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date	Wed, 20 Jan 2016 09:23:18 -0500
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0 4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	1 <html>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	2 <head>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	3 <title>MayaChemTools:Code:StatisticsUtil.pm</title>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	4 <meta http-equiv="content-type" content="text/html;charset=utf-8">
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	5 <link rel="stylesheet" type="text/css" href="../../../css/MayaChemToolsCode.css">
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	6 </head>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	7 <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10">
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	8 <br/>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	9 <center>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	10 <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	11 </center>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	12 <br/>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	13 <pre>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	14 <a name="package-StatisticsUtil-"></a> 1 <span class="k">package </span><span class="i">StatisticsUtil</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	15 2 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	16 3 <span class="c"># $RCSfile: StatisticsUtil.pm,v $</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	17 4 <span class="c"># $Date: 2015/02/28 20:47:18 $</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	18 5 <span class="c"># $Revision: 1.41 $</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	19 6 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	20 7 <span class="c"># Author: Manish Sud <msud@san.rr.com></span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	21 8 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	22 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	23 10 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	24 11 <span class="c"># This file is part of MayaChemTools.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	25 12 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	26 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	27 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	28 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	29 16 <span class="c"># later version.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	30 17 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	31 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	32 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	33 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	34 21 <span class="c"># details.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	35 22 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	36 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	37 24 <span class="c"># along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	38 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	39 26 <span class="c"># Boston, MA, 02111-1307, USA.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	40 27 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	41 28
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	42 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	43 30 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	44 31
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	45 32 <span class="k">use</span> <span class="w">vars</span> <span class="q">qw(@ISA @EXPORT @EXPORT_OK %EXPORT_TAGS)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	46 33
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	47 34 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	48 35 <span class="i">@EXPORT</span> = <span class="q">qw(Average AverageDeviation Covariance Correlation Euclidean Factorial FactorialDivison GeometricMean Frequency HarmonicMean KLargest KSmallest Kurtosis Maximum Minimum Mean Median Mode PearsonCorrelation Permutations Product Range RSquare Skewness Sum SumOfSquares StandardDeviation StandardDeviationN StandardError Standardize StandardScores StandardScoresN TrimMean Variance VarianceN)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	49 36 <span class="i">@EXPORT_OK</span> = <span class="q">qw()</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	50 37 <span class="i">%EXPORT_TAGS</span> = <span class="s">(</span><span class="w">all</span> <span class="cm">=></span> <span class="s">[</span><span class="i">@EXPORT</span><span class="cm">,</span> <span class="i">@EXPORT_OK</span><span class="s">]</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	51 38
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	52 39 <span class="c"># Compute the mean of an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	53 <a name="Average-"></a> 40 <span class="k">sub </span><span class="m">Average</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	54 41 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	55 42 <span class="k">return</span> <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	56 43 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	57 44
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	58 45 <span class="c"># Compute the average of the absolute deviation of an array of numbers: SUM( ABS(x[i] - Xmean) ) / n</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	59 <a name="AverageDeviation-"></a> 46 <span class="k">sub </span><span class="m">AverageDeviation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	60 47 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	61 48
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	62 49 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	63 50 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	64 51 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	65 52 <span class="k">my</span><span class="s">(</span><span class="i">$AverageDeviation</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SumOfDeviations</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	66 53
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	67 54 <span class="i">$AverageDeviation</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	68 55 <span class="i">$Mean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	69 56 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	70 57 <span class="i">$SumOfDeviations</span> += <span class="k">abs</span><span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	71 58 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	72 59 <span class="i">$AverageDeviation</span> = <span class="i">$SumOfDeviations</span> / <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	73 60
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	74 61 <span class="k">return</span> <span class="i">$AverageDeviation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	75 62 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	76 63
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	77 64 <span class="c"># Compute correlation coefficient between two arrays of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	78 <a name="Correlation-"></a> 65 <span class="k">sub </span><span class="m">Correlation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	79 66 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$YArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	80 67 <span class="k">return</span> <span class="i">PearsonCorrelation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$YArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	81 68 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	82 69
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	83 70 <span class="c"># Compute the covariance between two arrays of numbers: SUM( (x[i] - Xmean) (y[i] - Ymean) ) / n</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	84 <a name="Covariance-"></a> 71 <span class="k">sub </span><span class="m">Covariance</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	85 72 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$YArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	86 73
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	87 74 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">@$XArrayRef</span> && <span class="i">@$YArrayRef</span> && <span class="s">(</span><span class="i">@$XArrayRef</span> == <span class="i">@$YArrayRef</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	88 75 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	89 76 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	90 77 <span class="k">my</span><span class="s">(</span><span class="i">$Covariance</span><span class="cm">,</span> <span class="i">$XMean</span><span class="cm">,</span> <span class="i">$YMean</span><span class="cm">,</span> <span class="i">$Index</span><span class="cm">,</span> <span class="i">$ProductOfDeviations</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	91 78
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	92 79 <span class="i">$Covariance</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	93 80 <span class="i">$XMean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	94 81 <span class="i">$YMean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$YArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	95 82 <span class="i">$ProductOfDeviations</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	96 83 <span class="k">for</span> <span class="i">$Index</span> <span class="s">(</span><span class="n">0</span> .. <span class="i">$#</span>{<span class="i">@$XArrayRef</span>}<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	97 84 <span class="i">$ProductOfDeviations</span> += <span class="s">(</span><span class="s">(</span><span class="i">$XArrayRef</span>->[<span class="i">$Index</span>] - <span class="i">$XMean</span><span class="s">)</span> * <span class="s">(</span><span class="i">$YArrayRef</span>->[<span class="i">$Index</span>] - <span class="i">$YMean</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	98 85 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	99 86 <span class="i">$Covariance</span> = <span class="i">$ProductOfDeviations</span> / <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	100 87 <span class="k">return</span> <span class="i">$Covariance</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	101 88 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	102 89
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	103 90 <span class="c"># Compute the euclidean distance of an array of numbers: SQRT( SUM( x[i] ** 2) )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	104 <a name="Euclidean-"></a> 91 <span class="k">sub </span><span class="m">Euclidean</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	105 92 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	106 93
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	107 94 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	108 95 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	109 96 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	110 97 <span class="k">my</span><span class="s">(</span><span class="i">$SumOfSquares</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	111 98
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	112 99 <span class="i">$SumOfSquares</span> = <span class="i">SumOfSquares</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	113 100
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	114 101 <span class="k">return</span> <span class="k">sqrt</span> <span class="i">$SumOfSquares</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	115 102 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	116 103
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	117 104 <span class="c"># Compute factorial of a number...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	118 <a name="Factorial-"></a> 105 <span class="k">sub </span><span class="m">Factorial</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	119 106 <span class="k">my</span><span class="s">(</span><span class="i">$Num</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	120 107
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	121 108 <span class="k">return</span> <span class="i">_Factorial</span><span class="s">(</span><span class="i">$Num</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	122 109 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	123 110
