Package org.apache.commons.math4.legacy.analysis.differentiation

Class SparseGradient

java.lang.Object

org.apache.commons.math4.legacy.analysis.differentiation.SparseGradient

All Implemented Interfaces:

FieldElement<SparseGradient>, RealFieldElement<SparseGradient>

public final class SparseGradient
extends Object
implements RealFieldElement<SparseGradient>

First derivative computation with large number of variables.

This class plays a similar role to DerivativeStructure, with a focus on efficiency when dealing with large number of independent variables and most computation depend only on a few of them, and when only first derivative is desired. When these conditions are met, this class should be much faster than DerivativeStructure and use less memory.

Since:

3.3

Method Summary

Modifier and Type	Method	Description
SparseGradient	abs()
SparseGradient	acos()
SparseGradient	acosh()
SparseGradient	add(double c)
SparseGradient	add(SparseGradient a)
void	addInPlace(SparseGradient a)	Add in place.
SparseGradient	asin()
SparseGradient	asinh()
SparseGradient	atan()
SparseGradient	atan2(SparseGradient x)
static SparseGradient	atan2(SparseGradient y, SparseGradient x)	Two arguments arc tangent operation.
SparseGradient	atanh()
SparseGradient	cbrt()
SparseGradient	ceil()
SparseGradient	compose(double f0, double f1)	Compute composition of the instance by a univariate function.
SparseGradient	copySign(double sign)
SparseGradient	copySign(SparseGradient sign)
SparseGradient	cos()
SparseGradient	cosh()
static SparseGradient	createConstant(double value)	Factory method creating a constant.
static SparseGradient	createVariable(int idx, double value)	Factory method creating an independent variable.
SparseGradient	divide(double c)
SparseGradient	divide(SparseGradient a)
boolean	equals(Object other)	Test for the equality of two sparse gradients.
SparseGradient	exp()
SparseGradient	expm1()
SparseGradient	floor()
double	getDerivative(int index)	Get the derivative with respect to a particular index variable.
Field<SparseGradient>	getField()
double	getReal()
double	getValue()	Get the value of the function.
int	hashCode()	Get a hashCode for the derivative structure.
SparseGradient	hypot(SparseGradient y)
static SparseGradient	hypot(SparseGradient x, SparseGradient y)	Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2) avoiding intermediate overflow or underflow.
SparseGradient	linearCombination(double[] a, SparseGradient[] b)
SparseGradient	linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2)
SparseGradient	linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3)
SparseGradient	linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3, double a4, SparseGradient b4)
SparseGradient	linearCombination(SparseGradient[] a, SparseGradient[] b)
SparseGradient	linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2)
SparseGradient	linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3)
SparseGradient	linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3, SparseGradient a4, SparseGradient b4)
SparseGradient	log()
SparseGradient	log10()	Base 10 logarithm.
SparseGradient	log1p()
SparseGradient	multiply(double c)
SparseGradient	multiply(int n)
SparseGradient	multiply(SparseGradient a)
void	multiplyInPlace(SparseGradient a)	Multiply in place.
SparseGradient	negate()
int	numVars()	Find the number of variables.
SparseGradient	pow(double p)
static SparseGradient	pow(double a, SparseGradient x)	Compute ax where a is a double and x a SparseGradient.
SparseGradient	pow(int n)
SparseGradient	pow(SparseGradient e)
SparseGradient	reciprocal()
SparseGradient	remainder(double a)
SparseGradient	remainder(SparseGradient a)
SparseGradient	rint()
SparseGradient	rootN(int n)
long	round()
SparseGradient	scalb(int n)
SparseGradient	signum()
SparseGradient	sin()
SparseGradient	sinh()
SparseGradient	sqrt()
SparseGradient	subtract(double c)
SparseGradient	subtract(SparseGradient a)
SparseGradient	tan()
SparseGradient	tanh()
double	taylor(double... delta)	Evaluate Taylor expansion of a sparse gradient.
SparseGradient	toDegrees()	Convert radians to degrees, with error of less than 0.5 ULP.
SparseGradient	toRadians()	Convert degrees to radians, with error of less than 0.5 ULP.

Methods inherited from class java.lang.Object

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

Method Detail

createConstant

public static SparseGradient createConstant(double value)

Factory method creating a constant.

Parameters:

value - value of the constant

Returns:

a new instance

createVariable

public static SparseGradient createVariable(int idx,
                                            double value)

Factory method creating an independent variable.

Parameters:

idx - index of the variable

value - value of the variable

Returns:

a new instance

numVars

public int numVars()

Find the number of variables.

Returns:

number of variables

getDerivative

public double getDerivative(int index)

Get the derivative with respect to a particular index variable.

Parameters:

index - index to differentiate with.

