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array.js
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import { isInteger } from './number.js'
import { isNumber, isBigNumber, isArray, isString } from './is.js'
import { format } from './string.js'
import { DimensionError } from '../error/DimensionError.js'
import { IndexError } from '../error/IndexError.js'
import { deepStrictEqual } from './object.js'
/**
* Calculate the size of a multi dimensional array.
* This function checks the size of the first entry, it does not validate
* whether all dimensions match. (use function `validate` for that)
* @param {Array} x
* @Return {Number[]} size
*/
export function arraySize (x) {
const s = []
while (Array.isArray(x)) {
s.push(x.length)
x = x[0]
}
return s
}
/**
* Recursively validate whether each element in a multi dimensional array
* has a size corresponding to the provided size array.
* @param {Array} array Array to be validated
* @param {number[]} size Array with the size of each dimension
* @param {number} dim Current dimension
* @throws DimensionError
* @private
*/
function _validate (array, size, dim) {
let i
const len = array.length
if (len !== size[dim]) {
throw new DimensionError(len, size[dim])
}
if (dim < size.length - 1) {
// recursively validate each child array
const dimNext = dim + 1
for (i = 0; i < len; i++) {
const child = array[i]
if (!Array.isArray(child)) {
throw new DimensionError(size.length - 1, size.length, '<')
}
_validate(array[i], size, dimNext)
}
} else {
// last dimension. none of the childs may be an array
for (i = 0; i < len; i++) {
if (Array.isArray(array[i])) {
throw new DimensionError(size.length + 1, size.length, '>')
}
}
}
}
/**
* Validate whether each element in a multi dimensional array has
* a size corresponding to the provided size array.
* @param {Array} array Array to be validated
* @param {number[]} size Array with the size of each dimension
* @throws DimensionError
*/
export function validate (array, size) {
const isScalar = (size.length === 0)
if (isScalar) {
// scalar
if (Array.isArray(array)) {
throw new DimensionError(array.length, 0)
}
} else {
// array
_validate(array, size, 0)
}
}
/**
* Validate whether the source of the index matches the size of the Array
* @param {Array | Matrix} array Array to be validated
* @param {Index} index Index with the source information to validate
* @throws DimensionError
*/
export function validateIndexSourceSize (value, index) {
const valueSize = value.isMatrix ? value._size : arraySize(value)
const sourceSize = index._sourceSize
// checks if the source size is not null and matches the valueSize
sourceSize.forEach((sourceDim, i) => {
if (sourceDim !== null && sourceDim !== valueSize[i]) { throw new DimensionError(sourceDim, valueSize[i]) }
})
}
/**
* Test whether index is an integer number with index >= 0 and index < length
* when length is provided
* @param {number} index Zero-based index
* @param {number} [length] Length of the array
*/
export function validateIndex (index, length) {
if (index !== undefined) {
if (!isNumber(index) || !isInteger(index)) {
throw new TypeError('Index must be an integer (value: ' + index + ')')
}
if (index < 0 || (typeof length === 'number' && index >= length)) {
throw new IndexError(index, length)
}
}
}
/**
* Test if and index has empty values
* @param {number} index Zero-based index
*/
export function isEmptyIndex (index) {
for (let i = 0; i < index._dimensions.length; ++i) {
const dimension = index._dimensions[i]
if (dimension._data && isArray(dimension._data)) {
if (dimension._size[0] === 0) {
return true
}
} else if (dimension.isRange) {
if (dimension.start === dimension.end) {
return true
}
} else if (isString(dimension)) {
if (dimension.length === 0) {
return true
}
}
}
return false
}
/**
* Resize a multi dimensional array. The resized array is returned.
* @param {Array | number} array Array to be resized
* @param {number[]} size Array with the size of each dimension
* @param {*} [defaultValue=0] Value to be filled in in new entries,
* zero by default. Specify for example `null`,
* to clearly see entries that are not explicitly
* set.
