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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 name="4.3 Root-finding" href="rootfinding">
<p>
<a href="../apidocs/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.html">
UnivariateRealSolver</a>, <a href="../apidocs/org/apache/commons/math/analysis/solvers/DifferentiableUnivariateRealSolver.html">
DifferentiableUnivariateRealSolver</a> and <a href="../apidocs/org/apache/commons/math/analysis/solvers/PolynomialSolver.html">
<a href="../apidocs/org/apache/commons/math3/analysis/solvers/UnivariateRealSolver.html">
UnivariateRealSolver</a>, <a href="../apidocs/org/apache/commons/math3/analysis/solvers/DifferentiableUnivariateRealSolver.html">
DifferentiableUnivariateRealSolver</a> and <a href="../apidocs/org/apache/commons/math3/analysis/solvers/PolynomialSolver.html">
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/math/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.
<a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">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/math3/analysis/polynomials/PolynomialFunction.html">polynomial functions</a> respectively.
A root is the value where the function takes the value 0. Commons-Math
includes implementations of the several root-finding algorithms:
</p>
@ -107,84 +107,84 @@
<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>
<td><a href="../apidocs/org/apache/commons/math/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/solvers/BisectionSolver.html">Bisection</a></td>
<td><a href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>linear, guaranteed</td>
<td>yes</td>
<td>yes</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, guaranteed</td>
<td>yes</td>
<td>no</td>
</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>yes</td>
<td>yes</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, guaranteed</td>
<td>yes</td>
<td>yes</td>
</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/math/analysis/polynomials/PolynomialFunction.html">polynomial functions</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/math3/analysis/polynomials/PolynomialFunction.html">polynomial functions</a></td>
<td>cubic for simple root, linear for multiple root</td>
<td>yes</td>
<td>no</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>quadratic close to roots</td>
<td>yes</td>
<td>no</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>quadratic close to root</td>
<td>yes</td>
<td>no</td>
</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/math/analysis/DifferentiableUnivariateRealFunction.html">differentiable univariate real-valued functions</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/math3/analysis/DifferentiableUnivariateRealFunction.html">differentiable univariate real-valued functions</a></td>
<td>quadratic, non-guaranteed</td>
<td>no</td>
<td>no</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, guaranteed</td>
<td>yes</td>
<td>yes</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>linear, guaranteed</td>
<td>yes</td>
<td>yes</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear</td>
<td>yes</td>
<td>no</td>
</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/math/analysis/UnivariateRealFunction.html">univariate real-valued functions</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/math3/analysis/UnivariateRealFunction.html">univariate real-valued functions</a></td>
<td>super-linear, non-guaranteed</td>
<td>yes</td>
<td>no</td>
@ -240,9 +240,9 @@
ill-conditioned problems is to be solved, this number can be decreased in order
to avoid wasting time.
<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
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
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
@ -376,13 +376,13 @@ double c = UnivariateRealSolverUtils.forceSide(100, function,
</subsection>
<subsection name="4.4 Interpolation" href="interpolation">
<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
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>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
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,
including point not belonging to the original set.
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>.
</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
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>)
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
<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,
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
@ -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
partial derivatives of the function at those grid points.
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
<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>.
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
the data by computing the polynomial that best fits each of the one-dimensional
curves along each of the coordinate axes.
</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
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>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
<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,
including a point not belonging to the original set.
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
partial derivatives of the function at those grid points.
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
<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>.
</p>
</subsection>
<subsection name="4.5 Integration" href="integration">
<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
<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>.
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>
<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>
<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>
<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>
</ul>
</p>
</subsection>
<subsection name="4.6 Polynomials" href="polynomials">
<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
coefficients polynomials.
</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
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
Chebyshev, Hermite, Jacobi, Laguerre and Legendre polynomials. Coefficients are
computed using exact fractions so these factory methods can build polynomials

