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dorbdb.f
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*> \brief \b DORBDB
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DORBDB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
* X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
* TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* CHARACTER SIGNS, TRANS
* INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
* $ Q
* ..
* .. Array Arguments ..
* DOUBLE PRECISION PHI( * ), THETA( * )
* DOUBLE PRECISION TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
* $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
* $ X21( LDX21, * ), X22( LDX22, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DORBDB 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] SIGNS
*> \verbatim
*> 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).
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows and columns in X.
*> \endverbatim
*>
*> \param[in] P
*> \verbatim
*> P is INTEGER
*> The number of rows in X11 and X12. 0 <= P <= M.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*> Q is INTEGER
*> The number of columns in X11 and X21. 0 <= Q <=
*> MIN(P,M-P,M-Q).
*> \endverbatim
*>
*> \param[in,out] X11
*> \verbatim
*> X11 is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDX11
*> \verbatim
*> LDX11 is INTEGER
*> The leading dimension of X11. If TRANS = 'N', then LDX11 >=
*> P; else LDX11 >= Q.
*> \endverbatim
*>
*> \param[in,out] X12
*> \verbatim
*> X12 is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDX12
*> \verbatim
*> LDX12 is INTEGER
*> The leading dimension of X12. If TRANS = 'N', then LDX12 >=
*> P; else LDX11 >= M-Q.
*> \endverbatim
*>
*> \param[in,out] X21
*> \verbatim
*> X21 is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDX21
*> \verbatim
*> LDX21 is INTEGER
*> The leading dimension of X21. If TRANS = 'N', then LDX21 >=
*> M-P; else LDX21 >= Q.
*> \endverbatim
*>
*> \param[in,out] X22
*> \verbatim
*> X22 is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] LDX22
*> \verbatim
*> LDX22 is INTEGER
*> The leading dimension of X22. If TRANS = 'N', then LDX22 >=
*> M-P; else LDX22 >= M-Q.
*> \endverbatim
*>
*> \param[out] THETA
*> \verbatim
*> THETA is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[out] PHI
*> \verbatim
*> PHI is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[out] TAUP1
*> \verbatim
*> TAUP1 is DOUBLE PRECISION array, dimension (P)
*> The scalar factors of the elementary reflectors that define
*> P1.
*> \endverbatim
*>
*> \param[out] TAUP2
*> \verbatim
*> TAUP2 is DOUBLE PRECISION array, dimension (M-P)
*> The scalar factors of the elementary reflectors that define
*> P2.
*> \endverbatim
*>
*> \param[out] TAUQ1
*> \verbatim
*> TAUQ1 is DOUBLE PRECISION array, dimension (Q)
*> The scalar factors of the elementary reflectors that define
*> Q1.
*> \endverbatim
*>
*> \param[out] TAUQ2
*> \verbatim
*> TAUQ2 is DOUBLE PRECISION array, dimension (M-Q)
*> The scalar factors of the elementary reflectors that define
*> Q2.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION 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.
*
*> \date December 2016
*
*> \ingroup doubleOTHERcomputational
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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 DORCSD for details.
*>
*> P1, P2, Q1, and Q2 are represented as products of elementary
*> reflectors. See DORCSD for details on generating P1, P2, Q1, and Q2
*> using DORGQR and DORGLQ.
*> \endverbatim
*
*> \par References:
* ================
*>
*> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
*> Algorithms, 50(1):33-65, 2009.
*>
* =====================================================================
SUBROUTINE DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
$ X21, LDX21, X22, LDX22, THETA, PHI, TAUP1,
$ TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER SIGNS, TRANS
INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
$ Q
* ..
* .. Array Arguments ..
DOUBLE PRECISION PHI( * ), THETA( * )
DOUBLE PRECISION TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
$ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
$ X21( LDX21, * ), X22( LDX22, * )
* ..
*
* ====================================================================
*
* .. Parameters ..
DOUBLE PRECISION REALONE
PARAMETER ( REALONE = 1.0D0 )
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
* ..
* .. Local Scalars ..
LOGICAL COLMAJOR, LQUERY
INTEGER I, LWORKMIN, LWORKOPT
DOUBLE PRECISION Z1, Z2, Z3, Z4
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DLARF, DLARFGP, DSCAL, XERBLA
* ..
* .. External Functions ..
DOUBLE PRECISION DNRM2
LOGICAL LSAME
EXTERNAL DNRM2, LSAME
* ..
* .. Intrinsic Functions
INTRINSIC ATAN2, COS, MAX, SIN
* ..
* .. Executable Statements ..
