mXrap - XPolyMath

XPolyMath

require.mx('mxjs/base/xpolymath.js');

This library provides functions for polynomial operations

This is very much still a work in progress, the functionality here has only been tested with a few sample cases.

QuickRef

Complex
Complex.abs
Complex.add
Complex.copy
Complex.create
Complex.divide
Complex.isInfinite
Complex.isNaN
Complex.multiply
Complex.set
Complex.sqrt
Complex.subtract
Solver
Solver.zeros
ComplexNumber

Status	Name
	`Number` Complex.abs ( `ComplexNumber` ↓cp ) Returns the absolute value of a complex number.
	`ComplexNumber` Complex.add ( `ComplexNumber` ↓cp1, `ComplexNumber` ↓cp2, `ComplexNumber` ↑cp ) Addition of complex numbers: cp = cp1 + cp2.
	`ComplexNumber` Complex.copy ( `ComplexNumber` ↓cp1, `ComplexNumber` ↑cp ) Copies a complex number.
	`ComplexNumber` Complex.create ( `Number` ↓r, `Number` ↓i, `ComplexNumber` ↑cp ) Creates a complex number.
	`ComplexNumber` Complex.divide ( `ComplexNumber` ↓cp1, `ComplexNumber` ↓cp2, `ComplexNumber` ↑cp ) Division of complex numbers: cp = cp1 / cp2.
	`Boolean` Complex.isInfinite ( `ComplexNumber` ↓cp ) Returns if the complex number is infinite. The complex number is infinite if either of its components are infinite.
	`Boolean` Complex.isNaN ( `ComplexNumber` ↓cp ) Returns if the complex number is Not-A-Number. The complex number is Not-A-Number if either of its components are Not-A-Number.
	`ComplexNumber` Complex.multiply ( `ComplexNumber` ↓cp1, `ComplexNumber` ↓cp2, `ComplexNumber` ↑cp ) Multiplication of complex numbers: cp = cp1 x cp2.
	`ComplexNumber` Complex.set ( `Number` ↓r, `Number` ↓i, `ComplexNumber` ↑cp ) Sets the values of a complex number.
	`ComplexNumber` Complex.sqrt ( `ComplexNumber` ↓cp1, `ComplexNumber` ↑cp ) Square root of complex numbers: cp is the square root of cp1.
	`ComplexNumber` Complex.subtract ( `ComplexNumber` ↓cp1, `ComplexNumber` ↓cp2, `ComplexNumber` ↑cp ) Subtraction of complex numbers: cp = cp1 - cp2.
	`Number` Solver.zeros ( `Array` ↓coefficients, `Number` ↓coefficients_length, `Array` ↑roots, `Number` ↓opt_initial, `Number` ↓opt_max_evaluations, `Number` ↓opt_absolute_accuracy, `Number` ↓opt_relative_accuracy, `Number` ↓opt_function_value_accuracy ) Solve for the zeroes/roots of the specified real polynomial function using Laguerre's algorithm. The roots returned can be complex, so they are returned as an array of ComplexNumber(s).

Category: Complex

Methods for working with complex numbers

↑abs = Lib.Complex.abs ( ↓cp ) Alpha

Returns the absolute value of a complex number.

Parameters:

ComplexNumber ↓cp - - complex number

Returns: Number ↑abs - - absolute value of cp

↑cp = Lib.Complex.add ( ↓cp1, ↓cp2, ↑cp ) Alpha

Addition of complex numbers: cp = cp1 + cp2.

Parameters:

ComplexNumber ↓cp1 - - complex number, first operand
ComplexNumber ↓cp2 - - complex number, second operand
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

↑cp = Lib.Complex.copy ( ↓cp1, ↑cp ) Alpha

Copies a complex number.

Parameters:

ComplexNumber ↓cp1 - - complex number to copy
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

↑cp = Lib.Complex.create ( ↓r, ↓i, ↑cp ) Alpha

Creates a complex number.

Parameters:

Number ↓r - - real component of complex number
Number ↓i - - imaginary component of complex number
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

↑cp = Lib.Complex.divide ( ↓cp1, ↓cp2, ↑cp ) Alpha

Division of complex numbers: cp = cp1 / cp2.

