la.la

Class Function.Integral

java.lang.Object

la.la.Value

la.la.Function

la.la.Function.Native

la.la.Function.Native2

la.la.Function.Native3

la.la.Function.Integral

All Implemented Interfaces:

java.lang.Comparable<Value>

Enclosing class:

Function

public static class Function.Integral
extends Function.Native3

Integral : int → real → real → real. The key method is apply_nxx(n,lo,x). The Integral is done by Simpson's rule. Note that (this(n))(lo) is a Cts2Cts. Also see Cts2Cts.integral() and Cts2Cts.make_integral().

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 'This' Function.Integral is the Integral of '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
Integral(Function f) Construct the Integral of Cts2Cts 'f'.

Method Summary

Modifier and Type	Method and Description
double	apply_nxx(int n, double lo, double x) Integrate f from 'lo' to 'x' in 'n' steps using Simpson's rule; override it if there is a closed form.
Function.Cts2Cts	apply2(Value n, Value lo) Makes use of apply_nxx(n,lo,x).
Value	apply3(Value n, Value lo, Value x) Integrate f from 'lo' to 'x' in 'n' steps.

Methods inherited from class la.la.Function.Native3

apply

Methods inherited from class la.la.Function

bOp, fromBop, fromUop, main, toString, type, uOp

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

'This' Function.Integral is the Integral of 'f'.

Constructor Detail

Integral

public Integral(Function f)

Construct the Integral of Cts2Cts 'f'.

Method Detail

apply2

public Function.Cts2Cts apply2(Value n,
                               Value lo)

Makes use of apply_nxx(n,lo,x). Note, (this(n))(lo) is a Cts2Cts the derivative of which is f. E.g., if f(z) = z say, g(z) = ∫_lo..z x dx = {x²/2}_lo..z = (z² - lo²)/2, then g'(z) = z = f(z).

Overrides:

apply2 in class Function.Native3

apply3

public Value apply3(Value n,
                    Value lo,
                    Value x)

Integrate f from 'lo' to 'x' in 'n' steps. Method 'apply3' is what makes Integral a Function.Native3. Makes use of apply_nxx(n,lo,x).

Specified by:

apply3 in class Function.Native3

apply_nxx

public double apply_nxx(int n,
                        double lo,
                        double x)

Integrate f from 'lo' to 'x' in 'n' steps using Simpson's rule; override it if there is a closed form. 'n' is forced to be ≥3, and odd.