*
* Test input arguments
*
INFO = 0
COLMAJOR = .NOT. LSAME( TRANS, 'T' )
IF( .NOT. LSAME( SIGNS, 'O' ) ) THEN
Z1 = REALONE
Z2 = REALONE
Z3 = REALONE
Z4 = REALONE
ELSE
Z1 = REALONE
Z2 = -REALONE
Z3 = REALONE
Z4 = -REALONE
END IF
LQUERY = LWORK .EQ. -1
*
IF( M .LT. 0 ) THEN
INFO = -3
ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
INFO = -4
ELSE IF( Q .LT. 0 .OR. Q .GT. P .OR. Q .GT. M-P .OR.
$ Q .GT. M-Q ) THEN
INFO = -5
ELSE IF( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
INFO = -7
ELSE IF( .NOT.COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
INFO = -7
ELSE IF( COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
INFO = -9
ELSE IF( .NOT.COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
INFO = -9
ELSE IF( COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
INFO = -11
ELSE IF( .NOT.COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
INFO = -11
ELSE IF( COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
INFO = -13
ELSE IF( .NOT.COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
INFO = -13
END IF
*
* Compute workspace
*
IF( INFO .EQ. 0 ) THEN
LWORKOPT = M - Q
LWORKMIN = M - Q
WORK(1) = LWORKOPT
IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
INFO = -21
END IF
END IF
IF( INFO .NE. 0 ) THEN
CALL XERBLA( 'xORBDB', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Handle column-major and row-major separately
*
IF( COLMAJOR ) THEN
*
* Reduce columns 1, ..., Q of X11, X12, X21, and X22
*
DO I = 1, Q
*
IF( I .EQ. 1 ) THEN
CALL DSCAL( P-I+1, Z1, X11(I,I), 1 )
ELSE
CALL DSCAL( P-I+1, Z1*COS(PHI(I-1)), X11(I,I), 1 )
CALL DAXPY( P-I+1, -Z1*Z3*Z4*SIN(PHI(I-1)), X12(I,I-1),
$ 1, X11(I,I), 1 )
END IF
IF( I .EQ. 1 ) THEN
CALL DSCAL( M-P-I+1, Z2, X21(I,I), 1 )
ELSE
CALL DSCAL( M-P-I+1, Z2*COS(PHI(I-1)), X21(I,I), 1 )
CALL DAXPY( M-P-I+1, -Z2*Z3*Z4*SIN(PHI(I-1)), X22(I,I-1),
$ 1, X21(I,I), 1 )
END IF
*
THETA(I) = ATAN2( DNRM2( M-P-I+1, X21(I,I), 1 ),
$ DNRM2( P-I+1, X11(I,I), 1 ) )
*
IF( P .GT. I ) THEN
CALL DLARFGP( P-I+1, X11(I,I), X11(I+1,I), 1, TAUP1(I) )
ELSE IF( P .EQ. I ) THEN
CALL DLARFGP( P-I+1, X11(I,I), X11(I,I), 1, TAUP1(I) )
END IF
X11(I,I) = ONE
IF ( M-P .GT. I ) THEN
CALL DLARFGP( M-P-I+1, X21(I,I), X21(I+1,I), 1,
$ TAUP2(I) )
ELSE IF ( M-P .EQ. I ) THEN
CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I), 1, TAUP2(I) )
END IF
X21(I,I) = ONE
*
IF ( Q .GT. I ) THEN
CALL DLARF( 'L', P-I+1, Q-I, X11(I,I), 1, TAUP1(I),
$ X11(I,I+1), LDX11, WORK )
END IF
IF ( M-Q+1 .GT. I ) THEN
CALL DLARF( 'L', P-I+1, M-Q-I+1, X11(I,I), 1, TAUP1(I),
$ X12(I,I), LDX12, WORK )
END IF
IF ( Q .GT. I ) THEN
CALL DLARF( 'L', M-P-I+1, Q-I, X21(I,I), 1, TAUP2(I),
$ X21(I,I+1), LDX21, WORK )
END IF
IF ( M-Q+1 .GT. I ) THEN
CALL DLARF( 'L', M-P-I+1, M-Q-I+1, X21(I,I), 1, TAUP2(I),
$ X22(I,I), LDX22, WORK )
END IF
*
IF( I .LT. Q ) THEN
CALL DSCAL( Q-I, -Z1*Z3*SIN(THETA(I)), X11(I,I+1),
