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Base package name: Changed "math" -> "math3" in userguide links. 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1291806 13f79535-47bb-0310-9956-ffa450edef68
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Gilles Sadowski 2012-02-21 14:31:56 +00:00
parent bc2588f16d
commit 66ea7501d4
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102
src/site/xdoc/userguide/analysis.xml
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@ -93,13 +93,13 @@
</subsection> </subsection>
<subsection name="4.3 Root-finding" href="rootfinding"> <subsection name="4.3 Root-finding" href="rootfinding">
<p> <p>
<a href="../apidocs/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.html"> <a href="../apidocs/org/apache/commons/math3/analysis/solvers/UnivariateRealSolver.html">
UnivariateRealSolver</a>, <a href="../apidocs/org/apache/commons/math/analysis/solvers/DifferentiableUnivariateRealSolver.html"> UnivariateRealSolver</a>, <a href="../apidocs/org/apache/commons/math3/analysis/solvers/DifferentiableUnivariateRealSolver.html">
DifferentiableUnivariateRealSolver</a> and <a href="../apidocs/org/apache/commons/math/analysis/solvers/PolynomialSolver.html"> DifferentiableUnivariateRealSolver</a> and <a href="../apidocs/org/apache/commons/math3/analysis/solvers/PolynomialSolver.html">
PolynomialSolver</a> provide means to find roots of PolynomialSolver</a> provide means to find roots of
<a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a>, <a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a>,
<a href="../apidocs/org/apache/commons/math/analysis/DifferentiableUnivariateRealFunction.html">differentiable univariate real-valued functions</a>, <a href="../apidocs/org/apache/commons/math3/analysis/DifferentiableUnivariateRealFunction.html">differentiable univariate real-valued functions</a>,
and <a href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialFunction.html">polynomial functions</a> respectively. and <a href="../apidocs/org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html">polynomial functions</a> respectively.
A root is the value where the function takes the value 0. Commons-Math A root is the value where the function takes the value 0. Commons-Math
includes implementations of the several root-finding algorithms: includes implementations of the several root-finding algorithms:
</p> </p>
@ -107,84 +107,84 @@
<tr BGCOLOR="#CCCCFF"><td colspan="5"><font size="+2">Root solvers</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="5"><font size="+2">Root solvers</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Function type</td><td>Convergence</td><td>Needs initial bracketing</td><td>Bracket side selection</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Function type</td><td>Convergence</td><td>Needs initial bracketing</td><td>Bracket side selection</td></font></tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/BisectionSolver.html">Bisection</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/BisectionSolver.html">Bisection</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>linear, guaranteed</td> <td>linear, guaranteed</td>
<td>yes</td> <td>yes</td>
<td>yes</td> <td>yes</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/BrentSolver.html">Brent-Dekker</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/BrentSolver.html">Brent-Dekker</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, guaranteed</td> <td>super-linear, guaranteed</td>
<td>yes</td> <td>yes</td>
<td>no</td> <td>no</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/BracketingNthOrderBrentSolver.html">bracketing n<sup>th</sup> order Brent</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/BracketingNthOrderBrentSolver.html">bracketing n<sup>th</sup> order Brent</a></td>
<td>variable order, guaranteed</td> <td>variable order, guaranteed</td>
<td>yes</td> <td>yes</td>
<td>yes</td> <td>yes</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/IllinoisSolver.html">Illinois Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/IllinoisSolver.html">Illinois Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, guaranteed</td> <td>super-linear, guaranteed</td>
<td>yes</td> <td>yes</td>
<td>yes</td> <td>yes</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/LaguerreSolver.html">Laguerre's Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/LaguerreSolver.html">Laguerre's Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialFunction.html">polynomial functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html">polynomial functions</a></td>
<td>cubic for simple root, linear for multiple root</td> <td>cubic for simple root, linear for multiple root</td>
<td>yes</td> <td>yes</td>
<td>no</td> <td>no</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/MullerSolver.html">Muller's Method</a> using bracketing to deal with real-valued functions</td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/MullerSolver.html">Muller's Method</a> using bracketing to deal with real-valued functions</td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>quadratic close to roots</td> <td>quadratic close to roots</td>
<td>yes</td> <td>yes</td>
<td>no</td> <td>no</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/MullerSolver2.html">Muller's Method</a> using modulus to deal with real-valued functions</td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/MullerSolver2.html">Muller's Method</a> using modulus to deal with real-valued functions</td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>quadratic close to root</td> <td>quadratic close to root</td>
<td>yes</td> <td>yes</td>
<td>no</td> <td>no</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/NewtonSolver.html">Newton's Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/NewtonSolver.html">Newton's Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/DifferentiableUnivariateRealFunction.html">differentiable univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/DifferentiableUnivariateRealFunction.html">differentiable univariate real-valued functions</a></td>
<td>quadratic, non-guaranteed</td> <td>quadratic, non-guaranteed</td>
<td>no</td> <td>no</td>
<td>no</td> <td>no</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/PegasusSolver.html">Pegasus Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/PegasusSolver.html">Pegasus Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, guaranteed</td> <td>super-linear, guaranteed</td>
<td>yes</td> <td>yes</td>
<td>yes</td> <td>yes</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/RegulaFalsiSolver.html">Regula Falsi (false position) Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/RegulaFalsiSolver.html">Regula Falsi (false position) Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>linear, guaranteed</td> <td>linear, guaranteed</td>
<td>yes</td> <td>yes</td>
<td>yes</td> <td>yes</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/RiddersSolver.html">Ridder's Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/RiddersSolver.html">Ridder's Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear</td> <td>super-linear</td>
<td>yes</td> <td>yes</td>
<td>no</td> <td>no</td>
</tr> </tr>
<tr> <tr>
<td><a href="../apidocs/org/apache/commons/math/analysis/solvers/SecantSolver.html">Secant Method</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/solvers/SecantSolver.html">Secant Method</a></td>
<td><a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td> <td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, non-guaranteed</td> <td>super-linear, non-guaranteed</td>
<td>yes</td> <td>yes</td>
<td>no</td> <td>no</td>
@ -240,9 +240,9 @@
ill-conditioned problems is to be solved, this number can be decreased in order ill-conditioned problems is to be solved, this number can be decreased in order
to avoid wasting time. to avoid wasting time.
<a <a
href="../apidocs/org/apache/commons/math/analysis/solvers/BracketedUnivariateRealSolver.html">Bracketed href="../apidocs/org/apache/commons/math3/analysis/solvers/BracketedUnivariateRealSolver.html">Bracketed
solvers</a> also take an <a solvers</a> also take an <a
href="../apidocs/org/apache/commons/math/analysis/solvers/AllowedSolutions.html">allowedSolutions</a> href="../apidocs/org/apache/commons/math3/analysis/solvers/AllowedSolutions.html">allowedSolutions</a>
enum parameter to specify which side of the final convergence interval should be enum parameter to specify which side of the final convergence interval should be
selected as the root. It can be <code>ANY_SIDE</code>, <code>LEFT_SIDE</code>, <code>RIGHT_SIDE</code>, selected as the root. It can be <code>ANY_SIDE</code>, <code>LEFT_SIDE</code>, <code>RIGHT_SIDE</code>,
<code>BELOW_SIDE</code> or <code>ABOVE_SIDE</code>. Left and right are used to specify the root along <code>BELOW_SIDE</code> or <code>ABOVE_SIDE</code>. Left and right are used to specify the root along
@ -376,13 +376,13 @@ double c = UnivariateRealSolverUtils.forceSide(100, function,
</subsection> </subsection>
<subsection name="4.4 Interpolation" href="interpolation"> <subsection name="4.4 Interpolation" href="interpolation">
<p> <p>
A <a href="../apidocs/org/apache/commons/math/analysis/interpolation/UnivariateRealInterpolator.html"> A <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/UnivariateRealInterpolator.html">
UnivariateRealInterpolator</a> is used to find a univariate real-valued UnivariateRealInterpolator</a> is used to find a univariate real-valued
function <code>f</code> which for a given set of ordered pairs function <code>f</code> which for a given set of ordered pairs
(<code>x<sub>i</sub></code>,<code>y<sub>i</sub></code>) yields (<code>x<sub>i</sub></code>,<code>y<sub>i</sub></code>) yields
<code>f(x<sub>i</sub>)=y<sub>i</sub></code> to the best accuracy possible. The result <code>f(x<sub>i</sub>)=y<sub>i</sub></code> to the best accuracy possible. The result
is provided as an object implementing the <a is provided as an object implementing the <a
href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">
UnivariateRealFunction</a> interface. It can therefore be evaluated at any point, UnivariateRealFunction</a> interface. It can therefore be evaluated at any point,
including point not belonging to the original set. including point not belonging to the original set.
Currently, only an interpolator for generating natural cubic splines and a polynomial Currently, only an interpolator for generating natural cubic splines and a polynomial
@ -437,13 +437,13 @@ System.out println("f(" + interpolationX + ") = " + interpolatedY);</source>
href="http://www.dudziak.com/microsphere.pdf">MS thesis</a>. href="http://www.dudziak.com/microsphere.pdf">MS thesis</a>.
</p> </p>
<p> <p>
A <a href="../apidocs/org/apache/commons/math/analysis/interpolation/BivariateRealGridInterpolator.html"> A <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/BivariateRealGridInterpolator.html">
BivariateRealGridInterpolator</a> is used to find a bivariate real-valued BivariateRealGridInterpolator</a> is used to find a bivariate real-valued
function <code>f</code> which for a given set of tuples function <code>f</code> which for a given set of tuples
(<code>x<sub>i</sub></code>,<code>y<sub>j</sub></code>,<code>f<sub>ij</sub></code>) (<code>x<sub>i</sub></code>,<code>y<sub>j</sub></code>,<code>f<sub>ij</sub></code>)
yields <code>f(x<sub>i</sub>,y<sub>j</sub>)=f<sub>ij</sub></code> to the best accuracy yields <code>f(x<sub>i</sub>,y<sub>j</sub>)=f<sub>ij</sub></code> to the best accuracy
possible. The result is provided as an object implementing the possible. The result is provided as an object implementing the
<a href="../apidocs/org/apache/commons/math/analysis/BivariateRealFunction.html"> <a href="../apidocs/org/apache/commons/math3/analysis/BivariateRealFunction.html">
BivariateRealFunction</a> interface. It can therefore be evaluated at any point, BivariateRealFunction</a> interface. It can therefore be evaluated at any point,
including a point not belonging to the original set. including a point not belonging to the original set.
The arrays <code>x<sub>i</sub></code> and <code>y<sub>j</sub></code> must be The arrays <code>x<sub>i</sub></code> and <code>y<sub>j</sub></code> must be
@ -455,25 +455,25 @@ System.out println("f(" + interpolationX + ") = " + interpolatedY);</source>
are computed from the function values sampled on a grid, as well as the values of the are computed from the function values sampled on a grid, as well as the values of the
partial derivatives of the function at those grid points. partial derivatives of the function at those grid points.
From two-dimensional data sampled on a grid, the From two-dimensional data sampled on a grid, the
<a href="../apidocs/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolator.html"> <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolator.html">
BicubicSplineInterpolator</a> computes a BicubicSplineInterpolator</a> computes a
<a href="../apidocs/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.html"> <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/BicubicSplineInterpolatingFunction.html">
bicubic interpolating function</a>. bicubic interpolating function</a>.
Prior to computing an interpolating function, the Prior to computing an interpolating function, the
<a href="../apidocs/org/apache/commons/math/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.html"> <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/SmoothingPolynomialBicubicSplineInterpolator.html">
SmoothingPolynomialBicubicSplineInterpolator</a> class performs smoothing of SmoothingPolynomialBicubicSplineInterpolator</a> class performs smoothing of
the data by computing the polynomial that best fits each of the one-dimensional the data by computing the polynomial that best fits each of the one-dimensional
curves along each of the coordinate axes. curves along each of the coordinate axes.
</p> </p>
<p> <p>
A <a href="../apidocs/org/apache/commons/math/analysis/interpolation/TrivariateRealGridInterpolator.html"> A <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/TrivariateRealGridInterpolator.html">
TrivariateRealGridInterpolator</a> is used to find a trivariate real-valued TrivariateRealGridInterpolator</a> is used to find a trivariate real-valued
function <code>f</code> which for a given set of tuples function <code>f</code> which for a given set of tuples
(<code>x<sub>i</sub></code>,<code>y<sub>j</sub></code>,<code>z<sub>k</sub></code>, (<code>x<sub>i</sub></code>,<code>y<sub>j</sub></code>,<code>z<sub>k</sub></code>,
<code>f<sub>ijk</sub></code>) <code>f<sub>ijk</sub></code>)
yields <code>f(x<sub>i</sub>,y<sub>j</sub>,z<sub>k</sub>)=f<sub>ijk</sub></code> yields <code>f(x<sub>i</sub>,y<sub>j</sub>,z<sub>k</sub>)=f<sub>ijk</sub></code>
to the best accuracy possible. The result is provided as an object implementing the to the best accuracy possible. The result is provided as an object implementing the
<a href="../apidocs/org/apache/commons/math/analysis/TrivariateRealFunction.html"> <a href="../apidocs/org/apache/commons/math3/analysis/TrivariateRealFunction.html">
TrivariateRealFunction</a> interface. It can therefore be evaluated at any point, TrivariateRealFunction</a> interface. It can therefore be evaluated at any point,
including a point not belonging to the original set. including a point not belonging to the original set.
The arrays <code>x<sub>i</sub></code>, <code>y<sub>j</sub></code> and The arrays <code>x<sub>i</sub></code>, <code>y<sub>j</sub></code> and
@ -486,41 +486,41 @@ System.out println("f(" + interpolationX + ") = " + interpolatedY);</source>
are computed from the function values sampled on a grid, as well as the values of the are computed from the function values sampled on a grid, as well as the values of the
partial derivatives of the function at those grid points. partial derivatives of the function at those grid points.
From three-dimensional data sampled on a grid, the From three-dimensional data sampled on a grid, the
<a href="../apidocs/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolator.html"> <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolator.html">
TricubicSplineInterpolator</a> computes a TricubicSplineInterpolator</a> computes a
<a href="../apidocs/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.html"> <a href="../apidocs/org/apache/commons/math3/analysis/interpolation/TricubicSplineInterpolatingFunction.html">
tricubic interpolating function</a>. tricubic interpolating function</a>.
</p> </p>
</subsection> </subsection>
<subsection name="4.5 Integration" href="integration"> <subsection name="4.5 Integration" href="integration">
<p> <p>
A <a href="../apidocs/org/apache/commons/math/analysis/integration/UnivariateRealIntegrator.html"> A <a href="../apidocs/org/apache/commons/math3/analysis/integration/UnivariateRealIntegrator.html">
UnivariateRealIntegrator</a> provides the means to numerically integrate UnivariateRealIntegrator</a> provides the means to numerically integrate
<a href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html"> <a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">
univariate real-valued functions</a>. univariate real-valued functions</a>.
Commons-Math includes implementations of the following integration algorithms: <ul> Commons-Math includes implementations of the following integration algorithms: <ul>
<li><a href="../apidocs/org/apache/commons/math/analysis/integration/RombergIntegrator.html"> <li><a href="../apidocs/org/apache/commons/math3/analysis/integration/RombergIntegrator.html">
Romberg's method</a></li> Romberg's method</a></li>
<li><a href="../apidocs/org/apache/commons/math/analysis/integration/SimpsonIntegrator.html"> <li><a href="../apidocs/org/apache/commons/math3/analysis/integration/SimpsonIntegrator.html">
Simpson's method</a></li> Simpson's method</a></li>
<li><a href="../apidocs/org/apache/commons/math/analysis/integration/TrapezoidIntegrator.html"> <li><a href="../apidocs/org/apache/commons/math3/analysis/integration/TrapezoidIntegrator.html">
trapezoid method</a></li> trapezoid method</a></li>
<li><a href="../apidocs/org/apache/commons/math/analysis/integration/LegendreGaussIntegrator.html"> <li><a href="../apidocs/org/apache/commons/math3/analysis/integration/LegendreGaussIntegrator.html">
Legendre-Gauss method</a></li> Legendre-Gauss method</a></li>
</ul> </ul>
</p> </p>
</subsection> </subsection>
<subsection name="4.6 Polynomials" href="polynomials"> <subsection name="4.6 Polynomials" href="polynomials">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/analysis/polynomials/package-summary.html"> The <a href="../apidocs/org/apache/commons/math3/analysis/polynomials/package-summary.html">
org.apache.commons.math3.analysis.polynomials</a> package provides real org.apache.commons.math3.analysis.polynomials</a> package provides real
coefficients polynomials. coefficients polynomials.
</p> </p>
<p> <p>
The <a href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialFunction.html"> The <a href="../apidocs/org/apache/commons/math3/analysis/polynomials/PolynomialFunction.html">
PolynomialFunction</a> class is the most general one, using traditional PolynomialFunction</a> class is the most general one, using traditional
coefficients arrays. The coefficients arrays. The
<a href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.html"> <a href="../apidocs/org/apache/commons/math3/analysis/polynomials/PolynomialsUtils.html">
PolynomialsUtils</a> utility class provides static factory methods to build PolynomialsUtils</a> utility class provides static factory methods to build
Chebyshev, Hermite, Jacobi, Laguerre and Legendre polynomials. Coefficients are Chebyshev, Hermite, Jacobi, Laguerre and Legendre polynomials. Coefficients are
computed using exact fractions so these factory methods can build polynomials computed using exact fractions so these factory methods can build polynomials

