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csytrf.f
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1 *> \brief \b CSYTRF
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 CSYTRF( 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 *> CSYTRF computes the factorization of a complex symmetric matrix A
39 *> using the Bunch-Kaufman diagonal pivoting method. The form of the
40 *> 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 *> with 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 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 *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
93 *> interchanged and D(k,k) is a 1-by-1 diagonal block.
94 *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
95 *> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
96 *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
97 *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
98 *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
99 *> \endverbatim
100 *>
101 *> \param[out] WORK
102 *> \verbatim
103 *> WORK is COMPLEX array, dimension (MAX(1,LWORK))
104 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
105 *> \endverbatim
106 *>
107 *> \param[in] LWORK
108 *> \verbatim
109 *> LWORK is INTEGER
110 *> The length of WORK. LWORK >=1. For best performance
111 *> LWORK >= N*NB, where NB is the block size returned by ILAENV.
112 *>
113 *> If LWORK = -1, then a workspace query is assumed; the routine
114 *> only calculates the optimal size of the WORK array, returns
115 *> this value as the first entry of the WORK array, and no error
116 *> message related to LWORK is issued by XERBLA.
117 *> \endverbatim
118 *>
119 *> \param[out] INFO
120 *> \verbatim
121 *> INFO is INTEGER
122 *> = 0: successful exit
123 *> < 0: if INFO = -i, the i-th argument had an illegal value
124 *> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
125 *> has been completed, but the block diagonal matrix D is
126 *> exactly singular, and division by zero will occur if it
127 *> is used to solve a system of equations.
128 *> \endverbatim
129 *
130 * Authors:
131 * ========
132 *
133 *> \author Univ. of Tennessee
134 *> \author Univ. of California Berkeley
135 *> \author Univ. of Colorado Denver
136 *> \author NAG Ltd.
137 *
138 *> \date November 2011
139 *
140 *> \ingroup complexSYcomputational
141 *
142 *> \par Further Details:
143 * =====================
144 *>
145 *> \verbatim
146 *>
147 *> If UPLO = 'U', then A = U*D*U**T, where
148 *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
149 *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
150 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
151 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
152 *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
153 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
154 *>
155 *> ( I v 0 ) k-s
156 *> U(k) = ( 0 I 0 ) s
157 *> ( 0 0 I ) n-k
158 *> k-s s n-k
159 *>
160 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
161 *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
162 *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
163 *>
164 *> If UPLO = 'L', then A = L*D*L**T, where
165 *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
166 *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
167 *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
168 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
169 *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
170 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
171 *>
172 *> ( I 0 0 ) k-1
173 *> L(k) = ( 0 I 0 ) s
174 *> ( 0 v I ) n-k-s+1
175 *> k-1 s n-k-s+1
176 *>
177 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
178 *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
179 *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
180 *> \endverbatim
181 *>
182 * =====================================================================
183  SUBROUTINE csytrf( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
184 *
185 * -- LAPACK computational routine (version 3.4.0) --
186 * -- LAPACK is a software package provided by Univ. of Tennessee, --
187 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
188 * November 2011
189 *
190 * .. Scalar Arguments ..
191  CHARACTER uplo
192  INTEGER info, lda, lwork, n
193 * ..
194 * .. Array Arguments ..
195  INTEGER ipiv( * )
196  COMPLEX a( lda, * ), work( * )
197 * ..
198 *
199 * =====================================================================
200 *
201 * .. Local Scalars ..
202  LOGICAL lquery, upper
203  INTEGER iinfo, iws, j, k, kb, ldwork, lwkopt, nb, nbmin
204 * ..
205 * .. External Functions ..
206  LOGICAL lsame
207  INTEGER ilaenv
208  EXTERNAL lsame, ilaenv
209 * ..
210 * .. External Subroutines ..
211  EXTERNAL clasyf, csytf2, xerbla
212 * ..
213 * .. Intrinsic Functions ..
214  INTRINSIC max
215 * ..
216 * .. Executable Statements ..
217 *
218 * Test the input parameters.
219 *
220  info = 0
221  upper = lsame( uplo, 'U' )
222  lquery = ( lwork.EQ.-1 )
223  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
224  info = -1
225  ELSE IF( n.LT.0 ) THEN
226  info = -2
227  ELSE IF( lda.LT.max( 1, n ) ) THEN
228  info = -4
229  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
230  info = -7
231  END IF
232 *
233  IF( info.EQ.0 ) THEN
234 *
235 * Determine the block size
236 *
237  nb = ilaenv( 1, 'CSYTRF', uplo, n, -1, -1, -1 )
238  lwkopt = n*nb
239  work( 1 ) = lwkopt
240  END IF
241 *
242  IF( info.NE.0 ) THEN
243  CALL xerbla( 'CSYTRF', -info )
244  RETURN
245  ELSE IF( lquery ) THEN
246  RETURN
247  END IF
248 *
249  nbmin = 2
250  ldwork = n
251  IF( nb.GT.1 .AND. nb.LT.n ) THEN
252  iws = ldwork*nb
253  IF( lwork.LT.iws ) THEN
254  nb = max( lwork / ldwork, 1 )
255  nbmin = max( 2, ilaenv( 2, 'CSYTRF', uplo, n, -1, -1, -1 ) )
256  END IF
257  ELSE
258  iws = 1
259  END IF
260  IF( nb.LT.nbmin )
261  $ nb = n
262 *
263  IF( upper ) THEN
264 *
265 * Factorize A as U*D*U**T using the upper triangle of A
266 *
267 * K is the main loop index, decreasing from N to 1 in steps of
268 * KB, where KB is the number of columns factorized by CLASYF;
269 * KB is either NB or NB-1, or K for the last block
270 *
271  k = n
272  10 CONTINUE
273 *
274 * If K < 1, exit from loop
275 *
276  IF( k.LT.1 )
277  $ go to 40
278 *
279  IF( k.GT.nb ) THEN
280 *
281 * Factorize columns k-kb+1:k of A and use blocked code to
282 * update columns 1:k-kb
283 *
284  CALL clasyf( uplo, k, nb, kb, a, lda, ipiv, work, n, iinfo )
285  ELSE
286 *
287 * Use unblocked code to factorize columns 1:k of A
288 *
289  CALL csytf2( uplo, k, a, lda, ipiv, iinfo )
290  kb = k
291  END IF
292 *
293 * Set INFO on the first occurrence of a zero pivot
294 *
295  IF( info.EQ.0 .AND. iinfo.GT.0 )
296  $ info = iinfo
297 *
298 * Decrease K and return to the start of the main loop
299 *
300  k = k - kb
301  go to 10
302 *
303  ELSE
304 *
305 * Factorize A as L*D*L**T using the lower triangle of A
306 *
307 * K is the main loop index, increasing from 1 to N in steps of
308 * KB, where KB is the number of columns factorized by CLASYF;
309 * KB is either NB or NB-1, or N-K+1 for the last block
310 *
311  k = 1
312  20 CONTINUE
313 *
314 * If K > N, exit from loop
315 *
316  IF( k.GT.n )
317  $ go to 40
318 *
319  IF( k.LE.n-nb ) THEN
320 *
321 * Factorize columns k:k+kb-1 of A and use blocked code to
322 * update columns k+kb:n
323 *
324  CALL clasyf( uplo, n-k+1, nb, kb, a( k, k ), lda, ipiv( k ),
325  $ work, n, iinfo )
326  ELSE
327 *
328 * Use unblocked code to factorize columns k:n of A
329 *
330  CALL csytf2( uplo, n-k+1, a( k, k ), lda, ipiv( k ), iinfo )
331  kb = n - k + 1
332  END IF
333 *
334 * Set INFO on the first occurrence of a zero pivot
335 *
336  IF( info.EQ.0 .AND. iinfo.GT.0 )
337  $ info = iinfo + k - 1
338 *
339 * Adjust IPIV
340 *
341  DO 30 j = k, k + kb - 1
342  IF( ipiv( j ).GT.0 ) THEN
343  ipiv( j ) = ipiv( j ) + k - 1
344  ELSE
345  ipiv( j ) = ipiv( j ) - k + 1
346  END IF
347  30 CONTINUE
348 *
349 * Increase K and return to the start of the main loop
350 *
351  k = k + kb
352  go to 20
353 *
354  END IF
355 *
356  40 CONTINUE
357  work( 1 ) = lwkopt
358  RETURN
359 *
360 * End of CSYTRF
361 *
362  END