MathNet.Numerics

AppContext based switches to disable functionality, controllable through also in the host application through AppContext or by configuration with AppContextSwitchOverride. https://docs.microsoft.com/en-us/dotnet/framework/configure-apps/file-schema/runtime/appcontextswitchoverrides-element

Since AppContext is not supported on .NET Framework 4.0, a local implementation is used there instead, which cannot be controlled though configuration or through AppContext.

Useful extension methods for Arrays.

Copies the values from on array to another.

The source array. The destination array.

Copies the values from on array to another.

The source array. The destination array.

Copies the values from on array to another.

The source array. The destination array.

Copies the values from on array to another.

The source array. The destination array.

Enumerative Combinatorics and Counting.

Count the number of possible variations without repetition. The order matters and each object can be chosen only once.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen at most once. Maximum number of distinct variations.

Count the number of possible variations with repetition. The order matters and each object can be chosen more than once.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen 0, 1 or multiple times. Maximum number of distinct variations with repetition.

Count the number of possible combinations without repetition. The order does not matter and each object can be chosen only once.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen at most once. Maximum number of combinations.

Count the number of possible combinations with repetition. The order does not matter and an object can be chosen more than once.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen 0, 1 or multiple times. Maximum number of combinations with repetition.

Count the number of possible permutations (without repetition).

Number of (distinguishable) elements in the set. Maximum number of permutations without repetition.

Generate a random permutation, without repetition, by generating the index numbers 0 to N-1 and shuffle them randomly. Implemented using Fisher-Yates Shuffling.

An array of length N that contains (in any order) the integers of the interval [0, N). Number of (distinguishable) elements in the set. The random number generator to use. Optional; the default random source will be used if null.

Select a random permutation, without repetition, from a data array by reordering the provided array in-place. Implemented using Fisher-Yates Shuffling. The provided data array will be modified.

The data array to be reordered. The array will be modified by this routine. The random number generator to use. Optional; the default random source will be used if null.

Select a random permutation from a data sequence by returning the provided data in random order. Implemented using Fisher-Yates Shuffling.

The data elements to be reordered. The random number generator to use. Optional; the default random source will be used if null.

Generate a random combination, without repetition, by randomly selecting some of N elements.

Number of elements in the set. The random number generator to use. Optional; the default random source will be used if null. Boolean mask array of length N, for each item true if it is selected.

Generate a random combination, without repetition, by randomly selecting k of N elements.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen at most once. The random number generator to use. Optional; the default random source will be used if null. Boolean mask array of length N, for each item true if it is selected.

Select a random combination, without repetition, from a data sequence by selecting k elements in original order.

The data source to choose from. Number of elements (k) to choose from the data set. Each element is chosen at most once. The random number generator to use. Optional; the default random source will be used if null. The chosen combination, in the original order.

Generates a random combination, with repetition, by randomly selecting k of N elements.

Number of elements in the set. Number of elements to choose from the set. Elements can be chosen more than once. The random number generator to use. Optional; the default random source will be used if null. Integer mask array of length N, for each item the number of times it was selected.

Select a random combination, with repetition, from a data sequence by selecting k elements in original order.

The data source to choose from. Number of elements (k) to choose from the data set. Elements can be chosen more than once. The random number generator to use. Optional; the default random source will be used if null. The chosen combination with repetition, in the original order.

Generate a random variation, without repetition, by randomly selecting k of n elements with order. Implemented using partial Fisher-Yates Shuffling.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen at most once. The random number generator to use. Optional; the default random source will be used if null. An array of length K that contains the indices of the selections as integers of the interval [0, N).

Generate a random variation, without repetition, by randomly selecting k of n elements with order. This is an O(k) space-complexity implementation optimized for very large N.
The space complexity of Fisher-Yates Shuffling is O(n+k). When N is very large, the algorithm will be unexecutable in limited memory, and a more memory-efficient algorithm is needed.
You can explicitly cast N to if N is out of range of or memory, so that this special implementation is called. However, this implementation is slower than Fisher-Yates Shuffling: don't call it if time is more critical than space.
The K of type seems impossible, because the returned array is of size K and must all be stored in memory.

Number of elements in the set. Number of elements to choose from the set. Each element is chosen at most once. The random number generator to use. Optional; the default random source will be used if null. An array of length K that contains the indices of the selections as integers of the interval [0, N).

Select a random variation, without repetition, from a data sequence by randomly selecting k elements in random order. Implemented using partial Fisher-Yates Shuffling.

The data source to choose from. Number of elements (k) to choose from the set. Each element is chosen at most once. The random number generator to use. Optional; the default random source will be used if null. The chosen variation, in random order.

Generate a random variation, with repetition, by randomly selecting k of n elements with order.

Number of elements in the set. Number of elements to choose from the set. Elements can be chosen more than once. The random number generator to use. Optional; the default random source will be used if null. An array of length K that contains the indices of the selections as integers of the interval [0, N).

Select a random variation, with repetition, from a data sequence by randomly selecting k elements in random order.

32-bit single precision complex numbers class.

The class Complex32 provides all elementary operations on complex numbers. All the operators +, -, *, /, ==, != are defined in the canonical way. Additional complex trigonometric functions are also provided. Note that the Complex32 structures has two special constant values and .


            Complex32 x = new Complex32(1f,2f);
            Complex32 y = Complex32.FromPolarCoordinates(1f, Math.Pi);
            Complex32 z = (x + y) / (x - y);

For mathematical details about complex numbers, please have a look at the Wikipedia

The real component of the complex number.

The imaginary component of the complex number.

Initializes a new instance of the Complex32 structure with the given real and imaginary parts.

The value for the real component. The value for the imaginary component.

Creates a complex number from a point's polar coordinates.

A complex number. The magnitude, which is the distance from the origin (the intersection of the x-axis and the y-axis) to the number. The phase, which is the angle from the line to the horizontal axis, measured in radians.

Returns a new instance with a real number equal to zero and an imaginary number equal to zero.

Returns a new instance with a real number equal to one and an imaginary number equal to zero.

Returns a new instance with a real number equal to zero and an imaginary number equal to one.

Returns a new instance with real and imaginary numbers positive infinite.

Returns a new instance with real and imaginary numbers not a number.

Gets the real component of the complex number.

The real component of the complex number.

Gets the real imaginary component of the complex number.

The real imaginary component of the complex number.

Gets the phase or argument of this Complex32.

Phase always returns a value bigger than negative Pi and smaller or equal to Pi. If this Complex32 is zero, the Complex32 is assumed to be positive real with an argument of zero. The phase or argument of this Complex32

Gets the magnitude (or absolute value) of a complex number.

Assuming that magnitude of (inf,a) and (a,inf) and (inf,inf) is inf and (NaN,a), (a,NaN) and (NaN,NaN) is NaN The magnitude of the current instance.

