pass data between C++ Eigen Matrix and MATLAB mxArray with a cell array

I would like to pass data between Eigen Matrix/Vector and mex arrays. In the following code, I defined a mex array called y_output, which contains a cell array. The variable y_output will be passed to MATLAB. Each element in y_output is a vector but with different lengths. I would like to pass a pointer that points to Eigen vectors to the mex array y_output.

Notice that the data stored in y will be modified with a user-defined function. After calling the function, I would assume that the data stored in y_output will be modified corresponding. However, I cannot directly pass the pointer from y_output to y. Is there any way to make it possible? Thanks!

This question is similar but different from the one at Pass C++ Eigen matrix to Matlab mex output. This question is asking how to pass an array of matrices, while the question in that link is asking how to pass a matrix.

#include "mex.h"
#include "matrix.h"
#include <Eigen>


void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{


// prhs[0]: a cell array of length T, each element is a vector with different lengths
mwSize T =  mxGetNumberOfElements(prhs[0]);
mwSize* n = new mwSize[T];
Eigen::VectorXd* z = new Eigen::VectorXd[T];

for(int t=0; t<T; t++){
    n[t] = mxGetNumberOfElements(mxGetCell(prhs[0], t));
    z[t] = Eigen::Map<Eigen::VectorXd>(mxGetPr(mxGetCell(prhs[0], t)), n[t]);
}

// create a cell matrix with T rows and one columns
mxArray* y_output = mxCreateCellMatrix(T,1);

// create corresponding Eigen objects
Eigen::VectorXd* y = new Eigen::VectorXd[T]();

Eigen::VectorXd y_temp(n[0]); y_temp.setZero();

for(int t=0; t<T; t++){
    mxSetCell(y_output, t, mxCreateDoubleMatrix(n[t], 1, mxREAL));

    y[t] = Eigen::VectorXd::Zero(n[t]);
    y_temp.resize(n[t]);

    Eigen::Map<Eigen::VectorXd> y[t](mxGetPr(mxGetCell(y_output, t)), n[t]); // This is not correct!



}


// Myfun(y, z);

// set output
plhs[0] = y_output;

}

Solution

Your solution copies data around both for the input and the output of MyFunc. It is possible to pass both arguments using a std::vector of Eigen::Map objects. The following code is based on your answer. Lines starting with //-- were removed from your code and replaced by the line which follow.

As a sidenote: Avoid allocating arrays with new (in 99.99% of all cases), but use a std::vector instead. This takes care of deallocating all resources when the object gets out of scope. Also, in MyFunc you don't have to guess the size of y and z.

#include "mex.h"
#include "matrix.h"
//-- #include <Eigen> <-- this should be <Eigen/Eigen>, but likely Eigen/Core suffices
//                        Perhaps you also need to change your include-path 
#include <Eigen/Core>

#include <vector>

void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{

    // prhs[0]: a cell array of length T, each element is a vector with different lengths
    mwSize T =  mxGetNumberOfElements(prhs[0]);
    //-- mwSize* n = new mwSize[T];
    std::vector<mwSize> n(T);
    //-- Eigen::VectorXd* z = new Eigen::VectorXd[T];
    std::vector<Eigen::Map<const Eigen::VectorXd> > z; // input vector of Maps
    z.reserve(T);

    for(int t=0; t<T; t++){
        // Note: You don't actually seem to need n[t], except for creating y_output
        n[t] = mxGetNumberOfElements(mxGetCell(prhs[0], t));
        //-- z[t] = Eigen::Map<Eigen::VectorXd>(mxGetPr(mxGetCell(prhs[0], t)), n[t]);
        z.emplace_back(mxGetPr(mxGetCell(prhs[0], t)), n[t]);
    }

    // create a cell matrix with T rows and one columns
    mxArray* y_output = mxCreateCellMatrix(T,1);

    // create corresponding Eigen objects
    //-- Eigen::VectorXd* y = new Eigen::VectorXd[T]();
    std::vector<Eigen::Map<Eigen::VectorXd> > y; // output vector of Maps
    y.reserve(T);

    // This must be called after setting up y: 
    //-- Myfun(y, z);

    //-- double* ptemp;
    for(int t=0; t<T; t++){
        mxSetCell(y_output, t, mxCreateDoubleMatrix(n[t], 1, mxREAL));

        //-- ptemp = mxGetPr(mxGetCell(y_output, t));
        //-- // assign the data stored in y[t] to the contents in y_output.
        //-- for(int i=0; i<n[t]; i++){
        //--     //mxGetPr(mxGetCell(y_output, t))[i] = y[t](i);
        //--     ptemp[i] = y[t](i);
        //-- }
        y.emplace_back(mxGetPr(mxGetCell(y_output, t)), n[t]);
    }

    // Now call Myfun, but the function now needs to accept vectors of Eigen::Map, instead of pointers to VectorXd
    // It should be possible to keep the Code inside Myfun unchanged
    // Myfun(y, z);

    //-- ptemp = NULL;

    // set output
    plhs[0] = y_output;

}