1: *> \brief \b ZHEGV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHEGV + dependencies
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13: *> [ZIP]</a>
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15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
22: * LWORK, RWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION RWORK( * ), W( * )
30: * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
40: *> of a complex generalized Hermitian-definite eigenproblem, of the form
41: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
42: *> Here A and B are assumed to be Hermitian and B is also
43: *> positive definite.
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] ITYPE
50: *> \verbatim
51: *> ITYPE is INTEGER
52: *> Specifies the problem type to be solved:
53: *> = 1: A*x = (lambda)*B*x
54: *> = 2: A*B*x = (lambda)*x
55: *> = 3: B*A*x = (lambda)*x
56: *> \endverbatim
57: *>
58: *> \param[in] JOBZ
59: *> \verbatim
60: *> JOBZ is CHARACTER*1
61: *> = 'N': Compute eigenvalues only;
62: *> = 'V': Compute eigenvalues and eigenvectors.
63: *> \endverbatim
64: *>
65: *> \param[in] UPLO
66: *> \verbatim
67: *> UPLO is CHARACTER*1
68: *> = 'U': Upper triangles of A and B are stored;
69: *> = 'L': Lower triangles of A and B are stored.
70: *> \endverbatim
71: *>
72: *> \param[in] N
73: *> \verbatim
74: *> N is INTEGER
75: *> The order of the matrices A and B. N >= 0.
76: *> \endverbatim
77: *>
78: *> \param[in,out] A
79: *> \verbatim
80: *> A is COMPLEX*16 array, dimension (LDA, N)
81: *> On entry, the Hermitian matrix A. If UPLO = 'U', the
82: *> leading N-by-N upper triangular part of A contains the
83: *> upper triangular part of the matrix A. If UPLO = 'L',
84: *> the leading N-by-N lower triangular part of A contains
85: *> the lower triangular part of the matrix A.
86: *>
87: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
88: *> matrix Z of eigenvectors. The eigenvectors are normalized
89: *> as follows:
90: *> if ITYPE = 1 or 2, Z**H*B*Z = I;
91: *> if ITYPE = 3, Z**H*inv(B)*Z = I.
92: *> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
93: *> or the lower triangle (if UPLO='L') of A, including the
94: *> diagonal, is destroyed.
95: *> \endverbatim
96: *>
97: *> \param[in] LDA
98: *> \verbatim
99: *> LDA is INTEGER
100: *> The leading dimension of the array A. LDA >= max(1,N).
101: *> \endverbatim
102: *>
103: *> \param[in,out] B
104: *> \verbatim
105: *> B is COMPLEX*16 array, dimension (LDB, N)
106: *> On entry, the Hermitian positive definite matrix B.
107: *> If UPLO = 'U', the leading N-by-N upper triangular part of B
108: *> contains the upper triangular part of the matrix B.
109: *> If UPLO = 'L', the leading N-by-N lower triangular part of B
110: *> contains the lower triangular part of the matrix B.
111: *>
112: *> On exit, if INFO <= N, the part of B containing the matrix is
113: *> overwritten by the triangular factor U or L from the Cholesky
114: *> factorization B = U**H*U or B = L*L**H.
115: *> \endverbatim
116: *>
117: *> \param[in] LDB
118: *> \verbatim
119: *> LDB is INTEGER
120: *> The leading dimension of the array B. LDB >= max(1,N).
121: *> \endverbatim
122: *>
123: *> \param[out] W
124: *> \verbatim
125: *> W is DOUBLE PRECISION array, dimension (N)
126: *> If INFO = 0, the eigenvalues in ascending order.
127: *> \endverbatim
128: *>
129: *> \param[out] WORK
130: *> \verbatim
131: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
132: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
133: *> \endverbatim
134: *>
135: *> \param[in] LWORK
136: *> \verbatim
137: *> LWORK is INTEGER
138: *> The length of the array WORK. LWORK >= max(1,2*N-1).
139: *> For optimal efficiency, LWORK >= (NB+1)*N,
140: *> where NB is the blocksize for ZHETRD returned by ILAENV.
141: *>
142: *> If LWORK = -1, then a workspace query is assumed; the routine
143: *> only calculates the optimal size of the WORK array, returns
144: *> this value as the first entry of the WORK array, and no error
145: *> message related to LWORK is issued by XERBLA.