Gets the squared magnitude (or squared absolute value) of a complex number.

The squared magnitude of the current instance.

Gets the unity of this complex (same argument, but on the unit circle; exp(I*arg))

The unity of this Complex32.

Gets a value indicating whether the Complex32 is zero.

true if this instance is zero; otherwise, false.

Gets a value indicating whether the Complex32 is one.

true if this instance is one; otherwise, false.

Gets a value indicating whether the Complex32 is the imaginary unit.

true if this instance is ImaginaryOne; otherwise, false.

Gets a value indicating whether the provided Complex32evaluates to a value that is not a number.

true if this instance is ; otherwise, false.

Gets a value indicating whether the provided Complex32 evaluates to an infinite value.

true if this instance is infinite; otherwise, false. True if it either evaluates to a complex infinity or to a directed infinity.

Gets a value indicating whether the provided Complex32 is real.

true if this instance is a real number; otherwise, false.

Gets a value indicating whether the provided Complex32 is real and not negative, that is >= 0.

true if this instance is real nonnegative number; otherwise, false.

Exponential of this Complex32 (exp(x), E^x).

The exponential of this complex number.

Natural Logarithm of this Complex32 (Base E).

The natural logarithm of this complex number.

Common Logarithm of this Complex32 (Base 10).

The common logarithm of this complex number.

Logarithm of this Complex32 with custom base.

The logarithm of this complex number.

Raise this Complex32 to the given value.

The exponent. The complex number raised to the given exponent.

Raise this Complex32 to the inverse of the given value.

The root exponent. The complex raised to the inverse of the given exponent.

The Square (power 2) of this Complex32

The square of this complex number.

The Square Root (power 1/2) of this Complex32

The square root of this complex number.

Evaluate all square roots of this Complex32.

Evaluate all cubic roots of this Complex32.

Equality test.

One of complex numbers to compare. The other complex numbers to compare. true if the real and imaginary components of the two complex numbers are equal; false otherwise.

Inequality test.

One of complex numbers to compare. The other complex numbers to compare. true if the real or imaginary components of the two complex numbers are not equal; false otherwise.

Unary addition.

The complex number to operate on. Returns the same complex number.

Unary minus.

The complex number to operate on. The negated value of the .

Addition operator. Adds two complex numbers together.

The result of the addition. One of the complex numbers to add. The other complex numbers to add.

Subtraction operator. Subtracts two complex numbers.

The result of the subtraction. The complex number to subtract from. The complex number to subtract.

Addition operator. Adds a complex number and float together.

The result of the addition. The complex numbers to add. The float value to add.

Subtraction operator. Subtracts float value from a complex value.

The result of the subtraction. The complex number to subtract from. The float value to subtract.

Addition operator. Adds a complex number and float together.

The result of the addition. The float value to add. The complex numbers to add.

Subtraction operator. Subtracts complex value from a float value.

The result of the subtraction. The float vale to subtract from. The complex value to subtract.

Multiplication operator. Multiplies two complex numbers.

The result of the multiplication. One of the complex numbers to multiply. The other complex number to multiply.

Multiplication operator. Multiplies a complex number with a float value.

The result of the multiplication. The float value to multiply. The complex number to multiply.

Multiplication operator. Multiplies a complex number with a float value.

The result of the multiplication. The complex number to multiply. The float value to multiply.

Division operator. Divides a complex number by another.

Enhanced Smith's algorithm for dividing two complex numbers The result of the division. The dividend. The divisor.

Helper method for dividing.

Re first Im first Re second Im second

Division operator. Divides a float value by a complex number.

Algorithm based on Smith's algorithm The result of the division. The dividend. The divisor.

Division operator. Divides a complex number by a float value.

The result of the division. The dividend. The divisor.

Computes the conjugate of a complex number and returns the result.

Returns the multiplicative inverse of a complex number.

Converts the value of the current complex number to its equivalent string representation in Cartesian form.

The string representation of the current instance in Cartesian form.

Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified format for its real and imaginary parts.

The string representation of the current instance in Cartesian form. A standard or custom numeric format string. is not a valid format string.

Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified culture-specific formatting information.

The string representation of the current instance in Cartesian form, as specified by . An object that supplies culture-specific formatting information.

Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified format and culture-specific format information for its real and imaginary parts.

The string representation of the current instance in Cartesian form, as specified by and . A standard or custom numeric format string. An object that supplies culture-specific formatting information. is not a valid format string.

Checks if two complex numbers are equal. Two complex numbers are equal if their corresponding real and imaginary components are equal.

Returns true if the two objects are the same object, or if their corresponding real and imaginary components are equal, false otherwise. The complex number to compare to with.

The hash code for the complex number.

The hash code of the complex number. The hash code is calculated as System.Math.Exp(ComplexMath.Absolute(complexNumber)).

Checks if two complex numbers are equal. Two complex numbers are equal if their corresponding real and imaginary components are equal.

Returns true if the two objects are the same object, or if their corresponding real and imaginary components are equal, false otherwise. The complex number to compare to with.

Creates a complex number based on a string. The string can be in the following formats (without the quotes): 'n', 'ni', 'n +/- ni', 'ni +/- n', 'n,n', 'n,ni,' '(n,n)', or '(n,ni)', where n is a float.

A complex number containing the value specified by the given string. the string to parse. An that supplies culture-specific formatting information.

Parse a part (real or complex) from a complex number.

Start Token. Is set to true if the part identified itself as being imaginary. An that supplies culture-specific formatting information. Resulting part as float.

Converts the string representation of a complex number to a single-precision complex number equivalent. A return value indicates whether the conversion succeeded or failed.

A string containing a complex number to convert. The parsed value. If the conversion succeeds, the result will contain a complex number equivalent to value. Otherwise the result will contain complex32.Zero. This parameter is passed uninitialized

Converts the string representation of a complex number to single-precision complex number equivalent. A return value indicates whether the conversion succeeded or failed.

A string containing a complex number to convert. An that supplies culture-specific formatting information about value. The parsed value. If the conversion succeeds, the result will contain a complex number equivalent to value. Otherwise the result will contain complex32.Zero. This parameter is passed uninitialized

Explicit conversion of a real decimal to a Complex32.

The decimal value to convert. The result of the conversion.

Explicit conversion of a Complex to a Complex32.

The decimal value to convert. The result of the conversion.

Implicit conversion of a real byte to a Complex32.

The byte value to convert. The result of the conversion.

Implicit conversion of a real short to a Complex32.

The short value to convert. The result of the conversion.

Implicit conversion of a signed byte to a Complex32.

The signed byte value to convert. The result of the conversion.

Implicit conversion of a unsigned real short to a Complex32.

The unsigned short value to convert. The result of the conversion.

