Refs #324. Upgrade LAPACK to 3.5.0 version.
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Zhang Xianyi
313
lapack-netlib/SRC/cunbdb6.f
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313
lapack-netlib/SRC/cunbdb6.f
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*> \brief \b CUNBDB6
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download CUNBDB6 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cunbdb6.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunbdb6.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunbdb6.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
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* LDQ2, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
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* $ N
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* ..
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* .. Array Arguments ..
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* COMPLEX Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
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* ..
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*
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*
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*> \par Purpose:
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*> =============
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*>
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*>\verbatim
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*>
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*> CUNBDB6 orthogonalizes the column vector
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*> X = [ X1 ]
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*> [ X2 ]
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*> with respect to the columns of
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*> Q = [ Q1 ] .
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*> [ Q2 ]
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*> The columns of Q must be orthonormal.
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*>
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*> If the projection is zero according to Kahan's "twice is enough"
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*> criterion, then the zero vector is returned.
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*>
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*>\endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M1
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*> \verbatim
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*> M1 is INTEGER
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*> The dimension of X1 and the number of rows in Q1. 0 <= M1.
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*> \endverbatim
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*>
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*> \param[in] M2
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*> \verbatim
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*> M2 is INTEGER
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*> The dimension of X2 and the number of rows in Q2. 0 <= M2.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns in Q1 and Q2. 0 <= N.
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*> \endverbatim
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*>
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*> \param[in,out] X1
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*> \verbatim
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*> X1 is COMPLEX array, dimension (M1)
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*> On entry, the top part of the vector to be orthogonalized.
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*> On exit, the top part of the projected vector.
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*> \endverbatim
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*>
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*> \param[in] INCX1
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*> \verbatim
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*> INCX1 is INTEGER
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*> Increment for entries of X1.
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*> \endverbatim
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*>
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*> \param[in,out] X2
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*> \verbatim
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*> X2 is COMPLEX array, dimension (M2)
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*> On entry, the bottom part of the vector to be
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*> orthogonalized. On exit, the bottom part of the projected
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*> vector.
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*> \endverbatim
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*>
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*> \param[in] INCX2
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*> \verbatim
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*> INCX2 is INTEGER
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*> Increment for entries of X2.
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*> \endverbatim
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*>
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*> \param[in] Q1
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*> \verbatim
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*> Q1 is COMPLEX array, dimension (LDQ1, N)
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*> The top part of the orthonormal basis matrix.
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*> \endverbatim
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*>
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*> \param[in] LDQ1
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*> \verbatim
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*> LDQ1 is INTEGER
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*> The leading dimension of Q1. LDQ1 >= M1.
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*> \endverbatim
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*>
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*> \param[in] Q2
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*> \verbatim
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*> Q2 is COMPLEX array, dimension (LDQ2, N)
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*> The bottom part of the orthonormal basis matrix.
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*> \endverbatim
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*>
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*> \param[in] LDQ2
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*> \verbatim
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*> LDQ2 is INTEGER
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*> The leading dimension of Q2. LDQ2 >= M2.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= N.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit.
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*> < 0: if INFO = -i, the i-th argument had an illegal value.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date July 2012
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*
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*> \ingroup complexOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE CUNBDB6( M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2,
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$ LDQ2, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine (version 3.5.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* July 2012
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*
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* .. Scalar Arguments ..
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INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
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$ N
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* ..
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* .. Array Arguments ..
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COMPLEX Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ALPHASQ, REALONE, REALZERO
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PARAMETER ( ALPHASQ = 0.01E0, REALONE = 1.0E0,
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$ REALZERO = 0.0E0 )
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COMPLEX NEGONE, ONE, ZERO
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PARAMETER ( NEGONE = (-1.0E0,0.0E0), ONE = (1.0E0,0.0E0),
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$ ZERO = (0.0E0,0.0E0) )
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* ..
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* .. Local Scalars ..
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INTEGER I
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REAL NORMSQ1, NORMSQ2, SCL1, SCL2, SSQ1, SSQ2
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEMV, CLASSQ, XERBLA
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* ..
