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| <div class="subTitle">org.apache.commons.math3.optimization</div> |
| <h2 title="Class LeastSquaresConverter" class="title">Class LeastSquaresConverter</h2> |
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| <ul class="inheritance"> |
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| <ul class="inheritance"> |
| <li>org.apache.commons.math3.optimization.LeastSquaresConverter</li> |
| </ul> |
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| </ul> |
| <div class="description"> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <dl> |
| <dt>All Implemented Interfaces:</dt> |
| <dd><a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a></dd> |
| </dl> |
| <hr> |
| <div class="block"><strong>Deprecated.</strong> |
| <div class="block"><i>As of 3.1 (to be removed in 4.0).</i></div> |
| </div> |
| <br> |
| <pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> |
| public class <span class="strong">LeastSquaresConverter</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a> |
| implements <a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a></pre> |
| <div class="block">This class converts <a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis"><code>vectorial |
| objective functions</code></a> to <a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis"><code>scalar objective functions</code></a> |
| when the goal is to minimize them. |
| <p> |
| This class is mostly used when the vectorial objective function represents |
| a theoretical result computed from a point set applied to a model and |
| the models point must be adjusted to fit the theoretical result to some |
| reference observations. The observations may be obtained for example from |
| physical measurements whether the model is built from theoretical |
| considerations. |
| </p> |
| <p> |
| This class computes a possibly weighted squared sum of the residuals, which is |
| a scalar value. The residuals are the difference between the theoretical model |
| (i.e. the output of the vectorial objective function) and the observations. The |
| class implements the <a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis"><code>MultivariateFunction</code></a> interface and can therefore be |
| minimized by any optimizer supporting scalar objectives functions.This is one way |
| to perform a least square estimation. There are other ways to do this without using |
| this converter, as some optimization algorithms directly support vectorial objective |
| functions. |
| </p> |
| <p> |
| This class support combination of residuals with or without weights and correlations. |
| </p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>2.0</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: LeastSquaresConverter.java 1591835 2014-05-02 09:04:01Z tn $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis"><code>MultivariateFunction</code></a>, |
| <a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis"><code>MultivariateVectorFunction</code></a></dd></dl> |
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| <th class="colOne" scope="col">Constructor and Description</th> |
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| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/optimization/LeastSquaresConverter.html#LeastSquaresConverter(org.apache.commons.math3.analysis.MultivariateVectorFunction, double[])">LeastSquaresConverter</a></strong>(<a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateVectorFunction</a> function, |
| double[] observations)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Build a simple converter for uncorrelated residuals with the same weight.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/optimization/LeastSquaresConverter.html#LeastSquaresConverter(org.apache.commons.math3.analysis.MultivariateVectorFunction, double[], double[])">LeastSquaresConverter</a></strong>(<a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateVectorFunction</a> function, |
| double[] observations, |
| double[] weights)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Build a simple converter for uncorrelated residuals with the specific weights.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/optimization/LeastSquaresConverter.html#LeastSquaresConverter(org.apache.commons.math3.analysis.MultivariateVectorFunction, double[], org.apache.commons.math3.linear.RealMatrix)">LeastSquaresConverter</a></strong>(<a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateVectorFunction</a> function, |
| double[] observations, |
| <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> scale)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Build a simple converter for correlated residuals with the specific weights.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
| </ul> |
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| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/optimization/LeastSquaresConverter.html#value(double[])">value</a></strong>(double[] point)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Compute the value for the function at the given point.</div> |
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| <code><a href="http://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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://docs.oracle.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></li> |
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| <h3>Constructor Detail</h3> |
| <a name="LeastSquaresConverter(org.apache.commons.math3.analysis.MultivariateVectorFunction, double[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>LeastSquaresConverter</h4> |
| <pre>public LeastSquaresConverter(<a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateVectorFunction</a> function, |
| double[] observations)</pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Build a simple converter for uncorrelated residuals with the same weight.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - vectorial residuals function to wrap</dd><dd><code>observations</code> - observations to be compared to objective function to compute residuals</dd></dl> |
| </li> |
| </ul> |
| <a name="LeastSquaresConverter(org.apache.commons.math3.analysis.MultivariateVectorFunction, double[], double[])"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>LeastSquaresConverter</h4> |
| <pre>public LeastSquaresConverter(<a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateVectorFunction</a> function, |
| double[] observations, |
| double[] weights)</pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Build a simple converter for uncorrelated residuals with the specific weights. |
| <p> |
| The scalar objective function value is computed as: |
| <pre> |
| objective = ∑weight<sub>i</sub>(observation<sub>i</sub>-objective<sub>i</sub>)<sup>2</sup> |
| </pre> |
| </p> |
| <p> |
| Weights can be used for example to combine residuals with different standard |
| deviations. As an example, consider a residuals array in which even elements |
| are angular measurements in degrees with a 0.01° standard deviation and |
| odd elements are distance measurements in meters with a 15m standard deviation. |
| In this case, the weights array should be initialized with value |
| 1.0/(0.01<sup>2</sup>) in the even elements and 1.0/(15.0<sup>2</sup>) in the |
| odd elements (i.e. reciprocals of variances). |
| </p> |
| <p> |
| The array computed by the objective function, the observations array and the |
| weights array must have consistent sizes or a <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception"><code>DimensionMismatchException</code></a> |
| will be triggered while computing the scalar objective. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - vectorial residuals function to wrap</dd><dd><code>observations</code> - observations to be compared to objective function to compute residuals</dd><dd><code>weights</code> - weights to apply to the residuals</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the observations vector and the weights |
| vector dimensions do not match (objective function dimension is checked only when |
| the <a href="../../../../../org/apache/commons/math3/optimization/LeastSquaresConverter.html#value(double[])"><code>value(double[])</code></a> method is called)</dd></dl> |
| </li> |
| </ul> |
| <a name="LeastSquaresConverter(org.apache.commons.math3.analysis.MultivariateVectorFunction, double[], org.apache.commons.math3.linear.RealMatrix)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>LeastSquaresConverter</h4> |
| <pre>public LeastSquaresConverter(<a href="../../../../../org/apache/commons/math3/analysis/MultivariateVectorFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateVectorFunction</a> function, |
| double[] observations, |
| <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> scale)</pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Build a simple converter for correlated residuals with the specific weights. |
| <p> |
| The scalar objective function value is computed as: |
| <pre> |
| objective = y<sup>T</sup>y with y = scale×(observation-objective) |
| </pre> |
| </p> |
| <p> |
| The array computed by the objective function, the observations array and the |
| the scaling matrix must have consistent sizes or a <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception"><code>DimensionMismatchException</code></a> |
| will be triggered while computing the scalar objective. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>function</code> - vectorial residuals function to wrap</dd><dd><code>observations</code> - observations to be compared to objective function to compute residuals</dd><dd><code>scale</code> - scaling matrix</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the observations vector and the scale |
| matrix dimensions do not match (objective function dimension is checked only when |
| the <a href="../../../../../org/apache/commons/math3/optimization/LeastSquaresConverter.html#value(double[])"><code>value(double[])</code></a> method is called)</dd></dl> |
| </li> |
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| <h4>value</h4> |
| <pre>public double value(double[] point)</pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Compute the value for the function at the given point.</div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html#value(double[])">value</a></code> in interface <code><a href="../../../../../org/apache/commons/math3/analysis/MultivariateFunction.html" title="interface in org.apache.commons.math3.analysis">MultivariateFunction</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>point</code> - Point at which the function must be evaluated.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the function value for the given point.</dd></dl> |
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