Implicit conversion of a real int to a Complex32.

The int value to convert. The result of the conversion.

Implicit conversion of a BigInteger int to a Complex32.

The BigInteger value to convert. The result of the conversion.

Implicit conversion of a real long to a Complex32.

The long value to convert. The result of the conversion.

Implicit conversion of a real uint to a Complex32.

The uint value to convert. The result of the conversion.

Implicit conversion of a real ulong to a Complex32.

The ulong value to convert. The result of the conversion.

Implicit conversion of a real float to a Complex32.

The float value to convert. The result of the conversion.

Implicit conversion of a real double to a Complex32.

The double value to convert. The result of the conversion.

Converts this Complex32 to a .

A with the same values as this Complex32.

Returns the additive inverse of a specified complex number.

The result of the real and imaginary components of the value parameter multiplied by -1. A complex number.

Computes the conjugate of a complex number and returns the result.

The conjugate of . A complex number.

Adds two complex numbers and returns the result.

The sum of and . The first complex number to add. The second complex number to add.

Subtracts one complex number from another and returns the result.

The result of subtracting from . The value to subtract from (the minuend). The value to subtract (the subtrahend).

Returns the product of two complex numbers.

The product of the and parameters. The first complex number to multiply. The second complex number to multiply.

Divides one complex number by another and returns the result.

The quotient of the division. The complex number to be divided. The complex number to divide by.

Returns the multiplicative inverse of a complex number.

The reciprocal of . A complex number.

Returns the square root of a specified complex number.

The square root of . A complex number.

Gets the absolute value (or magnitude) of a complex number.

The absolute value of . A complex number.

Returns e raised to the power specified by a complex number.

The number e raised to the power . A complex number that specifies a power.

Returns a specified complex number raised to a power specified by a complex number.

The complex number raised to the power . A complex number to be raised to a power. A complex number that specifies a power.

Returns a specified complex number raised to a power specified by a single-precision floating-point number.

The complex number raised to the power . A complex number to be raised to a power. A single-precision floating-point number that specifies a power.

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

The natural (base e) logarithm of . A complex number.

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

The logarithm of in base . A complex number. The base of the logarithm.

Returns the base-10 logarithm of a specified complex number.

The base-10 logarithm of . A complex number.

Returns the sine of the specified complex number.

The sine of . A complex number.

Returns the cosine of the specified complex number.

The cosine of . A complex number.

Returns the tangent of the specified complex number.

The tangent of . A complex number.

Returns the angle that is the arc sine of the specified complex number.

The angle which is the arc sine of . A complex number.

Returns the angle that is the arc cosine of the specified complex number.

The angle, measured in radians, which is the arc cosine of . A complex number that represents a cosine.

Returns the angle that is the arc tangent of the specified complex number.

The angle that is the arc tangent of . A complex number.

Returns the hyperbolic sine of the specified complex number.

The hyperbolic sine of . A complex number.

Returns the hyperbolic cosine of the specified complex number.

The hyperbolic cosine of . A complex number.

Returns the hyperbolic tangent of the specified complex number.

The hyperbolic tangent of . A complex number.

Extension methods for the Complex type provided by System.Numerics

Gets the squared magnitude of the Complex number.

The number to perform this operation on. The squared magnitude of the Complex number.

Gets the squared magnitude of the Complex number.

The number to perform this operation on. The squared magnitude of the Complex number.

Gets the unity of this complex (same argument, but on the unit circle; exp(I*arg))

The unity of this Complex.

Gets the conjugate of the Complex number.

The number to perform this operation on. The semantic of setting the conjugate is such that


            // a, b of type Complex32
            a.Conjugate = b;

is equivalent to


            // a, b of type Complex32
            a = b.Conjugate

The conjugate of the number.

Returns the multiplicative inverse of a complex number.

Exponential of this Complex (exp(x), E^x).

The number to perform this operation on. The exponential of this complex number.

Natural Logarithm of this Complex (Base E).

The number to perform this operation on. The natural logarithm of this complex number.

Common Logarithm of this Complex (Base 10).

The common logarithm of this complex number.

Logarithm of this Complex with custom base.

The logarithm of this complex number.

Raise this Complex to the given value.

The number to perform this operation on. The exponent. The complex number raised to the given exponent.

Raise this Complex to the inverse of the given value.

The number to perform this operation on. The root exponent. The complex raised to the inverse of the given exponent.

The Square (power 2) of this Complex

The number to perform this operation on. The square of this complex number.

The Square Root (power 1/2) of this Complex

The number to perform this operation on. The square root of this complex number.

Evaluate all square roots of this Complex.

Evaluate all cubic roots of this Complex.

Gets a value indicating whether the Complex32 is zero.

The number to perform this operation on. true if this instance is zero; otherwise, false.

Gets a value indicating whether the Complex32 is one.

The number to perform this operation on. true if this instance is one; otherwise, false.

Gets a value indicating whether the Complex32 is the imaginary unit.

true if this instance is ImaginaryOne; otherwise, false. The number to perform this operation on.

Gets a value indicating whether the provided Complex32evaluates to a value that is not a number.

The number to perform this operation on. true if this instance is NaN; otherwise, false.

Gets a value indicating whether the provided Complex32 evaluates to an infinite value.

The number to perform this operation on. true if this instance is infinite; otherwise, false. True if it either evaluates to a complex infinity or to a directed infinity.

Gets a value indicating whether the provided Complex32 is real.

The number to perform this operation on. true if this instance is a real number; otherwise, false.

Gets a value indicating whether the provided Complex32 is real and not negative, that is >= 0.

The number to perform this operation on. true if this instance is real nonnegative number; otherwise, false.

Returns a Norm of a value of this type, which is appropriate for measuring how close this value is to zero.

Returns a Norm of the difference of two values of this type, which is appropriate for measuring how close together these two values are.

A complex number containing the value specified by the given string. The string to parse.

A complex number containing the value specified by the given string. the string to parse. An that supplies culture-specific formatting information.

Parse a part (real or complex) from a complex number.

Start Token. Is set to true if the part identified itself as being imaginary. An that supplies culture-specific formatting information. Resulting part as double.

Converts the string representation of a complex number to a double-precision complex number equivalent. A return value indicates whether the conversion succeeded or failed.

A string containing a complex number to convert. The parsed value. If the conversion succeeds, the result will contain a complex number equivalent to value. Otherwise the result will contain Complex.Zero. This parameter is passed uninitialized.

Converts the string representation of a complex number to double-precision complex number equivalent. A return value indicates whether the conversion succeeded or failed.

Creates a Complex32 number based on a string. The string can be in the following formats (without the quotes): 'n', 'ni', 'n +/- ni', 'ni +/- n', 'n,n', 'n,ni,' '(n,n)', or '(n,ni)', where n is a double.

