1*> \brief \b DTRMM
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
12*
13*       .. Scalar Arguments ..
14*       DOUBLE PRECISION ALPHA
15*       INTEGER LDA,LDB,M,N
16*       CHARACTER DIAG,SIDE,TRANSA,UPLO
17*       ..
18*       .. Array Arguments ..
19*       DOUBLE PRECISION A(LDA,*),B(LDB,*)
20*       ..
21*
22*
23*> \par Purpose:
24*  =============
25*>
26*> \verbatim
27*>
28*> DTRMM  performs one of the matrix-matrix operations
29*>
30*>    B := alpha*op( A )*B,   or   B := alpha*B*op( A ),
31*>
32*> where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or
33*> non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
34*>
35*>    op( A ) = A   or   op( A ) = A**T.
36*> \endverbatim
37*
38*  Arguments:
39*  ==========
40*
41*> \param[in] SIDE
42*> \verbatim
43*>          SIDE is CHARACTER*1
44*>           On entry,  SIDE specifies whether  op( A ) multiplies B from
45*>           the left or right as follows:
46*>
47*>              SIDE = 'L' or 'l'   B := alpha*op( A )*B.
48*>
49*>              SIDE = 'R' or 'r'   B := alpha*B*op( A ).
50*> \endverbatim
51*>
52*> \param[in] UPLO
53*> \verbatim
54*>          UPLO is CHARACTER*1
55*>           On entry, UPLO specifies whether the matrix A is an upper or
56*>           lower triangular matrix as follows:
57*>
58*>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
59*>
60*>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
61*> \endverbatim
62*>
63*> \param[in] TRANSA
64*> \verbatim
65*>          TRANSA is CHARACTER*1
66*>           On entry, TRANSA specifies the form of op( A ) to be used in
67*>           the matrix multiplication as follows:
68*>
69*>              TRANSA = 'N' or 'n'   op( A ) = A.
70*>
71*>              TRANSA = 'T' or 't'   op( A ) = A**T.
72*>
73*>              TRANSA = 'C' or 'c'   op( A ) = A**T.
74*> \endverbatim
75*>
76*> \param[in] DIAG
77*> \verbatim
78*>          DIAG is CHARACTER*1
79*>           On entry, DIAG specifies whether or not A is unit triangular
80*>           as follows:
81*>
82*>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
83*>
84*>              DIAG = 'N' or 'n'   A is not assumed to be unit
85*>                                  triangular.
86*> \endverbatim
87*>
88*> \param[in] M
89*> \verbatim
90*>          M is INTEGER
91*>           On entry, M specifies the number of rows of B. M must be at
92*>           least zero.
93*> \endverbatim
94*>
95*> \param[in] N
96*> \verbatim
97*>          N is INTEGER
98*>           On entry, N specifies the number of columns of B.  N must be
99*>           at least zero.
100*> \endverbatim
101*>
102*> \param[in] ALPHA
103*> \verbatim
104*>          ALPHA is DOUBLE PRECISION.
105*>           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
106*>           zero then  A is not referenced and  B need not be set before
107*>           entry.
108*> \endverbatim
109*>
110*> \param[in] A
111*> \verbatim
112*>           A is DOUBLE PRECISION array, dimension ( LDA, k ), where k is m
113*>           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.
114*>           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
115*>           upper triangular part of the array  A must contain the upper
116*>           triangular matrix  and the strictly lower triangular part of
117*>           A is not referenced.
118*>           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
119*>           lower triangular part of the array  A must contain the lower
120*>           triangular matrix  and the strictly upper triangular part of
121*>           A is not referenced.
122*>           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
123*>           A  are not referenced either,  but are assumed to be  unity.
124*> \endverbatim
125*>
126*> \param[in] LDA
127*> \verbatim
128*>          LDA is INTEGER
129*>           On entry, LDA specifies the first dimension of A as declared
130*>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
131*>           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
132*>           then LDA must be at least max( 1, n ).
133*> \endverbatim
134*>
135*> \param[in,out] B
136*> \verbatim
137*>          B is DOUBLE PRECISION array, dimension ( LDB, N )
138*>           Before entry,  the leading  m by n part of the array  B must
139*>           contain the matrix  B,  and  on exit  is overwritten  by the
140*>           transformed matrix.
141*> \endverbatim
142*>
143*> \param[in] LDB
144*> \verbatim
145*>          LDB is INTEGER
146*>           On entry, LDB specifies the first dimension of B as declared
147*>           in  the  calling  (sub)  program.   LDB  must  be  at  least
148*>           max( 1, m ).