12
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@ -34,7 +34,7 @@
</subsection> </subsection>
<subsection name="7.2 Complex Numbers" href="complex"> <subsection name="7.2 Complex Numbers" href="complex">
<p> <p>
<a href="../apidocs/org/apache/commons/math/complex/Complex.html"> <a href="../apidocs/org/apache/commons/math3/complex/Complex.html">
Complex</a> provides a complex number type that forms the basis for Complex</a> provides a complex number type that forms the basis for
the complex functionality found in commons-math. the complex functionality found in commons-math.
</p> </p>
@ -45,9 +45,9 @@
handling infinite and <code>NaN</code> values. No attempt is made handling infinite and <code>NaN</code> values. No attempt is made
to comply with ANSII/IEC C99x Annex G or any other standard for to comply with ANSII/IEC C99x Annex G or any other standard for
Complex arithmetic. See the class and method javadocs for the Complex arithmetic. See the class and method javadocs for the
<a href="../apidocs/org/apache/commons/math/complex/Complex.html"> <a href="../apidocs/org/apache/commons/math3/complex/Complex.html">
Complex</a> and Complex</a> and
<a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html"> <a href="../apidocs/org/apache/commons/math3/complex/ComplexUtils.html">
ComplexUtils</a> classes for details on computing formulas. ComplexUtils</a> classes for details on computing formulas.
</p> </p>
<p> <p>
@ -78,11 +78,11 @@ Complex answer = lhs.add(rhs); // add two complex numbers
</subsection> </subsection>
<subsection name="7.3 Complex Transcendental Functions" href="function"> <subsection name="7.3 Complex Transcendental Functions" href="function">
<p> <p>
<a href="../apidocs/org/apache/commons/math/complex/Complex.html"> <a href="../apidocs/org/apache/commons/math3/complex/Complex.html">
Complex</a> also provides implementations of serveral transcendental Complex</a> also provides implementations of serveral transcendental
functions involving complex number arguments. functions involving complex number arguments.
Prior to version 1.2, these functions were provided Prior to version 1.2, these functions were provided
by <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html"> by <a href="../apidocs/org/apache/commons/math3/complex/ComplexUtils.html">
ComplexUtils</a> in a way similar to the real number functions found in ComplexUtils</a> in a way similar to the real number functions found in
<code>java.lang.Math</code>, but this has been deprecated. <code>java.lang.Math</code>, but this has been deprecated.
These operations provide the means to compute the log, sine, tangent, These operations provide the means to compute the log, sine, tangent,
@ -98,7 +98,7 @@ Complex answer = first.log(); // natural logarithm.
<subsection name="7.4 Complex Formatting and Parsing" href="formatting"> <subsection name="7.4 Complex Formatting and Parsing" href="formatting">
<p> <p>
<code>Complex</code> instances can be converted to and from strings <code>Complex</code> instances can be converted to and from strings
using the<a href="../apidocs/org/apache/commons/math/complex/ComplexFormat.html"> using the<a href="../apidocs/org/apache/commons/math3/complex/ComplexFormat.html">
ComplexFormat</a> class. ComplexFormat</a> class.
<code>ComplexFormat</code> is a <code>java.text.Format</code> <code>ComplexFormat</code> is a <code>java.text.Format</code>
extension and, as such, is used like other formatting objects (e.g. extension and, as such, is used like other formatting objects (e.g.

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@ -70,19 +70,19 @@ double upperTail = 1.0 - t.cumulativeProbability(2.75); // P(T &gt;= 2.75)</sour
Since there are numerous distributions and Commons-Math only directly Since there are numerous distributions and Commons-Math only directly
supports a handful, it may be necessary to extend the distribution supports a handful, it may be necessary to extend the distribution
framework to satisfy individual needs. It is recommended that the framework to satisfy individual needs. It is recommended that the
<a href="../apidocs/org/apache/commons/math/distribution/Distribution.html">Distribution</a>, <a href="../apidocs/org/apache/commons/math3/distribution/Distribution.html">Distribution</a>,
<a href="../apidocs/org/apache/commons/math/distribution/ContinuousDistribution.html"> <a href="../apidocs/org/apache/commons/math3/distribution/ContinuousDistribution.html">
ContinuousDistribution</a>, ContinuousDistribution</a>,
<a href="../apidocs/org/apache/commons/math/distribution/DiscreteDistribution.html"> <a href="../apidocs/org/apache/commons/math3/distribution/DiscreteDistribution.html">
DiscreteDistribution</a>, and <a href="../apidocs/org/apache/commons/math/distribution/IntegerDistribution.html"> DiscreteDistribution</a>, and <a href="../apidocs/org/apache/commons/math3/distribution/IntegerDistribution.html">
IntegerDistribution</a> interfaces serve as IntegerDistribution</a> interfaces serve as
base types for any extension. These serve as the basis for all the base types for any extension. These serve as the basis for all the
distributions directly supported by Commons-Math and using those interfaces distributions directly supported by Commons-Math and using those interfaces
for implementation purposes will ensure any extension is compatible with the for implementation purposes will ensure any extension is compatible with the
remainder of Commons-Math. To aid in implementing a distribution extension, remainder of Commons-Math. To aid in implementing a distribution extension,
the <a href="../apidocs/org/apache/commons/math/distribution/AbstractDistribution.html"> the <a href="../apidocs/org/apache/commons/math3/distribution/AbstractDistribution.html">
AbstractDistribution</a>, <a href="../apidocs/org/apache/commons/math/distribution/AbstractContinuousDistribution.html"> AbstractDistribution</a>, <a href="../apidocs/org/apache/commons/math3/distribution/AbstractContinuousDistribution.html">
AbstractContinuousDistribution</a>, and <a href="../apidocs/org/apache/commons/math/distribution/AbstractIntegerDistribution.html"> AbstractContinuousDistribution</a>, and <a href="../apidocs/org/apache/commons/math3/distribution/AbstractIntegerDistribution.html">
AbstractIntegerDistribution</a> provide implementation building blocks and AbstractIntegerDistribution</a> provide implementation building blocks and
offer basic distribution functionality. By extending these abstract classes offer basic distribution functionality. By extending these abstract classes
directly, much of the repetitive distribution implementation is already directly, much of the repetitive distribution implementation is already

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@ -32,12 +32,12 @@
</subsection> </subsection>
<subsection name="15.2 Kalman Filter" href="kalman"> <subsection name="15.2 Kalman Filter" href="kalman">
<p> <p>
<a href="../apidocs/org/apache/commons/math/filter/KalmanFilter.html"> <a href="../apidocs/org/apache/commons/math3/filter/KalmanFilter.html">
KalmanFilter</a> provides a discrete-time filter to estimate KalmanFilter</a> provides a discrete-time filter to estimate
a stochastic linear process.</p> a stochastic linear process.</p>
<p>A Kalman filter is initialized with a <a href="../apidocs/org/apache/commons/math/filter/ProcessModel.html"> <p>A Kalman filter is initialized with a <a href="../apidocs/org/apache/commons/math3/filter/ProcessModel.html">
ProcessModel</a> and a <a href="../apidocs/org/apache/commons/math/filter/MeasurementModel.html"> ProcessModel</a> and a <a href="../apidocs/org/apache/commons/math3/filter/MeasurementModel.html">
MeasurementModel</a>, which contain the corresponding transformation and noise covariance matrices. MeasurementModel</a>, which contain the corresponding transformation and noise covariance matrices.
The parameter names used in the respective models correspond to the following names commonly used The parameter names used in the respective models correspond to the following names commonly used
in the mathematical literature: in the mathematical literature:

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@ -33,8 +33,8 @@
</subsection> </subsection>
<subsection name="9.2 Fraction Numbers" href="fraction"> <subsection name="9.2 Fraction Numbers" href="fraction">
<p> <p>
<a href="../apidocs/org/apache/commons/math/fraction/Fraction.html"> <a href="../apidocs/org/apache/commons/math3/fraction/Fraction.html">
Fraction</a> and <a href="../apidocs/org/apache/commons/math/fraction/BigFraction.html"> Fraction</a> and <a href="../apidocs/org/apache/commons/math3/fraction/BigFraction.html">
BigFraction</a> provide fraction number type that forms the basis for BigFraction</a> provide fraction number type that forms the basis for
the fraction functionality found in Commons-Math. The former one can be the fraction functionality found in Commons-Math. The former one can be
used for fractions whose numerators and denominators are small enough used for fractions whose numerators and denominators are small enough
@ -71,7 +71,7 @@ Fraction answer = lhs.add(rhs); // add two fractions
<subsection name="9.3 Fraction Formatting and Parsing" href="formatting"> <subsection name="9.3 Fraction Formatting and Parsing" href="formatting">
<p> <p>
<code>Fraction</code> instances can be converted to and from strings <code>Fraction</code> instances can be converted to and from strings
using the<a href="../apidocs/org/apache/commons/math/fraction/FractionFormat.html"> using the<a href="../apidocs/org/apache/commons/math3/fraction/FractionFormat.html">
FractionFormat</a> class. <code>FractionFormat</code> is a FractionFormat</a> class. <code>FractionFormat</code> is a
<code>java.text.Format</code> extension and, as such, is used like other <code>java.text.Format</code> extension and, as such, is used like other
formatting objects (e.g. <code>java.text.SimpleDateFormat</code>): formatting objects (e.g. <code>java.text.SimpleDateFormat</code>):

