1: *> \brief <b> ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER 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 ZHPEV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpev.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpev.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpev.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
22: * INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, LDZ, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION RWORK( * ), W( * )
30: * COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
40: *> complex Hermitian matrix in packed storage.
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] AP
67: *> \verbatim
68: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
69: *> On entry, the upper or lower triangle of the Hermitian matrix
70: *> A, packed columnwise in a linear array. The j-th column of A
71: *> is stored in the array AP as follows:
72: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
73: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
74: *>
75: *> On exit, AP is overwritten by values generated during the
76: *> reduction to tridiagonal form. If UPLO = 'U', the diagonal
77: *> and first superdiagonal of the tridiagonal matrix T overwrite
78: *> the corresponding elements of A, and if UPLO = 'L', the
79: *> diagonal and first subdiagonal of T overwrite the
80: *> corresponding elements of A.
81: *> \endverbatim
82: *>
83: *> \param[out] W
84: *> \verbatim
85: *> W is DOUBLE PRECISION array, dimension (N)
86: *> If INFO = 0, the eigenvalues in ascending order.
87: *> \endverbatim
88: *>
89: *> \param[out] Z
90: *> \verbatim
91: *> Z is COMPLEX*16 array, dimension (LDZ, N)
92: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
93: *> eigenvectors of the matrix A, with the i-th column of Z
94: *> holding the eigenvector associated with W(i).
95: *> If JOBZ = 'N', then Z is not referenced.
96: *> \endverbatim
97: *>
98: *> \param[in] LDZ
99: *> \verbatim
100: *> LDZ is INTEGER
101: *> The leading dimension of the array Z. LDZ >= 1, and if
102: *> JOBZ = 'V', LDZ >= max(1,N).
103: *> \endverbatim
104: *>
105: *> \param[out] WORK
106: *> \verbatim
107: *> WORK is COMPLEX*16 array, dimension (max(1, 2*N-1))
108: *> \endverbatim
109: *>
110: *> \param[out] RWORK
111: *> \verbatim
112: *> RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
113: *> \endverbatim
114: *>
115: *> \param[out] INFO
116: *> \verbatim
117: *> INFO is INTEGER
118: *> = 0: successful exit.
119: *> < 0: if INFO = -i, the i-th argument had an illegal value.
120: *> > 0: if INFO = i, the algorithm failed to converge; i
121: *> off-diagonal elements of an intermediate tridiagonal
122: *> form did not converge to zero.
123: *> \endverbatim
124: *
125: * Authors:
126: * ========
127: *
128: *> \author Univ. of Tennessee
129: *> \author Univ. of California Berkeley
130: *> \author Univ. of Colorado Denver
131: *> \author NAG Ltd.
132: *
133: *> \ingroup complex16OTHEReigen
134: *
135: * =====================================================================
136: SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
137: $ INFO )
138: *
139: * -- LAPACK driver routine --
140: * -- LAPACK is a software package provided by Univ. of Tennessee, --
141: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142: *
143: * .. Scalar Arguments ..
144: CHARACTER JOBZ, UPLO
145: INTEGER INFO, LDZ, N
146: * ..
147: * .. Array Arguments ..
148: DOUBLE PRECISION RWORK( * ), W( * )
149: COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
150: * ..
151: *
152: * =====================================================================
153: *
154: * .. Parameters ..
155: DOUBLE PRECISION ZERO, ONE
156: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
157: * ..
158: * .. Local Scalars ..
159: LOGICAL WANTZ
160: INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
161: $ ISCALE
162: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
163: $ SMLNUM
164: * ..
165: * .. External Functions ..
166: LOGICAL LSAME
167: DOUBLE PRECISION DLAMCH, ZLANHP
168: EXTERNAL LSAME, DLAMCH, ZLANHP
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEQR,
172: $ ZUPGTR
173: * ..
174: * .. Intrinsic Functions ..
175: INTRINSIC SQRT
176: * ..
177: * .. Executable Statements ..
178: *
179: * Test the input parameters.
180: *
181: WANTZ = LSAME( JOBZ, 'V' )
182: *
183: INFO = 0
184: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
185: INFO = -1
186: ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
187: $ THEN
188: INFO = -2
189: ELSE IF( N.LT.0 ) THEN
190: INFO = -3
191: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
192: INFO = -7
193: END IF
194: *
195: IF( INFO.NE.0 ) THEN
196: CALL XERBLA( 'ZHPEV ', -INFO )
197: RETURN
198: END IF
199: *
200: * Quick return if possible
201: *
202: IF( N.EQ.0 )
203: $ RETURN
204: *
205: IF( N.EQ.1 ) THEN
206: W( 1 ) = DBLE( AP( 1 ) )
207: RWORK( 1 ) = 1
208: IF( WANTZ )
209: $ Z( 1, 1 ) = ONE
210: RETURN
211: END IF
212: *
213: * Get machine constants.
214: *
215: SAFMIN = DLAMCH( 'Safe minimum' )
216: EPS = DLAMCH( 'Precision' )
217: SMLNUM = SAFMIN / EPS
218: BIGNUM = ONE / SMLNUM
219: RMIN = SQRT( SMLNUM )
220: RMAX = SQRT( BIGNUM )
221: *
222: * Scale matrix to allowable range, if necessary.
223: *
224: ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
225: ISCALE = 0
226: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
227: ISCALE = 1
228: SIGMA = RMIN / ANRM
229: ELSE IF( ANRM.GT.RMAX ) THEN
230: ISCALE = 1
231: SIGMA = RMAX / ANRM
232: END IF
233: IF( ISCALE.EQ.1 ) THEN
234: CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
235: END IF
236: *
237: * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
238: *
239: INDE = 1
240: INDTAU = 1
241: CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
242: $ IINFO )
243: *
244: * For eigenvalues only, call DSTERF. For eigenvectors, first call
245: * ZUPGTR to generate the orthogonal matrix, then call ZSTEQR.
246: *
247: IF( .NOT.WANTZ ) THEN
248: CALL DSTERF( N, W, RWORK( INDE ), INFO )
249: ELSE
250: INDWRK = INDTAU + N
251: CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
252: $ WORK( INDWRK ), IINFO )
253: INDRWK = INDE + N
254: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
255: $ RWORK( INDRWK ), INFO )
256: END IF
257: *
258: * If matrix was scaled, then rescale eigenvalues appropriately.
259: *
260: IF( ISCALE.EQ.1 ) THEN
261: IF( INFO.EQ.0 ) THEN
262: IMAX = N
263: ELSE
264: IMAX = INFO - 1
265: END IF
266: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
267: END IF
268: *
269: RETURN
270: *
271: * End of ZHPEV
272: *
273: END
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