Permutations Cycles Counting ... speed up
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Hi, this is my code for permutation cycles counting. Any idea how to vectorize it to get some additional speedup for large set of permutations?
function count = PermCyclesCount(p)
[nR,nE] = size(p);
count = zeros(nR,1);
for j = 1:nR
i = 0;
count(j) = 0;
while i < nE
i = i + 1;
if p(j,i) > 0
flag = false; % flag is just to trick the computer into entering the while loop
first = i;
while (first ~= i) || ~flag
flag = true;
r = first;
first = p(j,first);
p(j,r) = 0; % The entries in the cycle are changed to zero to indicate that they have been `used'
end
count(j) = count(j) + 1;
end
end
end
end
Some testing data:
[~,perms] = sort(rand(1000000,60),2);
tic;c= PermCyclesCount(perms);toc
Elapsed time is 1.559758 seconds.
Accepted Answer
% VERSION 1
[nR, nE] = size(p);
count = zeros(nR, 1);
for j = 1:nR
q = p(j, :); % <== Cut out a vector to operate on
i = 0;
while i < nE
i = i + 1;
if q(i) > 0
flag = false;
first = i;
while (first ~= i) || ~flag
flag = true;
r = first;
first = q(first);
q(r) = 0;
end
count(j) = count(j) + 1;
end
end
end
This tiny change let the code run in 1.41 instead of 2.37 sec on my computer.
And this in 1.25 sec without the flag:
% VERSION 2
[nR, nE] = size(p);
count = zeros(nR, 1);
for j = 1:nR
q = p(j, :);
for i = 1:nE
if q(i) > 0
f = q(i);
q(i) = 0;
while f ~= i
r = f;
f = q(f);
q(r) = 0;
end
count(j) = count(j) + 1;
end
end
end
3 Comments
Michal
on 20 Oct 2017
This code is 20% faster, if the data a provided in columnwise order:
[~,perms] = sort(rand(60, 1000000), 1);
% VERSION 2.1
[nE, nE] = size(p); % <== Swapped
count = zeros(nR, 1);
for j = 1:nR
q = p(:, j); % <== Copy column
for i = 1:nE
if q(i) > 0
f = q(i);
q(i) = 0;
while f ~= i
r = f;
f = q(f);
q(r) = 0;
end
count(j) = count(j) + 1;
end
end
end
The C code is even 33% faster - see in the other answer.
Does the creation of perms matter also? Then:
[~,perms] = sort(rand(60, 1000000),1); % 4.88 sec
perms = Shuffle(repmat((1:60).', 1, 1000000), 1); % 2.95 sec
Michal
on 23 Oct 2017
More Answers (3)
A C-Mex has about the double speed of the VERSION 2:
// VERSION 3
#include "mex.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
size_t nR, nE, j, i;
double *c, *p, *pr;
int *q, f, r;
// Get input:
nR = mxGetM(prhs[0]);
nE = mxGetN(prhs[0]);
p = mxGetPr(prhs[0]);
// Create output:
plhs[0] = mxCreateDoubleMatrix((mwSize) nR, 1, mxREAL);
c = mxGetPr(plhs[0]);
q = (int *) mxMalloc((nE + 1) * sizeof(int));
for (j = 0; j < nR; j++) {
// Copy row p(j, :) to q:
pr = p++;
for (i = 1; i <= nE; i++) {
q[i] = (int) (*pr); // One based indexing for q
pr += nR;
}
for (i = 1; i <= nE; i++) {
if (q[i] != 0) {
f = q[i];
q[i] = 0;
while (f != i) {
r = f;
f = q[f];
q[r] = 0;
}
*c += 1.0;
}
}
c++;
}
mxFree(q);
return;
}
This is 33% faster, if you provide the input in columnwise order instead:
[~,perms] = sort(rand(60, 1000000),1);
// VERSION 3.1
#include "mex.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
// !!! FOR [nE x nR] !!!
