LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ clavhe()

subroutine clavhe ( character uplo,
character trans,
character diag,
integer n,
integer nrhs,
complex, dimension( lda, * ) a,
integer lda,
integer, dimension( * ) ipiv,
complex, dimension( ldb, * ) b,
integer ldb,
integer info )

CLAVHE

Purpose:
!>
!> CLAVHE performs one of the matrix-vector operations
!>    x := A*x  or  x := A^H*x,
!> where x is an N element vector and  A is one of the factors
!> from the block U*D*U' or L*D*L' factorization computed by CHETRF.
!>
!> If TRANS = 'N', multiplies by U  or U * D  (or L  or L * D)
!> If TRANS = 'C', multiplies by U' or D * U' (or L' or D * L')
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>          Specifies whether the factor stored in A is upper or lower
!>          triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
[in]TRANS
!>          TRANS is CHARACTER*1
!>          Specifies the operation to be performed:
!>          = 'N':  x := A*x
!>          = 'C':   x := A^H*x
!>
[in]DIAG
!>          DIAG is CHARACTER*1
!>          Specifies whether or not the diagonal blocks are unit
!>          matrices.  If the diagonal blocks are assumed to be unit,
!>          then A = U or A = L, otherwise A = U*D or A = L*D.
!>          = 'U':  Diagonal blocks are assumed to be unit matrices.
!>          = 'N':  Diagonal blocks are assumed to be non-unit matrices.
!>
[in]N
!>          N is INTEGER
!>          The number of rows and columns of the matrix A.  N >= 0.
!>
[in]NRHS
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of vectors
!>          x to be multiplied by A.  NRHS >= 0.
!>
[in]A
!>          A is COMPLEX array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by CHETRF_ROOK.
!>          Stored as a 2-D triangular matrix.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
[in]IPIV
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D,
!>          as determined by CHETRF.
!>
!>          If UPLO = 'U':
!>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
!>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
!>               (If IPIV( k ) = k, no interchange was done).
!>
!>               If IPIV(k) = IPIV(k-1) < 0, then rows and
!>               columns k-1 and -IPIV(k) were interchanged,
!>               D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
!>
!>          If UPLO = 'L':
!>               If IPIV(k) > 0, then rows and columns k and IPIV(k)
!>               were interchanged and D(k,k) is a 1-by-1 diagonal block.
!>               (If IPIV( k ) = k, no interchange was done).
!>
!>               If IPIV(k) = IPIV(k+1) < 0, then rows and
!>               columns k+1 and -IPIV(k) were interchanged,
!>               D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
!>
[in,out]B
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, B contains NRHS vectors of length N.
!>          On exit, B is overwritten with the product A * B.
!>
[in]LDB
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 151 of file clavhe.f.

153*
154* -- LAPACK test routine --
155* -- LAPACK is a software package provided by Univ. of Tennessee, --
156* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157*
158* .. Scalar Arguments ..
159 CHARACTER DIAG, TRANS, UPLO
160 INTEGER INFO, LDA, LDB, N, NRHS
161* ..
162* .. Array Arguments ..
163 INTEGER IPIV( * )
164 COMPLEX A( LDA, * ), B( LDB, * )
165* ..
166*
167* =====================================================================
168*
169* .. Parameters ..
170 COMPLEX ONE
171 parameter( one = ( 1.0e+0, 0.0e+0 ) )
172* ..
173* .. Local Scalars ..
174 LOGICAL NOUNIT
175 INTEGER J, K, KP
176 COMPLEX D11, D12, D21, D22, T1, T2
177* ..
178* .. External Functions ..
179 LOGICAL LSAME
180 EXTERNAL lsame
181* ..
182* .. External Subroutines ..
183 EXTERNAL cgemv, cgeru, clacgv, cscal, cswap, xerbla
184* ..
185* .. Intrinsic Functions ..
186 INTRINSIC abs, conjg, max
187* ..
188* .. Executable Statements ..
189*
190* Test the input parameters.
