43 lines
1.7 KiB
Plaintext
43 lines
1.7 KiB
Plaintext
# Taylor Series
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def a
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[ 1.00000_00000_00000_00000, 0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
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-0.04200_26350_34095_23553, 0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
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-0.00962_19715_27876_97356, 0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
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-0.00021_52416_74114_95097, 0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
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-0.00000_12504_93482_14267, 0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
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0.00000_00061_16095_10448, 0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
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0.00000_00001_04342_67117, 0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
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0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
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0.00000_00000_00001_22678, -0.00000_00000_00000_11813, 0.00000_00000_00000_00119,
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0.00000_00000_00000_00141, -0.00000_00000_00000_00023, 0.00000_00000_00000_00002 ]
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end
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def taylor_gamma(x)
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y = x.to_f - 1
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1.0 / a.reverse.reduce(0) { |sum, an| sum * y + an }
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end
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# Lanczos Method
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def p
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[ 0.99999_99999_99809_93, 676.52036_81218_851, -1259.13921_67224_028,
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771.32342_87776_5313, -176.61502_91621_4059, 12.50734_32786_86905,
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-0.13857_10952_65720_12, 9.98436_95780_19571_6e-6, 1.50563_27351_49311_6e-7 ]
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end
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def lanczos_gamma(z)
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# Reflection formula
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z = z.to_f
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if z < 0.5
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Math::PI / (Math.sin(Math::PI * z) * lanczos_gamma(1 - z))
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else
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z -= 1
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x = p[0]
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(1..p.size - 1).each { |i| x += p[i] / (z + i) }
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t = z + p.size - 1.5
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Math.sqrt(2 * Math::PI) * t**(z + 0.5) * Math.exp(-t) * x
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end
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end
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puts " Taylor Series Lanczos Method Builtin Function"
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(1..27).each { |i| n = i/3.0; puts "gamma(%.2f) = %.14e %.14e %.14e" % [n, taylor_gamma(n), lanczos_gamma(n), Math.gamma(n)] }
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