org.apache.commons.math3.analysis.differentiation.DerivativeStructure

All Implemented Interfaces:: Serializable, FieldElement<DerivativeStructure>, RealFieldElement<DerivativeStructure>

public class DerivativeStructure extends Object implements RealFieldElement<DerivativeStructure>, Serializable

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

This class is the workhorse of the differentiation package.

This class is an implementation of the extension to Rall's numbers described in Dan Kalman's paper Doubly Recursive Multivariate Automatic Differentiation, Mathematics Magazine, vol. 75, no. 3, June 2002. 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. Dan Kalman's derivative structures hold all partial derivatives up to any specified order, with respect to any number of free parameters. Rall's numbers therefore can be seen as derivative structures for order one derivative and one free parameter, and real numbers can be seen as derivative structures with zero order derivative and no free parameters.

DerivativeStructure 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 no requiring users to compute the derivatives by themselves. Implementing complex expression can also be done by developing computation code using standard primitive double values and to use differentiators to create the DerivativeStructure-based instances. This method is simpler but may be limited in the accuracy and derivation orders and may be computationally intensive (this is typically the case for finite differences differentiator.

Instances of this class are guaranteed to be immutable.

Since:

3.1

See Also:

Constructor Summary

Constructors

Constructor

Description

DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2)

Linear combination constructor.

DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2, double a3, DerivativeStructure ds3)

Linear combination constructor.

DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2, double a3, DerivativeStructure ds3, double a4, DerivativeStructure ds4)

Linear combination constructor.

DerivativeStructure(int parameters, int order)

Build an instance with all values and derivatives set to 0.

DerivativeStructure(int parameters, int order, double value)

Build an instance representing a constant value.

DerivativeStructure(int parameters, int order, double... derivatives)

Build an instance from all its derivatives.

DerivativeStructure(int parameters, int order, int index, double value)

Build an instance representing a variable.
Method Summary

Modifier and Type

Method

Description

DerivativeStructure

abs()

absolute value.

DerivativeStructure

acos()

Arc cosine operation.

DerivativeStructure

acosh()

Inverse hyperbolic cosine operation.

DerivativeStructure

add(double a)

'+' operator.

DerivativeStructure

add(DerivativeStructure a)

Compute this + a.

DerivativeStructure

asin()

Arc sine operation.

DerivativeStructure

asinh()

Inverse hyperbolic sine operation.

DerivativeStructure

atan()

Arc tangent operation.

DerivativeStructure

atan2(DerivativeStructure x)

Two arguments arc tangent operation.

static DerivativeStructure

atan2(DerivativeStructure y, DerivativeStructure x)

Two arguments arc tangent operation.

DerivativeStructure

atanh()

Inverse hyperbolic tangent operation.

DerivativeStructure

cbrt()

Cubic root.

DerivativeStructure

ceil()

Get the smallest whole number larger than instance.

DerivativeStructure

compose(double... f)

Compute composition of the instance by a univariate function.

DerivativeStructure

copySign(double sign)

Returns the instance with the sign of the argument.

DerivativeStructure

copySign(DerivativeStructure sign)

Returns the instance with the sign of the argument.

DerivativeStructure

cos()

Cosine operation.

DerivativeStructure

cosh()

Hyperbolic cosine operation.

DerivativeStructure

createConstant(double c)

Create a constant compatible with instance order and number of parameters.

DerivativeStructure

divide(double a)

'÷' operator.

DerivativeStructure

divide(DerivativeStructure a)

Compute this ÷ a.

boolean

equals(Object other)

Test for the equality of two derivative structures.

DerivativeStructure

exp()

Exponential.

DerivativeStructure

expm1()

Exponential minus 1.

DerivativeStructure

floor()

Get the largest whole number smaller than instance.

double[]

getAllDerivatives()

Get all partial derivatives.

int

getExponent()

Return the exponent of the instance value, removing the bias.

