Algorithm conversion to Matlab Code

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Mar One
Mar One 2022-5-21
回答： Todd 2025-9-14
Hello, i have this ziggurat algorithm that i wish to convert to a matlab code if someone would know the correct matlab code for it

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回答（4 个）

Steven Lord
Steven Lord 2022-5-21
See this post on Cleve Moler's blog.
  2 个评论
Mar One
Mar One 2022-5-21
i need the matlab code for the algorithm if posible
Walter Roberson
Walter Roberson 2022-5-22
Calling randn() is the matlab code that implements the algorithm.

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Walter Roberson
Walter Roberson 2022-5-22
Soufi
Soufi 2024-11-9
how can i traduct algorithme to matlab
Todd
Todd 2025-9-14
Based on wikipedia, this is most likely from
@article{JSSv005i08,
title={The Ziggurat Method for Generating Random Variables},
volume={5},
url={https://www.jstatsoft.org/index.php/jss/article/view/v005i08},
doi={10.18637/jss.v005.i08},
abstract={We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers k<sub>i</sub>, and reals w<sub>i</sub>. Some 99% of the time, the required x is produced by: Generate a random 32-bit integer j and let i be the index formed from the rightmost 8 bits of j. If j < k, return x = j x w<sub>i</sub>. We illustrate with C code that provides for inline generation of both normal and exponential variables, with a short procedure for settting up the necessary tables.},
number={8},
journal={Journal of Statistical Software},
author={Marsaglia, George and Tsang, Wai Wan},
year={2000},
pages={1–7}
}
The algorithm's source code is then
\usepackage{algorithm}
\usepackage{algpseudocode}
\begin{algorithm}
\caption{Original Ziggurat Algorithm (optimizations omitted for clarity)}
\RequireItem{$N$}{$\triangleright$ Number of regions}
\RequireItem{$x[0..N],\,y[0..N]$}{$\triangleright$ Coordinates of regions}
\RequireItem{$\mathrm{PDF}(\cdot)$}{$\triangleright$ Probability density function}
\RequireItem{$\mathrm{RandReal}()$}{$\triangleright$ A uniform real in $[0,1]$}
\RequireItem{$\mathrm{RandInteger}(N)$}{$\triangleright$ A uniform integer in $[0,N]$}
\begin{algorithmic}[1]
\Function{Ziggurat}{}
\Loop
\State $j \gets \mathrm{RandInteger}(N)$
\State $x \gets x[j] \times \mathrm{RandReal}()$
\If{$x < x[j+1]$}
\State \Return $x$
\ElsIf{$j \neq 0\;$ and $\;\mathrm{RandReal}() \times (y[j+1] - y[j]) < \mathrm{PDF}(x) - y[j]$}
\State \Return $x$
\ElsIf{$j = 0$}
\State \Return \Call{Tail}{$x[1]$}
\EndIf
\EndLoop
\EndFunction
\end{algorithmic}
\end{algorithm}
with Matlab code:
function z = zigguratSample(N, x, y, pdf_func)
% ZIGGURATSAMPLE Sample one variate using the Ziggurat algorithm
% Inputs:
% N : number of regions (integer)
% x(0:N) : right-edge coordinate of regions
% y(0:N) : heights of regions
% pdf_func : function handle, pdf_func(x) returns f(x)
%
% Output:
% z : a variate drawn from the target density
while true
j = randi([0, N]); % uniform integer in 0..N
u = rand(); % uniform real in [0,1)
xj = x(j+1); % MATLAB indices are 1-based; x(1) = x[0], etc
xjp1 = x(j+2); % x[j+1]
yj = y(j+1);
yjp1 = y(j+2);
x_star = xj * rand(); % propose horizontal coordinate
if x_star < xjp1
z = x_star;
return;
elseif j ~= 0 && rand() * (yjp1 - yj) < (pdf_func(x_star) - yj)
z = x_star;
return;
elseif j == 0
z = tailSample(x(2), pdf_func); % tail case, using x[1] in 0-based
return;
end
% else continue loop
end
end
function f = pdf_normal(x)
% Example: standard normal pdf
f = exp(-0.5 * x.^2) / sqrt(2*pi);
end
function z = tailSample(x1, pdf_func)
% Tail sampler; for normal, use exponentials etc.
while true
u = rand();
v = rand();
x = -log(u) / x1;
y = -log(v);
if 2*y >= x^2
z = x + x1;
return;
end
end
end

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