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<html> <head> <title>MayaChemTools:Code:MathUtil.pm</title> <meta http-equiv="content-type" content="text/html;charset=utf-8"> <link rel="stylesheet" type="text/css" href="../../../css/MayaChemToolsCode.css"> </head> <body leftmargin="20" rightmargin="20" topmargin="10" bottommargin="10"> <br/> <center> <a href="http://www.mayachemtools.org" title="MayaChemTools Home"><img src="../../../images/MayaChemToolsLogo.gif" border="0" alt="MayaChemTools"></a> </center> <br/> <pre> <a name="package-MathUtil-"></a> 1 <span class="k">package </span><span class="i">MathUtil</span><span class="sc">;</span> 2 <span class="c">#</span> 3 <span class="c"># $RCSfile: MathUtil.pm,v $</span> 4 <span class="c"># $Date: 2015/02/28 20:47:17 $</span> 5 <span class="c"># $Revision: 1.28 $</span> 6 <span class="c">#</span> 7 <span class="c"># Author: Manish Sud <msud@san.rr.com></span> 8 <span class="c">#</span> 9 <span class="c"># Copyright (C) 2015 Manish Sud. All rights reserved.</span> 10 <span class="c">#</span> 11 <span class="c"># This file is part of MayaChemTools.</span> 12 <span class="c">#</span> 13 <span class="c"># MayaChemTools is free software; you can redistribute it and/or modify it under</span> 14 <span class="c"># the terms of the GNU Lesser General Public License as published by the Free</span> 15 <span class="c"># Software Foundation; either version 3 of the License, or (at your option) any</span> 16 <span class="c"># later version.</span> 17 <span class="c">#</span> 18 <span class="c"># MayaChemTools is distributed in the hope that it will be useful, but without</span> 19 <span class="c"># any warranty; without even the implied warranty of merchantability of fitness</span> 20 <span class="c"># for a particular purpose. See the GNU Lesser General Public License for more</span> 21 <span class="c"># details.</span> 22 <span class="c">#</span> 23 <span class="c"># You should have received a copy of the GNU Lesser General Public License</span> 24 <span class="c"># along with MayaChemTools; if not, see <http://www.gnu.org/licenses/> or</span> 25 <span class="c"># write to the Free Software Foundation Inc., 59 Temple Place, Suite 330,</span> 26 <span class="c"># Boston, MA, 02111-1307, USA.</span> 27 <span class="c">#</span> 28 29 <span class="k">use</span> <span class="w">strict</span><span class="sc">;</span> 30 <span class="k">use</span> <span class="w">Exporter</span><span class="sc">;</span> 31 <span class="k">use</span> <span class="w">Constants</span><span class="sc">;</span> 32 <span class="k">use</span> <span class="w">Math::Trig</span> <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 33 <span class="k">use</span> <span class="w">POSIX</span> <span class="s">(</span><span class="s">)</span><span class="sc">;</span> 34 35 <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> 36 37 <span class="i">@ISA</span> = <span class="q">qw(Exporter)</span><span class="sc">;</span> 38 <span class="i">@EXPORT</span> = <span class="q">qw(acos asin atan tan ceil floor log10 min max srandom random round GeneratePrimeNumbersUpToLimit GeneratePrimeNumbersUpToCount)</span><span class="sc">;</span> 39 <span class="i">@EXPORT_OK</span> = <span class="q">qw()</span><span class="sc">;</span> 40 41 <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> 42 <span class="s">)</span><span class="sc">;</span> 43 44 45 <span class="c"># Return next largest integer...</span> <a name="ceil-"></a> 46 <span class="k">sub </span><span class="m">ceil ($)</span> <span class="s">{</span> 47 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 48 49 <span class="k">return</span> <span class="i">POSIX::ceil</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 50 <span class="s">}</span> 51 52 <span class="c"># Return previous smallest integer...</span> <a name="floor-"></a> 53 <span class="k">sub </span><span class="m">floor ($)</span> <span class="s">{</span> 54 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 55 56 <span class="k">return</span> <span class="i">POSIX::floor</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 57 <span class="s">}</span> 58 59 <span class="c"># Calculate log value using base 10...