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	124 111 <span class="c"># Perform factorial division of two numbers...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	125 <a name="FactorialDivison-"></a> 112 <span class="k">sub </span><span class="m">FactorialDivison</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	126 113 <span class="k">my</span><span class="s">(</span><span class="i">$Numerator</span><span class="cm">,</span> <span class="i">$Denominator</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	127 114
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	128 115 <span class="c"># Only works for integer numbers...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	129 116 <span class="k">if</span> <span class="s">(</span><span class="i">$Numerator</span> <= <span class="n">0</span> \|\| <span class="s">(</span><span class="i">$Numerator</span> != <span class="k">int</span><span class="s">(</span><span class="i">$Numerator</span><span class="s">)</span><span class="s">)</span> \|\|
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	130 117 <span class="i">$Denominator</span> <= <span class="n">0</span> \|\| <span class="s">(</span><span class="i">$Denominator</span> != <span class="k">int</span><span class="s">(</span><span class="i">$Denominator</span><span class="s">)</span><span class="s">)</span> <span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	131 118 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	132 119 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	133 120 <span class="k">my</span><span class="s">(</span><span class="i">$LargerNum</span><span class="cm">,</span> <span class="i">$SmallerNum</span><span class="cm">,</span> <span class="i">$Result</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	134 121 <span class="i">$LargerNum</span> = <span class="s">(</span><span class="i">$Numerator</span> > <span class="i">$Denominator</span><span class="s">)</span> ? <span class="i">$Numerator</span> <span class="co">:</span> <span class="i">$Denominator</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	135 122 <span class="i">$SmallerNum</span> = <span class="s">(</span><span class="i">$Numerator</span> < <span class="i">$Denominator</span><span class="s">)</span> ? <span class="i">$Numerator</span> <span class="co">:</span> <span class="i">$Denominator</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	136 123
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	137 124 <span class="i">$Result</span> = <span class="i">_Factorial</span><span class="s">(</span><span class="i">$LargerNum</span><span class="cm">,</span> <span class="i">$SmallerNum</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	138 125 <span class="k">if</span> <span class="s">(</span><span class="i">$Numerator</span> < <span class="i">$Denominator</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	139 126 <span class="i">$Result</span> = <span class="n">1</span>/<span class="i">$Result</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	140 127 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	141 128 <span class="k">return</span> <span class="i">$Result</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	142 129 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	143 130
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	144 131 <span class="c"># Calculate factorial of a number upto a specific limit...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	145 <a name="_Factorial-"></a> 132 <span class="k">sub </span><span class="m">_Factorial</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	146 133 <span class="k">my</span><span class="s">(</span><span class="i">$Num</span><span class="cm">,</span> <span class="i">$Limit</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	147 134
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	148 135 <span class="c"># Only works for integer numbers...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	149 136 <span class="k">if</span> <span class="s">(</span><span class="i">$Num</span> <= <span class="n">0</span> \|\| <span class="s">(</span><span class="i">$Num</span> != <span class="k">int</span><span class="s">(</span><span class="i">$Num</span><span class="s">)</span><span class="s">)</span> \|\| <span class="i">$Limit</span> < <span class="n">1</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	150 137 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	151 138 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	152 139
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	153 140 <span class="k">my</span><span class="s">(</span><span class="i">$Result</span><span class="s">)</span> = <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	154 141
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	155 142 <span class="k">while</span> <span class="s">(</span><span class="i">$Num</span> > <span class="i">$Limit</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	156 143 <span class="i">$Result</span> *= <span class="i">$Num</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	157 144 <span class="i">$Num</span>--<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	158 145 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	159 146 <span class="k">return</span> <span class="i">$Result</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	160 147 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	161 148
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	162 149 <span class="c"># Generate all possible permuations or a specific permutations of items in an array</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	163 150 <span class="c"># and return a reference to an array containing array references to generated permuations...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	164 151 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	165 152 <span class="c"># This alogrithm is based on the example provided by Mark Jason-Dominus, and is available</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	166 153 <span class="c"># at CPAN as mjd_permute standalone script.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	167 154 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	168 <a name="Permutations-"></a> 155 <span class="k">sub </span><span class="m">Permutations</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	169 156 <span class="k">my</span><span class="s">(</span><span class="i">@DataToPermute</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	170 157 <span class="k">my</span><span class="s">(</span><span class="i">$PermutationNum</span><span class="cm">,</span> <span class="i">$NumOfPermutations</span><span class="cm">,</span> <span class="i">@Permutations</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	171 158
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	172 159 <span class="k">if</span> <span class="s">(</span>!<span class="i">@DataToPermute</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	173 160 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	174 161 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	175 162
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	176 163 <span class="i">@Permutations</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	177 164 <span class="i">$NumOfPermutations</span> = <span class="i">Factorial</span><span class="s">(</span><span class="k">scalar</span> <span class="i">@DataToPermute</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	178 165
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	179 166 <span class="k">for</span> <span class="s">(</span><span class="i">$PermutationNum</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$PermutationNum</span> < <span class="i">$NumOfPermutations</span><span class="sc">;</span> <span class="i">$PermutationNum</span>++<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	180 167 <span class="k">my</span> <span class="i">@Permutation</span> = <span class="i">@DataToPermute</span>[<span class="i">_PermutationNumToPermutation</span><span class="s">(</span><span class="i">$PermutationNum</span><span class="cm">,</span> <span class="i">$#DataToPermute</span><span class="s">)</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	181 168 <span class="k">push</span> <span class="i">@Permutations</span><span class="cm">,</span> \<span class="i">@Permutation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	182 169 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	183 170
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	184 171 <span class="k">return</span> \<span class="i">@Permutations</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	185 172 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	186 173
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	187 174 <span class="c"># Generte Nth permutation for a collection of specific size...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	188 175 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	189 <a name="_PermutationNumToPermutation-"></a> 176 <span class="k">sub </span><span class="m">_PermutationNumToPermutation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	190 177 <span class="k">my</span><span class="s">(</span><span class="i">$Num</span><span class="cm">,</span> <span class="i">$Size</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	191 178
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	192 179 <span class="k">return</span> <span class="i">_PatternToPermutation</span><span class="s">(</span><span class="i">_PermutationNumToPattern</span><span class="s">(</span><span class="i">$Num</span><span class="cm">,</span> <span class="i">$Size</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	193 180 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	194 181
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	195 182 <span class="c"># Generate Nth pattern for a collection of specific size...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	196 183 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	197 <a name="_PermutationNumToPattern-"></a> 184 <span class="k">sub </span><span class="m">_PermutationNumToPattern</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	198 185 <span class="k">my</span><span class="s">(</span><span class="i">$Num</span><span class="cm">,</span> <span class="i">$Size</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	199 186 <span class="k">my</span><span class="s">(</span><span class="i">$Index</span><span class="cm">,</span> <span class="i">@Pattern</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	200 187
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	201 188 <span class="i">$Index</span> = <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	202 189
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	203 190 <span class="k">while</span> <span class="s">(</span><span class="i">$Index</span> <= <span class="i">$Size</span> + <span class="n">1</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	204 191 <span class="k">push</span> <span class="i">@Pattern</span><span class="cm">,</span> <span class="i">$Num</span> % <span class="i">$Index</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	205 192 <span class="i">$Num</span> = <span class="k">int</span><span class="s">(</span><span class="i">$Num</span>/<span class="i">$Index</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	206 193 <span class="i">$Index</span>++<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	207 194 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	208 195
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	209 196 <span class="k">return</span> <span class="i">@Pattern</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	210 197 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	211 198
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	212 199 <span class="c"># Generate permutation of integers from pattern...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	213 200 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	214 <a name="_PatternToPermutation-"></a> 201 <span class="k">sub </span><span class="m">_PatternToPermutation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	215 202 <span class="k">my</span><span class="s">(</span><span class="i">@Pattern</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	216 203 <span class="k">my</span><span class="s">(</span><span class="i">@Source</span><span class="cm">,</span> <span class="i">@Permutation</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	217 204
