TMath (math 8.1.4 API)

java.lang.Object
- de.gsi.math.TMathConstants
- - de.gsi.math.TMath

public class TMath
extends TMathConstants

Constructor Summary

Constructors
Constructor and Description

TMath()

Constructors
Constructor and Description
`TMath()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`BesselI(int n, double x)`
`static double`	`BesselI0(double x)`
`static double`	`BesselI1(double x)`
`static double`	`BesselJ0(double x)`
`static double`	`BesselJ1(double x)`
`static double`	`BesselK(int n, double x)`
`static double`	`BesselK0(double x)`
`static double`	`BesselK1(double x)`
`static double`	`BesselY0(double x)`
`static double`	`BesselY1(double x)`
`static double`	`Beta(double p, double q)`
`static double`	`BetaCf(double x, double a, double b)`
`static double`	`BetaDist(double x, double p, double q)` Computes the probability density function of the Beta distribution (the distribution function is computed in BetaDistI).
`static double`	`BetaDistI(double x, double p, double q)`
`static double`	`BetaIncomplete(double x, double a, double b)`
`static long`	`BinarySearch(double[] array, int length, double value)` Binary search in an array of n values to locate value.
`static long`	`BinarySearch(float[] array, int length, float value)` Binary search in an array of n values to locate value.
`static long`	`BinarySearch(int[] array, int length, int value)` Binary search in an array of n values to locate value.
`static long`	`BinarySearch(long[] array, int length, long value)` Binary search in an array of n values to locate value.
`static long`	`BinarySearch(short[] array, int length, short value)` Binary search in an array of n values to locate value.
`static double`	`Binomial(int n, int k)`
`static double`	`BinomialI(double p, int n, int k)`
`static double`	`BreitWigner(double x, double mean, double gamma)` Calculate a Breit Wigner function with mean and gamma.
`static double`	`CauchyDist(double x, double t, double s)` Computes the density of Cauchy distribution at point x The Cauchy distribution, also called Lorentzian distribution, is a continuous distribution describing resonance behavior The mean and standard deviation of the Cauchy distribution are undefined.
`static double`	`ChisquareQuantile(double p, double ndf)` Evaluate the quantiles of the chi-squared probability distribution function.
`static double`	`CorrelationCoefficient(double[] x, double[] y, double[] w)` Calculate weighted correlation coefficient x y data and weights w as double
`static double`	`Covariance(double[] xx, double[] yy, double[] ww)` calculated weighted covariance xx and yy with weights ww
`static double[]`	`Cross(double[] v1, double[] v2, double[] out)` Calculate the Cross Product of two vectors:
`static float[]`	`Cross(float[] v1, float[] v2, float[] out)` Calculate the Cross Product of two vectors:
`static double[]`	`Difference(double[] a, double[] b)`
`static double[]`	`Difference(double[] a, double[] b, int length)` computes the difference between vectors
`static float[]`	`Difference(float[] a, float[] b)`
`static float[]`	`Difference(float[] a, float[] b, int length)` computes the difference between vectors
`static int[]`	`Difference(int[] a, int[] b)`
`static int[]`	`Difference(int[] a, int[] b, int length)` computes the difference between vectors
`static long[]`	`Difference(long[] a, long[] b)`
`static long[]`	`Difference(long[] a, long[] b, int length)` computes the difference between vectors
`static short[]`	`Difference(short[] a, short[] b)`
`static short[]`	`Difference(short[] a, short[] b, int length)` computes the difference between vectors
`static double`	`DiLog(double x)` The DiLogarithm function Code translated by from CERNLIB DILOG function C332
`static double`	`effectiveSampleNumber(double[] ww)`
`static double`	`Erf(double x)` Computation of the error function erf(x).
`static double`	`Erfc(double x)` Compute the complementary error function erfc(x).
`static double`	`ErfInverse(double x)` returns the inverse error function
`static double`	`Factorial(int n)` Compute factorial(n).
`static double`	`FDist(double F, double N, double M)`
`static double`	`FDistI(double F, double N, double M)`
`static double`	`Freq(double x)` Computation of the normal frequency function freq(x).
`static double`	`GamCf(double a, double x)` Computation of the incomplete gamma function P(a,x) via its continued fraction representation.
`static double`	`Gamma(double z)` Computation of gamma(z) for all z>0.
`static double`	`Gamma(double a, double x)` Computation of the normalized lower incomplete gamma function P(a,x) as defined in the Handbook of Mathematical Functions by Abramowitz and Stegun, formula 6.5.1 on page 260 .
`static double`	`GammaDist(double x, double gamma, double mu, double beta)`
`static double`	`GamSer(double a, double x)` Computation of the incomplete gamma function P(a,x) via its series representation.
`static double`	`Gauss(double x, double mean, double sigma, boolean norm)` Calculate a Gaussian function with mean and sigma.
`static double`	`GeometricMean(double[] data)`
`static double`	`GeometricMean(double[] a, int length)` geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
`static float`	`GeometricMean(float[] data)`
`static float`	`GeometricMean(float[] a, int length)` geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
`static int`	`GeometricMean(int[] data)`
`static int`	`GeometricMean(int[] a, int length)` geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
`static long`	`GeometricMean(long[] data)`
`static long`	`GeometricMean(long[] a, int length)` geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
`static short`	`GeometricMean(short[] data)`
`static short`	`GeometricMean(short[] a, int length)` geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
`static boolean`	`IsInside(double xp, double yp, int np, double[] x, double[] y)` Function which returns true if point xp,yp lies inside the polygon defined by the np points in arrays x and y, false otherwise NOTE that the polygon must be a closed polygon (1st and last point must be identical).
`static boolean`	`IsInside(float xp, float yp, int np, float[] x, float[] y)` Function which returns true if point xp,yp lies inside the polygon defined by the np points in arrays x and y, false otherwise NOTE that the polygon must be a closed polygon (1st and last point must be identical).
`static boolean`	`IsInside(int xp, int yp, int np, int[] x, int[] y)` Function which returns true if point xp,yp lies inside the polygon defined by the np points in arrays x and y, false otherwise NOTE that the polygon must be a closed polygon (1st and last point must be identical).
`static double`	`Landau(double x, double mpv, double sigma, boolean norm)` The LANDAU function with mpv(most probable value) and sigma.
`static double`	`LandauI(double x)`
`static double`	`LaplaceDist(double x, double alpha, double beta)`
`static double`	`LaplaceDistI(double x, double alpha, double beta)`
`static double`	`LnGamma(double z)` Computation of ln[gamma(z)] for all z>0.
`static long`	`LocationMaximum(double[] a, int length)`
