mathjs
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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
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JavaScript
'use strict'
const util = require('../../utils/index')
const DimensionError = require('../../error/DimensionError')
const array = util.array
const object = util.object
const string = util.string
const number = util.number
const isArray = Array.isArray
const isNumber = number.isNumber
const isInteger = number.isInteger
const isString = string.isString
const validateIndex = array.validateIndex
function factory (type, config, load, typed) {
const Matrix = load(require('./Matrix')) // force loading Matrix (do not use via type.Matrix)
const equalScalar = load(require('../../function/relational/equalScalar'))
const getArrayDataType = load(require('./utils/getArrayDataType'))
/**
* Sparse Matrix implementation. This type implements a Compressed Column Storage format
* for sparse matrices.
* @class SparseMatrix
*/
function SparseMatrix (data, datatype) {
if (!(this instanceof SparseMatrix)) { throw new SyntaxError('Constructor must be called with the new operator') }
if (datatype && !isString(datatype)) { throw new Error('Invalid datatype: ' + datatype) }
if (type.isMatrix(data)) {
// create from matrix
_createFromMatrix(this, data, datatype)
} else if (data && isArray(data.index) && isArray(data.ptr) && isArray(data.size)) {
// initialize fields
this._values = data.values
this._index = data.index
this._ptr = data.ptr
this._size = data.size
this._datatype = datatype || data.datatype
} else if (isArray(data)) {
// create from array
_createFromArray(this, data, datatype)
} else if (data) {
// unsupported type
throw new TypeError('Unsupported type of data (' + util.types.type(data) + ')')
} else {
// nothing provided
this._values = []
this._index = []
this._ptr = [0]
this._size = [0, 0]
this._datatype = datatype
}
}
function _createFromMatrix (matrix, source, datatype) {
// check matrix type
if (source.type === 'SparseMatrix') {
// clone arrays
matrix._values = source._values ? object.clone(source._values) : undefined
matrix._index = object.clone(source._index)
matrix._ptr = object.clone(source._ptr)
matrix._size = object.clone(source._size)
matrix._datatype = datatype || source._datatype
} else {
// build from matrix data
_createFromArray(matrix, source.valueOf(), datatype || source._datatype)
}
}
function _createFromArray (matrix, data, datatype) {
// initialize fields
matrix._values = []
matrix._index = []
matrix._ptr = []
matrix._datatype = datatype
// discover rows & columns, do not use math.size() to avoid looping array twice
const rows = data.length
let columns = 0
// equal signature to use
let eq = equalScalar
// zero value
let zero = 0
if (isString(datatype)) {
// find signature that matches (datatype, datatype)
eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar
// convert 0 to the same datatype
zero = typed.convert(0, datatype)
}
// check we have rows (empty array)
if (rows > 0) {
// column index
let j = 0
do {
// store pointer to values index
matrix._ptr.push(matrix._index.length)
// loop rows
for (let i = 0; i < rows; i++) {
// current row
const row = data[i]
// check row is an array
if (isArray(row)) {
// update columns if needed (only on first column)
if (j === 0 && columns < row.length) { columns = row.length }
// check row has column
if (j < row.length) {
// value
const v = row[j]
// check value != 0
if (!eq(v, zero)) {
// store value
matrix._values.push(v)
// index
matrix._index.push(i)
}
}
} else {
// update columns if needed (only on first column)
if (j === 0 && columns < 1) { columns = 1 }
// check value != 0 (row is a scalar)
if (!eq(row, zero)) {
// store value
matrix._values.push(row)
// index
matrix._index.push(i)
}
}
}
// increment index
j++
}
while (j < columns)
}
// store number of values in ptr
matrix._ptr.push(matrix._index.length)
// size
matrix._size = [rows, columns]
}
SparseMatrix.prototype = new Matrix()
/**
* Attach type information
*/
SparseMatrix.prototype.type = 'SparseMatrix'
SparseMatrix.prototype.isSparseMatrix = true
/**
* Get the matrix type
*
* Usage:
* const matrixType = matrix.getDataType() // retrieves the matrix type
*
* @memberOf SparseMatrix
* @return {string} type information; if multiple types are found from the Matrix, it will return "mixed"
*/
SparseMatrix.prototype.getDataType = function () {
return getArrayDataType(this._values)
}
/**
* Get the storage format used by the matrix.
*
* Usage:
* const format = matrix.storage() // retrieve storage format
*
* @memberof SparseMatrix
* @return {string} The storage format.
*/
SparseMatrix.prototype.storage = function () {
return 'sparse'
}
/**
* Get the datatype of the data stored in the matrix.
