Package org.drip.numerical.common

Class NumberUtil

java.lang.Object

org.drip.numerical.common.NumberUtil

public class NumberUtil
extends java.lang.Object

NumberUtil implements number utility functions. It exposes the following functions:

• Verify number/number array validity, and closeness/sign match
• Factorial Permutation/Combination functionality
• Dump multi-dimensional array contents
• Min/Max/Bound the array entries within limits

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Primitives/Array Manipulate Format Display Utilities

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
NumberUtil()

Method Summary

Modifier and Type	Method	Description
static int	BinaryDigitCount(int n)	Retrieve the Binary Digit Count
static double	Bound(double dblX, double dblFloor, double dblCeiling)	Bound the input to within (floor, Ceiling), i.e., compute Min (Max (floor, X), Ceiling)
static boolean	CanMeasureWater(int x, int y, int z)	You are given two jugs with capacities x and y liters.
static int	DivideIntegers(int dividend, int divisor)	Divide two integers without using multiplication, division, and mod operator.
static double	DoubleFactorial(int n)	Compute (2n - 1)!!
static int	Factorial(int n)	This function implements Factorial N.
static double	Fractional(double z)	Retrieve the Fractional Part of z
static long	GCD(long a, long b)	Greatest Common Divisor between Two Numbers
static double	HalfDownShiftedFactorial(int n)	Compute (n - 0.5)!
static boolean	IsInteger(double z)	Indicate if z is an Integer
static boolean	IsNegativeInteger(double z)	Indicate if z is a Negative Integer
static boolean	IsNonNegativeInteger(double z)	Indicate if z is a Non-Negative Integer
static boolean	IsNonPositiveInteger(double z)	Indicate if z is a Non-Positive Integer
static boolean	IsNumberSequenceAdditive(java.lang.String s)	Additive number is a string whose digits can form additive sequence.
static boolean	IsPositiveInteger(double z)	Indicate if z is a Positive Integer
static boolean	IsValid(double dbl)	Checks if the input double is Infinite or NaN
static boolean	IsValid(double[] adbl)	Checks if the input double array contains an Infinite or an NaN
static boolean	IsValid(long l)	Check if the Input Long is MIN_VALUE or MAX_VALUE
static boolean	IsValid(long[] al)	Check if the Input Long Array contains a MIN_VALUE or MAX_VALUE
static double	Maximum(double[] adbl)	Retrieve the Maximum Element in the specified Array
static double	Minimum(double[] adbl)	Retrieve the Minimum Element in the specified Array
static int	NCK(int n, int k)	This function implements N choose K.
static int	NextPrimePalindrome(int n)	Find the smallest prime palindrome greater than or equal to the input number.
static boolean	NormalizedPositive(double[] array)	Check if the Array Elements are Normalized and Positive
static int	NPK(int n, int k)	This function implements N Permute K.
static int	NthDigit(int n)	Identify the nth Digit of the Number
static long	NthUglyNumber(long n, long a, long b, long c)	Find the nth ugly number.
static double	PochhammerSymbol(double s, int k)	Compute the Pochhammer Symbol for the Specified s and k
static double	Power(double x, int n)	Compute the Integer Power of x
static double	PrimeFactorExponentTwo(int n)	Compute the Exponent 2 of Prime Factorization for a given Integer
static boolean	Print1DArray(java.lang.String strName, double[] adblA, boolean bBailOnNaN)	Print the contents of the 1D array
static boolean	Print1DArray(java.lang.String strName, double[] adblA, int iNumDecimal, boolean bBailOnNaN)	Print the contents of the 1D array to the Specified Decimal Location
static boolean	Print2DArray(java.lang.String strName, double[][] aadblA, boolean bBailOnNaN)	Print the contents of the 2D array
static boolean	Print2DArrayPair(java.lang.String strLeftLabel, java.lang.String strRightLabel, double[][] aadblLeft, double[][] aadblRight, boolean bBailOnNaN)	Print the Contents of the 2D Array Pair
static boolean	Print2DArrayTriplet(java.lang.String strLeftLabel, java.lang.String strMiddleLabel, java.lang.String strRightLabel, double[][] aadblLeft, double[][] aadblMiddle, double[][] aadblRight, boolean bBailOnNaN)	Print the Contents of the 2D Array Triplet
static boolean	PrintMatrix(java.lang.String strName, double[][] aadblA)	Print the Matrix Contents
static int	Quotient2(int dividend, int divisor)	Given two integers dividend and divisor, divide two integers without using multiplication, division, and mod operator.
static int	ReciprocalIntegerFloor(double z)	Retrieve the Reciprocal Integer Floor of z
static int	ReverseInteger(int number)	Given a signed 32-bit integer number, return number with its digits reversed.
static double	RisingPochhammerSymbol(double s, int k)	Compute the Rising Pochhammer Symbol for the Specified s and k
static boolean	SameSign(double[] adbl)	Check if the specified array contains elements all of the same sign
static double	Sign(double z)	Indicate the Sign of z
static double	SubFactorial(int n)	This function implements Sub-factorial N.
static int	TrailingFactorialZeros(int n)	Estimate the Trailing Factorial Zeros
static boolean	WithinTolerance(double dbl1, double dbl2)	Compare and checks if the two input numbers fall within a specified tolerance
static boolean	WithinTolerance(double dbl1, double dbl2, double dblAbsoluteTolerance, double dblRelativeTolerance)	Compare and checks if the two input numbers fall within a specified tolerance

