Author: erans
Date: Fri Apr 23 22:33:37 2010
New Revision: 937545
URL: http://svn.apache.org/viewvc?rev=937545&view=rev
Log:
Removed package names in links.
Modified:
commons/proper/math/trunk/src/site/xdoc/userguide/analysis.xml
Modified: commons/proper/math/trunk/src/site/xdoc/userguide/analysis.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/site/xdoc/userguide/analysis.xml?rev=937545&r1=937544&r2=937545&view=diff
==============================================================================
--- commons/proper/math/trunk/src/site/xdoc/userguide/analysis.xml (original)
+++ commons/proper/math/trunk/src/site/xdoc/userguide/analysis.xml Fri Apr 23
22:33:37 2010
@@ -47,8 +47,8 @@
<subsection name="4.2 Root-finding" href="rootfinding">
<p>
A <a
href="../apidocs/org/apache/commons/math/analysis/solvers/UnivariateRealSolver.html">
- org.apache.commons.math.analysis.solvers.UnivariateRealSolver.</a>
- provides the means to find roots of <a
href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate
real-valued functions</a>.
+ UnivariateRealSolver</a> provides the means to find roots of
+ <a
href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate
real-valued functions</a>.
A root is the value where the function takes the value 0.
Commons-Math
includes implementations of the following root-finding algorithms:
<ul>
<li><a
href="../apidocs/org/apache/commons/math/analysis/solvers/BisectionSolver.html">
@@ -93,11 +93,13 @@
<p>
In order to use the root-finding features, first a solver object must
be created. It is encouraged that all solver object creation occurs
- via the
<code>org.apache.commons.math.analysis.solvers.UnivariateRealSolverFactory</code>
- class. <code>UnivariateRealSolverFactory</code> is a simple factory
- used to create all of the solver objects supported by Commons-Math.
- The typical usage of <code>UnivariateRealSolverFactory</code>
- to create a solver object would be:</p>
+ via the <a
href="../apidocs/org/apache/commons/math/analysis/solvers/UnivariateRealSolverFactory.html">
+ UnivariateRealSolverFactory</a> class.
<code>UnivariateRealSolverFactory</code>
+ is a simple factory used to create all of the solver objects
supported by
+ Commons-Math.
+ The typical usage of <code>UnivariateRealSolverFactory</code> to
create a
+ solver object would be:
+ </p>
<source>UnivariateRealSolverFactory factory =
UnivariateRealSolverFactory.newInstance();
UnivariateRealSolver solver = factory.newDefaultSolver();</source>
<p>
@@ -105,13 +107,22 @@ UnivariateRealSolver solver = factory.ne
<code>UnivariateRealSolverFactory</code> are detailed below:
<table>
<tr><th>Solver</th><th>Factory Method</th><th>Notes on
Use</th></tr>
- <tr><td>Bisection</td><td>newBisectionSolver</td><td><div>Root
must be bracketted.</div><div>Linear, guaranteed convergence</div></td></tr>
- <tr><td>Brent</td><td>newBrentSolver</td><td><div>Root must be
bracketted.</div><div>Super-linear, guaranteed convergence</div></td></tr>
- <tr><td>Newton</td><td>newNewtonSolver</td><td><div>Uses single
value for initialization.</div><div>Super-linear, non-guaranteed
convergence</div><div>Function must be differentiable</div></td></tr>
- <tr><td>Secant</td><td>newSecantSolver</td><td><div>Root must be
bracketted.</div><div>Super-linear, non-guaranteed convergence</div></td></tr>
- <tr><td>Muller</td><td>newMullerSolver</td><td><div>Root must be
bracketted.</div><div>We restrict ourselves to real valued functions, not
complex ones</div></td></tr>
- <tr><td>Laguerre</td><td>newLaguerreSolver</td><td><div>Root must
be bracketted.</div><div>Function must be a polynomial</div></td></tr>
- <tr><td>Ridder</td><td>newRidderSolver</td><td><div>Root must be
bracketted.</div><div></div></td></tr>
+ <tr><td>Bisection</td><td>newBisectionSolver</td><td><div>Root
must be
+ bracketted.</div><div>Linear, guaranteed
convergence</div></td></tr>
+ <tr><td>Brent</td><td>newBrentSolver</td><td><div>Root must be
bracketted.</div>
+ <div>Super-linear, guaranteed convergence</div></td></tr>
+ <tr><td>Newton</td><td>newNewtonSolver</td><td><div>Uses single
value for
+ initialization.</div><div>Super-linear, non-guaranteed
convergence</div>
+ <div>Function must be differentiable</div></td></tr>
+ <tr><td>Secant</td><td>newSecantSolver</td><td><div>Root must be
bracketted.</div>
+ <div>Super-linear, non-guaranteed convergence</div></td></tr>
+ <tr><td>Muller</td><td>newMullerSolver</td><td><div>Root must be
bracketted.</div>
+ <div>We restrict ourselves to real valued functions, not
complex ones</div>
+ </td></tr>
+ <tr><td>Laguerre</td><td>newLaguerreSolver</td><td><div>Root must
be bracketted.</div>
+ <div>Function must be a polynomial</div></td></tr>
+ <tr><td>Ridder</td><td>newRidderSolver</td><td><div>Root must be
bracketted.</div>
+ <div></div></td></tr>
</table>
</p>
<p>
@@ -247,15 +258,14 @@ double c = solver.solve(function, 1.0, 5
<subsection name="4.3 Interpolation" href="interpolation">
<p>
A <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/UnivariateRealInterpolator.html">
-
org.apache.commons.math.analysis.interpolation.UnivariateRealInterpolator</a>
- is used to find a univariate real-valued function <code>f</code>
which
- for a given set of ordered pairs
+ 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">
- org.apache.commons.math.analysis.UnivariateRealFunction</a>
interface. It can therefore
- be evaluated at any point, including point not belonging to the
original set.