A complex number containing the value specified by the given string. the string to parse.

A complex number containing the value specified by the given string. the string to parse. An that supplies culture-specific formatting information.

Converts the string representation of a complex number to a single-precision complex number equivalent. A return value indicates whether the conversion succeeded or failed.

Converts the string representation of a complex number to single-precision complex number equivalent. A return value indicates whether the conversion succeeded or failed.

A string containing a complex number to convert. An that supplies culture-specific formatting information about value. The parsed value. If the conversion succeeds, the result will contain a complex number equivalent to value. Otherwise the result will contain Complex.Zero. This parameter is passed uninitialized.

A collection of frequently used mathematical constants.

The number e

The number log[2](e)

The number log[10](e)

The number log[e](2)

The number log[e](10)

The number log[e](pi)

The number log[e](2*pi)/2

The number 1/e

The number sqrt(e)

The number sqrt(2)

The number sqrt(3)

The number sqrt(1/2) = 1/sqrt(2) = sqrt(2)/2

The number sqrt(3)/2

The number pi

The number pi*2

The number pi/2

The number pi*3/2

The number pi/4

The number sqrt(pi)

The number sqrt(2pi)

The number sqrt(pi/2)

The number sqrt(2*pi*e)

The number log(sqrt(2*pi))

The number log(sqrt(2*pi*e))

The number log(2 * sqrt(e / pi))

The number 1/pi

The number 2/pi

The number 1/sqrt(pi)

The number 1/sqrt(2pi)

The number 2/sqrt(pi)

The number 2 * sqrt(e / pi)

The number (pi)/180 - factor to convert from Degree (deg) to Radians (rad).

The number (pi)/200 - factor to convert from NewGrad (grad) to Radians (rad).

The number ln(10)/20 - factor to convert from Power Decibel (dB) to Neper (Np). Use this version when the Decibel represent a power gain but the compared values are not powers (e.g. amplitude, current, voltage).

The number ln(10)/10 - factor to convert from Neutral Decibel (dB) to Neper (Np). Use this version when either both or neither of the Decibel and the compared values represent powers.

The Catalan constant

Sum(k=0 -> inf){ (-1)^k/(2*k + 1)2 }

The Euler-Mascheroni constant

lim(n -> inf){ Sum(k=1 -> n) { 1/k - log(n) } }

The number (1+sqrt(5))/2, also known as the golden ratio

The Glaisher constant

e^(1/12 - Zeta(-1))

The Khinchin constant

prod(k=1 -> inf){1+1/(k*(k+2))^log(k,2)}

The size of a double in bytes.

The size of an int in bytes.

The size of a float in bytes.

The size of a Complex in bytes.

Speed of Light in Vacuum: c_0 = 2.99792458e8 [m s^-1] (defined, exact; 2007 CODATA)

Magnetic Permeability in Vacuum: mu_0 = 4*Pi * 10^-7 [N A^-2 = kg m A^-2 s^-2] (defined, exact; 2007 CODATA)

Electric Permittivity in Vacuum: epsilon_0 = 1/(mu_0*c_0^2) [F m^-1 = A^2 s^4 kg^-1 m^-3] (defined, exact; 2007 CODATA)

Characteristic Impedance of Vacuum: Z_0 = mu_0*c_0 [Ohm = m^2 kg s^-3 A^-2] (defined, exact; 2007 CODATA)

Newtonian Constant of Gravitation: G = 6.67429e-11 [m^3 kg^-1 s^-2] (2007 CODATA)

Planck's constant: h = 6.62606896e-34 [J s = m^2 kg s^-1] (2007 CODATA)

Reduced Planck's constant: h_bar = h / (2*Pi) [J s = m^2 kg s^-1] (2007 CODATA)

Planck mass: m_p = (h_bar*c_0/G)^(1/2) [kg] (2007 CODATA)

Planck temperature: T_p = (h_bar*c_0^5/G)^(1/2)/k [K] (2007 CODATA)

Planck length: l_p = h_bar/(m_p*c_0) [m] (2007 CODATA)

Planck time: t_p = l_p/c_0 [s] (2007 CODATA)

Elementary Electron Charge: e = 1.602176487e-19 [C = A s] (2007 CODATA)

Magnetic Flux Quantum: theta_0 = h/(2*e) [Wb = m^2 kg s^-2 A^-1] (2007 CODATA)

Conductance Quantum: G_0 = 2*e^2/h [S = m^-2 kg^-1 s^3 A^2] (2007 CODATA)

Josephson Constant: K_J = 2*e/h [Hz V^-1] (2007 CODATA)

Von Klitzing Constant: R_K = h/e^2 [Ohm = m^2 kg s^-3 A^-2] (2007 CODATA)

Bohr Magneton: mu_B = e*h_bar/2*m_e [J T^-1] (2007 CODATA)

Nuclear Magneton: mu_N = e*h_bar/2*m_p [J T^-1] (2007 CODATA)

Fine Structure Constant: alpha = e^2/4*Pi*e_0*h_bar*c_0 [1] (2007 CODATA)

Rydberg Constant: R_infty = alpha^2*m_e*c_0/2*h [m^-1] (2007 CODATA)

Bor Radius: a_0 = alpha/4*Pi*R_infty [m] (2007 CODATA)

Hartree Energy: E_h = 2*R_infty*h*c_0 [J] (2007 CODATA)

Quantum of Circulation: h/2*m_e [m^2 s^-1] (2007 CODATA)

Fermi Coupling Constant: G_F/(h_bar*c_0)^3 [GeV^-2] (2007 CODATA)

Weak Mixin Angle: sin^2(theta_W) [1] (2007 CODATA)

Electron Mass: [kg] (2007 CODATA)

Electron Mass Energy Equivalent: [J] (2007 CODATA)

Electron Molar Mass: [kg mol^-1] (2007 CODATA)

Electron Compton Wavelength: [m] (2007 CODATA)

Classical Electron Radius: [m] (2007 CODATA)

Thomson Cross Section: [m^2] (2002 CODATA)

Electron Magnetic Moment: [J T^-1] (2007 CODATA)

Electon G-Factor: [1] (2007 CODATA)

Muon Mass: [kg] (2007 CODATA)

Muon Mass Energy Equivalent: [J] (2007 CODATA)

Muon Molar Mass: [kg mol^-1] (2007 CODATA)

Muon Compton Wavelength: [m] (2007 CODATA)

Muon Magnetic Moment: [J T^-1] (2007 CODATA)

Muon G-Factor: [1] (2007 CODATA)

Tau Mass: [kg] (2007 CODATA)

Tau Mass Energy Equivalent: [J] (2007 CODATA)

Tau Molar Mass: [kg mol^-1] (2007 CODATA)