Returns:

derivative with respect to a particular index variable

getValue

public double getValue()

Get the value of the function.

Returns:

value of the function.

getReal

public double getReal()

Specified by:

getReal in interface RealFieldElement<SparseGradient>

add

public SparseGradient add(SparseGradient a)

Specified by:

add in interface FieldElement<SparseGradient>

addInPlace

public void addInPlace(SparseGradient a)

Add in place.

This method is designed to be faster when used multiple times in a loop.

The instance is changed here, in order to not change the instance the add(SparseGradient) method should be used.

Parameters:

a - instance to add

add

public SparseGradient add(double c)

Specified by:

add in interface RealFieldElement<SparseGradient>

subtract

public SparseGradient subtract(SparseGradient a)

Specified by:

subtract in interface FieldElement<SparseGradient>

subtract

public SparseGradient subtract(double c)

Specified by:

subtract in interface RealFieldElement<SparseGradient>

multiply

public SparseGradient multiply(SparseGradient a)

Specified by:

multiply in interface FieldElement<SparseGradient>

multiplyInPlace

public void multiplyInPlace(SparseGradient a)

Multiply in place.

This method is designed to be faster when used multiple times in a loop.

The instance is changed here, in order to not change the instance the add(SparseGradient) method should be used.

Parameters:

a - instance to multiply

multiply

public SparseGradient multiply(double c)

Specified by:

multiply in interface RealFieldElement<SparseGradient>

multiply

public SparseGradient multiply(int n)

Specified by:

multiply in interface FieldElement<SparseGradient>

divide

public SparseGradient divide(SparseGradient a)

Specified by:

divide in interface FieldElement<SparseGradient>

divide

public SparseGradient divide(double c)

Specified by:

divide in interface RealFieldElement<SparseGradient>

negate

public SparseGradient negate()

Specified by:

negate in interface FieldElement<SparseGradient>

getField

public Field<SparseGradient> getField()

Specified by:

getField in interface FieldElement<SparseGradient>

remainder

public SparseGradient remainder(double a)

Specified by:

remainder in interface RealFieldElement<SparseGradient>

remainder

public SparseGradient remainder(SparseGradient a)

Specified by:

remainder in interface RealFieldElement<SparseGradient>

abs

public SparseGradient abs()

Specified by:

abs in interface RealFieldElement<SparseGradient>

ceil

public SparseGradient ceil()

Specified by:

ceil in interface RealFieldElement<SparseGradient>

floor

public SparseGradient floor()

Specified by:

floor in interface RealFieldElement<SparseGradient>

rint

public SparseGradient rint()

Specified by:

rint in interface RealFieldElement<SparseGradient>

round

public long round()

Specified by:

round in interface RealFieldElement<SparseGradient>

signum

public SparseGradient signum()

Specified by:

signum in interface RealFieldElement<SparseGradient>

copySign

public SparseGradient copySign(SparseGradient sign)

Specified by:

copySign in interface RealFieldElement<SparseGradient>

copySign

public SparseGradient copySign(double sign)

Specified by:

copySign in interface RealFieldElement<SparseGradient>

scalb

public SparseGradient scalb(int n)

Specified by:

scalb in interface RealFieldElement<SparseGradient>

hypot

public SparseGradient hypot(SparseGradient y)

Specified by:

hypot in interface RealFieldElement<SparseGradient>

hypot

public static SparseGradient hypot(SparseGradient x,
                                   SparseGradient y)

Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²) avoiding intermediate overflow or underflow.

• If either argument is infinite, then the result is positive infinity.
• else, if either argument is NaN then the result is NaN.

Parameters:

x - a value

y - a value

Returns:

sqrt(x² +y²)

reciprocal

public SparseGradient reciprocal()

Specified by:

reciprocal in interface FieldElement<SparseGradient>

Specified by:

reciprocal in interface RealFieldElement<SparseGradient>

sqrt

public SparseGradient sqrt()

Specified by:

sqrt in interface RealFieldElement<SparseGradient>

cbrt

public SparseGradient cbrt()

Specified by:

cbrt in interface RealFieldElement<SparseGradient>

rootN

public SparseGradient rootN(int n)

Specified by:

rootN in interface RealFieldElement<SparseGradient>

pow

public SparseGradient pow(double p)

Specified by:

pow in interface RealFieldElement<SparseGradient>

pow

public SparseGradient pow(int n)

Specified by:

pow in interface RealFieldElement<SparseGradient>

pow

public SparseGradient pow(SparseGradient e)

Specified by:

pow in interface RealFieldElement<SparseGradient>

pow

public static SparseGradient pow(double a,
                                 SparseGradient x)

Compute a^x where a is a double and x a SparseGradient.