12
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@ -34,7 +34,7 @@
</subsection>
<subsection name="7.2 Complex Numbers" href="complex">
<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
the complex functionality found in commons-math.
</p>
@ -45,9 +45,9 @@
handling infinite and <code>NaN</code> values. No attempt is made
to comply with ANSII/IEC C99x Annex G or any other standard for
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
<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.
</p>
<p>
@ -78,11 +78,11 @@ Complex answer = lhs.add(rhs); // add two complex numbers
</subsection>
<subsection name="7.3 Complex Transcendental Functions" href="function">
<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
functions involving complex number arguments.
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
<code>java.lang.Math</code>, but this has been deprecated.
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">
<p>
<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.
<code>ComplexFormat</code> is a <code>java.text.Format</code>
extension and, as such, is used like other formatting objects (e.g.

14
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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
supports a handful, it may be necessary to extend the distribution
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/math/distribution/ContinuousDistribution.html">
<a href="../apidocs/org/apache/commons/math3/distribution/Distribution.html">Distribution</a>,
<a href="../apidocs/org/apache/commons/math3/distribution/ContinuousDistribution.html">
ContinuousDistribution</a>,
<a href="../apidocs/org/apache/commons/math/distribution/DiscreteDistribution.html">
DiscreteDistribution</a>, and <a href="../apidocs/org/apache/commons/math/distribution/IntegerDistribution.html">
<a href="../apidocs/org/apache/commons/math3/distribution/DiscreteDistribution.html">
DiscreteDistribution</a>, and <a href="../apidocs/org/apache/commons/math3/distribution/IntegerDistribution.html">
IntegerDistribution</a> interfaces serve as
base types for any extension. These serve as the basis for all the
distributions directly supported by Commons-Math and using those interfaces
for implementation purposes will ensure any extension is compatible with the
remainder of Commons-Math. To aid in implementing a distribution extension,
the <a href="../apidocs/org/apache/commons/math/distribution/AbstractDistribution.html">
AbstractDistribution</a>, <a href="../apidocs/org/apache/commons/math/distribution/AbstractContinuousDistribution.html">
AbstractContinuousDistribution</a>, and <a href="../apidocs/org/apache/commons/math/distribution/AbstractIntegerDistribution.html">
the <a href="../apidocs/org/apache/commons/math3/distribution/AbstractDistribution.html">
AbstractDistribution</a>, <a href="../apidocs/org/apache/commons/math3/distribution/AbstractContinuousDistribution.html">
AbstractContinuousDistribution</a>, and <a href="../apidocs/org/apache/commons/math3/distribution/AbstractIntegerDistribution.html">
AbstractIntegerDistribution</a> provide implementation building blocks and
offer basic distribution functionality. By extending these abstract classes
directly, much of the repetitive distribution implementation is already

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@ -32,12 +32,12 @@
</subsection>
<subsection name="15.2 Kalman Filter" href="kalman">
<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
a stochastic linear process.</p>
<p>A Kalman filter is initialized with a <a href="../apidocs/org/apache/commons/math/filter/ProcessModel.html">
ProcessModel</a> and a <a href="../apidocs/org/apache/commons/math/filter/MeasurementModel.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/math3/filter/MeasurementModel.html">
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
in the mathematical literature:

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@ -33,8 +33,8 @@
</subsection>
<subsection name="9.2 Fraction Numbers" href="fraction">
<p>
<a href="../apidocs/org/apache/commons/math/fraction/Fraction.html">
Fraction</a> and <a href="../apidocs/org/apache/commons/math/fraction/BigFraction.html">
<a href="../apidocs/org/apache/commons/math3/fraction/Fraction.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
the fraction functionality found in Commons-Math. The former one can be
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">
<p>
<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
<code>java.text.Format</code> extension and, as such, is used like other
formatting objects (e.g. <code>java.text.SimpleDateFormat</code>):

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@ -33,15 +33,15 @@
</subsection>
<subsection name="14.2 GA Framework">
<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).
<a href="../apidocs/org/apache/commons/math/genetics/Population.html">
Populations,</a> consisting of <a href="../apidocs/org/apache/commons/math/genetics/Chromosome.html">
<a href="../apidocs/org/apache/commons/math3/genetics/Population.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
<a href="../apidocs/org/apache/commons/math/genetics/StoppingCondition.html">
StoppingCondition</a> is reached. Evolution is determined by <a href="../apidocs/org/apache/commons/math/genetics/SelectionPolicy.html">
SelectionPolicy</a>, <a href="../apidocs/org/apache/commons/math/genetics/MutationPolicy.html">
MutationPolicy</a> and <a href="../apidocs/org/apache/commons/math/genetics/Fitness.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/math3/genetics/SelectionPolicy.html">
SelectionPolicy</a>, <a href="../apidocs/org/apache/commons/math3/genetics/MutationPolicy.html">
MutationPolicy</a> and <a href="../apidocs/org/apache/commons/math3/genetics/Fitness.html">
Fitness</a>.
</p>
<p>
@ -64,10 +64,10 @@
<ul><li>Apply configured <code>SelectionPolicy</code> to select a pair of parents
from <code>current</code></li>
<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>
<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>,
apply configured <code>MutationPolicy</code> to each of the offspring</li>
<li>Add offspring individually to nextGeneration,
@ -106,27 +106,27 @@ Chromosome bestFinal = finalPopulation.getFittestChromosome();
<table>
<tr><th>Parameter</th><th>value in example</th><th>meaning</th></tr>
<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
child, and the second parts are copied crosswise.</td></tr>
<tr><td>crossoverRate</td>
<td>1</td>
<td>Always apply crossover</td></tr>
<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>
<tr><td>mutationRate</td>
<td>.1</td>
<td>Apply mutation with probability 0.1 - that is, 10% of the time.</td></tr>
<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
n random chromosomes without replacement from the population, and then selecting the fittest chromosome among them.</td></tr>
</table><br/>
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
<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.
</p>
</subsection>

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@ -36,8 +36,8 @@
</subsection>
<subsection name="11.2 Euclidean spaces" href="euclidean">
<p>
<a href="../apidocs/org/apache/commons/math/geometry/euclidean/oned/Interval.html">
Interval</a> and <a href="../apidocs/org/apache/commons/math/geometry/euclidean/oned/IntervalsSet.html">
<a href="../apidocs/org/apache/commons/math3/geometry/euclidean/oned/Interval.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
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).
@ -46,7 +46,7 @@
representation.
</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
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).
@ -55,7 +55,7 @@
or from a boundary representation.
</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
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).
@ -64,7 +64,7 @@
or from a boundary representation.
</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
that instances of this class are guaranteed
to be immutable, this greatly simplifies modelling dynamical systems
@ -86,12 +86,12 @@
is of course also implemented.
</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
input with text representation of 3D vectors.
</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 instances are also immutable objects, as Vector3D instances.
</p>
@ -165,7 +165,7 @@
</subsection>
<subsection name="11.3 Binary Space Partitioning" href="partitioning">
<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
to associate attributes with each cell. Each node in a BSP tree
represents a convex region which is partitioned in two convex

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@ -37,7 +37,7 @@
</subsection>
<subsection name="3.2 Real matrices" href="real_matrices">
<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
entries. The following basic matrix operations are supported:
<ul>
@ -72,18 +72,18 @@ RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
</p>
<p>
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
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
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.
</p>
</subsection>
<subsection name="3.3 Real vectors" href="real_vectors">
<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
entries. The following basic matrix operations are supported:
<ul>
@ -96,7 +96,7 @@ RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
</ul>
</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
textual format.
</p>
@ -104,7 +104,7 @@ RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
<subsection name="3.4 Solving linear systems" href="solve">
<p>
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
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
@ -151,11 +151,11 @@ RealVector solution = solver.solve(constants);
<table border="1" align="center">
<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><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/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/math/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/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/LUDecomposition.html">LU</a></td><td>square</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/math3/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/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/SingularValueDecomposition.html">SVD</a></td><td>any</td><td>least squares solution</td></tr>
</table>
</p>
<p>
@ -190,13 +190,13 @@ RealVector solution = solver.solve(constants);
<subsection name="3.6 Non-real fields (complex, fractions ...)" href="field">
<p>
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:
<ul>
<li><a href="../apidocs/org/apache/commons/math/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/math/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/complex/Complex.html">Complex</a></li>
<li><a href="../apidocs/org/apache/commons/math3/fraction/Fraction.html">Fraction</a></li>
<li><a href="../apidocs/org/apache/commons/math3/fraction/BigFraction.html">BigFraction</a></li>
<li><a href="../apidocs/org/apache/commons/math3/util/BigReal.html">BigReal</a></li>
</ul>
</p>
</subsection>

