Module org.bzdev.math

Package org.bzdev.math

Class RealValuedFunctionThree

java.lang.Object

org.bzdev.math.RealValuedFunctionVA

org.bzdev.math.RealValuedFunctionThree

All Implemented Interfaces:

RealValuedFunctThreeOps, RealValuedFunctVAOps, VADomainOps

public class RealValuedFunctionThree
extends RealValuedFunctionVA
implements RealValuedFunctThreeOps

Class defining a real-valued function with three real arguments.

This is intended for cases in which a function should be passed as an argument.

A subclass will typically override one or more of the methods valueAt, deriv1At, deriv2At, deriv3At, deriv11At, deriv12At, deriv13At, deriv21At, deriv22At, deriv23At, deriv31At, deriv32At, and deriv33At to provide the values for a function and its first and second partial derivative. For any that are not available, an UnsupportedOperationException will be thrown.

The class also provides scripting-language support. If a Scripting context is named scripting, the following EMCAScript code will implement a function and its derivatives:

     importClass(org.bzdev.RealValuedFunctionThree);
     ....
     // assume ourObject is a Java class with a method setFunction
     // that takes a RealValuedFunctionThree as its argument.
     funct = new RealValuedFunctionThree(scripting,
               {valueAt: function(x,y,z) {return Math.sin(x)*Math.cos(y)*z;},
                deriv1At: function(x,y,z) {return Math.cos(x)*Math.cos(y)*z;},
                deriv2At: function(x,y,z) {
                   return -Math.sin(x)*Math.sin(y)*z;
                },
                deriv3At: function(x,y,z) {return Math.sin(x) * Math.cos(y);},
                deriv11At: function(x,y,z) {
                    return -Math.sin(x) * Math.cos(y) * z;
                },
                deriv12At: function(x,y,z) {
                    return -Math.cos(x) * Math.sin(y) * z;
                },
                deriv13At: function(x,y,z) {return Math.cos(x)*Math.sin(y);},
                deriv21At: function(x,y,z) {
                    return -Math.cos(x) * Math.sin(y) * z;
                },
                deriv22At: function(x,y,z) {
                    return -Math.sin(x) * Math.cos(y) * z;}
                deriv23At: function(x,y,z) {
                    return -Math.sin(x) * Math.sin(y);
                }
                deriv31At: function(x,y,z) {
                    return Math.cos(x) * Math.cos(y);
                },
                deriv32At: function(x,y,z) {
                    return -Math.sin(x) * Math.sin(y);
                },
                deriv33At: function(x,y,z) {return 0.0;}
               };
     ourObject.setFunction(funct);
 

Alternatively, one may use the following code where the functions defining the derivatives are provided by name:

     importClass(org.bzdev.RealValuedFunctionThree);
     ...
     function f(x,y,z) {return Math.sin(x) * Math.cos(y) * z;}
     function f1(x,y,z) {return Math.cos(x) * Math.cos(y) * z;}
     function f2(x,y,z) {return -Math.sin(x) * Math.sin(y) * z;}
     function f3(x,y,z) {return Math.sin(x) * Math.cos(y);}
     function f11(x,y,z) {return -Math.sin(x) * Math.cos(y) * z;}
     function f12(x,y,z) {return  -Math.cos(x) * Math.sin(y) * z;}
     function f13(x,y,z) {return  Math.cos(x) * Math.cos(y);}
     function f21(x,y,z) {return -Math.cos(x) * Math.sin(y) * z;}
     function f22(x,y,z) {return -Math.sin(x) * Math.cos(y) * z;}
     function f23(x,y,z) {return -Math.sin(x) * Math.sin(y);}
     function f31(x,y,z) {return Math.cos(x) * Math.cos(y)}
     function f32(x,y,z) {return  -Math.sin(x) * Math.sin(y);}
     function f33(x,y,z) {return  0.0;}
     ...
     // assume ourObject is a Java class with a method setFunction
     // that takes a RealValuedFunction as its argument.
     funct = new RealValuedFunction(scripting, "f", "f1", "f2", "f3"
                                      "f11", "f12", "f13", 
                                      "f21", "f22", "f23",
                                      "f31", "f32", "f33");
     ourObject.setFunction(funct);
 

Nested Class Summary

Nested classes/interfaces inherited from class org.bzdev.math.RealValuedFunctionVA

