Binomial transform: Difference between revisions
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=={{header|Phix}}==
{{trans|C}}
<!--
<syntaxhighlight lang="phix">
with javascript_semantics
function bt_forward(sequence a)
sequence b = {}
for n=1 to length(a) do
atom bn = 0
for k=1 to n do
bn += choose(n-1, k-1) * a[k]
end for
b &= bn
end for
return b
end function
function bt_inverse(sequence b)
sequence a = {}
for n=1 to length(b) do
atom an = 0
for k=1 to n do
integer sgn = iff(odd(n-k) ? -1 : 1)
an += choose(n-1, k-1) * b[k] * sgn
end for
a &= an
end for
return a
end function
function bt_self_inverting(sequence a)
sequence b = {}
for n=1 to length(a) do
atom bn = 0
for k=1 to n do
integer sgn = iff(even(k) ? -1 : 1)
bn += choose(n-1, k-1) * a[k] * sgn
end for
b &= bn
end for
return b
end function
sequence tests = {{"Catalan number sequence:",
{1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012,
742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190}},
{"Prime flip-flop sequence:",
{0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0}},
{"Fibonacci number sequence:",
{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181}},
{"Padovan number sequence:",
{1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37}}}
function jd(sequence s) return join(s," ",fmt:="%d") end function
for t in tests do
sequence {name, s} = t, fwd = bt_forward(s), inv = bt_inverse(s),
si = bt_self_inverting(s)
printf(1,"%s\n%s\n", {name,jd(s)})
printf(1,"Forward binomial transform:\n%s\n",jd(fwd))
printf(1,"Inverse binomial transform:\n%s\n",jd(inv))
printf(1,"Round trip:\n%s\n",jd(bt_inverse(fwd)))
printf(1,"Self-inverting:\n%s\n",jd(si))
printf(1,"Re-inverted:\n%s\n\n",jd(bt_self_inverting(si)))
end for
</syntaxhighlight>
{{out}}
Same as C, etc.
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