`static long`	`LocationMaximum(float[] a, int length)`
`static long`	`LocationMaximum(int[] a, int length)`
`static long`	`LocationMaximum(long[] a, int length)`
`static long`	`LocationMinimum(double[] a, int length)`
`static long`	`LocationMinimum(float[] a, int length)`
`static long`	`LocationMinimum(int[] a, int length)`
`static long`	`LocationMinimum(long[] a, int length)`
`static long`	`LocationMinimum(short[] a, int length)`
`static double`	`LogNormal(double x, double sigma, double theta, double m)` Computes the density of LogNormal distribution at point x.
`static void`	`main(String[] argv)`
`static double`	`Maximum(double[] data)`
`static double`	`Maximum(double[] data, int length)`
`static float`	`Maximum(float[] data)`
`static float`	`Maximum(float[] data, int length)`
`static int`	`Maximum(int[] data)`
`static int`	`Maximum(int[] data, int length)`
`static long`	`Maximum(long[] data)`
`static long`	`Maximum(long[] data, int length)`
`static short`	`Maximum(short[] data)`
`static short`	`Maximum(short[] data, int length)`
`static double`	`Mean(double[] data)`
`static double`	`Mean(double[] data, int length)`
`static float`	`Mean(float[] data)`
`static float`	`Mean(float[] data, int length)`
`static int`	`Mean(int[] data)`
`static int`	`Mean(int[] data, int length)`
`static long`	`Mean(long[] data)`
`static long`	`Mean(long[] data, int length)`
`static short`	`Mean(short[] data)`
`static short`	`Mean(short[] data, int length)`
`static double`	`Median(double[] data)`
`static double`	`Median(double[] data, int length)`
`static float`	`Median(float[] data)`
`static float`	`Median(float[] data, int length)`
`static int`	`Median(int[] data)`
`static int`	`Median(int[] data, int length)`
`static long`	`Median(long[] data)`
`static long`	`Median(long[] data, int length)`
`static short`	`Median(short[] data)`
`static short`	`Median(short[] data, int length)`
`static double`	`Minimum(double[] data)`
`static double`	`Minimum(double[] data, int length)`
`static float`	`Minimum(float[] data)`
`static float`	`Minimum(float[] data, int length)`
`static int`	`Minimum(int[] data)`
`static int`	`Minimum(int[] data, int length)`
`static long`	`Minimum(long[] data)`
`static long`	`Minimum(long[] data, int length)`
`static short`	`Minimum(short[] data)`
`static short`	`Minimum(short[] data, int length)`
`static double[]`	`Normal2Plane(double[] p1, double[] p2, double[] p3, double[] normal)` Calculate a normal vector of a plane.
`static float[]`	`Normal2Plane(float[] p1, float[] p2, float[] p3, float[] normal)` Calculate a normal vector of a plane.
`static double`	`Normalize(double[] v)` Normalise a vector v in place.
`static float`	`Normalize(float[] v)` Normalise a vector 'v' in place.
`static double`	`NormCross(double[] v1, double[] v2, double[] out)` Calculate the Normalized Cross Product of two vectors
`static float`	`NormCross(float[] v1, float[] v2, float[] out)` Calculate the Normalized Cross Product of two vectors
`static double`	`NormQuantile(double p)` Computes quantiles for standard normal distribution N(0, 1) at probability p ALGORITHM AS241 APPL.
`static double`	`PeakToPeak(double[] data)`
`static double`	`PeakToPeak(double[] data, int length)`
`static float`	`PeakToPeak(float[] data)`
`static float`	`PeakToPeak(float[] data, int length)`
`static int`	`PeakToPeak(int[] data)`
`static int`	`PeakToPeak(int[] data, int length)`
`static long`	`PeakToPeak(long[] data)`
`static long`	`PeakToPeak(long[] data, int length)`
`static short`	`PeakToPeak(short[] data)`
`static short`	`PeakToPeak(short[] data, int length)`
`static boolean`	`Permute(int n, int[] a)` Simple recursive algorithm to find the permutations of n natural numbers, not necessarily all distinct adapted from CERNLIB routine PERMU.
`static double`	`Poisson(double x, double par)` compute the Poisson distribution function for (x,par) The Poisson PDF is implemented by means of Euler's Gamma-function (for the factorial), so for all integer arguments it is correct.
`static double`	`PoissonI(double x, double par)` compute the Poisson distribution function for (x,par) This is a non-smooth function
`static double`	`Prob(double chi2, int ndf)` Computation of the probability for a certain Chi-squared (chi2) and number of degrees of freedom (ndf).
`static double`	`RMS(double[] data)`
`static double`	`RMS(double[] data, int length)`
`static float`	`RMS(float[] data)`
`static float`	`RMS(float[] data, int length)`
`static int`	`RMS(int[] data)`
`static int`	`RMS(int[] data, int length)`
`static long`	`RMS(long[] data)`
`static long`	`RMS(long[] data, int length)`
`static short`	`RMS(short[] data)`
`static short`	`RMS(short[] data, int length)`
`static double`	`Sinc(double x, boolean norm)` Calculate the sinc = sin(x)/x function if norm ==true then sinc = sinc(pix)/(pix) is used
`static double[]`	`Sort(double[] a, int length, boolean down)` Sorts the input a array
`static float[]`	`Sort(float[] a, int length, boolean down)` Sorts the input a array
`static int[]`	`Sort(int[] a, int length, boolean down)` Sorts the input a array
`static long[]`	`Sort(long[] a, int length, boolean down)` Sorts the input a array
`static short[]`	`Sort(short[] a, int length, boolean down)` Sorts the input a array
`static double`	`StruveH0(double x)`
`static double`	`StruveH1(double x)`
`static double`	`StruveL0(double x)`
`static double`	`StruveL1(double x)`
`static double`	`Student(double T, double ndf)` Computes density function for Student's t- distribution (the probability function (integral of density) is computed in StudentI).
`static double`	`StudentI(double T, double ndf)` Calculates the cumulative distribution function of Student's t-distribution second parameter stands for number of degrees of freedom, not for the number of samples if x has Student's t-distribution, the function returns the probability of x being less than T.
`static double`	`StudentQuantile(double p, double ndf, boolean lower_tail)`
`static double[]`	`Sum(double[] a, double[] b)`
`static double[]`	`Sum(double[] a, double[] b, int length)` computes the sum of vectors
`static float[]`	`Sum(float[] a, float[] b)`
`static float[]`	`Sum(float[] a, float[] b, int length)` computes the sum of vectors
`static int[]`	`Sum(int[] a, int[] b)`
`static int[]`	`Sum(int[] a, int[] b, int length)` computes the sum of vectors
`static long[]`	`Sum(long[] a, long[] b)`
`static long[]`	`Sum(long[] a, long[] b, int length)` computes the sum of vectors
`static short[]`	`Sum(short[] a, short[] b)`
`static short[]`	`Sum(short[] a, short[] b, int length)` computes the sum of vectors
`static double`	`Variance(double[] aa, double[] ww)`
`static double`	`Vavilov(double x, double kappa, double beta2)`
`protected static double`	`VavilovDenEval(double rlam, double[] AC, double[] HC, int itype)` Internal function, called by Vavilov and VavilovSet
`static double`	`VavilovI(double x, double kappa, double beta2)`
`static void`	`VavilovSet(double rkappa, double beta2, boolean mode, double[] WCM, double[] AC, double[] HC, int[] itype, int[] npt)` Internal function, called by Vavilov and VavilovI

