Math

Members

Own

Interval

eps

(private, static) Interval

Description

Interval for interval arithmetics. Consists of the properties

See

JXG.Math.IntervalArithmetic

Source

math/ia.js, line 175

(static) eps : Number

Description: eps defines the closeness to zero. If the absolute value of a given number is smaller than eps, it is considered to be equal to zero.
Type: Number
Source: math/math.js, line 84

Inherited

none

Methods

Own

(static) Vieta(x) → {Array}

Theorem of Vieta: Given a set of simple zeroes x_0, ..., x_n of a polynomial f, compute the coefficients s_k, (k=0,...,n-1) of the polynomial of the form. See https://de.wikipedia.org/wiki/Elementarsymmetrisches_Polynom.

f(x) = (x-x_0)...(x-x_n) = x^n + sum_{k=1}^{n} (-1)^(k) s_{k-1} x^(n-k)

Parameters

Name	Type	Description
`x`	Array	Simple zeroes of the polynomial.

Returns

Coefficients of the polynomial.

Type: Array

Details

Source: math/math.js, line 1445

(static) acosh(x) → {Number}

Hyperbolic arc-cosine of a number.

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

Source: math/math.js, line 714

(static) acot(x) → {Number}

Computes the inverse cotangent of x.

Parameters

Name	Type	Description
`x`	Number	The number the inverse cotangent will be calculated of.

Returns

Inverse cotangent of the given value.

Type: Number

Details

Source: math/math.js, line 754

(static) and(a, b) → {Boolean}

Logical operator: a && b?

Parameters

Name	Type	Description
`a`	Boolean
`b`	Boolean

Returns

Type: Boolean

Details

Source: math/math.js, line 1258

(static) asinh(x) → {Number}

Hyperbolic arcsine of a number

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

Source: math/math.js, line 726

(static) axpy(a, x, y) → {Array}

Compute a * x + y for a scalar a and vectors x and y.

Parameters

Name	Type	Description
`a`	Number
`x`	Array
`y`	Array

Returns

Type: Array

Details

Source: math/math.js, line 622

(static) binomial(n, k) → {Number}

Computes the binomial coefficient n over k.

Parameters

Name	Type	Description
`n`	Number	Fraction will be ignored
`k`	Number	Fraction will be ignored

Returns

The binomial coefficient n over k

Type: Number

Details

Source: math/math.js, line 660

(static) cbrt(x) → {Number}

Computes cube root of real number Polyfill for Math.cbrt().

Parameters

Name	Type	Description
`x`	Number	Radicand

Returns

Cube root of x.

Type: Number

Details

Source: math/math.js, line 805

(static) clamp()

Clamp x within the interval [a, b]. If x is below a, increase it to a. If it's above b, decrease it to b.

Details

Source: math/math.js, line 128

(static) cosh(x) → {Number}

Calculates the cosine hyperbolicus of x.

Parameters

Name	Type	Description
`x`	Number	The number the cosine hyperbolicus will be calculated of.

Returns

Cosine hyperbolicus of the given value.

Type: Number

Details

Source: math/math.js, line 690

(static) cot(x) → {Number}

Computes the cotangent of x.

Parameters

Name	Type	Description
`x`	Number	The number the cotangent will be calculated of.

Returns

Cotangent of the given value.

Type: Number

Details

Source: math/math.js, line 741

(static) crossProduct(c1, c2) → {Array}

Calculates the cross product of two vectors both of length three. In case of homogeneous coordinates this is either

the intersection of two lines
the line through two points

Parameters

Name	Type	Description
`c1`	Array	Homogeneous coordinates of line or point 1
`c2`	Array	Homogeneous coordinates of line or point 2

Returns

vector of length 3: homogeneous coordinates of the resulting point / line.

Type: Array

Details

Source: math/math.js, line 584

(static) decToFraction(x, orderopt) → {Array}

Convert a floating point number to sign + integer + fraction. fraction is given as nominator and denominator.

Algorithm: approximate the floating point number by a continued fraction and simultaneously keep track of its convergents. Inspired by https://kevinboone.me/rationalize.html.

Example

JXG.Math.decToFraction(0.33333333);
// Result: [ 1, 0, 1, 3 ]

JXG.Math.decToFraction(0);
// Result: [ 1, 0, 0, 1 ]

JXG.Math.decToFraction(-10.66666666666667);
// Result: [-1, 10, 2, 3 ]

Parameters

Name	Type	Attributes	Default	Description
`x`	Number			Number which is to be converted
`order`	Number	<optional>	`0.001`	Small number determining the approximation precision.

