```001:       SUBROUTINE SSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
002: *     .. Scalar Arguments ..
003:       REAL ALPHA
004:       INTEGER INCX,INCY,LDA,N
005:       CHARACTER UPLO
006: *     ..
007: *     .. Array Arguments ..
008:       REAL A(LDA,*),X(*),Y(*)
009: *     ..
010: *
011: *  Purpose
012: *  =======
013: *
014: *  SSYR2  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 n
019: *  by n symmetric matrix.
020: *
021: *  Arguments
022: *  ==========
023: *
024: *  UPLO   - CHARACTER*1.
025: *           On entry, UPLO specifies whether the upper or lower
026: *           triangular part of the array A is to be referenced as
027: *           follows:
028: *
029: *              UPLO = 'U' or 'u'   Only the upper triangular part of A
030: *                                  is to be referenced.
031: *
032: *              UPLO = 'L' or 'l'   Only the lower triangular part of A
033: *                                  is to be referenced.
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: *  A      - REAL             array of DIMENSION ( LDA, n ).
069: *           Before entry with  UPLO = 'U' or 'u', the leading n by n
070: *           upper triangular part of the array A must contain the upper
071: *           triangular part of the symmetric matrix and the strictly
072: *           lower triangular part of A is not referenced. On exit, the
073: *           upper triangular part of the array A is overwritten by the
074: *           upper triangular part of the updated matrix.
075: *           Before entry with UPLO = 'L' or 'l', the leading n by n
076: *           lower triangular part of the array A must contain the lower
077: *           triangular part of the symmetric matrix and the strictly
078: *           upper triangular part of A is not referenced. On exit, the
079: *           lower triangular part of the array A is overwritten by the
080: *           lower triangular part of the updated matrix.
081: *
082: *  LDA    - INTEGER.
083: *           On entry, LDA specifies the first dimension of A as declared
084: *           in the calling (sub) program. LDA must be at least
085: *           max( 1, n ).
086: *           Unchanged on exit.
087: *
088: *  Further Details
089: *  ===============
090: *
091: *  Level 2 Blas routine.
092: *
093: *  -- Written on 22-October-1986.
094: *     Jack Dongarra, Argonne National Lab.
095: *     Jeremy Du Croz, Nag Central Office.
096: *     Sven Hammarling, Nag Central Office.
097: *     Richard Hanson, Sandia National Labs.
098: *
099: *  =====================================================================
100: *
101: *     .. Parameters ..
102:       REAL ZERO
103:       PARAMETER (ZERO=0.0E+0)
104: *     ..
105: *     .. Local Scalars ..
106:       REAL TEMP1,TEMP2
107:       INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
108: *     ..
109: *     .. External Functions ..
110:       LOGICAL LSAME
111:       EXTERNAL LSAME
112: *     ..
113: *     .. External Subroutines ..
114:       EXTERNAL XERBLA
115: *     ..
116: *     .. Intrinsic Functions ..
117:       INTRINSIC MAX
118: *     ..
119: *
120: *     Test the input parameters.
121: *
122:       INFO = 0
123:       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
124:           INFO = 1
125:       ELSE IF (N.LT.0) THEN
126:           INFO = 2
127:       ELSE IF (INCX.EQ.0) THEN
128:           INFO = 5
129:       ELSE IF (INCY.EQ.0) THEN
130:           INFO = 7
131:       ELSE IF (LDA.LT.MAX(1,N)) THEN
132:           INFO = 9
133:       END IF
134:       IF (INFO.NE.0) THEN
135:           CALL XERBLA('SSYR2 ',INFO)
136:           RETURN
137:       END IF
138: *
139: *     Quick return if possible.
140: *
141:       IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
142: *
143: *     Set up the start points in X and Y if the increments are not both
144: *     unity.
145: *
146:       IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
147:           IF (INCX.GT.0) THEN
148:               KX = 1
149:           ELSE
150:               KX = 1 - (N-1)*INCX
151:           END IF
152:           IF (INCY.GT.0) THEN
153:               KY = 1
154:           ELSE
155:               KY = 1 - (N-1)*INCY
156:           END IF
157:           JX = KX
158:           JY = KY
159:       END IF
160: *
161: *     Start the operations. In this version the elements of A are
162: *     accessed sequentially with one pass through the triangular part
163: *     of A.
164: *
165:       IF (LSAME(UPLO,'U')) THEN
166: *
167: *        Form  A  when A is stored in the upper triangle.
168: *
169:           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
170:               DO 20 J = 1,N
171:                   IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
172:                       TEMP1 = ALPHA*Y(J)
173:                       TEMP2 = ALPHA*X(J)
174:                       DO 10 I = 1,J
175:                           A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
176:    10                 CONTINUE
177:                   END IF
178:    20         CONTINUE
179:           ELSE
180:               DO 40 J = 1,N
181:                   IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
182:                       TEMP1 = ALPHA*Y(JY)
183:                       TEMP2 = ALPHA*X(JX)
184:                       IX = KX
185:                       IY = KY
186:                       DO 30 I = 1,J
187:                           A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
188:                           IX = IX + INCX
189:                           IY = IY + INCY
190:    30                 CONTINUE
191:                   END IF
192:                   JX = JX + INCX
193:                   JY = JY + INCY
194:    40         CONTINUE
195:           END IF
196:       ELSE
197: *
198: *        Form  A  when A is stored in the lower triangle.
199: *
200:           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
201:               DO 60 J = 1,N
202:                   IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
203:                       TEMP1 = ALPHA*Y(J)
204:                       TEMP2 = ALPHA*X(J)
205:                       DO 50 I = J,N
206:                           A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
207:    50                 CONTINUE
208:                   END IF
209:    60         CONTINUE
210:           ELSE
211:               DO 80 J = 1,N
212:                   IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
213:                       TEMP1 = ALPHA*Y(JY)
214:                       TEMP2 = ALPHA*X(JX)
215:                       IX = JX
216:                       IY = JY
217:                       DO 70 I = J,N
218:                           A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
219:                           IX = IX + INCX
220:                           IY = IY + INCY
221:    70                 CONTINUE
222:                   END IF
223:                   JX = JX + INCX
224:                   JY = JY + INCY
225:    80         CONTINUE
226:           END IF
227:       END IF
228: *
229:       RETURN
230: *
231: *     End of SSYR2 .
232: *
233:       END
234: ```