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DefinitelyTyped/types/mathjs/index.d.ts
Mark Wiemer afa55fd87e
Add MathNode.content optional property (#43435) 
This is used by ParenthesisNode
2020-04-02 10:22:02 -07:00

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// Type definitions for mathjs 6.0
// Project: https://mathjs.org/
// Definitions by: Ilya Shestakov <https://github.com/siavol>,
// Andy Patterson <https://github.com/andnp>,
// Brad Besserman <https://github.com/bradbesserman>,
// Pawel Krol <https://github.com/pawkrol>,
// Charlee Li <https://github.com/charlee>,
// Mark Wiemer <https://github.com/mark-wiemer>
// Definitions: https://github.com/DefinitelyTyped/DefinitelyTyped
// TypeScript Version: 2.2
import { Decimal } from "decimal.js";
declare const math: math.MathJsStatic;
export as namespace math;
export = math;
type NoLiteralType<T> =
T extends number ? number :
T extends string ? string :
T extends boolean ? boolean :
T;
declare namespace math {
type MathArray = number[] | number[][];
type MathType =
| number
| BigNumber
| Fraction
| Complex
| Unit
| MathArray
| Matrix;
type MathExpression = string | string[] | MathArray | Matrix;
type FactoryFunction<T> = (scope: any) => T;
// FactoryFunctionMap can be nested; all nested objects will be flattened
interface FactoryFunctionMap {
[key: string]: FactoryFunction<any> | FactoryFunctionMap;
}
type MathJsFunctionName = keyof MathJsStatic;
interface MathJsStatic extends FactoryDependencies {
e: number;
pi: number;
i: number;
Infinity: number;
LN2: number;
LN10: number;
LOG2E: number;
LOG10E: number;
NaN: number;
null: number;
phi: number;
SQRT1_2: number;
SQRT2: number;
tau: number;
uninitialized: any;
version: string;
expression: MathNode;
json: MathJsJson;
/*************************************************************************
* Core functions
************************************************************************/
/**
* Set configuration options for math.js, and get current options. Will
* emit a ‘config’ event, with arguments (curr, prev, changes).
* @param options Available options: {number} epsilon Minimum relative
* difference between two compared values, used by all comparison
* functions. {string} matrix A string ‘Matrix’ (default) or ‘Array’.
* {string} number A string ‘number’ (default), ‘BigNumber’, or
* ‘Fraction’ {number} precision The number of significant digits for
* BigNumbers. Not applicable for Numbers. {string} parenthesis How to
* display parentheses in LaTeX and string output. {string} randomSeed
* Random seed for seeded pseudo random number generator. Set to null to
* randomly seed.
* @returns Returns the current configuration
*/
config: (options: ConfigOptions) => ConfigOptions;
/**
* Create a typed-function which checks the types of the arguments and
* can match them against multiple provided signatures. The
* typed-function automatically converts inputs in order to find a
* matching signature. Typed functions throw informative errors in case
* of wrong input arguments.
* @param name Optional name for the typed-function
* @param signatures Object with one or multiple function signatures
* @returns The created typed-function.
*/
typed: (name: string, signatures: Record<string, (...args: any[]) => any>) => ((...args: any[]) => any);
/*************************************************************************
* Construction functions
************************************************************************/
/**
* Create a BigNumber, which can store numbers with arbitrary precision.
* When a matrix is provided, all elements will be converted to
* BigNumber.
* @param x Value for the big number, 0 by default.
* @returns The created bignumber
*/
bignumber(
x?:
| number
| string
| Fraction
| BigNumber
| MathArray
| Matrix
| boolean
| Fraction
| null
): BigNumber;
/**
* Create a boolean or convert a string or number to a boolean. In case
* of a number, true is returned for non-zero numbers, and false in case
* of zero. Strings can be 'true' or 'false', or can contain a number.
* When value is a matrix, all elements will be converted to boolean.
* @param x A value of any type
* @returns The boolean value
*/
boolean(
x: string | number | boolean | MathArray | Matrix | null
): boolean | MathArray | Matrix;
/**
* Wrap any value in a chain, allowing to perform chained operations on
* the value. All methods available in the math.js library can be called
* upon the chain, and then will be evaluated with the value itself as
* first argument. The chain can be closed by executing chain.done(),
* which returns the final value. The chain has a number of special
* functions: done() Finalize the chain and return the chain's value.
* valueOf() The same as done() toString() Executes math.format() onto
* the chain's value, returning a string representation of the value.
* @param value A value of any type on which to start a chained
* operation.
* @returns The created chain
*/
chain(value?: any): MathJsChain;
/**
* Create a complex value or convert a value to a complex value.
* @param args Arguments specifying the real and imaginary part of the
* complex number
* @returns Returns a complex value
*/
complex(arg?: Complex | string | PolarCoordinates): Complex;
complex(arg?: MathArray | Matrix): MathArray | Matrix;
/**
* @param re Argument specifying the real part of the complex number
* @param im Argument specifying the imaginary part of the complex
* number
* @returns Returns a complex value
*/
complex(re: number, im: number): Complex;
/**
* Create a user-defined unit and register it with the Unit type.
* @param name The name of the new unit. Must be unique. Example: ‘knot’
* @param definition Definition of the unit in terms of existing units.
* For example, ‘0.514444444 m / s’.
* @param options (optional) An object containing any of the following
* properties:</br>- prefixes {string} “none”, “short”, “long”,
* “binary_short”, or “binary_long”. The default is “none”.</br>-
* aliases {Array} Array of strings. Example: [‘knots’, ‘kt’,
* ‘kts’]</br>- offset {Numeric} An offset to apply when converting from
* the unit. For example, the offset for celsius is 273.15. Default is
* 0.
* @returns The new unit
*/
createUnit(
name: string,
definition?: string | UnitDefinition,
options?: CreateUnitOptions
): Unit;
/**
* Create a user-defined unit and register it with the Unit type.
* @param units Definition of the unit
* @param options
* @returns The new unit
*/
createUnit(
units: Record<string, string | UnitDefinition>,
options?: CreateUnitOptions
): Unit;
/**
* Create a fraction convert a value to a fraction.
* @param args Arguments specifying the numerator and denominator of the
* fraction
* @returns Returns a fraction
*/
fraction(
args: Fraction | MathArray | Matrix
): Fraction | MathArray | Matrix;
/**
* @param numerator Argument specifying the numerator of the fraction
* @param denominator Argument specifying the denominator of the
* fraction
* @returns Returns a fraction
*/
fraction(
numerator: number | string | MathArray | Matrix,
denominator?: number | string | MathArray | Matrix
): Fraction | MathArray | Matrix;
/**
* Create an index. An Index can store ranges having start, step, and
* end for multiple dimensions. Matrix.get, Matrix.set, and math.subset
* accept an Index as input.
* @param ranges Zero or more ranges or numbers.
* @returns Returns the created index
*/
index(...ranges: any[]): Index;
/**
* Create a Matrix. The function creates a new math.type.Matrix object
* from an Array. A Matrix has utility functions to manipulate the data
* in the matrix, like getting the size and getting or setting values in
* the matrix. Supported storage formats are 'dense' and 'sparse'.
* @param format The Matrix storage format
* @returns The created Matrix
*/
matrix(format?: "sparse" | "dense"): Matrix;
/**
* @param data A multi dimensional array
* @param format The Matrix storage format
* @param dataType The Matrix data type
* @returns The created Matrix
*/
matrix(
data: MathArray | Matrix,
format?: "sparse" | "dense",
dataType?: string
): Matrix;
/**
* Create a number or convert a string, boolean, or unit to a number.
* When value is a matrix, all elements will be converted to number.
* @param value Value to be converted
* @returns The created number
*/
number(
value?:
| string
| number
| BigNumber
| Fraction
| boolean
| MathArray
| Matrix
| Unit
| null
): number | MathArray | Matrix;
/**
* @param value Value to be converted
* @param valuelessUnit A valueless unit, used to convert a unit to a
* number
* @returns The created number
*/
number(unit: Unit, valuelessUnit: Unit | string): number;
/**
* Create a Sparse Matrix. The function creates a new math.type.Matrix
* object from an Array. A Matrix has utility functions to manipulate
* the data in the matrix, like getting the size and getting or setting
* values in the matrix.
* @param data A two dimensional array
* @param dataType Sparse Matrix data type
* @returns The created matrix
*/
sparse(data?: MathArray | Matrix, dataType?: string): Matrix;
/**
* Split a unit in an array of units whose sum is equal to the original
* unit.
* @param unit A unit to be split
* @param parts An array of strings or valueless units
* @returns An array of units
*/
splitUnit(unit: Unit, parts: Unit[]): Unit[];
/**
* Create a string or convert any object into a string. Elements of
* Arrays and Matrices are processed element wise.
* @param value A value to convert to a string
* @returns The created string
*/
string(
value: MathType | null
): string | MathArray | Matrix;
/**
* Create a unit. Depending on the passed arguments, the function will
* create and return a new math.type.Unit object. When a matrix is
* provided, all elements will be converted to units.
* @param unit The unit to be created
* @returns The created unit
*/
unit(unit: string): Unit;
/**
* @param value The value of the unit to be created
* @param unit The unit to be created
* @returns The created unit
*/
unit(value: number | MathArray | Matrix, unit: string): Unit;
/*************************************************************************
* Expression functions
************************************************************************/
/**
* Parse and compile an expression. Returns a an object with a function
* evaluate([scope]) to evaluate the compiled expression.
* @param expr The expression to be compiled
* @returns An object with the compiled expression
*/
compile(expr: MathExpression): EvalFunction;
/**
* @param exprs The expressions to be compiled
* @returns An array of objects with the compiled expressions
*/
compile(exprs: MathExpression[]): EvalFunction[];
/**
* Evaluate an expression.
* @param expr The expression to be evaluated
* @param scope Scope to read/write variables
* @returns The result of the expression
*/
evaluate(
expr: MathExpression | MathExpression[] | Matrix,
scope?: object
): any;
/**
* Retrieve help on a function or data type. Help files are retrieved
* from the documentation in math.expression.docs.
* @param search A function or function name for which to get help
* @returns A help object
*/
help(search: () => any): Help;
/**
* Parse an expression. Returns a node tree, which can be evaluated by
* invoking node.evaluate();
* @param expr Expression to be parsed
* @param options Available options: nodes - a set of custome nodes
* @returns A node
*/
parse(expr: MathExpression, options?: any): MathNode;
/**
* @param exprs Expressions to be parsed
* @param options Available options: nodes - a set of custome nodes
* @returns An arry of nodes
*/
parse(exprs: MathExpression[], options?: any): MathNode[];
/**
* Create a parser. The function creates a new math.expression.Parser
* object.
* @returns A Parser object
*/
parser(): Parser;
/*************************************************************************
* Algebra functions
************************************************************************/
/**
* @param expr The expression to differentiate
* @param variable The variable over which to differentiate
* @param options There is one option available, simplify, which is true
* by default. When false, output will not be simplified.
* @returns The derivative of expr
*/
derivative(
expr: MathNode | string,
variable: MathNode | string,
options?: {simplify: boolean}
): MathNode;
/**
* Solves the linear equation system by forwards substitution. Matrix
* must be a lower triangular matrix.
* @param L A N x N matrix or array (L)
* @param b A column vector with the b values
* @returns A column vector with the linear system solution (x)
*/
lsolve(
L: Matrix | MathArray,
b: Matrix | MathArray
): Matrix | MathArray;
/**
* Calculate the Matrix LU decomposition with partial pivoting. Matrix A
* is decomposed in two matrices (L, U) and a row permutation vector p
* where A[p,:] = L * U
* @param A A two dimensional matrix or array for which to get the LUP
* decomposition.
* @returns The lower triangular matrix, the upper triangular matrix and
* the permutation matrix.
*/
lup(
A?: Matrix | MathArray
): { L: MathArray | Matrix; U: MathArray | Matrix; P: number[] };
/**
* Solves the linear system A * x = b where A is an [n x n] matrix and b
* is a [n] column vector.
* @param A Invertible Matrix or the Matrix LU decomposition
* @param b Column Vector
* @param order The Symbolic Ordering and Analysis order, see slu for
* details. Matrix must be a SparseMatrix
* @param threshold Partial pivoting threshold (1 for partial pivoting),
* see slu for details. Matrix must be a SparseMatrix.
* @returns Column vector with the solution to the linear system A * x =
* b
*/
lusolve(
A: Matrix | MathArray | number,
b: Matrix | MathArray,
order?: number,
threshold?: number
): Matrix | MathArray;
/**
* Calculate the Matrix QR decomposition. Matrix A is decomposed in two
* matrices (Q, R) where Q is an orthogonal matrix and R is an upper
* triangular matrix.
* @param A A two dimensional matrix or array for which to get the QR
* decomposition.
* @returns Q: the orthogonal matrix and R: the upper triangular matrix
*/
qr(
A: Matrix | MathArray
): { Q: MathArray | Matrix; R: MathArray | Matrix };
/**
* Transform a rationalizable expression in a rational fraction. If
* rational fraction is one variable polynomial then converts the
* numerator and denominator in canonical form, with decreasing
* exponents, returning the coefficients of numerator.
* @param expr The expression to check if is a polynomial expression
* @param optional scope of expression or true for already evaluated
* rational expression at input
* @param detailed optional True if return an object, false if return
* expression node (default)
* @returns The rational polynomial of expr
*/
rationalize(expr: MathNode | string, optional?: object | boolean, detailed?: true): { expression: MathNode | string, variables: string[], coefficients: MathType[] };
rationalize(expr: MathNode | string, optional?: object | boolean, detailed?: false): MathNode;
/**
* Simplify an expression tree.
* @param expr The expression to be simplified
* @param rules A list of rules are applied to an expression, repeating
* over the list until no further changes are made. It’s possible to
* pass a custom set of rules to the function as second argument. A rule
* can be specified as an object, string, or function.
* @param scope Scope to variables
* @returns Returns the simplified form of expr
*/
simplify(
expr: MathNode | string,
rules?: Array<({ l: string; r: string } | string | ((node: MathNode) => MathNode))>,
scope?: object
): MathNode;
/**
* Calculate the Sparse Matrix LU decomposition with full pivoting.
* Sparse Matrix A is decomposed in two matrices (L, U) and two
* permutation vectors (pinv, q) where P * A * Q = L * U
* @param A A two dimensional sparse matrix for which to get the LU
* decomposition.
* @param order The Symbolic Ordering and Analysis order: 0 - Natural
* ordering, no permutation vector q is returned 1 - Matrix must be
* square, symbolic ordering and analisis is performed on M = A + A' 2 -
* Symbolic ordering and analysis is performed on M = A' * A. Dense
* columns from A' are dropped, A recreated from A'. This is appropriate
* for LU factorization of non-symmetric matrices. 3 - Symbolic ordering
* and analysis is performed on M = A' * A. This is best used for LU
* factorization is matrix M has no dense rows. A dense row is a row
* with more than 10*sqr(columns) entries.
* @param threshold Partial pivoting threshold (1 for partial pivoting)
* @returns The lower triangular matrix, the upper triangular matrix and
* the permutation vectors.
*/
slu(A: Matrix, order: number, threshold: number): object;
/**
* Solves the linear equation system by backward substitution. Matrix
* must be an upper triangular matrix. U * x = b
* @param U A N x N matrix or array (U)
* @param b A column vector with the b values
* @returns A column vector with the linear system solution (x)
*/
usolve(
U: Matrix | MathArray,
b: Matrix | MathArray
): Matrix | MathArray;
/*************************************************************************
* Arithmetic functions
************************************************************************/
/**
* Calculate the absolute value of a number. For matrices, the function
* is evaluated element wise.
* @param x A number or matrix for which to get the absolute value
* @returns Absolute value of x
*/
abs(x: number): number;
abs(x: BigNumber): BigNumber;
abs(x: Fraction): Fraction;
abs(x: Complex): Complex;
abs(x: MathArray): MathArray;
abs(x: Matrix): Matrix;
abs(x: Unit): Unit;
/**
* Add two values, x + y. For matrices, the function is evaluated
* element wise.
* @param x First value to add
* @param y Second value to add
* @returns Sum of x and y
*/
add(x: MathType, y: MathType): MathType;
/**
* Calculate the cubic root of a value. For matrices, the function is
* evaluated element wise.
* @param x Value for which to calculate the cubic root.
* @param allRoots Optional, false by default. Only applicable when x is
* a number or complex number. If true, all complex roots are returned,
* if false (default) the principal root is returned.
* @returns Returns the cubic root of x
*/
cbrt(x: number, allRoots?: boolean): number;
cbrt(x: BigNumber, allRoots?: boolean): BigNumber;
cbrt(x: Fraction, allRoots?: boolean): Fraction;
cbrt(x: Complex, allRoots?: boolean): Complex;
cbrt(x: MathArray, allRoots?: boolean): MathArray;
cbrt(x: Matrix, allRoots?: boolean): Matrix;
cbrt(x: Unit, allRoots?: boolean): Unit;
/**
* Round a value towards plus infinity If x is complex, both real and
* imaginary part are rounded towards plus infinity. For matrices, the
* function is evaluated element wise.
* @param x Number to be rounded
* @returns Rounded value
*/
ceil(x: number): number;
ceil(x: BigNumber): BigNumber;
ceil(x: Fraction): Fraction;
ceil(x: Complex): Complex;
ceil(x: MathArray): MathArray;
ceil(x: Matrix): Matrix;
ceil(x: Unit): Unit;
/**
* Compute the cube of a value, x * x * x. For matrices, the function is
* evaluated element wise.
* @param x Number for which to calculate the cube
* @returns Cube of x
*/
cube(x: number): number;
cube(x: BigNumber): BigNumber;
cube(x: Fraction): Fraction;
cube(x: Complex): Complex;
cube(x: MathArray): MathArray;
cube(x: Matrix): Matrix;
cube(x: Unit): Unit;
/**
* Divide two values, x / y. To divide matrices, x is multiplied with
* the inverse of y: x * inv(y).
* @param x Numerator
* @param y Denominator
* @returns Quotient, x / y
*/
divide(x: Unit, y: Unit): Unit;
divide(x: number, y: number): number;
divide(x: MathType, y: MathType): MathType;
/**
* Divide two matrices element wise. The function accepts both matrices
* and scalar values.
* @param x Numerator
* @param y Denominator
* @returns Quotient, x ./ y
*/
dotDivide(x: MathType, y: MathType): MathType;
/**
* Multiply two matrices element wise. The function accepts both
* matrices and scalar values.
* @param x Left hand value
* @param y Right hand value
* @returns Multiplication of x and y
*/
dotMultiply(x: MathType, y: MathType): MathType;
/**
* Calculates the power of x to y element wise.
* @param x The base
* @param y The exponent
* @returns The value of x to the power y
*/
dotPow(x: MathType, y: MathType): MathType;
/**
* Calculate the exponent of a value. For matrices, the function is
* evaluated element wise.
* @param x A number or matrix to exponentiate
* @returns Exponent of x
*/
exp(x: number): number;
exp(x: BigNumber): BigNumber;
exp(x: Complex): Complex;
exp(x: MathArray): MathArray;
exp(x: Matrix): Matrix;
/**
* Calculate the value of subtracting 1 from the exponential value. For
* matrices, the function is evaluated element wise.
