umcg.genetica.math.Fmath Maven / Gradle / Ivy
/*
* Class Fmath
*
* USAGE: Mathematical class that supplements java.lang.Math and contains:
* the main physical constants
* trigonemetric functions absent from java.lang.Math
* some useful additional mathematical functions
* some conversion functions
*
* WRITTEN BY: Dr Michael Thomas Flanagan
*
* DATE: June 2002
* AMENDED: 6 January 2006, 12 April 2006, 5 May 2006, 28 July 2006, 27 December 2006,
* 29 March 2007, 29 April 2007, 2,9,15 & 26 June 2007, 20 October 2007, 4-6 December 2007
* 27 February 2008, 25 April 2008, 26 April 2008, 13 May 2008, 25/26 May 2008, 3-7 July 2008
* 11 November 2010, 9-18 January 2011, 13 August 2011
*
* DOCUMENTATION:
* See Michael Thomas Flanagan's Java library on-line web pages:
* http://www.ee.ucl.ac.uk/~mflanaga/java/
* http://www.ee.ucl.ac.uk/~mflanaga/java/Fmath.html
*
* Copyright (c) 2002 - 2011
*
* PERMISSION TO COPY:
* Permission to use, copy and modify this software and its documentation for
* NON-COMMERCIAL purposes is granted, without fee, provided that an acknowledgement
* to the author, Michael Thomas Flanagan at www.ee.ucl.ac.uk/~mflanaga, appears in all copies.
*
* Dr Michael Thomas Flanagan makes no representations about the suitability
* or fitness of the software for any or for a particular purpose.
* Michael Thomas Flanagan shall not be liable for any damages suffered
* as a result of using, modifying or distributing this software or its derivatives.
*
***************************************************************************************/
package umcg.genetica.math;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.Vector;
public class Fmath{
// PHYSICAL CONSTANTS
public static final double N_AVAGADRO = 6.0221419947e23; /* mol^-1 */
public static final double K_BOLTZMANN = 1.380650324e-23; /* J K^-1 */
public static final double H_PLANCK = 6.6260687652e-34; /* J s */
public static final double H_PLANCK_RED = H_PLANCK/(2*Math.PI); /* J s */
public static final double C_LIGHT = 2.99792458e8; /* m s^-1 */
public static final double R_GAS = 8.31447215; /* J K^-1 mol^-1 */
public static final double F_FARADAY = 9.6485341539e4; /* C mol^-1 */
public static final double T_ABS = -273.15; /* Celsius */
public static final double Q_ELECTRON = -1.60217646263e-19; /* C */
public static final double M_ELECTRON = 9.1093818872e-31; /* kg */
public static final double M_PROTON = 1.6726215813e-27; /* kg */
public static final double M_NEUTRON = 1.6749271613e-27; /* kg */
public static final double EPSILON_0 = 8.854187817e-12; /* F m^-1 */
public static final double MU_0 = Math.PI*4e-7; /* H m^-1 (N A^-2) */
public static final double ETA_0 = MU_0*C_LIGHT; /* Ohms */
// MATHEMATICAL CONSTANTS
public static final double EULER_CONSTANT_GAMMA = 0.5772156649015627;
public static final double PI = Math.PI; /* 3.141592653589793D */
public static final double E = Math.E; /* 2.718281828459045D */
// HashMap for 'arithmetic integer' recognition nmethod
private static final Map integers = new HashMap();
static{
integers.put(Integer.class, BigDecimal.valueOf(Integer.MAX_VALUE));
integers.put(Long.class, BigDecimal.valueOf(Long.MAX_VALUE));
integers.put(Byte.class, BigDecimal.valueOf(Byte.MAX_VALUE));
integers.put(Short.class, BigDecimal.valueOf(Short.MAX_VALUE));
integers.put(BigInteger.class, BigDecimal.valueOf(-1));
}
// METHODS
// LOGARITHMS
// Log to base 10 of a double number
public static double log10(double a){
return Math.log(a)/Math.log(10.0D);
}
// Log to base 10 of a float number
public static float log10(float a){
return (float) (Math.log((double)a)/Math.log(10.0D));
}
// Base 10 antilog of a double
public static double antilog10(double x){
return Math.pow(10.0D, x);
}
// Base 10 antilog of a float
public static float antilog10(float x){
return (float)Math.pow(10.0D, (double)x);
}
// Log to base e of a double number
public static double log(double a){
return Math.log(a);
}
// Log to base e of a float number
public static float log(float a){
return (float)Math.log((double)a);
}
// Base e antilog of a double
public static double antilog(double x){
return Math.exp(x);
}
// Base e antilog of a float
public static float antilog(float x){
return (float)Math.exp((double)x);
}
// Log to base 2 of a double number
public static double log2(double a){
return Math.log(a)/Math.log(2.0D);
}
// Log to base 2 of a float number
public static float log2(float a){
return (float) (Math.log((double)a)/Math.log(2.0D));
}
// Base 2 antilog of a double
public static double antilog2(double x){
return Math.pow(2.0D, x);
}
// Base 2 antilog of a float
public static float antilog2(float x){
return (float)Math.pow(2.0D, (double)x);
}
// Log to base b of a double number and double base
