1       SUBROUTINE ZSYR( UPLO, N, ALPHA, X, INCX, A, LDA )
  2 *
  3 *  -- LAPACK auxiliary routine (version 3.2) --
  4 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  5 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  6 *     November 2006
  7 *
  8 *     .. Scalar Arguments ..
  9       CHARACTER          UPLO
 10       INTEGER            INCX, LDA, N
 11       COMPLEX*16         ALPHA
 12 *     ..
 13 *     .. Array Arguments ..
 14       COMPLEX*16         A( LDA, * ), X( * )
 15 *     ..
 16 *
 17 *  Purpose
 18 *  =======
 19 *
 20 *  ZSYR   performs the symmetric rank 1 operation
 21 *
 22 *     A := alpha*x*x**H + A,
 23 *
 24 *  where alpha is a complex scalar, x is an n element vector and A is an
 25 *  n by n symmetric matrix.
 26 *
 27 *  Arguments
 28 *  ==========
 29 *
 30 *  UPLO     (input) CHARACTER*1
 31 *           On entry, UPLO specifies whether the upper or lower
 32 *           triangular part of the array A is to be referenced as
 33 *           follows:
 34 *
 35 *              UPLO = 'U' or 'u'   Only the upper triangular part of A
 36 *                                  is to be referenced.
 37 *
 38 *              UPLO = 'L' or 'l'   Only the lower triangular part of A
 39 *                                  is to be referenced.
 40 *
 41 *           Unchanged on exit.
 42 *
 43 *  N        (input) INTEGER
 44 *           On entry, N specifies the order of the matrix A.
 45 *           N must be at least zero.
 46 *           Unchanged on exit.
 47 *
 48 *  ALPHA    (input) COMPLEX*16
 49 *           On entry, ALPHA specifies the scalar alpha.
 50 *           Unchanged on exit.
 51 *
 52 *  X        (input) COMPLEX*16 array, dimension at least
 53 *           ( 1 + ( N - 1 )*abs( INCX ) ).
 54 *           Before entry, the incremented array X must contain the N-
 55 *           element vector x.
 56 *           Unchanged on exit.
 57 *
 58 *  INCX     (input) INTEGER
 59 *           On entry, INCX specifies the increment for the elements of
 60 *           X. INCX must not be zero.
 61 *           Unchanged on exit.
 62 *
 63 *  A        (input/output) COMPLEX*16 array, dimension ( LDA, N )
 64 *           Before entry, with  UPLO = 'U' or 'u', the leading n by n
 65 *           upper triangular part of the array A must contain the upper
 66 *           triangular part of the symmetric matrix and the strictly
 67 *           lower triangular part of A is not referenced. On exit, the
 68 *           upper triangular part of the array A is overwritten by the
 69 *           upper triangular part of the updated matrix.
 70 *           Before entry, with UPLO = 'L' or 'l', the leading n by n
 71 *           lower triangular part of the array A must contain the lower
 72 *           triangular part of the symmetric matrix and the strictly
 73 *           upper triangular part of A is not referenced. On exit, the
 74 *           lower triangular part of the array A is overwritten by the
 75 *           lower triangular part of the updated matrix.
 76 *
 77 *  LDA      (input) INTEGER
 78 *           On entry, LDA specifies the first dimension of A as declared
 79 *           in the calling (sub) program. LDA must be at least
 80 *           max( 1, N ).
 81 *           Unchanged on exit.
 82 *
 83 * =====================================================================
 84 *
 85 *     .. Parameters ..
 86       COMPLEX*16         ZERO
 87       PARAMETER          ( ZERO = ( 0.0D+00.0D+0 ) )
 88 *     ..
 89 *     .. Local Scalars ..
 90       INTEGER            I, INFO, IX, J, JX, KX
 91       COMPLEX*16         TEMP
 92 *     ..
 93 *     .. External Functions ..
 94       LOGICAL            LSAME
 95       EXTERNAL           LSAME
 96 *     ..
 97 *     .. External Subroutines ..
 98       EXTERNAL           XERBLA
 99 *     ..
100 *     .. Intrinsic Functions ..
101       INTRINSIC          MAX
102 *     ..
103 *     .. Executable Statements ..
104 *
105 *     Test the input parameters.
106 *
107       INFO = 0
108       IF.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
109          INFO = 1
110       ELSE IF( N.LT.0 ) THEN
111          INFO = 2
112       ELSE IF( INCX.EQ.0 ) THEN
113          INFO = 5
114       ELSE IF( LDA.LT.MAX1, N ) ) THEN
115          INFO = 7
116       END IF
117       IF( INFO.NE.0 ) THEN
118          CALL XERBLA( 'ZSYR  ', INFO )
119          RETURN
120       END IF
121 *
122 *     Quick return if possible.
123 *
124       IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
125      $   RETURN
126 *
127 *     Set the start point in X if the increment is not unity.
128 *
129       IF( INCX.LE.0 ) THEN
130          KX = 1 - ( N-1 )*INCX
131       ELSE IF( INCX.NE.1 ) THEN
132          KX = 1
133       END IF
134 *
135 *     Start the operations. In this version the elements of A are
136 *     accessed sequentially with one pass through the triangular part
137 *     of A.
138 *
139       IF( LSAME( UPLO, 'U' ) ) THEN
140 *
141 *        Form  A  when A is stored in upper triangle.
142 *
143          IF( INCX.EQ.1 ) THEN
144             DO 20 J = 1, N
145                IF( X( J ).NE.ZERO ) THEN
146                   TEMP = ALPHA*X( J )
147                   DO 10 I = 1, J
148                      A( I, J ) = A( I, J ) + X( I )*TEMP
149    10             CONTINUE
150                END IF
151    20       CONTINUE
152          ELSE
153             JX = KX
154             DO 40 J = 1, N
155                IF( X( JX ).NE.ZERO ) THEN
156                   TEMP = ALPHA*X( JX )
157                   IX = KX
158                   DO 30 I = 1, J
159                      A( I, J ) = A( I, J ) + X( IX )*TEMP
160                      IX = IX + INCX
161    30             CONTINUE
162                END IF
163                JX = JX + INCX
164    40       CONTINUE
165          END IF
166       ELSE
167 *
168 *        Form  A  when A is stored in lower triangle.
169 *
170          IF( INCX.EQ.1 ) THEN
171             DO 60 J = 1, N
172                IF( X( J ).NE.ZERO ) THEN
173                   TEMP = ALPHA*X( J )
174                   DO 50 I = J, N
175                      A( I, J ) = A( I, J ) + X( I )*TEMP
176    50             CONTINUE
177                END IF
178    60       CONTINUE
179          ELSE
180             JX = KX
181             DO 80 J = 1, N
182                IF( X( JX ).NE.ZERO ) THEN
183                   TEMP = ALPHA*X( JX )
184                   IX = JX
185                   DO 70 I = J, N
186                      A( I, J ) = A( I, J ) + X( IX )*TEMP
187                      IX = IX + INCX
188    70             CONTINUE
189                END IF
190                JX = JX + INCX
191    80       CONTINUE
192          END IF
193       END IF
194 *
195       RETURN
196 *
197 *     End of ZSYR
198 *
199       END