RealValuedFunctionVA.Linear

Constructor Summary

Constructors

Constructor	Description
RealValuedFunctionThree()	Constructor.
RealValuedFunctionThree(RealValuedFunctThreeOps function)	Constructor given a function.
RealValuedFunctionThree(RealValuedFunctThreeOps function, RealValuedFunctThreeOps function1, RealValuedFunctThreeOps function2, RealValuedFunctThreeOps function3)	Constructor given a function and its first partial derivatives.
RealValuedFunctionThree(RealValuedFunctThreeOps function, RealValuedFunctThreeOps function1, RealValuedFunctThreeOps function2, RealValuedFunctThreeOps function3, RealValuedFunctThreeOps function11, RealValuedFunctThreeOps function12, RealValuedFunctThreeOps function13, RealValuedFunctThreeOps function21, RealValuedFunctThreeOps function22, RealValuedFunctThreeOps function23, RealValuedFunctThreeOps function31, RealValuedFunctThreeOps function32, RealValuedFunctThreeOps function33)	Constructor given a function and its first and second partial derivatives.
RealValuedFunctionThree(ScriptingContext scriptingContext, Object object)	Constructor when the function is provided by a script object.
RealValuedFunctionThree(ScriptingContext scriptingContext, String fname, String f1name, String f2name, String f3name)	Constructor when the function and its first derivatives are provided by functions defined in scripts.
RealValuedFunctionThree(ScriptingContext scriptingContext, String fname, String f1name, String f2name, String f3name, String f11name, String f12name, String f13name, String f21name, String f22name, String f23name, String f31name, String f32name, String f33name)	Constructor when the function and its first and second derivatives are provided by functions defined in scripts.

Method Summary

Modifier and Type	Method	Description
final RealValuedFunctThreeOps	deriv(int i)	Get a function that computes the value of partial derivative that would be computed by calling derivAt(int,double...).
RealValuedFunctThreeOps	deriv1()	Get a function computing $\frac{\partial f}{\partial x_1}$.
RealValuedFunctThreeOps	deriv11()	Get a function that computes $\frac{\partial^2 f}{\partial x_1^2}$ where f is this function.
double	deriv11At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_1^2}$ for a function f(x1x2).
RealValuedFunctThreeOps	deriv12()	Get a function that computes $\frac{\partial^2 f}{\partial x_1 \partial x_2}$ where f is this function.
double	deriv12At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_1 \partial x_2}$ where f is this function.
RealValuedFunctThreeOps	deriv13()	Get a function that computes $\frac{\partial^2 f}{\partial x_1 \partial x_3}$ where f is this function.
double	deriv13At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_1 \partial x_3}$ for a function f(x1x2).
double	deriv1At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial f}{\partial x_1}$ for a function f(x1x2).
RealValuedFunctThreeOps	deriv2()	Get a function computing $\frac{\partial f}{\partial x_2}$.
RealValuedFunctThreeOps	deriv21()	Get a function that computes $\frac{\partial^2 f}{\partial x_2 \partial x_1}$ where f is this function.
double	deriv21At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_2 \partial x_1}$ for a function f(x1x2).
RealValuedFunctThreeOps	deriv22()	Get a function that computes $\frac{\partial^2 f}{\partial x_2^2}$ where f is this function.
double	deriv22At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_2^2}$ for a function f(x1x2).
RealValuedFunctThreeOps	deriv23()	Get a function that computes $\frac{\partial^2 f}{\partial x_2 \partial x_3}$ where f is this function.
double	deriv23At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_2 \partial x_3}$ for a function f(x1x2).
double	deriv2At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial f}{\partial x_2}$ for a function f(x2x2).
RealValuedFunctThreeOps	deriv3()	Get a function computing $\frac{\partial f}{\partial x_3}$.
RealValuedFunctThreeOps	deriv31()	Get a function that computes $\frac{\partial^2 f}{\partial x_3 \partial x_1}$ where f is this function.
double	deriv31At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_3 \partial x_1}$ for a function f(x1x2).
RealValuedFunctThreeOps	deriv32()	Get a function that computes $\frac{\partial^2 f}{\partial x_3 \partial x_2}$ where f is this function.
double	deriv32At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_3 \partial x_2}$ for a function f(x1x2).
RealValuedFunctThreeOps	deriv33()	Get a function that computes $\frac{\partial^2 f}{\partial x_3^2}$ where f is this function.
double	deriv33At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_3^2}$ for a function f(x1x2).
double	deriv3At(double arg1, double arg2, double arg3)	Evaluate the partial derivative $\frac{\partial f}{\partial x_3}$ for the function f(x1,x2,x3).
final double	derivAt(int i, double... args)	Evaluate the partial derivative $\frac{\partial f}{\partial x_i}$ for a function f(x0,x1, ...).
boolean	domainMax1Closed()	Determine if the domain maximum for the first argument is in the domain.
boolean	domainMax2Closed()	Determine if the domain maximum for the second argument is in the domain.
boolean	domainMax3Closed()	Determine if the domain maximum for the third argument is in the domain.
final boolean	domainMaxClosed(int i)	Determine if the domain maximum for the ith argument, when the arguments are in the domain of the function, is in the function's domain.
boolean	domainMin1Closed()	Determine if the domain minimum for the first argument is in the domain.
boolean	domainMin2Closed()	Determine if the domain minimum for the second argument is in the domain.
boolean	domainMin3Closed()	Determine if the domain minimum for the third argument is in the domain.
final boolean	domainMinClosed(int i)	Determine if the domain minimum for the ith argument, when the arguments are in the domain of the function, is in the function's domain.
final double	getDomainMax(int i)	Get the least upper bound of the ith argument when the arguments are in the domain of the function.
double	getDomainMax1()	Get the maximum value of the first argument in the domain of the function.
double	getDomainMax2()	Get the maximum value of the second argument in the domain of the function.
double	getDomainMax3()	Get the maximum value of the third argument in the domain of the function.
final double	getDomainMin(int i)	Get the greatest lower bound of the ith argument when the arguments are in the domain of the function.
double	getDomainMin1()	Get the minimum value of the first argument in the domain of the function.
double	getDomainMin2()	Get the minimum value of the second argument in the domain of the function.
double	getDomainMin3()	Get the minimum value of the third argument in the domain of the function.
final boolean	isInDomain(double... args)	Determine if a point is within the domain of this function.
boolean	isInDomain(double x, double y, double z)	Determine if a point (x, y) is within the domain of a real-valued function of two arguments.
final RealValuedFunctThreeOps	secondDeriv(int i, int j)	Get a function that computes the value of partial derivative that would be computed by calling secondDerivAt(int,int,double...).
final double	secondDerivAt(int i, int j, double... args)	Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_i \partial z_j}$ for a function f(x0,x1, ...).
final double	valueAt(double... args)	Call the function.
double	valueAt(double arg1, double arg2, double arg3)	Call the function.