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@ -40,7 +40,7 @@
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
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.
</p>
<p>
@ -64,9 +64,9 @@
</p>
<p>
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
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:
<ul>
<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
should be used when more in-depth information is needed throughout the integration process. The user
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/math/ode/sampling/StepNormalizer.html">StepNormalizer</a> object wrapping
<a href="../apidocs/org/apache/commons/math3/ode/sampling/StepHandler.html">StepHandler</a> interface or a
<a href="../apidocs/org/apache/commons/math3/ode/sampling/StepNormalizer.html">StepNormalizer</a> object wrapping
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
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
@ -140,7 +140,7 @@ StepHandler stepHandler = new StepHandler() {
integrator.addStepHandler(stepHandler);
</source>
<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
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
@ -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.
</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
(<a href="../apidocs/org/apache/commons/math/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/DummyStepHandler.html">DummyStepHandler</a>,
<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
completely driven by the integration process, then most of the application code will be run inside a
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
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
<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
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
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,
however the user can specify it if he prefers to retain full control over the integration or if the
automatic guess is wrong.
@ -180,7 +180,7 @@ integrator.addStepHandler(stepHandler);
</p>
<p>
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
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.
@ -260,23 +260,23 @@ public int eventOccurred(double t, double[] y, boolean increasing) {
<table border="1" align="center">
<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><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/math/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/math/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/EulerIntegrator.html">Euler</a></td><td>1</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/math3/ode/nonstiff/ClassicalRungeKuttaIntegrator.html">Classical Runge-Kutta</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/math3/ode/nonstiff/ThreeEighthesIntegrator.html">3/8</a></td><td>4</td></tr>
</table>
</p>
<p>
<table border="1" align="center">
<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><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/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/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/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/math/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/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/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/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/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/AdamsBashforthIntegrator.html">Adams-Bashforth</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>
</p>
</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
the initial state or some parameter of the ODE, he will use the classes and interfaces
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
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.
@ -323,9 +323,9 @@ public int eventOccurred(double t, double[] y, boolean increasing) {
<p>
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
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
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:
</p>
<source>
@ -373,9 +373,9 @@ integrator.integrate(t0, y0, dy0dp, t, y, dydy0, dydp);
<p>
If the function f is simple, the user can simply provide the local jacobians
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
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:
</p>
<source>

