Value Members

1.  final def !=(arg0: Any): Boolean

   Definition Classes

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2.  final def ##(): Int

   Definition Classes

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3.  final def ==(arg0: Any): Boolean

   Definition Classes

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4.  final def asInstanceOf[T0]: T0

   Definition Classes

   Any

5.  def betaF(a: Double, b: Double): Double

   Compute the beta function 'B(a, b)' for the following two cases: (1) when 'a' or 'b' are integers and (2) when 'a' or 'b' are integers + 1/2.

   Compute the beta function 'B(a, b)' for the following two cases: (1) when 'a' or 'b' are integers and (2) when 'a' or 'b' are integers + 1/2.

   a

   the first parameter, a real number satisfying (1) or (2)

   b

   the second parameter, a real number satisfying (1) or (2)

   See also

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

6.  def choose(n: Int, k: Int, l: Int): Long

   Compute trinomial coefficients: 'n' choose '(k, l'), combinations of 'n' things, '(k, l)' at a time, using Pascal's Tetrahedron.

   Compute trinomial coefficients: 'n' choose '(k, l'), combinations of 'n' things, '(k, l)' at a time, using Pascal's Tetrahedron. Ex: Given 'n' balls, counts ways in which 'k' are chosen for group 1 and 'l' are chosen for group 2.

   n

   the total number of items

   k

   the of items to choose

   l

   the of items to choose (requires 0 <= k + l <= n)

   See also

   http://people.sju.edu/~pklingsb/bintrin.pdf

7.  def choose(n: Int, k: Int): Long

   Compute binomial coefficients: 'n' choose 'k', combinations of 'n' things, 'k' at a time, using Pascal's Triangle.

   Compute binomial coefficients: 'n' choose 'k', combinations of 'n' things, 'k' at a time, using Pascal's Triangle.

   n

   the total number of items

   k

   the of items to choose (requires k <= n)

   See also

   http://www.mathsisfun.com/pascals-triangle.html

8.  def chose(n: Int, k: Int): Long

   Compute 'n' choose 'k' (combinations of 'n' things, 'k' at a time).

   Compute 'n' choose 'k' (combinations of 'n' things, 'k' at a time). A more efficient implementation is given below.

   n

   the total number of items

   k

   the of items to choose (requires k <= n)

9.  def clone(): AnyRef

   Attributes

   protected[java.lang]

   Definition Classes

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   @throws( ... )

10.  final def eq(arg0: AnyRef): Boolean

    Definition Classes

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11.  def equals(arg0: Any): Boolean

    Definition Classes

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12.  def fac(k: Int): Double

    Compute 'k' factorial 'k!' using three techniques (requires 'k <= 170').

    Compute 'k' factorial 'k!' using three techniques (requires 'k <= 170').

    k

    the nonnegative integer-valued argument to the factorial function

13.  def finalize(): Unit

    Attributes

    protected[java.lang]

    Definition Classes

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    Annotations

    @throws( classOf[java.lang.Throwable] )

14.  final def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes

    Error

15.  def gammaF(a: Double): Double

    Compute the gamma function 'gamma (a)' using the Lanczos Approximation.

    Compute the gamma function 'gamma (a)' using the Lanczos Approximation.

    a

    the parameter, a real number

    See also

    http://en.wikipedia.org/wiki/Lanczos_approximation

16.  final def getClass(): Class[_]

    Definition Classes

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17.  def hashCode(): Int

    Definition Classes

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18.  def hyp2f1(a: Double, b: Double, c: Double, z: Double): Double

    Compute the Gauss Hypergeometric function '2F1(a, b, c; z)' using a power series expansion.

    Compute the Gauss Hypergeometric function '2F1(a, b, c; z)' using a power series expansion.

    a

    the first parameter, a real/complex number

    b

    the second parameter, a real/complex number

    c

    the third parameter, a real/complex number, may not be a negative integer

    z

    the variable, a real/complex number s.t. |z| < 1

    See also

    people.maths.ox.ac.uk/porterm/research/pearson_final.pdf

    en.wikipedia.org/wiki/Hypergeometric_function For faster or more robust algorithms,

    http://dx.doi.org/10.1016/j.cpc.2007.11.007

19.  def iBetaF(z: Double, a: Double, b: Double): Double

    Compute the incomplete beta function 'B(z; a, b)', a generalization of the beta function 'z = 1'.

    Compute the incomplete beta function 'B(z; a, b)', a generalization of the beta function 'z = 1'.

    z

    the variable, a real/complex number s.t. 0 <= |z| <= 1

    a

    the first parameter, a real/complex number > 0

    b

    the second parameter, a real/complex number > 0

    See also

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

20.  final def isInstanceOf[T0]: Boolean

    Definition Classes

    Any

21.  val lfac: Array[Long]

    Table of all factorial numbers that can be represented as a long (64-bit) integer

22.  def logfac(k: Int): Double

    Compute the natural log factorial 'ln (k!)' so 'k! = exp (logfac (k))'.