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	218 205 <span class="i">@Source</span> = <span class="s">(</span><span class="n">0</span> .. <span class="i">$#Pattern</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	219 206
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	220 207 <span class="k">while</span> <span class="s">(</span><span class="i">@Pattern</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	221 208 <span class="k">push</span> <span class="i">@Permutation</span><span class="cm">,</span> <span class="k">splice</span><span class="s">(</span><span class="i">@Source</span><span class="cm">,</span> <span class="s">(</span><span class="k">pop</span> <span class="i">@Pattern</span><span class="s">)</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	222 209 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	223 210
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	224 211 <span class="k">return</span> <span class="i">@Permutation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	225 212 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	226 213
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	227 214 <span class="c"># Compute the frequency of occurance of values in an array of numbers. Three different</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	228 215 <span class="c"># invocation methods are supported:</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	229 216 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	230 217 <span class="c"># Frequency(\@ArrayRef) : Using the smallest and largest values, group the numbers into</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	231 218 <span class="c"># 10 bins.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	232 219 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	233 220 <span class="c"># Frequency(\@ArrayRef, $NumOfBins) : Using the smallest and largest values, group the</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	234 221 <span class="c"># numbers into specified bins.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	235 222 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	236 223 <span class="c"># Frequency(\@ArrayRef, \@BinRange): Use bin range to goup the values into different bins.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	237 224 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	238 225 <span class="c"># A hash array is returned with keys and values representing range and frequency values respectively.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	239 226 <span class="c"># The frequency value for a specific key corresponds to all the values which are greater than</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	240 227 <span class="c"># the previous key and less than or equal to the current key. A key value representing maximum value is</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	241 228 <span class="c"># added for generating frequency distribution for specific number of bins, and whenever the maximum</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	242 229 <span class="c"># array value is greater than the maximum specified in bin range, it is also added to bin range.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	243 230 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	244 <a name="Frequency-"></a> 231 <span class="k">sub </span><span class="m">Frequency</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	245 232 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	246 233
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	247 234 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	248 235 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	249 236 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	250 237
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	251 238 <span class="k">my</span><span class="s">(</span><span class="i">$BinRange</span><span class="cm">,</span> <span class="i">$NumOfBins</span><span class="cm">,</span> <span class="i">$BinRangeSpecified</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	252 239
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	253 240 <span class="i">$BinRangeSpecified</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	254 241 <span class="i">$NumOfBins</span> = <span class="n">10</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	255 242 <span class="k">if</span> <span class="s">(</span><span class="i">@_</span> == <span class="n">2</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	256 243 <span class="k">if</span> <span class="s">(</span><span class="k">ref</span><span class="s">(</span><span class="i">$_</span>[<span class="n">1</span>]<span class="s">)</span> <span class="k">eq</span> <span class="q">'ARRAY'</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	257 244 <span class="i">$BinRange</span> = <span class="i">$_</span>[<span class="n">1</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	258 245 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">@$BinRange</span> && <span class="s">(</span><span class="i">@$BinRange</span> > <span class="n">1</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	259 246 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	260 247 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	261 248 <span class="c"># Make sure the bin range contains values in increasing order...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	262 249 <span class="k">my</span><span class="s">(</span><span class="i">$Index1</span><span class="cm">,</span> <span class="i">$Index2</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	263 250 <span class="k">for</span> <span class="i">$Index1</span> <span class="s">(</span><span class="n">0</span> .. <span class="i">$#</span>{<span class="i">@$BinRange</span>}<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	264 251 <span class="k">for</span> <span class="i">$Index2</span> <span class="s">(</span><span class="s">(</span><span class="i">$Index1</span> + <span class="n">1</span><span class="s">)</span> .. <span class="i">$#</span>{<span class="i">@$BinRange</span>}<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	265 252 <span class="k">if</span> <span class="s">(</span><span class="i">$BinRange</span>->[<span class="i">$Index1</span>] >= <span class="i">$BinRange</span>->[<span class="i">$Index2</span>]<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	266 253 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	267 254 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	268 255 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	269 256 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	270 257 <span class="i">$BinRangeSpecified</span> = <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	271 258 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	272 259 <span class="k">else</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	273 260 <span class="i">$NumOfBins</span> = <span class="i">$_</span>[<span class="n">1</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	274 261 <span class="k">if</span> <span class="s">(</span><span class="i">$NumOfBins</span> <= <span class="n">1</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	275 262 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	276 263 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	277 264 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	278 265 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	279 266
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	280 267 <span class="c"># Setup range keys...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	281 268 <span class="k">my</span><span class="s">(</span><span class="i">@RangeKeys</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	282 269 <span class="i">@RangeKeys</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	283 270
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	284 271 <span class="k">my</span><span class="s">(</span><span class="i">$MinValue</span><span class="cm">,</span> <span class="i">$MaxValue</span><span class="s">)</span> = <span class="i">Range</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	285 272 <span class="k">if</span> <span class="s">(</span><span class="i">$BinRangeSpecified</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	286 273 <span class="k">push</span> <span class="i">@RangeKeys</span><span class="cm">,</span> <span class="i">@$BinRange</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	287 274 <span class="k">if</span> <span class="s">(</span><span class="i">$MaxValue</span> > <span class="i">$RangeKeys</span>[<span class="i">$#RangeKeys</span>]<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	288 275 <span class="k">push</span> <span class="i">@RangeKeys</span><span class="cm">,</span> <span class="i">$MaxValue</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	289 276 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	290 277 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	291 278 <span class="k">else</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	292 279 <span class="k">my</span><span class="s">(</span><span class="i">$MinValue</span><span class="cm">,</span> <span class="i">$MaxValue</span><span class="s">)</span> = <span class="i">Range</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	293 280 <span class="k">my</span><span class="s">(</span><span class="i">$Interval</span><span class="s">)</span> = <span class="s">(</span><span class="i">$MaxValue</span> - <span class="i">$MinValue</span><span class="s">)</span>/<span class="i">$NumOfBins</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	294 281 <span class="k">my</span><span class="s">(</span><span class="i">$KeyValue</span><span class="s">)</span> = <span class="i">$MinValue</span> + <span class="i">$Interval</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	295 282 <span class="k">while</span> <span class="s">(</span><span class="i">$KeyValue</span> < <span class="i">$MaxValue</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	296 283 <span class="k">push</span> <span class="i">@RangeKeys</span><span class="cm">,</span> <span class="i">$KeyValue</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	297 284 <span class="i">$KeyValue</span> += <span class="i">$Interval</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	298 285 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	299 286 <span class="k">push</span> <span class="i">@RangeKeys</span><span class="cm">,</span> <span class="i">$MaxValue</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	300 287 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	301 288
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	302 289 <span class="c">#Setup frequency hash array...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	303 290 <span class="k">my</span><span class="s">(</span><span class="i">%FrequencyMap</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	304 291 <span class="i">%FrequencyMap</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	305 292
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	306 293 <span class="i">%FrequencyMap</span> = <span class="k">map</span> <span class="s">{</span> <span class="i">$_</span> <span class="cm">=></span> <span class="n">0</span> <span class="s">}</span> <span class="i">@RangeKeys</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	307 294
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	308 295 <span class="c"># Count values...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	309 296 <span class="k">my</span><span class="s">(</span><span class="i">$Key</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	310 297