*
* Usage:
* const format = matrix.datatype() // retrieve matrix datatype
*
* @memberof SparseMatrix
* @return {string} The datatype.
*/
SparseMatrix.prototype.datatype = function () {
return this._datatype
}
/**
* Create a new SparseMatrix
* @memberof SparseMatrix
* @param {Array} data
* @param {string} [datatype]
*/
SparseMatrix.prototype.create = function (data, datatype) {
return new SparseMatrix(data, datatype)
}
/**
* Get the matrix density.
*
* Usage:
* const density = matrix.density() // retrieve matrix density
*
* @memberof SparseMatrix
* @return {number} The matrix density.
*/
SparseMatrix.prototype.density = function () {
// rows & columns
const rows = this._size[0]
const columns = this._size[1]
// calculate density
return rows !== 0 && columns !== 0 ? (this._index.length / (rows * columns)) : 0
}
/**
* Get a subset of the matrix, or replace a subset of the matrix.
*
* Usage:
* const subset = matrix.subset(index) // retrieve subset
* const value = matrix.subset(index, replacement) // replace subset
*
* @memberof SparseMatrix
* @param {Index} index
* @param {Array | Maytrix | *} [replacement]
* @param {*} [defaultValue=0] Default value, filled in on new entries when
* the matrix is resized. If not provided,
* new matrix elements will be filled with zeros.
*/
SparseMatrix.prototype.subset = function (index, replacement, defaultValue) { // check it is a pattern matrix
if (!this._values) { throw new Error('Cannot invoke subset on a Pattern only matrix') }
// check arguments
switch (arguments.length) {
case 1:
return _getsubset(this, index)
// intentional fall through
case 2:
case 3:
return _setsubset(this, index, replacement, defaultValue)
default:
throw new SyntaxError('Wrong number of arguments')
}
}
function _getsubset (matrix, idx) {
// check idx
if (!type.isIndex(idx)) {
throw new TypeError('Invalid index')
}
const isScalar = idx.isScalar()
if (isScalar) {
// return a scalar
return matrix.get(idx.min())
}
// validate dimensions
const size = idx.size()
if (size.length !== matrix._size.length) {
throw new DimensionError(size.length, matrix._size.length)
}
// vars
let i, ii, k, kk
// validate if any of the ranges in the index is out of range
const min = idx.min()
const max = idx.max()
for (i = 0, ii = matrix._size.length; i < ii; i++) {
validateIndex(min[i], matrix._size[i])
validateIndex(max[i], matrix._size[i])
}
// matrix arrays
const mvalues = matrix._values
const mindex = matrix._index
const mptr = matrix._ptr
// rows & columns dimensions for result matrix
const rows = idx.dimension(0)
const columns = idx.dimension(1)
// workspace & permutation vector
const w = []
const pv = []
// loop rows in resulting matrix
rows.forEach(function (i, r) {
// update permutation vector
pv[i] = r[0]
// mark i in workspace
w[i] = true
})
// result matrix arrays
const values = mvalues ? [] : undefined
const index = []
const ptr = []
// loop columns in result matrix
columns.forEach(function (j) {
// update ptr
ptr.push(index.length)
// loop values in column j
for (k = mptr[j], kk = mptr[j + 1]; k < kk; k++) {
// row
i = mindex[k]
// check row is in result matrix
if (w[i] === true) {
// push index
index.push(pv[i])
// check we need to process values
if (values) { values.push(mvalues[k]) }
}
}
})
// update ptr
ptr.push(index.length)
// return matrix
return new SparseMatrix({
values: values,
index: index,
ptr: ptr,
size: size,
datatype: matrix._datatype
})
}
function _setsubset (matrix, index, submatrix, defaultValue) {
// check index
if (!index || index.isIndex !== true) {
throw new TypeError('Invalid index')
}
// get index size and check whether the index contains a single value
const iSize = index.size()
const isScalar = index.isScalar()
// calculate the size of the submatrix, and convert it into an Array if needed
let sSize
if (type.isMatrix(submatrix)) {
// submatrix size
sSize = submatrix.size()
// use array representation
submatrix = submatrix.toArray()
} else {
// get submatrix size (array, scalar)
sSize = array.size(submatrix)
}
// check index is a scalar
if (isScalar) {
// verify submatrix is a scalar
if (sSize.length !== 0) {
throw new TypeError('Scalar expected')
}
// set value
matrix.set(index.min(), submatrix, defaultValue)
} else {
// validate dimensions, index size must be one or two dimensions
if (iSize.length !== 1 && iSize.length !== 2) {
throw new DimensionError(iSize.length, matrix._size.length, '<')
}
// check submatrix and index have the same dimensions
if (sSize.length < iSize.length) {
// calculate number of missing outer dimensions
let i = 0
let outer = 0
while (iSize[i] === 1 && sSize[i] === 1) {
i++
}
while (iSize[i] === 1) {
outer++
i++
}
// unsqueeze both outer and inner dimensions
submatrix = array.unsqueeze(submatrix, iSize.length, outer, sSize)
}
// check whether the size of the submatrix matches the index size
if (!object.deepEqual(iSize, sSize)) {
throw new DimensionError(iSize, sSize, '>')
}
// offsets
const x0 = index.min()[0]
const y0 = index.min()[1]
// submatrix rows and columns
const m = sSize[0]
const n = sSize[1]
// loop submatrix
for (let x = 0; x < m; x++) {
// loop columns
for (let y = 0; y < n; y++) {
// value at i, j
const v = submatrix[x][y]
// invoke set (zero value will remove entry from matrix)
matrix.set([x + x0, y + y0], v, defaultValue)
}
}
}
return matrix
}
/**
* Get a single element from the matrix.