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* .. Intrinsic Function ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test input arguments
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*
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INFO = 0
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IF( M1 .LT. 0 ) THEN
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INFO = -1
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ELSE IF( M2 .LT. 0 ) THEN
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INFO = -2
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ELSE IF( N .LT. 0 ) THEN
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INFO = -3
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ELSE IF( INCX1 .LT. 1 ) THEN
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INFO = -5
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ELSE IF( INCX2 .LT. 1 ) THEN
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INFO = -7
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ELSE IF( LDQ1 .LT. MAX( 1, M1 ) ) THEN
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INFO = -9
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ELSE IF( LDQ2 .LT. MAX( 1, M2 ) ) THEN
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INFO = -11
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ELSE IF( LWORK .LT. N ) THEN
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INFO = -13
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END IF
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*
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IF( INFO .NE. 0 ) THEN
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CALL XERBLA( 'CUNBDB6', -INFO )
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RETURN
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END IF
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*
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* First, project X onto the orthogonal complement of Q's column
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* space
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*
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SCL1 = REALZERO
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SSQ1 = REALONE
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CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
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SCL2 = REALZERO
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SSQ2 = REALONE
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CALL CLASSQ( M2, X2, INCX2, SCL2, SSQ2 )
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NORMSQ1 = SCL1**2*SSQ1 + SCL2**2*SSQ2
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*
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IF( M1 .EQ. 0 ) THEN
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DO I = 1, N
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WORK(I) = ZERO
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END DO
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ELSE
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CALL CGEMV( 'C', M1, N, ONE, Q1, LDQ1, X1, INCX1, ZERO, WORK,
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$ 1 )
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END IF
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*
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CALL CGEMV( 'C', M2, N, ONE, Q2, LDQ2, X2, INCX2, ONE, WORK, 1 )
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*
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CALL CGEMV( 'N', M1, N, NEGONE, Q1, LDQ1, WORK, 1, ONE, X1,
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$ INCX1 )
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CALL CGEMV( 'N', M2, N, NEGONE, Q2, LDQ2, WORK, 1, ONE, X2,
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$ INCX2 )
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*
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SCL1 = REALZERO
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SSQ1 = REALONE
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CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
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SCL2 = REALZERO
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SSQ2 = REALONE
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CALL CLASSQ( M2, X2, INCX2, SCL2, SSQ2 )
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NORMSQ2 = SCL1**2*SSQ1 + SCL2**2*SSQ2
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*
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* If projection is sufficiently large in norm, then stop.
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* If projection is zero, then stop.
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* Otherwise, project again.
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*
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IF( NORMSQ2 .GE. ALPHASQ*NORMSQ1 ) THEN
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RETURN
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END IF
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*
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IF( NORMSQ2 .EQ. ZERO ) THEN
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RETURN
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END IF
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*
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NORMSQ1 = NORMSQ2
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*
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DO I = 1, N
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WORK(I) = ZERO
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END DO
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*
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IF( M1 .EQ. 0 ) THEN
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DO I = 1, N
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WORK(I) = ZERO
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END DO
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ELSE
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CALL CGEMV( 'C', M1, N, ONE, Q1, LDQ1, X1, INCX1, ZERO, WORK,
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$ 1 )
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END IF
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*
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CALL CGEMV( 'C', M2, N, ONE, Q2, LDQ2, X2, INCX2, ONE, WORK, 1 )
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*
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CALL CGEMV( 'N', M1, N, NEGONE, Q1, LDQ1, WORK, 1, ONE, X1,
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$ INCX1 )
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CALL CGEMV( 'N', M2, N, NEGONE, Q2, LDQ2, WORK, 1, ONE, X2,
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$ INCX2 )
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*
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SCL1 = REALZERO
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SSQ1 = REALONE
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CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
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SCL2 = REALZERO
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SSQ2 = REALONE
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CALL CLASSQ( M1, X1, INCX1, SCL1, SSQ1 )
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NORMSQ2 = SCL1**2*SSQ1 + SCL2**2*SSQ2
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*
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* If second projection is sufficiently large in norm, then do
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* nothing more. Alternatively, if it shrunk significantly, then
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* truncate it to zero.
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*
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IF( NORMSQ2 .LT. ALPHASQ*NORMSQ1 ) THEN
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DO I = 1, M1
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X1(I) = ZERO
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END DO
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DO I = 1, M2
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X2(I) = ZERO
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END DO
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END IF
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*
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RETURN
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*
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* End of CUNBDB6
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*
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END
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