org.apache.commons.nabla
Class NablaMath

java.lang.Object
  org.apache.commons.nabla.NablaMath

public class NablaMath
extends Object

Math-like utility class computing differentials.

This class provides mathematical functions similar to the functions provided by the standard java.lang.Math class but using DifferentialPair instances instead of doubles.

Method Summary

static DifferentialPair	abs(DifferentialPair a) Absolute value function.
static DifferentialPair	acos(DifferentialPair a) Inverse cosine function.
static DifferentialPair	acosh(DifferentialPair a) Inverse hyperbolic cosine function.
static DifferentialPair	asin(DifferentialPair a) Inverse sine function.
static DifferentialPair	asinh(DifferentialPair a) Inverse hyperbolic sine function.
static DifferentialPair	atan(DifferentialPair a) Inverse tangent function.
static DifferentialPair	atan2(DifferentialPair y, DifferentialPair x) Cartesian to polar conversion function.
static DifferentialPair	atan2(DifferentialPair y, double x) Cartesian to polar conversion function.
static DifferentialPair	atan2(double y, DifferentialPair x) Cartesian to polar conversion function.
static DifferentialPair	atanh(DifferentialPair a) Inverse hyperbolic tangent function.
static DifferentialPair	cbrt(DifferentialPair a) Cubic root function.
static DifferentialPair	ceil(DifferentialPair a) Ceil function.
static DifferentialPair	copySign(DifferentialPair magnitude, DifferentialPair sign) Sign copy function.
static DifferentialPair	copySign(DifferentialPair magnitude, double sign) Sign copy function.
static DifferentialPair	copySign(double magnitude, DifferentialPair sign) Sign copy function.
static DifferentialPair	cos(DifferentialPair a) Cosine function.
static DifferentialPair	cosh(DifferentialPair a) Hyperbolic cosine function.
static DifferentialPair	exp(DifferentialPair a) Exponential function.
static DifferentialPair	expm1(DifferentialPair a) Exponential minus 1 function.
static DifferentialPair	floor(DifferentialPair a) Floor function.
static DifferentialPair	hypot(DifferentialPair x, DifferentialPair y) Cartesian to polar conversion function.
static DifferentialPair	hypot(DifferentialPair x, double y) Cartesian to polar conversion function.
static DifferentialPair	hypot(double x, DifferentialPair y) Cartesian to polar conversion function.
static DifferentialPair	IEEEremainder(DifferentialPair f1, DifferentialPair f2) Remainder function.
static DifferentialPair	IEEEremainder(DifferentialPair f1, double f2) Remainder function.
static DifferentialPair	IEEEremainder(double f1, DifferentialPair f2) Remainder function.
static DifferentialPair	log(DifferentialPair a) Natural logarithm function.
static DifferentialPair	log10(DifferentialPair a) Base 10 logarithm function.
static DifferentialPair	log1p(DifferentialPair a) Shifted natural logarithm function.
static DifferentialPair	max(DifferentialPair a, DifferentialPair b) Max function.
static DifferentialPair	max(DifferentialPair a, double b) Max function.
static DifferentialPair	max(double a, DifferentialPair b) Max function.
static DifferentialPair	min(DifferentialPair a, DifferentialPair b) Min function.
static DifferentialPair	min(DifferentialPair a, double b) Min function.
static DifferentialPair	min(double a, DifferentialPair b) Min function.
static DifferentialPair	nextAfter(DifferentialPair start, DifferentialPair direction) Neighbor function.
static DifferentialPair	nextAfter(DifferentialPair start, double direction) Neighbor function.
static DifferentialPair	nextAfter(double start, DifferentialPair direction) Neighbor function.
static DifferentialPair	nextUp(DifferentialPair a) Neighbor function.
static DifferentialPair	pow(DifferentialPair a, DifferentialPair b) Power function.
static DifferentialPair	pow(DifferentialPair a, double b) Power function.
static DifferentialPair	pow(double a, DifferentialPair b) Power function.
static DifferentialPair	rint(DifferentialPair a) Rounding function.
static DifferentialPair	scalb(DifferentialPair a, int scale) Binary rescaling function.
static DifferentialPair	signum(DifferentialPair a) Sign function.
static DifferentialPair	sin(DifferentialPair a) Sine function.
static DifferentialPair	sinh(DifferentialPair a) Hyperbolic sine function.
static DifferentialPair	sqrt(DifferentialPair a) Square root function.
static DifferentialPair	tan(DifferentialPair a) Tangent function.
static DifferentialPair	tanh(DifferentialPair a) Hyperbolic tangent function.
static DifferentialPair	toDegrees(DifferentialPair a) Angular conversion function.
static DifferentialPair	toRadians(DifferentialPair a) Angular conversion function.
static DifferentialPair	ulp(DifferentialPair a) Unit in Last Position function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

exp

public static DifferentialPair exp(DifferentialPair a)

Exponential function.

