la.la

Class Function.Derivative

java.lang.Object

la.la.Value

la.la.Function

la.la.Function.Native

la.la.Function.Cts2Cts

la.la.Function.Derivative

All Implemented Interfaces:

java.lang.Comparable<Value>

Enclosing class:

Function

public static class Function.Derivative
extends Function.Cts2Cts

The default Derivative uses finite-differences. The key method is apply_xx(δ,x). Also see Cts2Cts.d_dx() and Cts2Cts.make_d_dx().

Nested Class Summary

Nested classes/interfaces inherited from class la.la.Function

Function.Cts2Cts, Function.Derivative, Function.Integral, Function.Native, Function.Native2, Function.Native3

Nested classes/interfaces inherited from class la.la.Value

Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple

Field Summary

Fields

Modifier and Type	Field and Description
Function.Cts2Cts	f The Cts2Cts "f" of which "this" is the Derivative, f'.

Fields inherited from class la.la.Value

C, comparator, CR, E, eight, ffalse, five, fiveR, four, fourR, half, negCR, negOne, negOneR, negTenR, nilVal, nine, None, one, oneR, PI, PIby2, point01, point1, point5, point9, quarter, seven, six, ten, tenR, three, threeR, triv, ttrue, two, twoR, zero, zeroR

Constructor Summary

Constructors

Constructor and Description
Derivative(Function f) Construct the Derivative of the Cts2Cts, 'f'.

Method Summary

Modifier and Type	Method and Description
double	apply_x(double x) Call apply_xx(δ,x) for some "small" δ.
double	apply_xx(double delta, double x) Compute the Derivative of f by finite differences here.
protected Function.Derivative	make_d_dx() The Derivative of 'this' is the second Derivative of f, by finite differences.
protected Function.Integral	make_integral() The indefinite Integral of 'this' Derivative is f, of course. So, lo∫x this(x) dx = f(x) − f(lo).

Methods inherited from class la.la.Function.Cts2Cts

apply, d_dx, d2_dx2, fromFunction, integral, NewtonRaphson, root, turning, uOp

Methods inherited from class la.la.Function

bOp, fromBop, fromUop, main, toString, type

Methods inherited from class la.la.Value

AoM, bOp, compareTo, cons, cts, elt, errMsg, error, force, isTuple, just, n, nElts, nlAoM, pair, print, quad, real, RTE, triple, tuple, UOE, x

Methods inherited from class java.lang.Object

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

Field Detail

f

public final Function.Cts2Cts f

The Cts2Cts "f" of which "this" is the Derivative, f'.

Constructor Detail

Derivative

public Derivative(Function f)

Construct the Derivative of the Cts2Cts, 'f'.

Method Detail

apply_x

public double apply_x(double x)

Call apply_xx(δ,x) for some "small" δ. If you don't want to take your chances with δ being chosen for you, set your own with apply_xx(δ,x).

Specified by:

apply_x in class Function.Cts2Cts

apply_xx

public double apply_xx(double delta,
                       double x)

Compute the Derivative of f by finite differences here. Called by apply_x(x). Return (f(x+δ/2) - f(x-δ/2) / δ. Override it if there is something better (a closed form).

make_d_dx

protected Function.Derivative make_d_dx()

The Derivative of 'this' is the second Derivative of f, by finite differences.

Overrides:

make_d_dx in class Function.Cts2Cts

make_integral

protected Function.Integral make_integral()

The indefinite Integral of 'this' Derivative is f, of course.
So, _lo∫^x this(x) dx = f(x) − f(lo).

Overrides:

make_integral in class Function.Cts2Cts