LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dsbgv.f
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00001 *> \brief \b DSBGST
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DSBGV + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbgv.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbgv.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
00022 *                         LDZ, WORK, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          JOBZ, UPLO
00026 *       INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       DOUBLE PRECISION   AB( LDAB, * ), BB( LDBB, * ), W( * ),
00030 *      $                   WORK( * ), Z( LDZ, * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> DSBGV computes all the eigenvalues, and optionally, the eigenvectors
00040 *> of a real generalized symmetric-definite banded eigenproblem, of
00041 *> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
00042 *> and banded, and B is also positive definite.
00043 *> \endverbatim
00044 *
00045 *  Arguments:
00046 *  ==========
00047 *
00048 *> \param[in] JOBZ
00049 *> \verbatim
00050 *>          JOBZ is CHARACTER*1
00051 *>          = 'N':  Compute eigenvalues only;
00052 *>          = 'V':  Compute eigenvalues and eigenvectors.
00053 *> \endverbatim
00054 *>
00055 *> \param[in] UPLO
00056 *> \verbatim
00057 *>          UPLO is CHARACTER*1
00058 *>          = 'U':  Upper triangles of A and B are stored;
00059 *>          = 'L':  Lower triangles of A and B are stored.
00060 *> \endverbatim
00061 *>
00062 *> \param[in] N
00063 *> \verbatim
00064 *>          N is INTEGER
00065 *>          The order of the matrices A and B.  N >= 0.
00066 *> \endverbatim
00067 *>
00068 *> \param[in] KA
00069 *> \verbatim
00070 *>          KA is INTEGER
00071 *>          The number of superdiagonals of the matrix A if UPLO = 'U',
00072 *>          or the number of subdiagonals if UPLO = 'L'. KA >= 0.
00073 *> \endverbatim
00074 *>
00075 *> \param[in] KB
00076 *> \verbatim
00077 *>          KB is INTEGER
00078 *>          The number of superdiagonals of the matrix B if UPLO = 'U',
00079 *>          or the number of subdiagonals if UPLO = 'L'. KB >= 0.
00080 *> \endverbatim
00081 *>
00082 *> \param[in,out] AB
00083 *> \verbatim
00084 *>          AB is DOUBLE PRECISION array, dimension (LDAB, N)
00085 *>          On entry, the upper or lower triangle of the symmetric band
00086 *>          matrix A, stored in the first ka+1 rows of the array.  The
00087 *>          j-th column of A is stored in the j-th column of the array AB
00088 *>          as follows:
00089 *>          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
00090 *>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
00091 *>
00092 *>          On exit, the contents of AB are destroyed.
00093 *> \endverbatim
00094 *>
00095 *> \param[in] LDAB
00096 *> \verbatim
00097 *>          LDAB is INTEGER
00098 *>          The leading dimension of the array AB.  LDAB >= KA+1.
00099 *> \endverbatim
00100 *>
00101 *> \param[in,out] BB
00102 *> \verbatim
00103 *>          BB is DOUBLE PRECISION array, dimension (LDBB, N)
00104 *>          On entry, the upper or lower triangle of the symmetric band
00105 *>          matrix B, stored in the first kb+1 rows of the array.  The
00106 *>          j-th column of B is stored in the j-th column of the array BB
00107 *>          as follows:
00108 *>          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
00109 *>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
00110 *>
00111 *>          On exit, the factor S from the split Cholesky factorization
00112 *>          B = S**T*S, as returned by DPBSTF.
00113 *> \endverbatim
00114 *>
00115 *> \param[in] LDBB
00116 *> \verbatim
00117 *>          LDBB is INTEGER
00118 *>          The leading dimension of the array BB.  LDBB >= KB+1.
00119 *> \endverbatim
00120 *>
00121 *> \param[out] W
00122 *> \verbatim
00123 *>          W is DOUBLE PRECISION array, dimension (N)
00124 *>          If INFO = 0, the eigenvalues in ascending order.
00125 *> \endverbatim
00126 *>
00127 *> \param[out] Z
00128 *> \verbatim
00129 *>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
00130 *>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
00131 *>          eigenvectors, with the i-th column of Z holding the
00132 *>          eigenvector associated with W(i). The eigenvectors are
00133 *>          normalized so that Z**T*B*Z = I.
00134 *>          If JOBZ = 'N', then Z is not referenced.
00135 *> \endverbatim
00136 *>
00137 *> \param[in] LDZ
00138 *> \verbatim
00139 *>          LDZ is INTEGER
00140 *>          The leading dimension of the array Z.  LDZ >= 1, and if
00141 *>          JOBZ = 'V', LDZ >= N.