* @memberof SparseMatrix
* @param {number[]} index Zero-based index
* @return {*} value
*/
SparseMatrix.prototype.get = function (index) {
if (!isArray(index)) { throw new TypeError('Array expected') }
if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }
// check it is a pattern matrix
if (!this._values) { throw new Error('Cannot invoke get on a Pattern only matrix') }
// row and column
const i = index[0]
const j = index[1]
// check i, j are valid
validateIndex(i, this._size[0])
validateIndex(j, this._size[1])
// find value index
const k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index)
// check k is prior to next column k and it is in the correct row
if (k < this._ptr[j + 1] && this._index[k] === i) { return this._values[k] }
return 0
}
/**
* Replace a single element in the matrix.
* @memberof SparseMatrix
* @param {number[]} index Zero-based index
* @param {*} value
* @param {*} [defaultValue] Default value, filled in on new entries when
* the matrix is resized. If not provided,
* new matrix elements will be set to zero.
* @return {SparseMatrix} self
*/
SparseMatrix.prototype.set = function (index, v, defaultValue) {
if (!isArray(index)) { throw new TypeError('Array expected') }
if (index.length !== this._size.length) { throw new DimensionError(index.length, this._size.length) }
// check it is a pattern matrix
if (!this._values) { throw new Error('Cannot invoke set on a Pattern only matrix') }
// row and column
const i = index[0]
const j = index[1]
// rows & columns
let rows = this._size[0]
let columns = this._size[1]
// equal signature to use
let eq = equalScalar
// zero value
let zero = 0
if (isString(this._datatype)) {
// find signature that matches (datatype, datatype)
eq = typed.find(equalScalar, [this._datatype, this._datatype]) || equalScalar
// convert 0 to the same datatype
zero = typed.convert(0, this._datatype)
}
// check we need to resize matrix
if (i > rows - 1 || j > columns - 1) {
// resize matrix
_resize(this, Math.max(i + 1, rows), Math.max(j + 1, columns), defaultValue)
// update rows & columns
rows = this._size[0]
columns = this._size[1]
}
// check i, j are valid
validateIndex(i, rows)
validateIndex(j, columns)
// find value index
const k = _getValueIndex(i, this._ptr[j], this._ptr[j + 1], this._index)
// check k is prior to next column k and it is in the correct row
if (k < this._ptr[j + 1] && this._index[k] === i) {
// check value != 0
if (!eq(v, zero)) {
// update value
this._values[k] = v
} else {
// remove value from matrix
_remove(k, j, this._values, this._index, this._ptr)
}
} else {
// insert value @ (i, j)
_insert(k, i, j, v, this._values, this._index, this._ptr)
}
return this
}
function _getValueIndex (i, top, bottom, index) {
// check row is on the bottom side
if (bottom - top === 0) { return bottom }
// loop rows [top, bottom[
for (let r = top; r < bottom; r++) {
// check we found value index
if (index[r] === i) { return r }
}
// we did not find row
return top
}
function _remove (k, j, values, index, ptr) {
// remove value @ k
values.splice(k, 1)
index.splice(k, 1)
// update pointers
for (let x = j + 1; x < ptr.length; x++) { ptr[x]-- }
}
function _insert (k, i, j, v, values, index, ptr) {
// insert value
values.splice(k, 0, v)
// update row for k
index.splice(k, 0, i)
// update column pointers
for (let x = j + 1; x < ptr.length; x++) { ptr[x]++ }
}
/**
* Resize the matrix to the given size. Returns a copy of the matrix when
* `copy=true`, otherwise return the matrix itself (resize in place).
