001:       SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
002: *     .. Scalar Arguments ..
003:       DOUBLE PRECISION ALPHA,BETA
004:       INTEGER LDA,LDB,LDC,M,N
005:       CHARACTER SIDE,UPLO
006: *     ..
007: *     .. Array Arguments ..
008:       DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
009: *     ..
010: *
011: *  Purpose
012: *  =======
013: *
014: *  DSYMM  performs one of the matrix-matrix operations
015: *
016: *     C := alpha*A*B + beta*C,
017: *
018: *  or
019: *
020: *     C := alpha*B*A + beta*C,
021: *
022: *  where alpha and beta are scalars,  A is a symmetric matrix and  B and
023: *  C are  m by n matrices.
024: *
025: *  Arguments
026: *  ==========
027: *
028: *  SIDE   - CHARACTER*1.
029: *           On entry,  SIDE  specifies whether  the  symmetric matrix  A
030: *           appears on the  left or right  in the  operation as follows:
031: *
032: *              SIDE = 'L' or 'l'   C := alpha*A*B + beta*C,
033: *
034: *              SIDE = 'R' or 'r'   C := alpha*B*A + beta*C,
035: *
036: *           Unchanged on exit.
037: *
038: *  UPLO   - CHARACTER*1.
039: *           On  entry,   UPLO  specifies  whether  the  upper  or  lower
040: *           triangular  part  of  the  symmetric  matrix   A  is  to  be
041: *           referenced as follows:
042: *
043: *              UPLO = 'U' or 'u'   Only the upper triangular part of the
044: *                                  symmetric matrix is to be referenced.
045: *
046: *              UPLO = 'L' or 'l'   Only the lower triangular part of the
047: *                                  symmetric matrix is to be referenced.
048: *
049: *           Unchanged on exit.
050: *
051: *  M      - INTEGER.
052: *           On entry,  M  specifies the number of rows of the matrix  C.
053: *           M  must be at least zero.
054: *           Unchanged on exit.
055: *
056: *  N      - INTEGER.
057: *           On entry, N specifies the number of columns of the matrix C.
058: *           N  must be at least zero.
059: *           Unchanged on exit.
060: *
061: *  ALPHA  - DOUBLE PRECISION.
062: *           On entry, ALPHA specifies the scalar alpha.
063: *           Unchanged on exit.
064: *
065: *  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is
066: *           m  when  SIDE = 'L' or 'l'  and is  n otherwise.
067: *           Before entry  with  SIDE = 'L' or 'l',  the  m by m  part of
068: *           the array  A  must contain the  symmetric matrix,  such that
069: *           when  UPLO = 'U' or 'u', the leading m by m upper triangular
070: *           part of the array  A  must contain the upper triangular part
071: *           of the  symmetric matrix and the  strictly  lower triangular
072: *           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
073: *           the leading  m by m  lower triangular part  of the  array  A
074: *           must  contain  the  lower triangular part  of the  symmetric
075: *           matrix and the  strictly upper triangular part of  A  is not
076: *           referenced.
077: *           Before entry  with  SIDE = 'R' or 'r',  the  n by n  part of
078: *           the array  A  must contain the  symmetric matrix,  such that
079: *           when  UPLO = 'U' or 'u', the leading n by n upper triangular
080: *           part of the array  A  must contain the upper triangular part
081: *           of the  symmetric matrix and the  strictly  lower triangular
082: *           part of  A  is not referenced,  and when  UPLO = 'L' or 'l',
083: *           the leading  n by n  lower triangular part  of the  array  A
084: *           must  contain  the  lower triangular part  of the  symmetric
085: *           matrix and the  strictly upper triangular part of  A  is not
086: *           referenced.
087: *           Unchanged on exit.
088: *
089: *  LDA    - INTEGER.
090: *           On entry, LDA specifies the first dimension of A as declared
091: *           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
092: *           LDA must be at least  max( 1, m ), otherwise  LDA must be at
093: *           least  max( 1, n ).
094: *           Unchanged on exit.
095: *
096: *  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
097: *           Before entry, the leading  m by n part of the array  B  must
098: *           contain the matrix B.
099: *           Unchanged on exit.
100: *
101: *  LDB    - INTEGER.
102: *           On entry, LDB specifies the first dimension of B as declared
103: *           in  the  calling  (sub)  program.   LDB  must  be  at  least
104: *           max( 1, m ).
105: *           Unchanged on exit.
106: *
107: *  BETA   - DOUBLE PRECISION.
108: *           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
109: *           supplied as zero then C need not be set on input.
110: *           Unchanged on exit.
111: *
112: *  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).
113: *           Before entry, the leading  m by n  part of the array  C must
114: *           contain the matrix  C,  except when  beta  is zero, in which
115: *           case C need not be set on entry.
116: *           On exit, the array  C  is overwritten by the  m by n updated
117: *           matrix.
118: *
119: *  LDC    - INTEGER.
120: *           On entry, LDC specifies the first dimension of C as declared
121: *           in  the  calling  (sub)  program.   LDC  must  be  at  least
122: *           max( 1, m ).
123: *           Unchanged on exit.
124: *
125: *  Further Details
126: *  ===============
127: *
128: *  Level 3 Blas routine.
129: *
130: *  -- Written on 8-February-1989.
131: *     Jack Dongarra, Argonne National Laboratory.
132: *     Iain Duff, AERE Harwell.
133: *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
134: *     Sven Hammarling, Numerical Algorithms Group Ltd.
135: *
136: *  =====================================================================
137: *
138: *     .. External Functions ..