00142 *> \endverbatim
00143 *>
00144 *> \param[out] WORK
00145 *> \verbatim
00146 *>          WORK is DOUBLE PRECISION array, dimension (3*N)
00147 *> \endverbatim
00148 *>
00149 *> \param[out] INFO
00150 *> \verbatim
00151 *>          INFO is INTEGER
00152 *>          = 0:  successful exit
00153 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00154 *>          > 0:  if INFO = i, and i is:
00155 *>             <= N:  the algorithm failed to converge:
00156 *>                    i off-diagonal elements of an intermediate
00157 *>                    tridiagonal form did not converge to zero;
00158 *>             > N:   if INFO = N + i, for 1 <= i <= N, then DPBSTF
00159 *>                    returned INFO = i: B is not positive definite.
00160 *>                    The factorization of B could not be completed and
00161 *>                    no eigenvalues or eigenvectors were computed.
00162 *> \endverbatim
00163 *
00164 *  Authors:
00165 *  ========
00166 *
00167 *> \author Univ. of Tennessee 
00168 *> \author Univ. of California Berkeley 
00169 *> \author Univ. of Colorado Denver 
00170 *> \author NAG Ltd. 
00171 *
00172 *> \date November 2011
00173 *
00174 *> \ingroup doubleOTHEReigen
00175 *
00176 *  =====================================================================
00177       SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
00178      $                  LDZ, WORK, INFO )
00179 *
00180 *  -- LAPACK driver routine (version 3.4.0) --
00181 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00182 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00183 *     November 2011
00184 *
00185 *     .. Scalar Arguments ..
00186       CHARACTER          JOBZ, UPLO
00187       INTEGER            INFO, KA, KB, LDAB, LDBB, LDZ, N
00188 *     ..
00189 *     .. Array Arguments ..
00190       DOUBLE PRECISION   AB( LDAB, * ), BB( LDBB, * ), W( * ),
00191      $                   WORK( * ), Z( LDZ, * )
00192 *     ..
00193 *
00194 *  =====================================================================
00195 *
00196 *     .. Local Scalars ..
00197       LOGICAL            UPPER, WANTZ
00198       CHARACTER          VECT
00199       INTEGER            IINFO, INDE, INDWRK
00200 *     ..
00201 *     .. External Functions ..
00202       LOGICAL            LSAME
00203       EXTERNAL           LSAME
00204 *     ..
00205 *     .. External Subroutines ..
00206       EXTERNAL           DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, XERBLA
00207 *     ..
00208 *     .. Executable Statements ..
00209 *
00210 *     Test the input parameters.
00211 *
00212       WANTZ = LSAME( JOBZ, 'V' )
00213       UPPER = LSAME( UPLO, 'U' )
00214 *
00215       INFO = 0
00216       IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
00217          INFO = -1
00218       ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
00219          INFO = -2
00220       ELSE IF( N.LT.0 ) THEN
00221          INFO = -3
00222       ELSE IF( KA.LT.0 ) THEN
00223          INFO = -4
00224       ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
00225          INFO = -5
00226       ELSE IF( LDAB.LT.KA+1 ) THEN
00227          INFO = -7
00228       ELSE IF( LDBB.LT.KB+1 ) THEN
00229          INFO = -9
00230       ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
00231          INFO = -12
00232       END IF
00233       IF( INFO.NE.0 ) THEN
00234          CALL XERBLA( 'DSBGV ', -INFO )
00235          RETURN
00236       END IF
00237 *
00238 *     Quick return if possible
00239 *
00240       IF( N.EQ.0 )
00241      $   RETURN
00242 *
00243 *     Form a split Cholesky factorization of B.
00244 *
00245       CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
00246       IF( INFO.NE.0 ) THEN
00247          INFO = N + INFO
00248          RETURN
00249       END IF
00250 *
00251 *     Transform problem to standard eigenvalue problem.
00252 *
00253       INDE = 1
00254       INDWRK = INDE + N
00255       CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
00256      $             WORK( INDWRK ), IINFO )
00257 *
00258 *     Reduce to tridiagonal form.
00259 *
00260       IF( WANTZ ) THEN
00261          VECT = 'U'
00262       ELSE
00263          VECT = 'N'
00264       END IF
00265       CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
00266      $             WORK( INDWRK ), IINFO )
00267 *
00268 *     For eigenvalues only, call DSTERF.  For eigenvectors, call SSTEQR.
00269 *
00270       IF( .NOT.WANTZ ) THEN
00271          CALL DSTERF( N, W, WORK( INDE ), INFO )
00272       ELSE
00273          CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
00274      $                INFO )
00275       END IF
00276       RETURN
00277 *
00278 *     End of DSBGV
00279 *
00280       END
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