LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dtrsm()

subroutine dtrsm ( character side,
character uplo,
character transa,
character diag,
integer m,
integer n,
double precision alpha,
double precision, dimension(lda,*) a,
integer lda,
double precision, dimension(ldb,*) b,
integer ldb )

DTRSM

Purpose:
!>
!> DTRSM  solves one of the matrix equations
!>
!>    op( A )*X = alpha*B,   or   X*op( A ) = alpha*B,
!>
!> where alpha is a scalar, X and B are m by n matrices, A is a unit, or
!> non-unit,  upper or lower triangular matrix  and  op( A )  is one  of
!>
!>    op( A ) = A   or   op( A ) = A**T.
!>
!> The matrix X is overwritten on B.
!>
Parameters
[in]SIDE
!>          SIDE is CHARACTER*1
!>           On entry, SIDE specifies whether op( A ) appears on the left
!>           or right of X as follows:
!>
!>              SIDE = 'L' or 'l'   op( A )*X = alpha*B.
!>
!>              SIDE = 'R' or 'r'   X*op( A ) = alpha*B.
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>           On entry, UPLO specifies whether the matrix A is an upper or
!>           lower triangular matrix as follows:
!>
!>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
!>
!>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
!>
[in]TRANSA
!>          TRANSA is CHARACTER*1
!>           On entry, TRANSA specifies the form of op( A ) to be used in
!>           the matrix multiplication as follows:
!>
!>              TRANSA = 'N' or 'n'   op( A ) = A.
!>
!>              TRANSA = 'T' or 't'   op( A ) = A**T.
!>
!>              TRANSA = 'C' or 'c'   op( A ) = A**T.
!>
[in]DIAG
!>          DIAG is CHARACTER*1
!>           On entry, DIAG specifies whether or not A is unit triangular
!>           as follows:
!>
!>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
!>
!>              DIAG = 'N' or 'n'   A is not assumed to be unit
!>                                  triangular.
!>
[in]M
!>          M is INTEGER
!>           On entry, M specifies the number of rows of B. M must be at
!>           least zero.
!>
[in]N
!>          N is INTEGER
!>           On entry, N specifies the number of columns of B.  N must be
!>           at least zero.
!>
[in]ALPHA
!>          ALPHA is DOUBLE PRECISION.
!>           On entry,  ALPHA specifies the scalar  alpha. When  alpha is
!>           zero then  A is not referenced and  B need not be set before
!>           entry.
!>
[in]A
!>          A is DOUBLE PRECISION array, dimension ( LDA, k ),
!>           where k is m when SIDE = 'L' or 'l'
!>             and k is n when SIDE = 'R' or 'r'.
!>           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k
!>           upper triangular part of the array  A must contain the upper
!>           triangular matrix  and the strictly lower triangular part of
!>           A is not referenced.
!>           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k
!>           lower triangular part of the array  A must contain the lower
!>           triangular matrix  and the strictly upper triangular part of
!>           A is not referenced.
!>           Note that when  DIAG = 'U' or 'u',  the diagonal elements of
!>           A  are not referenced either,  but are assumed to be  unity.
!>
[in]LDA
!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then
!>           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'
!>           then LDA must be at least max( 1, n ).
!>
[in,out]B
!>          B is DOUBLE PRECISION array, dimension ( LDB, N )
!>           Before entry,  the leading  m by n part of the array  B must
!>           contain  the  right-hand  side  matrix  B,  and  on exit  is
!>           overwritten by the solution matrix  X.
!>
[in]LDB
!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   LDB  must  be  at  least
!>           max( 1, m ).
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  Level 3 Blas routine.
!>
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>

Definition at line 180 of file dtrsm.f.

