Eigen provides the SparseMatrix class for representing sparse matrices, which are matrices that have a significant number of zero elements. Here are a few examples of how you can use the SparseMatrix class in Eigen:
- Creating a sparse matrix:
#include <Eigen/Sparse>
#include <iostream>
using namespace Eigen;
using namespace std;
int main() {
// Create a sparse matrix with 5 rows and 4 columns, and 7 non-zero elements
SparseMatrix<double> A(5, 4);
A.reserve(VectorXi::Constant(4, 2)); // Reserve space for 2 non-zero elements per column
A.insert(0, 0) = 1;
A.insert(1, 0) = 2;
A.insert(2, 1) = 3;
A.insert(3, 1) = 4;
A.insert(4, 2) = 5;
A.insert(2, 3) = 6;
A.insert(4, 3) = 7;
A.makeCompressed(); // Optimize the storage of the non-zero elements
cout << "A = " << endl << A << endl;
// Output: A = (5, 4) matrix with 7 non-zero elements
// 1.000 0.000 0.000 0.000
// 2.000 0.000 0.000 0.000
// 0.000 3.000 0.000 6.000
// 0.000 4.000 0.000 0.000
// 0.000 0.000 5.000 7.000
return 0;
}- Accessing elements of a sparse matrix:
#include <Eigen/Sparse>
#include <iostream>
using namespace Eigen;
using namespace std;
int main() {
SparseMatrix<double> A(5, 4);
// ... set up the matrix A as before ...
// Access element at row i and column j
double element = A.coeff(i, j);
return 0;
}- Matrix operations:
Eigen provides many functions for performing operations on sparse matrices, such as matrix-vector multiplication and matrix-matrix multiplication. Here are some examples:
#include <Eigen/Sparse>
#include <iostream>
using namespace Eigen;
using namespace std;
int main() {
SparseMatrix<double> A(5, 4);
// ... set up the matrix A as before ...
VectorXd x(4);
x.setRandom();
// Matrix-vector multiplication
VectorXd y = A * x;
cout << "y = " << endl << y << endl;
SparseMatrix<double> B(4, 3);
// ... set up the matrix B ...
// Matrix-matrix multiplication
SparseMatrix<double> C = A * B;
cout << "C = " << endl << C << endl;
return 0;
}
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