la_lapack::laed7 Interface Reference

LAED7: computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and optionally eigenvectors of a dense or banded Hermitian matrix that has been reduced to tridiagonal form. T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) where Z = Q**Hu, u is a vector of length N with ones in the CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in Q, and the eigenvalues are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the Z vector. For each such occurrence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine SLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by SLAED3). This routine also calculates the eigenvectors of the current problem. The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem. More...

Public Member Functions
pure subroutine	claed7 (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info)
	la_claed7
pure subroutine	dlaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info)
	la_dlaed7
	la_qlaed7
pure subroutine	slaed7 (icompq, n, qsiz, tlvls, curlvl, curpbm, d, q, ldq, indxq, rho, cutpnt, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, iwork, info)
	la_slaed7
	la_wlaed7
pure subroutine	zlaed7 (n, cutpnt, qsiz, tlvls, curlvl, curpbm, d, q, ldq, rho, indxq, qstore, qptr, prmptr, perm, givptr, givcol, givnum, work, rwork, iwork, info)
	la_zlaed7

Detailed Description

LAED7: computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and optionally eigenvectors of a dense or banded Hermitian matrix that has been reduced to tridiagonal form. T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out) where Z = Q**Hu, u is a vector of length N with ones in the CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in Q, and the eigenvalues are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the Z vector. For each such occurrence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine SLAED2. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by SLAED3). This routine also calculates the eigenvectors of the current problem. The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem.

Member Function/Subroutine Documentation

claed7()

pure subroutine la_lapack::laed7::claed7	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	cutpnt,
		integer(ilp), intent(in)	qsiz,
		integer(ilp), intent(in)	tlvls,
		integer(ilp), intent(in)	curlvl,
		integer(ilp), intent(in)	curpbm,
		real(sp), dimension(*), intent(inout)	d,
		complex(sp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		real(sp), intent(inout)	rho,
		integer(ilp), dimension(*), intent(out)	indxq,
		real(sp), dimension(*), intent(inout)	qstore,
		integer(ilp), dimension(*), intent(inout)	qptr,
		integer(ilp), dimension(*), intent(inout)	prmptr,
		integer(ilp), dimension(*), intent(inout)	perm,
		integer(ilp), dimension(*), intent(inout)	givptr,
		integer(ilp), dimension(2,*), intent(inout)	givcol,
		real(sp), dimension(2,*), intent(inout)	givnum,
		complex(sp), dimension(*), intent(out)	work,
		real(sp), dimension(*), intent(out)	rwork,
		integer(ilp), dimension(*), intent(out)	iwork,
		integer(ilp), intent(out)	info
	)

dlaed7()

pure subroutine la_lapack::laed7::dlaed7	(	integer(ilp), intent(in)	icompq,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	qsiz,
		integer(ilp), intent(in)	tlvls,
		integer(ilp), intent(in)	curlvl,
		integer(ilp), intent(in)	curpbm,
		real(dp), dimension(*), intent(inout)	d,
		real(dp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		integer(ilp), dimension(*), intent(out)	indxq,
		real(dp), intent(inout)	rho,
		integer(ilp), intent(in)	cutpnt,
		real(dp), dimension(*), intent(inout)	qstore,
		integer(ilp), dimension(*), intent(inout)	qptr,
		integer(ilp), dimension(*), intent(inout)	prmptr,
		integer(ilp), dimension(*), intent(inout)	perm,
		integer(ilp), dimension(*), intent(inout)	givptr,
		integer(ilp), dimension(2,*), intent(inout)	givcol,
		real(dp), dimension(2,*), intent(inout)	givnum,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), dimension(*), intent(out)	iwork,
		integer(ilp), intent(out)	info
	)

la_claed7()

la_lapack::laed7::la_claed7

la_dlaed7()

la_lapack::laed7::la_dlaed7

la_qlaed7()

la_lapack::laed7::la_qlaed7

la_slaed7()

la_lapack::laed7::la_slaed7

la_wlaed7()

la_lapack::laed7::la_wlaed7

la_zlaed7()

la_lapack::laed7::la_zlaed7

slaed7()

pure subroutine la_lapack::laed7::slaed7	(	integer(ilp), intent(in)	icompq,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	qsiz,
		integer(ilp), intent(in)	tlvls,
		integer(ilp), intent(in)	curlvl,
		integer(ilp), intent(in)	curpbm,
		real(sp), dimension(*), intent(inout)	d,
		real(sp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		integer(ilp), dimension(*), intent(out)	indxq,
		real(sp), intent(inout)	rho,
		integer(ilp), intent(in)	cutpnt,
		real(sp), dimension(*), intent(inout)	qstore,
		integer(ilp), dimension(*), intent(inout)	qptr,
		integer(ilp), dimension(*), intent(inout)	prmptr,
		integer(ilp), dimension(*), intent(inout)	perm,
		integer(ilp), dimension(*), intent(inout)	givptr,
		integer(ilp), dimension(2,*), intent(inout)	givcol,
		real(sp), dimension(2,*), intent(inout)	givnum,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), dimension(*), intent(out)	iwork,
		integer(ilp), intent(out)	info
	)

zlaed7()

pure subroutine la_lapack::laed7::zlaed7	(	integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	cutpnt,
		integer(ilp), intent(in)	qsiz,
		integer(ilp), intent(in)	tlvls,
		integer(ilp), intent(in)	curlvl,
		integer(ilp), intent(in)	curpbm,
		real(dp), dimension(*), intent(inout)	d,
		complex(dp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		real(dp), intent(inout)	rho,
		integer(ilp), dimension(*), intent(out)	indxq,
		real(dp), dimension(*), intent(inout)	qstore,
		integer(ilp), dimension(*), intent(inout)	qptr,
		integer(ilp), dimension(*), intent(inout)	prmptr,
		integer(ilp), dimension(*), intent(inout)	perm,
		integer(ilp), dimension(*), intent(inout)	givptr,
		integer(ilp), dimension(2,*), intent(inout)	givcol,
		real(dp), dimension(2,*), intent(inout)	givnum,
		complex(dp), dimension(*), intent(out)	work,
		real(dp), dimension(*), intent(out)	rwork,
		integer(ilp), dimension(*), intent(out)	iwork,
		integer(ilp), intent(out)	info
	)

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

• la_lapack.f90