1       SUBROUTINE STRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
  2 *     .. Scalar Arguments ..
  3       REAL ALPHA
  4       INTEGER LDA,LDB,M,N
  5       CHARACTER DIAG,SIDE,TRANSA,UPLO
  6 *     ..
  7 *     .. Array Arguments ..
  8       REAL A(LDA,*),B(LDB,*)
  9 *     ..
 10 *
 11 *  Purpose
 12 *  =======
 13 *
 14 *  STRMM  performs one of the matrix-matrix operations
 15 *
 16 *     B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
 17 *
 18 *  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
 19 *  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
 20 *
 21 *     op( A ) = A   or   op( A ) = A**T.
 22 *
 23 *  Arguments
 24 *  ==========
 25 *
 26 *  SIDE   - CHARACTER*1.
 27 *           On entry,  SIDE specifies whether  op( A ) multiplies B from
 28 *           the left or right as follows:
 29 *
 30 *              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
 31 *
 32 *              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
 33 *
 34 *           Unchanged on exit.
 35 *
 36 *  UPLO   - CHARACTER*1.
 37 *           On entry, UPLO specifies whether the matrix A is an upper or
 38 *           lower triangular matrix as follows:
 39 *
 40 *              UPLO = 'U' or 'u'   A is an upper triangular matrix.
 41 *
 42 *              UPLO = 'L' or 'l'   A is a lower triangular matrix.
 43 *
 44 *           Unchanged on exit.
 45 *
 46 *  TRANSA - CHARACTER*1.
 47 *           On entry, TRANSA specifies the form of op( A ) to be used in
 48 *           the matrix multiplication as follows:
 49 *
 50 *              TRANSA = 'N' or 'n'   op( A ) = A.
 51 *
 52 *              TRANSA = 'T' or 't'   op( A ) = A**T.
 53 *
 54 *              TRANSA = 'C' or 'c'   op( A ) = A**T.
 55 *
 56 *           Unchanged on exit.
 57 *
 58 *  DIAG   - CHARACTER*1.
 59 *           On entry, DIAG specifies whether or not A is unit triangular
 60 *           as follows:
 61 *
 62 *              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
 63 *
 64 *              DIAG = 'N' or 'n'   A is not assumed to be unit
 65 *                                  triangular.
 66 *
 67 *           Unchanged on exit.
 68 *
 69 *  M      - INTEGER.
 70 *           On entry, M specifies the number of rows of B. M must be at
 71 *           least zero.
 72 *           Unchanged on exit.
 73 *
 74 *  N      - INTEGER.
 75 *           On entry, N specifies the number of columns of B.  N must be
 76 *           at least zero.
 77 *           Unchanged on exit.
 78 *
 79 *  ALPHA  - REAL            .
 80 *           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
 81 *           zero then  A is not referenced and  B need not be set before
 82 *           entry.
 83 *           Unchanged on exit.
 84 *
 85 *  A      - REAL             array of DIMENSION ( LDA, k ), where k is m
 86 *           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
 87 *           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
 88 *           upper triangular part of the array  A must contain the upper
 89 *           triangular matrix  and the strictly lower triangular part of
 90 *           A is not referenced.
 91 *           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
 92 *           lower triangular part of the array  A must contain the lower
 93 *           triangular matrix  and the strictly upper triangular part of
 94 *           A is not referenced.
 95 *           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
 96 *           A  are not referenced either,  but are assumed to be  unity.
 97 *           Unchanged on exit.
 98 *
 99 *  LDA    - INTEGER.
100 *           On entry, LDA specifies the first dimension of A as declared
101 *           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
102 *           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
103 *           then LDA must be at least max( 1, n ).
104 *           Unchanged on exit.
105 *
106 *  B      - REAL             array of DIMENSION ( LDB, n ).
107 *           Before entry,  the leading  m by n part of the array  B must
108 *           contain the matrix  B,  and  on exit  is overwritten  by the
109 *           transformed matrix.
110 *
111 *  LDB    - INTEGER.
112 *           On entry, LDB specifies the first dimension of B as declared
113 *           in  the  calling  (sub)  program.   LDB  must  be  at  least
114 *           max( 1, m ).
115 *           Unchanged on exit.
116 *
117 *  Further Details
118 *  ===============
119 *
120 *  Level 3 Blas routine.
121 *
122 *  -- Written on 8-February-1989.
123 *     Jack Dongarra, Argonne National Laboratory.
124 *     Iain Duff, AERE Harwell.
125 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.
126 *     Sven Hammarling, Numerical Algorithms Group Ltd.
127 *
128 *  =====================================================================
129 *
130 *     .. External Functions ..
131       LOGICAL LSAME
132       EXTERNAL LSAME
133 *     ..
134 *     .. External Subroutines ..
135       EXTERNAL XERBLA
136 *     ..
137 *     .. Intrinsic Functions ..
138       INTRINSIC MAX
139 *     ..
140 *     .. Local Scalars ..
141       REAL TEMP
142       INTEGER I,INFO,J,K,NROWA
143       LOGICAL LSIDE,NOUNIT,UPPER
144 *     ..
145 *     .. Parameters ..
146       REAL ONE,ZERO
147       PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
148 *     ..
149 *
150 *     Test the input parameters.
151 *
152       LSIDE = LSAME(SIDE,'L')
153       IF (LSIDE) THEN
154           NROWA = M
155       ELSE
156           NROWA = N
157       END IF
158       NOUNIT = LSAME(DIAG,'N')
159       UPPER = LSAME(UPLO,'U')
160 *
161       INFO = 0
162       IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
163           INFO = 1
164       ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
165           INFO = 2
166       ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
167      +         (.NOT.LSAME(TRANSA,'T')) .AND.
168      +         (.NOT.LSAME(TRANSA,'C'))) THEN
169           INFO = 3
170       ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
171           INFO = 4
172       ELSE IF (M.LT.0THEN
173           INFO = 5
174       ELSE IF (N.LT.0THEN
175           INFO = 6
176       ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
177           INFO = 9
178       ELSE IF (LDB.LT.MAX(1,M)) THEN
179           INFO = 11
180       END IF
181       IF (INFO.NE.0THEN
182           CALL XERBLA('STRMM ',INFO)
183           RETURN
184       END IF
185 *
186 *     Quick return if possible.
187 *
188       IF (M.EQ.0 .OR. N.EQ.0RETURN
189 *
190 *     And when  alpha.eq.zero.
191 *
192       IF (ALPHA.EQ.ZERO) THEN
193           DO 20 J = 1,N
194               DO 10 I = 1,M
195                   B(I,J) = ZERO
196    10         CONTINUE
197    20     CONTINUE
198           RETURN
199       END IF
200 *
201 *     Start the operations.
202 *
203       IF (LSIDE) THEN
204           IF (LSAME(TRANSA,'N')) THEN
205 *
206 *           Form  B := alpha*A*B.
207 *
208               IF (UPPER) THEN
209                   DO 50 J = 1,N
210                       DO 40 K = 1,M
211                           IF (B(K,J).NE.ZERO) THEN
212                               TEMP = ALPHA*B(K,J)
213                               DO 30 I = 1,K - 1
214                                   B(I,J) = B(I,J) + TEMP*A(I,K)
215    30                         CONTINUE
216                               IF (NOUNIT) TEMP = TEMP*A(K,K)
217                               B(K,J) = TEMP
218                           END IF
219    40                 CONTINUE
220    50             CONTINUE
221               ELSE
222                   DO 80 J = 1,N
223                       DO 70 K = M,1,-1
224                           IF (B(K,J).NE.ZERO) THEN
225                               TEMP = ALPHA*B(K,J)
226                               B(K,J) = TEMP
227                               IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
228                               DO 60 I = K + 1,M
229                                   B(I,J) = B(I,J) + TEMP*A(I,K)
230    60                         CONTINUE
231                           END IF
232    70                 CONTINUE
233    80             CONTINUE
234               END IF
235           ELSE
236 *
237 *           Form  B := alpha*A**T*B.
238 *
239               IF (UPPER) THEN
240                   DO 110 J = 1,N
241                       DO 100 I = M,1,-1
242                           TEMP = B(I,J)
243                           IF (NOUNIT) TEMP = TEMP*A(I,I)
244                           DO 90 K = 1,I - 1
245                               TEMP = TEMP + A(K,I)*B(K,J)
246    90                     CONTINUE
247                           B(I,J) = ALPHA*TEMP
248   100                 CONTINUE
249   110             CONTINUE
250               ELSE
251                   DO 140 J = 1,N
252                       DO 130 I = 1,M
253                           TEMP = B(I,J)
254                           IF (NOUNIT) TEMP = TEMP*A(I,I)
255                           DO 120 K = I + 1,M
256                               TEMP = TEMP + A(K,I)*B(K,J)
257   120                     CONTINUE
258                           B(I,J) = ALPHA*TEMP
259   130                 CONTINUE
260   140             CONTINUE
261               END IF
262           END IF
263       ELSE
264           IF (LSAME(TRANSA,'N')) THEN
265 *
266 *           Form  B := alpha*B*A.
267 *
268               IF (UPPER) THEN
269                   DO 180 J = N,1,-1
270                       TEMP = ALPHA
271                       IF (NOUNIT) TEMP = TEMP*A(J,J)
272                       DO 150 I = 1,M
273                           B(I,J) = TEMP*B(I,J)
274   150                 CONTINUE
275                       DO 170 K = 1,J - 1
276                           IF (A(K,J).NE.ZERO) THEN
277                               TEMP = ALPHA*A(K,J)
278                               DO 160 I = 1,M
279                                   B(I,J) = B(I,J) + TEMP*B(I,K)
280   160                         CONTINUE
281                           END IF
282   170                 CONTINUE
283   180             CONTINUE
284               ELSE
285                   DO 220 J = 1,N
286                       TEMP = ALPHA
287                       IF (NOUNIT) TEMP = TEMP*A(J,J)
288                       DO 190 I = 1,M
289                           B(I,J) = TEMP*B(I,J)
290   190                 CONTINUE
291                       DO 210 K = J + 1,N
292                           IF (A(K,J).NE.ZERO) THEN
293                               TEMP = ALPHA*A(K,J)
294                               DO 200 I = 1,M
295                                   B(I,J) = B(I,J) + TEMP*B(I,K)
296   200                         CONTINUE
297                           END IF
298   210                 CONTINUE
299   220             CONTINUE
300               END IF
301           ELSE
302 *
303 *           Form  B := alpha*B*A**T.
304 *
305               IF (UPPER) THEN
306                   DO 260 K = 1,N
307                       DO 240 J = 1,K - 1
308                           IF (A(J,K).NE.ZERO) THEN
309                               TEMP = ALPHA*A(J,K)
310                               DO 230 I = 1,M
311                                   B(I,J) = B(I,J) + TEMP*B(I,K)
312   230                         CONTINUE
313                           END IF
314   240                 CONTINUE
315                       TEMP = ALPHA
316                       IF (NOUNIT) TEMP = TEMP*A(K,K)
317                       IF (TEMP.NE.ONE) THEN
318                           DO 250 I = 1,M
319                               B(I,K) = TEMP*B(I,K)
320   250                     CONTINUE
321                       END IF
322   260             CONTINUE
323               ELSE
324                   DO 300 K = N,1,-1
325                       DO 280 J = K + 1,N
326                           IF (A(J,K).NE.ZERO) THEN
327                               TEMP = ALPHA*A(J,K)
328                               DO 270 I = 1,M
329                                   B(I,J) = B(I,J) + TEMP*B(I,K)
330   270                         CONTINUE
331                           END IF
332   280                 CONTINUE
333                       TEMP = ALPHA
334                       IF (NOUNIT) TEMP = TEMP*A(K,K)
335                       IF (TEMP.NE.ONE) THEN
336                           DO 290 I = 1,M
337                               B(I,K) = TEMP*B(I,K)
338   290                     CONTINUE
339                       END IF
340   300             CONTINUE
341               END IF
342           END IF
343       END IF
344 *
345       RETURN
346 *
347 *     End of STRMM .
348 *
349       END