jsat.math

Class MathTricks

java.lang.Object

jsat.math.MathTricks

public class MathTricks
extends java.lang.Object

This class provides utilities for performing specific arithmetic patterns in numerically stable / efficient ways.

Method Summary

Modifier and Type	Method and Description
static double	hornerPoly(double[] coef, double x) This evaluates a polynomial using Horner's method.
static double	hornerPolyR(double[] coef, double x) This evaluates a polynomial using Horner's method.
static double	logSumExp(double[] vals, double maxValue) Provides a numerically table way to perform the log of a sum of exponentiations.
static double	logSumExp(Vec vals, double maxValue) Provides a numerically table way to perform the log of a sum of exponentiations.
static double	max(double... vals)
static double	min(double... vals)
static void	softmax(double[] x, boolean implicitExtra) Applies the softmax function to the given array of values, normalizing them so that each value is equal to exp(xj) / Σ∀ i exp(xi)
static void	softmax(Vec x, boolean implicitExtra) Applies the softmax function to the given array of values, normalizing them so that each value is equal to exp(xj) / Σ∀ i exp(xi) Note: If the input is sparse, this will end up destroying sparsity

Methods inherited from class java.lang.Object

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

Method Detail

max

public static double max(double... vals)

Parameters:

vals - an array of values to get the maximum of

Returns:

the maximum of all given values

min

public static double min(double... vals)

Parameters:

vals - an array of values to get the maximum of

Returns:

the maximum of all given values

logSumExp

public static double logSumExp(Vec vals,
                               double maxValue)

Provides a numerically table way to perform the log of a sum of exponentiations. The computed result is
log(∑ _{∀ val ∈ vals} exp(val) )

Parameters:

vals - the array of values to exponentiate and add

maxValue - the maximum value in the array

Returns:

the log of the sum of the exponentiated values

logSumExp

public static double logSumExp(double[] vals,
                               double maxValue)

Provides a numerically table way to perform the log of a sum of exponentiations. The computed result is
log(∑ _{∀ val ∈ vals} exp(val) )

Parameters:

vals - the array of values to exponentiate and add

maxValue - the maximum value in the array

Returns:

the log of the sum of the exponentiated values

softmax

public static void softmax(double[] x,
                           boolean implicitExtra)

Applies the softmax function to the given array of values, normalizing them so that each value is equal to

exp(x_j) / Σ_{∀ i} exp(x_i)

Parameters:

x - the array of values

implicitExtra - true if the softmax will assume there is an extra implicit value not included in the array with a value of 0.0

softmax

public static void softmax(Vec x,
                           boolean implicitExtra)

Applies the softmax function to the given array of values, normalizing them so that each value is equal to

exp(x_j) / Σ_{∀ i} exp(x_i)
Note: If the input is sparse, this will end up destroying sparsity

Parameters:

x - the array of values

implicitExtra - true if the softmax will assume there is an extra implicit value not included in the array with a value of 0.0

hornerPolyR

public static double hornerPolyR(double[] coef,
                                 double x)

This evaluates a polynomial using Horner's method. It is assumed that the polynomial is stored in reverse order in the array coef, ie: from c_n at index 0, and then decreasing.

Parameters:

coef - the polynomial with coefficients in reverse order

x - the value to evaluate the polynomial at

Returns:

the value of the polynomial at x

hornerPoly

public static double hornerPoly(double[] coef,
                                double x)

This evaluates a polynomial using Horner's method. It is assumed that the polynomial is stored in order in the array coef, ie: from c₀ at index 0, and then increasing with the index.

Parameters:

coef - the polynomial with coefficients in reverse order

x - the value to evaluate the polynomial at

Returns:

the value of the polynomial at x