* @return {Array} array The resized array
*/
export function resize (array, size, defaultValue) {
// check the type of the arguments
if (!Array.isArray(size)) {
throw new TypeError('Array expected')
}
if (size.length === 0) {
throw new Error('Resizing to scalar is not supported')
}
// check whether size contains positive integers
size.forEach(function (value) {
if (!isNumber(value) || !isInteger(value) || value < 0) {
throw new TypeError('Invalid size, must contain positive integers ' +
'(size: ' + format(size) + ')')
}
})
// convert number to an array
if (isNumber(array) || isBigNumber(array)) {
array = [array]
}
// recursively resize the array
const _defaultValue = (defaultValue !== undefined) ? defaultValue : 0
_resize(array, size, 0, _defaultValue)
return array
}
/**
* Recursively resize a multi dimensional array
* @param {Array} array Array to be resized
* @param {number[]} size Array with the size of each dimension
* @param {number} dim Current dimension
* @param {*} [defaultValue] Value to be filled in in new entries,
* undefined by default.
* @private
*/
function _resize (array, size, dim, defaultValue) {
let i
let elem
const oldLen = array.length
const newLen = size[dim]
const minLen = Math.min(oldLen, newLen)
// apply new length
array.length = newLen
if (dim < size.length - 1) {
// non-last dimension
const dimNext = dim + 1
// resize existing child arrays
for (i = 0; i < minLen; i++) {
// resize child array
elem = array[i]
if (!Array.isArray(elem)) {
elem = [elem] // add a dimension
array[i] = elem
}
_resize(elem, size, dimNext, defaultValue)
}
// create new child arrays
for (i = minLen; i < newLen; i++) {
// get child array
elem = []
array[i] = elem
// resize new child array
_resize(elem, size, dimNext, defaultValue)
}
} else {
// last dimension
// remove dimensions of existing values
for (i = 0; i < minLen; i++) {
while (Array.isArray(array[i])) {
array[i] = array[i][0]
}
}
// fill new elements with the default value
for (i = minLen; i < newLen; i++) {
array[i] = defaultValue
}
}
}
/**
* Re-shape a multi dimensional array to fit the specified dimensions
* @param {Array} array Array to be reshaped
* @param {number[]} sizes List of sizes for each dimension
* @returns {Array} Array whose data has been formatted to fit the
* specified dimensions
*
* @throws {DimensionError} If the product of the new dimension sizes does
* not equal that of the old ones
*/
export function reshape (array, sizes) {
const flatArray = flatten(array)
const currentLength = flatArray.length
if (!Array.isArray(array) || !Array.isArray(sizes)) {
throw new TypeError('Array expected')
}
if (sizes.length === 0) {
throw new DimensionError(0, currentLength, '!=')
}
sizes = processSizesWildcard(sizes, currentLength)
const newLength = product(sizes)
if (currentLength !== newLength) {
throw new DimensionError(
newLength,
currentLength,
'!='
)
}
try {
return _reshape(flatArray, sizes)
} catch (e) {
if (e instanceof DimensionError) {
throw new DimensionError(
newLength,
currentLength,
'!='
)
}
throw e
}
}
/**
* Replaces the wildcard -1 in the sizes array.
* @param {number[]} sizes List of sizes for each dimension. At most on wildcard.
* @param {number} currentLength Number of elements in the array.
* @throws {Error} If more than one wildcard or unable to replace it.
* @returns {number[]} The sizes array with wildcard replaced.
*/
export function processSizesWildcard (sizes, currentLength) {
const newLength = product(sizes)
const processedSizes = sizes.slice()
const WILDCARD = -1
const wildCardIndex = sizes.indexOf(WILDCARD)
const isMoreThanOneWildcard = sizes.indexOf(WILDCARD, wildCardIndex + 1) >= 0
if (isMoreThanOneWildcard) {
throw new Error('More than one wildcard in sizes')
}
const hasWildcard = wildCardIndex >= 0
const canReplaceWildcard = currentLength % newLength === 0
if (hasWildcard) {
if (canReplaceWildcard) {
processedSizes[wildCardIndex] = -currentLength / newLength
} else {
throw new Error('Could not replace wildcard, since ' + currentLength + ' is no multiple of ' + (-newLength))
}
}
return processedSizes
}
/**
* Computes the product of all array elements.