Methods inherited from class org.bzdev.math.RealValuedFunctionVA

jacobian, jacobian, maxArgLength, minArgLength

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.bzdev.math.RealValuedFunctThreeOps

maxArgLength, minArgLength

Constructor Details

RealValuedFunctionThree

public RealValuedFunctionThree()

Constructor.

RealValuedFunctionThree

public RealValuedFunctionThree(RealValuedFunctThreeOps function)

Constructor given a function. The argument implements RealValuedFunctThreeOps and can be a lambda expression with three arguments. The interface RealValuedFunctThreeOps provides a single method: RealValuedFunctThreeOps.valueAt(double,double,double) that, when called, provides the function's value.

Parameters:

function - the function

RealValuedFunctionThree

public RealValuedFunctionThree(RealValuedFunctThreeOps function,
 RealValuedFunctThreeOps function1,
 RealValuedFunctThreeOps function2,
 RealValuedFunctThreeOps function3)

Constructor given a function and its first partial derivatives. The arguments implement RealValuedFunctThreeOps and can be a lambda expression with three arguments. The interface RealValuedFunctThreeOps provides a single method: RealValuedFunctThreeOps.valueAt(double,double,double) that, when called, provides the function's value.

Parameters:

function - the function; null if not provided

function1 - the function that provides the value for the deriv1At(double,double,double); null if this partial derivative is not defined.

function2 - the function that provides the value for the deriv2At(double,double,double); null if this partial derivative is not defined.

function3 - the function that provides the value for the deriv3At(double,double,double); null if this partial derivative is not defined.

RealValuedFunctionThree

public RealValuedFunctionThree(RealValuedFunctThreeOps function,
 RealValuedFunctThreeOps function1,
 RealValuedFunctThreeOps function2,
 RealValuedFunctThreeOps function3,
 RealValuedFunctThreeOps function11,
 RealValuedFunctThreeOps function12,
 RealValuedFunctThreeOps function13,
 RealValuedFunctThreeOps function21,
 RealValuedFunctThreeOps function22,
 RealValuedFunctThreeOps function23,
 RealValuedFunctThreeOps function31,
 RealValuedFunctThreeOps function32,
 RealValuedFunctThreeOps function33)

Constructor given a function and its first and second partial derivatives. The arguments implement RealValuedFunctThreeOps and can be a lambda expression with three arguments. The interface RealValuedFunctThreeOps provides a single method: RealValuedFunctThreeOps.valueAt(double,double,double) that, when called, provides the function's value.

