org.hipparchus.analysis.differentiation.Gradient

All Implemented Interfaces:: Serializable, Derivative<Gradient>, Derivative1<Gradient>, DifferentialAlgebra, CalculusFieldElement<Gradient>, FieldElement<Gradient>

public class Gradient extends Object implements Derivative1<Gradient>, Serializable

Class representing both the value and the differentials of a function.

This class is a stripped-down version of DerivativeStructure with derivation order 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.

Gradient 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.

Since:

1.7

See Also:

Constructor Summary

Constructors

Constructor

Description

Gradient(double value, double... gradient)

Build an instance with values and derivative.

Gradient(DerivativeStructure ds)

Build an instance from a DerivativeStructure.
Method Summary

Modifier and Type

Method

Description

Gradient

abs()

absolute value.

Gradient

add(Gradient a)

Compute this + a.

Gradient

atan2(Gradient x)

Two arguments arc tangent operation.

Gradient

compose(double... f)

Compute composition of the instance by a univariate function.

Gradient

compose(double f0, double f1)

Compute composition of the instance by a univariate function differentiable at order 1.

static Gradient

constant(int freeParameters, double value)

Build an instance corresponding to a constant value.

Gradient

copySign(double sign)

Returns the instance with the sign of the argument.

Gradient

copySign(Gradient sign)

Returns the instance with the sign of the argument.

Gradient

divide(double a)

'÷' operator.

Gradient

divide(Gradient a)

Compute this ÷ a.

boolean

equals(Object other)

Test for the equality of two univariate derivatives.

GradientField

getField()

Get the Field to which the instance belongs.

int

getFreeParameters()

Get the number of free parameters.

double[]

getGradient()

Get the gradient part of the function.

double

getPartialDerivative(int n)

Get the partial derivative with respect to one parameter.

double

getPartialDerivative(int... orders)

Get a partial derivative.

double

getValue()

Get the value part of the function.

int

hashCode()

Get a hashCode for the univariate derivative.

Gradient

hypot(Gradient y)

Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.

Gradient

linearCombination(double[] a, Gradient[] b)

Compute a linear combination.

Gradient

linearCombination(double a1, Gradient b1, double a2, Gradient b2)

Compute a linear combination.

Gradient

linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3)

Compute a linear combination.

Gradient

linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3, double a4, Gradient b4)

Compute a linear combination.

Gradient

linearCombination(Gradient[] a, Gradient[] b)

Compute a linear combination.

Gradient

linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2)

Compute a linear combination.

Gradient

linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3)

Compute a linear combination.

Gradient

linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3, Gradient a4, Gradient b4)

Compute a linear combination.

Gradient

multiply(double a)

'×' operator.

Gradient

multiply(int n)

Compute n × this.

Gradient

multiply(Gradient a)

Compute this × a.

Gradient

negate()

Returns the additive inverse of this element.

Gradient

newInstance(double c)

Create an instance corresponding to a constant real value.

Gradient

pow(double p)

Power operation.

static Gradient

pow(double a, Gradient x)

Compute a^x where a is a double and x a Gradient

Gradient

pow(int n)

Integer power operation.

Gradient

remainder(Gradient a)

IEEE remainder operator.

Gradient

scalb(int n)

Multiply the instance by a power of 2.

FieldSinCos<Gradient>

sinCos()

Combined Sine and Cosine operation.

FieldSinhCosh<Gradient>

sinhCosh()

Combined hyperbolic sine and cosine operation.

Gradient

subtract(Gradient a)

Compute this - a.

double

taylor(double... delta)

Evaluate Taylor expansion a derivative structure.

Gradient

toDegrees()

Convert radians to degrees, with error of less than 0.5 ULP

DerivativeStructure

toDerivativeStructure()

Convert the instance to a DerivativeStructure.

Gradient

toRadians()

Convert degrees to radians, with error of less than 0.5 ULP

static Gradient

variable(int freeParameters, int index, double value)

Build a Gradient representing a variable.

Gradient

withValue(double v)

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
ceil, floor, getPi, isFinite, isInfinite, isNaN, norm, rint, round, sign, ulp

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative
add, getExponent, 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, sinh, sqrt, square, tan, tanh

Methods inherited from interface org.hipparchus.FieldElement
isZero

Constructor Details
- Gradient
  
  public Gradient(double value, double... gradient)
  
  Build an instance with values and derivative.
  
