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13 <html xmlns="http://www.w3.org/1999/xhtml">
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15 <title>Math - The Commons Math User Guide - Utilites</title>
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28 Commons Math User Guide
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64
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65
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66
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67 <h5>User Guide</h5>
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68 <ul>
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69
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70 <li class="none">
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71 <a href="../userguide/index.html">Contents</a>
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72 </li>
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73
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74 <li class="none">
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75 <a href="../userguide/overview.html">Overview</a>
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76 </li>
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79 <a href="../userguide/stat.html">Statistics</a>
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83 <a href="../userguide/random.html">Data Generation</a>
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87 <a href="../userguide/linear.html">Linear Algebra</a>
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88 </li>
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91 <a href="../userguide/analysis.html">Numerical Analysis</a>
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92 </li>
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95 <a href="../userguide/special.html">Special Functions</a>
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96 </li>
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98 <li class="none">
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99 <strong>Utilities</strong>
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100 </li>
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101
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102 <li class="none">
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103 <a href="../userguide/complex.html">Complex Numbers</a>
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104 </li>
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108 </li>
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109
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110 <li class="none">
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111 <a href="../userguide/fraction.html">Fractions</a>
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112 </li>
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115 <a href="../userguide/transform.html">Transform Methods</a>
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127 <a href="../userguide/ode.html">Ordinary Differential Equations</a>
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144
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145 </div>
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146 </div>
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147 <div id="bodyColumn">
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148 <div id="contentBox">
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149 <div class="section"><h2><a name="a6_Utilities"></a>6 Utilities</h2>
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150 <div class="section"><h3><a name="a6.1_Overview"></a>6.1 Overview</h3>
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151 <p>
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152 The <a href="../apidocs/org/apache/commons/math/util/package-summary.html">
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153 org.apache.commons.math.util</a> package collects a group of array utilities,
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154 value transformers, and numerical routines used by implementation classes in
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155 commons-math.
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156 </p>
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157 </div>
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158 <div class="section"><h3><a name="a6.2_Double_array_utilities"></a>6.2 Double array utilities</h3>
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159 <p>
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160 To maintain statistics based on a "rolling" window of values, a resizable
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161 array implementation was developed and is provided for reuse in the
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162 <code>util</code> package. The core functionality provided is described in
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163 the documentation for the interface,
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164 <a href="../apidocs/org/apache/commons/math/util/DoubleArray.html">
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165 org.apache.commons.math.util.DoubleArray.</a> This interface adds one
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166 method, <code>addElementRolling(double)</code> to basic list accessors.
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167 The <code>addElementRolling</code> method adds an element
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168 (the actual parameter) to the end of the list and removes the first element
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169 in the list.
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170 </p>
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171 <p>
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172 The <a href="../apidocs/org/apache/commons/math/util/ResizableDoubleArray.html">
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173 org.apache.commons.math.util.ResizableDoubleArray</a> class provides a
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174 configurable, array-backed implementation of the <code>DoubleArray</code>
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175 interface. When <code>addElementRolling</code> is invoked, the underlying
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176 array is expanded if necessary, the new element is added to the end of the
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177 array and the "usable window" of the array is moved forward, so that
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178 the first element is effectively discarded, what was the second becomes the
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179 first, and so on. To efficiently manage storage, two maintenance
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180 operations need to be periodically performed -- orphaned elements at the
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181 beginning of the array need to be reclaimed and space for new elements at
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182 the end needs to be created. Both of these operations are handled
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183 automatically, with frequency / effect driven by the configuration
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184 properties <code>expansionMode</code>, <code>expansionFactor</code> and
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185 <code>contractionCriteria.</code> See
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186 <a href="../apidocs/org/apache/commons/math/util/ResizableDoubleArray.html">
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187 ResizableDoubleArray</a>
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188 for details.
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189 </p>
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190 </div>
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191 <div class="section"><h3><a name="a6.3_intdouble_hash_map"></a>6.3 int/double hash map</h3>
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192 <p>
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193 The <a href="../apidocs/org/apache/commons/math/util/OpenIntToDoubleHashMap.html">
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194 org.apache.commons.math.util.OpenIntToDoubleHashMap</a> class provides a specialized
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195 hash map implementation for int/double. This implementation has a much smaller memory
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196 overhead than standard <code>java.util.HashMap</code> class. It uses open addressing
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197 and primitive arrays, which greatly reduces the number of intermediate objects and
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198 improve data locality.
