1: *> \brief <b> ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHEEV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zheev.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zheev.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zheev.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
22: * INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, LDA, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION RWORK( * ), W( * )
30: * COMPLEX*16 A( LDA, * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
40: *> complex Hermitian matrix A.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] JOBZ
47: *> \verbatim
48: *> JOBZ is CHARACTER*1
49: *> = 'N': Compute eigenvalues only;
50: *> = 'V': Compute eigenvalues and eigenvectors.
51: *> \endverbatim
52: *>
53: *> \param[in] UPLO
54: *> \verbatim
55: *> UPLO is CHARACTER*1
56: *> = 'U': Upper triangle of A is stored;
57: *> = 'L': Lower triangle of A is stored.
58: *> \endverbatim
59: *>
60: *> \param[in] N
61: *> \verbatim
62: *> N is INTEGER
63: *> The order of the matrix A. N >= 0.
64: *> \endverbatim
65: *>
66: *> \param[in,out] A
67: *> \verbatim
68: *> A is COMPLEX*16 array, dimension (LDA, N)
69: *> On entry, the Hermitian matrix A. If UPLO = 'U', the
70: *> leading N-by-N upper triangular part of A contains the
71: *> upper triangular part of the matrix A. If UPLO = 'L',
72: *> the leading N-by-N lower triangular part of A contains
73: *> the lower triangular part of the matrix A.
74: *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
75: *> orthonormal eigenvectors of the matrix A.
76: *> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
77: *> or the upper triangle (if UPLO='U') of A, including the
78: *> diagonal, is destroyed.
79: *> \endverbatim
80: *>
81: *> \param[in] LDA
82: *> \verbatim
83: *> LDA is INTEGER
84: *> The leading dimension of the array A. LDA >= max(1,N).
85: *> \endverbatim
86: *>
87: *> \param[out] W
88: *> \verbatim
89: *> W is DOUBLE PRECISION array, dimension (N)
90: *> If INFO = 0, the eigenvalues in ascending order.
91: *> \endverbatim
92: *>
93: *> \param[out] WORK
94: *> \verbatim
95: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
96: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
97: *> \endverbatim
98: *>
99: *> \param[in] LWORK
100: *> \verbatim
101: *> LWORK is INTEGER
102: *> The length of the array WORK. LWORK >= max(1,2*N-1).
103: *> For optimal efficiency, LWORK >= (NB+1)*N,
104: *> where NB is the blocksize for ZHETRD returned by ILAENV.
105: *>
106: *> If LWORK = -1, then a workspace query is assumed; the routine
107: *> only calculates the optimal size of the WORK array, returns
108: *> this value as the first entry of the WORK array, and no error
109: *> message related to LWORK is issued by XERBLA.
110: *> \endverbatim
111: *>
112: *> \param[out] RWORK
113: *> \verbatim
114: *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
115: *> \endverbatim
116: *>
117: *> \param[out] INFO
118: *> \verbatim
119: *> INFO is INTEGER
120: *> = 0: successful exit
121: *> < 0: if INFO = -i, the i-th argument had an illegal value
122: *> > 0: if INFO = i, the algorithm failed to converge; i
123: *> off-diagonal elements of an intermediate tridiagonal
124: *> form did not converge to zero.
125: *> \endverbatim
126: *
127: * Authors:
128: * ========
129: *
130: *> \author Univ. of Tennessee
131: *> \author Univ. of California Berkeley
132: *> \author Univ. of Colorado Denver
133: *> \author NAG Ltd.
134: *
135: *> \ingroup complex16HEeigen
136: *
137: * =====================================================================
138: SUBROUTINE ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
139: $ INFO )
140: *
141: * -- LAPACK driver routine --
142: * -- LAPACK is a software package provided by Univ. of Tennessee, --
143: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144: *
145: * .. Scalar Arguments ..
146: CHARACTER JOBZ, UPLO
147: INTEGER INFO, LDA, LWORK, N
148: * ..
149: * .. Array Arguments ..
150: DOUBLE PRECISION RWORK( * ), W( * )
151: COMPLEX*16 A( LDA, * ), WORK( * )
152: * ..
153: *
154: * =====================================================================
155: *
156: * .. Parameters ..
157: DOUBLE PRECISION ZERO, ONE
158: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
159: COMPLEX*16 CONE
160: PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) )
161: * ..