Tau Compton Wavelength: [m] (2007 CODATA)

Proton Mass: [kg] (2007 CODATA)

Proton Mass Energy Equivalent: [J] (2007 CODATA)

Proton Molar Mass: [kg mol^-1] (2007 CODATA)

Proton Compton Wavelength: [m] (2007 CODATA)

Proton Magnetic Moment: [J T^-1] (2007 CODATA)

Proton G-Factor: [1] (2007 CODATA)

Proton Shielded Magnetic Moment: [J T^-1] (2007 CODATA)

Proton Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)

Proton Shielded Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)

Neutron Mass: [kg] (2007 CODATA)

Neutron Mass Energy Equivalent: [J] (2007 CODATA)

Neutron Molar Mass: [kg mol^-1] (2007 CODATA)

Neuron Compton Wavelength: [m] (2007 CODATA)

Neutron Magnetic Moment: [J T^-1] (2007 CODATA)

Neutron G-Factor: [1] (2007 CODATA)

Neutron Gyro-Magnetic Ratio: [s^-1 T^-1] (2007 CODATA)

Deuteron Mass: [kg] (2007 CODATA)

Deuteron Mass Energy Equivalent: [J] (2007 CODATA)

Deuteron Molar Mass: [kg mol^-1] (2007 CODATA)

Deuteron Magnetic Moment: [J T^-1] (2007 CODATA)

Helion Mass: [kg] (2007 CODATA)

Helion Mass Energy Equivalent: [J] (2007 CODATA)

Helion Molar Mass: [kg mol^-1] (2007 CODATA)

Avogadro constant: [mol^-1] (2010 CODATA)

The SI prefix factor corresponding to 1 000 000 000 000 000 000 000 000

The SI prefix factor corresponding to 1 000 000 000 000 000 000 000

The SI prefix factor corresponding to 1 000 000 000 000 000 000

The SI prefix factor corresponding to 1 000 000 000 000 000

The SI prefix factor corresponding to 1 000 000 000 000

The SI prefix factor corresponding to 1 000 000 000

The SI prefix factor corresponding to 1 000 000

The SI prefix factor corresponding to 1 000

The SI prefix factor corresponding to 100

The SI prefix factor corresponding to 10

The SI prefix factor corresponding to 0.1

The SI prefix factor corresponding to 0.01

The SI prefix factor corresponding to 0.001

The SI prefix factor corresponding to 0.000 001

The SI prefix factor corresponding to 0.000 000 001

The SI prefix factor corresponding to 0.000 000 000 001

The SI prefix factor corresponding to 0.000 000 000 000 001

The SI prefix factor corresponding to 0.000 000 000 000 000 001

The SI prefix factor corresponding to 0.000 000 000 000 000 000 001

The SI prefix factor corresponding to 0.000 000 000 000 000 000 000 001

Sets parameters for the library.

Use a specific provider if configured, e.g. using environment variables, or fall back to the best providers.

Use the best provider available.

Use the Intel MKL native provider for linear algebra. Throws if it is not available or failed to initialize, in which case the previous provider is still active.

Try to use the Intel MKL native provider for linear algebra.

True if the provider was found and initialized successfully. False if it failed and the previous provider is still active.

Use the Nvidia CUDA native provider for linear algebra. Throws if it is not available or failed to initialize, in which case the previous provider is still active.

Try to use the Nvidia CUDA native provider for linear algebra.

True if the provider was found and initialized successfully. False if it failed and the previous provider is still active.

Use the OpenBLAS native provider for linear algebra. Throws if it is not available or failed to initialize, in which case the previous provider is still active.

Try to use the OpenBLAS native provider for linear algebra.

True if the provider was found and initialized successfully. False if it failed and the previous provider is still active.

Try to use any available native provider in an undefined order.

True if one of the native providers was found and successfully initialized. False if it failed and the previous provider is still active.

Gets or sets a value indicating whether the distribution classes check validate each parameter. For the multivariate distributions this could involve an expensive matrix factorization. The default setting of this property is true.

Gets or sets a value indicating whether to use thread safe random number generators (RNG). Thread safe RNG about two and half time slower than non-thread safe RNG.

true to use thread safe random number generators ; otherwise, false.

Optional path to try to load native provider binaries from.

Gets or sets a value indicating how many parallel worker threads shall be used when parallelization is applicable.

Default to the number of processor cores, must be between 1 and 1024 (inclusive).

Gets or sets the TaskScheduler used to schedule the worker tasks.

Gets or sets the order of the matrix when linear algebra provider must calculate multiply in parallel threads.

The order. Default 64, must be at least 3.

Gets or sets the number of elements a vector or matrix must contain before we multiply threads.

Number of elements. Default 300, must be at least 3.

Numerical Derivative.

Initialized a NumericalDerivative with the given points and center.

Initialized a NumericalDerivative with the default points and center for the given order.

Evaluates the derivative of a scalar univariate function.

Univariate function handle. Point at which to evaluate the derivative. Derivative order.

Creates a function handle for the derivative of a scalar univariate function.

Univariate function handle. Derivative order.

Evaluates the first derivative of a scalar univariate function.

Univariate function handle. Point at which to evaluate the derivative.

Creates a function handle for the first derivative of a scalar univariate function.

Univariate function handle.

Evaluates the second derivative of a scalar univariate function.

Univariate function handle. Point at which to evaluate the derivative.

Creates a function handle for the second derivative of a scalar univariate function.

Univariate function handle.

Evaluates the partial derivative of a multivariate function.

Multivariate function handle. Vector at which to evaluate the derivative. Index of independent variable for partial derivative. Derivative order.

Creates a function handle for the partial derivative of a multivariate function.

Multivariate function handle. Index of independent variable for partial derivative. Derivative order.

Evaluates the first partial derivative of a multivariate function.

Multivariate function handle. Vector at which to evaluate the derivative. Index of independent variable for partial derivative.

Creates a function handle for the first partial derivative of a multivariate function.

Multivariate function handle. Index of independent variable for partial derivative.

Evaluates the partial derivative of a bivariate function.

Bivariate function handle. First argument at which to evaluate the derivative. Second argument at which to evaluate the derivative. Index of independent variable for partial derivative. Derivative order.

Creates a function handle for the partial derivative of a bivariate function.

Bivariate function handle. Index of independent variable for partial derivative. Derivative order.

Evaluates the first partial derivative of a bivariate function.

Bivariate function handle. First argument at which to evaluate the derivative. Second argument at which to evaluate the derivative. Index of independent variable for partial derivative.

Creates a function handle for the first partial derivative of a bivariate function.

Bivariate function handle. Index of independent variable for partial derivative.

