How to find vector elements between two values, efficiently

I need to find all elements that fall between 2 values (L,U) in a matrix (A) with 2.8 million rows. I'm currently doing this:

[ind,~] = find(A(:,1) >= L & A(:,1) < U);

Variables U and L are updated 41 times inside a loop. This single line of code is slowing down the program by 20 minutes! Any ideas how can I speed this up?

[Angus]

The fastest way I can think of is the following:

data = randn(3000000,3);

inds = not(abs(sign(sign(L - data) + sign(U - data))));

this will give you a matrix of 1s and 0s indicating the indices where the values are between your two bounds (L, U); note not [L, U].

This should be lightening fast, for 3 columns and 3 million rows it computes in a fraction of a second.

[chirag]

just type this

op=A(A>l & A<U);

[Pratik Anandpara]

how to find its position from matrix,index of that element which we call...@chirag

Answer 1

[Matt Fig]

Do you need the actual indices or the values? If you only need the values, then it would probably be faster to do:

A(A(:,1) >= L & A(:,1) < U)

[Gonzalo]

I actually need the indices...

[Matt Fig]

Then you may be stuck unless there are other efficiencies you can make. One alternative that I can think of to get the indices would be to use a dummy variable. I am not sure if this would be faster or not. Make IDX before hand, if you are looping....

IDX = uint32(1:size(A,1));

ind = IDX(A(:,1) >= L & A(:,1) < U);

[Gonzalo]

This method reduces the time by 13,7%, which is good. Thanks.

Answer 2

[James Tursa]

You can try a mex approach. The following file does the exact calculation shown above. If you need to modify it for different columns etc let me know. To mex it, simply put the file someplace on your path, make that directory your current directory, then type

mex findrange.c

The mex program does the calculations fast at the expense of memory. It always allocates enough to hold the indexes of the entire column and then just sets the return size to the amount that it found without reallocating & copying. But from the looks of things this may be a relatively minor temporary memory waste.

/* File: findrange.c                                                */
/* IND = findrange(A,L,U) returns the same result as the following: */
/* IND = find(A(:,1)>=L & A(:,1)<U)                                 */
/* Programmer: James Tursa                                          */
#include "mex.h"
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
    mwSize i, k, m;
    double L, U;
    double *pr, *ind;

      if( nlhs > 1 ) {
          mexErrMsgTxt("Too many outputs.");
      }
      if( nrhs != 3 ) {
          mexErrMsgTxt("Need exactly 3 inputs.");
      }
      if( !mxIsDouble(prhs[0]) || mxIsSparse(prhs[0]) || mxGetNumberOfDimensions(prhs[0]) > 2 ) {
          mexErrMsgTxt("First argument must be full double 2D matrix.");
      }
      if( !mxIsNumeric(prhs[1]) || mxGetNumberOfElements(prhs[1]) != 1 ) {
          mexErrMsgTxt("2nd argument must be a scalar.");
      }
      if( !mxIsNumeric(prhs[2]) || mxGetNumberOfElements(prhs[2]) != 1 ) {
          mexErrMsgTxt("3rd argument must be a scalar.");
      }
      L = mxGetScalar(prhs[1]);
      U = mxGetScalar(prhs[2]);
      pr = mxGetPr(prhs[0]);
      m = mxGetM(prhs[0]);
      plhs[0] = mxCreateDoubleMatrix(m,1,mxREAL);
      ind = mxGetPr(plhs[0]);
      for( i=0; i<m; i++ ) {
          if( *pr >= L && *pr < U ) {
              *ind++ = i+1;
          }
          pr++;
      }
      mxSetM(plhs[0],ind-mxGetPr(plhs[0]));
  }

[Jan]

Instead of the DOUBLE output, an UINT32 vector would use the half memory:

uint32_T *ind, i, m;

plhs[0] = mxCreateNumericMatrix(m,1,mxUINT32_CLASS, mxREAL);

ind = (uint32_T *) mxGetData(plhs[0]);

With "for (i = 1; i <= m; i++), ... *ind++=i;" you can save some milliseconds.

[James Tursa]

DOUBLE vs UINT32 memory savings:

True. Whether this is an actual savings overall depends on what is done with the result downstream (which OP doesn't show). If operations are done with it that turn it into a double then the memory savings will turn into a memory waste instead.

Changing the loop index to start from 1 instead of 0:

Yeah, I saw that right after I posted it (I habitually start my loops from 0 in C), but then I thought ... "Why don't I just let Jan find it ..."

