LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dsygst.f
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1 *> \brief \b DSYGST
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download DSYGST + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsygst.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, ITYPE, LDA, LDB, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DSYGST reduces a real symmetric-definite generalized eigenproblem
38 *> to standard form.
39 *>
40 *> If ITYPE = 1, the problem is A*x = lambda*B*x,
41 *> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
42 *>
43 *> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
44 *> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
45 *>
46 *> B must have been previously factorized as U**T*U or L*L**T by DPOTRF.
47 *> \endverbatim
48 *
49 * Arguments:
50 * ==========
51 *
52 *> \param[in] ITYPE
53 *> \verbatim
54 *> ITYPE is INTEGER
55 *> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
56 *> = 2 or 3: compute U*A*U**T or L**T*A*L.
57 *> \endverbatim
58 *>
59 *> \param[in] UPLO
60 *> \verbatim
61 *> UPLO is CHARACTER*1
62 *> = 'U': Upper triangle of A is stored and B is factored as
63 *> U**T*U;
64 *> = 'L': Lower triangle of A is stored and B is factored as
65 *> L*L**T.
66 *> \endverbatim
67 *>
68 *> \param[in] N
69 *> \verbatim
70 *> N is INTEGER
71 *> The order of the matrices A and B. N >= 0.
72 *> \endverbatim
73 *>
74 *> \param[in,out] A
75 *> \verbatim
76 *> A is DOUBLE PRECISION array, dimension (LDA,N)
77 *> On entry, the symmetric matrix A. If UPLO = 'U', the leading
78 *> N-by-N upper triangular part of A contains the upper
79 *> triangular part of the matrix A, and the strictly lower
80 *> triangular part of A is not referenced. If UPLO = 'L', the
81 *> leading N-by-N lower triangular part of A contains the lower
82 *> triangular part of the matrix A, and the strictly upper
83 *> triangular part of A is not referenced.
84 *>
85 *> On exit, if INFO = 0, the transformed matrix, stored in the
86 *> same format as A.
87 *> \endverbatim
88 *>
89 *> \param[in] LDA
90 *> \verbatim
91 *> LDA is INTEGER
92 *> The leading dimension of the array A. LDA >= max(1,N).
93 *> \endverbatim
94 *>
95 *> \param[in] B
96 *> \verbatim
97 *> B is DOUBLE PRECISION array, dimension (LDB,N)
98 *> The triangular factor from the Cholesky factorization of B,
99 *> as returned by DPOTRF.
100 *> \endverbatim
101 *>
102 *> \param[in] LDB
103 *> \verbatim
104 *> LDB is INTEGER
105 *> The leading dimension of the array B. LDB >= max(1,N).
106 *> \endverbatim
107 *>
108 *> \param[out] INFO
109 *> \verbatim
110 *> INFO is INTEGER
111 *> = 0: successful exit
112 *> < 0: if INFO = -i, the i-th argument had an illegal value
113 *> \endverbatim
114 *
115 * Authors:
116 * ========
117 *
118 *> \author Univ. of Tennessee
119 *> \author Univ. of California Berkeley
120 *> \author Univ. of Colorado Denver
121 *> \author NAG Ltd.
122 *
123 *> \ingroup doubleSYcomputational
124 *
125 * =====================================================================
126  SUBROUTINE dsygst( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
127 *
128 * -- LAPACK computational routine --
129 * -- LAPACK is a software package provided by Univ. of Tennessee, --
130 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 *
132 * .. Scalar Arguments ..
133  CHARACTER UPLO
134  INTEGER INFO, ITYPE, LDA, LDB, N
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION A( LDA, * ), B( LDB, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION ONE, HALF
144  parameter( one = 1.0d0, half = 0.5d0 )
145 * ..
146 * .. Local Scalars ..
147  LOGICAL UPPER
148  INTEGER K, KB, NB
149 * ..
150 * .. External Subroutines ..
151  EXTERNAL dsygs2, dsymm, dsyr2k, dtrmm, dtrsm, xerbla
152 * ..
153 * .. Intrinsic Functions ..
154  INTRINSIC max, min
155 * ..
156 * .. External Functions ..
157  LOGICAL LSAME
158  INTEGER ILAENV
159  EXTERNAL lsame, ilaenv
160 * ..
161 * .. Executable Statements ..
162 *
163 * Test the input parameters.
164 *
165  info = 0
166  upper = lsame( uplo, 'U' )
167  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
168  info = -1
169  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
170  info = -2
171  ELSE IF( n.LT.0 ) THEN
172  info = -3
173  ELSE IF( lda.LT.max( 1, n ) ) THEN
174  info = -5
175  ELSE IF( ldb.LT.max( 1, n ) ) THEN
176  info = -7
177  END IF
178  IF( info.NE.0 ) THEN
179  CALL xerbla( 'DSYGST', -info )
180  RETURN
181  END IF
182 *
183 * Quick return if possible
184 *
185  IF( n.EQ.0 )
186  $ RETURN
187 *
188 * Determine the block size for this environment.
