org.hipparchus.analysis.differentiation

• ### Constructor Summary

Constructors
Constructor and Description
Gradient(DerivativeStructure ds)
Build an instance from a DerivativeStructure.
Gradient(double value, double... gradient)
Build an instance with values and derivative.
• ### Method Summary

All Methods
Modifier and Type Method and Description
Gradient abs()
absolute value.
Gradient acos()
Arc cosine operation.
Gradient acosh()
Inverse hyperbolic cosine operation.
Gradient add(double a)
'+' operator.
Gradient add(Gradient a)
Compute this + a.
Gradient asin()
Arc sine operation.
Gradient asinh()
Inverse hyperbolic sine operation.
Gradient atan()
Arc tangent operation.
Gradient atan2(Gradient x)
Two arguments arc tangent operation.
Gradient atanh()
Inverse hyperbolic tangent operation.
Gradient cbrt()
Cubic root.
Gradient ceil()
Get the smallest whole number larger than instance.
Gradient compose(double... f)
Compute composition of the instance by a univariate function.
static Gradient constant(int freeParameters, double value)
Build an instance corresponding to a constant value.
Gradient copySign(double sign)
Returns the instance with the sign of the argument.
Gradient copySign(Gradient sign)
Returns the instance with the sign of the argument.
Gradient cos()
Cosine operation.
Gradient cosh()
Hyperbolic cosine operation.
Gradient divide(double a)
'÷' operator.
Gradient divide(Gradient a)
Compute this ÷ a.
boolean equals(Object other)
Test for the equality of two univariate derivatives.
Gradient exp()
Exponential.
Gradient expm1()
Exponential minus 1.
Gradient floor()
Get the largest whole number smaller than instance.
int getExponent()
Return the exponent of the instance, removing the bias.
GradientField getField()
Get the Field to which the instance belongs.
int getFreeParameters()
Get the number of free parameters.
double[] getGradient()
Get the gradient part of the function.
int getOrder()
Get the derivation order.
double getPartialDerivative(int... orders)
Get a partial derivative.
double getPartialDerivative(int n)
Get the partial derivative with respect to one parameter.
Gradient getPi()
Get the Archimedes constant π.
double getReal()
Get the real value of the number.
double getValue()
Get the value part of the function.
int hashCode()
Get a hashCode for the univariate derivative.
Gradient hypot(Gradient y)
Returns the hypotenuse of a triangle with sides this and y - sqrt(this2 +y2) avoiding intermediate overflow or underflow.
Gradient linearCombination(double[] a, Gradient[] b)
Compute a linear combination.
Gradient linearCombination(double a1, Gradient b1, double a2, Gradient b2)
Compute a linear combination.
Gradient linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3)
Compute a linear combination.
Gradient linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3, double a4, Gradient b4)
Compute a linear combination.
Gradient linearCombination(Gradient[] a, Gradient[] b)
Compute a linear combination.
Gradient linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2)
Compute a linear combination.
Gradient linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3)
Compute a linear combination.
Gradient linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3, Gradient a4, Gradient b4)
Compute a linear combination.
Gradient log()
Natural logarithm.
Gradient log10()
Base 10 logarithm.
Gradient log1p()
Shifted natural logarithm.
Gradient multiply(double a)
'×' operator.
Gradient multiply(Gradient a)
Compute this × a.
Gradient multiply(int n)
Compute n × this.
Gradient negate()
Returns the additive inverse of this element.
Gradient newInstance(double c)
Create an instance corresponding to a constant real value.
Gradient pow(double p)
Power operation.
static Gradient pow(double a, Gradient x)
Compute ax where a is a double and x a Gradient
Gradient pow(Gradient e)
Power operation.
Gradient pow(int n)
Integer power operation.
Gradient reciprocal()
Returns the multiplicative inverse of this element.
Gradient remainder(double a)
IEEE remainder operator.
Gradient remainder(Gradient a)
IEEE remainder operator.
Gradient 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.
Gradient rootN(int n)
Nth root.
Gradient scalb(int n)
Multiply the instance by a power of 2.
Gradient sign()
Compute the sign of the instance.
Gradient sin()
Sine operation.
FieldSinCos<Gradient> sinCos()
Combined Sine and Cosine operation.
Gradient sinh()
Hyperbolic sine operation.
FieldSinhCosh<Gradient> sinhCosh()
Combined hyperbolic sine and sosine operation.
Gradient sqrt()
Square root.
Gradient subtract(double a)
'-' operator.
Gradient subtract(Gradient a)
Compute this - a.
Gradient tan()
Tangent operation.
Gradient tanh()
Hyperbolic tangent operation.
double taylor(double... delta)
Evaluate Taylor expansion a derivative structure.
Gradient toDegrees()
Convert radians to degrees, with error of less than 0.5 ULP
DerivativeStructure toDerivativeStructure()
Convert the instance to a DerivativeStructure.
Gradient toRadians()
Convert degrees to radians, with error of less than 0.5 ULP
Gradient ulp()
Compute least significant bit (Unit in Last Position) for a number.
static Gradient variable(int freeParameters, int index, double value)
Build a Gradient representing a variable.
• ### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface org.hipparchus.CalculusFieldElement

