la_lapack::gghrd Interface Reference

GGHRD: reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular. The form of the generalized eigenvalue problem is A*x = lambda*B*x, and B is typically made upper triangular by computing its QR factorization and moving the unitary matrix Q to the left side of the equation. This subroutine simultaneously reduces A to a Hessenberg matrix H: Q**H*A*Z = H and transforms B to another upper triangular matrix T: Q**H*B*Z = T in order to reduce the problem to its standard form H*y = lambda*T*y where y = Z**H*x. The unitary matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices Q1 and Z1, so that Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H If Q1 is the unitary matrix from the QR factorization of B in the original equation A*x = lambda*B*x, then GGHRD reduces the original problem to generalized Hessenberg form. More...

Public Member Functions
pure subroutine	cgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
	la_cgghrd
pure subroutine	dgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
	la_dgghrd
	la_qgghrd
pure subroutine	sgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
	la_sgghrd
	la_wgghrd
pure subroutine	zgghrd (compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, info)
	la_zgghrd

Detailed Description

GGHRD: reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular. The form of the generalized eigenvalue problem is A*x = lambda*B*x, and B is typically made upper triangular by computing its QR factorization and moving the unitary matrix Q to the left side of the equation. This subroutine simultaneously reduces A to a Hessenberg matrix H: Q**H*A*Z = H and transforms B to another upper triangular matrix T: Q**H*B*Z = T in order to reduce the problem to its standard form H*y = lambda*T*y where y = Z**H*x. The unitary matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices Q1 and Z1, so that Q1 * A * Z1**H = (Q1*Q) * H * (Z1*Z)**H Q1 * B * Z1**H = (Q1*Q) * T * (Z1*Z)**H If Q1 is the unitary matrix from the QR factorization of B in the original equation A*x = lambda*B*x, then GGHRD reduces the original problem to generalized Hessenberg form.

Member Function/Subroutine Documentation

cgghrd()

pure subroutine la_lapack::gghrd::cgghrd	(	character, intent(in)	compq,
		character, intent(in)	compz,
		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(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		complex(sp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		integer(ilp), intent(out)	info
	)

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dgghrd()

pure subroutine la_lapack::gghrd::dgghrd	(	character, intent(in)	compq,
		character, intent(in)	compz,
		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(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		real(dp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		integer(ilp), intent(out)	info
	)

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la_cgghrd()

la_lapack::gghrd::la_cgghrd

la_dgghrd()

la_lapack::gghrd::la_dgghrd

la_qgghrd()

la_lapack::gghrd::la_qgghrd

la_sgghrd()

la_lapack::gghrd::la_sgghrd

la_wgghrd()

la_lapack::gghrd::la_wgghrd

la_zgghrd()

la_lapack::gghrd::la_zgghrd

sgghrd()

pure subroutine la_lapack::gghrd::sgghrd	(	character, intent(in)	compq,
		character, intent(in)	compz,
		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(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		real(sp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		integer(ilp), intent(out)	info
	)

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zgghrd()

pure subroutine la_lapack::gghrd::zgghrd	(	character, intent(in)	compq,
		character, intent(in)	compz,
		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(ldq,*), intent(inout)	q,
		integer(ilp), intent(in)	ldq,
		complex(dp), dimension(ldz,*), intent(inout)	z,
		integer(ilp), intent(in)	ldz,
		integer(ilp), intent(out)	info
	)

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

• la_lapack.f90