public static double log10(double a, double b){
return Math.log(a)/Math.log(b);
}
// Log to base b of a double number and int base
public static double log10(double a, int b){
return Math.log(a)/Math.log((double)b);
}
// Log to base b of a float number and flaot base
public static float log10(float a, float b){
return (float) (Math.log((double)a)/Math.log((double)b));
}
// Log to base b of a float number and int base
public static float log10(float a, int b){
return (float) (Math.log((double)a)/Math.log((double)b));
}
// SQUARES
// Square of a double number
public static double square(double a){
return a*a;
}
// Square of a float number
public static float square(float a){
return a*a;
}
// Square of a BigDecimal number
public static BigDecimal square(BigDecimal a){
return a.multiply(a);
}
// Square of an int number
public static int square(int a){
return a*a;
}
// Square of a long number
public static long square(long a){
return a*a;
}
// Square of a BigInteger number
public static BigInteger square(BigInteger a){
return a.multiply(a);
}
// FACTORIALS
// factorial of n
// argument and return are integer, therefore limited to 0<=n<=12
// see below for long and double arguments
public static int factorial(int n){
if(n<0)throw new IllegalArgumentException("n must be a positive integer");
if(n>12)throw new IllegalArgumentException("n must less than 13 to avoid integer overflow\nTry long or double argument");
int f = 1;
for(int i=2; i<=n; i++)f*=i;
return f;
}
// factorial of n
// argument and return are long, therefore limited to 0<=n<=20
// see below for double argument
public static long factorial(long n){
if(n<0)throw new IllegalArgumentException("n must be a positive integer");
if(n>20)throw new IllegalArgumentException("n must less than 21 to avoid long integer overflow\nTry double argument");
long f = 1;
long iCount = 2L;
while(iCount<=n){
f*=iCount;
iCount += 1L;
}
return f;
}
// factorial of n
// Argument is of type BigInteger
public static BigInteger factorial(BigInteger n){
if(n.compareTo(BigInteger.ZERO)==-1)throw new IllegalArgumentException("\nn must be a positive integer\nIs a Gamma funtion [Fmath.gamma(x)] more appropriate?");
BigInteger one = BigInteger.ONE;
BigInteger f = one;
BigInteger iCount = new BigInteger("2");
while(iCount.compareTo(n)!=1){
f = f.multiply(iCount);
iCount = iCount.add(one);
}
one = null;
iCount = null;
return f;
}
// factorial of n
// Argument is of type double but must be, numerically, an integer
// factorial returned as double but is, numerically, should be an integer
// numerical rounding may makes this an approximation after n = 21
public static double factorial(double n){
if(n<0.0 || (n-Math.floor(n))!=0)throw new IllegalArgumentException("\nn must be a positive integer\nIs a Gamma funtion [Fmath.gamma(x)] more appropriate?");
double f = 1.0D;
double iCount = 2.0D;
while(iCount<=n){
f*=iCount;
iCount += 1.0D;
}
return f;
}
// factorial of n
// Argument is of type BigDecimal but must be, numerically, an integer
public static BigDecimal factorial(BigDecimal n){
if(n.compareTo(BigDecimal.ZERO)==-1 || !Fmath.isInteger(n))throw new IllegalArgumentException("\nn must be a positive integer\nIs a Gamma funtion [Fmath.gamma(x)] more appropriate?");
BigDecimal one = BigDecimal.ONE;
BigDecimal f = one;
BigDecimal iCount = new BigDecimal(2.0D);
while(iCount.compareTo(n)!=1){
f = f.multiply(iCount);
iCount = iCount.add(one);
}
one = null;
iCount = null;
return f;
}
// log to base e of the factorial of n
// log[e](factorial) returned as double
// numerical rounding may makes this an approximation
public static double logFactorial(int n){
if(n<0)throw new IllegalArgumentException("\nn must be a positive integer\nIs a Gamma funtion [Fmath.gamma(x)] more appropriate?");
double f = 0.0D;
for(int i=2; i<=n; i++)f+=Math.log(i);
return f;
}
// log to base e of the factorial of n
// Argument is of type double but must be, numerically, an integer
// log[e](factorial) returned as double
// numerical rounding may makes this an approximation
public static double logFactorial(long n){
if(n<0L)throw new IllegalArgumentException("\nn must be a positive integer\nIs a Gamma funtion [Fmath.gamma(x)] more appropriate?");
double f = 0.0D;
long iCount = 2L;
while(iCount<=n){
f+=Math.log(iCount);
iCount += 1L;
}
return f;
}
// log to base e of the factorial of n
// Argument is of type double but must be, numerically, an integer
// log[e](factorial) returned as double
// numerical rounding may makes this an approximation
public static double logFactorial(double n){
if(n<0 || (n-Math.floor(n))!=0)throw new IllegalArgumentException("\nn must be a positive integer\nIs a Gamma funtion [Fmath.gamma(x)] more appropriate?");
double f = 0.0D;
double iCount = 2.0D;
while(iCount<=n){
