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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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1 function A = dramadah(n, k)
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2 %DRAMADAH A (0,1) matrix whose inverse has large integer entries.
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3 % An anti-Hadamard matrix A is a matrix with elements 0 or 1 for
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4 % which MU(A) := NORM(INV(A),'FRO') is maximal.
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5 % A = DRAMADAH(N, K) is an N-by-N (0,1) matrix for which MU(A) is
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6 % relatively large, although not necessarily maximal.
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7 % Available types (the default is K = 1):
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8 % K = 1: A is Toeplitz, with ABS(DET(A)) = 1, and MU(A) > c(1.75)^N,
8f23314345f4 Create local repository for matrix toolboxes. Step #0 done.
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9 % where c is a constant.
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10 % K = 2: A is upper triangular and Toeplitz.
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11 % The inverses of both types have integer entries.
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12 %
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13 % Another interesting (0,1) matrix:
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14 % K = 3: A has maximal determinant among (0,1) lower Hessenberg
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15 % matrices: det(A) = the n'th Fibonacci number. A is Toeplitz.
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16 % The eigenvalues have an interesting distribution in the complex
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17 % plane.
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18
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19 % References:
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20 % R.L. Graham and N.J.A. Sloane, Anti-Hadamard matrices,
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21 % Linear Algebra and Appl., 62 (1984), pp. 113-137.
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22 % L. Ching, The maximum determinant of an nxn lower Hessenberg
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23 % (0,1) matrix, Linear Algebra and Appl., 183 (1993), pp. 147-153.
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24
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25 if nargin < 2, k = 1; end
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26
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27 if k == 1 % Toeplitz
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28
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29 c = ones(n,1);
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30 for i=2:4:n
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31 m = min(1,n-i);
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32 c(i:i+m) = zeros(m+1,1);
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33 end
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34 r = zeros(n,1);
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35 r(1:4) = [1 1 0 1];
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36 if n < 4, r = r(1:n); end
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37 A = toeplitz(c,r);
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38
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39 elseif k == 2 % Upper triangular and Toeplitz
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40
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41 c = zeros(n,1);
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42 c(1) = 1;
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43 r = ones(n,1);
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44 for i=3:2:n
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45 r(i) = 0;
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46 end
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47 A = toeplitz(c,r);
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48
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49 elseif k == 3 % Lower Hessenberg.
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50
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51 c = ones(n,1);
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52 for i=2:2:n, c(i)=0; end;
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53 A = toeplitz(c, [1 1 zeros(1,n-2)]);
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54
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55 end