Methods inherited from class de.gsi.math.TMathConstants
Abs, Abs, Abs, Abs, Abs, ACos, ASin, ATan, ATan2, C, Ccgs, Ceil, CeilNint, Cos, CosH, CUncertainty, DegToRad, E, EulerGamma, Even, Exp, Finite, Floor, FloorNint, G, Gcgs, GhbarC, GhbarCUncertainty, Gn, GnUncertainty, GUncertainty, H, Hbar, Hbarcgs, HbarUncertainty, HC, HCcgs, Hcgs, HUncertainty, Hypot, Hypot, InvPi, IsNaN, K, Kcgs, KUncertainty, Ldexp, Ln10, Log, Log10, Log2, Log2, LogE, Max, Max, Max, Max, Max, Min, Min, Min, Min, Min, MWair, Na, NaUncertainty, NextPrime, Nint, Nint, Odd, Pi, PiOver2, PiOver4, Power, Qe, QeUncertainty, R, RadToDeg, Range, Range, Range, Range, Rgair, RUncertainty, Sigma, SigmaUncertainty, Sign, Sign, Sign, Sign, Sign, Sin, SinH, Sqr, Sqrt, Sqrt2, Tan, TanH, TwoPi

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - TMath
```
public TMath()
```
- Method Detail
  - BesselI
```
public static double BesselI(int n,
                             double x)
```
  - BesselI0
```
public static double BesselI0(double x)
```
  - BesselI1
```
public static double BesselI1(double x)
```
  - BesselJ0
```
public static double BesselJ0(double x)
```
  - BesselJ1
```
public static double BesselJ1(double x)
```
  - BesselK
```
public static double BesselK(int n,
                             double x)
```
  - BesselK0
```
public static double BesselK0(double x)
```
  - BesselK1
```
public static double BesselK1(double x)
```
  - BesselY0
```
public static double BesselY0(double x)
```
  - BesselY1
```
public static double BesselY1(double x)
```
  - Beta
```
public static double Beta(double p,
                          double q)
```
  - BetaCf
```
public static double BetaCf(double x,
                            double a,
                            double b)
```
  - BetaDist
```
public static double BetaDist(double x,
                              double p,
                              double q)
```
    Computes the probability density function of the Beta distribution (the distribution function is computed in BetaDistI). The first argument is the point, where the function will be computed, second and third are the function parameters. Since the Beta distribution is bounded on both sides, it's often used to represent processes with natural lower and upper limits.
    
    Parameters:
    
    x - input value
    
    p - p parameter of beta function
    
    q - q parameter of beta function
    
    Returns:
    
    probability density function of the Beta distribution
  - BetaDistI
```
public static double BetaDistI(double x,
                               double p,
                               double q)
```
  - BetaIncomplete
```
public static double BetaIncomplete(double x,
                                    double a,
                                    double b)
```
  - BinarySearch
```
public static long BinarySearch(double[] array,
                                int length,
                                double value)
```
    Binary search in an array of n values to locate value. Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.
    
    Parameters:
    
    array - input vector
    
    length - <= data.length elements to be used
    
    value - to be searched
    
    Returns:
    
    index of found value, -1 otherwise
  - BinarySearch
```
public static long BinarySearch(float[] array,
                                int length,
                                float value)
```
    Binary search in an array of n values to locate value. Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.
    
    Parameters:
    
    array - input vector
    
    length - <= data.length elements to be used
    
    value - to be searched
    
    Returns:
    
    index of found value, -1 otherwise
  - BinarySearch
```
public static long BinarySearch(int[] array,
                                int length,
                                int value)
```
    Binary search in an array of n values to locate value. Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.
    
    Parameters:
    
    array - input vector
    
    length - <= data.length elements to be used
    
    value - to be searched
    
    Returns:
    
    index of found value, -1 otherwise
  - BinarySearch
```
public static long BinarySearch(long[] array,
                                int length,
                                long value)
```
    Binary search in an array of n values to locate value. Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.
    