f+=Math.log(iCount);
iCount += 1.0D;
}
return f;
}
// SIGN
/* returns -1 if x < 0 else returns 1 */
// double version
public static double sign(double x){
if (x<0.0){
return -1.0;
}
else{
return 1.0;
}
}
/* returns -1 if x < 0 else returns 1 */
// float version
public static float sign(float x){
if (x<0.0F){
return -1.0F;
}
else{
return 1.0F;
}
}
/* returns -1 if x < 0 else returns 1 */
// int version
public static int sign(int x){
if (x<0){
return -1;
}
else{
return 1;
}
}
/* returns -1 if x < 0 else returns 1 */
// long version
public static long sign(long x){
if (x<0){
return -1;
}
else{
return 1;
}
}
// ADDITIONAL TRIGONOMETRIC FUNCTIONS
// Returns the length of the hypotenuse of a and b
// i.e. sqrt(a*a+b*b) [without unecessary overflow or underflow]
// double version
public static double hypot(double aa, double bb){
double amod=Math.abs(aa);
double bmod=Math.abs(bb);
double cc = 0.0D, ratio = 0.0D;
if(amod==0.0){
cc=bmod;
}
else{
if(bmod==0.0){
cc=amod;
}
else{
if(amod>=bmod){
ratio=bmod/amod;
cc=amod*Math.sqrt(1.0 + ratio*ratio);
}
else{
ratio=amod/bmod;
cc=bmod*Math.sqrt(1.0 + ratio*ratio);
}
}
}
return cc;
}
// Returns the length of the hypotenuse of a and b
// i.e. sqrt(a*a+b*b) [without unecessary overflow or underflow]
// float version
public static float hypot(float aa, float bb){
return (float) hypot((double) aa, (double) bb);
}
// Angle (in radians) subtended at coordinate C
// given x, y coordinates of all apices, A, B and C, of a triangle
public static double angle(double xAtA, double yAtA, double xAtB, double yAtB, double xAtC, double yAtC){
double ccos = Fmath.cos(xAtA, yAtA, xAtB, yAtB, xAtC, yAtC);
return Math.acos(ccos);
}
// Angle (in radians) between sides sideA and sideB given all side lengths of a triangle
public static double angle(double sideAC, double sideBC, double sideAB){
double ccos = Fmath.cos(sideAC, sideBC, sideAB);
return Math.acos(ccos);
}
// Sine of angle subtended at coordinate C
// given x, y coordinates of all apices, A, B and C, of a triangle
public static double sin(double xAtA, double yAtA, double xAtB, double yAtB, double xAtC, double yAtC){
double angle = Fmath.angle(xAtA, yAtA, xAtB, yAtB, xAtC, yAtC);
return Math.sin(angle);
}
// Sine of angle between sides sideA and sideB given all side lengths of a triangle
public static double sin(double sideAC, double sideBC, double sideAB){
double angle = Fmath.angle(sideAC, sideBC, sideAB);
return Math.sin(angle);
}
// Sine given angle in radians
// for completion - returns Math.sin(arg)
public static double sin(double arg){
return Math.sin(arg);
}
// Inverse sine
// Fmath.asin Checks limits - Java Math.asin returns NaN if without limits
public static double asin(double a){
if(a<-1.0D && a>1.0D) throw new IllegalArgumentException("Fmath.asin argument (" + a + ") must be >= -1.0 and <= 1.0");
return Math.asin(a);
}
// Cosine of angle subtended at coordinate C
// given x, y coordinates of all apices, A, B and C, of a triangle
public static double cos(double xAtA, double yAtA, double xAtB, double yAtB, double xAtC, double yAtC){
double sideAC = Fmath.hypot(xAtA - xAtC, yAtA - yAtC);
double sideBC = Fmath.hypot(xAtB - xAtC, yAtB - yAtC);
double sideAB = Fmath.hypot(xAtA - xAtB, yAtA - yAtB);
return Fmath.cos(sideAC, sideBC, sideAB);
}
// Cosine of angle between sides sideA and sideB given all side lengths of a triangle
public static double cos(double sideAC, double sideBC, double sideAB){
return 0.5D*(sideAC/sideBC + sideBC/sideAC - (sideAB/sideAC)*(sideAB/sideBC));
}
// Cosine given angle in radians
// for completion - returns Java Math.cos(arg)
public static double cos(double arg){
return Math.cos(arg);
}
// Inverse cosine
// Fmath.asin Checks limits - Java Math.asin returns NaN if without limits
public static double acos(double a){
if(a<-1.0D || a>1.0D) throw new IllegalArgumentException("Fmath.acos argument (" + a + ") must be >= -1.0 and <= 1.0");
return Math.acos(a);
}
// Tangent of angle subtended at coordinate C
// given x, y coordinates of all apices, A, B and C, of a triangle
public static double tan(double xAtA, double yAtA, double xAtB, double yAtB, double xAtC, double yAtC){
double angle = Fmath.angle(xAtA, yAtA, xAtB, yAtB, xAtC, yAtC);
return Math.tan(angle);
}
// Tangent of angle between sides sideA and sideB given all side lengths of a triangle
public static double tan(double sideAC, double sideBC, double sideAB){
double angle = Fmath.angle(sideAC, sideBC, sideAB);
return Math.tan(angle);
}
// Tangent given angle in radians
// for completion - returns Math.tan(arg)
public static double tan(double arg){
return Math.tan(arg);
}
// Inverse tangent
// for completion - returns Math.atan(arg)
public static double atan(double a){
return Math.atan(a);
}