</span> <a name="log10-"></a> 60 <span class="k">sub </span><span class="m">log10 ($)</span> <span class="s">{</span> 61 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 62 63 <span class="k">return</span> <span class="i">CORE::</span><span class="k">log</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span>/<span class="i">CORE::</span><span class="k">log</span><span class="s">(</span><span class="n">10</span><span class="s">)</span><span class="sc">;</span> 64 <span class="s">}</span> 65 66 <span class="c"># Return the smaller of two numbers...</span> <a name="min-"></a> 67 <span class="k">sub </span><span class="m">min ($$)</span> <span class="s">{</span> 68 <span class="k">my</span><span class="s">(</span><span class="i">$Value1</span><span class="cm">,</span> <span class="i">$Value2</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 69 70 <span class="k">return</span> <span class="s">(</span><span class="i">$Value1</span> <= <span class="i">$Value2</span><span class="s">)</span> ? <span class="i">$Value1</span> <span class="co">:</span> <span class="i">$Value2</span><span class="sc">;</span> 71 <span class="s">}</span> 72 73 <span class="c"># Return the larger of two numbers...</span> <a name="max-"></a> 74 <span class="k">sub </span><span class="m">max ($$)</span> <span class="s">{</span> 75 <span class="k">my</span><span class="s">(</span><span class="i">$Value1</span><span class="cm">,</span> <span class="i">$Value2</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 76 77 <span class="k">return</span> <span class="s">(</span><span class="i">$Value1</span> >= <span class="i">$Value2</span><span class="s">)</span> ? <span class="i">$Value1</span> <span class="co">:</span> <span class="i">$Value2</span><span class="sc">;</span> 78 <span class="s">}</span> 79 80 <span class="c"># The random number generator implemented in MayaChemTools is a variant of linear</span> 81 <span class="c"># congruential generator (LCG) as described by Miller et al. [ Ref 120 ]. It is</span> 82 <span class="c"># also referred to as Lehmer random number generator or Park-Miller random number</span> 83 <span class="c"># generator.</span> 84 <span class="c">#</span> 85 <span class="c"># Unlike Perl's core random number generator function rand, the random number</span> 86 <span class="c"># generator implemented in MayaChemTools generates consistent random values</span> 87 <span class="c"># across different platforms - Windows, CygWin, Linux, Unix - for a specific random</span> 88 <span class="c"># seed.</span> 89 <span class="c">#</span> 90 91 <span class="c"># $RandomModulus = 2**31 - 1;</span> 92 <span class="c"># $RandomMultiplier = 16807;</span> 93 <span class="c"># $RandomQuotient = $RandomModulus / $RandomMultiplier;</span> 94 <span class="c"># $RandomRemainder = $RandomModulus % $RandomMultiplier</span> 95 <span class="c">#</span> 96 <span class="c"># $MaxRandomSeed = 2*31 -2</span> 97 <span class="c">#</span> 98 <span class="k">my</span><span class="s">(</span><span class="i">$MaxRandomSeed</span><span class="cm">,</span> <span class="i">$RandomSeed</span><span class="cm">,</span> <span class="i">$RandomModulus</span><span class="cm">,</span> <span class="i">$RandomMultiplier</span><span class="cm">,</span> <span class="i">$RandomQuotient</span><span class="cm">,</span> <span class="i">$RandomRemainder</span><span class="s">)</span><span class="sc">;</span> 99 100 <span class="i">$MaxRandomSeed</span> = <span class="n">2147483646</span><span class="sc">;</span> 101 <span class="i">$RandomSeed</span> = <span class="n">123456789</span><span class="sc">;</span> 102 103 <span class="i">$RandomModulus</span> = <span class="n">2147483647</span><span class="sc">;</span> 104 <span class="i">$RandomMultiplier</span> = <span class="n">16807</span><span class="sc">;</span> 105 <span class="i">$RandomQuotient</span> = <span class="n">127773</span><span class="sc">;</span> 106 <span class="i">$RandomRemainder</span> = <span class="n">2836</span><span class="sc">;</span> 107 108 <span class="c"># Set random number seed...</span> 109 <span class="c">#</span> 110 <span class="c"># The intial value of random number seed is recommeded to be an integer between 1</span> 111 <span class="c"># and 2**31 - 2 [Ref 120] which translates to be 1 and 2147483646</span> 112 <span class="c">#</span> <a name="srandom-"></a> 113 <span class="k">sub </span><span class="m">srandom ($)</span> <span class="s">{</span> 114 <span class="k">my</span><span class="s">(</span><span class="i">$Seed</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 115 116 <span class="k">if</span> <span class="s">(</span><span class="i">$Seed</span> <= <span class="n">0</span> <span class="s">)</span> <span class="s">{</span> 117 <span class="k">die</span> <span class="q">"Error: srandom: Specified seed value must be greater than 0..."