 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhetrs_rook()

 subroutine zhetrs_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 )

ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)

Purpose:
``` ZHETRS_ROOK solves a system of linear equations A*X = B with a complex
Hermitian matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHETRF_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**H; = 'L': Lower triangular, form is A = L*D*L**H.``` [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 ZHETRF_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 ZHETRF_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```
Contributors:
```  November 2013,  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 134 of file zhetrs_rook.f.

136 *
137 * -- LAPACK computational routine --
138 * -- LAPACK is a software package provided by Univ. of Tennessee, --
139 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140 *
141 * .. Scalar Arguments ..
142  CHARACTER UPLO
143  INTEGER INFO, LDA, LDB, N, NRHS
144 * ..
145 * .. Array Arguments ..
146  INTEGER IPIV( * )
147  COMPLEX*16 A( LDA, * ), B( LDB, * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  COMPLEX*16 ONE
154  parameter( one = ( 1.0d+0, 0.0d+0 ) )
155 * ..
156 * .. Local Scalars ..
157  LOGICAL UPPER
158  INTEGER J, K, KP
159  DOUBLE PRECISION S
160  COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
161 * ..
162 * .. External Functions ..
163  LOGICAL LSAME
164  EXTERNAL lsame
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL zgemv, zgeru, zlacgv, zdscal, zswap, xerbla
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC dconjg, max, dble
171 * ..
172 * .. Executable Statements ..
173 *
174  info = 0
175  upper = lsame( uplo, 'U' )
176  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
177  info = -1
178  ELSE IF( n.LT.0 ) THEN
179  info = -2
180  ELSE IF( nrhs.LT.0 ) THEN
181  info = -3
182  ELSE IF( lda.LT.max( 1, n ) ) THEN
183  info = -5
184  ELSE IF( ldb.LT.max( 1, n ) ) THEN
185  info = -8
186  END IF
187  IF( info.NE.0 ) THEN
188  CALL xerbla( 'ZHETRS_ROOK', -info )
189  RETURN
190  END IF
191 *
192 * Quick return if possible
193 *
194  IF( n.EQ.0 .OR. nrhs.EQ.0 )
195  \$ RETURN
196 *
197  IF( upper ) THEN
198 *
199 * Solve A*X = B, where A = U*D*U**H.
200 *
201 * First solve U*D*X = B, overwriting B with X.
202 *
203 * K is the main loop index, decreasing from N to 1 in steps of
204 * 1 or 2, depending on the size of the diagonal blocks.
205 *
206  k = n
207  10 CONTINUE
208 *
209 * If K < 1, exit from loop.
210 *
211  IF( k.LT.1 )
212  \$ GO TO 30
213 *
214  IF( ipiv( k ).GT.0 ) THEN
215 *
216 * 1 x 1 diagonal block
217 *
218 * Interchange rows K and IPIV(K).
219 *
220  kp = ipiv( k )
221  IF( kp.NE.k )
222  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
223 *
224 * Multiply by inv(U(K)), where U(K) is the transformation
225 * stored in column K of A.
226 *
227  CALL zgeru( k-1, nrhs, -one, a( 1, k ), 1, b( k, 1 ), ldb,
228  \$ b( 1, 1 ), ldb )
229 *
230 * Multiply by the inverse of the diagonal block.
231 *
232  s = dble( one ) / dble( a( k, k ) )
233  CALL zdscal( nrhs, s, b( k, 1 ), ldb )
234  k = k - 1
235  ELSE
236 *
237 * 2 x 2 diagonal block
238 *
239 * Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1)
240 *
241  kp = -ipiv( k )
242  IF( kp.NE.k )
243  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
244 *
245  kp = -ipiv( k-1)
246  IF( kp.NE.k-1 )
247  \$ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
248 *
249 * Multiply by inv(U(K)), where U(K) is the transformation
250 * stored in columns K-1 and K of A.
