genericObjectiveFunction

 objective function for optimal approximation
 
 THIS IS NO USER FUNCTION

• computeMatrixError compute error vector from matrices
• computeMeasureDec calculate measure from decomposition data
• computeProjectionFromGrass compute projection matrix from grassmann coordinates
• estimateHeMatrix compute the "closest" hE-vector in reach of the given hC-representation

• approxNonlinear approximation by nonlinear optimization

0001 function objectiveValue = genericObjectiveFunction(x, heMatrix, dec, ...
0002     par, grassStruct, sampleProjectionData)
0003 % objective function for optimal approximation
0004 %
0005 % THIS IS NO USER FUNCTION
0006 
0007 % The elk-library: convex geometry applied to crystallization modeling.
0008 %   Copyright (C) 2013 Alexander Reinhold
0009 %
0010 % This program is free software: you can redistribute it and/or modify it
0011 %   under the terms of the GNU General Public License as published by the
0012 %   Free Software Foundation, either version 3 of the License, or (at your
0013 %   option) any later version.
0014 %
0015 % This program is distributed in the hope that it will be useful, but
0016 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0017 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0018 %   General Public License for more details.
0019 %
0020 % You should have received a copy of the GNU General Public License along
0021 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0022 
0023 % projection matrix
0024 projectionMatrix = computeProjectionFromGrass(x, grassStruct);
0025 % define penalty function
0026 % penaltyValue = @(validRatio)((validRatio < par.penaltyRatioLimit)*...
0027 %     (par.penaltyRatioLimit - validRatio)*par.penaltySlope);
0028 
0029 %% projection
0030 if strcmpi(par.projectionType, 'true')
0031     heMatrixProjected = projectionMatrix * heMatrix;
0032 else
0033     %! DEV: this is temporarily not supported:
0034     error('elk:approximation:internalError', 'DEV: not supported');
0035     heMatrixProjected = estimateHeMatrix(heMatrix, projectionMatrix, ...
0036         sampleProjectionData);
0037     %/
0038 end
0039 
0040 %% evaluate error
0041 if strcmpi(par.errorType, 'PCA')
0042     % objective
0043     objectiveValue = sum((heMatrix(:) - heMatrixProjected(:)).^2);
0044 else
0045     % measure matrix (enforce validity)
0046     measureMatrix = computeMeasureDec(dec, 'hC', ...
0047         heMatrixProjected, par.measureList, [], [], 1);  
0048     
0049     % get ratio of columns that contribute to errors
0050 %     ratio = sum(fadeOutScaling) / length(fadeOutScaling);
0051     
0052     % error vector
0053     errorVector = computeMatrixError(par.measureValueMatrix, ...
0054         measureMatrix, par.errorType, par.errorGroupVector);
0055     
0056     % apply weights and penalty
0057 %     objectiveValue = par.measureWeightVector(:)'*errorVector + penaltyValue(ratio);
0058     objectiveValue = par.measureWeightVector(:)'*errorVector;
0059     
0060 end