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Classes

Namespace JXG.Math


      ↳ JXG.Math



Defined in: math.js.

Namespace Summary
Constructor Attributes Constructor Name and Description
 
JXG.Math
Math namespace.
Field Summary
Field Attributes Field Name and Description
<static>  
JXG.Math.acosh
Hyperbolic arc-cosine of a number.
<static>  
JXG.Math.asinh
Hyperbolic arcsine of a number
<static>  
JXG.Math.eps
eps defines the closeness to zero.
<static>  
JXG.Math.Interval
Interval for interval arithmetics.
Method Summary
Method Attributes Method Name and Description
<static>  
JXG.Math.acot(x)
Computes the inverse cotangent of x.
<static>  
JXG.Math.and(a, b)
Logical operator: a && b?
<static>  
JXG.Math.axpy(a, x, y)
Compute a * x + y for a scalar a and vectors x and y.
<static>  
JXG.Math.binomial(n, k)
Computes the binomial coefficient n over k.
<static>  
JXG.Math.cbrt(x)
Computes cube root of real number Polyfill for Math.cbrt().
<static>  
JXG.Math.clamp(x, a, b)
Clamp x within the interval [a, b].
<static>  
JXG.Math.cosh(x)
Calculates the cosine hyperbolicus of x.
<static>  
JXG.Math.cot(x)
Computes the cotangent of x.
<static>  
JXG.Math.crossProduct(c1, c2)
Calculates the cross product of two vectors both of length three.
<static>  
JXG.Math.decToFraction(x, order)
Convert a floating point number to sign + integer + fraction.
<static>  
JXG.Math.eq(a, b)
Logical test: a === b?
<static>  
JXG.Math.erf(x)
Error function, see https://en.wikipedia.org/wiki/Error_function.
<static>  
JXG.Math.erfc(x)
Complementary error function, i.e.
<static>  
JXG.Math.erfi(x)
Inverse of error function
<static>  
JXG.Math.factorial(n)
Compute the factorial of a positive integer.
<static>  
JXG.Math.frustum(l, r, t, b, n, f)
Generates a 4x4 matrix for 3D to 2D projections.
<static>  
JXG.Math.gamma(z)
Gamma function for real parameters by Lanczos approximation.
<static>  
JXG.Math.gcd(a, b)
Greatest common divisor (gcd) of two numbers.
<static>  
JXG.Math.geq(a, b)
Logical test: a >= b?
<static>  
JXG.Math.gt(a, b)
Logical test: a > b?
<static>  
JXG.Math.hstep(x)
Heaviside unit step function.
<static>  
JXG.Math.hypot(a)
Returns sqrt(a * a + b * b) for a variable number of arguments.
<static>  
JXG.Math.identity(n, m)
Generates an identity matrix.
<static>  
JXG.Math.innerProduct(a, b, n)
Inner product of two vectors a and b.
<static>  
JXG.Math.inverse(Ain)
Compute the inverse of an nxn matrix with Gauss elimination.
<static>  
JXG.Math.lcm(a, b)
Least common multiple (lcm) of two numbers.
<static>  
JXG.Math.leq(a, b)
Logical test: a <= b?
<static>  
JXG.Math.log(x, b)
Logarithm to arbitrary base b.
<static>  
JXG.Math.log10(x)
Logarithm to base 10.
<static>  
JXG.Math.log2(x)
Logarithm to base 2.
<static>  
JXG.Math.lt(a, b)
Logical test: a < b?
<static>  
JXG.Math.matMatMult(mat1, mat2)
Computes the product of the two matrices mat1*mat2.
<static>  
JXG.Math.matrix(n, m, init)
Initializes a matrix as an array of rows with the given value.
<static>  
JXG.Math.matVecMult(mat, vec)
Multiplies a vector vec to a matrix mat: mat * vec.
<static>  
JXG.Math.mod(a, m)
The JavaScript implementation of the % operator returns the symmetric modulo.
<static>  
JXG.Math.ndtr(x)
Normal distribution function
<static>  
JXG.Math.ndtri(x)
Inverse of normal distribution function
<static>  
JXG.Math.neq(a, b)
Logical test: a !== b?
