npm install dstructs-matrixMatrix
===
[![NPM version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][codecov-image]][codecov-url] [![Dependencies][dependencies-image]][dependencies-url]
> Matrices.
This module exports a [Matrix][matrix] data structure for efficient storage and computation of numeric values. The data structure provides an interface for accessing and modifying one or more stored values. Matrices find common use in linear algebra, numerical analysis, image manipulation, machine learning, and data processing.
---
1. Installation
1. Usage
- Matrix
* matrix()
- Properties
* dtype
* ndims
* shape
* offset
* strides
* length
* nbytes
* data
- Methods
* Set
- Matrix.prototype.set()
- Matrix.prototype.iset()
- Matrix.prototype.mset()
- Matrix.prototype.sset()
* Get
- Matrix.prototype.get()
- Matrix.prototype.iget()
- Matrix.prototype.mget()
- Matrix.prototype.sget()
* Accessor
- Matrix.prototype.toString()
- Matrix.prototype.toJSON()
- Constructor
- Raw
* matrix.raw()
1. Notes
- Linear Indexing
1. Examples
1. Tests
- Unit
- Coverage
1. License
---
`` bash`
$ npm install dstructs-matrix
For use in the browser, use [browserify][browserify].
` javascript`
var matrix = require( 'dstructs-matrix' );
#### matrix( [data,] shape[, dtype] )
Creates a new Matrix having a specified shape (dimensions => [rows,cols]).
` javascript`
var mat = matrix( [3,2] );
/*
[ 0 0
0 0
0 0 ]
*/
By default, the matrix elements are floating-point 64-bit numbers (float64). To specify a different data type, provide a dtype.
` javascript`
var mat = matrix( [2,2], 'int8' );
/*
[ 0 0
0 0 ]
*/
The following dtypes are accepted:
* int8
*
*
*
*
*
*
*
*
If a __linear__ numeric array is not provided, the function initializes a __zero-filled__ matrix. To initialize a matrix, provide a typed input data array, whose length matches the specified shape.
` javascript
var data = new Int8Array( 6 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
var mat = matrix( data, [2,3] ); // 2*3 = 6
/*
[ 0 1 2
3 4 5 ]
*/
`
To cast an input data array to a different data type, provide a dtype.
` javascript`
var mat = matrix( data, [2,2], 'uint32' );
/*
[ 0 1
2 3 ]
*/
If provided an Array instead of a typed array and no dtype is specified, the input data array is [cast][cast-arrays] to float64.
` javascript
var data = [ 10, 20, 30, 40, 50, 60 ];
var mat = matrix( data, [3,2] );
/*
[ 10 20
30 40
50 60 ]
*/
var dtype = mat.dtype;
// returns 'float64'
`
---
A Matrix has the following properties...
A __read-only__ property returning the underlying storage data type.
` javascript`
var dtype = mat.dtype;
// returns
A __read-only__ property returning the number of dimensions.
` javascript`
var ndims = mat.ndims;
// returns 2
A __read-only__ property returning the matrix shape.
` javascript`
var shape = mat.shape;
// returns [...]
A property returning the offset used to index into the underlying data store.
` javascript`
var offset = mat.offset;
// returns 0
By default, the offset is 0. While not __read-only__, most consumers should treat the offset as a __read-only__ property.
A __read-only__ property returning the strides used to index into the underlying data store.
` javascript`
var strides = mat.strides;
// returns [...]
While not __frozen__, most consumers should treat the strides elements as __read-only__ elements.
A __read-only__ property returning the matrix length; i.e., how many elements are in the Matrix, similar to [Array#length][array-length].
` javascript`
var len = mat.length;
// returns
__Note__: while a Matrix has a length property, a Matrix should __not__ be considered array-like, as array indexing with __not__ work as expected.