Methods inherited from class java.lang.Object

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

Constructor Details

NumberUtil

public NumberUtil()

Method Details

IsValid

public static final boolean IsValid(long l)

Check if the Input Long is MIN_VALUE or MAX_VALUE

Parameters:

l - Input Long

Returns:

TRUE - Input Long is MIN_VALUE or MAX_VALUE

IsValid

public static final boolean IsValid(long[] al)

Check if the Input Long Array contains a MIN_VALUE or MAX_VALUE

Parameters:

al - Input Long Array

Returns:

TRUE - Input Long Array contains a MIN_VALUE or MAX_VALUE

IsValid

public static final boolean IsValid(double dbl)

Checks if the input double is Infinite or NaN

Parameters:

dbl - Input double

Returns:

TRUE - Input double is Infinite or NaN

IsValid

public static final boolean IsValid(double[] adbl)

Checks if the input double array contains an Infinite or an NaN

Parameters:

adbl - Input double array

Returns:

TRUE - Input double contains an Infinite or an NaN

WithinTolerance

public static final boolean WithinTolerance(double dbl1,
double dbl2,
double dblAbsoluteTolerance,
double dblRelativeTolerance)

Compare and checks if the two input numbers fall within a specified tolerance

Parameters:

dbl1 - Number #1

dbl2 - Number #2

dblAbsoluteTolerance - Absolute Tolerance

dblRelativeTolerance - Relative Tolerance

Returns:

TRUE if they fall within the tolerance

WithinTolerance

public static final boolean WithinTolerance(double dbl1,
double dbl2)

Compare and checks if the two input numbers fall within a specified tolerance

Parameters:

dbl1 - Number #1

dbl2 - Number #2

Returns:

TRUE if they fall within the tolerance

Factorial

public static final int Factorial(int n)

This function implements Factorial N.

Parameters:

n - N

Returns:

Factorial N

SubFactorial

public static final double SubFactorial(int n)

This function implements Sub-factorial N.

Parameters:

n - N

Returns:

The Sub-factorial N

NPK

public static final int NPK(int n,
int k)

This function implements N Permute K.

Parameters:

n - N

k - K

Returns:

N Permute K

NCK

public static final int NCK(int n,
int k)

This function implements N choose K.

Parameters:

n - N

k - K

Returns:

N choose K

Bound

public static final double Bound(double dblX,
double dblFloor,
double dblCeiling)
                          throws java.lang.Exception

Bound the input to within (floor, Ceiling), i.e., compute Min (Max (floor, X), Ceiling)

Parameters:

dblX - Input Number

dblFloor - Floor

dblCeiling - Ceiling

Returns:

Min (Max (floor, X), Ceiling)

Throws:

java.lang.Exception - Thrown if the inputs are invalid

Minimum

public static final double Minimum(double[] adbl)
                            throws java.lang.Exception

Retrieve the Minimum Element in the specified Array

Parameters:

adbl - Array of elements

Returns:

The Minimum Element

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

Maximum

public static final double Maximum(double[] adbl)
                            throws java.lang.Exception

Retrieve the Maximum Element in the specified Array

Parameters:

adbl - Array of elements

Returns:

The Maximum Element

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

SameSign

public static final boolean SameSign(double[] adbl)
                              throws java.lang.Exception

Check if the specified array contains elements all of the same sign

Parameters:

adbl - Array of elements

Returns:

TRUE - Same Sign

Throws:

java.lang.Exception - Thrown if the Inputs are invalid

Print1DArray

public static final boolean Print1DArray(java.lang.String strName,
double[] adblA,
boolean bBailOnNaN)

Print the contents of the 1D array

Parameters:

strName - Label Name

adblA - The 1D array

bBailOnNaN - Bail on encountering an NaN

Returns:

TRUE - Print Successful

Print1DArray

public static final boolean Print1DArray(java.lang.String strName,
double[] adblA,
int iNumDecimal,
boolean bBailOnNaN)

