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91 <FONT SIZE="-1">
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92 org.apache.commons.math.random</FONT>
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93 <BR>
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94 Class CorrelatedRandomVectorGenerator</H2>
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95 <PRE>
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96 <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
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97 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.random.CorrelatedRandomVectorGenerator</B>
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98 </PRE>
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99 <DL>
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100 <DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random">RandomVectorGenerator</A></DD>
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101 </DL>
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102 <HR>
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103 <DL>
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104 <DT><PRE>public class <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.62"><B>CorrelatedRandomVectorGenerator</B></A><DT>extends <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random">RandomVectorGenerator</A></DL>
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105 </PRE>
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106
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107 <P>
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108 A <A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random"><CODE>RandomVectorGenerator</CODE></A> that generates vectors with with
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109 correlated components.
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110 <p>Random vectors with correlated components are built by combining
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111 the uncorrelated components of another random vector in such a way that
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112 the resulting correlations are the ones specified by a positive
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113 definite covariance matrix.</p>
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114 <p>The main use for correlated random vector generation is for Monte-Carlo
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115 simulation of physical problems with several variables, for example to
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116 generate error vectors to be added to a nominal vector. A particularly
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117 interesting case is when the generated vector should be drawn from a <a
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118 href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution">
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119 Multivariate Normal Distribution</a>. The approach using a Cholesky
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120 decomposition is quite usual in this case. However, it cas be extended
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121 to other cases as long as the underlying random generator provides
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122 <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random"><CODE>normalized values</CODE></A> like <A HREF="../../../../../org/apache/commons/math/random/GaussianRandomGenerator.html" title="class in org.apache.commons.math.random"><CODE>GaussianRandomGenerator</CODE></A> or <A HREF="../../../../../org/apache/commons/math/random/UniformRandomGenerator.html" title="class in org.apache.commons.math.random"><CODE>UniformRandomGenerator</CODE></A>.</p>
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123 <p>Sometimes, the covariance matrix for a given simulation is not
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124 strictly positive definite. This means that the correlations are
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125 not all independent from each other. In this case, however, the non
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126 strictly positive elements found during the Cholesky decomposition
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127 of the covariance matrix should not be negative either, they
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128 should be null. Another non-conventional extension handling this case
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129 is used here. Rather than computing <code>C = U<sup>T</sup>.U</code>
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130 where <code>C</code> is the covariance matrix and <code>U</code>
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131 is an uppertriangular matrix, we compute <code>C = B.B<sup>T</sup></code>
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132 where <code>B</code> is a rectangular matrix having
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133 more rows than columns. The number of columns of <code>B</code> is
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134 the rank of the covariance matrix, and it is the dimension of the
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135 uncorrelated random vector that is needed to compute the component
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136 of the correlated vector. This class handles this situation
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137 automatically.</p>
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138 <P>
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139
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140 <P>
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141 <DL>
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142 <DT><B>Since:</B></DT>
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143 <DD>1.2</DD>
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144 <DT><B>Version:</B></DT>
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145 <DD>$Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $</DD>
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146 </DL>
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147 <HR>
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148
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149 <P>
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150
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151 <!-- ======== CONSTRUCTOR SUMMARY ======== -->
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152
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153 <A NAME="constructor_summary"><!-- --></A>
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154 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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155 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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156 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
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157 <B>Constructor Summary</B></FONT></TH>
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158 </TR>
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159 <TR BGCOLOR="white" CLASS="TableRowColor">
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160 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(double[], org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</A></B>(double[] mean,
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161 <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance,
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162 double small,
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163 <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator)</CODE>
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164
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165 <BR>
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166 Simple constructor.</TD>
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167 </TR>
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168 <TR BGCOLOR="white" CLASS="TableRowColor">
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169 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</A></B>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance,
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170 double small,
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171 <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator)</CODE>
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172
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173 <BR>
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174 Simple constructor.</TD>
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175 </TR>
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176 </TABLE>
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177
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178 <!-- ========== METHOD SUMMARY =========== -->
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179
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180 <A NAME="method_summary"><!-- --></A>
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181 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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182 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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183 <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
