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                                    Wed Feb 26 2014                                     dsbtrd.f(3)