MathUtils (Hipparchus 2.0 API)

java.lang.Object
- org.hipparchus.util.MathUtils

```
public final class MathUtils
extends Object
```
Miscellaneous utility functions.

See Also:

ArithmeticUtils, Precision, MathArrays

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static class`	`MathUtils.FieldSumAndResidual<T extends FieldElement<T>>` Result class for `twoSum(FieldElement, FieldElement)` containing the sum and the residual error in the sum.
`static class`	`MathUtils.SumAndResidual` Result class for `twoSum(double, double)` containing the sum and the residual error in the sum.

Field Summary

Fields
Modifier and Type Field and Description

static double PI_SQUARED
\(\pi^2\)

static double SEMI_PI
\(\pi/2\).

static double TWO_PI
\(2\pi\)

Fields
Modifier and Type	Field and Description
`static double`	`PI_SQUARED` \(\pi^2\)
`static double`	`SEMI_PI` \(\pi/2\).
`static double`	`TWO_PI` \(2\pi\)

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static void`	`checkDimension(int dimension, int otherDimension)` Checks that the given dimensions match.
`static void`	`checkFinite(double x)` Check that the argument is a real number.
`static void`	`checkFinite(double[] val)` Check that all the elements are real numbers.
`static void`	`checkNotNull(Object o)` Checks that an object is not null.
`static void`	`checkNotNull(Object o, Localizable pattern, Object... args)` Checks that an object is not null.
`static void`	`checkRangeInclusive(double value, double lo, double hi)` Checks that the given value is strictly within the range [lo, hi].
`static void`	`checkRangeInclusive(long value, long lo, long hi)` Checks that the given value is strictly within the range [lo, hi].
`static byte`	`copySign(byte magnitude, byte sign)` Returns the first argument with the sign of the second argument.
`static int`	`copySign(int magnitude, int sign)` Returns the first argument with the sign of the second argument.
`static long`	`copySign(long magnitude, long sign)` Returns the first argument with the sign of the second argument.
`static short`	`copySign(short magnitude, short sign)` Returns the first argument with the sign of the second argument.
`static boolean`	`equals(double x, double y)` Returns `true` if the values are equal according to semantics of `Double.equals(Object)`.
`static int`	`hash(double value)` Returns an integer hash code representing the given double value.
`static int`	`hash(double[] value)` Returns an integer hash code representing the given double array.
`static <T extends CalculusFieldElement<T>> T`	`max(T e1, T e2)` Find the maximum of two field elements.
`static <T extends CalculusFieldElement<T>> T`	`min(T e1, T e2)` Find the minimum of two field elements.
`static double`	`normalizeAngle(double a, double center)` Normalize an angle in a 2π wide interval around a center value.
`static <T extends CalculusFieldElement<T>> T`	`normalizeAngle(T a, T center)` Normalize an angle in a 2π wide interval around a center value.
`static double`	`reduce(double a, double period, double offset)` Reduce `\|a - offset\|` to the primary interval `[0, \|period\|)`.
`static MathUtils.SumAndResidual`	`twoSum(double a, double b)` Sums `a` and `b` using Møller's 2Sum algorithm.
`static <T extends FieldElement<T>> MathUtils.FieldSumAndResidual<T>`	`twoSum(T a, T b)` Sums `a` and `b` using Møller's 2Sum algorithm.

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

- Field Detail
  - TWO_PI
```
public static final double TWO_PI
```
    \(2\pi\)
    
    See Also:
    
    Constant Field Values
  - PI_SQUARED
```
public static final double PI_SQUARED
```
    \(\pi^2\)
    
    See Also:
    
    Constant Field Values
  - SEMI_PI
```
public static final double SEMI_PI
```
    \(\pi/2\).
    
    See Also:
    
    Constant Field Values
- Method Detail
  - hash
```
public static int hash(double value)
```
    Returns an integer hash code representing the given double value.
    
    Parameters:
    
    value - the value to be hashed
    
    Returns:
    
    the hash code
  - equals
```
public static boolean equals(double x,
                             double y)
```
    Returns true if the values are equal according to semantics of Double.equals(Object).
    
    Parameters:
    
    x - Value
    
    y - Value
    
    Returns:
    
    new Double(x).equals(new Double(y))
  - hash
```
public static int hash(double[] value)
```
    Returns an integer hash code representing the given double array.
    