189 *
190  nb = ilaenv( 1, 'DSYGST', uplo, n, -1, -1, -1 )
191 *
192  IF( nb.LE.1 .OR. nb.GE.n ) THEN
193 *
194 * Use unblocked code
195 *
196  CALL dsygs2( itype, uplo, n, a, lda, b, ldb, info )
197  ELSE
198 *
199 * Use blocked code
200 *
201  IF( itype.EQ.1 ) THEN
202  IF( upper ) THEN
203 *
204 * Compute inv(U**T)*A*inv(U)
205 *
206  DO 10 k = 1, n, nb
207  kb = min( n-k+1, nb )
208 *
209 * Update the upper triangle of A(k:n,k:n)
210 *
211  CALL dsygs2( itype, uplo, kb, a( k, k ), lda,
212  $ b( k, k ), ldb, info )
213  IF( k+kb.LE.n ) THEN
214  CALL dtrsm( 'Left', uplo, 'Transpose', 'Non-unit',
215  $ kb, n-k-kb+1, one, b( k, k ), ldb,
216  $ a( k, k+kb ), lda )
217  CALL dsymm( 'Left', uplo, kb, n-k-kb+1, -half,
218  $ a( k, k ), lda, b( k, k+kb ), ldb, one,
219  $ a( k, k+kb ), lda )
220  CALL dsyr2k( uplo, 'Transpose', n-k-kb+1, kb, -one,
221  $ a( k, k+kb ), lda, b( k, k+kb ), ldb,
222  $ one, a( k+kb, k+kb ), lda )
223  CALL dsymm( 'Left', uplo, kb, n-k-kb+1, -half,
224  $ a( k, k ), lda, b( k, k+kb ), ldb, one,
225  $ a( k, k+kb ), lda )
226  CALL dtrsm( 'Right', uplo, 'No transpose',
227  $ 'Non-unit', kb, n-k-kb+1, one,
228  $ b( k+kb, k+kb ), ldb, a( k, k+kb ),
229  $ lda )
230  END IF
231  10 CONTINUE
232  ELSE
233 *
234 * Compute inv(L)*A*inv(L**T)
235 *
236  DO 20 k = 1, n, nb
237  kb = min( n-k+1, nb )
238 *
239 * Update the lower triangle of A(k:n,k:n)
240 *
241  CALL dsygs2( itype, uplo, kb, a( k, k ), lda,
242  $ b( k, k ), ldb, info )
243  IF( k+kb.LE.n ) THEN
244  CALL dtrsm( 'Right', uplo, 'Transpose', 'Non-unit',
245  $ n-k-kb+1, kb, one, b( k, k ), ldb,
246  $ a( k+kb, k ), lda )
247  CALL dsymm( 'Right', uplo, n-k-kb+1, kb, -half,
248  $ a( k, k ), lda, b( k+kb, k ), ldb, one,
249  $ a( k+kb, k ), lda )
250  CALL dsyr2k( uplo, 'No transpose', n-k-kb+1, kb,
251  $ -one, a( k+kb, k ), lda, b( k+kb, k ),
252  $ ldb, one, a( k+kb, k+kb ), lda )
253  CALL dsymm( 'Right', uplo, n-k-kb+1, kb, -half,
254  $ a( k, k ), lda, b( k+kb, k ), ldb, one,
255  $ a( k+kb, k ), lda )
256  CALL dtrsm( 'Left', uplo, 'No transpose',
257  $ 'Non-unit', n-k-kb+1, kb, one,
258  $ b( k+kb, k+kb ), ldb, a( k+kb, k ),
259  $ lda )
260  END IF
261  20 CONTINUE
262  END IF
263  ELSE
264  IF( upper ) THEN
265 *
266 * Compute U*A*U**T
267 *
268  DO 30 k = 1, n, nb
269  kb = min( n-k+1, nb )
270 *
271 * Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
272 *
273  CALL dtrmm( 'Left', uplo, 'No transpose', 'Non-unit',
274  $ k-1, kb, one, b, ldb, a( 1, k ), lda )
275  CALL dsymm( 'Right', uplo, k-1, kb, half, a( k, k ),
276  $ lda, b( 1, k ), ldb, one, a( 1, k ), lda )
277  CALL dsyr2k( uplo, 'No transpose', k-1, kb, one,
278  $ a( 1, k ), lda, b( 1, k ), ldb, one, a,
279  $ lda )
280  CALL dsymm( 'Right', uplo, k-1, kb, half, a( k, k ),
281  $ lda, b( 1, k ), ldb, one, a( 1, k ), lda )
282  CALL dtrmm( 'Right', uplo, 'Transpose', 'Non-unit',
283  $ k-1, kb, one, b( k, k ), ldb, a( 1, k ),
284  $ lda )
285  CALL dsygs2( itype, uplo, kb, a( k, k ), lda,
286  $ b( k, k ), ldb, info )
287  30 CONTINUE
288  ELSE
289 *
290 * Compute L**T*A*L
291 *
292  DO 40 k = 1, n, nb
293  kb = min( n-k+1, nb )
294 *
295 * Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
296 *
297  CALL dtrmm( 'Right', uplo, 'No transpose', 'Non-unit',
298  $ kb, k-1, one, b, ldb, a( k, 1 ), lda )
299  CALL dsymm( 'Left', uplo, kb, k-1, half, a( k, k ),
300  $ lda, b( k, 1 ), ldb, one, a( k, 1 ), lda )
301  CALL dsyr2k( uplo, 'Transpose', k-1, kb, one,
302  $ a( k, 1 ), lda, b( k, 1 ), ldb, one, a,
303  $ lda )
304  CALL dsymm( 'Left', uplo, kb, k-1, half, a( k, k ),
305  $ lda, b( k, 1 ), ldb, one, a( k, 1 ), lda )
306  CALL dtrmm( 'Left', uplo, 'Transpose', 'Non-unit', kb,
307  $ k-1, one, b( k, k ), ldb, a( k, 1 ), lda )
308  CALL dsygs2( itype, uplo, kb, a( k, k ), lda,
309  $ b( k, k ), ldb, info )
310  40 CONTINUE
311  END IF
312  END IF
313  END IF
314  RETURN
315 *
316 * End of DSYGST
317 *
318  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYMM
Definition: dsymm.f:189
subroutine dsyr2k(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DSYR2K
Definition: dsyr2k.f:192
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:177
subroutine dsygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
DSYGST
Definition: dsygst.f:127
subroutine dsygs2(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorizatio...
Definition: dsygs2.f:127