Annotation of rpl/lapack/lapack/zhegs2.f, revision 1.14
1.12 bertrand 1: *> \brief \b ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHEGS2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegs2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegs2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegs2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHEGS2( 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: *> ZHEGS2 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: *> Specifies whether the upper or lower triangular part of the
63: *> Hermitian matrix A is stored, and how B has been factorized.
64: *> = 'U': Upper triangular
65: *> = 'L': Lower triangular
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: *>
1.12 bertrand 95: *> \param[in,out] B
1.9 bertrand 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: *
1.12 bertrand 123: *> \date September 2012
1.9 bertrand 124: *
125: *> \ingroup complex16HEcomputational
126: *
127: * =====================================================================
1.1 bertrand 128: SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
129: *
1.12 bertrand 130: * -- LAPACK computational routine (version 3.4.2) --
1.1 bertrand 131: * -- LAPACK is a software package provided by Univ. of Tennessee, --
132: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.12 bertrand 133: * September 2012
1.1 bertrand 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, HALF
147: PARAMETER ( ONE = 1.0D+0, HALF = 0.5D+0 )
148: COMPLEX*16 CONE
149: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
150: * ..
151: * .. Local Scalars ..
152: LOGICAL UPPER
153: INTEGER K
154: DOUBLE PRECISION AKK, BKK
155: COMPLEX*16 CT
156: * ..
157: * .. External Subroutines ..
158: EXTERNAL XERBLA, ZAXPY, ZDSCAL, ZHER2, ZLACGV, ZTRMV,
159: $ ZTRSV
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC MAX
163: * ..
164: * .. External Functions ..
165: LOGICAL LSAME
166: EXTERNAL LSAME
167: * ..
168: * .. Executable Statements ..
169: *
170: * Test the input parameters.
171: *
172: INFO = 0
173: UPPER = LSAME( UPLO, 'U' )
174: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
175: INFO = -1
176: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
177: INFO = -2
178: ELSE IF( N.LT.0 ) THEN
179: INFO = -3
180: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
181: INFO = -5
182: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
183: INFO = -7
184: END IF
185: IF( INFO.NE.0 ) THEN
186: CALL XERBLA( 'ZHEGS2', -INFO )
187: RETURN
188: END IF
189: *
190: IF( ITYPE.EQ.1 ) THEN
191: IF( UPPER ) THEN
192: *
1.8 bertrand 193: * Compute inv(U**H)*A*inv(U)
1.1 bertrand 194: *
195: DO 10 K = 1, N
196: *
197: * Update the upper triangle of A(k:n,k:n)
198: *
199: AKK = A( K, K )
200: BKK = B( K, K )
201: AKK = AKK / BKK**2
202: A( K, K ) = AKK
203: IF( K.LT.N ) THEN
204: CALL ZDSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA )
205: CT = -HALF*AKK
206: CALL ZLACGV( N-K, A( K, K+1 ), LDA )
207: CALL ZLACGV( N-K, B( K, K+1 ), LDB )
208: CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ),
209: $ LDA )
210: CALL ZHER2( UPLO, N-K, -CONE, A( K, K+1 ), LDA,
211: $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA )
212: CALL ZAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ),
213: $ LDA )
214: CALL ZLACGV( N-K, B( K, K+1 ), LDB )
215: CALL ZTRSV( UPLO, 'Conjugate transpose', 'Non-unit',
216: $ N-K, B( K+1, K+1 ), LDB, A( K, K+1 ),
217: $ LDA )
218: CALL ZLACGV( N-K, A( K, K+1 ), LDA )
219: END IF
220: 10 CONTINUE
221: ELSE
222: *
1.8 bertrand 223: * Compute inv(L)*A*inv(L**H)
1.1 bertrand 224: *
225: DO 20 K = 1, N
226: *
227: * Update the lower triangle of A(k:n,k:n)
228: *
229: AKK = A( K, K )
230: BKK = B( K, K )
231: AKK = AKK / BKK**2
232: A( K, K ) = AKK
233: IF( K.LT.N ) THEN
234: CALL ZDSCAL( N-K, ONE / BKK, A( K+1, K ), 1 )
235: CT = -HALF*AKK
236: CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 )
237: CALL ZHER2( UPLO, N-K, -CONE, A( K+1, K ), 1,
238: $ B( K+1, K ), 1, A( K+1, K+1 ), LDA )
239: CALL ZAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 )
240: CALL ZTRSV( UPLO, 'No transpose', 'Non-unit', N-K,
241: $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 )
242: END IF
243: 20 CONTINUE
244: END IF
245: ELSE
246: IF( UPPER ) THEN
247: *
1.8 bertrand 248: * Compute U*A*U**H
1.1 bertrand 249: *
250: DO 30 K = 1, N
251: *
252: * Update the upper triangle of A(1:k,1:k)
253: *
254: AKK = A( K, K )
255: BKK = B( K, K )
256: CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
257: $ LDB, A( 1, K ), 1 )
258: CT = HALF*AKK
259: CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 )
260: CALL ZHER2( UPLO, K-1, CONE, A( 1, K ), 1, B( 1, K ), 1,
261: $ A, LDA )
262: CALL ZAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 )
263: CALL ZDSCAL( K-1, BKK, A( 1, K ), 1 )
264: A( K, K ) = AKK*BKK**2
265: 30 CONTINUE
266: ELSE
267: *
1.8 bertrand 268: * Compute L**H *A*L
1.1 bertrand 269: *
270: DO 40 K = 1, N
271: *
272: * Update the lower triangle of A(1:k,1:k)
273: *
274: AKK = A( K, K )
275: BKK = B( K, K )
276: CALL ZLACGV( K-1, A( K, 1 ), LDA )
277: CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1,
278: $ B, LDB, A( K, 1 ), LDA )
279: CT = HALF*AKK
280: CALL ZLACGV( K-1, B( K, 1 ), LDB )
281: CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA )
282: CALL ZHER2( UPLO, K-1, CONE, A( K, 1 ), LDA, B( K, 1 ),
283: $ LDB, A, LDA )
284: CALL ZAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA )
285: CALL ZLACGV( K-1, B( K, 1 ), LDB )
286: CALL ZDSCAL( K-1, BKK, A( K, 1 ), LDA )
287: CALL ZLACGV( K-1, A( K, 1 ), LDA )
288: A( K, K ) = AKK*BKK**2
289: 40 CONTINUE
290: END IF
291: END IF
292: RETURN
293: *
294: * End of ZHEGS2
295: *
296: END
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