Defines some mathematical functions to be used in derived and other classes. More...

Inheritance diagram for IG.Num.M:

Static Public Member Functions
static void	Swap (ref double a, ref double b)
	Swaps values of the two specified variables of type double. More...

static void	Swap (ref int a, ref int b)
	Swaps values of the two specified variables of type int. More...

static void	Swap (ref string a, ref string b)
	Swaps values of the two specified variables of type string. More...

static double	abs (double a)
	Absolute value. More...

static double	sign (double a)
	Returns a value indicating the sign of a number. More...

static double	ceil (double a)
	Returns the smallest integral value that is greater than or equal to the specified decimal number. More...

static double	floor (double a)
	Returns the largest integer less than or equal to the specified number. More...

static double	trunc (double a)
	Calculates the integral part of a specified number. More...

static double	min (double a, double b)
	Smallest of two numbers. More...

static double	max (double a, double b)
	Largest of two numbers. More...

static double	min (double a, double b, double c)
	Smallest of three numbers. More...

static double	max (double a, double b, double c)
	Largest of three numbers. More...

static double	min (double a, double b, double c, double d)
	Smallest of four numbers. More...

static double	max (double a, double b, double c, double d)
	Largest of four numbers. More...

static double	min (double a, double b, double c, double d, double e)
	Smallest of five numbers. More...

static double	max (double a, double b, double c, double d, double e)
	Largest of five numbers. More...

static double	min (double a, double b, double c, double d, double e, double f)
	Smallest of six numbers. More...

static double	max (double a, double b, double c, double d, double e, double f)
	Largest of six numbers. More...

static double	min (params double[] numbers)
	Minimal of the specified values. More...

static double	max (params double[] numbers)
	Maximal of the specified values. More...

static double	sum (params double[] numbers)
	Sum of the specified values. More...

static double	prod (params double[] numbers)
	Product of the specified values. More...

static double	pow (double a, double b)
	Returns a specified number raised to the specified power. More...

static double	sqr (double a)
	Returns the square of a specified number. More...

static double	cube (double a)
	Returns the square of a specified number. More...

static double	pow2 (double x)
	Square. More...

static double	pow3 (double x)
	3rd power. More...

static double	pow4 (double x)
	4th power. More...

static double	pow5 (double x)
	5th power. More...

static double	pow6 (double x)
	6th power. More...

static double	sqrt (double a)
	Returns the square root of a specified number. More...

static double	root2 (double a)
	Returns the square root of a specified number. More...

static double	root3 (double a)
	Returns the cubic root of a specified number. More...

static double	rand ()
	Returns a uniformly distributed random number greater than or equal to 0.0, and less or equal than 1.0. More...

static double	rand (double min, double max)
	Returns a uniformly distributed random number greater than or equal to min, and less or equal than max. More...

static double	randgauss (double mean, double standardDeviation)
	Returns a Gaussian distributed random number with the specified mean and standard deviation. More...

static double	exp (double a)
	Returns e raised to the specified power. More...

static double	log (double a)
	Returns the natural (base e) logarithm of a specified number. More...

static double	ln (double a)
	Returns the natural (base e) logarithm of a specified number. More...

static double	log10 (double a)
	Returns the base 10 logarithm of a specified number. More...

static double	lg (double a)
	Returns the base 10 logarithm of a specified number. More...

static double	log2 (double a)
	Returns the base 2 logarithm of a specified number. More...

static double	log (double a, double logBase)
	Returns the logarithm of a specified number in a specified base. More...

static double	deg (double x)
	Converts angle in radians to angle in degrees and returns it. More...

static double	rad (double x)
	Converts angle in degrees to angle in radians and returns it. More...

static double	sin (double a)
	Returns the sine of the specified angle. More...

static double	cos (double a)
	Returns the cosine of the specified angle. More...

static double	tg (double a)
	Returns the tangent of the specified angle. More...

static double	ctg (double x)
	Returns cotangent of the specified angle. More...

