LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zsytrs_rook.f
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1 *> \brief \b ZSYTRS_ROOK
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZSYTRS_ROOK( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, LDB, N, NRHS
26 * ..
27 * .. Array Arguments ..
28 * INTEGER IPIV( * )
29 * COMPLEX*16 A( LDA, * ), B( LDB, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZSYTRS_ROOK solves a system of linear equations A*X = B with
39 *> a complex symmetric matrix A using the factorization A = U*D*U**T or
40 *> A = L*D*L**T computed by ZSYTRF_ROOK.
41 *> \endverbatim
42 *
43 * Arguments:
44 * ==========
45 *
46 *> \param[in] UPLO
47 *> \verbatim
48 *> UPLO is CHARACTER*1
49 *> Specifies whether the details of the factorization are stored
50 *> as an upper or lower triangular matrix.
51 *> = 'U': Upper triangular, form is A = U*D*U**T;
52 *> = 'L': Lower triangular, form is A = L*D*L**T.
53 *> \endverbatim
54 *>
55 *> \param[in] N
56 *> \verbatim
57 *> N is INTEGER
58 *> The order of the matrix A. N >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in] NRHS
62 *> \verbatim
63 *> NRHS is INTEGER
64 *> The number of right hand sides, i.e., the number of columns
65 *> of the matrix B. NRHS >= 0.
66 *> \endverbatim
67 *>
68 *> \param[in] A
69 *> \verbatim
70 *> A is COMPLEX*16 array, dimension (LDA,N)
71 *> The block diagonal matrix D and the multipliers used to
72 *> obtain the factor U or L as computed by ZSYTRF_ROOK.
73 *> \endverbatim
74 *>
75 *> \param[in] LDA
76 *> \verbatim
77 *> LDA is INTEGER
78 *> The leading dimension of the array A. LDA >= max(1,N).
79 *> \endverbatim
80 *>
81 *> \param[in] IPIV
82 *> \verbatim
83 *> IPIV is INTEGER array, dimension (N)
84 *> Details of the interchanges and the block structure of D
85 *> as determined by ZSYTRF_ROOK.
86 *> \endverbatim
87 *>
88 *> \param[in,out] B
89 *> \verbatim
90 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
91 *> On entry, the right hand side matrix B.
92 *> On exit, the solution matrix X.
93 *> \endverbatim
94 *>
95 *> \param[in] LDB
96 *> \verbatim
97 *> LDB is INTEGER
98 *> The leading dimension of the array B. LDB >= max(1,N).
99 *> \endverbatim
100 *>
101 *> \param[out] INFO
102 *> \verbatim
103 *> INFO is INTEGER
104 *> = 0: successful exit
105 *> < 0: if INFO = -i, the i-th argument had an illegal value
106 *> \endverbatim
107 *
108 * Authors:
109 * ========
110 *
111 *> \author Univ. of Tennessee
112 *> \author Univ. of California Berkeley
113 *> \author Univ. of Colorado Denver
114 *> \author NAG Ltd.
115 *
116 *> \ingroup complex16SYcomputational
117 *
118 *> \par Contributors:
119 * ==================
120 *>
121 *> \verbatim
122 *>
123 *> December 2016, Igor Kozachenko,
124 *> Computer Science Division,
125 *> University of California, Berkeley
126 *>
127 *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
128 *> School of Mathematics,
129 *> University of Manchester
130 *>
131 *> \endverbatim
132 *
133 * =====================================================================
134  SUBROUTINE zsytrs_rook( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
135  \$ INFO )
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 CONE
154  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
155 * ..
156 * .. Local Scalars ..
157  LOGICAL UPPER
158  INTEGER J, K, KP
159  COMPLEX*16 AK, AKM1, AKM1K, BK, BKM1, DENOM
160 * ..
161 * .. External Functions ..
162  LOGICAL LSAME
163  EXTERNAL lsame
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL zgemv, zgeru, zscal, zswap, xerbla
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC max
170 * ..
171 * .. Executable Statements ..
172 *
173  info = 0
174  upper = lsame( uplo, 'U' )
175  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
176  info = -1
177  ELSE IF( n.LT.0 ) THEN
178  info = -2
179  ELSE IF( nrhs.LT.0 ) THEN
180  info = -3
181  ELSE IF( lda.LT.max( 1, n ) ) THEN
182  info = -5
183  ELSE IF( ldb.LT.max( 1, n ) ) THEN
184  info = -8
185  END IF
186  IF( info.NE.0 ) THEN
187  CALL xerbla( 'ZSYTRS_ROOK', -info )
188  RETURN
189  END IF
190 *
191 * Quick return if possible
192 *
193  IF( n.EQ.0 .OR. nrhs.EQ.0 )
194  \$ RETURN
195 *
196  IF( upper ) THEN
197 *
198 * Solve A*X = B, where A = U*D*U**T.
199 *
200 * First solve U*D*X = B, overwriting B with X.
201 *
202 * K is the main loop index, decreasing from N to 1 in steps of
203 * 1 or 2, depending on the size of the diagonal blocks.
204 *
205  k = n
206  10 CONTINUE
207 *
208 * If K < 1, exit from loop.
209 *
210  IF( k.LT.1 )
211  \$ GO TO 30
212 *
213  IF( ipiv( k ).GT.0 ) THEN
214 *
215 * 1 x 1 diagonal block
216 *
217 * Interchange rows K and IPIV(K).
218 *
219  kp = ipiv( k )
220  IF( kp.NE.k )
221  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
222 *
223 * Multiply by inv(U(K)), where U(K) is the transformation
224 * stored in column K of A.
