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