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From l..@apache.org
Subject svn commit: r857558 [21/39] - in /websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3: ./ analysis/ analysis/differentiation/ analysis/interpolation/ complex/ dfp/ distribution/ distribution/fitting/ ex...
Date Sat, 06 Apr 2013 23:42:02 GMT
Modified: websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizerTest.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizerTest.html (original)
+++ websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/PowellOptimizerTest.html Sat Apr  6 23:42:01 2013
@@ -21,237 +21,254 @@
 <FONT color="green">018</FONT>    <a name="line.18"></a>
 <FONT color="green">019</FONT>    import org.apache.commons.math3.analysis.MultivariateFunction;<a name="line.19"></a>
 <FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.SumSincFunction;<a name="line.20"></a>
-<FONT color="green">021</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;<a name="line.21"></a>
-<FONT color="green">022</FONT>    import org.apache.commons.math3.optim.PointValuePair;<a name="line.22"></a>
-<FONT color="green">023</FONT>    import org.apache.commons.math3.optim.InitialGuess;<a name="line.23"></a>
-<FONT color="green">024</FONT>    import org.apache.commons.math3.optim.MaxEval;<a name="line.24"></a>
-<FONT color="green">025</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction;<a name="line.25"></a>
-<FONT color="green">026</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.26"></a>
-<FONT color="green">027</FONT>    import org.junit.Assert;<a name="line.27"></a>
-<FONT color="green">028</FONT>    import org.junit.Test;<a name="line.28"></a>
-<FONT color="green">029</FONT>    <a name="line.29"></a>
-<FONT color="green">030</FONT>    /**<a name="line.30"></a>
-<FONT color="green">031</FONT>     * Test for {@link PowellOptimizer}.<a name="line.31"></a>
-<FONT color="green">032</FONT>     */<a name="line.32"></a>
-<FONT color="green">033</FONT>    public class PowellOptimizerTest {<a name="line.33"></a>
-<FONT color="green">034</FONT>    <a name="line.34"></a>
-<FONT color="green">035</FONT>        @Test<a name="line.35"></a>
-<FONT color="green">036</FONT>        public void testSumSinc() {<a name="line.36"></a>
-<FONT color="green">037</FONT>            final MultivariateFunction func = new SumSincFunction(-1);<a name="line.37"></a>
-<FONT color="green">038</FONT>    <a name="line.38"></a>
-<FONT color="green">039</FONT>            int dim = 2;<a name="line.39"></a>
-<FONT color="green">040</FONT>            final double[] minPoint = new double[dim];<a name="line.40"></a>
-<FONT color="green">041</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.41"></a>
-<FONT color="green">042</FONT>                minPoint[i] = 0;<a name="line.42"></a>
-<FONT color="green">043</FONT>            }<a name="line.43"></a>
-<FONT color="green">044</FONT>    <a name="line.44"></a>
-<FONT color="green">045</FONT>            double[] init = new double[dim];<a name="line.45"></a>
-<FONT color="green">046</FONT>    <a name="line.46"></a>
-<FONT color="green">047</FONT>            // Initial is minimum.<a name="line.47"></a>
-<FONT color="green">048</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.48"></a>
-<FONT color="green">049</FONT>                init[i] = minPoint[i];<a name="line.49"></a>
-<FONT color="green">050</FONT>            }<a name="line.50"></a>
-<FONT color="green">051</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9);<a name="line.51"></a>
-<FONT color="green">052</FONT>    <a name="line.52"></a>
-<FONT color="green">053</FONT>            // Initial is far from minimum.<a name="line.53"></a>
-<FONT color="green">054</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.54"></a>
-<FONT color="green">055</FONT>                init[i] = minPoint[i] + 3;<a name="line.55"></a>
-<FONT color="green">056</FONT>            }<a name="line.56"></a>
-<FONT color="green">057</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-5);<a name="line.57"></a>
-<FONT color="green">058</FONT>            // More stringent line search tolerance enhances the precision<a name="line.58"></a>
-<FONT color="green">059</FONT>            // of the result.<a name="line.59"></a>
-<FONT color="green">060</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9, 1e-7);<a name="line.60"></a>
-<FONT color="green">061</FONT>        }<a name="line.61"></a>
-<FONT color="green">062</FONT>    <a name="line.62"></a>
-<FONT color="green">063</FONT>        @Test<a name="line.63"></a>
-<FONT color="green">064</FONT>        public void testQuadratic() {<a name="line.64"></a>
-<FONT color="green">065</FONT>            final MultivariateFunction func = new MultivariateFunction() {<a name="line.65"></a>
-<FONT color="green">066</FONT>                    public double value(double[] x) {<a name="line.66"></a>
-<FONT color="green">067</FONT>                        final double a = x[0] - 1;<a name="line.67"></a>
-<FONT color="green">068</FONT>                        final double b = x[1] - 1;<a name="line.68"></a>
-<FONT color="green">069</FONT>                        return a * a + b * b + 1;<a name="line.69"></a>
-<FONT color="green">070</FONT>                    }<a name="line.70"></a>
-<FONT color="green">071</FONT>                };<a name="line.71"></a>
-<FONT color="green">072</FONT>    <a name="line.72"></a>
-<FONT color="green">073</FONT>            int dim = 2;<a name="line.73"></a>
-<FONT color="green">074</FONT>            final double[] minPoint = new double[dim];<a name="line.74"></a>
-<FONT color="green">075</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.75"></a>
-<FONT color="green">076</FONT>                minPoint[i] = 1;<a name="line.76"></a>
-<FONT color="green">077</FONT>            }<a name="line.77"></a>