251 *
252  CALL zgeru( k-2, nrhs, -one, a( 1, k ), 1, b( k, 1 ), ldb,
253  \$ b( 1, 1 ), ldb )
254  CALL zgeru( k-2, nrhs, -one, a( 1, k-1 ), 1, b( k-1, 1 ),
255  \$ ldb, b( 1, 1 ), ldb )
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 ) / dconjg( akm1k )
262  denom = akm1*ak - one
263  DO 20 j = 1, nrhs
264  bkm1 = b( k-1, j ) / akm1k
265  bk = b( k, j ) / dconjg( 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**H *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**H(K)), where U(K) is the transformation
293 * stored in column K of A.
294 *
295  IF( k.GT.1 ) THEN
296  CALL zlacgv( nrhs, b( k, 1 ), ldb )
297  CALL zgemv( 'Conjugate transpose', k-1, nrhs, -one, b,
298  \$ ldb, a( 1, k ), 1, one, b( k, 1 ), ldb )
299  CALL zlacgv( nrhs, b( k, 1 ), ldb )
300  END IF
301 *
302 * Interchange rows K and IPIV(K).
303 *
304  kp = ipiv( k )
305  IF( kp.NE.k )
306  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
307  k = k + 1
308  ELSE
309 *
310 * 2 x 2 diagonal block
311 *
312 * Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
313 * stored in columns K and K+1 of A.
314 *
315  IF( k.GT.1 ) THEN
316  CALL zlacgv( nrhs, b( k, 1 ), ldb )
317  CALL zgemv( 'Conjugate transpose', k-1, nrhs, -one, b,
318  \$ ldb, a( 1, k ), 1, one, b( k, 1 ), ldb )
319  CALL zlacgv( nrhs, b( k, 1 ), ldb )
320 *
321  CALL zlacgv( nrhs, b( k+1, 1 ), ldb )
322  CALL zgemv( 'Conjugate transpose', k-1, nrhs, -one, b,
323  \$ ldb, a( 1, k+1 ), 1, one, b( k+1, 1 ), ldb )
324  CALL zlacgv( nrhs, b( k+1, 1 ), ldb )
325  END IF
326 *
327 * Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1)
328 *
329  kp = -ipiv( k )
330  IF( kp.NE.k )
331  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
332 *
333  kp = -ipiv( k+1 )
334  IF( kp.NE.k+1 )
335  \$ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
336 *
337  k = k + 2
338  END IF
339 *
340  GO TO 40
341  50 CONTINUE
342 *
343  ELSE
344 *
345 * Solve A*X = B, where A = L*D*L**H.
346 *
347 * First solve L*D*X = B, overwriting B with X.
348 *
349 * K is the main loop index, increasing from 1 to N in steps of
350 * 1 or 2, depending on the size of the diagonal blocks.
351 *
352  k = 1
353  60 CONTINUE
354 *
355 * If K > N, exit from loop.
356 *
357  IF( k.GT.n )
358  \$ GO TO 80
359 *
360  IF( ipiv( k ).GT.0 ) THEN
361 *
362 * 1 x 1 diagonal block
363 *
364 * Interchange rows K and IPIV(K).
365 *
366  kp = ipiv( k )
367  IF( kp.NE.k )
368  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
369 *
370 * Multiply by inv(L(K)), where L(K) is the transformation
371 * stored in column K of A.
372 *
373  IF( k.LT.n )
374  \$ CALL zgeru( n-k, nrhs, -one, a( k+1, k ), 1, b( k, 1 ),
375  \$ ldb, b( k+1, 1 ), ldb )
376 *
377 * Multiply by the inverse of the diagonal block.
378 *
379  s = dble( one ) / dble( a( k, k ) )
380  CALL zdscal( nrhs, s, b( k, 1 ), ldb )
381  k = k + 1
382  ELSE
383 *
384 * 2 x 2 diagonal block
385 *
386 * Interchange rows K and -IPIV(K), then K+1 and -IPIV(K+1)
387 *
388  kp = -ipiv( k )
389  IF( kp.NE.k )
390  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
391 *
392  kp = -ipiv( k+1 )
393  IF( kp.NE.k+1 )
394  \$ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
395 *
396 * Multiply by inv(L(K)), where L(K) is the transformation
397 * stored in columns K and K+1 of A.
