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dsbgst.f(3) [debian man page]

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 3.4.1							  Sun May 26 2013						       dsbgst.f(3)

Check Out this Related Man Page

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 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) 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    (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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