    Parameters:
    
    array - input vector
    
    length - <= data.length elements to be used
    
    value - to be searched
    
    Returns:
    
    index of found value, -1 otherwise
  - BinarySearch
```
public static long BinarySearch(short[] array,
                                int length,
                                short value)
```
    Binary search in an array of n values to locate value. Array is supposed to be sorted prior to this call. If match is found, function returns position of element. If no match found, function gives nearest element smaller than value.
    
    Parameters:
    
    array - input vector
    
    length - <= data.length elements to be used
    
    value - to be searched
    
    Returns:
    
    index of found value, -1 otherwise
  - Binomial
```
public static double Binomial(int n,
                              int k)
```
  - BinomialI
```
public static double BinomialI(double p,
                               int n,
                               int k)
```
  - BreitWigner
```
public static double BreitWigner(double x,
                                 double mean,
                                 double gamma)
```
    Calculate a Breit Wigner function with mean and gamma.
    
    Parameters:
    
    x - input parameter
    
    mean - centre of distribution
    
    gamma - width of distribution
    
    Returns:
    
    the computed result
  - CauchyDist
```
public static double CauchyDist(double x,
                                double t,
                                double s)
```
    Computes the density of Cauchy distribution at point x The Cauchy distribution, also called Lorentzian distribution, is a continuous distribution describing resonance behavior The mean and standard deviation of the Cauchy distribution are undefined. The practical meaning of this is that collecting 1,000 data points gives no more accurate an estimate of the mean and standard deviation than does a single point. The formula was taken from "Engineering Statistics Handbook" on site http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm Implementation by Anna Kreshuk.
    
    Parameters:
    
    x - input value
    
    t - the location parameter
    
    s - the scale parameter
    
    Returns:
    
    Cauchy distribution at point x
  - ChisquareQuantile
```
public static double ChisquareQuantile(double p,
                                       double ndf)
```
    Evaluate the quantiles of the chi-squared probability distribution function. Algorithm AS 91 Appl. Statist. (1975) Vol.24, P.35 implemented by Anna Kreshuk. Incorporates the suggested changes in AS R85 (vol.40(1), pp.233-5, 1991)
    
    Parameters:
    
    p - the probability value, at which the quantile is computed
    
    ndf - number of degrees of freedom
    
    Returns:
    
    quantiles of the chi-squared probability distribution
  - CorrelationCoefficient
```
public static double CorrelationCoefficient(double[] x,
                                            double[] y,
                                            double[] w)
```
    Calculate weighted correlation coefficient x y data and weights w as double
    
    Parameters:
    
    x - input vector 1
    
    y - input vector 2
    
    w - wheights weight vector
    
    Returns:
    
    weighted correlation coefficient
  - Covariance
```
public static double Covariance(double[] xx,
                                double[] yy,
                                double[] ww)
```
    calculated weighted covariance xx and yy with weights ww
    
    Parameters:
    
    xx - input vector 1
    
    yy - input vector 2
    
    ww - weights
    
    Returns:
    
    weighted covariance
  - Cross
```
public static double[] Cross(double[] v1,
                             double[] v2,
                             double[] out)
```
    Calculate the Cross Product of two vectors:
    
    Parameters:
    
    v1 - input vector1
    
    v2 - input vector2
    
    out - output vector
    
    Returns:
    
    out = [v1 x v2]
  - Cross
```
public static float[] Cross(float[] v1,
                            float[] v2,
                            float[] out)
```
    Calculate the Cross Product of two vectors:
    
    Parameters:
    
    v1 - input vector1
    
    v2 - input vector2
    
    out - output vector
    
    Returns:
    
    out = [v1 x v2]
  - Difference
```
public static double[] Difference(double[] a,
                                  double[] b)
```
  - Difference
```
public static double[] Difference(double[] a,
                                  double[] b,
                                  int length)
```
    computes the difference between vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] - b[]
  - Difference
```
public static float[] Difference(float[] a,
                                 float[] b)
```
  - Difference
```
public static float[] Difference(float[] a,
                                 float[] b,
                                 int length)
```
    computes the difference between vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] - b[]
  - Difference
```
public static int[] Difference(int[] a,
                               int[] b)
```
  - Difference
```
public static int[] Difference(int[] a,
                               int[] b,
                               int length)
```
    computes the difference between vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] - b[]
  - Difference
```
public static long[] Difference(long[] a,
                                long[] b)
```
  - Difference
```
public static long[] Difference(long[] a,
                                long[] b,
                                int length)
```
    computes the difference between vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] - b[]
  - Difference
```
public static short[] Difference(short[] a,
                                 short[] b)
```
  - Difference
```
public static short[] Difference(short[] a,
                                 short[] b,
                                 int length)
```
    computes the difference between vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] - b[]
  - DiLog
```
public static double DiLog(double x)
```
    The DiLogarithm function Code translated by from CERNLIB DILOG function C332
    
    Parameters:
    
    x - input
    
    Returns:
    
    the computed result
  - effectiveSampleNumber
```
public static double effectiveSampleNumber(double[] ww)
```
  - Erf
```
public static double Erf(double x)
```
    Computation of the error function erf(x). Erf(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between 0 and x --- NvE 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    x - input
    
    Returns:
    
    the computed result
  - Erfc
```
public static double Erfc(double x)
```
    Compute the complementary error function erfc(x). Erfc(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between x and infinity Nve 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    x - input parameter
    
    Returns:
    
    the computed result
  - ErfInverse
```
public static double ErfInverse(double x)
```
    returns the inverse error function
    
    Parameters:
    
    x - must be <-1<x<1
    
    Returns:
    
    the computed result
  - Factorial
```
public static double Factorial(int n)
```
    Compute factorial(n).
    
    Parameters:
    
    n - input parameter
    
    Returns:
    
    the computed result
  - FDist
```
public static double FDist(double F,
                           double N,
                           double M)
```
  - FDistI
```
public static double FDistI(double F,
                            double N,
                            double M)
```
  - Freq
```
public static double Freq(double x)
```
    Computation of the normal frequency function freq(x). Freq(x) = (1/sqrt(2pi)) Integral(exp(-t^2/2))dt between -infinity and x. Translated from CERNLIB C300 by Rene Brun.
    