149*> \endverbatim
150*
151*  Authors:
152*  ========
153*
154*> \author Univ. of Tennessee
155*> \author Univ. of California Berkeley
156*> \author Univ. of Colorado Denver
157*> \author NAG Ltd.
158*
159*> \ingroup double_blas_level3
160*
161*> \par Further Details:
162*  =====================
163*>
164*> \verbatim
165*>
166*>  Level 3 Blas routine.
167*>
168*>  -- Written on 8-February-1989.
169*>     Jack Dongarra, Argonne National Laboratory.
170*>     Iain Duff, AERE Harwell.
171*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
172*>     Sven Hammarling, Numerical Algorithms Group Ltd.
173*> \endverbatim
174*>
175*  =====================================================================
176      SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
177*
178*  -- Reference BLAS level3 routine --
179*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
180*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181*
182*     .. Scalar Arguments ..
183      DOUBLE PRECISION ALPHA
184      INTEGER LDA,LDB,M,N
185      CHARACTER DIAG,SIDE,TRANSA,UPLO
186*     ..
187*     .. Array Arguments ..
188      DOUBLE PRECISION A(LDA,*),B(LDB,*)
189*     ..
190*
191*  =====================================================================
192*
193*     .. External Functions ..
194      LOGICAL LSAME
195      EXTERNAL LSAME
196*     ..
197*     .. External Subroutines ..
198      EXTERNAL XERBLA
199*     ..
200*     .. Intrinsic Functions ..
201      INTRINSIC MAX
202*     ..
203*     .. Local Scalars ..
204      DOUBLE PRECISION TEMP
205      INTEGER I,INFO,J,K,NROWA
206      LOGICAL LSIDE,NOUNIT,UPPER
207*     ..
208*     .. Parameters ..
209      DOUBLE PRECISION ONE,ZERO
210      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
211*     ..
212*
213*     Test the input parameters.
214*
215      LSIDE = LSAME(SIDE,'L')
216      IF (LSIDE) THEN
217          NROWA = M
218      ELSE
219          NROWA = N
220      END IF
221      NOUNIT = LSAME(DIAG,'N')
222      UPPER = LSAME(UPLO,'U')
223*
224      INFO = 0
225      IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
226          INFO = 1
227      ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
228          INFO = 2
229      ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
230     +         (.NOT.LSAME(TRANSA,'T')) .AND.
231     +         (.NOT.LSAME(TRANSA,'C'))) THEN
232          INFO = 3
233      ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
234          INFO = 4
235      ELSE IF (M.LT.0) THEN
236          INFO = 5
237      ELSE IF (N.LT.0) THEN
238          INFO = 6
239      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
240          INFO = 9
241      ELSE IF (LDB.LT.MAX(1,M)) THEN
242          INFO = 11
243      END IF
244      IF (INFO.NE.0) THEN
245          CALL XERBLA('DTRMM ',INFO)
246          RETURN
247      END IF
248*
249*     Quick return if possible.
250*
251      IF (M.EQ.0 .OR. N.EQ.0) RETURN
252*
253*     And when  alpha.eq.zero.
254*
255      IF (ALPHA.EQ.ZERO) THEN
256          DO 20 J = 1,N
257              DO 10 I = 1,M
258                  B(I,J) = ZERO
259   10         CONTINUE
260   20     CONTINUE
261          RETURN
262      END IF
263*
264*     Start the operations.
265*
266      IF (LSIDE) THEN
267          IF (LSAME(TRANSA,'N')) THEN
268*
269*           Form  B := alpha*A*B.
270*
271              IF (UPPER) THEN
272                  DO 50 J = 1,N
273                      DO 40 K = 1,M
274                          IF (B(K,J).NE.ZERO) THEN
275                              TEMP = ALPHA*B(K,J)
276                              DO 30 I = 1,K - 1
277                                  B(I,J) = B(I,J) + TEMP*A(I,K)
278   30                         CONTINUE
279                              IF (NOUNIT) TEMP = TEMP*A(K,K)
280                              B(K,J) = TEMP
281                          END IF
282   40                 CONTINUE
283   50             CONTINUE
284              ELSE
285                  DO 80 J = 1,N
286                      DO 70 K = M,1,-1
287                          IF (B(K,J).NE.ZERO) THEN
288                              TEMP = ALPHA*B(K,J)
289                              B(K,J) = TEMP
290                              IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
291                              DO 60 I = K + 1,M
292                                  B(I,J) = B(I,J) + TEMP*A(I,K)
293   60                         CONTINUE
294                          END IF
295   70                 CONTINUE
296   80             CONTINUE
297              END IF
298          ELSE
299*
300*           Form  B := alpha*A**T*B.
