OpenRadioss 2025.1.11
OpenRadioss project
Loading...
Searching...
No Matches
ztrsm.f
Go to the documentation of this file.
1*> \brief \b ZTRSM
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 ZTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
12*
13* .. Scalar Arguments ..
14* COMPLEX*16 ALPHA
15* INTEGER LDA,LDB,M,N
16* CHARACTER DIAG,SIDE,TRANSA,UPLO
17* ..
18* .. Array Arguments ..
19* COMPLEX*16 A(LDA,*),B(LDB,*)
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> ZTRSM solves one of the matrix equations
29*>
30*> op( A )*X = alpha*B, or X*op( A ) = alpha*B,
31*>
32*> where alpha is a scalar, X and B are m by n matrices, 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 or op( A ) = A**H.
36*>
37*> The matrix X is overwritten on B.
38*> \endverbatim
39*
40* Arguments:
41* ==========
42*
43*> \param[in] SIDE
44*> \verbatim
45*> SIDE is CHARACTER*1
46*> On entry, SIDE specifies whether op( A ) appears on the left
47*> or right of X as follows:
48*>
49*> SIDE = 'L' or 'l' op( A )*X = alpha*B.
50*>
51*> SIDE = 'R' or 'r' X*op( A ) = alpha*B.
52*> \endverbatim
53*>
54*> \param[in] UPLO
55*> \verbatim
56*> UPLO is CHARACTER*1
57*> On entry, UPLO specifies whether the matrix A is an upper or
58*> lower triangular matrix as follows:
59*>
60*> UPLO = 'U' or 'u' A is an upper triangular matrix.
61*>
62*> UPLO = 'L' or 'l' A is a lower triangular matrix.
63*> \endverbatim
64*>
65*> \param[in] TRANSA
66*> \verbatim
67*> TRANSA is CHARACTER*1
68*> On entry, TRANSA specifies the form of op( A ) to be used in
69*> the matrix multiplication as follows:
70*>
71*> TRANSA = 'N' or 'n' op( A ) = A.
72*>
73*> TRANSA = 'T' or 't' op( A ) = A**T.
74*>
75*> TRANSA = 'C' or 'c' op( A ) = A**H.
76*> \endverbatim
77*>
78*> \param[in] DIAG
79*> \verbatim
80*> DIAG is CHARACTER*1
81*> On entry, DIAG specifies whether or not A is unit triangular
82*> as follows:
83*>
84*> DIAG = 'U' or 'u' A is assumed to be unit triangular.
85*>
86*> DIAG = 'N' or 'n' A is not assumed to be unit
87*> triangular.
88*> \endverbatim
89*>
90*> \param[in] M
91*> \verbatim
92*> M is INTEGER
93*> On entry, M specifies the number of rows of B. M must be at
94*> least zero.
95*> \endverbatim
96*>
97*> \param[in] N
98*> \verbatim
99*> N is INTEGER
100*> On entry, N specifies the number of columns of B. N must be
101*> at least zero.
102*> \endverbatim
103*>
104*> \param[in] ALPHA
105*> \verbatim
106*> ALPHA is COMPLEX*16
107*> On entry, ALPHA specifies the scalar alpha. When alpha is
108*> zero then A is not referenced and B need not be set before
109*> entry.
110*> \endverbatim
111*>
112*> \param[in] A
113*> \verbatim
114*> A is COMPLEX*16 array, dimension ( LDA, k ),
115*> where k is m when SIDE = 'L' or 'l'
116*> and k is n when SIDE = 'R' or 'r'.
117*> Before entry with UPLO = 'U' or 'u', the leading k by k
118*> upper triangular part of the array A must contain the upper
119*> triangular matrix and the strictly lower triangular part of
120*> A is not referenced.
121*> Before entry with UPLO = 'L' or 'l', the leading k by k
122*> lower triangular part of the array A must contain the lower
123*> triangular matrix and the strictly upper triangular part of
124*> A is not referenced.
