Description of sllinrega

Home > sltoolbox > regression > sllinrega.m

sllinrega

PURPOSE

SLLINREGA Performs Augmented Multivariate Linear Regression

SYNOPSIS

function [A, b] = sllinrega(X, Y, varargin)

DESCRIPTION

SLLINREGA Performs Augmented Multivariate Linear Regression

 $ Syntax $
   - [A, b] = sllinrega(X, Y, ...)

 $ Arguments $
   - X:        The sample matrix of x
   - Y:        The sample matrix of y
   - A:        The solved transform matrix
   - b:        The solved shift vector

 $ Description $
   - [A, b] = sllinrega(X, Y, ...) solves the regression problem given
     by the following formula:
           y = A * x + b
     in least square error sense. The samples are stored in X and Y
     in column-wise manner.
     You can specify properties for regression as in sllinreg.

 $ Remarks $
   - The implementation is based on sllinreg with an augmented 
     formulation as follows:
           y = [A, b] * [x; 1]

 $ History $
   - Created by Dahua Lin, on Sep 15th, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• sllinreg SLLINREG Performs Multivariate Linear Regression and Ridge Regression
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

SOURCE CODE

0001 function [A, b] = sllinrega(X, Y, varargin)
0002 %SLLINREGA Performs Augmented Multivariate Linear Regression
0003 %
0004 % $ Syntax $
0005 %   - [A, b] = sllinrega(X, Y, ...)
0006 %
0007 % $ Arguments $
0008 %   - X:        The sample matrix of x
0009 %   - Y:        The sample matrix of y
0010 %   - A:        The solved transform matrix
0011 %   - b:        The solved shift vector
0012 %
0013 % $ Description $
0014 %   - [A, b] = sllinrega(X, Y, ...) solves the regression problem given
0015 %     by the following formula:
0016 %           y = A * x + b
0017 %     in least square error sense. The samples are stored in X and Y
0018 %     in column-wise manner.
0019 %     You can specify properties for regression as in sllinreg.
0020 %
0021 % $ Remarks $
0022 %   - The implementation is based on sllinreg with an augmented
0023 %     formulation as follows:
0024 %           y = [A, b] * [x; 1]
0025 %
0026 % $ History $
0027 %   - Created by Dahua Lin, on Sep 15th, 2006
0028 %
0029 
0030 %% parse and verify input arguments
0031 
0032 if nargin < 2
0033     raise_lackinput('sllinrega', 2);
0034 end
0035 
0036 if ~isnumeric(X) || ~isnumeric(Y) || ndims(X) ~= 2 || ndims(Y) ~= 2
0037     error('sltoolbox:invalidarg', ...
0038         'The X and Y should be both 2D numeric matrices');
0039 end
0040 
0041 %% main
0042 
0043 % augment formulation
0044 [dx, nx] = size(X);
0045 Xa = [X; ones(1, nx)];
0046 
0047 % solve
0048 Aa = sllinreg(Xa, Y, varargin{:});
0049 clear Xa;
0050 
0051 % extract
0052 A = Aa(:, 1:dx);
0053 b = Aa(:, dx+1);
0054 
0055 
0056 
0057 
0058 
0059 
0060

---

Generated on Wed 20-Sep-2006 12:43:11 by m2html © 2003