mathjs/src/utils/collection.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 { isCollection, isMatrix } from './is'
import { IndexError } from '../error/IndexError'
import { arraySize } from './array'

/**
 * Test whether an array contains collections
 * @param {Array} array
 * @returns {boolean} Returns true when the array contains one or multiple
 *                    collections (Arrays or Matrices). Returns false otherwise.
 */
export function containsCollections (array) {
  for (let i = 0; i < array.length; i++) {
    if (isCollection(array[i])) {
      return true
    }
  }
  return false
}

/**
 * Recursively loop over all elements in a given multi dimensional array
 * and invoke the callback on each of the elements.
 * @param {Array | Matrix} array
 * @param {Function} callback     The callback method is invoked with one
 *                                parameter: the current element in the array
 */
export function deepForEach (array, callback) {
  if (isMatrix(array)) {
    array = array.valueOf()
  }

  for (let i = 0, ii = array.length; i < ii; i++) {
    const value = array[i]

    if (Array.isArray(value)) {
      deepForEach(value, callback)
    } else {
      callback(value)
    }
  }
}

/**
 * Execute the callback function element wise for each element in array and any
 * nested array
 * Returns an array with the results
 * @param {Array | Matrix} array
 * @param {Function} callback   The callback is called with two parameters:
 *                              value1 and value2, which contain the current
 *                              element of both arrays.
 * @param {boolean} [skipZeros] Invoke callback function for non-zero values only.
 *
 * @return {Array | Matrix} res
 */
export function deepMap (array, callback, skipZeros) {
  if (array && (typeof array.map === 'function')) {
    // TODO: replace array.map with a for loop to improve performance
    return array.map(function (x) {
      return deepMap(x, callback, skipZeros)
    })
  } else {
    return callback(array)
  }
}

/**
 * Reduce a given matrix or array to a new matrix or
 * array with one less dimension, applying the given
 * callback in the selected dimension.
 * @param {Array | Matrix} mat
 * @param {number} dim
 * @param {Function} callback
 * @return {Array | Matrix} res
 */
export function reduce (mat, dim, callback) {
  const size = Array.isArray(mat) ? arraySize(mat) : mat.size()
  if (dim < 0 || (dim >= size.length)) {
    // TODO: would be more clear when throwing a DimensionError here
    throw new IndexError(dim, size.length)
  }

  if (isMatrix(mat)) {
    return mat.create(_reduce(mat.valueOf(), dim, callback))
  } else {
    return _reduce(mat, dim, callback)
  }
}

/**
 * Recursively reduce a matrix
 * @param {Array} mat
 * @param {number} dim
 * @param {Function} callback
 * @returns {Array} ret
 * @private
 */
function _reduce (mat, dim, callback) {
  let i, ret, val, tran

  if (dim <= 0) {
    if (!Array.isArray(mat[0])) {
      val = mat[0]
      for (i = 1; i < mat.length; i++) {
        val = callback(val, mat[i])
      }
      return val
    } else {
      tran = _switch(mat)
      ret = []
      for (i = 0; i < tran.length; i++) {
        ret[i] = _reduce(tran[i], dim - 1, callback)
      }
      return ret
    }
  } else {
    ret = []
    for (i = 0; i < mat.length; i++) {
      ret[i] = _reduce(mat[i], dim - 1, callback)
    }
    return ret
  }
}

/**
 * Transpose a matrix
 * @param {Array} mat
 * @returns {Array} ret
 * @private
 */
function _switch (mat) {
  const I = mat.length
  const J = mat[0].length
  let i, j
  const ret = []
  for (j = 0; j < J; j++) {
    const tmp = []
    for (i = 0; i < I; i++) {
      tmp.push(mat[i][j])
    }
    ret.push(tmp)
  }
  return ret
}

// TODO: document function scatter
export function scatter (a, j, w, x, u, mark, c, f, inverse, update, value) {
  // a arrays
  const avalues = a._values
  const aindex = a._index
  const aptr = a._ptr
  // c arrays
  const cindex = c._index

  // vars
  let k, k0, k1, i

  // check we need to process values (pattern matrix)
  if (x) {
    // values in j
    for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {
      // row
      i = aindex[k]
      // check value exists in current j
      if (w[i] !== mark) {
        // i is new entry in j
        w[i] = mark
        // add i to pattern of C
        cindex.push(i)
        // x(i) = A, check we need to call function this time
        if (update) {
          // copy value to workspace calling callback function
          x[i] = inverse ? f(avalues[k], value) : f(value, avalues[k])
          // function was called on current row
          u[i] = mark
        } else {
          // copy value to workspace
          x[i] = avalues[k]
        }
      } else {
        // i exists in C already
        x[i] = inverse ? f(avalues[k], x[i]) : f(x[i], avalues[k])
        // function was called on current row
        u[i] = mark
      }
    }
  } else {
    // values in j
    for (k0 = aptr[j], k1 = aptr[j + 1], k = k0; k < k1; k++) {
      // row
      i = aindex[k]
      // check value exists in current j
      if (w[i] !== mark) {
        // i is new entry in j
        w[i] = mark
        // add i to pattern of C
        cindex.push(i)
      } else {
        // indicate function was called on current row
        u[i] = mark
      }
    }
  }
}