</span><span class="sc">;</span> 118 <span class="s">}</span> 119 120 <span class="i">$RandomSeed</span> = <span class="s">(</span><span class="i">$Seed</span> > <span class="i">$MaxRandomSeed</span><span class="s">)</span> ? <span class="s">(</span><span class="i">$Seed</span> % <span class="i">$MaxRandomSeed</span><span class="s">)</span> <span class="co">:</span> <span class="i">$Seed</span><span class="sc">;</span> 121 122 <span class="k">return</span> <span class="i">$RandomSeed</span><span class="sc">;</span> 123 <span class="s">}</span> 124 125 <span class="c"># Retrun a random number between 0 and less than 1 or specified size...</span> 126 <span class="c">#</span> <a name="random-"></a> 127 <span class="k">sub </span><span class="m">random (;$)</span> <span class="s">{</span> 128 <span class="k">my</span><span class="s">(</span><span class="i">$Size</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 129 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">$LowValue</span><span class="cm">,</span> <span class="i">$HighValue</span><span class="s">)</span><span class="sc">;</span> 130 131 <span class="i">$Size</span> = <span class="k">defined</span> <span class="i">$Size</span> ? <span class="i">$Size</span> <span class="co">:</span> <span class="n">1.0</span><span class="sc">;</span> 132 133 <span class="i">$HighValue</span> = <span class="i">$RandomSeed</span> / <span class="i">$RandomQuotient</span><span class="sc">;</span> 134 <span class="i">$LowValue</span> = <span class="i">$RandomSeed</span> % <span class="i">$RandomQuotient</span><span class="sc">;</span> 135 136 <span class="i">$Value</span> = <span class="i">$RandomMultiplier</span> * <span class="i">$LowValue</span> - <span class="i">$RandomRemainder</span> * <span class="i">$HighValue</span><span class="sc">;</span> 137 138 <span class="i">$RandomSeed</span> = <span class="s">(</span><span class="i">$Value</span> > <span class="n">0</span><span class="s">)</span> ? <span class="i">$Value</span> <span class="co">:</span> <span class="s">(</span><span class="i">$Value</span> + <span class="i">$RandomModulus</span><span class="s">)</span><span class="sc">;</span> 139 140 <span class="k">return</span> <span class="s">(</span><span class="i">$RandomSeed</span> / <span class="i">$RandomModulus</span><span class="s">)</span> * <span class="i">$Size</span><span class="sc">;</span> 141 <span class="s">}</span> 142 143 <span class="c"># Round a integer/real number to:</span> 144 <span class="c"># . A nearest integer</span> 145 <span class="c"># . Specified number of decimal places</span> 146 <span class="c">#</span> <a name="round-"></a> 147 <span class="k">sub </span><span class="m">round ($;$)</span> <span class="s">{</span> 148 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="cm">,</span> <span class="i">$DecimalPlaces</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 149 <span class="k">my</span><span class="s">(</span><span class="i">$RoundedValue</span><span class="s">)</span><span class="sc">;</span> 150 151 <span class="k">if</span> <span class="s">(</span><span class="k">defined</span><span class="s">(</span><span class="i">$DecimalPlaces</span><span class="s">)</span> && <span class="i">$DecimalPlaces</span> > <span class="n">0</span><span class="s">)</span> <span class="s">{</span> 152 <span class="i">$RoundedValue</span> = <span class="k">sprintf</span> <span class="q">"%.${DecimalPlaces}f"</span><span class="cm">,</span> <span class="i">$Value</span><span class="sc">;</span> 153 <span class="s">}</span> 154 <span class="k">else</span> <span class="s">{</span> 155 <span class="k">if</span> <span class="s">(</span><span class="i">$Value</span> < <span class="n">0</span><span class="s">)</span> <span class="s">{</span> 156 <span class="i">$RoundedValue</span> = <span class="k">int</span><span class="s">(</span><span class="i">$Value</span> - <span class="n">0.5</span><span class="s">)</span><span class="sc">;</span> 157 <span class="s">}</span> 158 <span class="k">else</span> <span class="s">{</span> 159 <span class="i">$RoundedValue</span> = <span class="k">int</span><span class="s">(</span><span class="i">$Value</span> + <span class="n">0.5</span><span class="s">)</span><span class="sc">;</span> 160 <span class="s">}</span> 161 <span class="s">}</span> 162 <span class="k">return</span> <span class="i">$RoundedValue</span><span class="sc">;</span> 163 <span class="s">}</span> 164 165 <span class="c"># Return tangent of an angle expressed in radians.