Maths (nshmp-haz)

java.lang.Object
- gov.usgs.earthquake.nshmp.util.Maths

```
public final class Maths
extends Object
```
Miscellaneous math utilities. In some cases, these methods obviate the need for 3^rd party imports.

Author:

Peter Powers

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`PI_BY_2` Constant for π/2.
`static double`	`SQRT_2` The precomputed √2.
`static double`	`SQRT_2PI` The precomputed √2π.
`static double`	`TO_DEGREES` Conversion multiplier for radians to degrees.
`static double`	`TO_RADIANS` Conversion multiplier for degrees to radians.
`static double`	`TWO_PI` Constant for 2π.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static Converter<Double,Double>`	`decimalToProbabilityConverter(int percentScale)` Return a converter between decimal values and percentages.
`static double`	`epsilon(double μ, double σ, double x)` Standardized normal variate `ε = (x - μ) / σ`.
`static double`	`erf(double x)` Error function approximation of Abramowitz and Stegun, formula 7.1.26 in the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
`static double`	`hypot(double... values)` Variadic form of `hypot(double, double)`.
`static double`	`hypot(double v1, double v2)` Same as `Math.hypot(double, double)` without regard to intermediate under/over flow prior to internal call to `Math.sqrt(double)`.
`static double`	`hypot(double v1, double v2, double v3)` Three argument form of `hypot(double, double)`.
`static double`	`normalCcdf(double μ, double σ, double x)` Normal complementary cumulative distribution function.
`static double`	`normalPdf(double μ, double σ, double x)` Normal probability density function.
`static double`	`round(double value, double model)` Round a double to the nearest specified double.
`static double`	`round(double value, double model, RoundingMode mode)` Round a double to the nearest specified double.
`static double`	`round(double value, int scale)` Round a double to a specified number of decimal places according to `RoundingMode.HALF_UP`.
`static double`	`round(double value, int scale, RoundingMode mode)` Round a double to a specified number of decimal places according to the supplied `RoundingMode`.
`static double`	`stepFunction(double μ, double x)` Step function for which `f(x) =` { `1 if x ≤ μ; 0 if x > μ` }.

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

- Field Detail
  - PI_BY_2
```
public static final double PI_BY_2
```
    Constant for π/2.
    
    See Also:
    
    Constant Field Values
  - TWO_PI
```
public static final double TWO_PI
```
    Constant for 2π.
    
    See Also:
    
    Constant Field Values
  - TO_RADIANS
```
public static final double TO_RADIANS
```
    Conversion multiplier for degrees to radians.
  - TO_DEGREES
```
public static final double TO_DEGREES
```
    Conversion multiplier for radians to degrees.
  - SQRT_2
```
public static final double SQRT_2
```
    The precomputed √2.
  - SQRT_2PI
```
public static final double SQRT_2PI
```
    The precomputed √2π.
- Method Detail
  - epsilon
```
public static double epsilon(double μ,
                             double σ,
                             double x)
```
    Standardized normal variate ε = (x - μ) / σ.
    
    Parameters:
    
    μ - mean
    
    σ - standard deviation
  - erf
```
public static double erf(double x)
```
    Error function approximation of Abramowitz and Stegun, formula 7.1.26 in the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Although the approximation is only valid for x ≥ 0, because erf(x) is an odd function, erf(x) = −erf(−x) and negative values are supported.
  - hypot
```
public static double hypot(double v1,
                           double v2)
```
    Same as Math.hypot(double, double) without regard to intermediate under/over flow prior to internal call to Math.sqrt(double).
    
    Parameters:
    
    v1 - first value
    
    v2 - second value
    
    See Also:
    
    Math.hypot(double, double)
  - hypot
```
public static double hypot(double v1,
                           double v2,
                           double v3)
```
    Three argument form of hypot(double, double). Does not protect against intermediate under/over flow prior to internal call to Math.sqrt(double).
    
    Parameters:
    
    v1 - first value
    
    v2 - second value
    
    v3 - second value
    
    See Also:
    
    hypot(double, double)
  - hypot
```
public static double hypot(double... values)
```
    Variadic form of hypot(double, double). Does not protect against intermediate under/over flow prior to internal call to Math.sqrt(double).
    
    Parameters:
    
    values - to process
    
    See Also:
    
    hypot(double, double)
  - normalCcdf
```
public static double normalCcdf(double μ,
                                double σ,
                                double x)
```
    Normal complementary cumulative distribution function.
    
    Parameters:
    
    μ - mean
    
    σ - standard deviation
    
    x - variate
  - normalPdf
```
public static double normalPdf(double μ,
                               double σ,
                               double x)
```
    Normal probability density function.
    
    Parameters:
    
    μ - mean
    
    σ - standard deviation
    
    x - variate
  - stepFunction
```
public static double stepFunction(double μ,
                                  double x)
```
    Step function for which f(x) = { 1 if x ≤ μ; 0 if x > μ }.
    
    Parameters:
    
    μ - mean
    
    x - variate
  - round
```
public static double round(double value,
                           int scale)
```
    Round a double to a specified number of decimal places according to RoundingMode.HALF_UP. Internally this method uses the scaling and rounding capabilities of BigDecimal. Note that a negative scale will round value to the specified number of places above the decimal.
    
    Parameters:
    
    value - to round
    
    scale - the number of decimal places in the result
  - round
```
public static double round(double value,
                           int scale,
                           RoundingMode mode)
```
    Round a double to a specified number of decimal places according to the supplied RoundingMode. Internally this method uses the scaling and rounding capabilities of BigDecimal. Note that a negative scale will round value to the specified number of places above the decimal.
    
    Parameters:
    
    value - to round
    
    scale - the number of decimal places in the result
  - round
```
public static double round(double value,
                           double model)
```
    Round a double to the nearest specified double. Internally this method uses the scaling and rounding of BigDecimal according to RoundingMode.HALF_UP.
    
    Parameters:
    
    value - to round
    
    model - to round to
  - round
```
public static double round(double value,
                           double model,
                           RoundingMode mode)
```
    Round a double to the nearest specified double. Internally this method uses the scaling and rounding of BigDecimal according to a specified RoundingMode.
    
    Parameters:
    
    value - to round
    
    model - to round to
    
    mode - to round by
  - decimalToProbabilityConverter
```
public static Converter<Double,Double> decimalToProbabilityConverter(int percentScale)
```
    Return a converter between decimal values and percentages. The forward operation of this converter may be lossy in as much as the supplied decimal value will be rounded to the specified scale after conversion to a percentage. For instance:
    decimalToProbabilityConverter(2).convert(0.23456) = 23.46
    Reverse operations do not affect precision at this time.
    
    Parameters:
    
    percentScale - the number of decimal places in percentages output by this converter

Class Maths

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

PI_BY_2

TWO_PI

TO_RADIANS

TO_DEGREES

SQRT_2

SQRT_2PI

Method Detail

epsilon

erf

hypot

hypot

hypot

normalCcdf

normalPdf

stepFunction

round

round

round

round

decimalToProbabilityConverter