001:       SUBROUTINE ZSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
002: *     .. Scalar Arguments ..
003:       DOUBLE COMPLEX ALPHA,BETA
004:       INTEGER LDA,LDB,LDC,M,N
005:       CHARACTER SIDE,UPLO
006: *     ..
007: *     .. Array Arguments ..
008:       DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
009: *     ..
010: *
011: *  Purpose
012: *  =======
013: *
014: *  ZSYMM  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  - COMPLEX*16      .
062: *           On entry, ALPHA specifies the scalar alpha.
063: *           Unchanged on exit.
064: *
065: *  A      - COMPLEX*16       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      - COMPLEX*16       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   - COMPLEX*16      .
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      - COMPLEX*16       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: *
126: *  Level 3 Blas routine.
127: *
128: *  -- Written on 8-February-1989.
129: *     Jack Dongarra, Argonne National Laboratory.
130: *     Iain Duff, AERE Harwell.
131: *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
132: *     Sven Hammarling, Numerical Algorithms Group Ltd.
133: *
134: *
135: *     .. External Functions ..
136:       LOGICAL LSAME
137:       EXTERNAL LSAME
138: *     ..
139: *     .. External Subroutines ..
140:       EXTERNAL XERBLA
141: *     ..
142: *     .. Intrinsic Functions ..
143:       INTRINSIC MAX
144: *     ..
145: *     .. Local Scalars ..
146:       DOUBLE COMPLEX TEMP1,TEMP2
147:       INTEGER I,INFO,J,K,NROWA
148:       LOGICAL UPPER
149: *     ..
150: *     .. Parameters ..
151:       DOUBLE COMPLEX ONE
152:       PARAMETER (ONE= (1.0D+0,0.0D+0))
153:       DOUBLE COMPLEX ZERO
154:       PARAMETER (ZERO= (0.0D+0,0.0D+0))
155: *     ..
156: *
157: *     Set NROWA as the number of rows of A.
158: *
159:       IF (LSAME(SIDE,'L')) THEN
160:           NROWA = M
161:       ELSE
162:           NROWA = N
163:       END IF
164:       UPPER = LSAME(UPLO,'U')
165: *
166: *     Test the input parameters.
167: *
168:       INFO = 0
169:       IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
170:           INFO = 1
171:       ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
172:           INFO = 2
173:       ELSE IF (M.LT.0) THEN
174:           INFO = 3
175:       ELSE IF (N.LT.0) THEN
176:           INFO = 4
177:       ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
178:           INFO = 7
179:       ELSE IF (LDB.LT.MAX(1,M)) THEN
180:           INFO = 9
181:       ELSE IF (LDC.LT.MAX(1,M)) THEN
182:           INFO = 12
183:       END IF
184:       IF (INFO.NE.0) THEN
185:           CALL XERBLA('ZSYMM ',INFO)
186:           RETURN
187:       END IF
188: *
189: *     Quick return if possible.
190: *
191:       IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
192:      +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
193: *
194: *     And when  alpha.eq.zero.
195: *
196:       IF (ALPHA.EQ.ZERO) THEN
197:           IF (BETA.EQ.ZERO) THEN
198:               DO 20 J = 1,N
199:                   DO 10 I = 1,M
200:                       C(I,J) = ZERO
201:    10             CONTINUE
202:    20         CONTINUE
203:           ELSE
204:               DO 40 J = 1,N
205:                   DO 30 I = 1,M
206:                       C(I,J) = BETA*C(I,J)
207:    30             CONTINUE
208:    40         CONTINUE
209:           END IF
210:           RETURN
211:       END IF
212: *
213: *     Start the operations.
214: *
215:       IF (LSAME(SIDE,'L')) THEN
216: *
217: *        Form  C := alpha*A*B + beta*C.
218: *
219:           IF (UPPER) THEN
220:               DO 70 J = 1,N
221:                   DO 60 I = 1,M
222:                       TEMP1 = ALPHA*B(I,J)
223:                       TEMP2 = ZERO
224:                       DO 50 K = 1,I - 1
225:                           C(K,J) = C(K,J) + TEMP1*A(K,I)
226:                           TEMP2 = TEMP2 + B(K,J)*A(K,I)
227:    50                 CONTINUE
228:                       IF (BETA.EQ.ZERO) THEN
229:                           C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2
230:                       ELSE
231:                           C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) +
232:      +                             ALPHA*TEMP2
233:                       END IF
234:    60             CONTINUE
235:    70         CONTINUE
236:           ELSE
237:               DO 100 J = 1,N
238:                   DO 90 I = M,1,-1
239:                       TEMP1 = ALPHA*B(I,J)
240:                       TEMP2 = ZERO
241:                       DO 80 K = I + 1,M
242:                           C(K,J) = C(K,J) + TEMP1*A(K,I)
243:                           TEMP2 = TEMP2 + B(K,J)*A(K,I)
244:    80                 CONTINUE
245:                       IF (BETA.EQ.ZERO) THEN
246:                           C(I,J) = TEMP1*A(I,I) + ALPHA*TEMP2
247:                       ELSE
248:                           C(I,J) = BETA*C(I,J) + TEMP1*A(I,I) +
249:      +                             ALPHA*TEMP2
250:                       END IF
251:    90             CONTINUE
252:   100         CONTINUE
253:           END IF
254:       ELSE
255: *
256: *        Form  C := alpha*B*A + beta*C.
257: *
258:           DO 170 J = 1,N
259:               TEMP1 = ALPHA*A(J,J)
260:               IF (BETA.EQ.ZERO) THEN
261:                   DO 110 I = 1,M
262:                       C(I,J) = TEMP1*B(I,J)
263:   110             CONTINUE
264:               ELSE
265:                   DO 120 I = 1,M
266:                       C(I,J) = BETA*C(I,J) + TEMP1*B(I,J)
267:   120             CONTINUE
268:               END IF
269:               DO 140 K = 1,J - 1
270:                   IF (UPPER) THEN
271:                       TEMP1 = ALPHA*A(K,J)
272:                   ELSE
273:                       TEMP1 = ALPHA*A(J,K)
274:                   END IF
275:                   DO 130 I = 1,M
276:                       C(I,J) = C(I,J) + TEMP1*B(I,K)
277:   130             CONTINUE
278:   140         CONTINUE
279:               DO 160 K = J + 1,N
280:                   IF (UPPER) THEN
281:                       TEMP1 = ALPHA*A(J,K)
282:                   ELSE
283:                       TEMP1 = ALPHA*A(K,J)
284:                   END IF
285:                   DO 150 I = 1,M
286:                       C(I,J) = C(I,J) + TEMP1*B(I,K)
287:   150             CONTINUE
288:   160         CONTINUE
289:   170     CONTINUE
290:       END IF
291: *
292:       RETURN
293: *
294: *     End of ZSYMM .
295: *
296:       END
297: