Annotation of rpl/lapack/lapack/zhbgv.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZHBGST
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZHBGV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgv.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgv.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgv.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
! 22: * LDZ, WORK, RWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * CHARACTER JOBZ, UPLO
! 26: * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * DOUBLE PRECISION RWORK( * ), W( * )
! 30: * COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
! 31: * $ Z( LDZ, * )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
! 41: *> of a complex generalized Hermitian-definite banded eigenproblem, of
! 42: *> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
! 43: *> and banded, and B is also positive definite.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] JOBZ
! 50: *> \verbatim
! 51: *> JOBZ is CHARACTER*1
! 52: *> = 'N': Compute eigenvalues only;
! 53: *> = 'V': Compute eigenvalues and eigenvectors.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] UPLO
! 57: *> \verbatim
! 58: *> UPLO is CHARACTER*1
! 59: *> = 'U': Upper triangles of A and B are stored;
! 60: *> = 'L': Lower triangles of A and B are stored.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] N
! 64: *> \verbatim
! 65: *> N is INTEGER
! 66: *> The order of the matrices A and B. N >= 0.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] KA
! 70: *> \verbatim
! 71: *> KA is INTEGER
! 72: *> The number of superdiagonals of the matrix A if UPLO = 'U',
! 73: *> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] KB
! 77: *> \verbatim
! 78: *> KB is INTEGER
! 79: *> The number of superdiagonals of the matrix B if UPLO = 'U',
! 80: *> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[in,out] AB
! 84: *> \verbatim
! 85: *> AB is COMPLEX*16 array, dimension (LDAB, N)
! 86: *> On entry, the upper or lower triangle of the Hermitian band
! 87: *> matrix A, stored in the first ka+1 rows of the array. The
! 88: *> j-th column of A is stored in the j-th column of the array AB
! 89: *> as follows:
! 90: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
! 91: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
! 92: *>
! 93: *> On exit, the contents of AB are destroyed.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] LDAB
! 97: *> \verbatim
! 98: *> LDAB is INTEGER
! 99: *> The leading dimension of the array AB. LDAB >= KA+1.
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in,out] BB
! 103: *> \verbatim
! 104: *> BB is COMPLEX*16 array, dimension (LDBB, N)
! 105: *> On entry, the upper or lower triangle of the Hermitian band
! 106: *> matrix B, stored in the first kb+1 rows of the array. The
! 107: *> j-th column of B is stored in the j-th column of the array BB
! 108: *> as follows:
! 109: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
! 110: *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
! 111: *>
! 112: *> On exit, the factor S from the split Cholesky factorization
! 113: *> B = S**H*S, as returned by ZPBSTF.
! 114: *> \endverbatim
! 115: *>
! 116: *> \param[in] LDBB
! 117: *> \verbatim
! 118: *> LDBB is INTEGER
! 119: *> The leading dimension of the array BB. LDBB >= KB+1.
! 120: *> \endverbatim
! 121: *>
! 122: *> \param[out] W
! 123: *> \verbatim
! 124: *> W is DOUBLE PRECISION array, dimension (N)
! 125: *> If INFO = 0, the eigenvalues in ascending order.
! 126: *> \endverbatim
! 127: *>
! 128: *> \param[out] Z
! 129: *> \verbatim
! 130: *> Z is COMPLEX*16 array, dimension (LDZ, N)
! 131: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
! 132: *> eigenvectors, with the i-th column of Z holding the
! 133: *> eigenvector associated with W(i). The eigenvectors are
! 134: *> normalized so that Z**H*B*Z = I.
! 135: *> If JOBZ = 'N', then Z is not referenced.
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[in] LDZ
! 139: *> \verbatim
! 140: *> LDZ is INTEGER
! 141: *> The leading dimension of the array Z. LDZ >= 1, and if
! 142: *> JOBZ = 'V', LDZ >= N.