Class to calculate finite difference coefficients using Taylor series expansion method. For n points, coefficients are calculated up to the maximum derivative order possible (n-1). The current function value position specifies the "center" for surrounding coefficients. Selecting the first, middle or last positions represent forward, backwards and central difference methods.

Number of points for finite difference coefficients. Changing this value recalculates the coefficients table.

Initializes a new instance of the class.

Number of finite difference coefficients.

Gets the finite difference coefficients for a specified center and order.

Current function position with respect to coefficients. Must be within point range. Order of finite difference coefficients. Vector of finite difference coefficients.

Gets the finite difference coefficients for all orders at a specified center.

Current function position with respect to coefficients. Must be within point range. Rectangular array of coefficients, with columns specifying order.

Type of finite different step size.

The absolute step size value will be used in numerical derivatives, regardless of order or function parameters.

A base step size value, h, will be scaled according to the function input parameter. A common example is hx = h*(1+abs(x)), however this may vary depending on implementation. This definition only guarantees that the only scaling will be relative to the function input parameter and not the order of the finite difference derivative.

A base step size value, eps (typically machine precision), is scaled according to the finite difference coefficient order and function input parameter. The initial scaling according to finite different coefficient order can be thought of as producing a base step size, h, that is equivalent to scaling. This step size is then scaled according to the function input parameter. Although implementation may vary, an example of second order accurate scaling may be (eps)^(1/3)*(1+abs(x)).

Class to evaluate the numerical derivative of a function using finite difference approximations. Variable point and center methods can be initialized . This class can also be used to return function handles (delegates) for a fixed derivative order and variable. It is possible to evaluate the derivative and partial derivative of univariate and multivariate functions respectively.

Initializes a NumericalDerivative class with the default 3 point center difference method.

Initialized a NumericalDerivative class.

Number of points for finite difference derivatives. Location of the center with respect to other points. Value ranges from zero to points-1.

Sets and gets the finite difference step size. This value is for each function evaluation if relative step size types are used. If the base step size used in scaling is desired, see .

Setting then getting the StepSize may return a different value. This is not unusual since a user-defined step size is converted to a base-2 representable number to improve finite difference accuracy.

Sets and gets the base finite difference step size. This assigned value to this parameter is only used if is set to RelativeX. However, if the StepType is Relative, it will contain the base step size computed from based on the finite difference order.

Sets and gets the base finite difference step size. This parameter is only used if is set to Relative. By default this is set to machine epsilon, from which is computed.

Sets and gets the location of the center point for the finite difference derivative.

Number of times a function is evaluated for numerical derivatives.

Type of step size for computing finite differences. If set to absolute, dx = h. If set to relative, dx = (1+abs(x))*h^(2/(order+1)). This provides accurate results when h is approximately equal to the square-root of machine accuracy, epsilon.

Evaluates the derivative of equidistant points using the finite difference method.

Vector of points StepSize apart. Derivative order. Finite difference step size. Derivative of points of the specified order.

Evaluates the derivative of a scalar univariate function.

Supplying the optional argument currentValue will reduce the number of function evaluations required to calculate the finite difference derivative. Function handle. Point at which to compute the derivative. Derivative order. Current function value at center. Function derivative at x of the specified order.

Creates a function handle for the derivative of a scalar univariate function.

Input function handle. Derivative order. Function handle that evaluates the derivative of input function at a fixed order.

Evaluates the partial derivative of a multivariate function.

Multivariate function handle. Vector at which to evaluate the derivative. Index of independent variable for partial derivative. Derivative order. Current function value at center. Function partial derivative at x of the specified order.

Evaluates the partial derivatives of a multivariate function array.

This function assumes the input vector x is of the correct length for f. Multivariate vector function array handle. Vector at which to evaluate the derivatives. Index of independent variable for partial derivative. Derivative order. Current function value at center. Vector of functions partial derivatives at x of the specified order.

Creates a function handle for the partial derivative of a multivariate function.

Input function handle. Index of the independent variable for partial derivative. Derivative order. Function handle that evaluates partial derivative of input function at a fixed order.

Creates a function handle for the partial derivative of a vector multivariate function.

Input function handle. Index of the independent variable for partial derivative. Derivative order. Function handle that evaluates partial derivative of input function at fixed order.

Evaluates the mixed partial derivative of variable order for multivariate functions.

This function recursively uses to evaluate mixed partial derivative. Therefore, it is more efficient to call for higher order derivatives of a single independent variable. Multivariate function handle. Points at which to evaluate the derivative. Vector of indices for the independent variables at descending derivative orders. Highest order of differentiation. Current function value at center. Function mixed partial derivative at x of the specified order.

Evaluates the mixed partial derivative of variable order for multivariate function arrays.

This function recursively uses to evaluate mixed partial derivative. Therefore, it is more efficient to call for higher order derivatives of a single independent variable. Multivariate function array handle. Vector at which to evaluate the derivative. Vector of indices for the independent variables at descending derivative orders. Highest order of differentiation. Current function value at center. Function mixed partial derivatives at x of the specified order.

Creates a function handle for the mixed partial derivative of a multivariate function.

Input function handle. Vector of indices for the independent variables at descending derivative orders. Highest derivative order. Function handle that evaluates the fixed mixed partial derivative of input function at fixed order.

Creates a function handle for the mixed partial derivative of a multivariate vector function.

Input vector function handle. Vector of indices for the independent variables at descending derivative orders. Highest derivative order. Function handle that evaluates the fixed mixed partial derivative of input function at fixed order.

Resets the evaluation counter.

Class for evaluating the Hessian of a smooth continuously differentiable function using finite differences. By default, a central 3-point method is used.

Number of function evaluations.

Creates a numerical Hessian object with a three point central difference method.

Creates a numerical Hessian with a specified differentiation scheme.

Number of points for Hessian evaluation. Center point for differentiation.

Evaluates the Hessian of the scalar univariate function f at points x.

Scalar univariate function handle. Point at which to evaluate Hessian. Hessian tensor.

Evaluates the Hessian of a multivariate function f at points x.

This method of computing the Hessian is only valid for Lipschitz continuous functions. The function mirrors the Hessian along the diagonal since d2f/dxdy = d2f/dydx for continuously differentiable functions. Multivariate function handle.> Points at which to evaluate Hessian.> Hessian tensor.

Resets the function evaluation counter for the Hessian.

Class for evaluating the Jacobian of a function using finite differences. By default, a central 3-point method is used.

Number of function evaluations.

Creates a numerical Jacobian object with a three point central difference method.

Creates a numerical Jacobian with a specified differentiation scheme.

Number of points for Jacobian evaluation. Center point for differentiation.

Evaluates the Jacobian of scalar univariate function f at point x.

Scalar univariate function handle. Point at which to evaluate Jacobian. Jacobian vector.

Evaluates the Jacobian of a multivariate function f at vector x.