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	311 298 <span class="j">VALUE:</span> <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	312 299 <span class="k">for</span> <span class="i">$Key</span> <span class="s">(</span><span class="i">@RangeKeys</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	313 300 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> <= <span class="i">$Key</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	314 301 <span class="i">$FrequencyMap</span>{<span class="i">$Key</span>} += <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	315 302 <span class="k">next</span> <span class="j">VALUE</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	316 303 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	317 304 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	318 305 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	319 306 <span class="k">return</span> <span class="s">(</span><span class="i">%FrequencyMap</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	320 307 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	321 308
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	322 309 <span class="c"># Compute the geometric mean of an array of numbers: NthROOT( PRODUCT(x[i]) )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	323 <a name="GeometricMean-"></a> 310 <span class="k">sub </span><span class="m">GeometricMean</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	324 311 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	325 312
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	326 313 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	327 314 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	328 315 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	329 316 <span class="k">my</span><span class="s">(</span><span class="i">$Mean</span><span class="cm">,</span> <span class="i">$Product</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	330 317 <span class="i">$Product</span> = <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	331 318 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	332 319 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> <= <span class="n">0</span> <span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	333 320 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	334 321 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	335 322 <span class="i">$Product</span> *= <span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	336 323 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	337 324 <span class="i">$Mean</span> = <span class="i">$Product</span> ** <span class="s">(</span><span class="n">1</span> / <span class="i">@$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	338 325 <span class="k">return</span> <span class="i">$Mean</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	339 326 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	340 327
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	341 328 <span class="c"># Compute the harmonic mean of an array of numbers: 1 / ( SUM(1/x[i]) / n )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	342 <a name="HarmonicMean-"></a> 329 <span class="k">sub </span><span class="m">HarmonicMean</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	343 330 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	344 331
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	345 332 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	346 333 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	347 334 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	348 335 <span class="k">my</span><span class="s">(</span><span class="i">$Mean</span><span class="cm">,</span> <span class="i">$Sum</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	349 336 <span class="i">$Sum</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	350 337 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	351 338 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> <= <span class="n">0</span> <span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	352 339 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	353 340 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	354 341 <span class="i">$Sum</span> += <span class="n">1</span>/<span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	355 342 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	356 343 <span class="i">$Mean</span> = <span class="n">1</span>/<span class="s">(</span><span class="i">$Sum</span>/<span class="i">@$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	357 344 <span class="k">return</span> <span class="i">$Mean</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	358 345 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	359 346
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	360 347 <span class="c"># Return the k-largest value from an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	361 <a name="KLargest-"></a> 348 <span class="k">sub </span><span class="m">KLargest</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	362 349 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$K</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	363 350
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	364 351 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">@$XArrayRef</span> && <span class="s">(</span><span class="i">$K</span> > <span class="n">0</span><span class="s">)</span> && <span class="s">(</span><span class="i">$K</span> <= <span class="i">@$XArrayRef</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	365 352 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	366 353 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	367 354 <span class="k">my</span><span class="s">(</span><span class="i">$KLargest</span><span class="cm">,</span> <span class="i">@SortedXArray</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	368 355 <span class="i">@SortedXArray</span> = <span class="k">sort</span> <span class="s">{</span> <span class="i">$b</span> <=> <span class="i">$a</span> <span class="s">}</span> <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	369 356 <span class="i">$KLargest</span> = <span class="i">$SortedXArray</span>[<span class="i">$K</span> - <span class="n">1</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	370 357 <span class="k">return</span> <span class="i">$KLargest</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	371 358 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	372 359
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	373 360 <span class="c"># Return the k-smallest value from an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	374 <a name="KSmallest-"></a> 361 <span class="k">sub </span><span class="m">KSmallest</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	375 362 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$K</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	376 363
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	377 364 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">@$XArrayRef</span> && <span class="s">(</span><span class="i">$K</span> > <span class="n">0</span><span class="s">)</span> && <span class="s">(</span><span class="i">$K</span> <= <span class="i">@$XArrayRef</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	378 365 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	379 366 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	380 367 <span class="k">my</span><span class="s">(</span><span class="i">$KSmallest</span><span class="cm">,</span> <span class="i">@SortedXArray</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	381 368 <span class="i">@SortedXArray</span> = <span class="k">sort</span> <span class="s">{</span> <span class="i">$a</span> <=> <span class="i">$b</span> <span class="s">}</span> <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	382 369 <span class="i">$KSmallest</span> = <span class="i">$SortedXArray</span>[<span class="i">$K</span> - <span class="n">1</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	383 370 <span class="k">return</span> <span class="i">$KSmallest</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	384 371 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	385 372
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	386 373 <span class="c"># Compute the kurtosis of an array of numbers:</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	387 374 <span class="c"># [ {n(n + 1)/(n - 1)(n - 2)(n - 3)} SUM{ ((x[i] - Xmean)/STDDEV)^4 } ] - {3((n - 1)^2)}/{(n - 2)(n-3)}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	388 375 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	389 <a name="Kurtosis-"></a> 376 <span class="k">sub </span><span class="m">Kurtosis</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	390 377 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	391 378
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	392 379 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span> \|\| <span class="s">(</span><span class="s">(</span><span class="i">@$XArrayRef</span> - <span class="n">3</span><span class="s">)</span> <= <span class="n">0</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	393 380 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	394 381 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	395 382 <span class="k">my</span><span class="s">(</span><span class="i">$Kurtosis</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$StandardDeviation</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	396 383 <span class="i">$Mean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	397 384 <span class="k">if</span> <span class="s">(</span>!<span class="k">defined</span> <span class="i">$Mean</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	398 385 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	399 386 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	400 387 <span class="i">$StandardDeviation</span> = <span class="i">StandardDeviation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	401 388 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="k">defined</span> <span class="i">$StandardDeviation</span> && <span class="i">$StandardDeviation</span> != <span class="n">0</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	402 389 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	403 390 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	404 391
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	405 392 <span class="k">my</span><span class="s">(</span><span class="i">$SumOfScores</span><span class="cm">,</span> <span class="i">$SampleSize</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	406 393 <span class="i">$SumOfScores</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	407 394 <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	408 395 <span class="i">$SumOfScores</span> += <span class="s">(</span><span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span>/<span class="i">$StandardDeviation</span><span class="s">)</span> ** <span class="n">4</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	409 396 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	410 397 <span class="i">$SampleSize</span> = <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	411 398 <span class="i">$Kurtosis</span> = <span class="s">(</span><span class="s">(</span><span class="s">(</span><span class="i">$SampleSize</span> * <span class="s">(</span><span class="i">$SampleSize</span> + <span class="n">1</span><span class="s">)</span><span class="s">)</span>/<span class="s">(</span><span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">1</span><span class="s">)</span> * <span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">2</span><span class="s">)</span> * <span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">3</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> * <span class="i">$SumOfScores</span><span class="s">)</span> - <span class="s">(</span><span class="s">(</span><span class="n">3</span> * <span class="s">(</span><span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">1</span><span class="s">)</span> ** <span class="n">2</span><span class="s">)</span><span class="s">)</span>/<span class="s">(</span><span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">2</span><span class="s">)</span> * <span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">3</span><span class="s">)</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	412 399 <span class="k">return</span> <span class="i">$Kurtosis</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	413 400 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	414 401
