Class FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>
- java.lang.Object
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- org.hipparchus.analysis.differentiation.FieldUnivariateDerivative<T,FieldUnivariateDerivative2<T>>
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- org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2<T>
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- Type Parameters:
T
- the type of the function parameters and value
- All Implemented Interfaces:
DifferentialAlgebra
,FieldDerivative<T,FieldUnivariateDerivative2<T>>
,CalculusFieldElement<FieldUnivariateDerivative2<T>>
,FieldElement<FieldUnivariateDerivative2<T>>
public class FieldUnivariateDerivative2<T extends CalculusFieldElement<T>> extends FieldUnivariateDerivative<T,FieldUnivariateDerivative2<T>>
Class representing both the value and the differentials of a function.This class is a stripped-down version of
FieldDerivativeStructure
with only onefree parameter
andderivation order
limited to two. It should have less overhead thanFieldDerivativeStructure
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.
FieldUnivariateDerivative2
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
Derivative
-based classes (or in fact anyCalculusFieldElement
class) is a tedious and error-prone task but has the advantage of not requiring users to compute the derivatives by themselves and allowing to switch for one derivative implementation to another as they all share the same filed API.Instances of this class are guaranteed to be immutable.
- Since:
- 1.7
- See Also:
DerivativeStructure
,UnivariateDerivative1
,UnivariateDerivative2
,Gradient
,FieldDerivativeStructure
,FieldUnivariateDerivative1
,FieldGradient
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Constructor Summary
Constructors Constructor Description FieldUnivariateDerivative2(FieldDerivativeStructure<T> ds)
Build an instance from aFieldDerivativeStructure
.FieldUnivariateDerivative2(T f0, T f1, T f2)
Build an instance with values and derivative.
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Method Summary
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Methods inherited from class org.hipparchus.analysis.differentiation.FieldUnivariateDerivative
getFreeParameters, getPartialDerivative
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Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.hipparchus.CalculusFieldElement
isFinite, isInfinite, isNaN, norm, round
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Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative
add, ceil, floor, getExponent, getReal, pow, rint, sign, subtract, ulp
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Methods inherited from interface org.hipparchus.FieldElement
isZero
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Constructor Detail
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FieldUnivariateDerivative2
public FieldUnivariateDerivative2(T f0, T f1, T f2)
Build an instance with values and derivative.- Parameters:
f0
- value of the functionf1
- first derivative of the functionf2
- second derivative of the function
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FieldUnivariateDerivative2
public FieldUnivariateDerivative2(FieldDerivativeStructure<T> ds) throws MathIllegalArgumentException
Build an instance from aFieldDerivativeStructure
.- Parameters:
ds
- derivative structure- Throws:
MathIllegalArgumentException
- if eitherds
parameters is not 1 ords
order is not 2
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Method Detail
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newInstance
public FieldUnivariateDerivative2<T> newInstance(double value)
Create an instance corresponding to a constant real value.- Parameters:
value
- constant real value- Returns:
- instance corresponding to a constant real value
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newInstance
public FieldUnivariateDerivative2<T> newInstance(T value)
Create an instance corresponding to a constant Field value.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.
- Parameters:
value
- constant value- Returns:
- instance corresponding to a constant Field value
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withValue
public FieldUnivariateDerivative2<T> withValue(T value)
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.