181*
182* -- Reference BLAS level3 routine --
183* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
184* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
185*
186* .. Scalar Arguments ..
187 DOUBLE PRECISION ALPHA
188 INTEGER LDA,LDB,M,N
189 CHARACTER DIAG,SIDE,TRANSA,UPLO
190* ..
191* .. Array Arguments ..
192 DOUBLE PRECISION A(LDA,*),B(LDB,*)
193* ..
194*
195* =====================================================================
196*
197* .. External Functions ..
198 LOGICAL LSAME
199 EXTERNAL lsame
200* ..
201* .. External Subroutines ..
202 EXTERNAL xerbla
203* ..
204* .. Intrinsic Functions ..
205 INTRINSIC max
206* ..
207* .. Local Scalars ..
208 DOUBLE PRECISION TEMP
209 INTEGER I,INFO,J,K,NROWA
210 LOGICAL LSIDE,NOUNIT,UPPER
211* ..
212* .. Parameters ..
213 DOUBLE PRECISION ONE,ZERO
214 parameter(one=1.0d+0,zero=0.0d+0)
215* ..
216*
217* Test the input parameters.
218*
219 lside = lsame(side,'L')
220 IF (lside) THEN
221 nrowa = m
222 ELSE
223 nrowa = n
224 END IF
225 nounit = lsame(diag,'N')
226 upper = lsame(uplo,'U')
227*
228 info = 0
229 IF ((.NOT.lside) .AND. (.NOT.lsame(side,'R'))) THEN
230 info = 1
231 ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
232 info = 2
233 ELSE IF ((.NOT.lsame(transa,'N')) .AND.
234 + (.NOT.lsame(transa,'T')) .AND.
235 + (.NOT.lsame(transa,'C'))) THEN
236 info = 3
237 ELSE IF ((.NOT.lsame(diag,'U')) .AND.
238 + (.NOT.lsame(diag,'N'))) THEN
239 info = 4
240 ELSE IF (m.LT.0) THEN
241 info = 5
242 ELSE IF (n.LT.0) THEN
243 info = 6
244 ELSE IF (lda.LT.max(1,nrowa)) THEN
245 info = 9
246 ELSE IF (ldb.LT.max(1,m)) THEN
247 info = 11
248 END IF
249 IF (info.NE.0) THEN
250 CALL xerbla('DTRSM ',info)
251 RETURN
252 END IF
253*
254* Quick return if possible.
255*
256 IF (m.EQ.0 .OR. n.EQ.0) RETURN
257*
258* And when alpha.eq.zero.
259*
260 IF (alpha.EQ.zero) THEN
261 DO 20 j = 1,n
262 DO 10 i = 1,m
263 b(i,j) = zero
264 10 CONTINUE
265 20 CONTINUE
266 RETURN
267 END IF
268*
269* Start the operations.
270*
271 IF (lside) THEN
272 IF (lsame(transa,'N')) THEN
273*
274* Form B := alpha*inv( A )*B.
275*
276 IF (upper) THEN
277 DO 60 j = 1,n
278 IF (alpha.NE.one) THEN
279 DO 30 i = 1,m
280 b(i,j) = alpha*b(i,j)
281 30 CONTINUE
282 END IF
283 DO 50 k = m,1,-1
284 IF (b(k,j).NE.zero) THEN
285 IF (nounit) b(k,j) = b(k,j)/a(k,k)
286 DO 40 i = 1,k - 1
287 b(i,j) = b(i,j) - b(k,j)*a(i,k)
288 40 CONTINUE
289 END IF
290 50 CONTINUE
291 60 CONTINUE
292 ELSE
293 DO 100 j = 1,n
294 IF (alpha.NE.one) THEN
295 DO 70 i = 1,m
296 b(i,j) = alpha*b(i,j)
297 70 CONTINUE
298 END IF
299 DO 90 k = 1,m
300 IF (b(k,j).NE.zero) THEN
301 IF (nounit) b(k,j) = b(k,j)/a(k,k)
302 DO 80 i = k + 1,m
303 b(i,j) = b(i,j) - b(k,j)*a(i,k)
