CXML
        	    
LAPACK version 3.0
ssbgst(3)

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

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

      CHARACTER	     UPLO, VECT

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

      REAL	     AB( LDAB, * ), BB( LDBB, * ), WORK( * ), X( LDX, * )

DESCRIPTION
  SSBGST 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 SPBSTF, 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.

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 subdiagonals if UPLO = 'L'.	 KA >= 0.

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

  AB	  (input/output) 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 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) REAL array, dimension (LDBB,N)
	  The banded factor S from the split Cholesky factorization of B, as
	  returned by SPBSTF, 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) REAL 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) REAL array, dimension (2*N)

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