Package cern.jet.math

Class Arithmetic

  • public class Arithmetic
extends Constants
    Arithmetic functions.

    • Constructor Summary

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

    • Method Summary

      All Methods Static Methods Concrete Methods 
      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.

    • Field Detail

      • logFactorials

        protected static final double[] logFactorials

      • longFactorials

        protected static final long[] longFactorials

      • doubleFactorials

        protected static final double[] doubleFactorials

    • Constructor Detail

      • Arithmetic

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

    • Method Detail

      • 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.

      • 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)