- Parameters:
value
- zeroth-order derivative of new represented function- Returns:
- new object with changed value
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getAddendum
public FieldUnivariateDerivative2<T> 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 whene.getReal()
is finite (i.e. neither infinite nor NaN), thene.getAddendum().add(e.getReal())
ise
ande.subtract(e.getReal())
ise.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.- Returns:
- real value
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getValue
public T getValue()
Get the value part of the univariate derivative.- Returns:
- value part of the univariate derivative
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getDerivative
public T getDerivative(int n)
Get a derivative from the univariate derivative.- Specified by:
getDerivative
in classFieldUnivariateDerivative<T extends CalculusFieldElement<T>,FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>>
- Parameters:
n
- derivation order (must be between 0 andgetOrder()
, both inclusive)- Returns:
- nth derivative, or
NaN
if n is either negative or strictly larger thangetOrder()
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getOrder
public int getOrder()
Get the derivation order.- Returns:
- derivation order
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getFirstDerivative
public T getFirstDerivative()
Get the first derivative.- Returns:
- first derivative
- See Also:
getValue()
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getSecondDerivative
public T getSecondDerivative()
Get the second derivative.- Returns:
- second derivative
- See Also:
getValue()
,getFirstDerivative()
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getValueField
public Field<T> getValueField()
Get theField
the value and parameters of the function belongs to.- Returns:
Field
the value and parameters of the function belongs to
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toDerivativeStructure
public FieldDerivativeStructure<T> toDerivativeStructure()
Convert the instance to aFieldDerivativeStructure
.- Specified by:
toDerivativeStructure
in classFieldUnivariateDerivative<T extends CalculusFieldElement<T>,FieldUnivariateDerivative2<T extends CalculusFieldElement<T>>>
- Returns:
- derivative structure with same value and derivative as the instance
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add
public FieldUnivariateDerivative2<T> add(double a)
'+' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this+a
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add
public FieldUnivariateDerivative2<T> add(FieldUnivariateDerivative2<T> a)
Compute this + a.- Parameters:
a
- element to add- Returns:
- a new element representing this + a
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subtract
public FieldUnivariateDerivative2<T> subtract(double a)
'-' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this-a
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subtract
public FieldUnivariateDerivative2<T> subtract(FieldUnivariateDerivative2<T> a)
Compute this - a.- Parameters:
a
- element to subtract- Returns:
- a new element representing this - a
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multiply
public FieldUnivariateDerivative2<T> multiply(T a)
'×' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this×a
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multiply
public FieldUnivariateDerivative2<T> multiply(int n)
Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]- Parameters:
n
- Number of timesthis
must be added to itself.- Returns:
- A new element representing n × this.
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multiply
public FieldUnivariateDerivative2<T> multiply(double a)
'×' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this×a
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multiply
public FieldUnivariateDerivative2<T> multiply(FieldUnivariateDerivative2<T> a)
Compute this × a.- Parameters:
a
- element to multiply- Returns:
- a new element representing this × a
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square
public FieldUnivariateDerivative2<T> square()
Compute this × this.- Returns:
- a new element representing this × this
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divide
public FieldUnivariateDerivative2<T> divide(T a)
'÷' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this÷a
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divide
public FieldUnivariateDerivative2<T> divide(double a)
'÷' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this÷a
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divide
public FieldUnivariateDerivative2<T> divide(FieldUnivariateDerivative2<T> a)
Compute this ÷ a.- Parameters:
a
- element to divide by- Returns:
- a new element representing this ÷ a
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remainder
public FieldUnivariateDerivative2<T> remainder(T a)
IEEE remainder operator.- 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)
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remainder
public FieldUnivariateDerivative2<T> remainder(double a)
IEEE remainder operator.- 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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remainder
public FieldUnivariateDerivative2<T> remainder(FieldUnivariateDerivative2<T> a)
IEEE remainder operator.- 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
public FieldUnivariateDerivative2<T> negate()
Returns the additive inverse ofthis
element.- Returns:
- the opposite of
this
.