191*
192 info = 0
193 IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194 info = -1
195 ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'C' ) )
196 $ THEN
197 info = -2
198 ELSE IF( .NOT.lsame( diag, 'U' ) .AND. .NOT.lsame( diag, 'N' ) )
199 $ THEN
200 info = -3
201 ELSE IF( n.LT.0 ) THEN
202 info = -4
203 ELSE IF( lda.LT.max( 1, n ) ) THEN
204 info = -6
205 ELSE IF( ldb.LT.max( 1, n ) ) THEN
206 info = -9
207 END IF
208 IF( info.NE.0 ) THEN
209 CALL xerbla( 'CLAVHE ', -info )
210 RETURN
211 END IF
212*
213* Quick return if possible.
214*
215 IF( n.EQ.0 )
216 $ RETURN
217*
218 nounit = lsame( diag, 'N' )
219*------------------------------------------
220*
221* Compute B := A * B (No transpose)
222*
223*------------------------------------------
224 IF( lsame( trans, 'N' ) ) THEN
225*
226* Compute B := U*B
227* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
228*
229 IF( lsame( uplo, 'U' ) ) THEN
230*
231* Loop forward applying the transformations.
232*
233 k = 1
234 10 CONTINUE
235 IF( k.GT.n )
236 $ GO TO 30
237 IF( ipiv( k ).GT.0 ) THEN
238*
239* 1 x 1 pivot block
240*
241* Multiply by the diagonal element if forming U * D.
242*
243 IF( nounit )
244 $ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
245*
246* Multiply by P(K) * inv(U(K)) if K > 1.
247*
248 IF( k.GT.1 ) THEN
249*
250* Apply the transformation.
251*
252 CALL cgeru( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
253 $ ldb, b( 1, 1 ), ldb )
254*
255* Interchange if P(K) != I.
256*
257 kp = ipiv( k )
258 IF( kp.NE.k )
259 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
260 END IF
261 k = k + 1
262 ELSE
263*
264* 2 x 2 pivot block
265*
266* Multiply by the diagonal block if forming U * D.
267*
268 IF( nounit ) THEN
269 d11 = a( k, k )
270 d22 = a( k+1, k+1 )
271 d12 = a( k, k+1 )
272 d21 = conjg( d12 )
273 DO 20 j = 1, nrhs
274 t1 = b( k, j )
275 t2 = b( k+1, j )
276 b( k, j ) = d11*t1 + d12*t2
277 b( k+1, j ) = d21*t1 + d22*t2
278 20 CONTINUE
279 END IF
280*
281* Multiply by P(K) * inv(U(K)) if K > 1.
282*
283 IF( k.GT.1 ) THEN
284*
285* Apply the transformations.
286*
287 CALL cgeru( k-1, nrhs, one, a( 1, k ), 1, b( k, 1 ),
288 $ ldb, b( 1, 1 ), ldb )
289 CALL cgeru( k-1, nrhs, one, a( 1, k+1 ), 1,
290 $ b( k+1, 1 ), ldb, b( 1, 1 ), ldb )
291*
292* Interchange if P(K) != I.
293*
294 kp = abs( ipiv( k ) )
295 IF( kp.NE.k )
296 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
297 END IF
298 k = k + 2
299 END IF
300 GO TO 10
301 30 CONTINUE
302*
303* Compute B := L*B
304* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m)) .
305*
306 ELSE
307*
308* Loop backward applying the transformations to B.
309*
310 k = n
311 40 CONTINUE
312 IF( k.LT.1 )
313 $ GO TO 60
314*
315* Test the pivot index. If greater than zero, a 1 x 1
316* pivot was used, otherwise a 2 x 2 pivot was used.
317*
318 IF( ipiv( k ).GT.0 ) THEN
319*
320* 1 x 1 pivot block:
321*
322* Multiply by the diagonal element if forming L * D.
323*
324 IF( nounit )
325 $ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
326*
327* Multiply by P(K) * inv(L(K)) if K < N.
328*
329 IF( k.NE.n ) THEN
330 kp = ipiv( k )
331*
332* Apply the transformation.
333*
334 CALL cgeru( n-k, nrhs, one, a( k+1, k ), 1,
335 $ b( k, 1 ), ldb, b( k+1, 1 ), ldb )
336*
337* Interchange if a permutation was applied at the
338* K-th step of the factorization.