62
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@ -54,7 +54,7 @@
</p>
<p>
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>.
</p>
<p>
@ -63,21 +63,21 @@
are only four interfaces defining the common behavior of optimizers, one for each
supported type of objective function:
<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
href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">
href="../apidocs/org/apache/commons/math3/analysis/UnivariateRealFunction.html">
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
href="../apidocs/org/apache/commons/math/analysis/MultivariateRealFunction.html">
href="../apidocs/org/apache/commons/math3/analysis/MultivariateRealFunction.html">
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
href="../apidocs/org/apache/commons/math/analysis/DifferentiableMultivariateRealFunction.html">
href="../apidocs/org/apache/commons/math3/analysis/DifferentiableMultivariateRealFunction.html">
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
href="../apidocs/org/apache/commons/math/analysis/DifferentiableMultivariateVectorialFunction.html">
href="../apidocs/org/apache/commons/math3/analysis/DifferentiableMultivariateVectorialFunction.html">
differentiable multivariate vectorial functions</a></li>
</ul>
</p>
@ -85,14 +85,14 @@
<p>
Despite there are only four types of supported optimizers, it is possible to optimize
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
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
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
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.
</p>
@ -106,7 +106,7 @@
</subsection>
<subsection name="12.2 Univariate Functions" href="univariate">
<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
function <code>f</code>.
</p>
@ -157,16 +157,16 @@
The <code>direct</code> package provides four solvers:
<ul>
<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>
<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>
<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>
<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.
</li>
</ul>
@ -174,9 +174,9 @@
<p>
The first two simplex-based methods do not handle simple bounds constraints by themselves.
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
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
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
@ -230,15 +230,15 @@
<p>
Two optimizers are available in the general package, both devoted to least-squares
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
href="../apidocs/org/apache/commons/math/optimization/general/LevenbergMarquardtOptimizer.html">
href="../apidocs/org/apache/commons/math3/optimization/general/LevenbergMarquardtOptimizer.html">
Levenberg-Marquardt</a> method.
</p>
<p>
In order to solve a vectorial optimization problem, the user must provide it as
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
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
@ -303,7 +303,7 @@
</table>
<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:
</p>
@ -571,17 +571,17 @@ C: 16.324008168386605
</dd></dl>
<p>
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
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
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
solver).
</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.
</p>
</subsection>
@ -608,16 +608,16 @@ C: 16.324008168386605
</p>
<p>
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
provide their own implementation of the curve template as a class implementing
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
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
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
not an initial guess as they are able to compute them by themselves.
</p>

6
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@ -104,9 +104,9 @@
<p>
When the actual parameters provided to a method or the internal state of an object
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
<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
exceptions (and any other exceptions) are thrown are specified in the javadoc method
comments.
@ -118,7 +118,7 @@
<p>
As of version 2.2, the policy for dealing with null references is as
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
class does not inherit from the standard <code>NullPointerException</code> but is a subclass
of <code>MathIllegalArgumentException</code>.

62
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@ -68,7 +68,7 @@
<subsection name="2.2 Random numbers" href="deviates">
<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
of numbers. The API contracts of these methods use the following concepts:
<dl>
@ -87,10 +87,10 @@
ranges in the set of possible values of a random variable have
different probabilities of containing the value. Commons Math supports
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.
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
random deviates.
</dd>
@ -168,11 +168,11 @@ for (int i = 0; i &lt; 1000; i++) {
Some algorithms require random vectors instead of random scalars. When the
components of these vectors are uncorrelated, they may be generated simply
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
process by setting the mean and deviation of each component once and
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
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
@ -221,10 +221,10 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
<p>
In addition to multivariate normal distributions, correlated vectors from multivariate uniform
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
<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.
</p>
</subsection>
@ -345,41 +345,41 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
generation utilities and to provide a generic means to replace
<code>java.util.Random</code> in applications, a random generator
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
<code>java.util.Random</code> and any implementation of this
interface can be used as the source of random data for the commons-math
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.
This class provides default implementations of "derived" data generation
methods based on the primitive, <code>nextDouble()</code>.
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
<code>java.util.Random</code> and wraps and delegates calls to
a <code>RandomGenerator</code> instance.
</p>
<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:
<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>
<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>
<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
which in turn is extended by:
<ul>
<li><a href="../apidocs/org/apache/commons/math/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/math/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/math/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/math/random/Well44497b.html">Well44497b</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/MersenneTwister.html">MersenneTwister</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/Well512a.html">Well512a</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/Well1024a.html">Well1024a</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/Well19937a.html">Well19937a</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/Well19937c.html">Well19937c</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/Well44497a.html">Well44497a</a></li>
<li><a href="../apidocs/org/apache/commons/math3/random/Well44497b.html">Well44497b</a></li>
</ul>
</li>
</ul>
@ -450,21 +450,21 @@ RealMatrix covariance = MatrixUtils.createRealMatrix(cov); </source>
<table border="1" align="center">
<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><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/math/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/math/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/math/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/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/MersenneTwister.html">MersenneTwister</a></td><td>1</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/math3/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/Well1024a.html">Well1024a</a></td><td>between 0.63 and 0.73</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/math3/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/Well44497a.html">Well44497a</a></td><td>between 0.69 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>
</p>
<p>
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/math/random/Well44497b.html">Well44497b</a> are probably very good choices.
href="../apidocs/org/apache/commons/math3/random/Well19937c.html">Well19937c</a> and <a
href="../apidocs/org/apache/commons/math3/random/Well44497b.html">Well44497b</a> are probably very good choices.
</p>
<p>