This function assumes that the length of vector x consistent with the argument count of f. Multivariate function handle. Points at which to evaluate Jacobian. Jacobian vector.

Evaluates the Jacobian of a multivariate function f at vector x given a current function value.

To minimize the number of function evaluations, a user can supply the current value of the function to be used in computing the Jacobian. This value must correspond to the "center" location for the finite differencing. If a scheme is used where the center value is not evaluated, this will provide no added efficiency. This method also assumes that the length of vector x consistent with the argument count of f. Multivariate function handle. Points at which to evaluate Jacobian. Current function value at finite difference center. Jacobian vector.

Evaluates the Jacobian of a multivariate function array f at vector x.

Multivariate function array handle. Vector at which to evaluate Jacobian. Jacobian matrix.

Evaluates the Jacobian of a multivariate function array f at vector x given a vector of current function values.

To minimize the number of function evaluations, a user can supply a vector of current values of the functions to be used in computing the Jacobian. These value must correspond to the "center" location for the finite differencing. If a scheme is used where the center value is not evaluated, this will provide no added efficiency. This method also assumes that the length of vector x consistent with the argument count of f. Multivariate function array handle. Vector at which to evaluate Jacobian. Vector of current function values. Jacobian matrix.

Resets the function evaluation counter for the Jacobian.

Evaluates the Riemann-Liouville fractional derivative that uses the double exponential integration.

order = 1.0 : normal derivative order = 0.5 : semi-derivative order = -0.5 : semi-integral order = -1.0 : normal integral The analytic smooth function to differintegrate. The evaluation point. The order of fractional derivative. The reference point of integration. The expected relative accuracy of the Double-Exponential integration. Approximation of the differintegral of order n at x.

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Legendre integration.

order = 1.0 : normal derivative order = 0.5 : semi-derivative order = -0.5 : semi-integral order = -1.0 : normal integral The analytic smooth function to differintegrate. The evaluation point. The order of fractional derivative. The reference point of integration. The number of Gauss-Legendre points. Approximation of the differintegral of order n at x.

Evaluates the Riemann-Liouville fractional derivative that uses the Gauss-Kronrod integration.

order = 1.0 : normal derivative order = 0.5 : semi-derivative order = -0.5 : semi-integral order = -1.0 : normal integral The analytic smooth function to differintegrate. The evaluation point. The order of fractional derivative. The reference point of integration. The expected relative accuracy of the Gauss-Kronrod integration. The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points. Approximation of the differintegral of order n at x.

Metrics to measure the distance between two structures.

Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.

Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.

Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.

Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.

Euclidean Distance, i.e. the L2-norm of the difference.

Manhattan Distance, i.e. the L1-norm of the difference.

Chebyshev Distance, i.e. the Infinity-norm of the difference.

Minkowski Distance, i.e. the generalized p-norm of the difference.

Canberra Distance, a weighted version of the L1-norm of the difference.

Cosine Distance, representing the angular distance while ignoring the scale.

Hamming Distance, i.e. the number of positions that have different values in the vectors.

Pearson's distance, i.e. 1 - the person correlation coefficient.

Jaccard distance, i.e. 1 - the Jaccard index.

Thrown if a or b are null. Throw if a and b are of different lengths. Jaccard distance.

Jaccard distance, i.e. 1 - the Jaccard index.

Thrown if a or b are null. Throw if a and b are of different lengths. Jaccard distance.

Discrete Univariate Bernoulli distribution. The Bernoulli distribution is a distribution over bits. The parameter p specifies the probability that a 1 is generated. Wikipedia - Bernoulli distribution.

Initializes a new instance of the Bernoulli class.

The probability (p) of generating one. Range: 0 ≤ p ≤ 1. If the Bernoulli parameter is not in the range [0,1].

Initializes a new instance of the Bernoulli class.

The probability (p) of generating one. Range: 0 ≤ p ≤ 1. The random number generator which is used to draw random samples. If the Bernoulli parameter is not in the range [0,1].

A string representation of the distribution.

a string representation of the distribution.

Tests whether the provided values are valid parameters for this distribution.

The probability (p) of generating one. Range: 0 ≤ p ≤ 1.

Gets the probability of generating a one. Range: 0 ≤ p ≤ 1.

Gets or sets the random number generator which is used to draw random samples.

Gets the mean of the distribution.

Gets the standard deviation of the distribution.

Gets the variance of the distribution.

Gets the entropy of the distribution.

Gets the skewness of the distribution.

Gets the smallest element in the domain of the distributions which can be represented by an integer.

Gets the largest element in the domain of the distributions which can be represented by an integer.

Gets the mode of the distribution.

Gets all modes of the distribution.

Gets the median of the distribution.

Computes the probability mass (PMF) at k, i.e. P(X = k).

The location in the domain where we want to evaluate the probability mass function. the probability mass at location .

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).

The location in the domain where we want to evaluate the log probability mass function. the log probability mass at location .

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).

The location at which to compute the cumulative distribution function. the cumulative distribution at location .

Computes the probability mass (PMF) at k, i.e. P(X = k).

The location in the domain where we want to evaluate the probability mass function. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. the probability mass at location .

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).

The location in the domain where we want to evaluate the log probability mass function. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. the log probability mass at location .

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).

The location at which to compute the cumulative distribution function. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. the cumulative distribution at location .

Generates one sample from the Bernoulli distribution.

The random source to use. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. A random sample from the Bernoulli distribution.

Samples a Bernoulli distributed random variable.

A sample from the Bernoulli distribution.

Fills an array with samples generated from the distribution.

Samples an array of Bernoulli distributed random variables.

a sequence of samples from the distribution.

Samples a Bernoulli distributed random variable.

The random number generator to use. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. A sample from the Bernoulli distribution.

Samples a sequence of Bernoulli distributed random variables.

The random number generator to use. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. a sequence of samples from the distribution.

Fills an array with samples generated from the distribution.

The random number generator to use. The array to fill with the samples. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. a sequence of samples from the distribution.

Samples a Bernoulli distributed random variable.

The probability (p) of generating one. Range: 0 ≤ p ≤ 1. A sample from the Bernoulli distribution.

Samples a sequence of Bernoulli distributed random variables.

The probability (p) of generating one. Range: 0 ≤ p ≤ 1. a sequence of samples from the distribution.

Fills an array with samples generated from the distribution.

The array to fill with the samples. The probability (p) of generating one. Range: 0 ≤ p ≤ 1. a sequence of samples from the distribution.

Continuous Univariate Beta distribution. For details about this distribution, see Wikipedia - Beta distribution.

