la_lapack::bbcsd Interface Reference

BBCSD computes the CS decomposition of a unitary matrix in bidiagonal-block form. More...

Public Member Functions
pure subroutine	cbbcsd (jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta, phi, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, b11d, b11e, b12d, b12e, b21d, b21e, b22d, b22e, rwork, lrwork, info)
	la_cbbcsd
pure subroutine	dbbcsd (jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta, phi, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, b11d, b11e, b12d, b12e, b21d, b21e, b22d, b22e, work, lwork, info)
	la_dbbcsd
	la_qbbcsd
pure subroutine	sbbcsd (jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta, phi, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, b11d, b11e, b12d, b12e, b21d, b21e, b22d, b22e, work, lwork, info)
	la_sbbcsd
	la_wbbcsd
pure subroutine	zbbcsd (jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta, phi, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t, ldv2t, b11d, b11e, b12d, b12e, b21d, b21e, b22d, b22e, rwork, lrwork, info)
	la_zbbcsd

Detailed Description

BBCSD computes the CS decomposition of a unitary matrix in bidiagonal-block form.

$$\renewcommand\arraystretch{1.3} \left[ \begin{array}{c|ccc} B_{11} & B_{12} & 0 & 0 \\ 0 & 0 & -I & 0 \\ \hline B_{21} & B_{22} & 0 & 0 \\ 0 & 0 & 0 & I \\ C & -S & 0 & 0 \end{array} \right] = \left[ \begin{array}{c|c} U_1 & 0 \\ \hline 0 & U_2 \end{array} \right] \left[ \begin{array}{c|ccc} 0 & 0 & -I & 0 \\ \hline S & C & 0 & 0 \\ 0 & 0 & 0 & I \end{array} \right] \left[ \begin{array}{c|c} V_1^H & 0 \\ \hline 0 & V_2^H \end{array} \right]$$

X is $M \times M$, its top-left block is $P \times Q$, and $Q$ must be no larger than $P$, $M-P$, or $M-Q$. (If $Q$ is not the smallest index, then X must be transposed and/or permuted. This can be done in constant time using the TRANS and SIGNS options. See CUNCSD for details.)

The bidiagonal matrices $B_{11}$, $B_{12}$, $B_{21}$, and $B_{22}$ are represented implicitly by angles $\theta(1:Q)$ and $\phi(1:Q-1)$.

The unitary matrices $U_1$, $U_2$, $V_1^T$, and $V_2^T$ are input/output.

The input matrices are pre- or post-multiplied by the appropriate singular vector matrices.

Member Function/Subroutine Documentation

cbbcsd()

pure subroutine la_lapack::bbcsd::cbbcsd	(	character, intent(in)	jobu1,
		character, intent(in)	jobu2,
		character, intent(in)	jobv1t,
		character, intent(in)	jobv2t,
		character, intent(in)	trans,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		integer(ilp), intent(in)	q,
		real(sp), dimension(*), intent(inout)	theta,
		real(sp), dimension(*), intent(inout)	phi,
		complex(sp), dimension(ldu1,*), intent(inout)	u1,
		integer(ilp), intent(in)	ldu1,
		complex(sp), dimension(ldu2,*), intent(inout)	u2,
		integer(ilp), intent(in)	ldu2,
		complex(sp), dimension(ldv1t,*), intent(inout)	v1t,
		integer(ilp), intent(in)	ldv1t,
		complex(sp), dimension(ldv2t,*), intent(inout)	v2t,
		integer(ilp), intent(in)	ldv2t,
		real(sp), dimension(*), intent(out)	b11d,
		real(sp), dimension(*), intent(out)	b11e,
		real(sp), dimension(*), intent(out)	b12d,
		real(sp), dimension(*), intent(out)	b12e,
		real(sp), dimension(*), intent(out)	b21d,
		real(sp), dimension(*), intent(out)	b21e,
		real(sp), dimension( *), intent(out)	b22d,
		real(sp), dimension(*), intent(out)	b22e,
		real(sp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(in)	lrwork,
		integer(ilp), intent(out)	info )

