Description of sldiscrep

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sldiscrep

PURPOSE

SLDISCREP Evaluates the discrepancy of two arrays

SYNOPSIS

function d = sldiscrep(X1, X2, measure, r1)

DESCRIPTION

SLDISCREP Evaluates the discrepancy of two arrays

 $ Syntax $
   - d = sldiscrep(X1, X2, measure)
   - d = sldiscrep(X1, X2, measure, true)

 $ Arguments $
   - X1:       the first array
   - X2:       the second array
   - measure:  the name of measure
   - d:        the measure value

 $ Description $
   - d = sldiscrep(X1, X2, measure) evaluates the discrepancy between
     X1 and X2 according to the specified measure. 

     \*
     \t   Table 1. Discrepancy Measures
     \h    name        &     description
          'fro'        & Compute the Frobenius between two arrays
                         that is to sum the square differences and
                         compute the square root.
          'avgfro'     & Compute the average Frobenius norm between
                         two arrays, that is to average the square
                         differences, and compute the square root.
          'energy'     & Compute the total difference square energy.
          'avgenergy'  & Compute the average difference square energy.
          'maxdiffabs' & Compute the maximum element-wise absolute 
                         difference
          'maxdiffnrm' & Compute the maximum column-wise difference
                         norm.
     \*  

   - d = sldiscrep(X1, X2, measure, true) computes the relative measure
     with X1 as reference. By default, this mode is disabled.

 $ History $
   - Created by Dahua Lin, on Aug 17, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• slnorm SLNORM Compute the Lp-norms
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

• slfmm SLFMM Learns a Finite Mixture Model (FMM)

SOURCE CODE

0001 function d = sldiscrep(X1, X2, measure, r1)
0002 %SLDISCREP Evaluates the discrepancy of two arrays
0003 %
0004 % $ Syntax $
0005 %   - d = sldiscrep(X1, X2, measure)
0006 %   - d = sldiscrep(X1, X2, measure, true)
0007 %
0008 % $ Arguments $
0009 %   - X1:       the first array
0010 %   - X2:       the second array
0011 %   - measure:  the name of measure
0012 %   - d:        the measure value
0013 %
0014 % $ Description $
0015 %   - d = sldiscrep(X1, X2, measure) evaluates the discrepancy between
0016 %     X1 and X2 according to the specified measure.
0017 %
0018 %     \*
0019 %     \t   Table 1. Discrepancy Measures
0020 %     \h    name        &     description
0021 %          'fro'        & Compute the Frobenius between two arrays
0022 %                         that is to sum the square differences and
0023 %                         compute the square root.
0024 %          'avgfro'     & Compute the average Frobenius norm between
0025 %                         two arrays, that is to average the square
0026 %                         differences, and compute the square root.
0027 %          'energy'     & Compute the total difference square energy.
0028 %          'avgenergy'  & Compute the average difference square energy.
0029 %          'maxdiffabs' & Compute the maximum element-wise absolute
0030 %                         difference
0031 %          'maxdiffnrm' & Compute the maximum column-wise difference
0032 %                         norm.
0033 %     \*
0034 %
0035 %   - d = sldiscrep(X1, X2, measure, true) computes the relative measure
0036 %     with X1 as reference. By default, this mode is disabled.
0037 %
0038 % $ History $
0039 %   - Created by Dahua Lin, on Aug 17, 2006
0040 %
0041 
0042 %% parse and verify input arguments
0043 
0044 if nargin < 3
0045     raise_lackinput('sldiscrep', 3);
0046 end
0047 
0048 if ~isequal(size(X1), size(X2))
0049     error('sltoolbox:sizmismatch', ...
0050         'The sizes of X1 and X2 are different');
0051 end
0052 
0053 if nargin < 4 || isempty(r1)
0054     r1 = false;
0055 end
0056 
0057 %% compute
0058 
0059 switch measure
0060     case 'fro'
0061         D = X1(:) - X2(:);
0062         d = sqrt(sum(D.^2));
0063         clear D;
0064         if r1
0065             d0 = sqrt(sum(X1(:).^2));
0066             d = d / d0;
0067         end        
0068         
0069     case 'avgfro'
0070         n = numel(X1);
0071         D = X1(:) - X2(:);
0072         d = sqrt(sum(D.^2) / n);
0073         clear D;
0074         if r1
0075             d0 = sqrt(sum(X1(:).^2) / n);
0076             d = d / d0;
0077         end  
0078         
0079     case 'energy'
0080         D = X1(:) - X2(:);
0081         d = sum(D.^2);
0082         clear D;
0083         if r1
0084             d0 = sum(X1(:).^2);
0085             d = d / d0;
0086         end  
0087         
0088     case 'avgenergy'
0089         n = numel(X1);
0090         D = X1(:) - X2(:);
0091         d = sum(D.^2) / n;
0092         clear D;
0093         if r1
0094             d0 = sum(X1(:).^2) / n;
0095             d = d / d0;
0096         end  
0097         
0098     case 'maxdiffabs'
0099         if ~r1
0100             D = X1(:) - X2(:);
0101             d = max(abs(D));
0102         else
0103             D = (X1(:) - X2(:)) ./ X1(:);
0104             d = max(abs(D(:)));
0105         end
0106         
0107     case 'maxdiffnrm'
0108         if ~r1
0109             dn = slnorm(X1 - X2);
0110             d = max(dn(:));
0111         else
0112             dn = slnorm(X1 - X2);
0113             dn1 = slnorm(X1);
0114             d = max(dn(:) ./ dn1(:));
0115         end
0116         
0117     otherwise
0118         error('sltoolbox:invalidarg', ...
0119             'Invalid measure name %s', measure);
0120 end
0121 
0122 
0123     
0124 
0125 
0126

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