权重矩阵

回归就是求矩阵系数，那么一个这样的矩阵表达式:X*A=Y，如何求系数矩阵A呢，两边同时乘以X转置，得X‘*X*A=X’*Y;那么在下一步两边同时乘以X‘*X的逆得到，A = inv(X' * X) * X' * Y    ，这里是为了防止 矩阵X不满秩，所以先乘以一个转秩  

function [Bw, Ui] = dopWeightBasis(B, W)%% Purpose : This function generates a discrete orthogonal weighted  %           basis from a unitary basis function set. The weightings must%           either be a vector w or a matrix W. In the case of a vector of%           weighty they are used as the diagonal of the weighting matrix%           i.e. W = diag(w);%% Use (syntax):%       Pw = generateWeightedPoly(noPoints, degree, weights);%% Input Parameters :%       B: A unitary basis set from which the weighted basis functions ar%       eto be generated%       W: the weights which must be the same length as the number of%       points.%% Return Parameters :%       Bw: the weighted polynomial basis.%       Ui: The post multiplying matrix which einsures Bw = B * Ui%% Description and algorithms:%       This algorith is based on a method developed by Paul O'Leary and%       Matthew Harker.%% References : "Savitzky-Golay Smoothing for Multivariate Cyclic% Measurement Data", Paul O'Leary, Matthew Harker and Richard Neumayr,% Submitted to the National Indian Conference on Graphics and Computer% Vision 2010, Jaipur India.%% Author :  Paul O'Leary% Date :    15. Sept 2009% Version : 1.0%% (c) 2009 Paul O'Leary, Chair of Automation, University of Leoben, Leoben, Austria% email: [e-mail], url: automation.unileoben.ac.at%% History:%   Date:           Comment:%   15. Sept        Original version%%--------------------------------------------------------%% if a vector of weights is delivered then generate the seighting matrixif isvector(W)    factor = 10;    if ( min( W ) / max(W) )<= factor*eps        error('The weighting vector must be positive definite.');    end;    W = diag( W );end;%% test the inputs for correctness%[nW, mW] = size( W );%if ~(nW == mW)    error('The weigthing matrix must be square');end;%try    % test if W is positive definite    chol(W);catch me    error('The weighting matrix W must be positive semi definite');end;%[nB, mB] = size( B );if ~(nB == nW)    error('The dimensions of the basis function matrix B and W are not consistent');end;%---------------------------------------------------------------% Do the necessary computations to generate the weighted basis.%U = chol(B' * W * B);Ui = inv( U );%Bw = B * Ui;