How to print an Eigen tensor into a text file? - c++

Question

I am trying to print out a 3D matrix into a text file that can be read by a MATLAB code. The example I have here prints the tensor in a text file but when I try to open it in MATLAB it reads something like 256 x 16 instead of 16x16x16.
Example:
static const int nx = 16;
static const int ny = 16;
static const int nz = 16;double Lx = 128;
double Ly = 128;
double LZ = 128;
double dx = Lx / nx;
double dy = Ly / ny;
double dz = Lz / nz;
double a = (2 * EIGEN_PI)/Lx;
double b = (2 * EIGEN_PI)/ Ly;
Eigen::Tensor<double, 3> X(nx,ny,nz);
eXX.setZero();
Eigen::Tensor<double, 3> Y(nx,ny,nz);
eYY.setZero();
Eigen::Tensor<double, 3> Z(nx,ny,nz);
eZZ.setZero();
for(int i = 0; i< nx; i++){
for(int j = 0; j< ny; j++){
for(int k = 0; k< nz; k++){
X(k,i,j) = i*dx;
Y(j,i,k) = j*dy;
Z(j,i,k) = k*dz;
}
}
}
Eigen::Tensor<double, 3> Out(nx,ny,nz);
Out.setZero();
for(int i = 0; i< nx; i++){
for(int j = 0; j< ny; j++){
for(int k = 0; k< nz; k++){
Out(k,i,j) = sin(3. * a * Z(k,i,j)) * sin(a * X(k,i,j)) * cos(b * Y(k,i,j));
}
}
}
std::ofstream file("test.txt");
if (file.is_open())
{
file << Out << '\n';
}
I know I will probably have to write my own output routine instead os using the operator << since it treats a rank-3 tensor as a 2-d matrix for the purpose of output.