125*> Note that when DIAG = 'U' or 'u', the diagonal elements of
126*> A are not referenced either, but are assumed to be unity.
127*> \endverbatim
128*>
129*> \param[in] LDA
130*> \verbatim
131*> LDA is INTEGER
132*> On entry, LDA specifies the first dimension of A as declared
133*> in the calling (sub) program. When SIDE = 'L' or 'l' then
134*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
135*> then LDA must be at least max( 1, n ).
136*> \endverbatim
137*>
138*> \param[in,out] B
139*> \verbatim
140*> B is COMPLEX*16 array, dimension ( LDB, N )
141*> Before entry, the leading m by n part of the array B must
142*> contain the right-hand side matrix B, and on exit is
143*> overwritten by the solution matrix X.
144*> \endverbatim
145*>
146*> \param[in] LDB
147*> \verbatim
148*> LDB is INTEGER
149*> On entry, LDB specifies the first dimension of B as declared
150*> in the calling (sub) program. LDB must be at least
151*> max( 1, m ).
152*> \endverbatim
153*
154* Authors:
155* ========
156*
157*> \author Univ. of Tennessee
158*> \author Univ. of California Berkeley
159*> \author Univ. of Colorado Denver
160*> \author NAG Ltd.
161*
162*> \ingroup complex16_blas_level3
163*
164*> \par Further Details:
165* =====================
166*>
167*> \verbatim
168*>
169*> Level 3 Blas routine.
170*>
171*> -- Written on 8-February-1989.
172*> Jack Dongarra, Argonne National Laboratory.
173*> Iain Duff, AERE Harwell.
174*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
175*> Sven Hammarling, Numerical Algorithms Group Ltd.
176*> \endverbatim
177*>
178* =====================================================================
179 SUBROUTINE ztrsm(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
180*
181* -- Reference BLAS level3 routine --
182* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
183* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
184*
185* .. Scalar Arguments ..
186 COMPLEX*16 ALPHA
187 INTEGER LDA,LDB,M,N
188 CHARACTER DIAG,SIDE,TRANSA,UPLO
189* ..
190* .. Array Arguments ..
191 COMPLEX*16 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 dconjg,max
205* ..
206* .. Local Scalars ..
207 COMPLEX*16 TEMP
208 INTEGER I,INFO,J,K,NROWA
209 LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
210* ..
211* .. Parameters ..
212 COMPLEX*16 ONE
213 parameter(one= (1.0d+0,0.0d+0))
214 COMPLEX*16 ZERO
215 parameter(zero= (0.0d+0,0.0d+0))
216* ..
217*
218* Test the input parameters.
219*
220 lside = lsame(side,'L')
221 IF (lside) THEN
222 nrowa = m
223 ELSE
224 nrowa = n
225 END IF
226 noconj = lsame(transa,'T')
227 nounit = lsame(diag,'N')
228 upper = lsame(uplo,'U')
229*
230 info = 0
231 IF ((.NOT.lside) .AND. (.NOT.lsame(side,'R'))) THEN
232 info = 1
233 ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
234 info = 2
235 ELSE IF ((.NOT.lsame(transa,'N')) .AND.
236 + (.NOT.lsame(transa,'T')) .AND.
237 + (.NOT.lsame(transa,'C'))) THEN
238 info = 3
239 ELSE IF ((.NOT.lsame(diag,'u.AND..NOT.')) (LSAME(DIAG,'n'))) THEN
240 INFO = 4
241.LT. ELSE IF (M0) THEN
242 INFO = 5
243.LT. ELSE IF (N0) THEN
244 INFO = 6
245.LT. ELSE IF (LDAMAX(1,NROWA)) THEN
246 INFO = 9
247.LT. ELSE IF (LDBMAX(1,M)) THEN
248 INFO = 11
249 END IF
250.NE. IF (INFO0) THEN
251 CALL XERBLA('ztrsm ',INFO)
252 RETURN
253 END IF
254*
255* Quick return if possible.