* @param x A number or matrix to apply expm1
* @returns Exponent of x
*/
expm1(x: number): number;
expm1(x: BigNumber): BigNumber;
expm1(x: Complex): Complex;
expm1(x: MathArray): MathArray;
expm1(x: Matrix): Matrix;
/**
* Round a value towards zero. For matrices, the function is evaluated
* element wise.
* @param x Number to be rounded
* @returns Rounded value
*/
fix(x: number): number;
fix(x: BigNumber): BigNumber;
fix(x: Fraction): Fraction;
fix(x: Complex): Complex;
fix(x: MathArray): MathArray;
fix(x: Matrix): Matrix;
/**
* Round a value towards minus infinity. For matrices, the function is
* evaluated element wise.
* @param Number to be rounded
* @returns Rounded value
*/
floor(x: number): number;
floor(x: BigNumber): BigNumber;
floor(x: Fraction): Fraction;
floor(x: Complex): Complex;
floor(x: MathArray): MathArray;
floor(x: Matrix): Matrix;
/**
* Calculate the greatest common divisor for two or more values or
* arrays. For matrices, the function is evaluated element wise.
* @param args Two or more integer numbers
* @returns The greatest common divisor
*/
gcd(...args: number[]): number;
gcd(...args: BigNumber[]): BigNumber;
gcd(...args: Fraction[]): Fraction;
gcd(...args: MathArray[]): MathArray;
gcd(...args: Matrix[]): Matrix;
/**
* Calculate the hypotenusa of a list with values. The hypotenusa is
* defined as: hypot(a, b, c, ...) = sqrt(a^2 + b^2 + c^2 + ...) For
* matrix input, the hypotenusa is calculated for all values in the
* matrix.
* @param args A list with numeric values or an Array or Matrix. Matrix
* and Array input is flattened and returns a single number for the
* whole matrix.
* @returns Returns the hypothenuse of the input values.
*/
hypot(...args: number[]): number;
hypot(...args: BigNumber[]): BigNumber;
/**
* Calculate the least common multiple for two or more values or arrays.
* lcm is defined as: lcm(a, b) = abs(a * b) / gcd(a, b) For matrices,
* the function is evaluated element wise.
* @param a An integer number
* @param b An integer number
* @returns The least common multiple
*/
lcm(a: number, b: number): number;
lcm(a: BigNumber, b: BigNumber): BigNumber;
lcm(a: MathArray, b: MathArray): MathArray;
lcm(a: Matrix, b: Matrix): Matrix;
/**
* Calculate the logarithm of a value. For matrices, the function is
* evaluated element wise.
* @param x Value for which to calculate the logarithm.
* @param base Optional base for the logarithm. If not provided, the
* natural logarithm of x is calculated. Default value: e.
* @returns Returns the logarithm of x
*/
log<T extends number | BigNumber | Complex | MathArray | Matrix>(
x: T,
base?: number | BigNumber | Complex
): NoLiteralType<T>;
/**
* Calculate the 10-base of a value. This is the same as calculating
* log(x, 10). For matrices, the function is evaluated element wise.
* @param x Value for which to calculate the logarithm.
* @returns Returns the 10-base logarithm of x
*/
log10(x: number): number;
log10(x: BigNumber): BigNumber;
log10(x: Complex): Complex;
log10(x: MathArray): MathArray;
log10(x: Matrix): Matrix;
/**
* Calculate the logarithm of a value+1. For matrices, the function is
* evaluated element wise.
* @param x Value for which to calculate the logarithm.
* @returns Returns the logarithm of x+1
*/
log1p(x: number, base?: number | BigNumber | Complex): number;
log1p(x: BigNumber, base?: number | BigNumber | Complex): BigNumber;
log1p(x: Complex, base?: number | BigNumber | Complex): Complex;
log1p(x: MathArray, base?: number | BigNumber | Complex): MathArray;
log1p(x: Matrix, base?: number | BigNumber | Complex): Matrix;
/**
* Calculate the 2-base of a value. This is the same as calculating
* log(x, 2). For matrices, the function is evaluated element wise.
* @param x Value for which to calculate the logarithm.
* @returns Returns the 2-base logarithm of x
*/
log2(x: number): number;
log2(x: BigNumber): BigNumber;
log2(x: Complex): Complex;
log2(x: MathArray): MathArray;
log2(x: Matrix): Matrix;
/**
* Calculates the modulus, the remainder of an integer division. For
* matrices, the function is evaluated element wise. The modulus is
* defined as: x - y * floor(x / y)
* @see http://en.wikipedia.org/wiki/Modulo_operation.
* @param x Dividend
* @param y Divisor
* @returns Returns the remainder of x divided by y
*/
mod<T extends number | BigNumber | Fraction | MathArray | Matrix>(
x: T,
y: number | BigNumber | Fraction | MathArray | Matrix
): NoLiteralType<T>;
/**
* Multiply two values, x * y. The result is squeezed. For matrices, the
* matrix product is calculated.
* @param x The first value to multiply
* @param y The second value to multiply
* @returns Multiplication of x and y
*/
multiply<T extends Matrix | MathArray>(x: T, y: MathType): T;
multiply(x: Unit, y: Unit): Unit;
multiply(x: number, y: number): number;
multiply(x: MathType, y: MathType): MathType;
/**
* Calculate the norm of a number, vector or matrix. The second
* parameter p is optional. If not provided, it defaults to 2.
* @param x Value for which to calculate the norm
* @param p Vector space. Supported numbers include Infinity and
* -Infinity. Supported strings are: 'inf', '-inf', and 'fro' (The
* Frobenius norm) Default value: 2.
* @returns the p-norm
*/
norm(
x: number | BigNumber | Complex | MathArray | Matrix,
p?: number | BigNumber | string
): number | BigNumber;
/**
* Calculate the nth root of a value. The principal nth root of a
* positive real number A, is the positive real solution of the equation
* x^root = A For matrices, the function is evaluated element wise.
* @param a Value for which to calculate the nth root
* @param root The root. Default value: 2.
* @return The nth root of a
*/
nthRoot(
a: number | BigNumber | MathArray | Matrix | Complex,
root?: number | BigNumber
): number | Complex | MathArray | Matrix;
/**
* Calculates the power of x to y, x ^ y. Matrix exponentiation is
* supported for square matrices x, and positive integer exponents y.
* @param x The base
* @param y The exponent
* @returns x to the power y
*/
pow(x: MathType, y: number | BigNumber | Complex): MathType;
/**
* Round a value towards the nearest integer. For matrices, the function
* is evaluated element wise.
* @param x Number to be rounded
* @param n Number of decimals Default value: 0.
* @returns Rounded value of x
*/
round<T extends number | BigNumber | Fraction | Complex | MathArray | Matrix>(
x: T,
n?: number | BigNumber | MathArray
): NoLiteralType<T>;
/**
* Compute the sign of a value. The sign of a value x is: 1 when x > 1
* -1 when x < 0 0 when x == 0 For matrices, the function is evaluated
* element wise.
* @param x The number for which to determine the sign
* @returns The sign of x
*/
sign(x: number): number;
sign(x: BigNumber): BigNumber;
sign(x: Fraction): Fraction;
sign(x: Complex): Complex;
sign(x: MathArray): MathArray;
sign(x: Matrix): Matrix;
sign(x: Unit): Unit;
/**
* Calculate the square root of a value. For matrices, the function is
* evaluated element wise.
* @param x Value for which to calculate the square root
* @returns Returns the square root of x
*/
sqrt(x: number): number;
sqrt(x: BigNumber): BigNumber;
sqrt(x: Complex): Complex;
sqrt(x: MathArray): MathArray;
sqrt(x: Matrix): Matrix;
sqrt(x: Unit): Unit;
/**
* Compute the square of a value, x * x. For matrices, the function is
* evaluated element wise.
* @param x Number for which to calculate the square
* @returns Squared value
*/
square(x: number): number;
square(x: BigNumber): BigNumber;
square(x: Fraction): Fraction;
square(x: Complex): Complex;
square(x: MathArray): MathArray;
square(x: Matrix): Matrix;
square(x: Unit): Unit;
/**
* Subtract two values, x - y. For matrices, the function is evaluated
* element wise.
* @param x Initial value
* @param y Value to subtract from x
* @returns Subtraction of x and y
*/
subtract(x: MathType, y: MathType): MathType;
/**
* Inverse the sign of a value, apply a unary minus operation. For
* matrices, the function is evaluated element wise. Boolean values and
* strings will be converted to a number. For complex numbers, both real
* and complex value are inverted.
* @param x Number to be inverted
* @returns Retursn the value with inverted sign
*/
unaryMinus(x: number): number;
unaryMinus(x: BigNumber): BigNumber;
unaryMinus(x: Fraction): Fraction;
unaryMinus(x: Complex): Complex;
unaryMinus(x: MathArray): MathArray;
unaryMinus(x: Matrix): Matrix;
unaryMinus(x: Unit): Unit;
/**
* Unary plus operation. Boolean values and strings will be converted to
* a number, numeric values will be returned as is. For matrices, the
* function is evaluated element wise.
* @param x Input value
* @returns Returns the input value when numeric, converts to a number
* when input is non-numeric.
*/
unaryPlus(x: number): number;
unaryPlus(x: BigNumber): BigNumber;
unaryPlus(x: Fraction): Fraction;
unaryPlus(x: string): string;
unaryPlus(x: Complex): Complex;
unaryPlus(x: MathArray): MathArray;
unaryPlus(x: Matrix): Matrix;
unaryPlus(x: Unit): Unit;
/**
* Calculate the extended greatest common divisor for two values. See
* http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.
* @param a An integer number
* @param b An integer number
* @returns Returns an array containing 3 integers [div, m, n] where div
* = gcd(a, b) and a*m + b*n = div
*/
xgcd(a: number | BigNumber, b: number | BigNumber): MathArray;
/*************************************************************************
* Bitwise functions
************************************************************************/
/**
* Bitwise AND two values, x & y. For matrices, the function is
* evaluated element wise.
* @param x First value to and
* @param y Second value to and
* @returns AND of x and y
*/
bitAnd<T extends number | BigNumber | MathArray | Matrix>(
x: T,
y: number | BigNumber | MathArray | Matrix
): NoLiteralType<T>;
/**
* Bitwise NOT value, ~x. For matrices, the function is evaluated
* element wise. For units, the function is evaluated on the best prefix
* base.
* @param x Value to not
* @returns NOT of x
*/
bitNot(x: number): number;
bitNot(x: BigNumber): BigNumber;
bitNot(x: MathArray): MathArray;
bitNot(x: Matrix): Matrix;
/**
* Bitwise OR two values, x | y. For matrices, the function is evaluated
* element wise. For units, the function is evaluated on the lowest
* print base.
* @param x First value to or
* @param y Second value to or
* @returns OR of x and y
*/
bitOr(x: number, y: number): number;
bitOr(x: BigNumber, y: BigNumber): BigNumber;
bitOr(x: MathArray, y: MathArray): MathArray;
bitOr(x: Matrix, y: Matrix): Matrix;
/**
* Bitwise XOR two values, x ^ y. For matrices, the function is
* evaluated element wise.
* @param x First value to xor
* @param y Second value to xor
* @returns XOR of x and y
*/
bitXor<T extends number | BigNumber | MathArray | Matrix>(
x: T,
y: number | BigNumber | MathArray | Matrix
): NoLiteralType<T>;
/**
* Bitwise left logical shift of a value x by y number of bits, x << y.
* For matrices, the function is evaluated element wise. For units, the
* function is evaluated on the best prefix base.
* @param x Value to be shifted
* @param y Amount of shifts
* @returns x shifted left y times
*/
leftShift<T extends number | BigNumber | MathArray | Matrix>(
x: T,
y: number | BigNumber
): NoLiteralType<T>;
/**
* Bitwise right arithmetic shift of a value x by y number of bits, x >>
* y. For matrices, the function is evaluated element wise. For units,
* the function is evaluated on the best prefix base.
* @param x Value to be shifted
* @param y Amount of shifts
* @returns x sign-filled shifted right y times
*/
rightArithShift<T extends number | BigNumber | MathArray | Matrix>(
x: T,
y: number | BigNumber
): NoLiteralType<T>;
/**
* Bitwise right logical shift of value x by y number of bits, x >>> y.
* For matrices, the function is evaluated element wise. For units, the
* function is evaluated on the best prefix base.
* @param x Value to be shifted
* @param y Amount of shifts
* @returns x zero-filled shifted right y times
*/
rightLogShift<T extends number | MathArray | Matrix>(
x: T,
y: number
): NoLiteralType<T>;
/*************************************************************************
* Combinatorics functions
************************************************************************/
/**
* The Bell Numbers count the number of partitions of a set. A partition
* is a pairwise disjoint subset of S whose union is S. bellNumbers only
* takes integer arguments. The following condition must be enforced: n
* >= 0
* @param n Total number of objects in the set
* @returns B(n)
*/
bellNumbers(n: number): number;
bellNumbers(n: BigNumber): BigNumber;
/**
* The Catalan Numbers enumerate combinatorial structures of many
* different types. catalan only takes integer arguments. The following
* condition must be enforced: n >= 0
* @param n nth Catalan number
* @returns Cn(n)
*/
catalan(n: number): number;
catalan(n: BigNumber): BigNumber;
/**
* The composition counts of n into k parts. Composition only takes
* integer arguments. The following condition must be enforced: k <= n.
* @param n Total number of objects in the set
* @param k Number of objects in the subset
* @returns Returns the composition counts of n into k parts.
*/
composition<T extends number | BigNumber>(
n: T,
k: number | BigNumber
): NoLiteralType<T>;
/**
* The Stirling numbers of the second kind, counts the number of ways to
* partition a set of n labelled objects into k nonempty unlabelled
* subsets. stirlingS2 only takes integer arguments. The following
* condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) =
* 1
* @param n Total number of objects in the set
* @param k Number of objects in the subset
* @returns S(n,k)
*/
stirlingS2<T extends number | BigNumber>(
n: T,
k: number | BigNumber
): NoLiteralType<T>;
/*************************************************************************
* Complex functions
************************************************************************/
/**
* Compute the argument of a complex value. For a complex number a + bi,
* the argument is computed as atan2(b, a). For matrices, the function
* is evaluated element wise.
* @param x A complex number or array with complex numbers
* @returns The argument of x
*/
arg(x: number | Complex): number;
arg(x: BigNumber | Complex): BigNumber;
arg(x: MathArray): MathArray;
arg(x: Matrix): Matrix;
/**
* Compute the complex conjugate of a complex value. If x = a+bi, the
* complex conjugate of x is a - bi. For matrices, the function is
* evaluated element wise.
* @param x A complex number or array with complex numbers
* @returns The complex conjugate of x
*/
conj<T extends number | BigNumber | Complex | MathArray | Matrix>(
x: T
): NoLiteralType<T>;
/**
* Get the imaginary part of a complex number. For a complex number a +
* bi, the function returns b. For matrices, the function is evaluated
* element wise.
* @param x A complex number or array with complex numbers
* @returns The imaginary part of x
*/
im(
x: number | BigNumber | Complex | MathArray | Matrix
): number | BigNumber | MathArray | Matrix;
/**
* Get the real part of a complex number. For a complex number a + bi,
* the function returns a. For matrices, the function is evaluated
* element wise.
* @param x A complex number or array of complex numbers
* @returns The real part of x
*/
re(
x: number | BigNumber | Complex | MathArray | Matrix
): number | BigNumber | MathArray | Matrix;
/*************************************************************************
* Geometry functions
************************************************************************/
/**
* Calculates: The eucledian distance between two points in 2 and 3
* dimensional spaces. Distance between point and a line in 2 and 3
* dimensional spaces. Pairwise distance between a set of 2D or 3D
* points NOTE: When substituting coefficients of a line(a, b and c),
* use ax + by + c = 0 instead of ax + by = c For parametric equation of
* a 3D line, x0, y0, z0, a, b, c are from: (x−x0, y−y0, z−z0) = t(a, b,
* c)
* @param x Coordinates of the first point
* @param y Coordinates of the second point
* @returns Returns the distance from two/three points
*/
distance(
x: MathArray | Matrix | object,
y: MathArray | Matrix | object
): number | BigNumber;
/**
* Calculates the point of intersection of two lines in two or three
* dimensions and of a line and a plane in three dimensions. The inputs
* are in the form of arrays or 1 dimensional matrices. The line
* intersection functions return null if the lines do not meet. Note:
* Fill the plane coefficients as x + y + z = c and not as x + y + z + c
* = 0.
* @param w Co-ordinates of first end-point of first line
* @param x Co-ordinates of second end-point of first line
* @param y Co-ordinates of first end-point of second line OR
* Coefficients of the plane's equation
* @param z Co-ordinates of second end-point of second line OR null if
* the calculation is for line and plane
* @returns Returns the point of intersection of lines/lines-planes
*/
intersect(
w: MathArray | Matrix,
x: MathArray | Matrix,
y: MathArray | Matrix,
z: MathArray | Matrix
): MathArray;
/*************************************************************************
* Logical functions
************************************************************************/
/**
* Logical and. Test whether two values are both defined with a
* nonzero/nonempty value. For matrices, the function is evaluated
* element wise.
* @param x First value to and
* @param y Second value to and
* @returns Returns true when both inputs are defined with a
* nonzero/nonempty value.
*/
and(
x: number | BigNumber | Complex | Unit | MathArray | Matrix,
y: number | BigNumber | Complex | Unit | MathArray | Matrix
): boolean | MathArray | Matrix;
/**
* Logical not. Flips boolean value of a given parameter. For matrices,
* the function is evaluated element wise.
* @param x First value to not
* @returns Returns true when input is a zero or empty value.
*/
not(
x: number | BigNumber | Complex | Unit | MathArray | Matrix
): boolean | MathArray | Matrix;
/**
* Logical or. Test if at least one value is defined with a
* nonzero/nonempty value. For matrices, the function is evaluated
* element wise.
* @param x First value to or
* @param y Second value to or
* @returns Returns true when one of the inputs is defined with a
* nonzero/nonempty value.
*/
or(
x: number | BigNumber | Complex | Unit | MathArray | Matrix,
y: number | BigNumber | Complex | Unit | MathArray | Matrix
): boolean | MathArray | Matrix;
/**
* Logical xor. Test whether one and only one value is defined with a
* nonzero/nonempty value. For matrices, the function is evaluated
* element wise.
* @param x First value to xor
* @param y Second value to xor
* @returns Returns true when one and only one input is defined with a
* nonzero/nonempty value.
*/
xor(
x: number | BigNumber | Complex | Unit | MathArray | Matrix,
y: number | BigNumber | Complex | Unit | MathArray | Matrix
): boolean | MathArray | Matrix;
/*************************************************************************
* Matrix functions
************************************************************************/
/**
* Concatenate two or more matrices. dim: number is a zero-based
* dimension over which to concatenate the matrices. By default the last
* dimension of the matrices.
