LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ssytrf_rook.f
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1 *> \brief \b SSYTRF_ROOK
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSYTRF_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 * REAL A( LDA, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SSYTRF_ROOK computes the factorization of a real symmetric 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 symmetric 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 REAL array, dimension (LDA,N)
70 *> On entry, the symmetric 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 *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
95 *> were 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 *> If IPIV(k) > 0, then rows and columns k and IPIV(k)
104 *> were interchanged and D(k,k) is a 1-by-1 diagonal block.
105 *>
106 *> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
107 *> columns k and -IPIV(k) were interchanged and rows and
108 *> columns k+1 and -IPIV(k+1) were inerchaged,
109 *> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
110 *> \endverbatim
111 *>
112 *> \param[out] WORK
113 *> \verbatim
114 *> WORK is REAL array, dimension (MAX(1,LWORK)).
115 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
116 *> \endverbatim
117 *>
118 *> \param[in] LWORK
119 *> \verbatim
120 *> LWORK is INTEGER
121 *> The length of WORK. LWORK >=1. For best performance
122 *> LWORK >= N*NB, where NB is the block size returned by ILAENV.
123 *>
124 *> If LWORK = -1, then a workspace query is assumed; the routine
125 *> only calculates the optimal size of the WORK array, returns
126 *> this value as the first entry of the WORK array, and no error
127 *> message related to LWORK is issued by XERBLA.
128 *> \endverbatim
129 *>
130 *> \param[out] INFO
131 *> \verbatim
132 *> INFO is INTEGER
133 *> = 0: successful exit
134 *> < 0: if INFO = -i, the i-th argument had an illegal value
135 *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
136 *> has been completed, but the block diagonal matrix D is
137 *> exactly singular, and division by zero will occur if it
138 *> is used to solve a system of equations.
139 *> \endverbatim
140 *
141 * Authors:
142 * ========
143 *
144 *> \author Univ. of Tennessee
145 *> \author Univ. of California Berkeley
146 *> \author Univ. of Colorado Denver
147 *> \author NAG Ltd.
148 *
149 *> \date June 2016
150 *
151 *> \ingroup realSYcomputational
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 ssytrf_rook( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
210 *
211 * -- LAPACK computational routine (version 3.7.0) --
212 * -- LAPACK is a software package provided by Univ. of Tennessee, --
213 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
214 * June 2016
215 *
216 * .. Scalar Arguments ..
217  CHARACTER UPLO
218  INTEGER INFO, LDA, LWORK, N
219 * ..
220 * .. Array Arguments ..
221  INTEGER IPIV( * )
222  REAL 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  EXTERNAL lsame, ilaenv
235 * ..
236 * .. External Subroutines ..
237  EXTERNAL slasyf_rook, ssytf2_rook, xerbla
238 * ..
239 * .. Intrinsic Functions ..
240  INTRINSIC max
241 * ..
242 * .. Executable Statements ..
243 *
244 * Test the input parameters.
