IntervalArithmetic

Namespace

JXG.Math.IntervalArithmetic namespace. Interval arithmetic is a technique used to mitigate rounding and measurement errors in mathematical computation by computing function bounds. Instead of representing a value as a single number, interval arithmetic represents each value as a range.

For example, we wish to calculate the area of a rectangle from direct measurements using a standard meter stick with an uncertainty of 0.0005 m (half the “least count measurement” of 1 mm). We measure one side nominally as L=1, so 0.9995 ≤ L ≤ 1.0005, the other nominally as W=2 so the interval is [1.9995, 2.0005].

let L = JXG.Math.IntervalArithmetic.Interval(0.9995, 1.0005)
let W = JXG.Math.IntervalArithmetic.Interval(1.9995, 2.0005)

let A = JXG.Math.IntervalArithmetic.mul(L, W)

console.log('area:', A) // {hi: 2.0015002500000003, lo: 1.99850025}
Methods

Own

abs

acos

acot

add

asin

atan

cos

cosh

difference

div

divNegative

divNonZero

divPositive

divZero

equal

exp

fmod

geq

gt

hasInterval

hasValue

hull

intersection

intervalsOverlap

isEmpty

isWhole

leq

ln

log

log10

log2

lt

max

min

mul

multiplicativeInverse

negative

notEqual

nthRoot

positive

pow

sin

sinh

sqrt

sub

tan

tanh

union

width

zeroIn

(static) abs(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1072

(static) acos(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1251

(static) acot(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1265

(static) add(x, y)

Addition

Parameters

Name Type Description
x JXG.Math.Interval | Number
y JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 337

(static) asin(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1237

(static) atan(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1276

(static) cos(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1154

(static) cosh(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1298

(static) difference(x, y)

Difference of overlapping intervals x and y

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1026

(static) div(x, y)

Division

Parameters

Name Type Description
x JXG.Math.Interval | Number
y JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 475

(private, static) divNegative(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 668

(private, static) divNonZero(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 603

(private, static) divPositive(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 644

(private, static) divZero(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 691

(static) equal(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 1331

(static) exp(x)

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 905

(static) fmod(x, y)

x mod y: x - n * y

Parameters

Name Type Description
x JXG.Math.Interval | Number
y JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 707

(static) geq(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 1416

(static) gt(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 1380

(static) hasInterval(x, y)

Test if interval x contains interval y.

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 574

(static) hasValue(i, value)

Test if interval contains a specific value.

Parameters

Name Type Description
i JXG.Math.Interval
value Number

Returns

Boolean

Details

Source
math/ia.js, line 561

(static) hull(x, y)

Hull of intervals x and y

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 973

(static) intersection(x, y)

Intersection of intervals x and y

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 994

(static) intervalsOverlap(x, y)

Test if intervals x and y have non-zero intersection.

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 587

(static) isEmpty(i)

Test if interval is empty set.

Parameters

Name Type Description
i JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 533

(static) isWhole(i)

Test if interval is (-Infinity, Infinity).

Parameters

Name Type Description
i JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 542

(static) leq(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 1398

(static) ln(x)

Natural log, alias for JXG.Math.IntervalArithmetic#log.

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 937

(static) log(x)

Natural log

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 920

(static) log10(x)

Logarithm to base 10.

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 948

(static) log2(x)

Logarithm to base 2.

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 960

(static) lt(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 1362

(static) max(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1093

(static) min(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1113

(static) mul(x, y)

Multiplication

Parameters

Name Type Description
x JXG.Math.Interval | Number
y JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 371

(static) multiplicativeInverse(x)

1 / x

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 734

(static) negative(x)

Return -x

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 517

(static) notEqual(x, y)

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 1350

(static) nthRoot(x, n)

x1/n

Parameters

Name Type Description
x JXG.Math.Interval | Number
n Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 849

(static) positive(x)

Return +x (i.e. identity)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 507

(static) pow(x, power)

xpower

Parameters

Name Type Description
x JXG.Math.Interval | Number
power JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 767

(static) sin(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1201

(static) sinh(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1287

(static) sqrt(x)

sqrt(x)

Parameters

Name Type Description
x JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 836

(static) sub(x, y)

Subtraction

Parameters

Name Type Description
x JXG.Math.Interval | Number
y JXG.Math.Interval | Number

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 354

(static) tan(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1212

(static) tanh(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1315

(static) union(x, y)

Union of overlapping intervals x and y

Parameters

Name Type Description
x JXG.Math.Interval
y JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1013

(static) width(x)

Parameters

Name Type Description
x JXG.Math.Interval

Returns

JXG.Math.Interval

Details

Source
math/ia.js, line 1061

(static) zeroIn(i)

Test if interval contains 0.

Parameters

Name Type Description
i JXG.Math.Interval

Returns

Boolean

Details

Source
math/ia.js, line 551

Inherited

none

Details

IntervalArithmetic

Source
math/ia.js, line 287