-<FONT color="green">078</FONT>    <a name="line.78"></a>
-<FONT color="green">079</FONT>            double[] init = new double[dim];<a name="line.79"></a>
-<FONT color="green">080</FONT>    <a name="line.80"></a>
-<FONT color="green">081</FONT>            // Initial is minimum.<a name="line.81"></a>
-<FONT color="green">082</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.82"></a>
-<FONT color="green">083</FONT>                init[i] = minPoint[i];<a name="line.83"></a>
-<FONT color="green">084</FONT>            }<a name="line.84"></a>
-<FONT color="green">085</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);<a name="line.85"></a>
-<FONT color="green">086</FONT>    <a name="line.86"></a>
-<FONT color="green">087</FONT>            // Initial is far from minimum.<a name="line.87"></a>
-<FONT color="green">088</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.88"></a>
-<FONT color="green">089</FONT>                init[i] = minPoint[i] - 20;<a name="line.89"></a>
-<FONT color="green">090</FONT>            }<a name="line.90"></a>
-<FONT color="green">091</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);<a name="line.91"></a>
-<FONT color="green">092</FONT>        }<a name="line.92"></a>
+<FONT color="green">021</FONT>    import org.apache.commons.math3.optim.PointValuePair;<a name="line.21"></a>
+<FONT color="green">022</FONT>    import org.apache.commons.math3.optim.InitialGuess;<a name="line.22"></a>
+<FONT color="green">023</FONT>    import org.apache.commons.math3.optim.MaxEval;<a name="line.23"></a>
+<FONT color="green">024</FONT>    import org.apache.commons.math3.optim.SimpleBounds;<a name="line.24"></a>
+<FONT color="green">025</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;<a name="line.25"></a>
+<FONT color="green">026</FONT>    import org.apache.commons.math3.optim.nonlinear.scalar.ObjectiveFunction;<a name="line.26"></a>
+<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.MathUnsupportedOperationException;<a name="line.27"></a>
+<FONT color="green">028</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.28"></a>
+<FONT color="green">029</FONT>    import org.junit.Assert;<a name="line.29"></a>
+<FONT color="green">030</FONT>    import org.junit.Test;<a name="line.30"></a>
+<FONT color="green">031</FONT>    <a name="line.31"></a>
+<FONT color="green">032</FONT>    /**<a name="line.32"></a>
+<FONT color="green">033</FONT>     * Test for {@link PowellOptimizer}.<a name="line.33"></a>
+<FONT color="green">034</FONT>     */<a name="line.34"></a>
+<FONT color="green">035</FONT>    public class PowellOptimizerTest {<a name="line.35"></a>
+<FONT color="green">036</FONT>        @Test(expected=MathUnsupportedOperationException.class)<a name="line.36"></a>
+<FONT color="green">037</FONT>        public void testBoundsUnsupported() {<a name="line.37"></a>
+<FONT color="green">038</FONT>            final MultivariateFunction func = new SumSincFunction(-1);<a name="line.38"></a>
+<FONT color="green">039</FONT>            final PowellOptimizer optim = new PowellOptimizer(1e-8, 1e-5,<a name="line.39"></a>
+<FONT color="green">040</FONT>                                                              1e-4, 1e-4);<a name="line.40"></a>
+<FONT color="green">041</FONT>    <a name="line.41"></a>
+<FONT color="green">042</FONT>            optim.optimize(new MaxEval(100),<a name="line.42"></a>
+<FONT color="green">043</FONT>                           new ObjectiveFunction(func),<a name="line.43"></a>
+<FONT color="green">044</FONT>                           GoalType.MINIMIZE,<a name="line.44"></a>
+<FONT color="green">045</FONT>                           new InitialGuess(new double[] { -3, 0 }),<a name="line.45"></a>
+<FONT color="green">046</FONT>                           new SimpleBounds(new double[] { -5, -1 },<a name="line.46"></a>
+<FONT color="green">047</FONT>                                            new double[] { 5, 1 }));<a name="line.47"></a>
+<FONT color="green">048</FONT>        }<a name="line.48"></a>
+<FONT color="green">049</FONT>    <a name="line.49"></a>
+<FONT color="green">050</FONT>        @Test<a name="line.50"></a>
+<FONT color="green">051</FONT>        public void testSumSinc() {<a name="line.51"></a>
+<FONT color="green">052</FONT>            final MultivariateFunction func = new SumSincFunction(-1);<a name="line.52"></a>
+<FONT color="green">053</FONT>    <a name="line.53"></a>
+<FONT color="green">054</FONT>            int dim = 2;<a name="line.54"></a>
+<FONT color="green">055</FONT>            final double[] minPoint = new double[dim];<a name="line.55"></a>
+<FONT color="green">056</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.56"></a>
+<FONT color="green">057</FONT>                minPoint[i] = 0;<a name="line.57"></a>
+<FONT color="green">058</FONT>            }<a name="line.58"></a>
+<FONT color="green">059</FONT>    <a name="line.59"></a>
+<FONT color="green">060</FONT>            double[] init = new double[dim];<a name="line.60"></a>
+<FONT color="green">061</FONT>    <a name="line.61"></a>
+<FONT color="green">062</FONT>            // Initial is minimum.<a name="line.62"></a>
+<FONT color="green">063</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.63"></a>
+<FONT color="green">064</FONT>                init[i] = minPoint[i];<a name="line.64"></a>
+<FONT color="green">065</FONT>            }<a name="line.65"></a>
+<FONT color="green">066</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9);<a name="line.66"></a>
+<FONT color="green">067</FONT>    <a name="line.67"></a>
+<FONT color="green">068</FONT>            // Initial is far from minimum.<a name="line.68"></a>
+<FONT color="green">069</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.69"></a>
