Note: Currently can only save PETSc vectors to .mat files, not matrices (use the PETSCVIEWERBINARY and ${PETSC_DIR}/share/petsc/matlab/PetscBinaryRead.m to read matrices into MATLAB).
For parallel vectors obtained with DMCreateGlobalVector() or DMGetGlobalVector() the vectors are saved to the .mat file in natural ordering. You can use DMView() to save the DMDA information to the .mat file the fields in the MATLAB loaded da variable give the array dimensions so you can reshape the MATLAB vector to the same multidimensional shape as it had in PETSc for plotting etc. For example,
In your PETSc C/C++ code (assuming a two dimensional DMDA with one degree of freedom per node)
PetscObjectSetName((PetscObject)x,"x");
VecView(x,PETSC_VIEWER_MATLAB_WORLD);
PetscObjectSetName((PetscObject)da,"da");
DMView(x,PETSC_VIEWER_MATLAB_WORLD);
Then from MATLAB
load('matlaboutput.mat') % matlaboutput.mat is the default filename
xnew = zeros(da.n,da.m);
xnew(:) = x; % reshape one dimensional vector back to two dimensions
If you wish to put the same variable into the .mat file several times you need to give it a new name before each call to view.
Use PetscViewerMatlabPutArray() to just put an array of doubles into the .mat file