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92 org.apache.commons.math.optimization</FONT>
93 <BR>
94 Class LeastSquaresConverter</H2>
95 <PRE>
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>
97 <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.optimization.LeastSquaresConverter</B>
98 </PRE>
99 <DL>
100 <DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateRealFunction</A></DD>
101 </DL>
102 <HR>
103 <DL>
104 <DT><PRE>public class <A HREF="../../../../../src-html/org/apache/commons/math/optimization/LeastSquaresConverter.html#line.57"><B>LeastSquaresConverter</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/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateRealFunction</A></DL>
105 </PRE>
106
107 <P>
108 This class converts <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>vectorial
109 objective functions</CODE></A> to <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>scalar objective functions</CODE></A>
110 when the goal is to minimize them.
111 <p>
112 This class is mostly used when the vectorial objective function represents
113 a theoretical result computed from a point set applied to a model and
114 the models point must be adjusted to fit the theoretical result to some
115 reference observations. The observations may be obtained for example from
116 physical measurements whether the model is built from theoretical
117 considerations.
118 </p>
119 <p>
120 This class computes a possibly weighted squared sum of the residuals, which is
121 a scalar value. The residuals are the difference between the theoretical model
122 (i.e. the output of the vectorial objective function) and the observations. The
123 class implements the <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>MultivariateRealFunction</CODE></A> interface and can therefore be
124 minimized by any optimizer supporting scalar objectives functions.This is one way
125 to perform a least square estimation. There are other ways to do this without using
126 this converter, as some optimization algorithms directly support vectorial objective
127 functions.
128 </p>
129 <p>
130 This class support combination of residuals with or without weights and correlations.
131 </p>
132 <P>
133
134 <P>
135 <DL>
136 <DT><B>Since:</B></DT>
137 <DD>2.0</DD>
138 <DT><B>Version:</B></DT>
139 <DD>$Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $</DD>
140 <DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>MultivariateRealFunction</CODE></A>,
141 <A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis"><CODE>MultivariateVectorialFunction</CODE></A></DL>
142 <HR>
143
144 <P>
145
146 <!-- ======== CONSTRUCTOR SUMMARY ======== -->
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152 <B>Constructor Summary</B></FONT></TH>
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154 <TR BGCOLOR="white" CLASS="TableRowColor">
155 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html#LeastSquaresConverter(org.apache.commons.math.analysis.MultivariateVectorialFunction, double[])">LeastSquaresConverter</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateVectorialFunction</A>&nbsp;function,
156 double[]&nbsp;observations)</CODE>
157
158 <BR>
159 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a simple converter for uncorrelated residuals with the same weight.</TD>
160 </TR>
161 <TR BGCOLOR="white" CLASS="TableRowColor">
162 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html#LeastSquaresConverter(org.apache.commons.math.analysis.MultivariateVectorialFunction, double[], double[])">LeastSquaresConverter</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateVectorialFunction</A>&nbsp;function,
163 double[]&nbsp;observations,
164 double[]&nbsp;weights)</CODE>
165
166 <BR>
167 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a simple converter for uncorrelated residuals with the specific weights.</TD>
168 </TR>
169 <TR BGCOLOR="white" CLASS="TableRowColor">
170 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html#LeastSquaresConverter(org.apache.commons.math.analysis.MultivariateVectorialFunction, double[], org.apache.commons.math.linear.RealMatrix)">LeastSquaresConverter</A></B>(<A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateVectorialFunction</A>&nbsp;function,
171 double[]&nbsp;observations,
172 <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A>&nbsp;scale)</CODE>
173
174 <BR>
175 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Build a simple converter for correlated residuals with the specific weights.</TD>
176 </TR>
177 </TABLE>
178 &nbsp;
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188 <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
189 <CODE>&nbsp;double</CODE></FONT></TD>
190 <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html#value(double[])">value</A></B>(double[]&nbsp;point)</CODE>
191
192 <BR>
193 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compute the value for the function at the given point.</TD>
194 </TR>
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205 &nbsp;
206 <P>
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216 </TABLE>
217
218 <A NAME="LeastSquaresConverter(org.apache.commons.math.analysis.MultivariateVectorialFunction, double[])"><!-- --></A><H3>
219 LeastSquaresConverter</H3>
220 <PRE>
221 public <A HREF="../../../../../src-html/org/apache/commons/math/optimization/LeastSquaresConverter.html#line.75"><B>LeastSquaresConverter</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateVectorialFunction</A>&nbsp;function,
222 double[]&nbsp;observations)</PRE>
223 <DL>
224 <DD>Build a simple converter for uncorrelated residuals with the same weight.
