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<h2 title="Class NonNegativeLeastSquares" class="title">Class NonNegativeLeastSquares</h2>
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<pre>public class <span class="strong">NonNegativeLeastSquares</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 NonNegativeLeastSquares provides a method for solving a least squares
 minimization problem with nonnegativity constraints. The <TT>solve()</TT>
 method finds an approximate solution to the linear system of equations
 <B>Ax</B> = <B>b</B>, such that
 ||<B>Ax</B>&nbsp;-&nbsp;<B>b</B>||<SUP>2</SUP> is minimized, and such that
 <B>x</B> &gt;= <B>0</B>. The inputs to and outputs from the <TT>solve()</TT>
 method are stored in the fields of an instance of class
 NonNegativeLeastSquares.
 <P>
 The Java code is a translation of the Fortran subroutine <TT>NNLS</TT> from
 Charles L. Lawson and Richard J. Hanson, <I>Solving Least Squares
 Problems</I> (Society for Industrial and Applied Mathematics, 1995), page
 161.</div>
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<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
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<td class="colFirst"><code>double[][]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#a">a</a></strong></code>
<div class="block">The <I>M</I>x<I>N</I>-element <B>A</B> matrix for the least squares
 problem.</div>
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<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#b">b</a></strong></code>
<div class="block">The <I>M</I>-element <B>b</B> vector for the least squares problem.</div>
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<td class="colFirst"><code>int[]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#index">index</a></strong></code>
<div class="block">The <I>N</I>-element index vector.</div>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#M">M</a></strong></code>
<div class="block">The number of rows, typically the number of input data points, in the
 least squares problem.</div>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#N">N</a></strong></code>
<div class="block">The number of columns, typically the number of output parameters, in the
 least squares problem.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#normsqr">normsqr</a></strong></code>
<div class="block">The squared Euclidean norm of the residual vector, ||<B>Ax</B> -
 <B>b</B>||<SUP>2</SUP>.</div>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#nsetp">nsetp</a></strong></code>
<div class="block">The number of elements in the set <I>P;</I> that is, the number of
 positive values (inactive constraints).</div>
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<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.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/NonNegativeLeastSquares.html#NonNegativeLeastSquares(int, int)">NonNegativeLeastSquares</a></strong>(int&nbsp;M,
                       int&nbsp;N)</code>
<div class="block">Construct a new nonnegative least squares problem of the given size.</div>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/NonNegativeLeastSquares.html#solve()">solve</a></strong>()</code>
<div class="block">Solve this least squares minimization problem with nonnegativity
 constraints.</div>
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<h4>M</h4>
<pre>public final&nbsp;int M</pre>
<div class="block">The number of rows, typically the number of input data points, in the
 least squares problem.</div>
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<h4>N</h4>
<pre>public final&nbsp;int N</pre>
<div class="block">The number of columns, typically the number of output parameters, in the
 least squares problem.</div>
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<h4>a</h4>
<pre>public final&nbsp;double[][] a</pre>
<div class="block">The <I>M</I>x<I>N</I>-element <B>A</B> matrix for the least squares
 problem. On input to the <TT>solve()</TT> method, <TT>a</TT> contains the
 matrix <B>A</B>. On output, <TT>a</TT> has been replaced with <B>QA</B>,
 where <B>Q</B> is an <I>M</I>x<I>M</I>-element orthogonal matrix
 generated during the <TT>solve()</TT> method's execution.</div>
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<h4>b</h4>
<pre>public final&nbsp;double[] b</pre>
<div class="block">The <I>M</I>-element <B>b</B> vector for the least squares problem. On
 input to the <TT>solve()</TT> method, <TT>b</TT> contains the vector
 <B>b</B>. On output, <TT>b</TT> has been replaced with <B>Qb</B>, where
 <B>Q</B> is an <I>M</I>x<I>M</I>-element orthogonal matrix generated
 during the <TT>solve()</TT> method's execution.</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
 output from the <TT>solve()</TT> method, <TT>x</TT> contains the solution
 vector <B>x</B>.</div>
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<h4>index</h4>
<pre>public final&nbsp;int[] index</pre>
<div class="block">The <I>N</I>-element index vector. On output from the <TT>solve()</TT>
 method: <TT>index[0]</TT> through <TT>index[nsetp-1]</TT> contain the
 indexes of the elements in <B>x</B> that are in set <I>P,</I> the set of
 positive values; that is, the elements that are not forced to be zero
 (inactive constraints). <TT>index[nsetp]</TT> through <TT>index[N-1]</TT>
 contain the indexes of the elements in <B>x</B> that are in set <I>Z,</I>
 the set of zero values; that is, the elements that are forced to be zero
 (active constraints).</div>
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<h4>nsetp</h4>
<pre>public&nbsp;int nsetp</pre>
<div class="block">The number of elements in the set <I>P;</I> that is, the number of
 positive values (inactive constraints). An output of the <TT>solve()</TT>
 method.</div>
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<h4>normsqr</h4>
<pre>public&nbsp;double normsqr</pre>
<div class="block">The squared Euclidean norm of the residual vector, ||<B>Ax</B> -
 <B>b</B>||<SUP>2</SUP>. An output of the <TT>solve()</TT> method.</div>
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<h4>NonNegativeLeastSquares</h4>
<pre>public&nbsp;NonNegativeLeastSquares(int&nbsp;M,
                       int&nbsp;N)</pre>
<div class="block">Construct a new nonnegative least squares problem of the given size.
 Fields <TT>M</TT> and <TT>N</TT> are set to the given values. The array
 fields <TT>a</TT>, <TT>b</TT>, <TT>x</TT>, and <TT>index</TT> are
 allocated with the proper sizes but are not filled in.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>M</code> - Number of rows (input data points) in the least squares
            problem.</dd><dd><code>N</code> - Number of columns (output parameters) in the least squares
            problem.</dd>
<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>M</TT> &lt;= 0 or <TT>N</TT>
     &lt;= 0.</dd></dl>
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<h4>solve</h4>
<pre>public&nbsp;void&nbsp;solve()</pre>
<div class="block">Solve this least squares minimization problem with nonnegativity
 constraints. The <TT>solve()</TT> method finds an approximate solution to
 the linear system of equations <B>Ax</B> = <B>b</B>, such that
 ||<B>Ax</B>&nbsp;-&nbsp;<B>b</B>||<SUP>2</SUP> is minimized, and such
 that <B>x</B> &gt;= <B>0</B>. On input, the field <TT>a</TT> must be
 filled in with the matrix <B>A</B> and the field <TT>b</TT> must be
 filled in with the vector <B>b</B> for the problem to be solved. 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="../../../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 (more than 3<I>N</I> iterations).</dd></dl>
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