LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
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/
7 *
8 *> \htmlonly
9 *> Download ZHETRF_ROOK + dependencies
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetrf_rook.f">
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 ..
238  EXTERNAL zlahef_rook, zhetf2_rook, xerbla
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 *
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 ) = 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)
Download ZLAHEF_ROOK + dependencies <a href="http://www.netlib.org/cgi-bin/netlibfiles....
Definition: zlahef_rook.f:184