<static>  
JXG.Math.norm(a, n)
Euclidean norm of a vector.
<private> <static>  
JXG.Math.normalize(stdform)
Normalize the standard form [c, b0, b1, a, k, r, q0, q1].
<static>  
JXG.Math.not(a)
Logical operator: !a?
<static>  
JXG.Math.nthroot(x, n)
Compute n-th real root of a real number.
<static>  
JXG.Math.or(a, b)
Logical operator: a || b?
<static>  
JXG.Math.pow(base, exponent)
Compute base to the power of exponent.
<static>  
JXG.Math.projection(fov, ratio, n, f)
Generates a 4x4 matrix for 3D to 2D projections.
<static>  
JXG.Math.ratpow(base, m, n)
Compute base to the power of the rational exponent m / n.
<static>  
JXG.Math.relDif(a, b)
Determine the relative difference between two numbers.
<static>  
JXG.Math.roundToStep(value, step, min, max)
Special use of Math.round function to round not only to integers but also to chosen decimal values.
<static>  
JXG.Math.sign(x)
The sign() function returns the sign of a number, indicating whether the number is positive, negative or zero.
<static>  
JXG.Math.sinh(x)
Sine hyperbolicus of x.
<static>  
JXG.Math.squampow(base, exponent)
A square & multiply algorithm to compute base to the power of exponent.
<static>  
JXG.Math.toGL(m)
Converts a two dimensional array to a one dimensional Float32Array that can be processed by WebGL.
<static>  
JXG.Math.transpose(M)
Transposes a matrix given as a two dimensional array.
<static>  
JXG.Math.vector(n, init)
Initializes a vector of size n wih coefficients set to the init value (default 0)
<static>  
JXG.Math.Vieta(x)
Theorem of Vieta: Given a set of simple zeroes x_0, .
<static>  
JXG.Math.wrap(x, a, b)
Translate x into the interval [a, b) by adding a multiple of b - a.
<static>  
JXG.Math.wrapAndClamp(x, a, b, period)
A way of clamping a periodic variable.
<static>  
JXG.Math.xor(a, b)
Logical operator: either a or b?
Namespace Detail
JXG.Math
Math namespace. Contains mathematics related methods which are specific to JSXGraph or which extend the JavaScript Math class.
Field Detail
<static> {Number} JXG.Math.acosh
Hyperbolic arc-cosine of a number.
<static> {Number} JXG.Math.asinh
Hyperbolic arcsine of a number
<static> {Number} JXG.Math.eps
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.
<static> {Object} JXG.Math.Interval
Interval for interval arithmetics. Consists of the properties
Defined in: ia.js.
Method Detail
<static> {Number} JXG.Math.acot(x)
Computes the inverse cotangent of x.
Parameters:
{Number} x
The number the inverse cotangent will be calculated of.
Returns:
{Number} Inverse cotangent of the given value.
<static> {Boolean} JXG.Math.and(a, b)
Logical operator: a && b?
Parameters:
{Boolean} a
{Boolean} b
Returns:
{Boolean}
<static> JXG.Math.axpy(a, x, y)
Compute a * x + y for a scalar a and vectors x and y.
Parameters:
{Number} a
{Array} x
{Array} y
Returns:
<static> {Number} JXG.Math.binomial(n, k)
Computes the binomial coefficient n over k.
Parameters:
{Number} n
Fraction will be ignored
{Number} k
Fraction will be ignored
Returns:
{Number} The binomial coefficient n over k
<static> {Number} JXG.Math.cbrt(x)
Computes cube root of real number Polyfill for Math.cbrt().
Parameters:
{Number} x
Radicand
Returns:
{Number} Cube root of x.
<static> JXG.Math.clamp(x, a, b)
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.
Parameters:
x
a
b
<static> {Number} JXG.Math.cosh(x)
Calculates the cosine hyperbolicus of x.
Parameters:
{Number} x
The number the cosine hyperbolicus will be calculated of.