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@ -33,15 +33,15 @@
</subsection> </subsection>
<subsection name="14.2 GA Framework"> <subsection name="14.2 GA Framework">
<p> <p>
<a href="../apidocs/org/apache/commons/math/genetics/GeneticAlgorithm.html"> <a href="../apidocs/org/apache/commons/math3/genetics/GeneticAlgorithm.html">
GeneticAlgorithm</a> provides an execution framework for Genetic Algorithms (GA). GeneticAlgorithm</a> provides an execution framework for Genetic Algorithms (GA).
<a href="../apidocs/org/apache/commons/math/genetics/Population.html"> <a href="../apidocs/org/apache/commons/math3/genetics/Population.html">
Populations,</a> consisting of <a href="../apidocs/org/apache/commons/math/genetics/Chromosome.html"> Populations,</a> consisting of <a href="../apidocs/org/apache/commons/math3/genetics/Chromosome.html">
Chromosomes</a> are evolved by the <code>GeneticAlgorithm</code> until a Chromosomes</a> are evolved by the <code>GeneticAlgorithm</code> until a
<a href="../apidocs/org/apache/commons/math/genetics/StoppingCondition.html"> <a href="../apidocs/org/apache/commons/math3/genetics/StoppingCondition.html">
StoppingCondition</a> is reached. Evolution is determined by <a href="../apidocs/org/apache/commons/math/genetics/SelectionPolicy.html"> StoppingCondition</a> is reached. Evolution is determined by <a href="../apidocs/org/apache/commons/math3/genetics/SelectionPolicy.html">
SelectionPolicy</a>, <a href="../apidocs/org/apache/commons/math/genetics/MutationPolicy.html"> SelectionPolicy</a>, <a href="../apidocs/org/apache/commons/math3/genetics/MutationPolicy.html">
MutationPolicy</a> and <a href="../apidocs/org/apache/commons/math/genetics/Fitness.html"> MutationPolicy</a> and <a href="../apidocs/org/apache/commons/math3/genetics/Fitness.html">
Fitness</a>. Fitness</a>.
</p> </p>
<p> <p>
@ -64,10 +64,10 @@
<ul><li>Apply configured <code>SelectionPolicy</code> to select a pair of parents <ul><li>Apply configured <code>SelectionPolicy</code> to select a pair of parents
from <code>current</code></li> from <code>current</code></li>
<li>With probability = <li>With probability =
<a href="../apidocs/org/apache/commons/math/genetics/GeneticAlgorithm.html#getCrossoverRate()"> <a href="../apidocs/org/apache/commons/math3/genetics/GeneticAlgorithm.html#getCrossoverRate()">
getCrossoverRate()</a>, apply configured <code>CrossoverPolicy</code> to parents</li> getCrossoverRate()</a>, apply configured <code>CrossoverPolicy</code> to parents</li>
<li>With probability = <li>With probability =
<a href="../apidocs/org/apache/commons/math/genetics/GeneticAlgorithm.html#getMutationRate()"> <a href="../apidocs/org/apache/commons/math3/genetics/GeneticAlgorithm.html#getMutationRate()">
getMutationRate()</a>, getMutationRate()</a>,
apply configured <code>MutationPolicy</code> to each of the offspring</li> apply configured <code>MutationPolicy</code> to each of the offspring</li>
<li>Add offspring individually to nextGeneration, <li>Add offspring individually to nextGeneration,
@ -106,27 +106,27 @@ Chromosome bestFinal = finalPopulation.getFittestChromosome();
<table> <table>
<tr><th>Parameter</th><th>value in example</th><th>meaning</th></tr> <tr><th>Parameter</th><th>value in example</th><th>meaning</th></tr>
<tr><td>crossoverPolicy</td> <tr><td>crossoverPolicy</td>
<td><a href="../apidocs/org/apache/commons/math/genetics/OnePointCrossover.html">OnePointCrossover</a></td> <td><a href="../apidocs/org/apache/commons/math3/genetics/OnePointCrossover.html">OnePointCrossover</a></td>
<td>A random crossover point is selected and the first part from each parent is copied to the corresponding <td>A random crossover point is selected and the first part from each parent is copied to the corresponding
child, and the second parts are copied crosswise.</td></tr> child, and the second parts are copied crosswise.</td></tr>
<tr><td>crossoverRate</td> <tr><td>crossoverRate</td>
<td>1</td> <td>1</td>
<td>Always apply crossover</td></tr> <td>Always apply crossover</td></tr>
<tr><td>mutationPolicy</td> <tr><td>mutationPolicy</td>
<td><a href="../apidocs/org/apache/commons/math/genetics/RandomKeyMutation.html">RandomKeyMutation</a></td> <td><a href="../apidocs/org/apache/commons/math3/genetics/RandomKeyMutation.html">RandomKeyMutation</a></td>
<td>Changes a randomly chosen element of the array representation to a random value uniformly distributed in [0,1].</td></tr> <td>Changes a randomly chosen element of the array representation to a random value uniformly distributed in [0,1].</td></tr>
<tr><td>mutationRate</td> <tr><td>mutationRate</td>
<td>.1</td> <td>.1</td>
<td>Apply mutation with probability 0.1 - that is, 10% of the time.</td></tr> <td>Apply mutation with probability 0.1 - that is, 10% of the time.</td></tr>
<tr><td>selectionPolicy</td> <tr><td>selectionPolicy</td>
<td><a href="../apidocs/org/apache/commons/math/genetics/TournamentSelection.html">TournamentSelection</a></td> <td><a href="../apidocs/org/apache/commons/math3/genetics/TournamentSelection.html">TournamentSelection</a></td>
<td>Each of the two selected chromosomes is selected based on an n-ary tournament -- this is done by drawing <td>Each of the two selected chromosomes is selected based on an n-ary tournament -- this is done by drawing
n random chromosomes without replacement from the population, and then selecting the fittest chromosome among them.</td></tr> n random chromosomes without replacement from the population, and then selecting the fittest chromosome among them.</td></tr>
</table><br/> </table><br/>
The algorithm starts with an <code>initial</code> population of <code>Chromosomes.</code> and executes until The algorithm starts with an <code>initial</code> population of <code>Chromosomes.</code> and executes until
the specified <a href="../apidocs/org/apache/commons/math/genetics/StoppingCondition.html">StoppingCondition</a> the specified <a href="../apidocs/org/apache/commons/math3/genetics/StoppingCondition.html">StoppingCondition</a>
is reached. In the example above, a is reached. In the example above, a
<a href="../apidocs/org/apache/commons/math/genetics/FixedGenerationCount.html">FixedGenerationCount</a> <a href="../apidocs/org/apache/commons/math3/genetics/FixedGenerationCount.html">FixedGenerationCount</a>
stopping condition is used, which means the algorithm proceeds through a fixed number of generations. stopping condition is used, which means the algorithm proceeds through a fixed number of generations.
</p> </p>
</subsection> </subsection>

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@ -36,8 +36,8 @@
</subsection> </subsection>
<subsection name="11.2 Euclidean spaces" href="euclidean"> <subsection name="11.2 Euclidean spaces" href="euclidean">
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/oned/Interval.html"> <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/oned/Interval.html">
Interval</a> and <a href="../apidocs/org/apache/commons/math/geometry/euclidean/oned/IntervalsSet.html"> Interval</a> and <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/oned/IntervalsSet.html">
IntervalsSet</a> represent one dimensional regions. All classical set operations are available IntervalsSet</a> represent one dimensional regions. All classical set operations are available
for intervals sets: union, intersection, symmetric difference (exclusive or), difference, complement, for intervals sets: union, intersection, symmetric difference (exclusive or), difference, complement,
as well as region predicates (point inside/outside/on boundary, emptiness, other region contained). as well as region predicates (point inside/outside/on boundary, emptiness, other region contained).
@ -46,7 +46,7 @@
representation. representation.
</p> </p>
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/twod/PolygonsSet.html"> <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/twod/PolygonsSet.html">
PolygonsSet</a> represent two dimensional regions. All classical set operations are available PolygonsSet</a> represent two dimensional regions. All classical set operations are available
for polygons sets: union, intersection, symmetric difference (exclusive or), difference, complement, for polygons sets: union, intersection, symmetric difference (exclusive or), difference, complement,
as well as region predicates (point inside/outside/on boundary, emptiness, other region contained). as well as region predicates (point inside/outside/on boundary, emptiness, other region contained).
@ -55,7 +55,7 @@
or from a boundary representation. or from a boundary representation.
</p> </p>
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/threed/PolyhedronsSet.html"> <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/threed/PolyhedronsSet.html">
PolyhedronsSet</a> represent three dimensional regions. All classical set operations are available PolyhedronsSet</a> represent three dimensional regions. All classical set operations are available
for polyhedrons sets: union, intersection, symmetric difference (exclusive or), difference, complement, for polyhedrons sets: union, intersection, symmetric difference (exclusive or), difference, complement,
as well as region predicates (point inside/outside/on boundary, emptiness, other region contained). as well as region predicates (point inside/outside/on boundary, emptiness, other region contained).
@ -64,7 +64,7 @@
or from a boundary representation. or from a boundary representation.
</p> </p>
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/threed/Vector3D.html"> <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html">
Vector3D</a> provides a simple vector type. One important feature is Vector3D</a> provides a simple vector type. One important feature is
that instances of this class are guaranteed that instances of this class are guaranteed
to be immutable, this greatly simplifies modelling dynamical systems to be immutable, this greatly simplifies modelling dynamical systems
@ -86,12 +86,12 @@
is of course also implemented. is of course also implemented.
</p> </p>
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/threed/Vector3DFormat.html"> <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/threed/Vector3DFormat.html">
Vector3DFormat</a> is a specialized format for formatting output or parsing Vector3DFormat</a> is a specialized format for formatting output or parsing
input with text representation of 3D vectors. input with text representation of 3D vectors.
</p> </p>
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/threed/Rotation.html"> <a href="../apidocs/org/apache/commons/math3/geometry/euclidean/threed/Rotation.html">
Rotation</a> represents 3D rotations. Rotation</a> represents 3D rotations.
Rotation instances are also immutable objects, as Vector3D instances. Rotation instances are also immutable objects, as Vector3D instances.
</p> </p>
@ -165,7 +165,7 @@
</subsection> </subsection>
<subsection name="11.3 Binary Space Partitioning" href="partitioning"> <subsection name="11.3 Binary Space Partitioning" href="partitioning">
<p> <p>
<a href="../apidocs/org/apache/commons/math/geometry/partitioning/BSPTree.html"> <a href="../apidocs/org/apache/commons/math3/geometry/partitioning/BSPTree.html">
BSP trees</a> are an efficient way to represent space partitions and BSP trees</a> are an efficient way to represent space partitions and
to associate attributes with each cell. Each node in a BSP tree to associate attributes with each cell. Each node in a BSP tree
represents a convex region which is partitioned in two convex represents a convex region which is partitioned in two convex

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</subsection> </subsection>
<subsection name="3.2 Real matrices" href="real_matrices"> <subsection name="3.2 Real matrices" href="real_matrices">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/linear/RealMatrix.html"> The <a href="../apidocs/org/apache/commons/math3/linear/RealMatrix.html">
RealMatrix</a> interface represents a matrix with real numbers as RealMatrix</a> interface represents a matrix with real numbers as
entries. The following basic matrix operations are supported: entries. The following basic matrix operations are supported:
<ul> <ul>
@ -72,18 +72,18 @@ RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
</p> </p>
<p> <p>
The three main implementations of the interface are <a The three main implementations of the interface are <a
href="../apidocs/org/apache/commons/math/linear/Array2DRowRealMatrix.html"> href="../apidocs/org/apache/commons/math3/linear/Array2DRowRealMatrix.html">
Array2DRowRealMatrix</a> and <a Array2DRowRealMatrix</a> and <a
href="../apidocs/org/apache/commons/math/linear/BlockRealMatrix.html"> href="../apidocs/org/apache/commons/math3/linear/BlockRealMatrix.html">
BlockRealMatrix</a> for dense matrices (the second one being more suited to BlockRealMatrix</a> for dense matrices (the second one being more suited to
dimensions above 50 or 100) and <a dimensions above 50 or 100) and <a
href="../apidocs/org/apache/commons/math/linear/SparseRealMatrix.html"> href="../apidocs/org/apache/commons/math3/linear/SparseRealMatrix.html">
SparseRealMatrix</a> for sparse matrices. SparseRealMatrix</a> for sparse matrices.
</p> </p>
</subsection> </subsection>
<subsection name="3.3 Real vectors" href="real_vectors"> <subsection name="3.3 Real vectors" href="real_vectors">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/linear/RealVector.html"> The <a href="../apidocs/org/apache/commons/math3/linear/RealVector.html">
RealVector</a> interface represents a vector with real numbers as RealVector</a> interface represents a vector with real numbers as
entries. The following basic matrix operations are supported: entries. The following basic matrix operations are supported:
<ul> <ul>
@ -96,7 +96,7 @@ RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
</ul> </ul>
</p> </p>
<p> <p>
The <a href="../apidocs/org/apache/commons/math/linear/RealVectorFormat.html"> The <a href="../apidocs/org/apache/commons/math3/linear/RealVectorFormat.html">
RealVectorFormat</a> class handles input/output of vectors in a customizable RealVectorFormat</a> class handles input/output of vectors in a customizable
textual format. textual format.
</p> </p>
@ -104,7 +104,7 @@ RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
<subsection name="3.4 Solving linear systems" href="solve"> <subsection name="3.4 Solving linear systems" href="solve">
<p> <p>
The <code>solve()</code> methods of the <a The <code>solve()</code> methods of the <a
href="../apidocs/org/apache/commons/math/linear/DecompositionSolver.html">DecompositionSolver</a> href="../apidocs/org/apache/commons/math3/linear/DecompositionSolver.html">DecompositionSolver</a>
interface support solving linear systems of equations of the form AX=B, either interface support solving linear systems of equations of the form AX=B, either
in linear sense or in least square sense. A <code>RealMatrix</code> instance is in linear sense or in least square sense. A <code>RealMatrix</code> instance is
used to represent the coefficient matrix of the system. Solving the system is a used to represent the coefficient matrix of the system. Solving the system is a
@ -151,11 +151,11 @@ RealVector solution = solver.solve(constants);
<table border="1" align="center"> <table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Decomposition algorithms</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Decomposition algorithms</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>coefficients matrix</td><td>problem type</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>coefficients matrix</td><td>problem type</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/linear/LUDecomposition.html">LU</a></td><td>square</td><td>exact solution only</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/linear/LUDecomposition.html">LU</a></td><td>square</td><td>exact solution only</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/linear/CholeskyDecomposition.html">Cholesky</a></td><td>symmetric positive definite</td><td>exact solution only</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/linear/CholeskyDecomposition.html">Cholesky</a></td><td>symmetric positive definite</td><td>exact solution only</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/linear/QRDecomposition.html">QR</a></td><td>any</td><td>least squares solution</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/linear/QRDecomposition.html">QR</a></td><td>any</td><td>least squares solution</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/linear/EigenDecomposition.html">eigen decomposition</a></td><td>square</td><td>exact solution only</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/linear/EigenDecomposition.html">eigen decomposition</a></td><td>square</td><td>exact solution only</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/linear/SingularValueDecomposition.html">SVD</a></td><td>any</td><td>least squares solution</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/linear/SingularValueDecomposition.html">SVD</a></td><td>any</td><td>least squares solution</td></tr>
</table> </table>
</p> </p>
<p> <p>
@ -190,13 +190,13 @@ RealVector solution = solver.solve(constants);
<subsection name="3.6 Non-real fields (complex, fractions ...)" href="field"> <subsection name="3.6 Non-real fields (complex, fractions ...)" href="field">
<p> <p>
In addition to the real field, matrices and vectors using non-real <a In addition to the real field, matrices and vectors using non-real <a
href="../apidocs/org/apache/commons/math/FieldElement.html">field elements</a> can be used. href="../apidocs/org/apache/commons/math3/FieldElement.html">field elements</a> can be used.
The fields already supported by the library are: The fields already supported by the library are:
<ul> <ul>
<li><a href="../apidocs/org/apache/commons/math/complex/Complex.html">Complex</a></li> <li><a href="../apidocs/org/apache/commons/math3/complex/Complex.html">Complex</a></li>
<li><a href="../apidocs/org/apache/commons/math/fraction/Fraction.html">Fraction</a></li> <li><a href="../apidocs/org/apache/commons/math3/fraction/Fraction.html">Fraction</a></li>
<li><a href="../apidocs/org/apache/commons/math/fraction/BigFraction.html">BigFraction</a></li> <li><a href="../apidocs/org/apache/commons/math3/fraction/BigFraction.html">BigFraction</a></li>
<li><a href="../apidocs/org/apache/commons/math/util/BigReal.html">BigReal</a></li> <li><a href="../apidocs/org/apache/commons/math3/util/BigReal.html">BigReal</a></li>
</ul> </ul>
</p> </p>
</subsection> </subsection>

