la_lapack::ggev Interface Reference

GGEV: computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero. The right generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A,B) satisfies A * v(j) = lambda(j) * B * v(j). The left generalized eigenvector u(j) corresponding to the generalized eigenvalues lambda(j) of (A,B) satisfies u(j)**H * A = lambda(j) * u(j)**H * B where u(j)**H is the conjugate-transpose of u(j). More...

Public Member Functions
subroutine	cggev (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
	la_cggev
subroutine	dggev (jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai, beta, vl, ldvl, vr, ldvr, work, lwork, info)
	la_dggev
	la_qggev
subroutine	sggev (jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai, beta, vl, ldvl, vr, ldvr, work, lwork, info)
	la_sggev
	la_wggev
subroutine	zggev (jobvl, jobvr, n, a, lda, b, ldb, alpha, beta, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
	la_zggev

Detailed Description

GGEV: computes for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero. The right generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A,B) satisfies A * v(j) = lambda(j) * B * v(j). The left generalized eigenvector u(j) corresponding to the generalized eigenvalues lambda(j) of (A,B) satisfies u(j)**H * A = lambda(j) * u(j)**H * B where u(j)**H is the conjugate-transpose of u(j).

Member Function/Subroutine Documentation

cggev()

subroutine la_lapack::ggev::cggev	(	character, intent(in)	jobvl,
		character, intent(in)	jobvr,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(sp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		complex(sp), dimension(*), intent(out)	alpha,
		complex(sp), dimension(*), intent(out)	beta,
		complex(sp), dimension(ldvl,*), intent(out)	vl,
		integer(ilp), intent(in)	ldvl,
		complex(sp), dimension(ldvr,*), intent(out)	vr,
		integer(ilp), intent(in)	ldvr,
		complex(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		real(sp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(out)	info )

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dggev()

subroutine la_lapack::ggev::dggev	(	character, intent(in)	jobvl,
		character, intent(in)	jobvr,
		integer(ilp), intent(in)	n,
		real(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(dp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		real(dp), dimension(*), intent(out)	alphar,
		real(dp), dimension(*), intent(out)	alphai,
		real(dp), dimension(*), intent(out)	beta,
		real(dp), dimension(ldvl,*), intent(out)	vl,
		integer(ilp), intent(in)	ldvl,
		real(dp), dimension(ldvr,*), intent(out)	vr,
		integer(ilp), intent(in)	ldvr,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info )

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la_cggev()

la_lapack::ggev::la_cggev

la_dggev()

la_lapack::ggev::la_dggev

la_qggev()

la_lapack::ggev::la_qggev

la_sggev()

la_lapack::ggev::la_sggev

la_wggev()

la_lapack::ggev::la_wggev

la_zggev()

la_lapack::ggev::la_zggev

sggev()

subroutine la_lapack::ggev::sggev	(	character, intent(in)	jobvl,
		character, intent(in)	jobvr,
		integer(ilp), intent(in)	n,
		real(sp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		real(sp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		real(sp), dimension(*), intent(out)	alphar,
		real(sp), dimension(*), intent(out)	alphai,
		real(sp), dimension(*), intent(out)	beta,
		real(sp), dimension(ldvl,*), intent(out)	vl,
		integer(ilp), intent(in)	ldvl,
		real(sp), dimension(ldvr,*), intent(out)	vr,
		integer(ilp), intent(in)	ldvr,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info )

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zggev()

subroutine la_lapack::ggev::zggev	(	character, intent(in)	jobvl,
		character, intent(in)	jobvr,
		integer(ilp), intent(in)	n,
		complex(dp), dimension(lda,*), intent(inout)	a,
		integer(ilp), intent(in)	lda,
		complex(dp), dimension(ldb,*), intent(inout)	b,
		integer(ilp), intent(in)	ldb,
		complex(dp), dimension(*), intent(out)	alpha,
		complex(dp), dimension(*), intent(out)	beta,
		complex(dp), dimension(ldvl,*), intent(out)	vl,
		integer(ilp), intent(in)	ldvl,
		complex(dp), dimension(ldvr,*), intent(out)	vr,
		integer(ilp), intent(in)	ldvr,
		complex(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		real(dp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(out)	info )

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

• la_lapack.f90