Umberto Picchini

trapzf does not allow for unevenly sampled data, even though the comment claims it does. Matlab's trapz does allow for uneven data. To correct this, the following change must be made to the C code of trapzf, here called trapzfu. Note that the speedup on a 64-bit WinXP computer of trapfzu over trapz was about 10-fold. Unrolling the loop in trapzfu2.c provides another 20% improvement in speed.

--- trapzfu.c ------
/* F=trapzfu(X,Y) computes the integral of Y with respect to X using
    the trapezoidal method. X and Y must be vectors of the same length.
    For trapzf to work properly:
    X must be a STRICTLY monotonically increasing vector.
    X does not need to be evenly spaced.
 
    C. Quaia, National Eye Institute, NIH, DHHS
 */

#include "mex.h"

void trapzfu( double *area, double *xv, double *yv, int N) {
        register int i;
        
        *area = 0;
        for (i = 0; i < (N-1); i++) {
                *area = *area + (xv[i+1] - xv[i]) * (yv[i] + yv[i+1]);
        }
        *area = *area / 2;
}

void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
        int N, N1, N2;
        double *area;
        double *xv, *yv ;
        
        N1 = mxGetNumberOfElements(prhs[0]);
        N2 = mxGetNumberOfElements(prhs[1]);
        if (N1 != N2)
                mexErrMsgTxt("Input x and y must have the same length");
        else
                N = N1;
        if (N < 2)
                mexErrMsgTxt("The minimum length is 2");
        
        xv = mxGetPr(prhs[0]);
        yv = mxGetPr(prhs[1]);
        plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL);
        area = mxGetPr(plhs[0]);
        
        trapzfu(area, xv, yv, N);
}

------------ trapzfu2.c --------
/* F=trapzfu2(X,Y) computes the integral of Y with respect to X using
    the trapezoidal method. X and Y must be vectors of the same length.
    For trapzf to work properly:
    X must be a STRICTLY monotonically increasing vector.
    X does not need to be evenly spaced.

    L. Optican, NEI/NIH/DHHS

 */

#include "mex.h"

void trapzfu2( double *area, double *xv, double *yv, int N) {
        register int i, j,r;
        
        *area = 0;
        i = 0;
        r = (N - 1) % 4;
        for(; i < r; i++) {
                // *area += (xv[i+1] - xv[i]) * (yv[i] + yv[i+1]);
                *area += (xv[i+1] - xv[i]) * (yv[i+1] + yv[i]);
        }
        
        for(; i <= (N-4); i += 4) {
                *area += (xv[i+1] - xv[i]) * (yv[i+1] + yv[i]);
                *area += (xv[i+2] - xv[i+1]) * (yv[i+2] + yv[i+1]);
                *area += (xv[i+3] - xv[i+2]) * (yv[i+3] + yv[i+2]);
                *area += (xv[i+4] - xv[i+3]) * (yv[i+4] + yv[i+3]);
        }
        *area = *area / 2;
}

void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
        int N, N1, N2;
        double *area;
        double *xv, *yv ;
        
        N1 = mxGetNumberOfElements(prhs[0]);
        N2 = mxGetNumberOfElements(prhs[1]);
        if (N1 != N2)
                mexErrMsgTxt("Input x and y must have the same length");
        else
                N = N1;
        if (N < 2)
                mexErrMsgTxt("The minimum length is 2");
        
        xv = mxGetPr(prhs[0]);
        yv = mxGetPr(prhs[1]);
        plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL);
        area = mxGetPr(plhs[0]);
        
        trapzfu2(area, xv, yv, N);
}

thanks