// Inverse tangent - ratio numerator and denominator provided
// for completion - returns Math.atan2(arg)
public static double atan2(double a, double b){
return Math.atan2(a, b);
}
// Cotangent
public static double cot(double a){
return 1.0D/Math.tan(a);
}
// Inverse cotangent
public static double acot(double a){
return Math.atan(1.0D/a);
}
// Inverse cotangent - ratio numerator and denominator provided
public static double acot2(double a, double b){
return Math.atan2(b, a);
}
// Secant
public static double sec(double a){
return 1.0/Math.cos(a);
}
// Inverse secant
public static double asec(double a){
if(a<1.0D && a>-1.0D) throw new IllegalArgumentException("asec argument (" + a + ") must be >= 1 or <= -1");
return Math.acos(1.0/a);
}
// Cosecant
public static double csc(double a){
return 1.0D/Math.sin(a);
}
// Inverse cosecant
public static double acsc(double a){
if(a<1.0D && a>-1.0D) throw new IllegalArgumentException("acsc argument (" + a + ") must be >= 1 or <= -1");
return Math.asin(1.0/a);
}
// Exsecant
public static double exsec(double a){
return (1.0/Math.cos(a)-1.0D);
}
// Inverse exsecant
public static double aexsec(double a){
if(a<0.0D && a>-2.0D) throw new IllegalArgumentException("aexsec argument (" + a + ") must be >= 0.0 and <= -2");
return Math.asin(1.0D/(1.0D + a));
}
// Versine
public static double vers(double a){
return (1.0D - Math.cos(a));
}
// Inverse versine
public static double avers(double a){
if(a<0.0D && a>2.0D) throw new IllegalArgumentException("avers argument (" + a + ") must be <= 2 and >= 0");
return Math.acos(1.0D - a);
}
// Coversine
public static double covers(double a){
return (1.0D - Math.sin(a));
}
// Inverse coversine
public static double acovers(double a){
if(a<0.0D && a>2.0D) throw new IllegalArgumentException("acovers argument (" + a + ") must be <= 2 and >= 0");
return Math.asin(1.0D - a);
}
// Haversine
public static double hav(double a){
return 0.5D*Fmath.vers(a);
}
// Inverse haversine
public static double ahav(double a){
if(a<0.0D && a>1.0D) throw new IllegalArgumentException("ahav argument (" + a + ") must be >= 0 and <= 1");
return Fmath.acos(1.0D - 2.0D*a);
}
// Unnormalised sinc (unnormalised sine cardinal) sin(x)/x
public static double sinc(double a){
if(Math.abs(a)<1e-40){
return 1.0D;
}
else{
return Math.sin(a)/a;
}
}
// Normalised sinc (normalised sine cardinal) sin(pi.x)/(pi.x)
public static double nsinc(double a){
if(Math.abs(a)<1e-40){
return 1.0D;
}
else{
return Math.sin(Math.PI*a)/(Math.PI*a);
}
}
//Hyperbolic sine of a double number
public static double sinh(double a){
return 0.5D*(Math.exp(a)-Math.exp(-a));
}
// Inverse hyperbolic sine of a double number
public static double asinh(double a){
double sgn = 1.0D;
if(a<0.0D){
sgn = -1.0D;
a = -a;
}
return sgn*Math.log(a+Math.sqrt(a*a+1.0D));
}
//Hyperbolic cosine of a double number
public static double cosh(double a){
return 0.5D*(Math.exp(a)+Math.exp(-a));
}
// Inverse hyperbolic cosine of a double number
public static double acosh(double a){
if(a<1.0D) throw new IllegalArgumentException("acosh real number argument (" + a + ") must be >= 1");
return Math.log(a+Math.sqrt(a*a-1.0D));
}
//Hyperbolic tangent of a double number
public static double tanh(double a){
return sinh(a)/cosh(a);
}
// Inverse hyperbolic tangent of a double number
public static double atanh(double a){
double sgn = 1.0D;
if(a<0.0D){
sgn = -1.0D;
a = -a;
}
if(a>1.0D) throw new IllegalArgumentException("atanh real number argument (" + sgn*a + ") must be >= -1 and <= 1");
return 0.5D*sgn*(Math.log(1.0D + a)-Math.log(1.0D - a));
}
//Hyperbolic cotangent of a double number
public static double coth(double a){
return 1.0D/tanh(a);
}
// Inverse hyperbolic cotangent of a double number
public static double acoth(double a){
double sgn = 1.0D;
if(a<0.0D){
sgn = -1.0D;
a = -a;
}
if(a<1.0D) throw new IllegalArgumentException("acoth real number argument (" + sgn*a + ") must be <= -1 or >= 1");
return 0.5D*sgn*(Math.log(1.0D + a)-Math.log(a - 1.0D));
}
//Hyperbolic secant of a double number
public static double sech(double a){
return 1.0D/cosh(a);
}
// Inverse hyperbolic secant of a double number
public static double asech(double a){
if(a>1.0D || a<0.0D) throw new IllegalArgumentException("asech real number argument (" + a + ") must be >= 0 and <= 1");
return 0.5D*(Math.log(1.0D/a + Math.sqrt(1.0D/(a*a) - 1.0D)));
}
//Hyperbolic cosecant of a double number
public static double csch(double a){
return 1.0D/sinh(a);
}
// Inverse hyperbolic cosecant of a double number
public static double acsch(double a){
double sgn = 1.0D;
if(a<0.0D){
sgn = -1.0D;
a = -a;
}
return 0.5D*sgn*(Math.log(1.0/a + Math.sqrt(1.0D/(a*a) + 1.0D)));
}
// DETERMINING PRECISION i.e. number of mantissa places
public static int checkPrecision(double number){
