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annotate toolbox/ipjfact.m @ 2:c124219d7bfa draft

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Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author Antonio Pino Robles <data.script93@gmail.com>
date Thu, 07 May 2015 18:36:24 +0200
parents 8f23314345f4
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1 function [A, detA] = ipjfact(n, k)
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2 %IPJFACT A Hankel matrix with factorial elements.
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3 % A = IPJFACT(N, K) is the matrix with
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4 % A(i,j) = (i+j)! (K = 0, default)
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5 % A(i,j) = 1/(i+j)! (K = 1)
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6 % Both are Hankel matrices.
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7 % The determinant and inverse are known explicitly.
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8 % If a second output argument is present, d = DET(A) is returned:
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9 % [A, d] = IPJFACT(N, K);
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10
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11 % Suggested by P. R. Graves-Morris.
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12 %
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13 % Reference:
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14 % M.J.C. Gover, The explicit inverse of factorial Hankel matrices,
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15 % Dept. of Mathematics, University of Bradford, 1993.
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16
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17 if nargin == 1, k = 0; end
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18
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19 c = cumprod(2:n+1);
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20 d = cumprod(n+1:2*n) * c(n-1);
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21
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22 A = hankel(c, d);
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23
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24 if k == 1
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25 A = ones(n)./A;
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26 end
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27
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28 if nargout == 2
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29 d = 1;
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30 if k == 0
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31 for i=1:n-1
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32 d = d*prod(1:i+1)*prod(1:n-i);
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33 end
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34 d = d*prod(1:n+1);
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35 else
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36 for i=0:n-1
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37 d = d*prod(1:i)/prod(1:n+1+i);
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38 end
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39 if rem(n*(n-1)/2,2), d = -d; end
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40 end
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41 detA = d;
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42 end