` javascript
var data = new Float32Array( 10 );
var mat = matrix( data, [1,10] );
/*
[ 0 0 0 0 0 0 0 0 0 0 ]
*/
var value = mat.get( 1, 3 );
// returns 0
value = mat[ 3 ];
// returns undefined
`
A __read-only__ property returning the number of bytes consumed by the Matrix elements.
` javascript`
var nbytes = mat.nbytes;
// returns
A __read-only__ property pointing to the underlying storage array.
` javascript`
var data = mat.data;
// returns
---
A Matrix has the following methods...
These methods mutate a Matrix:
#### Matrix.prototype.set( i, j, value )
Sets a Matrix element located at a row and column index.
` javascript`
mat.set( 3, 1, 20 );
/*
[ 0 1
2 3
4 5
6 20
8 9 ]
*/
Set methods return the Matrix instance and are thus chainable.
` javascript`
mat
.set( 3, 1, 21 )
.set( 3, 1, 22 )
.set( 3, 1, 23 )
.set( 3, 1, 24 )
.get( 3, 1 );
// returns 24
__Note__: out-of-bounds row and column indices will silently fail.
#### Matrix.prototype.iset( index, value )
Sets a Matrix element located at a specified index. If index < 0, the index refers to a position relative to the Matrix length, where index = -1 corresponds to the last element.
` javascript
mat.iset( 7, 25 );
/*
[ 0 1
2 3
4 5
6 25
8 9 ]
*/
mat.iset( -3, 20 );
/*
[ 0 1
2 3
4 5
6 20
8 9 ]
*/
`
__Note__: out-of-bounds indices will silently fail.
#### Matrix.prototype.mset( idx[, cols], value[, thisArg] )
Sets multiple Matrix elements. If provided a single array, idx is treated as an array of linear indices. The value argument may be either a number primitive, a Matrix containing values to set, or a callback function.
` javascript
var data = new Int8Array( 10*10 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
// Create a 10x10 matrix:
var mat = matrix( data, [10,10] );
var submat = mat.mget( [0,2,4], [1,4,5] );
/*
[ 1 4 5
21 24 25
41 44 45 ]
*/
mat.mset( [1,4,5,21,24,25,41,44,45], 5 );
submat = mat.mget( [0,2,4], [1,4,5] );
/*
[ 5 5 5
5 5 5
5 5 5 ]
*/
var zeros = matrix( [1,3], 'int8' );
/*
[ 0 0 0 ]
*/
mat.mset( [2], [1,4,5], zeros );
submat = mat.mget( [0,2,4], [1,4,5] );
/*
[ 5 5 5
0 0 0
5 5 5 ]
*/
`
A callback is provided four arguments:
* __d__: current value
* __i__: row index
* __j__: column index
* __idx__: linear index
and is __expected__ to return a number primitive or a value which can be cast to a number primitive.
` javascript
function set( d, i, j, idx ) {
return '' + j + i;
}
mat.mset( [0], [1,4,5], set );
mat.mget( [0,2,4], [1,4,5] );
/*
[ 10 40 50
0 0 0
5 5 5 ]
*/
`
By default, the callback this context is set to the Matrix instance. To specify a different this context, provide a thisArg.
` javascript
function set( d, i, j, idx ) {
console.log( this );
// returns null
return '' + j + i;
}
mat.mset( [0], [1,4,5], set, null );
`
__Notes__:
* Negative indices are __not__ permitted.
* Out-of-bounds row and column indices will silently fail.
* Values which are set are cast to the target Matrix data type.Matrix
* A value must have dimensions which match the submatrix defined by row and column indices.Matrix
* If linear indices are provided, a value must have a length equal to the number of provided indices.
#### Matrix.prototype.sset( subsequence, value[, thisArg] )
Sets Matrix elements according to a specified [subsequence][indexspace]. The subsequence must specify __both__ row and column subsequences; e.g., '3:7,5:9', where 3:7 corresponds to row indices 3,4,5,6 and 5:9 corresponds to column indices 5,6,7,8. The second argument may be either a number primitive, a Matrix containing values to set, or a callback function.
