org.apache.mahout.math.jet.math
Class Bessel

java.lang.Object
  extended by org.apache.mahout.math.jet.math.Constants
      extended by org.apache.mahout.math.jet.math.Bessel

Deprecated. until unit tests are in place. Until this time, this class/interface is unsupported.

@Deprecated
public class Bessel
extends Constants


Field Summary
 
Fields inherited from class org.apache.mahout.math.jet.math.Constants
BIG, BIG_INVERSE, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI
 
Constructor Summary
protected Bessel()
          Deprecated. Makes this class non instantiable, but still let's others inherit from it.
 
Method Summary
static double i0(double x)
          Deprecated. Returns the modified Bessel function of order 0 of the argument.
static double i0e(double x)
          Deprecated. Returns the exponentially scaled modified Bessel function of order 0 of the argument.
static double i1(double x)
          Deprecated. Returns the modified Bessel function of order 1 of the argument.
static double i1e(double x)
          Deprecated. Returns the exponentially scaled modified Bessel function of order 1 of the argument.
static double j0(double x)
          Deprecated. Returns the Bessel function of the first kind of order 0 of the argument.
static double j1(double x)
          Deprecated. Returns the Bessel function of the first kind of order 1 of the argument.
static double jn(int n, double x)
          Deprecated. Returns the Bessel function of the first kind of order n of the argument.
static double k0(double x)
          Deprecated. Returns the modified Bessel function of the third kind of order 0 of the argument.
static double k0e(double x)
          Deprecated. Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
static double k1(double x)
          Deprecated. Returns the modified Bessel function of the third kind of order 1 of the argument.
static double k1e(double x)
          Deprecated. Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.
static double kn(int nn, double x)
          Deprecated. Returns the modified Bessel function of the third kind of order nn of the argument.
static double y0(double x)
          Deprecated. Returns the Bessel function of the second kind of order 0 of the argument.
static double y1(double x)
          Deprecated. Returns the Bessel function of the second kind of order 1 of the argument.
static double yn(int n, double x)
          Deprecated. Returns the Bessel function of the second kind of order n of the argument.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

Bessel

protected Bessel()
Deprecated. 
Makes this class non instantiable, but still let's others inherit from it.

Method Detail

i0

public static double i0(double x)
Deprecated. 
Returns the modified Bessel function of order 0 of the argument.

The function is defined as i0(x) = j0( ix ).

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:
x - the value to compute the bessel function of.

i0e

public static double i0e(double x)
Deprecated. 
Returns the exponentially scaled modified Bessel function of order 0 of the argument.

The function is defined as i0e(x) = exp(-|x|) j0( ix ).

Parameters:
x - the value to compute the bessel function of.

i1

public static double i1(double x)
Deprecated. 
Returns the modified Bessel function of order 1 of the argument.

The function is defined as i1(x) = -i j1( ix ).

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:
x - the value to compute the bessel function of.

i1e

public static double i1e(double x)
Deprecated. 
Returns the exponentially scaled modified Bessel function of order 1 of the argument.

The function is defined as i1(x) = -i exp(-|x|) j1( ix ).

Parameters:
x - the value to compute the bessel function of.

j0

public static double j0(double x)
Deprecated. 
Returns the Bessel function of the first kind of order 0 of the argument.

Parameters:
x - the value to compute the bessel function of.

j1

public static double j1(double x)
Deprecated. 
Returns the Bessel function of the first kind of order 1 of the argument.

Parameters:
x - the value to compute the bessel function of.

jn

public static double jn(int n,
                        double x)
Deprecated. 
Returns the Bessel function of the first kind of order n of the argument.

Parameters:
n - the order of the Bessel function.
x - the value to compute the bessel function of.

k0

public static double k0(double x)
Deprecated. 
Returns the modified Bessel function of the third kind of order 0 of the argument.

The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:
x - the value to compute the bessel function of.

k0e

public static double k0e(double x)
Deprecated. 
Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.

Parameters:
x - the value to compute the bessel function of.

k1

public static double k1(double x)
Deprecated. 
Returns the modified Bessel function of the third kind of order 1 of the argument.

The range is partitioned into the two intervals [0,2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.

Parameters:
x - the value to compute the bessel function of.

k1e

public static double k1e(double x)
Deprecated. 
Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.

k1e(x) = exp(x) * k1(x).

Parameters:
x - the value to compute the bessel function of.

kn

public static double kn(int nn,
                        double x)
Deprecated. 
Returns the modified Bessel function of the third kind of order nn of the argument.

The range is partitioned into the two intervals [0,9.55] and (9.55, infinity). An ascending power series is used in the low range, and an asymptotic expansion in the high range.

Parameters:
nn - the order of the Bessel function.
x - the value to compute the bessel function of.

y0

public static double y0(double x)
Deprecated. 
Returns the Bessel function of the second kind of order 0 of the argument.

Parameters:
x - the value to compute the bessel function of.

y1

public static double y1(double x)
Deprecated. 
Returns the Bessel function of the second kind of order 1 of the argument.

Parameters:
x - the value to compute the bessel function of.

yn

public static double yn(int n,
                        double x)
Deprecated. 
Returns the Bessel function of the second kind of order n of the argument.

Parameters:
n - the order of the Bessel function.
x - the value to compute the bessel function of.


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