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*> \brief \b DORBDB5
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DORBDB5 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorbdb5.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorbdb5.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorbdb5.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DORBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
* LDQ2, WORK, LWORK, INFO )
*
* .. Scalar Arguments ..
* INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
* $ N
* ..
* .. Array Arguments ..
* DOUBLE PRECISION Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*>\verbatim
*>
*> DORBDB5 orthogonalizes the column vector
*> X = [ X1 ]
*> [ X2 ]
*> with respect to the columns of
*> Q = [ Q1 ] .
*> [ Q2 ]
*> The columns of Q must be orthonormal.
*>
*> If the projection is zero according to Kahan's "twice is enough"
*> criterion, then some other vector from the orthogonal complement
*> is returned. This vector is chosen in an arbitrary but deterministic
*> way.
*>
*>\endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M1
*> \verbatim
*> M1 is INTEGER
*> The dimension of X1 and the number of rows in Q1. 0 <= M1.
*> \endverbatim
*>
*> \param[in] M2
*> \verbatim
*> M2 is INTEGER
*> The dimension of X2 and the number of rows in Q2. 0 <= M2.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns in Q1 and Q2. 0 <= N.
*> \endverbatim
*>
*> \param[in,out] X1
*> \verbatim
*> X1 is DOUBLE PRECISION array, dimension (M1)
*> On entry, the top part of the vector to be orthogonalized.
*> On exit, the top part of the projected vector.
*> \endverbatim
*>
*> \param[in] INCX1
*> \verbatim
*> INCX1 is INTEGER
*> Increment for entries of X1.
*> \endverbatim
*>
*> \param[in,out] X2
*> \verbatim
*> X2 is DOUBLE PRECISION array, dimension (M2)
*> On entry, the bottom part of the vector to be
*> orthogonalized. On exit, the bottom part of the projected
*> vector.
*> \endverbatim
*>
*> \param[in] INCX2
*> \verbatim
*> INCX2 is INTEGER
*> Increment for entries of X2.
*> \endverbatim
*>
*> \param[in] Q1
*> \verbatim
*> Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
*> The top part of the orthonormal basis matrix.
*> \endverbatim
*>
*> \param[in] LDQ1
*> \verbatim
*> LDQ1 is INTEGER
*> The leading dimension of Q1. LDQ1 >= M1.
*> \endverbatim
*>
*> \param[in] Q2
*> \verbatim
*> Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
*> The bottom part of the orthonormal basis matrix.
*> \endverbatim
*>
*> \param[in] LDQ2
*> \verbatim
*> LDQ2 is INTEGER
*> The leading dimension of Q2. LDQ2 >= M2.
*> \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 >= N.
*> \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 July 2012
*
*> \ingroup doubleOTHERcomputational
*
* =====================================================================
SUBROUTINE DORBDB5( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
$ LDQ2, 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..--
* July 2012
*
* .. Scalar Arguments ..
INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
$ N
* ..
* .. Array Arguments ..
DOUBLE PRECISION Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
INTEGER CHILDINFO, I, J
* ..
* .. External Subroutines ..
EXTERNAL DORBDB6, XERBLA
* ..
* .. External Functions ..
DOUBLE PRECISION DNRM2
EXTERNAL DNRM2
* ..
* .. Intrinsic Function ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test input arguments
*
INFO = 0
IF( M1 .LT. 0 ) THEN
INFO = -1
ELSE IF( M2 .LT. 0 ) THEN
INFO = -2
ELSE IF( N .LT. 0 ) THEN
INFO = -3
ELSE IF( INCX1 .LT. 1 ) THEN
INFO = -5
ELSE IF( INCX2 .LT. 1 ) THEN
INFO = -7
ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
INFO = -9
ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
INFO = -11
ELSE IF( LWORK .LT. N ) THEN
INFO = -13
END IF
*
IF( INFO .NE. 0 ) THEN
CALL XERBLA( 'DORBDB5', -INFO )
RETURN
END IF
*
* Project X onto the orthogonal complement of Q
*
CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2,
$ WORK, LWORK, CHILDINFO )
*
* If the projection is nonzero, then return
*
IF( DNRM2(M1,X1,INCX1) .NE. ZERO
$ .OR. DNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
RETURN
END IF
*
* Project each standard basis vector e_1,...,e_M1 in turn, stopping
* when a nonzero projection is found
*
DO I = 1, M1
DO J = 1, M1
X1(J) = ZERO
END DO
X1(I) = ONE
DO J = 1, M2
X2(J) = ZERO
END DO
CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
$ LDQ2, WORK, LWORK, CHILDINFO )
IF( DNRM2(M1,X1,INCX1) .NE. ZERO
$ .OR. DNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
RETURN
END IF
END DO
*
* Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn,
* stopping when a nonzero projection is found
*
DO I = 1, M2
DO J = 1, M1
X1(J) = ZERO
END DO
DO J = 1, M2
X2(J) = ZERO
END DO
X2(I) = ONE
CALL DORBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
$ LDQ2, WORK, LWORK, CHILDINFO )
IF( DNRM2(M1,X1,INCX1) .NE. ZERO
$ .OR. DNRM2(M2,X2,INCX2) .NE. ZERO ) THEN
RETURN
END IF
END DO
*
RETURN
*
* End of DORBDB5
*
END
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