1      SUBROUTINE CHERF  ( UPLO, N, ALPHA, X, INCX, A, LDA )
2*     .. Scalar Arguments ..
3      REAL               ALPHA
4      INTEGER            INCX, LDA, N
5      CHARACTER*1        UPLO
6*     .. Array Arguments ..
7      COMPLEX            A( LDA, * ), X( * )
8*     ..
9*
10*  Purpose
11*  =======
12*
13*  CHER   performs the hermitian rank 1 operation
14*
15*     A := alpha*x*conjg( x' ) + A,
16*
17*  where alpha is a real scalar, x is an n element vector and A is an
18*  n by n hermitian matrix.
19*
20*  Parameters
21*  ==========
22*
23*  UPLO   - CHARACTER*1.
24*           On entry, UPLO specifies whether the upper or lower
25*           triangular part of the array A is to be referenced as
26*           follows:
27*
28*              UPLO = 'U' or 'u'   Only the upper triangular part of A
29*                                  is to be referenced.
30*
31*              UPLO = 'L' or 'l'   Only the lower triangular part of A
32*                                  is to be referenced.
33*
34*           Unchanged on exit.
35*
36*  N      - INTEGER.
37*           On entry, N specifies the order of the matrix A.
38*           N must be at least zero.
39*           Unchanged on exit.
40*
41*  ALPHA  - REAL            .
42*           On entry, ALPHA specifies the scalar alpha.
43*           Unchanged on exit.
44*
45*  X      - COMPLEX          array of dimension at least
46*           ( 1 + ( n - 1 )*abs( INCX ) ).
47*           Before entry, the incremented array X must contain the n
48*           element vector x.
49*           Unchanged on exit.
50*
51*  INCX   - INTEGER.
52*           On entry, INCX specifies the increment for the elements of
53*           X. INCX must not be zero.
54*           Unchanged on exit.
55*
56*  A      - COMPLEX          array of DIMENSION ( LDA, n ).
57*           Before entry with  UPLO = 'U' or 'u', the leading n by n
58*           upper triangular part of the array A must contain the upper
59*           triangular part of the hermitian matrix and the strictly
60*           lower triangular part of A is not referenced. On exit, the
61*           upper triangular part of the array A is overwritten by the
62*           upper triangular part of the updated matrix.
63*           Before entry with UPLO = 'L' or 'l', the leading n by n
64*           lower triangular part of the array A must contain the lower
65*           triangular part of the hermitian matrix and the strictly
66*           upper triangular part of A is not referenced. On exit, the
67*           lower triangular part of the array A is overwritten by the
68*           lower triangular part of the updated matrix.
69*           Note that the imaginary parts of the diagonal elements need
70*           not be set, they are assumed to be zero, and on exit they
71*           are set to zero.
72*
73*  LDA    - INTEGER.
74*           On entry, LDA specifies the first dimension of A as declared
75*           in the calling (sub) program. LDA must be at least
76*           max( 1, n ).
77*           Unchanged on exit.
78*
79*
80*  Level 2 Blas routine.
81*
82*  -- Written on 22-October-1986.
83*     Jack Dongarra, Argonne National Lab.
84*     Jeremy Du Croz, Nag Central Office.
85*     Sven Hammarling, Nag Central Office.
86*     Richard Hanson, Sandia National Labs.
87*
88*
89*     .. Parameters ..
90      COMPLEX            ZERO
91      PARAMETER        ( ZERO = ( 0.0E+0, 0.0E+0 ) )
92*     .. Local Scalars ..
93      COMPLEX            TEMP
94      INTEGER            I, INFO, IX, J, JX, KX
95*     .. External Functions ..
96      LOGICAL            LSAME
97      EXTERNAL           LSAME
98*     .. External Subroutines ..
99      EXTERNAL           XERBLA
100*     .. Intrinsic Functions ..
101      INTRINSIC          CONJG, MAX, REAL
102*     ..
103*     .. Executable Statements ..