Field<DerivativeStructure>

getField()

Get the Field to which the instance belongs.

int

getFreeParameters()

Get the number of free parameters.

int

getOrder()

Get the derivation order.

double

getPartialDerivative(int... orders)

Get a partial derivative.

double

getReal()

Get the real value of the number.

double

getValue()

Get the value part of the derivative structure.

int

hashCode()

Get a hashCode for the derivative structure.

DerivativeStructure

hypot(DerivativeStructure y)

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

static DerivativeStructure

hypot(DerivativeStructure x, DerivativeStructure y)

Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²) avoiding intermediate overflow or underflow.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

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

Compute a linear combination.

DerivativeStructure

log()

Natural logarithm.

DerivativeStructure

log10()

Base 10 logarithm.

DerivativeStructure

log1p()

Shifted natural logarithm.

DerivativeStructure

multiply(double a)

'×' operator.

DerivativeStructure

multiply(int n)

Compute n × this.

DerivativeStructure

multiply(DerivativeStructure a)

Compute this × a.

DerivativeStructure

negate()

Returns the additive inverse of this element.

DerivativeStructure

pow(double p)

Power operation.

static DerivativeStructure

pow(double a, DerivativeStructure x)

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

DerivativeStructure

pow(int n)

Integer power operation.

DerivativeStructure

pow(DerivativeStructure e)

Power operation.

DerivativeStructure

reciprocal()

Returns the multiplicative inverse of this element.

DerivativeStructure

remainder(double a)

IEEE remainder operator.

DerivativeStructure

remainder(DerivativeStructure a)

IEEE remainder operator.

DerivativeStructure

rint()

Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.

DerivativeStructure

rootN(int n)

N^th root.

long

round()

Get the closest long to instance value.

DerivativeStructure

scalb(int n)

Multiply the instance by a power of 2.

DerivativeStructure

signum()

Compute the signum of the instance.

DerivativeStructure

sin()

Sine operation.

DerivativeStructure

sinh()

Hyperbolic sine operation.

DerivativeStructure

sqrt()

Square root.

DerivativeStructure

subtract(double a)

'-' operator.

DerivativeStructure

subtract(DerivativeStructure a)

Compute this - a.

DerivativeStructure

tan()

Tangent operation.

DerivativeStructure

tanh()

Hyperbolic tangent operation.

double

taylor(double... delta)

Evaluate Taylor expansion a derivative structure.

DerivativeStructure

toDegrees()

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

DerivativeStructure

toRadians()

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

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- DerivativeStructure
  
  public DerivativeStructure(int parameters, int order) throws NumberIsTooLargeException
  
  Build an instance with all values and derivatives set to 0.
  
  Parameters:
  
  parameters - number of free parameters
  
  order - derivation order
  
  Throws:
  
  NumberIsTooLargeException - if order is too large
- DerivativeStructure
  
  public DerivativeStructure(int parameters, int order, double value) throws NumberIsTooLargeException
  
  Build an instance representing a constant value.
  Parameters:
  
  parameters - number of free parameters
  
  order - derivation order
  
  value - value of the constant
  
  Throws:
  
  NumberIsTooLargeException - if order is too large
  
  See Also:
  
  DerivativeStructure(int, int, int, double)
- DerivativeStructure
  
  public DerivativeStructure(int parameters, int order, int index, double value) throws NumberIsTooLargeException
  
  Build an instance representing a variable.
  Instances built using this constructor 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:
  
  parameters - number of free parameters
  
  order - derivation order
  
  index - index of the variable (from 0 to parameters - 1)
  
  value - value of the variable
  
  Throws:
  
  NumberIsTooLargeException - if index >= parameters.
  