boolean test = true;
int prec = 0;
if(Fmath.isNaN(number))test=false;
if(Fmath.isPlusInfinity(number))test=false;
if(Fmath.isMinusInfinity(number))test=false;
while(test){
if(number==Fmath.truncate(number, prec)){
test = false;
}
else{
prec++;
if(prec>20)test=false;
}
}
return prec;
}
public static int checkPrecision(float number){
return checkPrecision((double)number);
}
// MANTISSA ROUNDING (TRUNCATING)
// returns a value of xDouble truncated to trunc decimal places
public static double truncate(double xDouble, int trunc){
double xTruncated = xDouble;
if(!Fmath.isNaN(xDouble)){
if(!Fmath.isPlusInfinity(xDouble)){
if(!Fmath.isMinusInfinity(xDouble)){
if(xDouble!=0.0D){
String xString = ((new Double(xDouble)).toString()).trim();
xTruncated = Double.parseDouble(truncateProcedure(xString, trunc));
}
}
}
}
return xTruncated;
}
// returns a value of xFloat truncated to trunc decimal places
public static float truncate(float xFloat, int trunc){
float xTruncated = xFloat;
if(!Fmath.isNaN(xFloat)){
if(!Fmath.isPlusInfinity(xFloat)){
if(!Fmath.isMinusInfinity(xFloat)){
if(xFloat!=0.0D){
String xString = ((new Float(xFloat)).toString()).trim();
xTruncated = Float.parseFloat(truncateProcedure(xString, trunc));
}
}
}
}
return xTruncated;
}
// private method for truncating a float or double expressed as a String
private static String truncateProcedure(String xValue, int trunc){
String xTruncated = xValue;
String xWorking = xValue;
String exponent = " ";
String first = "+";
int expPos = xValue.indexOf('E');
int dotPos = xValue.indexOf('.');
int minPos = xValue.indexOf('-');
if(minPos!=-1){
if(minPos==0){
xWorking = xWorking.substring(1);
first = "-";
dotPos--;
expPos--;
}
}
if(expPos>-1){
exponent = xWorking.substring(expPos);
xWorking = xWorking.substring(0,expPos);
}
String xPreDot = null;
String xPostDot = "0";
String xDiscarded = null;
String tempString = null;
double tempDouble = 0.0D;
if(dotPos>-1){
xPreDot = xWorking.substring(0,dotPos);
xPostDot = xWorking.substring(dotPos+1);
int xLength = xPostDot.length();
if(trunc1){
tempString += xDiscarded.substring(1);
}
else{
tempString += "0";
}
tempDouble = Math.round(Double.parseDouble(tempString));
if(trunc>0){
if(tempDouble>=5.0){
int[] xArray = new int[trunc+1];
xArray[0] = 0;
for(int i=0; i0){
if(xArray[iCounter]<10){
test = false;
}
else{
xArray[iCounter]=0;
iCounter--;
}
}
else{
test = false;
}
}
int preInt = Integer.parseInt(xPreDot);
preInt += xArray[0];
xPreDot = (new Integer(preInt)).toString();
tempString = "";
for(int i=1; i<=trunc; i++){
tempString += (new Integer(xArray[i])).toString();
}
xPostDot = tempString;
}
else{
xPostDot = xPostDot.substring(0, trunc);
}
}
else{
if(tempDouble>=5.0){
int preInt = Integer.parseInt(xPreDot);
preInt++;
xPreDot = (new Integer(preInt)).toString();
}
xPostDot = "0";
}
}
xTruncated = first + xPreDot.trim() + "." + xPostDot.trim() + exponent;
}
return xTruncated.trim();
}
// Returns true if x is infinite, i.e. is equal to either plus or minus infinity
// x is double
public static boolean isInfinity(double x){
boolean test=false;
if(x==Double.POSITIVE_INFINITY || x==Double.NEGATIVE_INFINITY)test=true;
return test;
}
// Returns true if x is infinite, i.e. is equal to either plus or minus infinity
// x is float
public static boolean isInfinity(float x){
boolean test=false;
if(x==Float.POSITIVE_INFINITY || x==Float.NEGATIVE_INFINITY)test=true;
return test;
}
// Returns true if x is plus infinity
// x is double
public static boolean isPlusInfinity(double x){
boolean test=false;
if(x==Double.POSITIVE_INFINITY)test=true;
return test;
}
// Returns true if x is plus infinity
// x is float
public static boolean isPlusInfinity(float x){
boolean test=false;
if(x==Float.POSITIVE_INFINITY)test=true;
return test;
}
// Returns true if x is minus infinity
// x is double
public static boolean isMinusInfinity(double x){
boolean test=false;
if(x==Double.NEGATIVE_INFINITY)test=true;
return test;
}
// Returns true if x is minus infinity
// x is float
public static boolean isMinusInfinity(float x){
boolean test=false;
if(x==Float.NEGATIVE_INFINITY)test=true;
return test;
}
// Returns true if x is 'Not a Number' (NaN)
// x is double
public static boolean isNaN(double x){
boolean test=false;
if(x!=x)test=true;
return test;
}
// Returns true if x is 'Not a Number' (NaN)
// x is float
public static boolean isNaN(float x){
boolean test=false;
if(x!=x)test=true;
return test;
}
// Returns true if x equals y
// x and y are double
// x may be float within range, PLUS_INFINITY, NEGATIVE_INFINITY, or NaN
// NB!! This method treats two NaNs as equal
public static boolean isEqual(double x, double y){
boolean test=false;
if(Fmath.isNaN(x)){
if(Fmath.isNaN(y))test=true;
}
else{