    Parameters:
    
    x - input parameter
    
    Returns:
    
    the computed result
  - GamCf
```
public static double GamCf(double a,
                           double x)
```
    Computation of the incomplete gamma function P(a,x) via its continued fraction representation. --- Nve 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    a - input parameter
    
    x - input parameter
    
    Returns:
    
    the computed result
  - Gamma
```
public static double Gamma(double z)
```
    Computation of gamma(z) for all z>0. C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86. --- Nve 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    z - input parameter
    
    Returns:
    
    gamma(z)
  - Gamma
```
public static double Gamma(double a,
                           double x)
```
    Computation of the normalized lower incomplete gamma function P(a,x) as defined in the Handbook of Mathematical Functions by Abramowitz and Stegun, formula 6.5.1 on page 260 . Its normalization is such that Gamma(a,+infinity) = 1 . Begin_Latex P(a, x) = #frac{1}{#Gamma(a) } #int_{0}^{x} t^{a-1} e^{-t} dt End_Latex --- Nve 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    a - input parameter
    
    x - input parameter
    
    Returns:
    
    the computed result
  - GammaDist
```
public static double GammaDist(double x,
                               double gamma,
                               double mu,
                               double beta)
```
  - GamSer
```
public static double GamSer(double a,
                            double x)
```
    Computation of the incomplete gamma function P(a,x) via its series representation. --- Nve 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    a - input parameter
    
    x - input parameter
    
    Returns:
    
    the computed result
  - Gauss
```
public static double Gauss(double x,
                           double mean,
                           double sigma,
                           boolean norm)
```
    Calculate a Gaussian function with mean and sigma. If norm=true (default is false) the result is divided by sqrt(2*Pi)*sigma.
    
    Parameters:
    
    x - input parameter
    
    mean - centre of distribution
    
    sigma - width of distribution
    
    norm - normalisation factor
    
    Returns:
    
    the computed result
  - GeometricMean
```
public static double GeometricMean(double[] a,
                                   int length)
```
    geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
    
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    geometric mean of an array a with length n.
  - GeometricMean
```
public static double GeometricMean(double[] data)
```
  - GeometricMean
```
public static float GeometricMean(float[] a,
                                  int length)
```
    geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
    
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    geometric mean of an array a with length n.
  - GeometricMean
```
public static float GeometricMean(float[] data)
```
  - GeometricMean
```
public static int GeometricMean(int[] a,
                                int length)
```
    geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
    
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    geometric mean of an array a with length n.
  - GeometricMean
```
public static int GeometricMean(int[] data)
```
  - GeometricMean
```
public static long GeometricMean(long[] a,
                                 int length)
```
    geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
    
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    geometric mean of an array a with length n.
  - GeometricMean
```
public static long GeometricMean(long[] data)
```
  - GeometricMean
```
public static short GeometricMean(short[] a,
                                  int length)
```
    geometric_mean = (\Prod_{i=0}^{n-1} \abs{a[i]})^{1/n}
    
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    geometric mean of an array a with length n.
  - GeometricMean
```
public static short GeometricMean(short[] data)
```
  - IsInside
```
public static boolean IsInside(double xp,
                               double yp,
                               int np,
                               double[] x,
                               double[] y)
```
    Function which returns true if point xp,yp lies inside the polygon defined by the np points in arrays x and y, false otherwise NOTE that the polygon must be a closed polygon (1st and last point must be identical).
    
    Parameters:
    
    xp - test point coordinate x
    
    yp - test point coordinate y
    
    np - number of polygon edges
    
    x - x coordinates of polygon
    
    y - y coordinates of polygon
    
    Returns:
    
    true if point xp,yp lies inside
  - IsInside
```
public static boolean IsInside(float xp,
                               float yp,
                               int np,
                               float[] x,
                               float[] y)
```
    Function which returns true if point xp,yp lies inside the polygon defined by the np points in arrays x and y, false otherwise NOTE that the polygon must be a closed polygon (1st and last point must be identical).
    
    Parameters:
    
    xp - test point coordinate x
    
    yp - test point coordinate y
    
    np - number of polygon edges
    
    x - x coordinates of polygon
    
    y - y coordinates of polygon
    
    Returns:
    
    true if point xp, yp lies inside the polygon defined
  - IsInside
```
public static boolean IsInside(int xp,
                               int yp,
                               int np,
                               int[] x,
                               int[] y)
```
    Function which returns true if point xp,yp lies inside the polygon defined by the np points in arrays x and y, false otherwise NOTE that the polygon must be a closed polygon (1st and last point must be identical).
    
    Parameters:
    
    xp - test point coordinate x
    
    yp - test point coordinate y
    
    np - number of polygon edges
    
    x - x coordinates of polygon
    
    y - y coordinates of polygon
    
    Returns:
    
    true if point xp, yp lies inside the polygon defined
  - Landau
```
public static double Landau(double x,
                            double mpv,
                            double sigma,
                            boolean norm)
```
    The LANDAU function with mpv(most probable value) and sigma. This function has been adapted from the CERNLIB routine G110 denlan. If norm=true (default is false) the result is divided by sigma
    
    Parameters:
    
    x - input variable
    
    mpv - most probable value
    
    sigma - width of distribution
    
    norm - normalisation of distribution
    
    Returns:
    
    the computed result
  - LandauI
```
public static double LandauI(double x)
```
  - LaplaceDist
```
public static double LaplaceDist(double x,
                                 double alpha,
                                 double beta)
```
  - LaplaceDistI
```
public static double LaplaceDistI(double x,
                                  double alpha,
                                  double beta)
```
  - LnGamma
```
public static double LnGamma(double z)
```
    Computation of ln[gamma(z)] for all z>0. C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86 The accuracy of the result is better than 2e-10. --- Nve 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    z - input paramater
    
