compute error vector from matrices
Syntax: errorVector = computeMatrixError(referenceMatrix, ...
sampleMatrix, errorType)
The following error types are supported, while a detailed definition can
be obtained <a href="matlab: help computeMatrixError>helpErrorDefinition">here</a>: relativeSquared, absoluteSquared, relativeMean,
absoluteMean, relativeTotal, absoluteTotal.
With errorType='all', all error vectors are returned in a structure with
fields according to the error types given above.
See also: approximateDec0001 function errorVector = computeMatrixError(matrixOne, matrixTwo, ... 0002 errorType, groupVector) 0003 % compute error vector from matrices 0004 % 0005 % Syntax: errorVector = computeMatrixError(referenceMatrix, ... 0006 % sampleMatrix, errorType) 0007 % 0008 % The following error types are supported, while a detailed definition can 0009 % be obtained <a href="matlab: help computeMatrixError>helpErrorDefinition">here</a>: relativeSquared, absoluteSquared, relativeMean, 0010 % absoluteMean, relativeTotal, absoluteTotal. 0011 % 0012 % With errorType='all', all error vectors are returned in a structure with 0013 % fields according to the error types given above. 0014 % 0015 % See also: approximateDec 0016 0017 % The elk-library: convex geometry applied to crystallization modeling. 0018 % Copyright (C) 2013 Alexander Reinhold 0019 % 0020 % This program is free software: you can redistribute it and/or modify it 0021 % under the terms of the GNU General Public License as published by the 0022 % Free Software Foundation, either version 3 of the License, or (at your 0023 % option) any later version. 0024 % 0025 % This program is distributed in the hope that it will be useful, but 0026 % WITHOUT ANY WARRANTY; without even the implied warranty of 0027 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0028 % General Public License for more details. 0029 % 0030 % You should have received a copy of the GNU General Public License along 0031 % with this program. If not, see <http://www.gnu.org/licenses/>. 0032 0033 %% Info 0034 % Note that weights for the elements might be applied before calling this 0035 % function. A weighted aggregation of all error components can be 0036 % obtained by a subsequent scalar product between errorVectors and a 0037 % weight vector. 0038 %/ 0039 0040 if ~exist('ratio', 'var') || isempty(ratio) 0041 ratio = 1; 0042 end 0043 0044 n = size(matrixOne, 2); 0045 nReal = n*ratio; 0046 errorMatrix = matrixOne - matrixTwo; 0047 switch lower(errorType) 0048 case 'relativesquared' 0049 errorVector = 1/nReal * sqrt(... 0050 sum((errorMatrix ./ matrixOne).^2, 2) ); 0051 0052 case 'relativemean' 0053 errorVector = 1/nReal * sum(abs(errorMatrix ./ matrixOne), 2); 0054 0055 case 'relativemax' 0056 errorVector = max(abs(errorMatrix ./ matrixOne), [], 2); 0057 0058 case 'absolutesquared' 0059 errorVector = (1/ratio) * sum(errorMatrix.^2, 2); 0060 0061 case 'absolute' 0062 errorVector = (1/ratio) * sum(abs(errorMatrix), 2); 0063 0064 case 'absolutemax' 0065 errorVector = max(abs(errorMatrix), [], 2); 0066 0067 case 'relativetotal' 0068 errorVector = (1/ratio) * (sum(matrixOne, 2) - sum(matrixTwo, 2)) ./ ... 0069 sum(matrixOne, 2); 0070 0071 case 'absolutetotal' 0072 errorVector = (1/ratio) * (sum(matrixOne, 2) - sum(matrixTwo, 2)); 0073 0074 case 'relativemaxgroupedmean' 0075 errorVector = 0*errorMatrix(:,1); 0076 for iGroup = 1:max(groupVector) 0077 errorVector = max(errorVector, abs((... 0078 sum(matrixOne(:, groupVector==iGroup), 2) - ... 0079 sum(matrixTwo(:, groupVector==iGroup), 2)) ./ ... 0080 sum(matrixOne(:, groupVector==iGroup), 2))); 0081 end 0082 0083 case 'all' 0084 errorVector.relativeSquared = ... 0085 computeMatrixError(matrixOne, matrixTwo, 'relativeSquared'); 0086 0087 errorVector.relativeMean = ... 0088 computeMatrixError(matrixOne, matrixTwo, 'relativeMean'); 0089 0090 errorVector.absoluteSquared = ... 0091 computeMatrixError(matrixOne, matrixTwo, 'absoluteSquared'); 0092 0093 errorVector.absoluteMean = ... 0094 computeMatrixError(matrixOne, matrixTwo, 'absolute'); 0095 0096 errorVector.relativeTotal = ... 0097 computeMatrixError(matrixOne, matrixTwo, 'relativeTotal'); 0098 0099 errorVector.absoluteTotal = ... 0100 computeMatrixError(matrixOne, matrixTwo, 'absoluteTotal'); 0101 0102 otherwise 0103 error('elk:approximation:wrongInput', ... 0104 ['Given error type ''' errorType '''is not supported']); 0105 0106 end 0107 0108 end 0109 0110 function helpErrorDefinition() 0111 % %%% Detailed Error definitions for <a href="matlab: help computeMatrixError">computeMatrixError</a> 0112 % n - total number of columns in matrixOne and matrixTwo 0113 % xi - reference value (column of matrixOne) 0114 % yi - sample value (column of matrixTwo) 0115 % e - aggregated error vector 0116 % 0117 % %% absoluteSquared 0118 % e = sum( (xi - yi).^2 ) 0119 % 0120 % %% relativeSquared 0121 % e = 1/n * sqrt(sum( ((xi - yi) ./ xi )^2 )) 0122 % 0123 % %% absolute 0124 % e = sum( abs(xi - yi) ) 0125 % 0126 % %% relativeMean 0127 % e = 1/n * sum( abs(xi - yi) ) 0128 % 0129 % %% absoluteTotal 0130 % e = ( sum( xi ) - sum( yi ) ) 0131 % 0132 % %% relativeTotal 0133 % e = ( sum( xi ) - sum( yi ) ) / sum( xi ) 0134 % 0135 % %% 0136 end