LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
zsytrf.f
Go to the documentation of this file.
1 *> \brief \b ZSYTRF
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZSYTRF + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrf.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrf.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrf.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZSYTRF( 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 *> ZSYTRF 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 *> 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 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*16 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 *> \ingroup complex16SYcomputational
139 *
140 *> \par Further Details:
141 * =====================
142 *>
143 *> \verbatim
144 *>
145 *> If UPLO = 'U', then A = U*D*U**T, where
146 *> U = P(n)*U(n)* ... *P(k)U(k)* ...,
147 *> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
148 *> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
149 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
150 *> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
151 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
152 *>
153 *> ( I v 0 ) k-s
154 *> U(k) = ( 0 I 0 ) s
155 *> ( 0 0 I ) n-k
156 *> k-s s n-k
157 *>
158 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
159 *> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
160 *> and A(k,k), and v overwrites A(1:k-2,k-1:k).
161 *>
162 *> If UPLO = 'L', then A = L*D*L**T, where
163 *> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
164 *> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
165 *> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
166 *> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
167 *> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
168 *> that if the diagonal block D(k) is of order s (s = 1 or 2), then
169 *>
170 *> ( I 0 0 ) k-1
171 *> L(k) = ( 0 I 0 ) s
172 *> ( 0 v I ) n-k-s+1
173 *> k-1 s n-k-s+1
174 *>
175 *> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
176 *> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
177 *> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
178 *> \endverbatim
179 *>
180 * =====================================================================
181  SUBROUTINE zsytrf( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
182 *
183 * -- LAPACK computational routine --
184 * -- LAPACK is a software package provided by Univ. of Tennessee, --
185 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
186 *
187 * .. Scalar Arguments ..
188  CHARACTER UPLO
189  INTEGER INFO, LDA, LWORK, N
190 * ..
191 * .. Array Arguments ..
192  INTEGER IPIV( * )
193  COMPLEX*16 A( LDA, * ), WORK( * )
194 * ..
195 *
196 * =====================================================================
197 *
198 * .. Local Scalars ..
199  LOGICAL LQUERY, UPPER
200  INTEGER IINFO, IWS, J, K, KB, LDWORK, LWKOPT, NB, NBMIN
201 * ..
202 * .. External Functions ..
203  LOGICAL LSAME
204  INTEGER ILAENV
205  EXTERNAL lsame, ilaenv
206 * ..
207 * .. External Subroutines ..
208  EXTERNAL xerbla, zlasyf, zsytf2
209 * ..
210 * .. Intrinsic Functions ..
211  INTRINSIC max
212 * ..
213 * .. Executable Statements ..
214 *
215 * Test the input parameters.
216 *
217  info = 0
218  upper = lsame( uplo, 'U' )
219  lquery = ( lwork.EQ.-1 )
220  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
221  info = -1
222  ELSE IF( n.LT.0 ) THEN
223  info = -2
224  ELSE IF( lda.LT.max( 1, n ) ) THEN
225  info = -4
226  ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
227  info = -7
228  END IF
229 *
230  IF( info.EQ.0 ) THEN
231 *
232 * Determine the block size
233 *
234  nb = ilaenv( 1, 'ZSYTRF', uplo, n, -1, -1, -1 )
235  lwkopt = n*nb
236  work( 1 ) = lwkopt
237  END IF
238 *
239  IF( info.NE.0 ) THEN
240  CALL xerbla( 'ZSYTRF', -info )
241  RETURN
242  ELSE IF( lquery ) THEN
243  RETURN
244  END IF
245 *
246  nbmin = 2
247  ldwork = n
248  IF( nb.GT.1 .AND. nb.LT.n ) THEN
249  iws = ldwork*nb
250  IF( lwork.LT.iws ) THEN
251  nb = max( lwork / ldwork, 1 )
252  nbmin = max( 2, ilaenv( 2, 'ZSYTRF', uplo, n, -1, -1, -1 ) )
253  END IF
254  ELSE
255  iws = 1
256  END IF
257  IF( nb.LT.nbmin )
258  $ nb = n
259 *
260  IF( upper ) THEN
261 *
262 * Factorize A as U*D*U**T using the upper triangle of A
263 *
264 * K is the main loop index, decreasing from N to 1 in steps of
265 * KB, where KB is the number of columns factorized by ZLASYF;
266 * KB is either NB or NB-1, or K for the last block
267 *
268  k = n
269  10 CONTINUE
270 *
271 * If K < 1, exit from loop
272 *
273  IF( k.LT.1 )
274  $ GO TO 40
275 *
276  IF( k.GT.nb ) THEN
277 *
278 * Factorize columns k-kb+1:k of A and use blocked code to
279 * update columns 1:k-kb
280 *
281  CALL zlasyf( uplo, k, nb, kb, a, lda, ipiv, work, n, iinfo )
282  ELSE
283 *
284 * Use unblocked code to factorize columns 1:k of A
285 *
286  CALL zsytf2( uplo, k, a, lda, ipiv, iinfo )
287  kb = k
288  END IF
289 *
290 * Set INFO on the first occurrence of a zero pivot
291 *
292  IF( info.EQ.0 .AND. iinfo.GT.0 )
293  $ info = iinfo
294 *
295 * Decrease K and return to the start of the main loop
296 *
297  k = k - kb
298  GO TO 10
299 *
300  ELSE
301 *
302 * Factorize A as L*D*L**T using the lower triangle of A
303 *
304 * K is the main loop index, increasing from 1 to N in steps of
305 * KB, where KB is the number of columns factorized by ZLASYF;
306 * KB is either NB or NB-1, or N-K+1 for the last block
307 *
308  k = 1
309  20 CONTINUE
310 *
311 * If K > N, exit from loop
312 *
313  IF( k.GT.n )
314  $ GO TO 40
315 *
316  IF( k.LE.n-nb ) THEN
317 *
318 * Factorize columns k:k+kb-1 of A and use blocked code to
319 * update columns k+kb:n
320 *
321  CALL zlasyf( uplo, n-k+1, nb, kb, a( k, k ), lda, ipiv( k ),
322  $ work, n, iinfo )
323  ELSE
324 *
325 * Use unblocked code to factorize columns k:n of A
326 *
327  CALL zsytf2( uplo, n-k+1, a( k, k ), lda, ipiv( k ), iinfo )
328  kb = n - k + 1
329  END IF
330 *
331 * Set INFO on the first occurrence of a zero pivot
332 *
333  IF( info.EQ.0 .AND. iinfo.GT.0 )
334  $ info = iinfo + k - 1
335 *
336 * Adjust IPIV
337 *
338  DO 30 j = k, k + kb - 1
339  IF( ipiv( j ).GT.0 ) THEN
340  ipiv( j ) = ipiv( j ) + k - 1
341  ELSE
342  ipiv( j ) = ipiv( j ) - k + 1
343  END IF
344  30 CONTINUE
345 *
346 * Increase K and return to the start of the main loop
347 *
348  k = k + kb
349  GO TO 20
350 *
351  END IF
352 *
353  40 CONTINUE
354  work( 1 ) = lwkopt
355  RETURN
356 *
357 * End of ZSYTRF
358 *
359  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zsytf2(UPLO, N, A, LDA, IPIV, INFO)
ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting ...
Definition: zsytf2.f:191
subroutine zlasyf(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO)
ZLASYF computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagona...
Definition: zlasyf.f:177
subroutine zsytrf(UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO)
ZSYTRF
Definition: zsytrf.f:182