SRC/dsbgst.f(3)

NAME
SRC/dsbgst.f

SYNOPSIS

  Functions/Subroutines
subroutine dsbgst (vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)
DSBGST

Function/Subroutine Documentation

  subroutine dsbgst (character vect, character uplo, integer n, integer ka, integer kb, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) work, integer info)

DSBGST

Purpose:

    !>
    !> DSBGST reduces a real symmetric-definite banded generalized
    !> eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y,
    !> such that C has the same bandwidth as A.
    !>
    !> B must have been previously factorized as S**T*S by DPBSTF, using a
    !> split Cholesky factorization. A is overwritten by C = X**T*A*X, where
    !> X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the
    !> bandwidth of A.
    !>

Parameters
    VECT

    !>          VECT is CHARACTER*1
    !>          = 'N':  do not form the transformation matrix X;
    !>          = 'V':  form X.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is 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'.  KA >= KB >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION 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 transformed matrix X**T*A*X, stored in the same
    !>          format as A.
    !>

    LDAB

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

    BB

    !>          BB is DOUBLE PRECISION array, dimension (LDBB,N)
    !>          The banded factor S from the split Cholesky factorization of
    !>          B, as returned by DPBSTF, stored in the first KB+1 rows of
    !>          the array.
    !>

    LDBB

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

    X

    !>          X is DOUBLE PRECISION array, dimension (LDX,N)
    !>          If VECT = 'V', the n-by-n matrix X.
    !>          If VECT = 'N', the array X is not referenced.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.
    !>          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 157 of file dsbgst.f.

Author

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