LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zsytrs_rook()

subroutine zsytrs_rook ( character uplo,
integer n,
integer nrhs,
complex*16, dimension( lda, * ) a,
integer lda,
integer, dimension( * ) ipiv,
complex*16, dimension( ldb, * ) b,
integer ldb,
integer info )

ZSYTRS_ROOK

Download ZSYTRS_ROOK + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> ZSYTRS_ROOK solves a system of linear equations A*X = B with
!> a complex symmetric matrix A using the factorization A = U*D*U**T or
!> A = L*D*L**T computed by ZSYTRF_ROOK.
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>          Specifies whether the details of the factorization are stored
!>          as an upper or lower triangular matrix.
!>          = 'U':  Upper triangular, form is A = U*D*U**T;
!>          = 'L':  Lower triangular, form is A = L*D*L**T.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
[in]NRHS
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
[in]A
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The block diagonal matrix D and the multipliers used to
!>          obtain the factor U or L as computed by ZSYTRF_ROOK.
!>
[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 ZSYTRF_ROOK.
!>
[in,out]B
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>
[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 = -i, the i-th argument had an illegal value
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
!>
!>   December 2016, Igor Kozachenko,
!>                  Computer Science Division,
!>                  University of California, Berkeley
!>
!>  September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
!>                  School of Mathematics,
!>                  University of Manchester
!>
!>

Definition at line 132 of file zsytrs_rook.f.