Returns:
{Number} Cosine hyperbolicus of the given value.
<static> {Number} JXG.Math.cot(x)
Computes the cotangent of x.
Parameters:
{Number} x
The number the cotangent will be calculated of.
Returns:
{Number} Cotangent of the given value.
<static> {Array} JXG.Math.crossProduct(c1, c2)
Calculates the cross product of two vectors both of length three. In case of homogeneous coordinates this is either
Parameters:
{Array} c1
Homogeneous coordinates of line or point 1
{Array} c2
Homogeneous coordinates of line or point 2
Returns:
{Array} vector of length 3: homogeneous coordinates of the resulting point / line.
<static> {Array} JXG.Math.decToFraction(x, order)
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.

Parameters:
{Number} x
Number which is to be converted
{Number} order Optional, Default: 0.001
Small number determining the approximation precision.
Returns:
{Array} [sign, leading, nominator, denominator] where sign is 1 or -1.
See:
JXG.toFraction
Examples:
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 ]
<static> {Boolean} JXG.Math.eq(a, b)
Logical test: a === b?
Parameters:
{Number} a
{Number} b
Returns:
{Boolean}
<static> {Number} JXG.Math.erf(x)
Error function, see https://en.wikipedia.org/wiki/Error_function.
Parameters:
{Number} x
Returns:
{Number}
See:
JXG.Math.ProbFuncs.erf
<static> {Number} JXG.Math.erfc(x)
Complementary error function, i.e. 1 - erf(x).
Parameters:
{Number} x
Returns:
{Number}
See:
JXG.Math.erf
JXG.Math.ProbFuncs.erfc
<static> {Number} JXG.Math.erfi(x)
Inverse of error function
Parameters:
{Number} x
Returns:
{Number}
See:
JXG.Math.erf
JXG.Math.ProbFuncs.erfi
<static> {Number} JXG.Math.factorial(n)
Compute the factorial of a positive integer. If a non-integer value is given, the fraction will be ignored.
Parameters:
{Number} n
Returns:
{Number} n! = n*(n-1)*...*2*1
<static> {Array} JXG.Math.frustum(l, r, t, b, n, f)
Generates a 4x4 matrix for 3D to 2D projections.
Parameters:
{Number} l
Left
{Number} r
Right
{Number} t
Top
{Number} b
Bottom
{Number} n
Near
{Number} f
Far
Returns:
{Array} 4x4 Matrix
<static> JXG.Math.gamma(z)
Gamma function for real parameters by Lanczos approximation. Implementation straight from https://en.wikipedia.org/wiki/Lanczos_approximation.
Parameters:
{Number} z
Returns:
Number
<static> {Number} JXG.Math.gcd(a, b)
Greatest common divisor (gcd) of two numbers. See {@link rosettacode.org}.
Parameters:
{Number} a
First number
{Number} b
Second number
Returns:
{Number} gcd(a, b) if a and b are numbers, NaN else.
<static> {Boolean} JXG.Math.geq(a, b)
Logical test: a >= b?
Parameters:
{Number} a
{Number} b
Returns:
{Boolean}
<static> {Boolean} JXG.Math.gt(a, b)
Logical test: a > b?
Parameters:
{Number} a
{Number} b
Returns:
{Boolean}
<static> JXG.Math.hstep(x)
Heaviside unit step function. Returns 0 for x <, 1 for x > 0, and 0.5 for x == 0.
Parameters:
{Number} x
Returns:
Number
<static> JXG.Math.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:
{Number} a
Variable number of arguments.
Returns:
Number
<static> {Array} JXG.Math.identity(n, m)
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:
{Number} n
Number of rows
{Number} m Optional, Default: n
Number of columns
Returns:
{Array} 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.
<static> {Number} JXG.Math.innerProduct(a, b, n)
Inner product of two vectors a and b. n is the length of the vectors.
Parameters:
{Array} a
Vector
{Array} b
Vector
{Number} n Optional
Length of the Vectors. If not given the length of the first vector is taken.
Returns:
{Number} The inner product of a and b.