* @param {number[]} array Array of factors
* @returns {number} Product of all elements
*/
function product (array) {
return array.reduce((prev, curr) => prev * curr, 1)
}
/**
* Iteratively re-shape a multi dimensional array to fit the specified dimensions
* @param {Array} array Array to be reshaped
* @param {number[]} sizes List of sizes for each dimension
* @returns {Array} Array whose data has been formatted to fit the
* specified dimensions
*/
function _reshape (array, sizes) {
// testing if there are enough elements for the requested shape
let tmpArray = array
let tmpArray2
// for each dimensions starting by the last one and ignoring the first one
for (let sizeIndex = sizes.length - 1; sizeIndex > 0; sizeIndex--) {
const size = sizes[sizeIndex]
tmpArray2 = []
// aggregate the elements of the current tmpArray in elements of the requested size
const length = tmpArray.length / size
for (let i = 0; i < length; i++) {
tmpArray2.push(tmpArray.slice(i * size, (i + 1) * size))
}
// set it as the new tmpArray for the next loop turn or for return
tmpArray = tmpArray2
}
return tmpArray
}
/**
* Squeeze a multi dimensional array
* @param {Array} array
* @param {Array} [size]
* @returns {Array} returns the array itself
*/
export function squeeze (array, size) {
const s = size || arraySize(array)
// squeeze outer dimensions
while (Array.isArray(array) && array.length === 1) {
array = array[0]
s.shift()
}
// find the first dimension to be squeezed
let dims = s.length
while (s[dims - 1] === 1) {
dims--
}
// squeeze inner dimensions
if (dims < s.length) {
array = _squeeze(array, dims, 0)
s.length = dims
}
return array
}
/**
* Recursively squeeze a multi dimensional array
* @param {Array} array
* @param {number} dims Required number of dimensions
* @param {number} dim Current dimension
* @returns {Array | *} Returns the squeezed array
* @private
*/
function _squeeze (array, dims, dim) {
let i, ii
if (dim < dims) {
const next = dim + 1
for (i = 0, ii = array.length; i < ii; i++) {
array[i] = _squeeze(array[i], dims, next)
}
} else {
while (Array.isArray(array)) {
array = array[0]
}
}
return array
}
/**
* Unsqueeze a multi dimensional array: add dimensions when missing
*
* Paramter `size` will be mutated to match the new, unqueezed matrix size.
*
* @param {Array} array
* @param {number} dims Desired number of dimensions of the array
* @param {number} [outer] Number of outer dimensions to be added
* @param {Array} [size] Current size of array.
* @returns {Array} returns the array itself
* @private
*/
export function unsqueeze (array, dims, outer, size) {
const s = size || arraySize(array)
// unsqueeze outer dimensions
if (outer) {
for (let i = 0; i < outer; i++) {
array = [array]
s.unshift(1)
}
}
// unsqueeze inner dimensions
array = _unsqueeze(array, dims, 0)
while (s.length < dims) {
s.push(1)
}
return array
}
/**
* Recursively unsqueeze a multi dimensional array
* @param {Array} array
* @param {number} dims Required number of dimensions
* @param {number} dim Current dimension
* @returns {Array | *} Returns the squeezed array
* @private
*/
function _unsqueeze (array, dims, dim) {
let i, ii
if (Array.isArray(array)) {
const next = dim + 1
for (i = 0, ii = array.length; i < ii; i++) {
array[i] = _unsqueeze(array[i], dims, next)
}
} else {
for (let d = dim; d < dims; d++) {
array = [array]
}
}
return array
}
/**
* Flatten a multi dimensional array, put all elements in a one dimensional
* array
* @param {Array} array A multi dimensional array
* @return {Array} The flattened array (1 dimensional)
*/
export function flatten (array) {
if (!Array.isArray(array)) {
// if not an array, return as is
return array
}
const flat = []
array.forEach(function callback (value) {
if (Array.isArray(value)) {
value.forEach(callback) // traverse through sub-arrays recursively
} else {
flat.push(value)
}
})
return flat
}
/**
* A safe map
* @param {Array} array
* @param {function} callback
*/
export function map (array, callback) {
return Array.prototype.map.call(array, callback)
}
/**
* A safe forEach
* @param {Array} array
* @param {function} callback
*/
export function forEach (array, callback) {
Array.prototype.forEach.call(array, callback)
}
/**
* A safe filter
* @param {Array} array
* @param {function} callback
*/
export function filter (array, callback) {
if (arraySize(array).length !== 1) {
