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function Ha = renyi_true(p,alpha) % renyi_true computes base-2 Renyi entropy of the input discrete distribution. % % This function returns the scalar Renyi entropy Ha when the input p is a % probability vector, or returns a row vector containing the Renyi entropy % of each column of the input probability matrix p. % % Remarks: % --- Renyi entropy is a non-decreasing function in alpha: % log2(S) = H_0 >= H_1 >= H_2 >= ... >= H_infty % --- Speicial cases of Renyi entropy include: % H_0 = log2(S) % H_1 = H(p) --- Shannon entropy % H_2 = -log2(sum(p.^2)) % H_infty = -log2(max(p)) % Error-check of the input distribution p0 = p(:); if any(imag(p0)) || any(isinf(p0)) || any(isnan(p0)) || any(p0<0) || any(p0>1) error('The probability elements must be real numbers between 0 and 1.'); elseif any(abs(sum(p)-1) > sqrt(eps)) error('Sum of the probability elements must equal 1.'); end if alpha < 0 error('The order of Renyi entropy must be non-negative.'); elseif alpha == 1 Ha = -sum(log2(p.^p)); else Ha = log2(sum(p.^alpha))/(1-alpha); end