mathjs/lib/esm/function/matrix/fft.js

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

import { arraySize } from '../../utils/array.js';
import { factory } from '../../utils/factory.js';
var name = 'fft';
var dependencies = ['typed', 'matrix', 'addScalar', 'multiplyScalar', 'divideScalar', 'exp', 'tau', 'i'];
export var createFft = /* #__PURE__ */factory(name, dependencies, _ref => {
  var {
    typed,
    matrix,
    addScalar,
    multiplyScalar,
    divideScalar,
    exp,
    tau,
    i: I
  } = _ref;
  /**
   * Calculate N-dimensional fourier transform
   *
   * Syntax:
   *
   *     math.fft(arr)
   *
   * Examples:
   *
   *    math.fft([[1, 0], [1, 0]]) // returns [[{re:2, im:0}, {re:2, im:0}], [{re:0, im:0}, {re:0, im:0}]]
   *
   *
   * See Also:
   *
   *      ifft
   *
   * @param {Array | Matrix} arr    An array or matrix
   * @return {Array | Matrix}       N-dimensional fourier transformation of the array
   */
  return typed(name, {
    Array: _ndFft,
    Matrix: function Matrix(matrix) {
      return matrix.create(_ndFft(matrix.toArray()));
    }
  });

  /**
   * Perform an N-dimensional Fourier transform
   *
   * @param {Array} arr      The array
   * @return {Array}         resulting array
   */
  function _ndFft(arr) {
    var size = arraySize(arr);
    if (size.length === 1) return _fft(arr, size[0]);
    // ndFft along dimension 1,...,N-1 then 1dFft along dimension 0
    return _1dFft(arr.map(slice => _ndFft(slice, size.slice(1))), 0);
  }

  /**
   * Perform an 1-dimensional Fourier transform
   *
   * @param {Array} arr      The array
   * @param {number} dim     dimension of the array to perform on
   * @return {Array}         resulting array
   */
  function _1dFft(arr, dim) {
    var size = arraySize(arr);
    if (dim !== 0) return new Array(size[0]).fill(0).map((_, i) => _1dFft(arr[i], dim - 1));
    if (size.length === 1) return _fft(arr);
    function _transpose(arr) {
      // Swap first 2 dimensions
      var size = arraySize(arr);
      return new Array(size[1]).fill(0).map((_, j) => new Array(size[0]).fill(0).map((_, i) => arr[i][j]));
    }
    return _transpose(_1dFft(_transpose(arr), 1));
  }

  /**
   * Perform an 1-dimensional Fourier transform
   *
   * @param {Array} arr      The array
   * @return {Array}         resulting array
   */
  function _fft(arr) {
    var len = arr.length;
    if (len === 1) return [arr[0]];
    if (len % 2 === 0) {
      var ret = [..._fft(arr.filter((_, i) => i % 2 === 0), len / 2), ..._fft(arr.filter((_, i) => i % 2 === 1), len / 2)];
      for (var k = 0; k < len / 2; k++) {
        var p = ret[k];
        var q = multiplyScalar(ret[k + len / 2], exp(multiplyScalar(multiplyScalar(tau, I), divideScalar(-k, len))));
        ret[k] = addScalar(p, q);
        ret[k + len / 2] = addScalar(p, multiplyScalar(-1, q));
      }
      return ret;
    }
    throw new Error('Can only calculate FFT of power-of-two size');
  }
});