throw new Error('Only one dimensional matrices supported')
}
return Array.prototype.filter.call(array, callback)
}
/**
* Filter values in a callback given a regular expression
* @param {Array} array
* @param {RegExp} regexp
* @return {Array} Returns the filtered array
* @private
*/
export function filterRegExp (array, regexp) {
if (arraySize(array).length !== 1) {
throw new Error('Only one dimensional matrices supported')
}
return Array.prototype.filter.call(array, (entry) => regexp.test(entry))
}
/**
* A safe join
* @param {Array} array
* @param {string} separator
*/
export function join (array, separator) {
return Array.prototype.join.call(array, separator)
}
/**
* Assign a numeric identifier to every element of a sorted array
* @param {Array} a An array
* @return {Array} An array of objects containing the original value and its identifier
*/
export function identify (a) {
if (!Array.isArray(a)) {
throw new TypeError('Array input expected')
}
if (a.length === 0) {
return a
}
const b = []
let count = 0
b[0] = { value: a[0], identifier: 0 }
for (let i = 1; i < a.length; i++) {
if (a[i] === a[i - 1]) {
count++
} else {
count = 0
}
b.push({ value: a[i], identifier: count })
}
return b
}
/**
* Remove the numeric identifier from the elements
* @param {array} a An array
* @return {array} An array of values without identifiers
*/
export function generalize (a) {
if (!Array.isArray(a)) {
throw new TypeError('Array input expected')
}
if (a.length === 0) {
return a
}
const b = []
for (let i = 0; i < a.length; i++) {
b.push(a[i].value)
}
return b
}
/**
* Check the datatype of a given object
* This is a low level implementation that should only be used by
* parent Matrix classes such as SparseMatrix or DenseMatrix
* This method does not validate Array Matrix shape
* @param {Array} array
* @param {function} typeOf Callback function to use to determine the type of a value
* @return {string}
*/
export function getArrayDataType (array, typeOf) {
let type // to hold type info
let length = 0 // to hold length value to ensure it has consistent sizes
for (let i = 0; i < array.length; i++) {
const item = array[i]
const isArray = Array.isArray(item)
// Saving the target matrix row size
if (i === 0 && isArray) {
length = item.length
}
// If the current item is an array but the length does not equal the targetVectorSize
if (isArray && item.length !== length) {
return undefined
}
const itemType = isArray
? getArrayDataType(item, typeOf) // recurse into a nested array
: typeOf(item)
if (type === undefined) {
type = itemType // first item
} else if (type !== itemType) {
return 'mixed'
} else {
// we're good, everything has the same type so far
}
}
return type
}
/**
* Return the last item from an array
* @param {array}
* @returns {*}
*/
export function last (array) {
return array[array.length - 1]
}
/**
* Get all but the last element of array.
* @param {array}
* @returns {*}
*/
export function initial (array) {
return array.slice(0, array.length - 1)
}
/**
* Recursively concatenate two matrices.
* The contents of the matrices is not cloned.
* @param {Array} a Multi dimensional array
* @param {Array} b Multi dimensional array
* @param {number} concatDim The dimension on which to concatenate (zero-based)
* @param {number} dim The current dim (zero-based)
* @return {Array} c The concatenated matrix
* @private
*/
function concatRecursive (a, b, concatDim, dim) {
if (dim < concatDim) {
// recurse into next dimension
if (a.length !== b.length) {
throw new DimensionError(a.length, b.length)
}
const c = []
for (let i = 0; i < a.length; i++) {
c[i] = concatRecursive(a[i], b[i], concatDim, dim + 1)
}
return c
} else {
// concatenate this dimension
return a.concat(b)
}
}
/**
* Concatenates many arrays in the specified direction
* @param {...Array} arrays All the arrays to concatenate
* @param {number} concatDim The dimension on which to concatenate (zero-based)
* @returns
*/
export function concat () {
const arrays = Array.prototype.slice.call(arguments, 0, -1)
const concatDim = Array.prototype.slice.call(arguments, -1)
if (arrays.length === 1) {
return arrays[0]
}
if (arrays.length > 1) {
return arrays.slice(1).reduce(function (A, B) { return concatRecursive(A, B, concatDim, 0) }, arrays[0])
} else {
throw new Error('Wrong number of arguments in function concat')
}
}
/**
* Receives two or more sizes and get's the broadcasted size for both.