+<FONT color="green">070</FONT>                init[i] = minPoint[i] + 3;<a name="line.70"></a>
+<FONT color="green">071</FONT>            }<a name="line.71"></a>
+<FONT color="green">072</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-5);<a name="line.72"></a>
+<FONT color="green">073</FONT>            // More stringent line search tolerance enhances the precision<a name="line.73"></a>
+<FONT color="green">074</FONT>            // of the result.<a name="line.74"></a>
+<FONT color="green">075</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9, 1e-7);<a name="line.75"></a>
+<FONT color="green">076</FONT>        }<a name="line.76"></a>
+<FONT color="green">077</FONT>    <a name="line.77"></a>
+<FONT color="green">078</FONT>        @Test<a name="line.78"></a>
+<FONT color="green">079</FONT>        public void testQuadratic() {<a name="line.79"></a>
+<FONT color="green">080</FONT>            final MultivariateFunction func = new MultivariateFunction() {<a name="line.80"></a>
+<FONT color="green">081</FONT>                    public double value(double[] x) {<a name="line.81"></a>
+<FONT color="green">082</FONT>                        final double a = x[0] - 1;<a name="line.82"></a>
+<FONT color="green">083</FONT>                        final double b = x[1] - 1;<a name="line.83"></a>
+<FONT color="green">084</FONT>                        return a * a + b * b + 1;<a name="line.84"></a>
+<FONT color="green">085</FONT>                    }<a name="line.85"></a>
+<FONT color="green">086</FONT>                };<a name="line.86"></a>
+<FONT color="green">087</FONT>    <a name="line.87"></a>
+<FONT color="green">088</FONT>            int dim = 2;<a name="line.88"></a>
+<FONT color="green">089</FONT>            final double[] minPoint = new double[dim];<a name="line.89"></a>
+<FONT color="green">090</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.90"></a>
+<FONT color="green">091</FONT>                minPoint[i] = 1;<a name="line.91"></a>
+<FONT color="green">092</FONT>            }<a name="line.92"></a>
 <FONT color="green">093</FONT>    <a name="line.93"></a>
-<FONT color="green">094</FONT>        @Test<a name="line.94"></a>
-<FONT color="green">095</FONT>        public void testMaximizeQuadratic() {<a name="line.95"></a>
-<FONT color="green">096</FONT>            final MultivariateFunction func = new MultivariateFunction() {<a name="line.96"></a>
-<FONT color="green">097</FONT>                    public double value(double[] x) {<a name="line.97"></a>
-<FONT color="green">098</FONT>                        final double a = x[0] - 1;<a name="line.98"></a>
-<FONT color="green">099</FONT>                        final double b = x[1] - 1;<a name="line.99"></a>
-<FONT color="green">100</FONT>                        return -a * a - b * b + 1;<a name="line.100"></a>
-<FONT color="green">101</FONT>                    }<a name="line.101"></a>
-<FONT color="green">102</FONT>                };<a name="line.102"></a>
-<FONT color="green">103</FONT>    <a name="line.103"></a>
-<FONT color="green">104</FONT>            int dim = 2;<a name="line.104"></a>
-<FONT color="green">105</FONT>            final double[] maxPoint = new double[dim];<a name="line.105"></a>
-<FONT color="green">106</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.106"></a>
-<FONT color="green">107</FONT>                maxPoint[i] = 1;<a name="line.107"></a>
-<FONT color="green">108</FONT>            }<a name="line.108"></a>
-<FONT color="green">109</FONT>    <a name="line.109"></a>
-<FONT color="green">110</FONT>            double[] init = new double[dim];<a name="line.110"></a>
-<FONT color="green">111</FONT>    <a name="line.111"></a>
-<FONT color="green">112</FONT>            // Initial is minimum.<a name="line.112"></a>
-<FONT color="green">113</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.113"></a>
-<FONT color="green">114</FONT>                init[i] = maxPoint[i];<a name="line.114"></a>
-<FONT color="green">115</FONT>            }<a name="line.115"></a>
-<FONT color="green">116</FONT>            doTest(func, maxPoint, init,  GoalType.MAXIMIZE, 1e-9, 1e-8);<a name="line.116"></a>
-<FONT color="green">117</FONT>    <a name="line.117"></a>
-<FONT color="green">118</FONT>            // Initial is far from minimum.<a name="line.118"></a>
-<FONT color="green">119</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.119"></a>
-<FONT color="green">120</FONT>                init[i] = maxPoint[i] - 20;<a name="line.120"></a>
-<FONT color="green">121</FONT>            }<a name="line.121"></a>
-<FONT color="green">122</FONT>            doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);<a name="line.122"></a>
-<FONT color="green">123</FONT>        }<a name="line.123"></a>
+<FONT color="green">094</FONT>            double[] init = new double[dim];<a name="line.94"></a>
+<FONT color="green">095</FONT>    <a name="line.95"></a>
+<FONT color="green">096</FONT>            // Initial is minimum.<a name="line.96"></a>
+<FONT color="green">097</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.97"></a>
+<FONT color="green">098</FONT>                init[i] = minPoint[i];<a name="line.98"></a>
+<FONT color="green">099</FONT>            }<a name="line.99"></a>
+<FONT color="green">100</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);<a name="line.100"></a>
+<FONT color="green">101</FONT>    <a name="line.101"></a>
+<FONT color="green">102</FONT>            // Initial is far from minimum.<a name="line.102"></a>
+<FONT color="green">103</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.103"></a>
+<FONT color="green">104</FONT>                init[i] = minPoint[i] - 20;<a name="line.104"></a>
+<FONT color="green">105</FONT>            }<a name="line.105"></a>