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abs
public FieldUnivariateDerivative2<T> abs()
absolute value.- Returns:
- abs(this)
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copySign
public FieldUnivariateDerivative2<T> copySign(T sign)
Returns the instance with the sign of the argument. A NaNsign
argument is treated as positive.- Parameters:
sign
- the sign for the returned value- Returns:
- the instance with the same sign as the
sign
argument
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copySign
public FieldUnivariateDerivative2<T> copySign(FieldUnivariateDerivative2<T> sign)
Returns the instance with the sign of the argument. A NaNsign
argument is treated as positive.- Parameters:
sign
- the sign for the returned value- Returns:
- the instance with the same sign as the
sign
argument
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copySign
public FieldUnivariateDerivative2<T> copySign(double sign)
Returns the instance with the sign of the argument. A NaNsign
argument is treated as positive.- Parameters:
sign
- the sign for the returned value- Returns:
- the instance with the same sign as the
sign
argument
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scalb
public FieldUnivariateDerivative2<T> scalb(int n)
Multiply the instance by a power of 2.- Parameters:
n
- power of 2- Returns:
- this × 2n
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hypot
public FieldUnivariateDerivative2<T> hypot(FieldUnivariateDerivative2<T> y)
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.
- Parameters:
y
- a value- Returns:
- sqrt(this2 +y2)
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reciprocal
public FieldUnivariateDerivative2<T> reciprocal()
Returns the multiplicative inverse ofthis
element.- Returns:
- the inverse of
this
.
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compose
public FieldUnivariateDerivative2<T> compose(T g0, T g1, T g2)
Compute composition of the instance by a function.- Parameters:
g0
- value of the function at the current point (i.e. atg(getValue())
)g1
- first derivative of the function at the current point (i.e. atg'(getValue())
)g2
- second derivative of the function at the current point (i.e. atg''(getValue())
)- Returns:
- g(this)
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sqrt
public FieldUnivariateDerivative2<T> sqrt()
Square root.- Returns:
- square root of the instance
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cbrt
public FieldUnivariateDerivative2<T> cbrt()
Cubic root.- Returns:
- cubic root of the instance
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rootN
public FieldUnivariateDerivative2<T> rootN(int n)
Nth root.- Parameters:
n
- order of the root- Returns:
- nth root of the instance
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getField
public FieldUnivariateDerivative2Field<T> getField()
Get theField
to which the instance belongs.- Returns:
Field
to which the instance belongs
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pow
public static <T extends CalculusFieldElement<T>> FieldUnivariateDerivative2<T> pow(double a, FieldUnivariateDerivative2<T> x)
Compute ax where a is a double and x aFieldUnivariateDerivative2
- Type Parameters:
T
- the type of the function parameters and value- Parameters:
a
- number to exponentiatex
- power to apply- Returns:
- ax
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pow
public FieldUnivariateDerivative2<T> pow(double p)
Power operation.- Parameters:
p
- power to apply- Returns:
- thisp
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pow
public FieldUnivariateDerivative2<T> pow(int n)
Integer power operation.- Parameters:
n
- power to apply- Returns:
- thisn
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exp
public FieldUnivariateDerivative2<T> exp()
Exponential.- Returns:
- exponential of the instance
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expm1
public FieldUnivariateDerivative2<T> expm1()
Exponential minus 1.- Returns:
- exponential minus one of the instance
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log
public FieldUnivariateDerivative2<T> log()
Natural logarithm.- Returns:
- logarithm of the instance
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log1p
public FieldUnivariateDerivative2<T> log1p()
Shifted natural logarithm.- Returns:
- logarithm of one plus the instance
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log10
public FieldUnivariateDerivative2<T> log10()
Base 10 logarithm.- Returns:
- base 10 logarithm of the instance
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cos
public FieldUnivariateDerivative2<T> cos()
Cosine operation.- Returns:
- cos(this)
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sin
public FieldUnivariateDerivative2<T> sin()
Sine operation.- Returns:
- sin(this)
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sinCos
public FieldSinCos<FieldUnivariateDerivative2<T>> sinCos()
Combined Sine and Cosine operation.- Returns:
- [sin(this), cos(this)]
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tan
public FieldUnivariateDerivative2<T> tan()
Tangent operation.- Returns:
- tan(this)
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acos
public FieldUnivariateDerivative2<T> acos()
Arc cosine operation.- Returns:
- acos(this)
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asin
public FieldUnivariateDerivative2<T> asin()
Arc sine operation.- Returns:
- asin(this)
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atan
public FieldUnivariateDerivative2<T> atan()
Arc tangent operation.- Returns:
- atan(this)
