Class Special

Set of special mathematic functions.

Inheritance

System.Object

Special

Namespace: ISynergy.Framework.Mathematics.Common

Assembly: ISynergy.Framework.Mathematics.dll

Syntax

public static class Special : object

Remarks

References:

Cephes Math Library, http://www.netlib.org/cephes/
John D. Cook, http://www.johndcook.com/

Methods

View Source

Acosec(Double)

Inverse cosecant.

Declaration

public static double Acosec(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Acosech(Double)

Inverse hyperbolic cosecant.

Declaration

public static double Acosech(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Acosh(Double)

Inverse hyperbolic cos.

Declaration

public static double Acosh(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Acotan(Double)

Inverse cotangent.

Declaration

public static double Acotan(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Acotanh(Double)

Inverse hyperbolic cotangent.

Declaration

public static double Acotanh(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Asec(Double)

Inverse secant.

Declaration

public static double Asec(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Asech(Double)

Inverse hyperbolic secant.

Declaration

public static double Asech(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Asinh(Double)

Inverse hyperbolic sin.

Declaration

public static double Asinh(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Atanh(Double)

Inverse hyperbolic tangent.

Declaration

public static double Atanh(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Binomial(Double, Double)

Computes the binomial coefficients C(n,k).

Declaration

public static double Binomial(double n, double k)

Parameters

Type	Name	Description
System.Double	n
System.Double	k

Returns

Type	Description
System.Double

View Source

Binomial(Int32, Int32)

Computes the binomial coefficients C(n,k).

Declaration

public static double Binomial(int n, int k)

Parameters

Type	Name	Description
System.Int32	n
System.Int32	k

Returns

Type	Description
System.Double

View Source

BSpline(Int32, Double)

Computes the Basic Spline of order n

Declaration

public static double BSpline(int n, double x)

Parameters

Type	Name	Description
System.Int32	n
System.Double	x

Returns

Type	Description
System.Double

View Source

Cosec(Double)

Cosecant.

Declaration

public static double Cosec(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Cosech(Double)

Hyperbolic secant.

Declaration

public static double Cosech(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Cotan(Double)

Cotangent.

Declaration

public static double Cotan(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Cotanh(Double)

Hyperbolic cotangent.

Declaration

public static double Cotanh(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Epslon(Double)

Estimates unit round-off in quantities of size x.

Declaration

public static double Epslon(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

Remarks

This is a port of the epslon function from EISPACK.

View Source

Erf(Double)

Error function of the specified value.

Declaration

public static double Erf(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Erfc(Double)

Complementary error function of the specified value.

Declaration

public static double Erfc(double value)

Parameters

Type	Name	Description
System.Double	value

Returns

Type	Description
System.Double

Remarks

http://mathworld.wolfram.com/Erfc.html

View Source

Expm1(Double)

Compute exp(x) - 1 without loss of precision for small values of x.

Declaration

public static double Expm1(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

Remarks

References:

http://www.johndcook.com/cpp_expm1.html

View Source

Factorial(Double)

Returns the extended factorial definition of a real number.

Declaration

public static double Factorial(double n)

Parameters

Type	Name	Description
System.Double	n

Returns

Type	Description
System.Double

View Source

Factorial(Int32)

Computes the factorial of a number (n!)

Declaration

public static double Factorial(int n)

Parameters

Type	Name	Description
System.Int32	n

Returns

Type	Description
System.Double

View Source

Ierf(Double)

Inverse error function (Erf(Double).

Declaration

public static double Ierf(double y)

Parameters

Type	Name	Description
System.Double	y

Returns

Type	Description
System.Double

View Source

Ierfc(Double)

Inverse complemented error function (Erfc(Double).

Declaration

public static double Ierfc(double y)

Parameters

Type	Name	Description
System.Double	y

Returns

Type	Description
System.Double

View Source

Log1m(Double)

Computes log(1-x) without losing precision for small values of x.

Declaration

public static double Log1m(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Log1p(Double)

Computes log(1+x) without losing precision for small values of x.

Declaration

public static double Log1p(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

Remarks

References:

http://www.johndcook.com/csharp_log_one_plus_x.html

View Source

Log1pexp(Double)

Computes log(1 + exp(x)) without losing precision.

Declaration

public static double Log1pexp(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

LogBinomial(Double, Double)

Computes the log binomial Coefficients Log[C(n,k)].