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@ -40,7 +40,7 @@
All integrators provide dense output. This means that besides computing the state vector All integrators provide dense output. This means that besides computing the state vector
at discrete times, they also provide a cheap mean to get both the state and its derivative at discrete times, they also provide a cheap mean to get both the state and its derivative
between the time steps. They do so through classes extending the between the time steps. They do so through classes extending the
<a href="../apidocs/org/apache/commons/math/ode/sampling/StepInterpolator.html">StepInterpolator</a> <a href="../apidocs/org/apache/commons/math3/ode/sampling/StepInterpolator.html">StepInterpolator</a>
abstract class, which are made available to the user at the end of each step. abstract class, which are made available to the user at the end of each step.
</p> </p>
<p> <p>
@ -64,9 +64,9 @@
</p> </p>
<p> <p>
The user should describe his problem in his own classes which should implement the The user should describe his problem in his own classes which should implement the
<a href="../apidocs/org/apache/commons/math/ode/FirstOrderDifferentialEquations.html">FirstOrderDifferentialEquations</a> <a href="../apidocs/org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html">FirstOrderDifferentialEquations</a>
interface. Then he should pass it to the integrator he prefers among all the classes that implement interface. Then he should pass it to the integrator he prefers among all the classes that implement
the <a href="../apidocs/org/apache/commons/math/ode/FirstOrderIntegrator.html">FirstOrderIntegrator</a> the <a href="../apidocs/org/apache/commons/math3/ode/FirstOrderIntegrator.html">FirstOrderIntegrator</a>
interface. The following example shows how to implement the simple two-dimensional problem: interface. The following example shows how to implement the simple two-dimensional problem:
<ul> <ul>
<li>y'<sub>0</sub>(t) = &#x3c9; &#xD7; (c<sub>1</sub> - y<sub>1</sub>(t))</li> <li>y'<sub>0</sub>(t) = &#x3c9; &#xD7; (c<sub>1</sub> - y<sub>1</sub>(t))</li>
@ -116,10 +116,10 @@ dp853.integrate(ode, 0.0, y, 16.0, y); // now y contains final state at time t=1
<code>FirstOrderIntegrator.integrate</code> method, as shown by previous example. The second one <code>FirstOrderIntegrator.integrate</code> method, as shown by previous example. The second one
should be used when more in-depth information is needed throughout the integration process. The user should be used when more in-depth information is needed throughout the integration process. The user
can register an object implementing the can register an object implementing the
<a href="../apidocs/org/apache/commons/math/ode/sampling/StepHandler.html">StepHandler</a> interface or a <a href="../apidocs/org/apache/commons/math3/ode/sampling/StepHandler.html">StepHandler</a> interface or a
<a href="../apidocs/org/apache/commons/math/ode/sampling/StepNormalizer.html">StepNormalizer</a> object wrapping <a href="../apidocs/org/apache/commons/math3/ode/sampling/StepNormalizer.html">StepNormalizer</a> object wrapping
a user-specified object implementing the a user-specified object implementing the
<a href="../apidocs/org/apache/commons/math/ode/sampling/FixedStepHandler.html">FixedStepHandler</a> interface <a href="../apidocs/org/apache/commons/math3/ode/sampling/FixedStepHandler.html">FixedStepHandler</a> interface
into the integrator before calling the <code>FirstOrderIntegrator.integrate</code> method. The user object into the integrator before calling the <code>FirstOrderIntegrator.integrate</code> method. The user object
will be called appropriately during the integration process, allowing the user to process intermediate will be called appropriately during the integration process, allowing the user to process intermediate
results. The default step handler does nothing. Considering again the previous example, we want to print the results. The default step handler does nothing. Considering again the previous example, we want to print the
@ -140,7 +140,7 @@ StepHandler stepHandler = new StepHandler() {
integrator.addStepHandler(stepHandler); integrator.addStepHandler(stepHandler);
</source> </source>
<p> <p>
<a href="../apidocs/org/apache/commons/math/ode/ContinuousOutputModel.html">ContinuousOutputModel</a> <a href="../apidocs/org/apache/commons/math3/ode/ContinuousOutputModel.html">ContinuousOutputModel</a>
is a special-purpose step handler that is able to store all steps and to provide transparent access to is a special-purpose step handler that is able to store all steps and to provide transparent access to
any intermediate result once the integration is over. An important feature of this class is that it any intermediate result once the integration is over. An important feature of this class is that it
implements the <code>Serializable</code> interface. This means that a complete continuous model of the implements the <code>Serializable</code> interface. This means that a complete continuous model of the
@ -149,10 +149,10 @@ integrator.addStepHandler(stepHandler);
Only the result of the integration is stored, there is no reference to the integrated problem by itself. Only the result of the integration is stored, there is no reference to the integrated problem by itself.
</p> </p>
<p> <p>
Other default implementations of the <a href="../apidocs/org/apache/commons/math/ode/sampling/StepHandler.html">StepHandler</a> Other default implementations of the <a href="../apidocs/org/apache/commons/math3/ode/sampling/StepHandler.html">StepHandler</a>
interface are available for general needs interface are available for general needs
(<a href="../apidocs/org/apache/commons/math/ode/sampling/DummyStepHandler.html">DummyStepHandler</a>, (<a href="../apidocs/org/apache/commons/math3/ode/sampling/DummyStepHandler.html">DummyStepHandler</a>,
<a href="../apidocs/org/apache/commons/math/ode/sampling/StepNormalizer.html">StepNormalizer</a>) and custom <a href="../apidocs/org/apache/commons/math3/ode/sampling/StepNormalizer.html">StepNormalizer</a>) and custom
implementations can be developed for specific needs. As an example, if an application is to be implementations can be developed for specific needs. As an example, if an application is to be
completely driven by the integration process, then most of the application code will be run inside a completely driven by the integration process, then most of the application code will be run inside a
step handler specific to this application. step handler specific to this application.
@ -161,11 +161,11 @@ integrator.addStepHandler(stepHandler);
Some integrators (the simple ones) use fixed steps that are set at creation time. The more efficient Some integrators (the simple ones) use fixed steps that are set at creation time. The more efficient
integrators use variable steps that are handled internally in order to control the integration error integrators use variable steps that are handled internally in order to control the integration error
with respect to a specified accuracy (these integrators extend the with respect to a specified accuracy (these integrators extend the
<a href="../apidocs/org/apache/commons/math/ode/AdaptiveStepsizeIntegrator.html">AdaptiveStepsizeIntegrator</a> <a href="../apidocs/org/apache/commons/math3/ode/AdaptiveStepsizeIntegrator.html">AdaptiveStepsizeIntegrator</a>
abstract class). In this case, the step handler which is called after each successful step shows up abstract class). In this case, the step handler which is called after each successful step shows up
the variable stepsize. The <a href="../apidocs/org/apache/commons/math/ode/sampling/StepNormalizer.html">StepNormalizer</a> the variable stepsize. The <a href="../apidocs/org/apache/commons/math3/ode/sampling/StepNormalizer.html">StepNormalizer</a>
class can be used to convert the variable stepsize into a fixed stepsize that can be handled by classes class can be used to convert the variable stepsize into a fixed stepsize that can be handled by classes
implementing the <a href="../apidocs/org/apache/commons/math/ode/sampling/FixedStepHandler.html">FixedStepHandler</a> implementing the <a href="../apidocs/org/apache/commons/math3/ode/sampling/FixedStepHandler.html">FixedStepHandler</a>
interface. Adaptive stepsize integrators can automatically compute the initial stepsize by themselves, interface. Adaptive stepsize integrators can automatically compute the initial stepsize by themselves,
however the user can specify it if he prefers to retain full control over the integration or if the however the user can specify it if he prefers to retain full control over the integration or if the
automatic guess is wrong. automatic guess is wrong.
@ -180,7 +180,7 @@ integrator.addStepHandler(stepHandler);
</p> </p>
<p> <p>
Discrete events detection is based on switching functions. The user provides Discrete events detection is based on switching functions. The user provides
a simple <a href="../apidocs/org/apache/commons/math/ode/events/EventHandler.html">g(t, y)</a> a simple <a href="../apidocs/org/apache/commons/math3/ode/events/EventHandler.html">g(t, y)</a>
function depending on the current time and state. The integrator will monitor function depending on the current time and state. The integrator will monitor
the value of the function throughout integration range and will trigger the the value of the function throughout integration range and will trigger the
event when its sign changes. The magnitude of the value is almost irrelevant. event when its sign changes. The magnitude of the value is almost irrelevant.
@ -260,23 +260,23 @@ public int eventOccurred(double t, double[] y, boolean increasing) {
<table border="1" align="center"> <table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Fixed Step Integrators</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Fixed Step Integrators</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Order</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/EulerIntegrator.html">Euler</a></td><td>1</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/EulerIntegrator.html">Euler</a></td><td>1</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/MidpointIntegrator.html">Midpoint</a></td><td>2</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/MidpointIntegrator.html">Midpoint</a></td><td>2</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/ClassicalRungeKuttaIntegrator.html">Classical Runge-Kutta</a></td><td>4</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/ClassicalRungeKuttaIntegrator.html">Classical Runge-Kutta</a></td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/GillIntegrator.html">Gill</a></td><td>4</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/GillIntegrator.html">Gill</a></td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/ThreeEighthesIntegrator.html">3/8</a></td><td>4</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/ThreeEighthesIntegrator.html">3/8</a></td><td>4</td></tr>
</table> </table>
</p> </p>
<p> <p>
<table border="1" align="center"> <table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan="3"><font size="+2">Adaptive Stepsize Integrators</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="3"><font size="+2">Adaptive Stepsize Integrators</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>Integration Order</td><td>Error Estimation Order</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.html">Higham and Hall</a></td><td>5</td><td>4</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/HighamHall54Integrator.html">Higham and Hall</a></td><td>5</td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.html">Dormand-Prince 5(4)</a></td><td>5</td><td>4</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/DormandPrince54Integrator.html">Dormand-Prince 5(4)</a></td><td>5</td><td>4</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.html">Dormand-Prince 8(5,3)</a></td><td>8</td><td>5 and 3</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/DormandPrince853Integrator.html">Dormand-Prince 8(5,3)</a></td><td>8</td><td>5 and 3</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/GraggBulirschStoerIntegrator.html">Gragg-Bulirsch-Stoer</a></td><td>variable (up to 18 by default)</td><td>variable</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html">Gragg-Bulirsch-Stoer</a></td><td>variable (up to 18 by default)</td><td>variable</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/AdamsBashforthIntegrator.html">Adams-Bashforth</a></td><td>variable</td><td>variable</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/AdamsBashforthIntegrator.html">Adams-Bashforth</a></td><td>variable</td><td>variable</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.html">Adams-Moulton</a></td><td>variable</td><td>variable</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/ode/nonstiff/AdamsMoultonIntegrator.html">Adams-Moulton</a></td><td>variable</td><td>variable</td></tr>
</table> </table>
</p> </p>
</subsection> </subsection>
@ -285,7 +285,7 @@ public int eventOccurred(double t, double[] y, boolean increasing) {
If in addition to state y(t) the user needs to compute the sensitivity of the state to If in addition to state y(t) the user needs to compute the sensitivity of the state to
the initial state or some parameter of the ODE, he will use the classes and interfaces the initial state or some parameter of the ODE, he will use the classes and interfaces
from the <a from the <a
href="../apidocs/org/apache/commons/math/ode/jacobians/package-summary.html">org.apache.commons.ode.jacobians</a> href="../apidocs/org/apache/commons/math3/ode/jacobians/package-summary.html">org.apache.commons.ode.jacobians</a>
package instead of the top level ode package. These classes compute the jacobians package instead of the top level ode package. These classes compute the jacobians
dy(t)/dy<sub>0</sub> and dy(t)/dp where y<sub>0</sub> is the initial state dy(t)/dy<sub>0</sub> and dy(t)/dp where y<sub>0</sub> is the initial state
and p is some ODE parameter. and p is some ODE parameter.
@ -323,9 +323,9 @@ public int eventOccurred(double t, double[] y, boolean increasing) {
<p> <p>
If the function f is too complex, the user can simply rely on internal differentiation If the function f is too complex, the user can simply rely on internal differentiation
using finite differences to compute these local jacobians. So rather than the <a using finite differences to compute these local jacobians. So rather than the <a
href="../apidocs/org/apache/commons/math/ode/FirstOrderDifferentialEquations.html">FirstOrderDifferentialEquations</a> href="../apidocs/org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html">FirstOrderDifferentialEquations</a>
interface he will implement the <a interface he will implement the <a
href="../apidocs/org/apache/commons/math/ode/jacobians/ParameterizedODE.html">ParameterizedODE</a> href="../apidocs/org/apache/commons/math3/ode/jacobians/ParameterizedODE.html">ParameterizedODE</a>
interface. Considering again our example where only &#x3c9; is considered a parameter, we get: interface. Considering again our example where only &#x3c9; is considered a parameter, we get:
</p> </p>
<source> <source>
@ -373,9 +373,9 @@ integrator.integrate(t0, y0, dy0dp, t, y, dydy0, dydp);
<p> <p>
If the function f is simple, the user can simply provide the local jacobians If the function f is simple, the user can simply provide the local jacobians
by himself. So rather than the <a by himself. So rather than the <a
href="../apidocs/org/apache/commons/math/ode/FirstOrderDifferentialEquations.html">FirstOrderDifferentialEquations</a> href="../apidocs/org/apache/commons/math3/ode/FirstOrderDifferentialEquations.html">FirstOrderDifferentialEquations</a>
interface he will implement the <a interface he will implement the <a
href="../apidocs/org/apache/commons/math/ode/jacobians/ODEWithJacobians.html">ODEWithJacobians</a> href="../apidocs/org/apache/commons/math3/ode/jacobians/ODEWithJacobians.html">ODEWithJacobians</a>
interface. Considering again our example where only &#x3c9; is considered a parameter, we get: interface. Considering again our example where only &#x3c9; is considered a parameter, we get:
</p> </p>
<source> <source>

