How to do Weighted Averaging of n conscutive values in an Array

Question

I have a 900×1 vector of values (in MATLAB). Each 9 consecutive values should be averaged -without overlap- result in a 100×1 vector of values. The problem is that the averaging should be weighted based on a weighting vector of [1 2 1;2 4 2;1 2 1]. Is there any efficient way to do that averaging? I’ve heard about conv function in MATLAB; Is it helpful?

Answer 1

conv works by sliding a kernel through your data. But in your case, you need the mask to be jumping through your data, so I don't think conv will work for you.

If you want to use existing MATLAB function, you can do this (I have to assume your weighting matrix has only one dimension) :

kernel = [1;2;1;2;4;2;1;2;1];
in_matrix = reshape(in_matrix, 9, 100);
base = sum(kernel);
out_matrix = bsxfun(@times, in_matrix, kernel);
result = sum(out_matrix,1)/base;

I don't know if there is any clever way to speed this up. bsxfun allows singleton expansion, but maybe not dimension reduction.

A faster way would be to use mex. Open a new file in editor, paste the following code and save file as weighted_average.c.

#include "mex.h"

void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
    double *in_matrix, *kernel, *out_matrix, base;              
    int niter;
    size_t nrows_data, nrows_kernel;                   

    /* Get number of element along first dimension of input matrix. */
    nrows_kernel = mxGetM(prhs[1]);    
    nrows_data = mxGetM(prhs[0]);

    /* Create output matrix*/
    plhs[0] = mxCreateDoubleMatrix((mwSize)nrows_data/nrows_kernel,1,mxREAL);

    /* Get a pointer to the real data */
    in_matrix = mxGetPr(prhs[0]);
    kernel = mxGetPr(prhs[1]);
    out_matrix = mxGetPr(plhs[0]);

    /* Sum the elements in weighting array */
    base = 0;
    for (int i = 0; i < nrows_kernel; i +=1)
    {
        base += kernel[i];
    }

    /* Perform calculation */
    niter = nrows_data/nrows_kernel;
    for (int i = 0; i < niter ; i += 1)
    {   
        for (int j = 0; j < nrows_kernel; j += 1)
        {
            out_matrix[i] += in_matrix[i*nrows_kernel+j]*kernel[j];
        }
        out_matrix[i] /= base;
    }    
}

Then in command window , type in

mex weighted_average.c

To use it:

result = weighted_average(input, kernel);

Note that both input and kernel have to be M x 1 matrix. On my computer, the first method took 0.0012 second. The second method took 0.00007 second. That's an order of magnitude faster than the first method.