SRC/ssbgvx.f(3)

NAME
SRC/ssbgvx.f

SYNOPSIS

  Functions/Subroutines
subroutine ssbgvx (jobz, range, uplo, n, ka, kb, ab, ldab, bb, ldbb, q, ldq, vl, vu, il, iu, abstol, m, w, z, ldz, work, iwork, ifail, info)
SSBGVX

Function/Subroutine Documentation

  subroutine ssbgvx (character jobz, character range, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( ldq, * ) q, integer ldq, real vl, real vu, integer il, integer iu, real abstol, integer m, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)

SSBGVX

Purpose:

    !>
    !> SSBGVX computes selected eigenvalues, and optionally, eigenvectors
    !> of a real generalized symmetric-definite banded eigenproblem, of
    !> the form A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric
    !> and banded, and B is also positive definite.  Eigenvalues and
    !> eigenvectors can be selected by specifying either all eigenvalues,
    !> a range of values or a range of indices for the desired eigenvalues.
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    RANGE

    !>          RANGE is CHARACTER*1
    !>          = 'A': all eigenvalues will be found.
    !>          = 'V': all eigenvalues in the half-open interval (VL,VU]
    !>                 will be found.
    !>          = 'I': the IL-th through IU-th eigenvalues will be found.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangles of A and B are stored;
    !>          = 'L':  Lower triangles of A and B are stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrices A and B.  N >= 0.
    !>

    KA

    !>          KA is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KA >= 0.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of superdiagonals of the matrix B if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KB >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB, N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first ka+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
    !>
    !>          On exit, the contents of AB are destroyed.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KA+1.
    !>

    BB

    !>          BB is REAL array, dimension (LDBB, N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix B, stored in the first kb+1 rows of the array.  The
    !>          j-th column of B is stored in the j-th column of the array BB
    !>          as follows:
    !>          if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
    !>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
    !>
    !>          On exit, the factor S from the split Cholesky factorization
    !>          B = S**T*S, as returned by SPBSTF.
    !>

    LDBB

    !>          LDBB is INTEGER
    !>          The leading dimension of the array BB.  LDBB >= KB+1.
    !>

    Q

    !>          Q is REAL array, dimension (LDQ, N)
    !>          If JOBZ = 'V', the n-by-n matrix used in the reduction of
    !>          A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
    !>          and consequently C to tridiagonal form.
    !>          If JOBZ = 'N', the array Q is not referenced.
    !>

    LDQ

    !>          LDQ is INTEGER
    !>          The leading dimension of the array Q.  If JOBZ = 'N',
    !>          LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
    !>

    VL

    !>          VL is REAL
    !>
    !>          If RANGE='V', the lower bound of the interval to
    !>          be searched for eigenvalues. VL < VU.
    !>          Not referenced if RANGE = 'A' or 'I'.
    !>

    VU

    !>          VU is REAL
    !>
    !>          If RANGE='V', the upper bound of the interval to
    !>          be searched for eigenvalues. VL < VU.
    !>          Not referenced if RANGE = 'A' or 'I'.
    !>

    IL

    !>          IL is INTEGER
    !>
    !>          If RANGE='I', the index of the
    !>          smallest eigenvalue to be returned.
    !>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
    !>          Not referenced if RANGE = 'A' or 'V'.
    !>

    IU

    !>          IU is INTEGER
    !>
    !>          If RANGE='I', the index of the
    !>          largest eigenvalue to be returned.
    !>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
    !>          Not referenced if RANGE = 'A' or 'V'.
    !>

    ABSTOL

    !>          ABSTOL is REAL
    !>          The absolute error tolerance for the eigenvalues.
    !>          An approximate eigenvalue is accepted as converged
    !>          when it is determined to lie in an interval [a,b]
    !>          of width less than or equal to
    !>
    !>                  ABSTOL + EPS *   max( |a|,|b| ) ,
    !>
    !>          where EPS is the machine precision.  If ABSTOL is less than
    !>          or equal to zero, then  EPS*|T|  will be used in its place,
    !>          where |T| is the 1-norm of the tridiagonal matrix obtained
    !>          by reducing A to tridiagonal form.
    !>
    !>          Eigenvalues will be computed most accurately when ABSTOL is
    !>          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
    !>          If this routine returns with INFO>0, indicating that some
    !>          eigenvectors did not converge, try setting ABSTOL to
    !>          2*SLAMCH('S').
    !>

    M

    !>          M is INTEGER
    !>          The total number of eigenvalues found.  0 <= M <= N.
    !>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
    !>

    W

    !>          W is REAL array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    Z

    !>          Z is REAL array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
    !>          eigenvectors, with the i-th column of Z holding the
    !>          eigenvector associated with W(i).  The eigenvectors are
    !>          normalized so Z**T*B*Z = I.
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is REAL array, dimension (7*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (5*N)
    !>

    IFAIL

    !>          IFAIL is INTEGER array, dimension (M)
    !>          If JOBZ = 'V', then if INFO = 0, the first M elements of
    !>          IFAIL are zero.  If INFO > 0, then IFAIL contains the
    !>          indices of the eigenvalues that failed to converge.
    !>          If JOBZ = 'N', then IFAIL is not referenced.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          <= N: if INFO = i, then i eigenvectors failed to converge.
    !>                  Their indices are stored in IFAIL.
    !>          > N:  SPBSTF returned an error code; i.e.,
    !>                if INFO = N + i, for 1 <= i <= N, then the leading
    !>                principal minor of order i of B is not positive.
    !>                The factorization of B could not be completed and
    !>                no eigenvalues or eigenvectors were computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 291 of file ssbgvx.f.

Author

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