Parameters:

a - function input value

Returns:

e^a

expm1

public static DifferentialPair expm1(DifferentialPair a)

Exponential minus 1 function.

Parameters:

a - function input value

Returns:

e^a-1

log

public static DifferentialPair log(DifferentialPair a)

Natural logarithm function.

Parameters:

a - function input value

Returns:

log(a)

log1p

public static DifferentialPair log1p(DifferentialPair a)

Shifted natural logarithm function.

Parameters:

a - function input value

Returns:

log(1+a)

log10

public static DifferentialPair log10(DifferentialPair a)

Base 10 logarithm function.

Parameters:

a - function input value

Returns:

log₁₀(a)

cos

public static DifferentialPair cos(DifferentialPair a)

Cosine function.

Parameters:

a - function input value

Returns:

cos(a)

sin

public static DifferentialPair sin(DifferentialPair a)

Sine function.

Parameters:

a - function input value

Returns:

sin(a)

tan

public static DifferentialPair tan(DifferentialPair a)

Tangent function.

Parameters:

a - function input value

Returns:

tan(a)

acos

public static DifferentialPair acos(DifferentialPair a)

Inverse cosine function.

Parameters:

a - function input value

Returns:

acos(a)

asin

public static DifferentialPair asin(DifferentialPair a)

Inverse sine function.

Parameters:

a - function input value

Returns:

asin(a)

atan

public static DifferentialPair atan(DifferentialPair a)

Inverse tangent function.

Parameters:

a - function input value

Returns:

atan(a)

atan2

public static DifferentialPair atan2(DifferentialPair y,
                                     double x)

Cartesian to polar conversion function.

Parameters:

y - cartesian ordinate of the point

x - cartesian abscissa of the point

Returns:

angular part of the polar coordinates of the point

atan2

public static DifferentialPair atan2(double y,
                                     DifferentialPair x)

Cartesian to polar conversion function.

Parameters:

y - cartesian ordinate of the point

x - cartesian abscissa of the point

Returns:

angular part of the polar coordinates of the point

atan2

public static DifferentialPair atan2(DifferentialPair y,
                                     DifferentialPair x)

Cartesian to polar conversion function.

Parameters:

y - cartesian ordinate of the point

x - cartesian abscissa of the point

Returns:

angular part of the polar coordinates of the point

hypot

public static DifferentialPair hypot(DifferentialPair x,
                                     double y)

Cartesian to polar conversion function.

Parameters:

x - cartesian abscissa of the point

y - cartesian ordinate of the point

Returns:

radius part of the polar coordinates of the point

hypot

public static DifferentialPair hypot(double x,
                                     DifferentialPair y)

Cartesian to polar conversion function.

Parameters:

x - cartesian abscissa of the point

y - cartesian ordinate of the point

Returns:

radius part of the polar coordinates of the point

hypot

public static DifferentialPair hypot(DifferentialPair x,
                                     DifferentialPair y)

Cartesian to polar conversion function.

Parameters:

x - cartesian abscissa of the point

y - cartesian ordinate of the point

Returns:

radius part of the polar coordinates of the point

cosh

public static DifferentialPair cosh(DifferentialPair a)

Hyperbolic cosine function.

Parameters:

a - function input value

Returns:

cosh(a)

sinh

public static DifferentialPair sinh(DifferentialPair a)

Hyperbolic sine function.

Parameters:

a - function input value

Returns:

sinh(a)

tanh

public static DifferentialPair tanh(DifferentialPair a)

Hyperbolic tangent function.

Parameters:

a - function input value

Returns:

tanh(a)

acosh

public static DifferentialPair acosh(DifferentialPair a)

Inverse hyperbolic cosine function.

Parameters:

a - function input value

Returns:

acosh(a)

asinh

public static DifferentialPair asinh(DifferentialPair a)

Inverse hyperbolic sine function.

Parameters:

a - function input value

Returns:

asinh(a)

atanh

public static DifferentialPair atanh(DifferentialPair a)

Inverse hyperbolic tangent function.

Parameters:

a - function input value

Returns:

atanh(a)

sqrt

public static DifferentialPair sqrt(DifferentialPair a)

Square root function.

Parameters:

a - function input value

Returns:

&sqrt;a

cbrt

public static DifferentialPair cbrt(DifferentialPair a)

Cubic root function.

Parameters:

a - function input value

Returns:

cbrt(a)

pow

public static DifferentialPair pow(DifferentialPair a,
                                   double b)

Power function.

Parameters:

a - base value

b - exponent value

Returns:

a^b

pow

public static DifferentialPair pow(double a,
                                   DifferentialPair b)

Power function.

Parameters:

a - base value

b - exponent value

Returns:

a^b

pow

public static DifferentialPair pow(DifferentialPair a,
                                   DifferentialPair b)

Power function.

Parameters:

a - base value

b - exponent value

Returns:

a^b

abs

public static DifferentialPair abs(DifferentialPair a)

Absolute value function.

