Module org.bzdev.math

Package org.bzdev.math

Class VectorValuedFunction

java.lang.Object

org.bzdev.math.VectorValuedFunctionVA

org.bzdev.math.VectorValuedFunction

All Implemented Interfaces:

RealValuedDomainOps, VADomainOps

Direct Known Subclasses:

BSplineArray, NurbsArray

public abstract class VectorValuedFunction
extends VectorValuedFunctionVA
implements RealValuedDomainOps

Base class for vector-valued functions with one argument. The vectors have real components, as does the argument, all of which are a double-precision number (type "double").

Subclasses must implement the following method:

• valueAt(double[],int,double). This method is expected to throw an IllegalArgumentException if its arguments are out of range.

If the default behavior (throwing an UnsupportedOperationException) is not appropriate, subclasses should implement one or more of the following methods:

• derivAt(double[],int,double). This method throws an UnsupportedOperationException by default.
• secondDerivAt(double[],int,double). This method throws an UnsupportedOperationException by default.
• RealValuedDomainOps.getDomainMin(). The default is -Double.MAX_VALUE.
• RealValuedDomainOps.getDomainMax(). The default is Double.MAX_VALUE.
• RealValuedDomainOps.domainMinClosed(). The default is "true".
• RealValuedDomainOps.domainMaxClosed(). The default is "true".
• RealValuedDomainOps.isInDomain(double). The default checks that the argument is within the range specified by the domain minimum and maximum, with the end points included or not depending on whether the end points are closed or open respectively.

Field Summary

Fields inherited from class org.bzdev.math.VectorValuedFunctionVA

dim

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	VectorValuedFunction(int dim)	Constructor.

Method Summary

Modifier and Type	Method	Description
final double[]	derivAt(double u)	Evaluate the function's first derivative.
void	derivAt(double[] array, int offset, double u)	Evaluate the function's first derivative, storing the results.
final void	derivAt(int i, double[] array, int offset, double... args)	Evaluate the first partial derivative, storing the results ∂f / ∂xi for a function f(x0,x1, ...).
boolean	domainMaxClosed()	Determine if the domain maximum is in the domain.
boolean	domainMaxClosed(int argIndex)	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	domainMinClosed()	Determine if the domain minimum is in the domain.
final boolean	domainMinClosed(int argIndex)	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.
double	getDomainMax()	Get the maximum value in the domain of the function.
final double	getDomainMax(int argIndex)	Get the least upper bound of the ith argument when the arguments are in the domain of the function.
double	getDomainMin()	Get the minimum value in the domain of the function.
final double	getDomainMin(int argIndex)	Get the greatest lower bound of the ith argument when the arguments are in the domain of the function implementing this interface.
boolean	isInDomain(double x)	Determine if an argument is within the domain of a function.
boolean	isInDomain(double... args)	Determine if a sequence of arguments represents arguments that are in the domain of the function implementing this interface.
final double[]	secondDerivAt(double u)	Evaluate the function's second derivative.
void	secondDerivAt(double[] array, int offset, double u)	Evaluate the function's second derivative, storing the results.
final void	secondDerivAt(int i, int j, double[] array, int offset, double... args)	Evaluate the second partial derivative ∂2f / ∂x1∂x1 for a function f(x1x2), storing the results in an array.
final double[]	valueAt(double u)	Call the function.
abstract void	valueAt(double[] array, int offset, double u)	Call the function, storing the value in an array.
final void	valueAt(double[] array, int offset, double... args)	Call the function, storing the results in an array.

Methods inherited from class org.bzdev.math.VectorValuedFunctionVA

derivAt, getDimension, maxArgLength, minArgLength, secondDerivAt, valueAt

Methods inherited from class java.lang.Object

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

Constructor Details

VectorValuedFunction

protected VectorValuedFunction(int dim)

Constructor.

Parameters:

dim - the dimension of the vectors that will be returned by various methods.

Method Details

getDomainMin

public final double getDomainMin(int argIndex)
                          throws IllegalArgumentException

Description copied from interface: VADomainOps

Get the greatest lower bound of the i^th argument when the arguments are in the domain of the function implementing this interface.

Specified by:

getDomainMin in interface VADomainOps

Overrides:

getDomainMin in class VectorValuedFunctionVA

Parameters:

argIndex - 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

getDomainMax

public final double getDomainMax(int argIndex)
                          throws IllegalArgumentException

Description copied from interface: VADomainOps

Get the least upper bound of the i^th argument when the arguments are in the domain of the function.

Specified by:

getDomainMax in interface VADomainOps

Overrides:

getDomainMax in class VectorValuedFunctionVA

Parameters:

argIndex - 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

domainMinClosed

public final boolean domainMinClosed(int argIndex)
                              throws IllegalArgumentException

Description copied from interface: VADomainOps

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.

Specified by:

domainMinClosed in interface VADomainOps

Overrides:

domainMinClosed in class VectorValuedFunctionVA

Parameters:

argIndex - 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

domainMaxClosed

public boolean domainMaxClosed(int argIndex)
                        throws IllegalArgumentException

Description copied from interface: VADomainOps

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.

Specified by:

domainMaxClosed in interface VADomainOps

Overrides:

domainMaxClosed in class VectorValuedFunctionVA

Parameters:

argIndex - 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

isInDomain

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

Description copied from interface: VADomainOps

Determine if a sequence of arguments represents arguments that are in the domain of the function implementing this interface.