if(Fmath.isPlusInfinity(x)){
if(Fmath.isPlusInfinity(y))test=true;
}
else{
if(Fmath.isMinusInfinity(x)){
if(Fmath.isMinusInfinity(y))test=true;
}
else{
if(x==y)test=true;
}
}
}
return test;
}
// Returns true if x equals y
// x and y are float
// x may be float within range, PLUS_INFINITY, NEGATIVE_INFINITY, or NaN
// NB!! This method treats two NaNs as equal
public static boolean isEqual(float x, float y){
boolean test=false;
if(Fmath.isNaN(x)){
if(Fmath.isNaN(y))test=true;
}
else{
if(Fmath.isPlusInfinity(x)){
if(Fmath.isPlusInfinity(y))test=true;
}
else{
if(Fmath.isMinusInfinity(x)){
if(Fmath.isMinusInfinity(y))test=true;
}
else{
if(x==y)test=true;
}
}
}
return test;
}
// Returns true if x equals y
// x and y are int
public static boolean isEqual(int x, int y){
boolean test=false;
if(x==y)test=true;
return test;
}
// Returns true if x equals y
// x and y are char
public static boolean isEqual(char x, char y){
boolean test=false;
if(x==y)test=true;
return test;
}
// Returns true if x equals y
// x and y are Strings
public static boolean isEqual(String x, String y){
boolean test=false;
if(x.equals(y))test=true;
return test;
}
// IS EQUAL WITHIN LIMITS
// Returns true if x equals y within limits plus or minus limit
// x and y are double
public static boolean isEqualWithinLimits(double x, double y, double limit){
boolean test=false;
if(Math.abs(x-y)<=Math.abs(limit))test=true;
return test;
}
// Returns true if x equals y within limits plus or minus limit
// x and y are float
public static boolean isEqualWithinLimits(float x, float y, float limit){
boolean test=false;
if(Math.abs(x-y)<=Math.abs(limit))test=true;
return test;
}
// Returns true if x equals y within limits plus or minus limit
// x and y are long
public static boolean isEqualWithinLimits(long x, long y, long limit){
boolean test=false;
if(Math.abs(x-y)<=Math.abs(limit))test=true;
return test;
}
// Returns true if x equals y within limits plus or minus limit
// x and y are int
public static boolean isEqualWithinLimits(int x, int y, int limit){
boolean test=false;
if(Math.abs(x-y)<=Math.abs(limit))test=true;
return test;
}
// Returns true if x equals y within limits plus or minus limit
// x and y are BigDecimal
public static boolean isEqualWithinLimits(BigDecimal x, BigDecimal y, BigDecimal limit){
boolean test=false;
if(((x.subtract(y)).abs()).compareTo(limit.abs())<=0)test = true;
return test;
}
// Returns true if x equals y within limits plus or minus limit
// x and y are BigInteger
public static boolean isEqualWithinLimits(BigInteger x, BigInteger y, BigInteger limit){
boolean test=false;
if(((x.subtract(y)).abs()).compareTo(limit.abs())<=0)test = true;
return test;
}
// IS EQUAL WITHIN A PERCENTAGE
// Returns true if x equals y within a percentage of the mean
// x and y are double
public static boolean isEqualWithinPerCent(double x, double y, double perCent){
boolean test=false;
double limit = Math.abs((x+y)*perCent/200.0D);
if(Math.abs(x-y)<=limit)test=true;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are float
public static boolean isEqualWithinPerCent(float x, float y, float perCent){
boolean test=false;
double limit = Math.abs((x+y)*perCent/200.0F);
if(Math.abs(x-y)<=limit)test=true;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are long, percentage provided as double
public static boolean isEqualWithinPerCent(long x, long y, double perCent){
boolean test=false;
double limit = Math.abs((x+y)*perCent/200.0D);
if(Math.abs(x-y)<=limit)test=true;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are long, percentage provided as int
public static boolean isEqualWithinPerCent(long x, long y, long perCent){
boolean test=false;
double limit = Math.abs((double)(x+y)*(double)perCent/200.0D);
if(Math.abs(x-y)<=limit)test=true;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are int, percentage provided as double
public static boolean isEqualWithinPerCent(int x, int y, double perCent){
boolean test=false;
double limit = Math.abs((double)(x+y)*perCent/200.0D);
if(Math.abs(x-y)<=limit)test=true;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are int, percentage provided as int
public static boolean isEqualWithinPerCent(int x, int y, int perCent){
boolean test=false;
double limit = Math.abs((double)(x+y)*(double)perCent/200.0D);
if(Math.abs(x-y)<=limit)test=true;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are BigDecimal
public static boolean isEqualWithinPerCent(BigDecimal x, BigDecimal y, BigDecimal perCent){
boolean test=false;
BigDecimal limit = (x.add(y)).multiply(perCent).multiply(new BigDecimal("0.005"));
if(((x.subtract(y)).abs()).compareTo(limit.abs())<=0)test = true;
limit = null;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are BigDInteger, percentage provided as BigDecimal