$ LDX11 )
CALL DAXPY( Q-I, Z2*Z3*COS(THETA(I)), X21(I,I+1), LDX21,
$ X11(I,I+1), LDX11 )
END IF
CALL DSCAL( M-Q-I+1, -Z1*Z4*SIN(THETA(I)), X12(I,I), LDX12 )
CALL DAXPY( M-Q-I+1, Z2*Z4*COS(THETA(I)), X22(I,I), LDX22,
$ X12(I,I), LDX12 )
*
IF( I .LT. Q )
$ PHI(I) = ATAN2( DNRM2( Q-I, X11(I,I+1), LDX11 ),
$ DNRM2( M-Q-I+1, X12(I,I), LDX12 ) )
*
IF( I .LT. Q ) THEN
IF ( Q-I .EQ. 1 ) THEN
CALL DLARFGP( Q-I, X11(I,I+1), X11(I,I+1), LDX11,
$ TAUQ1(I) )
ELSE
CALL DLARFGP( Q-I, X11(I,I+1), X11(I,I+2), LDX11,
$ TAUQ1(I) )
END IF
X11(I,I+1) = ONE
END IF
IF ( Q+I-1 .LT. M ) THEN
IF ( M-Q .EQ. I ) THEN
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
$ TAUQ2(I) )
ELSE
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
$ TAUQ2(I) )
END IF
END IF
X12(I,I) = ONE
*
IF( I .LT. Q ) THEN
CALL DLARF( 'R', P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
$ X11(I+1,I+1), LDX11, WORK )
CALL DLARF( 'R', M-P-I, Q-I, X11(I,I+1), LDX11, TAUQ1(I),
$ X21(I+1,I+1), LDX21, WORK )
END IF
IF ( P .GT. I ) THEN
CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
$ X12(I+1,I), LDX12, WORK )
END IF
IF ( M-P .GT. I ) THEN
CALL DLARF( 'R', M-P-I, M-Q-I+1, X12(I,I), LDX12,
$ TAUQ2(I), X22(I+1,I), LDX22, WORK )
END IF
*
END DO
*
* Reduce columns Q + 1, ..., P of X12, X22
*
DO I = Q + 1, P
*
CALL DSCAL( M-Q-I+1, -Z1*Z4, X12(I,I), LDX12 )
IF ( I .GE. M-Q ) THEN
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I), LDX12,
$ TAUQ2(I) )
ELSE
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I+1), LDX12,
$ TAUQ2(I) )
END IF
X12(I,I) = ONE
*
IF ( P .GT. I ) THEN
CALL DLARF( 'R', P-I, M-Q-I+1, X12(I,I), LDX12, TAUQ2(I),
$ X12(I+1,I), LDX12, WORK )
END IF
IF( M-P-Q .GE. 1 )
$ CALL DLARF( 'R', M-P-Q, M-Q-I+1, X12(I,I), LDX12,
$ TAUQ2(I), X22(Q+1,I), LDX22, WORK )
*
END DO
*
* Reduce columns P + 1, ..., M - Q of X12, X22
*
DO I = 1, M - P - Q
*
CALL DSCAL( M-P-Q-I+1, Z2*Z4, X22(Q+I,P+I), LDX22 )
IF ( I .EQ. M-P-Q ) THEN
CALL DLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I),
$ LDX22, TAUQ2(P+I) )
ELSE
CALL DLARFGP( M-P-Q-I+1, X22(Q+I,P+I), X22(Q+I,P+I+1),
$ LDX22, TAUQ2(P+I) )
END IF
X22(Q+I,P+I) = ONE
IF ( I .LT. M-P-Q ) THEN
CALL DLARF( 'R', M-P-Q-I, M-P-Q-I+1, X22(Q+I,P+I), LDX22,
$ TAUQ2(P+I), X22(Q+I+1,P+I), LDX22, WORK )
END IF
*
END DO
*
ELSE
*
* Reduce columns 1, ..., Q of X11, X12, X21, X22
*
DO I = 1, Q
*
IF( I .EQ. 1 ) THEN
CALL DSCAL( P-I+1, Z1, X11(I,I), LDX11 )
ELSE
CALL DSCAL( P-I+1, Z1*COS(PHI(I-1)), X11(I,I), LDX11 )
CALL DAXPY( P-I+1, -Z1*Z3*Z4*SIN(PHI(I-1)), X12(I-1,I),
$ LDX12, X11(I,I), LDX11 )
END IF
IF( I .EQ. 1 ) THEN
CALL DSCAL( M-P-I+1, Z2, X21(I,I), LDX21 )
ELSE
CALL DSCAL( M-P-I+1, Z2*COS(PHI(I-1)), X21(I,I), LDX21 )
CALL DAXPY( M-P-I+1, -Z2*Z3*Z4*SIN(PHI(I-1)), X22(I-1,I),
$ LDX22, X21(I,I), LDX21 )
END IF
*
THETA(I) = ATAN2( DNRM2( M-P-I+1, X21(I,I), LDX21 ),