+<FONT color="green">106</FONT>            doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);<a name="line.106"></a>
+<FONT color="green">107</FONT>        }<a name="line.107"></a>
+<FONT color="green">108</FONT>    <a name="line.108"></a>
+<FONT color="green">109</FONT>        @Test<a name="line.109"></a>
+<FONT color="green">110</FONT>        public void testMaximizeQuadratic() {<a name="line.110"></a>
+<FONT color="green">111</FONT>            final MultivariateFunction func = new MultivariateFunction() {<a name="line.111"></a>
+<FONT color="green">112</FONT>                    public double value(double[] x) {<a name="line.112"></a>
+<FONT color="green">113</FONT>                        final double a = x[0] - 1;<a name="line.113"></a>
+<FONT color="green">114</FONT>                        final double b = x[1] - 1;<a name="line.114"></a>
+<FONT color="green">115</FONT>                        return -a * a - b * b + 1;<a name="line.115"></a>
+<FONT color="green">116</FONT>                    }<a name="line.116"></a>
+<FONT color="green">117</FONT>                };<a name="line.117"></a>
+<FONT color="green">118</FONT>    <a name="line.118"></a>
+<FONT color="green">119</FONT>            int dim = 2;<a name="line.119"></a>
+<FONT color="green">120</FONT>            final double[] maxPoint = new double[dim];<a name="line.120"></a>
+<FONT color="green">121</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.121"></a>
+<FONT color="green">122</FONT>                maxPoint[i] = 1;<a name="line.122"></a>
+<FONT color="green">123</FONT>            }<a name="line.123"></a>
 <FONT color="green">124</FONT>    <a name="line.124"></a>
-<FONT color="green">125</FONT>        /**<a name="line.125"></a>
-<FONT color="green">126</FONT>         * Ensure that we do not increase the number of function evaluations when<a name="line.126"></a>
-<FONT color="green">127</FONT>         * the function values are scaled up.<a name="line.127"></a>
-<FONT color="green">128</FONT>         * Note that the tolerances parameters passed to the constructor must<a name="line.128"></a>
-<FONT color="green">129</FONT>         * still hold sensible values because they are used to set the line search<a name="line.129"></a>
-<FONT color="green">130</FONT>         * tolerances.<a name="line.130"></a>
-<FONT color="green">131</FONT>         */<a name="line.131"></a>
-<FONT color="green">132</FONT>        @Test<a name="line.132"></a>
-<FONT color="green">133</FONT>        public void testRelativeToleranceOnScaledValues() {<a name="line.133"></a>
-<FONT color="green">134</FONT>            final MultivariateFunction func = new MultivariateFunction() {<a name="line.134"></a>
-<FONT color="green">135</FONT>                    public double value(double[] x) {<a name="line.135"></a>
-<FONT color="green">136</FONT>                        final double a = x[0] - 1;<a name="line.136"></a>
-<FONT color="green">137</FONT>                        final double b = x[1] - 1;<a name="line.137"></a>
-<FONT color="green">138</FONT>                        return a * a * FastMath.sqrt(FastMath.abs(a)) + b * b + 1;<a name="line.138"></a>
-<FONT color="green">139</FONT>                    }<a name="line.139"></a>
-<FONT color="green">140</FONT>                };<a name="line.140"></a>
-<FONT color="green">141</FONT>    <a name="line.141"></a>
-<FONT color="green">142</FONT>            int dim = 2;<a name="line.142"></a>
-<FONT color="green">143</FONT>            final double[] minPoint = new double[dim];<a name="line.143"></a>
-<FONT color="green">144</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.144"></a>
-<FONT color="green">145</FONT>                minPoint[i] = 1;<a name="line.145"></a>
-<FONT color="green">146</FONT>            }<a name="line.146"></a>
-<FONT color="green">147</FONT>    <a name="line.147"></a>
-<FONT color="green">148</FONT>            double[] init = new double[dim];<a name="line.148"></a>
-<FONT color="green">149</FONT>            // Initial is far from minimum.<a name="line.149"></a>
-<FONT color="green">150</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.150"></a>
-<FONT color="green">151</FONT>                init[i] = minPoint[i] - 20;<a name="line.151"></a>
-<FONT color="green">152</FONT>            }<a name="line.152"></a>
-<FONT color="green">153</FONT>    <a name="line.153"></a>
-<FONT color="green">154</FONT>            final double relTol = 1e-10;<a name="line.154"></a>
-<FONT color="green">155</FONT>    <a name="line.155"></a>
-<FONT color="green">156</FONT>            final int maxEval = 1000;<a name="line.156"></a>
-<FONT color="green">157</FONT>            // Very small absolute tolerance to rely solely on the relative<a name="line.157"></a>
-<FONT color="green">158</FONT>            // tolerance as a stopping criterion<a name="line.158"></a>
-<FONT color="green">159</FONT>            final PowellOptimizer optim = new PowellOptimizer(relTol, 1e-100);<a name="line.159"></a>
-<FONT color="green">160</FONT>    <a name="line.160"></a>
-<FONT color="green">161</FONT>            final PointValuePair funcResult = optim.optimize(new MaxEval(maxEval),<a name="line.161"></a>
-<FONT color="green">162</FONT>                                                             new ObjectiveFunction(func),<a name="line.162"></a>
-<FONT color="green">163</FONT>                                                             GoalType.MINIMIZE,<a name="line.163"></a>
-<FONT color="green">164</FONT>                                                             new InitialGuess(init));<a name="line.164"></a>
-<FONT color="green">165</FONT>            final double funcValue = func.value(funcResult.getPoint());<a name="line.165"></a>
-<FONT color="green">166</FONT>            final int funcEvaluations = optim.getEvaluations();<a name="line.166"></a>
