sorbdb.f(3)							      LAPACK							       sorbdb.f(3)

NAME

       sorbdb.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sorbdb (TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK,
	   LWORK, INFO)
	   SORBDB

Function/Subroutine Documentation
   subroutine sorbdb (characterTRANS, characterSIGNS, integerM, integerP, integerQ, real, dimension( ldx11, * )X11, integerLDX11, real, dimension(
       ldx12, * )X12, integerLDX12, real, dimension( ldx21, * )X21, integerLDX21, real, dimension( ldx22, * )X22, integerLDX22, real, dimension( *
       )THETA, real, dimension( * )PHI, real, dimension( * )TAUP1, real, dimension( * )TAUP2, real, dimension( * )TAUQ1, real, dimension( *
       )TAUQ2, real, dimension( * )WORK, integerLWORK, integerINFO)
       SORBDB

       Purpose:

	    SORBDB 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 SORCSD
	    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.

       Parameters:
	   TRANS

		     TRANS is CHARACTER
		     = 'T':	 X, U1, U2, V1T, and V2T are stored in row-major
				 order;
		     otherwise:  X, U1, U2, V1T, and V2T are stored in column-
				 major order.

	   SIGNS

		     SIGNS is CHARACTER
		     = 'O':	 The lower-left block is made nonpositive (the
				 "other" convention);
		     otherwise:  The upper-right block is made nonpositive (the
				 "default" convention).

	   M

		     M is INTEGER
		     The number of rows and columns in X.

	   P

		     P is INTEGER
		     The number of rows in X11 and X12. 0 <= P <= M.

	   Q

		     Q is INTEGER
		     The number of columns in X11 and X21. 0 <= Q <=
		     MIN(P,M-P,M-Q).

	   X11

		     X11 is REAL array, dimension (LDX11,Q)
		     On entry, the top-left block of the orthogonal matrix to be
		     reduced. On exit, the form depends on TRANS:
		     If TRANS = 'N', then
			the columns of tril(X11) specify reflectors for P1,
			the rows of triu(X11,1) specify reflectors for Q1;
		     else TRANS = 'T', and
			the rows of triu(X11) specify reflectors for P1,
			the columns of tril(X11,-1) specify reflectors for Q1.

	   LDX11

		     LDX11 is INTEGER
		     The leading dimension of X11. If TRANS = 'N', then LDX11 >=
		     P; else LDX11 >= Q.

	   X12

		     X12 is REAL array, dimension (LDX12,M-Q)
		     On entry, the top-right block of the orthogonal matrix to
		     be reduced. On exit, the form depends on TRANS:
		     If TRANS = 'N', then
			the rows of triu(X12) specify the first P reflectors for
			Q2;
		     else TRANS = 'T', and
			the columns of tril(X12) specify the first P reflectors
			for Q2.

	   LDX12

		     LDX12 is INTEGER
		     The leading dimension of X12. If TRANS = 'N', then LDX12 >=
		     P; else LDX11 >= M-Q.

	   X21

		     X21 is REAL array, dimension (LDX21,Q)
		     On entry, the bottom-left block of the orthogonal matrix to
		     be reduced. On exit, the form depends on TRANS:
		     If TRANS = 'N', then
			the columns of tril(X21) specify reflectors for P2;
		     else TRANS = 'T', and
			the rows of triu(X21) specify reflectors for P2.

	   LDX21

		     LDX21 is INTEGER
		     The leading dimension of X21. If TRANS = 'N', then LDX21 >=
		     M-P; else LDX21 >= Q.

	   X22

		     X22 is REAL array, dimension (LDX22,M-Q)
		     On entry, the bottom-right block of the orthogonal matrix to
		     be reduced. On exit, the form depends on TRANS:
		     If TRANS = 'N', then
			the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
			M-P-Q reflectors for Q2,
		     else TRANS = 'T', and
			the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
			M-P-Q reflectors for P2.

	   LDX22

		     LDX22 is INTEGER
		     The leading dimension of X22. If TRANS = 'N', then LDX22 >=
		     M-P; else LDX22 >= M-Q.

	   THETA

		     THETA is REAL array, dimension (Q)
		     The entries of the bidiagonal blocks B11, B12, B21, B22 can
		     be computed from the angles THETA and PHI. See Further
		     Details.

	   PHI

		     PHI is REAL array, dimension (Q-1)
		     The entries of the bidiagonal blocks B11, B12, B21, B22 can
		     be computed from the angles THETA and PHI. See Further
		     Details.

	   TAUP1

		     TAUP1 is REAL array, dimension (P)
		     The scalar factors of the elementary reflectors that define
		     P1.

	   TAUP2

		     TAUP2 is REAL array, dimension (M-P)
		     The scalar factors of the elementary reflectors that define
		     P2.

	   TAUQ1

		     TAUQ1 is REAL array, dimension (Q)
		     The scalar factors of the elementary reflectors that define
		     Q1.

	   TAUQ2

		     TAUQ2 is REAL array, dimension (M-Q)
		     The scalar factors of the elementary reflectors that define
		     Q2.

	   WORK

		     WORK is REAL array, dimension (LWORK)

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK. LWORK >= M-Q.

		     If LWORK = -1, then a workspace query is assumed; the routine
		     only calculates the optimal size of the WORK array, returns
		     this value as the first entry of the WORK array, and no error
		     message related to LWORK is issued by XERBLA.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     The bidiagonal blocks B11, B12, B21, and B22 are represented
	     implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
	     PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
	     lower bidiagonal. Every entry in each bidiagonal band is a product
	     of a sine or cosine of a THETA with a sine or cosine of a PHI. See
	     [1] or SORCSD for details.

	     P1, P2, Q1, and Q2 are represented as products of elementary
	     reflectors. See SORCSD for details on generating P1, P2, Q1, and Q2
	     using SORGQR and SORGLQ.

       References:
	   [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

       Definition at line 286 of file sorbdb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sorbdb.f(3)