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<div class="subTitle">edu.rit.numeric</div>
<h2 title="Class NonLinearLeastSquares" class="title">Class NonLinearLeastSquares</h2>
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<pre>public class <span class="strong">NonLinearLeastSquares</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Class NonLinearLeastSquares provides a method for minimizing the sum of the
squares of a series of nonlinear functions. There are <I>M</I> functions,
each of which has <I>N</I> inputs. These functions are represented by an
object that implements interface <a href="../../../edu/rit/numeric/VectorFunction.html" title="interface in edu.rit.numeric">VectorFunction</a>. The
<TT>solve()</TT> method finds a vector <B>x</B> such that
&Sigma;<SUB><I>i</I></SUB>&nbsp;[<I>f</I><SUB><I>i</I></SUB>(<B>x</B>)]<SUP>2</SUP>
is minimized. The inputs to and outputs from the <TT>solve()</TT> method are
stored in the fields of an instance of class NonLinearLeastSquares. The
Levenberg-Marquardt method is used to find the solution.
<P>
The Java code is a translation of the Fortran subroutine <TT>LMDER</TT> from
the MINPACK library. MINPACK was developed by Jorge Mor&eacute;, Burt Garbow,
and Ken Hillstrom at Argonne National Laboratory. For further information,
see
<A HREF="http://www.netlib.org/minpack/" TARGET="_top">http://www.netlib.org/minpack/</A>.</div>
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<caption><span>Fields</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../edu/rit/numeric/VectorFunction.html" title="interface in edu.rit.numeric">VectorFunction</a></code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#fcn">fcn</a></strong></code>
<div class="block">The nonlinear functions <I>f</I><SUB><I>i</I></SUB>(<B>x</B>) to be
minimized.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[][]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#fjac">fjac</a></strong></code>
<div class="block">The <I>M</I>&times;<I>N</I>-element Jacobian matrix.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#fvec">fvec</a></strong></code>
<div class="block">The <I>M</I>-element result vector.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#info">info</a></strong></code>
<div class="block">Information about the outcome.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>int[]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#ipvt">ipvt</a></strong></code>
<div class="block">The <I>N</I>-element permutation vector for <TT>fjac</TT>.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#M">M</a></strong></code>
<div class="block">The number of functions.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#N">N</a></strong></code>
<div class="block">The number of arguments for each function.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#nprint">nprint</a></strong></code>
<div class="block">Debug printout flag.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#tol">tol</a></strong></code>
<div class="block">Tolerance.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#x">x</a></strong></code>
<div class="block">The <I>N</I>-element <B>x</B> vector for the least squares problem.</div>
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<td class="colOne"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#NonLinearLeastSquares(edu.rit.numeric.VectorFunction)">NonLinearLeastSquares</a></strong>(<a href="../../../edu/rit/numeric/VectorFunction.html" title="interface in edu.rit.numeric">VectorFunction</a>&nbsp;theFunction)</code>
<div class="block">Construct a new nonlinear least squares problem for the given functions.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#solve()">solve</a></strong>()</code>
<div class="block">Solve this nonlinear least squares minimization problem.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonLinearLeastSquares.html#subclassDebug(int)">subclassDebug</a></strong>(int&nbsp;iter)</code>
<div class="block">Print debugging information.</div>
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<code><a href="http://docs.oracle.com/javase/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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/7/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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<h4>fcn</h4>
<pre>public final&nbsp;<a href="../../../edu/rit/numeric/VectorFunction.html" title="interface in edu.rit.numeric">VectorFunction</a> fcn</pre>
<div class="block">The nonlinear functions <I>f</I><SUB><I>i</I></SUB>(<B>x</B>) to be
minimized.</div>
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<h4>M</h4>
<pre>public final&nbsp;int M</pre>
<div class="block">The number of functions.</div>
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<h4>N</h4>
<pre>public final&nbsp;int N</pre>
<div class="block">The number of arguments for each function.</div>
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<h4>x</h4>
<pre>public final&nbsp;double[] x</pre>
<div class="block">The <I>N</I>-element <B>x</B> vector for the least squares problem. On
input to the <TT>solve()</TT> method, <TT>x</TT> contains an initial
estimate of the solution vector. On output from the <TT>solve()</TT>
method, <TT>x</TT> contains the final solution vector.</div>
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<h4>fvec</h4>
<pre>public final&nbsp;double[] fvec</pre>
<div class="block">The <I>M</I>-element result vector. On output from the <TT>solve()</TT>
method, for <I>i</I> = 0 to <I>M</I>&minus;1,
<TT>fvec</TT><SUB><I>i</I></SUB> = <I>f</I><SUB><I>i</I></SUB>(<B>x</B>),
where <B>x</B> is the final solution vector.</div>
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<h4>fjac</h4>
<pre>public final&nbsp;double[][] fjac</pre>
<div class="block">The <I>M</I>&times;<I>N</I>-element Jacobian matrix. On output from the
<TT>solve()</TT> method, the upper <I>N</I>&times;<I>N</I> submatrix of
<TT>fjac</TT> contains an upper triangular matrix <B>R</B> with diagonal
elements of nonincreasing magnitude such that
<P>
<CENTER>
<B>P</B><SUP>T</SUP>&nbsp;(<B>J</B><SUP>T</SUP>&nbsp;<B>J</B>)&nbsp;<B>P</B>&emsp;=&emsp;<B>R</B><SUP>T</SUP>&nbsp;<B>R</B>
</CENTER>
<P>
where <B>P</B> is a permutation matrix and <B>J</B> is the final
calculated Jacobian. Column <I>j</I> of <B>P</B> is column
<TT>ipvt[j]</TT> (see below) of the identity matrix. The lower
trapezoidal part of <TT>fjac</TT> contains information generated during
the computation of <B>R</B>.
