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added lapack 3.7.0 with latest patches from git

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Werner Saar
2017-01-06 11:48:40 +01:00
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*> \brief \b CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CLAQPS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/claqps.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/claqps.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/claqps.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
* VN2, AUXV, F, LDF )
*
* .. Scalar Arguments ..
* INTEGER KB, LDA, LDF, M, N, NB, OFFSET
* ..
* .. Array Arguments ..
* INTEGER JPVT( * )
* REAL VN1( * ), VN2( * )
* COMPLEX A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLAQPS computes a step of QR factorization with column pivoting
*> of a complex M-by-N matrix A by using Blas-3. It tries to factorize
*> NB columns from A starting from the row OFFSET+1, and updates all
*> of the matrix with Blas-3 xGEMM.
*>
*> In some cases, due to catastrophic cancellations, it cannot
*> factorize NB columns. Hence, the actual number of factorized
*> columns is returned in KB.
*>
*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0
*> \endverbatim
*>
*> \param[in] OFFSET
*> \verbatim
*> OFFSET is INTEGER
*> The number of rows of A that have been factorized in
*> previous steps.
*> \endverbatim
*>
*> \param[in] NB
*> \verbatim
*> NB is INTEGER
*> The number of columns to factorize.
*> \endverbatim
*>
*> \param[out] KB
*> \verbatim
*> KB is INTEGER
*> The number of columns actually factorized.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the M-by-N matrix A.
*> On exit, block A(OFFSET+1:M,1:KB) is the triangular
*> factor obtained and block A(1:OFFSET,1:N) has been
*> accordingly pivoted, but no factorized.
*> The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
*> been updated.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] JPVT
*> \verbatim
*> JPVT is INTEGER array, dimension (N)
*> JPVT(I) = K <==> Column K of the full matrix A has been
*> permuted into position I in AP.
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is COMPLEX array, dimension (KB)
*> The scalar factors of the elementary reflectors.
*> \endverbatim
*>
*> \param[in,out] VN1
*> \verbatim
*> VN1 is REAL array, dimension (N)
*> The vector with the partial column norms.
*> \endverbatim
*>
*> \param[in,out] VN2
*> \verbatim
*> VN2 is REAL array, dimension (N)
*> The vector with the exact column norms.
*> \endverbatim
*>
*> \param[in,out] AUXV
*> \verbatim
*> AUXV is COMPLEX array, dimension (NB)
*> Auxiliar vector.
*> \endverbatim
*>
*> \param[in,out] F
*> \verbatim
*> F is COMPLEX array, dimension (LDF,NB)
*> Matrix F**H = L * Y**H * A.
*> \endverbatim
*>
*> \param[in] LDF
*> \verbatim
*> LDF is INTEGER
*> The leading dimension of the array F. LDF >= max(1,N).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complexOTHERauxiliary
*
*> \par Contributors:
* ==================
*>
*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
*> X. Sun, Computer Science Dept., Duke University, USA
*>
*> \n
*> Partial column norm updating strategy modified on April 2011
*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
*> University of Zagreb, Croatia.
*
*> \par References:
* ================
*>
*> LAPACK Working Note 176
*
*> \htmlonly
*> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
*> \endhtmlonly
*
* =====================================================================
SUBROUTINE CLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
$ VN2, AUXV, F, LDF )
*
* -- LAPACK auxiliary 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 ..
INTEGER KB, LDA, LDF, M, N, NB, OFFSET
* ..
* .. Array Arguments ..
INTEGER JPVT( * )
REAL VN1( * ), VN2( * )
COMPLEX A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
COMPLEX CZERO, CONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0,
$ CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER ITEMP, J, K, LASTRK, LSTICC, PVT, RK
REAL TEMP, TEMP2, TOL3Z
COMPLEX AKK
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CGEMV, CLARFG, CSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, CONJG, MAX, MIN, NINT, REAL, SQRT
* ..
* .. External Functions ..
INTEGER ISAMAX
REAL SCNRM2, SLAMCH
EXTERNAL ISAMAX, SCNRM2, SLAMCH
* ..
* .. Executable Statements ..
*
LASTRK = MIN( M, N+OFFSET )
LSTICC = 0
K = 0
TOL3Z = SQRT(SLAMCH('Epsilon'))
*
* Beginning of while loop.