static double	arccos (double a)
	Returns the angle whose cosine is the specified number. More...

static double	arcsin (double a)
	Returns the angle whose sine is the specified number. More...

static double	arctg (double a)
	Returns the angle whose tangent is the specified number. More...

static double	arcctg (double x)
	Arc cotangent, inverse of 1/tan(x). More...

static double	arctg2 (double a, double b)
	Returns the angle whose tangent is the quotient of two specified numbers. More...

static double	Sinh (double a)
	Returns the hyperbolic sine of the specified angle. More...

static double	sinh (double a)
	Returns the hyperbolic sine of the specified angle. More...

static double	sh (double a)
	Returns the hyperbolic sine of the specified angle. More...

static double	ch (double a)
	Returns the hyperbolic cosine of the specified angle. More...

static double	th (double a)
	Returns the hyperbolic tangent of the specified angle. More...

static double	cth (double x)
	Hyperblic cotangent, 1/Math.Tanh. More...

static double	arsh (double x)
	Inverse hyperbolic sine. More...

static double	arch (double x)
	Inverse hyperbolic cosine. More...

static double	arth (double x)
	Inverse hyperbolic tangent. More...

static double	arcth (double x)
	Inverse hyperbolic cotangent. More...

static bool	CheckFactorialsArray ()
	Tests ehether the factoirals in the hard-coded array (factorials64) of factorials are correct; Throws ArgumentException if any of them is incorrect. More...

static void	TestFactorials ()
	Writes to the console all factorials that can be calculatet. More...

static void	TestFactorials (int max)
	Writes to the console the first n factorials. More...

static long	fac (int factor)
	Returns factorial of the specified number. More...

static long	facCalculated (long n)
	Returns factorial of the specified number - less efficient approac, but does not rely on hard coded array. More...

static long	fallingPower (long n, long p)
	Calculates and returns the falling power of the specified number. More...

static long	binomial (long n, long k)
	Returns binomial coefficient n over k . More...

static void	TestBinomialCoefficients ()
	Writes the first few binomial coefficients to the console. More...

static void	TestBinomialCoefficients (int nMax)
	Writes binomial coefficients up to the specified number to the console. More...

static double	Mean (ICollection< double > sample)
	Returns mean value of the specified sample. More...

static double	Mean (IVector sample)
	Returns mean value of the specified sample. More...

static double	Average (ICollection< double > sample)
	Returns mean value of the specified sample. More...

static double	Average (IVector sample)
	Returns mean value of the specified sample. More...

static double	StandardDeviation (ICollection< double > sample)
	Returns estimation of the standard deviation of a random value based on the specified sample. More...

static double	StandardDeviation (IVector sample)
	Returns estimation of the standard deviation of a random value based on the specified sample. More...

Properties
static double	e `[get]`
	Natural logarithmic base. More...

static double	pi `[get]`
	Ratio of the circumference of a circle to its diameter. More...

static double	zero `[get]`
	Zero (value 0.0). More...

static double	one `[get]`
	One (value 1.0). More...

Static Private Attributes
static Int64[]	factorials64
	Array of all factorials that do not produce overflow. More...

static bool	factorialsArrayChecked = false
	Whether or not factorials array has been tested. More...

Detailed Description

Defines some mathematical functions to be used in derived and other classes.

* Standard mathematical functions and constants with short names are implemented, e.g. sin() instesd of Math.Sin().

** These functions are public and static such that they can be used out of the derived classes, too.

*** In particular, some script classes derive from this one, in order to use simple-named mathematical functions.

** Some functions are defined with several names, in order to reduce probability of errors in scripts.

Member Function Documentation

static void IG.Num.M.Swap	(	ref double	a,
		ref double	b
	)

inlinestatic

Swaps values of the two specified variables of type double.

Parameters

a	First variable.
b	Second variable.

References IG.Num.s.

Referenced by IG.Num.InputOutputElementDefinition.GetDistortedBounds().

static void IG.Num.M.Swap	(	ref int	a,
		ref int	b
	)

inlinestatic

Swaps values of the two specified variables of type int.