  Parameters:
  
  value - value of the function
  
  gradient - gradient of the function
- Gradient
  
  public Gradient(DerivativeStructure ds) throws MathIllegalArgumentException
  
  Build an instance from a DerivativeStructure.
  
  Parameters:
  
  ds - derivative structure
  
  Throws:
  
  MathIllegalArgumentException - if ds order is not 1
Method Details
- constant
  
  public static Gradient constant(int freeParameters, double value)
  
  Build an instance corresponding to a constant value.
  
  Parameters:
  
  freeParameters - number of free parameters (i.e. dimension of the gradient)
  
  value - constant value of the function
  
  Returns:
  
  a Gradient with a constant value and all derivatives set to 0.0
- variable
  
  public static Gradient variable(int freeParameters, int index, double value)
  
  Build a Gradient representing a variable.
  Instances built using this method are considered to be the free variables with respect to which differentials are computed. As such, their differential with respect to themselves is +1.
  
  Parameters:
  
  freeParameters - number of free parameters (i.e. dimension of the gradient)
  
  index - index of the variable (from 0 to getFreeParameters() - 1)
  
  value - value of the variable
  
  Returns:
  
  a Gradient with a constant value and all derivatives set to 0.0 except the one at index which will be set to 1.0
- newInstance
  
  public Gradient newInstance(double c)
  
  Create an instance corresponding to a constant real value.
  
  Specified by:
  
  newInstance in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  c - constant real value
  
  Returns:
  
  instance corresponding to a constant real value
- withValue
  
  public Gradient withValue(double v)
  
  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 interface Derivative<Gradient>
  
  Parameters:
  
  v - zeroth-order derivative of new represented function
  
  Returns:
  
  new object with changed value
- getValue
  
  public double getValue()
  
  Get the value part of the function.
  
  Specified by:
  
  getValue in interface Derivative<Gradient>
  
  Returns:
  
  value part of the value of the function
- getGradient
  
  public double[] getGradient()
  
  Get the gradient part of the function.
  Returns:
  
  gradient part of the value of the function
  
  See Also:
  
  getPartialDerivative(int)
- getFreeParameters
  
  public int getFreeParameters()
  
  Get the number of free parameters.
  
  Specified by:
  
  getFreeParameters in interface DifferentialAlgebra
  
  Returns:
  
  number of free parameters
- getPartialDerivative
  
  public double getPartialDerivative(int... orders) throws MathIllegalArgumentException
  
  Get a partial derivative.
  Specified by:
  
  getPartialDerivative in interface Derivative<Gradient>
  
  Parameters:
  
  orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)
  
  Returns:
  
  partial derivative
  
  Throws:
  
  MathIllegalArgumentException - if the numbers of variables does not match the instance
  
  See Also:
  
  Derivative.getValue()
- getPartialDerivative
  
  public double getPartialDerivative(int n) throws MathIllegalArgumentException
  
  Get the partial derivative with respect to one parameter.
  
  Parameters:
  
  n - index of the parameter (counting from 0)
  
  Returns:
  
  partial derivative with respect to the n^th parameter
  
  Throws:
  
  MathIllegalArgumentException - if n is either negative or larger or equal to getFreeParameters()
- toDerivativeStructure
  
  public DerivativeStructure toDerivativeStructure()
  
  Convert the instance to a DerivativeStructure.
  
  Returns:
  
  derivative structure with same value and derivative as the instance
- add
  
  public Gradient add(Gradient a)
  
  Compute this + a.
  
  Specified by:
  
  add in interface FieldElement<Gradient>
  
  Parameters:
  
  a - element to add
  
  Returns:
  
  a new element representing this + a
- subtract
  
  public Gradient subtract(Gradient a)
  
  Compute this - a.
  