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184 <B>Method Summary</B></FONT></TH>
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185 </TR>
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186 <TR BGCOLOR="white" CLASS="TableRowColor">
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187 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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188 <CODE> <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A></CODE></FONT></TD>
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189 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getGenerator()">getGenerator</A></B>()</CODE>
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190
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191 <BR>
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192 Get the underlying normalized components generator.</TD>
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193 </TR>
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194 <TR BGCOLOR="white" CLASS="TableRowColor">
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195 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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196 <CODE> int</CODE></FONT></TD>
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197 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRank()">getRank</A></B>()</CODE>
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198
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199 <BR>
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200 Get the rank of the covariance matrix.</TD>
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201 </TR>
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202 <TR BGCOLOR="white" CLASS="TableRowColor">
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203 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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204 <CODE> <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A></CODE></FONT></TD>
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205 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()">getRootMatrix</A></B>()</CODE>
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206
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207 <BR>
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208 Get the root of the covariance matrix.</TD>
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209 </TR>
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210 <TR BGCOLOR="white" CLASS="TableRowColor">
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211 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
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212 <CODE> double[]</CODE></FONT></TD>
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213 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#nextVector()">nextVector</A></B>()</CODE>
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214
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215 <BR>
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216 Generate a correlated random vector.</TD>
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217 </TR>
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218 </TABLE>
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219 <A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
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220 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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221 <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
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222 <TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
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223 </TR>
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224 <TR BGCOLOR="white" CLASS="TableRowColor">
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225 <TD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
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226 </TR>
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227 </TABLE>
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228
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229 <P>
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230
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231 <!-- ========= CONSTRUCTOR DETAIL ======== -->
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232
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233 <A NAME="constructor_detail"><!-- --></A>
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234 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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235 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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236 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
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237 <B>Constructor Detail</B></FONT></TH>
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238 </TR>
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239 </TABLE>
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240
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241 <A NAME="CorrelatedRandomVectorGenerator(double[], org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)"><!-- --></A><H3>
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242 CorrelatedRandomVectorGenerator</H3>
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243 <PRE>
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244 public <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.96"><B>CorrelatedRandomVectorGenerator</B></A>(double[] mean,
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245 <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance,
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246 double small,
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247 <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator)
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248 throws <A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A>,
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249 <A HREF="../../../../../org/apache/commons/math/DimensionMismatchException.html" title="class in org.apache.commons.math">DimensionMismatchException</A></PRE>
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250 <DL>
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251 <DD>Simple constructor.
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252 <p>Build a correlated random vector generator from its mean
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253 vector and covariance matrix.</p>
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254 <P>
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255 <DL>
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256 <DT><B>Parameters:</B><DD><CODE>mean</CODE> - expected mean values for all components<DD><CODE>covariance</CODE> - covariance matrix<DD><CODE>small</CODE> - diagonal elements threshold under which column are
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257 considered to be dependent on previous ones and are discarded<DD><CODE>generator</CODE> - underlying generator for uncorrelated normalized
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258 components
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259 <DT><B>Throws:</B>
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260 <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if there is a dimension
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261 mismatch between the mean vector and the covariance matrix
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262 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></CODE> - if the
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263 covariance matrix is not strictly positive definite
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264 <DD><CODE><A HREF="../../../../../org/apache/commons/math/DimensionMismatchException.html" title="class in org.apache.commons.math">DimensionMismatchException</A></CODE> - if the mean and covariance
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265 arrays dimensions don't match</DL>
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266 </DL>
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267 <HR>
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268
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269 <A NAME="CorrelatedRandomVectorGenerator(org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)"><!-- --></A><H3>
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270 CorrelatedRandomVectorGenerator</H3>
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271 <PRE>
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272 public <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.125"><B>CorrelatedRandomVectorGenerator</B></A>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance,
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273 double small,
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274 <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator)
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275 throws <A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></PRE>
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276 <DL>
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277 <DD>Simple constructor.
