nilgiri.math.autodiff
Class DifferentialFunction<X extends Field<X>>

java.lang.Object
  nilgiri.math.autodiff.DifferentialFunction<X>

Type Parameters:

X - A set forms a field.

All Implemented Interfaces:

Differential<Variable<X>,DifferentialFunction<X>>, CommutativeGroup<DifferentialFunction<X>>, CommutativeRing<DifferentialFunction<X>>, Field<DifferentialFunction<X>>, Group<DifferentialFunction<X>>, Ring<DifferentialFunction<X>>

Direct Known Subclasses:

AbstractBinaryFunction, AbstractUnaryFunction, Constant, Variable

public abstract class DifferentialFunction<X extends Field<X>>
extends java.lang.Object
implements Field<DifferentialFunction<X>>, Differential<Variable<X>,DifferentialFunction<X>>

A differential function whose value are in X. Partial derivatives of an object f of DifferentialFunction<X> are given by f.diff(x) where x is an object of Variable<X>.

Method Summary

abstract DifferentialFunction<X>	diff(Variable<X> i_v1) Returns an object of D whose value is the derivative with respect to i_v.
DifferentialFunction<X>	div(DifferentialFunction<X> i_v) Returns an object of X whose value is (this / i_v).
abstract X	getValue() Returns the value in X of the function.
DifferentialFunction<X>	inverse() Returns an object of X whose value is (1 / this).
boolean	isConstant() Returns true if this is a constant.
boolean	isVariable() Returns true if this is a variable.
DifferentialFunction<X>	minus(DifferentialFunction<X> i_v) Returns an object of X whose value is (this - i_v).
DifferentialFunction<X>	mul(DifferentialFunction<X> i_v) Returns an object of X whose value is the product (this * i_v).
DifferentialFunction<X>	mul(long i_n) Returns an object of X whose value is the summation (sum_{1}^{i_n}(this)).
DifferentialFunction<X>	negate() Returns an object of X whose value is (- this).
DifferentialFunction<X>	plus(DifferentialFunction<X> i_v) Returns an object of X whose value is (this + i_v).
DifferentialFunction<X>	pow(int i_n) Returns an object of X whose value is the power (this ^ i_n).
abstract java.lang.String	toString()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Method Detail

getValue

public abstract X getValue()

Returns the value in X of the function.

Returns:

the value.

toString

public abstract java.lang.String toString()

Overrides:

toString in class java.lang.Object

isConstant

public boolean isConstant()

Returns true if this is a constant.

Returns:

true if this is a constant.

isVariable

public boolean isVariable()

Returns true if this is a variable.

Returns:

true if this is a variable.

diff

public abstract DifferentialFunction<X> diff(Variable<X> i_v1)

Description copied from interface: Differential

Returns an object of D whose value is the derivative with respect to i_v.

Specified by:

diff in interface Differential<Variable<X extends Field<X>>,DifferentialFunction<X extends Field<X>>>

Returns:

the derivative with respect to i_v.

plus

public DifferentialFunction<X> plus(DifferentialFunction<X> i_v)

Description copied from interface: Group

Returns an object of X whose value is (this + i_v).

Specified by:

plus in interface Group<DifferentialFunction<X extends Field<X>>>

Returns:

this + i_v

minus

public DifferentialFunction<X> minus(DifferentialFunction<X> i_v)

Description copied from interface: Group

Returns an object of X whose value is (this - i_v).

Specified by:

minus in interface Group<DifferentialFunction<X extends Field<X>>>

Returns:

this - i_v

mul

public DifferentialFunction<X> mul(DifferentialFunction<X> i_v)

Description copied from interface: Ring

Returns an object of X whose value is the product (this * i_v).

Specified by:

mul in interface Ring<DifferentialFunction<X extends Field<X>>>

Returns:

this * i_v

div

public DifferentialFunction<X> div(DifferentialFunction<X> i_v)

Description copied from interface: Field

Returns an object of X whose value is (this / i_v).

Specified by:

div in interface Field<DifferentialFunction<X extends Field<X>>>

Returns:

this / i_v

inverse

public DifferentialFunction<X> inverse()

Description copied from interface: Field

Returns an object of X whose value is (1 / this).

Specified by:

inverse in interface Field<DifferentialFunction<X extends Field<X>>>

Returns:

1 / this

negate

public DifferentialFunction<X> negate()

Description copied from interface: Group

Returns an object of X whose value is (- this).

Specified by:

negate in interface Group<DifferentialFunction<X extends Field<X>>>

Returns:

- this

mul

public DifferentialFunction<X> mul(long i_n)

Description copied from interface: Group

Returns an object of X whose value is the summation (sum_{1}^{i_n}(this)). Group<X&rt guarantees the results for natural numbers only.

Specified by:

mul in interface Group<DifferentialFunction<X extends Field<X>>>

Parameters:

i_n - a natural number

Returns:

sum_{1}^{i_n}(this)

pow

public DifferentialFunction<X> pow(int i_n)

Description copied from interface: Ring

Returns an object of X whose value is the power (this ^ i_n). Ring guarantees the results for natural numbers only.

Specified by:

pow in interface Ring<DifferentialFunction<X extends Field<X>>>

Parameters:

i_n - a natural number

Returns:

this ^ i_n