134*
135* -- LAPACK computational routine --
136* -- LAPACK is a software package provided by Univ. of Tennessee, --
137* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*
139* .. Scalar Arguments ..
140 CHARACTER UPLO
141 INTEGER INFO, LDA, LDB, N, NRHS
142* ..
143* .. Array Arguments ..
144 INTEGER IPIV( * )
145 COMPLEX*16 A( LDA, * ), B( LDB, * )
146* ..
147*
148* =====================================================================
149*
150* .. Parameters ..
151 COMPLEX*16 CONE
152 parameter( cone = ( 1.0d+0, 0.0d+0 ) )
153* ..
154* .. Local Scalars ..
155 LOGICAL UPPER
156 INTEGER J, K, KP
157 COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
158* ..
159* .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL lsame
162* ..
163* .. External Subroutines ..
164 EXTERNAL zgemv, zgeru, zscal, zswap, xerbla
165* ..
166* .. Intrinsic Functions ..
167 INTRINSIC max
168* ..
169* .. Executable Statements ..
170*
171 info = 0
172 upper = lsame( uplo, 'U' )
173 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
174 info = -1
175 ELSE IF( n.LT.0 ) THEN
176 info = -2
177 ELSE IF( nrhs.LT.0 ) THEN
178 info = -3
179 ELSE IF( lda.LT.max( 1, n ) ) THEN
180 info = -5
181 ELSE IF( ldb.LT.max( 1, n ) ) THEN
182 info = -8
183 END IF
184 IF( info.NE.0 ) THEN
185 CALL xerbla( 'ZSYTRS_ROOK', -info )
186 RETURN
187 END IF
188*
189* Quick return if possible
190*
191 IF( n.EQ.0 .OR. nrhs.EQ.0 )
192 $ RETURN
193*
194 IF( upper ) THEN
195*
196* Solve A*X = B, where A = U*D*U**T.
197*
198* First solve U*D*X = B, overwriting B with X.
199*
200* K is the main loop index, decreasing from N to 1 in steps of
201* 1 or 2, depending on the size of the diagonal blocks.
202*
203 k = n
204 10 CONTINUE
205*
206* If K < 1, exit from loop.
207*
208 IF( k.LT.1 )
209 $ GO TO 30
210*
211 IF( ipiv( k ).GT.0 ) THEN
212*
213* 1 x 1 diagonal block
214*
215* Interchange rows K and IPIV(K).
216*
217 kp = ipiv( k )
218 IF( kp.NE.k )
219 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
220*
221* Multiply by inv(U(K)), where U(K) is the transformation
222* stored in column K of A.
223*
224 CALL zgeru( k-1, nrhs, -cone, a( 1, k ), 1, b( k, 1 ),
225 $ ldb,
226 $ b( 1, 1 ), ldb )
227*
228* Multiply by the inverse of the diagonal block.
229*
230 CALL zscal( nrhs, cone / a( k, k ), b( k, 1 ), ldb )
231 k = k - 1
232 ELSE
233*
234* 2 x 2 diagonal block
235*
236* Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
237*
238 kp = -ipiv( k )
239 IF( kp.NE.k )
240 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
241*
242 kp = -ipiv( k-1 )
243 IF( kp.NE.k-1 )
244 $ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
245*
246* Multiply by inv(U(K)), where U(K) is the transformation
247* stored in columns K-1 and K of A.
248*
249 IF( k.GT.2 ) THEN
250 CALL zgeru( k-2, nrhs,-cone, a( 1, k ), 1, b( k, 1 ),
251 $ ldb, b( 1, 1 ), ldb )
252 CALL zgeru( k-2, nrhs,-cone, a( 1, k-1 ), 1, b( k-1,
253 $ 1 ),
254 $ ldb, b( 1, 1 ), ldb )
255 END IF
256*
257* Multiply by the inverse of the diagonal block.
258*
259 akm1k = a( k-1, k )
260 akm1 = a( k-1, k-1 ) / akm1k
261 ak = a( k, k ) / akm1k
262 denom = akm1*ak - cone
263 DO 20 j = 1, nrhs
264 bkm1 = b( k-1, j ) / akm1k
265 bk = b( k, j ) / akm1k
266 b( k-1, j ) = ( ak*bkm1-bk ) / denom
267 b( k, j ) = ( akm1*bk-bkm1 ) / denom
268 20 CONTINUE
269 k = k - 2
270 END IF
271*
272 GO TO 10
273 30 CONTINUE
274*
275* Next solve U**T *X = B, overwriting B with X.
276*
277* K is the main loop index, increasing from 1 to N in steps of
278* 1 or 2, depending on the size of the diagonal blocks.
279*
280 k = 1
281 40 CONTINUE
282*
283* If K > N, exit from loop.
284*
285 IF( k.GT.n )
286 $ GO TO 50
287*
288 IF( ipiv( k ).GT.0 ) THEN
289*
290* 1 x 1 diagonal block
291*
292* Multiply by inv(U**T(K)), where U(K) is the transformation
293* stored in column K of A.
294*
295 IF( k.GT.1 )
296 $ CALL zgemv( 'Transpose', k-1, nrhs, -cone, b,
297 $ ldb, a( 1, k ), 1, cone, b( k, 1 ), ldb )
298*
299* Interchange rows K and IPIV(K).
300*
301 kp = ipiv( k )
302 IF( kp.NE.k )
303 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
304 k = k + 1
305 ELSE
306*
307* 2 x 2 diagonal block
308*
309* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
310* stored in columns K and K+1 of A.
311*
312 IF( k.GT.1 ) THEN
313 CALL zgemv( 'Transpose', k-1, nrhs, -cone, b,
314 $ ldb, a( 1, k ), 1, cone, b( k, 1 ), ldb )
315 CALL zgemv( 'Transpose', k-1, nrhs, -cone, b,