    Returns:
    
    ln[gamma(z)]
  - LocationMaximum
```
public static long LocationMaximum(double[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMaximum
```
public static long LocationMaximum(float[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMaximum
```
public static long LocationMaximum(int[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMaximum
```
public static long LocationMaximum(long[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMinimum
```
public static long LocationMinimum(double[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMinimum
```
public static long LocationMinimum(float[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMinimum
```
public static long LocationMinimum(int[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMinimum
```
public static long LocationMinimum(long[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LocationMinimum
```
public static long LocationMinimum(short[] a,
                                   int length)
```
    Parameters:
    
    a - input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    index of array with the minimum element. If more than one element is minimum returns first found.
  - LogNormal
```
public static double LogNormal(double x,
                               double sigma,
                               double theta,
                               double m)
```
    Computes the density of LogNormal distribution at point x. Variable X has lognormal distribution if Y=Ln(X) has normal distribution. The formula was taken from "Engineering Statistics Handbook" on site http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm Implementation by Anna Kreshuk.
    
    Parameters:
    
    x - input value
    
    sigma - the shape parameter
    
    theta - the location parameter
    
    m - the scale parameter
    
    Returns:
    
    density of LogNormal distribution at point x
  - main
```
public static void main(String[] argv)
```
  - Maximum
```
public static double Maximum(double[] data)
```
  - Maximum
```
public static double Maximum(double[] data,
                             int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of largest vector element
  - Maximum
```
public static float Maximum(float[] data)
```
  - Maximum
```
public static float Maximum(float[] data,
                            int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of largest vector element
  - Maximum
```
public static int Maximum(int[] data)
```
  - Maximum
```
public static int Maximum(int[] data,
                          int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of largest vector element
  - Maximum
```
public static long Maximum(long[] data)
```
  - Maximum
```
public static long Maximum(long[] data,
                           int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of largest vector element
  - Maximum
```
public static short Maximum(short[] data)
```
  - Maximum
```
public static short Maximum(short[] data,
                            int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of largest vector element
  - Mean
```
public static double Mean(double[] data)
```
  - Mean
```
public static double Mean(double[] data,
                          int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    average of vector elements
  - Mean
```
public static float Mean(float[] data)
```
  - Mean
```
public static float Mean(float[] data,
                         int length)
```
    Parameters:
    
    data - the input vector
    
    length - of the input vector
    
    Returns:
    
    average of vector elements
  - Mean
```
public static int Mean(int[] data)
```
  - Mean
```
public static int Mean(int[] data,
                       int length)
```
    Parameters:
    
    data - the input vector
    
    length - of the input vector
    
    Returns:
    
    average of vector elements
  - Mean
```
public static long Mean(long[] data)
```
  - Mean
```
public static long Mean(long[] data,
                        int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    average of vector elements
  - Mean
```
public static short Mean(short[] data)
```
  - Mean
```
public static short Mean(short[] data,
                         int length)
```
    Parameters:
    
    data - the input vector
    
    length - of the input vector
    
    Returns:
    
    average of vector elements
  - Median
```
public static double Median(double[] data)
```
  - Median
```
public static double Median(double[] data,
                            int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    median value of vector element
  - Median
```
public static float Median(float[] data)
```
  - Median
```
public static float Median(float[] data,
                           int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    median value of vector element
  - Median
```
public static int Median(int[] data)
```
  - Median
```
public static int Median(int[] data,
                         int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    median value of vector element
  - Median
```
public static long Median(long[] data)
```
  - Median
```
public static long Median(long[] data,
                          int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    median value of vector element
  - Median
```
public static short Median(short[] data)
```
  - Median
```
public static short Median(short[] data,
                           int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    median value of vector element
  - Minimum
```
public static double Minimum(double[] data)
```
  - Minimum
```
public static double Minimum(double[] data,
                             int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of smallest vector element
  - Minimum
```
public static float Minimum(float[] data)
```
  - Minimum
```
public static float Minimum(float[] data,
                            int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of smallest vector element
  - Minimum
```
public static int Minimum(int[] data)
```
  - Minimum
```
public static int Minimum(int[] data,
                          int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of smallest vector element
  - Minimum
```
public static long Minimum(long[] data)
```
  - Minimum
```
public static long Minimum(long[] data,
                           int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of smallest vector element
  - Minimum
```
public static short Minimum(short[] data)
```
  - Minimum
```
public static short Minimum(short[] data,
                            int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    value of smallest vector element
  - Normal2Plane
```
public static double[] Normal2Plane(double[] p1,
                                    double[] p2,
                                    double[] p3,
                                    double[] normal)
```
    Calculate a normal vector of a plane.
    
    Parameters:
    
    p1 - first 3D points belonged the plane to define it.
    
    p2 - second 3D points belonged the plane to define it.
    
    p3 - third 3D points belonged the plane to define it.
    
    normal - Pointer to 3D normal vector (normalised)
    
    Returns:
    
    the computed result
  - Normal2Plane
```
public static float[] Normal2Plane(float[] p1,
                                   float[] p2,
                                   float[] p3,
                                   float[] normal)
```
    Calculate a normal vector of a plane.
    
    Parameters:
    
    p1 - first 3D points belonged the plane to define it.
    
    p2 - second 3D points belonged the plane to define it.
    
    p3 - third 3D points belonged the plane to define it.
    
    normal - Pointer to 3D normal vector (normalised)
    
    Returns:
    
    the computed result
  - Normalize
```
public static double Normalize(double[] v)
```
    Normalise a vector v in place. Returns the norm of the original vector. This implementation (thanks Kevin Lynch <krlynch@bu.edu>) is protected against possible overflows. Find the largest element, and divide that one out.
    
    Parameters:
    
    v - input parameter vector
    
    Returns:
    
    the computed result
  - Normalize
```
public static float Normalize(float[] v)
```
    Normalise a vector 'v' in place.
    
    Parameters:
    
    v - input parameter vector
    
    Returns:
    
    the computed result the norm of the original vector.
  - NormCross
```
public static double NormCross(double[] v1,
                               double[] v2,
                               double[] out)
```
    Calculate the Normalized Cross Product of two vectors
    
    Parameters:
    
    v1 - input vector1
    
    v2 - input vector2
    
    out - output vector
    
    Returns:
    
    the computed result
  - NormCross
```
public static float NormCross(float[] v1,
                              float[] v2,
                              float[] out)
```
    Calculate the Normalized Cross Product of two vectors
    
    Parameters:
    
    v1 - input vector1
    
    v2 - input vector2
    
    out - output vector
    
    Returns:
    
    the computed result
  - NormQuantile
```
public static double NormQuantile(double p)
```
    Computes quantiles for standard normal distribution N(0, 1) at probability p ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3, 477-484.
    
    Parameters:
    
    p - input value
    
    Returns:
    
    quantiles for standard normal distribution N(0, 1) at probability p
  - PeakToPeak
```
public static double PeakToPeak(double[] data)
```
  - PeakToPeak
```
public static double PeakToPeak(double[] data,
                                int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    peak-to-peak value of vector element
  - PeakToPeak
```
public static float PeakToPeak(float[] data)
```
  - PeakToPeak
```
public static float PeakToPeak(float[] data,
                               int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    peak-to-peak value of vector element
  - PeakToPeak
```
public static int PeakToPeak(int[] data)
```
  - PeakToPeak
```
public static int PeakToPeak(int[] data,
                             int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    peak-to-peak value of vector element
  - PeakToPeak
```
public static long PeakToPeak(long[] data)
```
  - PeakToPeak
```
public static long PeakToPeak(long[] data,
                              int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    peak-to-peak value of vector element
  - PeakToPeak
```
public static short PeakToPeak(short[] data)
```
  - PeakToPeak
```
public static short PeakToPeak(short[] data,
                               int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    peak-to-peak value of vector element
  - Permute
```
public static boolean Permute(int n,
                              int[] a)
```
    Simple recursive algorithm to find the permutations of n natural numbers, not necessarily all distinct adapted from CERNLIB routine PERMU. The input array has to be initialised with a non descending sequence. The method returns false when all combinations are exhausted.
    
