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    1: *> \brief \b DSBGV
    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 December 2016
  173: *
  174: *> \ingroup doubleOTHEReigen
  175: *
  176: *  =====================================================================
  177:       SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
  178:      $                  LDZ, WORK, INFO )
  179: *
  180: *  -- LAPACK driver routine (version 3.7.0) --
  181: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  182: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  183: *     December 2016
  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