la_lapack::laqz0 Interface Reference

LAQZ0: computes the eigenvalues of a matrix pair (H,T), where H is an upper Hessenberg matrix and T is upper triangular, using the double-shift QZ method. Matrix pairs of this type are produced by the reduction to generalized upper Hessenberg form of a matrix pair (A,B): A = Q1*H*Z1**H, B = Q1*T*Z1**H, as computed by CGGHRD. If JOB='S', then the Hessenberg-triangular pair (H,T) is also reduced to generalized Schur form, H = Q*S*Z**H, T = Q*P*Z**H, where Q and Z are unitary matrices, P and S are an upper triangular matrices. Optionally, the unitary matrix Q from the generalized Schur factorization may be postmultiplied into an input matrix Q1, and the unitary matrix Z may be postmultiplied into an input matrix Z1. If Q1 and Z1 are the unitary matrices from CGGHRD that reduced the matrix pair (A,B) to generalized upper Hessenberg form, then the output matrices Q1*Q and Z1*Z are the unitary factors from the generalized Schur factorization of (A,B): A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently, of (A,B)) are computed as a pair of values (alpha,beta), where alpha is complex and beta real. If beta is nonzero, lambda = alpha / beta is an eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP) A*x = lambda*B*x and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the alternate form of the GNEP mu*A*y = B*y. Eigenvalues can be read directly from the generalized Schur form: alpha = S(i,i), beta = P(i,i). Ref: C.B. Moler Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), pp. 241–256. Ref: B. Kagstrom, D. Kressner, "Multishift Variants of the QZ Algorithm with Aggressive Early Deflation", SIAM J. Numer. Anal., 29(2006), pp. 199–227. Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift, multipole rational QZ method with agressive early deflation". More...

Public Member Functions
recursive subroutine	claqz0 (wants, wantq, wantz, n, ilo, ihi, a, lda, b, ldb, alpha, beta, q, ldq, z, ldz, work, lwork, rwork, rec, info)
	la_claqz0
recursive subroutine	dlaqz0 (wants, wantq, wantz, n, ilo, ihi, a, lda, b, ldb, alphar, alphai, beta, q, ldq, z, ldz, work, lwork, rec, info)
	la_dlaqz0
	la_qlaqz0
recursive subroutine	slaqz0 (wants, wantq, wantz, n, ilo, ihi, a, lda, b, ldb, alphar, alphai, beta, q, ldq, z, ldz, work, lwork, rec, info)
	la_slaqz0
	la_wlaqz0
recursive subroutine	zlaqz0 (wants, wantq, wantz, n, ilo, ihi, a, lda, b, ldb, alpha, beta, q, ldq, z, ldz, work, lwork, rwork, rec, info)
	la_zlaqz0

Detailed Description

LAQZ0: computes the eigenvalues of a matrix pair (H,T), where H is an upper Hessenberg matrix and T is upper triangular, using the double-shift QZ method. Matrix pairs of this type are produced by the reduction to generalized upper Hessenberg form of a matrix pair (A,B): A = Q1*H*Z1**H, B = Q1*T*Z1**H, as computed by CGGHRD. If JOB='S', then the Hessenberg-triangular pair (H,T) is also reduced to generalized Schur form, H = Q*S*Z**H, T = Q*P*Z**H, where Q and Z are unitary matrices, P and S are an upper triangular matrices. Optionally, the unitary matrix Q from the generalized Schur factorization may be postmultiplied into an input matrix Q1, and the unitary matrix Z may be postmultiplied into an input matrix Z1. If Q1 and Z1 are the unitary matrices from CGGHRD that reduced the matrix pair (A,B) to generalized upper Hessenberg form, then the output matrices Q1*Q and Z1*Z are the unitary factors from the generalized Schur factorization of (A,B): A = (Q1*Q)*S*(Z1*Z)**H, B = (Q1*Q)*P*(Z1*Z)**H. To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently, of (A,B)) are computed as a pair of values (alpha,beta), where alpha is complex and beta real. If beta is nonzero, lambda = alpha / beta is an eigenvalue of the generalized nonsymmetric eigenvalue problem (GNEP) A*x = lambda*B*x and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the alternate form of the GNEP mu*A*y = B*y. Eigenvalues can be read directly from the generalized Schur form: alpha = S(i,i), beta = P(i,i). Ref: C.B. Moler Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), pp. 241–256. Ref: B. Kagstrom, D. Kressner, "Multishift Variants of the QZ Algorithm with Aggressive Early Deflation", SIAM J. Numer. Anal., 29(2006), pp. 199–227. Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift, multipole rational QZ method with agressive early deflation".

Member Function/Subroutine Documentation

claqz0()

recursive subroutine la_lapack::laqz0::claqz0	(	character, intent(in)	wants,
		character, intent(in)	wantq,
		character, intent(in)	wantz,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ilo,
		integer(ilp), intent(in)	ihi,
		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(inout)	alpha,
		complex(sp), dimension(*), intent(inout)	beta,
		complex(sp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		complex(sp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		complex(sp), dimension(*), intent(inout)	work,
		integer(ilp), intent(in)	lwork,
		real(sp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(in)	rec,
		integer(ilp), intent(out)	info
	)

dlaqz0()

recursive subroutine la_lapack::laqz0::dlaqz0	(	character, intent(in)	wants,
		character, intent(in)	wantq,
		character, intent(in)	wantz,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ilo,
		integer(ilp), intent(in)	ihi,
		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(inout)	alphar,
		real(dp), dimension(*), intent(inout)	alphai,
		real(dp), dimension(*), intent(inout)	beta,
		real(dp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		real(dp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		real(dp), dimension(*), intent(inout)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(in)	rec,
		integer(ilp), intent(out)	info
	)

la_claqz0()

la_lapack::laqz0::la_claqz0

la_dlaqz0()

la_lapack::laqz0::la_dlaqz0

la_qlaqz0()

la_lapack::laqz0::la_qlaqz0

la_slaqz0()

la_lapack::laqz0::la_slaqz0

la_wlaqz0()

la_lapack::laqz0::la_wlaqz0

la_zlaqz0()

la_lapack::laqz0::la_zlaqz0

slaqz0()

recursive subroutine la_lapack::laqz0::slaqz0	(	character, intent(in)	wants,
		character, intent(in)	wantq,
		character, intent(in)	wantz,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ilo,
		integer(ilp), intent(in)	ihi,
		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(inout)	alphar,
		real(sp), dimension(*), intent(inout)	alphai,
		real(sp), dimension(*), intent(inout)	beta,
		real(sp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		real(sp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		real(sp), dimension(*), intent(inout)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(in)	rec,
		integer(ilp), intent(out)	info
	)

zlaqz0()

recursive subroutine la_lapack::laqz0::zlaqz0	(	character, intent(in)	wants,
		character, intent(in)	wantq,
		character, intent(in)	wantz,
		integer(ilp), intent(in)	n,
		integer(ilp), intent(in)	ilo,
		integer(ilp), intent(in)	ihi,
		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(inout)	alpha,
		complex(dp), dimension(*), intent(inout)	beta,
		complex(dp), dimension(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		complex(dp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		complex(dp), dimension(*), intent(inout)	work,
		integer(ilp), intent(in)	lwork,
		real(dp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(in)	rec,
		integer(ilp), intent(out)	info
	)

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

• la_lapack.f90