Package org.hipparchus.analysis.differentiation

Class SparseGradient

java.lang.Object

org.hipparchus.analysis.differentiation.SparseGradient

All Implemented Interfaces:

Serializable, Derivative<SparseGradient>, Derivative1<SparseGradient>, DifferentialAlgebra, CalculusFieldElement<SparseGradient>, FieldElement<SparseGradient>

public class SparseGradient
extends Object
implements Derivative1<SparseGradient>, 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.

See Also:

• Serialized Form

Method Summary

Modifier and Type	Method	Description
SparseGradient	abs()	absolute value.
SparseGradient	add(SparseGradient a)	Compute this + a.
void	addInPlace(SparseGradient a)	Add in place.
SparseGradient	atan2(SparseGradient x)	Two arguments arc tangent operation.
static SparseGradient	atan2(SparseGradient y, SparseGradient x)	Two arguments arc tangent operation.
SparseGradient	compose(double... f)	Compute composition of the instance by a univariate function.
SparseGradient	compose(double f0, double f1)	Compute composition of the instance by a univariate function differentiable at order 1.
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.
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(Object other)	Test for the equality of two sparse gradients.
SparseGradient	getAddendum()	Get the addendum to the real value of the number.
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.
int	getFreeParameters()	Get the number of free parameters.
double	getPartialDerivative(int... orders)	Get a partial derivative.
SparseGradient	getPi()	Get the Archimedes constant π.
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	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.
SparseGradient	newInstance(double v)	Create an instance corresponding to a constant real value.
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	remainder(double a)	IEEE remainder operator.
SparseGradient	remainder(SparseGradient a)	IEEE remainder operator.
SparseGradient	scalb(int n)	Multiply the instance by a power of 2.
SparseGradient	sqrt()	Square root.
SparseGradient	subtract(SparseGradient a)	Compute this - a.
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
SparseGradient	withValue(double v)	Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.hipparchus.CalculusFieldElement

ceil, floor, isFinite, isInfinite, isNaN, norm, rint, round, sign, ulp

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative

add, getExponent, getReal, pow, subtract

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative1

acos, acosh, asin, asinh, atan, atanh, cbrt, cos, cosh, exp, expm1, getOrder, log, log10, log1p, reciprocal, rootN, sin, sinCos, sinh, sinhCosh, square, tan, tanh

Methods inherited from interface org.hipparchus.FieldElement

isZero

Method Details

getFreeParameters

public int getFreeParameters()

Get the number of free parameters.

Specified by:

getFreeParameters in interface DifferentialAlgebra

Returns:

number of free parameters

getPartialDerivative

public double getPartialDerivative(int... orders)
                            throws MathIllegalArgumentException

Get a partial derivative.

Specified by:

getPartialDerivative in interface Derivative<SparseGradient>

Parameters:

orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)

Returns:

partial derivative

Throws:

MathIllegalArgumentException - if the numbers of variables does not match the instance

MathIllegalArgumentException - if sum of derivation orders is larger than the instance limits

See Also:

• Derivative.getValue()

newInstance

public SparseGradient newInstance(double v)

Create an instance corresponding to a constant real value.

Specified by:

newInstance in interface CalculusFieldElement<SparseGradient>

Parameters:

v - constant real value

Returns:

instance corresponding to a constant real value

withValue

public SparseGradient withValue(double v)

Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.

This default implementation is there so that no API gets broken by the next release, which is not a major one. Custom inheritors should probably overwrite it.

Specified by:

withValue in interface Derivative<SparseGradient>

Parameters:

v - zeroth-order derivative of new represented function

Returns:

new object with changed value

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

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

getAddendum

public SparseGradient getAddendum()

Get the addendum to the real value of the number.

The addendum is considered to be the part that when added back to the real part recovers the instance. This means that when e.getReal() is finite (i.e. neither infinite nor NaN), then e.getAddendum().add(e.getReal()) is e and e.subtract(e.getReal()) is e.getAddendum(). Beware that for non-finite numbers, these two equalities may not hold. The first equality (with the addition), always holds even for infinity and NaNs if the real part is independent of the addendum (this is the case for all derivatives types, as well as for complex and Dfp, but it is not the case for Tuple and FieldTuple). The second equality (with the subtraction), generally doesn't hold for non-finite numbers, because the subtraction generates NaNs.