* @param {...number[]} sizes Sizes to broadcast together
* @returns
*/
export function broadcastSizes (...sizes) {
const dimensions = sizes.map((s) => s.length)
const N = Math.max(...dimensions)
const sizeMax = new Array(N).fill(null)
// check for every size
for (let i = 0; i < sizes.length; i++) {
const size = sizes[i]
const dim = dimensions[i]
for (let j = 0; j < dim; j++) {
const n = N - dim + j
if (size[j] > sizeMax[n]) {
sizeMax[n] = size[j]
}
}
}
for (let i = 0; i < sizes.length; i++) {
checkBroadcastingRules(sizes[i], sizeMax)
}
return sizeMax
}
/**
* Checks if it's possible to broadcast a size to another size
* @param {number[]} size The size of the array to check
* @param {number[]} toSize The size of the array to validate if it can be broadcasted to
*/
export function checkBroadcastingRules (size, toSize) {
const N = toSize.length
const dim = size.length
for (let j = 0; j < dim; j++) {
const n = N - dim + j
if ((size[j] < toSize[n] && size[j] > 1) || (size[j] > toSize[n])) {
throw new Error(
`shape missmatch: missmatch is found in arg with shape (${size}) not possible to broadcast dimension ${dim} with size ${size[j]} to size ${toSize[n]}`
)
}
}
}
/**
* Broadcasts a single array to a certain size
* @param {array} array Array to be broadcasted
* @param {number[]} toSize Size to broadcast the array
* @returns The broadcasted array
*/
export function broadcastTo (array, toSize) {
let Asize = arraySize(array)
if (deepStrictEqual(Asize, toSize)) {
return array
}
checkBroadcastingRules(Asize, toSize)
const broadcastedSize = broadcastSizes(Asize, toSize)
const N = broadcastedSize.length
const paddedSize = [...Array(N - Asize.length).fill(1), ...Asize]
let A = clone(array)
// reshape A if needed to make it ready for concat
if (Asize.length < N) {
A = reshape(A, paddedSize)
Asize = arraySize(A)
}
// stretches the array on each dimension to make it the same size as index
for (let dim = 0; dim < N; dim++) {
if (Asize[dim] < broadcastedSize[dim]) {
A = stretch(A, broadcastedSize[dim], dim)
Asize = arraySize(A)
}
}
return A
}
/**
* Broadcasts arrays and returns the broadcasted arrays in an array
* @param {...Array | any} arrays
* @returns
*/
export function broadcastArrays (...arrays) {
if (arrays.length === 0) {
throw new Error('Insuficient number of argumnets in function broadcastArrays')
}
if (arrays.length === 1) {
return arrays[0]
}
const sizes = arrays.map(function (array) { return arraySize(array) })
const broadcastedSize = broadcastSizes(...sizes)
const broadcastedArrays = []
arrays.forEach(function (array) { broadcastedArrays.push(broadcastTo(array, broadcastedSize)) })
return broadcastedArrays
}
/**
* stretches a matrix up to a certain size in a certain dimension
* @param {Array} arrayToStretch
* @param {number[]} sizeToStretch
* @param {number} dimToStretch
* @returns
*/
export function stretch (arrayToStretch, sizeToStretch, dimToStretch) {
return concat(...Array(sizeToStretch).fill(arrayToStretch), dimToStretch)
}
/**
* Deep clones a multidimensional array
* @param {Array} array
* @returns cloned array
*/
export function clone (array) {
return Object.assign([], array)
}