isFinite, isInfinite, isNaN, norm, round
• ### Methods inherited from interface org.hipparchus.FieldElement

isZero
• ### Constructor Detail

public Gradient(double value,
double... gradient)
Build an instance with values and derivative.
Parameters:
value - value of the function
gradient - gradient of the function

public Gradient(DerivativeStructure ds)
throws MathIllegalArgumentException
Build an instance from a DerivativeStructure.
Parameters:
ds - derivative structure
Throws:
MathIllegalArgumentException - if ds order is not 1
• ### Method Detail

• #### constant

public static Gradient constant(int freeParameters,
double value)
Build an instance corresponding to a constant value.
Parameters:
freeParameters - number of free parameters (i.e. dimension of the gradient)
value - constant value of the function
Returns:
a Gradient with a constant value and all derivatives set to 0.0
• #### variable

public static Gradient variable(int freeParameters,
int index,
double value)
Build a Gradient representing a variable.

Instances built using this method are considered to be the free variables with respect to which differentials are computed. As such, their differential with respect to themselves is +1.

Parameters:
freeParameters - number of free parameters (i.e. dimension of the gradient)
index - index of the variable (from 0 to getFreeParameters() - 1)
value - value of the variable
Returns:
a Gradient with a constant value and all derivatives set to 0.0 except the one at index which will be set to 1.0
• #### newInstance

public Gradient newInstance(double c)
Create an instance corresponding to a constant real value.
Specified by:
newInstance in interface CalculusFieldElement<Gradient>
Parameters:
c - constant real value
Returns:
instance corresponding to a constant real value
• #### getReal

public double getReal()
Get the real value of the number.
Specified by:
getReal in interface FieldElement<Gradient>
Returns:
real value
• #### getValue

public double getValue()
Get the value part of the function.
Specified by:
getValue in interface Derivative<Gradient>
Returns:
value part of the value of the function

public double[] getGradient()
Get the gradient part of the function.
Returns:
gradient part of the value of the function
getPartialDerivative(int)
• #### getFreeParameters

public int getFreeParameters()
Get the number of free parameters.
Specified by:
getFreeParameters in interface Derivative<Gradient>
Returns:
number of free parameters
• #### getOrder

public int getOrder()
Get the derivation order.
Specified by:
getOrder in interface Derivative<Gradient>
Returns:
derivation order
• #### getPartialDerivative

public double getPartialDerivative(int... orders)
throws MathIllegalArgumentException
Get a partial derivative.
Specified by:
getPartialDerivative in interface Derivative<Gradient>
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
Derivative.getValue()
• #### getPartialDerivative

