1       SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
  2 *     .. Scalar Arguments ..
  3       DOUBLE PRECISION ALPHA
  4       INTEGER INCX,INCY,N
  5       CHARACTER UPLO
  6 *     ..
  7 *     .. Array Arguments ..
  8       DOUBLE PRECISION AP(*),X(*),Y(*)
  9 *     ..
 10 *
 11 *  Purpose
 12 *  =======
 13 *
 14 *  DSPR2  performs the symmetric rank 2 operation
 15 *
 16 *     A := alpha*x*y**T + alpha*y*x**T + A,
 17 *
 18 *  where alpha is a scalar, x and y are n element vectors 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  - DOUBLE PRECISION.
 43 *           On entry, ALPHA specifies the scalar alpha.
 44 *           Unchanged on exit.
 45 *
 46 *  X      - DOUBLE PRECISION 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 *  Y      - DOUBLE PRECISION array of dimension at least
 58 *           ( 1 + ( n - 1 )*abs( INCY ) ).
 59 *           Before entry, the incremented array Y must contain the n
 60 *           element vector y.
 61 *           Unchanged on exit.
 62 *
 63 *  INCY   - INTEGER.
 64 *           On entry, INCY specifies the increment for the elements of
 65 *           Y. INCY must not be zero.
 66 *           Unchanged on exit.
 67 *
 68 *  AP     - DOUBLE PRECISION array of DIMENSION at least
 69 *           ( ( n*( n + 1 ) )/2 ).
 70 *           Before entry with  UPLO = 'U' or 'u', the array AP must
 71 *           contain the upper triangular part of the symmetric matrix
 72 *           packed sequentially, column by column, so that AP( 1 )
 73 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
 74 *           and a( 2, 2 ) respectively, and so on. On exit, the array
 75 *           AP is overwritten by the upper triangular part of the
 76 *           updated matrix.
 77 *           Before entry with UPLO = 'L' or 'l', the array AP must
 78 *           contain the lower triangular part of the symmetric matrix
 79 *           packed sequentially, column by column, so that AP( 1 )
 80 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
 81 *           and a( 3, 1 ) respectively, and so on. On exit, the array
 82 *           AP is overwritten by the lower triangular part of the
 83 *           updated matrix.
 84 *
 85 *  Further Details
 86 *  ===============
 87 *
 88 *  Level 2 Blas routine.
 89 *
 90 *  -- Written on 22-October-1986.
 91 *     Jack Dongarra, Argonne National Lab.
 92 *     Jeremy Du Croz, Nag Central Office.
 93 *     Sven Hammarling, Nag Central Office.
 94 *     Richard Hanson, Sandia National Labs.
 95 *
 96 *  =====================================================================
 97 *
 98 *     .. Parameters ..
 99       DOUBLE PRECISION ZERO
100       PARAMETER (ZERO=0.0D+0)
101 *     ..
102 *     .. Local Scalars ..
103       DOUBLE PRECISION TEMP1,TEMP2
104       INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
105 *     ..
106 *     .. External Functions ..
107       LOGICAL LSAME
108       EXTERNAL LSAME
109 *     ..
110 *     .. External Subroutines ..
111       EXTERNAL XERBLA
112 *     ..
113 *
114 *     Test the input parameters.
115 *
116       INFO = 0
117       IF (.NOT.LSAME(UPLO,'U'.AND. .NOT.LSAME(UPLO,'L')) THEN
118           INFO = 1
119       ELSE IF (N.LT.0THEN
120           INFO = 2
121       ELSE IF (INCX.EQ.0THEN
122           INFO = 5
123       ELSE IF (INCY.EQ.0THEN
124           INFO = 7
125       END IF
126       IF (INFO.NE.0THEN
127           CALL XERBLA('DSPR2 ',INFO)
128           RETURN
129       END IF
130 *
131 *     Quick return if possible.
132 *
133       IF ((N.EQ.0.OR. (ALPHA.EQ.ZERO)) RETURN
134 *
135 *     Set up the start points in X and Y if the increments are not both
136 *     unity.
137 *
138       IF ((INCX.NE.1.OR. (INCY.NE.1)) THEN
139           IF (INCX.GT.0THEN
140               KX = 1
141           ELSE
142               KX = 1 - (N-1)*INCX
143           END IF
144           IF (INCY.GT.0THEN
145               KY = 1
146           ELSE
147               KY = 1 - (N-1)*INCY
148           END IF
149           JX = KX
150           JY = KY
151       END IF
152 *
153 *     Start the operations. In this version the elements of the array AP
154 *     are accessed sequentially with one pass through AP.
155 *
156       KK = 1
157       IF (LSAME(UPLO,'U')) THEN
158 *
159 *        Form  A  when upper triangle is stored in AP.
160 *
161           IF ((INCX.EQ.1.AND. (INCY.EQ.1)) THEN
162               DO 20 J = 1,N
163                   IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
164                       TEMP1 = ALPHA*Y(J)
165                       TEMP2 = ALPHA*X(J)
166                       K = KK
167                       DO 10 I = 1,J
168                           AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
169                           K = K + 1
170    10                 CONTINUE
171                   END IF
172                   KK = KK + J
173    20         CONTINUE
174           ELSE
175               DO 40 J = 1,N
176                   IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
177                       TEMP1 = ALPHA*Y(JY)
178                       TEMP2 = ALPHA*X(JX)
179                       IX = KX
180                       IY = KY
181                       DO 30 K = KK,KK + J - 1
182                           AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
183                           IX = IX + INCX
184                           IY = IY + INCY
185    30                 CONTINUE
186                   END IF
187                   JX = JX + INCX
188                   JY = JY + INCY
189                   KK = KK + J
190    40         CONTINUE
191           END IF
192       ELSE
193 *
194 *        Form  A  when lower triangle is stored in AP.
195 *
196           IF ((INCX.EQ.1.AND. (INCY.EQ.1)) THEN
197               DO 60 J = 1,N
198                   IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
199                       TEMP1 = ALPHA*Y(J)
200                       TEMP2 = ALPHA*X(J)
201                       K = KK
202                       DO 50 I = J,N
203                           AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2
204                           K = K + 1
205    50                 CONTINUE
206                   END IF
207                   KK = KK + N - J + 1
208    60         CONTINUE
209           ELSE
210               DO 80 J = 1,N
211                   IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
212                       TEMP1 = ALPHA*Y(JY)
213                       TEMP2 = ALPHA*X(JX)
214                       IX = JX
215                       IY = JY
216                       DO 70 K = KK,KK + N - J
217                           AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2
218                           IX = IX + INCX
219                           IY = IY + INCY
220    70                 CONTINUE
221                   END IF
222                   JX = JX + INCX
223                   JY = JY + INCY
224                   KK = KK + N - J + 1
225    80         CONTINUE
226           END IF
227       END IF
228 *
229       RETURN
230 *
231 *     End of DSPR2 .
232 *
233       END