Parameters

a	First variable.
b	Second variable.

References IG.Num.s.

static void IG.Num.M.Swap	(	ref string	a,
		ref string	b
	)

inlinestatic

Swaps values of the two specified variables of type string.

Parameters

a	First variable.
b	Second variable.

References IG.Num.s.

static double IG.Num.M.abs ( double a )

inlinestatic

Absolute value.

static double IG.Num.M.sign ( double a )

inlinestatic

Returns a value indicating the sign of a number.

static double IG.Num.M.ceil ( double a )

inlinestatic

Returns the smallest integral value that is greater than or equal to the specified decimal number.

static double IG.Num.M.floor ( double a )

inlinestatic

Returns the largest integer less than or equal to the specified number.

Referenced by IG.Forms.TimerControl.UpdateCdDisplay(), IG.Forms.TimerControl.UpdateCdInitialTime(), and IG.Forms.TimerControl.UpdateSwDisplay().

static double IG.Num.M.trunc ( double a )

inlinestatic

Calculates the integral part of a specified number.

static double IG.Num.M.min	(	double	a,
		double	b
	)

inlinestatic

Smallest of two numbers.

static double IG.Num.M.max	(	double	a,
		double	b
	)

inlinestatic

Largest of two numbers.

static double IG.Num.M.min	(	double	a,
		double	b,
		double	c
	)

inlinestatic

Smallest of three numbers.

static double IG.Num.M.max	(	double	a,
		double	b,
		double	c
	)

inlinestatic

Largest of three numbers.

static double IG.Num.M.min	(	double	a,
		double	b,
		double	c,
		double	d
	)

inlinestatic

Smallest of four numbers.

static double IG.Num.M.max	(	double	a,
		double	b,
		double	c,
		double	d
	)

inlinestatic

Largest of four numbers.

static double IG.Num.M.min	(	double	a,
		double	b,
		double	c,
		double	d,
		double	e
	)

inlinestatic

Smallest of five numbers.

static double IG.Num.M.max	(	double	a,
		double	b,
		double	c,
		double	d,
		double	e
	)

inlinestatic

Largest of five numbers.

static double IG.Num.M.min	(	double	a,
		double	b,
		double	c,
		double	d,
		double	e,
		double	f
	)

inlinestatic

Smallest of six numbers.

static double IG.Num.M.max	(	double	a,
		double	b,
		double	c,
		double	d,
		double	e,
		double	f
	)

inlinestatic

Largest of six numbers.

static double IG.Num.M.min ( params double[] numbers )

inlinestatic

Minimal of the specified values.

static double IG.Num.M.max ( params double[] numbers )

inlinestatic

Maximal of the specified values.

static double IG.Num.M.sum ( params double[] numbers )

inlinestatic

Sum of the specified values.

static double IG.Num.M.prod ( params double[] numbers )

inlinestatic

Product of the specified values.

static double IG.Num.M.pow	(	double	a,
		double	b
	)

inlinestatic

Returns a specified number raised to the specified power.

static double IG.Num.M.sqr ( double a )

inlinestatic

Returns the square of a specified number.

static double IG.Num.M.cube ( double a )

inlinestatic

Returns the square of a specified number.

static double IG.Num.M.pow2 ( double x )

inlinestatic

Square.

static double IG.Num.M.pow3 ( double x )

inlinestatic

3rd power.

static double IG.Num.M.pow4 ( double x )

inlinestatic

4th power.

static double IG.Num.M.pow5 ( double x )

inlinestatic

5th power.

static double IG.Num.M.pow6 ( double x )

inlinestatic

6th power.

static double IG.Num.M.sqrt ( double a )

inlinestatic

Returns the square root of a specified number.

static double IG.Num.M.root2 ( double a )

inlinestatic

Returns the square root of a specified number.

static double IG.Num.M.root3 ( double a )

inlinestatic

Returns the cubic root of a specified number.

static double IG.Num.M.rand ( )

inlinestatic

Returns a uniformly distributed random number greater than or equal to 0.0, and less or equal than 1.0.