Answer 3

[chirag]

just type this

op=A(A>l & A<U);

[Pratik Anandpara]

how to find its location from vector (index )

Answer 4

[Walter Roberson]

How "dense" are the values? It might be faster to use

[ind1, ~] = find(A(:,1)>=L);
ind = ind1(A(ind1,:)<U);

Or reversing the order of the test, putting the test less likely to succeed first.

This could be cost-effective if relatively few matches are found, reducing the number of ind1 subscripts that need to be looked up in the second step.

[Gonzalo]

It's very dense... I'll give this a try..

[Gonzalo]

This approach doesn't reduce the time.. but thanks anyway

Answer 5

[Angus]

The fastest way I can think of is the following:

data = randn(3000000,3);
inds = not(abs(sign(sign(L - data) + sign(U - data))));

this will give you a matrix of 1s and 0s indicating the indices where the values are between your two bounds (L, U); note not [L, U].

This should be lightening fast, for 3 columns and 3 million rows it computes in a fraction of a second.

[Matt Fig]

But surely this is not faster than:

idx = (A >= L & A < U);

You are calling SIGN 3 times, MINUS twice, PLUS once, ABS once - all on double data, then a logical negation. All that is involved above expression is two logical comparisons and a logical AND.

[Angus]

Matt. You're right it shouldn't be and isn't. It appeared and I believe I misread that this solution only lowered the execution time by 13.7% on a 20 minute execution time for merely the find statement. The example I gave above with 3 million rows and on 3 columns runs in sub 1 sec. Your answer definitely makes more sense.

[Erin Langenstein]

Hi, question: if I were to use inds = not(abs(sign(sign(L - Data) + sign(U - Data)))) and wanted to loop L and U through this with L = 0:1:170 and U = 1:1:171 but I want to get out a Different matrix for every U and L how would I do that? I tried two for loops but it just took forever and only used U = 170 and L= 171 thus only one matrix in the end. Thanks so much, Erin.

Answer 6

[Martin Muehlegger]

I have a datetime array pretty long like 121000 rows

A_time =            
'07-Mar-2019 07:07:42'
'07-Mar-2019 07:07:52'
'07-Mar-2019 07:08:02'
'07-Mar-2019 07:08:12'
'07-Mar-2019 07:08:22',...

and a smaller datetime matrix A_bg_date

A_bg_date = 
'07-Mar-2019 17:16:48'	'07-Mar-2019 17:18:20'
'08-Mar-2019 01:36:47'	'08-Mar-2019 01:38:30'
'08-Mar-2019 05:46:47'	'08-Mar-2019 05:48:24'
'08-Mar-2019 09:56:48'	'08-Mar-2019 09:58:25'
'08-Mar-2019 14:06:48'	'08-Mar-2019 14:08:25'

I would like to find the indices of A_time between A_bg_date(j,1) and A_bg_date(j, 2). (filter out certain timestemps)

I tried something like this:

A_time = datetime(A_MUP_res.stick_Data.stick_time,'ConvertFrom','datenum'); % timestemp
bg_times = zeros(1, length(A_time)); % create empty array to store
%  j = 1;
j = 1:length(A_bg_date);
for i = 1:length(A_time)
     %      j = 1:length(A_bg_date);
     bg_times = isbetween(A_time(i), A_bg_date(j,1), A_bg_date(j,4));
     bg_times = bg_times(i);
     %        j = j+1;
     %        bg_times(i) = isbetween(A_time(i), A_bg_date(2,1), A_bg_date(2,4));
end

I have either a index problem or i just get the indices of A_bg_date(1,1) to A_bg_date(1, 2) and it doesn't iterate through my A_bg_date matrix?

Answer 7

[Martin Muehlegger]

Found a solution....

made a index array for my main set (BG) and looped through the indices of my main set (i) and the indices of my subset (BG_A) (j) with a nested loop setting BG(i,1) = j puts the indices (length of subset) in the first row of your main matrix so that you can apply any kind of function to those timestemps

idx = 1:length(A_MUP_res.stick_Data.stick_duty_cps); % create indexrow filled later
% idx2 = zeros(length(A_MUP_res.stick_Data.stick_duty_cps),1);
idx = idx';
BG = horzcat(idx, A_MUP_res.stick_Data.stick_duty_cps); 
% j = 1:length(BG_A);
for i = 1:length(A_MUP_res.stick_Data.stick_duty_cps)
   for j = 1:length(BG_A)
       if BG(i,1) >= BG_A(j,1) && BG(i,1) <= BG_A(j,2) 
        BG(i,1) = j;
       end
   end
end
BG;
clear BG idx i j % clean workspace (OPTIONAL)