1 we can use something like this:
complex_function.f95

[COLOR=#a020f0]program[/color] complex_function
  [COLOR=#2e8b57][b]implicit[/b][/color] [COLOR=#2e8b57][b]none[/b][/color]

[COLOR=#2e8b57][b]  real[/b][/color], [COLOR=#2e8b57][b]parameter[/b][/color] :: pi [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]acos[/color]([COLOR=#804040][b]-[/b][/color][COLOR=#ff00ff]1.0[/color])
[COLOR=#2e8b57][b]  real[/b][/color] :: re_Z, im_Z
  [COLOR=#2e8b57][b]complex[/b][/color] :: Z, ZRSLT, cacos
  [COLOR=#2e8b57][b]complex[/b][/color], [COLOR=#2e8b57][b]parameter[/b][/color] :: J [COLOR=#804040][b]=[/b][/color] ([COLOR=#ff00ff]0.0[/color], [COLOR=#ff00ff]1.0[/color])

  [COLOR=#0000ff]! complex arccos(z)[/color]
  cacos (Z) [COLOR=#804040][b]=[/b][/color] [COLOR=#804040][b]-[/b][/color]J [COLOR=#804040][b]*[/b][/color] [COLOR=#008080]clog[/color](Z [COLOR=#804040][b]+[/b][/color] J[COLOR=#804040][b]*[/b][/color][COLOR=#008080]csqrt[/color]([COLOR=#ff00ff]1[/color] [COLOR=#804040][b]-[/b][/color] Z[COLOR=#804040][b]*[/b][/color]Z))

  [COLOR=#0000ff]! real argument[/color]
  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#804040][b]-[/b][/color][COLOR=#ff00ff]1[/color],[COLOR=#ff00ff]0[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#804040][b]-[/b][/color][COLOR=#ff00ff]0.5[/color],[COLOR=#ff00ff]0[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#ff00ff]0[/color],[COLOR=#ff00ff]0[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#ff00ff]0.5[/color],[COLOR=#ff00ff]0[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#ff00ff]1[/color],[COLOR=#ff00ff]0[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  [COLOR=#0000ff]! complex argument[/color]
  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#ff00ff]0[/color],[COLOR=#804040][b]-[/b][/color][COLOR=#ff00ff]1[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  re_Z [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]cos[/color](pi[COLOR=#804040][b]/[/b][/color][COLOR=#ff00ff]4.0[/color])
  im_Z [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]sin[/color](pi[COLOR=#804040][b]/[/b][/color][COLOR=#ff00ff]4.0[/color])
  Z [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]cmplx[/color](re_Z, im_Z)
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  re_Z [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]cos[/color](pi[COLOR=#804040][b]/[/b][/color][COLOR=#ff00ff]6.0[/color])
  im_Z [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]sin[/color](pi[COLOR=#804040][b]/[/b][/color][COLOR=#ff00ff]6.0[/color])
  Z [COLOR=#804040][b]=[/b][/color] [COLOR=#008080]cmplx[/color](re_Z, im_Z)
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  Z [COLOR=#804040][b]=[/b][/color] ([COLOR=#ff00ff]0[/color],[COLOR=#ff00ff]1[/color])
  ZRSLT [COLOR=#804040][b]=[/b][/color] cacos(Z)
  [COLOR=#804040][b]write[/b][/color]([COLOR=#804040][b]*[/b][/color],[COLOR=#ff00ff]100[/color]), Z, ZRSLT

  [COLOR=#6a5acd]100[/color] [COLOR=#804040][b]format[/b][/color] ([COLOR=#ff00ff]'Arccos('[/color],[COLOR=#008080]f6.3[/color],[COLOR=#ff00ff]' + J*'[/color],[COLOR=#008080]f6.3[/color],[COLOR=#ff00ff]') = '[/color],[COLOR=#008080]f10.8[/color],[COLOR=#ff00ff]' + J*'[/color],[COLOR=#008080]f10.8[/color])
[COLOR=#a020f0]end program[/color] complex_function

$ gfortran complex_function.f95 -o complex_function

$ complex_function
Arccos(-1.000 + J* 0.000) = 3.14159274 + J*-.00000000
Arccos(-0.500 + J* 0.000) = 2.09439516 + J*-.00000000
Arccos( 0.000 + J* 0.000) = 1.57079637 + J*-.00000000
Arccos( 0.500 + J* 0.000) = 1.04719758 + J*-.00000000
Arccos( 1.000 + J* 0.000) = 0.00000000 + J*-.00000000
Arccos( 0.000 + J*-1.000) = 1.57079637 + J*0.88137364
Arccos( 0.707 + J* 0.707) = 0.99893749 + J*-.76428539
Arccos( 0.866 + J* 0.500) = 0.78539819 + J*-.65847898
Arccos( 0.000 + J* 1.000) = 1.57079637 + J*-.88137364