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 of 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 of 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*> \date November 2011
160*
161*> \ingroup double_blas_level3
162*
163*> \par Further Details:
164*  =====================
165*>
166*> \verbatim
167*>
168*>  Level 3 Blas routine.
169*>
170*>  -- Written on 8-February-1989.
171*>     Jack Dongarra, Argonne National Laboratory.
172*>     Iain Duff, AERE Harwell.
173*>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
174*>     Sven Hammarling, Numerical Algorithms Group Ltd.
175*> \endverbatim
176*>
177*  =====================================================================
178      SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
179*
180*  -- Reference BLAS level3 routine (version 3.4.0) --
181*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
182*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
183*     November 2011
184*
185*     .. Scalar Arguments ..
186      DOUBLE PRECISION ALPHA
187      INTEGER LDA,LDB,M,N
188      CHARACTER DIAG,SIDE,TRANSA,UPLO
189*     ..
190*     .. Array Arguments ..
191      DOUBLE PRECISION A(LDA,*),B(LDB,*)
192*     ..
193*
194*  =====================================================================
195*
196*     .. External Functions ..
197      LOGICAL LSAME
198      EXTERNAL LSAME
199*     ..
200*     .. External Subroutines ..
201      EXTERNAL XERBLA
202*     ..
203*     .. Intrinsic Functions ..
204      INTRINSIC MAX
205*     ..
206*     .. Local Scalars ..
207      DOUBLE PRECISION TEMP
208      INTEGER I,INFO,J,K,NROWA
209      LOGICAL LSIDE,NOUNIT,UPPER
210*     ..
211*     .. Parameters ..
212      DOUBLE PRECISION ONE,ZERO
213      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
214*     ..
215*
216*     Test the input parameters.
217*
218      LSIDE = LSAME(SIDE,'L')
219      IF (LSIDE) THEN
220          NROWA = M
221      ELSE
222          NROWA = N
223      END IF
224      NOUNIT = LSAME(DIAG,'N')
225      UPPER = LSAME(UPLO,'U')
226*
227      INFO = 0
228      IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
229          INFO = 1
230      ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
231          INFO = 2
232      ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND.
233     +         (.NOT.LSAME(TRANSA,'T')) .AND.
234     +         (.NOT.LSAME(TRANSA,'C'))) THEN
235          INFO = 3
236      ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN
237          INFO = 4
238      ELSE IF (M.LT.0) THEN
239          INFO = 5
240      ELSE IF (N.LT.0) THEN
241          INFO = 6
242      ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
243          INFO = 9
244      ELSE IF (LDB.LT.MAX(1,M)) THEN
245          INFO = 11
246      END IF
247      IF (INFO.NE.0) THEN
248          CALL XERBLA('DTRMM ',INFO)
249          RETURN
250      END IF
251*
252*     Quick return if possible.
253*
254      IF (M.EQ.0 .OR. N.EQ.0) RETURN
255*
256*     And when  alpha.eq.zero.
257*
258      IF (ALPHA.EQ.ZERO) THEN
259          DO 20 J = 1,N
260              DO 10 I = 1,M
261                  B(I,J) = ZERO
262   10         CONTINUE
263   20     CONTINUE
264          RETURN
265      END IF
266*
267*     Start the operations.
268*
269      IF (LSIDE) THEN
270          IF (LSAME(TRANSA,'N')) THEN
271*
272*           Form  B := alpha*A*B.
273*
274              IF (UPPER) THEN
275                  DO 50 J = 1,N
276                      DO 40 K = 1,M
277                          IF (B(K,J).NE.ZERO) THEN
278                              TEMP = ALPHA*B(K,J)
279                              DO 30 I = 1,K - 1
280                                  B(I,J) = B(I,J) + TEMP*A(I,K)
281   30                         CONTINUE
282                              IF (NOUNIT) TEMP = TEMP*A(K,K)
283                              B(K,J) = TEMP
284                          END IF
285   40                 CONTINUE
286   50             CONTINUE
287              ELSE
288                  DO 80 J = 1,N
289                      DO 70 K = M,1,-1
290                          IF (B(K,J).NE.ZERO) THEN
291                              TEMP = ALPHA*B(K,J)
292                              B(K,J) = TEMP
293                              IF (NOUNIT) B(K,J) = B(K,J)*A(K,K)
294                              DO 60 I = K + 1,M
295                                  B(I,J) = B(I,J) + TEMP*A(I,K)
296   60                         CONTINUE
297                          END IF
298   70                 CONTINUE
299   80             CONTINUE
300              END IF
301          ELSE
302*
303*           Form  B := alpha*A**T*B.