162: * .. Local Scalars ..
163: LOGICAL LOWER, LQUERY, WANTZ
164: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
165: $ LLWORK, LWKOPT, NB
166: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
167: $ SMLNUM
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: INTEGER ILAENV
172: DOUBLE PRECISION DLAMCH, ZLANHE
173: EXTERNAL LSAME, ILAENV, DLAMCH, ZLANHE
174: * ..
175: * .. External Subroutines ..
176: EXTERNAL DSCAL, DSTERF, XERBLA, ZHETRD, ZLASCL, ZSTEQR,
177: $ ZUNGTR
178: * ..
179: * .. Intrinsic Functions ..
180: INTRINSIC MAX, SQRT
181: * ..
182: * .. Executable Statements ..
183: *
184: * Test the input parameters.
185: *
186: WANTZ = LSAME( JOBZ, 'V' )
187: LOWER = LSAME( UPLO, 'L' )
188: LQUERY = ( LWORK.EQ.-1 )
189: *
190: INFO = 0
191: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
192: INFO = -1
193: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
194: INFO = -2
195: ELSE IF( N.LT.0 ) THEN
196: INFO = -3
197: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
198: INFO = -5
199: END IF
200: *
201: IF( INFO.EQ.0 ) THEN
202: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
203: LWKOPT = MAX( 1, ( NB+1 )*N )
204: WORK( 1 ) = LWKOPT
205: *
206: IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY )
207: $ INFO = -8
208: END IF
209: *
210: IF( INFO.NE.0 ) THEN
211: CALL XERBLA( 'ZHEEV ', -INFO )
212: RETURN
213: ELSE IF( LQUERY ) THEN
214: RETURN
215: END IF
216: *
217: * Quick return if possible
218: *
219: IF( N.EQ.0 ) THEN
220: RETURN
221: END IF
222: *
223: IF( N.EQ.1 ) THEN
224: W( 1 ) = DBLE( A( 1, 1 ) )
225: WORK( 1 ) = 1
226: IF( WANTZ )
227: $ A( 1, 1 ) = CONE
228: RETURN
229: END IF
230: *
231: * Get machine constants.
232: *
233: SAFMIN = DLAMCH( 'Safe minimum' )
234: EPS = DLAMCH( 'Precision' )
235: SMLNUM = SAFMIN / EPS
236: BIGNUM = ONE / SMLNUM
237: RMIN = SQRT( SMLNUM )
238: RMAX = SQRT( BIGNUM )
239: *
240: * Scale matrix to allowable range, if necessary.
241: *
242: ANRM = ZLANHE( 'M', UPLO, N, A, LDA, RWORK )
243: ISCALE = 0
244: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
245: ISCALE = 1
246: SIGMA = RMIN / ANRM
247: ELSE IF( ANRM.GT.RMAX ) THEN
248: ISCALE = 1
249: SIGMA = RMAX / ANRM
250: END IF
251: IF( ISCALE.EQ.1 )
252: $ CALL ZLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
253: *
254: * Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
255: *
256: INDE = 1
257: INDTAU = 1
258: INDWRK = INDTAU + N
259: LLWORK = LWORK - INDWRK + 1
260: CALL ZHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ),
261: $ WORK( INDWRK ), LLWORK, IINFO )
262: *
263: * For eigenvalues only, call DSTERF. For eigenvectors, first call
264: * ZUNGTR to generate the unitary matrix, then call ZSTEQR.
265: *
266: IF( .NOT.WANTZ ) THEN
267: CALL DSTERF( N, W, RWORK( INDE ), INFO )
268: ELSE
269: CALL ZUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
270: $ LLWORK, IINFO )
271: INDWRK = INDE + N
272: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA,
273: $ RWORK( INDWRK ), INFO )
274: END IF
275: *
276: * If matrix was scaled, then rescale eigenvalues appropriately.
277: *
278: IF( ISCALE.EQ.1 ) THEN
279: IF( INFO.EQ.0 ) THEN
280: IMAX = N
281: ELSE
282: IMAX = INFO - 1
283: END IF
284: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
285: END IF
286: *
287: * Set WORK(1) to optimal complex workspace size.
288: *
289: WORK( 1 ) = LWKOPT
290: *
291: RETURN
292: *
293: * End of ZHEEV
294: *
295: END
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