104*
105*     Test the input parameters.
106*
107      INFO = 0
108      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
109     $         .NOT.LSAME( UPLO, 'L' )      )THEN
110         INFO = 1
111      ELSE IF( N.LT.0 )THEN
112         INFO = 2
113      ELSE IF( INCX.EQ.0 )THEN
114         INFO = 5
115      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
116         INFO = 7
117      END IF
118      IF( INFO.NE.0 )THEN
119         CALL XERBLA( 'CHER  ', INFO )
120         RETURN
121      END IF
122*
123*     Quick return if possible.
124*
125      IF( ( N.EQ.0 ).OR.( ALPHA.EQ.REAL( ZERO ) ) )
126     $   RETURN
127*
128*     Set the start point in X if the increment is not unity.
129*
130      IF( INCX.LE.0 )THEN
131         KX = 1 - ( N - 1 )*INCX
132      ELSE IF( INCX.NE.1 )THEN
133         KX = 1
134      END IF
135*
136*     Start the operations. In this version the elements of A are
137*     accessed sequentially with one pass through the triangular part
138*     of A.
139*
140      IF( LSAME( UPLO, 'U' ) )THEN
141*
142*        Form  A  when A is stored in upper triangle.
143*
144         IF( INCX.EQ.1 )THEN
145            DO 20, J = 1, N
146               IF( X( J ).NE.ZERO )THEN
147                  TEMP = ALPHA*CONJG( X( J ) )
148                  DO 10, I = 1, J - 1
149                     A( I, J ) = A( I, J ) + X( I )*TEMP
150   10             CONTINUE
151                  A( J, J ) = REAL( A( J, J ) ) + REAL( X( J )*TEMP )
152               ELSE
153                  A( J, J ) = REAL( A( J, J ) )
154               END IF
155   20       CONTINUE
156         ELSE
157            JX = KX
158            DO 40, J = 1, N
159               IF( X( JX ).NE.ZERO )THEN
160                  TEMP = ALPHA*CONJG( X( JX ) )
161                  IX   = KX
162                  DO 30, I = 1, J - 1
163                     A( I, J ) = A( I, J ) + X( IX )*TEMP
164                     IX        = IX        + INCX
165   30             CONTINUE
166                  A( J, J ) = REAL( A( J, J ) ) + REAL( X( JX )*TEMP )
167               ELSE
168                  A( J, J ) = REAL( A( J, J ) )
169               END IF
170               JX = JX + INCX
171   40       CONTINUE
172         END IF
173      ELSE
174*
175*        Form  A  when A is stored in lower triangle.
176*
177         IF( INCX.EQ.1 )THEN
178            DO 60, J = 1, N
179               IF( X( J ).NE.ZERO )THEN
180                  TEMP      = ALPHA*CONJG( X( J ) )
181                  A( J, J ) = REAL( A( J, J ) ) + REAL( TEMP*X( J ) )
182                  DO 50, I = J + 1, N
183                     A( I, J ) = A( I, J ) + X( I )*TEMP
184   50             CONTINUE
185               ELSE
186                  A( J, J ) = REAL( A( J, J ) )
187               END IF
188   60       CONTINUE
189         ELSE
190            JX = KX
191            DO 80, J = 1, N
192               IF( X( JX ).NE.ZERO )THEN
193                  TEMP      = ALPHA*CONJG( X( JX ) )
194                  A( J, J ) = REAL( A( J, J ) ) + REAL( TEMP*X( JX ) )
195                  IX        = JX
196                  DO 70, I = J + 1, N
197                     IX        = IX        + INCX
198                     A( I, J ) = A( I, J ) + X( IX )*TEMP
199   70             CONTINUE
200               ELSE
201                  A( J, J ) = REAL( A( J, J ) )
202               END IF
203               JX = JX + INCX
204   80       CONTINUE
205         END IF
206      END IF
207*
208      RETURN
209*
210*     End of CHER  .
211*
212      END
213