Parameters:

ComplexNumber ↓cp1 - - complex number, first operand
ComplexNumber ↓cp2 - - complex number, second operand
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

↑isInfinite = Lib.Complex.isInfinite ( ↓cp ) Alpha

Returns if the complex number is infinite. The complex number is infinite if either of its components are infinite.

Parameters:

ComplexNumber ↓cp - - complex number to check

Returns: Boolean ↑isInfinite - - true if cp is infinite, false otherwise

↑isNaN = Lib.Complex.isNaN ( ↓cp ) Alpha

Returns if the complex number is Not-A-Number. The complex number is Not-A-Number if either of its components are Not-A-Number.

Parameters:

ComplexNumber ↓cp - - complex number to check

Returns: Boolean ↑isNaN - - true if cp is Not-A-Number, false otherwise

↑cp = Lib.Complex.multiply ( ↓cp1, ↓cp2, ↑cp ) Alpha

Multiplication of complex numbers: cp = cp1 x cp2.

Parameters:

ComplexNumber ↓cp1 - - complex number, first operand
ComplexNumber ↓cp2 - - complex number, second operand
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

↑cp = Lib.Complex.set ( ↓r, ↓i, ↑cp ) Alpha

Sets the values of a complex number.

Parameters:

Number ↓r - - real component of complex number
Number ↓i - - imaginary component of complex number
ComplexNumber ↑cp - - complex number

Returns: ComplexNumber ↑cp - - complex number

↑cp = Lib.Complex.sqrt ( ↓cp1, ↑cp ) Alpha

Square root of complex numbers: cp is the square root of cp1.

Parameters:

ComplexNumber ↓cp1 - - complex number, first operand
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

↑cp = Lib.Complex.subtract ( ↓cp1, ↓cp2, ↑cp ) Alpha

Subtraction of complex numbers: cp = cp1 - cp2.

Parameters:

ComplexNumber ↓cp1 - - complex number, first operand
ComplexNumber ↓cp2 - - complex number, second operand
ComplexNumber ↑cp - - complex number. Optional - if not specified a new ComplexNumber is created and returned.

Returns: ComplexNumber ↑cp - - complex number

Category: Solver

Methods for solving polynomial functions

↑n = Lib.Solver.zeros ( ↓coefficients, ↓coefficients_length, ↑roots, ↓opt_initial, ↓opt_max_evaluations, ↓opt_absolute_accuracy, ↓opt_relative_accuracy, ↓opt_function_value_accuracy ) Alpha

Solve for the zeroes/roots of the specified real polynomial function using Laguerre's algorithm.

The roots returned can be complex, so they are returned as an array of ComplexNumber(s).

Parameters:

Array ↓coefficients - - an array specifying the coefficients. e.g. for 100 + 10x + 4x^2 + 3x^3 + x^5, the array would be [100, 10, 4, 3, 0, 1];
Number ↓coefficients_length - - the length of the above array
Array ↑roots - - output array to be populated with the ComplexNumber instances indicating the roots of the polynomial function
Number ↓opt_initial - - optional initial root for the Laguerre algorithm. By default this is 0.
Number ↓opt_max_evaluations - - optional max number of iterations for the Laguerre algorithm. By default this is Number.MAX_SAFE_INTEGER. An error will be thrown if the solution does not converge by this number of iterations.
Number ↓opt_absolute_accuracy - - optional absolute accuracy for the Laguerre algorithm. By default this is 1e-6.
Number ↓opt_relative_accuracy - - optional relative accuracy for the Laguerre algorithm. By default this is 1e-14.
Number ↓opt_function_value_accuracy - - optional function value accuracy for the Laguerre algorithm. By default this is 1e-15.

Returns: Number ↑n - - number of roots.

Class: ComplexNumber

A ComplexNumber encapsulates a complex number.

Status	Name
Member	`Number` i - an array containing the y coordinates of the points in this Path
Member	`Number` r - real component of the

Libraries

Categories

Classes

XPolyMath

Category: Complex

Category: Solver

Class: ComplexNumber