301*
302              IF (UPPER) THEN
303                  DO 110 J = 1,N
304                      DO 100 I = M,1,-1
305                          TEMP = B(I,J)
306                          IF (NOUNIT) TEMP = TEMP*A(I,I)
307                          DO 90 K = 1,I - 1
308                              TEMP = TEMP + A(K,I)*B(K,J)
309   90                     CONTINUE
310                          B(I,J) = ALPHA*TEMP
311  100                 CONTINUE
312  110             CONTINUE
313              ELSE
314                  DO 140 J = 1,N
315                      DO 130 I = 1,M
316                          TEMP = B(I,J)
317                          IF (NOUNIT) TEMP = TEMP*A(I,I)
318                          DO 120 K = I + 1,M
319                              TEMP = TEMP + A(K,I)*B(K,J)
320  120                     CONTINUE
321                          B(I,J) = ALPHA*TEMP
322  130                 CONTINUE
323  140             CONTINUE
324              END IF
325          END IF
326      ELSE
327          IF (LSAME(TRANSA,'N')) THEN
328*
329*           Form  B := alpha*B*A.
330*
331              IF (UPPER) THEN
332                  DO 180 J = N,1,-1
333                      TEMP = ALPHA
334                      IF (NOUNIT) TEMP = TEMP*A(J,J)
335                      DO 150 I = 1,M
336                          B(I,J) = TEMP*B(I,J)
337  150                 CONTINUE
338                      DO 170 K = 1,J - 1
339                          IF (A(K,J).NE.ZERO) THEN
340                              TEMP = ALPHA*A(K,J)
341                              DO 160 I = 1,M
342                                  B(I,J) = B(I,J) + TEMP*B(I,K)
343  160                         CONTINUE
344                          END IF
345  170                 CONTINUE
346  180             CONTINUE
347              ELSE
348                  DO 220 J = 1,N
349                      TEMP = ALPHA
350                      IF (NOUNIT) TEMP = TEMP*A(J,J)
351                      DO 190 I = 1,M
352                          B(I,J) = TEMP*B(I,J)
353  190                 CONTINUE
354                      DO 210 K = J + 1,N
355                          IF (A(K,J).NE.ZERO) THEN
356                              TEMP = ALPHA*A(K,J)
357                              DO 200 I = 1,M
358                                  B(I,J) = B(I,J) + TEMP*B(I,K)
359  200                         CONTINUE
360                          END IF
361  210                 CONTINUE
362  220             CONTINUE
363              END IF
364          ELSE
365*
366*           Form  B := alpha*B*A**T.
367*
368              IF (UPPER) THEN
369                  DO 260 K = 1,N
370                      DO 240 J = 1,K - 1
371                          IF (A(J,K).NE.ZERO) THEN
372                              TEMP = ALPHA*A(J,K)
373                              DO 230 I = 1,M
374                                  B(I,J) = B(I,J) + TEMP*B(I,K)
375  230                         CONTINUE
376                          END IF
377  240                 CONTINUE
378                      TEMP = ALPHA
379                      IF (NOUNIT) TEMP = TEMP*A(K,K)
380                      IF (TEMP.NE.ONE) THEN
381                          DO 250 I = 1,M
382                              B(I,K) = TEMP*B(I,K)
383  250                     CONTINUE
384                      END IF
385  260             CONTINUE
386              ELSE
387                  DO 300 K = N,1,-1
388                      DO 280 J = K + 1,N
389                          IF (A(J,K).NE.ZERO) THEN
390                              TEMP = ALPHA*A(J,K)
391                              DO 270 I = 1,M
392                                  B(I,J) = B(I,J) + TEMP*B(I,K)
393  270                         CONTINUE
394                          END IF
395  280                 CONTINUE
396                      TEMP = ALPHA
397                      IF (NOUNIT) TEMP = TEMP*A(K,K)
398                      IF (TEMP.NE.ONE) THEN
399                          DO 290 I = 1,M
400                              B(I,K) = TEMP*B(I,K)
401  290                     CONTINUE
402                      END IF
403  300             CONTINUE
404              END IF
405          END IF
406      END IF
407*
408      RETURN
409*
410*     End of DTRMM
411*
412      END
413