https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&feed=atom&action=history
Gamma and Beta function - Revision history
2024-03-19T03:32:33Z
Revision history for this page on the wiki
MediaWiki 1.35.5
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=32498&oldid=prev
Newacct at 10:18, 13 December 2009
2009-12-13T10:18:09Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:18, 13 December 2009</td>
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<td colspan="2" class="diff-lineno">Line 9:</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gammaln :: Double -> Double</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gammaln xx = let tmp' = (xx+5.5) - (xx+0.5)*log(xx+5.5)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gammaln xx = let tmp' = (xx+5.5) - (xx+0.5)*log(xx+5.5)</div></td>
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<td class="diff-marker">−</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> ser' = <del class="diffchange diffchange-inline">foldl</del> <del class="diffchange diffchange-inline">(</del>+<del class="diffchange diffchange-inline">)</del> <del class="diffchange diffchange-inline">ser</del> $ <del class="diffchange diffchange-inline">map</del> (<del class="diffchange diffchange-inline">\(y,c</del>) <del class="diffchange diffchange-inline">-></del> <del class="diffchange diffchange-inline">c/(</del>xx+<del class="diffchange diffchange-inline">y)) $ zip [</del>1..]<del class="diffchange diffchange-inline"> cof</del></div></td>
<td class="diff-marker">+</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> ser' = <ins class="diffchange diffchange-inline">ser</ins> + <ins class="diffchange diffchange-inline">sum</ins> $ <ins class="diffchange diffchange-inline">zipWith</ins> (<ins class="diffchange diffchange-inline">/</ins>) <ins class="diffchange diffchange-inline">cof</ins> <ins class="diffchange diffchange-inline">[</ins>xx+1..]</div></td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> in -tmp' + log(2.5066282746310005 * ser' / xx)</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> in -tmp' + log(2.5066282746310005 * ser' / xx)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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Newacct
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=25546&oldid=prev
Lazor: removed unnecessary 'where'
2009-01-07T17:14:47Z
<p>removed unnecessary 'where'</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:14, 7 January 2009</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gammaln xx = let tmp' = (xx+5.5) - (xx+0.5)*log(xx+5.5)</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gammaln xx = let tmp' = (xx+5.5) - (xx+0.5)*log(xx+5.5)</div></td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ser' = foldl (+) ser $ map (\(y,c) -> c/(xx+y)) $ zip [1..] cof</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ser' = foldl (+) ser $ map (\(y,c) -> c/(xx+y)) $ zip [1..] cof</div></td>
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<td class="diff-marker">−</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> in -tmp' + log(2.5066282746310005 * ser' / xx)<del class="diffchange diffchange-inline"> where</del></div></td>
<td class="diff-marker">+</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> in -tmp' + log(2.5066282746310005 * ser' / xx)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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Lazor
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=22393&oldid=prev
Lemming: parentheses
2008-08-11T15:20:49Z
<p>parentheses</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:20, 11 August 2008</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><haskell></div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><haskell></div></td>
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<td class="diff-marker">−</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>beta z w = exp <del class="diffchange diffchange-inline">(</del>(gammaln z<del class="diffchange diffchange-inline">)</del> + <del class="diffchange diffchange-inline">(</del>gammaln w<del class="diffchange diffchange-inline">)</del> - <del class="diffchange diffchange-inline">(</del>gammaln (z+w))</div></td>
<td class="diff-marker">+</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>beta z w = exp (gammaln z + gammaln w - gammaln (z+w))</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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Lemming
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=22392&oldid=prev
Lemming: dot
2008-08-11T15:20:13Z
<p>dot</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:20, 11 August 2008</td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