Declaration

public static double LogBinomial(double n, double k)

Parameters

Type	Name	Description
System.Double	n
System.Double	k

Returns

Type	Description
System.Double

View Source

LogBinomial(Int32, Int32)

Computes the log binomial Coefficients Log[C(n,k)].

Declaration

public static double LogBinomial(int n, int k)

Parameters

Type	Name	Description
System.Int32	n
System.Int32	k

Returns

Type	Description
System.Double

View Source

LogDiff(Double, Double)

Computes x + y without losing precision using ln(x) and ln(y).

Declaration

public static double LogDiff(double lnx, double lny)

Parameters

Type	Name	Description
System.Double	lnx
System.Double	lny

Returns

Type	Description
System.Double

View Source

LogFactorial(Double)

Returns the log factorial of a number (ln(n!))

Declaration

public static double LogFactorial(double n)

Parameters

Type	Name	Description
System.Double	n

Returns

Type	Description
System.Double

View Source

LogFactorial(Int32)

Returns the log factorial of a number (ln(n!))

Declaration

public static double LogFactorial(int n)

Parameters

Type	Name	Description
System.Int32	n

Returns

Type	Description
System.Double

View Source

LogSum(Double, Double)

Computes x + y without losing precision using ln(x) and ln(y).

Declaration

public static double LogSum(double lnx, double lny)

Parameters

Type	Name	Description
System.Double	lnx
System.Double	lny

Returns

Type	Description
System.Double

View Source

LogSum(Double[])

Computes x + y without losing precision using ln(x) and ln(y).

Declaration

public static double LogSum(double[] values)

Parameters

Type	Name	Description
System.Double[]	values

Returns

Type	Description
System.Double

View Source

LogSum(Single, Single)

Computes x + y without losing precision using ln(x) and ln(y).

Declaration

public static double LogSum(float lnx, float lny)

Parameters

Type	Name	Description
System.Single	lnx
System.Single	lny

Returns

Type	Description
System.Double

View Source

LogSumExp(Double[])

Computes sum(x) without losing precision using ln(x_0) ... ln(x_n).

Declaration

public static double LogSumExp(this double[] array)

Parameters

Type	Name	Description
System.Double[]	array

Returns

Type	Description
System.Double

View Source

P1evl(Double, Double[], Int32)

Evaluates polynomial of degree N with assumption that coef[N] = 1.0

Declaration

public static double P1evl(double x, double[] coef, int n)

Parameters

Type	Name	Description
System.Double	x
System.Double[]	coef
System.Int32	n

Returns

Type	Description
System.Double

View Source

Polevl(Double, Double[], Int32)

Evaluates polynomial of degree N

Declaration

public static double Polevl(double x, double[] coef, int n)

Parameters

Type	Name	Description
System.Double	x
System.Double[]	coef
System.Int32	n

Returns

Type	Description
System.Double

View Source

Sec(Double)

Secant.

Declaration

public static double Sec(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Sech(Double)

Hyperbolic secant.

Declaration

public static double Sech(double x)

Parameters

Type	Name	Description
System.Double	x

Returns

Type	Description
System.Double

View Source

Sign(Double, Double)

Returns a with the sign of b.

Declaration

public static double Sign(double a, double b)

Parameters

Type	Name	Description
System.Double	a
System.Double	b

Returns

Type	Description
System.Double	If B > 0 then the result is ABS(A), else it is -ABS(A).

Remarks

This is a port of the sign transfer function from EISPACK, and is is equivalent to C++'s std::copysign function.

View Source

Softmax(Double[])

Computes the Softmax function (also known as normalized Exponencial function) that "squashes"a vector or arbitrary real values into a vector of real values in the range (0, 1) that add up to 1.

Declaration

public static double[] Softmax(double[] input)

Parameters

Type	Name	Description
System.Double[]	input	The real values to be converted into the unit interval.

Returns

Type	Description
System.Double[]	A vector with the same number of dimensions as `input` but where values lie between 0 and 1.

View Source

Softmax(Double[], Double[])

Computes the Softmax function (also known as normalized Exponencial function) that "squashes"a vector or arbitrary real values into a vector of real values in the range (0, 1) that add up to 1.

Declaration

public static double[] Softmax(double[] input, double[] result)

Parameters

Type	Name	Description
System.Double[]	input	The real values to be converted into the unit interval.
System.Double[]	result	The location where to store the result of this operation.

Returns

Type	Description
System.Double[]	A vector with the same number of dimensions as `input` but where values lie between 0 and 1.