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@ -35,7 +35,7 @@
</subsection>
<subsection name="5.2 Erf functions" href="erf">
<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.
<table>
<tr><th>Function</th><th>Method</th><th>Reference</th></tr>
@ -45,7 +45,7 @@
</subsection>
<subsection name="5.3 Gamma functions" href="gamma">
<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.
<table>
<tr><th>Function</th><th>Method</th><th>Reference</th></tr>
@ -56,7 +56,7 @@
</subsection>
<subsection name="5.4 Beta funtions" href="beta">
<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.
<table>
<tr><th>Function</th><th>Method</th><th>Reference</th></tr>

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@ -63,12 +63,12 @@
</p>
<p>
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>.
This interface, implemented by all statistics, consists of
<code>evaluate()</code> methods that take double[] arrays as arguments
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>
<code>getResult()</code> and associated methods to support
"storageless" implementations that maintain counters, sums or other
@ -77,9 +77,9 @@
</p>
<p>
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
<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.
</p>
<p>
@ -89,9 +89,9 @@
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
(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
<a href="../apidocs/org/apache/commons/math/stat/descriptive/SummaryStatistics.html">
<a href="../apidocs/org/apache/commons/math3/stat/descriptive/SummaryStatistics.html">
SummaryStatistics.</a>
</p>
<p>
@ -109,18 +109,18 @@
<table>
<tr><th>Aggregate</th><th>Statistics Included</th><th>Values stored?</th>
<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,
sum, sum of squares, standard deviation, variance, percentiles, skewness,
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,
sum, sum of squares, standard deviation, variance</td><td>No</td><td>No</td></tr>
</table>
</p>
<p>
<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
gather statistics for multiple datasets as well as for a combined sample
including all of the data.
@ -134,19 +134,19 @@
<p>
Neither <code>DescriptiveStatistics</code> nor <code>SummaryStatistics</code>
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
<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
versions for applications that require concurrent access to statistical
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
<code>MultivariateSummaryStatistics.</code>
</p>
<p>
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
directly from double[] arrays.
</p>
@ -244,7 +244,7 @@ DescriptiveStatistics stats = new SynchronizedDescriptiveStatistics();
The first is to use an <code>AggregateSummaryStatistics</code> instance
to accumulate overall statistics contributed by <code>SummaryStatistics</code>
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>:
<source>
// 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
aggregate as well as the subsample. For applications that can wait to do the aggregation until all values
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.
This method should be used when aggregation needs to be done across threads.
<source>
@ -293,7 +293,7 @@ double totalSampleSum = aggregatedStats.getSum();
</subsection>
<subsection name="1.3 Frequency distributions">
<p>
<a href="../apidocs/org/apache/commons/math/stat/Frequency.html">
<a href="../apidocs/org/apache/commons/math3/stat/Frequency.html">
Frequency</a>
provides a simple interface for maintaining counts and percentages of discrete
values.
@ -357,7 +357,7 @@ System.out.println(f.getCumPct("z")); // displays 1
</subsection>
<subsection name="1.4 Simple regression">
<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
one independent variable estimating the linear model:
</p>
@ -393,7 +393,7 @@ System.out.println(f.getCumPct("z")); // displays 1
"compute" method that updates all statistics. Each of the getters performs
the necessary computations to return the requested statistic.</li>
<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>
property is false, the model is estimated without a constant term and
<code>getIntercept()</code> returns <code>0</code>.</li>
@ -511,9 +511,9 @@ System.out.println(regression.getInterceptStdErr() );
</subsection>
<subsection name="1.5 Multiple linear regression">
<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
<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:
</p>
<p>
@ -525,9 +525,9 @@ System.out.println(regression.getInterceptStdErr() );
of <b>error terms</b> or <b>residuals</b>.
</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
<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
classes for details on the algorithms and forumlas used.
</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
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
<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>,
<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
<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.