*
* @memberof SparseMatrix
* @param {number[]} size The new size the matrix should have.
* @param {*} [defaultValue=0] Default value, filled in on new entries.
* If not provided, the matrix elements will
* be filled with zeros.
* @param {boolean} [copy] Return a resized copy of the matrix
*
* @return {Matrix} The resized matrix
*/
SparseMatrix.prototype.resize = function (size, defaultValue, copy) {
// validate arguments
if (!isArray(size)) { throw new TypeError('Array expected') }
if (size.length !== 2) { throw new Error('Only two dimensions matrix are supported') }
// check sizes
size.forEach(function (value) {
if (!number.isNumber(value) || !number.isInteger(value) || value < 0) {
throw new TypeError('Invalid size, must contain positive integers ' +
'(size: ' + string.format(size) + ')')
}
})
// matrix to resize
const m = copy ? this.clone() : this
// resize matrix
return _resize(m, size[0], size[1], defaultValue)
}
function _resize (matrix, rows, columns, defaultValue) {
// value to insert at the time of growing matrix
let value = defaultValue || 0
// equal signature to use
let eq = equalScalar
// zero value
let zero = 0
if (isString(matrix._datatype)) {
// find signature that matches (datatype, datatype)
eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar
// convert 0 to the same datatype
zero = typed.convert(0, matrix._datatype)
// convert value to the same datatype
value = typed.convert(value, matrix._datatype)
}
// should we insert the value?
const ins = !eq(value, zero)
// old columns and rows
const r = matrix._size[0]
let c = matrix._size[1]
let i, j, k
// check we need to increase columns
if (columns > c) {
// loop new columns
for (j = c; j < columns; j++) {
// update matrix._ptr for current column
matrix._ptr[j] = matrix._values.length
// check we need to insert matrix._values
if (ins) {
// loop rows
for (i = 0; i < r; i++) {
// add new matrix._values
matrix._values.push(value)
// update matrix._index
matrix._index.push(i)
}
}
}
// store number of matrix._values in matrix._ptr
matrix._ptr[columns] = matrix._values.length
} else if (columns < c) {
// truncate matrix._ptr
matrix._ptr.splice(columns + 1, c - columns)
// truncate matrix._values and matrix._index
matrix._values.splice(matrix._ptr[columns], matrix._values.length)
matrix._index.splice(matrix._ptr[columns], matrix._index.length)
}
// update columns
c = columns
// check we need to increase rows
if (rows > r) {
// check we have to insert values
if (ins) {
// inserts
let n = 0
// loop columns
for (j = 0; j < c; j++) {
// update matrix._ptr for current column
matrix._ptr[j] = matrix._ptr[j] + n
// where to insert matrix._values
k = matrix._ptr[j + 1] + n
// pointer
let p = 0
// loop new rows, initialize pointer
for (i = r; i < rows; i++, p++) {
// add value
matrix._values.splice(k + p, 0, value)
// update matrix._index
matrix._index.splice(k + p, 0, i)
// increment inserts
n++
}
}
// store number of matrix._values in matrix._ptr
matrix._ptr[c] = matrix._values.length
}
} else if (rows < r) {
// deletes
let d = 0
// loop columns
for (j = 0; j < c; j++) {
// update matrix._ptr for current column
matrix._ptr[j] = matrix._ptr[j] - d
// where matrix._values start for next column
const k0 = matrix._ptr[j]
const k1 = matrix._ptr[j + 1] - d
// loop matrix._index
for (k = k0; k < k1; k++) {
// row
i = matrix._index[k]
// check we need to delete value and matrix._index
if (i > rows - 1) {
// remove value
matrix._values.splice(k, 1)
// remove item from matrix._index
matrix._index.splice(k, 1)
// increase deletes
d++
}
}
}
// update matrix._ptr for current column
matrix._ptr[j] = matrix._values.length
}
// update matrix._size
matrix._size[0] = rows
matrix._size[1] = columns
// return matrix
return matrix
}
/**
* Reshape the matrix to the given size. Returns a copy of the matrix when
* `copy=true`, otherwise return the matrix itself (reshape in place).
*
* NOTE: This might be better suited to copy by default, instead of modifying
* in place. For now, it operates in place to remain consistent with
* resize().
*
* @memberof SparseMatrix
* @param {number[]} size The new size the matrix should have.
