gov.nist.microanalysis.Utility
Class Math2

java.lang.Object
  gov.nist.microanalysis.Utility.Math2

public class Math2
extends java.lang.Object

Useful math functions not provided in the standard libraries.

Copyright: Pursuant to title 17 Section 105 of the United States Code this software is not subject to copyright protection and is in the public domain

Company: National Institute of Standards and Technology

Version:

1.0

Author:

Nicholas W. M. Ritchie

Field Summary

static double[]	MINUS_X_AXIS
static double[]	MINUS_Y_AXIS
static double[]	MINUS_Z_AXIS
static double[]	ORIGIN_3D
static double	SQRT_PI SQRT_PI - The square root of Pi ~ 1.772
static double[]	X_AXIS
static double[]	Y_AXIS
static double[]	Z_AXIS

Constructor Summary

Math2()

Method Summary

static double	angleBetween(double[] a, double[] b) angleBetween - Returns the angle between the vector a and vector b in radians.
static double[]	cross(double[] a, double[] b) cross - Computes the cross product of two three-vectors a and b
static double	distance(double[] p1, double[] p2) distance - What is the Euclidean distance between p1 and p2.
static double[]	divide(double[] a, double b) divide - Returns a vector containing a, a vector, divided by b, a scalar.
static double	dot(double[] a, double[] b) dot - Compute the dot product of two equal lengthed vectors
static double	erf(double x) erf - The error function (2/sqrt(pi))*Integrate[Exp[-t^2],{t,0,x}] Source: Numerical Recipes in C - 2nd Edition
static double	erfc(double x) erfc - The complementary error function (1-erf(x)) Source: Numerical Recipes in C - 2nd Edition
static double	expRand() expRand - Selects a random value from an exponential distibution.
static double	gammaln(double xx) gammaln - The natural log of the gamma function.
static double	gammap(double a, double x) gammap - Computes the incomplete gamma function P(a,x) by selecting between series and continued fraction representations based on the size of the arguments.
static double	li(double x) li - A naive implementation of the Logarithmic Integral
static double	magnitude(double[] p) magnitude - What is the length of the specified vector?
static double[]	minus(double[] a, double[] b) minus - Returns the vector sum a + b
static double[]	multiply(double a, double[] b) multiply - Returns a vector containing the product of a, a scalar, times b, a vector.
static double[]	negative(double[] a) Returns a vector in which each of the coordinates equals -1 times the coordinates in a.
static double[]	normalize(double[] p) normalize - Returns a copy of the input vector normalized to 1 length of 1.0.
static double[]	plus(double[] a, double[] b) plus - Returns the vector sum a + b
static double	sqr(double x) sqr - returns x*x
static double	sum(double[] da) sum - Returns the sum of the specified array

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

ORIGIN_3D

public static final double[] ORIGIN_3D

X_AXIS

public static final double[] X_AXIS

Y_AXIS

public static final double[] Y_AXIS

Z_AXIS

public static final double[] Z_AXIS

MINUS_X_AXIS

public static final double[] MINUS_X_AXIS

MINUS_Y_AXIS

public static final double[] MINUS_Y_AXIS

MINUS_Z_AXIS

public static final double[] MINUS_Z_AXIS

SQRT_PI

public static final double SQRT_PI

SQRT_PI - The square root of Pi ~ 1.772

Constructor Detail

Math2

public Math2()

Method Detail

sqr

public static final double sqr(double x)

sqr - returns x*x

Parameters:

x - double

Returns:

double

erf

public static final double erf(double x)

erf - The error function (2/sqrt(pi))*Integrate[Exp[-t^2],{t,0,x}]
Source: Numerical Recipes in C - 2nd Edition

Parameters:

x - double

Returns:

double

erfc

public static final double erfc(double x)

erfc - The complementary error function (1-erf(x))
Source: Numerical Recipes in C - 2nd Edition

Parameters:

x - double

Returns:

double

gammap

public static final double gammap(double a,
                                  double x)

gammap - Computes the incomplete gamma function P(a,x) by selecting between series and continued fraction representations based on the size of the arguments.
Source: Numerical Recipes in C - 2nd Edition

Parameters:

a - double

x - double

Returns:

double

gammaln

public static final double gammaln(double xx)

gammaln - The natural log of the gamma function.
Source: Numerical Recipes in C - 2nd Edition

Parameters:

xx - double

Returns:

double

expRand

public static final double expRand()

expRand - Selects a random value from an exponential distibution. The mean value returned is 1.0.

Returns:

double - Returns a random variable in the range [0,infinity)

distance

public static final double distance(double[] p1,
                                    double[] p2)

distance - What is the Euclidean distance between p1 and p2.

Parameters:

p1 -

p2 -

Returns:

double

magnitude

public static final double magnitude(double[] p)

magnitude - What is the length of the specified vector?

Parameters:

p -

Returns:

double

normalize

public static final double[] normalize(double[] p)

normalize - Returns a copy of the input vector normalized to 1 length of 1.0.

Parameters:

p - The vector to normalize

Returns:

A new vector containing the normalized result.

sum

public static final double sum(double[] da)

sum - Returns the sum of the specified array

Parameters:

da -

Returns:

The sum of the specified array

plus

public static final double[] plus(double[] a,
                                  double[] b)

plus - Returns the vector sum a + b

Parameters:

a -

b -

Returns:

The vector a+b

minus

public static final double[] minus(double[] a,
                                   double[] b)

minus - Returns the vector sum a + b

Parameters:

a -

b -

Returns:

The vector a+b

dot

public static final double dot(double[] a,
                               double[] b)

dot - Compute the dot product of two equal lengthed vectors

Parameters:

a -

b -

Returns:

The dot product of a and b

negative

public static final double[] negative(double[] a)

Returns a vector in which each of the coordinates equals -1 times the coordinates in a.

Parameters:

a -

Returns:

double [] = -a

cross

public static final double[] cross(double[] a,
                                   double[] b)

cross - Computes the cross product of two three-vectors a and b

Parameters:

a -

b -

Returns:

A three-vector perpendicular to both a and b and of length |a||b| sin(th) where th is the angle between a and b

multiply

public static final double[] multiply(double a,
                                      double[] b)

multiply - Returns a vector containing the product of a, a scalar, times b, a vector.

Parameters:

a -

b -

Returns:

A vector containing a*b

angleBetween

public static final double angleBetween(double[] a,
                                        double[] b)

angleBetween - Returns the angle between the vector a and vector b in radians.

Parameters:

a -

b -

Returns:

The angle 0.0 (parallel) to Pi (antiparallel)

divide

public static final double[] divide(double[] a,
                                    double b)

divide - Returns a vector containing a, a vector, divided by b, a scalar.

Parameters:

a -

b -

Returns:

A vector containing a/b

li

public static final double li(double x)

li - A naive implementation of the Logarithmic Integral

Parameters:

x -

Returns:

double