Class UnivariateDerivative1
- All Implemented Interfaces:
Serializable
,Comparable<UnivariateDerivative1>
,Derivative<UnivariateDerivative1>
,Derivative1<UnivariateDerivative1>
,DifferentialAlgebra
,CalculusFieldElement<UnivariateDerivative1>
,FieldElement<UnivariateDerivative1>
This class is a stripped-down version of DerivativeStructure
with only one free parameter
and derivation order
also limited to one.
It should have less overhead than DerivativeStructure
in its domain.
This class is an implementation of Rall's numbers. Rall's numbers are an extension to the real numbers used throughout mathematical expressions; they hold the derivative together with the value of a function.
UnivariateDerivative1
instances can be used directly thanks to
the arithmetic operators to the mathematical functions provided as
methods by this class (+, -, *, /, %, sin, cos ...).
Implementing complex expressions by hand using these classes is a tedious and error-prone task but has the advantage of having no limitation on the derivation order despite not requiring users to compute the derivatives by themselves.
Instances of this class are guaranteed to be immutable.
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Field Summary
Modifier and TypeFieldDescriptionstatic final UnivariateDerivative1
The constant value of π as aUnivariateDerivative1
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Constructor Summary
ConstructorDescriptionUnivariateDerivative1
(double f0, double f1) Build an instance with values and derivative.Build an instance from aDerivativeStructure
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Method Summary
Modifier and TypeMethodDescriptionabs()
absolute value.Compute this + a.Two arguments arc tangent operation.int
compose
(double... f) Compute composition of the instance by a univariate function.compose
(double ff0, double ff1) Compute composition of the instance by a univariate function differentiable at order 1.copySign
(double sign) Returns the instance with the sign of the argument.Returns the instance with the sign of the argument.divide
(double a) '÷' operator.Compute this ÷ a.boolean
Test for the equality of two univariate derivatives.double
getDerivative
(int n) Get a derivative from the univariate derivative.getField()
Get theField
to which the instance belongs.double
Get the first derivative.getPi()
Get the Archimedes constant π.double
getValue()
Get the value part of the function.int
hashCode()
Get a hashCode for the univariate derivative.Returns the hypotenuse of a triangle with sidesthis
andy
- sqrt(this2 +y2) avoiding intermediate overflow or underflow.linearCombination
(double[] a, UnivariateDerivative1[] b) Compute a linear combination.linearCombination
(double a1, UnivariateDerivative1 b1, double a2, UnivariateDerivative1 b2) Compute a linear combination.linearCombination
(double a1, UnivariateDerivative1 b1, double a2, UnivariateDerivative1 b2, double a3, UnivariateDerivative1 b3) Compute a linear combination.linearCombination
(double a1, UnivariateDerivative1 b1, double a2, UnivariateDerivative1 b2, double a3, UnivariateDerivative1 b3, double a4, UnivariateDerivative1 b4) Compute a linear combination.Compute a linear combination.linearCombination
(UnivariateDerivative1 a1, UnivariateDerivative1 b1, UnivariateDerivative1 a2, UnivariateDerivative1 b2) Compute a linear combination.linearCombination
(UnivariateDerivative1 a1, UnivariateDerivative1 b1, UnivariateDerivative1 a2, UnivariateDerivative1 b2, UnivariateDerivative1 a3, UnivariateDerivative1 b3) Compute a linear combination.linearCombination
(UnivariateDerivative1 a1, UnivariateDerivative1 b1, UnivariateDerivative1 a2, UnivariateDerivative1 b2, UnivariateDerivative1 a3, UnivariateDerivative1 b3, UnivariateDerivative1 a4, UnivariateDerivative1 b4) Compute a linear combination.multiply
(double a) '×' operator.multiply
(int n) Compute n × this.Compute this × a.negate()
Returns the additive inverse ofthis
element.newInstance
(double value) Create an instance corresponding to a constant real value.pow
(double p) Power operation.static UnivariateDerivative1
pow
(double a, UnivariateDerivative1 x) Compute ax where a is a double and x aUnivariateDerivative1
pow
(int n) Integer power operation.IEEE remainder operator.scalb
(int n) Multiply the instance by a power of 2.Compute this - a.double
taylor
(double delta) Evaluate Taylor expansion a univariate derivative.Convert radians to degrees, with error of less than 0.5 ULPConvert the instance to aDerivativeStructure
.Convert degrees to radians, with error of less than 0.5 ULPwithValue
(double value) 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 org.hipparchus.analysis.differentiation.UnivariateDerivative
getFreeParameters, getPartialDerivative
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, getPartialDerivative, getReal, pow, remainder, 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, sqrt, square, tan, tanh
Methods inherited from interface org.hipparchus.analysis.differentiation.DifferentialAlgebra
getFreeParameters
Methods inherited from interface org.hipparchus.FieldElement
isZero
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Field Details
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PI
The constant value of π as aUnivariateDerivative1
.- Since:
- 2.0
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Constructor Details
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UnivariateDerivative1
public UnivariateDerivative1(double f0, double f1) Build an instance with values and derivative.- Parameters:
f0
- value of the functionf1
- first derivative of the function
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UnivariateDerivative1
Build an instance from aDerivativeStructure
.- Parameters:
ds
- derivative structure- Throws:
MathIllegalArgumentException
- if eitherds
parameters is not 1 ords
order is not 1
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Method Details
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newInstance
Create an instance corresponding to a constant real value.- Specified by:
newInstance
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
value
- constant real value- Returns:
- instance corresponding to a constant real value
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withValue
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 interfaceDerivative<UnivariateDerivative1>
- Parameters:
value
- zeroth-order derivative of new represented function- Returns:
- new object with changed value
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getValue
public double getValue()Get the value part of the function.- Specified by:
getValue
in interfaceDerivative<UnivariateDerivative1>
- Returns:
- value part of the value of the function
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getDerivative
public double getDerivative(int n) Get a derivative from the univariate derivative.- Specified by:
getDerivative
in classUnivariateDerivative<UnivariateDerivative1>
- Parameters:
n
- derivation order (must be between 0 andDifferentialAlgebra.getOrder()