+ 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
interpolator are available. There is no interpolator factory,
mainly because the
interpolation algorithm is more determined by the kind of the
interpolated function
@@ -309,71 +319,66 @@ System.out println("f(" + interpolationX
</p>
<p>
A <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/BivariateRealGridInterpolator.html">
-
org.apache.commons.math.analysis.interpolation.BivariateRealGridInterpolator</a>
- is used to find a bivariate real-valued function <code>f</code> which
- for a given set of tuples
+ 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">
- org.apache.commons.math.analysis.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 sorted in
- increasing order in order to define a two-dimensional regular grid.
- </p>
- <p>
- In <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.html">
- bicubic interpolation</a>, the interpolation function is a
3rd-degree polynomial of two
- variables. The coefficients are computed from the function values
sampled on a regular grid,
- as well as the values of the partial derivatives of the function at
those grid points.
+ 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
+ sorted in increasing order in order to define a two-dimensional grid.
</p>
<p>
- From two-dimensional data sampled on a regular grid, the
+ In <a
href="http://en.wikipedia.org/wiki/Bicubic_interpolation";>bicubic
interpolation</a>,
+ the interpolation function is a 3rd-degree polynomial of two
variables. The coefficients
+ 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">
-
org.apache.commons.math.analysis.interpolation.BicubicSplineInterpolator</a>
- computes a <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/BicubicSplineInterpolatingFunction.html">
+ BicubicSplineInterpolator</a> computes a
+ <a
href="../apidocs/org/apache/commons/math/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">
-
org.apache.commons.math.analysis.interpolation.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.
+ 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">
-
org.apache.commons.math.analysis.interpolation.TrivariateRealGridInterpolator</a>
- is used to find a bivariate real-valued function <code>f</code> which
- for a given set of tuples
+ 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
+ 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">
- org.apache.commons.math.analysis.TrivariateRealFunction</a>
interface. It can therefore
- be evaluated at any point, including a point not belonging to the
original set.
+ 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
- <code>z<sub>k</sub></code> must be sorted in increasing order in
order to define a
- three-dimensional regular grid.
- </p>
- <p>
- In <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.html">
- tricubic interpolation</a>, the interpolation function is a
3rd-degree polynomial of two
- variables. The coefficients are computed from the function values
sampled on a regular grid,
- as well as the values of the partial derivatives of the function at
those grid points.
+ <code>z<sub>k</sub></code> must be sorted in increasing order in
order to define
+ a three-dimensional grid.
</p>
<p>
- From three-dimensional data sampled on a regular grid, the
+ In <a
href="http://en.wikipedia.org/wiki/Tricubic_interpolation";>tricubic
interpolation</a>,
+ the interpolation function is a 3rd-degree polynomial of three
variables. The coefficients
+ 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">
-
org.apache.commons.math.analysis.interpolation.TricubicSplineInterpolator</a>
- computes a <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.html">
+ TricubicSplineInterpolator</a> computes a
+ <a
href="../apidocs/org/apache/commons/math/analysis/interpolation/TricubicSplineInterpolatingFunction.html">
tricubic interpolating function</a>.
</p>
</subsection>
<subsection name="4.4 Integration" href="integration">
<p>
A <a
href="../apidocs/org/apache/commons/math/analysis/integration/UnivariateRealIntegrator.html">
-
org.apache.commons.math.analysis.integration.UnivariateRealIntegrator.</a>
- provides the means to numerically integrate <a
href="../apidocs/org/apache/commons/math/analysis/UnivariateRealFunction.html">univariate
real-valued functions</a>.
+ UnivariateRealIntegrator</a> provides the means to numerically
integrate
+ <a
href="../apidocs/org/apache/commons/math/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">
Romberg's method</a></li>
@@ -389,17 +394,18 @@ System.out println("f(" + interpolationX
<subsection name="4.5 Polynomials" href="polynomials">
<p>
The <a
href="../apidocs/org/apache/commons/math/analysis/polynomials/package-summary.html">
- org.apache.commons.math.analysis.polynomials</a> package provides
real coefficients
- polynomials.
+ org.apache.commons.math.analysis.polynomials</a> package provides
real
+ coefficients polynomials.
</p>
<p>
The <a
href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialFunction.html">
- org.apache.commons.math.analysis.polynomials.PolynomialFunction</a>
class is the most general
- one, using traditional coefficients arrays. The <a
-
href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.html">
- org.apache.commons.math.analysis.polynomials.PolynomialsUtils</a>
utility class provides static
- factory methods to build Chebyshev, Hermite, Lagrange and Legendre
polynomials. Coefficients
- are computed using exact fractions so these factory methods can
build polynomials up to any degree.
+ PolynomialFunction</a> class is the most general one, using
traditional
+ coefficients arrays. The
+ <a
href="../apidocs/org/apache/commons/math/analysis/polynomials/PolynomialsUtils.html">
+ PolynomialsUtils</a> utility class provides static factory methods
to build
+ Chebyshev, Hermite, Lagrange and Legendre polynomials. Coefficients
are
+ computed using exact fractions so these factory methods can build
polynomials
+ up to any degree.
</p>
</subsection>
</section>