public static boolean isEqualWithinPerCent(BigInteger x, BigInteger y, BigDecimal perCent){
boolean test=false;
BigDecimal xx = new BigDecimal(x);
BigDecimal yy = new BigDecimal(y);
BigDecimal limit = (xx.add(yy)).multiply(perCent).multiply(new BigDecimal("0.005"));
if(((xx.subtract(yy)).abs()).compareTo(limit.abs())<=0)test = true;
limit = null;
xx = null;
yy = null;
return test;
}
// Returns true if x equals y within a percentage of the mean
// x and y are BigDInteger, percentage provided as BigInteger
public static boolean isEqualWithinPerCent(BigInteger x, BigInteger y, BigInteger perCent){
boolean test=false;
BigDecimal xx = new BigDecimal(x);
BigDecimal yy = new BigDecimal(y);
BigDecimal pc = new BigDecimal(perCent);
BigDecimal limit = (xx.add(yy)).multiply(pc).multiply(new BigDecimal("0.005"));
if(((xx.subtract(yy)).abs()).compareTo(limit.abs())<=0)test = true;
limit = null;
xx = null;
yy = null;
pc = null;
return test;
}
// COMPARISONS
// Returns 0 if x == y
// Returns -1 if x < y
// Returns 1 if x > y
// x and y are double
public static int compare(double x, double y){
Double X = new Double(x);
Double Y = new Double(y);
return X.compareTo(Y);
}
// Returns 0 if x == y
// Returns -1 if x < y
// Returns 1 if x > y
// x and y are int
public static int compare(int x, int y){
Integer X = new Integer(x);
Integer Y = new Integer(y);
return X.compareTo(Y);
}
// Returns 0 if x == y
// Returns -1 if x < y
// Returns 1 if x > y
// x and y are long
public static int compare(long x, long y){
Long X = new Long(x);
Long Y = new Long(y);
return X.compareTo(Y);
}
// Returns 0 if x == y
// Returns -1 if x < y
// Returns 1 if x > y
// x and y are float
public static int compare(float x, float y){
Float X = new Float(x);
Float Y = new Float(y);
return X.compareTo(Y);
}
// Returns 0 if x == y
// Returns -1 if x < y
// Returns 1 if x > y
// x and y are short
public static int compare(byte x, byte y){
Byte X = new Byte(x);
Byte Y = new Byte(y);
return X.compareTo(Y);
}
// Returns 0 if x == y
// Returns -1 if x < y
// Returns 1 if x > y
// x and y are short
public static int compare(short x, short y){
Short X = new Short(x);
Short Y = new Short(y);
return X.compareTo(Y);
}
// COMPARE ARRAYS
// Returns true if arrays identical, false if not
// arrays - double[]
public static boolean compare(double[] array1, double[] array2){
boolean ret = true;
int n = array1.length;
int m = array2.length;
if(n!=m){
ret = false;
}
else{
for(int i=0; i=1970){
yearDiff += 365;
if(Fmath.leapYear(yearTest))yearDiff++;
yearTest--;
}
yearDiff *= 24L*60L*60L*1000L;
long monthDiff = 0L;
int monthTest = month -1;
while(monthTest>0){
monthDiff += monthDays[monthTest];
if(Fmath.leapYear(year))monthDiff++;
monthTest--;
}
monthDiff *= 24L*60L*60L*1000L;
ms = yearDiff + monthDiff + day*24L*60L*60L*1000L + hour*60L*60L*1000L + min*60L*1000L + sec*1000L;
return ms;
}
// DEPRECATED METHODS
// Several methods have been revised and moved to classes ArrayMaths, Conv or PrintToScreen
// ARRAY MAXIMUM (deprecated - see ArryMaths class)
// Maximum of a 1D array of doubles, aa
public static double maximum(double[] aa){
int n = aa.length;
double aamax=aa[0];
for(int i=1; iaamax)aamax=aa[i];
}
return aamax;
}
// Maximum of a 1D array of floats, aa
public static float maximum(float[] aa){
int n = aa.length;
float aamax=aa[0];
for(int i=1; iaamax)aamax=aa[i];
}
return aamax;
}
// Maximum of a 1D array of ints, aa
public static int maximum(int[] aa){
int n = aa.length;
int aamax=aa[0];
for(int i=1; iaamax)aamax=aa[i];
}
return aamax;
}
// Maximum of a 1D array of longs, aa
public static long maximum(long[] aa){
long n = aa.length;
long aamax=aa[0];
for(int i=1; iaamax)aamax=aa[i];
}
return aamax;
}
// Minimum of a 1D array of doubles, aa
public static double minimum(double[] aa){
int n = aa.length;
double aamin=aa[0];
for(int i=1; i double[]
public static double[] arrayMultByConstant(double[] aa, double constant){
int n = aa.length;
double[] bb = new double[n];
for(int i=0; i double[]
public static double[] arrayMultByConstant(int[] aa, double constant){
int n = aa.length;
double[] bb = new double[n];
for(int i=0; i double[]
public static double[] arrayMultByConstant(double[] aa, int constant){
int n = aa.length;
double[] bb = new double[n];
for(int i=0; i double[]
public static double[] arrayMultByConstant(int[] aa, int constant){
int n = aa.length;
double[] bb = new double[n];
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i arrayl = new ArrayList();
for(int i=0; i=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of floats
// returns -1 if none found
public static int indexOf(float[] array, float value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter]==value){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of longs
