1: *> \brief \b ZHEGST
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHEGST + 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/zhegst.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHEGST( 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: * COMPLEX*16 A( LDA, * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZHEGST reduces a complex Hermitian-definite generalized
38: *> eigenproblem to standard form.
39: *>
40: *> If ITYPE = 1, the problem is A*x = lambda*B*x,
41: *> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
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**H or L**H*A*L.
45: *>
46: *> B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] ITYPE
53: *> \verbatim
54: *> ITYPE is INTEGER
55: *> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
56: *> = 2 or 3: compute U*A*U**H or L**H*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**H*U;
64: *> = 'L': Lower triangle of A is stored and B is factored as
65: *> L*L**H.
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 COMPLEX*16 array, dimension (LDA,N)
77: *> On entry, the Hermitian 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,out] B
96: *> \verbatim
97: *> B is COMPLEX*16 array, dimension (LDB,N)
98: *> The triangular factor from the Cholesky factorization of B,
99: *> as returned by ZPOTRF.
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 September 2012
124: *
125: *> \ingroup complex16HEcomputational
126: *
127: * =====================================================================
128: SUBROUTINE ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
129: *
130: * -- LAPACK computational routine (version 3.4.2) --
131: * -- LAPACK is a software package provided by Univ. of Tennessee, --
132: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133: * September 2012
134: *
135: * .. Scalar Arguments ..
136: CHARACTER UPLO
137: INTEGER INFO, ITYPE, LDA, LDB, N
138: * ..
139: * .. Array Arguments ..
140: COMPLEX*16 A( LDA, * ), B( LDB, * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE
147: PARAMETER ( ONE = 1.0D+0 )
148: COMPLEX*16 CONE, HALF
149: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
150: $ HALF = ( 0.5D+0, 0.0D+0 ) )
151: * ..
152: * .. Local Scalars ..
153: LOGICAL UPPER
154: INTEGER K, KB, NB
155: * ..
156: * .. External Subroutines ..
157: EXTERNAL XERBLA, ZHEGS2, ZHEMM, ZHER2K, ZTRMM, ZTRSM
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC MAX, MIN
161: * ..
162: * .. External Functions ..
163: LOGICAL LSAME
164: INTEGER ILAENV
165: EXTERNAL LSAME, ILAENV
166: * ..
167: * .. Executable Statements ..
168: *
169: * Test the input parameters.
170: *
171: INFO = 0
172: UPPER = LSAME( UPLO, 'U' )
173: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
174: INFO = -1
175: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
176: INFO = -2
177: ELSE IF( N.LT.0 ) THEN
178: INFO = -3
179: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
180: INFO = -5
181: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
182: INFO = -7
183: END IF
184: IF( INFO.NE.0 ) THEN
185: CALL XERBLA( 'ZHEGST', -INFO )
186: RETURN
187: END IF
188: *
189: * Quick return if possible
190: *
191: IF( N.EQ.0 )
192: $ RETURN
193: *
194: * Determine the block size for this environment.
195: *
196: NB = ILAENV( 1, 'ZHEGST', UPLO, N, -1, -1, -1 )
197: *
198: IF( NB.LE.1 .OR. NB.GE.N ) THEN
199: *
200: * Use unblocked code
201: *
202: CALL ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
203: ELSE
204: *
205: * Use blocked code
206: *
207: IF( ITYPE.EQ.1 ) THEN
208: IF( UPPER ) THEN
209: *
210: * Compute inv(U**H)*A*inv(U)
211: *
212: DO 10 K = 1, N, NB
213: KB = MIN( N-K+1, NB )
214: *
215: * Update the upper triangle of A(k:n,k:n)
216: *