References IG.Num.RandomGenerator.Global, and IG.Num.IRandomGenerator.NextDoubleInclusive().

static double IG.Num.M.rand	(	double	min,
		double	max
	)

inlinestatic

Returns a uniformly distributed random number greater than or equal to min, and less or equal than max.

References IG.Num.RandomGenerator.Global, and IG.Num.IRandomGenerator.NextDoubleInclusive().

static double IG.Num.M.randgauss	(	double	mean,
		double	standardDeviation
	)

inlinestatic

Returns a Gaussian distributed random number with the specified mean and standard deviation.

Parameters

mean	Mean value of the distribution.
standardDeviation	Standard deviation of the distribution.

References IG.Num.RandomGaussian.Global, and IG.Num.RandomGaussian.NextGaussian().

static double IG.Num.M.exp ( double a )

inlinestatic

Returns e raised to the specified power.

static double IG.Num.M.log ( double a )

inlinestatic

Returns the natural (base e) logarithm of a specified number.

static double IG.Num.M.ln ( double a )

inlinestatic

Returns the natural (base e) logarithm of a specified number.

static double IG.Num.M.log10 ( double a )

inlinestatic

Returns the base 10 logarithm of a specified number.

static double IG.Num.M.lg ( double a )

inlinestatic

Returns the base 10 logarithm of a specified number.

static double IG.Num.M.log2 ( double a )

inlinestatic

Returns the base 2 logarithm of a specified number.

static double IG.Num.M.log	(	double	a,
		double	logBase
	)

inlinestatic

Returns the logarithm of a specified number in a specified base.

Parameters

a	Number whose logarithm is returned.
logBase	Base of the logarithm.

static double IG.Num.M.deg ( double x )

inlinestatic

Converts angle in radians to angle in degrees and returns it.

static double IG.Num.M.rad ( double x )

inlinestatic

Converts angle in degrees to angle in radians and returns it.

static double IG.Num.M.sin ( double a )

inlinestatic

Returns the sine of the specified angle.

static double IG.Num.M.cos ( double a )

inlinestatic

Returns the cosine of the specified angle.

static double IG.Num.M.tg ( double a )

inlinestatic

Returns the tangent of the specified angle.

static double IG.Num.M.ctg ( double x )

inlinestatic

Returns cotangent of the specified angle.

static double IG.Num.M.arccos ( double a )

inlinestatic

Returns the angle whose cosine is the specified number.

static double IG.Num.M.arcsin ( double a )

inlinestatic

Returns the angle whose sine is the specified number.

static double IG.Num.M.arctg ( double a )

inlinestatic

Returns the angle whose tangent is the specified number.

static double IG.Num.M.arcctg ( double x )

inlinestatic

Arc cotangent, inverse of 1/tan(x).

static double IG.Num.M.arctg2	(	double	a,
		double	b
	)

inlinestatic

Returns the angle whose tangent is the quotient of two specified numbers.

static double IG.Num.M.Sinh ( double a )

inlinestatic

Returns the hyperbolic sine of the specified angle.

static double IG.Num.M.sinh ( double a )

inlinestatic

Returns the hyperbolic sine of the specified angle.

static double IG.Num.M.sh ( double a )

inlinestatic

Returns the hyperbolic sine of the specified angle.

static double IG.Num.M.ch ( double a )

inlinestatic

Returns the hyperbolic cosine of the specified angle.

static double IG.Num.M.th ( double a )

inlinestatic

Returns the hyperbolic tangent of the specified angle.

static double IG.Num.M.cth ( double x )

inlinestatic

Hyperblic cotangent, 1/Math.Tanh.

static double IG.Num.M.arsh ( double x )

inlinestatic

Inverse hyperbolic sine.

