(octave.info)Sparse Matrices with Mex-Files

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A.2.6 Sparse Matrices with Mex-Files
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The Octave format for sparse matrices is identical to the mex format in
that it is a compressed column sparse format.  Also, in both
implementations sparse matrices are required to be two-dimensional.  The
only difference of importance to the programmer is that the real and
imaginary parts of the matrix are stored separately.

   The mex-file interface, in addition to using ‘mxGetM’, ‘mxGetN’,
‘mxSetM’, ‘mxSetN’, ‘mxGetPr’, ‘mxGetPi’, ‘mxSetPr’, and ‘mxSetPi’, also
supplies the following functions.

     mwIndex *mxGetIr (const mxArray *ptr);
     mwIndex *mxGetJc (const mxArray *ptr);
     mwSize mxGetNzmax (const mxArray *ptr);

     void mxSetIr (mxArray *ptr, mwIndex *ir);
     void mxSetJc (mxArray *ptr, mwIndex *jc);
     void mxSetNzmax (mxArray *ptr, mwSize nzmax);

‘mxGetNzmax’ gets the maximum number of elements that can be stored in
the sparse matrix.  This is not necessarily the number of nonzero
elements in the sparse matrix.  ‘mxGetJc’ returns an array with one
additional value than the number of columns in the sparse matrix.  The
difference between consecutive values of the array returned by ‘mxGetJc’
define the number of nonzero elements in each column of the sparse
matrix.  Therefore,

     mwSize nz, n;
     mwIndex *Jc;
     mxArray *m;
     ...
     n = mxGetN (m);
     Jc = mxGetJc (m);
     nz = Jc[n];

returns the actual number of nonzero elements stored in the matrix in
‘nz’.  As the arrays returned by ‘mxGetPr’ and ‘mxGetPi’ only contain
the nonzero values of the matrix, we also need a pointer to the rows of
the nonzero elements, and this is given by ‘mxGetIr’.  A complete
example of the use of sparse matrices in mex-files is given by the file
‘mysparse.c’ shown below.

     #include "mex.h"
     
     void
     mexFunction (int nlhs, mxArray *plhs[],
                  int nrhs, const mxArray *prhs[])
     {
       mwSize m, n, nz;
       mxArray *v;
       mwIndex i;
       double *pr, *pi;
       double *pr2, *pi2;
       mwIndex *ir, *jc;
       mwIndex *ir2, *jc2;
     
       if (nrhs != 1 || ! mxIsSparse (prhs[0]))
         mexErrMsgTxt ("ARG1 must be a sparse matrix");
     
       m = mxGetM (prhs[0]);
       n = mxGetN (prhs[0]);
       nz = mxGetNzmax (prhs[0]);
     
       if (mxIsComplex (prhs[0]))
         {
           mexPrintf ("Matrix is %d-by-%d complex sparse matrix", m, n);
           mexPrintf (" with %d elements\n", nz);
     
           pr = mxGetPr (prhs[0]);
           pi = mxGetPi (prhs[0]);
           ir = mxGetIr (prhs[0]);
           jc = mxGetJc (prhs[0]);
     
           i = n;
           while (jc[i] == jc[i-1] && i != 0) i--;
     
           mexPrintf ("last nonzero element (%d, %d) = (%g, %g)\n",
                      ir[nz-1]+ 1, i, pr[nz-1], pi[nz-1]);
     
           v = mxCreateSparse (m, n, nz, mxCOMPLEX);
           pr2 = mxGetPr (v);
           pi2 = mxGetPi (v);
           ir2 = mxGetIr (v);
           jc2 = mxGetJc (v);
     
           for (i = 0; i < nz; i++)
             {
               pr2[i] = 2 * pr[i];
               pi2[i] = 2 * pi[i];
               ir2[i] = ir[i];
             }
           for (i = 0; i < n + 1; i++)
             jc2[i] = jc[i];
     
           if (nlhs > 0)
             plhs[0] = v;
         }
       else if (mxIsLogical (prhs[0]))
         {
           mxLogical *pbr, *pbr2;
           mexPrintf ("Matrix is %d-by-%d logical sparse matrix", m, n);
           mexPrintf (" with %d elements\n", nz);
     
           pbr = mxGetLogicals (prhs[0]);
           ir = mxGetIr (prhs[0]);
           jc = mxGetJc (prhs[0]);
     
           i = n;
           while (jc[i] == jc[i-1] && i != 0) i--;
           mexPrintf ("last nonzero element (%d, %d) = %d\n",
                      ir[nz-1]+ 1, i, pbr[nz-1]);
     
           v = mxCreateSparseLogicalMatrix (m, n, nz);
           pbr2 = mxGetLogicals (v);
           ir2 = mxGetIr (v);
           jc2 = mxGetJc (v);
     
           for (i = 0; i < nz; i++)
             {
               pbr2[i] = pbr[i];
               ir2[i] = ir[i];
             }
           for (i = 0; i < n + 1; i++)
             jc2[i] = jc[i];
     
           if (nlhs > 0)
             plhs[0] = v;
         }
       else
         {
           mexPrintf ("Matrix is %d-by-%d real sparse matrix", m, n);
           mexPrintf (" with %d elements\n", nz);
     
           pr = mxGetPr (prhs[0]);
           ir = mxGetIr (prhs[0]);
           jc = mxGetJc (prhs[0]);
     
           i = n;
           while (jc[i] == jc[i-1] && i != 0) i--;
           mexPrintf ("last nonzero element (%d, %d) = %g\n",
                      ir[nz-1]+ 1, i, pr[nz-1]);
     
           v = mxCreateSparse (m, n, nz, mxREAL);
           pr2 = mxGetPr (v);
           ir2 = mxGetIr (v);
           jc2 = mxGetJc (v);
     
           for (i = 0; i < nz; i++)
             {
               pr2[i] = 2 * pr[i];
               ir2[i] = ir[i];
             }
           for (i = 0; i < n + 1; i++)
             jc2[i] = jc[i];
     
           if (nlhs > 0)
             plhs[0] = v;
         }
     }

   A sample usage of ‘mysparse’ is

     sm = sparse ([1, 0; 0, pi]);
     mysparse (sm)
     ⇒
     Matrix is 2-by-2 real sparse matrix with 2 elements
     last nonzero element (2, 2) = 3.14159