LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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zhetrf_rook.f
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1*> \brief \b ZHETRF_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/
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZHETRF_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*16 A( LDA, * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZHETRF_ROOK computes the factorization of a complex 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*16 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*16 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*> \ingroup complex16HEcomputational
154*
155*> \par Further Details:
156* =====================
157*>
158*> \verbatim
159*>
160*> If UPLO = 'U', then A = U*D*U**T, where
161*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
162*> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
163*> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
164*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
165*> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
166*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
167*>
168*> ( I v 0 ) k-s
169*> U(k) = ( 0 I 0 ) s
170*> ( 0 0 I ) n-k
171*> k-s s n-k
172*>
173*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
174*> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
175*> and A(k,k), and v overwrites A(1:k-2,k-1:k).
176*>
177*> If UPLO = 'L', then A = L*D*L**T, where
178*> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
179*> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
180*> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
181*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
182*> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
183*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
184*>
185*> ( I 0 0 ) k-1
186*> L(k) = ( 0 I 0 ) s
187*> ( 0 v I ) n-k-s+1
188*> k-1 s n-k-s+1
189*>
190*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
191*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
192*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
193*> \endverbatim
194*
195*> \par Contributors:
196* ==================
197*>
198*> \verbatim
199*>
200*> June 2016, Igor Kozachenko,
201*> Computer Science Division,
202*> University of California, Berkeley
203*>
204*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
205*> School of Mathematics,
206*> University of Manchester
207*>
208*> \endverbatim
209*
210* =====================================================================
211 SUBROUTINE zhetrf_rook( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
212*
213* -- LAPACK computational routine --
214* -- LAPACK is a software package provided by Univ. of Tennessee, --
215* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
216*
217* .. Scalar Arguments ..
218 CHARACTER UPLO
219 INTEGER INFO, LDA, LWORK, N
220* ..
221* .. Array Arguments ..
222 INTEGER IPIV( * )
223 COMPLEX*16 A( LDA, * ), WORK( * )
224* ..
225*
226* =====================================================================
227*
228* .. Local Scalars ..
229 LOGICAL LQUERY, UPPER
230 INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
231* ..
232* .. External Functions ..
233 LOGICAL LSAME
234 INTEGER ILAENV
235 EXTERNAL lsame, ilaenv
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, 'ZHETRF_ROOK', uplo, n, -1, -1, -1 )
265 lwkopt = max( 1, n*nb )
266 work( 1 ) = lwkopt
267 END IF
268*
269 IF( info.NE.0 ) THEN
270 CALL xerbla( 'ZHETRF_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, 'ZHETRF_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 ZLAHEF_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 zlahef_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 zhetf2_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 ZLAHEF_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 zlahef_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 zhetf2_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*
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 ) = lwkopt
390 RETURN
391*
392* End of ZHETRF_ROOK
393*
394 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zhetf2_rook(UPLO, N, A, LDA, IPIV, INFO)
ZHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: zhetf2_rook.f:194
subroutine zhetrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZHETRF_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bun...
Definition: zhetrf_rook.f:212
subroutine zlahef_rook(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)