LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
chetrf_rook.f
Go to the documentation of this file.
1 *> \brief \b CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetrf_rook.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetrf_rook.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetrf_rook.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, LWORK, N
26 * ..
27 * .. Array Arguments ..
28 * INTEGER IPIV( * )
29 * COMPLEX A( LDA, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CHETRF_ROOK computes the factorization of a comlex Hermitian matrix A
39 *> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
40 *> The form of the factorization is
41 *>
42 *> A = U*D*U**T or A = L*D*L**T
43 *>
44 *> where U (or L) is a product of permutation and unit upper (lower)
45 *> triangular matrices, and D is Hermitian and block diagonal with
46 *> 1-by-1 and 2-by-2 diagonal blocks.
47 *>
48 *> This is the blocked version of the algorithm, calling Level 3 BLAS.
49 *> \endverbatim
50 *
51 * Arguments:
52 * ==========
53 *
54 *> \param[in] UPLO
55 *> \verbatim
56 *> UPLO is CHARACTER*1
57 *> = 'U': Upper triangle of A is stored;
58 *> = 'L': Lower triangle of A is stored.
59 *> \endverbatim
60 *>
61 *> \param[in] N
62 *> \verbatim
63 *> N is INTEGER
64 *> The order of the matrix A. N >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in,out] A
68 *> \verbatim
69 *> A is COMPLEX array, dimension (LDA,N)
70 *> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
71 *> N-by-N upper triangular part of A contains the upper
72 *> triangular part of the matrix A, and the strictly lower
73 *> triangular part of A is not referenced. If UPLO = 'L', the
74 *> leading N-by-N lower triangular part of A contains the lower
75 *> triangular part of the matrix A, and the strictly upper
76 *> triangular part of A is not referenced.
77 *>
78 *> On exit, the block diagonal matrix D and the multipliers used
79 *> to obtain the factor U or L (see below for further details).
80 *> \endverbatim
81 *>
82 *> \param[in] LDA
83 *> \verbatim
84 *> LDA is INTEGER
85 *> The leading dimension of the array A. LDA >= max(1,N).
86 *> \endverbatim
87 *>
88 *> \param[out] IPIV
89 *> \verbatim
90 *> IPIV is INTEGER array, dimension (N)
91 *> Details of the interchanges and the block structure of D.
92 *>
93 *> If UPLO = 'U':
94 *> Only the last KB elements of IPIV are set.
95 *>
96 *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
97 *> interchanged and D(k,k) is a 1-by-1 diagonal block.
98 *>
99 *> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
100 *> columns k and -IPIV(k) were interchanged and rows and
101 *> columns k-1 and -IPIV(k-1) were inerchaged,
102 *> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
103 *>
104 *> If UPLO = 'L':
105 *> Only the first KB elements of IPIV are set.
106 *>
107 *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
108 *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
109 *>
110 *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
111 *> columns k and -IPIV(k) were interchanged and rows and
112 *> columns k+1 and -IPIV(k+1) were inerchaged,
113 *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
114 *> \endverbatim
115 *>
116 *> \param[out] WORK
117 *> \verbatim
118 *> WORK is COMPLEX array, dimension (MAX(1,LWORK)).
119 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
120 *> \endverbatim
121 *>
122 *> \param[in] LWORK
123 *> \verbatim
124 *> LWORK is INTEGER
125 *> The length of WORK. LWORK >=1. For best performance
126 *> LWORK >= N*NB, where NB is the block size returned by ILAENV.
127 *>
128 *> If LWORK = -1, then a workspace query is assumed; the routine
129 *> only calculates the optimal size of the WORK array, returns
130 *> this value as the first entry of the WORK array, and no error
131 *> message related to LWORK is issued by XERBLA.
132 *> \endverbatim
133 *>
134 *> \param[out] INFO
135 *> \verbatim
136 *> INFO is INTEGER
137 *> = 0: successful exit
138 *> < 0: if INFO = -i, the i-th argument had an illegal value
139 *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
140 *> has been completed, but the block diagonal matrix D is
141 *> exactly singular, and division by zero will occur if it
142 *> is used to solve a system of equations.
143 *> \endverbatim
144 *
145 * Authors:
146 * ========
147 *
148 *> \author Univ. of Tennessee
149 *> \author Univ. of California Berkeley
150 *> \author Univ. of Colorado Denver
151 *> \author NAG Ltd.
152 *
153 *> \date June 2016
154 *
155 *> \ingroup complexHEcomputational
156 *
157 *> \par Further Details:
158 * =====================
159 *>
160 *> \verbatim
161 *>
162 *> If UPLO = 'U', then A = U*D*U**T, where
163 *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
164 *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
165 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
166 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
167 *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
168 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
169 *>
170 *> ( I v 0 ) k-s
171 *> U(k) = ( 0 I 0 ) s
172 *> ( 0 0 I ) n-k
173 *> k-s s n-k
174 *>
175 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
176 *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
177 *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
178 *>
179 *> If UPLO = 'L', then A = L*D*L**T, where
180 *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
181 *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
182 *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
183 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
184 *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
185 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
186 *>
187 *> ( I 0 0 ) k-1
188 *> L(k) = ( 0 I 0 ) s
189 *> ( 0 v I ) n-k-s+1
190 *> k-1 s n-k-s+1
191 *>
192 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
193 *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
194 *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
195 *> \endverbatim
196 *
197 *> \par Contributors:
198 * ==================
199 *>
200 *> \verbatim
201 *>
202 *> June 2016, Igor Kozachenko,
203 *> Computer Science Division,
204 *> University of California, Berkeley
205 *>
206 *> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
207 *> School of Mathematics,
208 *> University of Manchester
209 *>
210 *> \endverbatim
211 *
212 * =====================================================================
213  SUBROUTINE chetrf_rook( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
214 *
215 * -- LAPACK computational routine (version 3.6.1) --
216 * -- LAPACK is a software package provided by Univ. of Tennessee, --
217 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
218 * June 2016
219 *
220 * .. Scalar Arguments ..
221  CHARACTER UPLO
222  INTEGER INFO, LDA, LWORK, N
223 * ..
224 * .. Array Arguments ..
225  INTEGER IPIV( * )
226  COMPLEX A( lda, * ), WORK( * )
227 * ..
228 *
229 * =====================================================================
230 *
231 * .. Local Scalars ..
232  LOGICAL LQUERY, UPPER
233  INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
234 * ..
235 * .. External Functions ..
236  LOGICAL LSAME
237  INTEGER ILAENV
238  EXTERNAL lsame, ilaenv
239 * ..
240 * .. External Subroutines ..
241  EXTERNAL clahef_rook, chetf2_rook, xerbla
242 * ..
243 * .. Intrinsic Functions ..
244  INTRINSIC max
245 * ..
246 * .. Executable Statements ..
247 *
248 * Test the input parameters.