Parameters:

function - the function; null if not provided

function1 - the function that provides the value for the deriv1At(double,double,double); null if this partial derivative is not defined.

function2 - the function that provides the value for the deriv2At(double,double,double); null if this partial derivative is not defined.

function3 - the function that provides the value for the deriv3At(double,double,double); null if this partial derivative is not defined.

function11 - the function that provides the value for the deriv11At(double,double,double); null if this partial derivative is not defined.

function12 - the function that provides the value for the deriv21At(double,double,double); null if this partial derivative is not defined.

function13 - the function that provides the value for the deriv13At(double,double,double); null if this partial derivative is not defined.

function21 - the function that provides the value for the deriv21At(double,double,double); null if this partial derivative is not defined.

function22 - the function that provides the value for the deriv22At(double,double,double); null if this partial derivative is not defined.

function23 - the function that provides the value for the deriv23At(double,double,double); null if this partial derivative is not defined.

function31 - the function that provides the value for the deriv31At(double,double,double); null if this partial derivative is not defined.

function32 - the function that provides the value for the deriv32At(double,double,double); null if this partial derivative is not defined.

function33 - the function that provides the value for the deriv33At(double,double,double); null if this partial derivative is not defined.

RealValuedFunctionThree

public RealValuedFunctionThree(ScriptingContext scriptingContext,
 Object object)

Constructor when the function is provided by a script object. The parameter 'object' is expected to be either an instance of RealValuedFunctionThree or an object defined by a scripting language with methods named "valueAt", "deriv1At" "deriv2At", "deriv11At", "deriv12At", deriv21At", and "deriv22At". Each of these methods takes two arguments, both real numbers, and returns a number. For a real-valued function f(x₁,x₂), these methods are defined as follows:

• valueAt returns f(x₁,x₂).
• deriv1At returns $\frac{\partial f}{\partial x_1}$ evaluated at the point (x₁,x₂,x₃).
• deriv2At returns $\frac{\partial f}{\partial x_2}$ evaluated at the point (x₁,x₂,x₃).
• deriv3At returns $\frac{\partial f}{\partial x_3}$ evaluated at the point (x₁,x₂,x₃).
• deriv11At returns $\frac{\partial^2 f}{\partial x_1^2}$ evaluated at the point (x₁,x₂,x₃).
• deriv12At returns $\frac{\partial^2 f}{\partial x_1 \partial x_2}$ evaluated at the point (x₁,x₂,x₃).
• deriv13At returns $\frac{\partial^2 f}{\partial x_1 \partial x_3}$ evaluated at the point (x₁,x₂,x₃).
• deriv21At returns $\frac{\partial^2 f}{\partial x_2 \partial x_1}$ evaluated at the point (x₁,x₂).
• deriv22At returns $\frac{\partial^2 f}{\partial x_2^2}$ evaluated at the point (x₁,x₂,x₃).
• deriv23At returns $\frac{\partial^2 f}{\partial x_2 \partial x_3}$ evaluated at the point (x₁,x₂,x₃).
• deriv31At returns $\frac{\partial^2 f}{\partial x_3 \partial x_1}$ evaluated at the point (x₁,x₂,x₃).
• deriv32At returns $\frac{\partial^2 f}{\partial x_3 \partial x_2}$ evaluated at the point (x₁,x₂,x₃).
• deriv33At returns $\frac{\partial^2 f}{\partial x_3^2}$ evaluated at the point (x₁,x₂,x₃).

Parameters:

scriptingContext - the scripting context

object - an object from a scripting environment defining the methods defined above or a subset of those methods

RealValuedFunctionThree

public RealValuedFunctionThree(ScriptingContext scriptingContext,
 String fname,
 String f1name,
 String f2name,
 String f3name)

Constructor when the function and its first derivatives are provided by functions defined in scripts. The script functions are expected to define up to three functions, and their names are used as the arguments for this method.

