la_lapack::orbdb Interface Reference

ORBDB: simultaneously bidiagonalizes the blocks of an M-by-M partitioned orthogonal matrix X: [ B11 | B12 0 0 ] [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**T X = [--------—] = [------—] [-------------—] [------—] . [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ] [ 0 | 0 0 I ] X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is not the case, then X must be transposed and/or permuted. This can be done in constant time using the TRANS and SIGNS options. See DORCSD for details.) The orthogonal matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by- (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are represented implicitly by Householder vectors. B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented implicitly by angles THETA, PHI. More...

Public Member Functions
subroutine	dorbdb (trans, signs, m, p, q, x11, ldx11, x12, ldx12, x21, ldx21, x22, ldx22, theta, phi, taup1, taup2, tauq1, tauq2, work, lwork, info)
	la_dorbdb
	la_qorbdb
subroutine	sorbdb (trans, signs, m, p, q, x11, ldx11, x12, ldx12, x21, ldx21, x22, ldx22, theta, phi, taup1, taup2, tauq1, tauq2, work, lwork, info)
	la_sorbdb

Detailed Description

ORBDB: simultaneously bidiagonalizes the blocks of an M-by-M partitioned orthogonal matrix X: [ B11 | B12 0 0 ] [ X11 | X12 ] [ P1 | ] [ 0 | 0 -I 0 ] [ Q1 | ]**T X = [--------—] = [------—] [-------------—] [------—] . [ X21 | X22 ] [ | P2 ] [ B21 | B22 0 0 ] [ | Q2 ] [ 0 | 0 0 I ] X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is not the case, then X must be transposed and/or permuted. This can be done in constant time using the TRANS and SIGNS options. See DORCSD for details.) The orthogonal matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by- (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are represented implicitly by Householder vectors. B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented implicitly by angles THETA, PHI.

Member Function/Subroutine Documentation

dorbdb()

subroutine la_lapack::orbdb::dorbdb	(	character, intent(in)	trans,
		character, intent(in)	signs,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		integer(ilp), intent(in)	q,
		real(dp), dimension(ldx11,*), intent(inout)	x11,
		integer(ilp), intent(in)	ldx11,
		real(dp), dimension(ldx12,*), intent(inout)	x12,
		integer(ilp), intent(in)	ldx12,
		real(dp), dimension(ldx21,*), intent(inout)	x21,
		integer(ilp), intent(in)	ldx21,
		real(dp), dimension(ldx22,*), intent(inout)	x22,
		integer(ilp), intent(in)	ldx22,
		real(dp), dimension(*), intent(out)	theta,
		real(dp), dimension(*), intent(out)	phi,
		real(dp), dimension(*), intent(out)	taup1,
		real(dp), dimension(*), intent(out)	taup2,
		real(dp), dimension(*), intent(out)	tauq1,
		real(dp), dimension(*), intent(out)	tauq2,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

la_dorbdb()

la_lapack::orbdb::la_dorbdb

la_qorbdb()

la_lapack::orbdb::la_qorbdb

la_sorbdb()

la_lapack::orbdb::la_sorbdb

sorbdb()

subroutine la_lapack::orbdb::sorbdb	(	character, intent(in)	trans,
		character, intent(in)	signs,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		integer(ilp), intent(in)	q,
		real(sp), dimension(ldx11,*), intent(inout)	x11,
		integer(ilp), intent(in)	ldx11,
		real(sp), dimension(ldx12,*), intent(inout)	x12,
		integer(ilp), intent(in)	ldx12,
		real(sp), dimension(ldx21,*), intent(inout)	x21,
		integer(ilp), intent(in)	ldx21,
		real(sp), dimension(ldx22,*), intent(inout)	x22,
		integer(ilp), intent(in)	ldx22,
		real(sp), dimension(*), intent(out)	theta,
		real(sp), dimension(*), intent(out)	phi,
		real(sp), dimension(*), intent(out)	taup1,
		real(sp), dimension(*), intent(out)	taup2,
		real(sp), dimension(*), intent(out)	tauq1,
		real(sp), dimension(*), intent(out)	tauq2,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info
	)

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

• la_lapack.f90