lib/complex.lib

   1 import ( "math.lib" );
   2 square = _ <: *;
   3
   4 // Complex in cartesian coordinates
   5 carte_cplx = _, _: (_, 1 : vectorize), (_, 1 : vectorize) : #;
   6
   7 // Cartesian complex : basic operations
   8 ccplx_real = _, 0 : [];
   9 ccplx_imag = _, 1 : [];
  10 ccplx_conj = _ <: ccplx_real, ccplx_imag : _, (0, _ : -) : carte_cplx;
  11 ccplx_modul2 = _ <: ccplx_real, ccplx_imag : square, square : +;
  12 ccplx_modul = ccplx_modul2 : sqrt;
  13
  14 //real_not_zero = _ <: (ccplx_imag, ccplx_real : / : atan);
  15 //real_compare = _ <: (ccplx_real, 0 : >), (ccplx_real, 0 : <) : + <: _, (-(1), 0 : <);
  16 //real_zero = _ <: (ccplx_imag, 0 : > : *(PI) : /(2)), (ccplx_imag, 0 : < : _, (0, 1 : -) : * : *(PI) : /(2)) : +;
  17 //ccplx_angle = _ <: (real_not_zero, real_compare, real_zero : *, * : +), (ccplx_real, 0 : < : _, PI : *) : +;
  18 ccplx_angle = _ <: ccplx_imag, ccplx_real : atan2;
  19
  20 ccplx_div_real = _, _ <: ccplx_real, _, ccplx_imag, _ : /, / : carte_cplx;
  21
  22 // cartesian complex : add, sub, mul and div
  23 ccplx_add = +;
  24 ccplx_sub = -;
  25
  26 ccplx_mul = _, _ <: ccplx_real, ccplx_real, ccplx_imag, ccplx_imag,ccplx_real, ccplx_imag, ccplx_imag, ccplx_real : *, *, *, * : -, + : carte_cplx;
  27
  28 ccplx_div = _, _ <: ccplx_real, ccplx_real, ccplx_imag, ccplx_imag, ccplx_imag, ccplx_real, ccplx_real, ccplx_imag, !, ccplx_real, !, ccplx_imag : *, *, *, *, square, square : +, -, + : carte_cplx, _ : ccplx_div_real;
  29 //ccplx_div = _, _ <: _, ccplx_conj, !, _ : ccplx_mul, ccplx_modul2 : ccplx_div_real;
  30
  31 // Complex in polar coordinates
  32 polar_cplx = _, _: (_, 1 : vectorize), (_, 1 : vectorize) : #;
  33 pcplx_modul = _, 0 : [];
  34 pcplx_angle = _, 1 : [];
  35 pcplx_real = _ <: pcplx_modul, (pcplx_angle : cos) : *;
  36 pcplx_imag = _ <: pcplx_modul, (pcplx_angle : sin) : *;
  37
  38 // conversion between cartesian complex and polar complex
  39 sca_abs = _ <: _, (>(0) : *(2) : -(1)) : *;
  40 sca2pcplx = _ <: sca_abs, (<(0) : *(PI)) : polar_cplx;
  41 polar2carte = _ <: pcplx_real, pcplx_imag : carte_cplx;
  42 carte2polar = _ <: ccplx_modul, ccplx_angle : polar_cplx;
  43
  44 // Polar complex : add, sub, mul and div
  45 pcplx_add = _, _ : polar2carte, polar2carte : ccplx_add : carte2polar;
  46 pcplx_sub = _, _ : polar2carte, polar2carte : ccplx_sub : carte2polar;
  47 pcplx_mul = _, _ <: (pcplx_modul, pcplx_modul : *), (pcplx_angle, pcplx_angle : +) : polar_cplx;
  48
  49 pcplx_div = _, _ <: (pcplx_modul, pcplx_modul : /), (pcplx_angle, pcplx_angle : -) : polar_cplx;
  50
  51 //functions used in FFT
  52 real_pcplx_mul = _, ( _ <: pcplx_modul, pcplx_angle) : *, _ : polar_cplx;
  53 pcplx_moduls(n) = par(i, n, pcplx_modul);
  54
  55