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dbbcsd()

pure subroutine la_lapack::bbcsd::dbbcsd	(	character, intent(in)	jobu1,
		character, intent(in)	jobu2,
		character, intent(in)	jobv1t,
		character, intent(in)	jobv2t,
		character, intent(in)	trans,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		integer(ilp), intent(in)	q,
		real(dp), dimension(*), intent(inout)	theta,
		real(dp), dimension(*), intent(inout)	phi,
		real(dp), dimension(ldu1,*), intent(inout)	u1,
		integer(ilp), intent(in)	ldu1,
		real(dp), dimension(ldu2,*), intent(inout)	u2,
		integer(ilp), intent(in)	ldu2,
		real(dp), dimension(ldv1t,*), intent(inout)	v1t,
		integer(ilp), intent(in)	ldv1t,
		real(dp), dimension(ldv2t,*), intent(inout)	v2t,
		integer(ilp), intent(in)	ldv2t,
		real(dp), dimension(*), intent(out)	b11d,
		real(dp), dimension(*), intent(out)	b11e,
		real(dp), dimension(*), intent(out)	b12d,
		real(dp), dimension(*), intent(out)	b12e,
		real(dp), dimension(*), intent(out)	b21d,
		real(dp), dimension(*), intent(out)	b21e,
		real(dp), dimension( *), intent(out)	b22d,
		real(dp), dimension(*), intent(out)	b22e,
		real(dp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info )

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la_cbbcsd()

la_lapack::bbcsd::la_cbbcsd

la_dbbcsd()

la_lapack::bbcsd::la_dbbcsd

la_qbbcsd()

la_lapack::bbcsd::la_qbbcsd

la_sbbcsd()

la_lapack::bbcsd::la_sbbcsd

la_wbbcsd()

la_lapack::bbcsd::la_wbbcsd

la_zbbcsd()

la_lapack::bbcsd::la_zbbcsd

sbbcsd()

pure subroutine la_lapack::bbcsd::sbbcsd	(	character, intent(in)	jobu1,
		character, intent(in)	jobu2,
		character, intent(in)	jobv1t,
		character, intent(in)	jobv2t,
		character, intent(in)	trans,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		integer(ilp), intent(in)	q,
		real(sp), dimension(*), intent(inout)	theta,
		real(sp), dimension(*), intent(inout)	phi,
		real(sp), dimension(ldu1,*), intent(inout)	u1,
		integer(ilp), intent(in)	ldu1,
		real(sp), dimension(ldu2,*), intent(inout)	u2,
		integer(ilp), intent(in)	ldu2,
		real(sp), dimension(ldv1t,*), intent(inout)	v1t,
		integer(ilp), intent(in)	ldv1t,
		real(sp), dimension(ldv2t,*), intent(inout)	v2t,
		integer(ilp), intent(in)	ldv2t,
		real(sp), dimension(*), intent(out)	b11d,
		real(sp), dimension(*), intent(out)	b11e,
		real(sp), dimension(*), intent(out)	b12d,
		real(sp), dimension(*), intent(out)	b12e,
		real(sp), dimension(*), intent(out)	b21d,
		real(sp), dimension(*), intent(out)	b21e,
		real(sp), dimension( *), intent(out)	b22d,
		real(sp), dimension(*), intent(out)	b22e,
		real(sp), dimension(*), intent(out)	work,
		integer(ilp), intent(in)	lwork,
		integer(ilp), intent(out)	info )

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zbbcsd()

pure subroutine la_lapack::bbcsd::zbbcsd	(	character, intent(in)	jobu1,
		character, intent(in)	jobu2,
		character, intent(in)	jobv1t,
		character, intent(in)	jobv2t,
		character, intent(in)	trans,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	p,
		integer(ilp), intent(in)	q,
		real(dp), dimension(*), intent(inout)	theta,
		real(dp), dimension(*), intent(inout)	phi,
		complex(dp), dimension(ldu1,*), intent(inout)	u1,
		integer(ilp), intent(in)	ldu1,
		complex(dp), dimension(ldu2,*), intent(inout)	u2,
		integer(ilp), intent(in)	ldu2,
		complex(dp), dimension(ldv1t,*), intent(inout)	v1t,
		integer(ilp), intent(in)	ldv1t,
		complex(dp), dimension(ldv2t,*), intent(inout)	v2t,
		integer(ilp), intent(in)	ldv2t,
		real(dp), dimension(*), intent(out)	b11d,
		real(dp), dimension(*), intent(out)	b11e,
		real(dp), dimension(*), intent(out)	b12d,
		real(dp), dimension(*), intent(out)	b12e,
		real(dp), dimension(*), intent(out)	b21d,
		real(dp), dimension(*), intent(out)	b21e,
		real(dp), dimension( *), intent(out)	b22d,
		real(dp), dimension(*), intent(out)	b22e,
		real(dp), dimension(*), intent(out)	rwork,
		integer(ilp), intent(in)	lrwork,
		integer(ilp), intent(out)	info )

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

• la_lapack.f90