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dsbgst.f(3)				      LAPACK				      dsbgst.f(3)

NAME
       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 (characterVECT, characterUPLO, integerN, integerKA, integerKB, double
       precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldbb, * )BB,
       integerLDBB, double precision, dimension( ldx, * )X, integerLDX, double precision,
       dimension( * )WORK, integerINFO)
       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.

       Date:
	   November 2011

       Definition at line 159 of file dsbgst.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dsbgst.f(3)
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