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278 <p>Build a null mean random correlated vector generator from its
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279 covariance matrix.</p>
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280 <P>
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281 <DL>
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282 <DT><B>Parameters:</B><DD><CODE>covariance</CODE> - covariance matrix<DD><CODE>small</CODE> - diagonal elements threshold under which column are
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283 considered to be dependent on previous ones and are discarded<DD><CODE>generator</CODE> - underlying generator for uncorrelated normalized
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284 components
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285 <DT><B>Throws:</B>
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286 <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></CODE> - if the
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287 covariance matrix is not strictly positive definite</DL>
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288 </DL>
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289
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290 <!-- ============ METHOD DETAIL ========== -->
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291
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292 <A NAME="method_detail"><!-- --></A>
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293 <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
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294 <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
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295 <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
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296 <B>Method Detail</B></FONT></TH>
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297 </TR>
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298 </TABLE>
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299
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300 <A NAME="getGenerator()"><!-- --></A><H3>
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301 getGenerator</H3>
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302 <PRE>
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303 public <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.145"><B>getGenerator</B></A>()</PRE>
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304 <DL>
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305 <DD>Get the underlying normalized components generator.
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306 <P>
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307 <DD><DL>
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308 </DL>
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309 </DD>
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310 <DD><DL>
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311
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312 <DT><B>Returns:</B><DD>underlying uncorrelated components generator</DL>
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313 </DD>
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314 </DL>
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315 <HR>
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316
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317 <A NAME="getRootMatrix()"><!-- --></A><H3>
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318 getRootMatrix</H3>
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319 <PRE>
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320 public <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.155"><B>getRootMatrix</B></A>()</PRE>
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321 <DL>
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322 <DD>Get the root of the covariance matrix.
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323 The root is the rectangular matrix <code>B</code> such that
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324 the covariance matrix is equal to <code>B.B<sup>T</sup></code>
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325 <P>
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326 <DD><DL>
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327 </DL>
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328 </DD>
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329 <DD><DL>
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330
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331 <DT><B>Returns:</B><DD>root of the square matrix<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRank()"><CODE>getRank()</CODE></A></DL>
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332 </DD>
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333 </DL>
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334 <HR>
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335
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336 <A NAME="getRank()"><!-- --></A><H3>
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337 getRank</H3>
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338 <PRE>
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339 public int <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.166"><B>getRank</B></A>()</PRE>
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340 <DL>
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341 <DD>Get the rank of the covariance matrix.
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342 The rank is the number of independent rows in the covariance
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343 matrix, it is also the number of columns of the rectangular
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344 matrix of the decomposition.
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345 <P>
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346 <DD><DL>
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347 </DL>
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348 </DD>
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349 <DD><DL>
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350
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351 <DT><B>Returns:</B><DD>rank of the square matrix.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()"><CODE>getRootMatrix()</CODE></A></DL>
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352 </DD>
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353 </DL>
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354 <HR>
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355
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356 <A NAME="nextVector()"><!-- --></A><H3>
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357 nextVector</H3>
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358 <PRE>
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359 public double[] <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.283"><B>nextVector</B></A>()</PRE>
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360 <DL>
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361 <DD>Generate a correlated random vector.
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362 <P>
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363 <DD><DL>
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364 <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html#nextVector()">nextVector</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random">RandomVectorGenerator</A></CODE></DL>
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365 </DD>
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366 <DD><DL>
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367
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368 <DT><B>Returns:</B><DD>a random vector as an array of double. The returned array
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369 is created at each call, the caller can do what it wants with it.</DL>
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370 </DD>
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371 </DL>
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372 <!-- ========= END OF CLASS DATA ========= -->
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373 <HR>
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374
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375
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376 <!-- ======= START OF BOTTOM NAVBAR ====== -->
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384 <TR ALIGN="center" VALIGN="top">
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385 <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A> </TD>
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388 <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="class-use/CorrelatedRandomVectorGenerator.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A> </TD>
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396 <TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM>
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398 </TD>
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