LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ctrmm()

 subroutine ctrmm ( character SIDE, character UPLO, character TRANSA, character DIAG, integer M, integer N, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(ldb,*) B, integer LDB )

CTRMM

Purpose:
``` CTRMM  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   or   op( A ) = A**H.```
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**H.``` [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 COMPLEX 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 COMPLEX 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 COMPLEX 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 ctrmm.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 COMPLEX ALPHA
184 INTEGER LDA,LDB,M,N
185 CHARACTER DIAG,SIDE,TRANSA,UPLO
186* ..
187* .. Array Arguments ..
188 COMPLEX 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 conjg,max
202* ..
203* .. Local Scalars ..
204 COMPLEX TEMP
205 INTEGER I,INFO,J,K,NROWA
206 LOGICAL LSIDE,NOCONJ,NOUNIT,UPPER
207* ..
208* .. Parameters ..
209 COMPLEX ONE
210 parameter(one= (1.0e+0,0.0e+0))
211 COMPLEX ZERO
212 parameter(zero= (0.0e+0,0.0e+0))
213* ..
214*
215* Test the input parameters.
216*
217 lside = lsame(side,'L')
218 IF (lside) THEN
219 nrowa = m
220 ELSE
221 nrowa = n
222 END IF
223 noconj = lsame(transa,'T')
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('CTRMM ',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 or B := alpha*A**H*B.
304*
305 IF (upper) THEN
306 DO 120 j = 1,n
307 DO 110 i = m,1,-1
308 temp = b(i,j)
309 IF (noconj) THEN
310 IF (nounit) temp = temp*a(i,i)
311 DO 90 k = 1,i - 1
312 temp = temp + a(k,i)*b(k,j)
313 90 CONTINUE
314 ELSE
315 IF (nounit) temp = temp*conjg(a(i,i))
316 DO 100 k = 1,i - 1
317 temp = temp + conjg(a(k,i))*b(k,j)
318 100 CONTINUE
319 END IF
320 b(i,j) = alpha*temp
321 110 CONTINUE
322 120 CONTINUE
323 ELSE
324 DO 160 j = 1,n
325 DO 150 i = 1,m
326 temp = b(i,j)
327 IF (noconj) THEN
328 IF (nounit) temp = temp*a(i,i)
329 DO 130 k = i + 1,m
330 temp = temp + a(k,i)*b(k,j)
331 130 CONTINUE
332 ELSE
333 IF (nounit) temp = temp*conjg(a(i,i))
334 DO 140 k = i + 1,m
335 temp = temp + conjg(a(k,i))*b(k,j)
336 140 CONTINUE
337 END IF
338 b(i,j) = alpha*temp
339 150 CONTINUE
340 160 CONTINUE
341 END IF
342 END IF
343 ELSE
344 IF (lsame(transa,'N')) THEN
345*
346* Form B := alpha*B*A.
347*
348 IF (upper) THEN
349 DO 200 j = n,1,-1
350 temp = alpha
351 IF (nounit) temp = temp*a(j,j)
352 DO 170 i = 1,m
353 b(i,j) = temp*b(i,j)
354 170 CONTINUE
355 DO 190 k = 1,j - 1
356 IF (a(k,j).NE.zero) THEN
357 temp = alpha*a(k,j)
358 DO 180 i = 1,m
359 b(i,j) = b(i,j) + temp*b(i,k)
360 180 CONTINUE
361 END IF
362 190 CONTINUE
363 200 CONTINUE
364 ELSE
365 DO 240 j = 1,n
366 temp = alpha
367 IF (nounit) temp = temp*a(j,j)
368 DO 210 i = 1,m
369 b(i,j) = temp*b(i,j)
370 210 CONTINUE
371 DO 230 k = j + 1,n
372 IF (a(k,j).NE.zero) THEN
373 temp = alpha*a(k,j)
374 DO 220 i = 1,m
375 b(i,j) = b(i,j) + temp*b(i,k)
376 220 CONTINUE
377 END IF
378 230 CONTINUE
379 240 CONTINUE
380 END IF
381 ELSE
382*
383* Form B := alpha*B*A**T or B := alpha*B*A**H.
384*
385 IF (upper) THEN
386 DO 280 k = 1,n
387 DO 260 j = 1,k - 1
388 IF (a(j,k).NE.zero) THEN
389 IF (noconj) THEN
390 temp = alpha*a(j,k)
391 ELSE
392 temp = alpha*conjg(a(j,k))
393 END IF
394 DO 250 i = 1,m
395 b(i,j) = b(i,j) + temp*b(i,k)
396 250 CONTINUE
397 END IF
398 260 CONTINUE
399 temp = alpha
400 IF (nounit) THEN
401 IF (noconj) THEN
402 temp = temp*a(k,k)
403 ELSE
404 temp = temp*conjg(a(k,k))
405 END IF
406 END IF
407 IF (temp.NE.one) THEN
408 DO 270 i = 1,m
409 b(i,k) = temp*b(i,k)
410 270 CONTINUE
411 END IF
412 280 CONTINUE
413 ELSE
414 DO 320 k = n,1,-1
415 DO 300 j = k + 1,n
416 IF (a(j,k).NE.zero) THEN
417 IF (noconj) THEN
418 temp = alpha*a(j,k)
419 ELSE
420 temp = alpha*conjg(a(j,k))
421 END IF
422 DO 290 i = 1,m
423 b(i,j) = b(i,j) + temp*b(i,k)
424 290 CONTINUE
425 END IF
426 300 CONTINUE
427 temp = alpha
428 IF (nounit) THEN
429 IF (noconj) THEN
430 temp = temp*a(k,k)
431 ELSE
432 temp = temp*conjg(a(k,k))
433 END IF
434 END IF
435 IF (temp.NE.one) THEN
436 DO 310 i = 1,m
437 b(i,k) = temp*b(i,k)
438 310 CONTINUE
439 END IF
440 320 CONTINUE
441 END IF
442 END IF
443 END IF
444*
445 RETURN
446*
447* End of CTRMM
448*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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