LAPACK 3.12.1
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chetrf_rook.f
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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*
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15*
16* Definition:
17* ===========
18*
19* SUBROUTINE CHETRF_ROOK( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
20*
21* .. Scalar Arguments ..
22* CHARACTER UPLO
23* INTEGER INFO, LDA, LWORK, N
24* ..
25* .. Array Arguments ..
26* INTEGER IPIV( * )
27* COMPLEX A( LDA, * ), WORK( * )
28* ..
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> CHETRF_ROOK computes the factorization of a complex Hermitian matrix A
37*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method.
38*> The form of the factorization is
39*>
40*> A = U*D*U**T or A = L*D*L**T
41*>
42*> where U (or L) is a product of permutation and unit upper (lower)
43*> triangular matrices, and D is Hermitian and block diagonal with
44*> 1-by-1 and 2-by-2 diagonal blocks.
45*>
46*> This is the blocked version of the algorithm, calling Level 3 BLAS.
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] UPLO
53*> \verbatim
54*> UPLO is CHARACTER*1
55*> = 'U': Upper triangle of A is stored;
56*> = 'L': Lower triangle of A is stored.
57*> \endverbatim
58*>
59*> \param[in] N
60*> \verbatim
61*> N is INTEGER
62*> The order of the matrix A. N >= 0.
63*> \endverbatim
64*>
65*> \param[in,out] A
66*> \verbatim
67*> A is COMPLEX array, dimension (LDA,N)
68*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
69*> N-by-N upper triangular part of A contains the upper
70*> triangular part of the matrix A, and the strictly lower
71*> triangular part of A is not referenced. If UPLO = 'L', the
72*> leading N-by-N lower triangular part of A contains the lower
73*> triangular part of the matrix A, and the strictly upper
74*> triangular part of A is not referenced.
75*>
76*> On exit, the block diagonal matrix D and the multipliers used
77*> to obtain the factor U or L (see below for further details).
78*> \endverbatim
79*>
80*> \param[in] LDA
81*> \verbatim
82*> LDA is INTEGER
83*> The leading dimension of the array A. LDA >= max(1,N).
84*> \endverbatim
85*>
86*> \param[out] IPIV
87*> \verbatim
88*> IPIV is INTEGER array, dimension (N)
89*> Details of the interchanges and the block structure of D.
90*>
91*> If UPLO = 'U':
92*> Only the last KB elements of IPIV are set.
93*>
94*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
95*> interchanged and D(k,k) is a 1-by-1 diagonal block.
96*>
97*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
98*> columns k and -IPIV(k) were interchanged and rows and
99*> columns k-1 and -IPIV(k-1) were inerchaged,
100*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
101*>
102*> If UPLO = 'L':
103*> Only the first KB elements of IPIV are set.
104*>
105*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
106*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
107*>
108*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
109*> columns k and -IPIV(k) were interchanged and rows and
110*> columns k+1 and -IPIV(k+1) were inerchaged,
111*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
112*> \endverbatim
113*>
114*> \param[out] WORK
115*> \verbatim
116*> WORK is COMPLEX array, dimension (MAX(1,LWORK)).
117*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
118*> \endverbatim
119*>
120*> \param[in] LWORK
121*> \verbatim
122*> LWORK is INTEGER
123*> The length of WORK. LWORK >= 1. For best performance
124*> LWORK >= N*NB, where NB is the block size returned by ILAENV.
125*>
126*> If LWORK = -1, then a workspace query is assumed; the routine
127*> only calculates the optimal size of the WORK array, returns
128*> this value as the first entry of the WORK array, and no error
129*> message related to LWORK is issued by XERBLA.
130*> \endverbatim
131*>
132*> \param[out] INFO
133*> \verbatim
134*> INFO is INTEGER
135*> = 0: successful exit
136*> < 0: if INFO = -i, the i-th argument had an illegal value
137*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
138*> has been completed, but the block diagonal matrix D is
139*> exactly singular, and division by zero will occur if it
140*> is used to solve a system of equations.
141*> \endverbatim
142*
143* Authors:
144* ========
145*
146*> \author Univ. of Tennessee
147*> \author Univ. of California Berkeley
148*> \author Univ. of Colorado Denver
149*> \author NAG Ltd.
150*
151*> \ingroup hetrf_rook
152*
153*> \par Further Details:
154* =====================
155*>
156*> \verbatim
157*>
158*> If UPLO = 'U', then A = U*D*U**T, where
159*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
160*> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
161*> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
162*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
163*> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
164*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
165*>
166*> ( I v 0 ) k-s
167*> U(k) = ( 0 I 0 ) s
168*> ( 0 0 I ) n-k
169*> k-s s n-k
170*>
171*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
172*> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
173*> and A(k,k), and v overwrites A(1:k-2,k-1:k).
174*>
175*> If UPLO = 'L', then A = L*D*L**T, where
176*> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
177*> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
178*> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
179*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
180*> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
181*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
182*>
183*> ( I 0 0 ) k-1
184*> L(k) = ( 0 I 0 ) s
185*> ( 0 v I ) n-k-s+1
186*> k-1 s n-k-s+1
187*>
188*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
189*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
190*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
191*> \endverbatim
192*
193*> \par Contributors:
194* ==================
195*>
196*> \verbatim
197*>
198*> June 2016, Igor Kozachenko,
199*> Computer Science Division,
200*> University of California, Berkeley
201*>
202*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
203*> School of Mathematics,
204*> University of Manchester
205*>
206*> \endverbatim
207*
208* =====================================================================
209 SUBROUTINE chetrf_rook( UPLO, N, A, LDA, IPIV, WORK, LWORK,
210 $ INFO )
211*
212* -- LAPACK computational routine --
213* -- LAPACK is a software package provided by Univ. of Tennessee, --
214* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
215*
216* .. Scalar Arguments ..
