1       SUBROUTINE DLAUUM( UPLO, N, A, LDA, INFO )
  2 *
  3 *  -- LAPACK auxiliary routine (version 3.3.1) --
  4 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  5 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  6 *  -- April 2011                                                      --
  7 *
  8 *     .. Scalar Arguments ..
  9       CHARACTER          UPLO
 10       INTEGER            INFO, LDA, N
 11 *     ..
 12 *     .. Array Arguments ..
 13       DOUBLE PRECISION   A( LDA, * )
 14 *     ..
 15 *
 16 *  Purpose
 17 *  =======
 18 *
 19 *  DLAUUM computes the product U * U**T or L**T * L, where the triangular
 20 *  factor U or L is stored in the upper or lower triangular part of
 21 *  the array A.
 22 *
 23 *  If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
 24 *  overwriting the factor U in A.
 25 *  If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
 26 *  overwriting the factor L in A.
 27 *
 28 *  This is the blocked form of the algorithm, calling Level 3 BLAS.
 29 *
 30 *  Arguments
 31 *  =========
 32 *
 33 *  UPLO    (input) CHARACTER*1
 34 *          Specifies whether the triangular factor stored in the array A
 35 *          is upper or lower triangular:
 36 *          = 'U':  Upper triangular
 37 *          = 'L':  Lower triangular
 38 *
 39 *  N       (input) INTEGER
 40 *          The order of the triangular factor U or L.  N >= 0.
 41 *
 42 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 43 *          On entry, the triangular factor U or L.
 44 *          On exit, if UPLO = 'U', the upper triangle of A is
 45 *          overwritten with the upper triangle of the product U * U**T;
 46 *          if UPLO = 'L', the lower triangle of A is overwritten with
 47 *          the lower triangle of the product L**T * L.
 48 *
 49 *  LDA     (input) INTEGER
 50 *          The leading dimension of the array A.  LDA >= max(1,N).
 51 *
 52 *  INFO    (output) INTEGER
 53 *          = 0: successful exit
 54 *          < 0: if INFO = -k, the k-th argument had an illegal value
 55 *
 56 *  =====================================================================
 57 *
 58 *     .. Parameters ..
 59       DOUBLE PRECISION   ONE
 60       PARAMETER          ( ONE = 1.0D+0 )
 61 *     ..
 62 *     .. Local Scalars ..
 63       LOGICAL            UPPER
 64       INTEGER            I, IB, NB
 65 *     ..
 66 *     .. External Functions ..
 67       LOGICAL            LSAME
 68       INTEGER            ILAENV
 69       EXTERNAL           LSAME, ILAENV
 70 *     ..
 71 *     .. External Subroutines ..
 72       EXTERNAL           DGEMM, DLAUU2, DSYRK, DTRMM, XERBLA
 73 *     ..
 74 *     .. Intrinsic Functions ..
 75       INTRINSIC          MAXMIN
 76 *     ..
 77 *     .. Executable Statements ..
 78 *
 79 *     Test the input parameters.
 80 *
 81       INFO = 0
 82       UPPER = LSAME( UPLO, 'U' )
 83       IF.NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
 84          INFO = -1
 85       ELSE IF( N.LT.0 ) THEN
 86          INFO = -2
 87       ELSE IF( LDA.LT.MAX1, N ) ) THEN
 88          INFO = -4
 89       END IF
 90       IF( INFO.NE.0 ) THEN
 91          CALL XERBLA( 'DLAUUM'-INFO )
 92          RETURN
 93       END IF
 94 *
 95 *     Quick return if possible
 96 *
 97       IF( N.EQ.0 )
 98      $   RETURN
 99 *
100 *     Determine the block size for this environment.
101 *
102       NB = ILAENV( 1'DLAUUM', UPLO, N, -1-1-1 )
103 *
104       IF( NB.LE.1 .OR. NB.GE.N ) THEN
105 *
106 *        Use unblocked code
107 *
108          CALL DLAUU2( UPLO, N, A, LDA, INFO )
109       ELSE
110 *
111 *        Use blocked code
112 *
113          IF( UPPER ) THEN
114 *
115 *           Compute the product U * U**T.
116 *
117             DO 10 I = 1, N, NB
118                IB = MIN( NB, N-I+1 )
119                CALL DTRMM( 'Right''Upper''Transpose''Non-unit',
120      $                     I-1, IB, ONE, A( I, I ), LDA, A( 1, I ),
121      $                     LDA )
122                CALL DLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
123                IF( I+IB.LE.N ) THEN
124                   CALL DGEMM( 'No transpose''Transpose', I-1, IB,
125      $                        N-I-IB+1, ONE, A( 1, I+IB ), LDA,
126      $                        A( I, I+IB ), LDA, ONE, A( 1, I ), LDA )
127                   CALL DSYRK( 'Upper''No transpose', IB, N-I-IB+1,
128      $                        ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
129      $                        LDA )
130                END IF
131    10       CONTINUE
132          ELSE
133 *
134 *           Compute the product L**T * L.
135 *
136             DO 20 I = 1, N, NB
137                IB = MIN( NB, N-I+1 )
138                CALL DTRMM( 'Left''Lower''Transpose''Non-unit', IB,
139      $                     I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA )
140                CALL DLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
141                IF( I+IB.LE.N ) THEN
142                   CALL DGEMM( 'Transpose''No transpose', IB, I-1,
143      $                        N-I-IB+1, ONE, A( I+IB, I ), LDA,
144      $                        A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA )
145                   CALL DSYRK( 'Lower''Transpose', IB, N-I-IB+1, ONE,
146      $                        A( I+IB, I ), LDA, ONE, A( I, I ), LDA )
147                END IF
148    20       CONTINUE
149          END IF
150       END IF
151 *
152       RETURN
153 *
154 *     End of DLAUUM
155 *
156       END