Talk:Ziggurat algorithm

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Diagram needed

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Basically, something like Fig. 1 on p.2 of Marsaglia's paper, or Fig. 5 from the Thomas et al. paper (linked from article References). An improvement would be to add labels "y₀", "y₁", etc. along the y-axis and "x₀", "x₁", etc. above the points.

Without that picture, the best wording is awfully hard to follow.

For a normal distribution, the function to plot is y = y^-x²/2, and the 8-layer Ziggurat points on it are

x[0] = 2.3383716982472527044692   y[0] = 0.0649595117330380202104
x[1] = 1.9819049364005106693290   y[1] = 0.1402998180884519367696
x[2] = 1.7165081257767795707347   y[2] = 0.2291908828832851165061
x[3] = 1.4853586756432938545359   y[3] = 0.3318257830466926345376
x[4] = 1.2629701985308330330774   y[4] = 0.4504325835506035839847
x[5] = 1.0273863717802284625238   y[5] = 0.5899241094185249870813
x[6] = 0.7383689179764494421219   y[6] = 0.7614016031422429793942
x[7] = 0.0000000000000000000000   y[7] = 1.0000000000000000003253

Here's a sample gnuplot input file:

#set terminal svg
#set output "zig.svg"
unset label
set label "x-1" at 2.7120530222393384079012,0.0649595117330380202104 cent offset 0,0.5
set label "x0" at 2.3383716982472527044692,0.1402998180884519367696 cent offset 0,0.5
set label "x1" at 1.9819049364005106693290,0.2291908828832851165061 cent offset 0,0.5
set label "x2" at 1.7165081257767795707347,0.3318257830466926345376 cent offset 0,0.5
set label "x3" at 1.4853586756432938545359,0.4504325835506035839847 cent offset 0,0.5
set label "x4" at 1.2629701985308330330774,0.5899241094185249870813 cent offset 0,0.5
set label "x5" at 1.0273863717802284625238,0.7614016031422429793942 cent offset 0,0.5 
set label "x6" at 0.7383689179764494421219,1.0000000000000000000000 cent offset 0,0.5

set label "y0" at 0,0.0649595117330380202104 right offset -0.5,0
set label "y1" at 0,0.1402998180884519367696 right offset -0.5,0
set label "y2" at 0,0.2291908828832851165061 right offset -0.5,0.2
set label "y3" at 0,0.3318257830466926345376 right offset -0.5,0
set label "y4" at 0,0.4504325835506035839847 right offset -0.5,0
set label "y5" at 0,0.5899241094185249870813 right offset -0.5,-0.7
set label "y6" at 0,0.7614016031422429793942 right offset -0.5,0
set label "y7" at 0,1.0000000000000000000000 right offset -2.5,0

set xrange [0:3.5]
set yrange [0:1.05]
plot exp(-x**2/2) title "exp(-x^2/2)" with lines linewidth 2, "zig.dat" ti "" with lines

And the corresponding input file zig.dat:

0.0000000000000000000000        1.0000000000000000000000
0.7383689179764494421219        1.0000000000000000000000
0.7383689179764494421219        0.5899241094185249870813

0.0000000000000000000000        0.7614016031422429793942
1.0273863717802284625238        0.7614016031422429793942
1.0273863717802284625238        0.4504325835506035839847

0.0000000000000000000000        0.5899241094185249870813
1.2629701985308330330774        0.5899241094185249870813
1.2629701985308330330774        0.3318257830466926345376

0.0000000000000000000000        0.4504325835506035839847
1.4853586756432938545359        0.4504325835506035839847
1.4853586756432938545359        0.2291908828832851165061

0.0000000000000000000000        0.3318257830466926345376
1.7165081257767795707347        0.3318257830466926345376
1.7165081257767795707347        0.1402998180884519367696

0.0000000000000000000000        0.2291908828832851165061
1.9819049364005106693290        0.2291908828832851165061
1.9819049364005106693290        0.0649595117330380202104

0.0000000000000000000000        0.1402998180884519367696
2.3383716982472527044692        0.1402998180884519367696
2.3383716982472527044692        0.0000000000000000000000

0.0000000000000000000000        0.0649595117330380202104
2.7120530222393384079012        0.0649595117330380202104
2.7120530222393384079012        0.0000000000000000000000

71.41.210.146 16:33, 19 June 2007 (UTC)[reply]