// returns -1 if none found
public static int indexOf(long[] array, long value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter]==value){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of ints
// returns -1 if none found
public static int indexOf(int[] array, int value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter]==value){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of bytes
// returns -1 if none found
public static int indexOf(byte[] array, byte value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter]==value){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of shorts
// returns -1 if none found
public static int indexOf(short[] array, short value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter]==value){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of chars
// returns -1 if none found
public static int indexOf(char[] array, char value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter]==value){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of Strings
// returns -1 if none found
public static int indexOf(String[] array, String value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter].equals(value)){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// finds the index of the first occurence of the element equal to a given value in an array of Objects
// returns -1 if none found
public static int indexOf(Object[] array, Object value){
int index = -1;
boolean test = true;
int counter = 0;
while(test){
if(array[counter].equals(value)){
index = counter;
test = false;
}
else{
counter++;
if(counter>=array.length)test = false;
}
}
return index;
}
// FIND VALUE OF AND FIND VALUE OF ARRAY ELEMENTS NEAREST TO A VALUE (deprecated - see ArryMaths class)
// finds the value of nearest element value in array to the argument value
public static double nearestElementValue(double[] array, double value){
double diff = Math.abs(array[0] - value);
double nearest = array[0];
for(int i=1; i=0.0D){
diff0 = value - array[ii];
nearest = array[ii];
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = min;
diff0 = min - value;
test = false;
}
}
}
for(int i=0; i=0.0D && diff1=0.0D){
diff0 = value - array[ii];
nearest = ii;
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = minI;
diff0 = min - value;
test = false;
}
}
}
for(int i=0; i=0.0D && diff1max)max = array[ii];
if((array[ii] - value )>=0.0D){
diff0 = value - array[ii];
nearest = array[ii];
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = max;
diff0 = value - max;
test = false;
}
}
}
for(int i=0; i=0.0D && diff1max){
max = array[ii];
maxI = ii;
}
if((array[ii] - value )>=0.0D){
diff0 = value - array[ii];
nearest = ii;
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = maxI;
diff0 = value - max;
test = false;
}
}
}
for(int i=0; i=0.0D && diff1=0){
diff0 = value - array[ii];
nearest = array[ii];
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = min;
diff0 = min - value;
test = false;
}
}
}
for(int i=0; i=0 && diff1=0){
diff0 = value - array[ii];
nearest = ii;
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = minI;
diff0 = min - value;
test = false;
}
}
}
for(int i=0; i=0 && diff1max)max = array[ii];
if((array[ii] - value )>=0){
diff0 = value - array[ii];
nearest = array[ii];
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = max;
diff0 = value - max;
test = false;
}
}
}
for(int i=0; i=0 && diff1max){
max = array[ii];
maxI = ii;
}
if((array[ii] - value )>=0){
diff0 = value - array[ii];
nearest = ii;
test = false;
}
else{
ii++;
if(ii>array.length-1){
nearest = maxI;
diff0 = value - max;
test = false;
}
}
}
for(int i=0; i=0 && diff10)sum += i;
return sum;
}
// PRODUCT OF ALL ELEMENTS (deprecated - see ArryMaths class)
// Product of all array elements - double array
public static double arrayProduct(double[]array){
double product = 1.0D;
for(double i:array)product *= i;
return product;
}
// Product of all array elements - float array
public static float arrayProduct(float[]array){
float product = 1.0F;
for(float i:array)product *= i;
return product;
}
// Product of all array elements - int array
public static int arrayProduct(int[]array){
int product = 1;
for(int i:array)product *= i;
return product;
}
// Product of all array elements - long array
public static long arrayProduct(long[]array){
long product = 1L;
for(long i:array)product *= i;
return product;
}
// CONCATENATE TWO ARRAYS (deprecated - see ArryMaths class)
// Concatenate two double arrays
public static double[] concatenate(double[] aa, double[] bb){
int aLen = aa.length;
int bLen = bb.length;
int cLen = aLen + bLen;
double[] cc = new double[cLen];
for(int i=0; i selectSortVector(double[] aa){
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