mathjs
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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif
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JavaScript
;
Object.defineProperty(exports, "__esModule", {
value: true
});
exports.createPow = void 0;
var _factory = require("../../utils/factory.js");
var _number = require("../../utils/number.js");
var _array = require("../../utils/array.js");
var _index = require("../../plain/number/index.js");
var name = 'pow';
var dependencies = ['typed', 'config', 'identity', 'multiply', 'matrix', 'inv', 'fraction', 'number', 'Complex'];
var createPow = exports.createPow = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
var typed = _ref.typed,
config = _ref.config,
identity = _ref.identity,
multiply = _ref.multiply,
matrix = _ref.matrix,
inv = _ref.inv,
number = _ref.number,
fraction = _ref.fraction,
Complex = _ref.Complex;
/**
* Calculates the power of x to y, `x ^ y`.
*
* Matrix exponentiation is supported for square matrices `x` and integers `y`:
* when `y` is nonnegative, `x` may be any square matrix; and when `y` is
* negative, `x` must be invertible, and then this function returns
* inv(x)^(-y).
*
* For cubic roots of negative numbers, the function returns the principal
* root by default. In order to let the function return the real root,
* math.js can be configured with `math.config({predictable: true})`.
* To retrieve all cubic roots of a value, use `math.cbrt(x, true)`.
*
* Syntax:
*
* math.pow(x, y)
*
* Examples:
*
* math.pow(2, 3) // returns number 8
*
* const a = math.complex(2, 3)
* math.pow(a, 2) // returns Complex -5 + 12i
*
* const b = [[1, 2], [4, 3]]
* math.pow(b, 2) // returns Array [[9, 8], [16, 17]]
*
* const c = [[1, 2], [4, 3]]
* math.pow(c, -1) // returns Array [[-0.6, 0.4], [0.8, -0.2]]
*
* See also:
*
* multiply, sqrt, cbrt, nthRoot
*
* @param {number | BigNumber | Complex | Unit | Array | Matrix} x The base
* @param {number | BigNumber | Complex} y The exponent
* @return {number | BigNumber | Complex | Array | Matrix} The value of `x` to the power `y`
*/
return typed(name, {
'number, number': _pow,
'Complex, Complex': function ComplexComplex(x, y) {
return x.pow(y);
},
'BigNumber, BigNumber': function BigNumberBigNumber(x, y) {
if (y.isInteger() || x >= 0 || config.predictable) {
return x.pow(y);
} else {
return new Complex(x.toNumber(), 0).pow(y.toNumber(), 0);
}
},
'Fraction, Fraction': function FractionFraction(x, y) {
var result = x.pow(y);
if (result != null) {
return result;
}
if (config.predictable) {
throw new Error('Result of pow is non-rational and cannot be expressed as a fraction');
} else {
return _pow(x.valueOf(), y.valueOf());
}
},
'Array, number': _powArray,
'Array, BigNumber': function ArrayBigNumber(x, y) {
return _powArray(x, y.toNumber());
},
'Matrix, number': _powMatrix,
'Matrix, BigNumber': function MatrixBigNumber(x, y) {
return _powMatrix(x, y.toNumber());
},
'Unit, number | BigNumber': function UnitNumberBigNumber(x, y) {
return x.pow(y);
}
});
/**
* Calculates the power of x to y, x^y, for two numbers.
* @param {number} x
* @param {number} y
* @return {number | Complex} res
* @private
*/
function _pow(x, y) {
// Alternatively could define a 'realmode' config option or something, but
// 'predictable' will work for now
if (config.predictable && !(0, _number.isInteger)(y) && x < 0) {
// Check to see if y can be represented as a fraction
try {
var yFrac = fraction(y);
var yNum = number(yFrac);
if (y === yNum || Math.abs((y - yNum) / y) < 1e-14) {
if (yFrac.d % 2 === 1) {
return (yFrac.n % 2 === 0 ? 1 : -1) * Math.pow(-x, y);
}
}
} catch (ex) {
// fraction() throws an error if y is Infinity, etc.
}
// Unable to express y as a fraction, so continue on
}
// **for predictable mode** x^Infinity === NaN if x < -1
// N.B. this behavour is different from `Math.pow` which gives
// (-2)^Infinity === Infinity
if (config.predictable && (x < -1 && y === Infinity || x > -1 && x < 0 && y === -Infinity)) {
return NaN;
}
if ((0, _number.isInteger)(y) || x >= 0 || config.predictable) {
return (0, _index.powNumber)(x, y);
} else {
// TODO: the following infinity checks are duplicated from powNumber. Deduplicate this somehow
// x^Infinity === 0 if -1 < x < 1
// A real number 0 is returned instead of complex(0)
if (x * x < 1 && y === Infinity || x * x > 1 && y === -Infinity) {
return 0;
}
return new Complex(x, 0).pow(y, 0);
}
}
/**
* Calculate the power of a 2d array
* @param {Array} x must be a 2 dimensional, square matrix
* @param {number} y a integer value (positive if `x` is not invertible)
* @returns {Array}
* @private
*/
function _powArray(x, y) {
if (!(0, _number.isInteger)(y)) {
throw new TypeError('For A^b, b must be an integer (value is ' + y + ')');
}
// verify that A is a 2 dimensional square matrix
var s = (0, _array.arraySize)(x);
if (s.length !== 2) {
throw new Error('For A^b, A must be 2 dimensional (A has ' + s.length + ' dimensions)');
}
if (s[0] !== s[1]) {
throw new Error('For A^b, A must be square (size is ' + s[0] + 'x' + s[1] + ')');
}
if (y < 0) {
try {
return _powArray(inv(x), -y);
} catch (error) {
if (error.message === 'Cannot calculate inverse, determinant is zero') {
throw new TypeError('For A^b, when A is not invertible, b must be a positive integer (value is ' + y + ')');
}
throw error;
}
}
var res = identity(s[0]).valueOf();
var px = x;
while (y >= 1) {
if ((y & 1) === 1) {
res = multiply(px, res);
}
y >>= 1;
px = multiply(px, px);
}
return res;
}
/**
* Calculate the power of a 2d matrix
* @param {Matrix} x must be a 2 dimensional, square matrix
* @param {number} y a positive, integer value
* @returns {Matrix}
* @private
*/
function _powMatrix(x, y) {
return matrix(_powArray(x.valueOf(), y));
}
});