<static> {Array} JXG.Math.inverse(Ain)
Compute the inverse of an nxn matrix with Gauss elimination.
Parameters:
{Array} Ain
Returns:
{Array} Inverse matrix of Ain
<static> {Number} JXG.Math.lcm(a, b)
Least common multiple (lcm) of two numbers.
Parameters:
{Number} a
First number
{Number} b
Second number
Returns:
{Number} lcm(a, b) if a and b are numbers, NaN else.
<static> {Boolean} JXG.Math.leq(a, b)
Logical test: a <= b?
Parameters:
{Number} a
{Number} b
Returns:
{Boolean}
<static> {Number} JXG.Math.log(x, b)
Logarithm to arbitrary base b. If b is not given, natural log is taken, i.e. b = e.
Parameters:
{Number} x
{Number} b
base
Returns:
{Number} log(x, b) Logarithm of x to base b, that is log(x)/log(b).
<static> {Number} JXG.Math.log10(x)
Logarithm to base 10.
Parameters:
{Number} x
Returns:
{Number} log10(x) Logarithm of x to base 10.
<static> {Number} JXG.Math.log2(x)
Logarithm to base 2.
Parameters:
{Number} x
Returns:
{Number} log2(x) Logarithm of x to base 2.
<static> {Boolean} JXG.Math.lt(a, b)
Logical test: a < b?
Parameters:
{Number} a
{Number} b
Returns:
{Boolean}
<static> {Array} JXG.Math.matMatMult(mat1, mat2)
Computes the product of the two matrices mat1*mat2.
Parameters:
{Array} mat1
Two dimensional array of numbers
{Array} mat2
Two dimensional array of numbers
Returns:
{Array} Two dimensional Array of numbers containing result
<static> {Array} JXG.Math.matrix(n, m, init)
Initializes a matrix as an array of rows with the given value.
Parameters:
{Number} n
Number of rows
{Number} m Optional, Default: n
Number of columns
{Number} init Optional, Default: 0
Initial value for each coefficient
Returns:
{Array} A n times m-matrix represented by a two-dimensional array. The inner arrays hold the columns, the outer array holds the rows.
<static> {Array} JXG.Math.matVecMult(mat, vec)
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.
Parameters:
{Array} mat
Two dimensional array of numbers. The inner arrays describe the columns, the outer ones the matrix' rows.
{Array} vec
Array of numbers
Returns:
{Array} Array of numbers containing the result
Examples:
var A = [[2, 1],
         [1, 3]],
    b = [4, 5],
    c;
c = JXG.Math.matVecMult(A, b)
// c === [13, 19];
<static> {Number} JXG.Math.mod(a, m)
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:
{Number} a
{Number} m
Returns:
{Number} Mathematical modulo a mod m
<static> {Number} JXG.Math.ndtr(x)
Normal distribution function
Parameters:
{Number} x
Returns:
{Number}
See:
JXG.Math.ProbFuncs.ndtr
<static> {Number} JXG.Math.ndtri(x)
Inverse of normal distribution function
Parameters:
{Number} x
Returns:
{Number}
See:
JXG.Math.ndtr
JXG.Math.ProbFuncs.ndtri
<static> {Boolean} JXG.Math.neq(a, b)
Logical test: a !== b?
Parameters:
{Number} a
{Number} b
Returns:
{Boolean}
<static> {Number} JXG.Math.norm(a, n)
Euclidean norm of a vector.
Parameters:
{Array} a
Array containing a vector.
{Number} n
(Optional) length of the array.
Returns:
{Number} Euclidean norm of the vector.
<private> <static> {Array} JXG.Math.normalize(stdform)
Normalize the standard form [c, b0, b1, a, k, r, q0, q1].
Parameters:
{Array} stdform
The standard form to be normalized.
Returns:
{Array} The normalized standard form.
<static> {Boolean} JXG.Math.not(a)
Logical operator: !a?
Parameters:
{Boolean} a
Returns:
{Boolean}
<static> {Number} JXG.Math.nthroot(x, n)
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
Parameters:
{Number} x
radicand. Must be non-negative, if n even.
