mathjs/src/utils/array.js at develop · rvramesh/mathjs · GitHub

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import { isInteger } from './number.js'

import { isNumber } from './is.js'

import { format } from './string.js'

import { DimensionError } from '../error/DimensionError.js'

import { IndexError } from '../error/IndexError.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)

}

/**

* 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 (!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)

}

/**

* Resize a multi dimensional array. The resized array is returned.

* @param {Array} array Array to be resized

* @param {Array.<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) {

// TODO: add support for scalars, having size=[] ?

// check the type of the arguments

if (!Array.isArray(array) || !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) + ')')

}

})

// 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 {Array.<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 {Array.<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 {Array.<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 {Array<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 {Array.<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.

export function initial (array) {

return array.slice(0, array.length - 1)

}

/**

* Test whether an array or string contains an item

* @param {Array | string} array

* @param {*} item

* @return {boolean}

export function contains (array, item) {

return array.indexOf(item) !== -1

}

mathjs/src/utils/array.js at develop · rvramesh/mathjs · GitHub

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