jiangchengfeiyi-xiaochengxu/node_modules/mathjs/lib/esm/function/arithmetic/nthRoot.js

import { factory } from '../../utils/factory.js';
import { createMatAlgo01xDSid } from '../../type/matrix/utils/matAlgo01xDSid.js';
import { createMatAlgo02xDS0 } from '../../type/matrix/utils/matAlgo02xDS0.js';
import { createMatAlgo06xS0S0 } from '../../type/matrix/utils/matAlgo06xS0S0.js';
import { createMatAlgo11xS0s } from '../../type/matrix/utils/matAlgo11xS0s.js';
import { createMatrixAlgorithmSuite } from '../../type/matrix/utils/matrixAlgorithmSuite.js';
import { nthRootNumber } from '../../plain/number/index.js';
var name = 'nthRoot';
var dependencies = ['typed', 'matrix', 'equalScalar', 'BigNumber', 'concat'];
export var createNthRoot = /* #__PURE__ */factory(name, dependencies, _ref => {
  var {
    typed,
    matrix,
    equalScalar,
    BigNumber: _BigNumber,
    concat
  } = _ref;
  var matAlgo01xDSid = createMatAlgo01xDSid({
    typed
  });
  var matAlgo02xDS0 = createMatAlgo02xDS0({
    typed,
    equalScalar
  });
  var matAlgo06xS0S0 = createMatAlgo06xS0S0({
    typed,
    equalScalar
  });
  var matAlgo11xS0s = createMatAlgo11xS0s({
    typed,
    equalScalar
  });
  var matrixAlgorithmSuite = createMatrixAlgorithmSuite({
    typed,
    matrix,
    concat
  });

  /**
   * 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.
   *
   * Syntax:
   *
   *     math.nthRoot(a)
   *     math.nthRoot(a, root)
   *
   * Examples:
   *
   *     math.nthRoot(9, 2)    // returns 3 (since 3^2 == 9)
   *     math.sqrt(9)          // returns 3 (since 3^2 == 9)
   *     math.nthRoot(64, 3)   // returns 4 (since 4^3 == 64)
   *
   * See also:
   *
   *     sqrt, pow
   *
   * @param {number | BigNumber | Array | Matrix | Complex} a
   *              Value for which to calculate the nth root
   * @param {number | BigNumber} [root=2]    The root.
   * @return {number | Complex | Array | Matrix} Returns the nth root of `a`
   */
  function complexErr() {
    throw new Error('Complex number not supported in function nthRoot. Use nthRoots instead.');
  }
  return typed(name, {
    number: nthRootNumber,
    'number, number': nthRootNumber,
    BigNumber: x => _bigNthRoot(x, new _BigNumber(2)),
    'BigNumber, BigNumber': _bigNthRoot,
    Complex: complexErr,
    'Complex, number': complexErr,
    Array: typed.referTo('DenseMatrix,number', selfDn => x => selfDn(matrix(x), 2).valueOf()),
    DenseMatrix: typed.referTo('DenseMatrix,number', selfDn => x => selfDn(x, 2)),
    SparseMatrix: typed.referTo('SparseMatrix,number', selfSn => x => selfSn(x, 2)),
    'SparseMatrix, SparseMatrix': typed.referToSelf(self => (x, y) => {
      // density must be one (no zeros in matrix)
      if (y.density() === 1) {
        // sparse + sparse
        return matAlgo06xS0S0(x, y, self);
      } else {
        // throw exception
        throw new Error('Root must be non-zero');
      }
    }),
    'DenseMatrix, SparseMatrix': typed.referToSelf(self => (x, y) => {
      // density must be one (no zeros in matrix)
      if (y.density() === 1) {
        // dense + sparse
        return matAlgo01xDSid(x, y, self, false);
      } else {
        // throw exception
        throw new Error('Root must be non-zero');
      }
    }),
    'Array, SparseMatrix': typed.referTo('DenseMatrix,SparseMatrix', selfDS => (x, y) => selfDS(matrix(x), y)),
    'number | BigNumber, SparseMatrix': typed.referToSelf(self => (x, y) => {
      // density must be one (no zeros in matrix)
      if (y.density() === 1) {
        // sparse - scalar
        return matAlgo11xS0s(y, x, self, true);
      } else {
        // throw exception
        throw new Error('Root must be non-zero');
      }
    })
  }, matrixAlgorithmSuite({
    scalar: 'number | BigNumber',
    SD: matAlgo02xDS0,
    Ss: matAlgo11xS0s,
    sS: false
  }));

  /**
   * Calculate the nth root of a for BigNumbers, solve x^root == a
   * https://rosettacode.org/wiki/Nth_root#JavaScript
   * @param {BigNumber} a
   * @param {BigNumber} root
   * @private
   */
  function _bigNthRoot(a, root) {
    var precision = _BigNumber.precision;
    var Big = _BigNumber.clone({
      precision: precision + 2
    });
    var zero = new _BigNumber(0);
    var one = new Big(1);
    var inv = root.isNegative();
    if (inv) {
      root = root.neg();
    }
    if (root.isZero()) {
      throw new Error('Root must be non-zero');
    }
    if (a.isNegative() && !root.abs().mod(2).equals(1)) {
      throw new Error('Root must be odd when a is negative.');
    }

    // edge cases zero and infinity
    if (a.isZero()) {
      return inv ? new Big(Infinity) : 0;
    }
    if (!a.isFinite()) {
      return inv ? zero : a;
    }
    var x = a.abs().pow(one.div(root));
    // If a < 0, we require that root is an odd integer,
    // so (-1) ^ (1/root) = -1
    x = a.isNeg() ? x.neg() : x;
    return new _BigNumber((inv ? one.div(x) : x).toPrecision(precision));
  }
});
export var createNthRootNumber = /* #__PURE__ */factory(name, ['typed'], _ref2 => {
  var {
    typed
  } = _ref2;
  return typed(name, {
    number: nthRootNumber,
    'number, number': nthRootNumber
  });
});