217 CHARACTER UPLO
218 INTEGER INFO, LDA, LWORK, N
219* ..
220* .. Array Arguments ..
221 INTEGER IPIV( * )
222 COMPLEX A( LDA, * ), WORK( * )
223* ..
224*
225* =====================================================================
226*
227* .. Local Scalars ..
228 LOGICAL LQUERY, UPPER
229 INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
230* ..
231* .. External Functions ..
232 LOGICAL LSAME
233 INTEGER ILAENV
234 REAL SROUNDUP_LWORK
235 EXTERNAL lsame, ilaenv, sroundup_lwork
236* ..
237* .. External Subroutines ..
239* ..
240* .. Intrinsic Functions ..
241 INTRINSIC max
242* ..
243* .. Executable Statements ..
244*
245* Test the input parameters.
246*
247 info = 0
248 upper = lsame( uplo, 'U' )
249 lquery = ( lwork.EQ.-1 )
250 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
251 info = -1
252 ELSE IF( n.LT.0 ) THEN
253 info = -2
254 ELSE IF( lda.LT.max( 1, n ) ) THEN
255 info = -4
256 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
257 info = -7
258 END IF
259*
260 IF( info.EQ.0 ) THEN
261*
262* Determine the block size
263*
264 nb = ilaenv( 1, 'CHETRF_ROOK', uplo, n, -1, -1, -1 )
265 lwkopt = max( 1, n*nb )
266 work( 1 ) = sroundup_lwork( lwkopt )
267 END IF
268*
269 IF( info.NE.0 ) THEN
270 CALL xerbla( 'CHETRF_ROOK', -info )
271 RETURN
272 ELSE IF( lquery ) THEN
273 RETURN
274 END IF
275*
276 nbmin = 2
277 ldwork = n
278 IF( nb.GT.1 .AND. nb.LT.n ) THEN
279 iws = ldwork*nb
280 IF( lwork.LT.iws ) THEN
281 nb = max( lwork / ldwork, 1 )
282 nbmin = max( 2, ilaenv( 2, 'CHETRF_ROOK',
283 $ uplo, n, -1, -1, -1 ) )
284 END IF
285 ELSE
286 iws = 1
287 END IF
288 IF( nb.LT.nbmin )
289 $ nb = n
290*
291 IF( upper ) THEN
292*
293* Factorize A as U*D*U**T using the upper triangle of A
294*
295* K is the main loop index, decreasing from N to 1 in steps of
296* KB, where KB is the number of columns factorized by CLAHEF_ROOK;
297* KB is either NB or NB-1, or K for the last block
298*
299 k = n
300 10 CONTINUE
301*
302* If K < 1, exit from loop
303*
304 IF( k.LT.1 )
305 $ GO TO 40
306*
307 IF( k.GT.nb ) THEN
308*
309* Factorize columns k-kb+1:k of A and use blocked code to
310* update columns 1:k-kb
311*
312 CALL clahef_rook( uplo, k, nb, kb, a, lda,
313 $ ipiv, work, ldwork, iinfo )
314 ELSE
315*
316* Use unblocked code to factorize columns 1:k of A
317*
318 CALL chetf2_rook( uplo, k, a, lda, ipiv, iinfo )
319 kb = k
320 END IF
321*
322* Set INFO on the first occurrence of a zero pivot
323*
324 IF( info.EQ.0 .AND. iinfo.GT.0 )
325 $ info = iinfo
326*
327* No need to adjust IPIV
328*
329* Decrease K and return to the start of the main loop
330*
331 k = k - kb
332 GO TO 10
333*
334 ELSE
335*
336* Factorize A as L*D*L**T using the lower triangle of A
337*
338* K is the main loop index, increasing from 1 to N in steps of
339* KB, where KB is the number of columns factorized by CLAHEF_ROOK;
340* KB is either NB or NB-1, or N-K+1 for the last block
341*
342 k = 1
343 20 CONTINUE
344*
345* If K > N, exit from loop
346*
347 IF( k.GT.n )
348 $ GO TO 40
349*
350 IF( k.LE.n-nb ) THEN
351*
352* Factorize columns k:k+kb-1 of A and use blocked code to
353* update columns k+kb:n
354*
355 CALL clahef_rook( uplo, n-k+1, nb, kb, a( k, k ), lda,
356 $ ipiv( k ), work, ldwork, iinfo )
357 ELSE
358*
359* Use unblocked code to factorize columns k:n of A
360*
361 CALL chetf2_rook( uplo, n-k+1, a( k, k ), lda, ipiv( k ),
362 $ iinfo )
363 kb = n - k + 1
364 END IF
365*
366* Set INFO on the first occurrence of a zero pivot
367*
368 IF( info.EQ.0 .AND. iinfo.GT.0 )
369 $ info = iinfo + k - 1
370*
371* Adjust IPIV
372*
373 DO 30 j = k, k + kb - 1
374 IF( ipiv( j ).GT.0 ) THEN
375 ipiv( j ) = ipiv( j ) + k - 1
376 ELSE
377 ipiv( j ) = ipiv( j ) - k + 1
378 END IF
379 30 CONTINUE
380*
381* Increase K and return to the start of the main loop
382*
383 k = k + kb
384 GO TO 20
385*
386 END IF
387*
388 40 CONTINUE
389 work( 1 ) = sroundup_lwork( lwkopt )
390 RETURN
391*
392* End of CHETRF_ROOK
393*
394 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chetf2_rook(uplo, n, a, lda, ipiv, info)
CHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
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...
subroutine clahef_rook(uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)
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