Annotation of rpl/lapack/lapack/zhbev.f, revision 1.17
1.8 bertrand 1: *> \brief <b> ZHBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download ZHBEV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbev.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbev.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbev.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
22: * RWORK, INFO )
1.14 bertrand 23: *
1.8 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, KD, LDAB, LDZ, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION RWORK( * ), W( * )
30: * COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
31: * ..
1.14 bertrand 32: *
1.8 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
40: *> a complex Hermitian band 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] KD
67: *> \verbatim
68: *> KD is INTEGER
69: *> The number of superdiagonals of the matrix A if UPLO = 'U',
70: *> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
71: *> \endverbatim
72: *>
73: *> \param[in,out] AB
74: *> \verbatim
75: *> AB is COMPLEX*16 array, dimension (LDAB, N)
76: *> On entry, the upper or lower triangle of the Hermitian band
77: *> matrix A, stored in the first KD+1 rows of the array. The
78: *> j-th column of A is stored in the j-th column of the array AB
79: *> as follows:
80: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
81: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
82: *>
83: *> On exit, AB is overwritten by values generated during the
84: *> reduction to tridiagonal form. If UPLO = 'U', the first
85: *> superdiagonal and the diagonal of the tridiagonal matrix T
86: *> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
87: *> the diagonal and first subdiagonal of T are returned in the
88: *> first two rows of AB.
89: *> \endverbatim
90: *>
91: *> \param[in] LDAB
92: *> \verbatim
93: *> LDAB is INTEGER
94: *> The leading dimension of the array AB. LDAB >= KD + 1.
95: *> \endverbatim
96: *>
97: *> \param[out] W
98: *> \verbatim
99: *> W is DOUBLE PRECISION array, dimension (N)
100: *> If INFO = 0, the eigenvalues in ascending order.
101: *> \endverbatim
102: *>
103: *> \param[out] Z
104: *> \verbatim
105: *> Z is COMPLEX*16 array, dimension (LDZ, N)
106: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
107: *> eigenvectors of the matrix A, with the i-th column of Z
108: *> holding the eigenvector associated with W(i).
109: *> If JOBZ = 'N', then Z is not referenced.
110: *> \endverbatim
111: *>
112: *> \param[in] LDZ
113: *> \verbatim
114: *> LDZ is INTEGER
115: *> The leading dimension of the array Z. LDZ >= 1, and if
116: *> JOBZ = 'V', LDZ >= max(1,N).
117: *> \endverbatim
118: *>
119: *> \param[out] WORK
120: *> \verbatim
121: *> WORK is COMPLEX*16 array, dimension (N)
122: *> \endverbatim
123: *>
124: *> \param[out] RWORK
125: *> \verbatim
126: *> RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
127: *> \endverbatim
128: *>
129: *> \param[out] INFO
130: *> \verbatim
131: *> INFO is INTEGER
132: *> = 0: successful exit.
133: *> < 0: if INFO = -i, the i-th argument had an illegal value.
134: *> > 0: if INFO = i, the algorithm failed to converge; i
135: *> off-diagonal elements of an intermediate tridiagonal
136: *> form did not converge to zero.
137: *> \endverbatim
138: *
139: * Authors:
140: * ========
141: *
1.14 bertrand 142: *> \author Univ. of Tennessee
143: *> \author Univ. of California Berkeley
144: *> \author Univ. of Colorado Denver
145: *> \author NAG Ltd.
1.8 bertrand 146: *
147: *> \ingroup complex16OTHEReigen
148: *
149: * =====================================================================
1.1 bertrand 150: SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
151: $ RWORK, INFO )
152: *
1.17 ! bertrand 153: * -- LAPACK driver routine --
1.1 bertrand 154: * -- LAPACK is a software package provided by Univ. of Tennessee, --
155: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156: *
157: * .. Scalar Arguments ..
158: CHARACTER JOBZ, UPLO
159: INTEGER INFO, KD, LDAB, LDZ, N
160: * ..
161: * .. Array Arguments ..
162: DOUBLE PRECISION RWORK( * ), W( * )
163: COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
164: * ..
165: *
166: * =====================================================================
167: *
168: * .. Parameters ..
169: DOUBLE PRECISION ZERO, ONE
170: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
171: * ..
172: * .. Local Scalars ..
173: LOGICAL LOWER, WANTZ
174: INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
175: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
176: $ SMLNUM
177: * ..
178: * .. External Functions ..
179: LOGICAL LSAME
180: DOUBLE PRECISION DLAMCH, ZLANHB
181: EXTERNAL LSAME, DLAMCH, ZLANHB
182: * ..
183: * .. External Subroutines ..
184: EXTERNAL DSCAL, DSTERF, XERBLA, ZHBTRD, ZLASCL, ZSTEQR
185: * ..
186: * .. Intrinsic Functions ..
187: INTRINSIC SQRT
188: * ..
189: * .. Executable Statements ..
190: *
191: * Test the input parameters.
192: *
193: WANTZ = LSAME( JOBZ, 'V' )
194: LOWER = LSAME( UPLO, 'L' )
195: *
196: INFO = 0
197: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
198: INFO = -1
199: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
200: INFO = -2
201: ELSE IF( N.LT.0 ) THEN
202: INFO = -3
203: ELSE IF( KD.LT.0 ) THEN
204: INFO = -4
205: ELSE IF( LDAB.LT.KD+1 ) THEN
206: INFO = -6
207: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
208: INFO = -9
209: END IF
210: *
211: IF( INFO.NE.0 ) THEN
212: CALL XERBLA( 'ZHBEV ', -INFO )
213: RETURN
214: END IF
215: *
216: * Quick return if possible
217: *
218: IF( N.EQ.0 )
219: $ RETURN
220: *
221: IF( N.EQ.1 ) THEN
222: IF( LOWER ) THEN
1.17 ! bertrand 223: W( 1 ) = DBLE( AB( 1, 1 ) )
1.1 bertrand 224: ELSE
1.17 ! bertrand 225: W( 1 ) = DBLE( AB( KD+1, 1 ) )
1.1 bertrand 226: END IF
227: IF( WANTZ )
228: $ Z( 1, 1 ) = ONE
229: RETURN
230: END IF
231: *
232: * Get machine constants.
233: *
234: SAFMIN = DLAMCH( 'Safe minimum' )
235: EPS = DLAMCH( 'Precision' )
236: SMLNUM = SAFMIN / EPS
237: BIGNUM = ONE / SMLNUM
238: RMIN = SQRT( SMLNUM )
239: RMAX = SQRT( BIGNUM )
240: *
241: * Scale matrix to allowable range, if necessary.
242: *
243: ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
244: ISCALE = 0
245: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
246: ISCALE = 1
247: SIGMA = RMIN / ANRM
248: ELSE IF( ANRM.GT.RMAX ) THEN
249: ISCALE = 1
250: SIGMA = RMAX / ANRM
251: END IF
252: IF( ISCALE.EQ.1 ) THEN
253: IF( LOWER ) THEN
254: CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
255: ELSE
256: CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
257: END IF
258: END IF
259: *
260: * Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
261: *
262: INDE = 1
263: CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
264: $ LDZ, WORK, IINFO )
265: *
266: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
267: *
268: IF( .NOT.WANTZ ) THEN
269: CALL DSTERF( N, W, RWORK( INDE ), INFO )
270: ELSE
271: INDRWK = INDE + N
272: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
273: $ RWORK( INDRWK ), 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: RETURN
288: *
289: * End of ZHBEV
290: *
291: END
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