    Parameters:
    
    n - size of input vector
    
    a - input vector
    
    Returns:
    
    false when all combinations are exhausted
  - Poisson
```
public static double Poisson(double x,
                             double par)
```
    compute the Poisson distribution function for (x,par) The Poisson PDF is implemented by means of Euler's Gamma-function (for the factorial), so for all integer arguments it is correct. BUT for non-integer values it IS NOT equal to the Poisson distribution. see PoissonI to get a non-smooth function. Note that for large values of par, it is better to call Gaus(x,par,sqrt(par),true) Begin_Html
    
    Parameters:
    
    x - input value
    
    par - input parameter
    
    Returns:
    
    the computed result
  - PoissonI
```
public static double PoissonI(double x,
                              double par)
```
    compute the Poisson distribution function for (x,par) This is a non-smooth function
    
    Parameters:
    
    x - input value
    
    par - input parameter
    
    Returns:
    
    the computed result
  - Prob
```
public static double Prob(double chi2,
                          int ndf)
```
    Computation of the probability for a certain Chi-squared (chi2) and number of degrees of freedom (ndf). Calculations are based on the incomplete gamma function P(a,x), where a=ndf/2 and x=chi2/2. P(a,x) represents the probability that the observed Chi-squared for a correct model should be less than the value chi2. The returned probability corresponds to 1-P(a,x), which denotes the probability that an observed Chi-squared exceeds the value chi2 by chance, even for a correct model. --- NvE 14-nov-1998 UU-SAP Utrecht
    
    Parameters:
    
    chi2 - input
    
    ndf - number of degrees of freedom
    
    Returns:
    
    the computed result
  - RMS
```
public static double RMS(double[] data)
```
  - RMS
```
public static double RMS(double[] data,
                         int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    un-biased r.m.s. of vector elements
  - RMS
```
public static float RMS(float[] data)
```
  - RMS
```
public static float RMS(float[] data,
                        int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    un-biased r.m.s. of vector elements
  - RMS
```
public static int RMS(int[] data)
```
  - RMS
```
public static int RMS(int[] data,
                      int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    un-biased r.m.s. of vector elements
  - RMS
```
public static long RMS(long[] data)
```
  - RMS
```
public static long RMS(long[] data,
                       int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= d data.length elements to be used
    
    Returns:
    
    un-biased r.m.s. of vector elements
  - RMS
```
public static short RMS(short[] data)
```
  - RMS
```
public static short RMS(short[] data,
                        int length)
```
    Parameters:
    
    data - the input vector
    
    length - <= data.length elements to be used
    
    Returns:
    
    un-biased r.m.s. of vector elements
  - Sinc
```
public static double Sinc(double x,
                          boolean norm)
```
    Calculate the sinc = sin(x)/x function if norm ==true then sinc = sinc(pi*x)/(pi*x) is used
    
    Parameters:
    
    x - input parameter
    
    norm - normalisation factor
    
    Returns:
    
    the computed result
  - Sort
```
public static double[] Sort(double[] a,
                            int length,
                            boolean down)
```
    Sorts the input a array
    
    Parameters:
    
    a - the input array
    
    length - <= data.length elements to be used
    
    down - true: ascending , false: descending order
    
    Returns:
    
    the sorted array
  - Sort
```
public static float[] Sort(float[] a,
                           int length,
                           boolean down)
```
    Sorts the input a array
    
    Parameters:
    
    a - the input array
    
    length - <= data.length elements to be used
    
    down - true: ascending , false: descending order
    
    Returns:
    
    the sorted array
  - Sort
```
public static int[] Sort(int[] a,
                         int length,
                         boolean down)
```
    Sorts the input a array
    
    Parameters:
    
    a - the input array
    
    length - <= data.length elements to be used
    
    down - true: ascending , false: descending order
    
    Returns:
    
    the sorted array
  - Sort
```
public static long[] Sort(long[] a,
                          int length,
                          boolean down)
```
    Sorts the input a array
    