Parameters:

scriptingContext - the scripting context

fname - the name of a scripting-language function of three arguments; null if the valueAt method is not supported

f1name - the name of a scripting-language function of three arguments providing the desired function's first derivative with respect to the first argument; null if the deriv1At method is not supported

f2name - the name of a scripting-language function of three arguments providing the desired function's first derivative with respect to the second argument; null if the deriv2At method is not supported

f3name - the name of a scripting-language function of three arguments providing the desired function's first derivative with respect to the third argument; null if the deriv3At method is not supported

RealValuedFunctionThree

public RealValuedFunctionThree(ScriptingContext scriptingContext,
 String fname,
 String f1name,
 String f2name,
 String f3name,
 String f11name,
 String f12name,
 String f13name,
 String f21name,
 String f22name,
 String f23name,
 String f31name,
 String f32name,
 String f33name)

Constructor when the function and its first and second derivatives are provided by functions defined in scripts. The script functions are expected to define up to three functions, and their names are used as the arguments for this method.

Parameters:

scriptingContext - the scripting context

fname - the name of a scripting-language function of three arguments; null if the valueAt method is not supported

f1name - the name of a scripting-language function of three arguments providing the desired function's first derivative with respect to the first argument; null if the deriv1At method is not supported

f2name - the name of a scripting-language function of three arguments providing the desired function's first derivative with respect to the second argument; null if the deriv2At method is not supported

f3name - the name of a scripting-language function of three arguments providing the desired function's first derivative with respect to the third argument; null if the deriv3At method is not supported

f11name - the name of the scripting-language function of three arguments providing the value for deriv11At(double,double,double).

f12name - the name of the scripting-language function of three arguments providing the value for deriv12At(double,double,double).

f13name - the name of the scripting-language function of three arguments providing the value for deriv13At(double,double,double).

f21name - the name of the scripting-language function of three arguments providing the value for deriv21At(double,double,double).

f22name - the name of the scripting-language function of three arguments providing the value for deriv22At(double,double,double).

f23name - the name of the scripting-language function of three arguments providing the value for deriv23At(double,double,double).

f31name - the name of the scripting-language function of three arguments providing the value for deriv31At(double,double,double).

f32name - the name of the scripting-language function of three arguments providing the value for deriv32At(double,double,double).

f33name - the name of the scripting-language function of three arguments providing the value for deriv33At(double,double,double).

Method Details

getDomainMin

public final double getDomainMin(int i)
                          throws IllegalArgumentException,
IllegalStateException

Description copied from class: RealValuedFunctionVA

Get the greatest lower bound of the i^th argument when the arguments are in the domain of the function. The implementation will either return the most negative double-precision number or the result of calling a method named getDomainMin (with the same arguments as this method) provided by an object created by a scripting language. If an object created via a scripting language is not passed to a constructor, and a different value is appropriate, this method should be overridden.

Specified by:

getDomainMin in interface VADomainOps

Overrides:

getDomainMin in class RealValuedFunctionVA

Parameters:

i - the index determining the argument for which this method applies (0^th, 1^st, ...)

Returns:

the minimum value

Throws:

IllegalArgumentException - the argument is out of range

IllegalStateException - the function was not fully initialized.

getDomainMax

public final double getDomainMax(int i)
                          throws IllegalArgumentException,
IllegalStateException

Description copied from class: RealValuedFunctionVA

Get the least upper bound of the i^th argument when the arguments are in the domain of the function. The implementation will either return the largest double-precision number or the result of calling a method named getDomainMax (with the same arguments as this method) provided by an object created by a scripting language. If an object created via a scripting language is not passed to a constructor, and a different value is appropriate, this method should be overridden.

Specified by:

getDomainMax in interface VADomainOps

Overrides:

getDomainMax in class RealValuedFunctionVA

Parameters:

i - the index determining the argument for which this method applies (0^th, 1^st, ...)

Returns:

the maximum value

Throws:

IllegalArgumentException - the argument is out of range

IllegalStateException - the function was not fully initialized.

domainMinClosed

public final boolean domainMinClosed(int i)
                              throws IllegalArgumentException,
IllegalStateException

Description copied from class: RealValuedFunctionVA

Determine if the domain minimum for the i^th argument, when the arguments are in the domain of the function, is in the function's domain. The implementation will either return true or the result of calling a method named getDomainMinClosed (with the same arguments as this method) provided by an object created by a scripting language. If an object created via a scripting language is not passed to a constructor, and a different value is appropriate, this method should be overridden.

Specified by:

domainMinClosed in interface VADomainOps

Overrides:

domainMinClosed in class RealValuedFunctionVA

Parameters:

i - the index determining the argument for which this method applies (0^th, 1^st, ...)

