209 lines
6.2 KiB
JavaScript
209 lines
6.2 KiB
JavaScript
import { factory } from '../../utils/factory.js';
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import { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js';
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import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js';
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import { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js';
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import { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js';
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import { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js';
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import { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js';
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import { nthRootNumber } from '../../plain/number/index.js';
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var name = 'nthRoot';
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var dependencies = ['typed', 'matrix', 'equalScalar', 'BigNumber'];
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export var createNthRoot = /* #__PURE__ */factory(name, dependencies, _ref => {
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var {
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typed,
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matrix,
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equalScalar,
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BigNumber: _BigNumber
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} = _ref;
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var algorithm01 = createAlgorithm01({
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typed
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});
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var algorithm02 = createAlgorithm02({
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typed,
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equalScalar
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});
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var algorithm06 = createAlgorithm06({
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typed,
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equalScalar
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});
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var algorithm11 = createAlgorithm11({
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typed,
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equalScalar
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});
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var algorithm13 = createAlgorithm13({
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typed
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});
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var algorithm14 = createAlgorithm14({
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typed
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});
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/**
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* Calculate the nth root of a value.
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* The principal nth root of a positive real number A, is the positive real
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* solution of the equation
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*
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* x^root = A
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*
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* For matrices, the function is evaluated element wise.
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*
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* Syntax:
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*
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* math.nthRoot(a)
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* math.nthRoot(a, root)
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*
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* Examples:
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*
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* math.nthRoot(9, 2) // returns 3, as 3^2 == 9
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* math.sqrt(9) // returns 3, as 3^2 == 9
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* math.nthRoot(64, 3) // returns 4, as 4^3 == 64
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*
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* See also:
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*
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* sqrt, pow
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*
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* @param {number | BigNumber | Array | Matrix | Complex} a
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* Value for which to calculate the nth root
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* @param {number | BigNumber} [root=2] The root.
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* @return {number | Complex | Array | Matrix} Returns the nth root of `a`
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*/
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var complexErr = '' + 'Complex number not supported in function nthRoot. ' + 'Use nthRoots instead.';
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return typed(name, {
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number: function number(x) {
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return nthRootNumber(x, 2);
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},
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'number, number': nthRootNumber,
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BigNumber: function BigNumber(x) {
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return _bigNthRoot(x, new _BigNumber(2));
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},
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Complex: function Complex(x) {
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throw new Error(complexErr);
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},
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'Complex, number': function ComplexNumber(x, y) {
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throw new Error(complexErr);
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},
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'BigNumber, BigNumber': _bigNthRoot,
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'Array | Matrix': function ArrayMatrix(x) {
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return this(x, 2);
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},
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'SparseMatrix, SparseMatrix': function SparseMatrixSparseMatrix(x, y) {
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// density must be one (no zeros in matrix)
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if (y.density() === 1) {
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// sparse + sparse
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return algorithm06(x, y, this);
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} else {
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// throw exception
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throw new Error('Root must be non-zero');
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}
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},
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'SparseMatrix, DenseMatrix': function SparseMatrixDenseMatrix(x, y) {
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return algorithm02(y, x, this, true);
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},
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'DenseMatrix, SparseMatrix': function DenseMatrixSparseMatrix(x, y) {
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// density must be one (no zeros in matrix)
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if (y.density() === 1) {
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// dense + sparse
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return algorithm01(x, y, this, false);
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} else {
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// throw exception
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throw new Error('Root must be non-zero');
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}
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},
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'DenseMatrix, DenseMatrix': function DenseMatrixDenseMatrix(x, y) {
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return algorithm13(x, y, this);
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},
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'Array, Array': function ArrayArray(x, y) {
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// use matrix implementation
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return this(matrix(x), matrix(y)).valueOf();
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},
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'Array, Matrix': function ArrayMatrix(x, y) {
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// use matrix implementation
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return this(matrix(x), y);
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},
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'Matrix, Array': function MatrixArray(x, y) {
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// use matrix implementation
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return this(x, matrix(y));
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},
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'SparseMatrix, number | BigNumber': function SparseMatrixNumberBigNumber(x, y) {
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return algorithm11(x, y, this, false);
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},
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'DenseMatrix, number | BigNumber': function DenseMatrixNumberBigNumber(x, y) {
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return algorithm14(x, y, this, false);
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},
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'number | BigNumber, SparseMatrix': function numberBigNumberSparseMatrix(x, y) {
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// density must be one (no zeros in matrix)
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if (y.density() === 1) {
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// sparse - scalar
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return algorithm11(y, x, this, true);
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} else {
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// throw exception
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throw new Error('Root must be non-zero');
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}
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},
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'number | BigNumber, DenseMatrix': function numberBigNumberDenseMatrix(x, y) {
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return algorithm14(y, x, this, true);
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},
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'Array, number | BigNumber': function ArrayNumberBigNumber(x, y) {
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// use matrix implementation
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return this(matrix(x), y).valueOf();
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},
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'number | BigNumber, Array': function numberBigNumberArray(x, y) {
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// use matrix implementation
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return this(x, matrix(y)).valueOf();
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}
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});
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/**
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* Calculate the nth root of a for BigNumbers, solve x^root == a
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* https://rosettacode.org/wiki/Nth_root#JavaScript
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* @param {BigNumber} a
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* @param {BigNumber} root
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* @private
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*/
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function _bigNthRoot(a, root) {
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var precision = _BigNumber.precision;
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var Big = _BigNumber.clone({
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precision: precision + 2
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});
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var zero = new _BigNumber(0);
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var one = new Big(1);
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var inv = root.isNegative();
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if (inv) {
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root = root.neg();
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}
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if (root.isZero()) {
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throw new Error('Root must be non-zero');
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}
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if (a.isNegative() && !root.abs().mod(2).equals(1)) {
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throw new Error('Root must be odd when a is negative.');
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} // edge cases zero and infinity
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if (a.isZero()) {
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return inv ? new Big(Infinity) : 0;
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}
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if (!a.isFinite()) {
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return inv ? zero : a;
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}
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var x = a.abs().pow(one.div(root)); // If a < 0, we require that root is an odd integer,
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// so (-1) ^ (1/root) = -1
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x = a.isNeg() ? x.neg() : x;
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return new _BigNumber((inv ? one.div(x) : x).toPrecision(precision));
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}
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});
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export var createNthRootNumber = /* #__PURE__ */factory(name, ['typed'], _ref2 => {
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var {
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typed
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} = _ref2;
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return typed(name, {
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number: nthRootNumber,
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'number, number': nthRootNumber
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});
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}); |