*> \brief \b DLAUUM 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 *> Download DLAUUM + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAUUM 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 DOUBLE PRECISION 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. * *> \ingroup doubleOTHERauxiliary * * ===================================================================== SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL UPPER INTEGER I, IB, NB * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL DGEMM, DLAUU2, DSYRK, DTRMM, 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( 'DLAUUM', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Determine the block size for this environment. * NB = ILAENV( 1, 'DLAUUM', UPLO, N, -1, -1, -1 ) * IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL DLAUU2( 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 DTRMM( 'Right', 'Upper', 'Transpose', 'Non-unit', \$ I-1, IB, ONE, A( I, I ), LDA, A( 1, I ), \$ LDA ) CALL DLAUU2( 'Upper', IB, A( I, I ), LDA, INFO ) IF( I+IB.LE.N ) THEN CALL DGEMM( '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 DSYRK( '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 DTRMM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB, \$ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA ) CALL DLAUU2( 'Lower', IB, A( I, I ), LDA, INFO ) IF( I+IB.LE.N ) THEN CALL DGEMM( '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 DSYRK( '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 DLAUUM * END