62
src/site/xdoc/userguide/optimization.xml
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@ -54,7 +54,7 @@
</p> </p>
<p> <p>
The type of goal, i.e. minimization or maximization, is defined by the enumerated The type of goal, i.e. minimization or maximization, is defined by the enumerated
<a href="../apidocs/org/apache/commons/math/optimization/GoalType.html"> <a href="../apidocs/org/apache/commons/math3/optimization/GoalType.html">
GoalType</a> which has only two values: <code>MAXIMIZE</code> and <code>MINIMIZE</code>. GoalType</a> which has only two values: <code>MAXIMIZE</code> and <code>MINIMIZE</code>.
</p> </p>
<p> <p>
@ -63,21 +63,21 @@
are only four interfaces defining the common behavior of optimizers, one for each are only four interfaces defining the common behavior of optimizers, one for each
supported type of objective function: supported type of objective function:
<ul> <ul>
<li><a href="../apidocs/org/apache/commons/math/optimization/UnivariateRealOptimizer.html"> <li><a href="../apidocs/org/apache/commons/math3/optimization/UnivariateRealOptimizer.html">
UnivariateRealOptimizer</a> for <a UnivariateRealOptimizer</a> for <a
href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">
univariate real functions</a></li> univariate real functions</a></li>
<li><a href="../apidocs/org/apache/commons/math/optimization/MultivariateRealOptimizer.html"> <li><a href="../apidocs/org/apache/commons/math3/optimization/MultivariateRealOptimizer.html">
MultivariateRealOptimizer</a> for <a MultivariateRealOptimizer</a> for <a
href="../apidocs/org/apache/commons/math/analysis/MultivariateRealFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/MultivariateRealFunction.html">
multivariate real functions</a></li> multivariate real functions</a></li>
<li><a href="../apidocs/org/apache/commons/math/optimization/DifferentiableMultivariateRealOptimizer.html"> <li><a href="../apidocs/org/apache/commons/math3/optimization/DifferentiableMultivariateRealOptimizer.html">
DifferentiableMultivariateRealOptimizer</a> for <a DifferentiableMultivariateRealOptimizer</a> for <a
href="../apidocs/org/apache/commons/math/analysis/DifferentiableMultivariateRealFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/DifferentiableMultivariateRealFunction.html">
differentiable multivariate real functions</a></li> differentiable multivariate real functions</a></li>
<li><a href="../apidocs/org/apache/commons/math/optimization/DifferentiableMultivariateVectorialOptimizer.html"> <li><a href="../apidocs/org/apache/commons/math3/optimization/DifferentiableMultivariateVectorialOptimizer.html">
DifferentiableMultivariateVectorialOptimizer</a> for <a DifferentiableMultivariateVectorialOptimizer</a> for <a
href="../apidocs/org/apache/commons/math/analysis/DifferentiableMultivariateVectorialFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/DifferentiableMultivariateVectorialFunction.html">
differentiable multivariate vectorial functions</a></li> differentiable multivariate vectorial functions</a></li>
</ul> </ul>
</p> </p>
@ -85,14 +85,14 @@
<p> <p>
Despite there are only four types of supported optimizers, it is possible to optimize Despite there are only four types of supported optimizers, it is possible to optimize
a transform a <a a transform a <a
href="../apidocs/org/apache/commons/math/analysis/MultivariateVectorialFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/MultivariateVectorialFunction.html">
non-differentiable multivariate vectorial function</a> by converting it to a <a non-differentiable multivariate vectorial function</a> by converting it to a <a
href="../apidocs/org/apache/commons/math/analysis/MultivariateRealFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/MultivariateRealFunction.html">
non-differentiable multivariate real function</a> thanks to the <a non-differentiable multivariate real function</a> thanks to the <a
href="../apidocs/org/apache/commons/math/optimization/LeastSquaresConverter.html"> href="../apidocs/org/apache/commons/math3/optimization/LeastSquaresConverter.html">
LeastSquaresConverter</a> helper class. The transformed function can be optimized using LeastSquaresConverter</a> helper class. The transformed function can be optimized using
any implementation of the <a any implementation of the <a
href="../apidocs/org/apache/commons/math/optimization/MultivariateRealOptimizer.html"> href="../apidocs/org/apache/commons/math3/optimization/MultivariateRealOptimizer.html">
MultivariateRealOptimizer</a> interface. MultivariateRealOptimizer</a> interface.
</p> </p>
@ -106,7 +106,7 @@
</subsection> </subsection>
<subsection name="12.2 Univariate Functions" href="univariate"> <subsection name="12.2 Univariate Functions" href="univariate">
<p> <p>
A <a href="../apidocs/org/apache/commons/math/optimization/UnivariateRealOptimizer.html"> A <a href="../apidocs/org/apache/commons/math3/optimization/UnivariateRealOptimizer.html">
UnivariateRealOptimizer</a> is used to find the minimal values of a univariate real-valued UnivariateRealOptimizer</a> is used to find the minimal values of a univariate real-valued
function <code>f</code>. function <code>f</code>.
</p> </p>
@ -157,16 +157,16 @@
The <code>direct</code> package provides four solvers: The <code>direct</code> package provides four solvers:
<ul> <ul>
<li>the classical <a <li>the classical <a
href="../apidocs/org/apache/commons/math/optimization/direct/NelderMeadSimplex.html"> href="../apidocs/org/apache/commons/math3/optimization/direct/NelderMeadSimplex.html">
Nelder-Mead</a> method,</li> Nelder-Mead</a> method,</li>
<li>Virginia Torczon's <a <li>Virginia Torczon's <a
href="../apidocs/org/apache/commons/math/optimization/direct/MultiDirectionalSimplex.html"> href="../apidocs/org/apache/commons/math3/optimization/direct/MultiDirectionalSimplex.html">
multi-directional</a> method,</li> multi-directional</a> method,</li>
<li>Nikolaus Hansen's <a <li>Nikolaus Hansen's <a
href="../apidocs/org/apache/commons/math/optimization/direct/CMAESOptimizer.html"> href="../apidocs/org/apache/commons/math3/optimization/direct/CMAESOptimizer.html">
</a>Covariance Matrix Adaptation Evolution Strategy (CMA-ES),</li> </a>Covariance Matrix Adaptation Evolution Strategy (CMA-ES),</li>
<li>Mike Powell's <a <li>Mike Powell's <a
href="../apidocs/org/apache/commons/math/optimization/direct/BOBYQAOptimizer.html"> href="../apidocs/org/apache/commons/math3/optimization/direct/BOBYQAOptimizer.html">
BOBYQA</a> method. BOBYQA</a> method.
</li> </li>
</ul> </ul>
@ -174,9 +174,9 @@
<p> <p>
The first two simplex-based methods do not handle simple bounds constraints by themselves. The first two simplex-based methods do not handle simple bounds constraints by themselves.
However there are two adapters(<a However there are two adapters(<a
href="../apidocs/org/apache/commons/math/optimization/direct/MultivariateRealFunctionMappingAdapter.html"> href="../apidocs/org/apache/commons/math3/optimization/direct/MultivariateRealFunctionMappingAdapter.html">
MultivariateRealFunctionMappingAdapter</a> and <a MultivariateRealFunctionMappingAdapter</a> and <a
href="../apidocs/org/apache/commons/math/optimization/direct/MultivariateRealFunctionPenaltyAdapter.html"> href="../apidocs/org/apache/commons/math3/optimization/direct/MultivariateRealFunctionPenaltyAdapter.html">
MultivariateRealFunctionPenaltyAdapter</a>) that can be used to wrap the user function in MultivariateRealFunctionPenaltyAdapter</a>) that can be used to wrap the user function in
such a way the wrapped function is unbounded and can be used with these optimizers, despite such a way the wrapped function is unbounded and can be used with these optimizers, despite
the fact the underlying function is still bounded and will be called only with feasible the fact the underlying function is still bounded and will be called only with feasible
@ -230,15 +230,15 @@
<p> <p>
Two optimizers are available in the general package, both devoted to least-squares Two optimizers are available in the general package, both devoted to least-squares
problems. The first one is based on the <a problems. The first one is based on the <a
href="../apidocs/org/apache/commons/math/optimization/general/GaussNewtonOptimizer.html"> href="../apidocs/org/apache/commons/math3/optimization/general/GaussNewtonOptimizer.html">
Gauss-Newton</a> method. The second one is the <a Gauss-Newton</a> method. The second one is the <a
href="../apidocs/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.html"> href="../apidocs/org/apache/commons/math3/optimization/general/LevenbergMarquardtOptimizer.html">
Levenberg-Marquardt</a> method. Levenberg-Marquardt</a> method.
</p> </p>
<p> <p>
In order to solve a vectorial optimization problem, the user must provide it as In order to solve a vectorial optimization problem, the user must provide it as
an object implementing the <a an object implementing the <a
href="../apidocs/org/apache/commons/math/analysis/DifferentiableMultivariateVectorialFunction.html"> href="../apidocs/org/apache/commons/math3/analysis/DifferentiableMultivariateVectorialFunction.html">
DifferentiableMultivariateVectorialFunction</a> interface. The object will be provided to DifferentiableMultivariateVectorialFunction</a> interface. The object will be provided to
the <code>estimate</code> method of the optimizer, along with the target and weight arrays, the <code>estimate</code> method of the optimizer, along with the target and weight arrays,
thus allowing the optimizer to compute the residuals at will. The last parameter to the thus allowing the optimizer to compute the residuals at will. The last parameter to the
@ -303,7 +303,7 @@
</table> </table>
<p> <p>
First we need to implement the interface <a href="../apidocs/org/apache/commons/math/analysis/DifferentiableMultivariateVectorialFunction.html">DifferentiableMultivariateVectorialFunction</a>. First we need to implement the interface <a href="../apidocs/org/apache/commons/math3/analysis/DifferentiableMultivariateVectorialFunction.html">DifferentiableMultivariateVectorialFunction</a>.
This requires the implementation of the method signatures: This requires the implementation of the method signatures:
</p> </p>
@ -571,17 +571,17 @@ C: 16.324008168386605
</dd></dl> </dd></dl>
<p> <p>
In addition to least squares solving, the <a In addition to least squares solving, the <a
href="../apidocs/org/apache/commons/math/optimization/general/NonLinearConjugateGradientOptimizer.html"> href="../apidocs/org/apache/commons/math3/optimization/general/NonLinearConjugateGradientOptimizer.html">
NonLinearConjugateGradientOptimizer</a> class provides a non-linear conjugate gradient algorithm NonLinearConjugateGradientOptimizer</a> class provides a non-linear conjugate gradient algorithm
to optimize <a to optimize <a
href="../apidocs/org/apache/commons/math/optimization/DifferentiableMultivariateRealFunction.html"> href="../apidocs/org/apache/commons/math3/optimization/DifferentiableMultivariateRealFunction.html">
DifferentiableMultivariateRealFunction</a>. Both the Fletcher-Reeves and the Polak-Ribi&#232;re DifferentiableMultivariateRealFunction</a>. Both the Fletcher-Reeves and the Polak-Ribi&#232;re
search direction update methods are supported. It is also possible to set up a preconditioner search direction update methods are supported. It is also possible to set up a preconditioner
or to change the line-search algorithm of the inner loop if desired (the default one is a Brent or to change the line-search algorithm of the inner loop if desired (the default one is a Brent
solver). solver).
</p> </p>
<p> <p>
The <a href="../apidocs/org/apache/commons/math/optimization/general/PowellOptimizer.html"> The <a href="../apidocs/org/apache/commons/math3/optimization/general/PowellOptimizer.html">
PowellOptimizer</a> provides an optimization method for non-differentiable functions. PowellOptimizer</a> provides an optimization method for non-differentiable functions.
</p> </p>
</subsection> </subsection>
@ -608,16 +608,16 @@ C: 16.324008168386605
</p> </p>
<p> <p>
The <a The <a
href="../apidocs/org/apache/commons/math/optimization/fitting/CurveFitter.html"> href="../apidocs/org/apache/commons/math3/optimization/fitting/CurveFitter.html">
CurveFitter</a> class provides curve fitting for general curves. Users must CurveFitter</a> class provides curve fitting for general curves. Users must
provide their own implementation of the curve template as a class implementing provide their own implementation of the curve template as a class implementing
the <a the <a
href="../apidocs/org/apache/commons/math/optimization/fitting/ParametricRealFunction.html"> href="../apidocs/org/apache/commons/math3/optimization/fitting/ParametricRealFunction.html">
ParametricRealFunction</a> interface and they must provide the initial guess of the ParametricRealFunction</a> interface and they must provide the initial guess of the
parameters. The more specialized <a parameters. The more specialized <a
href="../apidocs/org/apache/commons/math/optimization/fitting/PolynomialFitter.html"> href="../apidocs/org/apache/commons/math3/optimization/fitting/PolynomialFitter.html">
PolynomialFitter</a> and <a PolynomialFitter</a> and <a
href="../apidocs/org/apache/commons/math/optimization/fitting/HarmonicFitter.html"> href="../apidocs/org/apache/commons/math3/optimization/fitting/HarmonicFitter.html">
HarmonicFitter</a> classes require neither an implementation of the parametric real function HarmonicFitter</a> classes require neither an implementation of the parametric real function
not an initial guess as they are able to compute them by themselves. not an initial guess as they are able to compute them by themselves.
</p> </p>

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@ -104,9 +104,9 @@
<p> <p>
When the actual parameters provided to a method or the internal state of an object When the actual parameters provided to a method or the internal state of an object
make a computation meaningless, a make a computation meaningless, a
<a href="../apidocs/org/apache/commons/math/exception/MathIllegalArgumentException.html"> <a href="../apidocs/org/apache/commons/math3/exception/MathIllegalArgumentException.html">
IllegalArgumentException</a> or IllegalArgumentException</a> or
<a href="../apidocs/org/apache/commons/math/exception/MathIllegalStateException.html"> <a href="../apidocs/org/apache/commons/math3/exception/MathIllegalStateException.html">
MathIllegalStateException</a> may be thrown. Exact conditions under which runtime MathIllegalStateException</a> may be thrown. Exact conditions under which runtime
exceptions (and any other exceptions) are thrown are specified in the javadoc method exceptions (and any other exceptions) are thrown are specified in the javadoc method
comments. comments.
@ -118,7 +118,7 @@
<p> <p>
As of version 2.2, the policy for dealing with null references is as As of version 2.2, the policy for dealing with null references is as
follows: When an argument is unexpectedly null, a follows: When an argument is unexpectedly null, a
<a href="../apidocs/org/apache/commons/math/exception/NullArgumentException.html"> <a href="../apidocs/org/apache/commons/math3/exception/NullArgumentException.html">
NullArgumentException</a> is raised for signalling the illegal argument. Note that this NullArgumentException</a> is raised for signalling the illegal argument. Note that this
class does not inherit from the standard <code>NullPointerException</code> but is a subclass class does not inherit from the standard <code>NullPointerException</code> but is a subclass
of <code>MathIllegalArgumentException</code>. of <code>MathIllegalArgumentException</code>.