    Compute the natural log factorial 'ln (k!)' so 'k! = exp (logfac (k))'. The formula is a log transformation of Ramanujan's Factorial Approximation.

    k

    the value to take the log factorial of

23.  def mfac(k: Int): Long

    For small 'k', compute 'k' factorial by iterative multiplication.

    For small 'k', compute 'k' factorial by iterative multiplication.
    k! = k * (k-1) * ... * 2 * 1
    

    k

    the nonnegative integer-valued argument to the factorial function

24.  def mortici(k: Int): Double

    Compute 'k!' using Mortici's Factorial Approximation (more accurate than Stirling's 2nd Order Factorial Approximation).

    Compute 'k!' using Mortici's Factorial Approximation (more accurate than Stirling's 2nd Order Factorial Approximation).

    k

    the nonnegative integer-valued argument to the factorial function

    See also

    http://but.unitbv.ro/BU2010/Series%20III/BULETIN%20III%20PDF/Mathematics/Mortici.pdf

25.  final def ne(arg0: AnyRef): Boolean

    Definition Classes

    AnyRef

26.  final def notify(): Unit

    Definition Classes

    AnyRef

27.  final def notifyAll(): Unit

    Definition Classes

    AnyRef

28.  val pascalTet: Array[Array[Array[Int]]]

    Initial part of Pascal's Tetrahedron, precomputed to speed calculations (Trinomial Coefficients)

    Initial part of Pascal's Tetrahedron, precomputed to speed calculations (Trinomial Coefficients)

    See also

    https://sites.google.com/site/pascalloids/pascal-s-pyramid-3-var

29.  val pascalTri: Array[Array[Int]]

    Initial part of Pascal's Triangle, precomputed to speed calculations (Binomial Coefficients)

30.  def perm(n: Int, k: Int): Long

    Compute permutations of 'k' items selected from 'n' total items.

    Compute permutations of 'k' items selected from 'n' total items.

    n

    the total number of items

    k

    the of items selected

31.  def rBetaC(z: Double, a: Double, b: Double): Double

    Compute the complement of the regularized (incomplete) beta function '1.0 - I(z; a, b) = I(1.0 - z; b, a)'.

    Compute the complement of the regularized (incomplete) beta function '1.0 - I(z; a, b) = I(1.0 - z; b, a)'.

    z

    the variable, a real/complex number s.t. 0 <= |z| <= 1

    a

    the first parameter, a real/complex number > 0

    b

    the second parameter, a real/complex number > 0

32.  def rBetaF(z: Double, a: Double, b: Double): Double

    Compute the regularized (incomplete) beta function 'I(z; a, b)'.

    Compute the regularized (incomplete) beta function 'I(z; a, b)'.

    z

    the variable, a real/complex number s.t. 0 <= |z| <= 1

    a

    the first parameter, a real/complex number > 0

    b

    the second parameter, a real/complex number > 0

    See also

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

33.  def ramanujan(k: Int): Double

    Compute 'k!' using Ramanujan's Factorial Approximation (more accurate than Mortici's Factorial Approximation).

    Compute 'k!' using Ramanujan's Factorial Approximation (more accurate than Mortici's Factorial Approximation).

    k

    the nonnegative integer-valued argument to the factorial function

    See also

    http://files.ele-math.com/articles/jmi-05-53.pdf

34.  def rfac(k: Int, x: Double = 1.0): Double

    Compute the 'k'th degree rising factorial of 'x'.

    Compute the 'k'th degree rising factorial of 'x'. When 'x = 1', this is the regular factorial function 'k!'. Also known as Pochhammer's symbol. Caveat: only works when 'k' is a nonnegative integer

    k

    the number of factors in the product

    x

    the base number to start the product

35.  def stirling(k: Int): Double

    Compute 'k!' using Stirling's 2-nd Order Factorial Approximation.

    Compute 'k!' using Stirling's 2-nd Order Factorial Approximation.

    k

    the nonnegative integer-valued argument to the factorial function

    See also

    http://en.wikipedia.org/wiki/Stirling%27s_approximation

36.  final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes

    AnyRef

37.  def toString(): String

    Definition Classes

    AnyRef → Any

38.  final def wait(): Unit

    Definition Classes

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    Annotations

    @throws( ... )

39.  final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

40.  final def wait(arg0: Long): Unit

    Definition Classes

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    Annotations

    @throws( ... )