* @param args Two or more matrices
* @returns Concatenated matrix
*/
concat(...args: Array<MathArray | Matrix>): MathArray | Matrix;
/**
* Calculate the cross product for two vectors in three dimensional
* space. The cross product of A = [a1, a2, a3] and B =[b1, b2, b3] is
* defined as: cross(A, B) = [ a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1
* * b2 - a2 * b1 ]
* @param x First vector
* @param y Second vector
* @returns Returns the cross product of x and y
*/
cross(x: MathArray | Matrix, y: MathArray | Matrix): Matrix | MathArray;
/**
* Calculate the determinant of a matrix.
* @param x A Matrix
* @returns the determinant of x
*/
det(x: MathArray | Matrix): number;
/**
* Create a diagonal matrix or retrieve the diagonal of a matrix. When x
* is a vector, a matrix with vector x on the diagonal will be returned.
* When x is a two dimensional matrix, the matrixes kth diagonal will be
* returned as vector. When k is positive, the values are placed on the
* super diagonal. When k is negative, the values are placed on the sub
* diagonal.
* @param X A two dimensional matrix or a vector
* @param k The diagonal where the vector will be filled in or
* retrieved. Default value: 0.
* @param format The matrix storage format. Default value: 'dense'.
* @returns Diagonal matrix from input vector, or diagonal from input
* matrix
*/
diag(X: MathArray | Matrix, format?: string): Matrix;
diag(
X: MathArray | Matrix,
k: number | BigNumber,
format?: string
): Matrix | MathArray;
/**
* Calculate the dot product of two vectors. The dot product of A = [a1,
* a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as: dot(A,
* B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn
* @param x First vector
* @param y Second vector
* @returns Returns the dot product of x and y
*/
dot(x: MathArray | Matrix, y: MathArray | Matrix): number;
/**
* Compute the matrix exponential, expm(A) = e^A. The matrix must be
* square. Not to be confused with exp(a), which performs element-wise
* exponentiation. The exponential is calculated using the Padé
* approximant with scaling and squaring; see “Nineteen Dubious Ways to
* Compute the Exponential of a Matrix,” by Moler and Van Loan.
* @param x A square matrix
* @returns The exponential of x
*/
expm(x: Matrix): Matrix;
/**
* Create a 2-dimensional identity matrix with size m x n or n x n. The
* matrix has ones on the diagonal and zeros elsewhere.
* @param size The size for the matrix
* @param format The Matrix storage format
* @returns A matrix with ones on the diagonal
*/
identity(
size: number | number[] | Matrix | MathArray,
format?: string
): Matrix | MathArray | number;
/**
* @param m The x dimension for the matrix
* @param n The y dimension for the matrix
* @param format The Matrix storage format
* @returns A matrix with ones on the diagonal
*/
identity(m: number, n: number, format?: string): Matrix | MathArray | number;
/**
* Filter the items in an array or one dimensional matrix.
* @param x A one dimensional matrix or array to filter
* @param test A function or regular expression to test items. All
* entries for which test returns true are returned. When test is a
* function, it is invoked with three parameters: the value of the
* element, the index of the element, and the matrix/array being
* traversed. The function must return a boolean.
*/
filter(
x: Matrix | MathArray | string[],
test: ((value: any, index: any, matrix: Matrix | MathArray | string[]) => boolean) | RegExp
): Matrix | MathArray;
/**
* Flatten a multi dimensional matrix into a single dimensional matrix.
* @param x Matrix to be flattened
* @returns Returns the flattened matrix
*/
flatten<T extends MathArray | Matrix>(x: T): T;
/**
* Iterate over all elements of a matrix/array, and executes the given
* callback function.
* @param x The matrix to iterate on.
* @param callback The callback function is invoked with three
* parameters: the value of the element, the index of the element, and
* the Matrix/array being traversed.
*/
forEach<T extends Matrix | MathArray>(x: T, callback: ((value: any, index: any, matrix: T) => void)): void;
/**
* Calculate the inverse of a square matrix.
* @param x Matrix to be inversed
* @returns The inverse of x
*/
inv<T extends number | Complex | MathArray | Matrix>(
x: T
): NoLiteralType<T>;
/**
* Calculate the kronecker product of two matrices or vectors
* @param x First vector
* @param y Second vector
* @returns Returns the kronecker product of x and y
*/
kron(x: Matrix | MathArray, y: Matrix | MathArray): Matrix;
/**
* Iterate over all elements of a matrix/array, and executes the given
* callback function.
* @param x The matrix to iterate on.
* @param callback The callback function is invoked with three
* parameters: the value of the element, the index of the element, and
* the Matrix/array being traversed.
* @returns Transformed map of x
*/
map<T extends Matrix | MathArray>(x: T, callback: ((value: any, index: any, matrix: T) => MathType | string)): T;
/**
* Create a matrix filled with ones. The created matrix can have one or
* multiple dimensions.
* @param size The size of each dimension of the matrix
* @param format The matrix storage format
* @returns A matrix filled with ones
*/
ones(size: number | number[], format?: string): MathArray | Matrix;
/**
* @param m The x dimension of the matrix
* @param n The y dimension of the amtrix
* @param format The matrix storage format
* @returns A matrix filled with ones
*/
ones(m: number, n: number, format?: string): MathArray | Matrix;
/**
* Partition-based selection of an array or 1D matrix. Will find the kth
* smallest value, and mutates the input array. Uses Quickselect.
* @param x A one dimensional matrix or array to sort
* @param k The kth smallest value to be retrieved; zero-based index
* @param compare An optional comparator function. The function is
* called as compare(a, b), and must return 1 when a > b, -1 when a < b,
* and 0 when a == b. Default value: 'asc'.
* @returns Returns the kth lowest value.
*/
partitionSelect(
x: MathArray | Matrix,
k: number,
compare?: "asc" | "desc" | ((a: any, b: any) => number)
): any;
/**
* Create an array from a range. By default, the range end is excluded.
* This can be customized by providing an extra parameter includeEnd.
* @param str A string 'start:end' or 'start:step:end'
* @param start Start of the range
* @param end End of the range, excluded by default, included when
* parameter includeEnd=true
* @param step Step size. Default value is 1.
* @param includeEnd: Option to specify whether to include the end or
* not. False by default
* @returns Parameters describing the ranges start, end, and optional
* step.
*/
range(str: string, includeEnd?: boolean): Matrix;
range(
start: number | BigNumber,
end: number | BigNumber,
includeEnd?: boolean
): Matrix;
range(
start: number | BigNumber,
end: number | BigNumber,
step: number | BigNumber,
includeEnd?: boolean
): Matrix;
/**
* Reshape a multi dimensional array to fit the specified dimensions
* @param x Matrix to be reshaped
* @param sizes One dimensional array with integral sizes for each
* dimension
* @returns A reshaped clone of matrix x
*/
reshape<T extends MathArray | Matrix>(
x: T,
sizes: number[]
): T;
/**
* Resize a matrix
* @param x Matrix to be resized
* @param size One dimensional array with numbers
* @param defaultValue Zero by default, except in case of a string, in
* that case defaultValue = ' ' Default value: 0.
* @returns A resized clone of matrix x
*/
resize<T extends MathArray | Matrix>(
x: T,
size: MathArray | Matrix,
defaultValue?: number | string
): T;
/**
* Calculate the size of a matrix or scalar.
* @param A matrix
* @returns A vector with the size of x
*/
size(
x: boolean | number | Complex | Unit | string | MathArray | Matrix
): MathArray | Matrix;
/**
* Sort the items in a matrix
* @param x A one dimensional matrix or array to sort
* @param compare An optional _comparator function or name. The function
* is called as compare(a, b), and must return 1 when a > b, -1 when a <
* b, and 0 when a == b. Default value: ‘asc’
* @returns Returns the sorted matrix
*/
sort<T extends Matrix | MathArray>(
x: T,
compare: ((a: any, b: any) => number) | "asc" | "desc" | "natural"
): T;
/**
* Calculate the principal square root of a square matrix. The principal
* square root matrix X of another matrix A is such that X * X = A.
* @param A The square matrix A
* @returns The principal square root of matrix A
*/
sqrtm<T extends MathArray | Matrix>(A: T): T;
/**
* Squeeze a matrix, remove inner and outer singleton dimensions from a
* matrix.
* @param x Matrix to be squeezed
* @returns Squeezed matrix
*/
squeeze<T extends MathArray | Matrix>(x: T): T;
/**
* Get or set a subset of a matrix or string.
* @param value An array, matrix, or string
* @param index An index containing ranges for each dimension
* @param replacement An array, matrix, or scalar. If provided, the
* subset is replaced with replacement. If not provided, the subset is
* returned
* @param defaultValue Default value, filled in on new entries when the
* matrix is resized. If not provided, math.matrix elements will be left
* undefined. Default value: undefined.
* @returns Either the retrieved subset or the updated matrix
*/
subset<T extends MathArray | Matrix | string>(
value: T,
index: Index,
replacement?: any,
defaultValue?: any
): T;
/**
* Calculate the trace of a matrix: the sum of the elements on the main
* diagonal of a square matrix.
* @param x A matrix
* @returns The trace of x
*/
trace(x: MathArray | Matrix): number;
/**
* Transpose a matrix. All values of the matrix are reflected over its
* main diagonal. Only two dimensional matrices are supported.
* @param x Matrix to be transposed
* @returns The transposed matrix
*/
transpose<T extends MathArray | Matrix>(x: T): T;
/**
* Create a matrix filled with zeros. The created matrix can have one or
* multiple dimensions.
* @param size The size of each dimension of the matrix
* @param format The matrix storage format
* @returns A matrix filled with zeros
*/
zeros(size: number | number[], format?: string): MathArray | Matrix;
/**
* @param m The x dimension of the matrix
* @param n The y dimension of the matrix
* @param format The matrix storage format
* @returns A matrix filled with zeros
*/
zeros(m: number, n: number, format?: string): MathArray | Matrix;
/*************************************************************************
* Probability functions
************************************************************************/
/**
* Compute the number of ways of picking k unordered outcomes from n
* possibilities. Combinations only takes integer arguments. The
* following condition must be enforced: k <= n.
* @param n Total number of objects in the set
* @param k Number of objects in the subset
* @returns Number of possible combinations
*/
combinations<T extends number | BigNumber>(
n: T,
k: number | BigNumber
): NoLiteralType<T>;
/**
* Compute the factorial of a value Factorial only supports an integer
* value as argument. For matrices, the function is evaluated element
* wise.
* @param n An integer number
* @returns The factorial of n
*/
factorial<T extends number | BigNumber | MathArray | Matrix>(
n: T
): NoLiteralType<T>;
/**
* Compute the gamma function of a value using Lanczos approximation for
* small values, and an extended Stirling approximation for large
* values. For matrices, the function is evaluated element wise.
* @param n A real or complex number
* @returns The gamma of n
*/
gamma(n: number | MathArray | Matrix): number | MathArray | Matrix;
/**
* Calculate the Kullback-Leibler (KL) divergence between two
* distributions
* @param q First vector
* @param p Second vector
* @returns Returns disance between q and p
*/
kldivergence(q: MathArray | Matrix, p: MathArray | Matrix): number;
/**
* Multinomial Coefficients compute the number of ways of picking a1,
* a2, ..., ai unordered outcomes from n possibilities. multinomial
* takes one array of integers as an argument. The following condition
* must be enforced: every ai <= 0
* @param a Integer number of objects in the subset
* @returns multinomial coefficent
*/
multinomial<T extends number | BigNumber>(a: T[]): NoLiteralType<T>;
/**
* Compute the number of ways of obtaining an ordered subset of k
* elements from a set of n elements. Permutations only takes integer
* arguments. The following condition must be enforced: k <= n.
* @param n The number of objects in total
* @param k The number of objects in the subset
* @returns The number of permutations
*/
permutations<T extends number | BigNumber>(
n: T,
k?: number | BigNumber
): NoLiteralType<T>;
/**
* Random pick a value from a one dimensional array. Array element is
* picked using a random function with uniform distribution.
* @param array A one dimensional array
* @param number An int or float
* @param weights An array of ints or floats
* @returns Returns a single random value from array when number is 1 or
* undefined. Returns an array with the configured number of elements
* when number is > 1.
*/
pickRandom(
array: number[],
number?: number,
weights?: number[]
): number | number[];
/**
* Return a random number larger or equal to min and smaller than max
* using a uniform distribution.
* @param size If provided, an array or matrix with given size and
* filled with random values is returned
* @param min Minimum boundary for the random value, included
* @param max Maximum boundary for the random value, excluded
* @returns A random number
*/
random(min?: number, max?: number): number;
random<T extends MathArray | Matrix>(
size: T,
min?: number,
max?: number
): T;
/**
* Return a random integer number larger or equal to min and smaller
* than max using a uniform distribution.
* @param size If provided, an array or matrix with given size and
* filled with random values is returned
* @param min Minimum boundary for the random value, included
* @param max Maximum boundary for the random value, excluded
* @returns A random number
*/
randomInt(min: number, max?: number): number;
randomInt<T extends MathArray | Matrix>(
size: T,
min?: number,
max?: number
): T;
/*************************************************************************
* Relational functions
************************************************************************/
/**
* Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x
* == y. x and y are considered equal when the relative difference
* between x and y is smaller than the configured epsilon. The function
* cannot be used to compare values smaller than approximately 2.22e-16.
* For matrices, the function is evaluated element wise.
* @param x First value to compare
* @param y Second value to compare
* @returns Returns the result of the comparison: 1 when x > y, -1 when
* x < y, and 0 when x == y.
*/
compare(
x: MathType | string,
y: MathType | string
): number | BigNumber | Fraction | MathArray | Matrix;
/**
* Compare two values of any type in a deterministic, natural way. For
* numeric values, the function works the same as math.compare. For
* types of values that can’t be compared mathematically, the function
* compares in a natural way.
* @param x First value to compare
* @param y Second value to compare
* @returns Returns the result of the comparison: 1 when x > y, -1 when
* x < y, and 0 when x == y.
*/
compareNatural(x: any, y: any): number;
/**
* Compare two strings lexically. Comparison is case sensitive. Returns
* 1 when x > y, -1 when x < y, and 0 when x == y. For matrices, the
* function is evaluated element wise.
* @param x First string to compare
* @param y Second string to compare
* @returns Returns the result of the comparison: 1 when x > y, -1 when
* x < y, and 0 when x == y.
*/
compareText(
x: string | MathArray | Matrix,
y: string | MathArray | Matrix
): number | MathArray | Matrix;
/**
* Test element wise whether two matrices are equal. The function
* accepts both matrices and scalar values.
* @param x First matrix to compare
* @param y Second amtrix to compare
* @returns Returns true when the input matrices have the same size and
* each of their elements is equal.
*/
deepEqual(
x: MathType,
y: MathType
): number | BigNumber | Fraction | Complex | Unit | MathArray | Matrix;
/**
* Test whether two values are equal.
*
* The function tests whether the relative difference between x and y is
* smaller than the configured epsilon. The function cannot be used to
* compare values smaller than approximately 2.22e-16. For matrices, the
* function is evaluated element wise. In case of complex numbers, x.re
* must equal y.re, and x.im must equal y.im. Values null and undefined
* are compared strictly, thus null is only equal to null and nothing
* else, and undefined is only equal to undefined and nothing else.
* @param x First value to compare
* @param y Second value to compare
* @returns Returns true when the compared values are equal, else
* returns false
*/
equal(
x: MathType | string,
y: MathType | string
): boolean | MathArray | Matrix;
/**
* Check equality of two strings. Comparison is case sensitive. For
* matrices, the function is evaluated element wise.
* @param x First string to compare
* @param y Second string to compare
* @returns Returns true if the values are equal, and false if not.
*/
equalText(
x: string | MathArray | Matrix,
y: string | MathArray | Matrix
): number | MathArray | Matrix;
/**
* Test whether value x is larger than y. The function returns true when
* x is larger than y and the relative difference between x and y is
* larger than the configured epsilon. The function cannot be used to
* compare values smaller than approximately 2.22e-16. For matrices, the
* function is evaluated element wise.
* @param x First value to compare
* @param y Second value to vcompare
* @returns Returns true when x is larger than y, else returns false
*/
larger(
x: MathType | string,
y: MathType | string
): boolean | MathArray | Matrix;
/**
* Test whether value x is larger or equal to y. The function returns
* true when x is larger than y or the relative difference between x and
* y is smaller than the configured epsilon. The function cannot be used
* to compare values smaller than approximately 2.22e-16. For matrices,
* the function is evaluated element wise.
* @param x First value to compare
* @param y Second value to vcompare
* @returns Returns true when x is larger than or equal to y, else
* returns false
*/
largerEq(
x: MathType | string,
y: MathType | string
): boolean | MathArray | Matrix;
/**
* Test whether value x is smaller than y. The function returns true
* when x is smaller than y and the relative difference between x and y
* is smaller than the configured epsilon. The function cannot be used
* to compare values smaller than approximately 2.22e-16. For matrices,
* the function is evaluated element wise.
* @param x First value to compare
* @param y Second value to vcompare
* @returns Returns true when x is smaller than y, else returns false
*/
smaller(
x: MathType | string,
y: MathType | string
): boolean | MathArray | Matrix;
/**
* Test whether value x is smaller or equal to y. The function returns
* true when x is smaller than y or the relative difference between x
* and y is smaller than the configured epsilon. The function cannot be
* used to compare values smaller than approximately 2.22e-16. For
* matrices, the function is evaluated element wise.
* @param x First value to compare
* @param y Second value to vcompare
* @returns Returns true when x is smaller than or equal to y, else
* returns false
*/
smallerEq(
x: MathType | string,
y: MathType | string
): boolean | MathArray | Matrix;
/**
* Test whether two values are unequal. The function tests whether the
* relative difference between x and y is larger than the configured
* epsilon. The function cannot be used to compare values smaller than
* approximately 2.22e-16. For matrices, the function is evaluated
* element wise. In case of complex numbers, x.re must unequal y.re, or
* x.im must unequal y.im. Values null and undefined are compared
* strictly, thus null is unequal with everything except null, and
* undefined is unequal with everything except undefined.
* @param x First value to compare
* @param y Second value to vcompare
* @returns Returns true when the compared values are unequal, else
* returns false
*/
unequal(
x: MathType | string,
y: MathType | string
): boolean | MathArray | Matrix;
/*************************************************************************
* Set functions
************************************************************************/
/**
* Create the cartesian product of two (multi)sets. Multi-dimension
* arrays will be converted to single-dimension arrays before the
* operation.
* @param a1 A (multi)set
* @param a2 A (multi)set
* @returns The cartesian product of two (multi)sets
*/
setCartesian<T extends MathArray | Matrix>(
a1: T,
a2: MathArray | Matrix
): T;
/**
* Create the difference of two (multi)sets: every element of set1, that
* is not the element of set2. Multi-dimension arrays will be converted
* to single-dimension arrays before the operation
* @param a1 A (multi)set
* @param a2 A (multi)set
* @returns The difference of two (multi)sets
*/
setDifference<T extends MathArray | Matrix>(
a1: T,
a2: MathArray | Matrix
): T;
/**
* Collect the distinct elements of a multiset. A multi-dimension array
* will be converted to a single-dimension array before the operation.