217: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
218: $ B( K, K ), LDB, INFO )
219: IF( K+KB.LE.N ) THEN
220: CALL ZTRSM( 'Left', UPLO, 'Conjugate transpose',
221: $ 'Non-unit', KB, N-K-KB+1, CONE,
222: $ B( K, K ), LDB, A( K, K+KB ), LDA )
223: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
224: $ A( K, K ), LDA, B( K, K+KB ), LDB,
225: $ CONE, A( K, K+KB ), LDA )
226: CALL ZHER2K( UPLO, 'Conjugate transpose', N-K-KB+1,
227: $ KB, -CONE, A( K, K+KB ), LDA,
228: $ B( K, K+KB ), LDB, ONE,
229: $ A( K+KB, K+KB ), LDA )
230: CALL ZHEMM( 'Left', UPLO, KB, N-K-KB+1, -HALF,
231: $ A( K, K ), LDA, B( K, K+KB ), LDB,
232: $ CONE, A( K, K+KB ), LDA )
233: CALL ZTRSM( 'Right', UPLO, 'No transpose',
234: $ 'Non-unit', KB, N-K-KB+1, CONE,
235: $ B( K+KB, K+KB ), LDB, A( K, K+KB ),
236: $ LDA )
237: END IF
238: 10 CONTINUE
239: ELSE
240: *
241: * Compute inv(L)*A*inv(L**H)
242: *
243: DO 20 K = 1, N, NB
244: KB = MIN( N-K+1, NB )
245: *
246: * Update the lower triangle of A(k:n,k:n)
247: *
248: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
249: $ B( K, K ), LDB, INFO )
250: IF( K+KB.LE.N ) THEN
251: CALL ZTRSM( 'Right', UPLO, 'Conjugate transpose',
252: $ 'Non-unit', N-K-KB+1, KB, CONE,
253: $ B( K, K ), LDB, A( K+KB, K ), LDA )
254: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
255: $ A( K, K ), LDA, B( K+KB, K ), LDB,
256: $ CONE, A( K+KB, K ), LDA )
257: CALL ZHER2K( UPLO, 'No transpose', N-K-KB+1, KB,
258: $ -CONE, A( K+KB, K ), LDA,
259: $ B( K+KB, K ), LDB, ONE,
260: $ A( K+KB, K+KB ), LDA )
261: CALL ZHEMM( 'Right', UPLO, N-K-KB+1, KB, -HALF,
262: $ A( K, K ), LDA, B( K+KB, K ), LDB,
263: $ CONE, A( K+KB, K ), LDA )
264: CALL ZTRSM( 'Left', UPLO, 'No transpose',
265: $ 'Non-unit', N-K-KB+1, KB, CONE,
266: $ B( K+KB, K+KB ), LDB, A( K+KB, K ),
267: $ LDA )
268: END IF
269: 20 CONTINUE
270: END IF
271: ELSE
272: IF( UPPER ) THEN
273: *
274: * Compute U*A*U**H
275: *
276: DO 30 K = 1, N, NB
277: KB = MIN( N-K+1, NB )
278: *
279: * Update the upper triangle of A(1:k+kb-1,1:k+kb-1)
280: *
281: CALL ZTRMM( 'Left', UPLO, 'No transpose', 'Non-unit',
282: $ K-1, KB, CONE, B, LDB, A( 1, K ), LDA )
283: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
284: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
285: $ LDA )
286: CALL ZHER2K( UPLO, 'No transpose', K-1, KB, CONE,
287: $ A( 1, K ), LDA, B( 1, K ), LDB, ONE, A,
288: $ LDA )
289: CALL ZHEMM( 'Right', UPLO, K-1, KB, HALF, A( K, K ),
290: $ LDA, B( 1, K ), LDB, CONE, A( 1, K ),
291: $ LDA )
292: CALL ZTRMM( 'Right', UPLO, 'Conjugate transpose',
293: $ 'Non-unit', K-1, KB, CONE, B( K, K ), LDB,
294: $ A( 1, K ), LDA )
295: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
296: $ B( K, K ), LDB, INFO )
297: 30 CONTINUE
298: ELSE
299: *
300: * Compute L**H*A*L
301: *
302: DO 40 K = 1, N, NB
303: KB = MIN( N-K+1, NB )
304: *
305: * Update the lower triangle of A(1:k+kb-1,1:k+kb-1)
306: *
307: CALL ZTRMM( 'Right', UPLO, 'No transpose', 'Non-unit',
308: $ KB, K-1, CONE, B, LDB, A( K, 1 ), LDA )
309: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
310: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
311: $ LDA )
312: CALL ZHER2K( UPLO, 'Conjugate transpose', K-1, KB,
313: $ CONE, A( K, 1 ), LDA, B( K, 1 ), LDB,
314: $ ONE, A, LDA )
315: CALL ZHEMM( 'Left', UPLO, KB, K-1, HALF, A( K, K ),
316: $ LDA, B( K, 1 ), LDB, CONE, A( K, 1 ),
317: $ LDA )
318: CALL ZTRMM( 'Left', UPLO, 'Conjugate transpose',
319: $ 'Non-unit', KB, K-1, CONE, B( K, K ), LDB,
320: $ A( K, 1 ), LDA )
321: CALL ZHEGS2( ITYPE, UPLO, KB, A( K, K ), LDA,
322: $ B( K, K ), LDB, INFO )
323: 40 CONTINUE
324: END IF
325: END IF
326: END IF
327: RETURN
328: *
329: * End of ZHEGST
330: *
331: END
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