, both inclusive)- Returns:
- nth derivative
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getFirstDerivative
public double getFirstDerivative()Get the first derivative.- Returns:
- first derivative
- See Also:
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toDerivativeStructure
Convert the instance to aDerivativeStructure
.- Specified by:
toDerivativeStructure
in classUnivariateDerivative<UnivariateDerivative1>
- Returns:
- derivative structure with same value and derivative as the instance
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add
Compute this + a.- Specified by:
add
in interfaceFieldElement<UnivariateDerivative1>
- Parameters:
a
- element to add- Returns:
- a new element representing this + a
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subtract
Compute this - a.- Specified by:
subtract
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Specified by:
subtract
in interfaceFieldElement<UnivariateDerivative1>
- Parameters:
a
- element to subtract- Returns:
- a new element representing this - a
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multiply
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 interfaceCalculusFieldElement<UnivariateDerivative1>
- Specified by:
multiply
in interfaceFieldElement<UnivariateDerivative1>
- Parameters:
n
- Number of timesthis
must be added to itself.- Returns:
- A new element representing n × this.
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multiply
'×' operator.- Specified by:
multiply
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a
- right hand side parameter of the operator- Returns:
- this×a
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multiply
Compute this × a.- Specified by:
multiply
in interfaceFieldElement<UnivariateDerivative1>
- Parameters:
a
- element to multiply- Returns:
- a new element representing this × a
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divide
'÷' operator.- Specified by:
divide
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a
- right hand side parameter of the operator- Returns:
- this÷a
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divide
Compute this ÷ a.- Specified by:
divide
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Specified by:
divide
in interfaceFieldElement<UnivariateDerivative1>
- Parameters:
a
- element to divide by- Returns:
- a new element representing this ÷ a
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remainder
IEEE remainder operator.- Specified by:
remainder
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a
- right hand side parameter of the operator- Returns:
- this - n × a where n is the closest integer to this/a
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negate
Returns the additive inverse ofthis
element.- Specified by:
negate
in interfaceFieldElement<UnivariateDerivative1>
- Returns:
- the opposite of
this
.
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abs
absolute value.- Specified by:
abs
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Returns:
- abs(this)
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copySign
Returns the instance with the sign of the argument. A NaNsign
argument is treated as positive.- Specified by:
copySign
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
sign
- the sign for the returned value- Returns:
- the instance with the same sign as the
sign
argument
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copySign
Returns the instance with the sign of the argument. A NaNsign
argument is treated as positive.- Specified by:
copySign
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
sign
- the sign for the returned value- Returns:
- the instance with the same sign as the
sign
argument
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scalb
Multiply the instance by a power of 2.- Specified by:
scalb
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
n
- power of 2- Returns:
- this × 2n
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hypot
Returns the hypotenuse of a triangle with sidesthis
andy
- 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 interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
y
- a value- Returns:
- sqrt(this2 +y2)
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compose
Compute composition of the instance by a univariate function.- Specified by:
compose
in interfaceDerivative<UnivariateDerivative1>
- Parameters:
f
- array of value and derivatives of the function at the current point (i.e. [f(Derivative.getValue()
), f'(Derivative.getValue()
), f''(Derivative.getValue()
)...]).- Returns:
- f(this)
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compose
Compute composition of the instance by a univariate function differentiable at order 1.- Specified by:
compose
in interfaceDerivative1<UnivariateDerivative1>
- Parameters:
ff0
- value of functionff1
- first-order derivative- Returns:
- f(this)
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getField
Get theField
to which the instance belongs.- Specified by:
getField
in interfaceFieldElement<UnivariateDerivative1>
- Returns:
Field
to which the instance belongs
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pow
Compute ax where a is a double and x aUnivariateDerivative1
- Parameters:
a
- number to exponentiatex
- power to apply- Returns:
- ax
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pow
Power operation.- Specified by:
pow
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
p
- power to apply- Returns:
- thisp
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pow
Integer power operation.- Specified by:
pow
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
n
- power to apply- Returns:
- thisn
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atan2
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 computesatan2(this, x)
, i.e. the instance represents they
argument and thex
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 languagesatan2
two-arguments arc tangent and putsx
as its first argument.- Specified by:
atan2
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
x
- second argument of the arc tangent- Returns:
- atan2(this, x)
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toDegrees
Convert radians to degrees, with error of less than 0.5 ULP- Specified by:
toDegrees
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Returns:
- instance converted into degrees
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toRadians
Convert degrees to radians, with error of less than 0.5 ULP- Specified by:
toRadians
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Returns:
- instance converted into radians
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taylor
public double taylor(double delta) Evaluate Taylor expansion a univariate derivative.- Parameters:
delta
- parameter offset Δx- Returns:
- value of the Taylor expansion at x + Δx
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linearCombination
public UnivariateDerivative1 linearCombination(UnivariateDerivative1[] a, UnivariateDerivative1[] b) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.
