simple-squiggle

nthRoot.js (6350B)

---

 import { factory } from '../../utils/factory.js';
 import { createAlgorithm01 } from '../../type/matrix/utils/algorithm01.js';
 import { createAlgorithm02 } from '../../type/matrix/utils/algorithm02.js';
 import { createAlgorithm06 } from '../../type/matrix/utils/algorithm06.js';
 import { createAlgorithm11 } from '../../type/matrix/utils/algorithm11.js';
 import { createAlgorithm13 } from '../../type/matrix/utils/algorithm13.js';
 import { createAlgorithm14 } from '../../type/matrix/utils/algorithm14.js';
 import { nthRootNumber } from '../../plain/number/index.js';
 var name = 'nthRoot';
 var dependencies = ['typed', 'matrix', 'equalScalar', 'BigNumber'];
 export var createNthRoot = /* #__PURE__ */factory(name, dependencies, _ref => {
   var {
     typed,
     matrix,
     equalScalar,
     BigNumber: _BigNumber
   } = _ref;
   var algorithm01 = createAlgorithm01({
     typed
   });
   var algorithm02 = createAlgorithm02({
     typed,
     equalScalar
   });
   var algorithm06 = createAlgorithm06({
     typed,
     equalScalar
   });
   var algorithm11 = createAlgorithm11({
     typed,
     equalScalar
   });
   var algorithm13 = createAlgorithm13({
     typed
   });
   var algorithm14 = createAlgorithm14({
     typed
   });
   /**
    * 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, as 3^2 == 9
    *     math.sqrt(9)          // returns 3, as 3^2 == 9
    *     math.nthRoot(64, 3)   // returns 4, as 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`
    */
 
   var complexErr = '' + 'Complex number not supported in function nthRoot. ' + 'Use nthRoots instead.';
   return typed(name, {
     number: function number(x) {
       return nthRootNumber(x, 2);
     },
     'number, number': nthRootNumber,
     BigNumber: function BigNumber(x) {
       return _bigNthRoot(x, new _BigNumber(2));
     },
     Complex: function Complex(x) {
       throw new Error(complexErr);
     },
     'Complex, number': function ComplexNumber(x, y) {
       throw new Error(complexErr);
     },
     'BigNumber, BigNumber': _bigNthRoot,
     'Array | Matrix': function ArrayMatrix(x) {
       return this(x, 2);
     },
     'SparseMatrix, SparseMatrix': function SparseMatrixSparseMatrix(x, y) {
       // density must be one (no zeros in matrix)
       if (y.density() === 1) {
         // sparse + sparse
         return algorithm06(x, y, this);
       } else {
         // throw exception
         throw new Error('Root must be non-zero');
       }
     },
     'SparseMatrix, DenseMatrix': function SparseMatrixDenseMatrix(x, y) {
       return algorithm02(y, x, this, true);
     },
     'DenseMatrix, SparseMatrix': function DenseMatrixSparseMatrix(x, y) {
       // density must be one (no zeros in matrix)
       if (y.density() === 1) {
         // dense + sparse
         return algorithm01(x, y, this, false);
       } else {
         // throw exception
         throw new Error('Root must be non-zero');
       }
     },
     'DenseMatrix, DenseMatrix': function DenseMatrixDenseMatrix(x, y) {
       return algorithm13(x, y, this);
     },
     'Array, Array': function ArrayArray(x, y) {
       // use matrix implementation
       return this(matrix(x), matrix(y)).valueOf();
     },
     'Array, Matrix': function ArrayMatrix(x, y) {
       // use matrix implementation
       return this(matrix(x), y);
     },
     'Matrix, Array': function MatrixArray(x, y) {
       // use matrix implementation
       return this(x, matrix(y));
     },
     'SparseMatrix, number | BigNumber': function SparseMatrixNumberBigNumber(x, y) {
       return algorithm11(x, y, this, false);
     },
     'DenseMatrix, number | BigNumber': function DenseMatrixNumberBigNumber(x, y) {
       return algorithm14(x, y, this, false);
     },
     'number | BigNumber, SparseMatrix': function numberBigNumberSparseMatrix(x, y) {
       // density must be one (no zeros in matrix)
       if (y.density() === 1) {
         // sparse - scalar
         return algorithm11(y, x, this, true);
       } else {
         // throw exception
         throw new Error('Root must be non-zero');
       }
     },
     'number | BigNumber, DenseMatrix': function numberBigNumberDenseMatrix(x, y) {
       return algorithm14(y, x, this, true);
     },
     'Array, number | BigNumber': function ArrayNumberBigNumber(x, y) {
       // use matrix implementation
       return this(matrix(x), y).valueOf();
     },
     'number | BigNumber, Array': function numberBigNumberArray(x, y) {
       // use matrix implementation
       return this(x, matrix(y)).valueOf();
     }
   });
   /**
    * 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
   });
 });