* @param a A multiset
* @returns A set containing the distinct elements of the multiset
*/
setDistinct<T extends MathArray | Matrix>(a: T): T;
/**
* Create the intersection of two (multi)sets. Multi-dimension arrays
* will be converted to single-dimension arrays before the operation.
* @param a1 A (multi)set
* @param a2 A (multi)set
* @returns The intersection of two (multi)sets
*/
setIntersect<T extends MathArray | Matrix>(
a1: T,
a2: MathArray | Matrix
): T;
/**
* Check whether a (multi)set is a subset of another (multi)set. (Every
* element of set1 is the element of set2.) Multi-dimension arrays will
* be converted to single-dimension arrays before the operation.
* @param a1 A (multi)set
* @param a2 A (multi)set
* @returns True if a1 is subset of a2, else false
*/
setIsSubset(a1: MathArray | Matrix, a2: MathArray | Matrix): boolean;
/**
* Count the multiplicity of an element in a multiset. A multi-dimension
* array will be converted to a single-dimension array before the
* operation.
* @param e An element in the multiset
* @param a A multiset
* @returns The number of how many times the multiset contains the
* element
*/
setMultiplicity(
e: number | BigNumber | Fraction | Complex,
a: MathArray | Matrix
): number;
/**
* Create the powerset of a (multi)set. (The powerset contains very
* possible subsets of a (multi)set.) A multi-dimension array will be
* converted to a single-dimension array before the operation.
* @param a A multiset
* @returns The powerset of the (multi)set
*/
setPowerset<T extends MathArray | Matrix>(a: T): T;
/**
* Count the number of elements of a (multi)set. When a second parameter
* is ‘true’, count only the unique values. A multi-dimension array will
* be converted to a single-dimension array before the operation.
* @param a A multiset
* @returns The number of elements of the (multi)set
*/
setSize(a: MathArray | Matrix): number;
/**
* Create the symmetric difference of two (multi)sets. Multi-dimension
* arrays will be converted to single-dimension arrays before the
* operation.
* @param a1 A (multi)set
* @param a2 A (multi)set
* @returns The symmetric difference of two (multi)sets
*/
setSymDifference<T extends MathArray | Matrix>(
a1: T,
a2: MathArray | Matrix
): T;
/**
* Create the union of two (multi)sets. Multi-dimension arrays will be
* converted to single-dimension arrays before the operation.
* @param a1 A (multi)set
* @param a2 A (multi)set
* @returns The union of two (multi)sets
*/
setUnion<T extends MathArray | Matrix>(
a1: T,
a2: MathArray | Matrix
): T;
/*************************************************************************
* Special functions
************************************************************************/
/**
* Compute the erf function of a value using a rational Chebyshev
* approximations for different intervals of x.
* @param x A real number
* @returns The erf of x
*/
erf<T extends number | MathArray | Matrix>(x: T): NoLiteralType<T>;
/*************************************************************************
* Statistics functions
************************************************************************/
/**
* Compute the median absolute deviation of a matrix or a list with
* values. The median absolute deviation is defined as the median of the
* absolute deviations from the median.
* @param array A single matrix or multiple scalar values.
* @returns The median absolute deviation
*/
mad(array: MathArray | Matrix): any;
/**
* Compute the maximum value of a matrix or a list with values. In case
* of a multi dimensional array, the maximum of the flattened array will
* be calculated. When dim is provided, the maximum over the selected
* dimension will be calculated. Parameter dim is zero-based.
* @param args A single matrix or multiple scalar values
* @returns The maximum value
*/
max(...args: MathType[]): any;
/**
* @param A A single matrix
* @param dim The maximum over the selected dimension
* @returns The maximum value
*/
max(A: MathArray | Matrix, dim?: number): any;
/**
* Compute the mean value of matrix or a list with values. In case of a
* multi dimensional array, the mean of the flattened array will be
* calculated. When dim is provided, the maximum over the selected
* dimension will be calculated. Parameter dim is zero-based.
* @param args A single matrix or multiple scalar values
* @returns The mean of all values
*/
mean(...args: MathType[]): any;
/**
* @param A A single matrix
* @param dim The mean over the selected dimension
* @returns The mean of all values
*/
mean(A: MathArray | Matrix, dim?: number): any;
/**
* Compute the median of a matrix or a list with values. The values are
* sorted and the middle value is returned. In case of an even number of
* values, the average of the two middle values is returned. Supported
* types of values are: Number, BigNumber, Unit In case of a (multi
* dimensional) array or matrix, the median of all elements will be
* calculated.
* @param args A single matrix or or multiple scalar values
* @returns The median
*/
median(...args: MathType[]): any;
/**
* Compute the maximum value of a matrix or a list of values. In case of
* a multi dimensional array, the maximum of the flattened array will be
* calculated. When dim is provided, the maximum over the selected
* dimension will be calculated. Parameter dim is zero-based.
* @param args A single matrix or or multiple scalar values
* @returns The minimum value
*/
min(...args: MathType[]): any;
/**
* @param A A single matrix
* @param dim The minimum over the selected dimension
* @returns The minimum value
*/
min(A: MathArray | Matrix, dim?: number): any;
/**
* Computes the mode of a set of numbers or a list with values(numbers
* or characters). If there are more than one modes, it returns a list
* of those values.
* @param args A single matrix
* @returns The mode of all values
*/
mode(...args: MathType[]): any;
/**
* Compute the product of a matrix or a list with values. In case of a
* (multi dimensional) array or matrix, the sum of all elements will be
* calculated.
* @param args A single matrix or multiple scalar values
* @returns The product of all values
*/
prod(...args: MathType[]): any;
/**
* Compute the prob order quantile of a matrix or a list with values.
* The sequence is sorted and the middle value is returned. Supported
* types of sequence values are: Number, BigNumber, Unit Supported types
* of probability are: Number, BigNumber In case of a (multi
* dimensional) array or matrix, the prob order quantile of all elements
* will be calculated.
* @param A A single matrix or array
* @param probOrN prob is the order of the quantile, while N is the
* amount of evenly distributed steps of probabilities; only one of
* these options can be provided
* @param sorted =false is data sorted in ascending order
* @returns Quantile(s)
*/
quantileSeq(
A: MathArray | Matrix,
prob: number | BigNumber | MathArray,
sorted?: boolean
): number | BigNumber | Unit | MathArray;
/**
* Compute the standard deviation of a matrix or a list with values. The
* standard deviations is defined as the square root of the variance:
* std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or
* matrix, the standard deviation over all elements will be calculated.
* Optionally, the type of normalization can be specified as second
* parameter. The parameter normalization can be one of the following
* values: 'unbiased' (default) The sum of squared errors is divided by
* (n - 1) 'uncorrected' The sum of squared errors is divided by n
* 'biased' The sum of squared errors is divided by (n + 1)
* @param array A single matrix or multiple scalar values
* @param normalization Determines how to normalize the variance. Choose
* ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value:
* ‘unbiased’.
* @returns The standard deviation
*/
std(
array: MathArray | Matrix,
normalization?: "unbiased" | "uncorrected" | "biased" | "unbiased"
): number;
/**
* Compute the sum of a matrix or a list with values. In case of a
* (multi dimensional) array or matrix, the sum of all elements will be
* calculated.
* @param args A single matrix or multiple scalar values
* @returns The sum of all values
*/
sum(...args: Array<number | BigNumber | Fraction>): any;
/**
* @param array A single matrix
* @returns The sum of all values
*/
sum(array: MathArray | Matrix): any;
/**
* Compute the variance of a matrix or a list with values. In case of a
* (multi dimensional) array or matrix, the variance over all elements
* will be calculated. Optionally, the type of normalization can be
* specified as second parameter. The parameter normalization can be one
* of the following values: 'unbiased' (default) The sum of squared
* errors is divided by (n - 1) 'uncorrected' The sum of squared errors
* is divided by n 'biased' The sum of squared errors is divided by (n +
* 1) Note that older browser may not like the variable name var. In
* that case, the function can be called as math['var'](...) instead of
* math.variance(...).
* @param args A single matrix or multiple scalar values
* @returns The variance
*/
variance(...args: Array<number | BigNumber | Fraction>): any;
/**
* @param array A single matrix
* @param normalization normalization Determines how to normalize the
* variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’.
* Default value: ‘unbiased’.
* @returns The variance
*/
variance(
array: MathArray | Matrix,
normalization?: "unbiased" | "uncorrected" | "biased" | "unbiased"
): any;
/*************************************************************************
* String functions
************************************************************************/
/**
* Format a value of any type into a string.
* @param value The value to be formatted
* @param options An object with formatting options.
* @param callback A custom formatting function, invoked for all numeric
* elements in value, for example all elements of a matrix, or the real
* and imaginary parts of a complex number. This callback can be used to
* override the built-in numeric notation with any type of formatting.
* Function callback is called with value as parameter and must return a
* string.
* @see http://mathjs.org/docs/reference/functions/format.html
* @returns The formatted value
*/
format(
value: any,
options?: FormatOptions | number | ((item: any) => string),
callback?: ((value: any) => string)
): string;
/**
* Interpolate values into a string template.
* @param template A string containing variable placeholders.
* @param values An object containing variables which will be filled in
* in the template.
* @param precision Number of digits to format numbers. If not provided,
* the value will not be rounded.
* @param options Formatting options, or the number of digits to format
* numbers. See function math.format for a description of all options.
* @returns Interpolated string
*/
print(
template: string,
values: any,
precision?: number,
options?: number | object
): void;
/*************************************************************************
* Trigonometry functions
************************************************************************/
/**
* Calculate the inverse cosine of a value. For matrices, the function
* is evaluated element wise.
* @param x Function input
* @returns The arc cosine of x
*/
acos(x: number): number;
acos(x: BigNumber): BigNumber;
acos(x: Complex): Complex;
acos(x: MathArray): MathArray;
acos(x: Matrix): Matrix;
/**
* Calculate the hyperbolic arccos of a value, defined as acosh(x) =
* ln(sqrt(x^2 - 1) + x). For matrices, the function is evaluated
* element wise.
* @param x Function input
* @returns The hyperbolic arccosine of x
*/
acosh(x: number): number;
acosh(x: BigNumber): BigNumber;
acosh(x: Complex): Complex;
acosh(x: MathArray): MathArray;
acosh(x: Matrix): Matrix;
/**
* Calculate the inverse cotangent of a value. For matrices, the
* function is evaluated element wise.
* @param x Function input
* @returns The arc cotangent of x
*/
acot(x: number): number;
acot(x: BigNumber): BigNumber;
acot(x: MathArray): MathArray;
acot(x: Matrix): Matrix;
/**
* Calculate the hyperbolic arccotangent of a value, defined as acoth(x)
* = (ln((x+1)/x) + ln(x/(x-1))) / 2. For matrices, the function is
* evaluated element wise.
* @param x Function input
* @returns The hyperbolic arccotangent of x
*/
acoth(x: number): number;
acoth(x: BigNumber): BigNumber;
acoth(x: MathArray): MathArray;
acoth(x: Matrix): Matrix;
/**
* Calculate the inverse cosecant of a value. For matrices, the function
* is evaluated element wise.
* @param x Function input
* @returns The arc cosecant of x
*/
acsc(x: number): number;
acsc(x: BigNumber): BigNumber;
acsc(x: MathArray): MathArray;
acsc(x: Matrix): Matrix;
/**
* Calculate the hyperbolic arccosecant of a value, defined as acsch(x)
* = ln(1/x + sqrt(1/x^2 + 1)). For matrices, the function is evaluated
* element wise.
* @param x Function input
* @returns The hyperbolic arccosecant of x
*/
acsch(x: number): number;
acsch(x: BigNumber): BigNumber;
acsch(x: MathArray): MathArray;
acsch(x: Matrix): Matrix;
/**
* Calculate the inverse secant of a value. For matrices, the function
* is evaluated element wise.
* @param x Function input
* @returns The arc secant of x
*/
asec(x: number): number;
asec(x: BigNumber): BigNumber;
asec(x: MathArray): MathArray;
asec(x: Matrix): Matrix;
/**
* Calculate the hyperbolic arcsecant of a value, defined as asech(x) =
* ln(sqrt(1/x^2 - 1) + 1/x). For matrices, the function is evaluated
* element wise.
* @param x Function input
* @returns The hyperbolic arcsecant of x
*/
asech(x: number): number;
asech(x: BigNumber): BigNumber;
asech(x: MathArray): MathArray;
asech(x: Matrix): Matrix;
/**
* Calculate the inverse sine of a value. For matrices, the function is
* evaluated element wise.
* @param x Function input
* @returns The arc sine of x
*/
asin(x: number): number;
asin(x: BigNumber): BigNumber;
asin(x: Complex): Complex;
asin(x: MathArray): MathArray;
asin(x: Matrix): Matrix;
/**
* Calculate the hyperbolic arcsine of a value, defined as asinh(x) =
* ln(x + sqrt(x^2 + 1)). For matrices, the function is evaluated
* element wise.
* @param x Function input
* @returns The hyperbolic arcsine of x
*/
asinh(x: number): number;
asinh(x: BigNumber): BigNumber;
asinh(x: MathArray): MathArray;
asinh(x: Matrix): Matrix;
/**
* Calculate the inverse tangent of a value. For matrices, the function
* is evaluated element wise.
* @param x Function input
* @returns The arc tangent of x
*/
atan(x: number): number;
atan(x: BigNumber): BigNumber;
atan(x: MathArray): MathArray;
atan(x: Matrix): Matrix;
/**
* Calculate the inverse tangent function with two arguments, y/x. By
* providing two arguments, the right quadrant of the computed angle can
* be determined. For matrices, the function is evaluated element wise.
* @param x Function input
* @returns Four quadrant inverse tangent
*/
atan2(y: number, x: number): number;
atan2(y: MathArray | Matrix, x: MathArray | Matrix): MathArray | Matrix;
/**
* Calculate the hyperbolic arctangent of a value, defined as atanh(x) =
* ln((1 + x)/(1 - x)) / 2. For matrices, the function is evaluated
* element wise.
* @param x Function input
* @returns The hyperbolic arctangent of x
*/
atanh(x: number): number;
atanh(x: BigNumber): BigNumber;
atanh(x: MathArray): MathArray;
atanh(x: Matrix): Matrix;
/**
* Calculate the cosine of a value. For matrices, the function is
* evaluated element wise.
* @param x Function input
* @returns The cosine of x
*/
cos(x: number | Unit): number;
cos(x: BigNumber): BigNumber;
cos(x: Complex): Complex;
cos(x: MathArray): MathArray;
cos(x: Matrix): Matrix;
/**
* Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2
* * (exp(x) + exp(-x)). For matrices, the function is evaluated element
* wise.
* @param x Function input
* @returns The hyperbolic cosine of x
*/
cosh(x: number | Unit): number;
cosh(x: BigNumber): BigNumber;
cosh(x: Complex): Complex;
cosh(x: MathArray): MathArray;
cosh(x: Matrix): Matrix;
/**
* Calculate the cotangent of a value. cot(x) is defined as 1 / tan(x).
* For matrices, the function is evaluated element wise.
* @param x Function input
* @returns The cotangent of x
*/
cot(x: number | Unit): number;
cot(x: Complex): Complex;
cot(x: MathArray): MathArray;
cot(x: Matrix): Matrix;
/**
* Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1
* / tanh(x). For matrices, the function is evaluated element wise.
* @param x Function input
* @returns The hyperbolic cotangent of x
*/
coth(x: number | Unit): number;
coth(x: Complex): Complex;
coth(x: MathArray): MathArray;
coth(x: Matrix): Matrix;
/**
* Calculate the cosecant of a value, defined as csc(x) = 1/sin(x). For
* matrices, the function is evaluated element wise.
* @param x Function input
* @returns The cosecant hof x
*/
csc(x: number | Unit): number;
csc(x: Complex): Complex;
csc(x: MathArray): MathArray;
csc(x: Matrix): Matrix;
/**
* Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1
* / sinh(x). For matrices, the function is evaluated element wise.
* @param x Function input
* @returns The hyperbolic cosecant of x
*/
csch(x: number | Unit): number;
csch(x: Complex): Complex;
csch(x: MathArray): MathArray;
csch(x: Matrix): Matrix;
/**
* Calculate the secant of a value, defined as sec(x) = 1/cos(x). For
* matrices, the function is evaluated element wise.
* @param x Function input
* @returns The secant of x
*/
sec(x: number | Unit): number;
sec(x: Complex): Complex;
sec(x: MathArray): MathArray;
sec(x: Matrix): Matrix;
/**
* Calculate the hyperbolic secant of a value, defined as sech(x) = 1 /
* cosh(x). For matrices, the function is evaluated element wise.
* @param x Function input
* @returns The hyperbolic secant of x
*/
sech(x: number | Unit): number;
sech(x: Complex): Complex;
sech(x: MathArray): MathArray;
sech(x: Matrix): Matrix;
/**
* Calculate the sine of a value. For matrices, the function is
* evaluated element wise.
* @param x Function input
* @returns The sine of x
*/
sin(x: number | Unit): number;
sin(x: BigNumber): BigNumber;
sin(x: Complex): Complex;
sin(x: MathArray): MathArray;
sin(x: Matrix): Matrix;
/**
* Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 *
* (exp(x) - exp(-x)). For matrices, the function is evaluated element
* wise.
* @param x Function input
* @returns The hyperbolic sine of x
*/
sinh(x: number | Unit): number;
sinh(x: BigNumber): BigNumber;
sinh(x: Complex): Complex;
sinh(x: MathArray): MathArray;
sinh(x: Matrix): Matrix;
/**
* Calculate the tangent of a value. tan(x) is equal to sin(x) / cos(x).
* For matrices, the function is evaluated element wise.
* @param x Function input
* @returns The tangent of x
*/
tan(x: number | Unit): number;
tan(x: BigNumber): BigNumber;
tan(x: Complex): Complex;
tan(x: MathArray): MathArray;
tan(x: Matrix): Matrix;
/**
* Calculate the hyperbolic tangent of a value, defined as tanh(x) =
* (exp(2 * x) - 1) / (exp(2 * x) + 1). For matrices, the function is
* evaluated element wise.
* @param x Function input
* @returns The hyperbolic tangent of x
*/
tanh(x: number | Unit): number;
tanh(x: BigNumber): BigNumber;
tanh(x: Complex): Complex;
tanh(x: MathArray): MathArray;
tanh(x: Matrix): Matrix;
/*************************************************************************
* Unit functions
************************************************************************/
/**
* Change the unit of a value. For matrices, the function is evaluated
* element wise.
* @param x The unit to be converted.
* @param unit New unit. Can be a string like "cm" or a unit without
* value.
* @returns Value with changed, fixed unit
*/
to(
x: Unit | MathArray | Matrix,
unit: Unit | string
): Unit | MathArray | Matrix;
/*************************************************************************
* Utils functions
************************************************************************/
/**
* Clone an object.
* @param x Object to be cloned
* @returns A clone of object x
*/
clone(x: any): any;
/**
* Test whether a value is an integer number. The function supports
* number, BigNumber, and Fraction. The function is evaluated
* element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x contains a numeric, integer value.
* Throws an error in case of an unknown data type.