  See Also:
  
  DerivativeStructure(int, int, double)
- DerivativeStructure
  
  public DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2) throws DimensionMismatchException
  
  Linear combination constructor. The derivative structure built will be a1 * ds1 + a2 * ds2
  
  Parameters:
  
  a1 - first scale factor
  
  ds1 - first base (unscaled) derivative structure
  
  a2 - second scale factor
  
  ds2 - second base (unscaled) derivative structure
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders are inconsistent
- DerivativeStructure
  
  public DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2, double a3, DerivativeStructure ds3) throws DimensionMismatchException
  
  Linear combination constructor. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3
  
  Parameters:
  
  a1 - first scale factor
  
  ds1 - first base (unscaled) derivative structure
  
  a2 - second scale factor
  
  ds2 - second base (unscaled) derivative structure
  
  a3 - third scale factor
  
  ds3 - third base (unscaled) derivative structure
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders are inconsistent
- DerivativeStructure
  
  public DerivativeStructure(double a1, DerivativeStructure ds1, double a2, DerivativeStructure ds2, double a3, DerivativeStructure ds3, double a4, DerivativeStructure ds4) throws DimensionMismatchException
  
  Linear combination constructor. The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
  
  Parameters:
  
  a1 - first scale factor
  
  ds1 - first base (unscaled) derivative structure
  
  a2 - second scale factor
  
  ds2 - second base (unscaled) derivative structure
  
  a3 - third scale factor
  
  ds3 - third base (unscaled) derivative structure
  
  a4 - fourth scale factor
  
  ds4 - fourth base (unscaled) derivative structure
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders are inconsistent
- DerivativeStructure
  
  public DerivativeStructure(int parameters, int order, double... derivatives) throws DimensionMismatchException, NumberIsTooLargeException
  
  Build an instance from all its derivatives.
  Parameters:
  
  parameters - number of free parameters
  
  order - derivation order
  
  derivatives - derivatives sorted according to DSCompiler.getPartialDerivativeIndex(int...)
  
  Throws:
  
  DimensionMismatchException - if derivatives array does not match the size expected by the compiler
  
  NumberIsTooLargeException - if order is too large
  
  See Also:
  
  getAllDerivatives()
Method Details
- getFreeParameters
  
  public int getFreeParameters()
  
  Get the number of free parameters.
  
  Returns:
  
  number of free parameters
- getOrder
  
  public int getOrder()
  
  Get the derivation order.
  
  Returns:
  
  derivation order
- createConstant
  
  public DerivativeStructure createConstant(double c)
  
  Create a constant compatible with instance order and number of parameters.
  This method is a convenience factory method, it simply calls new DerivativeStructure(getFreeParameters(), getOrder(), c)
  Parameters:
  
  c - value of the constant
  
  Returns:
  
  a constant compatible with instance order and number of parameters
  
  Since:
  
  3.3
  
  See Also:
  
  DerivativeStructure(int, int, double)
- getReal
  
  public double getReal()
  
  Get the real value of the number.
  
  Specified by:
  
  getReal in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  real value
  
  Since:
  
  3.2
- getValue
  
  public double getValue()
  
  Get the value part of the derivative structure.
  Returns:
  
  value part of the derivative structure
  
  See Also:
  
  getPartialDerivative(int...)
- getPartialDerivative
  
  public double getPartialDerivative(int... orders) throws DimensionMismatchException, NumberIsTooLargeException
  
  Get a partial derivative.
  Parameters:
  
  orders - derivation orders with respect to each variable (if all orders are 0, the value is returned)
  
  Returns:
  
  partial derivative
  
  Throws:
  
  DimensionMismatchException - if the numbers of variables does not match the instance
  
  NumberIsTooLargeException - if sum of derivation orders is larger than the instance limits
  
  See Also:
  
  getValue()
- getAllDerivatives
  
  public double[] getAllDerivatives()
  
  Get all partial derivatives.
  
  Returns:
  
  a fresh copy of partial derivatives, in an array sorted according to DSCompiler.getPartialDerivativeIndex(int...)
- add
  
  public DerivativeStructure add(double a)
  
  '+' operator.
  
  Specified by:
  
  add in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this+a
  
  Since:
  
  3.2
- add
  
  public DerivativeStructure add(DerivativeStructure a) throws DimensionMismatchException
  
  Compute this + a.
  
  Specified by:
  
  add in interface FieldElement<DerivativeStructure>
  
  Parameters:
  
  a - element to add
  
  Returns:
  
  a new element representing this + a
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
- subtract
  
  public DerivativeStructure subtract(double a)
  
  '-' operator.
  