339*
340 IF( kp.NE.k )
341 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
342 END IF
343 k = k - 1
344*
345 ELSE
346*
347* 2 x 2 pivot block:
348*
349* Multiply by the diagonal block if forming L * D.
350*
351 IF( nounit ) THEN
352 d11 = a( k-1, k-1 )
353 d22 = a( k, k )
354 d21 = a( k, k-1 )
355 d12 = conjg( d21 )
356 DO 50 j = 1, nrhs
357 t1 = b( k-1, j )
358 t2 = b( k, j )
359 b( k-1, j ) = d11*t1 + d12*t2
360 b( k, j ) = d21*t1 + d22*t2
361 50 CONTINUE
362 END IF
363*
364* Multiply by P(K) * inv(L(K)) if K < N.
365*
366 IF( k.NE.n ) THEN
367*
368* Apply the transformation.
369*
370 CALL cgeru( n-k, nrhs, one, a( k+1, k ), 1,
371 $ b( k, 1 ), ldb, b( k+1, 1 ), ldb )
372 CALL cgeru( n-k, nrhs, one, a( k+1, k-1 ), 1,
373 $ b( k-1, 1 ), ldb, b( k+1, 1 ), ldb )
374*
375* Interchange if a permutation was applied at the
376* K-th step of the factorization.
377*
378 kp = abs( ipiv( k ) )
379 IF( kp.NE.k )
380 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
381 END IF
382 k = k - 2
383 END IF
384 GO TO 40
385 60 CONTINUE
386 END IF
387*--------------------------------------------------
388*
389* Compute B := A^H * B (conjugate transpose)
390*
391*--------------------------------------------------
392 ELSE
393*
394* Form B := U^H*B
395* where U = P(m)*inv(U(m))* ... *P(1)*inv(U(1))
396* and U^H = inv(U^H(1))*P(1)* ... *inv(U^H(m))*P(m)
397*
398 IF( lsame( uplo, 'U' ) ) THEN
399*
400* Loop backward applying the transformations.
401*
402 k = n
403 70 IF( k.LT.1 )
404 $ GO TO 90
405*
406* 1 x 1 pivot block.
407*
408 IF( ipiv( k ).GT.0 ) THEN
409 IF( k.GT.1 ) THEN
410*
411* Interchange if P(K) != I.
412*
413 kp = ipiv( k )
414 IF( kp.NE.k )
415 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
416*
417* Apply the transformation
418* y = y - B' conjg(x),
419* where x is a column of A and y is a row of B.
420*
421 CALL clacgv( nrhs, b( k, 1 ), ldb )
422 CALL cgemv( 'Conjugate', k-1, nrhs, one, b, ldb,
423 $ a( 1, k ), 1, one, b( k, 1 ), ldb )
424 CALL clacgv( nrhs, b( k, 1 ), ldb )
425 END IF
426 IF( nounit )
427 $ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
428 k = k - 1
429*
430* 2 x 2 pivot block.
431*
432 ELSE
433 IF( k.GT.2 ) THEN
434*
435* Interchange if P(K) != I.
436*
437 kp = abs( ipiv( k ) )
438 IF( kp.NE.k-1 )
439 $ CALL cswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ),
440 $ ldb )
441*
442* Apply the transformations
443* y = y - B' conjg(x),
444* where x is a block column of A and y is a block
445* row of B.
446*
447 CALL clacgv( nrhs, b( k, 1 ), ldb )
448 CALL cgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
449 $ a( 1, k ), 1, one, b( k, 1 ), ldb )
450 CALL clacgv( nrhs, b( k, 1 ), ldb )
451*
452 CALL clacgv( nrhs, b( k-1, 1 ), ldb )
453 CALL cgemv( 'Conjugate', k-2, nrhs, one, b, ldb,
454 $ a( 1, k-1 ), 1, one, b( k-1, 1 ), ldb )
455 CALL clacgv( nrhs, b( k-1, 1 ), ldb )
456 END IF
457*
458* Multiply by the diagonal block if non-unit.