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199 </p>
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200 </div>
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201 <div class="section"><h3><a name="a6.4_Continued_Fractions"></a>6.4 Continued Fractions</h3>
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202 <p>
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203 The <a href="../apidocs/org/apache/commons/math/util/ContinuedFraction.html">
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204 org.apache.commons.math.util.ContinuedFraction</a> class provides a generic
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205 way to create and evaluate continued fractions. The easiest way to create a
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206 continued fraction is to subclass <code>ContinuedFraction</code> and
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207 override the <code>getA</code> and <code>getB</code> methods which return
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208 the continued fraction terms. The precise definition of these terms is
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209 explained in <a href="http://mathworld.wolfram.com/ContinuedFraction.html" class="externalLink">
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210 Continued Fraction, equation (1)</a> from MathWorld.
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211 </p>
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212 <p>
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213 As an example, the constant Pi could be computed using the continued fraction
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214 defined at <a href="http://functions.wolfram.com/Constants/Pi/10/0002/" class="externalLink">
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215 http://functions.wolfram.com/Constants/Pi/10/0002/</a>. The following
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216 anonymous class provides the implementation:
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217 <div class="source"><pre>ContinuedFraction c = new ContinuedFraction() {
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218 public double getA(int n, double x) {
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219 switch(n) {
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220 case 0: return 3.0;
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221 default: return 6.0;
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222 }
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223 }
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224
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225 public double getB(int n, double x) {
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226 double y = (2.0 * n) - 1.0;
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227 return y * y;
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228 }
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229 }</pre>
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230 </div>
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231 </p>
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232 <p>
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233 Then, to evalute Pi, simply call any of the <code>evalute</code> methods
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234 (Note, the point of evalution in this example is meaningless since Pi is a
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235 constant).
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236 </p>
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237 <p>
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238 For a more practical use of continued fractions, consider the exponential
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239 function with the continued fraction definition of
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240 <a href="http://functions.wolfram.com/ElementaryFunctions/Exp/10/" class="externalLink">
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241 http://functions.wolfram.com/ElementaryFunctions/Exp/10/</a>. The
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242 following anonymous class provides its implementation:
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243 <div class="source"><pre>ContinuedFraction c = new ContinuedFraction() {
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244 public double getA(int n, double x) {
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245 if (n % 2 == 0) {
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246 switch(n) {
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247 case 0: return 1.0;
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248 default: return 2.0;
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249 }
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250 } else {
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251 return n;
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252 }
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253 }
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254
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255 public double getB(int n, double x) {
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256 if (n % 2 == 0) {
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257 return -x;
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258 } else {
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259 return x;
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260 }
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261 }
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262 }</pre>
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263 </div>
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264 </p>
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265 <p>
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266 Then, to evalute <i>e</i><sup>x</sup> for any value x, simply call any of the
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267 <code>evalute</code> methods.
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268 </p>
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269 </div>
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270 <div class="section"><h3><a name="a6.5_binomial_coefficients_factorials_and_other_common_math_functions"></a>6.5 binomial coefficients, factorials and other common math functions</h3>
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271 <p>
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272 A collection of reusable math functions is provided in the
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273 <a href="../apidocs/org/apache/commons/math/util/MathUtils.html">MathUtils</a>
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274 utility class. MathUtils currently includes methods to compute the following: <ul><li>
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275 Binomial coeffiecients -- "n choose k" available as an (exact) long value,
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276 <code>binomialCoefficient(int, int)</code> for small n, k; as a double,
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277 <code>binomialCoefficientDouble(int, int)</code> for larger values; and in
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278 a "super-sized" version, <code>binomialCoefficientLog(int, int)</code>
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279 that returns the natural logarithm of the value.</li>
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280 <li>
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281 Factorials -- like binomial coefficients, these are available as exact long
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282 values, <code>factorial(int)</code>; doubles,
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283 <code>factorialDouble(int)</code>; or logs, <code>factorialLog(int)</code>. </li>
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284 <li>
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285 Hyperbolic sine and cosine functions --
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286 <code>cosh(double), sinh(double)</code></li>
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287 <li>
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288 sign (+1 if argument > 0, 0 if x = 0, and -1 if x < 0) and
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289 indicator (+1.0 if argument >= 0 and -1.0 if argument < 0) functions
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290 for variables of all primitive numeric types.</li>
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291 <li>
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292 a hash function, <code>hash(double),</code> returning a long-valued
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293 hash code for a double value.
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294 </li>
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295 <li>
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296 Convience methods to round floating-point number to arbitrary precision.
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297 </li>
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298 <li>
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299 Least common multiple and greatest common denominator functions.
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300 </li>
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301 </ul>
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302 </p>
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303 </div>
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304 </div>
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305
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306 </div>
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307 </div>
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309 <hr/>
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310 </div>
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311 <div id="footer">
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312 <div class="xright">©
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313 2003-2010
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321
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322
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323 </div>
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327 </div>
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