249 *
250  info = 0
251  upper = lsame( uplo, 'U' )
252  lquery = ( lwork.EQ.-1 )
253  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
254  info = -1
255  ELSE IF( n.LT.0 ) THEN
256  info = -2
257  ELSE IF( lda.LT.max( 1, n ) ) THEN
258  info = -4
259  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
260  info = -7
261  END IF
262 *
263  IF( info.EQ.0 ) THEN
264 *
265 * Determine the block size
266 *
267  nb = ilaenv( 1, 'CHETRF_ROOK', uplo, n, -1, -1, -1 )
268  lwkopt = max( 1, n*nb )
269  work( 1 ) = lwkopt
270  END IF
271 *
272  IF( info.NE.0 ) THEN
273  CALL xerbla( 'CHETRF_ROOK', -info )
274  RETURN
275  ELSE IF( lquery ) THEN
276  RETURN
277  END IF
278 *
279  nbmin = 2
280  ldwork = n
281  IF( nb.GT.1 .AND. nb.LT.n ) THEN
282  iws = ldwork*nb
283  IF( lwork.LT.iws ) THEN
284  nb = max( lwork / ldwork, 1 )
285  nbmin = max( 2, ilaenv( 2, 'CHETRF_ROOK',
286  \$ uplo, n, -1, -1, -1 ) )
287  END IF
288  ELSE
289  iws = 1
290  END IF
291  IF( nb.LT.nbmin )
292  \$ nb = n
293 *
294  IF( upper ) THEN
295 *
296 * Factorize A as U*D*U**T using the upper triangle of A
297 *
298 * K is the main loop index, decreasing from N to 1 in steps of
299 * KB, where KB is the number of columns factorized by CLAHEF_ROOK;
300 * KB is either NB or NB-1, or K for the last block
301 *
302  k = n
303  10 CONTINUE
304 *
305 * If K < 1, exit from loop
306 *
307  IF( k.LT.1 )
308  \$ GO TO 40
309 *
310  IF( k.GT.nb ) THEN
311 *
312 * Factorize columns k-kb+1:k of A and use blocked code to
313 * update columns 1:k-kb
314 *
315  CALL clahef_rook( uplo, k, nb, kb, a, lda,
316  \$ ipiv, work, ldwork, iinfo )
317  ELSE
318 *
319 * Use unblocked code to factorize columns 1:k of A
320 *
321  CALL chetf2_rook( uplo, k, a, lda, ipiv, iinfo )
322  kb = k
323  END IF
324 *
325 * Set INFO on the first occurrence of a zero pivot
326 *
327  IF( info.EQ.0 .AND. iinfo.GT.0 )
328  \$ info = iinfo
329 *
330 * No need to adjust IPIV
331 *
332 * Decrease K and return to the start of the main loop
333 *
334  k = k - kb
335  GO TO 10
336 *
337  ELSE
338 *
339 * Factorize A as L*D*L**T using the lower triangle of A
340 *
341 * K is the main loop index, increasing from 1 to N in steps of
342 * KB, where KB is the number of columns factorized by CLAHEF_ROOK;
343 * KB is either NB or NB-1, or N-K+1 for the last block
344 *
345  k = 1
346  20 CONTINUE
347 *
348 * If K > N, exit from loop
349 *
350  IF( k.GT.n )
351  \$ GO TO 40
352 *
353  IF( k.LE.n-nb ) THEN
354 *
355 * Factorize columns k:k+kb-1 of A and use blocked code to
356 * update columns k+kb:n
357 *
358  CALL clahef_rook( uplo, n-k+1, nb, kb, a( k, k ), lda,
359  \$ ipiv( k ), work, ldwork, iinfo )
360  ELSE
361 *
362 * Use unblocked code to factorize columns k:n of A
363 *
364  CALL chetf2_rook( uplo, n-k+1, a( k, k ), lda, ipiv( k ),
365  \$ iinfo )
366  kb = n - k + 1
367  END IF
368 *
369 * Set INFO on the first occurrence of a zero pivot
370 *
371  IF( info.EQ.0 .AND. iinfo.GT.0 )
372  \$ info = iinfo + k - 1
373 *
375 *
376  DO 30 j = k, k + kb - 1
377  IF( ipiv( j ).GT.0 ) THEN
378  ipiv( j ) = ipiv( j ) + k - 1
379  ELSE
380  ipiv( j ) = ipiv( j ) - k + 1
381  END IF
382  30 CONTINUE
383 *
384 * Increase K and return to the start of the main loop
385 *
386  k = k + kb
387  GO TO 20
388 *
389  END IF
390 *
391  40 CONTINUE
392  work( 1 ) = lwkopt
393  RETURN
394 *
395 * End of CHETRF_ROOK
396 *
397  END
subroutine chetrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
CHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: chetrf_rook.f:214
subroutine chetf2_rook(UPLO, N, A, LDA, IPIV, INFO)
CHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: chetf2_rook.f:196
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine clahef_rook(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)