62
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@ -68,7 +68,7 @@
<subsection name="2.2 Random numbers" href="deviates"> <subsection name="2.2 Random numbers" href="deviates">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/random/RandomData.html"> The <a href="../apidocs/org/apache/commons/math3/random/RandomData.html">
RandomData</a> interface defines methods for generating random sequences RandomData</a> interface defines methods for generating random sequences
of numbers. The API contracts of these methods use the following concepts: of numbers. The API contracts of these methods use the following concepts:
<dl> <dl>
@ -87,10 +87,10 @@
ranges in the set of possible values of a random variable have ranges in the set of possible values of a random variable have
different probabilities of containing the value. Commons Math supports different probabilities of containing the value. Commons Math supports
generating random sequences from each of the distributions in the generating random sequences from each of the distributions in the
<a href="../apidocs/org/apache/commons/math/distribution/package-summary.html"> <a href="../apidocs/org/apache/commons/math3/distribution/package-summary.html">
distributions</a> package. distributions</a> package.
The javadoc for the <code>nextXxx</code> methods in The javadoc for the <code>nextXxx</code> methods in
<a href="../apidocs/org/apache/commons/math/random/RandomDataImpl.html"> <a href="../apidocs/org/apache/commons/math3/random/RandomDataImpl.html">
RandomDataImpl</a> describes the algorithms used to generate RandomDataImpl</a> describes the algorithms used to generate
random deviates. random deviates.
</dd> </dd>
@ -168,11 +168,11 @@ for (int i = 0; i &lt; 1000; i++) {
Some algorithms require random vectors instead of random scalars. When the Some algorithms require random vectors instead of random scalars. When the
components of these vectors are uncorrelated, they may be generated simply components of these vectors are uncorrelated, they may be generated simply
one at a time and packed together in the vector. The <a one at a time and packed together in the vector. The <a
href="../apidocs/org/apache/commons/math/random/UncorrelatedRandomVectorGenerator.html"> href="../apidocs/org/apache/commons/math3/random/UncorrelatedRandomVectorGenerator.html">
UncorrelatedRandomVectorGenerator</a> class simplifies this UncorrelatedRandomVectorGenerator</a> class simplifies this
process by setting the mean and deviation of each component once and process by setting the mean and deviation of each component once and
generating complete vectors. When the components are correlated however, generating complete vectors. When the components are correlated however,
generating them is much more difficult. The <a href="../apidocs/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html"> generating them is much more difficult. The <a href="../apidocs/org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html">
CorrelatedRandomVectorGenerator</a> class provides this service. In this CorrelatedRandomVectorGenerator</a> class provides this service. In this
case, the user must set up a complete covariance matrix instead of a simple case, the user must set up a complete covariance matrix instead of a simple
standard deviations vector. This matrix gathers both the variance and the standard deviations vector. This matrix gathers both the variance and the
@ -221,10 +221,10 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
<p> <p>
In addition to multivariate normal distributions, correlated vectors from multivariate uniform In addition to multivariate normal distributions, correlated vectors from multivariate uniform
distributions can be generated by creating a distributions can be generated by creating a
<a href="../apidocs/org/apache/commons/math/random/UniformRandomGenerator.html">UniformRandomGenerator</a> <a href="../apidocs/org/apache/commons/math3/random/UniformRandomGenerator.html">UniformRandomGenerator</a>
in place of the in place of the
<code>GaussianRandomGenerator</code> above. More generally, any <code>GaussianRandomGenerator</code> above. More generally, any
<a href="../apidocs/org/apache/commons/math/random/NormalizedRandomGenerator.html">NormalizedRandomGenerator</a> <a href="../apidocs/org/apache/commons/math3/random/NormalizedRandomGenerator.html">NormalizedRandomGenerator</a>
may be used. may be used.
</p> </p>
</subsection> </subsection>
@ -345,41 +345,41 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
generation utilities and to provide a generic means to replace generation utilities and to provide a generic means to replace
<code>java.util.Random</code> in applications, a random generator <code>java.util.Random</code> in applications, a random generator
adaptor framework has been added to commons-math. The adaptor framework has been added to commons-math. The
<a href="../apidocs/org/apache/commons/math/random/RandomGenerator.html"> <a href="../apidocs/org/apache/commons/math3/random/RandomGenerator.html">
RandomGenerator</a> interface abstracts the public interface of RandomGenerator</a> interface abstracts the public interface of
<code>java.util.Random</code> and any implementation of this <code>java.util.Random</code> and any implementation of this
interface can be used as the source of random data for the commons-math interface can be used as the source of random data for the commons-math
data generation classes. An abstract base class, data generation classes. An abstract base class,
<a href="../apidocs/org/apache/commons/math/random/AbstractRandomGenerator.html"> <a href="../apidocs/org/apache/commons/math3/random/AbstractRandomGenerator.html">
AbstractRandomGenerator</a> is provided to make implementation easier. AbstractRandomGenerator</a> is provided to make implementation easier.
This class provides default implementations of "derived" data generation This class provides default implementations of "derived" data generation
methods based on the primitive, <code>nextDouble()</code>. methods based on the primitive, <code>nextDouble()</code>.
To support generic replacement of <code>java.util.Random</code>, the To support generic replacement of <code>java.util.Random</code>, the
<a href="../apidocs/org/apache/commons/math/random/RandomAdaptor.html"> <a href="../apidocs/org/apache/commons/math3/random/RandomAdaptor.html">
RandomAdaptor</a> class is provided, which extends RandomAdaptor</a> class is provided, which extends
<code>java.util.Random</code> and wraps and delegates calls to <code>java.util.Random</code> and wraps and delegates calls to
a <code>RandomGenerator</code> instance. a <code>RandomGenerator</code> instance.
</p> </p>
<p>Commons-math provides by itself several implementations of the <a <p>Commons-math provides by itself several implementations of the <a
href="../apidocs/org/apache/commons/math/random/RandomGenerator.html"> href="../apidocs/org/apache/commons/math3/random/RandomGenerator.html">
RandomGenerator</a> interface: RandomGenerator</a> interface:
<ul> <ul>
<li><a href="../apidocs/org/apache/commons/math/random/JDKRandomGenerator.html">JDKRandomGenerator</a> <li><a href="../apidocs/org/apache/commons/math3/random/JDKRandomGenerator.html">JDKRandomGenerator</a>
that extends the JDK provided generator</li> that extends the JDK provided generator</li>
<li><a href="../apidocs/org/apache/commons/math/random/AbstractRandomGenerator.html"> <li><a href="../apidocs/org/apache/commons/math3/random/AbstractRandomGenerator.html">
AbstractRandomGenerator</a> as a helper for users generators</li> AbstractRandomGenerator</a> as a helper for users generators</li>
<li><a href="../apidocs/org/apache/commons/math/random/BitStreamGenerator.html"> <li><a href="../apidocs/org/apache/commons/math3/random/BitStreamGenerator.html">
BitStreamGenerator</a> which is an abstract class for several generators and BitStreamGenerator</a> which is an abstract class for several generators and
which in turn is extended by: which in turn is extended by:
<ul> <ul>
<li><a href="../apidocs/org/apache/commons/math/random/MersenneTwister.html">MersenneTwister</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/MersenneTwister.html">MersenneTwister</a></li>
<li><a href="../apidocs/org/apache/commons/math/random/Well512a.html">Well512a</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/Well512a.html">Well512a</a></li>
<li><a href="../apidocs/org/apache/commons/math/random/Well1024a.html">Well1024a</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/Well1024a.html">Well1024a</a></li>
<li><a href="../apidocs/org/apache/commons/math/random/Well19937a.html">Well19937a</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/Well19937a.html">Well19937a</a></li>
<li><a href="../apidocs/org/apache/commons/math/random/Well19937c.html">Well19937c</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/Well19937c.html">Well19937c</a></li>
<li><a href="../apidocs/org/apache/commons/math/random/Well44497a.html">Well44497a</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/Well44497a.html">Well44497a</a></li>
<li><a href="../apidocs/org/apache/commons/math/random/Well44497b.html">Well44497b</a></li> <li><a href="../apidocs/org/apache/commons/math3/random/Well44497b.html">Well44497b</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -450,21 +450,21 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
<table border="1" align="center"> <table border="1" align="center">
<tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example of performances</font></td></tr> <tr BGCOLOR="#CCCCFF"><td colspan="2"><font size="+2">Example of performances</font></td></tr>
<tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation rate (relative to MersenneTwister)</td></font></tr> <tr BGCOLOR="#EEEEFF"><font size="+1"><td>Name</td><td>generation rate (relative to MersenneTwister)</td></font></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/MersenneTwister.html">MersenneTwister</a></td><td>1</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/MersenneTwister.html">MersenneTwister</a></td><td>1</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/JDKRandomGenerator.html">JDKRandomGenerator</a></td><td>between 0.96 and 1.16</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/JDKRandomGenerator.html">JDKRandomGenerator</a></td><td>between 0.96 and 1.16</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/Well512a.html">Well512a</a></td><td>between 0.85 and 0.88</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/Well512a.html">Well512a</a></td><td>between 0.85 and 0.88</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/Well1024a.html">Well1024a</a></td><td>between 0.63 and 0.73</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/Well1024a.html">Well1024a</a></td><td>between 0.63 and 0.73</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/Well19937a.html">Well19937a</a></td><td>between 0.70 and 0.71</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/Well19937a.html">Well19937a</a></td><td>between 0.70 and 0.71</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/Well19937c.html">Well19937c</a></td><td>between 0.57 and 0.71</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/Well19937c.html">Well19937c</a></td><td>between 0.57 and 0.71</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/Well44497a.html">Well44497a</a></td><td>between 0.69 and 0.71</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/Well44497a.html">Well44497a</a></td><td>between 0.69 and 0.71</td></tr>
<tr><td><a href="../apidocs/org/apache/commons/math/random/Well44497b.html">Well44497b</a></td><td>between 0.65 and 0.71</td></tr> <tr><td><a href="../apidocs/org/apache/commons/math3/random/Well44497b.html">Well44497b</a></td><td>between 0.65 and 0.71</td></tr>
</table> </table>
</p> </p>
<p> <p>
So for most simulation problems, the better generators like <a So for most simulation problems, the better generators like <a
href="../apidocs/org/apache/commons/math/random/Well19937c.html">Well19937c</a> and <a href="../apidocs/org/apache/commons/math3/random/Well19937c.html">Well19937c</a> and <a
href="../apidocs/org/apache/commons/math/random/Well44497b.html">Well44497b</a> are probably very good choices. href="../apidocs/org/apache/commons/math3/random/Well44497b.html">Well44497b</a> are probably very good choices.
</p> </p>
<p> <p>

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@ -35,7 +35,7 @@
</subsection> </subsection>
<subsection name="5.2 Erf functions" href="erf"> <subsection name="5.2 Erf functions" href="erf">
<p> <p>
<a href="../apidocs/org/apache/commons/math/special/Erf.html">Erf</a> contains <a href="../apidocs/org/apache/commons/math3/special/Erf.html">Erf</a> contains
several useful functions involving the Error Function, Erf. several useful functions involving the Error Function, Erf.
<table> <table>
<tr><th>Function</th><th>Method</th><th>Reference</th></tr> <tr><th>Function</th><th>Method</th><th>Reference</th></tr>
@ -45,7 +45,7 @@
</subsection> </subsection>
<subsection name="5.3 Gamma functions" href="gamma"> <subsection name="5.3 Gamma functions" href="gamma">
<p> <p>
<a href="../apidocs/org/apache/commons/math/special/Gamma.html">Gamma</a> <a href="../apidocs/org/apache/commons/math3/special/Gamma.html">Gamma</a>
contains several useful functions involving the Gamma Function. contains several useful functions involving the Gamma Function.
<table> <table>
<tr><th>Function</th><th>Method</th><th>Reference</th></tr> <tr><th>Function</th><th>Method</th><th>Reference</th></tr>
@ -56,7 +56,7 @@
</subsection> </subsection>
<subsection name="5.4 Beta funtions" href="beta"> <subsection name="5.4 Beta funtions" href="beta">
<p> <p>
<a href="../apidocs/org/apache/commons/math/special/Beta.html">Beta</a> <a href="../apidocs/org/apache/commons/math3/special/Beta.html">Beta</a>
contains several useful functions involving the Beta Function. contains several useful functions involving the Beta Function.
<table> <table>
<tr><th>Function</th><th>Method</th><th>Reference</th></tr> <tr><th>Function</th><th>Method</th><th>Reference</th></tr>