  Specified by:
  
  subtract in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this-a
  
  Since:
  
  3.2
- subtract
  
  public DerivativeStructure subtract(DerivativeStructure a) throws DimensionMismatchException
  
  Compute this - a.
  
  Specified by:
  
  subtract in interface FieldElement<DerivativeStructure>
  
  Parameters:
  
  a - element to subtract
  
  Returns:
  
  a new element representing this - a
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
- multiply
  
  public DerivativeStructure multiply(int n)
  
  Compute n × this. Multiplication by an integer number is defined as the following sum n × this = ∑_i=1ⁿ this.
  
  Specified by:
  
  multiply in interface FieldElement<DerivativeStructure>
  
  Parameters:
  
  n - Number of times this must be added to itself.
  
  Returns:
  
  A new element representing n × this.
- multiply
  
  public DerivativeStructure multiply(double a)
  
  '×' operator.
  
  Specified by:
  
  multiply in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this×a
  
  Since:
  
  3.2
- multiply
  
  public DerivativeStructure multiply(DerivativeStructure a) throws DimensionMismatchException
  
  Compute this × a.
  
  Specified by:
  
  multiply in interface FieldElement<DerivativeStructure>
  
  Parameters:
  
  a - element to multiply
  
  Returns:
  
  a new element representing this × a
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
- divide
  
  public DerivativeStructure divide(double a)
  
  '÷' operator.
  
  Specified by:
  
  divide in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this÷a
  
  Since:
  
  3.2
- divide
  
  public DerivativeStructure divide(DerivativeStructure a) throws DimensionMismatchException
  
  Compute this ÷ a.
  
  Specified by:
  
  divide in interface FieldElement<DerivativeStructure>
  
  Parameters:
  
  a - element to divide by
  
  Returns:
  
  a new element representing this ÷ a
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
- remainder
  
  public DerivativeStructure remainder(double a)
  
  IEEE remainder operator.
  
  Specified by:
  
  remainder in interface RealFieldElement<DerivativeStructure>
  
  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)
- remainder
  
  public DerivativeStructure remainder(DerivativeStructure a) throws DimensionMismatchException
  
  IEEE remainder operator.
  
  Specified by:
  
  remainder in interface RealFieldElement<DerivativeStructure>
  
  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)
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- negate
  
  public DerivativeStructure negate()
  
  Returns the additive inverse of this element.
  
  Specified by:
  
  negate in interface FieldElement<DerivativeStructure>
  
  Returns:
  
  the opposite of this.
- abs
  
  public DerivativeStructure abs()
  
  absolute value.
  
  Specified by:
  
  abs in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  abs(this)
  
  Since:
  
  3.2
- ceil
  
  public DerivativeStructure ceil()
  
  Get the smallest whole number larger than instance.
  
  Specified by:
  
  ceil in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  ceil(this)
  
  Since:
  
  3.2
- floor
  
  public DerivativeStructure floor()
  
  Get the largest whole number smaller than instance.
  
  Specified by:
  
  floor in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  floor(this)
  
  Since:
  
  3.2
- rint
  
  public DerivativeStructure rint()
  
  Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
  
  Specified by:
  
  rint in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
  
  Since:
  
  3.2
- round
  
  public long round()
  
  Get the closest long to instance value.
  
  Specified by:
  
  round in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  closest long to RealFieldElement.getReal()
- signum
  
  public DerivativeStructure signum()
  
  Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
  
  Specified by:
  
  signum in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
  
  Since:
  
  3.2
- copySign
  
  public DerivativeStructure copySign(DerivativeStructure sign)
  
  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
  
  Specified by:
  
  copySign in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  sign - the sign for the returned value
  
  Returns:
  
  the instance with the same sign as the sign argument
  
  Since:
  
  3.2
- copySign
  
  public DerivativeStructure 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 RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  sign - the sign for the returned value
  
  Returns:
  
  the instance with the same sign as the sign argument
  
  Since:
  
  3.2
- getExponent
  
  public int getExponent()
  
  Return the exponent of the instance value, removing the bias.
  For double numbers of the form 2^x, the unbiased exponent is exactly x.
  