316 $ ldb, a( 1, k+1 ), 1, cone, b( k+1, 1 ), ldb )
317 END IF
318*
319* Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1).
320*
321 kp = -ipiv( k )
322 IF( kp.NE.k )
323 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
324*
325 kp = -ipiv( k+1 )
326 IF( kp.NE.k+1 )
327 $ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
328*
329 k = k + 2
330 END IF
331*
332 GO TO 40
333 50 CONTINUE
334*
335 ELSE
336*
337* Solve A*X = B, where A = L*D*L**T.
338*
339* First solve L*D*X = B, overwriting B with X.
340*
341* K is the main loop index, increasing from 1 to N in steps of
342* 1 or 2, depending on the size of the diagonal blocks.
343*
344 k = 1
345 60 CONTINUE
346*
347* If K > N, exit from loop.
348*
349 IF( k.GT.n )
350 $ GO TO 80
351*
352 IF( ipiv( k ).GT.0 ) THEN
353*
354* 1 x 1 diagonal block
355*
356* Interchange rows K and IPIV(K).
357*
358 kp = ipiv( k )
359 IF( kp.NE.k )
360 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
361*
362* Multiply by inv(L(K)), where L(K) is the transformation
363* stored in column K of A.
364*
365 IF( k.LT.n )
366 $ CALL zgeru( n-k, nrhs, -cone, a( k+1, k ), 1, b( k,
367 $ 1 ),
368 $ ldb, b( k+1, 1 ), ldb )
369*
370* Multiply by the inverse of the diagonal block.
371*
372 CALL zscal( nrhs, cone / a( k, k ), b( k, 1 ), ldb )
373 k = k + 1
374 ELSE
375*
376* 2 x 2 diagonal block
377*
378* Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1)
379*
380 kp = -ipiv( k )
381 IF( kp.NE.k )
382 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
383*
384 kp = -ipiv( k+1 )
385 IF( kp.NE.k+1 )
386 $ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
387*
388* Multiply by inv(L(K)), where L(K) is the transformation
389* stored in columns K and K+1 of A.
390*
391 IF( k.LT.n-1 ) THEN
392 CALL zgeru( n-k-1, nrhs,-cone, a( k+2, k ), 1, b( k,
393 $ 1 ),
394 $ ldb, b( k+2, 1 ), ldb )
395 CALL zgeru( n-k-1, nrhs,-cone, a( k+2, k+1 ), 1,
396 $ b( k+1, 1 ), ldb, b( k+2, 1 ), ldb )
397 END IF
398*
399* Multiply by the inverse of the diagonal block.
400*
401 akm1k = a( k+1, k )
402 akm1 = a( k, k ) / akm1k
403 ak = a( k+1, k+1 ) / akm1k
404 denom = akm1*ak - cone
405 DO 70 j = 1, nrhs
406 bkm1 = b( k, j ) / akm1k
407 bk = b( k+1, j ) / akm1k
408 b( k, j ) = ( ak*bkm1-bk ) / denom
409 b( k+1, j ) = ( akm1*bk-bkm1 ) / denom
410 70 CONTINUE
411 k = k + 2
412 END IF
413*
414 GO TO 60
415 80 CONTINUE
416*
417* Next solve L**T *X = B, overwriting B with X.
418*
419* K is the main loop index, decreasing from N to 1 in steps of
420* 1 or 2, depending on the size of the diagonal blocks.
421*
422 k = n
423 90 CONTINUE
424*
425* If K < 1, exit from loop.
426*
427 IF( k.LT.1 )
428 $ GO TO 100
429*
430 IF( ipiv( k ).GT.0 ) THEN
431*
432* 1 x 1 diagonal block
433*
434* Multiply by inv(L**T(K)), where L(K) is the transformation
435* stored in column K of A.
436*
437 IF( k.LT.n )
438 $ CALL zgemv( 'Transpose', n-k, nrhs, -cone, b( k+1,
439 $ 1 ),
440 $ ldb, a( k+1, k ), 1, cone, b( k, 1 ), ldb )
441*
442* Interchange rows K and IPIV(K).
443*
444 kp = ipiv( k )
445 IF( kp.NE.k )
446 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
447 k = k - 1
448 ELSE
449*
450* 2 x 2 diagonal block
451*
452* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
453* stored in columns K-1 and K of A.
454*
455 IF( k.LT.n ) THEN
456 CALL zgemv( 'Transpose', n-k, nrhs, -cone, b( k+1,
457 $ 1 ),
458 $ ldb, a( k+1, k ), 1, cone, b( k, 1 ), ldb )
459 CALL zgemv( 'Transpose', n-k, nrhs, -cone, b( k+1,
460 $ 1 ),
461 $ ldb, a( k+1, k-1 ), 1, cone, b( k-1, 1 ),
462 $ ldb )
463 END IF
464*
465* Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
466*
467 kp = -ipiv( k )
468 IF( kp.NE.k )
469 $ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
470*
471 kp = -ipiv( k-1 )
472 IF( kp.NE.k-1 )
473 $ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
474*
475 k = k - 2
476 END IF
477*
478 GO TO 90
479 100 CONTINUE
480 END IF
481*
482 RETURN
483*
484* End of ZSYTRS_ROOK
485*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zgemv
subroutine zgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZGEMV
Definition zgemv.f:160
zgeru
subroutine zgeru(m, n, alpha, x, incx, y, incy, a, lda)
ZGERU
Definition zgeru.f:130
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
zscal
subroutine zscal(n, za, zx, incx)
ZSCAL
Definition zscal.f:78
zswap
subroutine zswap(n, zx, incx, zy, incy)
ZSWAP
Definition zswap.f:81
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