304 80 CONTINUE
305 END IF
306 90 CONTINUE
307 100 CONTINUE
308 END IF
309 ELSE
310*
311* Form B := alpha*inv( A**T )*B.
312*
313 IF (upper) THEN
314 DO 130 j = 1,n
315 DO 120 i = 1,m
316 temp = alpha*b(i,j)
317 DO 110 k = 1,i - 1
318 temp = temp - a(k,i)*b(k,j)
319 110 CONTINUE
320 IF (nounit) temp = temp/a(i,i)
321 b(i,j) = temp
322 120 CONTINUE
323 130 CONTINUE
324 ELSE
325 DO 160 j = 1,n
326 DO 150 i = m,1,-1
327 temp = alpha*b(i,j)
328 DO 140 k = i + 1,m
329 temp = temp - a(k,i)*b(k,j)
330 140 CONTINUE
331 IF (nounit) temp = temp/a(i,i)
332 b(i,j) = temp
333 150 CONTINUE
334 160 CONTINUE
335 END IF
336 END IF
337 ELSE
338 IF (lsame(transa,'N')) THEN
339*
340* Form B := alpha*B*inv( A ).
341*
342 IF (upper) THEN
343 DO 210 j = 1,n
344 IF (alpha.NE.one) THEN
345 DO 170 i = 1,m
346 b(i,j) = alpha*b(i,j)
347 170 CONTINUE
348 END IF
349 DO 190 k = 1,j - 1
350 IF (a(k,j).NE.zero) THEN
351 DO 180 i = 1,m
352 b(i,j) = b(i,j) - a(k,j)*b(i,k)
353 180 CONTINUE
354 END IF
355 190 CONTINUE
356 IF (nounit) THEN
357 temp = one/a(j,j)
358 DO 200 i = 1,m
359 b(i,j) = temp*b(i,j)
360 200 CONTINUE
361 END IF
362 210 CONTINUE
363 ELSE
364 DO 260 j = n,1,-1
365 IF (alpha.NE.one) THEN
366 DO 220 i = 1,m
367 b(i,j) = alpha*b(i,j)
368 220 CONTINUE
369 END IF
370 DO 240 k = j + 1,n
371 IF (a(k,j).NE.zero) THEN
372 DO 230 i = 1,m
373 b(i,j) = b(i,j) - a(k,j)*b(i,k)
374 230 CONTINUE
375 END IF
376 240 CONTINUE
377 IF (nounit) THEN
378 temp = one/a(j,j)
379 DO 250 i = 1,m
380 b(i,j) = temp*b(i,j)
381 250 CONTINUE
382 END IF
383 260 CONTINUE
384 END IF
385 ELSE
386*
387* Form B := alpha*B*inv( A**T ).
388*
389 IF (upper) THEN
390 DO 310 k = n,1,-1
391 IF (nounit) THEN
392 temp = one/a(k,k)
393 DO 270 i = 1,m
394 b(i,k) = temp*b(i,k)
395 270 CONTINUE
396 END IF
397 DO 290 j = 1,k - 1
398 IF (a(j,k).NE.zero) THEN
399 temp = a(j,k)
400 DO 280 i = 1,m
401 b(i,j) = b(i,j) - temp*b(i,k)
402 280 CONTINUE
403 END IF
404 290 CONTINUE
405 IF (alpha.NE.one) THEN
406 DO 300 i = 1,m
407 b(i,k) = alpha*b(i,k)
408 300 CONTINUE
409 END IF
410 310 CONTINUE
411 ELSE
412 DO 360 k = 1,n
413 IF (nounit) THEN
414 temp = one/a(k,k)
415 DO 320 i = 1,m
416 b(i,k) = temp*b(i,k)
417 320 CONTINUE
418 END IF
419 DO 340 j = k + 1,n
420 IF (a(j,k).NE.zero) THEN
421 temp = a(j,k)
422 DO 330 i = 1,m
423 b(i,j) = b(i,j) - temp*b(i,k)
424 330 CONTINUE
425 END IF
426 340 CONTINUE
427 IF (alpha.NE.one) THEN
428 DO 350 i = 1,m
429 b(i,k) = alpha*b(i,k)
430 350 CONTINUE
431 END IF
432 360 CONTINUE
433 END IF
434 END IF
435 END IF
436*
437 RETURN
438*
439* End of DTRSM
440*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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