* @param {boolean} [copy] Return a reshaped copy of the matrix
*
* @return {Matrix} The reshaped matrix
*/
SparseMatrix.prototype.reshape = function (size, copy) {
// validate arguments
if (!isArray(size)) { throw new TypeError('Array expected') }
if (size.length !== 2) { throw new Error('Sparse matrices can only be reshaped in two dimensions') }
// check sizes
size.forEach(function (value) {
if (!number.isNumber(value) || !number.isInteger(value) || value < 0) {
throw new TypeError('Invalid size, must contain positive integers ' +
'(size: ' + string.format(size) + ')')
}
})
// m * n must not change
if (this._size[0] * this._size[1] !== size[0] * size[1]) {
throw new Error('Reshaping sparse matrix will result in the wrong number of elements')
}
// matrix to reshape
const m = copy ? this.clone() : this
// return unchanged if the same shape
if (this._size[0] === size[0] && this._size[1] === size[1]) {
return m
}
// Convert to COO format (generate a column index)
const colIndex = []
for (let i = 0; i < m._ptr.length; i++) {
for (let j = 0; j < m._ptr[i + 1] - m._ptr[i]; j++) {
colIndex.push(i)
}
}
// Clone the values array
const values = m._values.slice()
// Clone the row index array
const rowIndex = m._index.slice()
// Transform the (row, column) indices
for (let i = 0; i < m._index.length; i++) {
const r1 = rowIndex[i]
const c1 = colIndex[i]
const flat = r1 * m._size[1] + c1
colIndex[i] = flat % size[1]
rowIndex[i] = Math.floor(flat / size[1])
}
// Now reshaping is supposed to preserve the row-major order, BUT these sparse matrices are stored
// in column-major order, so we have to reorder the value array now. One option is to use a multisort,
// sorting several arrays based on some other array.
// OR, we could easily just:
// 1. Remove all values from the matrix
m._values.length = 0
m._index.length = 0
m._ptr.length = size[1] + 1
m._size = size.slice()
for (let i = 0; i < m._ptr.length; i++) {
m._ptr[i] = 0
}
// 2. Re-insert all elements in the proper order (simplified code from SparseMatrix.prototype.set)
// This step is probably the most time-consuming
for (let h = 0; h < values.length; h++) {
const i = rowIndex[h]
const j = colIndex[h]
const v = values[h]
const k = _getValueIndex(i, m._ptr[j], m._ptr[j + 1], m._index)
_insert(k, i, j, v, m._values, m._index, m._ptr)
}
// The value indices are inserted out of order, but apparently that's... still OK?
return m
}
/**
* Create a clone of the matrix
* @memberof SparseMatrix
* @return {SparseMatrix} clone
*/
SparseMatrix.prototype.clone = function () {
const m = new SparseMatrix({
values: this._values ? object.clone(this._values) : undefined,
index: object.clone(this._index),
ptr: object.clone(this._ptr),
size: object.clone(this._size),
datatype: this._datatype
})
return m
}
/**
* Retrieve the size of the matrix.
* @memberof SparseMatrix
* @returns {number[]} size
*/
SparseMatrix.prototype.size = function () {
return this._size.slice(0) // copy the Array
}
/**
* Create a new matrix with the results of the callback function executed on
* each entry of the matrix.
* @memberof SparseMatrix
* @param {Function} callback The callback function is invoked with three
* parameters: the value of the element, the index
* of the element, and the Matrix being traversed.
* @param {boolean} [skipZeros] Invoke callback function for non-zero values only.
*
* @return {SparseMatrix} matrix
*/
SparseMatrix.prototype.map = function (callback, skipZeros) {
// check it is a pattern matrix
if (!this._values) { throw new Error('Cannot invoke map on a Pattern only matrix') }
// matrix instance
const me = this
// rows and columns
const rows = this._size[0]
const columns = this._size[1]
// invoke callback
const invoke = function (v, i, j) {
// invoke callback
return callback(v, [i, j], me)
}
// invoke _map
return _map(this, 0, rows - 1, 0, columns - 1, invoke, skipZeros)
}
/**
* Create a new matrix with the results of the callback function executed on the interval
* [minRow..maxRow, minColumn..maxColumn].
