dlauum.f

          SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDA, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DLAUUM computes the product U * U' or L' * 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.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          Specifies whether the triangular factor stored in the array A
    *          is upper or lower triangular:
    *          = 'U':  Upper triangular
    *          = 'L':  Lower triangular
    *
    *  N       (input) INTEGER
    *          The order of the triangular factor U or L.  N >= 0.
    *
    *  A       (input/output) 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';
    *          if UPLO = 'L', the lower triangle of A is overwritten with
    *          the lower triangle of the product L' * L.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -k, the k-th argument had an illegal value
    *
    *  =====================================================================
    *
    *     .. 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'.
    *
                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' * 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