Referenced by IG.Num.Func.Cubic.Zeros().

static double IG.Num.M.arch ( double x )

inlinestatic

Inverse hyperbolic cosine.

Referenced by IG.Num.Func.Cubic.Zeros().

static double IG.Num.M.arth ( double x )

inlinestatic

Inverse hyperbolic tangent.

static double IG.Num.M.arcth ( double x )

inlinestatic

Inverse hyperbolic cotangent.

static bool IG.Num.M.CheckFactorialsArray ( )

inlinestatic

Tests ehether the factoirals in the hard-coded array (factorials64) of factorials are correct; Throws ArgumentException if any of them is incorrect.

Returns: true if test is successful.

static void IG.Num.M.TestFactorials ( )

inlinestatic

Writes to the console all factorials that can be calculatet.

static void IG.Num.M.TestFactorials ( int max )

inlinestatic

Writes to the console the first n factorials.

Parameters

max	Largest number whose factorial will be calculated.

static long IG.Num.M.fac ( int factor )

inlinestatic

Returns factorial of the specified number.

static long IG.Num.M.facCalculated ( long n )

inlinestatic

Returns factorial of the specified number - less efficient approac, but does not rely on hard coded array.

static long IG.Num.M.fallingPower	(	long	n,
		long	p
	)

inlinestatic

Calculates and returns the falling power of the specified number.

Parameters

n
p

See http://en.wikipedia.org/wiki/Falling_power

static long IG.Num.M.binomial	(	long	n,
		long	k
	)

inlinestatic

Returns binomial coefficient n over k .

Parameters

n
k

static void IG.Num.M.TestBinomialCoefficients ( )

inlinestatic

Writes the first few binomial coefficients to the console.

static void IG.Num.M.TestBinomialCoefficients ( int nMax )

inlinestatic

Writes binomial coefficients up to the specified number to the console.

Parameters

nMax	Maximal enumerator until which coefficients are written.

static double IG.Num.M.Mean ( ICollection< double > sample )

inlinestatic

Returns mean value of the specified sample.

Parameters

sample Collection containing observations within the sample.

static double IG.Num.M.Mean ( IVector sample )

inlinestatic

Returns mean value of the specified sample.

Parameters

sample Vector containing observations within the sample.

static double IG.Num.M.Average ( ICollection< double > sample )

inlinestatic

Returns mean value of the specified sample.

Parameters

sample Collection containing observations within the sample.

static double IG.Num.M.Average ( IVector sample )

inlinestatic

Returns mean value of the specified sample.

Parameters

sample Vector containing observations contained in the sample.

static double IG.Num.M.StandardDeviation ( ICollection< double > sample )

inlinestatic

Returns estimation of the standard deviation of a random value based on the specified sample.

Parameters

sample Collection containing all observations of the sample.

static double IG.Num.M.StandardDeviation ( IVector sample )

inlinestatic

Returns estimation of the standard deviation of a random value based on the specified sample.

Parameters

sample Vector containing all observations of the sample.

Member Data Documentation

Int64 [] IG.Num.M.factorials64

staticprivate

Initial value:

= { 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 
                                       362880, 3628800, 39916800, 479001600, 6227020800, 87178291200,
                                       1307674368000, 20922789888000, 355687428096000, 6402373705728000,
                                       121645100408832000, 2432902008176640000 }

Array of all factorials that do not produce overflow.

bool IG.Num.M.factorialsArrayChecked = false

staticprivate

Whether or not factorials array has been tested.

Property Documentation

double IG.Num.M.e

staticget

Natural logarithmic base.

double IG.Num.M.pi

staticget

Ratio of the circumference of a circle to its diameter.

double IG.Num.M.zero

staticget

Zero (value 0.0).

double IG.Num.M.one

staticget

One (value 1.0).

The documentation for this class was generated from the following file:

igbase/utilities/UtilMath.cs

Static Public Member Functions

Properties

Static Private Attributes

Detailed Description

Member Function Documentation

Member Data Documentation

Property Documentation