Returns

[sign, leading, nominator, denominator] where sign is 1 or -1.

Type: Array

Details

See

JXG.toFraction

Source

math/math.js, line 1319

(static) eq(a, b) → {Boolean}

Logical test: a === b?

Parameters

Name	Type	Description
`a`	Number
`b`	Number

Returns

Type: Boolean

Details

Source: math/math.js, line 1236

(static) erf(x) → {Number}

Error function, see https://en.wikipedia.org/wiki/Error_function.

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

See

JXG.Math.ProbFuncs.erf

Source

math/math.js, line 1064

(static) erfc(x) → {Number}

Complementary error function, i.e. 1 - erf(x).

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

See

Source

math/math.js, line 1076

(static) erfi(x) → {Number}

Inverse of error function

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

See

Source

math/math.js, line 1088

(static) factorial(n) → {Number}

Compute the factorial of a positive integer. If a non-integer value is given, the fraction will be ignored.

Parameters

Name	Type	Description
`n`	Number

Returns

n! = n*(n-1)*...21

Type: Number

Details

Source: math/math.js, line 639

(static) frustum(l, r, t, b, n, f) → {Array}

Generates a 4x4 matrix for 3D to 2D projections.

Parameters

Name	Type	Description
`l`	Number	Left
`r`	Number	Right
`t`	Number	Top
`b`	Number	Bottom
`n`	Number	Near
`f`	Number	Far

Returns

4x4 Matrix

Type: Array

Details

Source: math/math.js, line 233

(static) gamma(z)

Gamma function for real parameters by Lanczos approximation. Implementation straight from https://en.wikipedia.org/wiki/Lanczos_approximation.

Parameters

Name	Type	Description
`z`	Number

Returns

Number

Details

Source: math/math.js, line 1152

(static) gcd(a, b) → {Number}

Greatest common divisor (gcd) of two numbers. See href="https:\\/\\/rosettacode.org/wiki/Greatest_common_divisor#JavaScript">rosettacode.org.

Parameters

Name	Type	Description
`a`	Number	First number
`b`	Number	Second number

Returns

gcd(a, b) if a and b are numbers, NaN else.

Type: Number

Details

Source: math/math.js, line 960

(static) geq(a, b) → {Boolean}

Logical test: a >= b?

Parameters

Name	Type	Description
`a`	Number
`b`	Number

Returns

Type: Boolean

Details

Source: math/math.js, line 1225

(static) gt(a, b) → {Boolean}

Logical test: a > b?

Parameters

Name	Type	Description
`a`	Number
`b`	Number

Returns

Type: Boolean

Details

Source: math/math.js, line 1214

(static) hstep(x)

Heaviside unit step function. Returns 0 for x <, 1 for x > 0, and 0.5 for x == 0.

Parameters

Name	Type	Description
`x`	Number

Returns

Number

Details

Source: math/math.js, line 1140

(static) hypot(a)

Returns sqrt(a * a + b * b) for a variable number of arguments. This is a naive implementation which might be faster than Math.hypot. The latter is numerically more stable.

Parameters

Name	Type	Description
`a`	Number	Variable number of arguments.

Returns

Number

Details

Source: math/math.js, line 1123

(static) identity(n, mopt) → {Array}

Generates an identity matrix. If n is a number and m is undefined or not a number, a square matrix is generated, if n and m are both numbers, an nxm matrix is generated.

Parameters

Name	Type	Attributes	Default	Description
`n`	Number			Number of rows
`m`	Number	<optional>	`n`	Number of columns

Returns

A square matrix of length n with all coefficients equal to 0 except a_(i,i), i out of (1, ..., n), if m is undefined or not a number or a n times m-matrix with a_(i,j) = 0 and a_(i,i) = 1 if m is a number.

Type: Array

Details

Source: math/math.js, line 207

(static) innerProduct(a, b, nopt) → {Number}

Inner product of two vectors a and b. n is the length of the vectors.

Parameters

Name	Type	Attributes	Description
`a`	Array		Vector
`b`	Array		Vector
`n`	Number	<optional>	Length of the Vectors. If not given the length of the first vector is taken.

Returns

The inner product of a and b.

Type: Number

Details

Source: math/math.js, line 558

(static) inverse(A) → {Array}

Compute the inverse of an \((n \times n)\)-matrix by Gauss elimination.