-<FONT color="green">167</FONT>    <a name="line.167"></a>
-<FONT color="green">168</FONT>            final double scale = 1e10;<a name="line.168"></a>
-<FONT color="green">169</FONT>            final MultivariateFunction funcScaled = new MultivariateFunction() {<a name="line.169"></a>
-<FONT color="green">170</FONT>                    public double value(double[] x) {<a name="line.170"></a>
-<FONT color="green">171</FONT>                        return scale * func.value(x);<a name="line.171"></a>
-<FONT color="green">172</FONT>                    }<a name="line.172"></a>
-<FONT color="green">173</FONT>                };<a name="line.173"></a>
-<FONT color="green">174</FONT>    <a name="line.174"></a>
-<FONT color="green">175</FONT>            final PointValuePair funcScaledResult = optim.optimize(new MaxEval(maxEval),<a name="line.175"></a>
-<FONT color="green">176</FONT>                                                                   new ObjectiveFunction(funcScaled),<a name="line.176"></a>
-<FONT color="green">177</FONT>                                                                   GoalType.MINIMIZE,<a name="line.177"></a>
-<FONT color="green">178</FONT>                                                                   new InitialGuess(init));<a name="line.178"></a>
-<FONT color="green">179</FONT>            final double funcScaledValue = funcScaled.value(funcScaledResult.getPoint());<a name="line.179"></a>
-<FONT color="green">180</FONT>            final int funcScaledEvaluations = optim.getEvaluations();<a name="line.180"></a>
-<FONT color="green">181</FONT>    <a name="line.181"></a>
-<FONT color="green">182</FONT>            // Check that both minima provide the same objective funciton values,<a name="line.182"></a>
-<FONT color="green">183</FONT>            // within the relative function tolerance.<a name="line.183"></a>
-<FONT color="green">184</FONT>            Assert.assertEquals(1, funcScaledValue / (scale * funcValue), relTol);<a name="line.184"></a>
-<FONT color="green">185</FONT>    <a name="line.185"></a>
-<FONT color="green">186</FONT>            // Check that the numbers of evaluations are the same.<a name="line.186"></a>
-<FONT color="green">187</FONT>            Assert.assertEquals(funcEvaluations, funcScaledEvaluations);<a name="line.187"></a>
-<FONT color="green">188</FONT>        }<a name="line.188"></a>
+<FONT color="green">125</FONT>            double[] init = new double[dim];<a name="line.125"></a>
+<FONT color="green">126</FONT>    <a name="line.126"></a>
+<FONT color="green">127</FONT>            // Initial is minimum.<a name="line.127"></a>
+<FONT color="green">128</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.128"></a>
+<FONT color="green">129</FONT>                init[i] = maxPoint[i];<a name="line.129"></a>
+<FONT color="green">130</FONT>            }<a name="line.130"></a>
+<FONT color="green">131</FONT>            doTest(func, maxPoint, init,  GoalType.MAXIMIZE, 1e-9, 1e-8);<a name="line.131"></a>
+<FONT color="green">132</FONT>    <a name="line.132"></a>
+<FONT color="green">133</FONT>            // Initial is far from minimum.<a name="line.133"></a>
+<FONT color="green">134</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.134"></a>
+<FONT color="green">135</FONT>                init[i] = maxPoint[i] - 20;<a name="line.135"></a>
+<FONT color="green">136</FONT>            }<a name="line.136"></a>
+<FONT color="green">137</FONT>            doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);<a name="line.137"></a>
+<FONT color="green">138</FONT>        }<a name="line.138"></a>
+<FONT color="green">139</FONT>    <a name="line.139"></a>
+<FONT color="green">140</FONT>        /**<a name="line.140"></a>
+<FONT color="green">141</FONT>         * Ensure that we do not increase the number of function evaluations when<a name="line.141"></a>
+<FONT color="green">142</FONT>         * the function values are scaled up.<a name="line.142"></a>
+<FONT color="green">143</FONT>         * Note that the tolerances parameters passed to the constructor must<a name="line.143"></a>
+<FONT color="green">144</FONT>         * still hold sensible values because they are used to set the line search<a name="line.144"></a>
+<FONT color="green">145</FONT>         * tolerances.<a name="line.145"></a>
+<FONT color="green">146</FONT>         */<a name="line.146"></a>
+<FONT color="green">147</FONT>        @Test<a name="line.147"></a>
+<FONT color="green">148</FONT>        public void testRelativeToleranceOnScaledValues() {<a name="line.148"></a>
+<FONT color="green">149</FONT>            final MultivariateFunction func = new MultivariateFunction() {<a name="line.149"></a>
+<FONT color="green">150</FONT>                    public double value(double[] x) {<a name="line.150"></a>
+<FONT color="green">151</FONT>                        final double a = x[0] - 1;<a name="line.151"></a>
+<FONT color="green">152</FONT>                        final double b = x[1] - 1;<a name="line.152"></a>
+<FONT color="green">153</FONT>                        return a * a * FastMath.sqrt(FastMath.abs(a)) + b * b + 1;<a name="line.153"></a>
+<FONT color="green">154</FONT>                    }<a name="line.154"></a>
+<FONT color="green">155</FONT>                };<a name="line.155"></a>
+<FONT color="green">156</FONT>    <a name="line.156"></a>
+<FONT color="green">157</FONT>            int dim = 2;<a name="line.157"></a>
+<FONT color="green">158</FONT>            final double[] minPoint = new double[dim];<a name="line.158"></a>
+<FONT color="green">159</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.159"></a>
+<FONT color="green">160</FONT>                minPoint[i] = 1;<a name="line.160"></a>
+<FONT color="green">161</FONT>            }<a name="line.161"></a>