*/
function _map (matrix, minRow, maxRow, minColumn, maxColumn, callback, skipZeros) {
// result arrays
const values = []
const index = []
const ptr = []
// equal signature to use
let eq = equalScalar
// zero value
let zero = 0
if (isString(matrix._datatype)) {
// find signature that matches (datatype, datatype)
eq = typed.find(equalScalar, [matrix._datatype, matrix._datatype]) || equalScalar
// convert 0 to the same datatype
zero = typed.convert(0, matrix._datatype)
}
// invoke callback
const invoke = function (v, x, y) {
// invoke callback
v = callback(v, x, y)
// check value != 0
if (!eq(v, zero)) {
// store value
values.push(v)
// index
index.push(x)
}
}
// loop columns
for (let j = minColumn; j <= maxColumn; j++) {
// store pointer to values index
ptr.push(values.length)
// k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
const k0 = matrix._ptr[j]
const k1 = matrix._ptr[j + 1]
if (skipZeros) {
// loop k within [k0, k1[
for (let k = k0; k < k1; k++) {
// row index
const i = matrix._index[k]
// check i is in range
if (i >= minRow && i <= maxRow) {
// value @ k
invoke(matrix._values[k], i - minRow, j - minColumn)
}
}
} else {
// create a cache holding all defined values
const values = {}
for (let k = k0; k < k1; k++) {
const i = matrix._index[k]
values[i] = matrix._values[k]
}
// loop over all rows (indexes can be unordered so we can't use that),
// and either read the value or zero
for (let i = minRow; i <= maxRow; i++) {
const value = (i in values) ? values[i] : 0
invoke(value, i - minRow, j - minColumn)
}
}
}
// store number of values in ptr
ptr.push(values.length)
// return sparse matrix
return new SparseMatrix({
values: values,
index: index,
ptr: ptr,
size: [maxRow - minRow + 1, maxColumn - minColumn + 1]
})
}
/**
* Execute a callback function on each entry of the matrix.
* @memberof SparseMatrix
* @param {Function} callback The callback function is invoked with three
* parameters: the value of the element, the index
* of the element, and the Matrix being traversed.
* @param {boolean} [skipZeros] Invoke callback function for non-zero values only.
*/
SparseMatrix.prototype.forEach = function (callback, skipZeros) {
// check it is a pattern matrix
if (!this._values) { throw new Error('Cannot invoke forEach on a Pattern only matrix') }
// matrix instance
const me = this
// rows and columns
const rows = this._size[0]
const columns = this._size[1]
// loop columns
for (let j = 0; j < columns; j++) {
// k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
const k0 = this._ptr[j]
const k1 = this._ptr[j + 1]
if (skipZeros) {
// loop k within [k0, k1[
for (let k = k0; k < k1; k++) {
// row index
const i = this._index[k]
// value @ k
callback(this._values[k], [i, j], me)
}
} else {
// create a cache holding all defined values
const values = {}
for (let k = k0; k < k1; k++) {
const i = this._index[k]
values[i] = this._values[k]
}
// loop over all rows (indexes can be unordered so we can't use that),
// and either read the value or zero
for (let i = 0; i < rows; i++) {
const value = (i in values) ? values[i] : 0
callback(value, [i, j], me)
}
}
}
}
/**
* Create an Array with a copy of the data of the SparseMatrix
* @memberof SparseMatrix
* @returns {Array} array
*/
SparseMatrix.prototype.toArray = function () {
return _toArray(this._values, this._index, this._ptr, this._size, true)
}
/**
* Get the primitive value of the SparseMatrix: a two dimensions array
* @memberof SparseMatrix
* @returns {Array} array
*/
SparseMatrix.prototype.valueOf = function () {
return _toArray(this._values, this._index, this._ptr, this._size, false)
}
function _toArray (values, index, ptr, size, copy) {
// rows and columns
const rows = size[0]
const columns = size[1]
// result
const a = []
// vars
let i, j
// initialize array
for (i = 0; i < rows; i++) {
a[i] = []
for (j = 0; j < columns; j++) { a[i][j] = 0 }
}
// loop columns
for (j = 0; j < columns; j++) {
// k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
const k0 = ptr[j]
const k1 = ptr[j + 1]
// loop k within [k0, k1[
for (let k = k0; k < k1; k++) {
// row index
i = index[k]
// set value (use one for pattern matrix)
a[i][j] = values ? (copy ? object.clone(values[k]) : values[k]) : 1
}
}
return a
}
/**
* Get a string representation of the matrix, with optional formatting options.
* @memberof SparseMatrix
* @param {Object | number | Function} [options] Formatting options. See
* lib/utils/number:format for a
* description of the available
* options.
* @returns {string} str
*/
SparseMatrix.prototype.format = function (options) {
// rows and columns
const rows = this._size[0]
const columns = this._size[1]
// density
const density = this.density()
// rows & columns
let str = 'Sparse Matrix [' + string.format(rows, options) + ' x ' + string.format(columns, options) + '] density: ' + string.format(density, options) + '\n'
// loop columns
for (let j = 0; j < columns; j++) {
// k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
const k0 = this._ptr[j]
const k1 = this._ptr[j + 1]
// loop k within [k0, k1[
for (let k = k0; k < k1; k++) {
// row index
const i = this._index[k]
// append value
str += '\n (' + string.format(i, options) + ', ' + string.format(j, options) + ') ==> ' + (this._values ? string.format(this._values[k], options) : 'X')
}
}
return str
}
/**
* Get a string representation of the matrix
* @memberof SparseMatrix
* @returns {string} str
*/
SparseMatrix.prototype.toString = function () {
return string.format(this.toArray())
}
/**
* Get a JSON representation of the matrix
* @memberof SparseMatrix
* @returns {Object}
*/
SparseMatrix.prototype.toJSON = function () {
return {
mathjs: 'SparseMatrix',
values: this._values,
index: this._index,
ptr: this._ptr,
size: this._size,
datatype: this._datatype
}
}
/**
* Get the kth Matrix diagonal.
