## edu.stanford.nlp.math
Class SloppyMath

    java.lang.Object
      edu.stanford.nlp.math.SloppyMath

    public final class SloppyMath

extends Object

The class `SloppyMath` contains methods for performing basic numeric operations. In some cases, such as max and min, they cut a few corners in the implementation for the sake of efficiency. In particular, they may not handle special notions like NaN and -0.0 correctly. This was the origin of the class name, but many other methods are just useful math additions, such as logSum. This class just has static math methds.

Author:
  Christopher Manning

Method Summary
`static double` `chiSquare2by2(int k, int n, int r, int m)` Find a 2x2 chi-square value.
`static double` `exactBinomial(int k, int n, double p)` Find a one tailed exact binomial test probability.
`static double` `factorial(int x)` Uses floating point so that it can represent the really big numbers that come up.
`static double` `gamma(double n)`
`static double` `hypergeometric(int k, int n, int r, int m)` Find a hypergeometric distribution.
`static double` `intPow(double b, int e)` Exponentiation like we learned in grade school: multiply b by itself e times.
`static float` `intPow(float b, int e)` Exponentiation like we learned in grade school: multiply b by itself e times.
`static int` `intPow(int b, int e)` Exponentiation like we learned in grade school: multiply b by itself e times.
`static boolean` `isCloseTo(double a, double b)`
`static boolean` `isDangerous(double d)` Returns true if the argument is a "dangerous" double to have around, namely one that is infinite, NaN or zero.
`static boolean` `isVeryDangerous(double d)` Returns true if the argument is a "very dangerous" double to have around, namely one that is infinite or NaN.
`static double` `lgamma(double x)`
`static double` `log(double num, double base)` Convenience method for log to a different base
`static double` `logAdd(double lx, double ly)` Returns the log of the sum of two numbers, which are themselves input in log form.
`static float` `logAdd(float lx, float ly)` Returns the log of the sum of two numbers, which are themselves input in log form.
`static void` `main(String[] args)` Tests the hypergeometric distribution code, or other functions provided in this module.
`static int` `max(Collection<Integer> vals)`
`static double` `max(double a, double b)` Returns the greater of two `double` values.
`static float` `max(float a, float b)` Returns the greater of two `float` values.
`static int` `max(int a, int b, int c)` Returns the minimum of three int values.
`static double` `min(double a, double b)` Returns the smaller of two `double` values.
`static float` `min(float a, float b)` Returns the smaller of two `float` values.
`static int` `min(int a, int b, int c)` Returns the minimum of three int values.
`static int` `nChooseK(int n, int k)` Computes n choose k in an efficient way.
`static double` `oneTailedFishersExact(int k, int n, int r, int m)` Find a one-tailed Fisher's exact probability.
`static double` `poisson(int x, double lambda)`
`static double` `pow(double a, double b)` Returns an approximation to Math.pow(a,b) that is ~27x faster with a margin of error possibly around ~10%.
`static double` `round(double x)` Round a double to the nearest integer, via conventional rules (.5 rounds up, .49 rounds down), and return the result, still as a double.
`static double` `round(double x, int precision)` Round a double to the given number of decimal places, rounding to the nearest value via conventional rules (5 rounds up, 49 rounds down).
`static double` `sigmoid(double x)` Compute the sigmoid function with mean zero.

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

Method Detail

### round

    public static double round(double x)

  Round a double to the nearest integer, via conventional rules (.5 rounds up, .49 rounds down), and return the result, still as a double.

  Parameters:
    `x` - What to round
  Returns:
    The rounded value

### round

    public static double round(double x,
                               int precision)

  Round a double to the given number of decimal places, rounding to the nearest value via conventional rules (5 rounds up, 49 rounds down). E.g. round(3.1416, 2) == 3.14, round(431.5, -2) == 400, round(431.5, 0) = 432

### max

    public static int max(int a,
                          int b,
                          int c)

  Returns the minimum of three int values.

  Returns:
    The minimum of three int values.

### max

    public static int max(Collection<Integer> vals)

### lgamma

    public static double lgamma(double x)

  Returns:
    an approximation of the log of the Gamma function * of x. Laczos Approximation Reference: Numerical Recipes in C http://www.library.cornell.edu/nr/cbookcpdf.html from www.cs.berkeley.edu/~milch/blog/versions/blog-0.1.3/blog/distrib

### min

    public static int min(int a,
                          int b,
                          int c)

  Returns the minimum of three int values.

### max

    public static float max(float a,
                            float b)

  Returns the greater of two `float` values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. Does none of the special checks for NaN or -0.0f that `Math.max` does.

  Parameters:
    `a` - an argument.
    `b` - another argument.
  Returns:
    the larger of `a` and `b`.

### max

    public static double max(double a,
                             double b)

  Returns the greater of two `double` values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. Does none of the special checks for NaN or -0.0f that `Math.max` does.

  Parameters:
    `a` - an argument.
    `b` - another argument.
  Returns:
    the larger of `a` and `b`.

### min

    public static float min(float a,
                            float b)

  Returns the smaller of two `float` values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. Does none of the special checks for NaN or -0.0f that `Math.max` does.

  Parameters:
    `a` - an argument.
    `b` - another argument.
  Returns:
    the smaller of `a` and `b.`

### min

    public static double min(double a,
                             double b)

  Returns the smaller of two `double` values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. Does none of the special checks for NaN or -0.0f that `Math.max` does.

  Parameters:
    `a` - an argument.
    `b` - another argument.
  Returns:
    the smaller of `a` and `b`.

### isDangerous

    public static boolean isDangerous(double d)

  Returns true if the argument is a "dangerous" double to have around, namely one that is infinite, NaN or zero.