  Returns:
  
  exponent for instance in IEEE754 representation, without bias
- scalb
  
  public DerivativeStructure scalb(int n)
  
  Multiply the instance by a power of 2.
  
  Specified by:
  
  scalb in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  n - power of 2
  
  Returns:
  
  this × 2ⁿ
  
  Since:
  
  3.2
- hypot
  
  public DerivativeStructure hypot(DerivativeStructure y) throws DimensionMismatchException
  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 RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  y - a value
  
  Returns:
  
  sqrt(this² +y²)
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- hypot
  
  public static DerivativeStructure hypot(DerivativeStructure x, DerivativeStructure y) throws DimensionMismatchException
  Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +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:
  
  x - a value
  
  y - a value
  
  Returns:
  
  sqrt(x² +y²)
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- compose
  
  public DerivativeStructure compose(double... f) throws DimensionMismatchException
  
  Compute composition of the instance by a univariate function.
  
  Parameters:
  
  f - array of value and derivatives of the function at the current point (i.e. [f(getValue()), f'(getValue()), f''(getValue())...]).
  
  Returns:
  
  f(this)
  
  Throws:
  
  DimensionMismatchException - if the number of derivatives in the array is not equal to order + 1
- reciprocal
  
  public DerivativeStructure reciprocal()
  
  Returns the multiplicative inverse of this element.
  
  Specified by:
  
  reciprocal in interface FieldElement<DerivativeStructure>
  
  Specified by:
  
  reciprocal in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  the inverse of this.
- sqrt
  
  public DerivativeStructure sqrt()
  
  Square root.
  
  Specified by:
  
  sqrt in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  square root of the instance
  
  Since:
  
  3.2
- cbrt
  
  public DerivativeStructure cbrt()
  
  Cubic root.
  
  Specified by:
  
  cbrt in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  cubic root of the instance
  
  Since:
  
  3.2
- rootN
  
  public DerivativeStructure rootN(int n)
  
  N^th root.
  
  Specified by:
  
  rootN in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  n - order of the root
  
  Returns:
  
  n^th root of the instance
  
  Since:
  
  3.2
- getField
  
  public Field<DerivativeStructure> getField()
  
  Get the Field to which the instance belongs.
  
  Specified by:
  
  getField in interface FieldElement<DerivativeStructure>
  
  Returns:
  
  Field to which the instance belongs
- pow
  
  public static DerivativeStructure pow(double a, DerivativeStructure x)
  
  Compute a^x where a is a double and x a DerivativeStructure
  
  Parameters:
  
  a - number to exponentiate
  
  x - power to apply
  
  Returns:
  
  a^x
  
  Since:
  
  3.3
- pow
  
  public DerivativeStructure pow(double p)
  
  Power operation.
  
  Specified by:
  
  pow in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  p - power to apply
  
  Returns:
  
  this^p
  
  Since:
  
  3.2
- pow
  
  public DerivativeStructure pow(int n)
  
  Integer power operation.
  
  Specified by:
  
  pow in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  n - power to apply
  
  Returns:
  
  thisⁿ
  
  Since:
  
  3.2
- pow
  
  public DerivativeStructure pow(DerivativeStructure e) throws DimensionMismatchException
  
  Power operation.
  
  Specified by:
  
  pow in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  e - exponent
  
  Returns:
  
  this^e
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- exp
  
  public DerivativeStructure exp()
  
  Exponential.
  
  Specified by:
  
  exp in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  exponential of the instance
  
  Since:
  
  3.2
- expm1
  
  public DerivativeStructure expm1()
  
  Exponential minus 1.
  
  Specified by:
  
  expm1 in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  exponential minus one of the instance
  
  Since:
  
  3.2
- log
  
  public DerivativeStructure log()
  
  Natural logarithm.
  
  Specified by:
  
  log in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  logarithm of the instance
  
  Since:
  
  3.2
- log1p
  
  public DerivativeStructure log1p()
  
  Shifted natural logarithm.
  
  Specified by:
  
  log1p in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  logarithm of one plus the instance
  
  Since:
  
  3.2
- log10
  
  public DerivativeStructure log10()
  
  Base 10 logarithm.
  
