Package org.hipparchus.util
Class MathUtils
java.lang.Object
org.hipparchus.util.MathUtils
Miscellaneous utility functions.
- See Also:
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Nested Class Summary
Modifier and TypeClassDescriptionstatic final class
MathUtils.FieldSumAndResidual<T extends FieldElement<T>>
Result class fortwoSum(FieldElement, FieldElement)
containing the sum and the residual error in the sum.static final class
Result class fortwoSum(double, double)
containing the sum and the residual error in the sum. -
Field Summary
Modifier and TypeFieldDescriptionstatic final double
\(\pi^2\)static final double
\(\pi/2\).static final double
\(2\pi\) -
Method Summary
Modifier and TypeMethodDescriptionstatic 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
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) Returnstrue
if the values are equal according to semantics ofDouble.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>>
Tmax
(T e1, T e2) Find the maximum of two field elements.static <T extends CalculusFieldElement<T>>
Tmin
(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>>
TnormalizeAngle
(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) Sumsa
andb
using Møller's 2Sum algorithm.static <T extends FieldElement<T>>
MathUtils.FieldSumAndResidual<T>twoSum
(T a, T b) Sumsa
andb
using Møller's 2Sum algorithm.
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Field Details
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TWO_PI
public static final double TWO_PI\(2\pi\)- See Also:
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PI_SQUARED
public static final double PI_SQUARED\(\pi^2\)- See Also:
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SEMI_PI
public static final double SEMI_PI\(\pi/2\).- See Also:
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Method Details
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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
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equals
public static boolean equals(double x, double y) Returnstrue
if the values are equal according to semantics ofDouble.equals(Object)
.- Parameters:
x
- Valuey
- Value- Returns:
Double.valueOf(x).equals(Double.valueOf(y))
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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
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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 normalizecenter
- center of the desired 2π interval for the result- Returns:
- a-2kπ with integer k and center-π <= a-2kπ <= center+π
- normalize an angle between 0 and 2π:
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normalizeAngle
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 normalizecenter
- center of the desired 2π interval for the result- Returns:
- a-2kπ with integer k and center-π <= a-2kπ <= center+π
- normalize an angle between 0 and 2π:
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max
Find the maximum of two field elements.- Type Parameters:
T
- the type of the field elements- Parameters:
e1
- first elemente2
- second element- Returns:
- max(a1, e2)
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min
Find the minimum of two field elements.- Type Parameters:
T
- the type of the field elements- Parameters:
e1
- first elemente2
- second element- Returns:
- min(a1, e2)
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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 isNaN
.- Parameters:
a
- Value to reduce.period
- Period.offset
- Value that will be mapped to0
.- Returns:
- the value, within the interval
[0 |period|)
, that corresponds toa
.
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copySign
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 thesign
argument. - Throws:
MathRuntimeException
- ifmagnitude == Byte.MIN_VALUE
andsign >= 0
.
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copySign
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 thesign
argument. - Throws:
MathRuntimeException
- ifmagnitude == Short.MIN_VALUE
andsign >= 0
.
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copySign
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 thesign
argument. - Throws:
MathRuntimeException
- ifmagnitude == Integer.MIN_VALUE
andsign >= 0
.
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copySign
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 thesign
argument. - Throws:
MathRuntimeException
- ifmagnitude == Long.MIN_VALUE
andsign >= 0
.
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checkFinite
Check that the argument is a real number.- Parameters:
x
- Argument.- Throws:
MathIllegalArgumentException
- ifx
is not a finite real number.
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checkFinite
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.
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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 inpattern
.- Throws:
NullArgumentException
- ifo
isnull
.
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checkNotNull
Checks that an object is not null.- Parameters:
o
- Object to be checked.- Throws:
NullArgumentException
- ifo
isnull
.
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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
- ifvalue
is strictly outside [lo, hi].
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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
- ifvalue
is strictly outside [lo, hi].
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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.
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twoSum
Sumsa
andb
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 summandb
- second summand- Returns:
- sum and residual error in the sum
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twoSum
Sumsa
andb
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 summandb
- second summand- Returns:
- sum and residual error in the sum
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