Print the contents of the 1D array to the Specified Decimal Location

Parameters:

strName - Label Name

adblA - The 1D array

iNumDecimal - Number of Decimal Places to Display

bBailOnNaN - Bail on encountering an NaN

Returns:

TRUE - Print Successful

Print2DArray

public static final boolean Print2DArray(java.lang.String strName,
double[][] aadblA,
boolean bBailOnNaN)

Print the contents of the 2D array

Parameters:

strName - Label Name

aadblA - The 2D array

bBailOnNaN - Bail on encountering an NaN

Returns:

TRUE - Print Successful

Print2DArrayPair

public static final boolean Print2DArrayPair(java.lang.String strLeftLabel,
java.lang.String strRightLabel,
double[][] aadblLeft,
double[][] aadblRight,
boolean bBailOnNaN)

Print the Contents of the 2D Array Pair

Parameters:

strLeftLabel - Left Label

strRightLabel - Right Label

aadblLeft - The Left 2D array

aadblRight - The Right 2D array

bBailOnNaN - Bail on encountering an NaN

Returns:

TRUE - Print Successful

Print2DArrayTriplet

public static final boolean Print2DArrayTriplet(java.lang.String strLeftLabel,
java.lang.String strMiddleLabel,
java.lang.String strRightLabel,
double[][] aadblLeft,
double[][] aadblMiddle,
double[][] aadblRight,
boolean bBailOnNaN)

Print the Contents of the 2D Array Triplet

Parameters:

strLeftLabel - Left Label

strMiddleLabel - Middle Label

strRightLabel - Right Label

aadblLeft - The Left 2D array

aadblMiddle - The Middle 2D array

aadblRight - The Right 2D array

bBailOnNaN - Bail on encountering an NaN

Returns:

TRUE - Print Successful

PrintMatrix

public static final boolean PrintMatrix(java.lang.String strName,
double[][] aadblA)

Print the Matrix Contents

Parameters:

strName - Name of the Matrix

aadblA - Matrix

Returns:

TRUE - Matrix Contents Successfully printed

HalfDownShiftedFactorial

public static final double HalfDownShiftedFactorial(int n)
                                             throws java.lang.Exception

Compute (n - 0.5)!

Parameters:

n - n

Returns:

(n - 0.5)! Value

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

DoubleFactorial

public static final double DoubleFactorial(int n)
                                    throws java.lang.Exception

Compute (2n - 1)!!

Parameters:

n - n

Returns:

(2n - 1)!!

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

RisingPochhammerSymbol

public static final double RisingPochhammerSymbol(double s,
int k)
                                           throws java.lang.Exception

Compute the Rising Pochhammer Symbol for the Specified s and k

Parameters:

s - s

k - k

Returns:

The Rising Pochhammer Symbol

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

PochhammerSymbol

public static final double PochhammerSymbol(double s,
int k)
                                     throws java.lang.Exception

Compute the Pochhammer Symbol for the Specified s and k

Parameters:

s - s

k - k

Returns:

Pochhammer Symbol

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

IsInteger

public static final boolean IsInteger(double z)
                               throws java.lang.Exception

Indicate if z is an Integer

Parameters:

z - Z

Returns:

TRUE - z is an Integer

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

IsPositiveInteger

public static final boolean IsPositiveInteger(double z)
                                       throws java.lang.Exception

Indicate if z is a Positive Integer

Parameters:

z - Z

Returns:

TRUE - z is a Positive Integer

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

IsNonPositiveInteger

public static final boolean IsNonPositiveInteger(double z)
                                          throws java.lang.Exception

Indicate if z is a Non-Positive Integer

Parameters:

z - Z

Returns:

TRUE - z is a Non-Positive Integer

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

IsNegativeInteger

public static final boolean IsNegativeInteger(double z)
                                       throws java.lang.Exception

Indicate if z is a Negative Integer

Parameters:

z - Z

Returns:

TRUE - z is a Negative Integer

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

IsNonNegativeInteger

public static final boolean IsNonNegativeInteger(double z)
                                          throws java.lang.Exception

Indicate if z is a Non-Negative Integer

Parameters:

z - Z

Returns:

TRUE - z is a Non-Negative Integer

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Sign

public static final double Sign(double z)
                         throws java.lang.Exception

Indicate the Sign of z

Parameters:

z - Z

Returns:

Sign of z

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

NormalizedPositive

public static final boolean NormalizedPositive(double[] array)

Check if the Array Elements are Normalized and Positive

Parameters:

array - Array

Returns:

TRUE - The Array Elements are Normalized and Positive

Fractional

public static final double Fractional(double z)
                               throws java.lang.Exception