Specified by:

isInDomain in interface VADomainOps

Overrides:

isInDomain in class VectorValuedFunctionVA

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

getDomainMin

public double getDomainMin()

Description copied from interface: RealValuedDomainOps

Get the minimum value in the domain of the function.

Specified by:

getDomainMin in interface RealValuedDomainOps

Returns:

the minimum value

getDomainMax

public double getDomainMax()

Description copied from interface: RealValuedDomainOps

Get the maximum value in the domain of the function.

Specified by:

getDomainMax in interface RealValuedDomainOps

Returns:

the maximum value

domainMinClosed

public boolean domainMinClosed()

Description copied from interface: RealValuedDomainOps

Determine if the domain minimum is in the domain.

Specified by:

domainMinClosed in interface RealValuedDomainOps

Returns:

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

domainMaxClosed

public boolean domainMaxClosed()

Description copied from interface: RealValuedDomainOps

Determine if the domain maximum is in the domain.

Specified by:

domainMaxClosed in interface RealValuedDomainOps

Returns:

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

isInDomain

public boolean isInDomain(double x)
                   throws UnsupportedOperationException

Description copied from interface: RealValuedDomainOps

Determine if an argument is within the domain of a function.

Specified by:

isInDomain in interface RealValuedDomainOps

Parameters:

x - a value to test

Returns:

true if x is in this function's domain; false otherwise

Throws:

UnsupportedOperationException - domain membership could not be determined.

valueAt

public final void valueAt(double[] array,
 int offset,
 double... args)
                   throws IllegalArgumentException,
UnsupportedOperationException

Description copied from class: VectorValuedFunctionVA

Call the function, storing the results in an array.

Overrides:

valueAt in class VectorValuedFunctionVA

Parameters:

array - the array used to store the results.

offset - the offset into the array at which to store the results.

args - the function's arguments

Throws:

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

UnsupportedOperationException - the operation is not supported.

derivAt

public final void derivAt(int i,
 double[] array,
 int offset,
 double... args)
                   throws IllegalArgumentException,
UnsupportedOperationException

Description copied from class: VectorValuedFunctionVA

Evaluate the first partial derivative, storing the results ∂f / ∂x_i for a function f(x₀,x₁, ...).

Overrides:

derivAt in class VectorValuedFunctionVA

Parameters:

i - the index indicating that the partial derivative is computed for the i^th argument

array - the array used to store the results.

offset - the offset into the array at which to store the results.

args - the function f's arguments

Throws:

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

UnsupportedOperationException - the operation is not supported.

secondDerivAt

public final void secondDerivAt(int i,
 int j,
 double[] array,
 int offset,
 double... args)
                         throws IllegalArgumentException,
UnsupportedOperationException

Description copied from class: VectorValuedFunctionVA

Evaluate the second partial derivative ∂²f / ∂x₁∂x₁ for a function f(x₁x₂), storing the results in an array.

Overrides:

secondDerivAt in class VectorValuedFunctionVA

Parameters:

i - the index indicating that the partial derivative is computed for the i^th argument

j - the index indicating that the partial derivative is computed for the j^th argument

array - the array used to store the results.

offset - the offset into the array at which to store the results.

args - the function f's arguments

Throws:

IllegalArgumentException - the function's arguments were out of range

UnsupportedOperationException - the operation is not supported.

valueAt

public final double[] valueAt(double u)
                       throws IllegalArgumentException

Call the function.

Parameters:

u - the function's argument

Returns:

the value of the function for the given argument

Throws:

IllegalArgumentException - the function's argument was out of range

valueAt

public abstract void valueAt(double[] array,
 int offset,
 double u)
                      throws IllegalArgumentException

Call the function, storing the value in an array.

Parameters:

array - the array used to store the results of the function call.

offset - the offset into the array at which to store the results of the function call.

u - the function's argument

Throws:

IllegalArgumentException - the function's argument was out of range

derivAt

public final double[] derivAt(double u)
                       throws IllegalArgumentException,
UnsupportedOperationException

Evaluate the function's first derivative.

Parameters:

u - the function's argument

Returns:

the value of the function's derivative for the given argument

Throws:

IllegalArgumentException - the function's argument was out of range

UnsupportedOperationException - the operation is not supported.

derivAt

public void derivAt(double[] array,
 int offset,
 double u)
             throws IllegalArgumentException,
UnsupportedOperationException

Evaluate the function's first derivative, storing the results.

Parameters:

array - the array used to store the results.

offset - the offset into the array at which to store the results.

u - the function's argument

Throws:

IllegalArgumentException - the function's argument was out of range

UnsupportedOperationException - the operation is not supported.

secondDerivAt

public final double[] secondDerivAt(double u)
                             throws IllegalArgumentException,
UnsupportedOperationException

Evaluate the function's second derivative.

Parameters:

u - the function's argument

Returns:

the value of the function's second derivative for the given argument

Throws:

IllegalArgumentException - the function's argument was out of range

UnsupportedOperationException - the operation is not supported.

secondDerivAt

public void secondDerivAt(double[] array,
 int offset,
 double u)
                   throws IllegalArgumentException,
UnsupportedOperationException

Evaluate the function's second derivative, storing the results.

Parameters:

array - the array used to store the results.

offset - the offset into the array at which to store the results.

u - the function's argument

Throws:

IllegalArgumentException - the function's argument was out of range

UnsupportedOperationException - the operation is not supported.