#### A.2.2 Working with Matrices and Arrays in Mex-Files

The basic mex type of all variables is `mxArray`. Any object, such as a matrix, cell array, or structure, is stored in this basic type. `mxArray` serves essentially the same purpose as the `octave_value` class in oct-files in that it acts as a container for all the more specialized types.

The `mxArray` structure contains at a minimum, the name of the variable it represents, its dimensions, its type, and whether the variable is real or complex. It can also contain a number of additional fields depending on the type of the `mxArray`. There are a number of functions to create `mxArray` structures, including `mxCreateDoubleMatrix`, `mxCreateCellArray`, `mxCreateSparse`, and the generic `mxCreateNumericArray`.

The basic function to access the data in an array is `mxGetPr`. Because the mex interface assumes that real and imaginary parts of a complex array are stored separately, there is an equivalent function `mxGetPi` that gets the imaginary part. Both of these functions are only for use with double precision matrices. The generic functions `mxGetData` and `mxGetImagData` perform the same operation for all matrix types. For example:

    mxArray *m;
    mwSize *dims;
    UINT32_T *pr;

    dims = (mwSize *) mxMalloc (2 * sizeof (mwSize));
    dims[0] = 2; dims[1] = 2;
    m = mxCreateNumericArray (2, dims, mxUINT32_CLASS, mxREAL);
    pr = (UINT32_T *) mxGetData (m);

There are also the functions `mxSetPr`, etc., that perform the inverse, and set the data of an array to use the block of memory pointed to by the argument of `mxSetPr`.

Note the type `mwSize` used above, and also `mwIndex`, are defined as the native precision of the indexing in Octave on the platform on which the mex-file is built. This allows both 32- and 64-bit platforms to support mex-files. `mwSize` is used to define array dimensions and the maximum number or elements, while `mwIndex` is used to define indexing into arrays.

An example that demonstrates how to work with arbitrary real or complex double precision arrays is given by the file `mypow2.c` shown below.

    #include "mex.h"

    void
    mexFunction (int nlhs, mxArray *plhs[],
                 int nrhs, const mxArray *prhs[])
    {
      mwSize n;
      mwIndex i;
      double *vri, *vro;

      if (nrhs != 1 || ! mxIsDouble (prhs[0]))
        mexErrMsgTxt ("ARG1 must be a double matrix");

      n = mxGetNumberOfElements (prhs[0]);
      plhs[0] = mxCreateNumericArray (mxGetNumberOfDimensions (prhs[0]),
                                      mxGetDimensions (prhs[0]),
                                      mxGetClassID (prhs[0]),
                                      mxIsComplex (prhs[0]));
      vri = mxGetPr (prhs[0]);
      vro = mxGetPr (plhs[0]);

      if (mxIsComplex (prhs[0]))
        {
          double *vii, *vio;
          vii = mxGetPi (prhs[0]);
          vio = mxGetPi (plhs[0]);

          for (i = 0; i < n; i++)
            {
              vro[i] = vri[i] * vri[i] - vii[i] * vii[i];
              vio[i] = 2 * vri[i] * vii[i];
            }
        }
      else
        {
          for (i = 0; i < n; i++)
            vro[i] = vri[i] * vri[i];
        }
    }

An example of its use is

    b = randn (4,1) + 1i * randn (4,1);
    all (b.^2 == mypow2 (b))
    ⇒ 1

The example above uses the functions `mxGetDimensions`, `mxGetNumberOfElements`, and `mxGetNumberOfDimensions` to work with the dimensions of multi-dimensional arrays. The functions `mxGetM`, and `mxGetN` are also available to find the number of rows and columns in a 2-D matrix (MxN matrix).