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	415 402 <span class="c"># Return the smallest value from an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	416 <a name="Minimum-"></a> 403 <span class="k">sub </span><span class="m">Minimum</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	417 404 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	418 405 <span class="k">return</span> <span class="i">KSmallest</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	419 406 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	420 407
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	421 408 <span class="c"># Return the largest value from an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	422 <a name="Maximum-"></a> 409 <span class="k">sub </span><span class="m">Maximum</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	423 410 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	424 411 <span class="k">return</span> <span class="i">KLargest</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	425 412 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	426 413
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	427 414 <span class="c"># Compute the mean of an array of numbers: SUM( x[i] ) / n</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	428 <a name="Mean-"></a> 415 <span class="k">sub </span><span class="m">Mean</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	429 416 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	430 417
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	431 418 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	432 419 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	433 420 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	434 421 <span class="k">my</span><span class="s">(</span><span class="i">$Mean</span><span class="cm">,</span> <span class="i">$Sum</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	435 422 <span class="i">$Sum</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	436 423 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	437 424 <span class="i">$Sum</span> += <span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	438 425 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	439 426 <span class="i">$Mean</span> = <span class="i">$Sum</span> / <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	440 427 <span class="k">return</span> <span class="i">$Mean</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	441 428 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	442 429
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	443 430 <span class="c"># Compute the median value of an array of numbers. For an even number array, it's</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	444 431 <span class="c"># the average of two middle values.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	445 432 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	446 433 <span class="c"># For even values of n: Xsorted[(n - 1)/2 + 1]</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	447 434 <span class="c"># For odd values of n: (Xsorted[n/2] + Xsorted[n/2 + 1])/2</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	448 435 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	449 <a name="Median-"></a> 436 <span class="k">sub </span><span class="m">Median</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	450 437 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	451 438
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	452 439 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	453 440 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	454 441 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	455 442 <span class="k">my</span><span class="s">(</span><span class="i">$Median</span><span class="cm">,</span> <span class="i">@SortedXArray</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	456 443 <span class="i">$Median</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	457 444 <span class="i">@SortedXArray</span> = <span class="k">sort</span> <span class="s">{</span> <span class="i">$a</span> <=> <span class="i">$b</span> <span class="s">}</span> <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	458 445 <span class="k">if</span> <span class="s">(</span><span class="i">@$XArrayRef</span> % <span class="n">2</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	459 446 <span class="k">my</span><span class="s">(</span><span class="i">$MidIndex</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	460 447 <span class="i">$MidIndex</span> = <span class="k">int</span><span class="s">(</span><span class="i">@SortedXArray</span> - <span class="n">1</span><span class="s">)</span>/<span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	461 448 <span class="i">$Median</span> = <span class="i">$SortedXArray</span>[<span class="i">$MidIndex</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	462 449 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	463 450 <span class="k">else</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	464 451 <span class="c"># Even number array...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	465 452 <span class="k">my</span><span class="s">(</span><span class="i">$MidPosition</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	466 453 <span class="i">$MidPosition</span> = <span class="k">int</span><span class="s">(</span><span class="i">@SortedXArray</span> / <span class="n">2</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	467 454 <span class="i">$Median</span> = <span class="s">(</span><span class="i">$SortedXArray</span>[<span class="i">$MidPosition</span> - <span class="n">1</span>] + <span class="i">$SortedXArray</span>[<span class="i">$MidPosition</span>]<span class="s">)</span> / <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	468 455 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	469 456 <span class="k">return</span> <span class="i">$Median</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	470 457 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	471 458
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	472 459 <span class="c"># Return the most frequently occuring value in an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	473 <a name="Mode-"></a> 460 <span class="k">sub </span><span class="m">Mode</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	474 461 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	475 462
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	476 463 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	477 464 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	478 465 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	479 466 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">%ValueToCountMap</span><span class="cm">,</span> <span class="i">@CountList</span><span class="cm">,</span> <span class="i">@SortedCountList</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	480 467 <span class="i">%ValueToCountMap</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	481 468 <span class="i">@CountList</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	482 469 <span class="i">@SortedCountList</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	483 470 <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	484 471 <span class="k">if</span> <span class="s">(</span><span class="k">exists</span> <span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>}<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	485 472 <span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>} += <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	486 473 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	487 474 <span class="k">else</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	488 475 <span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>} = <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	489 476 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	490 477 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	491 478 <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="k">keys</span> <span class="i">%ValueToCountMap</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	492 479 <span class="k">push</span> <span class="i">@CountList</span><span class="cm">,</span> <span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>}<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	493 480 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	494 481 <span class="i">@SortedCountList</span> = <span class="k">sort</span> <span class="s">{</span> <span class="i">$b</span> <=> <span class="i">$a</span> <span class="s">}</span> <span class="i">@CountList</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	495 482
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	496 483 <span class="c"># Make sure the frequency of mode value is greater than one and check for</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	497 484 <span class="c"># multiple modes as well...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	498 485 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	499 486 <span class="k">my</span><span class="s">(</span><span class="i">$ModeCount</span><span class="cm">,</span> <span class="i">$ModeValue</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	500 487 <span class="i">$ModeCount</span> = <span class="i">$SortedCountList</span>[<span class="n">0</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	501 488 <span class="k">if</span> <span class="s">(</span><span class="i">$ModeCount</span> <= <span class="n">1</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	502 489 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	503 490 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	504 491 <span class="c"># Get the first mode value...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	505 492 <span class="j">VALUE:</span> <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="k">keys</span> <span class="i">%ValueToCountMap</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	506 493 <span class="k">if</span> <span class="s">(</span><span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>} == <span class="i">$ModeCount</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	507 494 <span class="i">$ModeValue</span> = <span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	508 495 <span class="c"># Set it to zero to skip it next time...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	509 496 <span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>} = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	510 497 <span class="k">last</span> <span class="j">VALUE</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	511 498 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	512 499 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	513 500
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	514 501 <span class="k">if</span> <span class="s">(</span><span class="k">wantarray</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	515 502 <span class="c"># Retrieve all the modes...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	516 503 <span class="k">my</span><span class="s">(</span><span class="i">@Modes</span><span class="cm">,</span> <span class="i">$Count</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	517 504 <span class="i">@Modes</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	518 505 <span class="k">push</span> <span class="i">@Modes</span><span class="cm">,</span> <span class="i">$ModeValue</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	519 506 <span class="k">for</span> <span class="i">$Count</span> <span class="s">(</span><span class="i">@SortedCountList</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	520 507 <span class="k">if</span> <span class="s">(</span><span class="i">$Count</span> == <span class="i">$ModeCount</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	521 508 <span class="j">VALUE:</span> <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="k">keys</span> <span class="i">%ValueToCountMap</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	522 509 <span class="k">if</span> <span class="s">(</span><span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>} == <span class="i">$ModeCount</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	523 510 <span class="k">push</span> <span class="i">@Modes</span><span class="cm">,</span> <span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	524 511 <span class="c"># Set it to zero to skip it next time...</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	525 512 <span class="i">$ValueToCountMap</span>{<span class="i">$Value</span>} = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	526 513 <span class="k">last</span> <span class="j">VALUE</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	527 514 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	528 515 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	529 516 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	530 517 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	531 518 <span class="k">return</span> <span class="k">sort</span> <span class="s">{</span><span class="i">$b</span> <=> <span class="i">$a</span><span class="s">}</span> <span class="i">@Modes</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	532 519 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	533 520 <span class="k">else</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	534 521 <span class="k">return</span> <span class="i">$ModeValue</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	535 522 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	536 523 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	537 524