` javascript
var data = new Float32Array( 10*10 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
// Create a 10x10 matrix:
var mat = matrix( data, [10,10] );
var submat = mat.sget( '3:7,5:9' );
/*
[ 35 36 37 38
45 46 47 48
55 56 57 58
65 66 67 68 ]
*/
var zeros = matrix( [2,2], 'float32' );
/*
[ 0 0
0 0 ]
*/
mat.sset( '4:6,6:8', zeros );
submat = mat.sget( '3:7,5:9' );
/*
[ 35 36 37 38
45 0 0 48
55 0 0 58
65 66 67 68 ]
*/
`
A callback is provided four arguments:
* __d__: value at a subsequence index
* __i__: row index
* __j__: column index
* __idx__: linear index
and is __expected__ to return a number primitive or a value which can be cast to a number primitive.
` javascript
function set( d, i, j, idx ) {
return '' + j + i;
}
mat.sset( '4:6,6:8', set );
submat = mat.sget( '3:7,5:9' );
/*
[ 35 36 37 38
45 64 74 48
55 65 75 58
65 66 67 68 ]
*/
`
By default, the callback this context is set to the Matrix instance. To specify a different this context, provide a thisArg.
` javascript
function set( d, i, j, idx ) {
console.log( this );
// returns null
return '' + j + i;
}
mat.sset( '4:6,6:8', set, null );
`
__Notes__:
* Values which are set are cast to the target Matrix data type.Matrix
* Out-of-bounds row and column indices will silently fail.
* A provided must have dimensions which match the submatrix defined by row and column subsequences.
* For further subsequence documentation, see [compute-indexspace][indexspace].
===
These methods provide access to Matrix elements:
#### Matrix.prototype.get( i, j )
Returns a Matrix element located at a row and column index.
` javascript
var data = new Float32Array( 10 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
var mat = matrix( data, [5,2] );
/*
[ 0 1
2 3
4 5
6 7
8 9 ]
*/
var values = mat.get( 3, 1 );
// returns 7
`
__Note__: out-of-bounds row and column indices will return a value of undefined.
#### Matrix.prototype.iget( index )
Returns a Matrix element located at a specified index. If index < 0, the index refers to a position relative to the Matrix length, where index = -1 corresponds to the last element.
` javascript
var value = mat.iget( 7 );
// returns 7
value = mat.iget( -3 );
// returns 7
`
__Note__: out-of-bounds indices will return a value of undefined.
#### Matrix.prototype.mget( idx[, cols] )
Returns multiple Matrix elements. If provided a single argument, the method treats idx as an array of linear indices (idx[i] >= 0) and returns a new Matrix instance having a single row. Otherwise, idx and cols are integer arrays which specify row and column indices and the method returns a new Matrix instance having dimensions determined by the number of defined rows and columns.
` javascript
var data = new Int8Array( 10 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i*2;
}
var mat = matrix( data, [5,2] );
/*
[ 0 2
4 6
8 10
12 14
16 18 ]
*/
// Scramble the second column:
var vals = mat.mget( [1,5,3,9,7] );
/*
[ 2, 10, 6, 18, 14 ]
*/
// Extract select rows and columns in arbitrary order:
var mat1 = mat.mget( [1,3,2], [1] );
/*
[ 4
14
8 ]
*/
`
If idx and/or cols is null, all rows (columns) are extracted.
` javascript
// Replicate a column:
var rep = mat.mget( null, [1,1,1,1,1] );
/*
[ 2 2 2 2 2
6 6 6 6 6
10 10 10 10 10
14 14 14 14 14
18 18 18 18 18 ]
*/
// Tile select rows and columns:
var tile = mat.mget( [1,2,1,2], [0,1,0,1] );
/*
[
4 6 4 6
8 10 8 10
4 6 4 6
8 10 8 10
]
*/
`
__Note__: out-of-bounds indices are ignored.
#### Matrix.prototype.sget( subsequence )
Returns Matrix elements in a new Matrix according to a specified [subsequence][indexspace]. The subsequence must specify __both__ row and column subsequences; e.g., '3:7,5:9', where 3:7 corresponds to row indices 3,4,5,6 and 5:9 corresponds to column indices 5,6,7,8. If a subsequence does not correspond to any Matrix elements, the method returns an empty Matrix.
