MathTricks (Java Statistical Analysis Tool 0.0.8 API)

java.lang.Object
- jsat.math.MathTricks

```
public class MathTricks
extends Object
```
This class provides utilities for performing specific arithmetic patterns in numerically stable / efficient ways.

Author:

Edward Raff

Field Summary

Fields
Modifier and Type	Field and Description
`static Function`	`absFunc` Convenience object for taking the `abs` of the first index
`static Function`	`expFunc` Convenience object for taking the `exp` of the first index
`static Function`	`invsFunc` Convenience object for taking the inverse (x^-1) of the first index.
`static Function`	`logFunc` Convenience object for taking the `log` of the first index
`static Function`	`sqrdFunc` Convenience object for taking the squared value of the first index
`static Function`	`sqrtFunc` Convenience object for taking the `square root` of the first index

Method Summary

All Methods Static Methods Concrete Methods
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(x_j) / Σ_{∀ i} exp(x_i)
`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

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - sqrtFunc
```
public static final Function sqrtFunc
```
    Convenience object for taking the square root of the first index
  - sqrdFunc
```
public static final Function sqrdFunc
```
    Convenience object for taking the squared value of the first index
  - invsFunc
```
public static final Function invsFunc
```
    Convenience object for taking the inverse (x^-1) of the first index.
  - logFunc
```
public static final Function logFunc
```
    Convenience object for taking the log of the first index
  - expFunc
```
public static final Function expFunc
```
    Convenience object for taking the exp of the first index
  - absFunc
```
public static final Function absFunc
```
    Convenience object for taking the abs of the first index
- 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

Class MathTricks

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

sqrtFunc

sqrdFunc

invsFunc

logFunc

expFunc

absFunc

Method Detail

max

min

logSumExp

logSumExp

softmax

softmax

hornerPolyR

hornerPoly