Retrieve the Fractional Part of z

Parameters:

z - Z

Returns:

The Fractional Part of z

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

ReciprocalIntegerFloor

public static final int ReciprocalIntegerFloor(double z)
                                        throws java.lang.Exception

Retrieve the Reciprocal Integer Floor of z

Parameters:

z - Z

Returns:

The Reciprocal Integer Floor of z

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

PrimeFactorExponentTwo

public static final double PrimeFactorExponentTwo(int n)
                                           throws java.lang.Exception

Compute the Exponent 2 of Prime Factorization for a given Integer

Parameters:

n - The Integer

Returns:

Exponent 2 of Prime Factorization for a given Integer

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

BinaryDigitCount

public static final int BinaryDigitCount(int n)

Retrieve the Binary Digit Count

Parameters:

n - N

Returns:

The Binary Digit Count

DivideIntegers

public static final int DivideIntegers(int dividend,
int divisor)
                                throws java.lang.Exception

Divide two integers without using multiplication, division, and mod operator. The integer division should truncate toward zero, which means losing its fractional part. For example, truncate(8.345) = 8 and truncate(-2.7335) = -2.

Parameters:

dividend - Dividend

divisor - Divisor

Returns:

The quotient after dividing dividend by divisor

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Power

public static final double Power(double x,
int n)
                          throws java.lang.Exception

Compute the Integer Power of x

Parameters:

x - x

n - n

Returns:

Integer Power of x

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

NextPrimePalindrome

public static final int NextPrimePalindrome(int n)

Find the smallest prime palindrome greater than or equal to the input number. Recall that a number is prime if it's only divisors are 1 and itself, and it is greater than 1. For example, 2,3,5,7,11 and 13 are primes. Recall that a number is a palindrome if it reads the same from left to right as it does from right to left. For example, 12321 is a palindrome.

Parameters:

n - The Number

Returns:

The Next Prime Palindrome

GCD

public static final long GCD(long a,
long b)

Greatest Common Divisor between Two Numbers

Parameters:

a - First Number

b - Second Number

Returns:

The GCD

NthUglyNumber

public static final long NthUglyNumber(long n,
long a,
long b,
long c)

Find the n^th ugly number. Ugly numbers are positive integers which are divisible by a or b or c.

Parameters:

n - n

a - A

b - B

c - C

Returns:

The n^th Ugly Number

IsNumberSequenceAdditive

public static final boolean IsNumberSequenceAdditive(java.lang.String s)

Additive number is a string whose digits can form additive sequence. A valid additive sequence should contain at least three numbers. Except for the first two numbers, each subsequent number in the sequence must be the sum of the preceding two. Given a string containing only digits '0'-'9', write a function to determine if it's an additive number. Note: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.

Parameters:

s - The Input String

Returns:

TRUE - Input is an Additive Number

TrailingFactorialZeros

public static final int TrailingFactorialZeros(int n)

Estimate the Trailing Factorial Zeros

Parameters:

n - Factorial NUmber

Returns:

Number of Training Factor Zeros

CanMeasureWater

public static final boolean CanMeasureWater(int x,
int y,
int z)

You are given two jugs with capacities x and y liters. There is an infinite amount of water supply available. You need to determine whether it is possible to measure exactly z liters using these two jugs. If z liters of water is measurable, you must have z liters of water contained within one or both buckets by the end. Operations allowed: Fill any of the jugs completely with water. Empty any of the jugs. Pour water from one jug into another till the other jug is completely full or the first jug itself is empty.

Parameters:

x - x

y - y

z - z

Returns:

TRUE - The Measurement can be successfully carried out

NthDigit

public static final int NthDigit(int n)

Identify the n^th Digit of the Number

Parameters:

n - The Number

Returns:

The n^th Digit

Quotient2

public static final int Quotient2(int dividend,
int divisor)

Given two integers dividend and divisor, divide two integers without using multiplication, division, and mod operator. Return the quotient after dividing dividend by divisor. The integer division should truncate toward zero, which means losing its fractional part. For example, truncate(8.345) = 8 and truncate(-2.7335) = -2. Note: Assume we are dealing with an environment that could only store integers within the 32-bit signed integer range: [−2³¹, 2³¹ − 1]. For this problem, assume that your function returns 2³¹ − 1 when the division result overflows.

Parameters:

dividend - Dividend

divisor - Divisor

Returns:

Quotient

ReverseInteger

public static final int ReverseInteger(int number)

Given a signed 32-bit integer number, return number with its digits reversed. If reversing number causes the value to go outside the signed 32-bit integer range [-2³¹, 2³¹ - 1], then return 0.

Parameters:

number - The Given Number

Returns:

The Reverse