139:       LOGICAL LSAME
140:       EXTERNAL LSAME
141: *     ..
142: *     .. External Subroutines ..
143:       EXTERNAL XERBLA
144: *     ..
145: *     .. Intrinsic Functions ..
146:       INTRINSIC MAX
147: *     ..
148: *     .. Local Scalars ..
149:       DOUBLE PRECISION TEMP1,TEMP2
150:       INTEGER I,INFO,J,K,NROWA
151:       LOGICAL UPPER
152: *     ..
153: *     .. Parameters ..
154:       DOUBLE PRECISION ONE,ZERO
155:       PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
156: *     ..
157: *
158: *     Set NROWA as the number of rows of A.
159: *
160:       IF (LSAME(SIDE,'L')) THEN
161:           NROWA = M
162:       ELSE
163:           NROWA = N
164:       END IF
165:       UPPER = LSAME(UPLO,'U')
166: *
167: *     Test the input parameters.
168: *
169:       INFO = 0
170:       IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
171:           INFO = 1
172:       ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
173:           INFO = 2
174:       ELSE IF (M.LT.0) THEN
175:           INFO = 3
176:       ELSE IF (N.LT.0) THEN
177:           INFO = 4
178:       ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
179:           INFO = 7
180:       ELSE IF (LDB.LT.MAX(1,M)) THEN
181:           INFO = 9
182:       ELSE IF (LDC.LT.MAX(1,M)) THEN
183:           INFO = 12
184:       END IF
185:       IF (INFO.NE.0) THEN
186:           CALL XERBLA('DSYMM ',INFO)
187:           RETURN
188:       END IF
189: *
190: *     Quick return if possible.
191: *
192:       IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
193:      +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
194: *
195: *     And when  alpha.eq.zero.
196: *
197:       IF (ALPHA.EQ.ZERO) THEN
198:           IF (BETA.EQ.ZERO) THEN
199:               DO 20 J = 1,N
200:                   DO 10 I = 1,M
201:                       C(I,J) = ZERO
202:    10             CONTINUE
203:    20         CONTINUE
204:           ELSE
205:               DO 40 J = 1,N
206:                   DO 30 I = 1,M
207:                       C(I,J) = BETA*C(I,J)
208:    30             CONTINUE
209:    40         CONTINUE
210:           END IF
211:           RETURN
212:       END IF
213: *
214: *     Start the operations.
215: *
216:       IF (LSAME(SIDE,'L')) THEN
217: *
218: *        Form  C := alpha*A*B + beta*C.
219: *
220:           IF (UPPER) THEN
221:               DO 70 J = 1,N
222:                   DO 60 I = 1,M
223:                       TEMP1 = ALPHA*B(I,J)
224:                       TEMP2 = ZERO
225:                       DO 50 K = 1,I - 1
226:                           C(K,J) = C(K,J) + TEMP1*A(K,I)
227:                           TEMP2 = TEMP2 + B(K,J)*A(K,I)
228:    50                 CONTINUE
229:                       IF (BETA.EQ.ZERO) THEN
230:                           C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2
231:                       ELSE
232:                           C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) +
233:      +                             ALPHA*TEMP2
234:                       END IF
235:    60             CONTINUE
236:    70         CONTINUE
237:           ELSE
238:               DO 100 J = 1,N
239:                   DO 90 I = M,1,-1
240:                       TEMP1 = ALPHA*B(I,J)
241:                       TEMP2 = ZERO
242:                       DO 80 K = I + 1,M
243:                           C(K,J) = C(K,J) + TEMP1*A(K,I)
244:                           TEMP2 = TEMP2 + B(K,J)*A(K,I)
245:    80                 CONTINUE
246:                       IF (BETA.EQ.ZERO) THEN
247:                           C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2
248:                       ELSE
249:                           C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) +
250:      +                             ALPHA*TEMP2
251:                       END IF
252:    90             CONTINUE
253:   100         CONTINUE
254:           END IF
255:       ELSE
256: *
257: *        Form  C := alpha*B*A + beta*C.
258: *
259:           DO 170 J = 1,N
260:               TEMP1 = ALPHA*A(J,J)
261:               IF (BETA.EQ.ZERO) THEN
262:                   DO 110 I = 1,M
263:                       C(I,J) = TEMP1*B(I,J)
264:   110             CONTINUE
265:               ELSE
266:                   DO 120 I = 1,M
267:                       C(I,J) = BETA*C(I,J) + TEMP1*B(I,J)
268:   120             CONTINUE
269:               END IF
270:               DO 140 K = 1,J - 1
271:                   IF (UPPER) THEN
272:                       TEMP1 = ALPHA*A(K,J)
273:                   ELSE
274:                       TEMP1 = ALPHA*A(J,K)
275:                   END IF
276:                   DO 130 I = 1,M
277:                       C(I,J) = C(I,J) + TEMP1*B(I,K)
278:   130             CONTINUE
279:   140         CONTINUE
280:               DO 160 K = J + 1,N
281:                   IF (UPPER) THEN
282:                       TEMP1 = ALPHA*A(J,K)
283:                   ELSE
284:                       TEMP1 = ALPHA*A(K,J)
285:                   END IF
286:                   DO 150 I = 1,M
287:                       C(I,J) = C(I,J) + TEMP1*B(I,K)
288:   150             CONTINUE
289:   160         CONTINUE
290:   170     CONTINUE
291:       END IF
292: *
293:       RETURN
294: *
295: *     End of DSYMM .
296: *
297:       END
298: