1       SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
  2 *     .. Scalar Arguments ..
  3       COMPLEX ALPHA
  4       INTEGER LDA,LDB,M,N
  5       CHARACTER DIAG,SIDE,TRANSA,UPLO
  6 *     ..
  7 *     .. Array Arguments ..
  8       COMPLEX A(LDA,*),B(LDB,*)
  9 *     ..
 10 *
 11 *  Purpose
 12 *  =======
 13 *
 14 *  CTRMM  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   or   op( A ) = A**H.
 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**H.
 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  - COMPLEX         .
 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      - COMPLEX          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      - COMPLEX          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 CONJG,MAX
139 *     ..
140 *     .. Local Scalars ..
141       COMPLEX TEMP
142       INTEGER I,INFO,J,K,NROWA
143       LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
144 *     ..
145 *     .. Parameters ..
146       COMPLEX ONE
147       PARAMETER (ONE= (1.0E+0,0.0E+0))
148       COMPLEX ZERO
149       PARAMETER (ZERO= (0.0E+0,0.0E+0))
150 *     ..
151 *
152 *     Test the input parameters.
153 *
154       LSIDE = LSAME(SIDE,'L')
155       IF (LSIDE) THEN
156           NROWA = M
157       ELSE
158           NROWA = N
159       END IF
160       NOCONJ = LSAME(TRANSA,'T')
161       NOUNIT = LSAME(DIAG,'N')
162       UPPER = LSAME(UPLO,'U')
163 *
164       INFO = 0
165       IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
166           INFO = 1
167       ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
168           INFO = 2
169       ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
170      +         (.NOT.LSAME(TRANSA,'T')) .AND.
171      +         (.NOT.LSAME(TRANSA,'C'))) THEN
172           INFO = 3
173       ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
174           INFO = 4
175       ELSE IF (M.LT.0THEN
176           INFO = 5
177       ELSE IF (N.LT.0THEN
178           INFO = 6
179       ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
180           INFO = 9
181       ELSE IF (LDB.LT.MAX(1,M)) THEN
182           INFO = 11
183       END IF
184       IF (INFO.NE.0THEN
185           CALL XERBLA('CTRMM ',INFO)
186           RETURN
187       END IF
188 *
189 *     Quick return if possible.
190 *
191       IF (M.EQ.0 .OR. N.EQ.0RETURN
192 *
193 *     And when  alpha.eq.zero.
194 *
195       IF (ALPHA.EQ.ZERO) THEN
196           DO 20 J = 1,N
197               DO 10 I = 1,M
198                   B(I,J) = ZERO
199    10         CONTINUE
200    20     CONTINUE
201           RETURN
202       END IF
203 *
204 *     Start the operations.
205 *
206       IF (LSIDE) THEN
207           IF (LSAME(TRANSA,'N')) THEN
208 *
209 *           Form  B := alpha*A*B.
210 *
211               IF (UPPER) THEN
212                   DO 50 J = 1,N
213                       DO 40 K = 1,M
214                           IF (B(K,J).NE.ZERO) THEN
215                               TEMP = ALPHA*B(K,J)
216                               DO 30 I = 1,K - 1
217                                   B(I,J) = B(I,J) + TEMP*A(I,K)
218    30                         CONTINUE
219                               IF (NOUNIT) TEMP = TEMP*A(K,K)
220                               B(K,J) = TEMP
221                           END IF
222    40                 CONTINUE
223    50             CONTINUE
224               ELSE
225                   DO 80 J = 1,N
226                       DO 70 K = M,1,-1
227                           IF (B(K,J).NE.ZERO) THEN
228                               TEMP = ALPHA*B(K,J)
229                               B(K,J) = TEMP
230                               IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
231                               DO 60 I = K + 1,M
232                                   B(I,J) = B(I,J) + TEMP*A(I,K)
233    60                         CONTINUE
234                           END IF
235    70                 CONTINUE
236    80             CONTINUE
237               END IF
238           ELSE
239 *
240 *           Form  B := alpha*A**T*B   or   B := alpha*A**H*B.
241 *
242               IF (UPPER) THEN
243                   DO 120 J = 1,N
244                       DO 110 I = M,1,-1
245                           TEMP = B(I,J)
246                           IF (NOCONJ) THEN
247                               IF (NOUNIT) TEMP = TEMP*A(I,I)
248                               DO 90 K = 1,I - 1
249                                   TEMP = TEMP + A(K,I)*B(K,J)
250    90                         CONTINUE
251                           ELSE
252                               IF (NOUNIT) TEMP = TEMP*CONJG(A(I,I))
253                               DO 100 K = 1,I - 1
254                                   TEMP = TEMP + CONJG(A(K,I))*B(K,J)
255   100                         CONTINUE
256                           END IF
257                           B(I,J) = ALPHA*TEMP
258   110                 CONTINUE
259   120             CONTINUE
260               ELSE
261                   DO 160 J = 1,N
262                       DO 150 I = 1,M
263                           TEMP = B(I,J)
264                           IF (NOCONJ) THEN
265                               IF (NOUNIT) TEMP = TEMP*A(I,I)
266                               DO 130 K = I + 1,M
267                                   TEMP = TEMP + A(K,I)*B(K,J)
268   130                         CONTINUE
269                           ELSE
270                               IF (NOUNIT) TEMP = TEMP*CONJG(A(I,I))
271                               DO 140 K = I + 1,M
272                                   TEMP = TEMP + CONJG(A(K,I))*B(K,J)
273   140                         CONTINUE
274                           END IF
275                           B(I,J) = ALPHA*TEMP
276   150                 CONTINUE
277   160             CONTINUE
278               END IF
279           END IF
280       ELSE
281           IF (LSAME(TRANSA,'N')) THEN
282 *
283 *           Form  B := alpha*B*A.
284 *
285               IF (UPPER) THEN
286                   DO 200 J = N,1,-1
287                       TEMP = ALPHA
288                       IF (NOUNIT) TEMP = TEMP*A(J,J)
289                       DO 170 I = 1,M
290                           B(I,J) = TEMP*B(I,J)
291   170                 CONTINUE
292                       DO 190 K = 1,J - 1
293                           IF (A(K,J).NE.ZERO) THEN
294                               TEMP = ALPHA*A(K,J)
295                               DO 180 I = 1,M
296                                   B(I,J) = B(I,J) + TEMP*B(I,K)
297   180                         CONTINUE
298                           END IF
299   190                 CONTINUE
300   200             CONTINUE
301               ELSE
302                   DO 240 J = 1,N
303                       TEMP = ALPHA
304                       IF (NOUNIT) TEMP = TEMP*A(J,J)
305                       DO 210 I = 1,M
306                           B(I,J) = TEMP*B(I,J)
307   210                 CONTINUE
308                       DO 230 K = J + 1,N
309                           IF (A(K,J).NE.ZERO) THEN
310                               TEMP = ALPHA*A(K,J)
311                               DO 220 I = 1,M
312                                   B(I,J) = B(I,J) + TEMP*B(I,K)
313   220                         CONTINUE
314                           END IF
315   230                 CONTINUE
316   240             CONTINUE
317               END IF
318           ELSE
319 *
320 *           Form  B := alpha*B*A**T   or   B := alpha*B*A**H.
321 *
322               IF (UPPER) THEN
323                   DO 280 K = 1,N
324                       DO 260 J = 1,K - 1
325                           IF (A(J,K).NE.ZERO) THEN
326                               IF (NOCONJ) THEN
327                                   TEMP = ALPHA*A(J,K)
328                               ELSE
329                                   TEMP = ALPHA*CONJG(A(J,K))
330                               END IF
331                               DO 250 I = 1,M
332                                   B(I,J) = B(I,J) + TEMP*B(I,K)
333   250                         CONTINUE
334                           END IF
335   260                 CONTINUE
336                       TEMP = ALPHA
337                       IF (NOUNIT) THEN
338                           IF (NOCONJ) THEN
339                               TEMP = TEMP*A(K,K)
340                           ELSE
341                               TEMP = TEMP*CONJG(A(K,K))
342                           END IF
343                       END IF
344                       IF (TEMP.NE.ONE) THEN
345                           DO 270 I = 1,M
346                               B(I,K) = TEMP*B(I,K)
347   270                     CONTINUE
348                       END IF
349   280             CONTINUE
350               ELSE
351                   DO 320 K = N,1,-1
352                       DO 300 J = K + 1,N
353                           IF (A(J,K).NE.ZERO) THEN
354                               IF (NOCONJ) THEN
355                                   TEMP = ALPHA*A(J,K)
356                               ELSE
357                                   TEMP = ALPHA*CONJG(A(J,K))
358                               END IF
359                               DO 290 I = 1,M
360                                   B(I,J) = B(I,J) + TEMP*B(I,K)
361   290                         CONTINUE
362                           END IF
363   300                 CONTINUE
364                       TEMP = ALPHA
365                       IF (NOUNIT) THEN
366                           IF (NOCONJ) THEN
367                               TEMP = TEMP*A(K,K)
368                           ELSE
369                               TEMP = TEMP*CONJG(A(K,K))
370                           END IF
371                       END IF
372                       IF (TEMP.NE.ONE) THEN
373                           DO 310 I = 1,M
374                               B(I,K) = TEMP*B(I,K)
375   310                     CONTINUE
376                       END IF
377   320             CONTINUE
378               END IF
379           END IF
380       END IF
381 *
382       RETURN
383 *
384 *     End of CTRMM .
385 *
386       END