function A = fiedler(c)
%FIEDLER Fiedler matrix - symmetric.
% A = FIEDLER(C), where C is an n-vector, is the n-by-n symmetric
% matrix with elements ABS(C(i)-C(j)).
% Special case: if C is a scalar, then A = FIEDLER(1:C)
% (i.e. A(i,j) = ABS(i-j)).
% Properties:
% FIEDLER(N) has a dominant positive eigenvalue and all the other
% eigenvalues are negative (Szego 1936).
% Explicit formulas for INV(A) and DET(A) are given in (Todd 1977)
% and attributed to Fiedler. These indicate that INV(A) is
% tridiagonal except for nonzero (1,n) and (n,1) elements.
% [I think these formulas are valid only if the elements of
% C are in increasing or decreasing order---NJH.]
% References:
% G. Szego, Solution to problem 3705, Amer. Math. Monthly,
% 43 (1936), pp. 246-259.
% J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra,
% Birkhauser, Basel, and Academic Press, New York, 1977, p. 159.
n = max(size(c));
% Handle scalar c.
if n == 1
n = c;
c = 1:n;
end
c = c(:).'; % Ensure c is a row vector.
A = ones(n,1)*c;
A = abs(A - A.'); % NB. array transpose.