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java.lang.Objectorg.apache.mahout.collections.Constants
org.apache.mahout.collections.Arithmetic
public final class Arithmetic
Arithmetic functions.
| Field Summary |
|---|
| Fields inherited from class org.apache.mahout.collections.Constants |
|---|
BIG, BIGINV, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI |
| 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 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 |
| Method Detail |
|---|
public static double binomial(double n,
long k)
public static double binomial(long n,
long k)
public static long ceil(double value)
long >= value. 1.0 -> 1, 1.2 -> 2, 1.9 -> 2. This
method is safer than using (long) Math.ceil(value), because of possible rounding error.
public static double chbevl(double x,
double[] coef,
int N)
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.
x - argument to the polynomial.coef - the coefficients of the polynomial.N - the number of coefficients.public static long floor(double value)
long <= value.
1.0 -> 1, 1.2 -> 1, 1.9 -> 1 <dt> 2.0 -> 2, 2.2 -> 2, 2.9 -> 2
public static double log(double base,
double value)
public static double log10(double value)
public static double log2(double value)
public static double logFactorial(int k)
k - must hold k >= 0.public static long longFactorial(int k)
k - must hold k >= 0 && k < 21.public static double stirlingCorrection(int k)
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) + STIRLING_CORRECTION(k + 1)
log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + STIRLING_CORRECTION(k)
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