{Number} n
index of the root. must be strictly positive integer.
Returns:
{Number} returns real root or NaN
Examples:
nthroot(16, 4): 2
nthroot(-27, 3): -3
nthroot(-4, 2): NaN
<static> {Boolean} JXG.Math.or(a, b)
Logical operator: a || b?
Parameters:
{Boolean} a
{Boolean} b
Returns:
{Boolean}
<static> {Number} JXG.Math.pow(base, exponent)
Compute base to the power of exponent.
Parameters:
{Number} base
{Number} exponent
Returns:
{Number} base to the power of exponent.
<static> {Array} JXG.Math.projection(fov, ratio, n, f)
Generates a 4x4 matrix for 3D to 2D projections.
Parameters:
{Number} fov
Field of view in vertical direction, given in rad.
{Number} ratio
Aspect ratio of the projection plane.
{Number} n
Near
{Number} f
Far
Returns:
{Array} 4x4 Projection Matrix
<static> {Number} JXG.Math.ratpow(base, m, n)
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:
{Number} base
{Number} m
numerator of exponent
{Number} n
denominator of exponent
Returns:
{Number} base to the power of exponent.
<static> {Number} JXG.Math.relDif(a, b)
Determine the relative difference between two numbers.
Parameters:
{Number} a
First number
{Number} b
Second number
Returns:
{Number} Relative difference between a and b: |a-b| / max(|a|, |b|)
<static> {Number} JXG.Math.roundToStep(value, step, min, max)
Special use of Math.round function to round not only to integers but also to chosen decimal values.
Parameters:
{Number} value
Value to be rounded.
{Number} step
Distance between the values to be rounded to. (default: 1.0)
{Number} min Optional
If set, it will be returned the maximum of value and min.
{Number} max Optional
If set, it will be returned the minimum of value and max.
Returns:
{Number} Fitted value.
<static> {Number} JXG.Math.sign(x)
The sign() function returns the sign of a number, indicating whether the number is positive, negative or zero.
Parameters:
{Number} x
A Number
Returns:
{Number} 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.
<static> {Number} JXG.Math.sinh(x)
Sine hyperbolicus of x.
Parameters:
{Number} x
The number the sine hyperbolicus will be calculated of.
Returns:
{Number} Sine hyperbolicus of the given value.
<static> {Number} JXG.Math.squampow(base, exponent)
A square & multiply algorithm to compute base to the power of exponent. Implementated by Wolfgang Riedl.
Parameters:
{Number} base
{Number} exponent
Returns:
{Number} Base to the power of exponent
<static> {Float32Array} JXG.Math.toGL(m)
Converts a two dimensional array to a one dimensional Float32Array that can be processed by WebGL.
Parameters:
{Array} m
A matrix in a two dimensional array.
Returns:
{Float32Array} 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.
<static> {Array} JXG.Math.transpose(M)
Transposes a matrix given as a two dimensional array.
Parameters:
{Array} M
The matrix to be transposed
Returns:
{Array} The transpose of M
<static> {Array} JXG.Math.vector(n, init)
Initializes a vector of size n wih coefficients set to the init value (default 0)
Parameters:
{Number} n
Length of the vector
{Number} init Optional, Default: 0
Initial value for each coefficient
Returns:
{Array} An array of length n
<static> {Array} JXG.Math.Vieta(x)
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:
{Array} x
Simple zeroes of the polynomial.
Returns:
{Array} Coefficients of the polynomial.
<static> JXG.Math.wrap(x, a, b)
Translate x into the interval [a, b) by adding a multiple of b - a.
Parameters:
{Number} x
{Number} a
{Number} b
<static> JXG.Math.wrapAndClamp(x, a, b, period)
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.
Parameters:
x
a
b
period
<static> {Boolean} JXG.Math.xor(a, b)
Logical operator: either a or b?
Parameters:
{Boolean} a
{Boolean} b
Returns:
{Boolean}
Documentation generated by JsDoc Toolkit 2.4.0 on Fri Nov 08 2024 12:13:05 GMT+0100 (Mitteleuropäische Normalzeit)