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@ -63,12 +63,12 @@
</p> </p>
<p> <p>
The top level interface is The top level interface is
<a href="../apidocs/org/apache/commons/math/stat/descriptive/UnivariateStatistic.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/UnivariateStatistic.html">
UnivariateStatistic</a>. UnivariateStatistic</a>.
This interface, implemented by all statistics, consists of This interface, implemented by all statistics, consists of
<code>evaluate()</code> methods that take double[] arrays as arguments <code>evaluate()</code> methods that take double[] arrays as arguments
and return the value of the statistic. This interface is extended by and return the value of the statistic. This interface is extended by
<a href="../apidocs/org/apache/commons/math/stat/descriptive/StorelessUnivariateStatistic.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/StorelessUnivariateStatistic.html">
StorelessUnivariateStatistic</a>, which adds <code>increment(),</code> StorelessUnivariateStatistic</a>, which adds <code>increment(),</code>
<code>getResult()</code> and associated methods to support <code>getResult()</code> and associated methods to support
"storageless" implementations that maintain counters, sums or other "storageless" implementations that maintain counters, sums or other
@ -77,9 +77,9 @@
</p> </p>
<p> <p>
Abstract implementations of the top level interfaces are provided in Abstract implementations of the top level interfaces are provided in
<a href="../apidocs/org/apache/commons/math/stat/descriptive/AbstractUnivariateStatistic.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/AbstractUnivariateStatistic.html">
AbstractUnivariateStatistic</a> and AbstractUnivariateStatistic</a> and
<a href="../apidocs/org/apache/commons/math/stat/descriptive/AbstractStorelessUnivariateStatistic.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/AbstractStorelessUnivariateStatistic.html">
AbstractStorelessUnivariateStatistic</a> respectively. AbstractStorelessUnivariateStatistic</a> respectively.
</p> </p>
<p> <p>
@ -89,9 +89,9 @@
compute the statistic). There are several ways to instantiate and use statistics. compute the statistic). There are several ways to instantiate and use statistics.
Statistics can be instantiated and used directly, but it is generally more convenient Statistics can be instantiated and used directly, but it is generally more convenient
(and efficient) to access them using the provided aggregates, (and efficient) to access them using the provided aggregates,
<a href="../apidocs/org/apache/commons/math/stat/descriptive/DescriptiveStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/DescriptiveStatistics.html">
DescriptiveStatistics</a> and DescriptiveStatistics</a> and
<a href="../apidocs/org/apache/commons/math/stat/descriptive/SummaryStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/SummaryStatistics.html">
SummaryStatistics.</a> SummaryStatistics.</a>
</p> </p>
<p> <p>
@ -109,18 +109,18 @@
<table> <table>
<tr><th>Aggregate</th><th>Statistics Included</th><th>Values stored?</th> <tr><th>Aggregate</th><th>Statistics Included</th><th>Values stored?</th>
<th>"Rolling" capability?</th></tr><tr><td> <th>"Rolling" capability?</th></tr><tr><td>
<a href="../apidocs/org/apache/commons/math/stat/descriptive/DescriptiveStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/DescriptiveStatistics.html">
DescriptiveStatistics</a></td><td>min, max, mean, geometric mean, n, DescriptiveStatistics</a></td><td>min, max, mean, geometric mean, n,
sum, sum of squares, standard deviation, variance, percentiles, skewness, sum, sum of squares, standard deviation, variance, percentiles, skewness,
kurtosis, median</td><td>Yes</td><td>Yes</td></tr><tr><td> kurtosis, median</td><td>Yes</td><td>Yes</td></tr><tr><td>
<a href="../apidocs/org/apache/commons/math/stat/descriptive/SummaryStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/SummaryStatistics.html">
SummaryStatistics</a></td><td>min, max, mean, geometric mean, n, SummaryStatistics</a></td><td>min, max, mean, geometric mean, n,
sum, sum of squares, standard deviation, variance</td><td>No</td><td>No</td></tr> sum, sum of squares, standard deviation, variance</td><td>No</td><td>No</td></tr>
</table> </table>
</p> </p>
<p> <p>
<code>SummaryStatistics</code> can be aggregated using <code>SummaryStatistics</code> can be aggregated using
<a href="../apidocs/org/apache/commons/math/stat/descriptive/AggregateSummaryStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/AggregateSummaryStatistics.html">
AggregateSummaryStatistics.</a> This class can be used to concurrently AggregateSummaryStatistics.</a> This class can be used to concurrently
gather statistics for multiple datasets as well as for a combined sample gather statistics for multiple datasets as well as for a combined sample
including all of the data. including all of the data.
@ -134,19 +134,19 @@
<p> <p>
Neither <code>DescriptiveStatistics</code> nor <code>SummaryStatistics</code> Neither <code>DescriptiveStatistics</code> nor <code>SummaryStatistics</code>
is thread-safe. is thread-safe.
<a href="../apidocs/org/apache/commons/math/stat/descriptive/SynchronizedDescriptiveStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/SynchronizedDescriptiveStatistics.html">
SynchronizedDescriptiveStatistics</a> and SynchronizedDescriptiveStatistics</a> and
<a href="../apidocs/org/apache/commons/math/stat/descriptive/SynchronizedSummaryStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/SynchronizedSummaryStatistics.html">
SynchronizedSummaryStatistics</a>, respectively, provide thread-safe SynchronizedSummaryStatistics</a>, respectively, provide thread-safe
versions for applications that require concurrent access to statistical versions for applications that require concurrent access to statistical
aggregates by multiple threads. aggregates by multiple threads.
<a href="../apidocs/org/apache/commons/math/stat/descriptive/SynchronizedMultiVariateSummaryStatistics.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/SynchronizedMultiVariateSummaryStatistics.html">
SynchronizedMultivariateSummaryStatistics</a> provides thread-safe SynchronizedMultivariateSummaryStatistics</a> provides thread-safe
<code>MultivariateSummaryStatistics.</code> <code>MultivariateSummaryStatistics.</code>
</p> </p>
<p> <p>
There is also a utility class, There is also a utility class,
<a href="../apidocs/org/apache/commons/math/stat/StatUtils.html"> <a href="../apidocs/org/apache/commons/math3/stat/StatUtils.html">
StatUtils</a>, that provides static methods for computing statistics StatUtils</a>, that provides static methods for computing statistics
directly from double[] arrays. directly from double[] arrays.
</p> </p>
@ -244,7 +244,7 @@ DescriptiveStatistics stats = new SynchronizedDescriptiveStatistics();
The first is to use an <code>AggregateSummaryStatistics</code> instance The first is to use an <code>AggregateSummaryStatistics</code> instance
to accumulate overall statistics contributed by <code>SummaryStatistics</code> to accumulate overall statistics contributed by <code>SummaryStatistics</code>
instances created using instances created using
<a href="../apidocs/org/apache/commons/math/stat/descriptive/AggregateSummaryStatistics.html#createContributingStatistics()"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/AggregateSummaryStatistics.html#createContributingStatistics()">
AggregateSummaryStatistics.createContributingStatistics()</a>: AggregateSummaryStatistics.createContributingStatistics()</a>:
<source> <source>
// Create a AggregateSummaryStatistics instance to accumulate the overall statistics // Create a AggregateSummaryStatistics instance to accumulate the overall statistics
@ -265,7 +265,7 @@ double totalSampleSum = aggregate.getSum();
<code>SummaryStatistics</code> instance maintained by the aggregate and each value addition updates the <code>SummaryStatistics</code> instance maintained by the aggregate and each value addition updates the
aggregate as well as the subsample. For applications that can wait to do the aggregation until all values aggregate as well as the subsample. For applications that can wait to do the aggregation until all values
have been added, a static have been added, a static
<a href="../apidocs/org/apache/commons/math/stat/descriptive/AggregateSummaryStatistics.html#aggregate(java.util.Collection)"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/AggregateSummaryStatistics.html#aggregate(java.util.Collection)">
aggregate</a> method is available, as shown in the following example. aggregate</a> method is available, as shown in the following example.
This method should be used when aggregation needs to be done across threads. This method should be used when aggregation needs to be done across threads.
<source> <source>
@ -293,7 +293,7 @@ double totalSampleSum = aggregatedStats.getSum();
</subsection> </subsection>
<subsection name="1.3 Frequency distributions"> <subsection name="1.3 Frequency distributions">
<p> <p>
<a href="../apidocs/org/apache/commons/math/stat/Frequency.html"> <a href="../apidocs/org/apache/commons/math3/stat/Frequency.html">
Frequency</a> Frequency</a>
provides a simple interface for maintaining counts and percentages of discrete provides a simple interface for maintaining counts and percentages of discrete
values. values.
@ -357,7 +357,7 @@ System.out.println(f.getCumPct("z")); // displays 1
</subsection> </subsection>
<subsection name="1.4 Simple regression"> <subsection name="1.4 Simple regression">
<p> <p>
<a href="../apidocs/org/apache/commons/math/stat/regression/SimpleRegression.html"> <a href="../apidocs/org/apache/commons/math3/stat/regression/SimpleRegression.html">
SimpleRegression</a> provides ordinary least squares regression with SimpleRegression</a> provides ordinary least squares regression with
one independent variable estimating the linear model: one independent variable estimating the linear model:
</p> </p>
@ -393,7 +393,7 @@ System.out.println(f.getCumPct("z")); // displays 1
"compute" method that updates all statistics. Each of the getters performs "compute" method that updates all statistics. Each of the getters performs
the necessary computations to return the requested statistic.</li> the necessary computations to return the requested statistic.</li>
<li> The intercept term may be suppressed by passing <code>false</code> to the <li> The intercept term may be suppressed by passing <code>false</code> to the
<a href="../apidocs/org/apache/commons/math/stat/regression/SimpleRegression.html#SimpleRegression(boolean)"> <a href="../apidocs/org/apache/commons/math3/stat/regression/SimpleRegression.html#SimpleRegression(boolean)">
SimpleRegression(boolean)</a> constructor. When the <code>hasIntercept</code> SimpleRegression(boolean)</a> constructor. When the <code>hasIntercept</code>
property is false, the model is estimated without a constant term and property is false, the model is estimated without a constant term and
<code>getIntercept()</code> returns <code>0</code>.</li> <code>getIntercept()</code> returns <code>0</code>.</li>
@ -511,9 +511,9 @@ System.out.println(regression.getInterceptStdErr() );
</subsection> </subsection>
<subsection name="1.5 Multiple linear regression"> <subsection name="1.5 Multiple linear regression">
<p> <p>
<a href="../apidocs/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.html"> <a href="../apidocs/org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html">
OLSMultipleLinearRegression</a> and OLSMultipleLinearRegression</a> and
<a href="../apidocs/org/apache/commons/math/stat/regression/GLSMultipleLinearRegression.html"> <a href="../apidocs/org/apache/commons/math3/stat/regression/GLSMultipleLinearRegression.html">
GLSMultipleLinearRegression</a> provide least squares regression to fit the linear model: GLSMultipleLinearRegression</a> provide least squares regression to fit the linear model:
</p> </p>
<p> <p>
@ -525,9 +525,9 @@ System.out.println(regression.getInterceptStdErr() );
of <b>error terms</b> or <b>residuals</b>. of <b>error terms</b> or <b>residuals</b>.
</p> </p>
<p> <p>
<a href="../apidocs/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.html"> <a href="../apidocs/org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html">
OLSMultipleLinearRegression</a> provides Ordinary Least Squares Regression, and OLSMultipleLinearRegression</a> provides Ordinary Least Squares Regression, and
<a href="../apidocs/org/apache/commons/math/stat/regression/GLSMultipleLinearRegression.html"> <a href="../apidocs/org/apache/commons/math3/stat/regression/GLSMultipleLinearRegression.html">
GLSMultipleLinearRegression</a> implements Generalized Least Squares. See the javadoc for these GLSMultipleLinearRegression</a> implements Generalized Least Squares. See the javadoc for these
classes for details on the algorithms and forumlas used. classes for details on the algorithms and forumlas used.
</p> </p>
@ -535,11 +535,11 @@ System.out.println(regression.getInterceptStdErr() );
Data for OLS models can be loaded in a single double[] array, consisting of concatenated rows of data, each containing Data for OLS models can be loaded in a single double[] array, consisting of concatenated rows of data, each containing
the regressand (Y) value, followed by regressor values; or using a double[][] array with rows corresponding to the regressand (Y) value, followed by regressor values; or using a double[][] array with rows corresponding to
observations. GLS models also require a double[][] array representing the covariance matrix of the error terms. See observations. GLS models also require a double[][] array representing the covariance matrix of the error terms. See
<a href="../apidocs/org/apache/commons/math/stat/regression/AbstractMultipleLinearRegression.html#newSampleData(double[], int, int)"> <a href="../apidocs/org/apache/commons/math3/stat/regression/AbstractMultipleLinearRegression.html#newSampleData(double[], int, int)">
AbstractMultipleLinearRegression#newSampleData(double[],int,int)</a>, AbstractMultipleLinearRegression#newSampleData(double[],int,int)</a>,
<a href="../apidocs/org/apache/commons/math/stat/regression/OLSMultipleLinearRegression.html#newSampleData(double[], double[][])"> <a href="../apidocs/org/apache/commons/math3/stat/regression/OLSMultipleLinearRegression.html#newSampleData(double[], double[][])">
OLSMultipleLinearRegression#newSampleData(double[], double[][])</a> and OLSMultipleLinearRegression#newSampleData(double[], double[][])</a> and
<a href="../apidocs/org/apache/commons/math/stat/regression/GLSMultipleLinearRegression.html#newSampleData(double[], double[][], double[][])"> <a href="../apidocs/org/apache/commons/math3/stat/regression/GLSMultipleLinearRegression.html#newSampleData(double[], double[][], double[][])">
GLSMultipleLinearRegression#newSampleData(double[],double[][],double[][])</a> for details. GLSMultipleLinearRegression#newSampleData(double[],double[][],double[][])</a> for details.
</p> </p>
<p> <p>
@ -617,16 +617,16 @@ regression.newSampleData(y, x, omega);
<subsection name="1.6 Rank transformations"> <subsection name="1.6 Rank transformations">
<p> <p>
Some statistical algorithms require that input data be replaced by ranks. Some statistical algorithms require that input data be replaced by ranks.
The <a href="../apidocs/org/apache/commons/math/stat/ranking/package-summary.html"> The <a href="../apidocs/org/apache/commons/math3/stat/ranking/package-summary.html">
org.apache.commons.math3.stat.ranking</a> package provides rank transformation. org.apache.commons.math3.stat.ranking</a> package provides rank transformation.
<a href="../apidocs/org/apache/commons/math/stat/ranking/RankingAlgorithm.html"> <a href="../apidocs/org/apache/commons/math3/stat/ranking/RankingAlgorithm.html">
RankingAlgorithm</a> defines the interface for ranking. RankingAlgorithm</a> defines the interface for ranking.
<a href="../apidocs/org/apache/commons/math/stat/ranking/NaturalRanking.html"> <a href="../apidocs/org/apache/commons/math3/stat/ranking/NaturalRanking.html">
NaturalRanking</a> provides an implementation that has two configuration options. NaturalRanking</a> provides an implementation that has two configuration options.
<ul> <ul>
<li><a href="../apidocs/org/apache/commons/math/stat/ranking/TiesStrategy.html"> <li><a href="../apidocs/org/apache/commons/math3/stat/ranking/TiesStrategy.html">
Ties strategy</a> deterimines how ties in the source data are handled by the ranking</li> Ties strategy</a> deterimines how ties in the source data are handled by the ranking</li>
<li><a href="../apidocs/org/apache/commons/math/stat/ranking/NaNStrategy.html"> <li><a href="../apidocs/org/apache/commons/math3/stat/ranking/NaNStrategy.html">
NaN strategy</a> determines how NaN values in the source data are handled.</li> NaN strategy</a> determines how NaN values in the source data are handled.</li>
</ul> </ul>
</p> </p>
@ -650,22 +650,22 @@ new NaturalRanking(NaNStrategy.REMOVED,TiesStrategy.SEQUENTIAL).rank(exampleData
values larger than any other value (including <code>Double.POSITIVE_INFINITY</code>). The values larger than any other value (including <code>Double.POSITIVE_INFINITY</code>). The
default <code>TiesStrategy</code> is <code>TiesStrategy.AVERAGE,</code> which assigns tied default <code>TiesStrategy</code> is <code>TiesStrategy.AVERAGE,</code> which assigns tied
values the average of the ranks applicable to the sequence of ties. See the values the average of the ranks applicable to the sequence of ties. See the
<a href="../apidocs/org/apache/commons/math/stat/ranking/NaturalRanking.html"> <a href="../apidocs/org/apache/commons/math3/stat/ranking/NaturalRanking.html">
NaturalRanking</a> for more examples and <a href="../apidocs/org/apache/commons/math/stat/ranking/TiesStrategy.html"> NaturalRanking</a> for more examples and <a href="../apidocs/org/apache/commons/math3/stat/ranking/TiesStrategy.html">
TiesStrategy</a> and <a href="../apidocs/org/apache/commons/math/stat/ranking/NaNStrategy.html">NaNStrategy</a> TiesStrategy</a> and <a href="../apidocs/org/apache/commons/math3/stat/ranking/NaNStrategy.html">NaNStrategy</a>
for details on these configuration options. for details on these configuration options.
</p> </p>
</subsection> </subsection>
<subsection name="1.7 Covariance and correlation"> <subsection name="1.7 Covariance and correlation">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/stat/correlation/package-summary.html"> The <a href="../apidocs/org/apache/commons/math3/stat/correlation/package-summary.html">
org.apache.commons.math3.stat.correlation</a> package computes covariances org.apache.commons.math3.stat.correlation</a> package computes covariances
and correlations for pairs of arrays or columns of a matrix. and correlations for pairs of arrays or columns of a matrix.
<a href="../apidocs/org/apache/commons/math/stat/correlation/Covariance.html"> <a href="../apidocs/org/apache/commons/math3/stat/correlation/Covariance.html">
Covariance</a> computes covariances, Covariance</a> computes covariances,
<a href="../apidocs/org/apache/commons/math/stat/correlation/PearsonsCorrelation.html"> <a href="../apidocs/org/apache/commons/math3/stat/correlation/PearsonsCorrelation.html">
PearsonsCorrelation</a> provides Pearson's Product-Moment correlation coefficients and PearsonsCorrelation</a> provides Pearson's Product-Moment correlation coefficients and
<a href="../apidocs/org/apache/commons/math/stat/correlation/SpearmansCorrelation.html"> <a href="../apidocs/org/apache/commons/math3/stat/correlation/SpearmansCorrelation.html">
SpearmansCorrelation</a> computes Spearman's rank correlation. SpearmansCorrelation</a> computes Spearman's rank correlation.
</p> </p>
<p> <p>
@ -681,17 +681,17 @@ new NaturalRanking(NaNStrategy.REMOVED,TiesStrategy.SEQUENTIAL).rank(exampleData
defaults to <code>true.</code> defaults to <code>true.</code>
</li> </li>
<li> <li>
<a href="../apidocs/org/apache/commons/math/stat/correlation/PearsonsCorrelation.html"> <a href="../apidocs/org/apache/commons/math3/stat/correlation/PearsonsCorrelation.html">
PearsonsCorrelation</a> computes correlations defined by the formula <br></br> PearsonsCorrelation</a> computes correlations defined by the formula <br></br>
<code>cor(X, Y) = sum[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / [(n - 1)s(X)s(Y)]</code><br/> <code>cor(X, Y) = sum[(x<sub>i</sub> - E(X))(y<sub>i</sub> - E(Y))] / [(n - 1)s(X)s(Y)]</code><br/>
where <code>E(X)</code> and <code>E(Y)</code> are means of <code>X</code> and <code>Y</code> where <code>E(X)</code> and <code>E(Y)</code> are means of <code>X</code> and <code>Y</code>
and <code>s(X)</code>, <code>s(Y)</code> are standard deviations. and <code>s(X)</code>, <code>s(Y)</code> are standard deviations.
</li> </li>
<li> <li>
<a href="../apidocs/org/apache/commons/math/stat/correlation/SpearmansCorrelation.html"> <a href="../apidocs/org/apache/commons/math3/stat/correlation/SpearmansCorrelation.html">
SpearmansCorrelation</a> applies a rank transformation to the input data and computes Pearson's SpearmansCorrelation</a> applies a rank transformation to the input data and computes Pearson's
correlation on the ranked data. The ranking algorithm is configurable. By default, correlation on the ranked data. The ranking algorithm is configurable. By default,
<a href="../apidocs/org/apache/commons/math/stat/ranking/NaturalRanking.html"> <a href="../apidocs/org/apache/commons/math3/stat/ranking/NaturalRanking.html">
NaturalRanking</a> with default strategies for handling ties and NaN values is used. NaturalRanking</a> with default strategies for handling ties and NaN values is used.
</li> </li>
</ul> </ul>
@ -805,7 +805,7 @@ new PearsonsCorrelation().correlation(ranking.rank(x), ranking.rank(y))
<subsection name="1.8 Statistical tests"> <subsection name="1.8 Statistical tests">
<p> <p>
The interfaces and implementations in the The interfaces and implementations in the
<a href="../apidocs/org/apache/commons/math/stat/inference/"> <a href="../apidocs/org/apache/commons/math3/stat/inference/">
org.apache.commons.math3.stat.inference</a> package provide org.apache.commons.math3.stat.inference</a> package provide
<a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm"> <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm">
Student's t</a>, Student's t</a>,
@ -817,19 +817,19 @@ new PearsonsCorrelation().correlation(ranking.rank(x), ranking.rank(y))
p-values</a> associated with <code>t-</code>, p-values</a> associated with <code>t-</code>,
<code>Chi-Square</code> and <code>One-Way ANOVA</code> tests. The <code>Chi-Square</code> and <code>One-Way ANOVA</code> tests. The
interfaces are interfaces are
<a href="../apidocs/org/apache/commons/math/stat/inference/TTest.html"> <a href="../apidocs/org/apache/commons/math3/stat/inference/TTest.html">
TTest</a>, TTest</a>,
<a href="../apidocs/org/apache/commons/math/stat/inference/ChiSquareTest.html"> <a href="../apidocs/org/apache/commons/math3/stat/inference/ChiSquareTest.html">
ChiSquareTest</a>, and ChiSquareTest</a>, and
<a href="../apidocs/org/apache/commons/math/stat/inference/OneWayAnova.html"> <a href="../apidocs/org/apache/commons/math3/stat/inference/OneWayAnova.html">
OneWayAnova</a> with provided implementations OneWayAnova</a> with provided implementations
<a href="../apidocs/org/apache/commons/math/stat/inference/TTestImpl.html"> <a href="../apidocs/org/apache/commons/math3/stat/inference/TTestImpl.html">
TTestImpl</a>, TTestImpl</a>,
<a href="../apidocs/org/apache/commons/math/stat/inference/ChiSquareTestImpl.html"> <a href="../apidocs/org/apache/commons/math3/stat/inference/ChiSquareTestImpl.html">
ChiSquareTestImpl</a> and ChiSquareTestImpl</a> and
<a href="../apidocs/org/apache/commons/math/stat/inference/OneWayAnovaImpl.html"> <a href="../apidocs/org/apache/commons/math3/stat/inference/OneWayAnovaImpl.html">
OneWayAnovaImpl</a>, respectively. OneWayAnovaImpl</a>, respectively.
The <a href="../apidocs/org/apache/commons/math/stat/inference/TestUtils.html"> The <a href="../apidocs/org/apache/commons/math3/stat/inference/TestUtils.html">
TestUtils</a> class provides static methods to get test instances or TestUtils</a> class provides static methods to get test instances or
to compute test statistics directly. The examples below all use the to compute test statistics directly. The examples below all use the
static methods in <code>TestUtils</code> to execute tests. To get static methods in <code>TestUtils</code> to execute tests. To get
@ -889,7 +889,7 @@ System.out.println(TestUtils.t(mu, observed));
<code>mu.</code> <code>mu.</code>
</dd> </dd>
<dd>To compare the mean of a dataset described by a <dd>To compare the mean of a dataset described by a
<a href="../apidocs/org/apache/commons/math/stat/descriptive/StatisticalSummary.html"> <a href="../apidocs/org/apache/commons/math3/stat/descriptive/StatisticalSummary.html">
StatisticalSummary</a> to a fixed value: StatisticalSummary</a> to a fixed value:
<source> <source>
double[] observed ={1d, 2d, 3d}; double[] observed ={1d, 2d, 3d};

