MATLAB Application Program Interface Reference

The MATLAB language works with only a single object type -- the MATLAB array. All MATLAB variables, including scalars, vectors, matrices, strings, cell arrays, and structures are stored as MATLAB arrays. The mxArray declaration corresponds to the internal data structure that MATLAB uses to represent arrays. The MATLAB array is the C language definition of a MATLAB variable. This mxArray structure contains, among other things:

The MATLAB variable's name
Its dimensions
Its type
Whether the variable is real or complex. If the variable contains complex numbers as elements, the MATLAB array includes vectors containing the real and imaginary parts
Whether the variable is a sparse matrix

Matrices, or m-by-n arrays, that are not sparse are called full. In the case of a full matrix, the mxArray structure contains parameters called pr and pi. pr contains the real part of the matrix data; pi contains the imaginary data, if there is any. Both pr and pi are one-dimensional arrays of double-precision numbers. The elements of the matrix are stored in these arrays columnwise. This is how Fortran stores matrices; MATLAB uses this convention because it was originally written in Fortran.

Sparse matrices have a different storage convention in MATLAB. The parameters pr and pi are still arrays of double-precision numbers, but there are now three new parameters, nzmax, ir, and jc:

nzmax is an integer that contains the length of ir, pr, and if it exists, pi. It is the maximum number possible number of nonzero elements in the sparse matrix.
ir points to an integer array of length nzmax containing the row indices of the corresponding elements in pr and pi.
jc points to an integer array of length N+1 that contains column index information. For j in the range 0jN-1, jc[j] is the index in ir, pr (and pi if it exists) of the first nonzero entry in the jth column and jc[j+1]-1 index of the last nonzero entry. As a result, jc[N] is also equal to nnz, the number of nonzero entries in the matrix. If nnz is less than nzmax, then more nonzero entries can be inserted in the array without allocating additional storage.

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