phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
ea86668bfcbc6dd9aa56477ec2dae9cd79e2fe8a
lapack/SRC/sorbdb4.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

376 lines
12 KiB
FortranFixed
Raw Blame History

*> \brief \b SORBDB4
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SORBDB4 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorbdb4.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorbdb4.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorbdb4.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
* TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK,
* INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21
* ..
* .. Array Arguments ..
* REAL PHI(*), THETA(*)
* REAL PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*),
* $ WORK(*), X11(LDX11,*), X21(LDX21,*)
* ..
*
*
*> \par Purpose:
* =============
*>
*>\verbatim
*>
*> SORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*>
*> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ]
*> [-----] = [---------] [-----] Q1**T .
*> [ X21 ] [ | P2 ] [ B21 ]
*> [ 0 ]
*>
*> X11 is P-by-Q, and X21 is (M-P)-by-Q. M-Q must be no larger than P,
*> M-P, or Q. Routines SORBDB1, SORBDB2, and SORBDB3 handle cases in
*> which M-Q is not the minimum dimension.
*>
*> The orthogonal matrices P1, P2, and Q1 are P-by-P, (M-P)-by-(M-P),
*> and (M-Q)-by-(M-Q), respectively. They are represented implicitly by
*> Householder vectors.
*>
*> B11 and B12 are (M-Q)-by-(M-Q) bidiagonal matrices represented
*> implicitly by angles THETA, PHI.
*>
*>\endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows X11 plus the number of rows in X21.
*> \endverbatim
*>
*> \param[in] P
*> \verbatim
*> P is INTEGER
*> The number of rows in X11. 0 <= P <= M.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*> Q is INTEGER
*> The number of columns in X11 and X21. 0 <= Q <= M and
*> M-Q <= min(P,M-P,Q).
*> \endverbatim
*>
*> \param[in,out] X11
*> \verbatim
*> X11 is REAL array, dimension (LDX11,Q)
*> On entry, the top block of the matrix X to be reduced. On
*> exit, the columns of tril(X11) specify reflectors for P1 and
*> the rows of triu(X11,1) specify reflectors for Q1.
*> \endverbatim
*>
*> \param[in] LDX11
*> \verbatim
*> LDX11 is INTEGER
*> The leading dimension of X11. LDX11 >= P.
*> \endverbatim
*>
*> \param[in,out] X21
*> \verbatim
*> X21 is REAL array, dimension (LDX21,Q)
*> On entry, the bottom block of the matrix X to be reduced. On
*> exit, the columns of tril(X21) specify reflectors for P2.
*> \endverbatim
*>
*> \param[in] LDX21
*> \verbatim
*> LDX21 is INTEGER
*> The leading dimension of X21. LDX21 >= M-P.
*> \endverbatim
*>
*> \param[out] THETA
*> \verbatim
*> THETA is REAL array, dimension (Q)
*> The entries of the bidiagonal blocks B11, B21 are defined by
*> THETA and PHI. See Further Details.
*> \endverbatim
*>
*> \param[out] PHI
*> \verbatim
*> PHI is REAL array, dimension (Q-1)
*> The entries of the bidiagonal blocks B11, B21 are defined by
*> THETA and PHI. See Further Details.
*> \endverbatim
*>
*> \param[out] TAUP1
*> \verbatim
*> TAUP1 is REAL array, dimension (P)
*> The scalar factors of the elementary reflectors that define
*> P1.
*> \endverbatim
*>
*> \param[out] TAUP2
*> \verbatim
*> TAUP2 is REAL array, dimension (M-P)
*> The scalar factors of the elementary reflectors that define
*> P2.
*> \endverbatim
*>
*> \param[out] TAUQ1
*> \verbatim
*> TAUQ1 is REAL array, dimension (Q)
*> The scalar factors of the elementary reflectors that define
*> Q1.
*> \endverbatim
*>
*> \param[out] PHANTOM
*> \verbatim
*> PHANTOM is REAL array, dimension (M)
*> The routine computes an M-by-1 column vector Y that is
*> orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
*> PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
*> Y(P+1:M), respectively.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
*>
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup realOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> The upper-bidiagonal blocks B11, B21 are represented implicitly by
*> angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). 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, and Q1 are represented as products of elementary reflectors.
*> See SORCSD2BY1 for details on generating P1, P2, and Q1 using SORGQR
*> and SORGLQ.
*> \endverbatim
*
*> \par References:
* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*>
* =====================================================================
SUBROUTINE SORBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, PHI,
$ TAUP1, TAUP2, TAUQ1, PHANTOM, WORK, LWORK,
$ INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER INFO, LWORK, M, P, Q, LDX11, LDX21
* ..
* .. Array Arguments ..
REAL PHI(*), THETA(*)
REAL PHANTOM(*), TAUP1(*), TAUP2(*), TAUQ1(*),
$ WORK(*), X11(LDX11,*), X21(LDX21,*)
* ..
*
* ====================================================================
*
* .. Parameters ..
REAL NEGONE, ONE, ZERO
PARAMETER ( NEGONE = -1.0E0, ONE = 1.0E0, ZERO = 0.0E0 )
* ..
* .. Local Scalars ..
REAL C, S
INTEGER CHILDINFO, I, ILARF, IORBDB5, J, LLARF,
$ LORBDB5, LWORKMIN, LWORKOPT
LOGICAL LQUERY
* ..
* .. External Subroutines ..
EXTERNAL SLARF, SLARFGP, SORBDB5, SROT, SSCAL, XERBLA
* ..
* .. External Functions ..
REAL SNRM2
EXTERNAL SNRM2
* ..
* .. Intrinsic Function ..
INTRINSIC ATAN2, COS, MAX, SIN, SQRT
* ..