225 *
226  CALL zgeru( k-1, nrhs, -cone, a( 1, k ), 1, b( k, 1 ), ldb,
227  \$ b( 1, 1 ), ldb )
228 *
229 * Multiply by the inverse of the diagonal block.
230 *
231  CALL zscal( nrhs, cone / a( k, k ), b( k, 1 ), ldb )
232  k = k - 1
233  ELSE
234 *
235 * 2 x 2 diagonal block
236 *
237 * Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
238 *
239  kp = -ipiv( k )
240  IF( kp.NE.k )
241  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
242 *
243  kp = -ipiv( k-1 )
244  IF( kp.NE.k-1 )
245  \$ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
246 *
247 * Multiply by inv(U(K)), where U(K) is the transformation
248 * stored in columns K-1 and K of A.
249 *
250  IF( k.GT.2 ) THEN
251  CALL zgeru( k-2, nrhs,-cone, a( 1, k ), 1, b( k, 1 ),
252  \$ ldb, b( 1, 1 ), ldb )
253  CALL zgeru( k-2, nrhs,-cone, a( 1, k-1 ), 1, b( k-1, 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, 1 ),
367  \$ ldb, b( k+1, 1 ), ldb )
368 *
369 * Multiply by the inverse of the diagonal block.
370 *
371  CALL zscal( nrhs, cone / a( k, k ), b( k, 1 ), ldb )
372  k = k + 1
373  ELSE
374 *
375 * 2 x 2 diagonal block
376 *
377 * Interchange rows K and -IPIV(K) THEN K+1 and -IPIV(K+1)
378 *
379  kp = -ipiv( k )
380  IF( kp.NE.k )
381  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
382 *
383  kp = -ipiv( k+1 )
384  IF( kp.NE.k+1 )
385  \$ CALL zswap( nrhs, b( k+1, 1 ), ldb, b( kp, 1 ), ldb )
386 *
387 * Multiply by inv(L(K)), where L(K) is the transformation
388 * stored in columns K and K+1 of A.
389 *
390  IF( k.LT.n-1 ) THEN
391  CALL zgeru( n-k-1, nrhs,-cone, a( k+2, k ), 1, b( k, 1 ),
392  \$ ldb, b( k+2, 1 ), ldb )
393  CALL zgeru( n-k-1, nrhs,-cone, a( k+2, k+1 ), 1,
394  \$ b( k+1, 1 ), ldb, b( k+2, 1 ), ldb )
395  END IF
396 *
397 * Multiply by the inverse of the diagonal block.
398 *
399  akm1k = a( k+1, k )
400  akm1 = a( k, k ) / akm1k
401  ak = a( k+1, k+1 ) / akm1k
402  denom = akm1*ak - cone
403  DO 70 j = 1, nrhs
404  bkm1 = b( k, j ) / akm1k
405  bk = b( k+1, j ) / akm1k
406  b( k, j ) = ( ak*bkm1-bk ) / denom
407  b( k+1, j ) = ( akm1*bk-bkm1 ) / denom
408  70 CONTINUE
409  k = k + 2
410  END IF
411 *
412  GO TO 60
413  80 CONTINUE
414 *
415 * Next solve L**T *X = B, overwriting B with X.
416 *
417 * K is the main loop index, decreasing from N to 1 in steps of
418 * 1 or 2, depending on the size of the diagonal blocks.
419 *
420  k = n
421  90 CONTINUE
422 *
423 * If K < 1, exit from loop.
424 *
425  IF( k.LT.1 )
426  \$ GO TO 100
427 *
428  IF( ipiv( k ).GT.0 ) THEN
429 *
430 * 1 x 1 diagonal block
431 *
432 * Multiply by inv(L**T(K)), where L(K) is the transformation
433 * stored in column K of A.
434 *
435  IF( k.LT.n )
436  \$ CALL zgemv( 'Transpose', n-k, nrhs, -cone, b( k+1, 1 ),
437  \$ ldb, a( k+1, k ), 1, cone, b( k, 1 ), ldb )
438 *
439 * Interchange rows K and IPIV(K).
440 *
441  kp = ipiv( k )
442  IF( kp.NE.k )
443  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
444  k = k - 1
445  ELSE
446 *
447 * 2 x 2 diagonal block
448 *
449 * Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
450 * stored in columns K-1 and K of A.
451 *
452  IF( k.LT.n ) THEN
453  CALL zgemv( 'Transpose', n-k, nrhs, -cone, b( k+1, 1 ),
454  \$ ldb, a( k+1, k ), 1, cone, b( k, 1 ), ldb )
455  CALL zgemv( 'Transpose', n-k, nrhs, -cone, b( k+1, 1 ),
456  \$ ldb, a( k+1, k-1 ), 1, cone, b( k-1, 1 ),
457  \$ ldb )
458  END IF
459 *
460 * Interchange rows K and -IPIV(K) THEN K-1 and -IPIV(K-1)
461 *
462  kp = -ipiv( k )
463  IF( kp.NE.k )
464  \$ CALL zswap( nrhs, b( k, 1 ), ldb, b( kp, 1 ), ldb )
465 *
466  kp = -ipiv( k-1 )
467  IF( kp.NE.k-1 )
468  \$ CALL zswap( nrhs, b( k-1, 1 ), ldb, b( kp, 1 ), ldb )
469 *
470  k = k - 2
471  END IF
472 *
473  GO TO 90
474  100 CONTINUE
475  END IF
476 *
477  RETURN
478 *
479 * End of ZSYTRS_ROOK
480 *
481  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.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 zsytrs_rook(UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
ZSYTRS_ROOK
Definition: zsytrs_rook.f:136