### isVeryDangerous

    public static boolean isVeryDangerous(double d)

  Returns true if the argument is a "very dangerous" double to have around, namely one that is infinite or NaN.

### isCloseTo

    public static boolean isCloseTo(double a,
                                    double b)

### gamma

    public static double gamma(double n)

### log

    public static double log(double num,
                             double base)

  Convenience method for log to a different base

### logAdd

    public static float logAdd(float lx,
                               float ly)

  Returns the log of the sum of two numbers, which are themselves input in log form. This uses natural logarithms. Reasonable care is taken to do this as efficiently as possible (under the assumption that the numbers might differ greatly in magnitude), with high accuracy, and without numerical overflow. Also, handle correctly the case of arguments being -Inf (e.g., probability 0).

  Parameters:
    `lx` - First number, in log form
    `ly` - Second number, in log form
  Returns:
    log(exp(lx) + exp(ly))

### logAdd

    public static double logAdd(double lx,
                                double ly)

  Returns the log of the sum of two numbers, which are themselves input in log form. This uses natural logarithms. Reasonable care is taken to do this as efficiently as possible (under the assumption that the numbers might differ greatly in magnitude), with high accuracy, and without numerical overflow. Also, handle correctly the case of arguments being -Inf (e.g., probability 0).

  Parameters:
    `lx` - First number, in log form
    `ly` - Second number, in log form
  Returns:
    log(exp(lx) + exp(ly))

### nChooseK

    public static int nChooseK(int n,
                               int k)

  Computes n choose k in an efficient way. Works with k == 0 or k == n but undefined if k < 0 or k > n

  Returns:
    fact(n) / fact(k) * fact(n-k)

### pow

    public static double pow(double a,
                             double b)

  Returns an approximation to Math.pow(a,b) that is ~27x faster with a margin of error possibly around ~10%. From http://martin.ankerl.com/2007/10/04/optimized-pow-approximation-for-java-and-c-c/

### intPow

    public static int intPow(int b,
                             int e)

  Exponentiation like we learned in grade school: multiply b by itself e times. Uses power of two trick. e must be nonnegative!!! no checking!!! For e <= 0, the exponent is treated as 0, and 1 is returned. 0^0 also returns 1.

  Parameters:
    `b` - base
    `e` - exponent
  Returns:
    b^e

### intPow

    public static float intPow(float b,
                               int e)

  Exponentiation like we learned in grade school: multiply b by itself e times. Uses power of two trick. e must be nonnegative!!! no checking!!!

  Parameters:
    `b` - base
    `e` - exponent
  Returns:
    b^e

### intPow

    public static double intPow(double b,
                                int e)

  Exponentiation like we learned in grade school: multiply b by itself e times. Uses power of two trick. e must be nonnegative!!! no checking!!!

  Parameters:
    `b` - base
    `e` - exponent
  Returns:
    b^e

### hypergeometric

    public static double hypergeometric(int k,
                                        int n,
                                        int r,
                                        int m)

  Find a hypergeometric distribution. This uses exact math, trying fairly hard to avoid numeric overflow by interleaving multiplications and divisions. (To do: make it even better at avoiding overflow, by using loops that will do either a multiple or divide based on the size of the intermediate result.)

  Parameters:
    `k` - The number of black balls drawn
    `n` - The total number of balls
    `r` - The number of black balls
    `m` - The number of balls drawn
  Returns:
    The hypergeometric value

### exactBinomial

    public static double exactBinomial(int k,
                                       int n,
                                       double p)

  Find a one tailed exact binomial test probability. Finds the chance of this or a higher result

  Parameters:
    `k` - number of successes
    `n` - Number of trials
    `p` - Probability of a success

### oneTailedFishersExact

    public static double oneTailedFishersExact(int k,
                                               int n,
                                               int r,
                                               int m)

  Find a one-tailed Fisher's exact probability. Chance of having seen this or a more extreme departure from what you would have expected given independence. I.e., k >= the value passed in. Warning: this was done just for collocations, where you are concerned with the case of k being larger than predicted. It doesn't correctly handle other cases, such as k being smaller than expected.

  Parameters:
    `k` - The number of black balls drawn
    `n` - The total number of balls
    `r` - The number of black balls
    `m` - The number of balls drawn
  Returns:
    The Fisher's exact p-value

### chiSquare2by2

    public static double chiSquare2by2(int k,
                                       int n,
                                       int r,
                                       int m)

  Find a 2x2 chi-square value. Note: could do this more neatly using simplified formula for 2x2 case.

  Parameters:
    `k` - The number of black balls drawn
    `n` - The total number of balls
    `r` - The number of black balls
    `m` - The number of balls drawn
  Returns:
    The Fisher's exact p-value

### sigmoid

    public static double sigmoid(double x)

  Compute the sigmoid function with mean zero. Care is taken to compute an accurate answer without numerical overflow. (Added by rajatr)

  Parameters:
    `x` - Point to compute sigmoid at.
  Returns:
    Value of the sigmoid, given by 1/(1+exp(-x))

### poisson

    public static double poisson(int x,
                                 double lambda)

### factorial

    public static double factorial(int x)

  Uses floating point so that it can represent the really big numbers that come up.

  Parameters:
    `x` - Argumet to take factorial of
  Returns:
    Factorial of argument

### main

    public static void main(String[] args)

  Tests the hypergeometric distribution code, or other functions provided in this module.

  Parameters:
    `args` - Either none, and the log add rountines are tested, or the following 4 arguments: k (cell), n (total), r (row), m (col)

Stanford NLP Group