```001:       SUBROUTINE SSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
002: *     .. Scalar Arguments ..
003:       REAL ALPHA
004:       INTEGER INCX,INCY,N
005:       CHARACTER UPLO
006: *     ..
007: *     .. Array Arguments ..
008:       REAL AP(*),X(*),Y(*)
009: *     ..
010: *
011: *  Purpose
012: *  =======
013: *
014: *  SSPR2  performs the symmetric rank 2 operation
015: *
016: *     A := alpha*x*y' + alpha*y*x' + A,
017: *
018: *  where alpha is a scalar, x and y are n element vectors and A is an
019: *  n by n symmetric matrix, supplied in packed form.
020: *
021: *  Arguments
022: *  ==========
023: *
024: *  UPLO   - CHARACTER*1.
025: *           On entry, UPLO specifies whether the upper or lower
026: *           triangular part of the matrix A is supplied in the packed
027: *           array AP as follows:
028: *
029: *              UPLO = 'U' or 'u'   The upper triangular part of A is
030: *                                  supplied in AP.
031: *
032: *              UPLO = 'L' or 'l'   The lower triangular part of A is
033: *                                  supplied in AP.
034: *
035: *           Unchanged on exit.
036: *
037: *  N      - INTEGER.
038: *           On entry, N specifies the order of the matrix A.
039: *           N must be at least zero.
040: *           Unchanged on exit.
041: *
042: *  ALPHA  - REAL            .
043: *           On entry, ALPHA specifies the scalar alpha.
044: *           Unchanged on exit.
045: *
046: *  X      - REAL             array of dimension at least
047: *           ( 1 + ( n - 1 )*abs( INCX ) ).
048: *           Before entry, the incremented array X must contain the n
049: *           element vector x.
050: *           Unchanged on exit.
051: *
052: *  INCX   - INTEGER.
053: *           On entry, INCX specifies the increment for the elements of
054: *           X. INCX must not be zero.
055: *           Unchanged on exit.
056: *
057: *  Y      - REAL             array of dimension at least
058: *           ( 1 + ( n - 1 )*abs( INCY ) ).
059: *           Before entry, the incremented array Y must contain the n
060: *           element vector y.
061: *           Unchanged on exit.
062: *
063: *  INCY   - INTEGER.
064: *           On entry, INCY specifies the increment for the elements of
065: *           Y. INCY must not be zero.
066: *           Unchanged on exit.
067: *
068: *  AP     - REAL             array of DIMENSION at least
069: *           ( ( n*( n + 1 ) )/2 ).
070: *           Before entry with  UPLO = 'U' or 'u', the array AP must
071: *           contain the upper triangular part of the symmetric matrix
072: *           packed sequentially, column by column, so that AP( 1 )
073: *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
074: *           and a( 2, 2 ) respectively, and so on. On exit, the array
075: *           AP is overwritten by the upper triangular part of the
076: *           updated matrix.
077: *           Before entry with UPLO = 'L' or 'l', the array AP must
078: *           contain the lower triangular part of the symmetric matrix
079: *           packed sequentially, column by column, so that AP( 1 )
080: *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
081: *           and a( 3, 1 ) respectively, and so on. On exit, the array
082: *           AP is overwritten by the lower triangular part of the
083: *           updated matrix.
084: *
085: *  Further Details
086: *  ===============
087: *
088: *  Level 2 Blas routine.
089: *
090: *  -- Written on 22-October-1986.
091: *     Jack Dongarra, Argonne National Lab.
092: *     Jeremy Du Croz, Nag Central Office.
093: *     Sven Hammarling, Nag Central Office.
094: *     Richard Hanson, Sandia National Labs.
095: *
096: *  =====================================================================
097: *
098: *     .. Parameters ..
099:       REAL ZERO
100:       PARAMETER (ZERO=0.0E+0)
101: *     ..
102: *     .. Local Scalars ..
103:       REAL 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.0) THEN
120:           INFO = 2
121:       ELSE IF (INCX.EQ.0) THEN
122:           INFO = 5
123:       ELSE IF (INCY.EQ.0) THEN
124:           INFO = 7
125:       END IF
126:       IF (INFO.NE.0) THEN
127:           CALL XERBLA('SSPR2 ',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.0) THEN
140:               KX = 1
141:           ELSE
142:               KX = 1 - (N-1)*INCX
143:           END IF
144:           IF (INCY.GT.0) THEN
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 SSPR2 .
232: *
233:       END
234: ```