$ DNRM2( P-I+1, X11(I,I), LDX11 ) )
*
CALL DLARFGP( P-I+1, X11(I,I), X11(I,I+1), LDX11, TAUP1(I) )
X11(I,I) = ONE
IF ( I .EQ. M-P ) THEN
CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I), LDX21,
$ TAUP2(I) )
ELSE
CALL DLARFGP( M-P-I+1, X21(I,I), X21(I,I+1), LDX21,
$ TAUP2(I) )
END IF
X21(I,I) = ONE
*
IF ( Q .GT. I ) THEN
CALL DLARF( 'R', Q-I, P-I+1, X11(I,I), LDX11, TAUP1(I),
$ X11(I+1,I), LDX11, WORK )
END IF
IF ( M-Q+1 .GT. I ) THEN
CALL DLARF( 'R', M-Q-I+1, P-I+1, X11(I,I), LDX11,
$ TAUP1(I), X12(I,I), LDX12, WORK )
END IF
IF ( Q .GT. I ) THEN
CALL DLARF( 'R', Q-I, M-P-I+1, X21(I,I), LDX21, TAUP2(I),
$ X21(I+1,I), LDX21, WORK )
END IF
IF ( M-Q+1 .GT. I ) THEN
CALL DLARF( 'R', M-Q-I+1, M-P-I+1, X21(I,I), LDX21,
$ TAUP2(I), X22(I,I), LDX22, WORK )
END IF
*
IF( I .LT. Q ) THEN
CALL DSCAL( Q-I, -Z1*Z3*SIN(THETA(I)), X11(I+1,I), 1 )
CALL DAXPY( Q-I, Z2*Z3*COS(THETA(I)), X21(I+1,I), 1,
$ X11(I+1,I), 1 )
END IF
CALL DSCAL( M-Q-I+1, -Z1*Z4*SIN(THETA(I)), X12(I,I), 1 )
CALL DAXPY( M-Q-I+1, Z2*Z4*COS(THETA(I)), X22(I,I), 1,
$ X12(I,I), 1 )
*
IF( I .LT. Q )
$ PHI(I) = ATAN2( DNRM2( Q-I, X11(I+1,I), 1 ),
$ DNRM2( M-Q-I+1, X12(I,I), 1 ) )
*
IF( I .LT. Q ) THEN
IF ( Q-I .EQ. 1) THEN
CALL DLARFGP( Q-I, X11(I+1,I), X11(I+1,I), 1,
$ TAUQ1(I) )
ELSE
CALL DLARFGP( Q-I, X11(I+1,I), X11(I+2,I), 1,
$ TAUQ1(I) )
END IF
X11(I+1,I) = ONE
END IF
IF ( M-Q .GT. I ) THEN
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1,
$ TAUQ2(I) )
ELSE
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I,I), 1,
$ TAUQ2(I) )
END IF
X12(I,I) = ONE
*
IF( I .LT. Q ) THEN
CALL DLARF( 'L', Q-I, P-I, X11(I+1,I), 1, TAUQ1(I),
$ X11(I+1,I+1), LDX11, WORK )
CALL DLARF( 'L', Q-I, M-P-I, X11(I+1,I), 1, TAUQ1(I),
$ X21(I+1,I+1), LDX21, WORK )
END IF
CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I),
$ X12(I,I+1), LDX12, WORK )
IF ( M-P-I .GT. 0 ) THEN
CALL DLARF( 'L', M-Q-I+1, M-P-I, X12(I,I), 1, TAUQ2(I),
$ X22(I,I+1), LDX22, WORK )
END IF
*
END DO
*
* Reduce columns Q + 1, ..., P of X12, X22
*
DO I = Q + 1, P
*
CALL DSCAL( M-Q-I+1, -Z1*Z4, X12(I,I), 1 )
CALL DLARFGP( M-Q-I+1, X12(I,I), X12(I+1,I), 1, TAUQ2(I) )
X12(I,I) = ONE
*
IF ( P .GT. I ) THEN
CALL DLARF( 'L', M-Q-I+1, P-I, X12(I,I), 1, TAUQ2(I),
$ X12(I,I+1), LDX12, WORK )
END IF
IF( M-P-Q .GE. 1 )
$ CALL DLARF( 'L', M-Q-I+1, M-P-Q, X12(I,I), 1, TAUQ2(I),
$ X22(I,Q+1), LDX22, WORK )
*
END DO
*
* Reduce columns P + 1, ..., M - Q of X12, X22
*
DO I = 1, M - P - Q
*
CALL DSCAL( M-P-Q-I+1, Z2*Z4, X22(P+I,Q+I), 1 )
IF ( M-P-Q .EQ. I ) THEN
CALL DLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I,Q+I), 1,
$ TAUQ2(P+I) )
ELSE
CALL DLARFGP( M-P-Q-I+1, X22(P+I,Q+I), X22(P+I+1,Q+I), 1,
$ TAUQ2(P+I) )
CALL DLARF( 'L', M-P-Q-I+1, M-P-Q-I, X22(P+I,Q+I), 1,
$ TAUQ2(P+I), X22(P+I,Q+I+1), LDX22, WORK )
END IF
X22(P+I,Q+I) = ONE
*
END DO
*
END IF
*
RETURN
*
* End of DORBDB
*
END