la_lapack::geesx Interface Reference

GEESX: computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). Optionally, it also orders the eigenvalues on the diagonal of the real Schur form so that selected eigenvalues are at the top left; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues (RCONDV). The leading columns of Z form an orthonormal basis for this invariant subspace. For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where these quantities are called s and sep respectively). A real matrix is in real Schur form if it is upper quasi-triangular with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the form [ a b ] [ c a ] where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). More...

Public Member Functions
subroutine	cgeesx (jobvs, sort, select, sense, n, a, lda, sdim, w, vs, ldvs, rconde, rcondv, work, lwork, rwork, bwork, info)
	la_cgeesx
subroutine	dgeesx (jobvs, sort, select, sense, n, a, lda, sdim, wr, wi, vs, ldvs, rconde, rcondv, work, lwork, iwork, liwork, bwork, info)
	la_dgeesx
	la_qgeesx
subroutine	sgeesx (jobvs, sort, select, sense, n, a, lda, sdim, wr, wi, vs, ldvs, rconde, rcondv, work, lwork, iwork, liwork, bwork, info)
	la_sgeesx
	la_wgeesx
subroutine	zgeesx (jobvs, sort, select, sense, n, a, lda, sdim, w, vs, ldvs, rconde, rcondv, work, lwork, rwork, bwork, info)
	la_zgeesx

Detailed Description

GEESX: computes for an N-by-N real nonsymmetric matrix A, the eigenvalues, the real Schur form T, and, optionally, the matrix of Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). Optionally, it also orders the eigenvalues on the diagonal of the real Schur form so that selected eigenvalues are at the top left; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues (RCONDV). The leading columns of Z form an orthonormal basis for this invariant subspace. For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where these quantities are called s and sep respectively). A real matrix is in real Schur form if it is upper quasi-triangular with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the form [ a b ] [ c a ] where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).

Member Function/Subroutine Documentation

cgeesx()

subroutine la_lapack::geesx::cgeesx	(	character, intent(in)	jobvs,
		character, intent(in)	sort,
		procedure(la_select_c)	select,
		character, intent(in)	sense,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		integer(ilp), intent(out)	sdim,
		complex(sp), dimension(*), intent(out)	w,
		complex(sp), dimension(ldvs,*), intent(out)	vs,
		integer(ilp), intent(in)	ldvs,
		real(sp), intent(out)	rconde,
		real(sp), intent(out)	rcondv,
		complex(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		real(sp), dimension(*), intent(out)	rwork,
		logical(lk), dimension(*), intent(out)	bwork,
		integer(ilp), intent(out)	info )

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dgeesx()

subroutine la_lapack::geesx::dgeesx	(	character, intent(in)	jobvs,
		character, intent(in)	sort,
		procedure(la_select_d)	select,
		character, intent(in)	sense,
		integer(ilp), intent(in)	n,
		real(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		integer(ilp), intent(out)	sdim,
		real(dp), dimension(*), intent(out)	wr,
		real(dp), dimension(*), intent(out)	wi,
		real(dp), dimension(ldvs,*), intent(out)	vs,
		integer(ilp), intent(in)	ldvs,
		real(dp), intent(out)	rconde,
		real(dp), intent(out)	rcondv,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), dimension(*), intent(out)	iwork,
		integer(ilp), intent(in)	liwork,
		logical(lk), dimension(*), intent(out)	bwork,
		integer(ilp), intent(out)	info )

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la_cgeesx()

la_lapack::geesx::la_cgeesx

la_dgeesx()

la_lapack::geesx::la_dgeesx

la_qgeesx()

la_lapack::geesx::la_qgeesx

la_sgeesx()

la_lapack::geesx::la_sgeesx

la_wgeesx()

la_lapack::geesx::la_wgeesx

la_zgeesx()

la_lapack::geesx::la_zgeesx

sgeesx()

subroutine la_lapack::geesx::sgeesx	(	character, intent(in)	jobvs,
		character, intent(in)	sort,
		procedure(la_select_s)	select,
		character, intent(in)	sense,
		integer(ilp), intent(in)	n,
		real(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		integer(ilp), intent(out)	sdim,
		real(sp), dimension(*), intent(out)	wr,
		real(sp), dimension(*), intent(out)	wi,
		real(sp), dimension(ldvs,*), intent(out)	vs,
		integer(ilp), intent(in)	ldvs,
		real(sp), intent(out)	rconde,
		real(sp), intent(out)	rcondv,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), dimension(*), intent(out)	iwork,
		integer(ilp), intent(in)	liwork,
		logical(lk), dimension(*), intent(out)	bwork,
		integer(ilp), intent(out)	info )

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zgeesx()

subroutine la_lapack::geesx::zgeesx	(	character, intent(in)	jobvs,
		character, intent(in)	sort,
		procedure(la_select_z)	select,
		character, intent(in)	sense,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		integer(ilp), intent(out)	sdim,
		complex(dp), dimension(*), intent(out)	w,
		complex(dp), dimension(ldvs,*), intent(out)	vs,
		integer(ilp), intent(in)	ldvs,
		real(dp), intent(out)	rconde,
		real(dp), intent(out)	rcondv,
		complex(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		real(dp), dimension(*), intent(out)	rwork,
		logical(lk), dimension(*), intent(out)	bwork,
		integer(ilp), intent(out)	info )

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

• la_lapack.F90