template<typename _MatrixType>
class Eigen::IterScaling< _MatrixType >

iterative scaling algorithm to equilibrate rows and column norms in matrices

This class can be used as a preprocessing tool to accelerate the convergence of iterative methods

This feature is useful to limit the pivoting amount during LU/ILU factorization The scaling strategy as presented here preserves the symmetry of the problem NOTE It is assumed that the matrix does not have empty row or column,

Example with key steps

VectorXd x(n), b(n);
SparseMatrix<double> A;
// fill A and b;
IterScaling<SparseMatrix<double> > scal; 
// Compute the left and right scaling vectors. The matrix is equilibrated at output
scal.computeRef(A); 
// Scale the right hand side
b = scal.LeftScaling().cwiseProduct(b); 
// Now, solve the equilibrated linear system with any available solver
 
// Scale back the computed solution
x = scal.RightScaling().cwiseProduct(x); 

Template Parameters

_MatrixType

the type of the matrix. It should be a real square sparsematrix

References : D. Ruiz and B. Ucar, A Symmetry Preserving Algorithm for Matrix Scaling, INRIA Research report RR-7552

See also

IncompleteLUT