Basic functions

Functions related to codes

function entropy(pmf, base)
    pmf = pmf/sum(pmf)
    return sum(pmf.*log(1./pmf)/log(base))
end
entropy(pmf) = entropy(pmf, 2)

entropy (generic function with 2 methods)

avgLength(code, pmf) = sum(map(length, code).*pmf)/sum(pmf)

avgLength (generic function with 1 method)

function blockPmf(pmf1, n, pmfm)
# Input pmf1: the probability vector of single symbols.
# Input pmfm: the probability vector of symbols of block length m
# Output pmfn: the pmf of symbols of block length n
    m = floor(log(length(pmfm))/log(length(pmf1)))
    pmfn = copy(pmfm)
    for k = m+1:n
        pmfn_next = Float64[]
        for p in pmfn
            push!(pmfn_next, p.*pmf1...)
        end
        pmfn = copy(pmfn_next)
    end
    return pmfn
end
blockPmf(pmf1, n) = blockPmf(pmf1, n, pmf1)

blockPmf (generic function with 2 methods)

Functions of collections

function minValues(A, r) 
# returns the r smallest numbers in A, and also removes the values from the original list
# r should be positive integer
    min_vals = Float64[]
    idx_list = Int64[]
    for i = 1:r
        (min, idx) = findmin(A)
        append!(idx_list, idx)
        deleteat!(A, idx)
        append!(min_vals, min)
    end
    return min_vals, idx_list
end

minValues (generic function with 1 method)

Functions for testing coding schemes

function testScheme(args...)
    if length(args) == 3
        (f, base, pmf) = args
        code = f(pmf, base)
        scale = log(base)/log(2)
    elseif length(args) == 2
        (f, pmf) = args
        base = 2
        code = f(pmf)
        scale = 1
    end
    print("---------------------------\n")
    print("Testing scheme: ", f, ".\n")
    print("pmf: ", pmf, "\n")
    print("Code: ", code, ".\n")
    pmf = pmf/sum(pmf)
    print("The average length: \t", avgLength(code, pmf)*scale, " [bits].\n")
    pmf = pmf[pmf .> 0]
    print("The entropy of the pmf: ", entropy(pmf), " [bits].\n\n")
end

testScheme (generic function with 1 method)

function testMultiSchemes(fs, bases, pmf)
    scales = log(bases)/log(2)
    print("---------------------------\n")
    print("pmf: ", pmf, "\n")
    pmf = pmf[pmf .> 0]
    n = length(pmf)
    print("The entropy of the pmf: ", entropy(pmf), " [bits].\n\n")
    for i in 1:length(fs)
        code = fs[i](pmf, bases[i])
        print(pmf/sum(pmf), "\n")
        print(fs[i], 
        " w/ base: ", bases[i], 
        ", code: ", code, 
        ", the average length: ", avgLength(code[1:n], pmf)*scales[i], " [bits].\n")
    end
end

testMultiSchemes (generic function with 1 method)