    Parameters:
    
    value - the value to be hashed (may be null)
    
    Returns:
    
    the hash code
  - normalizeAngle
```
public static double normalizeAngle(double a,
                                    double center)
```
    Normalize an angle in a 2π wide interval around a center value.
    This method has three main uses:
    - normalize an angle between 0 and 2π:
      a = MathUtils.normalizeAngle(a, FastMath.PI);
    - normalize an angle between -π and +π
      a = MathUtils.normalizeAngle(a, 0.0);
    - compute the angle between two defining angular positions:
      angle = MathUtils.normalizeAngle(end, start) - start;
    Note that due to numerical accuracy and since π cannot be represented exactly, the result interval is closed, it cannot be half-closed as would be more satisfactory in a purely mathematical view.
    Parameters:
    
    a - angle to normalize
    
    center - center of the desired 2π interval for the result
    
    Returns:
    
    a-2kπ with integer k and center-π <= a-2kπ <= center+π
  - normalizeAngle
```
public static <T extends CalculusFieldElement<T>> T normalizeAngle(T a,
                                                                   T center)
```
    Normalize an angle in a 2π wide interval around a center value.
    This method has three main uses:
    - normalize an angle between 0 and 2π:
      a = MathUtils.normalizeAngle(a, FastMath.PI);
    - normalize an angle between -π and +π
      a = MathUtils.normalizeAngle(a, zero);
    - compute the angle between two defining angular positions:
      angle = MathUtils.normalizeAngle(end, start).subtract(start);
    Note that due to numerical accuracy and since π cannot be represented exactly, the result interval is closed, it cannot be half-closed as would be more satisfactory in a purely mathematical view.
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    a - angle to normalize
    
    center - center of the desired 2π interval for the result
    
    Returns:
    
    a-2kπ with integer k and center-π <= a-2kπ <= center+π
  - max
```
public static <T extends CalculusFieldElement<T>> T max(T e1,
                                                        T e2)
```
    Find the maximum of two field elements.
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    e1 - first element
    
    e2 - second element
    
    Returns:
    
    max(a1, e2)
  - min
```
public static <T extends CalculusFieldElement<T>> T min(T e1,
                                                        T e2)
```
    Find the minimum of two field elements.
    
    Type Parameters:
    
    T - the type of the field elements
    
    Parameters:
    
    e1 - first element
    
    e2 - second element
    
    Returns:
    
    min(a1, e2)
  - reduce
```
public static double reduce(double a,
                            double period,
                            double offset)
```
    Reduce |a - offset| to the primary interval [0, |period|).
    
    Specifically, the value returned is
    a - |period| * floor((a - offset) / |period|) - offset.
    
    If any of the parameters are NaN or infinite, the result is NaN.
    
    Parameters:
    
    a - Value to reduce.
    
    period - Period.
    
    offset - Value that will be mapped to 0.
    
    Returns:
    
    the value, within the interval [0 |period|), that corresponds to a.
  - copySign
```
public static byte copySign(byte magnitude,
                            byte sign)
                     throws MathRuntimeException
```
    Returns the first argument with the sign of the second argument.
    
    Parameters:
    
    magnitude - Magnitude of the returned value.
    
    sign - Sign of the returned value.
    
    Returns:
    
    a value with magnitude equal to magnitude and with the same sign as the sign argument.
    
    Throws:
    
    MathRuntimeException - if magnitude == Byte.MIN_VALUE and sign >= 0.
  - copySign
```
public static short copySign(short magnitude,
                             short sign)
                      throws MathRuntimeException
```
    Returns the first argument with the sign of the second argument.
    
    Parameters:
    
    magnitude - Magnitude of the returned value.
    
    sign - Sign of the returned value.
    
    Returns:
    
    a value with magnitude equal to magnitude and with the same sign as the sign argument.
    
    Throws:
    
    MathRuntimeException - if magnitude == Short.MIN_VALUE and sign >= 0.
  - copySign
```
public static int copySign(int magnitude,
                           int sign)
                    throws MathRuntimeException
```
    Returns the first argument with the sign of the second argument.
    
    Parameters:
    
    magnitude - Magnitude of the returned value.
    
    sign - Sign of the returned value.
    
    Returns:
    
    a value with magnitude equal to magnitude and with the same sign as the sign argument.
    
    Throws:
    
    MathRuntimeException - if magnitude == Integer.MIN_VALUE and sign >= 0.
  - copySign
```
public static long copySign(long magnitude,
                            long sign)
                     throws MathRuntimeException
```
    Returns the first argument with the sign of the second argument.
    
