Eigen: How to initialize a sparse matrix with some sub sparse matrix

Question

in eigen, we can initialize a matrix or vector with some other matrix or vector like this:

MatrixXf matA(2, 2);
matA << 1, 2, 3, 4;
MatrixXf matB(4, 4);
matB << matA, matA/10, matA/10, matA;
std::cout << matB << std::endl;

what i want to achieve:

SparseMatrix<double> matA(2, 2);
matA.coeffRef(0, 0) = 1;
matA.coeffRef(1, 1) = 1;
SparseMatrix<double> matB(4, 4);
matB << matA, matA/10, matA/10, matA;
std::cout << matB << std::endl;

then i get a matrix like this:

1   0   0.1 0
0   1   0   0.1
0.1 0   1   0
0   0.1 0   0.1

but, it doesn't work for sparse matrix, so does eigen have built-in initializer like this? or i need to write it myself, if so? how?

Answer 1

You cannot have such an initializer because of the storage format. From the manual Sparse matrix manipulations > Block operations:

However, for performance reasons, writing to a sub-sparse-matrix is much more limited, and currently only contiguous sets of columns (resp. rows) of a column-major (resp. row-major) SparseMatrix are writable. Moreover, this information has to be known at compile-time, leaving out methods such as block(...) and corner*(...).

The only option you have is to convert everything to dense matrices, use the comma initializer and convert back to sparse.

#include <iostream>
#include <Eigen/Sparse>

using namespace Eigen;
typedef SparseMatrix<double> SparseMatrixXd;

int main()
{
  SparseMatrixXd matA(2, 2);
  matA.coeffRef(0, 0) = 1;
  matA.coeffRef(1, 1) = 1;
  SparseMatrixXd matB(4, 4);
  MatrixXd matC(4,4);
  matC <<
    MatrixXd(matA),
    MatrixXd(matA)/10,
    MatrixXd(matA)/10,
    MatrixXd(matA);
  matB = matC.sparseView();
  std::cout << matB << std::endl;
}

Alternatively you can use the unsupported Kronecker product module for this exact example.

#include <iostream>
#include <Eigen/Sparse>
#include <unsupported/Eigen/KroneckerProduct>

using namespace Eigen;
typedef SparseMatrix<double> SparseMatrixXd;

int main()
{
  SparseMatrixXd matA(2, 2);
  matA.coeffRef(0, 0) = 1;
  matA.coeffRef(1, 1) = 1;
  SparseMatrixXd matB(4, 4);
  matB =
    kroneckerProduct( (MatrixXd(2,2) << 1,0,0,1).finished(), matA ) +
    kroneckerProduct( (MatrixXd(2,2) << 0,1,1,0).finished(), matA/10);
  std::cout << matB << std::endl;
}