  Specified by:
  
  subtract in interface CalculusFieldElement<Gradient>
  
  Specified by:
  
  subtract in interface FieldElement<Gradient>
  
  Parameters:
  
  a - element to subtract
  
  Returns:
  
  a new element representing this - a
- multiply
  
  public Gradient multiply(int n)
  
  Compute n × this. Multiplication by an integer number is defined as the following sum \[ n \times \mathrm{this} = \sum_{i=1}^n \mathrm{this} \]
  
  Specified by:
  
  multiply in interface CalculusFieldElement<Gradient>
  
  Specified by:
  
  multiply in interface FieldElement<Gradient>
  
  Parameters:
  
  n - Number of times this must be added to itself.
  
  Returns:
  
  A new element representing n × this.
- multiply
  
  public Gradient multiply(double a)
  
  '×' operator.
  
  Specified by:
  
  multiply in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this×a
- multiply
  
  public Gradient multiply(Gradient a)
  
  Compute this × a.
  
  Specified by:
  
  multiply in interface FieldElement<Gradient>
  
  Parameters:
  
  a - element to multiply
  
  Returns:
  
  a new element representing this × a
- divide
  
  public Gradient divide(double a)
  
  '÷' operator.
  
  Specified by:
  
  divide in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this÷a
- divide
  
  public Gradient divide(Gradient a)
  
  Compute this ÷ a.
  
  Specified by:
  
  divide in interface CalculusFieldElement<Gradient>
  
  Specified by:
  
  divide in interface FieldElement<Gradient>
  
  Parameters:
  
  a - element to divide by
  
  Returns:
  
  a new element representing this ÷ a
- remainder
  
  public Gradient remainder(Gradient a)
  
  IEEE remainder operator.
  
  Specified by:
  
  remainder in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this - n × a where n is the closest integer to this/a
- negate
  
  public Gradient negate()
  
  Returns the additive inverse of this element.
  
  Specified by:
  
  negate in interface FieldElement<Gradient>
  
  Returns:
  
  the opposite of this.
- abs
  
  public Gradient abs()
  
  absolute value.
  
  Specified by:
  
  abs in interface CalculusFieldElement<Gradient>
  
  Returns:
  
  abs(this)
- copySign
  
  public Gradient copySign(Gradient sign)
  
  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
  
  Specified by:
  
  copySign in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  sign - the sign for the returned value
  
  Returns:
  
  the instance with the same sign as the sign argument
- copySign
  
  public Gradient copySign(double sign)
  
  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
  
  Specified by:
  
  copySign in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  sign - the sign for the returned value
  
  Returns:
  
  the instance with the same sign as the sign argument
- scalb
  
  public Gradient scalb(int n)
  
  Multiply the instance by a power of 2.
  
  Specified by:
  
  scalb in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  n - power of 2
  
  Returns:
  
  this × 2ⁿ
- hypot
  
  public Gradient hypot(Gradient y)
  Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
  
  If either argument is infinite, then the result is positive infinity.
  
  else, if either argument is NaN then the result is NaN.
  Specified by:
  
  hypot in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  y - a value
  
  Returns:
  
  sqrt(this² +y²)
- compose
  
  public Gradient compose(double... f)
  
  Compute composition of the instance by a univariate function.
  
  Specified by:
  
  compose in interface Derivative<Gradient>
  
  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)
- compose
  
  public Gradient compose(double f0, double f1)
  
  Compute composition of the instance by a univariate function differentiable at order 1.
  
  Specified by:
  
  compose in interface Derivative1<Gradient>
  
  Parameters:
  
  f0 - value of function
  
  f1 - first-order derivative
  
  Returns:
  
  f(this)
- getField
  
  public GradientField getField()
  
  Get the Field to which the instance belongs.
  
  Specified by:
  
  getField in interface FieldElement<Gradient>
  
  Returns:
  
  Field to which the instance belongs
- pow
  
  public static Gradient pow(double a, Gradient x)
  
  Compute a^x where a is a double and x a Gradient
  
  Parameters:
  
  a - number to exponentiate
  
  x - power to apply
  
  Returns:
  
  a^x
- pow
  
  public Gradient pow(double p)
  
  Power operation.
  
  Specified by:
  
  pow in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  p - power to apply
  
  Returns:
  
  this^p
- pow
  
  public Gradient pow(int n)
  
  Integer power operation.
  
  Specified by:
  
  pow in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  n - power to apply
  
  Returns:
  
  thisⁿ
- sinCos
  
  public FieldSinCos<Gradient> sinCos()
  
  Combined Sine and Cosine operation.
  
