64 lines
2.3 KiB
Matlab
64 lines
2.3 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 [DP6,DP6inv] = Q6_plication(p,progress)
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if nargin <2
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progress =0;
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end
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reverseStr = ''; counti=1;
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np = p*(p+1)*(p+2)*(p+3)*(p+4)*(p+5)/(1*2*3*4*5*6);
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DP6 = spalloc(p^6,p*(p+1)*(p+2)*(p+3)*(p+4)*(p+5)/(1*2*3*4*5*6),p^6);
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for i1=1:p
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for i2=i1:p
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for i3=i2:p
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for i4=i3:p
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for i5=i4:p
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for i6=i5:p
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if progress && (rem(counti,100)== 0)
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msg = sprintf(' Q6-plication 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(' Q6-plication 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([i6 i5 i4 i3 i2 i1]);
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for r = 1:size(idx,1)
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ii1 = idx(r,1); ii2= idx(r,2); ii3=idx(r,3); ii4=idx(r,4); ii5=idx(r,5); ii6=idx(r,6);
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n = ii1 + (ii2-1)*p + (ii3-1)*p^2 + (ii4-1)*p^3 + (ii5-1)*p^4 + (ii6-1)*p^5;
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m = mue(p,i6,i5,i4,i3,i2,i1);
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DP6(n,m)=1;
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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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end
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end
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DP6inv = (transpose(DP6)*DP6)\transpose(DP6);
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function m = mue(p,i1,i2,i3,i4,i5,i6)
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m = binom_coef(p,6,1) - binom_coef(p,1,i1+1) - binom_coef(p,2,i2+1) - binom_coef(p,3,i3+1) - binom_coef(p,4,i4+1) - binom_coef(p,5,i5+1) - binom_coef(p,6,i6+1);
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m = round(m);
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end
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function N = binom_coef(p,q,i)
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t = q; r =p+q-i;
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if t==0
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N=1;
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else
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N=1;
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for h = 0:(t-1)
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N = N*(r-h);
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end
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N=N/factorial(t);
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end
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end
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end
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