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	538 525
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	539 526 <span class="c"># Compute the Pearson correlation coefficient between two arrays of numbers:</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	540 527 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	541 528 <span class="c"># SUM( (x[i] - Xmean)(y[i] - Ymean) ) / SQRT( SUM( (x[i] - Xmean)^2 )(SUM( (y[i] - Ymean)^2 )) )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	542 529 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	543 530 <span class="c"># It returns values in the range from -1.0 to 1.0</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	544 <a name="PearsonCorrelation-"></a> 531 <span class="k">sub </span><span class="m">PearsonCorrelation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	545 532 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$YArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	546 533
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	547 534 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">@$XArrayRef</span> && <span class="i">@$YArrayRef</span> && <span class="s">(</span><span class="i">@$XArrayRef</span> == <span class="i">@$YArrayRef</span><span class="s">)</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	548 535 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	549 536 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	550 537 <span class="k">my</span><span class="s">(</span><span class="i">$Correlation</span><span class="cm">,</span> <span class="i">$XMean</span><span class="cm">,</span> <span class="i">$YMean</span><span class="cm">,</span> <span class="i">$Index</span><span class="cm">,</span> <span class="i">$XValueDeviation</span><span class="cm">,</span> <span class="i">$YValueDeviation</span><span class="cm">,</span> <span class="i">$SquareOfXDeviations</span><span class="cm">,</span> <span class="i">$SquareOfYDeviations</span><span class="cm">,</span> <span class="i">$ProductOfDeviations</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	551 538
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	552 539 <span class="i">$Correlation</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	553 540 <span class="i">$XMean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	554 541 <span class="i">$YMean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$YArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	555 542 <span class="i">$ProductOfDeviations</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$SquareOfXDeviations</span> = <span class="n">0</span><span class="sc">;</span> <span class="i">$SquareOfYDeviations</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	556 543 <span class="k">for</span> <span class="i">$Index</span> <span class="s">(</span><span class="n">0</span> .. <span class="i">$#</span>{<span class="i">@$XArrayRef</span>}<span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	557 544 <span class="i">$XValueDeviation</span> = <span class="i">$XArrayRef</span>->[<span class="i">$Index</span>] - <span class="i">$XMean</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	558 545 <span class="i">$YValueDeviation</span> = <span class="i">$YArrayRef</span>->[<span class="i">$Index</span>] - <span class="i">$YMean</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	559 546 <span class="i">$ProductOfDeviations</span> += <span class="s">(</span><span class="i">$XValueDeviation</span> * <span class="i">$YValueDeviation</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	560 547 <span class="i">$SquareOfXDeviations</span> += <span class="i">$XValueDeviation</span> ** <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	561 548 <span class="i">$SquareOfYDeviations</span> += <span class="i">$YValueDeviation</span> ** <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	562 549 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	563 550 <span class="i">$Correlation</span> = <span class="i">$ProductOfDeviations</span> / <span class="k">sqrt</span><span class="s">(</span><span class="i">$SquareOfXDeviations</span> * <span class="i">$SquareOfYDeviations</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	564 551 <span class="k">return</span> <span class="i">$Correlation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	565 552 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	566 553
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	567 554 <span class="c"># Return the smallest and largest values from an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	568 <a name="Range-"></a> 555 <span class="k">sub </span><span class="m">Range</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	569 556 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	570 557
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	571 558 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	572 559 <span class="k">return</span> <span class="s">(</span><span class="k">undef</span><span class="cm">,</span> <span class="k">undef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	573 560 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	574 561 <span class="k">my</span><span class="s">(</span><span class="i">$Smallest</span><span class="cm">,</span> <span class="i">$Largest</span><span class="cm">,</span> <span class="i">@SortedXArray</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	575 562 <span class="i">@SortedXArray</span> = <span class="k">sort</span> <span class="s">{</span> <span class="i">$a</span> <=> <span class="i">$b</span> <span class="s">}</span> <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	576 563 <span class="i">$Smallest</span> = <span class="i">$SortedXArray</span>[<span class="n">0</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	577 564 <span class="i">$Largest</span> = <span class="i">$SortedXArray</span>[<span class="i">$#SortedXArray</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	578 565 <span class="k">return</span> <span class="s">(</span><span class="i">$Smallest</span><span class="cm">,</span> <span class="i">$Largest</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	579 566 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	580 567
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	581 568 <span class="c"># Compute square of the Pearson correlation coefficient between two arrays of numbers.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	582 569 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	583 <a name="RSquare-"></a> 570 <span class="k">sub </span><span class="m">RSquare</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	584 571 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$YArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	585 572 <span class="k">my</span><span class="s">(</span><span class="i">$RSquare</span><span class="cm">,</span> <span class="i">$Correlation</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	586 573
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	587 574 <span class="i">$RSquare</span> = <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	588 575 <span class="i">$Correlation</span> = <span class="i">PearsonCorrelation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$YArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	589 576 <span class="k">if</span> <span class="s">(</span><span class="k">defined</span> <span class="i">$Correlation</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	590 577 <span class="i">$RSquare</span> = <span class="i">$Correlation</span> ** <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	591 578 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	592 579 <span class="k">return</span> <span class="i">$RSquare</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	593 580 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	594 581
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	595 582 <span class="c"># Compute the skewness of an array of numbers:</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	596 583 <span class="c"># {n/(n - 1)(n - 2)} SUM{ ((x[i] - Xmean)/STDDEV)^3 }</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	597 584 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	598 <a name="Skewness-"></a> 585 <span class="k">sub </span><span class="m">Skewness</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	599 586 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	600 587
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	601 588 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span> \|\| <span class="s">(</span><span class="s">(</span><span class="i">@$XArrayRef</span> - <span class="n">2</span><span class="s">)</span> <= <span class="n">0</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	602 589 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	603 590 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	604 591 <span class="k">my</span><span class="s">(</span><span class="i">$Skewness</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$StandardDeviation</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	605 592 <span class="i">$Mean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	606 593 <span class="k">if</span> <span class="s">(</span>!<span class="k">defined</span> <span class="i">$Mean</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	607 594 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	608 595 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	609 596 <span class="i">$StandardDeviation</span> = <span class="i">StandardDeviation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	610 597 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="k">defined</span> <span class="i">$StandardDeviation</span> && <span class="i">$StandardDeviation</span> != <span class="n">0</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	611 598 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	612 599 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	613 600
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	614 601 <span class="k">my</span><span class="s">(</span><span class="i">$SumOfScores</span><span class="cm">,</span> <span class="i">$SampleSize</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	615 602 <span class="i">$SumOfScores</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	616 603 <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	617 604 <span class="i">$SumOfScores</span> += <span class="s">(</span><span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span>/<span class="i">$StandardDeviation</span><span class="s">)</span> ** <span class="n">3</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	618 605 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	619 606 <span class="i">$SampleSize</span> = <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	620 607 <span class="i">$Skewness</span> = <span class="s">(</span><span class="i">$SampleSize</span>/<span class="s">(</span><span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">1</span><span class="s">)</span> * <span class="s">(</span><span class="i">$SampleSize</span> - <span class="n">2</span><span class="s">)</span> <span class="s">)</span><span class="s">)</span> * <span class="i">$SumOfScores</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	621 608 <span class="k">return</span> <span class="i">$Skewness</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	622 609 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	623 610