Parameters:

a - function input value

Returns:

|a|

signum

public static DifferentialPair signum(DifferentialPair a)

Sign function.

Parameters:

a - function input value

Returns:

-1, 0 or +1 according to the sign of a

copySign

public static DifferentialPair copySign(DifferentialPair magnitude,
                                        double sign)

Sign copy function.

Parameters:

magnitude - function input value

sign - sign reference

Returns:

either magnitude or -magnitude to match sign

copySign

public static DifferentialPair copySign(double magnitude,
                                        DifferentialPair sign)

Sign copy function.

Parameters:

magnitude - function input value

sign - sign reference

Returns:

either magnitude or -magnitude to match sign

copySign

public static DifferentialPair copySign(DifferentialPair magnitude,
                                        DifferentialPair sign)

Sign copy function.

Parameters:

magnitude - function input value

sign - sign reference

Returns:

either magnitude or -magnitude to match sign

floor

public static DifferentialPair floor(DifferentialPair a)

Floor function.

Parameters:

a - function input value

Returns:

largest integer value smaller than a or equal to a

rint

public static DifferentialPair rint(DifferentialPair a)

Rounding function.

Parameters:

a - function input value

Returns:

closest integer value to a

ceil

public static DifferentialPair ceil(DifferentialPair a)

Ceil function.

Parameters:

a - function input value

Returns:

smallest integer value greater than a or equal to a

nextUp

public static DifferentialPair nextUp(DifferentialPair a)

Neighbor function.

Parameters:

a - function input value

Returns:

smallest representable double value ly greater than a

nextAfter

public static DifferentialPair nextAfter(DifferentialPair start,
                                         double direction)

Neighbor function.

Parameters:

start - function input value

direction - direction of neighboring (relative to a)

Returns:

closest double value different than a in given direction

nextAfter

public static DifferentialPair nextAfter(double start,
                                         DifferentialPair direction)

Neighbor function.

Parameters:

start - function input value

direction - direction of neighboring (relative to a)

Returns:

closest double value different than a in given direction

nextAfter

public static DifferentialPair nextAfter(DifferentialPair start,
                                         DifferentialPair direction)

Neighbor function.

Parameters:

start - function input value

direction - direction of neighboring (relative to a)

Returns:

closest double value different than a in given direction

ulp

public static DifferentialPair ulp(DifferentialPair a)

Unit in Last Position function.

Parameters:

a - function input value

Returns:

value of the least significant bit of a

scalb

public static DifferentialPair scalb(DifferentialPair a,
                                     int scale)

Binary rescaling function.

Parameters:

a - function input value

scale - exponent part of the 2^scale multiplication factor

Returns:

a × 2^scale

IEEEremainder

public static DifferentialPair IEEEremainder(DifferentialPair f1,
                                             double f2)

Remainder function.

Parameters:

f1 - dividend

f2 - divisor

Returns:

remainder of f1/f2, following IEEE754 conventions

IEEEremainder

public static DifferentialPair IEEEremainder(double f1,
                                             DifferentialPair f2)

Remainder function.

Parameters:

f1 - dividend

f2 - divisor

Returns:

remainder of f1/f2, following IEEE754 conventions

IEEEremainder

public static DifferentialPair IEEEremainder(DifferentialPair f1,
                                             DifferentialPair f2)

Remainder function.

Parameters:

f1 - dividend

f2 - divisor

Returns:

remainder of f1/f2, following IEEE754 conventions

toDegrees

public static DifferentialPair toDegrees(DifferentialPair a)

Angular conversion function.

Parameters:

a - angle in radians

Returns:

angle converted to degrees

toRadians

public static DifferentialPair toRadians(DifferentialPair a)

Angular conversion function.

Parameters:

a - angle in degrees

Returns:

angle converted to radians

max

public static DifferentialPair max(DifferentialPair a,
                                   double b)

Max function.

Parameters:

a - first function input value

b - second function input value

Returns:

maximal value from the (a, b) pair

max

public static DifferentialPair max(double a,
                                   DifferentialPair b)

Max function.

Parameters:

a - first function input value

b - second function input value

Returns:

maximal value from the (a, b) pair

max

public static DifferentialPair max(DifferentialPair a,
                                   DifferentialPair b)

Max function.

Parameters:

a - first function input value

b - second function input value

Returns:

maximal value from the (a, b) pair

min

public static DifferentialPair min(DifferentialPair a,
                                   double b)

Min function.

Parameters:

a - first function input value

b - second function input value

Returns:

minimal value from the (a, b) pair

min

public static DifferentialPair min(double a,
                                   DifferentialPair b)

Min function.

Parameters:

a - first function input value

b - second function input value

Returns:

minimal value from the (a, b) pair

min

public static DifferentialPair min(DifferentialPair a,
                                   DifferentialPair b)

Min function.

Parameters:

a - first function input value

b - second function input value

Returns:

minimal value from the (a, b) pair