83 lines
3.0 KiB
Matlab
83 lines
3.0 KiB
Matlab
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% By Willi Mutschler, September 26, 2016. Email: willi@mutschler.eu
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% Quadruplication Matrix as defined by
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% Meijer (2005) - Matrix algebra for higher order moments. Linear Algebra and its Applications, 410,pp. 112<31>134
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%
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% Inputs:
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% p: size of vector
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% Outputs:
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% QP: quadruplication matrix
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% QPinv: Moore-Penrose inverse of QP
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%
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function [QP,QPinv] = quadruplication(p,progress,sparseflag)
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if nargin <2
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progress =0;
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end
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if nargin < 3
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sparseflag = 1;
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end
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reverseStr = ''; counti=1;
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np = p*(p+1)*(p+2)*(p+3)/24;
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if sparseflag
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QP = spalloc(p^4,p*(p+1)*(p+2)*(p+3)/24,p^4);
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else
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QP = zeros(p^4,p*(p+1)*(p+2)*(p+3)/24);
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end
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if nargout > 1
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if sparseflag
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QPinv = spalloc(p*(p+1)*(p+2)*(p+3)/24,p*(p+1)*(p+2)*(p+3)/24,p^4);
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else
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QPinv = zeros(p*(p+1)*(p+2)*(p+3)/24,p*(p+1)*(p+2)*(p+3)/24);
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end
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end
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for l=1:p
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for k=l:p
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for j=k:p
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for i=j:p
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if progress && (rem(counti,100)== 0)
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msg = sprintf(' Quadruplication Matrix Processed %d/%d', counti, np); fprintf([reverseStr, msg]); reverseStr = repmat(sprintf('\b'), 1, length(msg));
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elseif progress && (counti==np)
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msg = sprintf(' Quadruplication Matrix Processed %d/%d\n', counti, np); fprintf([reverseStr, msg]); reverseStr = repmat(sprintf('\b'), 1, length(msg));
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end
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idx = uperm([i j k l]);
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for r = 1:size(idx,1)
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ii = idx(r,1); jj= idx(r,2); kk=idx(r,3); ll=idx(r,4);
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n = ii + (jj-1)*p + (kk-1)*p^2 + (ll-1)*p^3;
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m = mue(p,i,j,k,l);
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QP(n,m)=1;
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if nargout > 1
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if i==j && j==k && k==l
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QPinv(m,n)=1;
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elseif i==j && j==k && k>l
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QPinv(m,n)=1/4;
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elseif i>j && j==k && k==l
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QPinv(m,n)=1/4;
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elseif i==j && j>k && k==l
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QPinv(m,n) = 1/6;
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elseif i>j && j>k && k==l
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QPinv(m,n) = 1/12;
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elseif i>j && j==k && k>l
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QPinv(m,n) = 1/12;
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elseif i==j && j>k && k>l
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QPinv(m,n) = 1/12;
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elseif i>j && j>k && k>l
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QPinv(m,n) = 1/24;
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end
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end
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end
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counti = counti+1;
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end
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end
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end
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end
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%QPinv = (transpose(QP)*QP)\transpose(QP);
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function m = mue(p,i,j,k,l)
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m = i + (j-1)*p + 1/2*(k-1)*p^2 + 1/6*(l-1)*p^3 - 1/2*j*(j-1) + 1/6*k*(k-1)*(k-2) - 1/24*l*(l-1)*(l-2)*(l-3) - 1/2*(k-1)^2*p + 1/6*(l-1)^3*p - 1/4*(l-1)*(l-2)*p^2 - 1/4*l*(l-1)*p + 1/6*(l-1)*p;
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m = round(m);
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end
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end
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