*/
isInteger(
x: number | BigNumber | Fraction | MathArray | Matrix
): boolean;
/**
* Test whether a value is NaN (not a number). The function supports
* types number, BigNumber, Fraction, Unit and Complex. The function is
* evaluated element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x is NaN. Throws an error in case of an
* unknown data type.
*/
isNaN(
x: number | BigNumber | Fraction | MathArray | Matrix | Unit
): boolean;
/**
* Test whether a value is negative: smaller than zero. The function
* supports types number, BigNumber, Fraction, and Unit. The function is
* evaluated element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x is larger than zero. Throws an error in
* case of an unknown data type.
*/
isNegative(
x: number | BigNumber | Fraction | MathArray | Matrix | Unit
): boolean;
/**
* Test whether a value is an numeric value. The function is evaluated
* element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x is a number, BigNumber, Fraction, or
* boolean. Returns false for other types. Throws an error in case of
* unknown types.
*/
isNumeric(x: any): x is number | BigNumber | Fraction | boolean;
/**
* Test whether a value is positive: larger than zero. The function
* supports types number, BigNumber, Fraction, and Unit. The function is
* evaluated element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x is larger than zero. Throws an error in
* case of an unknown data type.
*/
isPositive(
x: number | BigNumber | Fraction | MathArray | Matrix | Unit
): boolean;
/**
* Test whether a value is prime: has no divisors other than itself and
* one. The function supports type number, bignumber. The function is
* evaluated element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x is larger than zero. Throws an error in
* case of an unknown data type.
*/
isPrime(x: number | BigNumber | MathArray | Matrix): boolean;
/**
* Test whether a value is zero. The function can check for zero for
* types number, BigNumber, Fraction, Complex, and Unit. The function is
* evaluated element-wise in case of Array or Matrix input.
* @param x Value to be tested
* @returns Returns true when x is zero. Throws an error in case of an
* unknown data type.
*/
isZero(
x:
| number
| BigNumber
| Fraction
| MathArray
| Matrix
| Unit
| Complex
): boolean;
/**
* Determine the type of a variable.
* @param x The variable for which to test the type
* @returns Returns the name of the type. Primitive types are lower
* case, non-primitive types are upper-camel-case. For example ‘number’,
* ‘string’, ‘Array’, ‘Date’.
*/
typeOf(x: any): string;
/**
* Import functions from an object or a module
* To avoid errors when using one of the imported functions extend module like this:
*
* @example
* // imported_math_functions.ts
* declare module 'mathjs' {
* interface MathJsStatic {
* hello(a: number): number;
* }
* }
*
* @param object An object with functions to be imported.
* @param options An object with import options.
*/
import(object: ImportObject | ImportObject[], options: ImportOptions): void;
}
/*************************************************************************
* Factory and Dependencies
************************************************************************/
interface FactoryDependencies {
create: (factories: FactoryFunctionMap, config: ConfigOptions) => Partial<MathJsStatic>;
factory: <T>(
name: string,
dependencies: MathJsFunctionName[],
create: (injected: Partial<MathJsStatic>) => T,
meta?: any,
) => FactoryFunction<T>;
all: FactoryFunctionMap;
typedDependencies: FactoryFunctionMap;
ResultSetDependencies: FactoryFunctionMap;
BigNumberDependencies: FactoryFunctionMap;
ComplexDependencies: FactoryFunctionMap;
FractionDependencies: FactoryFunctionMap;
RangeDependencies: FactoryFunctionMap;
MatrixDependencies: FactoryFunctionMap;
DenseMatrixDependencies: FactoryFunctionMap;
cloneDependencies: FactoryFunctionMap;
isIntegerDependencies: FactoryFunctionMap;
isNegativeDependencies: FactoryFunctionMap;
isNumericDependencies: FactoryFunctionMap;
hasNumericValueDependencies: FactoryFunctionMap;
isPositiveDependencies: FactoryFunctionMap;
isZeroDependencies: FactoryFunctionMap;
isNaNDependencies: FactoryFunctionMap;
typeOfDependencies: FactoryFunctionMap;
typeofDependencies: FactoryFunctionMap;
equalScalarDependencies: FactoryFunctionMap;
SparseMatrixDependencies: FactoryFunctionMap;
numberDependencies: FactoryFunctionMap;
stringDependencies: FactoryFunctionMap;
booleanDependencies: FactoryFunctionMap;
bignumberDependencies: FactoryFunctionMap;
complexDependencies: FactoryFunctionMap;
fractionDependencies: FactoryFunctionMap;
matrixDependencies: FactoryFunctionMap;
splitUnitDependencies: FactoryFunctionMap;
unaryMinusDependencies: FactoryFunctionMap;
unaryPlusDependencies: FactoryFunctionMap;
absDependencies: FactoryFunctionMap;
applyDependencies: FactoryFunctionMap;
addScalarDependencies: FactoryFunctionMap;
cbrtDependencies: FactoryFunctionMap;
ceilDependencies: FactoryFunctionMap;
cubeDependencies: FactoryFunctionMap;
expDependencies: FactoryFunctionMap;
expm1Dependencies: FactoryFunctionMap;
fixDependencies: FactoryFunctionMap;
floorDependencies: FactoryFunctionMap;
gcdDependencies: FactoryFunctionMap;
lcmDependencies: FactoryFunctionMap;
log10Dependencies: FactoryFunctionMap;
log2Dependencies: FactoryFunctionMap;
modDependencies: FactoryFunctionMap;
multiplyScalarDependencies: FactoryFunctionMap;
multiplyDependencies: FactoryFunctionMap;
nthRootDependencies: FactoryFunctionMap;
signDependencies: FactoryFunctionMap;
sqrtDependencies: FactoryFunctionMap;
squareDependencies: FactoryFunctionMap;
subtractDependencies: FactoryFunctionMap;
xgcdDependencies: FactoryFunctionMap;
dotMultiplyDependencies: FactoryFunctionMap;
bitAndDependencies: FactoryFunctionMap;
bitNotDependencies: FactoryFunctionMap;
bitOrDependencies: FactoryFunctionMap;
bitXorDependencies: FactoryFunctionMap;
argDependencies: FactoryFunctionMap;
conjDependencies: FactoryFunctionMap;
imDependencies: FactoryFunctionMap;
reDependencies: FactoryFunctionMap;
notDependencies: FactoryFunctionMap;
orDependencies: FactoryFunctionMap;
xorDependencies: FactoryFunctionMap;
concatDependencies: FactoryFunctionMap;
columnDependencies: FactoryFunctionMap;
crossDependencies: FactoryFunctionMap;
diagDependencies: FactoryFunctionMap;
eyeDependencies: FactoryFunctionMap;
filterDependencies: FactoryFunctionMap;
flattenDependencies: FactoryFunctionMap;
forEachDependencies: FactoryFunctionMap;
getMatrixDataTypeDependencies: FactoryFunctionMap;
identityDependencies: FactoryFunctionMap;
kronDependencies: FactoryFunctionMap;
mapDependencies: FactoryFunctionMap;
onesDependencies: FactoryFunctionMap;
rangeDependencies: FactoryFunctionMap;
reshapeDependencies: FactoryFunctionMap;
resizeDependencies: FactoryFunctionMap;
rowDependencies: FactoryFunctionMap;
sizeDependencies: FactoryFunctionMap;
squeezeDependencies: FactoryFunctionMap;
subsetDependencies: FactoryFunctionMap;
transposeDependencies: FactoryFunctionMap;
ctransposeDependencies: FactoryFunctionMap;
zerosDependencies: FactoryFunctionMap;
erfDependencies: FactoryFunctionMap;
modeDependencies: FactoryFunctionMap;
prodDependencies: FactoryFunctionMap;
formatDependencies: FactoryFunctionMap;
printDependencies: FactoryFunctionMap;
toDependencies: FactoryFunctionMap;
isPrimeDependencies: FactoryFunctionMap;
numericDependencies: FactoryFunctionMap;
divideScalarDependencies: FactoryFunctionMap;
powDependencies: FactoryFunctionMap;
roundDependencies: FactoryFunctionMap;
logDependencies: FactoryFunctionMap;
log1pDependencies: FactoryFunctionMap;
nthRootsDependencies: FactoryFunctionMap;
dotPowDependencies: FactoryFunctionMap;
dotDivideDependencies: FactoryFunctionMap;
lsolveDependencies: FactoryFunctionMap;
usolveDependencies: FactoryFunctionMap;
leftShiftDependencies: FactoryFunctionMap;
rightArithShiftDependencies: FactoryFunctionMap;
rightLogShiftDependencies: FactoryFunctionMap;
andDependencies: FactoryFunctionMap;
compareDependencies: FactoryFunctionMap;
compareNaturalDependencies: FactoryFunctionMap;
compareTextDependencies: FactoryFunctionMap;
equalDependencies: FactoryFunctionMap;
equalTextDependencies: FactoryFunctionMap;
smallerDependencies: FactoryFunctionMap;
smallerEqDependencies: FactoryFunctionMap;
largerDependencies: FactoryFunctionMap;
largerEqDependencies: FactoryFunctionMap;
deepEqualDependencies: FactoryFunctionMap;
unequalDependencies: FactoryFunctionMap;
partitionSelectDependencies: FactoryFunctionMap;
sortDependencies: FactoryFunctionMap;
maxDependencies: FactoryFunctionMap;
minDependencies: FactoryFunctionMap;
ImmutableDenseMatrixDependencies: FactoryFunctionMap;
IndexDependencies: FactoryFunctionMap;
FibonacciHeapDependencies: FactoryFunctionMap;
SpaDependencies: FactoryFunctionMap;
UnitDependencies: FactoryFunctionMap;
unitDependencies: FactoryFunctionMap;
sparseDependencies: FactoryFunctionMap;
createUnitDependencies: FactoryFunctionMap;
acosDependencies: FactoryFunctionMap;
acoshDependencies: FactoryFunctionMap;
acotDependencies: FactoryFunctionMap;
acothDependencies: FactoryFunctionMap;
acscDependencies: FactoryFunctionMap;
acschDependencies: FactoryFunctionMap;
asecDependencies: FactoryFunctionMap;
asechDependencies: FactoryFunctionMap;
asinDependencies: FactoryFunctionMap;
asinhDependencies: FactoryFunctionMap;
atanDependencies: FactoryFunctionMap;
atan2Dependencies: FactoryFunctionMap;
atanhDependencies: FactoryFunctionMap;
cosDependencies: FactoryFunctionMap;
coshDependencies: FactoryFunctionMap;
cotDependencies: FactoryFunctionMap;
cothDependencies: FactoryFunctionMap;
cscDependencies: FactoryFunctionMap;
cschDependencies: FactoryFunctionMap;
secDependencies: FactoryFunctionMap;
sechDependencies: FactoryFunctionMap;
sinDependencies: FactoryFunctionMap;
sinhDependencies: FactoryFunctionMap;
tanDependencies: FactoryFunctionMap;
tanhDependencies: FactoryFunctionMap;
setCartesianDependencies: FactoryFunctionMap;
setDifferenceDependencies: FactoryFunctionMap;
setDistinctDependencies: FactoryFunctionMap;
setIntersectDependencies: FactoryFunctionMap;
setIsSubsetDependencies: FactoryFunctionMap;
setMultiplicityDependencies: FactoryFunctionMap;
setPowersetDependencies: FactoryFunctionMap;
setSizeDependencies: FactoryFunctionMap;
setSymDifferenceDependencies: FactoryFunctionMap;
setUnionDependencies: FactoryFunctionMap;
addDependencies: FactoryFunctionMap;
hypotDependencies: FactoryFunctionMap;
normDependencies: FactoryFunctionMap;
dotDependencies: FactoryFunctionMap;
traceDependencies: FactoryFunctionMap;
indexDependencies: FactoryFunctionMap;
NodeDependencies: FactoryFunctionMap;
AccessorNodeDependencies: FactoryFunctionMap;
ArrayNodeDependencies: FactoryFunctionMap;
AssignmentNodeDependencies: FactoryFunctionMap;
BlockNodeDependencies: FactoryFunctionMap;
ConditionalNodeDependencies: FactoryFunctionMap;
ConstantNodeDependencies: FactoryFunctionMap;
FunctionAssignmentNodeDependencies: FactoryFunctionMap;
IndexNodeDependencies: FactoryFunctionMap;
ObjectNodeDependencies: FactoryFunctionMap;
OperatorNodeDependencies: FactoryFunctionMap;
ParenthesisNodeDependencies: FactoryFunctionMap;
RangeNodeDependencies: FactoryFunctionMap;
RelationalNodeDependencies: FactoryFunctionMap;
SymbolNodeDependencies: FactoryFunctionMap;
FunctionNodeDependencies: FactoryFunctionMap;
parseDependencies: FactoryFunctionMap;
compileDependencies: FactoryFunctionMap;
evaluateDependencies: FactoryFunctionMap;
evalDependencies: FactoryFunctionMap;
ParserDependencies: FactoryFunctionMap;
parserDependencies: FactoryFunctionMap;
lupDependencies: FactoryFunctionMap;
qrDependencies: FactoryFunctionMap;
sluDependencies: FactoryFunctionMap;
lusolveDependencies: FactoryFunctionMap;
HelpDependencies: FactoryFunctionMap;
ChainDependencies: FactoryFunctionMap;
helpDependencies: FactoryFunctionMap;
chainDependencies: FactoryFunctionMap;
detDependencies: FactoryFunctionMap;
invDependencies: FactoryFunctionMap;
expmDependencies: FactoryFunctionMap;
sqrtmDependencies: FactoryFunctionMap;
divideDependencies: FactoryFunctionMap;
distanceDependencies: FactoryFunctionMap;
intersectDependencies: FactoryFunctionMap;
sumDependencies: FactoryFunctionMap;
meanDependencies: FactoryFunctionMap;
medianDependencies: FactoryFunctionMap;
madDependencies: FactoryFunctionMap;
varianceDependencies: FactoryFunctionMap;
varDependencies: FactoryFunctionMap;
quantileSeqDependencies: FactoryFunctionMap;
stdDependencies: FactoryFunctionMap;
combinationsDependencies: FactoryFunctionMap;
gammaDependencies: FactoryFunctionMap;
factorialDependencies: FactoryFunctionMap;
kldivergenceDependencies: FactoryFunctionMap;
multinomialDependencies: FactoryFunctionMap;
permutationsDependencies: FactoryFunctionMap;
pickRandomDependencies: FactoryFunctionMap;
randomDependencies: FactoryFunctionMap;
randomIntDependencies: FactoryFunctionMap;
stirlingS2Dependencies: FactoryFunctionMap;
bellNumbersDependencies: FactoryFunctionMap;
catalanDependencies: FactoryFunctionMap;
compositionDependencies: FactoryFunctionMap;
simplifyDependencies: FactoryFunctionMap;
derivativeDependencies: FactoryFunctionMap;
rationalizeDependencies: FactoryFunctionMap;
reviverDependencies: FactoryFunctionMap;
eDependencies: FactoryFunctionMap;
EDependencies: FactoryFunctionMap;
falseDependencies: FactoryFunctionMap;
iDependencies: FactoryFunctionMap;
InfinityDependencies: FactoryFunctionMap;
LN10Dependencies: FactoryFunctionMap;
LN2Dependencies: FactoryFunctionMap;
LOG10EDependencies: FactoryFunctionMap;
LOG2EDependencies: FactoryFunctionMap;
NaNDependencies: FactoryFunctionMap;
nullDependencies: FactoryFunctionMap;
phiDependencies: FactoryFunctionMap;
piDependencies: FactoryFunctionMap;
PIDependencies: FactoryFunctionMap;
SQRT1_2Dependencies: FactoryFunctionMap;
SQRT2Dependencies: FactoryFunctionMap;
tauDependencies: FactoryFunctionMap;
trueDependencies: FactoryFunctionMap;
versionDependencies: FactoryFunctionMap;
atomicMassDependencies: FactoryFunctionMap;
avogadroDependencies: FactoryFunctionMap;
bohrMagnetonDependencies: FactoryFunctionMap;
bohrRadiusDependencies: FactoryFunctionMap;
boltzmannDependencies: FactoryFunctionMap;
classicalElectronRadiusDependencies: FactoryFunctionMap;
conductanceQuantumDependencies: FactoryFunctionMap;
coulombDependencies: FactoryFunctionMap;
deuteronMassDependencies: FactoryFunctionMap;
efimovFactorDependencies: FactoryFunctionMap;
electricConstantDependencies: FactoryFunctionMap;
electronMassDependencies: FactoryFunctionMap;
elementaryChargeDependencies: FactoryFunctionMap;
faradayDependencies: FactoryFunctionMap;
fermiCouplingDependencies: FactoryFunctionMap;
fineStructureDependencies: FactoryFunctionMap;
firstRadiationDependencies: FactoryFunctionMap;
gasConstantDependencies: FactoryFunctionMap;
gravitationConstantDependencies: FactoryFunctionMap;
gravityDependencies: FactoryFunctionMap;
hartreeEnergyDependencies: FactoryFunctionMap;
inverseConductanceQuantumDependencies: FactoryFunctionMap;
klitzingDependencies: FactoryFunctionMap;
loschmidtDependencies: FactoryFunctionMap;
magneticConstantDependencies: FactoryFunctionMap;
magneticFluxQuantumDependencies: FactoryFunctionMap;
molarMassDependencies: FactoryFunctionMap;
molarMassC12Dependencies: FactoryFunctionMap;
molarPlanckConstantDependencies: FactoryFunctionMap;
molarVolumeDependencies: FactoryFunctionMap;
neutronMassDependencies: FactoryFunctionMap;
nuclearMagnetonDependencies: FactoryFunctionMap;
planckChargeDependencies: FactoryFunctionMap;
planckConstantDependencies: FactoryFunctionMap;
planckLengthDependencies: FactoryFunctionMap;
planckMassDependencies: FactoryFunctionMap;
planckTemperatureDependencies: FactoryFunctionMap;
planckTimeDependencies: FactoryFunctionMap;
protonMassDependencies: FactoryFunctionMap;
quantumOfCirculationDependencies: FactoryFunctionMap;
reducedPlanckConstantDependencies: FactoryFunctionMap;
rydbergDependencies: FactoryFunctionMap;
sackurTetrodeDependencies: FactoryFunctionMap;
secondRadiationDependencies: FactoryFunctionMap;
speedOfLightDependencies: FactoryFunctionMap;
stefanBoltzmannDependencies: FactoryFunctionMap;
thomsonCrossSectionDependencies: FactoryFunctionMap;
vacuumImpedanceDependencies: FactoryFunctionMap;
weakMixingAngleDependencies: FactoryFunctionMap;
wienDisplacementDependencies: FactoryFunctionMap;
applyTransformDependencies: FactoryFunctionMap;
columnTransformDependencies: FactoryFunctionMap;
filterTransformDependencies: FactoryFunctionMap;
forEachTransformDependencies: FactoryFunctionMap;
indexTransformDependencies: FactoryFunctionMap;
mapTransformDependencies: FactoryFunctionMap;
maxTransformDependencies: FactoryFunctionMap;
meanTransformDependencies: FactoryFunctionMap;
minTransformDependencies: FactoryFunctionMap;
rangeTransformDependencies: FactoryFunctionMap;
rowTransformDependencies: FactoryFunctionMap;
subsetTransformDependencies: FactoryFunctionMap;
concatTransformDependencies: FactoryFunctionMap;
stdTransformDependencies: FactoryFunctionMap;
sumTransformDependencies: FactoryFunctionMap;
varianceTransformDependencies: FactoryFunctionMap;
}
interface Matrix {
type: string;
storage(): string;
datatype(): string;
create(data: MathArray, datatype?: string): void;
density(): number;
subset(index: Index, replacement?: any, defaultValue?: any): Matrix;
get(index: number[]): any;
set(
index: number[],
value: any,
defaultValue?: number | string
): Matrix;
resize(
size: MathArray | Matrix,
defaultValue?: number | string
): Matrix;
clone(): Matrix;
size(): number[];
map(
callback: (a: any, b: number, c: Matrix) => any,
skipZeros?: boolean
): Matrix;
forEach(
callback: (a: any, b: number, c: Matrix) => void,
skipZeros?: boolean
): void;
toArray(): MathArray | Matrix;
valueOff(): MathArray | Matrix;
format(options?: FormatOptions | number | ((value: any) => string)): string;
toString(): string;
toJSON(): any;
diagonal(k?: number | BigNumber): any[];
swapRows(i: number, j: number): Matrix;
}
interface BigNumber extends Decimal {} // tslint:disable-line no-empty-interface
interface Fraction {
s: number;
n: number;
d: number;
}
interface Complex {
re: number;
im: number;
clone(): Complex;
equals(other: Complex): boolean;
format(precision?: number): string;
fromJSON(json: object): Complex;
fromPolar(polar: object): Complex;
fromPolar(r: number, phi: number): Complex;
toJSON(): object;
toPolar(): PolarCoordinates;
toString(): string;
compare(a: Complex, b: Complex): number;
}
interface PolarCoordinates {
r: number;
phi: number;
}
interface MathJSON {
mathjs?: string;
value: number;
unit: string;
fixPrefix?: boolean;
}
interface Unit {
valueOf(): string;
clone(): Unit;
hasBase(base: any): boolean;
equalBase(unit: Unit): boolean;
equals(unit: Unit): boolean;
multiply(unit: Unit): Unit;
divide(unit: Unit): Unit;
pow(unit: Unit): Unit;
abs(unit: Unit): Unit;
to(unit: string): Unit;
toNumber(unit: string): number;
toNumeric(unit: string): number | Fraction | BigNumber;
toSI(): Unit;
toString(): string;
toJSON(): MathJSON;
formatUnits(): string;
format(options: FormatOptions): string;
splitUnit(parts: ReadonlyArray<string | Unit>): Unit[];
}
interface CreateUnitOptions {
prefixes?: "none" | "short" | "long" | "binary_short" | "binary_long";
aliases?: string[];
offset?: number;
override?: boolean;
}
interface UnitDefinition {
definition?: string | Unit;
prefixes?: string;
offset?: number;
aliases?: string[];
}
interface Index {} // tslint:disable-line no-empty-interface
interface EvalFunction {
evaluate(scope?: any): any;
}
interface MathNode {
isNode: boolean;
isAccessorNode?: boolean;
isArrayNode?: boolean;
isAssignmentNode?: boolean;
isBlockNode?: boolean;
isConditionalnode?: boolean;
isConstantNode?: boolean;
isFunctionAssignmentNode?: boolean;
isFunctionNode?: boolean;
isIndexNode?: boolean;
isObjectNode?: boolean;
isOperatorNode?: boolean;
isParenthesisNode?: boolean;
isRangeNode?: boolean;
isSymbolNode?: boolean;
isUpdateNode?: boolean;
comment?: string;
content?: MathNode;
op?: string;
fn?: string;
args?: MathNode[];
type: string;
name?: string;
value?: any;
/**
* Create a shallow clone of the node. The node itself is cloned, its
* childs are not cloned.