<P>
<TT>fjac</TT> is used to calculate the covariance matrix of the solution.
This calculation is not yet implemented.</div>
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<h4>ipvt</h4>
<pre>public final&nbsp;int[] ipvt</pre>
<div class="block">The <I>N</I>-element permutation vector for <TT>fjac</TT>. On output from
the <TT>solve()</TT> method, <TT>ipvt</TT> defines a permutation matrix
<B>P</B> such that <B>JP</B> = <B>QR</B>, where <B>J</B> is the final
calculated Jacobian, <B>Q</B> is orthogonal (not stored), and <B>R</B> is
upper triangular with diagonal elements of nonincreasing magnitude.
Column <I>j</I> of <B>P</B> is column <TT>ipvt[j]</TT> of the identity
matrix.</div>
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<h4>tol</h4>
<pre>public&nbsp;double tol</pre>
<div class="block">Tolerance. An input to the <TT>solve()</TT> method. Must be &gt;= 0.
Termination occurs when the algorithm estimates either that the relative
error in the sum of squares is at most <TT>tol</TT> or that the relative
error between <TT>x</TT> and the solution is at most <TT>tol</TT>. The
default tolerance is 1&times;10<SUP>&minus;6</SUP>.</div>
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<h4>info</h4>
<pre>public&nbsp;int info</pre>
<div class="block">Information about the outcome. An output of the <TT>solve()</TT> method.
The possible values are:
<UL>
<LI>
0 -- Improper input parameters. Also, an IllegalArgumentException is
thrown.
<LI>
1 -- Algorithm estimates that the relative error in the sum of squares is
at most <TT>tol</TT>.
<LI>
2 -- Algorithm estimates that the relative error between <TT>x</TT> and
the solution is at most <TT>tol</TT>.
<LI>
3 -- Conditions for <TT>info</TT> = 1 and <TT>info</TT> = 2 both hold.
<LI>
4 -- <TT>fvec</TT> is orthogonal to the columns of the Jacobian to
machine precision.
<LI>
5 -- Number of function evaluations has reached 100(<I>N</I>+1). Also, a
TooManyIterationsException is thrown.
<LI>
6 -- <TT>tol</TT> is too small. No further reduction in the sum of
squares is possible.
<LI>
7 -- <TT>tol</TT> is too small. No further improvement in the approximate
solution <TT>x</TT> is possible.
</UL></div>
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<h4>nprint</h4>
<pre>public&nbsp;int nprint</pre>
<div class="block">Debug printout flag. An input to the <TT>solve()</TT> method. If
<TT>nprint</TT> &gt; 0, the <TT>subclassDebug()</TT> method is called at
the beginning of the first iteration and every <TT>nprint</TT> iterations
thereafter and immediately prior to return. If <TT>nprint</TT> &lt;= 0,
the <TT>subclassDebug()</TT> method is not called. The default setting is
0.</div>
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<h4>NonLinearLeastSquares</h4>
<pre>public&nbsp;NonLinearLeastSquares(<a href="../../../edu/rit/numeric/VectorFunction.html" title="interface in edu.rit.numeric">VectorFunction</a>&nbsp;theFunction)</pre>
<div class="block">Construct a new nonlinear least squares problem for the given functions.
Field <TT>fcn</TT> is set to <TT>theFunction</TT>. Fields <TT>M</TT> and
<TT>N</TT> are set by calling the <TT>resultLength()</TT> and
<TT>argumentLength()</TT> methods of <TT>theFunction</TT>. The vector and
matrix fields <TT>x</TT>, <TT>fvec</TT>, <TT>fjac</TT>, and <TT>ipvt</TT>
are allocated with the proper sizes but are not filled in.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>theFunction</code> - Nonlinear functions to be minimized.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - (unchecked exception) Thrown if <TT>theFunction</TT> is null.</dd>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <I>M</I> &lt;= 0, <I>N</I> &lt;= 0,
or <I>M</I> &lt; <I>N</I>.</dd></dl>
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<h4>solve</h4>
<pre>public&nbsp;void&nbsp;solve()</pre>
<div class="block">Solve this nonlinear least squares minimization problem. The
<TT>solve()</TT> method finds a vector <B>x</B> such that
&Sigma;<SUB><I>i</I></SUB>&nbsp;[<I>f</I><SUB><I>i</I></SUB>(<B>x</B>)]<SUP>2</SUP>
is minimized. On input, the field <TT>x</TT> must be filled in with an
initial estimate of the solution vector, and the field <TT>tol</TT> must
be set to the desired tolerance. On output, the other fields are filled
in with the solution as explained in the documentation for each field.</div>
<dl><dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>tol</TT> &lt;= 0.</dd>
<dd><code><a href="../../../edu/rit/numeric/TooManyIterationsException.html" title="class in edu.rit.numeric">TooManyIterationsException</a></code> - (unchecked exception) Thrown if too many iterations occurred without
finding a minimum (100(<I>N</I>+1) iterations).</dd></dl>
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<pre>protected&nbsp;void&nbsp;subclassDebug(int&nbsp;iter)</pre>
<div class="block">Print debugging information. If the <TT>nprint</TT> field is greater than
zero, the <TT>subclassDebug()</TT> method is called at the beginning of
the first iteration and every <TT>nprint</TT> iterations thereafter and
immediately prior to return. The fields of this object contain the
current state of the algorithm. The fields of this object must not be
altered.
<P>
The default implementation of the <TT>subclassDebug()</TT> method does
nothing. A subclass can override the <TT>subclassDebug()</TT> method to
do something, such as print debugging information.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>iter</code> - Iteration number.</dd></dl>
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