Annotation of rpl/lapack/lapack/zhbev.f, revision 1.14
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: *
1.14 ! bertrand 147: *> \date December 2016
1.8 bertrand 148: *
149: *> \ingroup complex16OTHEReigen
150: *
151: * =====================================================================
1.1 bertrand 152: SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
153: $ RWORK, INFO )
154: *
1.14 ! bertrand 155: * -- LAPACK driver routine (version 3.7.0) --
1.1 bertrand 156: * -- LAPACK is a software package provided by Univ. of Tennessee, --
157: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 158: * December 2016
1.1 bertrand 159: *
160: * .. Scalar Arguments ..
161: CHARACTER JOBZ, UPLO
162: INTEGER INFO, KD, LDAB, LDZ, N
163: * ..
164: * .. Array Arguments ..
165: DOUBLE PRECISION RWORK( * ), W( * )
166: COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
167: * ..
168: *
169: * =====================================================================
170: *
171: * .. Parameters ..
172: DOUBLE PRECISION ZERO, ONE
173: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
174: * ..
175: * .. Local Scalars ..
176: LOGICAL LOWER, WANTZ
177: INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
178: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
179: $ SMLNUM
180: * ..
181: * .. External Functions ..
182: LOGICAL LSAME
183: DOUBLE PRECISION DLAMCH, ZLANHB
184: EXTERNAL LSAME, DLAMCH, ZLANHB
185: * ..
186: * .. External Subroutines ..
187: EXTERNAL DSCAL, DSTERF, XERBLA, ZHBTRD, ZLASCL, ZSTEQR
188: * ..
189: * .. Intrinsic Functions ..
190: INTRINSIC SQRT
191: * ..
192: * .. Executable Statements ..
193: *
194: * Test the input parameters.
195: *
196: WANTZ = LSAME( JOBZ, 'V' )
197: LOWER = LSAME( UPLO, 'L' )
198: *
199: INFO = 0
200: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
201: INFO = -1
202: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
203: INFO = -2
204: ELSE IF( N.LT.0 ) THEN
205: INFO = -3
206: ELSE IF( KD.LT.0 ) THEN
207: INFO = -4
208: ELSE IF( LDAB.LT.KD+1 ) THEN
209: INFO = -6
210: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
211: INFO = -9
212: END IF
213: *
214: IF( INFO.NE.0 ) THEN
215: CALL XERBLA( 'ZHBEV ', -INFO )
216: RETURN
217: END IF
218: *
219: * Quick return if possible
220: *
221: IF( N.EQ.0 )
222: $ RETURN
223: *
224: IF( N.EQ.1 ) THEN
225: IF( LOWER ) THEN
226: W( 1 ) = AB( 1, 1 )
227: ELSE
228: W( 1 ) = AB( KD+1, 1 )
229: END IF
230: IF( WANTZ )
231: $ Z( 1, 1 ) = ONE
232: RETURN
233: END IF
234: *
235: * Get machine constants.
236: *
237: SAFMIN = DLAMCH( 'Safe minimum' )
238: EPS = DLAMCH( 'Precision' )
239: SMLNUM = SAFMIN / EPS
240: BIGNUM = ONE / SMLNUM
241: RMIN = SQRT( SMLNUM )
242: RMAX = SQRT( BIGNUM )
243: *
244: * Scale matrix to allowable range, if necessary.
245: *
246: ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
247: ISCALE = 0
248: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
249: ISCALE = 1
250: SIGMA = RMIN / ANRM
251: ELSE IF( ANRM.GT.RMAX ) THEN
252: ISCALE = 1
253: SIGMA = RMAX / ANRM
254: END IF
255: IF( ISCALE.EQ.1 ) THEN
256: IF( LOWER ) THEN
257: CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
258: ELSE
259: CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
260: END IF
261: END IF
262: *
263: * Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
264: *
265: INDE = 1
266: CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
267: $ LDZ, WORK, IINFO )
268: *
269: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
270: *
271: IF( .NOT.WANTZ ) THEN
272: CALL DSTERF( N, W, RWORK( INDE ), INFO )
273: ELSE
274: INDRWK = INDE + N
275: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
276: $ RWORK( INDRWK ), INFO )
277: END IF
278: *
279: * If matrix was scaled, then rescale eigenvalues appropriately.
280: *
281: IF( ISCALE.EQ.1 ) THEN
282: IF( INFO.EQ.0 ) THEN
283: IMAX = N
284: ELSE
285: IMAX = INFO - 1
286: END IF
287: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
288: END IF
289: *
290: RETURN
291: *
292: * End of ZHBEV
293: *
294: END
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