How to vectorize the find function?

This is my code:

for i=1:size(Z,3)
    indmax(i)=find(abs(Z(1,:,i))>z90(1,1,i),1);
    indmin(i)=find(abs(Z(1,:,i))>z10(1,1,i),1);
end
trise(:,1)=(t(indmax)-t(indmin));

The variable Z is normally 3 or 6 rows, many columns and 5-10 pages. Something like:

size(Z)= 6 1920 8

The variables z10 and z90 have the same number of rows and pages as Z and 1 column. Something like:

size(z10)=size(z90)=6 1 8

I would actually need to repeat this code 6 more times (1 for each row).

Is there a way to vectorize this?

Answer 1

[Sean de Wolski]

%small sample because you only looped over first row
Z = rand(1,5,8)*2.5;
z90 = rand(1,1,8);
z10 = rand(1,1,8);

%Your way
for i=1:size(Z,3)
  indmax(i)=find(abs(Z(1,:,i))>z90(1,1,i),1);
  indmin(i)=find(abs(Z(1,:,i))>z10(1,1,i),1);
end

%Vectozed way:
[jk, indmx] = max(bsxfun(@gt,abs(Z),z90),[],2);
[jk, indmn] = max(bsxfun(@gt,abs(Z),z10),[],2);
indmx = squeeze(indmx);
indmn = squeeze(indmin);

isequal(indmin,indmn) 
isequal(indmax,indmx.') %transpose rowvec

This method is extended to the full size, though just looping over the six rows is probably just as easy/fast. I.e. loop 1:6, extract trise on each iteration.

[Matt Fig]

And the (you knew this was coming, right?) obligatory timings...

function [] = timeitagain

Z = rand(6,1920,8)*2.5;

z90 = rand(6,1,8);

z10 = rand(6,1,8);

% Proper for loop...

tic

for jj = size(Z,1):-1:1

for ii=size(Z,3):-1:1

R = abs(Z(jj,:,ii));

indmax(jj,ii)=find(R>z90(jj,1,ii),1);

indmin(jj,ii)=find(R>z10(jj,1,ii),1);

end

end

toc

%Vectozed way:

tic

[jk, indmx] = max(bsxfun(@gt,abs(Z),z90),[],2);

[jk, indmn] = max(bsxfun(@gt,abs(Z),z10),[],2);

indmx = squeeze(indmx);

indmn = squeeze(indmin);

toc

isequal(indmin,indmn)

isequal(indmax,indmx) %transpose rowvec

Now running from the command line:

Elapsed time is 0.001451 seconds.

Elapsed time is 0.012311 seconds.

[Sean de Wolski]

At first your results made me sad. But vectorizing consistently wins by more 30% on my system! (I squeezed the ABS out of both of your and my bsx).

function [t1 t2] = timeitagain

Z = rand(6,1920,8)*2.5;

z90 = rand(6,1,8);

z10 = rand(6,1,8);

% Proper for loop...

tic

Z2 = abs(Z);

for jj = size(Z,1):-1:1

for ii=size(Z,3):-1:1

R = Z2(jj,:,ii);

indmax(jj,ii)=find(R>z90(jj,1,ii),1);

indmin(jj,ii)=find(R>z10(jj,1,ii),1);

end

end

t1 = toc;

%Vectozed way:

tic

Z3 = abs(Z);

[~, indmx] = max(bsxfun(@gt,Z3,z90),[],2);

[~, indmn] = max(bsxfun(@gt,Z3,z10),[],2);

indmx = squeeze(indmx);

indmn = squeeze(indmn);

t2 = toc;

if ~isequal(indmin,indmn) || ~isequal(indmax,indmx)

error('Sean you failed vectorizing!');

end

Called with:

t1 = 0;

t2 = 0;

for ii = 1:10

[t1c t2c] = timeitagain;

t1 = t1+t1c;

t2 = t2+t2c;

end

t1/t2

%{

ans =

1.3154

ans =

1.3181

ans =

1.3993

ans =

1.3189

%}

[Sean de Wolski]

Ps. How's your new laptop?

[Matt Fig]

Figures, it must be improvements in newer versions. I am still using 2007b.

My new laptop was delayed a day. "Out for delivery" today though!!

(P.S. Lenovo w520 fully loaded...)

[Sean de Wolski]

^^^^Jealous.

[Bernard Küsel]

Thanks for the help!

Answer 2

[Doug Hull]

Why vectorize?

Just add another for loop for the rows.

[Bernard Küsel]

The problem is that this section is inside a bigger loop that repeats 13770 times. This part added to the loop for the rows is adding about 10min to the whole simulation, which takes about 40min (without this section). I was wondering if I could make it faster.

[Matt Fig]

You will find that pre-allocating your arrays will speed your code up tremendously if your data is that large.

[Doug Hull]

Your question is then about speeding up the code, not about vectorizing?

[Bernard Küsel]

Yeah, sorry about that.. It's just that vectorizing usually speeds up the code.