C++ - MATLAB : updating a Sparse Matrix blockwise

Question

Matlab code here

 N = 4096;
 x       =   linspace(-1,1,N);     
 A = sparse(100000,100000); 
 index = 1:32;

 A(index,index)    =   kernel(x(index),x(index));
  //kernel here outputs a 32 x 32 matrix 

I have to convert the MATLAB code to C++,but I am stuck at sparse function, I tried using:

 N=4096;
 Eigen::VectorXd x = Eigen::VectorXd::LinSpaced(N,-1,1); 
 Eigen::SparseMatrix<double> A(Asize,Asize);
 A.block(1,1,index.size(), index.size()) = Kernel();

But SparseMatrix has block as read only function and therefore can't be useful for updating the matrix.

Another Point:

I have gone through the Eigen documentation and checked a different form of SparseMatrix declaration :

 typedef Eigen::Triplet<double> T;
 std::vector<T>tripleList;
 tripleList.reserve(nnz);

 for(...)
 {
  // ...
  tripletList.push_back(T(i,j,v_ij));   //?? what are these values?
  }
 A.setFromTriplets(tripleList.begin(), tripleList.end());

But I don't understand what should be value of nnz, should it be the value that I get from Matlab code and what value should I push through the for loop? Will they be random, how do I select the "pushed values" given that matrix size is so large.

Also, the last question remains, how will the sparse matrix after declaration gets updated block-wise?

Answer 1

In general, Eigen sparse matrix blocks are const. The exception to this rule is eg m.col(i) in a column major matrix or .row(i) in a row major one.

As for your second point, nnz is the number of non-zeros. By specifying how many non-zeros the matrix needs to hold at the beginning, you minimize the number of reallocations/copies needed when constructing the sparse matrix. See the documentation . Also, note that other overload is useful if you know how many elements are needed in each column. Regarding the for loop, assume you had three arrays: columnIndices , rowIndices and values , all of length nnz . Your for loop would look like:

for(int i = 0; i < nnz; i++)
{
    tripletList.push_back(T(columnIndices[i], rowIndices[i], values[i]));
}

Alternatively, you could compute the values for each triplet within the for loop.