public double getPartialDerivative(int n)
throws MathIllegalArgumentException
Get the partial derivative with respect to one parameter.
Parameters:
n - index of the parameter (counting from 0)
Returns:
partial derivative with respect to the nth parameter
Throws:
MathIllegalArgumentException - if n is either negative or larger or equal to getFreeParameters()
• #### toDerivativeStructure

public DerivativeStructure toDerivativeStructure()
Convert the instance to a DerivativeStructure.
Returns:
derivative structure with same value and derivative as the instance

public Gradient add(double a)
'+' operator.
Specified by:
add in interface CalculusFieldElement<Gradient>
Parameters:
a - right hand side parameter of the operator
Returns:
this+a

public Gradient add(Gradient a)
Compute this + a.
Specified by:
add in interface FieldElement<Gradient>
Parameters:
a - element to add
Returns:
a new element representing this + a
• #### subtract

public Gradient subtract(double a)
'-' operator.
Specified by:
subtract in interface CalculusFieldElement<Gradient>
Parameters:
a - right hand side parameter of the operator
Returns:
this-a
• #### subtract

public Gradient subtract(Gradient a)
Compute this - a.
Specified by:
subtract in interface FieldElement<Gradient>
Parameters:
a - element to subtract
Returns:
a new element representing this - a
• #### multiply

public Gradient 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<Gradient>
Parameters:
n - Number of times this must be added to itself.
Returns:
A new element representing n × this.
• #### multiply

public Gradient multiply(double a)
'×' operator.
Specified by:
multiply in interface CalculusFieldElement<Gradient>
Parameters:
a - right hand side parameter of the operator
Returns:
this×a
• #### multiply

public Gradient multiply(Gradient a)
Compute this × a.
Specified by:
multiply in interface FieldElement<Gradient>
Parameters:
a - element to multiply
Returns:
a new element representing this × a
• #### divide

public Gradient divide(double a)
'÷' operator.
Specified by:
divide in interface CalculusFieldElement<Gradient>
Parameters:
a - right hand side parameter of the operator
Returns:
this÷a
• #### divide

public Gradient divide(Gradient a)
Compute this ÷ a.
Specified by:
divide in interface FieldElement<Gradient>
Parameters:
a - element to divide by
Returns:
a new element representing this ÷ a
• #### remainder

public Gradient remainder(double a)
IEEE remainder operator.
Specified by:
remainder in interface CalculusFieldElement<Gradient>
Parameters:
a - right hand side parameter of the operator
Returns:
this - n × a where n is the closest integer to this/a
• #### remainder

public Gradient remainder(Gradient a)
IEEE remainder operator.
Specified by:
remainder in interface CalculusFieldElement<Gradient>
Parameters:
a - right hand side parameter of the operator
Returns:
this - n × a where n is the closest integer to this/a
• #### negate

public Gradient negate()
Returns the additive inverse of this element.
Specified by:
negate in interface FieldElement<Gradient>
Returns:
the opposite of this.
• #### abs

public Gradient abs()
absolute value.

Just another name for CalculusFieldElement.norm()

Specified by:
abs in interface CalculusFieldElement<Gradient>
Returns:
abs(this)
• #### ceil

public Gradient ceil()
Get the smallest whole number larger than instance.
Specified by:
ceil in interface CalculusFieldElement<Gradient>
Returns:
ceil(this)
• #### floor

public Gradient floor()
Get the largest whole number smaller than instance.
Specified by:
floor in interface CalculusFieldElement<Gradient>
Returns:
floor(this)
• #### rint

public Gradient 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 CalculusFieldElement<Gradient>
Returns:
a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
• #### sign

public Gradient sign()
Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)
Specified by:
sign in interface CalculusFieldElement<Gradient>
Returns:
-1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
• #### copySign

public Gradient copySign(Gradient sign)
Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
Specified by:
copySign in interface CalculusFieldElement<Gradient>
Parameters:
sign - the sign for the returned value
Returns:
the instance with the same sign as the sign argument
• #### copySign

public Gradient 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<Gradient>
Parameters:
sign - the sign for the returned value
Returns:
the instance with the same sign as the sign argument
• #### getExponent

public int getExponent()
Return the exponent of the instance, removing the bias.

