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67 lines
2.6 KiB
Matlab
67 lines
2.6 KiB
Matlab
% Generates a 1D orthonormal polynomial base
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% polys = legendrepoly1D_2(X,maxorder,w);
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% The weighting function has not been tested extensively
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% Manuel Guizar - March 10, 2009
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% Copyright (c) 2016, Manuel Guizar Sicairos, James R. Fienup, University of Rochester
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% All rights reserved.
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%
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% Redistribution and use in source and binary forms, with or without
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% modification, are permitted provided that the following conditions are
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% met:
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%
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% * Redistributions of source code must retain the above copyright
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% notice, this list of conditions and the following disclaimer.
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% * Redistributions in binary form must reproduce the above copyright
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% notice, this list of conditions and the following disclaimer in
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% the documentation and/or other materials provided with the distribution
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% * Neither the name of the University of Rochester nor the names
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% of its contributors may be used to endorse or promote products derived
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% from this software without specific prior written permission.
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%
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% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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% POSSIBILITY OF SUCH DAMAGE.
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function polys = legendrepoly1D_2(X,maxorder,w)
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if nargin < 3
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w = 1;
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end
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[nc nr] = size(X);
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polys = ones(nc,nr);
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%%% Generation of polynomials
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for ii = 0:maxorder,
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polys(:,:,ii+1) = (X.^(ii));
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end
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%%% Normalization
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for ii = 1:length(polys(1,1,:)),
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% polys(:,:,ii) = polys(:,:,ii)/sqrt(sum(sum(abs(polys(:,:,ii)).^2)));
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polys(:,:,ii) = polys(:,:,ii)/sqrt(sum(sum(w.*abs(polys(:,:,ii)).^2)));
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end
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%%% Orthonormalization
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for ii = 2:length(polys(1,1,:)),
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for jj = 1:ii-1,
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polys(:,:,ii) = polys(:,:,ii) - sum(sum(polys(:,:,ii).*polys(:,:,jj).*w))*polys(:,:,jj);
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end
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polys(:,:,ii) = polys(:,:,ii)/sqrt(sum(sum(w.*polys(:,:,ii).^2)));
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end
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% polys(:,:,3) = polys(:,:,3) - sum(sum(polys(:,:,3).*polys(:,:,1)))*polys(:,:,1);
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% polys(:,:,3) = polys(:,:,3)/sum(sum(polys(:,:,3).^2));
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