la_lapack::pteqr Interface Reference

PTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor. This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. This means that if the eigenvalues range over many orders of magnitude in size, then the small eigenvalues and corresponding eigenvectors will be computed more accurately than, for example, with the standard QR method. The eigenvectors of a full or band positive definite Hermitian matrix can also be found if CHETRD, CHPTRD, or CHBTRD has been used to reduce this matrix to tridiagonal form. (The reduction to tridiagonal form, however, may preclude the possibility of obtaining high relative accuracy in the small eigenvalues of the original matrix, if these eigenvalues range over many orders of magnitude.) More...

Public Member Functions
pure subroutine	cpteqr (compz, n, d, e, z, ldz, work, info)
	la_cpteqr
pure subroutine	dpteqr (compz, n, d, e, z, ldz, work, info)
	la_dpteqr
	la_qpteqr
pure subroutine	spteqr (compz, n, d, e, z, ldz, work, info)
	la_spteqr
	la_wpteqr
pure subroutine	zpteqr (compz, n, d, e, z, ldz, work, info)
	la_zpteqr

Detailed Description

PTEQR: computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor. This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. This means that if the eigenvalues range over many orders of magnitude in size, then the small eigenvalues and corresponding eigenvectors will be computed more accurately than, for example, with the standard QR method. The eigenvectors of a full or band positive definite Hermitian matrix can also be found if CHETRD, CHPTRD, or CHBTRD has been used to reduce this matrix to tridiagonal form. (The reduction to tridiagonal form, however, may preclude the possibility of obtaining high relative accuracy in the small eigenvalues of the original matrix, if these eigenvalues range over many orders of magnitude.)

Member Function/Subroutine Documentation

cpteqr()

pure subroutine la_lapack::pteqr::cpteqr	(	character, intent(in)	compz,
		integer(ilp), intent(in)	n,
		real(sp), dimension(*), intent(inout)	d,
		real(sp), dimension(*), intent(inout)	e,
		complex(sp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(out)	info
	)

dpteqr()

pure subroutine la_lapack::pteqr::dpteqr	(	character, intent(in)	compz,
		integer(ilp), intent(in)	n,
		real(dp), dimension(*), intent(inout)	d,
		real(dp), dimension(*), intent(inout)	e,
		real(dp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(out)	info
	)

la_cpteqr()

la_lapack::pteqr::la_cpteqr

la_dpteqr()

la_lapack::pteqr::la_dpteqr

la_qpteqr()

la_lapack::pteqr::la_qpteqr

la_spteqr()

la_lapack::pteqr::la_spteqr

la_wpteqr()

la_lapack::pteqr::la_wpteqr

la_zpteqr()

la_lapack::pteqr::la_zpteqr

spteqr()

pure subroutine la_lapack::pteqr::spteqr	(	character, intent(in)	compz,
		integer(ilp), intent(in)	n,
		real(sp), dimension(*), intent(inout)	d,
		real(sp), dimension(*), intent(inout)	e,
		real(sp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(out)	info
	)

zpteqr()

pure subroutine la_lapack::pteqr::zpteqr	(	character, intent(in)	compz,
		integer(ilp), intent(in)	n,
		real(dp), dimension(*), intent(inout)	d,
		real(dp), dimension(*), intent(inout)	e,
		complex(dp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(out)	info
	)

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The documentation for this interface was generated from the following file:

• la_lapack.f90