+<FONT color="green">162</FONT>    <a name="line.162"></a>
+<FONT color="green">163</FONT>            double[] init = new double[dim];<a name="line.163"></a>
+<FONT color="green">164</FONT>            // Initial is far from minimum.<a name="line.164"></a>
+<FONT color="green">165</FONT>            for (int i = 0; i &lt; dim; i++) {<a name="line.165"></a>
+<FONT color="green">166</FONT>                init[i] = minPoint[i] - 20;<a name="line.166"></a>
+<FONT color="green">167</FONT>            }<a name="line.167"></a>
+<FONT color="green">168</FONT>    <a name="line.168"></a>
+<FONT color="green">169</FONT>            final double relTol = 1e-10;<a name="line.169"></a>
+<FONT color="green">170</FONT>    <a name="line.170"></a>
+<FONT color="green">171</FONT>            final int maxEval = 1000;<a name="line.171"></a>
+<FONT color="green">172</FONT>            // Very small absolute tolerance to rely solely on the relative<a name="line.172"></a>
+<FONT color="green">173</FONT>            // tolerance as a stopping criterion<a name="line.173"></a>
+<FONT color="green">174</FONT>            final PowellOptimizer optim = new PowellOptimizer(relTol, 1e-100);<a name="line.174"></a>
+<FONT color="green">175</FONT>    <a name="line.175"></a>
+<FONT color="green">176</FONT>            final PointValuePair funcResult = optim.optimize(new MaxEval(maxEval),<a name="line.176"></a>
+<FONT color="green">177</FONT>                                                             new ObjectiveFunction(func),<a name="line.177"></a>
+<FONT color="green">178</FONT>                                                             GoalType.MINIMIZE,<a name="line.178"></a>
+<FONT color="green">179</FONT>                                                             new InitialGuess(init));<a name="line.179"></a>
+<FONT color="green">180</FONT>            final double funcValue = func.value(funcResult.getPoint());<a name="line.180"></a>
+<FONT color="green">181</FONT>            final int funcEvaluations = optim.getEvaluations();<a name="line.181"></a>
+<FONT color="green">182</FONT>    <a name="line.182"></a>
+<FONT color="green">183</FONT>            final double scale = 1e10;<a name="line.183"></a>
+<FONT color="green">184</FONT>            final MultivariateFunction funcScaled = new MultivariateFunction() {<a name="line.184"></a>
+<FONT color="green">185</FONT>                    public double value(double[] x) {<a name="line.185"></a>
+<FONT color="green">186</FONT>                        return scale * func.value(x);<a name="line.186"></a>
+<FONT color="green">187</FONT>                    }<a name="line.187"></a>
+<FONT color="green">188</FONT>                };<a name="line.188"></a>
 <FONT color="green">189</FONT>    <a name="line.189"></a>
-<FONT color="green">190</FONT>        /**<a name="line.190"></a>
-<FONT color="green">191</FONT>         * @param func Function to optimize.<a name="line.191"></a>
-<FONT color="green">192</FONT>         * @param optimum Expected optimum.<a name="line.192"></a>
-<FONT color="green">193</FONT>         * @param init Starting point.<a name="line.193"></a>
-<FONT color="green">194</FONT>         * @param goal Minimization or maximization.<a name="line.194"></a>
-<FONT color="green">195</FONT>         * @param fTol Tolerance (relative error on the objective function) for<a name="line.195"></a>
-<FONT color="green">196</FONT>         * "Powell" algorithm.<a name="line.196"></a>
-<FONT color="green">197</FONT>         * @param pointTol Tolerance for checking that the optimum is correct.<a name="line.197"></a>
-<FONT color="green">198</FONT>         */<a name="line.198"></a>
-<FONT color="green">199</FONT>        private void doTest(MultivariateFunction func,<a name="line.199"></a>
-<FONT color="green">200</FONT>                            double[] optimum,<a name="line.200"></a>
-<FONT color="green">201</FONT>                            double[] init,<a name="line.201"></a>
-<FONT color="green">202</FONT>                            GoalType goal,<a name="line.202"></a>
-<FONT color="green">203</FONT>                            double fTol,<a name="line.203"></a>
-<FONT color="green">204</FONT>                            double pointTol) {<a name="line.204"></a>
-<FONT color="green">205</FONT>            final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));<a name="line.205"></a>
-<FONT color="green">206</FONT>    <a name="line.206"></a>
-<FONT color="green">207</FONT>            final PointValuePair result = optim.optimize(new MaxEval(1000),<a name="line.207"></a>
-<FONT color="green">208</FONT>                                                         new ObjectiveFunction(func),<a name="line.208"></a>
-<FONT color="green">209</FONT>                                                         goal,<a name="line.209"></a>
-<FONT color="green">210</FONT>                                                         new InitialGuess(init));<a name="line.210"></a>
-<FONT color="green">211</FONT>            final double[] point = result.getPoint();<a name="line.211"></a>
-<FONT color="green">212</FONT>    <a name="line.212"></a>
-<FONT color="green">213</FONT>            for (int i = 0, dim = optimum.length; i &lt; dim; i++) {<a name="line.213"></a>
-<FONT color="green">214</FONT>                Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),<a name="line.214"></a>
-<FONT color="green">215</FONT>                                    optimum[i], point[i], pointTol);<a name="line.215"></a>
-<FONT color="green">216</FONT>            }<a name="line.216"></a>
-<FONT color="green">217</FONT>        }<a name="line.217"></a>
-<FONT color="green">218</FONT>    <a name="line.218"></a>
-<FONT color="green">219</FONT>        /**<a name="line.219"></a>