*
10 CONTINUE
IF( ( K.LT.NB ) .AND. ( LSTICC.EQ.0 ) ) THEN
K = K + 1
RK = OFFSET + K
*
* Determine ith pivot column and swap if necessary
*
PVT = ( K-1 ) + ISAMAX( N-K+1, VN1( K ), 1 )
IF( PVT.NE.K ) THEN
CALL CSWAP( M, A( 1, PVT ), 1, A( 1, K ), 1 )
CALL CSWAP( K-1, F( PVT, 1 ), LDF, F( K, 1 ), LDF )
ITEMP = JPVT( PVT )
JPVT( PVT ) = JPVT( K )
JPVT( K ) = ITEMP
VN1( PVT ) = VN1( K )
VN2( PVT ) = VN2( K )
END IF
*
* Apply previous Householder reflectors to column K:
* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**H.
*
IF( K.GT.1 ) THEN
DO 20 J = 1, K - 1
F( K, J ) = CONJG( F( K, J ) )
20 CONTINUE
CALL CGEMV( 'No transpose', M-RK+1, K-1, -CONE, A( RK, 1 ),
$ LDA, F( K, 1 ), LDF, CONE, A( RK, K ), 1 )
DO 30 J = 1, K - 1
F( K, J ) = CONJG( F( K, J ) )
30 CONTINUE
END IF
*
* Generate elementary reflector H(k).
*
IF( RK.LT.M ) THEN
CALL CLARFG( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) )
ELSE
CALL CLARFG( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) )
END IF
*
AKK = A( RK, K )
A( RK, K ) = CONE
*
* Compute Kth column of F:
*
* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**H*A(RK:M,K).
*
IF( K.LT.N ) THEN
CALL CGEMV( 'Conjugate transpose', M-RK+1, N-K, TAU( K ),
$ A( RK, K+1 ), LDA, A( RK, K ), 1, CZERO,
$ F( K+1, K ), 1 )
END IF
*
* Padding F(1:K,K) with zeros.
*
DO 40 J = 1, K
F( J, K ) = CZERO
40 CONTINUE
*
* Incremental updating of F:
* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**H
* *A(RK:M,K).
*
IF( K.GT.1 ) THEN
CALL CGEMV( 'Conjugate transpose', M-RK+1, K-1, -TAU( K ),
$ A( RK, 1 ), LDA, A( RK, K ), 1, CZERO,
$ AUXV( 1 ), 1 )
*
CALL CGEMV( 'No transpose', N, K-1, CONE, F( 1, 1 ), LDF,
$ AUXV( 1 ), 1, CONE, F( 1, K ), 1 )
END IF
*
* Update the current row of A:
* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**H.
*
IF( K.LT.N ) THEN
CALL CGEMM( 'No transpose', 'Conjugate transpose', 1, N-K,
$ K, -CONE, A( RK, 1 ), LDA, F( K+1, 1 ), LDF,
$ CONE, A( RK, K+1 ), LDA )
END IF
*
* Update partial column norms.
*
IF( RK.LT.LASTRK ) THEN
DO 50 J = K + 1, N
IF( VN1( J ).NE.ZERO ) THEN
*
* NOTE: The following 4 lines follow from the analysis in
* Lapack Working Note 176.
*
TEMP = ABS( A( RK, J ) ) / VN1( J )
TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2
IF( TEMP2 .LE. TOL3Z ) THEN
VN2( J ) = REAL( LSTICC )
LSTICC = J
ELSE
VN1( J ) = VN1( J )*SQRT( TEMP )
END IF
END IF
50 CONTINUE
END IF
*
A( RK, K ) = AKK
*
* End of while loop.
*
GO TO 10
END IF
KB = K
RK = OFFSET + KB
*
* Apply the block reflector to the rest of the matrix:
* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**H.
*
IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
CALL CGEMM( 'No transpose', 'Conjugate transpose', M-RK, N-KB,
$ KB, -CONE, A( RK+1, 1 ), LDA, F( KB+1, 1 ), LDF,
$ CONE, A( RK+1, KB+1 ), LDA )
END IF
*
* Recomputation of difficult columns.
*
60 CONTINUE
IF( LSTICC.GT.0 ) THEN
ITEMP = NINT( VN2( LSTICC ) )
VN1( LSTICC ) = SCNRM2( M-RK, A( RK+1, LSTICC ), 1 )
*
* NOTE: The computation of VN1( LSTICC ) relies on the fact that
* SNRM2 does not fail on vectors with norm below the value of
* SQRT(DLAMCH('S'))
*
VN2( LSTICC ) = VN1( LSTICC )
LSTICC = ITEMP
GO TO 60
END IF
*
RETURN
*
* End of CLAQPS
*
END