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linearCombination
Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.
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linearCombination
public UnivariateDerivative1 linearCombination(UnivariateDerivative1 a1, UnivariateDerivative1 b1, UnivariateDerivative1 a2, UnivariateDerivative1 b2) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a1
- first factor of the first termb1
- second factor of the first terma2
- first factor of the second termb2
- second factor of the second term- Returns:
- a1×b1 + a2×b2
- See Also:
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linearCombination
public UnivariateDerivative1 linearCombination(double a1, UnivariateDerivative1 b1, double a2, UnivariateDerivative1 b2) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a1
- first factor of the first termb1
- second factor of the first terma2
- first factor of the second termb2
- second factor of the second term- Returns:
- a1×b1 + a2×b2
- See Also:
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linearCombination
public UnivariateDerivative1 linearCombination(UnivariateDerivative1 a1, UnivariateDerivative1 b1, UnivariateDerivative1 a2, UnivariateDerivative1 b2, UnivariateDerivative1 a3, UnivariateDerivative1 b3) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a1
- first factor of the first termb1
- second factor of the first terma2
- first factor of the second termb2
- second factor of the second terma3
- first factor of the third termb3
- second factor of the third term- Returns:
- a1×b1 + a2×b2 + a3×b3
- See Also:
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linearCombination
public UnivariateDerivative1 linearCombination(double a1, UnivariateDerivative1 b1, double a2, UnivariateDerivative1 b2, double a3, UnivariateDerivative1 b3) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a1
- first factor of the first termb1
- second factor of the first terma2
- first factor of the second termb2
- second factor of the second terma3
- first factor of the third termb3
- second factor of the third term- Returns:
- a1×b1 + a2×b2 + a3×b3
- See Also:
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linearCombination
public UnivariateDerivative1 linearCombination(UnivariateDerivative1 a1, UnivariateDerivative1 b1, UnivariateDerivative1 a2, UnivariateDerivative1 b2, UnivariateDerivative1 a3, UnivariateDerivative1 b3, UnivariateDerivative1 a4, UnivariateDerivative1 b4) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a1
- first factor of the first termb1
- second factor of the first terma2
- first factor of the second termb2
- second factor of the second terma3
- first factor of the third termb3
- second factor of the third terma4
- first factor of the fourth termb4
- second factor of the fourth term- Returns:
- a1×b1 + a2×b2 + a3×b3 + a4×b4
- See Also:
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linearCombination
public UnivariateDerivative1 linearCombination(double a1, UnivariateDerivative1 b1, double a2, UnivariateDerivative1 b2, double a3, UnivariateDerivative1 b3, double a4, UnivariateDerivative1 b4) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Parameters:
a1
- first factor of the first termb1
- second factor of the first terma2
- first factor of the second termb2
- second factor of the second terma3
- first factor of the third termb3
- second factor of the third terma4
- first factor of the fourth termb4
- second factor of the fourth term- Returns:
- a1×b1 + a2×b2 + a3×b3 + a4×b4
- See Also:
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getPi
Get the Archimedes constant π.Archimedes constant is the ratio of a circle's circumference to its diameter.
- Specified by:
getPi
in interfaceCalculusFieldElement<UnivariateDerivative1>
- Returns:
- Archimedes constant π
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equals
Test for the equality of two univariate derivatives.univariate derivatives are considered equal if they have the same derivatives.
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hashCode
public int hashCode()Get a hashCode for the univariate derivative. -
compareTo
Comparison performed considering that derivatives are intrinsically linked to monomials in the corresponding Taylor expansion and that the higher the degree, the smaller the term.
- Specified by:
compareTo
in interfaceComparable<UnivariateDerivative1>
- Since:
- 3.0
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