256*
257.EQ..OR..EQ. IF (M0 N0) RETURN
258*
259* And when alpha.eq.zero.
260*
261.EQ. IF (ALPHAZERO) THEN
262 DO 20 J = 1,N
263 DO 10 I = 1,M
264 B(I,J) = ZERO
265 10 CONTINUE
266 20 CONTINUE
267 RETURN
268 END IF
269*
270* Start the operations.
271*
272 IF (LSIDE) THEN
273 IF (LSAME(TRANSA,'n')) THEN
274*
275* Form B := alpha*inv( A )*B.
276*
277 IF (UPPER) THEN
278 DO 60 J = 1,N
279.NE. IF (ALPHAONE) THEN
280 DO 30 I = 1,M
281 B(I,J) = ALPHA*B(I,J)
282 30 CONTINUE
283 END IF
284 DO 50 K = M,1,-1
285.NE. IF (B(K,J)ZERO) THEN
286 IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
287 DO 40 I = 1,K - 1
288 B(I,J) = B(I,J) - B(K,J)*A(I,K)
289 40 CONTINUE
290 END IF
291 50 CONTINUE
292 60 CONTINUE
293 ELSE
294 DO 100 J = 1,N
295.NE. IF (ALPHAONE) THEN
296 DO 70 I = 1,M
297 B(I,J) = ALPHA*B(I,J)
298 70 CONTINUE
299 END IF
300 DO 90 K = 1,M
301.NE. IF (B(K,J)ZERO) THEN
302 IF (NOUNIT) B(K,J) = B(K,J)/A(K,K)
303 DO 80 I = K + 1,M
304 B(I,J) = B(I,J) - B(K,J)*A(I,K)
305 80 CONTINUE
306 END IF
307 90 CONTINUE
308 100 CONTINUE
309 END IF
310 ELSE
311*
312* Form B := alpha*inv( A**T )*B
313* or B := alpha*inv( A**H )*B.
314*
315 IF (UPPER) THEN
316 DO 140 J = 1,N
317 DO 130 I = 1,M
318 TEMP = ALPHA*B(I,J)
319 IF (NOCONJ) THEN
320 DO 110 K = 1,I - 1
321 TEMP = TEMP - A(K,I)*B(K,J)
322 110 CONTINUE
323 IF (NOUNIT) TEMP = TEMP/A(I,I)
324 ELSE
325 DO 120 K = 1,I - 1
326 TEMP = TEMP - DCONJG(A(K,I))*B(K,J)
327 120 CONTINUE
328 IF (NOUNIT) TEMP = TEMP/DCONJG(A(I,I))
329 END IF
330 B(I,J) = TEMP
331 130 CONTINUE
332 140 CONTINUE
333 ELSE
334 DO 180 J = 1,N
335 DO 170 I = M,1,-1
336 TEMP = ALPHA*B(I,J)
337 IF (NOCONJ) THEN
338 DO 150 K = I + 1,M
339 TEMP = TEMP - A(K,I)*B(K,J)
340 150 CONTINUE
341 IF (NOUNIT) TEMP = TEMP/A(I,I)
342 ELSE
343 DO 160 K = I + 1,M
344 TEMP = TEMP - DCONJG(A(K,I))*B(K,J)
345 160 CONTINUE
346 IF (NOUNIT) TEMP = TEMP/DCONJG(A(I,I))
347 END IF
348 B(I,J) = TEMP
349 170 CONTINUE
350 180 CONTINUE
351 END IF
352 END IF
353 ELSE
354 IF (LSAME(TRANSA,'n')) THEN
355*
356* Form B := alpha*B*inv( A ).