Parameters

Name	Type	Description
`A`	Array	matrix

Returns

Inverse matrix of A or empty array (i.e. []) in case A is singular.

Type: Array

Details

Source: math/math.js, line 448

(static) lcm(a, b) → {Number}

Least common multiple (lcm) of two numbers.

Parameters

Name	Type	Description
`a`	Number	First number
`b`	Number	Second number

Returns

lcm(a, b) if a and b are numbers, NaN else.

Type: Number

Details

Source: math/math.js, line 995

(static) leq(a, b) → {Boolean}

Logical test: a <= b?

Parameters

Name	Type	Description
`a`	Number
`b`	Number

Returns

Type: Boolean

Details

Source: math/math.js, line 1203

(static) log(x, b) → {Number}

Logarithm to arbitrary base b. If b is not given, natural log is taken, i.e. b = e.

Parameters

Name	Type	Description
`x`	Number
`b`	Number	base

Returns

log(x, b) Logarithm of x to base b, that is log(x)/log(b).

Type: Number

Details

Source: math/math.js, line 887

(static) log10(x) → {Number}

Logarithm to base 10.

Parameters

Name	Type	Description
`x`	Number

Returns

log10(x) Logarithm of x to base 10.

Type: Number

Details

Source: math/math.js, line 868

(static) log2(x) → {Number}

Logarithm to base 2.

Parameters

Name	Type	Description
`x`	Number

Returns

log2(x) Logarithm of x to base 2.

Type: Number

Details

Source: math/math.js, line 877

(static) lt(a, b) → {Boolean}

Logical test: a < b?

Parameters

Name	Type	Description
`a`	Number
`b`	Number

Returns

Type: Boolean

Details

Source: math/math.js, line 1192

(static) matMatAdd(mat1, mat2) → {Array}

Compute the sum of two matrices: mat1 + mat2. Returns a new matrix object.

Parameters

Name	Type	Description
`mat1`	Array	Two-dimensional array of numbers
`mat2`	Array	Two-dimensional array of numbers

Returns

Two-dimensional Array of numbers containing result

Type: Array

Details

Source: math/math.js, line 405

(static) matMatMult(mat1, mat2) → {Array}

Computes the product of the two matrices: mat1 * mat2. Returns a new matrix array.

Parameters

Name	Type	Description
`mat1`	Array	Two-dimensional array of numbers
`mat2`	Array	Two-dimensional array of numbers

Returns

Two-dimensional Array of numbers containing result

Type: Array

Details

Source: math/math.js, line 357

(static) matNumberMult(mat, alpha) → {Array}

Multiply a matrix mat by a scalar alpha: mat * scalar

Parameters

Name	Type	Description
`mat`	Array	Two-dimensional array of numbers
`alpha`	Number	Scalar

Returns

Two-dimensional Array of numbers containing result

Type: Array

Details

Source: math/math.js, line 383

(static) matVecMult(mat, vec) → {Array}

Multiplies a vector vec to a matrix mat: mat * vec. The matrix is interpreted by this function as an array of rows. Please note: This function does not check if the dimensions match.

Example

var A = [[2, 1],
         [2, 3]],
    b = [4, 5],
    c;
c = JXG.Math.matVecMult(A, b);
// c === [13, 23];

Parameters

Name	Type	Description
`mat`	Array	Two-dimensional array of numbers. The inner arrays describe the columns, the outer ones the matrix' rows.
`vec`	Array	Array of numbers

Returns

Array of numbers containing the result

Type: Array

Details

Source: math/math.js, line 289

(static) matrix(n, mopt, initopt) → {Array}

Initializes a matrix as an array of rows with the given value.

Parameters

Name	Type	Attributes	Default	Description
`n`	Number			Number of rows
`m`	Number	<optional>	`n`	Number of columns
`init`	Number	<optional>	`0`	Initial value for each coefficient

Returns

A n times m-matrix represented by a two-dimensional array. The inner arrays hold the columns, the outer array holds the rows.

Type: Array

Details

Source: math/math.js, line 181

(static) mod(a, m) → {Number}

The JavaScript implementation of the % operator returns the symmetric modulo. mod and "%" are both identical if a >= 0 and m >= 0 but the results differ if a or m < 0.