</p>
<p>
@ -617,16 +617,16 @@ regression.newSampleData(y, x, omega);
<subsection name="1.6 Rank transformations">
<p>
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.
<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.
<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.
<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>
<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>
</ul>
</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
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
<a href="../apidocs/org/apache/commons/math/stat/ranking/NaturalRanking.html">
NaturalRanking</a> for more examples and <a href="../apidocs/org/apache/commons/math/stat/ranking/TiesStrategy.html">
TiesStrategy</a> and <a href="../apidocs/org/apache/commons/math/stat/ranking/NaNStrategy.html">NaNStrategy</a>
<a href="../apidocs/org/apache/commons/math3/stat/ranking/NaturalRanking.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/math3/stat/ranking/NaNStrategy.html">NaNStrategy</a>
for details on these configuration options.
</p>
</subsection>
<subsection name="1.7 Covariance and correlation">
<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
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,
<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
<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.
</p>
<p>
@ -681,17 +681,17 @@ new NaturalRanking(NaNStrategy.REMOVED,TiesStrategy.SEQUENTIAL).rank(exampleData
defaults to <code>true.</code>
</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>
<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>
and <code>s(X)</code>, <code>s(Y)</code> are standard deviations.
</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
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.
</li>
</ul>
@ -805,7 +805,7 @@ new PearsonsCorrelation().correlation(ranking.rank(x), ranking.rank(y))
<subsection name="1.8 Statistical tests">
<p>
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
<a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm">
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>,
<code>Chi-Square</code> and <code>One-Way ANOVA</code> tests. The
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>,
<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
<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
<a href="../apidocs/org/apache/commons/math/stat/inference/TTestImpl.html">
<a href="../apidocs/org/apache/commons/math3/stat/inference/TTestImpl.html">
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
<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.
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
to compute test statistics directly. The examples below all use the
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>
</dd>
<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:
<source>
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
provide both direct and inverse transforms.
<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>
<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>
<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>
<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>
</ul>
</p>

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

@ -31,7 +31,7 @@
<subsection name="6.1 Overview" href="overview">
<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,
value transformers, and numerical routines used by implementation classes in
commons-math.
@ -44,7 +44,7 @@
array implementation was developed and is provided for reuse in the
<code>util</code> package. The core functionality provided is described in
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,
<code>addElementRolling(double)</code> to basic list accessors.
The <code>addElementRolling</code> method adds an element
@ -52,7 +52,7 @@
in the list.
</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
implementation of the <code>DoubleArray</code> interface.
When <code>addElementRolling</code> is invoked, the underlying
@ -66,7 +66,7 @@
automatically, with frequency / effect driven by the configuration
properties <code>expansionMode</code>, <code>expansionFactor</code> and
<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>
for details.
</p>
@ -74,7 +74,7 @@
<subsection name="6.3 int/double hash map" href="int_double_hash_map">
<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
implementation for int/double. This implementation has a much smaller memory
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">
<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
continued fractions. The easiest way to create a continued fraction is
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">
<p>
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>
<li>
Binomial coefficients -- "n choose k" available as an (exact) long value,
@ -245,7 +245,7 @@
</subsection>
<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
(identifying points in a multidimensional space) to a single index (e.g. identifying
a location in a one-dimensional array.