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
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygst.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsygst.f">
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: *> \date December 2016
124: *
125: *> \ingroup doubleSYcomputational
126: *
127: * =====================================================================
128: SUBROUTINE DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
129: *
130: * -- LAPACK computational routine (version 3.7.0) --
131: * -- LAPACK is a software package provided by Univ. of Tennessee, --
132: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133: * December 2016
134: *
135: * .. Scalar Arguments ..
136: CHARACTER UPLO
137: INTEGER INFO, ITYPE, LDA, LDB, N
138: * ..
139: * .. Array Arguments ..
140: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE, HALF
147: PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL UPPER
151: INTEGER K, KB, NB
152: * ..
153: * .. External Subroutines ..
154: EXTERNAL DSYGS2, DSYMM, DSYR2K, DTRMM, DTRSM, XERBLA
155: * ..
156: * .. Intrinsic Functions ..
157: INTRINSIC MAX, MIN
158: * ..
159: * .. External Functions ..
160: LOGICAL LSAME
161: INTEGER ILAENV
162: EXTERNAL LSAME, ILAENV
163: * ..
164: * .. Executable Statements ..
165: *
166: * Test the input parameters.
167: *
168: INFO = 0
169: UPPER = LSAME( UPLO, 'U' )
170: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
171: INFO = -1
172: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
173: INFO = -2
174: ELSE IF( N.LT.0 ) THEN
175: INFO = -3
176: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
177: INFO = -5
178: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
179: INFO = -7
180: END IF
181: IF( INFO.NE.0 ) THEN
182: CALL XERBLA( 'DSYGST', -INFO )
183: RETURN
184: END IF
185: *
186: * Quick return if possible
187: *
188: IF( N.EQ.0 )
189: $ RETURN
190: *
191: * Determine the block size for this environment.
192: *
193: NB = ILAENV( 1, 'DSYGST', UPLO, N, -1, -1, -1 )
194: *
195: IF( NB.LE.1 .OR. NB.GE.N ) THEN
196: *
197: * Use unblocked code
198: *
199: CALL DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
200: ELSE
201: *
202: * Use blocked code
203: *
204: IF( ITYPE.EQ.1 ) THEN
205: IF( UPPER ) THEN
206: *
207: * Compute inv(U**T)*A*inv(U)
208: *
209: DO 10 K = 1, N, NB
210: KB = MIN( N-K+1, NB )
211: *
212: * Update the upper triangle of A(k:n,k:n)
213: *
214: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
215: $ B( K, K ), LDB, INFO )
216: IF( K+KB.LE.N ) THEN
217: CALL DTRSM( 'Left', UPLO, 'Transpose', 'Non-unit',
218: $ KB, N-K-KB+1, ONE, B( K, K ), LDB,
219: $ A( K, K+KB ), LDA )
220: CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
221: $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
222: $ A( K, K+KB ), LDA )
223: CALL DSYR2K( UPLO, 'Transpose', N-K-KB+1, KB, -ONE,
224: $ A( K, K+KB ), LDA, B( K, K+KB ), LDB,
225: $ ONE, A( K+KB, K+KB ), LDA )
226: CALL DSYMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
227: $ A( K, K ), LDA, B( K, K+KB ), LDB, ONE,
228: $ A( K, K+KB ), LDA )
229: CALL DTRSM( 'Right', UPLO, 'No transpose',
230: $ 'Non-unit', KB, N-K-KB+1, ONE,
231: $ B( K+KB, K+KB ), LDB, A( K, K+KB ),
232: $ LDA )
233: END IF
234: 10 CONTINUE
235: ELSE
236: *
237: * Compute inv(L)*A*inv(L**T)
238: *
239: DO 20 K = 1, N, NB
240: KB = MIN( N-K+1, NB )
241: *
242: * Update the lower triangle of A(k:n,k:n)
243: *
244: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
245: $ B( K, K ), LDB, INFO )
246: IF( K+KB.LE.N ) THEN
247: CALL DTRSM( 'Right', UPLO, 'Transpose', 'Non-unit',
248: $ N-K-KB+1, KB, ONE, B( K, K ), LDB,
249: $ A( K+KB, K ), LDA )
250: CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
251: $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
252: $ A( K+KB, K ), LDA )
253: CALL DSYR2K( UPLO, 'No transpose', N-K-KB+1, KB,
254: $ -ONE, A( K+KB, K ), LDA, B( K+KB, K ),
255: $ LDB, ONE, A( K+KB, K+KB ), LDA )
256: CALL DSYMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
257: $ A( K, K ), LDA, B( K+KB, K ), LDB, ONE,
258: $ A( K+KB, K ), LDA )
259: CALL DTRSM( 'Left', UPLO, 'No transpose',
260: $ 'Non-unit', N-K-KB+1, KB, ONE,
261: $ B( K+KB, K+KB ), LDB, A( K+KB, K ),
262: $ LDA )
263: END IF
264: 20 CONTINUE
265: END IF
266: ELSE
267: IF( UPPER ) THEN
268: *
269: * Compute U*A*U**T
270: *
271: DO 30 K = 1, N, NB
272: KB = MIN( N-K+1, NB )
273: *
274: * Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
275: *
276: CALL DTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
277: $ K-1, KB, ONE, B, LDB, A( 1, K ), LDA )
278: CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
279: $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
280: CALL DSYR2K( UPLO, 'No transpose', K-1, KB, ONE,
281: $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
282: $ LDA )
283: CALL DSYMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
284: $ LDA, B( 1, K ), LDB, ONE, A( 1, K ), LDA )
285: CALL DTRMM( 'Right', UPLO, 'Transpose', 'Non-unit',
286: $ K-1, KB, ONE, B( K, K ), LDB, A( 1, K ),
287: $ LDA )
288: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
289: $ B( K, K ), LDB, INFO )
290: 30 CONTINUE
291: ELSE
292: *
293: * Compute L**T*A*L
294: *
295: DO 40 K = 1, N, NB
296: KB = MIN( N-K+1, NB )
297: *
298: * Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
299: *
300: CALL DTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
301: $ KB, K-1, ONE, B, LDB, A( K, 1 ), LDA )
302: CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
303: $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
304: CALL DSYR2K( UPLO, 'Transpose', K-1, KB, ONE,
305: $ A( K, 1 ), LDA, B( K, 1 ), LDB, ONE, A,
306: $ LDA )
307: CALL DSYMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
308: $ LDA, B( K, 1 ), LDB, ONE, A( K, 1 ), LDA )
309: CALL DTRMM( 'Left', UPLO, 'Transpose', 'Non-unit', KB,
310: $ K-1, ONE, B( K, K ), LDB, A( K, 1 ), LDA )
311: CALL DSYGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
312: $ B( K, K ), LDB, INFO )
313: 40 CONTINUE
314: END IF
315: END IF
316: END IF
317: RETURN
318: *
319: * End of DSYGST
320: *
321: END
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