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atan2
public FieldUnivariateDerivative2<T> atan2(FieldUnivariateDerivative2<T> 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 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.- Parameters:
x
- second argument of the arc tangent- Returns:
- atan2(this, x)
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cosh
public FieldUnivariateDerivative2<T> cosh()
Hyperbolic cosine operation.- Returns:
- cosh(this)
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sinh
public FieldUnivariateDerivative2<T> sinh()
Hyperbolic sine operation.- Returns:
- sinh(this)
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sinhCosh
public FieldSinhCosh<FieldUnivariateDerivative2<T>> sinhCosh()
Combined hyperbolic sine and cosine operation.- Returns:
- [sinh(this), cosh(this)]
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tanh
public FieldUnivariateDerivative2<T> tanh()
Hyperbolic tangent operation.- Returns:
- tanh(this)
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acosh
public FieldUnivariateDerivative2<T> acosh()
Inverse hyperbolic cosine operation.- Returns:
- acosh(this)
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asinh
public FieldUnivariateDerivative2<T> asinh()
Inverse hyperbolic sine operation.- Returns:
- asin(this)
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atanh
public FieldUnivariateDerivative2<T> atanh()
Inverse hyperbolic tangent operation.- Returns:
- atanh(this)
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toDegrees
public FieldUnivariateDerivative2<T> toDegrees()
Convert radians to degrees, with error of less than 0.5 ULP- Returns:
- instance converted into degrees
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toRadians
public FieldUnivariateDerivative2<T> toRadians()
Convert degrees to radians, with error of less than 0.5 ULP- Returns:
- instance converted into radians
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taylor
public T 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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taylor
public T taylor(T 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 FieldUnivariateDerivative2<T> linearCombination(T[] a, FieldUnivariateDerivative2<T>[] b)
Compute a linear combination.- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.- Throws:
MathIllegalArgumentException
- if arrays dimensions don't match
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T>[] a, FieldUnivariateDerivative2<T>[] b)
Compute a linear combination.- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(double[] a, FieldUnivariateDerivative2<T>[] b)
Compute a linear combination.- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2)
Compute a linear combination.- 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:
CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
,CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2)
Compute a linear combination.- 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:
CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
,CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2, FieldUnivariateDerivative2<T> a3, FieldUnivariateDerivative2<T> b3)
Compute a linear combination.- 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:
CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
,CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(T a1, FieldUnivariateDerivative2<T> b1, T a2, FieldUnivariateDerivative2<T> b2, T a3, FieldUnivariateDerivative2<T> b3)
Compute a linear combination.- 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
- Throws:
MathIllegalArgumentException
- if number of free parameters or orders are inconsistent- See Also:
linearCombination(double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2)
,linearCombination(double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2, double, FieldUnivariateDerivative2)
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2, double a3, FieldUnivariateDerivative2<T> b3)
Compute a linear combination.- 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:
CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
,CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(FieldUnivariateDerivative2<T> a1, FieldUnivariateDerivative2<T> b1, FieldUnivariateDerivative2<T> a2, FieldUnivariateDerivative2<T> b2, FieldUnivariateDerivative2<T> a3, FieldUnivariateDerivative2<T> b3, FieldUnivariateDerivative2<T> a4, FieldUnivariateDerivative2<T> b4)
Compute a linear combination.- 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:
CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
,CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
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linearCombination
public FieldUnivariateDerivative2<T> linearCombination(double a1, FieldUnivariateDerivative2<T> b1, double a2, FieldUnivariateDerivative2<T> b2, double a3, FieldUnivariateDerivative2<T> b3, double a4, FieldUnivariateDerivative2<T> b4)
Compute a linear combination.- 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:
CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
,CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
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getPi
public FieldUnivariateDerivative2<T> getPi()
Get the Archimedes constant π.Archimedes constant is the ratio of a circle's circumference to its diameter.
- Returns:
- Archimedes constant π
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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.
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