` javascript
var submatrix;
submatrix = mat.sget( ':,:' ); // Copy a matrix
/*
[ 0 1
2 3
4 5
6 7
8 9 ]
*/
submatrix = mat.sget( '1:4,:' );
/*
[ 2 3
4 5
6 7 ]
*/
submatrix = mat.sget( '::-1,:' ); // flip top-to-bottom
/*
[ 8 9
6 7
4 5
2 3
0 1 ]
*/
submatrix = mat.sget( ':,::-1' ); // flip left-to-right
/*
[ 1 0
3 2
5 4
7 6
9 8 ]
*/
submatrix = mat.sget( '50:100,:' );
/*
[]
*/
`
__Notes__:
* Out-of-bounds indices are ignored.
* For further subsequence documentation, see [compute-indexspace][indexspace].
===
These methods do not mutate a Matrix and return some representation of a Matrix:
#### Matrix.prototype.toString()
Returns a string representation of a Matrix. This method is similar to [Array#toString][array-string], except that rows are delineated by __semicolons__ and column values are delineated by __commas__.
` javascript
var data = new Int8Array( 10 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
var mat = matrix( data, [5,2] );
var str = mat.toString();
// 0,1;2,3;4,5;6,7;8,9
`
To construct an array of arrays from the string representation,
` javascript
var rows,
cols,
i, j;
rows = str.split( ';' );
for ( i = 0; i < rows.length; i++ ) {
cols = rows[ i ].split( ',' );
rows[ i ] = new Array( cols.length );
for ( j = 0; j < cols.length; j++ ) {
rows[ i ][ j ] = parseFloat( cols[ j ] );
}
}
`
#### Matrix.prototype.toJSON()
Returns a [JSON][json] representation of a Matrix. [JSON#stringify][json-stringify] implicitly calls this method when stringifying a Matrix instance.
` javascript
var data = new Int8Array( 10 );
for ( var i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
var mat = matrix( data, [5,2] );
/*
[ 0 1
2 3
4 5
6 7
8 9 ]
*/
var json = mat.toJSON();
/*
{
"type": "Matrix",
"dtype": "int8",
"shape": [5,2],
"offset": 0,
"strides": [2,1],
"raw": false,
"data": [0,1,2,3,4,5,6,7,8,9]
}
*/
`
To a [revive][json-parse] a Matrix from a [JSON][json] string,
` javascript
// Matrix reviver:
var reviver = require( 'dstructs-matrix-reviver' );
// Stringify a matrix (implicitly calls .toJSON):
var str = JSON.stringify( mat );
// returns '{"type":"Matrix","dtype":"int8","shape":[5,2],"offset":0,"strides":[2,1],"raw":false,"data":[0,1,2,3,4,5,6,7,8,9]}'
// Revive a Matrix from a JSON string:
var mat = JSON.parse( str, reviver );
/*
[ 0 1
2 3
4 5
6 7
8 9 ]
*/
`
A Matrix has a constructor having the following interface...
#### mat.constructor( data, dtype, shape, offset, strides )
Creates a new Matrix having a specified shape, offset, strides, dtype, and underlying typed data store.
` javascript
var data = new Float32Array( 10 );
var mat1 = matrix( data, [5,2] );
/*
[ 0 0
0 0
0 0
0 0
0 0 ]
*/
var mat2 = new mat1.constructor( data, mat1.dtype, [2,5], 0, [5,1] );
/*
[ 0 0 0 0 0
0 0 0 0 0 ]
*/
`
__Note__: while more performant, constructing a Matrix in this manner should be carefully considered. Arguments are not validated or sanity checked.
