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DSBGST(3F)							    DSBGST(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     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    [Toc]    [Back]

     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.

ARGUMENTS    [Toc]    [Back]

     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) 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,jka)<=i<=j;
	if UPLO	= 'L', AB(1+i-j,j)    =	A(i,j) for



									Page 1






DSBGST(3F)							    DSBGST(3F)



	     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.
DSBGST(3F)							    DSBGST(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     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    [Toc]    [Back]

     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.

ARGUMENTS    [Toc]    [Back]

     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) 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,jka)<=i<=j;
	if UPLO	= 'L', AB(1+i-j,j)    =	A(i,j) for



									Page 1






DSBGST(3F)							    DSBGST(3F)



	     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.


									PPPPaaaaggggeeee 2222
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