la.la

Class Function.Cts2Cts.Integral

java.lang.Object

la.la.Value

la.la.Function

la.la.Function.Native

la.la.Function.Native2

la.la.Function.Cts2Cts2Cts

la.la.Function.Cts2Cts.Integral

All Implemented Interfaces:

java.lang.Comparable<Value>

Enclosing class:

Function.Cts2Cts

public class Function.Cts2Cts.Integral
extends Function.Cts2Cts2Cts

Integral: Cts→Cts→Cts (±) integrates f from 'lo' to 'hi'. The key method is apply_nxx(n,lo,x). For use by Cts2Cts.make_integral() and hence Cts2Cts.integral(). The Integral is performed numerically by Simpson's rule. If there is a closed-form, F, for the indefinite integral use exactIntegral(F).

Nested Class Summary

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

Function.Native.WithInverse

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

Function.Cts2Cts, Function.Cts2Cts2Cts, Function.CtsD2CtsD, Function.HasInverse, 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 'f' is a synonym for 'Cts2Cts.this' and 'this' Integral is the (definite) 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() Construct the definite 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' numerically in 'n' steps using Simpson's rule, called by apply_xx.
Function.Cts2Cts	apply_x(double lox) Returns a Cts→Cts which (i) will take hix & call apply_xx(lox,hix), and (ii) has the Derivative f.
double	apply_xx(double lox, double hix) Calls apply_nxx(n,lox,hix) with a small default value of 'n' to integrate f numerically.
Function.Cts2Cts	apply(Value lo) Calls apply_x(lo.x()).

Methods inherited from class la.la.Function.Cts2Cts2Cts

apply2

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

'f' is a synonym for 'Cts2Cts.this' and 'this' Integral is the (definite) Integral of 'f'.

Constructor Detail

Integral

public Integral()

Construct the definite Integral of Cts2Cts f.

Method Detail

apply

public Function.Cts2Cts apply(Value lo)

Calls apply_x(lo.x()). An Integral has roughly the type Cts→Cts→Cts.

Overrides:

apply in class Function.Cts2Cts2Cts

apply_x

public Function.Cts2Cts apply_x(double lox)

Returns a Cts→Cts which (i) will take hix & call apply_xx(lox,hix), and (ii) has the Derivative f.

apply_xx

public double apply_xx(double lox,
                       double hix)

Calls apply_nxx(n,lox,hix) with a small default value of 'n' to integrate f numerically. If you want to set 'n' yourself, override apply_xx and/or apply_nxx. (See exactIntegral(F) if there is a closed-form for the indefinite integral.)

Specified by:

apply_xx in class Function.Cts2Cts2Cts

apply_nxx

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

Integrate f from 'lo' to 'x' numerically in 'n' steps using Simpson's rule, called by apply_xx. Note, 'n' is forced to be ≥3, and odd. See exactIntegral if there is a closed-form for the indefinite integral.