com.numericalmethod.suanshu.analysis.function

Class FunctionOps

java.lang.Object

com.numericalmethod.suanshu.analysis.function.FunctionOps

public class FunctionOps
extends java.lang.Object

These are some commonly used mathematical functions.

Constructor Summary

Constructors

Constructor and Description
FunctionOps()

Method Summary

Modifier and Type	Method and Description
static double	combination(int n, int k) Compute the combination function or binomial coefficient.
static double	dotProduct(double[] x1, double[] x2) \(x_1 \cdot x_2\) This operation is called inner product when used in the context of vector space.
static long	dotProduct(long[] x1, long[] x2) \(x_1 \cdot x_2\) This operation is called inner product when used in the context of vector space.
static double	factorial(int n) n!
static double	linearInterpolate(double x, double x0, double y0, double x1, double y1) Linear interpolation between two points.
static long	mod(long x, long m) Compute the positive modulus of a number.
static long	modpow(long base, long exponent, long modulus) be mod m
static double	permutation(int n, int k) Compute the permutation function.

Methods inherited from class java.lang.Object

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

Constructor Detail

FunctionOps

public FunctionOps()

Method Detail

modpow

public static long modpow(long base,
                          long exponent,
                          long modulus)

 be mod m
 

We use the fact that

 (a * b) mod m = ((a mod m) * (b mod m)) mod m
 

This code may fail without being noticed for very large numbers because overflow in integer operations does not throw any exception in the JVM.

Parameters:

base - positive integer b

exponent - positive integer e

modulus - positive integer m

Returns:

b^e mod m

Throws:

java.lang.IllegalArgumentException - if not all inputs are positive integers

See Also:

• Wikipedia: Modular exponentiation
• Wikipedia: Right-to-left binary method
• "Bruce Schneier, "p. 244," Applied Cryptography, 2e, ISBN 0-471-11709-9."

mod

public static long mod(long x,
                       long m)

Compute the positive modulus of a number. If x is positive, we return x mod m; otherwise, we return the smallest positive integer less than m, having the same modulo. For example,

 -1 mod 5 = 4
 

Parameters:

x - an integer

m - the modulus

Returns:

x mod m

See Also:

Wikipedia: Modulo operation

dotProduct

public static long dotProduct(long[] x1,
                              long[] x2)

\(x_1 \cdot x_2\)

This operation is called inner product when used in the context of vector space.

Parameters:

x1 - a long array

x2 - a long array

Returns:

\(x_1 \cdot x_2\)

See Also:

Wikipedia: Dot product

dotProduct

public static double dotProduct(double[] x1,
                                double[] x2)

\(x_1 \cdot x_2\)

This operation is called inner product when used in the context of vector space.

Parameters:

x1 - a double array

x2 - a double array

Returns:

\(x_1 \cdot x_2\)

See Also:

Wikipedia: Dot product

factorial

public static double factorial(int n)

n!

Parameters:

n - an integer

Returns:

n!

See Also:

Wikipedia: Factorial

combination

public static double combination(int n,
                                 int k)

Compute the combination function or binomial coefficient. It is the number of subsets of size k in a larger set of n elements.

Parameters:

n - the size of the full set

k - the size of a combination

Returns:

\(\frac{n!}{(n-k)! k!}\)

See Also:

Wikipedia: Combination

permutation

public static double permutation(int n,
                                 int k)

Compute the permutation function. It is the number of size-k-permutations from a larger set of n elements.

Parameters:

n - the size of the full set

k - the size of a permutation

Returns:

\(\frac{n!}{(n-k)!}\)

See Also:

Wikipedia: Permutation

linearInterpolate

public static double linearInterpolate(double x,
                                       double x0,
                                       double y0,
                                       double x1,
                                       double y1)

Linear interpolation between two points.

Parameters:

x - x

x0 - x0

y0 - y0

x1 - x1

y1 - y1

Returns:

the linear interpolation between two points

See Also:

Wikipedia: Linear interpolation between two known points