  Returns:
  
  base 10 logarithm of the instance
- cos
  
  public DerivativeStructure cos()
  
  Cosine operation.
  
  Specified by:
  
  cos in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  cos(this)
  
  Since:
  
  3.2
- sin
  
  public DerivativeStructure sin()
  
  Sine operation.
  
  Specified by:
  
  sin in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  sin(this)
  
  Since:
  
  3.2
- tan
  
  public DerivativeStructure tan()
  
  Tangent operation.
  
  Specified by:
  
  tan in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  tan(this)
  
  Since:
  
  3.2
- acos
  
  public DerivativeStructure acos()
  
  Arc cosine operation.
  
  Specified by:
  
  acos in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  acos(this)
  
  Since:
  
  3.2
- asin
  
  public DerivativeStructure asin()
  
  Arc sine operation.
  
  Specified by:
  
  asin in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  asin(this)
  
  Since:
  
  3.2
- atan
  
  public DerivativeStructure atan()
  
  Arc tangent operation.
  
  Specified by:
  
  atan in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  atan(this)
  
  Since:
  
  3.2
- atan2
  
  public DerivativeStructure atan2(DerivativeStructure x) throws DimensionMismatchException
  
  Two arguments arc tangent operation.
  
  Specified by:
  
  atan2 in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  x - second argument of the arc tangent
  
  Returns:
  
  atan2(this, x)
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders are inconsistent
  
  Since:
  
  3.2
- atan2
  
  public static DerivativeStructure atan2(DerivativeStructure y, DerivativeStructure x) throws DimensionMismatchException
  
  Two arguments arc tangent operation.
  
  Parameters:
  
  y - first argument of the arc tangent
  
  x - second argument of the arc tangent
  
  Returns:
  
  atan2(y, x)
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- cosh
  
  public DerivativeStructure cosh()
  
  Hyperbolic cosine operation.
  
  Specified by:
  
  cosh in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  cosh(this)
  
  Since:
  
  3.2
- sinh
  
  public DerivativeStructure sinh()
  
  Hyperbolic sine operation.
  
  Specified by:
  
  sinh in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  sinh(this)
  
  Since:
  
  3.2
- tanh
  
  public DerivativeStructure tanh()
  
  Hyperbolic tangent operation.
  
  Specified by:
  
  tanh in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  tanh(this)
  
  Since:
  
  3.2
- acosh
  
  public DerivativeStructure acosh()
  
  Inverse hyperbolic cosine operation.
  
  Specified by:
  
  acosh in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  acosh(this)
  
  Since:
  
  3.2
- asinh
  
  public DerivativeStructure asinh()
  
  Inverse hyperbolic sine operation.
  
  Specified by:
  
  asinh in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  asin(this)
  
  Since:
  
  3.2
- atanh
  
  public DerivativeStructure atanh()
  
  Inverse hyperbolic tangent operation.
  
  Specified by:
  
  atanh in interface RealFieldElement<DerivativeStructure>
  
  Returns:
  
  atanh(this)
  
  Since:
  
  3.2
- toDegrees
  
  public DerivativeStructure toDegrees()
  
  Convert radians to degrees, with error of less than 0.5 ULP
  
  Returns:
  
  instance converted into degrees
- toRadians
  
  public DerivativeStructure toRadians()
  
  Convert degrees to radians, with error of less than 0.5 ULP
  
  Returns:
  
  instance converted into radians
- taylor
  
  public double taylor(double... delta) throws MathArithmeticException
  
  Evaluate Taylor expansion a derivative structure.
  
  Parameters:
  
  delta - parameters offsets (Δx, Δy, ...)
  
  Returns:
  
  value of the Taylor expansion at x + Δx, y + Δy, ...
  
  Throws:
  
  MathArithmeticException - if factorials becomes too large
- linearCombination
  
  public DerivativeStructure linearCombination(DerivativeStructure[] a, DerivativeStructure[] b) throws DimensionMismatchException
  
  Compute a linear combination.
  
