Class FieldGradient<T extends CalculusFieldElement<T>>
- Type Parameters:
T
- the type of the function parameters and value
- All Implemented Interfaces:
DifferentialAlgebra
,FieldDerivative<T,
,FieldGradient<T>> FieldDerivative1<T,
,FieldGradient<T>> CalculusFieldElement<FieldGradient<T>>
,FieldElement<FieldGradient<T>>
This class is a stripped-down version of FieldDerivativeStructure
with derivation order
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.
FieldGradient
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
.FieldGradient
(T value, T... gradient) Build an instance with values and derivative. -
Method Summary
Modifier and TypeMethodDescriptionabs()
absolute value.add
(double a) '+' operator.add
(FieldGradient<T> a) Compute this + a.atan2
(FieldGradient<T> x) Two arguments arc tangent operation.Compute composition of the instance by a function.static <T extends CalculusFieldElement<T>>
FieldGradient<T>constant
(int freeParameters, T value) Build an instance corresponding to a constant value.copySign
(double sign) Returns the instance with the sign of the argument.copySign
(FieldGradient<T> sign) Returns the instance with the sign of the argument.Returns the instance with the sign of the argument.divide
(double a) '÷' operator.divide
(FieldGradient<T> a) Compute this ÷ a.'÷' operator.boolean
Test for the equality of two univariate derivatives.getField()
Get theField
to which the instance belongs.int
Get the number of free parameters.T[]
Get the gradient part of the function.getPartialDerivative
(int n) Get the partial derivative with respect to one parameter.getPartialDerivative
(int... orders) Get a partial derivative.getPi()
Get the Archimedes constant π.getValue()
Get the value part of the function.Get theField
the value and parameters of the function belongs to.int
hashCode()
Get a hashCode for the univariate derivative.hypot
(FieldGradient<T> y) Returns the hypotenuse of a triangle with sidesthis
andy
- sqrt(this2 +y2) avoiding intermediate overflow or underflow.linearCombination
(double[] a, FieldGradient<T>[] b) Compute a linear combination.linearCombination
(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2) Compute a linear combination.linearCombination
(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2, double a3, FieldGradient<T> b3) Compute a linear combination.linearCombination
(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2, double a3, FieldGradient<T> b3, double a4, FieldGradient<T> b4) Compute a linear combination.linearCombination
(FieldGradient<T>[] a, FieldGradient<T>[] b) Compute a linear combination.linearCombination
(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2) Compute a linear combination.linearCombination
(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2, FieldGradient<T> a3, FieldGradient<T> b3) Compute a linear combination.linearCombination
(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2, FieldGradient<T> a3, FieldGradient<T> b3, FieldGradient<T> a4, FieldGradient<T> b4) Compute a linear combination.linearCombination
(T[] a, FieldGradient<T>[] b) Compute a linear combination.linearCombination
(T a1, FieldGradient<T> b1, T a2, FieldGradient<T> b2, T a3, FieldGradient<T> b3) Compute a linear combination.multiply
(double a) '×' operator.multiply
(int n) Compute n × this.multiply
(FieldGradient<T> a) Compute this × a.'×' operator.negate()
Returns the additive inverse ofthis
element.newInstance
(double c) Create an instance corresponding to a constant real value.newInstance
(T c) Create an instance corresponding to a constant Field value.pow
(double p) Power operation.static <T extends CalculusFieldElement<T>>
FieldGradient<T>pow
(double a, FieldGradient<T> x) Compute ax where a is a double and x aFieldGradient
pow
(int n) Integer power operation.remainder
(double a) IEEE remainder operator.remainder
(FieldGradient<T> a) IEEE remainder operator.IEEE remainder operator.rootN
(int n) Nth root.scalb
(int n) Multiply the instance by a power of 2.sinCos()
Combined Sine and Cosine operation.sinhCosh()
Combined hyperbolic sine and cosine operation.subtract
(double a) '-' operator.subtract
(FieldGradient<T> a) Compute this - a.taylor
(double... delta) Evaluate Taylor expansion of a gradient.Evaluate Taylor expansion of a gradient.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 ULPstatic <T extends CalculusFieldElement<T>>
FieldGradient<T>variable
(int freeParameters, int index, T value) Build aGradient
representing a variable.Create a new object with new value (zeroth-order derivative, as passed as input) and same derivatives of order one and above.Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.hipparchus.CalculusFieldElement
isFinite, isInfinite, isNaN, norm, round
Methods inherited from interface org.hipparchus.analysis.differentiation.FieldDerivative
add, ceil, floor, getExponent, 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, sinh, sqrt, square, tan, tanh
Methods inherited from interface org.hipparchus.FieldElement
isZero
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Constructor Details
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FieldGradient
Build an instance with values and derivative.- Parameters:
value
- value of the functiongradient
- gradient of the function
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FieldGradient
Build an instance from aDerivativeStructure
.- Parameters:
ds
- derivative structure- Throws:
MathIllegalArgumentException
- ifds
order is not 1
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Method Details
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constant
public static <T extends CalculusFieldElement<T>> FieldGradient<T> constant(int freeParameters, T value) Build an instance corresponding to a constant value.- Type Parameters:
T
- the type of the function parameters and value- Parameters:
freeParameters
- number of free parameters (i.e. dimension of the gradient)value
- constant value of the function- Returns:
- a
FieldGradient
with a constant value and all derivatives set to 0.0
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variable
public static <T extends CalculusFieldElement<T>> FieldGradient<T> variable(int freeParameters, int index, T value) Build aGradient
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.
