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RedHat 9 (Linux i386) - man page for dsbgst (redhat section l)

DSBGST(l)					)					DSBGST(l)

NAME
       DSBGST - reduce a real symmetric-definite banded generalized eigenproblem A*x = lambda*B*x
       to standard form C*y = lambda*y,

SYNOPSIS
       SUBROUTINE DSBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO )

	   CHARACTER	  UPLO, VECT

	   INTEGER	  INFO, KA, KB, LDAB, LDBB, LDX, N

	   DOUBLE	  PRECISION AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )

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 factor-
       ization. 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.

ARGUMENTS
       VECT    (input) CHARACTER*1
	       = 'N':  do not form the transformation matrix X;
	       = 'V':  form X.

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The order of the matrices A and B.  N >= 0.

       KA      (input) INTEGER
	       The  number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-
	       diagonals if UPLO = 'L'.  KA >= 0.

       KB      (input) INTEGER
	       The number of superdiagonals of the matrix B if UPLO = 'U', or the number of  sub-
	       diagonals if UPLO = 'L'.  KA >= KB >= 0.

       AB      (input/output) 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 col-
	       umn  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    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KA+1.

       BB      (input) 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    (input) INTEGER
	       The leading dimension of the array BB.  LDBB >= KB+1.

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

       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value.

LAPACK version 3.0			   15 June 2000 				DSBGST(l)


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