C# Class YAMP.Numerics.Helpers

Provides some commonly used methods for numeric algorithms.

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_oe static_oe property

Provides access to the first 21 bernoulli numbers.

public static Double[] BernoulliNumbers
return	Double[]

LanczosD public_oe static_oe property

Provides access do some Lanczos numbers.

public static Double[] LanczosD
return	Double[]

LogPI public_oe static_oe property

Value of ln(Pi)

public static Double LogPI
return	Double

LogTwo public_oe static_oe property

Value of ln(2)

public static Double LogTwo
return	Double

SqrtPI public_oe static_oe property

Value of Sqrt(Pi)

public static Double SqrtPI
return	Double

SqrtThree public_oe static_oe property

Value of Sqrt(3)

public static Double SqrtThree
return	Double

SqrtTwo public_oe static_oe property

Value of Sqrt(2)

public static Double SqrtTwo
return	Double

SqrtTwoPI public_oe static_oe property

Value of Sqrt(2 * Pi)

public static Double SqrtTwoPI
return	Double

TwoPIpow public_oe static_oe property

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

public static Double[] TwoPIpow
return	Double[]