--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/dramadah.m	Thu May 07 18:36:24 2015 +0200
@@ -0,0 +1,55 @@
+function A = dramadah(n, k)
+%DRAMADAH  A (0,1) matrix whose inverse has large integer entries.
+%          An anti-Hadamard matrix A is a matrix with elements 0 or 1 for
+%          which MU(A) := NORM(INV(A),'FRO') is maximal.
+%          A = DRAMADAH(N, K) is an N-by-N (0,1) matrix for which MU(A) is
+%          relatively large, although not necessarily maximal.
+%          Available types (the default is K = 1):
+%          K = 1: A is Toeplitz, with ABS(DET(A)) = 1, and MU(A) > c(1.75)^N,
+%                 where c is a constant.
+%          K = 2: A is upper triangular and Toeplitz.
+%          The inverses of both types have integer entries.
+%
+%          Another interesting (0,1) matrix:
+%          K = 3: A has maximal determinant among (0,1) lower Hessenberg
+%          matrices: det(A) = the n'th Fibonacci number.  A is Toeplitz.
+%          The eigenvalues have an interesting distribution in the complex
+%          plane.
+
+%          References:
+%          R.L. Graham and N.J.A. Sloane, Anti-Hadamard matrices,
+%             Linear Algebra and Appl., 62 (1984), pp. 113-137.
+%          L. Ching, The maximum determinant of an nxn lower Hessenberg
+%             (0,1) matrix, Linear Algebra and Appl., 183 (1993), pp. 147-153.
+
+if nargin < 2, k = 1; end
+
+if k == 1  % Toeplitz
+
+   c = ones(n,1);
+   for i=2:4:n
+       m = min(1,n-i);
+       c(i:i+m) = zeros(m+1,1);
+   end
+   r = zeros(n,1);
+   r(1:4) = [1 1 0 1];
+   if n < 4, r = r(1:n); end
+   A = toeplitz(c,r);
+
+elseif k == 2  % Upper triangular and Toeplitz
+
+   c = zeros(n,1);
+   c(1) = 1;
+   r = ones(n,1);
+   for i=3:2:n
+       r(i) = 0;
+   end
+   A = toeplitz(c,r);
+
+elseif k == 3  % Lower Hessenberg.
+
+   c = ones(n,1);
+   for i=2:2:n, c(i)=0; end;
+   A = toeplitz(c, [1 1 zeros(1,n-2)]);
+
+end