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## dsbgst()

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

Download DSBGST + dependencies [TGZ] [ZIP] [TXT]

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

  [in]

  VECT

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

  [in]

  UPLO

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

  [in]

  N

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

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in,out]

  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.
      !>

  [in]

  LDAB

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

  [in]

  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.
      !>

  [in]

  LDBB

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

  [out]

  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.
      !>

  [in]

  LDX

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

  [out]

  WORK

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

  [out]

  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.