  Specified by:
  
  sinCos in interface CalculusFieldElement<Gradient>
  
  Specified by:
  
  sinCos in interface Derivative1<Gradient>
  
  Returns:
  
  [sin(this), cos(this)]
- atan2
  
  public Gradient atan2(Gradient x)
  
  Two arguments arc tangent operation.
  Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.
  
  Specified by:
  
  atan2 in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  x - second argument of the arc tangent
  
  Returns:
  
  atan2(this, x)
- sinhCosh
  
  public FieldSinhCosh<Gradient> sinhCosh()
  
  Combined hyperbolic sine and cosine operation.
  
  Specified by:
  
  sinhCosh in interface CalculusFieldElement<Gradient>
  
  Specified by:
  
  sinhCosh in interface Derivative1<Gradient>
  
  Returns:
  
  [sinh(this), cosh(this)]
- toDegrees
  
  public Gradient toDegrees()
  
  Convert radians to degrees, with error of less than 0.5 ULP
  
  Specified by:
  
  toDegrees in interface CalculusFieldElement<Gradient>
  
  Returns:
  
  instance converted into degrees
- toRadians
  
  public Gradient toRadians()
  
  Convert degrees to radians, with error of less than 0.5 ULP
  
  Specified by:
  
  toRadians in interface CalculusFieldElement<Gradient>
  
  Returns:
  
  instance converted into radians
- taylor
  
  public double taylor(double... delta)
  
  Evaluate Taylor expansion a derivative structure.
  
  Parameters:
  
  delta - parameters offsets (Δx, Δy, ...)
  
  Returns:
  
  value of the Taylor expansion at x + Δx, y + Δy, ...
- linearCombination
  
  public Gradient linearCombination(Gradient[] a, Gradient[] b)
  
  Compute a linear combination.
  
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a - Factors.
  
  b - Factors.
  
  Returns:
  
  Σ_i a_i b_i.
- linearCombination
  
  public Gradient linearCombination(double[] a, Gradient[] b)
  
  Compute a linear combination.
  
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a - Factors.
  
  b - Factors.
  
  Returns:
  
  Σ_i a_i b_i.
- linearCombination
  
  public Gradient linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - 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)
- linearCombination
  
  public Gradient linearCombination(double a1, Gradient b1, double a2, Gradient b2)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - 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)
- linearCombination
  
  public Gradient linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - 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)
- linearCombination
  
  public Gradient linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - 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)
- linearCombination
  
  public Gradient linearCombination(Gradient a1, Gradient b1, Gradient a2, Gradient b2, Gradient a3, Gradient b3, Gradient a4, Gradient b4)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - second factor of the third term
  
  a4 - first factor of the fourth term
  
  b4 - 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)
- linearCombination
  
  public Gradient linearCombination(double a1, Gradient b1, double a2, Gradient b2, double a3, Gradient b3, double a4, Gradient b4)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Gradient>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - second factor of the third term
  
  a4 - first factor of the fourth term
  
  b4 - 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)
- equals
  
  public boolean equals(Object other)
  
  Test for the equality of two univariate derivatives.
  univariate derivatives are considered equal if they have the same derivatives.
  
  Overrides:
  
  equals in class Object
  
  Parameters:
  
  other - Object to test for equality to this
  
  Returns:
  
  true if two univariate derivatives are equal
- hashCode
  
  public int hashCode()
  
  Get a hashCode for the univariate derivative.
  
  Overrides:
  
  hashCode in class Object
  
  Returns:
  
  a hash code value for this object

Class Gradient

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative

Methods inherited from interface org.hipparchus.analysis.differentiation.Derivative1

Methods inherited from interface org.hipparchus.FieldElement

Constructor Details

Gradient

Gradient

Method Details

constant

variable

newInstance

withValue

getValue

getGradient

getFreeParameters

getPartialDerivative

getPartialDerivative

toDerivativeStructure

add

subtract

multiply

multiply

multiply

divide

divide

remainder

negate

abs

copySign

copySign

scalb

hypot

compose

compose

getField

pow

pow

pow

sinCos

atan2

sinhCosh

toDegrees

toRadians

taylor

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

linearCombination

equals

hashCode