How to loop through matrix elements in mex c++ function for MATLAB?

Question

I am trying to index write an external c++ function for MATLAB using mex to manipulate matrices, and am not able to use multidimensional indexing. There are examples provided here, but I have not found how to fix the problem I describe below. I have a sample matrix:

>> mat
mat =
 1    10
 2    20
 3    30
 4    40
 5    50

Currently I use a linear index through the matrix which works:

#include <mex.h>
#include <iostream>
using namespace std;
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) 
{ 
 //1.get pointer to input graph_list and allocate it    
    double *graph_list = mxGetPr(prhs[0]);
    mwSize mrows = mxGetM(prhs[0]);
    mwSize ncols = mxGetN(prhs[0]);  
    cout<< mrows<<" rows\n";
    cout<< ncols<<" cols\n";
    int mm, nn;
    for (nn=0;nn<ncols;nn++) {
        for (mm=0;mm<mrows;mm++){
            cout << graph_list[nn*(mrows) +mm]  <<"\n";            
        }
    }     
}

This produces:

>> mexTryAlex(mat)    
5 rows
2 cols
1
2
3
4
5
10
20
30
40
50

When I change the definition of graph_list and try 2D indexing to graph_list there is a compilation error with mex:

double **graph_list = mxGetPr(prhs[0]);
cout << graph_list[nn][mm];

EDIT: here is the error message received

>> mex mexTryAlex.cpp
Warning: You are using gcc version "4.4.3-4ubuntu5)".  The version
     currently supported with MEX is "4.3.4".
     For a list of currently supported compilers see: 
     http://www.mathworks.com/support/compilers/current_release/
mexTryAlex.cpp: In function ‘void mexFunction(int, mxArray**, int, const mxArray**)’:
mexTryAlex.cpp:16: error: cannot convert ‘double*’ to ‘double**’ in initialization
mex: compile of ' "mexTryAlex.cpp"' failed.
??? Error using ==> mex at 208
Unable to complete successfully.

Answer 1

The compiler says it all.

In C, a 2D array is like an array of arrays. Therefore, a 2D array is fundamentally different from a 1D array; it's an array of pointers, in which each element contains a pointer to an array (hence a double-pointer, double**).

You're asking mxGetPr() to return a double**, but it returns a double*, e.g., a pointer to the first element of a 1D array. This 1D array can only be indexed linearly.

My guess is that MATLAB does this it this way to keep indexing arrays consistent -- would you really expect/want a double**** for a 4-D array?

Moreover, mxGetPr() cannot be overloaded by return type (it's C after all).

In order to be able to double-index a 1D array, you could sneak in a little macro:

#define A(i,j) A[(i) + (j)*numrows]

and use it like so

double *A = mxGetPr(...);
int numrows = 4;   /* or get with mxGetM() or so) */

double blah = A(3,2); /* call to MACRO */

Obviously, as with all macros, there's a few things to look out for:

1. there's no bounds checking
2. C is 0-based, and Matlab 1-based, making all indices different
3. All arrays will have to be called 'A'

You could write a function to mitigate these drawbacks:

double getValue(double** array, int row, int* dims);

(or use mxCalcSingleSubscript as pointed out by Shai), but that doesn't really improve expressive power IMHO:

double blah = getValue(array, 3,4, dims);
/* or the ugliness from mxCalcSingleSubscript(); */

You could also write in C++, make a Matrix-type class with an operator(), construct it with the pointer and dimensions from mxGetPr() and mxGetDims() etc., compile in Matlab using g++ or equivalent, but that introduces a whole host of other problems and adds way much more complexity than needed for most cases.

Therefore, to avoid all of this mess, I just always compute the index in-place :)