*
* @memberof SparseMatrix
* @param {number | BigNumber} [k=0] The kth diagonal where the vector will retrieved.
*
* @returns {Matrix} The matrix vector with the diagonal values.
*/
SparseMatrix.prototype.diagonal = function (k) {
// validate k if any
if (k) {
// convert BigNumber to a number
if (type.isBigNumber(k)) { k = k.toNumber() }
// is must be an integer
if (!isNumber(k) || !isInteger(k)) {
throw new TypeError('The parameter k must be an integer number')
}
} else {
// default value
k = 0
}
const kSuper = k > 0 ? k : 0
const kSub = k < 0 ? -k : 0
// rows & columns
const rows = this._size[0]
const columns = this._size[1]
// number diagonal values
const n = Math.min(rows - kSub, columns - kSuper)
// diagonal arrays
const values = []
const index = []
const ptr = []
// initial ptr value
ptr[0] = 0
// loop columns
for (let j = kSuper; j < columns && values.length < n; j++) {
// k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
const k0 = this._ptr[j]
const k1 = this._ptr[j + 1]
// loop x within [k0, k1[
for (let x = k0; x < k1; x++) {
// row index
const i = this._index[x]
// check row
if (i === j - kSuper + kSub) {
// value on this column
values.push(this._values[x])
// store row
index[values.length - 1] = i - kSub
// exit loop
break
}
}
}
// close ptr
ptr.push(values.length)
// return matrix
return new SparseMatrix({
values: values,
index: index,
ptr: ptr,
size: [n, 1]
})
}
/**
* Generate a matrix from a JSON object
* @memberof SparseMatrix
* @param {Object} json An object structured like
* `{"mathjs": "SparseMatrix", "values": [], "index": [], "ptr": [], "size": []}`,
* where mathjs is optional
* @returns {SparseMatrix}
*/
SparseMatrix.fromJSON = function (json) {
return new SparseMatrix(json)
}
/**
* Create a diagonal matrix.
*
* @memberof SparseMatrix
* @param {Array} size The matrix size.
* @param {number | Array | Matrix } value The values for the diagonal.
* @param {number | BigNumber} [k=0] The kth diagonal where the vector will be filled in.
* @param {string} [datatype] The Matrix datatype, values must be of this datatype.
*
* @returns {SparseMatrix}
*/
SparseMatrix.diagonal = function (size, value, k, defaultValue, datatype) {
if (!isArray(size)) { throw new TypeError('Array expected, size parameter') }
if (size.length !== 2) { throw new Error('Only two dimensions matrix are supported') }
// map size & validate
size = size.map(function (s) {
// check it is a big number
if (type.isBigNumber(s)) {
// convert it
s = s.toNumber()
}
// validate arguments
if (!isNumber(s) || !isInteger(s) || s < 1) {
throw new Error('Size values must be positive integers')
}
return s
})
// validate k if any
if (k) {
// convert BigNumber to a number
if (type.isBigNumber(k)) { k = k.toNumber() }
// is must be an integer
if (!isNumber(k) || !isInteger(k)) {
throw new TypeError('The parameter k must be an integer number')
}
} else {
// default value
k = 0
}
// equal signature to use
let eq = equalScalar
// zero value
let zero = 0
if (isString(datatype)) {
// find signature that matches (datatype, datatype)
eq = typed.find(equalScalar, [datatype, datatype]) || equalScalar
// convert 0 to the same datatype
zero = typed.convert(0, datatype)
}
const kSuper = k > 0 ? k : 0
const kSub = k < 0 ? -k : 0
// rows and columns
const rows = size[0]
const columns = size[1]
// number of non-zero items
const n = Math.min(rows - kSub, columns - kSuper)
// value extraction function
let _value
// check value
if (isArray(value)) {
// validate array
if (value.length !== n) {
// number of values in array must be n
throw new Error('Invalid value array length')
}
// define function
_value = function (i) {
// return value @ i
return value[i]
}
} else if (type.isMatrix(value)) {
// matrix size
const ms = value.size()
// validate matrix
if (ms.length !== 1 || ms[0] !== n) {
// number of values in array must be n
throw new Error('Invalid matrix length')
}
// define function
_value = function (i) {
// return value @ i
return value.get([i])
}
} else {
// define function
_value = function () {
// return value
return value
}
}
// create arrays
const values = []
const index = []
const ptr = []
// loop items
for (let j = 0; j < columns; j++) {
// number of rows with value
ptr.push(values.length)
// diagonal index
const i = j - kSuper
// check we need to set diagonal value
if (i >= 0 && i < n) {
// get value @ i
const v = _value(i)
// check for zero
if (!eq(v, zero)) {
// column
index.push(i + kSub)
// add value
values.push(v)
}
}
}
// last value should be number of values
ptr.push(values.length)
// create SparseMatrix
return new SparseMatrix({
values: values,
index: index,
ptr: ptr,
size: [rows, columns]
})
}
/**
* Swap rows i and j in Matrix.
