*> \brief \b SLAUUM computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm).
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slauum.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SLAUUM( UPLO, N, A, LDA, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
* REAL A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLAUUM computes the product U * U**T or L**T * L, where the triangular
*> factor U or L is stored in the upper or lower triangular part of
*> the array A.
*>
*> If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
*> overwriting the factor U in A.
*> If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
*> overwriting the factor L in A.
*>
*> This is the blocked form of the algorithm, calling Level 3 BLAS.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the triangular factor stored in the array A
*> is upper or lower triangular:
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the triangular factor U or L. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is REAL array, dimension (LDA,N)
*> On entry, the triangular factor U or L.
*> On exit, if UPLO = 'U', the upper triangle of A is
*> overwritten with the upper triangle of the product U * U**T;
*> if UPLO = 'L', the lower triangle of A is overwritten with
*> the lower triangle of the product L**T * L.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -k, the k-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 realOTHERauxiliary
*
* =====================================================================
SUBROUTINE SLAUUM( UPLO, N, A, LDA, INFO )
*
* -- 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 ..
CHARACTER UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
REAL A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IB, NB
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLAUU2, SSYRK, STRMM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SLAUUM', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Determine the block size for this environment.
*
NB = ILAENV( 1, 'SLAUUM', UPLO, N, -1, -1, -1 )
*
IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code
*
CALL SLAUU2( UPLO, N, A, LDA, INFO )
ELSE
*
* Use blocked code
*
IF( UPPER ) THEN
*
* Compute the product U * U**T.
*
DO 10 I = 1, N, NB
IB = MIN( NB, N-I+1 )
CALL STRMM( 'Right', 'Upper', 'Transpose', 'Non-unit',
$ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
$ LDA )
CALL SLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
IF( I+IB.LE.N ) THEN
CALL SGEMM( 'No transpose', 'Transpose', I-1, IB,
$ N-I-IB+1, ONE, A( 1, I+IB ), LDA,
$ A( I, I+IB ), LDA, ONE, A( 1, I ), LDA )
CALL SSYRK( 'Upper', 'No transpose', IB, N-I-IB+1,
$ ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
$ LDA )
END IF
10 CONTINUE
ELSE
*
* Compute the product L**T * L.
*
DO 20 I = 1, N, NB
IB = MIN( NB, N-I+1 )
CALL STRMM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB,
$ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
CALL SLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
IF( I+IB.LE.N ) THEN
CALL SGEMM( 'Transpose', 'No transpose', IB, I-1,
$ N-I-IB+1, ONE, A( I+IB, I ), LDA,
$ A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA )
CALL SSYRK( 'Lower', 'Transpose', IB, N-I-IB+1, ONE,
$ A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
END IF
20 CONTINUE
END IF
END IF
*
RETURN
*
* End of SLAUUM
*
END