*/
clone(): MathNode;
/**
* Create a deep clone of the node. Both the node as well as all its
* childs are cloned recursively.
*/
cloneDeep(): MathNode;
/**
* Compile an expression into optimized JavaScript code. compile returns
* an object with a function evaluate([scope]) to evaluate. Example:
*/
compile(): EvalFunction;
/**
* Compile and eval an expression, this is the equivalent of doing
* node.compile().evaluate(scope). Example:
*/
evaluate(expr?: any): any;
/**
* Test whether this node equals an other node. Does a deep comparison
* of the values of both nodes.
*/
equals(other: MathNode): boolean;
/**
*
* Filter nodes in an expression tree. The callback function is called
* as callback(node: MathNode, path: string, parent: MathNode) : boolean
* for every node in the tree, and must return a boolean. The function
* filter returns an array with nodes for which the test returned true.
* Parameter path is a string containing a relative JSON Path.
*
* Example:
*
* ```
* var node = math.parse('x^2 + x/4 + 3*y');
* var filtered = node.filter(function (node) {
* return node.isSymbolMathNode && node.name == 'x';
* });
* // returns an array with two entries: two SymbolMathNodes 'x'
* ```
*
* The callback function is called as callback(node: MathNode, path:
* string, parent: MathNode) : boolean for every node in the tree, and
* must return a boolean. The function filter returns an array with
* nodes for which the test returned true. Parameter path is a string
* containing a relative JSON Path.
* @return Returns an array with nodes for which test returned true
*/
filter(
callback: (node: MathNode, path: string, parent: MathNode) => any
): MathNode[];
/**
* [forEach description]
*/
forEach(
callback: (node: MathNode, path: string, parent: MathNode) => any
): MathNode[];
/**
* Transform a node. Creates a new MathNode having it’s child's be the
* results of calling the provided callback function for each of the
* child's of the original node. The callback function is called as
* `callback(child: MathNode, path: string, parent: MathNode)` and must
* return a MathNode. Parameter path is a string containing a relative
* JSON Path.
*
*
* See also transform, which is a recursive version of map.
*/
map(
callback: (
node: MathNode,
path: string,
parent: MathNode
) => MathNode
): MathNode;
/**
* Get a HTML representation of the parsed expression.
*/
toHtml(options?: object): string;
/**
* Get a string representation of the parsed expression. This is not
* exactly the same as the original input.
*/
toString(options?: object): string;
/**
* Get a LaTeX representation of the expression.
*/
toTex(options?: object): string;
/**
* Recursively transform an expression tree via a transform function.
* Similar to Array.map, but recursively executed on all nodes in the
* expression tree. The callback function is a mapping function
* accepting a node, and returning a replacement for the node or the
* original node. Function callback is called as callback(node:
* MathNode, path: string, parent: MathNode) for every node in the tree,
* and must return a MathNode. Parameter path is a string containing a
* relative JSON Path.
*
* For example, to replace all nodes of type SymbolMathNode having name
* ‘x’ with a ConstantMathNode with value 3:
* ```js
* var node = math.parse('x^2 + 5*x');
* var transformed = node.transform(function (node, path, parent) {
* if (node.SymbolMathNode && node.name == 'x') {
* return new math.expression.node.ConstantMathNode(3);
* }
* else {
* return node;
* }
* });
* transformed.toString(); // returns '(3 ^ 2) + (5 * 3)'
* ```
*/
transform(
callback: (
node: MathNode,
path: string,
parent: MathNode
) => MathNode
): MathNode;
/**
* `traverse(callback)`
*
* Recursively traverse all nodes in a node tree. Executes given
* callback for this node and each of its child nodes. Similar to
* Array.forEach, except recursive. The callback function is a mapping
* function accepting a node, and returning a replacement for the node
* or the original node. Function callback is called as callback(node:
* MathNode, path: string, parent: MathNode) for every node in the tree.
* Parameter path is a string containing a relative JSON Path. Example:
*
* ```
* var node = math.parse('3 * x + 2');
* node.traverse(function (node, path, parent) {
* switch (node.type) {
* case 'OperatorMathNode': console.log(node.type, node.op); break;
* case 'ConstantMathNode': console.log(node.type, node.value); break;
* case 'SymbolMathNode': console.log(node.type, node.name); break;
* default: console.log(node.type);
* }
* });
* // outputs:
* // OperatorMathNode +
* // OperatorMathNode *
* // ConstantMathNode 3
* // SymbolMathNode x
* // ConstantMathNode 2
* ```
*/
traverse(
callback: (node: MathNode, path: string, parent: MathNode) => void
): any;
}
interface Parser {
evaluate(expr: string): any;
get(variable: string): any;
getAll(): { [key: string]: any; };
set: (variable: string, value: any) => void;
clear: () => void;
}
interface Distribution {
random(size: any, min?: any, max?: any): any;
randomInt(min: any, max?: any): any;
pickRandom(array: any): any;
}
interface FormatOptions {
/**
* Number notation. Choose from: 'fixed' Always use regular number
* notation. For example '123.40' and '14000000' 'exponential' Always
* use exponential notation. For example '1.234e+2' and '1.4e+7' 'auto'
* (default) Regular number notation for numbers having an absolute
* value between lower and upper bounds, and uses exponential notation
* elsewhere. Lower bound is included, upper bound is excluded. For
* example '123.4' and '1.4e7'.
*/
notation?: "fixed" | "exponential" | "engineering" | "auto";
/**
* A number between 0 and 16 to round the digits of the number. In case
* of notations 'exponential' and 'auto', precision defines the total
* number of significant digits returned and is undefined by default. In
* case of notation 'fixed', precision defines the number of significant
* digits after the decimal point, and is 0 by default.
*/
precision?: number;
/**
* Exponent determining the lower boundary for formatting a value with
* an exponent when notation='auto. Default value is -3.
*/
lowerExp?: number;
/**
* Exponent determining the upper boundary for formatting a value with
* an exponent when notation='auto. Default value is 5.
*/
upperExp?: number;
/**
* Available values: 'ratio' (default) or 'decimal'. For example
* format(fraction(1, 3)) will output '1/3' when 'ratio' is configured,
* and will output 0.(3) when 'decimal' is configured.
*/
fraction?: string;
}
interface Help {
toString(): string;
toJSON(): string;
}
interface ConfigOptions {
epsilon?: number;
matrix?: string;
number?: string;
precision?: number;
parenthesis?: string;
randomSeed?: string;
}
interface MathJsJson {
/**
* Returns reviver function that can be used as reviver in JSON.parse function.
*/
reviver(): (key: any, value: any) => any;
}
interface MathJsChain {
done(): any;
/*************************************************************************
* Construction functions
************************************************************************/
/**
* Create a BigNumber, which can store numbers with arbitrary precision.
* When a matrix is provided, all elements will be converted to
* BigNumber.
*/
bignumber(): MathJsChain;
/**
* Create a boolean or convert a string or number to a boolean. In case
* of a number, true is returned for non-zero numbers, and false in case
* of zero. Strings can be 'true' or 'false', or can contain a number.
* When value is a matrix, all elements will be converted to boolean.
*/
boolean(): MathJsChain;
/**
* Create a complex value or convert a value to a complex value.
* @param im Argument specifying the imaginary part of the complex
* number
*/
complex(im?: number): MathJsChain;
/**
* Create a user-defined unit and register it with the Unit type.
* @param definition Definition of the unit in terms of existing units.
* For example, ‘0.514444444 m / s’.
* @param options (optional) An object containing any of the following
* properties:</br>- prefixes {string} “none”, “short”, “long”,
* “binary_short”, or “binary_long”. The default is “none”.</br>-
* aliases {Array} Array of strings. Example: [‘knots’, ‘kt’,
* ‘kts’]</br>- offset {Numeric} An offset to apply when converting from
* the unit. For example, the offset for celsius is 273.15. Default is
* 0.
*/
createUnit(
definition?: string | UnitDefinition,
options?: CreateUnitOptions
): MathJsChain;
/**
* Create a user-defined unit and register it with the Unit type.
* @param options (optional) An object containing any of the following
* properties:</br>- prefixes {string} “none”, “short”, “long”,
* “binary_short”, or “binary_long”. The default is “none”.</br>-
* aliases {Array} Array of strings. Example: [‘knots’, ‘kt’,
* ‘kts’]</br>- offset {Numeric} An offset to apply when converting from
* the unit. For example, the offset for celsius is 273.15. Default is
* 0.
*/
createUnit(options?: CreateUnitOptions): MathJsChain;
/**
* Create a fraction convert a value to a fraction.
* @param denominator Argument specifying the denominator of the
* fraction
*/
fraction(
denominator?: number | string | MathArray | Matrix
): MathJsChain;
/**
* Create an index. An Index can store ranges having start, step, and
* end for multiple dimensions. Matrix.get, Matrix.set, and math.subset
* accept an Index as input.
*/
index(): MathJsChain;
/**
* Create a Matrix. The function creates a new math.type.Matrix object
* from an Array. A Matrix has utility functions to manipulate the data
* in the matrix, like getting the size and getting or setting values in
* the matrix. Supported storage formats are 'dense' and 'sparse'.
*/
matrix(format?: "sparse" | "dense", dataType?: string): MathJsChain;
/**
* Create a number or convert a string, boolean, or unit to a number.
* When value is a matrix, all elements will be converted to number.
* @param valuelessUnit A valueless unit, used to convert a unit to a
* number
*/
number(valuelessUnit?: Unit | string): MathJsChain;
/**
* Create a Sparse Matrix. The function creates a new math.type.Matrix
* object from an Array. A Matrix has utility functions to manipulate
* the data in the matrix, like getting the size and getting or setting
* values in the matrix.
* @param dataType Sparse Matrix data type
*/
sparse(dataType?: string): MathJsChain;
/**
* Split a unit in an array of units whose sum is equal to the original
* unit.
* @param parts An array of strings or valueless units
*/
splitUnit(parts: Unit[]): MathJsChain;
/**
* Create a string or convert any object into a string. Elements of
* Arrays and Matrices are processed element wise.
*/
string(): MathJsChain;
/**
* Create a unit. Depending on the passed arguments, the function will
* create and return a new math.type.Unit object. When a matrix is
* provided, all elements will be converted to units.
* @param unit The unit to be created
*/
unit(unit?: string): MathJsChain;
/*************************************************************************
* Expression functions
************************************************************************/
/**
* Parse and compile an expression. Returns a an object with a function
* evaluate([scope]) to evaluate the compiled expression.
*/
compile(): MathJsChain;
/**
* Evaluate an expression.
* @param scope Scope to read/write variables
*/
evaluate(scope?: object): MathJsChain;
/**
* Retrieve help on a function or data type. Help files are retrieved
* from the documentation in math.expression.docs.
*/
help(): MathJsChain;
/**
* Parse an expression. Returns a node tree, which can be evaluated by
* invoking node.evaluate();
* @param options Available options: nodes - a set of custome nodes
*/
parse(options?: any): MathJsChain;
/**
* @param options Available options: nodes - a set of custome nodes
*/
parse(options?: any): MathJsChain;
/**
* Create a parser. The function creates a new math.expression.Parser
* object.
*/
parser(): MathJsChain;
/*************************************************************************
* Algebra functions
************************************************************************/
/**
* @param variable The variable over which to differentiate
* @param options There is one option available, simplify, which is true
* by default. When false, output will not be simplified.
*/
derivative(variable: MathNode | string, options?: {simplify: boolean}): MathJsChain;
/**
* Solves the linear equation system by forwards substitution. Matrix
* must be a lower triangular matrix.
* @param b A column vector with the b values
*/
lsolve(b: Matrix | MathArray): MathJsChain;
/**
* Calculate the Matrix LU decomposition with partial pivoting. Matrix A
* is decomposed in two matrices (L, U) and a row permutation vector p
* where A[p,:] = L * U
*/
lup(): MathJsChain;
/**
* Solves the linear system A * x = b where A is an [n x n] matrix and b
* is a [n] column vector.
* @param b Column Vector
* @param order The Symbolic Ordering and Analysis order, see slu for
* details. Matrix must be a SparseMatrix
* @param threshold Partial pivoting threshold (1 for partial pivoting),
* see slu for details. Matrix must be a SparseMatrix.
*/
lusolve(
b: Matrix | MathArray,
order?: number,
threshold?: number
): MathJsChain;
/**
* Calculate the Matrix QR decomposition. Matrix A is decomposed in two
* matrices (Q, R) where Q is an orthogonal matrix and R is an upper
* triangular matrix.
*/
qr(): MathJsChain;
/**
* Transform a rationalizable expression in a rational fraction. If
* rational fraction is one variable polynomial then converts the
* numerator and denominator in canonical form, with decreasing
* exponents, returning the coefficients of numerator.
* @param optional scope of expression or true for already evaluated
* rational expression at input
* @param detailed optional True if return an object, false if return
* expression node (default)
*/
rationalize(optional?: object | boolean, detailed?: boolean): MathJsChain;
/**
* Simplify an expression tree.
* @param rules A list of rules are applied to an expression, repeating
* over the list until no further changes are made. It’s possible to
* pass a custom set of rules to the function as second argument. A rule
* can be specified as an object, string, or function.
* @param scope Scope to variables
*/
simplify(
rules?: Array<({ l: string; r: string } | string | ((node: MathNode) => MathNode))>,
scope?: object
): MathJsChain;
/**
* Calculate the Sparse Matrix LU decomposition with full pivoting.
* Sparse Matrix A is decomposed in two matrices (L, U) and two
* permutation vectors (pinv, q) where P * A * Q = L * U
* @param order The Symbolic Ordering and Analysis order: 0 - Natural
* ordering, no permutation vector q is returned 1 - Matrix must be
* square, symbolic ordering and analisis is performed on M = A + A' 2 -
* Symbolic ordering and analysis is performed on M = A' * A. Dense
* columns from A' are dropped, A recreated from A'. This is appropriate
* for LU factorization of non-symmetric matrices. 3 - Symbolic ordering
* and analysis is performed on M = A' * A. This is best used for LU
* factorization is matrix M has no dense rows. A dense row is a row
* with more than 10*sqr(columns) entries.
* @param threshold Partial pivoting threshold (1 for partial pivoting)
*/
slu(order: number, threshold: number): MathJsChain;
/**
* Solves the linear equation system by backward substitution. Matrix
* must be an upper triangular matrix. U * x = b
* @param b A column vector with the b values
*/
usolve(b: Matrix | MathArray): MathJsChain;
/*************************************************************************
* Arithmetic functions
************************************************************************/
/**
* Calculate the absolute value of a number. For matrices, the function
* is evaluated element wise.
*/
abs(): MathJsChain;
/**
* Add two values, x + y. For matrices, the function is evaluated
* element wise.
* @param y Second value to add
*/
add(y: MathType): MathJsChain;
/**
* Calculate the cubic root of a value. For matrices, the function is
* evaluated element wise.
* @param allRoots Optional, false by default. Only applicable when x is
* a number or complex number. If true, all complex roots are returned,
* if false (default) the principal root is returned.
*/
cbrt(allRoots?: boolean): MathJsChain;
/**
* Round a value towards plus infinity If x is complex, both real and
* imaginary part are rounded towards plus infinity. For matrices, the
* function is evaluated element wise.
*/
ceil(): MathJsChain;
/**
* Compute the cube of a value, x * x * x. For matrices, the function is
* evaluated element wise.
