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dsbtrd.f(3)				      LAPACK				      dsbtrd.f(3)

NAME
       dsbtrd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dsbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
	   DSBTRD

Function/Subroutine Documentation
   subroutine dsbtrd (characterVECT, characterUPLO, integerN, integerKD, double precision,
       dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )D, double precision,
       dimension( * )E, double precision, dimension( ldq, * )Q, integerLDQ, double precision,
       dimension( * )WORK, integerINFO)
       DSBTRD

       Purpose:

	    DSBTRD reduces a real symmetric band matrix A to symmetric
	    tridiagonal form T by an orthogonal similarity transformation:
	    Q**T * A * Q = T.

       Parameters:
	   VECT

		     VECT is CHARACTER*1
		     = 'N':  do not form Q;
		     = 'V':  form Q;
		     = 'U':  update a matrix X, by forming X*Q.

	   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 matrix A.  N >= 0.

	   KD

		     KD is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'.  KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
		     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
		     On exit, the diagonal elements of AB are overwritten by the
		     diagonal elements of the tridiagonal matrix T; if KD > 0, the
		     elements on the first superdiagonal (if UPLO = 'U') or the
		     first subdiagonal (if UPLO = 'L') are overwritten by the
		     off-diagonal elements of T; the rest of AB is overwritten by
		     values generated during the reduction.

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The diagonal elements of the tridiagonal matrix T.

	   E

		     E is DOUBLE PRECISION array, dimension (N-1)
		     The off-diagonal elements of the tridiagonal matrix T:
		     E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

	   Q

		     Q is DOUBLE PRECISION array, dimension (LDQ,N)
		     On entry, if VECT = 'U', then Q must contain an N-by-N
		     matrix X; if VECT = 'N' or 'V', then Q need not be set.

		     On exit:
		     if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
		     if VECT = 'U', Q contains the product X*Q;
		     if VECT = 'N', the array Q is not referenced.

	   LDQ

		     LDQ is INTEGER
		     The leading dimension of the array Q.
		     LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (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

       Further Details:

	     Modified by Linda Kaufman, Bell Labs.

       Definition at line 163 of file dsbtrd.f.

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

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