Returns:

true if the domain minimum is in the domain; false if it is the greatest lower bound for the domain

Throws:

IllegalArgumentException - the argument is out of range

IllegalStateException - the function was not fully initialized.

domainMaxClosed

public final boolean domainMaxClosed(int i)
                              throws IllegalArgumentException,
IllegalStateException

Description copied from class: RealValuedFunctionVA

Determine if the domain maximum for the i^th argument, when the arguments are in the domain of the function, is in the function's domain. The implementation will either return true or the result of calling a method named getDomainMaxClosed (with the same arguments as this method) provided by an object created by a scripting language. If an object created via a scripting language is not passed to a constructor, and a different value is appropriate, this method should be overridden.

Specified by:

domainMaxClosed in interface VADomainOps

Overrides:

domainMaxClosed in class RealValuedFunctionVA

Parameters:

i - the index determining the argument for which this method applies (0^th, 1^st, ...)

Returns:

true if the domain maximum is in the domain; false if it is the least upper bound for the domain

Throws:

IllegalArgumentException - the argument is out of range

IllegalStateException - the function was not fully initialized.

getDomainMin1

public double getDomainMin1()
                     throws IllegalStateException

Get the minimum value of the first argument in the domain of the function.

Returns:

the minimum value

Throws:

IllegalStateException - the function was not fully initialized.

getDomainMax1

public double getDomainMax1()
                     throws IllegalStateException

Get the maximum value of the first argument in the domain of the function.

Returns:

the maximum value

Throws:

IllegalStateException - the function was not fully initialized.

getDomainMin2

public double getDomainMin2()
                     throws IllegalStateException

Get the minimum value of the second argument in the domain of the function.

Returns:

the minimum value

Throws:

IllegalStateException - the function was not fully initialized.

getDomainMax2

public double getDomainMax2()
                     throws IllegalStateException

Get the maximum value of the second argument in the domain of the function.

Returns:

the maximum value

Throws:

IllegalStateException - the function was not fully initialized.

getDomainMin3

public double getDomainMin3()
                     throws IllegalStateException

Get the minimum value of the third argument in the domain of the function.

Returns:

the minimum value

Throws:

IllegalStateException - the function was not fully initialized.

getDomainMax3

public double getDomainMax3()
                     throws IllegalStateException

Get the maximum value of the third argument in the domain of the function.

Returns:

the maximum value

Throws:

IllegalStateException - the function was not fully initialized.

domainMin1Closed

public boolean domainMin1Closed()
                         throws IllegalStateException

Determine if the domain minimum for the first argument is in the domain.

Returns:

true if the domain minimum is in the domain; false if it is the greatest lower bound for the domain

Throws:

IllegalStateException - the function was not fully initialized.

domainMax1Closed

public boolean domainMax1Closed()
                         throws IllegalStateException

Determine if the domain maximum for the first argument is in the domain.

Returns:

true if the domain maximum is in the domain; false if it is the least upper bound for the domain

Throws:

IllegalStateException - the function was not fully initialized.

domainMin2Closed

public boolean domainMin2Closed()
                         throws IllegalStateException

Determine if the domain minimum for the second argument is in the domain.

Returns:

true if the domain minimum is in the domain; false if it is the greatest lower bound for the domain

Throws:

IllegalStateException - the function was not fully initialized.

domainMax2Closed

public boolean domainMax2Closed()
                         throws IllegalStateException

Determine if the domain maximum for the second argument is in the domain.

Returns:

true if the domain maximum is in the domain; false if it is the least upper bound for the domain

Throws:

IllegalStateException - the function was not fully initialized.

domainMin3Closed

public boolean domainMin3Closed()
                         throws IllegalStateException

Determine if the domain minimum for the third argument is in the domain.

Returns:

true if the domain minimum is in the domain; false if it is the greatest lower bound for the domain

Throws:

IllegalStateException - the function was not fully initialized.

domainMax3Closed

public boolean domainMax3Closed()
                         throws IllegalStateException

Determine if the domain maximum for the third argument is in the domain.

Returns:

true if the domain maximum is in the domain; false if it is the least upper bound for the domain

Throws:

IllegalStateException - the function was not fully initialized.

isInDomain

public final boolean isInDomain(double... args)
                         throws UnsupportedOperationException,
IllegalArgumentException,
IllegalStateException

Description copied from class: RealValuedFunctionVA

Determine if a point is within the domain of this function.

