Class FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>
- Type Parameters:
T
- the type of the function parameters and value
- All Implemented Interfaces:
DifferentialAlgebra
,FieldDerivative<T,
,FieldUnivariateDerivative1<T>> FieldDerivative1<T,
,FieldUnivariateDerivative1<T>> CalculusFieldElement<FieldUnivariateDerivative1<T>>
,FieldElement<FieldUnivariateDerivative1<T>>
This class is a stripped-down version of FieldDerivativeStructure
with only one free parameter
and derivation order
also limited to one.
It should have less overhead than FieldDerivativeStructure
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.
FieldUnivariateDerivative1
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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Constructor Summary
ConstructorDescriptionBuild an instance from aDerivativeStructure
.FieldUnivariateDerivative1
(T f0, T f1) Build an instance with values and derivative. -
Method Summary
Modifier and TypeMethodDescriptionabs()
absolute value.add
(double a) '+' operator.Compute this + a.Two arguments arc tangent operation.Compute composition of the instance by a function.copySign
(double sign) Returns the instance with the sign of the argument.copySign
(FieldUnivariateDerivative1<T> 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.'÷' operator.boolean
Test for the equality of two univariate derivatives.getDerivative
(int n) Get a derivative from the univariate derivative.getField()
Get theField
to which the instance belongs.Get the first derivative.getPi()
Get the Archimedes constant π.getValue()
Get the value part of the univariate derivative.Get theField
the value and parameters of the function belongs to.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, FieldUnivariateDerivative1<T>[] b) Compute a linear combination.linearCombination
(double a1, FieldUnivariateDerivative1<T> b1, double a2, FieldUnivariateDerivative1<T> b2) Compute a linear combination.linearCombination
(double a1, FieldUnivariateDerivative1<T> b1, double a2, FieldUnivariateDerivative1<T> b2, double a3, FieldUnivariateDerivative1<T> b3) Compute a linear combination.linearCombination
(double a1, FieldUnivariateDerivative1<T> b1, double a2, FieldUnivariateDerivative1<T> b2, double a3, FieldUnivariateDerivative1<T> b3, double a4, FieldUnivariateDerivative1<T> b4) Compute a linear combination.Compute a linear combination.linearCombination
(FieldUnivariateDerivative1<T> a1, FieldUnivariateDerivative1<T> b1, FieldUnivariateDerivative1<T> a2, FieldUnivariateDerivative1<T> b2) Compute a linear combination.linearCombination
(FieldUnivariateDerivative1<T> a1, FieldUnivariateDerivative1<T> b1, FieldUnivariateDerivative1<T> a2, FieldUnivariateDerivative1<T> b2, FieldUnivariateDerivative1<T> a3, FieldUnivariateDerivative1<T> b3) Compute a linear combination.linearCombination
(FieldUnivariateDerivative1<T> a1, FieldUnivariateDerivative1<T> b1, FieldUnivariateDerivative1<T> a2, FieldUnivariateDerivative1<T> b2, FieldUnivariateDerivative1<T> a3, FieldUnivariateDerivative1<T> b3, FieldUnivariateDerivative1<T> a4, FieldUnivariateDerivative1<T> b4) Compute a linear combination.linearCombination
(T[] a, FieldUnivariateDerivative1<T>[] b) Compute a linear combination.linearCombination
(T a1, FieldUnivariateDerivative1<T> b1, T a2, FieldUnivariateDerivative1<T> b2, T a3, FieldUnivariateDerivative1<T> b3) Compute a linear combination.multiply
(double a) '×' operator.multiply
(int n) Compute n × this.Compute this × a.'×' operator.negate()
Returns the additive inverse ofthis
element.newInstance
(double value) Create an instance corresponding to a constant real value.newInstance
(T value) Create an instance corresponding to a constant Field value.pow
(double p) Power operation.static <T extends CalculusFieldElement<T>>
FieldUnivariateDerivative1<T>pow
(double a, FieldUnivariateDerivative1<T> x) Compute ax where a is a double and x aFieldUnivariateDerivative1
pow
(int n) Integer power operation.remainder
(double a) IEEE remainder operator.IEEE remainder operator.IEEE remainder operator.rootN
(int n) Nth root.scalb
(int n) Multiply the instance by a power of 2.subtract
(double a) '-' operator.Compute this - a.taylor
(double delta) Evaluate Taylor expansion of a univariate derivative.Evaluate Taylor expansion of a univariate derivative.Convert radians to degrees, with error of less than 0.5 ULPConvert the instance to aFieldDerivativeStructure
.Convert degrees to radians, with error of less than 0.5 ULPCreate 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.FieldUnivariateDerivative
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
isFinite, isInfinite, isNaN, norm, round
Methods inherited from interface org.hipparchus.analysis.differentiation.DifferentialAlgebra
getFreeParameters
Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative
add, ceil, floor, getExponent, getPartialDerivative, getReal, pow, rint, sign, subtract, ulp
Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative1