    Parameters:
    
    a - the input array
    
    length - <= data.length elements to be used
    
    down - true: ascending , false: descending order
    
    Returns:
    
    the sorted array
  - Sort
```
public static short[] Sort(short[] a,
                           int length,
                           boolean down)
```
    Sorts the input a array
    
    Parameters:
    
    a - the input array
    
    length - <= data.length elements to be used
    
    down - true: ascending , false: descending order
    
    Returns:
    
    the sorted array
  - StruveH0
```
public static double StruveH0(double x)
```
  - StruveH1
```
public static double StruveH1(double x)
```
  - StruveL0
```
public static double StruveL0(double x)
```
  - StruveL1
```
public static double StruveL1(double x)
```
  - Student
```
public static double Student(double T,
                             double ndf)
```
    Computes density function for Student's t- distribution (the probability function (integral of density) is computed in StudentI). First parameter stands for x - the actual variable of the density function p(x) and the point at which the density is calculated. Second parameter stands for number of degrees of freedom. About Student distribution: Student's t-distribution is used for many significance tests, for example, for the Student's t-tests for the statistical significance of difference between two sample means and for confidence intervals for the difference between two population means. Example: suppose we have a random sample of size n drawn from normal distribution with mean Mu and st.deviation Sigma. Then the variable t = (sample_mean - Mu)/(sample_deviation / sqrt(n)) has Student's t-distribution with n-1 degrees of freedom. NOTE that this function's second argument is number of degrees of freedom, not the sample size. As the number of degrees of freedom grows, t-distribution approaches Normal(0,1) distribution. Implementation by Anna Kreshuk.
    
    Parameters:
    
    T - input value
    
    ndf - number of degrees of freedom
    
    Returns:
    
    value of the density function for Student's t- distribution
  - StudentI
```
public static double StudentI(double T,
                              double ndf)
```
    Calculates the cumulative distribution function of Student's t-distribution second parameter stands for number of degrees of freedom, not for the number of samples if x has Student's t-distribution, the function returns the probability of x being less than T. Implementation by Anna Kreshuk.
    
    Parameters:
    
    T - input value
    
    ndf - number of degrees of freedom
    
    Returns:
    
    cumulative distribution function of Student's t-distribution
  - StudentQuantile
```
public static double StudentQuantile(double p,
                                     double ndf,
                                     boolean lower_tail)
```
  - Sum
```
public static double[] Sum(double[] a,
                           double[] b)
```
  - Sum
```
public static double[] Sum(double[] a,
                           double[] b,
                           int length)
```
    computes the sum of vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] + b[]
  - Sum
```
public static float[] Sum(float[] a,
                          float[] b)
```
  - Sum
```
public static float[] Sum(float[] a,
                          float[] b,
                          int length)
```
    computes the sum of vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] + b[]
  - Sum
```
public static int[] Sum(int[] a,
                        int[] b)
```
  - Sum
```
public static int[] Sum(int[] a,
                        int[] b,
                        int length)
```
    computes the sum of vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] + b[]
  - Sum
```
public static long[] Sum(long[] a,
                         long[] b)
```
  - Sum
```
public static long[] Sum(long[] a,
                         long[] b,
                         int length)
```
    computes the sum of vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] + b[]
  - Sum
```
public static short[] Sum(short[] a,
                          short[] b)
```
  - Sum
```
public static short[] Sum(short[] a,
                          short[] b,
                          int length)
```
    computes the sum of vectors
    
    Parameters:
    
    a - input vector a
    
    b - input vector b
    
    length - minimum length to be taken into account
    
    Returns:
    
    ret[] = a[] + b[]
  - Variance
```
public static double Variance(double[] aa,
                              double[] ww)
```
  - Vavilov
```
public static double Vavilov(double x,
                             double kappa,
                             double beta2)
```
  - VavilovDenEval
```
protected static double VavilovDenEval(double rlam,
                                       double[] AC,
                                       double[] HC,
                                       int itype)
```
    Internal function, called by Vavilov and VavilovSet
    
    Parameters:
    
    rlam - ???
    
    AC - ???
    
    HC - ???
    
    itype - ???
    
    Returns:
    
    internal value
  - VavilovI
```
public static double VavilovI(double x,
                              double kappa,
                              double beta2)
```
  - VavilovSet
```
public static void VavilovSet(double rkappa,
                              double beta2,
                              boolean mode,
                              double[] WCM,
                              double[] AC,
                              double[] HC,
                              int[] itype,
                              int[] npt)
```
    Internal function, called by Vavilov and VavilovI
    
    Parameters:
    
    rkappa - ???
    
    beta2 - ???
    
    mode - ???
    
    WCM - ???
    
    AC - ???
    
    HC - ???
    
    itype - ???
    
    npt - ???

Class TMath

Constructor Summary

Method Summary

Methods inherited from class de.gsi.math.TMathConstants

Methods inherited from class java.lang.Object

Constructor Detail

TMath

Method Detail

BesselI

BesselI0

BesselI1

BesselJ0

BesselJ1

BesselK

BesselK0

BesselK1

BesselY0

BesselY1

Beta

BetaCf

BetaDist

BetaDistI

BetaIncomplete

BinarySearch

BinarySearch

BinarySearch

BinarySearch

BinarySearch

Binomial

BinomialI

BreitWigner

CauchyDist

ChisquareQuantile

CorrelationCoefficient

Covariance

Cross

Cross

Difference

Difference

Difference

Difference

Difference

Difference

Difference

Difference

Difference

Difference

DiLog

effectiveSampleNumber

Erf

Erfc

ErfInverse

Factorial

FDist

FDistI

Freq

GamCf

Gamma

Gamma

GammaDist

GamSer

Gauss

GeometricMean

GeometricMean

GeometricMean

GeometricMean

GeometricMean

GeometricMean

GeometricMean

GeometricMean

GeometricMean

GeometricMean

IsInside

IsInside

IsInside

Landau

LandauI

LaplaceDist

LaplaceDistI

LnGamma