fdet_chebyshev_seq2.m

空间统计工具箱

function [lowerbounds, chebyshevest, upperbounds, alphafine]=fdet_chebyshev_seq2(d, alphafine)
%
%[lowerbounds, chebyshevest, upperbounds, alphafine]=fdet_chebyshev_seq2(d, alphafine)
%
%%This function returns a sequence of quadratic lower Taylor series bounds, quadratic Chebyshev approximations, and upper
%Taylor series bounds for the log-determinant of (I-aD(1:i,1:i)) for i=1...n. The routine
%assumes the input matrix d is symmetric with a zeros on the diagonal.  As a default the elements of  a  go from 0 to 1 or can take the optional
%vector alphafine containing elements between 1 and -1. The computation of 
%log-determinants for negative values of a does not require more time, but may cause other routines to take more time.
%
%
%INPUT:
%
%The n by n symmetric weight matrix d with zeros on the diagonal.
%
%The optional n by 1 vector alphafine containing values for a. These values should lie between 
%1 and -1 (for this routine). As a default, alphafine has 1,00 elements with
%the initial element at 0 and the largest element is 0.99.
%
%
%OUTPUT:
%
%alphafine is a iter by 1 grid of values of the dependence parameter a ordered from negative to positive
%lowerbounds is a iter by n matrix of the lower Taylor bound for the log-determinant.
%chebyshevest is a iter by n matrix of the quadratic Chebyshev approximation.
%upperbounds is a iter by n matrix of the upper Taylor bound for the log-determinant.
%
%
%NOTES:
%
%The chebyshev approximation appeared in:
%
%Pace, R. Kelley, and James LeSage, 
%"Chebyshev Approximation of Log-determinants of Spatial Weight Matrices,"
%Computational Statistics and Data Analysis, forthcoming.
%
%The use of determinant sequences appeared in:
%
%Pace, R. Kelley, and James LeSage, 揝patial Autoregressive Local Estimation,