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	624 611 <span class="c"># Compute the standard deviation of an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	625 <a name="StandardDeviation-"></a> 612 <span class="k">sub </span><span class="m">StandardDeviation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	626 613 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	627 614 <span class="k">return</span> <span class="i">_CalculateStandardDeviation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">2</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	628 615 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	629 616
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	630 617 <span class="c"># Compute the standard deviation of an array of numbers representing entire population</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	631 <a name="StandardDeviationN-"></a> 618 <span class="k">sub </span><span class="m">StandardDeviationN</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	632 619 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	633 620 <span class="k">return</span> <span class="i">_CalculateStandardDeviation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	634 621 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	635 622
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	636 623 <span class="c"># Compute the standard deviation of an array of numbers.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	637 624 <span class="c"># Mode 1: SQRT ( SUM( (x[i] - mean)^2 ) / n )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	638 625 <span class="c"># Mode 2: SQRT ( SUM( (x[i] - mean)^2 ) / (n - 1) )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	639 626 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	640 <a name="_CalculateStandardDeviation-"></a> 627 <span class="k">sub </span><span class="m">_CalculateStandardDeviation</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	641 628 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$Mode</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	642 629
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	643 630 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	644 631 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	645 632 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	646 633 <span class="k">my</span><span class="s">(</span><span class="i">$StandardDeviation</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SquareOfDeviations</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$N</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	647 634
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	648 635 <span class="i">$StandardDeviation</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	649 636 <span class="i">$Mean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	650 637 <span class="i">$SquareOfDeviations</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	651 638 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	652 639 <span class="i">$SquareOfDeviations</span> += <span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span> ** <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	653 640 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	654 641 <span class="i">$N</span> = <span class="s">(</span><span class="i">$Mode</span> == <span class="n">1</span><span class="s">)</span> ? <span class="i">@$XArrayRef</span> <span class="co">:</span> <span class="s">(</span><span class="i">@$XArrayRef</span> - <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	655 642 <span class="i">$StandardDeviation</span> = <span class="k">sqrt</span><span class="s">(</span><span class="i">$SquareOfDeviations</span> / <span class="i">$N</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	656 643
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	657 644 <span class="k">return</span> <span class="i">$StandardDeviation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	658 645 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	659 646
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	660 647 <span class="c"># Compute the standard error using standard deviation and sample size</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	661 <a name="StandardError-"></a> 648 <span class="k">sub </span><span class="m">StandardError</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	662 649 <span class="k">my</span><span class="s">(</span><span class="i">$StandardDeviation</span><span class="cm">,</span> <span class="i">$Count</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	663 650
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	664 651 <span class="k">if</span> <span class="s">(</span><span class="i">$Count</span> <= <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	665 652 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	666 653 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	667 654 <span class="k">my</span><span class="s">(</span><span class="i">$StandardError</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	668 655 <span class="i">$StandardError</span> = <span class="i">$StandardDeviation</span> / <span class="k">sqrt</span><span class="s">(</span><span class="i">$Count</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	669 656
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	670 657 <span class="k">return</span> <span class="i">$StandardError</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	671 658 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	672 659
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	673 660 <span class="c"># Standardize the value using mean and standard deviation</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	674 <a name="Standardize-"></a> 661 <span class="k">sub </span><span class="m">Standardize</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	675 662 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$StandardDeviation</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	676 663
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	677 664 <span class="k">if</span> <span class="s">(</span><span class="i">$StandardDeviation</span> <= <span class="n">0</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	678 665 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	679 666 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	680 667 <span class="k">my</span><span class="s">(</span><span class="i">$StandardizedValue</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	681 668 <span class="i">$StandardizedValue</span> = <span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span>/<span class="i">$StandardDeviation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	682 669
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	683 670 <span class="k">return</span> <span class="i">$StandardizedValue</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	684 671 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	685 672
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	686 673 <span class="c"># Compute the standard deviation above the mean for an array of numbers.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	687 <a name="StandardScores-"></a> 674 <span class="k">sub </span><span class="m">StandardScores</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	688 675 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	689 676 <span class="k">return</span> <span class="i">_CalculateStandardScores</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">2</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	690 677 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	691 678
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	692 679 <span class="c"># Compute the standard deviation above the mean for an array of numbers representing entire population</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	693 <a name="StandardScoresN-"></a> 680 <span class="k">sub </span><span class="m">StandardScoresN</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	694 681 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	695 682 <span class="k">return</span> <span class="i">_CalculateStandardScores</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	696 683 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	697 684
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	698 685 <span class="c"># Compute the standard deviation above the mean for an array of numbers.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	699 686 <span class="c"># Mode 1: (x[i] - mean) / n</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	700 687 <span class="c"># Mode 2: (x[i] - mean) / (n - 1)</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	701 688 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	702 <a name="_CalculateStandardScores-"></a> 689 <span class="k">sub </span><span class="m">_CalculateStandardScores</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	703 690 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$Mode</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	704 691
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	705 692 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	706 693 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	707 694 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	708 695 <span class="k">my</span><span class="s">(</span><span class="i">@StandardScores</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$StandardDeviation</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	709 696
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	710 697 <span class="i">$Mean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	711 698 <span class="i">$StandardDeviation</span> = <span class="i">_CalculateStandardDeviation</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$Mode</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	712 699 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$StandardDeviation</span><span class="s">)</span> && <span class="i">$StandardDeviation</span> > <span class="n">0</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	713 700 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	714 701 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	715 702 <span class="i">@StandardScores</span> = <span class="s">(</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	716 703 <span class="k">for</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	717 704 <span class="k">push</span> <span class="i">@StandardScores</span><span class="cm">,</span> <span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span>/<span class="i">$StandardDeviation</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	718 705 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	719 706
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	720 707 <span class="k">return</span> <span class="i">@StandardScores</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	721 708 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	722 709
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	723 710 <span class="c"># Compute the product of an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	724 <a name="Product-"></a> 711 <span class="k">sub </span><span class="m">Product</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	725 712 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	726 713
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	727 714 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	728 715 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	729 716 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	730 717 <span class="k">my</span><span class="s">(</span><span class="i">$Product</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	731 718 <span class="i">$Product</span> = <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	732 719 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	733 720 <span class="i">$Product</span> *= <span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	734 721 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	735 722 <span class="k">return</span> <span class="i">$Product</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	736 723 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	737 724