*/
cube(): MathJsChain;
/**
* Divide two values, x / y. To divide matrices, x is multiplied with
* the inverse of y: x * inv(y).
* @param y Denominator
*/
divide(y: MathType): MathJsChain;
/**
* Divide two matrices element wise. The function accepts both matrices
* and scalar values.
* @param y Denominator
*/
dotDivide(y: MathType): MathJsChain;
/**
* Multiply two matrices element wise. The function accepts both
* matrices and scalar values.
* @param y Right hand value
*/
dotMultiply(y: MathType): MathJsChain;
/**
* Calculates the power of x to y element wise.
* @param y The exponent
*/
dotPow(y: MathType): MathJsChain;
/**
* Calculate the exponent of a value. For matrices, the function is
* evaluated element wise.
*/
exp(): MathJsChain;
/**
* Calculate the value of subtracting 1 from the exponential value. For
* matrices, the function is evaluated element wise.
*/
expm1(): MathJsChain;
/**
* Round a value towards zero. For matrices, the function is evaluated
* element wise.
*/
fix(): MathJsChain;
/**
* Round a value towards minus infinity. For matrices, the function is
* evaluated element wise.
*/
floor(): MathJsChain;
/**
* Calculate the greatest common divisor for two or more values or
* arrays. For matrices, the function is evaluated element wise.
*/
gcd(): MathJsChain;
/**
* Calculate the hypotenusa of a list with values. The hypotenusa is
* defined as: hypot(a, b, c, ...) = sqrt(a^2 + b^2 + c^2 + ...) For
* matrix input, the hypotenusa is calculated for all values in the
* matrix.
*/
hypot(): MathJsChain;
/**
* Calculate the least common multiple for two or more values or arrays.
* lcm is defined as: lcm(a, b) = abs(a * b) / gcd(a, b) For matrices,
* the function is evaluated element wise.
* @param b An integer number
*/
lcm(b: number | BigNumber | MathArray | Matrix): MathJsChain;
/**
* Calculate the logarithm of a value. For matrices, the function is
* evaluated element wise.
* @param base Optional base for the logarithm. If not provided, the
* natural logarithm of x is calculated. Default value: e.
*/
log(base?: number | BigNumber | Complex): MathJsChain;
/**
* Calculate the 10-base of a value. This is the same as calculating
* log(x, 10). For matrices, the function is evaluated element wise.
*/
log10(): MathJsChain;
/**
* Calculate the logarithm of a value+1. For matrices, the function is
* evaluated element wise.
*/
log1p(base?: number | BigNumber | Complex): MathJsChain;
/**
* Calculate the 2-base of a value. This is the same as calculating
* log(x, 2). For matrices, the function is evaluated element wise.
*/
log2(): MathJsChain;
/**
* Calculates the modulus, the remainder of an integer division. For
* matrices, the function is evaluated element wise. The modulus is
* defined as: x - y * floor(x / y)
* @see http://en.wikipedia.org/wiki/Modulo_operation.
* @param y Divisor
*/
mod(y: number | BigNumber | Fraction | MathArray | Matrix): MathJsChain;
/**
* Multiply two values, x * y. The result is squeezed. For matrices, the
* matrix product is calculated.
* @param y The second value to multiply
*/
multiply(y: MathType): MathJsChain;
/**
* Calculate the norm of a number, vector or matrix. The second
* parameter p is optional. If not provided, it defaults to 2.
* @param p Vector space. Supported numbers include Infinity and
* -Infinity. Supported strings are: 'inf', '-inf', and 'fro' (The
* Frobenius norm) Default value: 2.
*/
norm(p?: number | BigNumber | string): MathJsChain;
/**
* Calculate the nth root of a value. The principal nth root of a
* positive real number A, is the positive real solution of the equation
* x^root = A For matrices, the function is evaluated element wise.
* @param root The root. Default value: 2.
*/
nthRoot(root?: number | BigNumber): MathJsChain;
/**
* Calculates the power of x to y, x ^ y. Matrix exponentiation is
* supported for square matrices x, and positive integer exponents y.
* @param y The exponent
*/
pow(): MathJsChain;
/**
* Round a value towards the nearest integer. For matrices, the function
* is evaluated element wise.
* @param n Number of decimals Default value: 0.
*/
round(n?: number | BigNumber | MathArray): MathJsChain;
/**
* Compute the sign of a value. The sign of a value x is: 1 when x > 1
* -1 when x < 0 0 when x == 0 For matrices, the function is evaluated
* element wise.
* @param x The number for which to determine the sign
* @returns The sign of x
*/
sign(): MathJsChain;
/**
* Calculate the square root of a value. For matrices, the function is
* evaluated element wise.
*/
sqrt(): MathJsChain;
/**
* Compute the square of a value, x * x. For matrices, the function is
* evaluated element wise.
*/
square(): MathJsChain;
/**
* Subtract two values, x - y. For matrices, the function is evaluated
* element wise.
* @param y Value to subtract from x
*/
subtract(y: MathType): MathJsChain;
/**
* Inverse the sign of a value, apply a unary minus operation. For
* matrices, the function is evaluated element wise. Boolean values and
* strings will be converted to a number. For complex numbers, both real
* and complex value are inverted.
*/
unaryMinus(): MathJsChain;
/**
* Unary plus operation. Boolean values and strings will be converted to
* a number, numeric values will be returned as is. For matrices, the
* function is evaluated element wise.
*/
unaryPlus(): MathJsChain;
/**
* Calculate the extended greatest common divisor for two values. See
* http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm.
* @param b An integer number
*/
xgcd(b: number | BigNumber): MathJsChain;
/*************************************************************************
* Bitwise functions
************************************************************************/
/**
* Bitwise AND two values, x & y. For matrices, the function is
* evaluated element wise.
* @param y Second value to and
*/
bitAnd(y: number | BigNumber | MathArray | Matrix): MathJsChain;
/**
* Bitwise NOT value, ~x. For matrices, the function is evaluated
* element wise. For units, the function is evaluated on the best prefix
* base.
*/
bitNot(): MathJsChain;
/**
* Bitwise OR two values, x | y. For matrices, the function is evaluated
* element wise. For units, the function is evaluated on the lowest
* print base.
* @param y Second value to or
*/
bitOr(y: number | BigNumber | MathArray | Matrix): MathJsChain;
/**
* Bitwise XOR two values, x ^ y. For matrices, the function is
* evaluated element wise.
* @param y Second value to xor
*/
bitXor(y: number | BigNumber | MathArray | Matrix): MathJsChain;
/**
* Bitwise left logical shift of a value x by y number of bits, x << y.
* For matrices, the function is evaluated element wise. For units, the
* function is evaluated on the best prefix base.
* @param y Amount of shifts
*/
leftShift(y: number | BigNumber): MathJsChain;
/**
* Bitwise right arithmetic shift of a value x by y number of bits, x >>
* y. For matrices, the function is evaluated element wise. For units,
* the function is evaluated on the best prefix base.
* @param y Amount of shifts
*/
rightArithShift(y: number | BigNumber): MathJsChain;
/**
* Bitwise right logical shift of value x by y number of bits, x >>> y.
* For matrices, the function is evaluated element wise. For units, the
* function is evaluated on the best prefix base.
* @param y Amount of shifts
*/
rightLogShift(y: number): MathJsChain;
/*************************************************************************
* Combinatorics functions
************************************************************************/
/**
* The Bell Numbers count the number of partitions of a set. A partition
* is a pairwise disjoint subset of S whose union is S. bellNumbers only
* takes integer arguments. The following condition must be enforced: n
* >= 0
*/
bellNumbers(): MathJsChain;
/**
* The Catalan Numbers enumerate combinatorial structures of many
* different types. catalan only takes integer arguments. The following
* condition must be enforced: n >= 0
*/
catalan(): MathJsChain;
/**
* The composition counts of n into k parts. Composition only takes
* integer arguments. The following condition must be enforced: k <= n.
* @param k Number of objects in the subset
*/
composition(k: number | BigNumber): MathJsChain;
/**
* The Stirling numbers of the second kind, counts the number of ways to
* partition a set of n labelled objects into k nonempty unlabelled
* subsets. stirlingS2 only takes integer arguments. The following
* condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) =
* 1
* @param k Number of objects in the subset
*/
stirlingS2(k: number | BigNumber): MathJsChain;
/*************************************************************************
* Complex functions
************************************************************************/
/**
* Compute the argument of a complex value. For a complex number a + bi,
* the argument is computed as atan2(b, a). For matrices, the function
* is evaluated element wise.
*/
arg(): MathJsChain;
/**
* Compute the complex conjugate of a complex value. If x = a+bi, the
* complex conjugate of x is a - bi. For matrices, the function is
* evaluated element wise.
*/
conj(): MathJsChain;
/**
* Get the imaginary part of a complex number. For a complex number a +
* bi, the function returns b. For matrices, the function is evaluated
* element wise.
*/
im(): MathJsChain;
/**
* Get the real part of a complex number. For a complex number a + bi,
* the function returns a. For matrices, the function is evaluated
* element wise.
*/
re(): MathJsChain;
/*************************************************************************
* Geometry functions
************************************************************************/
/**
* Calculates: The eucledian distance between two points in 2 and 3
* dimensional spaces. Distance between point and a line in 2 and 3
* dimensional spaces. Pairwise distance between a set of 2D or 3D
* points NOTE: When substituting coefficients of a line(a, b and c),
* use ax + by + c = 0 instead of ax + by = c For parametric equation of
* a 3D line, x0, y0, z0, a, b, c are from: (x−x0, y−y0, z−z0) = t(a, b,
* c)
* @param y Coordinates of the second point
*/
distance(y: MathArray | Matrix | object): MathJsChain;
/**
* Calculates the point of intersection of two lines in two or three
* dimensions and of a line and a plane in three dimensions. The inputs
* are in the form of arrays or 1 dimensional matrices. The line
* intersection functions return null if the lines do not meet. Note:
* Fill the plane coefficients as x + y + z = c and not as x + y + z + c
* = 0.
* @param x Co-ordinates of second end-point of first line
* @param y Co-ordinates of first end-point of second line OR
* Coefficients of the plane's equation
* @param z Co-ordinates of second end-point of second line OR null if
* the calculation is for line and plane
*/
intersect(
x: MathArray | Matrix,
y: MathArray | Matrix,
z: MathArray | Matrix
): MathJsChain;
/*************************************************************************
* Logical functions
************************************************************************/
/**
* Logical and. Test whether two values are both defined with a
* nonzero/nonempty value. For matrices, the function is evaluated
* element wise.
* @param y Second value to and
*/
and(
y: number | BigNumber | Complex | Unit | MathArray | Matrix
): MathJsChain;
/**
* Logical not. Flips boolean value of a given parameter. For matrices,
* the function is evaluated element wise.
*/
not(): MathJsChain;
/**
* Logical or. Test if at least one value is defined with a
* nonzero/nonempty value. For matrices, the function is evaluated
* element wise.
* @param y Second value to or
*/
or(
y: number | BigNumber | Complex | Unit | MathArray | Matrix
): MathJsChain;
/**
* Logical xor. Test whether one and only one value is defined with a
* nonzero/nonempty value. For matrices, the function is evaluated
* element wise.
* @param y Second value to xor
*/
xor(
y: number | BigNumber | Complex | Unit | MathArray | Matrix
): MathJsChain;
/*************************************************************************
* Matrix functions
************************************************************************/
/**
* Concatenate two or more matrices. dim: number is a zero-based
* dimension over which to concatenate the matrices. By default the last
* dimension of the matrices.
*/
concat(): MathJsChain;
/**
* Calculate the cross product for two vectors in three dimensional
* space. The cross product of A = [a1, a2, a3] and B =[b1, b2, b3] is
* defined as: cross(A, B) = [ a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1
* * b2 - a2 * b1 ]
* @param y Second vector
*/
cross(y: MathArray | Matrix): MathJsChain;
/**
* Calculate the determinant of a matrix.
*/
det(): MathJsChain;
/**
* Create a diagonal matrix or retrieve the diagonal of a matrix. When x
* is a vector, a matrix with vector x on the diagonal will be returned.
* When x is a two dimensional matrix, the matrixes kth diagonal will be
* returned as vector. When k is positive, the values are placed on the
* super diagonal. When k is negative, the values are placed on the sub
* diagonal.
* @param k The diagonal where the vector will be filled in or
* retrieved. Default value: 0.
* @param format The matrix storage format. Default value: 'dense'.
*/
diag(format?: string): MathJsChain;
diag(k: number | BigNumber, format?: string): MathJsChain;
/**
* Calculate the dot product of two vectors. The dot product of A = [a1,
* a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as: dot(A,
* B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn
* @param y Second vector
*/
dot(y: MathArray | Matrix): MathJsChain;
/**
* Compute the matrix exponential, expm(A) = e^A. The matrix must be
* square. Not to be confused with exp(a), which performs element-wise
* exponentiation. The exponential is calculated using the Padé
* approximant with scaling and squaring; see “Nineteen Dubious Ways to
* Compute the Exponential of a Matrix,” by Moler and Van Loan.
*/
expm(): MathJsChain;
/**
* Create a 2-dimensional identity matrix with size m x n or n x n. The
* matrix has ones on the diagonal and zeros elsewhere.
* @param format The Matrix storage format
*/
identity(format?: string): MathJsChain;
/**
* @param n The y dimension for the matrix
* @param format The Matrix storage format
*/
identity(n: number, format?: string): MathJsChain;
/**
* Filter the items in an array or one dimensional matrix.
*/
filter(test: ((value: any, index: any, matrix: Matrix | MathArray) => Matrix | MathArray)| RegExp): MathJsChain;
/**
* Flatten a multi dimensional matrix into a single dimensional matrix.
*/
flatten(): MathJsChain;
/**
* Iterate over all elements of a matrix/array, and executes the given
* callback function.
*/
forEach(callback: ((value: any, index: any, matrix: Matrix | MathArray) => void)): MathJsChain;
/**
* Calculate the inverse of a square matrix.
*/
inv(): MathJsChain;
/**
* Calculate the kronecker product of two matrices or vectors
* @param y Second vector
*/
kron(y: Matrix | MathArray): MathJsChain;
/**
* Iterate over all elements of a matrix/array, and executes the given
* callback function.
* @param callback The callback function is invoked with three
* parameters: the value of the element, the index of the element, and
* the Matrix/array being traversed.
*/
map(callback: ((value: any, index: any, matrix: Matrix | MathArray) => Matrix | MathArray)): MathJsChain;
/**
* Create a matrix filled with ones. The created matrix can have one or
* multiple dimensions.
* @param format The matrix storage format
*/
ones(format?: string): MathJsChain;
/**
* @param format The matrix storage format
*/
ones(n: number, format?: string): MathJsChain;
/**
* Partition-based selection of an array or 1D matrix. Will find the kth
* smallest value, and mutates the input array. Uses Quickselect.
* @param k The kth smallest value to be retrieved; zero-based index
* @param compare An optional comparator function. The function is
* called as compare(a, b), and must return 1 when a > b, -1 when a < b,
* and 0 when a == b. Default value: 'asc'.
*/
partitionSelect(
k: number,
compare?: "asc" | "desc" | ((a: any, b: any) => number)
): MathJsChain;
/**
* Create an array from a range. By default, the range end is excluded.
* This can be customized by providing an extra parameter includeEnd.
* @param end End of the range, excluded by default, included when
* parameter includeEnd=true
* @param step Step size. Default value is 1.
* @param includeEnd: Option to specify whether to include the end or
* not. False by default
*/
range(includeEnd?: boolean): Matrix;
range(end: number | BigNumber, includeEnd?: boolean): MathJsChain;
range(
end: number | BigNumber,
step: number | BigNumber,
includeEnd?: boolean
): MathJsChain;
/**
* Reshape a multi dimensional array to fit the specified dimensions
* @param sizes One dimensional array with integral sizes for each
* dimension
*/
reshape(sizes: number[]): MathJsChain;
/**
* Resize a matrix
* @param size One dimensional array with numbers
* @param defaultValue Zero by default, except in case of a string, in
* that case defaultValue = ' ' Default value: 0.
*/
resize(
size: MathArray | Matrix,
defaultValue?: number | string
): MathJsChain;
/**
* Calculate the size of a matrix or scalar.
*/
size(): MathJsChain;
/**
* Sort the items in a matrix
* @param compare An optional _comparator function or name. The function
* is called as compare(a, b), and must return 1 when a > b, -1 when a <
* b, and 0 when a == b. Default value: ‘asc’
*/
sort(compare: ((a: any, b: any) => number) | "asc" | "desc" | "natural"): MathJsChain;
/**
* Calculate the principal square root of a square matrix. The principal
* square root matrix X of another matrix A is such that X * X = A.
*/
sqrtm(): MathJsChain;
/**
* Squeeze a matrix, remove inner and outer singleton dimensions from a
* matrix.
*/
squeeze(): MathJsChain;
/**
* Get or set a subset of a matrix or string.
* @param index An index containing ranges for each dimension
* @param replacement An array, matrix, or scalar. If provided, the
* subset is replaced with replacement. If not provided, the subset is
* returned
* @param defaultValue Default value, filled in on new entries when the
* matrix is resized. If not provided, math.matrix elements will be left
* undefined. Default value: undefined.
*/
subset(
index: Index,
replacement?: any,
defaultValue?: any
): MathJsChain;
/**
* Calculate the trace of a matrix: the sum of the elements on the main
* diagonal of a square matrix.
*/
trace(): MathJsChain;
/**
* Transpose a matrix. All values of the matrix are reflected over its
* main diagonal. Only two dimensional matrices are supported.
*/
transpose(): MathJsChain;
/**
* Create a matrix filled with zeros. The created matrix can have one or
* multiple dimensions.
* @param format The matrix storage format
* @returns A matrix filled with zeros
*/
zeros(format?: string): MathJsChain;
/**
* @param n The y dimension of the matrix
* @param format The matrix storage format
*/
zeros(n: number, format?: string): MathJsChain;
/*************************************************************************
* Probability functions
************************************************************************/
/**
* Compute the number of ways of picking k unordered outcomes from n
* possibilities. Combinations only takes integer arguments. The
* following condition must be enforced: k <= n.
* @param k Number of objects in the subset
*/
combinations(k: number | BigNumber): MathJsChain;
/**
* Compute the factorial of a value Factorial only supports an integer
* value as argument. For matrices, the function is evaluated element
* wise.
*/
factorial(): MathJsChain;
/**
* Compute the gamma function of a value using Lanczos approximation for
* small values, and an extended Stirling approximation for large
* values. For matrices, the function is evaluated element wise.
*/
gamma(): MathJsChain;
/**
* Calculate the Kullback-Leibler (KL) divergence between two
* distributions
* @param p Second vector
*/
kldivergence(p: MathArray | Matrix): MathJsChain;
/**
* Multinomial Coefficients compute the number of ways of picking a1,
* a2, ..., ai unordered outcomes from n possibilities. multinomial
* takes one array of integers as an argument. The following condition
* must be enforced: every ai <= 0
*/
multinomial(): MathJsChain;
/**
* Compute the number of ways of obtaining an ordered subset of k
* elements from a set of n elements. Permutations only takes integer
* arguments. The following condition must be enforced: k <= n.