*
* @memberof SparseMatrix
* @param {number} i Matrix row index 1
* @param {number} j Matrix row index 2
*
* @return {Matrix} The matrix reference
*/
SparseMatrix.prototype.swapRows = function (i, j) {
// check index
if (!isNumber(i) || !isInteger(i) || !isNumber(j) || !isInteger(j)) {
throw new Error('Row index must be positive integers')
}
// check dimensions
if (this._size.length !== 2) {
throw new Error('Only two dimensional matrix is supported')
}
// validate index
validateIndex(i, this._size[0])
validateIndex(j, this._size[0])
// swap rows
SparseMatrix._swapRows(i, j, this._size[1], this._values, this._index, this._ptr)
// return current instance
return this
}
/**
* Loop rows with data in column j.
*
* @param {number} j Column
* @param {Array} values Matrix values
* @param {Array} index Matrix row indeces
* @param {Array} ptr Matrix column pointers
* @param {Function} callback Callback function invoked for every row in column j
*/
SparseMatrix._forEachRow = function (j, values, index, ptr, callback) {
// indeces for column j
const k0 = ptr[j]
const k1 = ptr[j + 1]
// loop
for (let k = k0; k < k1; k++) {
// invoke callback
callback(index[k], values[k])
}
}
/**
* Swap rows x and y in Sparse Matrix data structures.
*
* @param {number} x Matrix row index 1
* @param {number} y Matrix row index 2
* @param {number} columns Number of columns in matrix
* @param {Array} values Matrix values
* @param {Array} index Matrix row indeces
* @param {Array} ptr Matrix column pointers
*/
SparseMatrix._swapRows = function (x, y, columns, values, index, ptr) {
// loop columns
for (let j = 0; j < columns; j++) {
// k0 <= k < k1 where k0 = _ptr[j] && k1 = _ptr[j+1]
const k0 = ptr[j]
const k1 = ptr[j + 1]
// find value index @ x
const kx = _getValueIndex(x, k0, k1, index)
// find value index @ x
const ky = _getValueIndex(y, k0, k1, index)
// check both rows exist in matrix
if (kx < k1 && ky < k1 && index[kx] === x && index[ky] === y) {
// swap values (check for pattern matrix)
if (values) {
const v = values[kx]
values[kx] = values[ky]
values[ky] = v
}
// next column
continue
}
// check x row exist & no y row
if (kx < k1 && index[kx] === x && (ky >= k1 || index[ky] !== y)) {
// value @ x (check for pattern matrix)
const vx = values ? values[kx] : undefined
// insert value @ y
index.splice(ky, 0, y)
if (values) { values.splice(ky, 0, vx) }
// remove value @ x (adjust array index if needed)
index.splice(ky <= kx ? kx + 1 : kx, 1)
if (values) { values.splice(ky <= kx ? kx + 1 : kx, 1) }
// next column
continue
}
// check y row exist & no x row
if (ky < k1 && index[ky] === y && (kx >= k1 || index[kx] !== x)) {
// value @ y (check for pattern matrix)
const vy = values ? values[ky] : undefined
// insert value @ x
index.splice(kx, 0, x)
if (values) { values.splice(kx, 0, vy) }
// remove value @ y (adjust array index if needed)
index.splice(kx <= ky ? ky + 1 : ky, 1)
if (values) { values.splice(kx <= ky ? ky + 1 : ky, 1) }
}
}
}
// register this type in the base class Matrix
type.Matrix._storage.sparse = SparseMatrix
return SparseMatrix
}
exports.name = 'SparseMatrix'
exports.path = 'type'
exports.factory = factory
exports.lazy = false // no lazy loading, as we alter type.Matrix._storage