* .. Executable Statements ..
*
* Test input arguments
*
INFO = 0
LQUERY = LWORK .EQ. -1
*
IF( M .LT. 0 ) THEN
INFO = -1
ELSE IF( P .LT. M-Q .OR. M-P .LT. M-Q ) THEN
INFO = -2
ELSE IF( Q .LT. M-Q .OR. Q .GT. M ) THEN
INFO = -3
ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
INFO = -5
ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
INFO = -7
END IF
*
* Compute workspace
*
IF( INFO .EQ. 0 ) THEN
ILARF = 2
LLARF = MAX( Q-1, P-1, M-P-1 )
IORBDB5 = 2
LORBDB5 = Q
LWORKOPT = ILARF + LLARF - 1
LWORKOPT = MAX( LWORKOPT, IORBDB5 + LORBDB5 - 1 )
LWORKMIN = LWORKOPT
WORK(1) = LWORKOPT
IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
INFO = -14
END IF
END IF
IF( INFO .NE. 0 ) THEN
CALL XERBLA( 'SORBDB4', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Reduce columns 1, ..., M-Q of X11 and X21
*
DO I = 1, M-Q
*
IF( I .EQ. 1 ) THEN
DO J = 1, M
PHANTOM(J) = ZERO
END DO
CALL SORBDB5( P, M-P, Q, PHANTOM(1), 1, PHANTOM(P+1), 1,
$ X11, LDX11, X21, LDX21, WORK(IORBDB5),
$ LORBDB5, CHILDINFO )
CALL SSCAL( P, NEGONE, PHANTOM(1), 1 )
CALL SLARFGP( P, PHANTOM(1), PHANTOM(2), 1, TAUP1(1) )
CALL SLARFGP( M-P, PHANTOM(P+1), PHANTOM(P+2), 1, TAUP2(1) )
THETA(I) = ATAN2( PHANTOM(1), PHANTOM(P+1) )
C = COS( THETA(I) )
S = SIN( THETA(I) )
PHANTOM(1) = ONE
PHANTOM(P+1) = ONE
CALL SLARF( 'L', P, Q, PHANTOM(1), 1, TAUP1(1), X11, LDX11,
$ WORK(ILARF) )
CALL SLARF( 'L', M-P, Q, PHANTOM(P+1), 1, TAUP2(1), X21,
$ LDX21, WORK(ILARF) )
ELSE
CALL SORBDB5( P-I+1, M-P-I+1, Q-I+1, X11(I,I-1), 1,
$ X21(I,I-1), 1, X11(I,I), LDX11, X21(I,I),
$ LDX21, WORK(IORBDB5), LORBDB5, CHILDINFO )
CALL SSCAL( P-I+1, NEGONE, X11(I,I-1), 1 )
CALL SLARFGP( P-I+1, X11(I,I-1), X11(I+1,I-1), 1, TAUP1(I) )
CALL SLARFGP( M-P-I+1, X21(I,I-1), X21(I+1,I-1), 1,
$ TAUP2(I) )
THETA(I) = ATAN2( X11(I,I-1), X21(I,I-1) )
C = COS( THETA(I) )
S = SIN( THETA(I) )
X11(I,I-1) = ONE
X21(I,I-1) = ONE
CALL SLARF( 'L', P-I+1, Q-I+1, X11(I,I-1), 1, TAUP1(I),
$ X11(I,I), LDX11, WORK(ILARF) )
CALL SLARF( 'L', M-P-I+1, Q-I+1, X21(I,I-1), 1, TAUP2(I),
$ X21(I,I), LDX21, WORK(ILARF) )
END IF
*
CALL SROT( Q-I+1, X11(I,I), LDX11, X21(I,I), LDX21, S, -C )
CALL SLARFGP( Q-I+1, X21(I,I), X21(I,I+1), LDX21, TAUQ1(I) )
C = X21(I,I)
X21(I,I) = ONE
CALL SLARF( 'R', P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
$ X11(I+1,I), LDX11, WORK(ILARF) )
CALL SLARF( 'R', M-P-I, Q-I+1, X21(I,I), LDX21, TAUQ1(I),
$ X21(I+1,I), LDX21, WORK(ILARF) )
IF( I .LT. M-Q ) THEN
S = SQRT( SNRM2( P-I, X11(I+1,I), 1 )**2
$ + SNRM2( M-P-I, X21(I+1,I), 1 )**2 )
PHI(I) = ATAN2( S, C )
END IF
*
END DO
*
* Reduce the bottom-right portion of X11 to [ I 0 ]
*
DO I = M - Q + 1, P
CALL SLARFGP( Q-I+1, X11(I,I), X11(I,I+1), LDX11, TAUQ1(I) )
X11(I,I) = ONE
CALL SLARF( 'R', P-I, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
$ X11(I+1,I), LDX11, WORK(ILARF) )
CALL SLARF( 'R', Q-P, Q-I+1, X11(I,I), LDX11, TAUQ1(I),
$ X21(M-Q+1,I), LDX21, WORK(ILARF) )
END DO
*
* Reduce the bottom-right portion of X21 to [ 0 I ]
*
DO I = P + 1, Q
CALL SLARFGP( Q-I+1, X21(M-Q+I-P,I), X21(M-Q+I-P,I+1), LDX21,
$ TAUQ1(I) )
X21(M-Q+I-P,I) = ONE
CALL SLARF( 'R', Q-I, Q-I+1, X21(M-Q+I-P,I), LDX21, TAUQ1(I),
$ X21(M-Q+I-P+1,I), LDX21, WORK(ILARF) )
END DO
*
RETURN
*
* End of SORBDB4
*
END
Reference in New Issue View Git Blame Copy Permalink