459*
460 IF( nounit ) THEN
461 d11 = a( k-1, k-1 )
462 d22 = a( k, k )
463 d12 = a( k-1, k )
464 d21 = conjg( d12 )
465 DO 80 j = 1, nrhs
466 t1 = b( k-1, j )
467 t2 = b( k, j )
468 b( k-1, j ) = d11*t1 + d12*t2
469 b( k, j ) = d21*t1 + d22*t2
470 80 CONTINUE
471 END IF
472 k = k - 2
473 END IF
474 GO TO 70
475 90 CONTINUE
476*
477* Form B := L^H*B
478* where L = P(1)*inv(L(1))* ... *P(m)*inv(L(m))
479* and L^H = inv(L^H(m))*P(m)* ... *inv(L^H(1))*P(1)
480*
481 ELSE
482*
483* Loop forward applying the L-transformations.
484*
485 k = 1
486 100 CONTINUE
487 IF( k.GT.n )
488 $ GO TO 120
489*
490* 1 x 1 pivot block
491*
492 IF( ipiv( k ).GT.0 ) THEN
493 IF( k.LT.n ) THEN
494*
495* Interchange if P(K) != I.
496*
497 kp = ipiv( k )
498 IF( kp.NE.k )
499 $ CALL cswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
500*
501* Apply the transformation
502*
503 CALL clacgv( nrhs, b( k, 1 ), ldb )
504 CALL cgemv( 'Conjugate', n-k, nrhs, one, b( k+1, 1 ),
505 $ ldb, a( k+1, k ), 1, one, b( k, 1 ), ldb )
506 CALL clacgv( nrhs, b( k, 1 ), ldb )
507 END IF
508 IF( nounit )
509 $ CALL cscal( nrhs, a( k, k ), b( k, 1 ), ldb )
510 k = k + 1
511*
512* 2 x 2 pivot block.
513*
514 ELSE
515 IF( k.LT.n-1 ) THEN
516*
517* Interchange if P(K) != I.
518*
519 kp = abs( ipiv( k ) )
520 IF( kp.NE.k+1 )
521 $ CALL cswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ),
522 $ ldb )
523*
524* Apply the transformation
525*
526 CALL clacgv( nrhs, b( k+1, 1 ), ldb )
527 CALL cgemv( 'Conjugate', n-k-1, nrhs, one,
528 $ b( k+2, 1 ), ldb, a( k+2, k+1 ), 1, one,
529 $ b( k+1, 1 ), ldb )
530 CALL clacgv( nrhs, b( k+1, 1 ), ldb )
531*
532 CALL clacgv( nrhs, b( k, 1 ), ldb )
533 CALL cgemv( 'Conjugate', n-k-1, nrhs, one,
534 $ b( k+2, 1 ), ldb, a( k+2, k ), 1, one,
535 $ b( k, 1 ), ldb )
536 CALL clacgv( nrhs, b( k, 1 ), ldb )
537 END IF
538*
539* Multiply by the diagonal block if non-unit.
540*
541 IF( nounit ) THEN
542 d11 = a( k, k )
543 d22 = a( k+1, k+1 )
544 d21 = a( k+1, k )
545 d12 = conjg( d21 )
546 DO 110 j = 1, nrhs
547 t1 = b( k, j )
548 t2 = b( k+1, j )
549 b( k, j ) = d11*t1 + d12*t2
550 b( k+1, j ) = d21*t1 + d22*t2
551 110 CONTINUE
552 END IF
553 k = k + 2
554 END IF
555 GO TO 100
556 120 CONTINUE
557 END IF
558*
559 END IF
560 RETURN
561*
562* End of CLAVHE
563*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
cgemv
subroutine cgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
CGEMV
Definition cgemv.f:160
cgeru
subroutine cgeru(m, n, alpha, x, incx, y, incy, a, lda)
CGERU
Definition cgeru.f:130
clacgv
subroutine clacgv(n, x, incx)
CLACGV conjugates a complex vector.
Definition clacgv.f:72
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
cscal
subroutine cscal(n, ca, cx, incx)
CSCAL
Definition cscal.f:78
cswap
subroutine cswap(n, cx, incx, cy, incy)
CSWAP
Definition cswap.f:81
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