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  a - Factors.
  
  b - Factors.
  
  Returns:
  
  Σ_i a_i b_i.
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- linearCombination
  
  public DerivativeStructure linearCombination(double[] a, DerivativeStructure[] b) throws DimensionMismatchException
  
  Compute a linear combination.
  
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  Parameters:
  
  a - Factors.
  
  b - Factors.
  
  Returns:
  
  Σ_i a_i b_i.
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
- linearCombination
  
  public DerivativeStructure linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2) throws DimensionMismatchException
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  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
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
  
  See Also:
  
  RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)
  
  RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
- linearCombination
  
  public DerivativeStructure linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2) throws DimensionMismatchException
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  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
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
  
  See Also:
  
  RealFieldElement.linearCombination(double, Object, double, Object, double, Object)
  
  RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
- linearCombination
  
  public DerivativeStructure linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2, DerivativeStructure a3, DerivativeStructure b3) throws DimensionMismatchException
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  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
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
  
  See Also:
  
  RealFieldElement.linearCombination(Object, Object, Object, Object)
  
  RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
- linearCombination
  
  public DerivativeStructure linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2, double a3, DerivativeStructure b3) throws DimensionMismatchException
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  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
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
  
  See Also:
  
  RealFieldElement.linearCombination(double, Object, double, Object)
  
  RealFieldElement.linearCombination(double, Object, double, Object, double, Object, double, Object)
- linearCombination
  
  public DerivativeStructure linearCombination(DerivativeStructure a1, DerivativeStructure b1, DerivativeStructure a2, DerivativeStructure b2, DerivativeStructure a3, DerivativeStructure b3, DerivativeStructure a4, DerivativeStructure b4) throws DimensionMismatchException
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  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 third term
  
  b4 - second factor of the third term
  
  Returns:
  
  a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
  
  See Also:
  
  RealFieldElement.linearCombination(Object, Object, Object, Object)
  
  RealFieldElement.linearCombination(Object, Object, Object, Object, Object, Object)
- linearCombination
  
  public DerivativeStructure linearCombination(double a1, DerivativeStructure b1, double a2, DerivativeStructure b2, double a3, DerivativeStructure b3, double a4, DerivativeStructure b4) throws DimensionMismatchException
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface RealFieldElement<DerivativeStructure>
  
  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 third term
  
  b4 - second factor of the third term
  
  Returns:
  
  a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
  
  Throws:
  
  DimensionMismatchException - if number of free parameters or orders do not match
  
  Since:
  
  3.2
  
  See Also:
  
  RealFieldElement.linearCombination(double, Object, double, Object)
  
  RealFieldElement.linearCombination(double, Object, double, Object, double, Object)
- equals
  
  public boolean equals(Object other)
  
  Test for the equality of two derivative structures.
  Derivative structures are considered equal if they have the same number of free parameters, the same derivation order, and the same derivatives.
  
  Overrides:
  
  equals in class Object
  
  Parameters:
  
  other - Object to test for equality to this
  
  Returns:
  
  true if two derivative structures are equal
  
  Since:
  
  3.2
- hashCode
  
  public int hashCode()
  
  Get a hashCode for the derivative structure.
  
  Overrides:
  
  hashCode in class Object
  
  Returns:
  
  a hash code value for this object
  
  Since:
  
  3.2

Class DerivativeStructure

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Details

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

DerivativeStructure

Method Details

getFreeParameters

getOrder

createConstant

getReal

getValue

getPartialDerivative

getAllDerivatives

add

add

subtract

subtract

multiply

multiply

multiply

divide

divide

remainder

remainder

negate

abs

ceil

floor

rint

round

signum

copySign

copySign

getExponent

scalb

hypot

hypot

compose

reciprocal

sqrt

cbrt

rootN

getField

pow

pow

pow

pow

exp

expm1

log

log1p

log10

cos

sin

tan

acos

asin

atan

atan2

atan2

cosh

sinh

tanh

acosh

asinh

atanh

toDegrees

toRadians

taylor

linearCombination

linearCombination

linearCombination

linearCombination