Adding Sparse Matrix Indexing

Summary:

Looking over the Eigen docs I think we can support the following in the stan language

data {
  int N; // rows
  int M; // cols
  int nz_vals; // number of nonzero values
  int nz_vec_vals; // number of nonzero values in vector
  int nz_rows[nnz_vals]; // row position of nonzero values
  int nz_cols[nnz_vals]; // col position of nonzero values
  int nz_vec_rows[nnz_vals]; // row position of nonzero vector values
  matrix[N, M] A_mat; // basic matrix
  sparse_matrix[nz_rows, nz_cols, N, M] A_sparse; // sparse matrix
  sparse_vector[nz_vec_rows, N] A_sparse_vec; // sparse vector
}

transformed data {
  sparse_matrix[N, M] A_sparse_mod = A_sparse;
  sparse_vector[N] A_sparse_vec_mod = A_sparse_vec;

  // Coeff access anywhere (slow but doable, fine for preallocated nnz areas)
  A_sparse_mod[1, 5] = 10.0;
  // Row / Column assignment:
  //     From sparse vec 
  A_sparse_mod[1, ] = sparse_vector; // stored as column major so efficient
  A_sparse[, 1] = sparse_vector; // bad performance but low effort
  //    From normal mat (possible but why?)
  A_sparse_mod[1:10, 1:10] = A_mat[1:10, 1:10]; 
  A_sparse_mod[1, ] = A_mat[1, ];
  A_sparse_mod[, 1] = A_mat[, 1];
  //  
}

@avehtari which of these would we want? All of them? Am I missing any?

Current Version:

v2.22.0