num::kernel::subspace Namespace Reference

Functions
real	mgs_orthogonalize (const std::vector< Vector > &basis, Vector &v, std::vector< real > &h, idx k)
	Modified Gram-Schmidt against basis[0..k-1].
real	mgs_orthogonalize (const Matrix &basis, idx k, Vector &v)
	Modified Gram-Schmidt against columns 0..k-1 of a row-major matrix.
template<class Op > requires requires(const Op& A, const Vector& x, Vector& y) { A.apply(x, y); }
real	arnoldi_step (const Op &A, std::vector< Vector > &basis, std::vector< real > &h, idx k, Vector &scratch, real breakdown_tol=real(1e-14))
	One Arnoldi step: expand the orthonormal basis by one vector.

Function Documentation

arnoldi_step()

template<class Op >
requires requires(const Op& A, const Vector& x, Vector& y) { A.apply(x, y); }

real num::kernel::subspace::arnoldi_step	(	const Op &	A,
		std::vector< Vector > &	basis,
		std::vector< real > &	h,
		idx	k,
		Vector &	scratch,
		real	breakdown_tol = real(1e-14)
	)

One Arnoldi step: expand the orthonormal basis by one vector.

Definition at line 24 of file subspace.hpp.

References num::beta(), mgs_orthogonalize(), and num::scale().

mgs_orthogonalize() [1/2]

real num::kernel::subspace::mgs_orthogonalize	(	const Matrix &	basis,
		idx	k,
		Vector &	v
	)

Modified Gram-Schmidt against columns 0..k-1 of a row-major matrix.

Definition at line 20 of file subspace.cpp.

References num::norm(), and num::BasicMatrix< T >::rows().

mgs_orthogonalize() [2/2]

real num::kernel::subspace::mgs_orthogonalize	(	const std::vector< Vector > &	basis,
		Vector &	v,
		std::vector< real > &	h,
		idx	k
	)

Modified Gram-Schmidt against basis[0..k-1].

Definition at line 9 of file subspace.cpp.

References num::axpy(), num::dot(), and num::norm().

Referenced by arnoldi_step(), num::expv(), num::gmres(), and num::lanczos().