org.apache.commons.math3.analysis.differentiation

Class SparseGradient

java.lang.Object

org.apache.commons.math3.analysis.differentiation.SparseGradient

All Implemented Interfaces:

java.io.Serializable, FieldElement<SparseGradient>, RealFieldElement<SparseGradient>

public class SparseGradient
extends java.lang.Object
implements RealFieldElement<SparseGradient>, java.io.Serializable

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

See Also:

Serialized Form

Method Summary

Modifier and Type	Method and Description
SparseGradient	abs() absolute value.
SparseGradient	acos() Arc cosine operation.
SparseGradient	acosh() Inverse hyperbolic cosine operation.
SparseGradient	add(double c) '+' operator.
SparseGradient	add(SparseGradient a) Compute this + a.
void	addInPlace(SparseGradient a) Add in place.
SparseGradient	asin() Arc sine operation.
SparseGradient	asinh() Inverse hyperbolic sine operation.
SparseGradient	atan() Arc tangent operation.
SparseGradient	atan2(SparseGradient x) Two arguments arc tangent operation.
static SparseGradient	atan2(SparseGradient y, SparseGradient x) Two arguments arc tangent operation.
SparseGradient	atanh() Inverse hyperbolic tangent operation.
SparseGradient	cbrt() Cubic root.
SparseGradient	ceil() Get the smallest whole number larger than instance.
SparseGradient	compose(double f0, double f1) Compute composition of the instance by a univariate function.
SparseGradient	copySign(double sign) Returns the instance with the sign of the argument.
SparseGradient	copySign(SparseGradient sign) Returns the instance with the sign of the argument.
SparseGradient	cos() Cosine operation.
SparseGradient	cosh() Hyperbolic cosine operation.
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) '÷' operator.
SparseGradient	divide(SparseGradient a) Compute this ÷ a.
boolean	equals(java.lang.Object other) Test for the equality of two sparse gradients.
SparseGradient	exp() Exponential.
SparseGradient	expm1() Exponential minus 1.
SparseGradient	floor() Get the largest whole number smaller than instance.
double	getDerivative(int index) Get the derivative with respect to a particular index variable.
Field<SparseGradient>	getField() Get the Field to which the instance belongs.
double	getReal() Get the real value of the number.
double	getValue() Get the value of the function.
int	hashCode() Get a hashCode for the derivative structure.
SparseGradient	hypot(SparseGradient y) Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
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) Compute a linear combination.
SparseGradient	linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2) Compute a linear combination.
SparseGradient	linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3) Compute a linear combination.
SparseGradient	linearCombination(double a1, SparseGradient b1, double a2, SparseGradient b2, double a3, SparseGradient b3, double a4, SparseGradient b4) Compute a linear combination.
SparseGradient	linearCombination(SparseGradient[] a, SparseGradient[] b) Compute a linear combination.
SparseGradient	linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2) Compute a linear combination.
SparseGradient	linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3) Compute a linear combination.
SparseGradient	linearCombination(SparseGradient a1, SparseGradient b1, SparseGradient a2, SparseGradient b2, SparseGradient a3, SparseGradient b3, SparseGradient a4, SparseGradient b4) Compute a linear combination.
SparseGradient	log() Natural logarithm.
SparseGradient	log10() Base 10 logarithm.
SparseGradient	log1p() Shifted natural logarithm.
SparseGradient	multiply(double c) '×' operator.
SparseGradient	multiply(int n) Compute n × this.
SparseGradient	multiply(SparseGradient a) Compute this × a.
void	multiplyInPlace(SparseGradient a) Multiply in place.
SparseGradient	negate() Returns the additive inverse of this element.
int	numVars() Find the number of variables.
SparseGradient	pow(double p) Power operation.
static SparseGradient	pow(double a, SparseGradient x) Compute ax where a is a double and x a SparseGradient
SparseGradient	pow(int n) Integer power operation.
SparseGradient	pow(SparseGradient e) Power operation.
SparseGradient	reciprocal() Returns the multiplicative inverse of this element.
SparseGradient	remainder(double a) IEEE remainder operator.
SparseGradient	remainder(SparseGradient a) IEEE remainder operator.
SparseGradient	rint() Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
SparseGradient	rootN(int n) Nth root.
long	round() Get the closest long to instance value.
SparseGradient	scalb(int n) Multiply the instance by a power of 2.
SparseGradient	signum() Compute the signum of the instance.
SparseGradient	sin() Sine operation.
SparseGradient	sinh() Hyperbolic sine operation.
SparseGradient	sqrt() Square root.
SparseGradient	subtract(double c) '-' operator.
SparseGradient	subtract(SparseGradient a) Compute this - a.
SparseGradient	tan() Tangent operation.
SparseGradient	tanh() Hyperbolic tangent operation.
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

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()

Get the real value of the number.