304*
305              IF (UPPER) THEN
306                  DO 110 J = 1,N
307                      DO 100 I = M,1,-1
308                          TEMP = B(I,J)
309                          IF (NOUNIT) TEMP = TEMP*A(I,I)
310                          DO 90 K = 1,I - 1
311                              TEMP = TEMP + A(K,I)*B(K,J)
312   90                     CONTINUE
313                          B(I,J) = ALPHA*TEMP
314  100                 CONTINUE
315  110             CONTINUE
316              ELSE
317                  DO 140 J = 1,N
318                      DO 130 I = 1,M
319                          TEMP = B(I,J)
320                          IF (NOUNIT) TEMP = TEMP*A(I,I)
321                          DO 120 K = I + 1,M
322                              TEMP = TEMP + A(K,I)*B(K,J)
323  120                     CONTINUE
324                          B(I,J) = ALPHA*TEMP
325  130                 CONTINUE
326  140             CONTINUE
327              END IF
328          END IF
329      ELSE
330          IF (LSAME(TRANSA,'N')) THEN
331*
332*           Form  B := alpha*B*A.
333*
334              IF (UPPER) THEN
335                  DO 180 J = N,1,-1
336                      TEMP = ALPHA
337                      IF (NOUNIT) TEMP = TEMP*A(J,J)
338                      DO 150 I = 1,M
339                          B(I,J) = TEMP*B(I,J)
340  150                 CONTINUE
341                      DO 170 K = 1,J - 1
342                          IF (A(K,J).NE.ZERO) THEN
343                              TEMP = ALPHA*A(K,J)
344                              DO 160 I = 1,M
345                                  B(I,J) = B(I,J) + TEMP*B(I,K)
346  160                         CONTINUE
347                          END IF
348  170                 CONTINUE
349  180             CONTINUE
350              ELSE
351                  DO 220 J = 1,N
352                      TEMP = ALPHA
353                      IF (NOUNIT) TEMP = TEMP*A(J,J)
354                      DO 190 I = 1,M
355                          B(I,J) = TEMP*B(I,J)
356  190                 CONTINUE
357                      DO 210 K = J + 1,N
358                          IF (A(K,J).NE.ZERO) THEN
359                              TEMP = ALPHA*A(K,J)
360                              DO 200 I = 1,M
361                                  B(I,J) = B(I,J) + TEMP*B(I,K)
362  200                         CONTINUE
363                          END IF
364  210                 CONTINUE
365  220             CONTINUE
366              END IF
367          ELSE
368*
369*           Form  B := alpha*B*A**T.
370*
371              IF (UPPER) THEN
372                  DO 260 K = 1,N
373                      DO 240 J = 1,K - 1
374                          IF (A(J,K).NE.ZERO) THEN
375                              TEMP = ALPHA*A(J,K)
376                              DO 230 I = 1,M
377                                  B(I,J) = B(I,J) + TEMP*B(I,K)
378  230                         CONTINUE
379                          END IF
380  240                 CONTINUE
381                      TEMP = ALPHA
382                      IF (NOUNIT) TEMP = TEMP*A(K,K)
383                      IF (TEMP.NE.ONE) THEN
384                          DO 250 I = 1,M
385                              B(I,K) = TEMP*B(I,K)
386  250                     CONTINUE
387                      END IF
388  260             CONTINUE
389              ELSE
390                  DO 300 K = N,1,-1
391                      DO 280 J = K + 1,N
392                          IF (A(J,K).NE.ZERO) THEN
393                              TEMP = ALPHA*A(J,K)
394                              DO 270 I = 1,M
395                                  B(I,J) = B(I,J) + TEMP*B(I,K)
396  270                         CONTINUE
397                          END IF
398  280                 CONTINUE
399                      TEMP = ALPHA
400                      IF (NOUNIT) TEMP = TEMP*A(K,K)
401                      IF (TEMP.NE.ONE) THEN
402                          DO 290 I = 1,M
403                              B(I,K) = TEMP*B(I,K)
404  290                     CONTINUE
405                      END IF
406  300             CONTINUE
407              END IF
408          END IF
409      END IF
410*
411      RETURN
412*
413*     End of DTRMM .
414*
415      END
416