</span> <a name="tan-"></a> 166 <span class="k">sub </span><span class="m">tan</span> <span class="s">{</span> 167 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 168 169 <span class="k">return</span> <span class="s">(</span><span class="i">CORE::</span><span class="k">sin</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span>/<span class="i">CORE::</span><span class="k">cos</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="s">)</span><span class="sc">;</span> 170 <span class="s">}</span> 171 172 <span class="c"># Return inverse sine of an angle expressed in radians.</span> 173 <span class="c">#</span> 174 <span class="c"># For a right angle triangle defined by sides X and Y in a unit circle, Pythagorean theorem implies</span> 175 <span class="c"># X**2 + Y**2 = 1 and sin value corresponds to Y. So asin is equivalent to atan2(Y, sqrt(1-Y**2)).</span> 176 <span class="c"># However, taking sqrt of negative numbers is problematic; Math::Trig::asin handles it using complex</span> 177 <span class="c"># numbers.</span> 178 <span class="c">#</span> <a name="asin-"></a> 179 <span class="k">sub </span><span class="m">asin ($)</span> <span class="s">{</span> 180 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 181 182 <span class="k">return</span> <span class="i">Math::Trig::asin</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 183 <span class="s">}</span> 184 185 <span class="c"># Return inverse cosine of an angle expressed in radians.</span> 186 <span class="c">#</span> 187 <span class="c"># For a right angle triangle defined by sides X and Y in a unit circle, Pythagorean theorem implies</span> 188 <span class="c"># X**2 + Y**2 = 1 and cos value corresponds to X. So asin is equivalent to atan2(sqrt(1-X**2), X)</span> 189 <span class="c"># However, taking sqrt of negative numbers is problematic; Math::Trig::acos handles it using complex</span> 190 <span class="c"># numbers.</span> 191 <span class="c">#</span> <a name="acos-"></a> 192 <span class="k">sub </span><span class="m">acos ($)</span> <span class="s">{</span> 193 <span class="k">my</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 194 195 <span class="k">return</span> <span class="i">Math::Trig::acos</span><span class="s">(</span><span class="i">$Value</span><span class="s">)</span><span class="sc">;</span> 196 <span class="s">}</span> 197 198 <span class="c"># Generate prime numbers up to a specified limit and return a reference to an</span> 199 <span class="c"># array containing the prime numbers.</span> 200 <span class="c">#</span> 201 <span class="c"># By default, the first 1000 prime numbers are generated. The 1000th prime</span> 202 <span class="c"># number is 7919 and that's why default limit is set to 7920.</span> 203 <span class="c">#</span> <a name="GeneratePrimeNumbersUpToLimit-"></a> 204 <span class="k">sub </span><span class="m">GeneratePrimeNumbersUpToLimit (;$)</span> <span class="s">{</span> 205 <span class="k">my</span><span class="s">(</span><span class="i">$Limit</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 206 207 <span class="i">$Limit</span> = <span class="k">defined</span> <span class="i">$Limit</span> ? <span class="i">$Limit</span> <span class="co">:</span> <span class="n">7920</span><span class="sc">;</span> 208 209 <span class="k">return</span> <span class="i">_GeneratePrimeNumbers</span><span class="s">(</span><span class="q">'ByLimit'</span><span class="cm">,</span> <span class="i">$Limit</span><span class="s">)</span> 210 <span class="s">}</span> 211 212 <span class="c"># Generate prime numbers up to specified count of prime numbers and return a</span> 213 <span class="c"># reference to an array containing the prime numbers.</span> 214 <span class="c">#</span> 215 <span class="c"># By default, the first 1000 prime numbers are generated. The 1000th prime</span> 216 <span class="c"># number is 7919.</span> 217 <span class="c">#</span> <a name="GeneratePrimeNumbersUpToCount-"></a> 218 <span class="k">sub </span><span class="m">GeneratePrimeNumbersUpToCount (;$)</span> <span class="s">{</span> 219 <span class="k">my</span><span class="s">(</span><span class="i">$Count</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 220 221 <span class="i">$Count</span> = <span class="k">defined</span> <span class="i">$Count</span> ? <span class="i">$Count</span> <span class="co">:</span> <span class="n">1000</span><span class="sc">;</span> 222 223 <span class="k">return</span> <span class="i">_GeneratePrimeNumbers</span><span class="s">(</span><span class="q">'ByCount'</span><span class="cm">,</span> <span class="i">$Count</span><span class="s">)</span> 224 <span class="s">}</span> 225 226 <span class="c"># Generate prime numbers up to specified limit or count and return a reference</span> 227 <span class="c"># to an array containing the prime numbers.</span> 228 <span class="c">#</span> 229 <span class="c"># The algorithm to generate prime numbers is a modification of Sieve of Erastothenes</span> 230 <span class="c"># prime number generator.</span> 231 <span class="c">#</span> <a name="_GeneratePrimeNumbers-"></a> 232 <span class="k">sub </span><span class="m">_GeneratePrimeNumbers</span> <span class="s">{</span> 233 <span class="k">my</span><span class="s">(</span><span class="i">$Mode</span><span class="cm">,</span> <span class="i">$Value</span><span class="s">)</span> = <span class="i">@_</span><span class="sc">;</span> 234 <span class="k">my</span><span class="s">(</span><span class="i">$ByLimit</span><span class="cm">,</span> <span class="i">$PrimeNumber</span><span class="cm">,</span> <span class="i">$Number</span><span class="cm">,</span> <span class="i">$SqrtOfNumber</span><span class="cm">,</span> <span class="i">$NumberIsPrime</span><span class="cm">,</span> <span class="i">@PrimeNumbers</span><span class="s">)</span><span class="sc">;</span> 235 236 <span class="i">$ByLimit</span> = <span class="s">(</span><span class="i">$Mode</span> =~ <span class="q">/^ByLimit$/i</span><span class="s">)</span> ? <span class="n">1</span> <span class="co">:</span> <span class="n">0</span><span class="sc">;</span> 237 238 <span class="i">@PrimeNumbers</span> = <span class="s">(</span><span class="n">2</span><span class="cm">,</span> <span class="n">3</span><span class="s">)</span><span class="sc">;</span> 239 <span class="i">$Number</span> = <span class="n">3</span><span class="sc">;</span> 240 241 <span class="c"># while ($Number <= $Limit) {</span> 242 <span class="k">while</span> <span class="s">(</span><span class="i">$ByLimit</span> ? <span class="s">(</span><span class="i">$Number</span> < <span class="i">$Value</span><span class="s">)</span> <span class="co">:</span> <span class="s">(</span><span class="i">@PrimeNumbers</span> < <span class="i">$Value</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 243 <span class="i">$Number</span> += <span class="n">2</span><span class="sc">;</span> 244 <span class="i">$SqrtOfNumber</span> = <span class="k">sqrt</span> <span class="i">$Number</span><span class="sc">;</span> 245 246 <span class="i">$NumberIsPrime</span> = <span class="n">1</span><span class="sc">;</span> 247 <span class="j">PRIMENUMBER:</span> <span class="k">for</span> <span class="i">$PrimeNumber</span> <span class="s">(</span><span class="i">@PrimeNumbers</span><span class="s">)</span> <span class="s">{</span> 248 <span class="k">if</span> <span class="s">(</span><span class="i">$PrimeNumber</span> > <span class="i">$SqrtOfNumber</span><span class="s">)</span> <span class="s">{</span> 249 <span class="k">last</span> <span class="j">PRIMENUMBER</span><span class="sc">;</span> 250 <span class="s">}</span> 251 <span class="k">if</span> <span class="s">(</span>!<span class="s">(</span><span class="i">$Number</span> % <span class="i">$PrimeNumber</span><span class="s">)</span><span class="s">)</span> <span class="s">{</span> 252 <span class="i">$NumberIsPrime</span> = <span class="n">0</span><span class="sc">;</span> 253 <span class="k">last</span> <span class="j">PRIMENUMBER</span><span class="sc">;</span> 254 <span class="s">}</span> 255 <span class="s">}</span> 256 <span class="k">if</span> <span class="s">(</span><span class="i">$NumberIsPrime</span><span class="s">)</span> <span class="s">{</span> 257 <span class="k">push</span> <span class="i">@PrimeNumbers</span><span class="cm">,</span> <span class="i">$Number</span><span class="sc">;</span> 258 <span class="s">}</span> 259 <span class="s">}</span> 260 <span class="k">return</span> \<span class="i">@PrimeNumbers</span><span class="sc">;</span> 261 <span class="s">}</span> 262 <a name="EOF-"></a></pre> <p> </p> <br /> <center> <img src="../../../images/h2o2.png"> </center> </body> </html>