Binomial transform: Difference between revisions
Added XPL0 example.
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Round trip:
1 0 0 1 0 1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
</pre>
=={{header|XPL0}}==
{{trans|C}}
<syntaxhighlight lang "XPL0">func real Factorial(N);
int N, I;
real F;
[F:= 1.;
for I:= 2 to N do F:= F * float(I);
return F;
];
func real Binomial(N, K);
int N, K;
return Factorial(N) / Factorial(N-K) / Factorial(K);
proc BinomialFwd(A, B, M);
real A, B; int M;
int N, K;
[for N:= 0 to M-1 do
[B(N):= 0.;
for K:= 0 to N do
B(N):= B(N) + Binomial(N, K) * A(K);
];
];
proc BinomialInv(A, B, M);
real A, B; int M;
int N, K, Sign;
[for N:= 0 to M-1 do
[A(N):= 0.;
for K:= 0 to N do
[Sign:= if N-K & 1 then -1 else 1;
A(N):= A(N) + float(Sign) * Binomial(N, K) * B(K);
];
];
];
real Fwd(20), Inv(20), Seqs;
int Title, I, J;
[Seqs:= [
[1., 1., 2., 5., 14., 42., 132., 429., 1430., 4862., 16796., 58786., 208012.,
742900., 2674440., 9694845., 35357670., 129644790., 477638700., 1767263190.],
[0., 1., 1., 0., 1., 0., 1., 0., 0., 0., 1., 0., 1., 0., 0., 0., 1., 0., 1., 0.],
[0., 1., 1., 2., 3., 5., 8., 13., 21., 34., 55., 89., 144., 233., 377., 610.,
987., 1597., 2584., 4181.],
[1., 0., 0., 1., 0., 1., 1., 1., 2., 2., 3., 4., 5., 7., 9., 12., 16., 21., 28., 37.]];
Title:= [
"Catalan number sequence:",
"Prime flip-flop sequence:",
"Fibonacci number sequence:",
"Padovan number sequence:" ];
Format(1,0);
for I:= 0 to 4-1 do
[Text(0, Title(I)); CrLf(0);
for J:= 0 to 20-1 do [RlOut(0, Seqs(I,J)); ChOut(0, ^ )];
Text(0, "^m^jForward binomial transform:^m^j");
BinomialFwd(Seqs(I), Fwd, 20);
for J:= 0 to 20-1 do [RlOut(0, Fwd(J)); ChOut(0, ^ )];
Text(0, "^m^jInverse binomial transform:^m^j");
BinomialInv(Inv, Seqs(I), 20);
for J:= 0 to 20-1 do [RlOut(0, Inv(J)); ChOut(0, ^ )];
Text(0, "^m^jRound trip:^m^j");
BinomialInv(Inv, Fwd, 20);
for J:= 0 to 20-1 do [RlOut(0, Inv(J)); ChOut(0, ^ )];
if I < 3 then CrLf(0);
CrLf(0);
];
]</syntaxhighlight>
{{out}}
<pre>
Catalan number sequence:
1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440 9694845 35357670 129644790 477638700 1767263190
Forward binomial transform:
1 2 5 15 51 188 731 2950 12235 51822 223191 974427 4302645 19181100 86211885 390248055 1777495635 8140539950 37463689775 173164232965
Inverse binomial transform:
1 0 1 1 3 6 15 36 91 232 603 1585 4213 11298 30537 83097 227475 625992 1730787 4805595
Round trip:
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
Forward binomial transform:
0 1 3 6 11 20 37 70 134 255 476 869 1564 2821 5201 9948 19793 40562 84271 174952
Inverse binomial transform:
0 1 -1 0 3 -10 25 -56 118 -237 456 -847 1540 -2795 5173 -9918 19761 -40528 84235 -174914
Round trip:
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
Forward binomial transform:
0 1 3 8 21 55 144 377 987 2584 6765 17711 46368 121393 317811 832040 2178309 5702887 14930352 39088169
Inverse binomial transform:
0 1 -1 2 -3 5 -8 13 -21 34 -55 89 -144 233 -377 610 -987 1597 -2584 4181
Round trip:
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
Forward binomial transform:
1 1 1 2 5 12 28 65 151 351 816 1897 4410 10252 23833 55405 128801 299426 696081 1618192
Inverse binomial transform:
1 -1 1 0 -3 10 -24 49 -89 145 -208 245 -174 -176 1121 -3185 7137 -13920 24301 -37926
Round trip:
1 0 0 1 0 1 1 1 2 2 3 4 5 7 9 12 16 21 28 37
</pre>
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