8
src/site/xdoc/userguide/transform.xml
View File

@ -31,13 +31,13 @@
This package provides a few transformers for signal analysis. All transformers This package provides a few transformers for signal analysis. All transformers
provide both direct and inverse transforms. provide both direct and inverse transforms.
<ul> <ul>
<li><a href="../apidocs/org/apache/commons/math/transform/FastFourierTransformer.html"> <li><a href="../apidocs/org/apache/commons/math3/transform/FastFourierTransformer.html">
FastFourierTransformer</a> (produces <code>Complex</code> results)</li> FastFourierTransformer</a> (produces <code>Complex</code> results)</li>
<li><a href="../apidocs/org/apache/commons/math/transform/FastCosineTransformer.html"> <li><a href="../apidocs/org/apache/commons/math3/transform/FastCosineTransformer.html">
FastCosineTransformer</a> (produces real results)</li> FastCosineTransformer</a> (produces real results)</li>
<li><a href="../apidocs/org/apache/commons/math/transform/FastSineTransformer.html"> <li><a href="../apidocs/org/apache/commons/math3/transform/FastSineTransformer.html">
FastSineTransformer</a> (produces real results)</li> FastSineTransformer</a> (produces real results)</li>
<li><a href="../apidocs/org/apache/commons/math/transform/FastHadamardTransformer.html"> <li><a href="../apidocs/org/apache/commons/math3/transform/FastHadamardTransformer.html">
FastHadamardTransformer</a> (produces real results)</li> FastHadamardTransformer</a> (produces real results)</li>
</ul> </ul>
</p> </p>

16
src/site/xdoc/userguide/utilities.xml
View File

@ -31,7 +31,7 @@
<subsection name="6.1 Overview" href="overview"> <subsection name="6.1 Overview" href="overview">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/util/package-summary.html"> The <a href="../apidocs/org/apache/commons/math3/util/package-summary.html">
org.apache.commons.math3.util</a> package collects a group of array utilities, org.apache.commons.math3.util</a> package collects a group of array utilities,
value transformers, and numerical routines used by implementation classes in value transformers, and numerical routines used by implementation classes in
commons-math. commons-math.
@ -44,7 +44,7 @@
array implementation was developed and is provided for reuse in the array implementation was developed and is provided for reuse in the
<code>util</code> package. The core functionality provided is described in <code>util</code> package. The core functionality provided is described in
the documentation for the interface, the documentation for the interface,
<a href="../apidocs/org/apache/commons/math/util/DoubleArray.html"> <a href="../apidocs/org/apache/commons/math3/util/DoubleArray.html">
DoubleArray</a>. This interface adds one method, DoubleArray</a>. This interface adds one method,
<code>addElementRolling(double)</code> to basic list accessors. <code>addElementRolling(double)</code> to basic list accessors.
The <code>addElementRolling</code> method adds an element The <code>addElementRolling</code> method adds an element
@ -52,7 +52,7 @@
in the list. in the list.
</p> </p>
<p> <p>
The <a href="../apidocs/org/apache/commons/math/util/ResizableDoubleArray.html"> The <a href="../apidocs/org/apache/commons/math3/util/ResizableDoubleArray.html">
ResizableDoubleArray</a> class provides a configurable, array-backed ResizableDoubleArray</a> class provides a configurable, array-backed
implementation of the <code>DoubleArray</code> interface. implementation of the <code>DoubleArray</code> interface.
When <code>addElementRolling</code> is invoked, the underlying When <code>addElementRolling</code> is invoked, the underlying
@ -66,7 +66,7 @@
automatically, with frequency / effect driven by the configuration automatically, with frequency / effect driven by the configuration
properties <code>expansionMode</code>, <code>expansionFactor</code> and properties <code>expansionMode</code>, <code>expansionFactor</code> and
<code>contractionCriteria.</code> See <code>contractionCriteria.</code> See
<a href="../apidocs/org/apache/commons/math/util/ResizableDoubleArray.html"> <a href="../apidocs/org/apache/commons/math3/util/ResizableDoubleArray.html">
ResizableDoubleArray</a> ResizableDoubleArray</a>
for details. for details.
</p> </p>
@ -74,7 +74,7 @@
<subsection name="6.3 int/double hash map" href="int_double_hash_map"> <subsection name="6.3 int/double hash map" href="int_double_hash_map">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/util/OpenIntToDoubleHashMap.html"> The <a href="../apidocs/org/apache/commons/math3/util/OpenIntToDoubleHashMap.html">
OpenIntToDoubleHashMap</a> class provides a specialized hash map OpenIntToDoubleHashMap</a> class provides a specialized hash map
implementation for int/double. This implementation has a much smaller memory implementation for int/double. This implementation has a much smaller memory
overhead than standard <code>java.util.HashMap</code> class. It uses open addressing overhead than standard <code>java.util.HashMap</code> class. It uses open addressing
@ -85,7 +85,7 @@
<subsection name="6.4 Continued Fractions" href="continued_fractions"> <subsection name="6.4 Continued Fractions" href="continued_fractions">
<p> <p>
The <a href="../apidocs/org/apache/commons/math/util/ContinuedFraction.html"> The <a href="../apidocs/org/apache/commons/math3/util/ContinuedFraction.html">
ContinuedFraction</a> class provides a generic way to create and evaluate ContinuedFraction</a> class provides a generic way to create and evaluate
continued fractions. The easiest way to create a continued fraction is continued fractions. The easiest way to create a continued fraction is
to subclass <code>ContinuedFraction</code> and override the to subclass <code>ContinuedFraction</code> and override the
@ -149,7 +149,7 @@
<subsection name="6.5 Binomial coefficients, factorials and other common math functions" href="binomial_coefficients_factorials_and_other_common_math_functions"> <subsection name="6.5 Binomial coefficients, factorials and other common math functions" href="binomial_coefficients_factorials_and_other_common_math_functions">
<p> <p>
A collection of reusable math functions is provided in the A collection of reusable math functions is provided in the
<a href="../apidocs/org/apache/commons/math/util/MathUtils.html">MathUtils</a> <a href="../apidocs/org/apache/commons/math3/util/MathUtils.html">MathUtils</a>
utility class. MathUtils currently includes methods to compute the following: <ul> utility class. MathUtils currently includes methods to compute the following: <ul>
<li> <li>
Binomial coefficients -- "n choose k" available as an (exact) long value, Binomial coefficients -- "n choose k" available as an (exact) long value,
@ -245,7 +245,7 @@
</subsection> </subsection>
<subsection name="6.7 Miscellaneous" href="miscellaneous"> <subsection name="6.7 Miscellaneous" href="miscellaneous">
The <a href="../apidocs/org/apache/commons/math/util/MultidimensionalCounter.html"> The <a href="../apidocs/org/apache/commons/math3/util/MultidimensionalCounter.html">
MultidimensionalCounter</a> is a utility class that converts a set of indices MultidimensionalCounter</a> is a utility class that converts a set of indices
(identifying points in a multidimensional space) to a single index (e.g. identifying (identifying points in a multidimensional space) to a single index (e.g. identifying
a location in a one-dimensional array. a location in a one-dimensional array.