Specified by:

getReal in interface RealFieldElement<SparseGradient>

Returns:

real value

add

public SparseGradient add(SparseGradient a)

Compute this + a.

Specified by:

add in interface FieldElement<SparseGradient>

Parameters:

a - element to add

Returns:

a new element representing this + a

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)

'+' operator.

Specified by:

add in interface RealFieldElement<SparseGradient>

Parameters:

c - right hand side parameter of the operator

Returns:

this+a

subtract

public SparseGradient subtract(SparseGradient a)

Compute this - a.

Specified by:

subtract in interface FieldElement<SparseGradient>

Parameters:

a - element to subtract

Returns:

a new element representing this - a

subtract

public SparseGradient subtract(double c)

'-' operator.

Specified by:

subtract in interface RealFieldElement<SparseGradient>

Parameters:

c - right hand side parameter of the operator

Returns:

this-a

multiply

public SparseGradient multiply(SparseGradient a)

Compute this × a.

Specified by:

multiply in interface FieldElement<SparseGradient>

Parameters:

a - element to multiply

Returns:

a new element representing this × a

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)

'×' operator.

Specified by:

multiply in interface RealFieldElement<SparseGradient>

Parameters:

c - right hand side parameter of the operator

Returns:

this×a

multiply

public SparseGradient multiply(int n)

Compute n × this. Multiplication by an integer number is defined as the following sum n × this = ∑_i=1ⁿ this.

Specified by:

multiply in interface FieldElement<SparseGradient>

Parameters:

n - Number of times this must be added to itself.

Returns:

A new element representing n × this.

divide

public SparseGradient divide(SparseGradient a)

Compute this ÷ a.

Specified by:

divide in interface FieldElement<SparseGradient>

Parameters:

a - element to divide by

Returns:

a new element representing this ÷ a

divide

public SparseGradient divide(double c)

'÷' operator.

Specified by:

divide in interface RealFieldElement<SparseGradient>

Parameters:

c - right hand side parameter of the operator

Returns:

this÷a

negate

public SparseGradient negate()

Returns the additive inverse of this element.

Specified by:

negate in interface FieldElement<SparseGradient>

Returns:

the opposite of this.

getField

public Field<SparseGradient> getField()

Get the Field to which the instance belongs.

Specified by:

getField in interface FieldElement<SparseGradient>

Returns:

Field to which the instance belongs

remainder

public SparseGradient remainder(double a)

IEEE remainder operator.

Specified by:

remainder in interface RealFieldElement<SparseGradient>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)

remainder

public SparseGradient remainder(SparseGradient a)

IEEE remainder operator.

Specified by:

remainder in interface RealFieldElement<SparseGradient>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)

abs

public SparseGradient abs()

absolute value.

Specified by:

abs in interface RealFieldElement<SparseGradient>

Returns:

abs(this)

ceil

public SparseGradient ceil()

Get the smallest whole number larger than instance.

Specified by:

ceil in interface RealFieldElement<SparseGradient>

Returns:

ceil(this)

floor

public SparseGradient floor()

Get the largest whole number smaller than instance.

Specified by:

floor in interface RealFieldElement<SparseGradient>

Returns:

floor(this)

rint

public SparseGradient rint()

Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.

Specified by:

rint in interface RealFieldElement<SparseGradient>

Returns:

a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5

round

public long round()

Get the closest long to instance value.

Specified by:

round in interface RealFieldElement<SparseGradient>

Returns:

closest long to RealFieldElement.getReal()

signum

public SparseGradient signum()

Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise

Specified by:

signum in interface RealFieldElement<SparseGradient>

Returns:

-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

copySign

public SparseGradient copySign(SparseGradient sign)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

Specified by:

copySign in interface RealFieldElement<SparseGradient>

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

copySign

public SparseGradient copySign(double sign)

Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.

Specified by:

copySign in interface RealFieldElement<SparseGradient>

Parameters:

sign - the sign for the returned value

Returns:

the instance with the same sign as the sign argument

scalb

public SparseGradient scalb(int n)

Multiply the instance by a power of 2.

Specified by:

scalb in interface RealFieldElement<SparseGradient>

Parameters:

n - power of 2

Returns:

this × 2ⁿ

hypot

public SparseGradient hypot(SparseGradient y)

Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +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.

Specified by:

hypot in interface RealFieldElement<SparseGradient>

Parameters:

y - a value

Returns:

sqrt(this² +y²)

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()

Returns the multiplicative inverse of this element.

Specified by:

reciprocal in interface FieldElement<SparseGradient>

Specified by:

reciprocal in interface RealFieldElement<SparseGradient>

Returns:

the inverse of this.

sqrt

public SparseGradient sqrt()

Square root.

Specified by:

sqrt in interface RealFieldElement<SparseGradient>

Returns:

square root of the instance

cbrt

public SparseGradient cbrt()

Cubic root.