acos, acosh, asin, asinh, atan, atanh, cbrt, cos, cosh, exp, expm1, getOrder, log, log10, log1p, reciprocal, sin, sinCos, sinh, sinhCosh, sqrt, square, tan, tanh
Methods inherited from interface org.hipparchus.FieldElement
isZero
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Constructor Details
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FieldUnivariateDerivative1
Build an instance with values and derivative.- Parameters:
f0
- value of the functionf1
- first derivative of the function
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FieldUnivariateDerivative1
public FieldUnivariateDerivative1(FieldDerivativeStructure<T> ds) throws MathIllegalArgumentException 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<T extends CalculusFieldElement<T>>
- Parameters:
value
- constant real value- Returns:
- instance corresponding to a constant real value
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newInstance
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.
- Specified by:
newInstance
in interfaceFieldDerivative<T extends CalculusFieldElement<T>,
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>> - Parameters:
value
- constant value- Returns:
- instance corresponding to a constant Field 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 interfaceFieldDerivative<T extends CalculusFieldElement<T>,
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>> - Parameters:
value
- zeroth-order derivative of new represented function- Returns:
- new object with changed value
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getValue
Get the value part of the univariate derivative.- Specified by:
getValue
in interfaceFieldDerivative<T extends CalculusFieldElement<T>,
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>> - Returns:
- value part of the univariate derivative
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getDerivative
Get a derivative from the univariate derivative.- Specified by:
getDerivative
in classFieldUnivariateDerivative<T extends CalculusFieldElement<T>,
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>> - Parameters:
n
- derivation order (must be between 0 andDifferentialAlgebra.getOrder()
, both inclusive)- Returns:
- nth derivative, or
NaN
if n is either negative or strictly larger thanDifferentialAlgebra.getOrder()
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getFirstDerivative
Get the first derivative.- Returns:
- first derivative
- See Also:
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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
Convert the instance to aFieldDerivativeStructure
.- Specified by:
toDerivativeStructure
in classFieldUnivariateDerivative<T extends CalculusFieldElement<T>,
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>> - Returns:
- derivative structure with same value and derivative as the instance
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add
'+' operator.- Specified by:
add
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- right hand side parameter of the operator- Returns:
- this+a
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add
Compute this + a.- Specified by:
add
in interfaceFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- element to add- Returns:
- a new element representing this + a
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subtract
'-' operator.- Specified by:
subtract
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- right hand side parameter of the operator- Returns:
- this-a
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subtract
Compute this - a.- Specified by:
subtract
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Specified by:
subtract
in interfaceFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- element to subtract- Returns:
- a new element representing this - a
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multiply
'×' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- 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<T extends CalculusFieldElement<T>>
- Specified by:
multiply
in interfaceFieldElement<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- Parameters:
a
- element to multiply- Returns:
- a new element representing this × a
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divide
'÷' operator.- Parameters:
a
- right hand side parameter of the operator- Returns:
- this÷a
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divide
'÷' operator.- Specified by:
divide
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- Specified by:
divide
in interfaceFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- element to divide by- Returns:
- a new element representing this ÷ a
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remainder
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
IEEE remainder operator.- Specified by:
remainder
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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
IEEE remainder operator.- Specified by:
remainder
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- Returns:
- the opposite of
this
.