-<FONT color="green">220</FONT>         * @param func Function to optimize.<a name="line.220"></a>
-<FONT color="green">221</FONT>         * @param optimum Expected optimum.<a name="line.221"></a>
-<FONT color="green">222</FONT>         * @param init Starting point.<a name="line.222"></a>
-<FONT color="green">223</FONT>         * @param goal Minimization or maximization.<a name="line.223"></a>
-<FONT color="green">224</FONT>         * @param fTol Tolerance (relative error on the objective function) for<a name="line.224"></a>
-<FONT color="green">225</FONT>         * "Powell" algorithm.<a name="line.225"></a>
-<FONT color="green">226</FONT>         * @param fLineTol Tolerance (relative error on the objective function)<a name="line.226"></a>
-<FONT color="green">227</FONT>         * for the internal line search algorithm.<a name="line.227"></a>
-<FONT color="green">228</FONT>         * @param pointTol Tolerance for checking that the optimum is correct.<a name="line.228"></a>
-<FONT color="green">229</FONT>         */<a name="line.229"></a>
-<FONT color="green">230</FONT>        private void doTest(MultivariateFunction func,<a name="line.230"></a>
-<FONT color="green">231</FONT>                            double[] optimum,<a name="line.231"></a>
-<FONT color="green">232</FONT>                            double[] init,<a name="line.232"></a>
-<FONT color="green">233</FONT>                            GoalType goal,<a name="line.233"></a>
-<FONT color="green">234</FONT>                            double fTol,<a name="line.234"></a>
-<FONT color="green">235</FONT>                            double fLineTol,<a name="line.235"></a>
-<FONT color="green">236</FONT>                            double pointTol) {<a name="line.236"></a>
-<FONT color="green">237</FONT>            final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),<a name="line.237"></a>
-<FONT color="green">238</FONT>                                                              fLineTol, Math.ulp(1d));<a name="line.238"></a>
-<FONT color="green">239</FONT>    <a name="line.239"></a>
-<FONT color="green">240</FONT>            final PointValuePair result = optim.optimize(new MaxEval(1000),<a name="line.240"></a>
-<FONT color="green">241</FONT>                                                         new ObjectiveFunction(func),<a name="line.241"></a>
-<FONT color="green">242</FONT>                                                         goal,<a name="line.242"></a>
-<FONT color="green">243</FONT>                                                         new InitialGuess(init));<a name="line.243"></a>
-<FONT color="green">244</FONT>            final double[] point = result.getPoint();<a name="line.244"></a>
-<FONT color="green">245</FONT>    <a name="line.245"></a>
-<FONT color="green">246</FONT>            for (int i = 0, dim = optimum.length; i &lt; dim; i++) {<a name="line.246"></a>
-<FONT color="green">247</FONT>                Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),<a name="line.247"></a>
-<FONT color="green">248</FONT>                                    optimum[i], point[i], pointTol);<a name="line.248"></a>
-<FONT color="green">249</FONT>            }<a name="line.249"></a>
-<FONT color="green">250</FONT>        }<a name="line.250"></a>
-<FONT color="green">251</FONT>    }<a name="line.251"></a>
+<FONT color="green">190</FONT>            final PointValuePair funcScaledResult = optim.optimize(new MaxEval(maxEval),<a name="line.190"></a>
+<FONT color="green">191</FONT>                                                                   new ObjectiveFunction(funcScaled),<a name="line.191"></a>
+<FONT color="green">192</FONT>                                                                   GoalType.MINIMIZE,<a name="line.192"></a>
+<FONT color="green">193</FONT>                                                                   new InitialGuess(init));<a name="line.193"></a>
+<FONT color="green">194</FONT>            final double funcScaledValue = funcScaled.value(funcScaledResult.getPoint());<a name="line.194"></a>
+<FONT color="green">195</FONT>            final int funcScaledEvaluations = optim.getEvaluations();<a name="line.195"></a>
+<FONT color="green">196</FONT>    <a name="line.196"></a>
+<FONT color="green">197</FONT>            // Check that both minima provide the same objective funciton values,<a name="line.197"></a>
+<FONT color="green">198</FONT>            // within the relative function tolerance.<a name="line.198"></a>
+<FONT color="green">199</FONT>            Assert.assertEquals(1, funcScaledValue / (scale * funcValue), relTol);<a name="line.199"></a>
+<FONT color="green">200</FONT>    <a name="line.200"></a>
+<FONT color="green">201</FONT>            // Check that the numbers of evaluations are the same.<a name="line.201"></a>
+<FONT color="green">202</FONT>            Assert.assertEquals(funcEvaluations, funcScaledEvaluations);<a name="line.202"></a>
+<FONT color="green">203</FONT>        }<a name="line.203"></a>
+<FONT color="green">204</FONT>    <a name="line.204"></a>
+<FONT color="green">205</FONT>        /**<a name="line.205"></a>
+<FONT color="green">206</FONT>         * @param func Function to optimize.<a name="line.206"></a>
+<FONT color="green">207</FONT>         * @param optimum Expected optimum.<a name="line.207"></a>
+<FONT color="green">208</FONT>         * @param init Starting point.<a name="line.208"></a>
+<FONT color="green">209</FONT>         * @param goal Minimization or maximization.<a name="line.209"></a>
+<FONT color="green">210</FONT>         * @param fTol Tolerance (relative error on the objective function) for<a name="line.210"></a>
+<FONT color="green">211</FONT>         * "Powell" algorithm.<a name="line.211"></a>
+<FONT color="green">212</FONT>         * @param pointTol Tolerance for checking that the optimum is correct.<a name="line.212"></a>