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<td class="diff-marker">−</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>the beta function relates to the gamma function by <math>\Beta(z,w)= \frac{\Gamma(z)<del class="diffchange diffchange-inline">*</del>\Gamma(w)}{\Gamma(z+w)}</math>, so we can compute the Beta function using gammaln like this:</div></td>
<td class="diff-marker">+</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>the beta function relates to the gamma function by <math>\Beta(z,w)= \frac{\Gamma(z)<ins class="diffchange diffchange-inline">\cdot</ins>\Gamma(w)}{\Gamma(z+w)}</math>, so we can compute the Beta function using gammaln like this:</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><haskell></div></td>
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Lemming
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=22391&oldid=prev
Lemming: Gamma symbol
2008-08-11T15:19:51Z
<p>Gamma symbol</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:19, 11 August 2008</td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></haskell></div></td>
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<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
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<td class="diff-marker">−</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>the beta function relates to the gamma function by <math><del class="diffchange diffchange-inline">B</del>(z,w)= \frac{Gamma(z)*Gamma(w)}{Gamma(z+w)}</math>, so we can compute the Beta function using gammaln like this:</div></td>
<td class="diff-marker">+</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>the beta function relates to the gamma function by <math><ins class="diffchange diffchange-inline">\Beta</ins>(z,w)= \frac{<ins class="diffchange diffchange-inline">\</ins>Gamma(z)*<ins class="diffchange diffchange-inline">\</ins>Gamma(w)}{<ins class="diffchange diffchange-inline">\</ins>Gamma(z+w)}</math>, so we can compute the Beta function using gammaln like this:</div></td>
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<td class="diff-marker"> </td>
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Lemming
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=15237&oldid=prev
Lazor at 02:20, 23 August 2007
2007-08-23T02:20:03Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:20, 23 August 2007</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><haskell></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><haskell></div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>cof :: [Double]</div></td>
<td class="diff-marker"> </td>
<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>cof :: [Double]</div></td>
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<td class="diff-marker">−</td>
<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>cof = [76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,0.<del class="diffchange diffchange-inline">01208650973866179</del>,-0.<del class="diffchange diffchange-inline">00005395239384953</del>]</div></td>
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<td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>cof = [76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,0.<ins class="diffchange diffchange-inline">001208650973866179</ins>,-0.<ins class="diffchange diffchange-inline">000005395239384953</ins>]</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>ser :: Double</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>ser :: Double</div></td>
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Lazor
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=15236&oldid=prev
Lazor at 02:14, 23 August 2007
2007-08-23T02:14:29Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:14, 23 August 2007</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>beta z w = exp ((gammaln z) + (gammaln w) - (gammaln (z+w))</div></td>
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Lazor
https://wiki.haskell.org/index.php?title=Gamma_and_Beta_function&diff=15235&oldid=prev
Lazor at 02:14, 23 August 2007
2007-08-23T02:14:08Z
<p></p>
<p><b>New page</b></p><div>The Gamma and Beta function as described in 'Numerical Recipes in C++', the approximation is taken from [Lanczos, C. 1964 SIAM Journal on Numerical Analysis, ser. B, vol. 1, pp. 86-96]<br />
<haskell><br />
cof :: [Double]<br />
cof = [76.18009172947146,-86.50532032941677,24.01409824083091,-1.231739572450155,0.01208650973866179,-0.00005395239384953]<br />
<br />
ser :: Double<br />
ser = 1.000000000190015<br />
<br />
gammaln :: Double -> Double<br />
gammaln xx = let tmp' = (xx+5.5) - (xx+0.5)*log(xx+5.5)<br />
ser' = foldl (+) ser $ map (\(y,c) -> c/(xx+y)) $ zip [1..] cof<br />
in -tmp' + log(2.5066282746310005 * ser' / xx) where<br />
</haskell><br />
<br />
the beta function relates to the gamma function by <math>B(z,w)= \frac{Gamma(z)*Gamma(w)}{Gamma(z+w)}</math>, so we can compute the Beta function using gammaln like this:<br />
<br />
<haskell><br />
beta z w = exp ((gammaln z) + (gammaln w) - (gammaln (z+w))<br />
</haskell></div>
Lazor