    Parameters:
    
    magnitude - Magnitude of the returned value.
    
    sign - Sign of the returned value.
    
    Returns:
    
    a value with magnitude equal to magnitude and with the same sign as the sign argument.
    
    Throws:
    
    MathRuntimeException - if magnitude == Long.MIN_VALUE and sign >= 0.
  - checkFinite
```
public static void checkFinite(double x)
                        throws MathIllegalArgumentException
```
    Check that the argument is a real number.
    
    Parameters:
    
    x - Argument.
    
    Throws:
    
    MathIllegalArgumentException - if x is not a finite real number.
  - checkFinite
```
public static void checkFinite(double[] val)
                        throws MathIllegalArgumentException
```
    Check that all the elements are real numbers.
    
    Parameters:
    
    val - Arguments.
    
    Throws:
    
    MathIllegalArgumentException - if any values of the array is not a finite real number.
  - checkNotNull
```
public static void checkNotNull(Object o,
                                Localizable pattern,
                                Object... args)
                         throws NullArgumentException
```
    Checks that an object is not null.
    
    Parameters:
    
    o - Object to be checked.
    
    pattern - Message pattern.
    
    args - Arguments to replace the placeholders in pattern.
    
    Throws:
    
    NullArgumentException - if o is null.
  - checkNotNull
```
public static void checkNotNull(Object o)
                         throws NullArgumentException
```
    Checks that an object is not null.
    
    Parameters:
    
    o - Object to be checked.
    
    Throws:
    
    NullArgumentException - if o is null.
  - checkRangeInclusive
```
public static void checkRangeInclusive(long value,
                                       long lo,
                                       long hi)
```
    Checks that the given value is strictly within the range [lo, hi].
    
    Parameters:
    
    value - value to be checked.
    
    lo - the lower bound (inclusive).
    
    hi - the upper bound (inclusive).
    
    Throws:
    
    MathIllegalArgumentException - if value is strictly outside [lo, hi].
  - checkRangeInclusive
```
public static void checkRangeInclusive(double value,
                                       double lo,
                                       double hi)
```
    Checks that the given value is strictly within the range [lo, hi].
    
    Parameters:
    
    value - value to be checked.
    
    lo - the lower bound (inclusive).
    
    hi - the upper bound (inclusive).
    
    Throws:
    
    MathIllegalArgumentException - if value is strictly outside [lo, hi].
  - checkDimension
```
public static void checkDimension(int dimension,
                                  int otherDimension)
```
    Checks that the given dimensions match.
    
    Parameters:
    
    dimension - the first dimension.
    
    otherDimension - the second dimension.
    
    Throws:
    
    MathIllegalArgumentException - if length != otherLength.
  - twoSum
```
public static MathUtils.SumAndResidual twoSum(double a,
                                              double b)
```
    Sums a and b using Møller's 2Sum algorithm.
    References:
    - Møller, Ole. "Quasi double-precision in floating point addition." BIT 5, 37–50 (1965).
    - Shewchuk, Richard J. "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates." Discrete & Computational Geometry 18, 305–363 (1997).
    - https://en.wikipedia.org/wiki/2Sum
    Parameters:
    
    a - first summand
    
    b - second summand
    
    Returns:
    
    sum and residual error in the sum
  - twoSum
```
public static <T extends FieldElement<T>> MathUtils.FieldSumAndResidual<T> twoSum(T a,
                                                                                  T b)
```
    Sums a and b using Møller's 2Sum algorithm.
    References:
    - Møller, Ole. "Quasi double-precision in floating point addition." BIT 5, 37–50 (1965).
    - Shewchuk, Richard J. "Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates." Discrete & Computational Geometry 18, 305–363 (1997).
    - https://en.wikipedia.org/wiki/2Sum
    Type Parameters:
    
    T - field element type
    
    Parameters:
    
    a - first summand
    
    b - second summand
    
    Returns:
    
    sum and residual error in the sum

Class MathUtils

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

TWO_PI

PI_SQUARED

SEMI_PI

Method Detail

hash

equals

hash

normalizeAngle

normalizeAngle

max

min

reduce

copySign

copySign

copySign

copySign

checkFinite

checkFinite

checkNotNull

checkNotNull

checkRangeInclusive

checkRangeInclusive

checkDimension

twoSum

twoSum