Specified by:

cbrt in interface RealFieldElement<SparseGradient>

Returns:

cubic root of the instance

rootN

public SparseGradient rootN(int n)

N^th root.

Specified by:

rootN in interface RealFieldElement<SparseGradient>

Parameters:

n - order of the root

Returns:

n^th root of the instance

pow

public SparseGradient pow(double p)

Power operation.

Specified by:

pow in interface RealFieldElement<SparseGradient>

Parameters:

p - power to apply

Returns:

this^p

pow

public SparseGradient pow(int n)

Integer power operation.

Specified by:

pow in interface RealFieldElement<SparseGradient>

Parameters:

n - power to apply

Returns:

thisⁿ

pow

public SparseGradient pow(SparseGradient e)

Power operation.

Specified by:

pow in interface RealFieldElement<SparseGradient>

Parameters:

e - exponent

Returns:

this^e

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()

Exponential.

Specified by:

exp in interface RealFieldElement<SparseGradient>

Returns:

exponential of the instance

expm1

public SparseGradient expm1()

Exponential minus 1.

Specified by:

expm1 in interface RealFieldElement<SparseGradient>

Returns:

exponential minus one of the instance

log

public SparseGradient log()

Natural logarithm.

Specified by:

log in interface RealFieldElement<SparseGradient>

Returns:

logarithm of the instance

log10

public SparseGradient log10()

Base 10 logarithm.

Returns:

base 10 logarithm of the instance

log1p

public SparseGradient log1p()

Shifted natural logarithm.

Specified by:

log1p in interface RealFieldElement<SparseGradient>

Returns:

logarithm of one plus the instance

cos

public SparseGradient cos()

Cosine operation.

Specified by:

cos in interface RealFieldElement<SparseGradient>

Returns:

cos(this)

sin

public SparseGradient sin()

Sine operation.

Specified by:

sin in interface RealFieldElement<SparseGradient>

Returns:

sin(this)

tan

public SparseGradient tan()

Tangent operation.

Specified by:

tan in interface RealFieldElement<SparseGradient>

Returns:

tan(this)

acos

public SparseGradient acos()

Arc cosine operation.

Specified by:

acos in interface RealFieldElement<SparseGradient>

Returns:

acos(this)

asin

public SparseGradient asin()

Arc sine operation.

Specified by:

asin in interface RealFieldElement<SparseGradient>

Returns:

asin(this)

atan

public SparseGradient atan()

Arc tangent operation.

Specified by:

atan in interface RealFieldElement<SparseGradient>

Returns:

atan(this)

atan2

public SparseGradient atan2(SparseGradient x)

Two arguments arc tangent operation.

Specified by:

atan2 in interface RealFieldElement<SparseGradient>

Parameters:

x - second argument of the arc tangent

Returns:

atan2(this, x)

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()

Hyperbolic cosine operation.

Specified by:

cosh in interface RealFieldElement<SparseGradient>

Returns:

cosh(this)

sinh

public SparseGradient sinh()

Hyperbolic sine operation.

Specified by:

sinh in interface RealFieldElement<SparseGradient>

Returns:

sinh(this)

tanh

public SparseGradient tanh()

Hyperbolic tangent operation.

Specified by:

tanh in interface RealFieldElement<SparseGradient>

Returns:

tanh(this)

acosh

public SparseGradient acosh()

Inverse hyperbolic cosine operation.

Specified by:

acosh in interface RealFieldElement<SparseGradient>

Returns:

acosh(this)

asinh

public SparseGradient asinh()

Inverse hyperbolic sine operation.

Specified by:

asinh in interface RealFieldElement<SparseGradient>

Returns:

asin(this)

atanh

public SparseGradient atanh()

Inverse hyperbolic tangent operation.

Specified by:

atanh in interface RealFieldElement<SparseGradient>

Returns:

atanh(this)

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)
                                 throws DimensionMismatchException

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

DimensionMismatchException - if arrays dimensions don't match

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

See Also:

RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object), RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

Returns:

a₁×b₁ + a₂×b₂

See Also:

RealFieldElement.linearCombination(double, Object, double, Object, double, Object), RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

See Also:

RealFieldElement.linearCombination(Object, Object, Object, Object), RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃

See Also:

RealFieldElement.linearCombination(double, Object, double, Object), RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the third term

b4 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

RealFieldElement.linearCombination(Object, Object, Object, Object), RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface RealFieldElement<SparseGradient>

Parameters:

a1 - first factor of the first term

b1 - second factor of the first term

a2 - first factor of the second term

b2 - second factor of the second term

a3 - first factor of the third term

b3 - second factor of the third term

a4 - first factor of the third term

b4 - second factor of the third term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

RealFieldElement.linearCombination(double, Object, double, Object), RealFieldElement.linearCombination(double, Object, double, Object, double, Object)

equals

public boolean equals(java.lang.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 java.lang.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 java.lang.Object

Returns:

a hash code value for this object

Since:

3.2