* @param k The number of objects in the subset
*/
permutations(k?: number | BigNumber): MathJsChain;
/**
* Random pick a value from a one dimensional array. Array element is
* picked using a random function with uniform distribution.
* @param number An int or float
* @param weights An array of ints or floats
*/
pickRandom(number?: number, weights?: number[]): MathJsChain;
/**
* Return a random number larger or equal to min and smaller than max
* using a uniform distribution.
* @param min Minimum boundary for the random value, included
* @param max Maximum boundary for the random value, excluded
*/
// tslint:disable-next-line unified-signatures
random(max?: number): MathJsChain;
// tslint:disable-next-line unified-signatures
random(min: number, max: number): MathJsChain;
/**
* Return a random integer number larger or equal to min and smaller
* than max using a uniform distribution.
* @param min Minimum boundary for the random value, included
* @param max Maximum boundary for the random value, excluded
*/
// tslint:disable-next-line unified-signatures
randomInt(max?: number): MathJsChain;
// tslint:disable-next-line unified-signatures
randomInt(min: number, max: number): MathJsChain;
/*************************************************************************
* Relational functions
************************************************************************/
/**
* Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x
* == y. x and y are considered equal when the relative difference
* between x and y is smaller than the configured epsilon. The function
* cannot be used to compare values smaller than approximately 2.22e-16.
* For matrices, the function is evaluated element wise.
* @param y Second value to compare
*/
compare(y: MathType | string): MathJsChain;
/**
* Compare two values of any type in a deterministic, natural way. For
* numeric values, the function works the same as math.compare. For
* types of values that can’t be compared mathematically, the function
* compares in a natural way.
* @param y Second value to compare
*/
compareNatural(y: any): MathJsChain;
/**
* Compare two strings lexically. Comparison is case sensitive. Returns
* 1 when x > y, -1 when x < y, and 0 when x == y. For matrices, the
* function is evaluated element wise.
* @param y Second string to compare
*/
compareText(y: string | MathArray | Matrix): MathJsChain;
/**
* Test element wise whether two matrices are equal. The function
* accepts both matrices and scalar values.
* @param y Second amtrix to compare
*/
deepEqual(y: MathType): MathJsChain;
/**
* Test whether two values are equal.
*
* The function tests whether the relative difference between x and y is
* smaller than the configured epsilon. The function cannot be used to
* compare values smaller than approximately 2.22e-16. For matrices, the
* function is evaluated element wise. In case of complex numbers, x.re
* must equal y.re, and x.im must equal y.im. Values null and undefined
* are compared strictly, thus null is only equal to null and nothing
* else, and undefined is only equal to undefined and nothing else.
* @param y Second value to compare
*/
equal(y: MathType | string): MathJsChain;
/**
* Check equality of two strings. Comparison is case sensitive. For
* matrices, the function is evaluated element wise.
* @param y Second string to compare
*/
equalText(y: string | MathArray | Matrix): MathJsChain;
/**
* Test whether value x is larger than y. The function returns true when
* x is larger than y and the relative difference between x and y is
* larger than the configured epsilon. The function cannot be used to
* compare values smaller than approximately 2.22e-16. For matrices, the
* function is evaluated element wise.
* @param y Second value to compare
*/
larger(y: MathType | string): MathJsChain;
/**
* Test whether value x is larger or equal to y. The function returns
* true when x is larger than y or the relative difference between x and
* y is smaller than the configured epsilon. The function cannot be used
* to compare values smaller than approximately 2.22e-16. For matrices,
* the function is evaluated element wise.
* @param y Second value to vcompare
*/
largerEq(y: MathType | string): MathJsChain;
/**
* Test whether value x is smaller than y. The function returns true
* when x is smaller than y and the relative difference between x and y
* is smaller than the configured epsilon. The function cannot be used
* to compare values smaller than approximately 2.22e-16. For matrices,
* the function is evaluated element wise.
* @param y Second value to vcompare
*/
smaller(y: MathType | string): MathJsChain;
/**
* Test whether value x is smaller or equal to y. The function returns
* true when x is smaller than y or the relative difference between x
* and y is smaller than the configured epsilon. The function cannot be
* used to compare values smaller than approximately 2.22e-16. For
* matrices, the function is evaluated element wise.
* @param y Second value to compare
*/
smallerEq(y: MathType | string): MathJsChain;
/**
* Test whether two values are unequal. The function tests whether the
* relative difference between x and y is larger than the configured
* epsilon. The function cannot be used to compare values smaller than
* approximately 2.22e-16. For matrices, the function is evaluated
* element wise. In case of complex numbers, x.re must unequal y.re, or
* x.im must unequal y.im. Values null and undefined are compared
* strictly, thus null is unequal with everything except null, and
* undefined is unequal with everything except undefined.
* @param y Second value to vcompare
*/
unequal(y: MathType | string): MathJsChain;
/*************************************************************************
* Set functions
************************************************************************/
/**
* Create the cartesian product of two (multi)sets. Multi-dimension
* arrays will be converted to single-dimension arrays before the
* operation.
* @param a2 A (multi)set
*/
setCartesian(a2: MathArray | Matrix): MathJsChain;
/**
* Create the difference of two (multi)sets: every element of set1, that
* is not the element of set2. Multi-dimension arrays will be converted
* to single-dimension arrays before the operation
* @param a2 A (multi)set
*/
setDifference(a2: MathArray | Matrix): MathJsChain;
/**
* Collect the distinct elements of a multiset. A multi-dimension array
* will be converted to a single-dimension array before the operation.
*/
setDistinct(): MathJsChain;
/**
* Create the intersection of two (multi)sets. Multi-dimension arrays
* will be converted to single-dimension arrays before the operation.
* @param a2 A (multi)set
*/
setIntersect(a2: MathArray | Matrix): MathJsChain;
/**
* Check whether a (multi)set is a subset of another (multi)set. (Every
* element of set1 is the element of set2.) Multi-dimension arrays will
* be converted to single-dimension arrays before the operation.
* @param a2 A (multi)set
*/
setIsSubset(a2: MathArray | Matrix): MathJsChain;
/**
* Count the multiplicity of an element in a multiset. A multi-dimension
* array will be converted to a single-dimension array before the
* operation.
* @param a A multiset
*/
setMultiplicity(a: MathArray | Matrix): MathJsChain;
/**
* Create the powerset of a (multi)set. (The powerset contains very
* possible subsets of a (multi)set.) A multi-dimension array will be
* converted to a single-dimension array before the operation.
*/
setPowerset(): MathJsChain;
/**
* Count the number of elements of a (multi)set. When a second parameter
* is ‘true’, count only the unique values. A multi-dimension array will
* be converted to a single-dimension array before the operation.
*/
setSize(): MathJsChain;
/**
* Create the symmetric difference of two (multi)sets. Multi-dimension
* arrays will be converted to single-dimension arrays before the
* operation.
* @param a2 A (multi)set
*/
setSymDifference(a2: MathArray | Matrix): MathJsChain;
/**
* Create the union of two (multi)sets. Multi-dimension arrays will be
* converted to single-dimension arrays before the operation.
* @param a2 A (multi)set
*/
setUnion(a2: MathArray | Matrix): MathJsChain;
/*************************************************************************
* Special functions
************************************************************************/
/**
* Compute the erf function of a value using a rational Chebyshev
* approximations for different intervals of x.
*/
erf(): MathJsChain;
/*************************************************************************
* Statistics functions
************************************************************************/
/**
* Compute the median absolute deviation of a matrix or a list with
* values. The median absolute deviation is defined as the median of the
* absolute deviations from the median.
*/
mad(): MathJsChain;
/**
* Compute the maximum value of a matrix or a list with values. In case
* of a multi dimensional array, the maximum of the flattened array will
* be calculated. When dim is provided, the maximum over the selected
* dimension will be calculated. Parameter dim is zero-based.
* @param dim The maximum over the selected dimension
*/
max(dim?: number): MathJsChain;
/**
* Compute the mean value of matrix or a list with values. In case of a
* multi dimensional array, the mean of the flattened array will be
* calculated. When dim is provided, the maximum over the selected
* dimension will be calculated. Parameter dim is zero-based.
* @param dim The mean over the selected dimension
*/
mean(dim?: number): MathJsChain;
/**
* Compute the median of a matrix or a list with values. The values are
* sorted and the middle value is returned. In case of an even number of
* values, the average of the two middle values is returned. Supported
* types of values are: Number, BigNumber, Unit In case of a (multi
* dimensional) array or matrix, the median of all elements will be
* calculated.
*/
median(): MathJsChain;
/**
* Compute the maximum value of a matrix or a list of values. In case of
* a multi dimensional array, the maximum of the flattened array will be
* calculated. When dim is provided, the maximum over the selected
* dimension will be calculated. Parameter dim is zero-based.
* @param dim The minimum over the selected dimension
*/
min(dim?: number): MathJsChain;
/**
* Computes the mode of a set of numbers or a list with values(numbers
* or characters). If there are more than one modes, it returns a list
* of those values.
*/
mode(): MathJsChain;
/**
* Compute the product of a matrix or a list with values. In case of a
* (multi dimensional) array or matrix, the sum of all elements will be
* calculated.
*/
prod(): MathJsChain;
/**
* Compute the prob order quantile of a matrix or a list with values.
* The sequence is sorted and the middle value is returned. Supported
* types of sequence values are: Number, BigNumber, Unit Supported types
* of probability are: Number, BigNumber In case of a (multi
* dimensional) array or matrix, the prob order quantile of all elements
* will be calculated.
* @param probOrN prob is the order of the quantile, while N is the
* amount of evenly distributed steps of probabilities; only one of
* these options can be provided
* @param sorted =false is data sorted in ascending order
*/
quantileSeq(
prob: number | BigNumber | MathArray,
sorted?: boolean
): MathJsChain;
/**
* Compute the standard deviation of a matrix or a list with values. The
* standard deviations is defined as the square root of the variance:
* std(A) = sqrt(variance(A)). In case of a (multi dimensional) array or
* matrix, the standard deviation over all elements will be calculated.
* Optionally, the type of normalization can be specified as second
* parameter. The parameter normalization can be one of the following
* values: 'unbiased' (default) The sum of squared errors is divided by
* (n - 1) 'uncorrected' The sum of squared errors is divided by n
* 'biased' The sum of squared errors is divided by (n + 1)
* @param array A single matrix or multiple scalar values
* @param normalization Determines how to normalize the variance. Choose
* ‘unbiased’ (default), ‘uncorrected’, or ‘biased’. Default value:
* ‘unbiased’.
* @returns The standard deviation
*/
std(
normalization?: "unbiased" | "uncorrected" | "biased" | "unbiased"
): MathJsChain;
/**
* Compute the sum of a matrix or a list with values. In case of a
* (multi dimensional) array or matrix, the sum of all elements will be
* calculated.
*/
sum(): MathJsChain;
/**
* Compute the variance of a matrix or a list with values. In case of a
* (multi dimensional) array or matrix, the variance over all elements
* will be calculated. Optionally, the type of normalization can be
* specified as second parameter. The parameter normalization can be one
* of the following values: 'unbiased' (default) The sum of squared
* errors is divided by (n - 1) 'uncorrected' The sum of squared errors
* is divided by n 'biased' The sum of squared errors is divided by (n +
* 1) Note that older browser may not like the variable name var. In
* that case, the function can be called as math['var'](...) instead of
* math.variance(...).
* @param normalization normalization Determines how to normalize the
* variance. Choose ‘unbiased’ (default), ‘uncorrected’, or ‘biased’.
* Default value: ‘unbiased’.
* @returns The variance
*/
variance(
normalization?: "unbiased" | "uncorrected" | "biased" | "unbiased"
): MathJsChain;
/*************************************************************************
* String functions
************************************************************************/
/**
* Format a value of any type into a string.
* @param options An object with formatting options.
* @param callback A custom formatting function, invoked for all numeric
* elements in value, for example all elements of a matrix, or the real
* and imaginary parts of a complex number. This callback can be used to
* override the built-in numeric notation with any type of formatting.
* Function callback is called with value as parameter and must return a
* string.
* @see http://mathjs.org/docs/reference/functions/format.html
*/
format(
value: any,
options?: FormatOptions | number | ((item: any) => string),
callback?: ((value: any) => string)
): MathJsChain;
/**
* Interpolate values into a string template.
* @param values An object containing variables which will be filled in
* in the template.
* @param precision Number of digits to format numbers. If not provided,
* the value will not be rounded.
* @param options Formatting options, or the number of digits to format
* numbers. See function math.format for a description of all options.
*/
print(
values: any,
precision?: number,
options?: number | object
): MathJsChain;
/*************************************************************************
* Trigonometry functions
************************************************************************/
/**
* Calculate the inverse cosine of a value. For matrices, the function
* is evaluated element wise.
*/
acos(): MathJsChain;
/**
* Calculate the hyperbolic arccos of a value, defined as acosh(x) =
* ln(sqrt(x^2 - 1) + x). For matrices, the function is evaluated
* element wise.
*/
acosh(): MathJsChain;
/**
* Calculate the inverse cotangent of a value. For matrices, the
* function is evaluated element wise.
*/
acot(): MathJsChain;
/**
* Calculate the hyperbolic arccotangent of a value, defined as acoth(x)
* = (ln((x+1)/x) + ln(x/(x-1))) / 2. For matrices, the function is
* evaluated element wise.
*/
acoth(): MathJsChain;
/**
* Calculate the inverse cosecant of a value. For matrices, the function
* is evaluated element wise.
*/
acsc(): MathJsChain;
/**
* Calculate the hyperbolic arccosecant of a value, defined as acsch(x)
* = ln(1/x + sqrt(1/x^2 + 1)). For matrices, the function is evaluated
* element wise.
*/
acsch(): MathJsChain;
/**
* Calculate the inverse secant of a value. For matrices, the function
* is evaluated element wise.
*/
asec(): MathJsChain;
/**
* Calculate the hyperbolic arcsecant of a value, defined as asech(x) =
* ln(sqrt(1/x^2 - 1) + 1/x). For matrices, the function is evaluated
* element wise.
*/
asech(): MathJsChain;
/**
* Calculate the inverse sine of a value. For matrices, the function is
* evaluated element wise.
*/
asin(): MathJsChain;
/**
* Calculate the hyperbolic arcsine of a value, defined as asinh(x) =
* ln(x + sqrt(x^2 + 1)). For matrices, the function is evaluated
* element wise.
*/
asinh(): MathJsChain;
/**
* Calculate the inverse tangent of a value. For matrices, the function
* is evaluated element wise.
*/
atan(): MathJsChain;
/**
* Calculate the inverse tangent function with two arguments, y/x. By
* providing two arguments, the right quadrant of the computed angle can
* be determined. For matrices, the function is evaluated element wise.
*/
atan2(): MathJsChain;
/**
* Calculate the hyperbolic arctangent of a value, defined as atanh(x) =
* ln((1 + x)/(1 - x)) / 2. For matrices, the function is evaluated
* element wise.
*/
atanh(): MathJsChain;
/**
* Calculate the cosine of a value. For matrices, the function is
* evaluated element wise.
*/
cos(): MathJsChain;
/**
* Calculate the hyperbolic cosine of a value, defined as cosh(x) = 1/2
* * (exp(x) + exp(-x)). For matrices, the function is evaluated element
* wise.
*/
cosh(): MathJsChain;
/**
* Calculate the cotangent of a value. cot(x) is defined as 1 / tan(x).
* For matrices, the function is evaluated element wise.
*/
cot(): MathJsChain;
/**
* Calculate the hyperbolic cotangent of a value, defined as coth(x) = 1
* / tanh(x). For matrices, the function is evaluated element wise.
*/
coth(): MathJsChain;
/**
* Calculate the cosecant of a value, defined as csc(x) = 1/sin(x). For
* matrices, the function is evaluated element wise.
*/
csc(): MathJsChain;
/**
* Calculate the hyperbolic cosecant of a value, defined as csch(x) = 1
* / sinh(x). For matrices, the function is evaluated element wise.
*/
csch(): MathJsChain;
/**
* Calculate the secant of a value, defined as sec(x) = 1/cos(x). For
* matrices, the function is evaluated element wise.
*/
sec(): MathJsChain;
/**
* Calculate the hyperbolic secant of a value, defined as sech(x) = 1 /
* cosh(x). For matrices, the function is evaluated element wise.
*/
sech(): MathJsChain;
/**
* Calculate the sine of a value. For matrices, the function is
* evaluated element wise.
*/
sin(): MathJsChain;
/**
* Calculate the hyperbolic sine of a value, defined as sinh(x) = 1/2 *
* (exp(x) - exp(-x)). For matrices, the function is evaluated element
* wise.
*/
sinh(): MathJsChain;
/**
* Calculate the tangent of a value. tan(x) is equal to sin(x) / cos(x).
* For matrices, the function is evaluated element wise.
*/
tan(): MathJsChain;
/**
* Calculate the hyperbolic tangent of a value, defined as tanh(x) =
* (exp(2 * x) - 1) / (exp(2 * x) + 1). For matrices, the function is
* evaluated element wise.
*/
tanh(): MathJsChain;
/*************************************************************************
* Unit functions
************************************************************************/
/**
* Change the unit of a value. For matrices, the function is evaluated
* element wise.
* @param unit New unit. Can be a string like "cm" or a unit without
* value.
*/
to(unit: Unit | string): MathJsChain;
/*************************************************************************
* Utils functions
************************************************************************/
/**
* Clone an object.
*/
clone(): MathJsChain;
/**
* Test whether a value is an integer number. The function supports
* number, BigNumber, and Fraction. The function is evaluated
* element-wise in case of Array or Matrix input.
*/
isInteger(): MathJsChain;
/**
* Test whether a value is NaN (not a number). The function supports
* types number, BigNumber, Fraction, Unit and Complex. The function is
* evaluated element-wise in case of Array or Matrix input.
*/
isNaN(): MathJsChain;
/**
* Test whether a value is negative: smaller than zero. The function
* supports types number, BigNumber, Fraction, and Unit. The function is
* evaluated element-wise in case of Array or Matrix input.
*/
isNegative(): MathJsChain;
/**
* Test whether a value is an numeric value. The function is evaluated
* element-wise in case of Array or Matrix input.
*/
isNumeric(): MathJsChain;
/**
* Test whether a value is positive: larger than zero. The function
* supports types number, BigNumber, Fraction, and Unit. The function is
* evaluated element-wise in case of Array or Matrix input.
*/
isPositive(): MathJsChain;
/**
* Test whether a value is prime: has no divisors other than itself and
* one. The function supports type number, bignumber. The function is
* evaluated element-wise in case of Array or Matrix input.
*/
isPrime(): MathJsChain;
/**
* Test whether a value is zero. The function can check for zero for
* types number, BigNumber, Fraction, Complex, and Unit. The function is
* evaluated element-wise in case of Array or Matrix input.
*/
isZero(): MathJsChain;
/**
* Determine the type of a variable.
*/
typeOf(): MathJsChain;
}
interface ImportOptions {
override?: boolean;
silent?: boolean;
wrap?: boolean;
}
interface ImportObject {
[key: string]: any;
}
}
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