The default behavior of this method assumes the domain is a rectangular region and uses the methods RealValuedFunctionVA.getDomainMin(int), RealValuedFunctionVA.getDomainMax(int), RealValuedFunctionVA.domainMinClosed(int), RealValuedFunctionVA.domainMaxClosed(int), to determine if the arguments represent a point in the functions domain. If the domain is not rectangular with each side either in or not in the domain, then this method must be overridden. If it is not possible with a reasonable amount of computation to determine that a point is in the domain, an UnsupportedOperationException may be thrown. If this exception is thrown, it should be thrown regardless of the arguments.

Specified by:

isInDomain in interface VADomainOps

Overrides:

isInDomain in class RealValuedFunctionVA

Parameters:

args - the arguments (x₀,x₁,...) giving the coordinates of a point

Returns:

true if the point (x₀,x₁,...) is in this function's domain; false otherwise

Throws:

UnsupportedOperationException - domain membership could not be determined.

IllegalArgumentException - an argument is out of range

IllegalStateException - the function was not fully initialized.

isInDomain

public boolean isInDomain(double x,
 double y,
 double z)
                   throws UnsupportedOperationException,
IllegalStateException

Determine if a point (x, y) is within the domain of a real-valued function of two arguments.

The default behavior of this method assumes the domain is a rectangular region and uses the methods getDomainMin1(), getDomainMin2(), getDomainMax1(), getDomainMax2() domainMin1Closed(), domainMin2Closed(), domainMax1Closed(), and domainMax2Closed() to determine if the arguments represent a point in the functions domain. If the domain is not rectangular with each side either in or not in the domain, then this method must be overridden. If it is not possible with a reasonable amount of computation to determine that a point is in the domain, an UnsupportedOperationException may be thrown. If this exception is thrown, it should be thrown regardless of the arguments.

Parameters:

x - the 1st coordinate

y - the 2nd coordinate

z - the 3rd coordinate

Returns:

true if the point (x, y) is in this function's domain; false otherwise

Throws:

UnsupportedOperationException - domain membership could not be determined.

IllegalStateException

valueAt

public final double valueAt(double... args)
                     throws IllegalArgumentException,
UnsupportedOperationException

Description copied from class: RealValuedFunctionVA

Call the function.

Specified by:

valueAt in interface RealValuedFunctThreeOps

Specified by:

valueAt in interface RealValuedFunctVAOps

Overrides:

valueAt in class RealValuedFunctionVA

Parameters:

args - the function's arguments

Returns:

the value of the function for the given arguments

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

valueAt

public double valueAt(double arg1,
 double arg2,
 double arg3)
               throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Call the function.

Specified by:

valueAt in interface RealValuedFunctThreeOps

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the function for the given arguments

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv

public final RealValuedFunctThreeOps deriv(int i)

Get a function that computes the value of partial derivative that would be computed by calling derivAt(int,double...).

Parameters:

i - the index of the argument (0 for the first argument, 1 for the second, etc.)

Returns:

the function

derivAt

public final double derivAt(int i,
 double... args)
                     throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial f}{\partial x_i}$ for a function f(x₀,x₁, ...).

This method calls a method named deriv<i+1>At(...) where i is the value of the first argument. One should usually override those methods instead of this one.

Overrides:

derivAt in class RealValuedFunctionVA

Parameters:

i - the index indicating that the partial derivative is computed for the i^th argument, numbered from zero

args - the function f's arguments

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv1

public RealValuedFunctThreeOps deriv1()

Get a function computing $\frac{\partial f}{\partial x_1}$.

Returns:

a function that computes $\frac{\partial f}{\partial x_1}$ where f is this real-valued function

deriv1At

public double deriv1At(double arg1,
 double arg2,
 double arg3)
                throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial f}{\partial x_1}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv2

public RealValuedFunctThreeOps deriv2()

Get a function computing $\frac{\partial f}{\partial x_2}$.

Returns:

a function that computes $\frac{\partial f}{\partial x_2}$ where f is this real-valued function

deriv2At

public double deriv2At(double arg1,
 double arg2,
 double arg3)
                throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial f}{\partial x_2}$ for a function f(x₂x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv3

public RealValuedFunctThreeOps deriv3()

Get a function computing $\frac{\partial f}{\partial x_3}$.

Returns:

a function that computes $\frac{\partial f}{\partial x_3}$ where f is this real-valued function

deriv3At

public double deriv3At(double arg1,
 double arg2,
 double arg3)
                throws IllegalArgumentException,
UnsupportedOperationException

Evaluate the partial derivative $\frac{\partial f}{\partial x_3}$ for the function f(x₁,x₂,x₃).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

secondDeriv

public final RealValuedFunctThreeOps secondDeriv(int i,
 int j)

Get a function that computes the value of partial derivative that would be computed by calling secondDerivAt(int,int,double...).