Parameters

Name	Type	Description
`a`	Number
`m`	Number

Returns

Mathematical modulo \(a \bmod m\)

Type: Number

Details

Source: math/math.js, line 108

(static) ndtr(x) → {Number}

Normal distribution function

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

See

JXG.Math.ProbFuncs.ndtr

Source

math/math.js, line 1099

(static) ndtri(x) → {Number}

Inverse of normal distribution function

Parameters

Name	Type	Description
`x`	Number

Returns

Type: Number

Details

See

Source

math/math.js, line 1111

(static) neq(a, b) → {Boolean}

Logical test: a !== b?

Parameters

Name	Type	Description
`a`	Number
`b`	Number

Returns

Type: Boolean

Details

Source: math/math.js, line 1247

(static) norm(a, n) → {Number}

Euclidean norm of a vector.

Parameters

Name	Type	Description
`a`	Array	Array containing a vector.
`n`	Number	(Optional) length of the array.

Returns

Euclidean norm of the vector.

Type: Number

Details

Source: math/math.js, line 599

(private, static) normalize(stdform) → {Array}

Normalize the standard form [c, b0, b1, a, k, r, q0, q1].

Parameters

Name	Type	Description
`stdform`	Array	The standard form to be normalized.

Returns

The normalized standard form.

Type: Array

Details

Source: math/math.js, line 1368

(static) not(a) → {Boolean}

Logical operator: !a?

Parameters

Name	Type	Description
`a`	Boolean

Returns

Type: Boolean

Details

Source: math/math.js, line 1268

(static) nthroot(x, n) → {Number}

Compute n-th real root of a real number. n must be strictly positive integer. If n is odd, the real n-th root exists and is negative. For n even, for negative valuees of x NaN is returned

Example

nthroot(16, 4): 2
nthroot(-27, 3): -3
nthroot(-4, 2): NaN

Parameters

Name	Type	Description
`x`	Number	radicand. Must be non-negative, if n even.
`n`	Number	index of the root. must be strictly positive integer.

Returns

returns real root or NaN

Type: Number

Details

Source: math/math.js, line 771

(static) or(a, b) → {Boolean}

Logical operator: a || b?

Parameters

Name	Type	Description
`a`	Boolean
`b`	Boolean

Returns

Type: Boolean

Details

Source: math/math.js, line 1279

(static) pow(base, exponent) → {Number}

Compute base to the power of exponent.

Parameters

Name	Type	Description
`base`	Number
`exponent`	Number

Returns

base to the power of exponent.

Type: Number

Details

Source: math/math.js, line 817

(static) projection(fov, ratio, n, f) → {Array}

Generates a 4x4 matrix for 3D to 2D projections.

Parameters

Name	Type	Description
`fov`	Number	Field of view in vertical direction, given in rad.
`ratio`	Number	Aspect ratio of the projection plane.
`n`	Number	Near
`f`	Number	Far

Returns

4x4 Projection Matrix

Type: Array

Details

Source: math/math.js, line 267

(static) ratpow(base, m, n) → {Number}

Compute base to the power of the rational exponent m / n. This function first reduces the fraction m/n and then computes JXG.Math.pow(base, m/n).

This function is necessary to have the same results for e.g. (-8)^(1/3) = (-8)^(2/6) = -2

Parameters

Name	Type	Description
`base`	Number
`m`	Number	numerator of exponent
`n`	Number	denominator of exponent

Returns

base to the power of exponent.

Type: Number

Details

Source: math/math.js, line 850

(static) relDif(a, b) → {Number}

Determine the relative difference between two numbers.

Parameters

Name	Type	Description
`a`	Number	First number
`b`	Number	Second number

Returns

Relative difference between a and b: |a-b| / max(|a|, |b|)

Type: Number

Details

Source: math/math.js, line 92

(static) roundToStep(value, step, minopt, maxopt) → {Number}

Special use of Math.round function to round not only to integers but also to chosen decimal values.

Parameters

Name	Type	Attributes	Description
`value`	Number		Value to be rounded.
`step`	Number		Distance between the values to be rounded to. (default: 1.0)
`min`	Number	<optional>	If set, it will be returned the maximum of value and min.
`max`	Number	<optional>	If set, it will be returned the minimum of value and max.

Returns

Fitted value.

Type: Number

Details

Source: math/math.js, line 1019

(static) sign(x) → {Number}

The sign() function returns the sign of a number, indicating whether the number is positive, negative or zero.

Parameters

Name	Type	Description
`x`	Number	A Number

Returns

This function has 5 kinds of return values, 1, -1, 0, -0, NaN, which represent "positive number", "negative number", "positive zero", "negative zero" and NaN respectively.

Type: Number

Details

Source: math/math.js, line 907

(static) sinh(x) → {Number}

Sine hyperbolicus of x.

