This document presents code for quickly finding the index of the last value in a sorted array that is less than a given value x. It uses a binary search approach implemented recursively in MATLAB and as a MEX function for faster performance. Benchmarking shows the MEX version is much faster than the MATLAB implementation when performing many lookups on a large array.

1. ts=linspace(0,20,500000);
tic;
for i=1:1000
f=min(find(ts>10));
end;
toc
function [data,x,lower,upper]= find_halfspace_rec(data,x,lower,upper);
mp=floor((lower+upper)/2);
if mp~=lower
if data(mp)<x
[data,x,lower,upper]= find_halfspace_rec(data,x,mp,upper);
else
[data,x,lower,upper]= find_halfspace_rec(data,x,lower,mp);
end;
end;
function l = find_halfspace(data,x);
% returns the number of the last sample in the ASCENDING array data that is
% &lt; x using a simple half space search
upper = numel(data); lower = 1;
[data,x,l,u] = find_halfspace_rec(data,x,lower,upper);
ts=linspace(0,20,500000);
tic;
Fast lookup in sorted array | Jakob Voigts http://jvoigts.scripts.mit.edu/blog/fast-sorted-array-lookup/
第 1 頁，共 3 頁 2015/3/9 下午 06:18

2. for i=1:1000
f=find_halfspace(ts,10);
end;
toc
#include "mex.h"
/*
* find_halfspace_mex.c
* same as find_halfspace.m
*/
int binary_search(double a[], int low, int high, double target[]) {
int result=-1;
while (low = a[middle])
low = middle + 1;
else
return middle;
result=middle;
}
return result+1;
}
void find_halfspace_mex(double y[], double x[],double f[],int low, int high)
{
y[0]=binary_search(x, low, high, f);
}
void mexFunction( int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[] )
{
double *x,*y, *f;
size_t mrows,ncols,maxsize;
/* Check for proper number of arguments. */
if(nrhs!=2) {
mexErrMsgIdAndTxt( "MATLAB:find_halfspace_mex:invalidNumInputs", "two inputs required."
} else if(nlhs&gt;1) {
mexErrMsgIdAndTxt( "MATLAB:timestwo:maxlhs", "Too many output arguments.");
}
/* The input must be a noncomplex scalar double.*/
mrows = mxGetM(prhs[0]);
ncols = mxGetN(prhs[0]);
if (mrows&gt;ncols)
maxsize = mrows;
else
maxsize = ncols;
/* Create matrix for the return argument. */
plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL);
/* Assign pointers to each input and output. */
x = mxGetPr(prhs[0]);
f = mxGetPr(prhs[1]);
y = mxGetPr(plhs[0]);
if ((mrows==0)||(ncols==0))
y[0]=-1;
else
find_halfspace_mex(y,x,f,0,maxsize);
Fast lookup in sorted array | Jakob Voigts http://jvoigts.scripts.mit.edu/blog/fast-sorted-array-lookup/
第 2 頁，共 3 頁 2015/3/9 下午 06:18

3. }
ts=linspace(0,20,500000);
tic;
for i=1:1000
f=find_halfspace_mex(ts,10);
end;
toc
Fast lookup in sorted array | Jakob Voigts http://jvoigts.scripts.mit.edu/blog/fast-sorted-array-lookup/
第 3 頁，共 3 頁 2015/3/9 下午 06:18