Parameters:

i - the argument index for the first derivative

j - the argument index for the second derivative

Returns:

the function

secondDerivAt

public final double secondDerivAt(int i,
 int j,
 double... args)
                           throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_i \partial z_j}$ for a function f(x₀,x₁, ...).

This method calls a method named deriv<i+1><j+1>At(...) where i and j are the values of the first two arguments. One should usually override those methods instead of this one.

Overrides:

secondDerivAt in class RealValuedFunctionVA

Parameters:

i - the index indicating that the partial derivative is computed for the i^th argument, numbered from 0

j - the index indicating that the partial derivative is computed for the j^th argument, numbered from 0

args - the function f's arguments

Returns:

the value of the partial derivative $\frac{\partial^2 f}{\partial x_i \partial z_j}$ for the given arguments x₀, x₁, ...

Throws:

IllegalArgumentException - the function's arguments were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv11

public RealValuedFunctThreeOps deriv11()

Get a function that computes $\frac{\partial^2 f}{\partial x_1^2}$ where f is this function.

Returns:

a function that computes $\frac{\partial^2 f}{\partial x_1^2}$

deriv11At

public double deriv11At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_1^2}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv12

public RealValuedFunctThreeOps deriv12()

Get a function that computes $\frac{\partial^2 f}{\partial x_1 \partial x_2}$ where f is this function.

Returns:

a function that computes $\frac{\partial^2 f}{\partial x_1 \partial x_2}$ where f is this function. ∂²f / (∂x₁ ∂x₂)

deriv12At

public double deriv12At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_1 \partial x_2}$ where f is this function. * ∂²f / (∂x₁ ∂x₂) for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv13

public RealValuedFunctThreeOps deriv13()

Get a function that computes $\frac{\partial^2 f}{\partial x_1 \partial x_3}$ where f is this function.

Returns:

a function that computes $\frac{\partial^2 f}{\partial x_1 \partial x_3}$

deriv13At

public double deriv13At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_1 \partial x_3}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv21

public RealValuedFunctThreeOps deriv21()

Get a function that computes $\frac{\partial^2 f}{\partial x_2 \partial x_1}$ where f is this function.

Returns:

a function that computes $\frac{\partial^2 f}{\partial x_2 \partial x_1}$

deriv21At

public double deriv21At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_2 \partial x_1}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv22

public RealValuedFunctThreeOps deriv22()

Get a function that computes $\frac{\partial^2 f}{\partial x_2^2}$ where f is this function.

Returns:

a function that computes ∂²f / ∂x₂²

deriv22At

public double deriv22At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_2^2}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv23

public RealValuedFunctThreeOps deriv23()

Get a function that computes $\frac{\partial^2 f}{\partial x_2 \partial x_3}$ where f is this function.

Returns:

a function that computes ∂²f / ∂x₂³

deriv23At

public double deriv23At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_2 \partial x_3}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv31

public RealValuedFunctThreeOps deriv31()

Get a function that computes $\frac{\partial^2 f}{\partial x_3 \partial x_1}$ where f is this function.

Returns:

a function that computes ∂²f / ∂x₃¹

deriv31At

public double deriv31At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_3 \partial x_1}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv32

public RealValuedFunctThreeOps deriv32()

Get a function that computes $\frac{\partial^2 f}{\partial x_3 \partial x_2}$ where f is this function.

Returns:

a function that computes $\frac{\partial^2 f}{\partial x_3 \partial x_2}$

deriv32At

public double deriv32At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_3 \partial x_2}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.

deriv33

public RealValuedFunctThreeOps deriv33()

Get a function that computes $\frac{\partial^2 f}{\partial x_3^2}$ where f is this function.

Returns:

a function that computes $\frac{\partial^2 f}{\partial x_3^2}$

deriv33At

public double deriv33At(double arg1,
 double arg2,
 double arg3)
                 throws IllegalArgumentException,
UnsupportedOperationException,
IllegalStateException

Evaluate the partial derivative $\frac{\partial^2 f}{\partial x_3^2}$ for a function f(x₁x₂).

Parameters:

arg1 - the function's first argument

arg2 - the function's second argument

arg3 - the function's third argument

Returns:

the value of the partial derivative for the given argument

Throws:

IllegalArgumentException - the function's argument(s) were out of range

UnsupportedOperationException - the operation is not supported.

IllegalStateException - the function was not fully initialized.