Algebra (Ignite 2.5.0)

java.lang.Object
- org.apache.ignite.ml.math.Constants
- - org.apache.ignite.ml.math.Algebra

```
public class Algebra
extends Constants
```
Miscellaneous arithmetic and algebra functions. Lifted from Apache Mahout.

Field Summary
- Fields inherited from class org.apache.ignite.ml.math.Constants
  BIG, BIGINV, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI

Constructor Summary

Constructors
Constructor and Description

Algebra()

Constructors
Constructor and Description
`Algebra()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and 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 val)` 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`	`evalPoly(double x, double[] coef, int n)` Evaluates the given polynomial of degree `N` at `x`.
`static double`	`evalPoly1(double x, double[] coef, int n)` Evaluates the given polynomial of degree `N` at `x`, assuming coefficient of N is 1.0.
`static long`	`floor(double val)` Returns the largest `long <= value`.
`static double`	`hypot(double a, double b)` Gets `sqrt(a^2 + b^2)` without under/overflow.
`static double`	`log(double base, double val)` Returns `log<sub>base</sub>value`.
`static double`	`log10(double val)` Returns `log<sub>10</sub>value`.
`static double`	`log2(double val)` Returns `log<sub>2</sub>value`.
`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

- Constructor Detail
 - Algebra
```
public Algebra()
```
- 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).
 Parameters:
 
 n - Size of set.
 
 k - Size of subset.
 
 Returns:
 
 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 ).
 Parameters:
 
 n - Size of set.
 
 k - Size of subset.
 
 Returns:
 
 Binomial coefficient.
 - ceil
```
public static long ceil(double val)
```
 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.
 
 Parameters:
 
 val - Value for ceil.
 
 Returns:
 
 Ceil of the given value.
 - chbevl
```
public static double chbevl(double x,
 double[] coef,
 int N)
```
 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 - Coefficients of the polynomial.
 
 N - Number of coefficients.
 - floor
```
public static long floor(double val)
```
 Returns the largest long <= value.
 Examples: 1.0 -> 1, 1.2 -> 1, 1.9 -> 1 <dt> 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 val)
```
 Returns logbasevalue.
 - log10
```
public static double log10(double val)
```
 Returns log10value.
 - log2
```
public static double log2(double val)
```
 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 Stirling's approximation.
 
 Parameters:
 
 k - must hold k >= 0.
 - longFactorial
```
public static long longFactorial(int k)
```
 Instantly returns the factorial k!.
 
 Parameters:
 
 k - must hold k >= 0 && k < 21
 - 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) + STIRLING_CORRECTION(k + 1) log k! = (k + 1/2)log(k) - k + (1/2)log(2Pi) + STIRLING_CORRECTION(k)
 - evalPoly1
```
public static double evalPoly1(double x,
 double[] coef,
 int n)
```
 Evaluates the given polynomial of degree N at x, assuming coefficient of N is 1.0. Otherwise same as evalPoly(double, double[], int).
```
 2 N
 y = C + C x + C x +...+ C x
 0 1 2 N
 
```
 where
```
 C = 1
 N
 
```
 and hence is omitted from the array.
 Coefficients are stored in reverse order:
```
 coef[0] = C , ..., coef[N-1] = C .
 N-1 0
 
```
 Calling arguments are otherwise the same as evalPoly(double, double[], int).
 In the interest of speed, there are no checks for out of bounds arithmetic.
 Parameters:
 
 x - Argument to the polynomial.
 
 coef - Coefficients of the polynomial.
 
 n - Degree of the polynomial.
 - evalPoly
```
public static double evalPoly(double x,
 double[] coef,
 int n)
```
 Evaluates the given polynomial of degree N at x.
```
 2 N
 y = C + C x + C x +...+ C x
 0 1 2 N
 
```
 Coefficients are stored in reverse order:
```
 coef[0] = C , ..., coef[N] = C .
 N 0
 
```
 In the interest of speed, there are no checks for out of bounds arithmetic.
 Parameters:
 
 x - Argument to the polynomial.
 
 coef - Coefficients of the polynomial.
 
 n - Degree of the polynomial.
 - hypot
```
public static double hypot(double a,
 double b)
```
 Gets sqrt(a^2 + b^2) without under/overflow.
 
 Parameters:
 
 a - First side value.
 
 b - Second side value.
 
 Returns:
 
 Hypotenuse value.

Class Algebra

Field Summary

Fields inherited from class org.apache.ignite.ml.math.Constants

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Algebra

Method Detail

binomial

binomial

ceil

chbevl

floor

log

log10

log2

logFactorial

longFactorial

stirlingCorrection

evalPoly1

evalPoly

hypot