146: *> \endverbatim
147: *>
148: *> \param[out] RWORK
149: *> \verbatim
150: *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
151: *> \endverbatim
152: *>
153: *> \param[out] INFO
154: *> \verbatim
155: *> INFO is INTEGER
156: *> = 0: successful exit
157: *> < 0: if INFO = -i, the i-th argument had an illegal value
158: *> > 0: ZPOTRF or ZHEEV returned an error code:
159: *> <= N: if INFO = i, ZHEEV failed to converge;
160: *> i off-diagonal elements of an intermediate
161: *> tridiagonal form did not converge to zero;
162: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
163: *> minor of order i of B is not positive definite.
164: *> The factorization of B could not be completed and
165: *> no eigenvalues or eigenvectors were computed.
166: *> \endverbatim
167: *
168: * Authors:
169: * ========
170: *
171: *> \author Univ. of Tennessee
172: *> \author Univ. of California Berkeley
173: *> \author Univ. of Colorado Denver
174: *> \author NAG Ltd.
175: *
176: *> \ingroup complex16HEeigen
177: *
178: * =====================================================================
179: SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
180: $ LWORK, RWORK, INFO )
181: *
182: * -- LAPACK driver routine --
183: * -- LAPACK is a software package provided by Univ. of Tennessee, --
184: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
185: *
186: * .. Scalar Arguments ..
187: CHARACTER JOBZ, UPLO
188: INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
189: * ..
190: * .. Array Arguments ..
191: DOUBLE PRECISION RWORK( * ), W( * )
192: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
193: * ..
194: *
195: * =====================================================================
196: *
197: * .. Parameters ..
198: COMPLEX*16 ONE
199: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
200: * ..
201: * .. Local Scalars ..
202: LOGICAL LQUERY, UPPER, WANTZ
203: CHARACTER TRANS
204: INTEGER LWKOPT, NB, NEIG
205: * ..
206: * .. External Functions ..
207: LOGICAL LSAME
208: INTEGER ILAENV
209: EXTERNAL LSAME, ILAENV
210: * ..
211: * .. External Subroutines ..
212: EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
213: * ..
214: * .. Intrinsic Functions ..
215: INTRINSIC MAX
216: * ..
217: * .. Executable Statements ..
218: *
219: * Test the input parameters.
220: *
221: WANTZ = LSAME( JOBZ, 'V' )
222: UPPER = LSAME( UPLO, 'U' )
223: LQUERY = ( LWORK.EQ.-1 )
224: *
225: INFO = 0
226: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
227: INFO = -1
228: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
229: INFO = -2
230: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
231: INFO = -3
232: ELSE IF( N.LT.0 ) THEN
233: INFO = -4
234: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
235: INFO = -6
236: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
237: INFO = -8
238: END IF
239: *
240: IF( INFO.EQ.0 ) THEN
241: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
242: LWKOPT = MAX( 1, ( NB + 1 )*N )
243: WORK( 1 ) = LWKOPT
244: *
245: IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN
246: INFO = -11
247: END IF
248: END IF
249: *
250: IF( INFO.NE.0 ) THEN
251: CALL XERBLA( 'ZHEGV ', -INFO )
252: RETURN
253: ELSE IF( LQUERY ) THEN
254: RETURN
255: END IF
256: *
257: * Quick return if possible
258: *
259: IF( N.EQ.0 )
260: $ RETURN
261: *
262: * Form a Cholesky factorization of B.
263: *
264: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
265: IF( INFO.NE.0 ) THEN
266: INFO = N + INFO
267: RETURN
268: END IF
269: *
270: * Transform problem to standard eigenvalue problem and solve.
271: *
272: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
273: CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
274: *
275: IF( WANTZ ) THEN
276: *
277: * Backtransform eigenvectors to the original problem.
278: *
279: NEIG = N
280: IF( INFO.GT.0 )
281: $ NEIG = INFO - 1
282: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
283: *
284: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
285: * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
286: *
287: IF( UPPER ) THEN
288: TRANS = 'N'
289: ELSE
290: TRANS = 'C'
291: END IF
292: *
293: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
294: $ B, LDB, A, LDA )
295: *
296: ELSE IF( ITYPE.EQ.3 ) THEN
297: *
298: * For B*A*x=(lambda)*x;
299: * backtransform eigenvectors: x = L*y or U**H *y
300: *
301: IF( UPPER ) THEN
302: TRANS = 'C'
303: ELSE
304: TRANS = 'N'
305: END IF
306: *
307: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
308: $ B, LDB, A, LDA )
309: END IF
310: END IF
311: *
312: WORK( 1 ) = LWKOPT
313: *
314: RETURN
315: *
316: * End of ZHEGV
317: *
318: END
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