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