Package cern.jet.math

Class Arithmetic

java.lang.Object
cern.jet.math.Constants
cern.jet.math.Arithmetic
public class Arithmetic extends Constants
Arithmetic functions.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected static final double[]
    doubleFactorials
     
    protected static final double[]
    logFactorials
     
    protected static final long[]
    longFactorials
     

    Fields inherited from class cern.jet.math.Constants

    big, biginv, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    Arithmetic()
    Makes this class non instantiable, but still let's others inherit from it.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    binomial(double n, long k)
    Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
    static double
    binomial(long n, long k)
    Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
    static long
    ceil(double value)
    Returns the smallest long >= value.
    static double
    chbevl(double x, double[] coef, int N)
    Evaluates the series of Chebyshev polynomials Ti at argument x/2.
    static double
    factorial(int k)
    Instantly returns the factorial k!
    static long
    floor(double value)
    Returns the largest long <= value.
    static double
    log(double base, double value)
    Returns logbasevalue.
    static double
    log10(double value)
    Returns log10value.
    static double
    log2(double value)
    Returns log2value.
    static double
    logFactorial(int k)
    Returns log(k!)
    static long
    longFactorial(int k)
    Instantly returns the factorial k!
    static double
    stirlingCorrection(int k)
    Returns the StirlingCorrection.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • logFactorials

      protected static final double[] logFactorials

    • longFactorials

      protected static final long[] longFactorials

    • doubleFactorials

      protected static final double[] doubleFactorials

  • Constructor Details

    • Arithmetic

      protected Arithmetic()
      Makes this class non instantiable, but still let's others inherit from it.

  • Method Details

    • binomial

      public static double binomial(double n, long k)
      Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial coefficient is defined as (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).
      • k<0: 0.
      • k==0: 1.
      • k==1: n.
      • else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).
      Returns:
      the binomial coefficient.

    • binomial

      public static double binomial(long n, long k)
      Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k". The binomial coefficient is defined as
      • k<0: 0.
      • k==0 || k==n: 1.
      • k==1 || k==n-1: n.
      • else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).
      Returns:
      the binomial coefficient.

    • ceil

      public static long ceil(double value)
      Returns the smallest long >= value. Examples: 1.0 -> 1, 1.2 -> 2, 1.9 -> 2. This method is safer than using (long) Math.ceil(value), because of possible rounding error.

    • chbevl

      public static double chbevl(double x, double[] coef, int N) throws ArithmeticException
      Evaluates the series of Chebyshev polynomials Ti at argument x/2. The series is given by 
              N-1
         - '
  y  =   >   coef[i] T (x/2)
         -            i
        i=0
      Coefficients are stored in reverse order, i.e. the zero order term is last in the array. Note N is the number of coefficients, not the order.

      If coefficients are for the interval a to b, x must have been transformed to x -> 2(2x - b - a)/(b-a) before entering the routine. This maps x from (a, b) to (-1, 1), over which the Chebyshev polynomials are defined.

      If the coefficients are for the inverted interval, in which (a, b) is mapped to (1/b, 1/a), the transformation required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity, this becomes x -> 4a/x - 1.

      SPEED:

      Taking advantage of the recurrence properties of the Chebyshev polynomials, the routine requires one more addition per loop than evaluating a nested polynomial of the same degree.

      Parameters:
      x - argument to the polynomial.
      coef - the coefficients of the polynomial.
      N - the number of coefficients.
      Throws:
      ArithmeticException

    • factorial

      public static double factorial(int k)
      Instantly returns the factorial k!.
      Parameters:
      k - must hold k >= 0.

    • floor

      public static long floor(double value)
      Returns the largest long <= value. Examples: 1.0 -> 1, 1.2 -> 1, 1.9 -> 1 2.0 -> 2, 2.2 -> 2, 2.9 -> 2 This method is safer than using (long) Math.floor(value), because of possible rounding error.

    • log

      public static double log(double base, double value)
      Returns logbasevalue.

    • log10

      public static double log10(double value)
      Returns log10value.

    • log2

      public static double log2(double value)
      Returns log2value.

    • logFactorial

      public static double logFactorial(int k)
      Returns log(k!). Tries to avoid overflows. For k<30 simply looks up a table in O(1). For k>=30 uses stirlings approximation.
      Parameters:
      k - must hold k >= 0.

    • longFactorial

      public static long longFactorial(int k) throws IllegalArgumentException
      Instantly returns the factorial k!.
      Parameters:
      k - must hold k >= 0 && k < 21.
      Throws:
      IllegalArgumentException

    • stirlingCorrection

      public static double stirlingCorrection(int k)
      Returns the StirlingCorrection.

      Correction term of the Stirling approximation for log(k!) (series in 1/k, or table values for small k) with int parameter k.

      log k! = (k + 1/2)log(k + 1) - (k + 1) + (1/2)log(2Pi) + stirlingCorrection(k + 1)

      log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + stirlingCorrection(k)