! 143: *> \endverbatim
! 144: *>
! 145: *> \param[out] WORK
! 146: *> \verbatim
! 147: *> WORK is COMPLEX*16 array, dimension (N)
! 148: *> \endverbatim
! 149: *>
! 150: *> \param[out] RWORK
! 151: *> \verbatim
! 152: *> RWORK is DOUBLE PRECISION array, dimension (3*N)
! 153: *> \endverbatim
! 154: *>
! 155: *> \param[out] INFO
! 156: *> \verbatim
! 157: *> INFO is INTEGER
! 158: *> = 0: successful exit
! 159: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 160: *> > 0: if INFO = i, and i is:
! 161: *> <= N: the algorithm failed to converge:
! 162: *> i off-diagonal elements of an intermediate
! 163: *> tridiagonal form did not converge to zero;
! 164: *> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
! 165: *> returned INFO = i: B is not positive definite.
! 166: *> The factorization of B could not be completed and
! 167: *> no eigenvalues or eigenvectors were computed.
! 168: *> \endverbatim
! 169: *
! 170: * Authors:
! 171: * ========
! 172: *
! 173: *> \author Univ. of Tennessee
! 174: *> \author Univ. of California Berkeley
! 175: *> \author Univ. of Colorado Denver
! 176: *> \author NAG Ltd.
! 177: *
! 178: *> \date November 2011
! 179: *
! 180: *> \ingroup complex16OTHEReigen
! 181: *
! 182: * =====================================================================
1.1 bertrand 183: SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
184: $ LDZ, WORK, RWORK, INFO )
185: *
1.8 ! bertrand 186: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 187: * -- LAPACK is a software package provided by Univ. of Tennessee, --
188: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 189: * November 2011
1.1 bertrand 190: *
191: * .. Scalar Arguments ..
192: CHARACTER JOBZ, UPLO
193: INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
194: * ..
195: * .. Array Arguments ..
196: DOUBLE PRECISION RWORK( * ), W( * )
197: COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
198: $ Z( LDZ, * )
199: * ..
200: *
201: * =====================================================================
202: *
203: * .. Local Scalars ..
204: LOGICAL UPPER, WANTZ
205: CHARACTER VECT
206: INTEGER IINFO, INDE, INDWRK
207: * ..
208: * .. External Functions ..
209: LOGICAL LSAME
210: EXTERNAL LSAME
211: * ..
212: * .. External Subroutines ..
213: EXTERNAL DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR
214: * ..
215: * .. Executable Statements ..
216: *
217: * Test the input parameters.
218: *
219: WANTZ = LSAME( JOBZ, 'V' )
220: UPPER = LSAME( UPLO, 'U' )
221: *
222: INFO = 0
223: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
224: INFO = -1
225: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
226: INFO = -2
227: ELSE IF( N.LT.0 ) THEN
228: INFO = -3
229: ELSE IF( KA.LT.0 ) THEN
230: INFO = -4
231: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
232: INFO = -5
233: ELSE IF( LDAB.LT.KA+1 ) THEN
234: INFO = -7
235: ELSE IF( LDBB.LT.KB+1 ) THEN
236: INFO = -9
237: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
238: INFO = -12
239: END IF
240: IF( INFO.NE.0 ) THEN
241: CALL XERBLA( 'ZHBGV ', -INFO )
242: RETURN
243: END IF
244: *
245: * Quick return if possible
246: *
247: IF( N.EQ.0 )
248: $ RETURN
249: *
250: * Form a split Cholesky factorization of B.
251: *
252: CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
253: IF( INFO.NE.0 ) THEN
254: INFO = N + INFO
255: RETURN
256: END IF
257: *
258: * Transform problem to standard eigenvalue problem.
259: *
260: INDE = 1
261: INDWRK = INDE + N
262: CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
263: $ WORK, RWORK( INDWRK ), IINFO )
264: *
265: * Reduce to tridiagonal form.
266: *
267: IF( WANTZ ) THEN
268: VECT = 'U'
269: ELSE
270: VECT = 'N'
271: END IF
272: CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
273: $ LDZ, WORK, IINFO )
274: *
275: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
276: *
277: IF( .NOT.WANTZ ) THEN
278: CALL DSTERF( N, W, RWORK( INDE ), INFO )
279: ELSE
280: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
281: $ RWORK( INDWRK ), INFO )
282: END IF
283: RETURN
284: *
285: * End of ZHBGV
286: *
287: END
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