1       SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
  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, N
 11       COMPLEX*16         ALPHA
 12 *     ..
 13 *     .. Array Arguments ..
 14       COMPLEX*16         AP( * ), X( * )
 15 *     ..
 16 *
 17 *  Purpose
 18 *  =======
 19 *
 20 *  ZSPR    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, supplied in packed form.
 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 matrix A is supplied in the packed
 33 *           array AP as follows:
 34 *
 35 *              UPLO = 'U' or 'u'   The upper triangular part of A is
 36 *                                  supplied in AP.
 37 *
 38 *              UPLO = 'L' or 'l'   The lower triangular part of A is
 39 *                                  supplied in AP.
 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 *  AP       (input/output) COMPLEX*16 array, dimension at least
 64 *           ( ( N*( N + 1 ) )/2 ).
 65 *           Before entry, with  UPLO = 'U' or 'u', the array AP must
 66 *           contain the upper triangular part of the symmetric matrix
 67 *           packed sequentially, column by column, so that AP( 1 )
 68 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
 69 *           and a( 2, 2 ) respectively, and so on. On exit, the array
 70 *           AP is overwritten by the upper triangular part of the
 71 *           updated matrix.
 72 *           Before entry, with UPLO = 'L' or 'l', the array AP must
 73 *           contain the lower triangular part of the symmetric matrix
 74 *           packed sequentially, column by column, so that AP( 1 )
 75 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
 76 *           and a( 3, 1 ) respectively, and so on. On exit, the array
 77 *           AP is overwritten by the lower triangular part of the
 78 *           updated matrix.
 79 *           Note that the imaginary parts of the diagonal elements need
 80 *           not be set, they are assumed to be zero, and on exit they
 81 *           are set to zero.
 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, K, KK, KX
 91       COMPLEX*16         TEMP
 92 *     ..
 93 *     .. External Functions ..
 94       LOGICAL            LSAME
 95       EXTERNAL           LSAME
 96 *     ..
 97 *     .. External Subroutines ..
 98       EXTERNAL           XERBLA
 99 *     ..
100 *     .. Executable Statements ..
101 *
102 *     Test the input parameters.
103 *
104       INFO = 0
105       IF.NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
106          INFO = 1
107       ELSE IF( N.LT.0 ) THEN
108          INFO = 2
109       ELSE IF( INCX.EQ.0 ) THEN
110          INFO = 5
111       END IF
112       IF( INFO.NE.0 ) THEN
113          CALL XERBLA( 'ZSPR  ', INFO )
114          RETURN
115       END IF
116 *
117 *     Quick return if possible.
118 *
119       IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
120      $   RETURN
121 *
122 *     Set the start point in X if the increment is not unity.
123 *
124       IF( INCX.LE.0 ) THEN
125          KX = 1 - ( N-1 )*INCX
126       ELSE IF( INCX.NE.1 ) THEN
127          KX = 1
128       END IF
129 *
130 *     Start the operations. In this version the elements of the array AP
131 *     are accessed sequentially with one pass through AP.
132 *
133       KK = 1
134       IF( LSAME( UPLO, 'U' ) ) THEN
135 *
136 *        Form  A  when upper triangle is stored in AP.
137 *
138          IF( INCX.EQ.1 ) THEN
139             DO 20 J = 1, N
140                IF( X( J ).NE.ZERO ) THEN
141                   TEMP = ALPHA*X( J )
142                   K = KK
143                   DO 10 I = 1, J - 1
144                      AP( K ) = AP( K ) + X( I )*TEMP
145                      K = K + 1
146    10             CONTINUE
147                   AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP
148                ELSE
149                   AP( KK+J-1 ) = AP( KK+J-1 )
150                END IF
151                KK = KK + J
152    20       CONTINUE
153          ELSE
154             JX = KX
155             DO 40 J = 1, N
156                IF( X( JX ).NE.ZERO ) THEN
157                   TEMP = ALPHA*X( JX )
158                   IX = KX
159                   DO 30 K = KK, KK + J - 2
160                      AP( K ) = AP( K ) + X( IX )*TEMP
161                      IX = IX + INCX
162    30             CONTINUE
163                   AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP
164                ELSE
165                   AP( KK+J-1 ) = AP( KK+J-1 )
166                END IF
167                JX = JX + INCX
168                KK = KK + J
169    40       CONTINUE
170          END IF
171       ELSE
172 *
173 *        Form  A  when lower triangle is stored in AP.
174 *
175          IF( INCX.EQ.1 ) THEN
176             DO 60 J = 1, N
177                IF( X( J ).NE.ZERO ) THEN
178                   TEMP = ALPHA*X( J )
179                   AP( KK ) = AP( KK ) + TEMP*X( J )
180                   K = KK + 1
181                   DO 50 I = J + 1, N
182                      AP( K ) = AP( K ) + X( I )*TEMP
183                      K = K + 1
184    50             CONTINUE
185                ELSE
186                   AP( KK ) = AP( KK )
187                END IF
188                KK = KK + N - J + 1
189    60       CONTINUE
190          ELSE
191             JX = KX
192             DO 80 J = 1, N
193                IF( X( JX ).NE.ZERO ) THEN
194                   TEMP = ALPHA*X( JX )
195                   AP( KK ) = AP( KK ) + TEMP*X( JX )
196                   IX = JX
197                   DO 70 K = KK + 1, KK + N - J
198                      IX = IX + INCX
199                      AP( K ) = AP( K ) + X( IX )*TEMP
200    70             CONTINUE
201                ELSE
202                   AP( KK ) = AP( KK )
203                END IF
204                JX = JX + INCX
205                KK = KK + N - J + 1
206    80       CONTINUE
207          END IF
208       END IF
209 *
210       RETURN
211 *
212 *     End of ZSPR
213 *
214       END