1       SUBROUTINE ZLAUUM( 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       COMPLEX*16         A( LDA, * )
 14 *     ..
 15 *
 16 *  Purpose
 17 *  =======
 18 *
 19 *  ZLAUUM computes the product U * U**H or L**H * 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) COMPLEX*16 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**H;
 46 *          if UPLO = 'L', the lower triangle of A is overwritten with
 47 *          the lower triangle of the product L**H * 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       COMPLEX*16         CONE
 62       PARAMETER          ( CONE = ( 1.0D+00.0D+0 ) )
 63 *     ..
 64 *     .. Local Scalars ..
 65       LOGICAL            UPPER
 66       INTEGER            I, IB, NB
 67 *     ..
 68 *     .. External Functions ..
 69       LOGICAL            LSAME
 70       INTEGER            ILAENV
 71       EXTERNAL           LSAME, ILAENV
 72 *     ..
 73 *     .. External Subroutines ..
 74       EXTERNAL           XERBLA, ZGEMM, ZHERK, ZLAUU2, ZTRMM
 75 *     ..
 76 *     .. Intrinsic Functions ..
 77       INTRINSIC          MAXMIN
 78 *     ..
 79 *     .. Executable Statements ..
 80 *
 81 *     Test the input parameters.
 82 *
 83       INFO = 0
 84       UPPER = LSAME( UPLO, 'U' )
 85       IF.NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
 86          INFO = -1
 87       ELSE IF( N.LT.0 ) THEN
 88          INFO = -2
 89       ELSE IF( LDA.LT.MAX1, N ) ) THEN
 90          INFO = -4
 91       END IF
 92       IF( INFO.NE.0 ) THEN
 93          CALL XERBLA( 'ZLAUUM'-INFO )
 94          RETURN
 95       END IF
 96 *
 97 *     Quick return if possible
 98 *
 99       IF( N.EQ.0 )
100      $   RETURN
101 *
102 *     Determine the block size for this environment.
103 *
104       NB = ILAENV( 1'ZLAUUM', UPLO, N, -1-1-1 )
105 *
106       IF( NB.LE.1 .OR. NB.GE.N ) THEN
107 *
108 *        Use unblocked code
109 *
110          CALL ZLAUU2( UPLO, N, A, LDA, INFO )
111       ELSE
112 *
113 *        Use blocked code
114 *
115          IF( UPPER ) THEN
116 *
117 *           Compute the product U * U**H.
118 *
119             DO 10 I = 1, N, NB
120                IB = MIN( NB, N-I+1 )
121                CALL ZTRMM( 'Right''Upper''Conjugate transpose',
122      $                     'Non-unit', I-1, IB, CONE, A( I, I ), LDA,
123      $                     A( 1, I ), LDA )
124                CALL ZLAUU2( 'Upper', IB, A( I, I ), LDA, INFO )
125                IF( I+IB.LE.N ) THEN
126                   CALL ZGEMM( 'No transpose''Conjugate transpose',
127      $                        I-1, IB, N-I-IB+1, CONE, A( 1, I+IB ),
128      $                        LDA, A( I, I+IB ), LDA, CONE, A( 1, I ),
129      $                        LDA )
130                   CALL ZHERK( 'Upper''No transpose', IB, N-I-IB+1,
131      $                        ONE, A( I, I+IB ), LDA, ONE, A( I, I ),
132      $                        LDA )
133                END IF
134    10       CONTINUE
135          ELSE
136 *
137 *           Compute the product L**H * L.
138 *
139             DO 20 I = 1, N, NB
140                IB = MIN( NB, N-I+1 )
141                CALL ZTRMM( 'Left''Lower''Conjugate transpose',
142      $                     'Non-unit', IB, I-1, CONE, A( I, I ), LDA,
143      $                     A( I, 1 ), LDA )
144                CALL ZLAUU2( 'Lower', IB, A( I, I ), LDA, INFO )
145                IF( I+IB.LE.N ) THEN
146                   CALL ZGEMM( 'Conjugate transpose''No transpose', IB,
147      $                        I-1, N-I-IB+1, CONE, A( I+IB, I ), LDA,
148      $                        A( I+IB, 1 ), LDA, CONE, A( I, 1 ), LDA )
149                   CALL ZHERK( 'Lower''Conjugate transpose', IB,
150      $                        N-I-IB+1, ONE, A( I+IB, I ), LDA, ONE,
151      $                        A( I, I ), LDA )
152                END IF
153    20       CONTINUE
154          END IF
155       END IF
156 *
157       RETURN
158 *
159 *     End of ZLAUUM
160 *
161       END