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	738 725 <span class="c"># Compute the sum of an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	739 <a name="Sum-"></a> 726 <span class="k">sub </span><span class="m">Sum</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	740 727 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	741 728
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	742 729 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	743 730 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	744 731 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	745 732 <span class="k">my</span><span class="s">(</span><span class="i">$Sum</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	746 733 <span class="i">$Sum</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	747 734 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	748 735 <span class="i">$Sum</span> += <span class="i">$Value</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	749 736 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	750 737 <span class="k">return</span> <span class="i">$Sum</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	751 738 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	752 739
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	753 740 <span class="c"># Compute the sum of squares of an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	754 <a name="SumOfSquares-"></a> 741 <span class="k">sub </span><span class="m">SumOfSquares</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	755 742 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	756 743
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	757 744 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	758 745 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	759 746 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	760 747 <span class="k">my</span><span class="s">(</span><span class="i">$SumOfSquares</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	761 748 <span class="i">$SumOfSquares</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	762 749 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	763 750 <span class="i">$SumOfSquares</span> += <span class="i">$Value</span> ** <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	764 751 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	765 752 <span class="k">return</span> <span class="i">$SumOfSquares</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	766 753 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	767 754
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	768 755 <span class="c"># Compute the mean of an array of numbers by excluding a fraction of</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	769 756 <span class="c"># numbers from the top and bottom of the data set.</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	770 <a name="TrimMean-"></a> 757 <span class="k">sub </span><span class="m">TrimMean</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	771 758 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$FractionToExclude</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	772 759
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	773 760 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">@$XArrayRef</span> && <span class="i">$FractionToExclude</span> > <span class="n">0</span> && <span class="i">$FractionToExclude</span> <= <span class="n">1</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	774 761 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	775 762 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	776 763 <span class="k">my</span><span class="s">(</span><span class="i">$NumberToExclude</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	777 764 <span class="i">$NumberToExclude</span> = <span class="k">int</span><span class="s">(</span><span class="i">@$XArrayRef</span> * <span class="i">$FractionToExclude</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	778 765 <span class="i">$NumberToExclude</span> = <span class="s">(</span><span class="i">$NumberToExclude</span> % <span class="n">2</span><span class="s">)</span> ? <span class="s">(</span><span class="i">$NumberToExclude</span> - <span class="n">1</span><span class="s">)</span> <span class="co">:</span> <span class="i">$NumberToExclude</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	779 766 <span class="k">if</span> <span class="s">(</span><span class="i">$NumberToExclude</span> == <span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	780 767 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	781 768 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	782 769 <span class="k">my</span><span class="s">(</span><span class="i">$Mean</span><span class="cm">,</span> <span class="i">$Sum</span><span class="cm">,</span> <span class="i">$Index</span><span class="cm">,</span> <span class="i">$FirstIndex</span><span class="cm">,</span> <span class="i">$LastIndex</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	783 770 <span class="i">$FirstIndex</span> = <span class="i">$NumberToExclude</span>/<span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	784 771 <span class="i">$LastIndex</span> = <span class="i">@$XArrayRef</span> - <span class="s">(</span><span class="i">$NumberToExclude</span>/<span class="n">2</span><span class="s">)</span> - <span class="n">1</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	785 772 <span class="i">$Sum</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	786 773 <span class="k">my</span><span class="s">(</span><span class="i">@SortedXArray</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	787 774 <span class="i">@SortedXArray</span> = <span class="k">sort</span> <span class="s">{</span> <span class="i">$a</span> <=> <span class="i">$b</span> <span class="s">}</span> <span class="i">@$XArrayRef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	788 775 <span class="k">for</span> <span class="i">$Index</span> <span class="s">(</span><span class="i">$FirstIndex</span> .. <span class="i">$LastIndex</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	789 776 <span class="i">$Sum</span> += <span class="i">$SortedXArray</span>[<span class="i">$Index</span>]<span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	790 777 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	791 778 <span class="i">$Mean</span> = <span class="i">$Sum</span>/<span class="s">(</span><span class="i">@SortedXArray</span> - <span class="i">$NumberToExclude</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	792 779 <span class="k">return</span> <span class="i">$Mean</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	793 780 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	794 781
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	795 782 <span class="c"># Compute the variance of an array of numbers</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	796 <a name="Variance-"></a> 783 <span class="k">sub </span><span class="m">Variance</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	797 784 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	798 785 <span class="k">return</span> <span class="i">_CalculateVariance</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">2</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	799 786 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	800 787
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	801 788 <span class="c"># Compute the variance of an array of numbers representing entire population</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	802 <a name="VarianceN-"></a> 789 <span class="k">sub </span><span class="m">VarianceN</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	803 790 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	804 791 <span class="k">return</span> <span class="i">_CalculateVariance</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	805 792 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	806 793
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	807 794 <span class="c"># Compute the variance of an array of numbers:</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	808 795 <span class="c"># Mode 1: SUM( (x[i] - Xmean)^2 / n )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	809 796 <span class="c"># Mode 2: SUM( (x[i] - Xmean)^2 / (n - 1) )</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	810 797 <span class="c">#</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	811 <a name="_CalculateVariance-"></a> 798 <span class="k">sub </span><span class="m">_CalculateVariance</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	812 799 <span class="k">my</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="cm">,</span> <span class="i">$Mode</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	813 800
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	814 801 <span class="k">if</span> <span class="s">(</span>!<span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	815 802 <span class="k">return</span> <span class="k">undef</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	816 803 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	817 804 <span class="k">my</span><span class="s">(</span><span class="i">$Variance</span><span class="cm">,</span> <span class="i">$Value</span><span class="cm">,</span> <span class="i">$SquareOfDeviations</span><span class="cm">,</span> <span class="i">$Mean</span><span class="cm">,</span> <span class="i">$N</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	818 805
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	819 806 <span class="i">$Variance</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	820 807 <span class="i">$Mean</span> = <span class="i">Mean</span><span class="s">(</span><span class="i">$XArrayRef</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	821 808 <span class="i">$SquareOfDeviations</span> = <span class="n">0</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	822 809 <span class="k">foreach</span> <span class="i">$Value</span> <span class="s">(</span><span class="i">@$XArrayRef</span><span class="s">)</span> <span class="s">{</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	823 810 <span class="i">$SquareOfDeviations</span> += <span class="s">(</span><span class="i">$Value</span> - <span class="i">$Mean</span><span class="s">)</span> ** <span class="n">2</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	824 811 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	825 812 <span class="i">$N</span> = <span class="s">(</span><span class="i">$Mode</span> == <span class="n">1</span><span class="s">)</span> ? <span class="i">@$XArrayRef</span> <span class="co">:</span> <span class="s">(</span><span class="i">@$XArrayRef</span> - <span class="n">1</span><span class="s">)</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	826 813 <span class="i">$Variance</span> = <span class="i">$SquareOfDeviations</span> / <span class="i">$N</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	827 814
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	828 815 <span class="k">return</span> <span class="i">$Variance</span><span class="sc">;</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	829 816 <span class="s">}</span>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	830 817
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	831 <a name="EOF-"></a></pre>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	832 <p> </p>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	833 <br />
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	834 <center>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	835 <img src="../../../images/h2o2.png">
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	836 </center>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	837 </body>
4816e4a8ae95 Uploaded deepakjadmin parents: diff changeset	838 </html>

Mercurial > repos > deepakjadmin > mayatool3_test2

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