245 *
246  info = 0
247  upper = lsame( uplo, 'U' )
248  lquery = ( lwork.EQ.-1 )
249  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
250  info = -1
251  ELSE IF( n.LT.0 ) THEN
252  info = -2
253  ELSE IF( lda.LT.max( 1, n ) ) THEN
254  info = -4
255  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
256  info = -7
257  END IF
258 *
259  IF( info.EQ.0 ) THEN
260 *
261 * Determine the block size
262 *
263  nb = ilaenv( 1, 'SSYTRF_ROOK', uplo, n, -1, -1, -1 )
264  lwkopt = max( 1, n*nb )
265  work( 1 ) = lwkopt
266  END IF
267 *
268  IF( info.NE.0 ) THEN
269  CALL xerbla( 'SSYTRF_ROOK', -info )
270  RETURN
271  ELSE IF( lquery ) THEN
272  RETURN
273  END IF
274 *
275  nbmin = 2
276  ldwork = n
277  IF( nb.GT.1 .AND. nb.LT.n ) THEN
278  iws = ldwork*nb
279  IF( lwork.LT.iws ) THEN
280  nb = max( lwork / ldwork, 1 )
281  nbmin = max( 2, ilaenv( 2, 'SSYTRF_ROOK',
282  $ uplo, n, -1, -1, -1 ) )
283  END IF
284  ELSE
285  iws = 1
286  END IF
287  IF( nb.LT.nbmin )
288  $ nb = n
289 *
290  IF( upper ) THEN
291 *
292 * Factorize A as U*D*U**T using the upper triangle of A
293 *
294 * K is the main loop index, decreasing from N to 1 in steps of
295 * KB, where KB is the number of columns factorized by SLASYF_ROOK;
296 * KB is either NB or NB-1, or K for the last block
297 *
298  k = n
299  10 CONTINUE
300 *
301 * If K < 1, exit from loop
302 *
303  IF( k.LT.1 )
304  $ GO TO 40
305 *
306  IF( k.GT.nb ) THEN
307 *
308 * Factorize columns k-kb+1:k of A and use blocked code to
309 * update columns 1:k-kb
310 *
311  CALL slasyf_rook( uplo, k, nb, kb, a, lda,
312  $ ipiv, work, ldwork, iinfo )
313  ELSE
314 *
315 * Use unblocked code to factorize columns 1:k of A
316 *
317  CALL ssytf2_rook( uplo, k, a, lda, ipiv, iinfo )
318  kb = k
319  END IF
320 *
321 * Set INFO on the first occurrence of a zero pivot
322 *
323  IF( info.EQ.0 .AND. iinfo.GT.0 )
324  $ info = iinfo
325 *
326 * No need to adjust IPIV
327 *
328 * Decrease K and return to the start of the main loop
329 *
330  k = k - kb
331  GO TO 10
332 *
333  ELSE
334 *
335 * Factorize A as L*D*L**T using the lower triangle of A
336 *
337 * K is the main loop index, increasing from 1 to N in steps of
338 * KB, where KB is the number of columns factorized by SLASYF_ROOK;
339 * KB is either NB or NB-1, or N-K+1 for the last block
340 *
341  k = 1
342  20 CONTINUE
343 *
344 * If K > N, exit from loop
345 *
346  IF( k.GT.n )
347  $ GO TO 40
348 *
349  IF( k.LE.n-nb ) THEN
350 *
351 * Factorize columns k:k+kb-1 of A and use blocked code to
352 * update columns k+kb:n
353 *
354  CALL slasyf_rook( uplo, n-k+1, nb, kb, a( k, k ), lda,
355  $ ipiv( k ), work, ldwork, iinfo )
356  ELSE
357 *
358 * Use unblocked code to factorize columns k:n of A
359 *
360  CALL ssytf2_rook( uplo, n-k+1, a( k, k ), lda, ipiv( k ),
361  $ iinfo )
362  kb = n - k + 1
363  END IF
364 *
365 * Set INFO on the first occurrence of a zero pivot
366 *
367  IF( info.EQ.0 .AND. iinfo.GT.0 )
368  $ info = iinfo + k - 1
369 *
370 * Adjust IPIV
371 *
372  DO 30 j = k, k + kb - 1
373  IF( ipiv( j ).GT.0 ) THEN
374  ipiv( j ) = ipiv( j ) + k - 1
375  ELSE
376  ipiv( j ) = ipiv( j ) - k + 1
377  END IF
378  30 CONTINUE
379 *
380 * Increase K and return to the start of the main loop
381 *
382  k = k + kb
383  GO TO 20
384 *
385  END IF
386 *
387  40 CONTINUE
388  work( 1 ) = lwkopt
389  RETURN
390 *
391 * End of SSYTRF_ROOK
392 *
393  END
subroutine ssytrf_rook(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
SSYTRF_ROOK
Definition: ssytrf_rook.f:210
subroutine slasyf_rook(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
SLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufm...
Definition: slasyf_rook.f:186
subroutine ssytf2_rook(UPLO, N, A, LDA, IPIV, INFO)
SSYTF2_ROOK computes the factorization of a real symmetric indefinite matrix using the bounded Bunch-...
Definition: ssytf2_rook.f:196
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62