- Type Parameters:
T
- the type of the function parameters and value- Parameters:
freeParameters
- number of free parameters (i.e. dimension of the gradient)index
- index of the variable (from 0 togetFreeParameters()
- 1)value
- value of the variable- Returns:
- a
FieldGradient
with a constant value and all derivatives set to 0.0 except the one atindex
which will be set to 1.0
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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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newInstance
Create an instance corresponding to a constant real value.- Specified by:
newInstance
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Parameters:
c
- 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>,
FieldGradient<T extends CalculusFieldElement<T>>> - Parameters:
c
- 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>,
FieldGradient<T extends CalculusFieldElement<T>>> - Parameters:
v
- zeroth-order derivative of new represented function- Returns:
- new object with changed value
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getValue
Get the value part of the function.- Specified by:
getValue
in interfaceFieldDerivative<T extends CalculusFieldElement<T>,
FieldGradient<T extends CalculusFieldElement<T>>> - Returns:
- value part of the value of the function
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getGradient
Get the gradient part of the function.- Returns:
- gradient part of the value of the function
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getFreeParameters
public int getFreeParameters()Get the number of free parameters.- Specified by:
getFreeParameters
in interfaceDifferentialAlgebra
- Returns:
- number of free parameters
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getPartialDerivative
Get a partial derivative.- Specified by:
getPartialDerivative
in interfaceFieldDerivative<T extends CalculusFieldElement<T>,
FieldGradient<T extends CalculusFieldElement<T>>> - 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- See Also:
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getPartialDerivative
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 togetFreeParameters()
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toDerivativeStructure
Convert the instance to aFieldDerivativeStructure
.- 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:
n
- right hand side parameter of the operator- Returns:
- this×n
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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>,
FieldGradient<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>> FieldGradient<T> pow(double a, FieldGradient<T> x) Compute ax where a is a double and x aFieldGradient
- 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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sinCos
Combined Sine and Cosine operation.- Specified by:
sinCos
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Specified by:
sinCos
in interfaceFieldDerivative1<T extends CalculusFieldElement<T>,
FieldGradient<T extends CalculusFieldElement<T>>> - Returns:
- [sin(this), cos(this)]
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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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sinhCosh
Combined hyperbolic sine and cosine operation.- Specified by:
sinhCosh
in interfaceCalculusFieldElement<T extends CalculusFieldElement<T>>
- Specified by:
sinhCosh
in interfaceFieldDerivative1<T extends CalculusFieldElement<T>,
FieldGradient<T extends CalculusFieldElement<T>>> - Returns:
- [sinh(this), cosh(this)]
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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 gradient.- Parameters:
delta
- parameters offsets (Δx, Δy, ...)- Returns:
- value of the Taylor expansion at x + Δx, y + Δy, ...
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taylor
Evaluate Taylor expansion of a gradient.- Parameters:
delta
- parameters offsets (Δx, Δy, ...)- Returns:
- value of the Taylor expansion at x + Δx, y + Δy, ...
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linearCombination
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
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
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 FieldGradient<T> linearCombination(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<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 FieldGradient<T> linearCombination(double a1, FieldGradient<T> b1, double a2, FieldGradient<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 FieldGradient<T> linearCombination(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2, FieldGradient<T> a3, FieldGradient<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 FieldGradient<T> linearCombination(T a1, FieldGradient<T> b1, T a2, FieldGradient<T> b2, T a3, FieldGradient<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 FieldGradient<T> linearCombination(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2, double a3, FieldGradient<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:
-
linearCombination
public FieldGradient<T> linearCombination(FieldGradient<T> a1, FieldGradient<T> b1, FieldGradient<T> a2, FieldGradient<T> b2, FieldGradient<T> a3, FieldGradient<T> b3, FieldGradient<T> a4, FieldGradient<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 FieldGradient<T> linearCombination(double a1, FieldGradient<T> b1, double a2, FieldGradient<T> b2, double a3, FieldGradient<T> b3, double a4, FieldGradient<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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