There are a few special cases for the parameterization of the Beta distribution. When both shape parameters are positive infinity, the Beta distribution degenerates to a point distribution at 0.5. When one of the shape parameters is positive infinity, the distribution degenerates to a point distribution at the positive infinity. When both shape parameters are 0.0, the Beta distribution degenerates to a Bernoulli distribution with parameter 0.5. When one shape parameter is 0.0, the distribution degenerates to a point distribution at the non-zero shape parameter.

Initializes a new instance of the Beta class.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0.

Initializes a new instance of the Beta class.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. The random number generator which is used to draw random samples.

A string representation of the distribution.

A string representation of the Beta distribution.

Tests whether the provided values are valid parameters for this distribution.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0.

Gets the α shape parameter of the Beta distribution. Range: α ≥ 0.

Gets the β shape parameter of the Beta distribution. Range: β ≥ 0.

Gets or sets the random number generator which is used to draw random samples.

Gets the mean of the Beta distribution.

Gets the variance of the Beta distribution.

Gets the standard deviation of the Beta distribution.

Gets the entropy of the Beta distribution.

Gets the skewness of the Beta distribution.

Gets the mode of the Beta distribution; when there are multiple answers, this routine will return 0.5.

Gets the median of the Beta distribution.

Gets the minimum of the Beta distribution.

Gets the maximum of the Beta distribution.

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.

The location at which to compute the density. the density at .

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).

The location at which to compute the log density. the log density at .

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).

The location at which to compute the cumulative distribution function. the cumulative distribution at location .

Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.

The location at which to compute the inverse cumulative density. the inverse cumulative density at . WARNING: currently not an explicit implementation, hence slow and unreliable.

Generates a sample from the Beta distribution.

a sample from the distribution.

Fills an array with samples generated from the distribution.

Generates a sequence of samples from the Beta distribution.

a sequence of samples from the distribution.

Samples Beta distributed random variables by sampling two Gamma variables and normalizing.

The random number generator to use. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a random number from the Beta distribution.

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. The location at which to compute the density. the density at .

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. The location at which to compute the density. the log density at .

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).

The location at which to compute the cumulative distribution function. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. the cumulative distribution at location .

Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.

The location at which to compute the inverse cumulative density. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. the inverse cumulative density at . WARNING: currently not an explicit implementation, hence slow and unreliable.

Generates a sample from the distribution.

The random number generator to use. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a sample from the distribution.

Generates a sequence of samples from the distribution.

The random number generator to use. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a sequence of samples from the distribution.

Fills an array with samples generated from the distribution.

The random number generator to use. The array to fill with the samples. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a sequence of samples from the distribution.

Generates a sample from the distribution.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a sample from the distribution.

Generates a sequence of samples from the distribution.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a sequence of samples from the distribution.

Fills an array with samples generated from the distribution.

The array to fill with the samples. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. a sequence of samples from the distribution.

Discrete Univariate Beta-Binomial distribution. The beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution. It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics to capture overdispersion in binomial type distributed data. Wikipedia - Beta-Binomial distribution.

Initializes a new instance of the class.

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0.

Initializes a new instance of the class.

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0. The random number generator which is used to draw random samples.

Returns a that represents this instance.

A that represents this instance.

Tests whether the provided values are valid parameters for this distribution.

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0.

Tests whether the provided values are valid parameters for this distribution.

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0. The location in the domain where we want to evaluate the probability mass function.

Gets the mean of the distribution.

Gets the variance of the distribution.

Gets the standard deviation of the distribution.

Gets the entropy of the distribution.

Gets the skewness of the distribution.

Gets the mode of the distribution

Gets the median of the distribution.

Gets the smallest element in the domain of the distributions which can be represented by an integer.

Gets the largest element in the domain of the distributions which can be represented by an integer.

Computes the probability mass (PMF) at k, i.e. P(X = k).

The location in the domain where we want to evaluate the probability mass function. the probability mass at location .

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).

The location in the domain where we want to evaluate the log probability mass function. the log probability mass at location .

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).

The location at which to compute the cumulative distribution function. the cumulative distribution at location

Computes the probability mass (PMF) at k, i.e. P(X = k).

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0. The location in the domain where we want to evaluate the probability mass function. the probability mass at location .

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0. The location in the domain where we want to evaluate the probability mass function. the log probability mass at location .

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).

The number of Bernoulli trials n - n is a positive integer Shape parameter alpha of the Beta distribution. Range: a > 0. Shape parameter beta of the Beta distribution. Range: b > 0. The location at which to compute the cumulative distribution function. the cumulative distribution at location .

Samples BetaBinomial distributed random variables by sampling a Beta distribution then passing to a Binomial distribution.

The random number generator to use. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. The number of trials (n). Range: n ≥ 0. a random number from the BetaBinomial distribution.

Samples a BetaBinomial distributed random variable.

a sample from the distribution.

Fills an array with samples generated from the distribution.

Samples an array of BetaBinomial distributed random variables.

a sequence of samples from the distribution.

Samples a BetaBinomial distributed random variable.

Fills an array with samples generated from the distribution.

Samples an array of BetaBinomial distributed random variables.

The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. The number of trials (n). Range: n ≥ 0. a sequence of samples from the distribution.

Fills an array with samples generated from the distribution.

The array to fill with the samples. The α shape parameter of the Beta distribution. Range: α ≥ 0. The β shape parameter of the Beta distribution. Range: β ≥ 0. The number of trials (n). Range: n ≥ 0.

Initializes a new instance of the BetaScaled class.

The α shape parameter of the BetaScaled distribution. Range: α > 0. The β shape parameter of the BetaScaled distribution. Range: β > 0. The location (μ) of the distribution. The scale (σ) of the distribution. Range: σ > 0. The random number generator which is used to draw random samples.

Create a Beta PERT distribution, used in risk analysis and other domains where an expert forecast is used to construct an underlying beta distribution.

The minimum value. The maximum value. The most likely value (mode). The random number generator which is used to draw random samples. The Beta distribution derived from the PERT parameters.

A string representation of the distribution.

A string representation of the BetaScaled distribution.

Tests whether the provided values are valid parameters for this distribution.

Gets the α shape parameter of the BetaScaled distribution. Range: α > 0.

Gets the β shape parameter of the BetaScaled distribution. Range: β > 0.

Gets the location (μ) of the BetaScaled distribution.

Gets the scale (σ) of the BetaScaled distribution. Range: σ > 0.

Gets or sets the random number generator which is used to draw random samples.

Gets the mean of the BetaScaled distribution.

Gets the variance of the BetaScaled distribution.

Gets the standard deviation of the BetaScaled distribution.

Gets the entropy of the BetaScaled distribution.

Gets the skewness of the BetaScaled distribution.

Gets the mode of the BetaScaled distribution; when there are multiple answers, this routine will return 0.5.

Gets the median of the BetaScaled distribution.

Gets the minimum of the BetaScaled distribution.

Gets the maximum of the BetaScaled distribution.