size_t nR, nE, j, i;
double *c, *p, *pr;
int *q, f, r, ic;
// Get input:
nE = mxGetM(prhs[0]);
nR = mxGetN(prhs[0]);
p = mxGetPr(prhs[0]);
// Create output:
plhs[0] = mxCreateDoubleMatrix((mwSize) nR, 1, mxREAL);
c = mxGetPr(plhs[0]);
q = (int *) mxMalloc((nE + 1) * sizeof(int));
for (j = 0; j < nR; j++) {
// Copy row p(j, :) to q:
pr = p;
for (i = 1; i <= nE; i++) {
q[i] = (int) (*pr++); // One based indexing for q
}
ic = 0;
for (i = 1; i <= nE; i++) {
if (q[i] != 0) {
f = q[i];
q[i] = 0;
while (f != i) {
r = f;
f = q[f];
q[r] = 0;
}
ic++;
}
}
*c++ = (double) ic;
pr += nE;
}
mxFree(q);
return;
}
Jos (10584)
on 20 Oct 2017
Not vectorised, but less checking, not sure if it is faster
nR = size(p,1) ;
count2 = zeros(nR,1) ;
tf = ~isnan(p) ;
for j = 1:nR
r1 = find(tf(j,:), 1 ,'first') ; % find the first cycle
while ~isempty(r1) % is there a cycle
count2(j) = count2(j) + 1 ;
while tf(j,r1)
tf(j,r1) = false ;
r2 = p(j,r1) ;
r1 = r2 ;
end
r1 = find(tf(j,:),1,'first') ; % find the next cycle
end
end
9 Comments
Michal
on 20 Oct 2017
Jos (10584)
on 20 Oct 2017
haha! Good for you that you checked :)
Did you profile your code to see where the bottlenecks are?
Michal
on 20 Oct 2017
Jos (10584)
on 20 Oct 2017
and your own code?
@Michal Kvasnicka: if you expect that running the profiler somehow magically will use no system resources and that all code will run at exactly the same speed when it is boing profiled then you will always be disappointed. Nowhere in the profiler documentation
does it state that everything will run at exactly the same speed, but it does state that "Profiling is a way to measure where a program spends time." Running extra code (i.e. the profiler itself) requires system resources, and therefore this can affect the timing.
Michal
on 20 Oct 2017
Jan
on 20 Oct 2017
The profiler disables the JIT acceleration, which could re-order the code lines to improve speed. This cannot be allowed, if the time per line should be measured.
But the JIT accelerator is essential for the run time of such loops. Therefore the profiler has a limited use here. You can determine the commands which take the most time, but not the code blocks.
Michal
on 20 Oct 2017
Jos (10584)
on 20 Oct 2017
Edited: Jos (10584)
on 20 Oct 2017
This is upto 10 times faster than your code (and indeed about 100 times faster than my previous code):
[nR, nE] = size(p) ;
count3 = zeros(nR,1) ;
tf = true(nR,nE) ;
for Ri = 1:nR
for Ei = 1:nE,
if tf(Ri,Ei)
count3(Ri) = count3(Ri) + 1 ;
while tf(Ri,Ei)
tf(Ri,Ei) = false ;
r = p(Ri,Ei) ;
Ei = r ;
end
end
end
end
2 Comments
Michal
on 20 Oct 2017
An improved version of Jos' code:
[nR, nE] = size(p) ;
count = zeros(nR,1) ;
tf = true(nE, nR) ; % Transposed to operate on column
for Ri = 1:nR
q = p(Ri, :); % Vector cut out
for Ei = 1:nE
k = Ei;
if tf(k, Ri)
count(Ri) = count(Ri) + 1 ;
while tf(k, Ri)
tf(k, Ri) = false ;
r = q(k) ;
k = r ;
end
end
end
end
To my surprise using a vector tf = true(nE, 1) is not faster.
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