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Diffstat (limited to 'noao/onedspec/splot/voigt.x')
-rw-r--r-- | noao/onedspec/splot/voigt.x | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/noao/onedspec/splot/voigt.x b/noao/onedspec/splot/voigt.x new file mode 100644 index 00000000..08a44c78 --- /dev/null +++ b/noao/onedspec/splot/voigt.x @@ -0,0 +1,71 @@ +# VOIGT -- Compute the real (Voigt function) and imaginary parts of the +# complex function w(z)=exp(-z**2)*erfc(-i*z) in the upper half-plane +# z=x+iy. The maximum relative error of the real part is 2E-6 and the +# imaginary part is 5E-6. +# +# From: Humlicek, J. Quant. Spectrosc. Radiat. Transfer, V21, p309, 1979. + +procedure voigt (xarg, yarg, wr, wi) + +real xarg #I Real part of argument +real yarg #I Imaginary part of argument +real wr #O Real part of function +real wi #O Imaginary part of function + +int i +real x, y, y1, y2, y3, d, d1, d2, d3, d4, r, r2 +real t[6], c[6], s[6] + +data t/.314240376,.947788391,1.59768264,2.27950708,3.02063703,3.8897249/ +data c/1.01172805,-.75197147,1.2557727e-2,1.00220082e-2,-2.42068135e-4, + 5.00848061e-7/ +data s/1.393237,.231152406,-.155351466,6.21836624e-3,9.19082986e-5, + -6.27525958e-7/ + +begin + x = xarg + y = abs (yarg) + wr = 0. + wi = 0. + y1 = y + 1.5 + y2 = y1 * y1 + + # Region II + if (y < 0.85 && abs(x) > 18.1*y+1.65) { + if (abs(x) < 12) + wr = exp (-x * x) + y3 = y + 3 + do i = 1, 6 { + r = x - t[i] + r2 = r * r + d = 1 / (r2 + y2) + d1 = y1 * d + d2 = r * d + wr = wr + y * (c[i] * (r * d2 - 1.5 * d1) + s[i] * y3 * d2) / + (r2 + 2.25) + r = x + t[i] + r2 = r * r + d = 1 / (r2 + y2) + d3 = y1 * d + d4 = r * d + wr = wr + y * (c[i] * (r * d4 - 1.5 * d3) - s[i] * y3 * d4) / + (r2 + 2.25) + wi = wi + c[i] * (d2 + d4) + s[i] * (d1 - d3) + } + + # Region I + } else { + do i = 1, 6 { + r = x - t[i] + d = 1 / (r * r + y2) + d1 = y1 * d + d2 = r * d + r = x + t[i] + d = 1 / (r * r + y2) + d3 = y1 * d + d4 = r * d + wr = wr + c[i] * (d1 + d3) - s[i] * (d2 - d4) + wi = wi + c[i] * (d2 + d4) + s[i] * (d1 - d3) + } + } +end |