For double numbers of the form 2x, the unbiased exponent is exactly x.

Specified by:
getExponent in interface CalculusFieldElement<Gradient>
Returns:
exponent for the instance, without bias
• #### scalb

public Gradient scalb(int n)
Multiply the instance by a power of 2.
Specified by:
scalb in interface CalculusFieldElement<Gradient>
Parameters:
n - power of 2
Returns:
this × 2n
• #### ulp

public Gradient ulp()
Compute least significant bit (Unit in Last Position) for a number.

The ulp function is a step function, hence all its derivatives are 0.

Specified by:
ulp in interface CalculusFieldElement<Gradient>
Returns:
ulp(this)
Since:
2.0
• #### hypot

public Gradient hypot(Gradient 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<Gradient>
Parameters:
y - a value
Returns:
sqrt(this2 +y2)
• #### reciprocal

public Gradient reciprocal()
Returns the multiplicative inverse of this element.
Specified by:
reciprocal in interface CalculusFieldElement<Gradient>
Specified by:
reciprocal in interface FieldElement<Gradient>
Returns:
the inverse of this.
• #### sqrt

public Gradient sqrt()
Square root.
Specified by:
sqrt in interface CalculusFieldElement<Gradient>
Returns:
square root of the instance
• #### cbrt

public Gradient cbrt()
Cubic root.
Specified by:
cbrt in interface CalculusFieldElement<Gradient>
Returns:
cubic root of the instance
• #### rootN

public Gradient rootN(int n)
Nth root.
Specified by:
rootN in interface CalculusFieldElement<Gradient>
Parameters:
n - order of the root
Returns:
nth root of the instance
• #### getField

public GradientField getField()
Get the Field to which the instance belongs.
Specified by:
getField in interface FieldElement<Gradient>
Returns:
Field to which the instance belongs
• #### pow

public static Gradient pow(double a,
Gradient x)
Compute ax where a is a double and x a Gradient
Parameters:
a - number to exponentiate
x - power to apply
Returns:
ax
• #### pow

public Gradient pow(double p)
Power operation.
Specified by:
pow in interface CalculusFieldElement<Gradient>
Parameters:
p - power to apply
Returns:
thisp
• #### pow

public Gradient pow(int n)
Integer power operation.
Specified by:
pow in interface CalculusFieldElement<Gradient>
Parameters:
n - power to apply
Returns:
thisn
• #### pow

public Gradient pow(Gradient e)
Power operation.
Specified by:
pow in interface CalculusFieldElement<Gradient>
Parameters:
e - exponent
Returns:
thise
• #### exp

public Gradient exp()
Exponential.
Specified by:
exp in interface CalculusFieldElement<Gradient>
Returns:
exponential of the instance
• #### expm1

public Gradient expm1()
Exponential minus 1.
Specified by:
expm1 in interface CalculusFieldElement<Gradient>
Returns:
exponential minus one of the instance
• #### log

public Gradient log()
Natural logarithm.
Specified by:
log in interface CalculusFieldElement<Gradient>
Returns:
logarithm of the instance
• #### log1p

public Gradient log1p()
Shifted natural logarithm.
Specified by:
log1p in interface CalculusFieldElement<Gradient>
Returns:
logarithm of one plus the instance
• #### log10

public Gradient log10()
Base 10 logarithm.
Specified by:
log10 in interface CalculusFieldElement<Gradient>
Returns:
base 10 logarithm of the instance
• #### cos

public Gradient cos()
Cosine operation.
Specified by:
cos in interface CalculusFieldElement<Gradient>
Returns:
cos(this)
• #### sin

public Gradient sin()
Sine operation.
Specified by:
sin in interface CalculusFieldElement<Gradient>
Returns:
sin(this)
• #### sinCos