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abs
absolute value.- Specified by:
abs
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Returns:
- abs(this)
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copySign
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
Returns the instance with the sign of the argument. A NaNsign
argument is treated as positive.- Specified by:
copySign
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- Parameters:
y
- a value- Returns:
- sqrt(this2 +y2)
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compose
Compute composition of the instance by a function.- Specified by:
compose
in interfaceFieldDerivative1<T extends CalculusFieldElement<T>,
FieldUnivariateDerivative1<T extends CalculusFieldElement<T>>> - 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())
)- Returns:
- g(this)
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rootN
Nth root.- Specified by:
rootN
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
n
- order of the root- Returns:
- nth root of the instance
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getField
Get theField
to which the instance belongs.- Specified by:
getField
in interfaceFieldElement<T extends CalculusFieldElement<T>>
- Returns:
Field
to which the instance belongs
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pow
public static <T extends CalculusFieldElement<T>> FieldUnivariateDerivative1<T> pow(double a, FieldUnivariateDerivative1<T> x) Compute ax where a is a double and x aFieldUnivariateDerivative1
- 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
Power operation.- Specified by:
pow
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
p
- power to apply- Returns:
- thisp
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pow
Integer power operation.- Specified by:
pow
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- Returns:
- instance converted into radians
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taylor
Evaluate Taylor expansion of a univariate derivative.- Parameters:
delta
- parameter offset Δx- Returns:
- value of the Taylor expansion at x + Δx
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taylor
Evaluate Taylor expansion of a univariate derivative.- Parameters:
delta
- parameter offset Δx- Returns:
- value of the Taylor expansion at x + Δx
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linearCombination
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 FieldUnivariateDerivative1<T> linearCombination(FieldUnivariateDerivative1<T>[] a, FieldUnivariateDerivative1<T>[] b) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.
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linearCombination
public FieldUnivariateDerivative1<T> linearCombination(double[] a, FieldUnivariateDerivative1<T>[] b) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
a
- Factors.b
- Factors.- Returns:
Σi ai bi
.
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linearCombination
public FieldUnivariateDerivative1<T> linearCombination(FieldUnivariateDerivative1<T> a1, FieldUnivariateDerivative1<T> b1, FieldUnivariateDerivative1<T> a2, FieldUnivariateDerivative1<T> b2) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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 FieldUnivariateDerivative1<T> linearCombination(double a1, FieldUnivariateDerivative1<T> b1, double a2, FieldUnivariateDerivative1<T> b2) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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 FieldUnivariateDerivative1<T> linearCombination(FieldUnivariateDerivative1<T> a1, FieldUnivariateDerivative1<T> b1, FieldUnivariateDerivative1<T> a2, FieldUnivariateDerivative1<T> b2, FieldUnivariateDerivative1<T> a3, FieldUnivariateDerivative1<T> b3) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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 FieldUnivariateDerivative1<T> linearCombination(T a1, FieldUnivariateDerivative1<T> b1, T a2, FieldUnivariateDerivative1<T> b2, T a3, FieldUnivariateDerivative1<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:
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linearCombination
public FieldUnivariateDerivative1<T> linearCombination(double a1, FieldUnivariateDerivative1<T> b1, double a2, FieldUnivariateDerivative1<T> b2, double a3, FieldUnivariateDerivative1<T> b3) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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 FieldUnivariateDerivative1<T> linearCombination(FieldUnivariateDerivative1<T> a1, FieldUnivariateDerivative1<T> b1, FieldUnivariateDerivative1<T> a2, FieldUnivariateDerivative1<T> b2, FieldUnivariateDerivative1<T> a3, FieldUnivariateDerivative1<T> b3, FieldUnivariateDerivative1<T> a4, FieldUnivariateDerivative1<T> b4) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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 FieldUnivariateDerivative1<T> linearCombination(double a1, FieldUnivariateDerivative1<T> b1, double a2, FieldUnivariateDerivative1<T> b2, double a3, FieldUnivariateDerivative1<T> b3, double a4, FieldUnivariateDerivative1<T> b4) Compute a linear combination.- Specified by:
linearCombination
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- 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<T extends CalculusFieldElement<T>>
- 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.
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