398 *
399  IF( k.LT.n-1 ) THEN
400  CALL zgeru( n-k-1, nrhs, -one, a( k+2, k ), 1, b( k, 1 ),
401  \$ ldb, b( k+2, 1 ), ldb )
402  CALL zgeru( n-k-1, nrhs, -one, a( k+2, k+1 ), 1,
403  \$ b( k+1, 1 ), ldb, b( k+2, 1 ), ldb )
404  END IF
405 *
406 * Multiply by the inverse of the diagonal block.
407 *
408  akm1k = a( k+1, k )
409  akm1 = a( k, k ) / dconjg( akm1k )
410  ak = a( k+1, k+1 ) / akm1k
411  denom = akm1*ak - one
412  DO 70 j = 1, nrhs
413  bkm1 = b( k, j ) / dconjg( akm1k )
414  bk = b( k+1, j ) / akm1k
415  b( k, j ) = ( ak*bkm1-bk ) / denom
416  b( k+1, j ) = ( akm1*bk-bkm1 ) / denom
417  70 CONTINUE
418  k = k + 2
419  END IF
420 *
421  GO TO 60
422  80 CONTINUE
423 *
424 * Next solve L**H *X = B, overwriting B with X.
425 *
426 * K is the main loop index, decreasing from N to 1 in steps of
427 * 1 or 2, depending on the size of the diagonal blocks.
428 *
429  k = n
430  90 CONTINUE
431 *
432 * If K < 1, exit from loop.
433 *
434  IF( k.LT.1 )
435  \$ GO TO 100
436 *
437  IF( ipiv( k ).GT.0 ) THEN
438 *
439 * 1 x 1 diagonal block
440 *
441 * Multiply by inv(L**H(K)), where L(K) is the transformation
442 * stored in column K of A.
443 *
444  IF( k.LT.n ) THEN
445  CALL zlacgv( nrhs, b( k, 1 ), ldb )
446  CALL zgemv( 'Conjugate transpose', n-k, nrhs, -one,
447  \$ b( k+1, 1 ), ldb, a( k+1, k ), 1, one,
448  \$ b( k, 1 ), ldb )
449  CALL zlacgv( nrhs, b( k, 1 ), ldb )
450  END IF
451 *
452 * Interchange rows K and IPIV(K).
453 *
454  kp = ipiv( k )
455  IF( kp.NE.k )
456  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
457  k = k - 1
458  ELSE
459 *
460 * 2 x 2 diagonal block
461 *
462 * Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
463 * stored in columns K-1 and K of A.
464 *
465  IF( k.LT.n ) THEN
466  CALL zlacgv( nrhs, b( k, 1 ), ldb )
467  CALL zgemv( 'Conjugate transpose', n-k, nrhs, -one,
468  \$ b( k+1, 1 ), ldb, a( k+1, k ), 1, one,
469  \$ b( k, 1 ), ldb )
470  CALL zlacgv( nrhs, b( k, 1 ), ldb )
471 *
472  CALL zlacgv( nrhs, b( k-1, 1 ), ldb )
473  CALL zgemv( 'Conjugate transpose', n-k, nrhs, -one,
474  \$ b( k+1, 1 ), ldb, a( k+1, k-1 ), 1, one,
475  \$ b( k-1, 1 ), ldb )
476  CALL zlacgv( nrhs, b( k-1, 1 ), ldb )
477  END IF
478 *
479 * Interchange rows K and -IPIV(K), then K-1 and -IPIV(K-1)
480 *
481  kp = -ipiv( k )
482  IF( kp.NE.k )
483  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
484 *
485  kp = -ipiv( k-1 )
486  IF( kp.NE.k-1 )
487  \$ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
488 *
489  k = k - 2
490  END IF
491 *
492  GO TO 90
493  100 CONTINUE
494  END IF
495 *
496  RETURN
497 *
498 * End of ZHETRS_ROOK
499 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:130
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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