public FieldSinCos<Gradient> sinCos()
Combined Sine and Cosine operation.
Specified by:
sinCos in interface CalculusFieldElement<Gradient>
Returns:
[sin(this), cos(this)]
• #### tan

public Gradient tan()
Tangent operation.
Specified by:
tan in interface CalculusFieldElement<Gradient>
Returns:
tan(this)
• #### acos

public Gradient acos()
Arc cosine operation.
Specified by:
acos in interface CalculusFieldElement<Gradient>
Returns:
acos(this)
• #### asin

public Gradient asin()
Arc sine operation.
Specified by:
asin in interface CalculusFieldElement<Gradient>
Returns:
asin(this)
• #### atan

public Gradient atan()
Arc tangent operation.
Specified by:
atan in interface CalculusFieldElement<Gradient>
Returns:
atan(this)
• #### atan2

public Gradient atan2(Gradient 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<Gradient>
Parameters:
x - second argument of the arc tangent
Returns:
atan2(this, x)
• #### cosh

public Gradient cosh()
Hyperbolic cosine operation.
Specified by:
cosh in interface CalculusFieldElement<Gradient>
Returns:
cosh(this)
• #### sinh

public Gradient sinh()
Hyperbolic sine operation.
Specified by:
sinh in interface CalculusFieldElement<Gradient>
Returns:
sinh(this)
• #### sinhCosh

public FieldSinhCosh<Gradient> sinhCosh()
Combined hyperbolic sine and sosine operation.
Specified by:
sinhCosh in interface CalculusFieldElement<Gradient>
Returns:
[sinh(this), cosh(this)]
• #### tanh

public Gradient tanh()
Hyperbolic tangent operation.
Specified by:
tanh in interface CalculusFieldElement<Gradient>
Returns:
tanh(this)
• #### acosh

public Gradient acosh()
Inverse hyperbolic cosine operation.
Specified by:
acosh in interface CalculusFieldElement<Gradient>
Returns:
acosh(this)
• #### asinh

public Gradient asinh()
Inverse hyperbolic sine operation.
Specified by:
asinh in interface CalculusFieldElement<Gradient>
Returns:
asin(this)
• #### atanh

public Gradient atanh()
Inverse hyperbolic tangent operation.
Specified by:
atanh in interface CalculusFieldElement<Gradient>
Returns:
atanh(this)
• #### toDegrees

public Gradient toDegrees()
Convert radians to degrees, with error of less than 0.5 ULP
Specified by:
toDegrees in interface CalculusFieldElement<Gradient>
Returns:
instance converted into degrees

public Gradient toRadians()
Convert degrees to radians, with error of less than 0.5 ULP
Specified by:
toRadians in interface CalculusFieldElement<Gradient>
Returns:
• #### taylor

public double taylor(double... delta)
Evaluate Taylor expansion a derivative structure.
Parameters:
delta - parameters offsets (Δx, Δy, ...)
Returns:
value of the Taylor expansion at x + Δx, y + Δy, ...
• #### linearCombination

public Gradient linearCombination(Gradient[] a,
Gradient[] b)
Compute a linear combination.
Specified by:
linearCombination in interface CalculusFieldElement<Gradient>
Parameters:
a - Factors.
b - Factors.
Returns:
Σi ai bi.
• #### linearCombination

public Gradient linearCombination(double[] a,
Gradient[] b)
Compute a linear combination.
Specified by:
linearCombination in interface CalculusFieldElement<Gradient>
Parameters:
a - Factors.
b - Factors.
Returns:
Σi ai bi.
• #### getPi

public Gradient 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<Gradient>
Returns:
Archimedes constant π
• #### equals

public boolean equals(Object other)
Test for the equality of two univariate derivatives.

univariate derivatives are considered equal if they have the same derivatives.

Overrides:
equals in class Object
Parameters:
other - Object to test for equality to this
Returns:
true if two univariate derivatives are equal
• #### hashCode

public int hashCode()
Get a hashCode for the univariate derivative.
Overrides:
hashCode in class Object
Returns:
a hash code value for this object