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Binomial transform: Difference between revisions

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Binomial transform (view source)

Revision as of 10:11, 9 May 2023

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m (→‎{{header|Phix}}: minor tidy)
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">bt_forward</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integersequence</span> <span style="color: #000000;">lb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">){}</span>
<span style="color: #004080008080;">sequencefor</span> <span style="color: #000000;">bn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8000000;">repeat1</span> <span style="color: #0000FF008080;">(to</span> <span style="color: #0000007060A8;">0length</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>▼
<span style="color: #004080;">atom</span> <span style="color: #000000;">bn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">bn</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">choose</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">bn</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">b</span>
Line 806 ⟶ 805:
<span style="color: #008080;">function</span> <span style="color: #000000;">bt_inverse</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integersequence</span> <span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">){}</span>
<span style="color: #004080008080;">sequencefor</span> <span style="color: #000000;">an</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8000000;">repeat1</span> <span style="color: #0000FF008080;">(to</span> <span style="color: #0000007060A8;">0length</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">an</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
Line 814 ⟶ 812:
<span style="color: #000000;">an</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">choose</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">sgn</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">an</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">a</span>
Line 820 ⟶ 818:
<span style="color: #008080;">function</span> <span style="color: #000000;">bt_self_inverting</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integersequence</span> <span style="color: #000000;">lb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">){}</span>
<span style="color: #004080008080;">sequencefor</span> <span style="color: #000000;">bn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8000000;">repeat1</span> <span style="color: #0000FF008080;">(to</span> <span style="color: #0000007060A8;">0length</span><span style="color: #0000FF;">,(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">bn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
Line 828 ⟶ 825:
<span style="color: #000000;">bn</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">choose</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">sgn</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">bn</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">b</span>
Line 846 ⟶ 843:
<span style="color: #008080;">for</span> <span style="color: #000000;">t</span> <span style="color: #008080;">in</span> <span style="color: #000000;">tests</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">name</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">fwd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bt_forward</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">inv</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bt_inverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span>
▲ <span style="color: #008080;">for</span> <span style="color: #000000;">nsi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1bt_self_inverting</span> <span style="color: #0080800000FF;">to(</span> <span style="color: #000000;">ls</span> <span style="color: #0080800000FF;">do)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s\n%s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">name</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)})</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fwd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bt_forward</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">inv</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">bt_inverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Forward binomial transform:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fwd</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Inverse binomial transform:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">inv</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Round trip:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bt_inverse</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fwd</span><span style="color: #0000FF;">)))</span>
<span style="color: #0000007060A8;">fwdprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Self-inverting:\n%s\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bt_self_invertingjd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ssi</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"SelfRe-invertinginverted:\n%s\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fwdbt_self_inverting</span><span style="color: #0000FF;">(</span><span style="color: #000000;">si</span><span style="color: #0000FF;">)))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Re-inverted:\n%s\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bt_self_inverting</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fwd</span><span style="color: #0000FF;">)))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
Same as C, etc.
 
=={{header|Python}}==
Petelomax
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