Parameters:

a - number to exponentiate

x - power to apply

Returns:

a^x

exp

public SparseGradient exp()

Specified by:

exp in interface RealFieldElement<SparseGradient>

expm1

public SparseGradient expm1()

Specified by:

expm1 in interface RealFieldElement<SparseGradient>

log

public SparseGradient log()

Specified by:

log in interface RealFieldElement<SparseGradient>

log10

public SparseGradient log10()

Base 10 logarithm.

Specified by:

log10 in interface RealFieldElement<SparseGradient>

Returns:

base 10 logarithm of the instance

log1p

public SparseGradient log1p()

Specified by:

log1p in interface RealFieldElement<SparseGradient>

cos

public SparseGradient cos()

Specified by:

cos in interface RealFieldElement<SparseGradient>

sin

public SparseGradient sin()

Specified by:

sin in interface RealFieldElement<SparseGradient>

tan

public SparseGradient tan()

Specified by:

tan in interface RealFieldElement<SparseGradient>

acos

public SparseGradient acos()

Specified by:

acos in interface RealFieldElement<SparseGradient>

asin

public SparseGradient asin()

Specified by:

asin in interface RealFieldElement<SparseGradient>

atan

public SparseGradient atan()

Specified by:

atan in interface RealFieldElement<SparseGradient>

atan2

public SparseGradient atan2(SparseGradient x)

Specified by:

atan2 in interface RealFieldElement<SparseGradient>

atan2

public static SparseGradient atan2(SparseGradient y,
                                   SparseGradient x)

Two arguments arc tangent operation.

Parameters:

y - first argument of the arc tangent

x - second argument of the arc tangent

Returns:

atan2(y, x)

cosh

public SparseGradient cosh()

Specified by:

cosh in interface RealFieldElement<SparseGradient>

sinh

public SparseGradient sinh()

Specified by:

sinh in interface RealFieldElement<SparseGradient>

tanh

public SparseGradient tanh()

Specified by:

tanh in interface RealFieldElement<SparseGradient>

acosh

public SparseGradient acosh()

Specified by:

acosh in interface RealFieldElement<SparseGradient>

asinh

public SparseGradient asinh()

Specified by:

asinh in interface RealFieldElement<SparseGradient>

atanh

public SparseGradient atanh()

Specified by:

atanh in interface RealFieldElement<SparseGradient>

toDegrees

public SparseGradient toDegrees()

Convert radians to degrees, with error of less than 0.5 ULP.

Returns:

instance converted into degrees

toRadians

public SparseGradient toRadians()

Convert degrees to radians, with error of less than 0.5 ULP.

Returns:

instance converted into radians

taylor

public double taylor(double... delta)

Evaluate Taylor expansion of a sparse gradient.

Parameters:

delta - parameters offsets (Δx, Δy, ...)

Returns:

value of the Taylor expansion at x + Δx, y + Δy, ...

compose

public SparseGradient compose(double f0,
                              double f1)

Compute composition of the instance by a univariate function.

Parameters:

f0 - value of the function at (i.e. f(getValue()))

f1 - first derivative of the function at the current point (i.e. f'(getValue()))

Returns:

f(this)

linearCombination

public SparseGradient linearCombination(SparseGradient[] a,
                                        SparseGradient[] b)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(double[] a,
                                        SparseGradient[] b)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(SparseGradient a1,
                                        SparseGradient b1,
                                        SparseGradient a2,
                                        SparseGradient b2)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(double a1,
                                        SparseGradient b1,
                                        double a2,
                                        SparseGradient b2)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(SparseGradient a1,
                                        SparseGradient b1,
                                        SparseGradient a2,
                                        SparseGradient b2,
                                        SparseGradient a3,
                                        SparseGradient b3)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(double a1,
                                        SparseGradient b1,
                                        double a2,
                                        SparseGradient b2,
                                        double a3,
                                        SparseGradient b3)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(SparseGradient a1,
                                        SparseGradient b1,
                                        SparseGradient a2,
                                        SparseGradient b2,
                                        SparseGradient a3,
                                        SparseGradient b3,
                                        SparseGradient a4,
                                        SparseGradient b4)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

linearCombination

public SparseGradient linearCombination(double a1,
                                        SparseGradient b1,
                                        double a2,
                                        SparseGradient b2,
                                        double a3,
                                        SparseGradient b3,
                                        double a4,
                                        SparseGradient b4)

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

equals

public boolean equals(Object other)

Test for the equality of two sparse gradients.

Sparse gradients are considered equal if they have the same value and the same derivatives.

Overrides:

equals in class Object

Parameters:

other - Object to test for equality to this

Returns:

true if two sparse gradients are equal

hashCode

public int hashCode()

Get a hashCode for the derivative structure.

Overrides:

hashCode in class Object

Returns:

a hash code value for this object

Since:

3.2