Parameters

Name	Type	Description
`x`	Number	The number the sine hyperbolicus will be calculated of.

Returns

Sine hyperbolicus of the given value.

Type: Number

Details

Source: math/math.js, line 702

(static) squampow(base, exponent) → {Number}

A square & multiply algorithm to compute base to the power of exponent. Implementated by Wolfgang Riedl.

Parameters

Name	Type	Description
`base`	Number
`exponent`	Number

Returns

Base to the power of exponent

Type: Number

Details

Source: math/math.js, line 925

(static) toGL(m) → {Float32Array}

Converts a two-dimensional array to a one-dimensional Float32Array that can be processed by WebGL.

Parameters

Name	Type	Description
`m`	Array	A matrix in a two-dimensional array.

Returns

A one-dimensional array containing the matrix in column wise notation. Provides a fall back to the default JavaScript Array if Float32Array is not available.

Type: Float32Array

Details

Source: math/math.js, line 1411

(static) trace(M) → {Number}

Trace of a square matrix, given as a two-dimensional array.

Parameters

Name	Type	Description
`M`	Array	Square matrix

Returns

The trace of M, NaN if M is not square.

Type: Number

Details

Source: math/math.js, line 533

(static) transpose(M) → {Array}

Transposes a matrix given as a two-dimensional array.

Parameters

Name	Type	Description
`M`	Array	The matrix to be transposed

Returns

The transpose of M

Type: Array

Details

Source: math/math.js, line 424

(static) vecMatMult(vec, mat) → {Array}

Multiplies a vector vec to a matrix mat from the left: vec * mat. The matrix is interpreted by this function as an array of rows. Please note: This function does not check if the dimensions match.

Example

var A = [[2, 1],
         [2, 3]],
    b = [4, 5],
    c;
c = JXG.Math.vecMatMult(b, A);
// c === [18, 16];

Parameters

Name	Type	Description
`vec`	Array	Array of numbers
`mat`	Array	Two-dimensional array of numbers. The inner arrays describe the columns, the outer ones the matrix' rows.

Returns

Array of numbers containing the result

Type: Array

Details

Source: math/math.js, line 327

(static) vector(n, initopt) → {Array}

Initializes a vector of size n wih coefficients set to the init value (default 0)

Parameters

Name	Type	Attributes	Default	Description
`n`	Number			Length of the vector
`init`	Number	<optional>	`0`	Initial value for each coefficient

Returns

An array of length n

Type: Array

Details

Source: math/math.js, line 160

(static) wrap(x, a, b)

Translate x into the interval [a, b) by adding a multiple of b - a.

Parameters

Name	Type	Description
`x`	Number
`a`	Number
`b`	Number

Details

Source: math/math.js, line 119

(static) wrapAndClamp()

A way of clamping a periodic variable. If x is congruent mod period to a point in [a, b], return that point. Otherwise, wrap it into [mid - period/2, mid + period/2], where mid is the mean of a and b, and then clamp it to [a, b] from there.

Details

Source: math/math.js, line 139

(static) xor(a, b) → {Boolean}

Logical operator: either a or b?

Parameters

Name	Type	Description
`a`	Boolean
`b`	Boolean

Returns

Type: Boolean

Details

Source: math/math.js, line 1290

Inherited

none

Details

Source: math/math.js, line 78

Classes

BoxQuadtree: Instantiate a new box quadtree.
ImplicitPlot
Quadtree: Instantiate a new quadtree.

Namespaces

Clip: JXG.Math.Clip namespace.
Extrapolate: JXG.Math.Extrapolate namespace.
Geometry: JXG.Math.Geometry namespace.
IntervalArithmetic: JXG.Math.IntervalArithmetic namespace.
Metapost: The JXG.Math.Metapost namespace holds algorithms converted from Metapost by D.E.
Nlp: The JXG.Math.Nlp namespace holds numerical algorithms for non-linear optimization, mainly the port of COBYLA.
Numerics: The JXG.Math.Numerics namespace holds numerical algorithms, constants, and variables.
Plot: The JXG.Math.Plot namespace holds various functions for plotting of curves.
Poly: The JXG.Math.Poly namespace holds algorithms to create and manipulate polynomials.
ProbFuncs: The JXG.Math.ProbFuncs namespace bundles various probability functions, e.g.
Statistics: JXG.Math.Statistics namespace with functions for mathematical statistics.
Tiling: The JXG.Math.Tiling namespace.