LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

◆ dtrmm()

 subroutine dtrmm ( 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 )

DTRMM

Purpose:
DTRMM  performs one of the matrix-matrix operations

B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

where  alpha  is a scalar,  B  is an m by n matrix,  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.
Parameters
 [in] SIDE SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B. SIDE = 'R' or 'r' B := alpha*B*op( A ). [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 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 matrix B, and on exit is overwritten by the transformed matrix. [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 ).
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 176 of file dtrmm.f.

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*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
Here is the call graph for this function:
Here is the caller graph for this function: