C# Class YAMP.Numerics.Helpers

Provides some commonly used methods for numeric algorithms.

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Public Properties

Property	Type	Description
BernoulliNumbers	Double[]
LanczosD	Double[]
LogPI	Double
LogTwo	Double
SqrtPI	Double
SqrtThree	Double
SqrtTwo	Double
SqrtTwoPI	Double
TwoPIpow	Double[]

Public Methods

Method	Description
BinomialCoefficient ( Double n, Double k ) : Double	Computes the real binomial coefficient (almost general) given two values, n choose k.
BinomialCoefficient ( ScalarValue n, ScalarValue k ) : ScalarValue	Computes the complex binomial coefficient (very general) given two values, n choose k.
ChebEval ( ChebSeries cs, Double x ) : Double	Evaluate a real Chebyshev polynomial on an interval, given the coefficients.
ChebEval ( Int32 n, Double coefficients, Double x ) : Double	Evaluate a real Chebyshev polynomial on an interval, given the coefficients.
ChebEval ( ChebSeries cs, ScalarValue z ) : ScalarValue	Evaluate a complex Chebyshev polynomial on an interval, given the coefficients.
ComputeRoots ( Int32 N, Int32 sign ) : ScalarValue[]	computes the N-th roots of unity, which are the factors in a length-N Fourier transform.
Factorial ( Int32 n ) : Double	Computes the factorial of an integer and returns a double with the result.
GCD ( Int32 A, Int32 B ) : Int32	Computes the greatest common divisor of two numbers.
Hypot ( Double a, Double b ) : Double	Computes the length of a right triangle's hypotenuse.
IsPrimeNumber ( Int32 n ) : System.Boolean	Returns a boolean if the given integer is a prime number.
PowMod ( Int32 b, Int32 e, Int32 m ) : Int32	Computes a power of an integer in modular arithmetic.
Power ( ScalarValue z, Int32 n ) : ScalarValue	Takes the power of z to an integer n.

Private Methods

Method	Description
IsProbablyPrime ( Int32 n, Int32 m, Int32 s, Int32 d, Int32 w ) : System.Boolean

Method Details

BinomialCoefficient() public static method

Computes the real binomial coefficient (almost general) given two values, n choose k.

public static BinomialCoefficient ( Double n, Double k ) : Double
n	Double	We have n elements.
k	Double	We choose k elements.
return	Double

BinomialCoefficient() public static method

Computes the complex binomial coefficient (very general) given two values, n choose k.

public static BinomialCoefficient ( ScalarValue n, ScalarValue k ) : ScalarValue
n	ScalarValue	We have n elements.
k	ScalarValue	We choose k elements.
return	ScalarValue

ChebEval() public static method

Evaluate a real Chebyshev polynomial on an interval, given the coefficients.

public static ChebEval ( ChebSeries cs, Double x ) : Double
cs	ChebSeries	The coefficients to consider.
x	Double	The real evaluation argument.
return	Double

ChebEval() public static method

Evaluate a real Chebyshev polynomial on an interval, given the coefficients.

public static ChebEval ( Int32 n, Double coefficients, Double x ) : Double
n	System.Int32	The order for the summation of the polynomial.
coefficients	Double	The coefficients to consider.
x	Double	The real evaluation argument.
return	Double

ChebEval() public static method

Evaluate a complex Chebyshev polynomial on an interval, given the coefficients.

public static ChebEval ( ChebSeries cs, ScalarValue z ) : ScalarValue
cs	ChebSeries	The coefficients to consider.
z	ScalarValue	The complex evaluation argument.
return	ScalarValue

ComputeRoots() public static method

computes the N-th roots of unity, which are the factors in a length-N Fourier transform.

public static ComputeRoots ( Int32 N, Int32 sign ) : ScalarValue[]
N	System.Int32	What number of roots.
sign	System.Int32	The sign to take.
return	ScalarValue[]

Factorial() public static method

Computes the factorial of an integer and returns a double with the result.

public static Factorial ( Int32 n ) : Double
n	System.Int32	The argument to take the factorial.
return	Double

GCD() public static method

Computes the greatest common divisor of two numbers.

public static GCD ( Int32 A, Int32 B ) : Int32
A	System.Int32	The first number.
B	System.Int32	The second number.
return	System.Int32

Hypot() public static method

Computes the length of a right triangle's hypotenuse.

public static Hypot ( Double a, Double b ) : Double
a	Double	The length of one side.
b	Double	The length of another side.
return	Double

IsPrimeNumber() public static method

Returns a boolean if the given integer is a prime number.

public static IsPrimeNumber ( Int32 n ) : System.Boolean
n	System.Int32	The integer to examine.
return	System.Boolean

PowMod() public static method

Computes a power of an integer in modular arithmetic.

public static PowMod ( Int32 b, Int32 e, Int32 m ) : Int32
b	System.Int32	The base, which must be positive.
e	System.Int32	The exponent, which must be positive.
m	System.Int32	The modulus, which must be positive.
return	System.Int32

Power() public static method

Takes the power of z to an integer n.

public static Power ( ScalarValue z, Int32 n ) : ScalarValue
z	ScalarValue	The complex value z in C.
n	System.Int32	The power n in N.
return	ScalarValue

Property Details

BernoulliNumbers public static property

Provides access to the first 21 bernoulli numbers.

public static Double[] BernoulliNumbers
return	Double[]

LanczosD public static property

Provides access do some Lanczos numbers.

public static Double[] LanczosD
return	Double[]

LogPI public static property

Value of ln(Pi)

public static Double LogPI
return	Double

LogTwo public static property

Value of ln(2)

public static Double LogTwo
return	Double

SqrtPI public static property

Value of Sqrt(Pi)

public static Double SqrtPI
return	Double

SqrtThree public static property

Value of Sqrt(3)

public static Double SqrtThree
return	Double

SqrtTwo public static property

Value of Sqrt(2)

public static Double SqrtTwo
return	Double

SqrtTwoPI public static property

Value of Sqrt(2 * Pi)

public static Double SqrtTwoPI
return	Double

TwoPIpow public static property

Provides access to (2*pi)^(10*n) with n = 0, ..., 17.

public static Double[] TwoPIpow
return	Double[]