357*
358 IF (UPPER) THEN
359 DO 230 J = 1,N
360.NE. IF (ALPHAONE) THEN
361 DO 190 I = 1,M
362 B(I,J) = ALPHA*B(I,J)
363 190 CONTINUE
364 END IF
365 DO 210 K = 1,J - 1
366.NE. IF (A(K,J)ZERO) THEN
367 DO 200 I = 1,M
368 B(I,J) = B(I,J) - A(K,J)*B(I,K)
369 200 CONTINUE
370 END IF
371 210 CONTINUE
372 IF (NOUNIT) THEN
373 TEMP = ONE/A(J,J)
374 DO 220 I = 1,M
375 B(I,J) = TEMP*B(I,J)
376 220 CONTINUE
377 END IF
378 230 CONTINUE
379 ELSE
380 DO 280 J = N,1,-1
381.NE. IF (ALPHAONE) THEN
382 DO 240 I = 1,M
383 B(I,J) = ALPHA*B(I,J)
384 240 CONTINUE
385 END IF
386 DO 260 K = J + 1,N
387.NE. IF (A(K,J)ZERO) THEN
388 DO 250 I = 1,M
389 B(I,J) = B(I,J) - A(K,J)*B(I,K)
390 250 CONTINUE
391 END IF
392 260 CONTINUE
393 IF (NOUNIT) THEN
394 TEMP = ONE/A(J,J)
395 DO 270 I = 1,M
396 B(I,J) = TEMP*B(I,J)
397 270 CONTINUE
398 END IF
399 280 CONTINUE
400 END IF
401 ELSE
402*
403* Form B := alpha*B*inv( A**T )
404* or B := alpha*B*inv( A**H ).
405*
406 IF (UPPER) THEN
407 DO 330 K = N,1,-1
408 IF (NOUNIT) THEN
409 IF (NOCONJ) THEN
410 TEMP = ONE/A(K,K)
411 ELSE
412 TEMP = ONE/DCONJG(A(K,K))
413 END IF
414 DO 290 I = 1,M
415 B(I,K) = TEMP*B(I,K)
416 290 CONTINUE
417 END IF
418 DO 310 J = 1,K - 1
419.NE. IF (A(J,K)ZERO) THEN
420 IF (NOCONJ) THEN
421 TEMP = A(J,K)
422 ELSE
423 TEMP = DCONJG(A(J,K))
424 END IF
425 DO 300 I = 1,M
426 B(I,J) = B(I,J) - TEMP*B(I,K)
427 300 CONTINUE
428 END IF
429 310 CONTINUE
430.NE. IF (ALPHAONE) THEN
431 DO 320 I = 1,M
432 B(I,K) = ALPHA*B(I,K)
433 320 CONTINUE
434 END IF
435 330 CONTINUE
436 ELSE
437 DO 380 K = 1,N
438 IF (NOUNIT) THEN
439 IF (NOCONJ) THEN
440 TEMP = ONE/A(K,K)
441 ELSE
442 TEMP = ONE/DCONJG(A(K,K))
443 END IF
444 DO 340 I = 1,M
445 B(I,K) = TEMP*B(I,K)
446 340 CONTINUE
447 END IF
448 DO 360 J = K + 1,N
449.NE. IF (A(J,K)ZERO) THEN
450 IF (NOCONJ) THEN
451 TEMP = A(J,K)
452 ELSE
453 TEMP = DCONJG(A(J,K))
454 END IF
455 DO 350 I = 1,M
456 B(I,J) = B(I,J) - TEMP*B(I,K)
457 350 CONTINUE
458 END IF
459 360 CONTINUE
460.NE. IF (ALPHAONE) THEN
461 DO 370 I = 1,M
462 B(I,K) = ALPHA*B(I,K)
463 370 CONTINUE
464 END IF
465 380 CONTINUE
466 END IF
467 END IF
468 END IF
469*
470 RETURN
471*
472* End of ZTRSM
473*
474 END
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
ztrsm
subroutine ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRSM
Definition ztrsm.f:180
max
#define max(a, b)
Definition macros.h:21