1       SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP)
  2 *     .. Scalar Arguments ..
  3       REAL ALPHA
  4       INTEGER INCX,N
  5       CHARACTER UPLO
  6 *     ..
  7 *     .. Array Arguments ..
  8       REAL AP(*),X(*)
  9 *     ..
 10 *
 11 *  Purpose
 12 *  =======
 13 *
 14 *  SSPR    performs the symmetric rank 1 operation
 15 *
 16 *     A := alpha*x*x**T + A,
 17 *
 18 *  where alpha is a real scalar, x is an n element vector and A is an
 19 *  n by n symmetric matrix, supplied in packed form.
 20 *
 21 *  Arguments
 22 *  ==========
 23 *
 24 *  UPLO   - CHARACTER*1.
 25 *           On entry, UPLO specifies whether the upper or lower
 26 *           triangular part of the matrix A is supplied in the packed
 27 *           array AP as follows:
 28 *
 29 *              UPLO = 'U' or 'u'   The upper triangular part of A is
 30 *                                  supplied in AP.
 31 *
 32 *              UPLO = 'L' or 'l'   The lower triangular part of A is
 33 *                                  supplied in AP.
 34 *
 35 *           Unchanged on exit.
 36 *
 37 *  N      - INTEGER.
 38 *           On entry, N specifies the order of the matrix A.
 39 *           N must be at least zero.
 40 *           Unchanged on exit.
 41 *
 42 *  ALPHA  - REAL            .
 43 *           On entry, ALPHA specifies the scalar alpha.
 44 *           Unchanged on exit.
 45 *
 46 *  X      - REAL             array of dimension at least
 47 *           ( 1 + ( n - 1 )*abs( INCX ) ).
 48 *           Before entry, the incremented array X must contain the n
 49 *           element vector x.
 50 *           Unchanged on exit.
 51 *
 52 *  INCX   - INTEGER.
 53 *           On entry, INCX specifies the increment for the elements of
 54 *           X. INCX must not be zero.
 55 *           Unchanged on exit.
 56 *
 57 *  AP     - REAL             array of DIMENSION at least
 58 *           ( ( n*( n + 1 ) )/2 ).
 59 *           Before entry with  UPLO = 'U' or 'u', the array AP must
 60 *           contain the upper triangular part of the symmetric matrix
 61 *           packed sequentially, column by column, so that AP( 1 )
 62 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
 63 *           and a( 2, 2 ) respectively, and so on. On exit, the array
 64 *           AP is overwritten by the upper triangular part of the
 65 *           updated matrix.
 66 *           Before entry with UPLO = 'L' or 'l', the array AP must
 67 *           contain the lower triangular part of the symmetric matrix
 68 *           packed sequentially, column by column, so that AP( 1 )
 69 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
 70 *           and a( 3, 1 ) respectively, and so on. On exit, the array
 71 *           AP is overwritten by the lower triangular part of the
 72 *           updated matrix.
 73 *
 74 *  Further Details
 75 *  ===============
 76 *
 77 *  Level 2 Blas routine.
 78 *
 79 *  -- Written on 22-October-1986.
 80 *     Jack Dongarra, Argonne National Lab.
 81 *     Jeremy Du Croz, Nag Central Office.
 82 *     Sven Hammarling, Nag Central Office.
 83 *     Richard Hanson, Sandia National Labs.
 84 *
 85 *  =====================================================================
 86 *
 87 *     .. Parameters ..
 88       REAL ZERO
 89       PARAMETER (ZERO=0.0E+0)
 90 *     ..
 91 *     .. Local Scalars ..
 92       REAL TEMP
 93       INTEGER I,INFO,IX,J,JX,K,KK,KX
 94 *     ..
 95 *     .. External Functions ..
 96       LOGICAL LSAME
 97       EXTERNAL LSAME
 98 *     ..
 99 *     .. External Subroutines ..
100       EXTERNAL XERBLA
101 *     ..
102 *
103 *     Test the input parameters.
104 *
105       INFO = 0
106       IF (.NOT.LSAME(UPLO,'U'.AND. .NOT.LSAME(UPLO,'L')) THEN
107           INFO = 1
108       ELSE IF (N.LT.0THEN
109           INFO = 2
110       ELSE IF (INCX.EQ.0THEN
111           INFO = 5
112       END IF
113       IF (INFO.NE.0THEN
114           CALL XERBLA('SSPR  ',INFO)
115           RETURN
116       END IF
117 *
118 *     Quick return if possible.
119 *
120       IF ((N.EQ.0.OR. (ALPHA.EQ.ZERO)) RETURN
121 *
122 *     Set the start point in X if the increment is not unity.
123 *
124       IF (INCX.LE.0THEN
125           KX = 1 - (N-1)*INCX
126       ELSE IF (INCX.NE.1THEN
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.1THEN
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
144                           AP(K) = AP(K) + X(I)*TEMP
145                           K = K + 1
146    10                 CONTINUE
147                   END IF
148                   KK = KK + J
149    20         CONTINUE
150           ELSE
151               JX = KX
152               DO 40 J = 1,N
153                   IF (X(JX).NE.ZERO) THEN
154                       TEMP = ALPHA*X(JX)
155                       IX = KX
156                       DO 30 K = KK,KK + J - 1
157                           AP(K) = AP(K) + X(IX)*TEMP
158                           IX = IX + INCX
159    30                 CONTINUE
160                   END IF
161                   JX = JX + INCX
162                   KK = KK + J
163    40         CONTINUE
164           END IF
165       ELSE
166 *
167 *        Form  A  when lower triangle is stored in AP.
168 *
169           IF (INCX.EQ.1THEN
170               DO 60 J = 1,N
171                   IF (X(J).NE.ZERO) THEN
172                       TEMP = ALPHA*X(J)
173                       K = KK
174                       DO 50 I = J,N
175                           AP(K) = AP(K) + X(I)*TEMP
176                           K = K + 1
177    50                 CONTINUE
178                   END IF
179                   KK = KK + N - J + 1
180    60         CONTINUE
181           ELSE
182               JX = KX
183               DO 80 J = 1,N
184                   IF (X(JX).NE.ZERO) THEN
185                       TEMP = ALPHA*X(JX)
186                       IX = JX
187                       DO 70 K = KK,KK + N - J
188                           AP(K) = AP(K) + X(IX)*TEMP
189                           IX = IX + INCX
190    70                 CONTINUE
191                   END IF
192                   JX = JX + INCX
193                   KK = KK + N - J + 1
194    80         CONTINUE
195           END IF
196       END IF
197 *
198       RETURN
199 *
200 *     End of SSPR  .
201 *
202       END