225 <P>
226 <DL>
227 <DT><B>Parameters:</B><DD><CODE>function</CODE> - vectorial residuals function to wrap<DD><CODE>observations</CODE> - observations to be compared to objective function to compute residuals</DL>
228 </DL>
229 <HR>
230
231 <A NAME="LeastSquaresConverter(org.apache.commons.math.analysis.MultivariateVectorialFunction, double[], double[])"><!-- --></A><H3>
232 LeastSquaresConverter</H3>
233 <PRE>
234 public <A HREF="../../../../../src-html/org/apache/commons/math/optimization/LeastSquaresConverter.html#line.111"><B>LeastSquaresConverter</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateVectorialFunction</A>&nbsp;function,
235 double[]&nbsp;observations,
236 double[]&nbsp;weights)
237 throws <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></PRE>
238 <DL>
239 <DD>Build a simple converter for uncorrelated residuals with the specific weights.
240 <p>
241 The scalar objective function value is computed as:
242 <pre>
243 objective = &sum;weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup>
244 </pre>
245 </p>
246 <p>
247 Weights can be used for example to combine residuals with different standard
248 deviations. As an example, consider a residuals array in which even elements
249 are angular measurements in degrees with a 0.01&deg; standard deviation and
250 odd elements are distance measurements in meters with a 15m standard deviation.
251 In this case, the weights array should be initialized with value
252 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the
253 odd elements (i.e. reciprocals of variances).
254 </p>
255 <p>
256 The array computed by the objective function, the observations array and the
257 weights array must have consistent sizes or a <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math"><CODE>FunctionEvaluationException</CODE></A> will be
258 triggered while computing the scalar objective.
259 </p>
260 <P>
261 <DL>
262 <DT><B>Parameters:</B><DD><CODE>function</CODE> - vectorial residuals function to wrap<DD><CODE>observations</CODE> - observations to be compared to objective function to compute residuals<DD><CODE>weights</CODE> - weights to apply to the residuals
263 <DT><B>Throws:</B>
264 <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 the observations vector and the weights
265 vector dimensions don't match (objective function dimension is checked only when
266 the <A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html#value(double[])"><CODE>value(double[])</CODE></A> method is called)</DL>
267 </DL>
268 <HR>
269
270 <A NAME="LeastSquaresConverter(org.apache.commons.math.analysis.MultivariateVectorialFunction, double[], org.apache.commons.math.linear.RealMatrix)"><!-- --></A><H3>
271 LeastSquaresConverter</H3>
272 <PRE>
273 public <A HREF="../../../../../src-html/org/apache/commons/math/optimization/LeastSquaresConverter.html#line.144"><B>LeastSquaresConverter</B></A>(<A HREF="../../../../../org/apache/commons/math/analysis/MultivariateVectorialFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateVectorialFunction</A>&nbsp;function,
274 double[]&nbsp;observations,
275 <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A>&nbsp;scale)
276 throws <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></PRE>
277 <DL>
278 <DD>Build a simple converter for correlated residuals with the specific weights.
279 <p>
280 The scalar objective function value is computed as:
281 <pre>
282 objective = y<sup>T</sup>y with y = scale&times;(observation-objective)
283 </pre>
284 </p>
285 <p>
286 The array computed by the objective function, the observations array and the
287 the scaling matrix must have consistent sizes or a <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math"><CODE>FunctionEvaluationException</CODE></A>
288 will be triggered while computing the scalar objective.
289 </p>
290 <P>
291 <DL>
292 <DT><B>Parameters:</B><DD><CODE>function</CODE> - vectorial residuals function to wrap<DD><CODE>observations</CODE> - observations to be compared to objective function to compute residuals<DD><CODE>scale</CODE> - scaling matrix
293 <DT><B>Throws:</B>
294 <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 the observations vector and the scale
295 matrix dimensions don't match (objective function dimension is checked only when
296 the <A HREF="../../../../../org/apache/commons/math/optimization/LeastSquaresConverter.html#value(double[])"><CODE>value(double[])</CODE></A> method is called)</DL>
297 </DL>
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309 <A NAME="value(double[])"><!-- --></A><H3>
310 value</H3>
311 <PRE>
312 public double <A HREF="../../../../../src-html/org/apache/commons/math/optimization/LeastSquaresConverter.html#line.159"><B>value</B></A>(double[]&nbsp;point)
313 throws <A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></PRE>
314 <DL>
315 <DD>Compute the value for the function at the given point.
316 <P>
317 <DD><DL>
318 <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html#value(double[])">value</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/analysis/MultivariateRealFunction.html" title="interface in org.apache.commons.math.analysis">MultivariateRealFunction</A></CODE></DL>
319 </DD>
320 <DD><DL>
321 <DT><B>Parameters:</B><DD><CODE>point</CODE> - point at which the function must be evaluated
322 <DT><B>Returns:</B><DD>function value for the given point
323 <DT><B>Throws:</B>
324 <DD><CODE><A HREF="../../../../../org/apache/commons/math/FunctionEvaluationException.html" title="class in org.apache.commons.math">FunctionEvaluationException</A></CODE> - if the function evaluation fails</DL>
325 </DD>
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