Arithmetic (Colt 1.2.0 - API Specification)

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cern.jet.math
Class Arithmetic

java.lang.Object
  cern.jet.math.Constants
      cern.jet.math.Arithmetic

public class Arithmetic
extends Constants

Arithmetic functions.

Method Summary
`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 `log_basevalue`.
`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

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

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 log_basevalue. 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) Overview Package Class Use Tree Deprecated Index Help Colt 1.2.0 PREV CLASS NEXT CLASS FRAMES NO FRAMES SUMMARY: NESTED | FIELD | CONSTR | METHOD DETAIL: FIELD | CONSTR | METHOD Jump to the Colt Homepage

cern.jet.math Class Arithmetic

binomial

binomial

ceil

chbevl

factorial

floor

log

log10

log2

logFactorial

longFactorial

stirlingCorrection

cern.jet.math
Class Arithmetic