Specified by:

getAddendum in interface CalculusFieldElement<SparseGradient>

Returns:

real value

getValue

public double getValue()

Get the value of the function.

Specified by:

getValue in interface Derivative<SparseGradient>

Returns:

value of the function.

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

subtract

public SparseGradient subtract(SparseGradient a)

Compute this - a.

Specified by:

subtract in interface CalculusFieldElement<SparseGradient>

Specified by:

subtract in interface FieldElement<SparseGradient>

Parameters:

a - element to subtract

Returns:

a new element representing 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 CalculusFieldElement<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 \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]

Specified by:

multiply in interface CalculusFieldElement<SparseGradient>

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 CalculusFieldElement<SparseGradient>

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 CalculusFieldElement<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 CalculusFieldElement<SparseGradient>

Specified by:

remainder in interface Derivative<SparseGradient>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a

remainder

public SparseGradient remainder(SparseGradient a)

IEEE remainder operator.

Specified by:

remainder in interface CalculusFieldElement<SparseGradient>

Parameters:

a - right hand side parameter of the operator

Returns:

this - n × a where n is the closest integer to this/a

abs

public SparseGradient abs()

absolute value.

Specified by:

abs in interface CalculusFieldElement<SparseGradient>

Returns:

abs(this)

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 CalculusFieldElement<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 CalculusFieldElement<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 CalculusFieldElement<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 CalculusFieldElement<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)

sqrt

public SparseGradient sqrt()

Square root.

Specified by:

sqrt in interface CalculusFieldElement<SparseGradient>

Specified by:

sqrt in interface Derivative1<SparseGradient>

Returns:

square root of the instance

pow

public SparseGradient pow(double p)

Power operation.

Specified by:

pow in interface CalculusFieldElement<SparseGradient>

Parameters:

p - power to apply

Returns:

this^p

pow

public SparseGradient pow(int n)

Integer power operation.

Specified by:

pow in interface CalculusFieldElement<SparseGradient>

Parameters:

n - power to apply

Returns:

thisⁿ

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

atan2

public SparseGradient atan2(SparseGradient x)

Two arguments arc tangent operation.

Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.

Specified by:

atan2 in interface CalculusFieldElement<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)

toDegrees

public SparseGradient toDegrees()

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

Specified by:

toDegrees in interface CalculusFieldElement<SparseGradient>

Returns:

instance converted into degrees

toRadians

public SparseGradient toRadians()

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

Specified by:

toRadians in interface CalculusFieldElement<SparseGradient>

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... f)

Compute composition of the instance by a univariate function.

Specified by:

compose in interface Derivative<SparseGradient>

Parameters:

f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).

Returns:

f(this)

Throws:

MathIllegalArgumentException - if the number of elements in the array is not equal to 2 (i.e. value and first derivative)

compose

public SparseGradient compose(double f0,
 double f1)

Compute composition of the instance by a univariate function differentiable at order 1.

Specified by:

compose in interface Derivative1<SparseGradient>

Parameters:

f0 - value of function

f1 - first-order derivative

Returns:

f(this)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<SparseGradient>

Parameters:

a - Factors.

b - Factors.

Returns:

Σi ai bi.

Throws:

MathIllegalArgumentException - if arrays dimensions don't match

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<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 CalculusFieldElement<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:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

linearCombination

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

Compute a linear combination.

Specified by:

linearCombination in interface CalculusFieldElement<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:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

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 CalculusFieldElement<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:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

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 CalculusFieldElement<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:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)

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 CalculusFieldElement<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 fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
• CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)

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 CalculusFieldElement<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 fourth term

b4 - second factor of the fourth term

Returns:

a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄

See Also:

• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
• CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)

getPi

public SparseGradient getPi()

Get the Archimedes constant π.

Archimedes constant is the ratio of a circle's circumference to its diameter.

Specified by:

getPi in interface CalculusFieldElement<SparseGradient>

Returns:

Archimedes constant π

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