+<FONT color="green">213</FONT>         */<a name="line.213"></a>
+<FONT color="green">214</FONT>        private void doTest(MultivariateFunction func,<a name="line.214"></a>
+<FONT color="green">215</FONT>                            double[] optimum,<a name="line.215"></a>
+<FONT color="green">216</FONT>                            double[] init,<a name="line.216"></a>
+<FONT color="green">217</FONT>                            GoalType goal,<a name="line.217"></a>
+<FONT color="green">218</FONT>                            double fTol,<a name="line.218"></a>
+<FONT color="green">219</FONT>                            double pointTol) {<a name="line.219"></a>
+<FONT color="green">220</FONT>            final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));<a name="line.220"></a>
+<FONT color="green">221</FONT>    <a name="line.221"></a>
+<FONT color="green">222</FONT>            final PointValuePair result = optim.optimize(new MaxEval(1000),<a name="line.222"></a>
+<FONT color="green">223</FONT>                                                         new ObjectiveFunction(func),<a name="line.223"></a>
+<FONT color="green">224</FONT>                                                         goal,<a name="line.224"></a>
+<FONT color="green">225</FONT>                                                         new InitialGuess(init));<a name="line.225"></a>
+<FONT color="green">226</FONT>            final double[] point = result.getPoint();<a name="line.226"></a>
+<FONT color="green">227</FONT>    <a name="line.227"></a>
+<FONT color="green">228</FONT>            for (int i = 0, dim = optimum.length; i &lt; dim; i++) {<a name="line.228"></a>
+<FONT color="green">229</FONT>                Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),<a name="line.229"></a>
+<FONT color="green">230</FONT>                                    optimum[i], point[i], pointTol);<a name="line.230"></a>
+<FONT color="green">231</FONT>            }<a name="line.231"></a>
+<FONT color="green">232</FONT>        }<a name="line.232"></a>
+<FONT color="green">233</FONT>    <a name="line.233"></a>
+<FONT color="green">234</FONT>        /**<a name="line.234"></a>
+<FONT color="green">235</FONT>         * @param func Function to optimize.<a name="line.235"></a>
+<FONT color="green">236</FONT>         * @param optimum Expected optimum.<a name="line.236"></a>
+<FONT color="green">237</FONT>         * @param init Starting point.<a name="line.237"></a>
+<FONT color="green">238</FONT>         * @param goal Minimization or maximization.<a name="line.238"></a>
+<FONT color="green">239</FONT>         * @param fTol Tolerance (relative error on the objective function) for<a name="line.239"></a>
+<FONT color="green">240</FONT>         * "Powell" algorithm.<a name="line.240"></a>
+<FONT color="green">241</FONT>         * @param fLineTol Tolerance (relative error on the objective function)<a name="line.241"></a>
+<FONT color="green">242</FONT>         * for the internal line search algorithm.<a name="line.242"></a>
+<FONT color="green">243</FONT>         * @param pointTol Tolerance for checking that the optimum is correct.<a name="line.243"></a>
+<FONT color="green">244</FONT>         */<a name="line.244"></a>
+<FONT color="green">245</FONT>        private void doTest(MultivariateFunction func,<a name="line.245"></a>
+<FONT color="green">246</FONT>                            double[] optimum,<a name="line.246"></a>
+<FONT color="green">247</FONT>                            double[] init,<a name="line.247"></a>
+<FONT color="green">248</FONT>                            GoalType goal,<a name="line.248"></a>
+<FONT color="green">249</FONT>                            double fTol,<a name="line.249"></a>
+<FONT color="green">250</FONT>                            double fLineTol,<a name="line.250"></a>
+<FONT color="green">251</FONT>                            double pointTol) {<a name="line.251"></a>
+<FONT color="green">252</FONT>            final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),<a name="line.252"></a>
+<FONT color="green">253</FONT>                                                              fLineTol, Math.ulp(1d));<a name="line.253"></a>
+<FONT color="green">254</FONT>    <a name="line.254"></a>
+<FONT color="green">255</FONT>            final PointValuePair result = optim.optimize(new MaxEval(1000),<a name="line.255"></a>
+<FONT color="green">256</FONT>                                                         new ObjectiveFunction(func),<a name="line.256"></a>
+<FONT color="green">257</FONT>                                                         goal,<a name="line.257"></a>
+<FONT color="green">258</FONT>                                                         new InitialGuess(init));<a name="line.258"></a>
+<FONT color="green">259</FONT>            final double[] point = result.getPoint();<a name="line.259"></a>
+<FONT color="green">260</FONT>    <a name="line.260"></a>
+<FONT color="green">261</FONT>            for (int i = 0, dim = optimum.length; i &lt; dim; i++) {<a name="line.261"></a>
+<FONT color="green">262</FONT>                Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),<a name="line.262"></a>
+<FONT color="green">263</FONT>                                    optimum[i], point[i], pointTol);<a name="line.263"></a>
+<FONT color="green">264</FONT>            }<a name="line.264"></a>
+<FONT color="green">265</FONT>    <a name="line.265"></a>
+<FONT color="green">266</FONT>            Assert.assertTrue(optim.getIterations() &gt; 0);<a name="line.266"></a>
+<FONT color="green">267</FONT>        }<a name="line.267"></a>
+<FONT color="green">268</FONT>    }<a name="line.268"></a>
 
 
 



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