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

The basic mex type of all variables is `mxArray`. All variables, such as matrices, cell arrays or structures are all stored in this basic type, and this type serves basically the same purpose as the octave_value class in oct-files. That is it acts as a container for the more specialized types.

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

The basic functions to access the data contained in an array is `mxGetPr`. As the mex interface assumes that the real and imaginary parts of a complex array are stored separately, there is an equivalent function `mxGetPi` that get the imaginary part. Both of these functions are for use only with double precision matrices. There also exists the generic function `mxGetData` and `mxGetImagData` that perform the same operation on 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 `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 dimension and maximum number or elements, while `mwIndex` is used to define indexing into arrays.

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

         /*

         Copyright (C) 2006, 2007 John W. Eaton

         This file is part of Octave.

         Octave is free software; you can redistribute it and/or
         modify it under the terms of the GNU General Public License
         as published by the Free Software Foundation; either
         version 3  of the License, or (at your option) any later
         version.

         Octave is distributed in the hope that it will be useful,
         but WITHOUT ANY WARRANTY; without even the implied warranty
         of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
         See the GNU General Public License for more details.

         You should have received a copy of the GNU General Public
         License along with Octave; see the file COPYING.  If not,
         see <http://www.gnu.org/licenses/>.

         */

         #include "mex.h"

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

           if (nrhs != 1 || ! mxIsNumeric (prhs[0]))
             mexErrMsgTxt ("expects matrix");

           n = mxGetNumberOfElements (prhs[0]);
           plhs[0] = (mxArray *) 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];
             }
         }

with an example of its use

         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 matrix.