---
For performance, a lower-level interface is provided which forgoes some of the guarantees of the above API, such as input argument validation and measures to prevent Matrices from becoming corrupted. While use of the above API is encouraged in REPL environments, use of the lower-level interface may be warranted when arguments are of a known type or when many Matrices must be created.
#### matrix.raw( [data,] shape[, dtype] )
Creates a new Matrix having a specified shape.
` javascript
var data = new Float32Array( 10 );
var mat = matrix.raw( data, [5,2] );
/*
[ 0 0
0 0
0 0
0 0
0 0 ]
*/
`
If the input data type is known, Matrix creation is significantly faster.
` javascript`
var mat = matrix.raw( data, [5,2], 'float32' );
/*
[ 0 0
0 0
0 0
0 0
0 0 ]
*/
__Notes__:
* The shape and dtype parameters are the same as for the higher-level Matrix interface.dtype
* Specifying a does __not__ cast the data to a different storage type. Instead, providing the argument circumvents the need to determine the input data type, resulting in increased performance.data
* Input __must__ be a typed array. Unlike the higher-level Matrix interface, plain arrays are __not__ cast to float64. Providing a plain array can lead to subtle bugs and affect performance.Matrix
* properties and methods are the same as for the higher-level API, with the exception that Matrix properties are __no__ longer read-only and methods do __not__ perform input argument validation.Matrix
* Setting properties is __not__ recommended as the can become corrupted; e.g., incompatible dimensions, out-of-bounds indexing, etc. In contrast to the strict API above, setting Matrix properties will __not__ result in an error being thrown. Accordingly, property modification may introduce silent bugs.Matrix
* The lower-level constructor has the same interface as the higher-level Matrix constructor.
---
#### Linear Indexing
A linear index corresponds to an element position in a flattened Matrix arranged in [__row-major__][row-major-order] order. For example, consider a [__zero-filled__][zeros] 5x2 matrix, its subscripts, and its corresponding linear indices.
` javascript
/*
Matrix Subscripts Indices
[ 0 0 [ a00 a01 [ 0 1
0 0 a10 a11 2 3
A = 0 0 => a20 a21 => 4 5
0 0 a30 a31 6 7
0 0 ] a40 a41 ] 8 9 ]
*/
`
---
` javascript
var matrix = require( 'dstructs-matrix' );
// Create a new 2x2 matrix:
var mat = matrix( [2,2] );
console.log( mat );
// Inspect the initialized matrix elements:
console.log( mat.get( 1, 1 ) );
// Set a matrix element:
console.log( mat.set( 1, 1, 5 ) );
// Confirm that the matrix element was set:
console.log( mat.get( 1, 1 ) );
// Convert the matrix to a string:
console.log( mat.toString() );
// Convert the matrix to JSON:
console.log( mat.toJSON() );
`
To run the example code from the top-level application directory,
` bash`
$ node ./examples/index.js
---
Unit tests use the [Mocha][mocha] test framework with [Chai][chai] assertions. To run the tests, execute the following command in the top-level application directory:
` bash`
$ make test
All new feature development should have corresponding unit tests to validate correct functionality.
This repository uses [Istanbul][istanbul] as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:
` bash`
$ make test-cov
Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,
` bash``
$ make view-cov
---
[MIT license][mit-license].
Copyright © 2015. The [Compute.io][compute-io] Authors.
[npm-image]: http://img.shields.io/npm/v/dstructs-matrix.svg
[npm-url]: https://npmjs.org/package/dstructs-matrix
[travis-image]: http://img.shields.io/travis/dstructs/matrix/master.svg
[travis-url]: https://travis-ci.org/dstructs/matrix
[codecov-image]: https://img.shields.io/codecov/c/github/dstructs/matrix/master.svg
[codecov-url]: https://codecov.io/github/dstructs/matrix?branch=master
[dependencies-image]: http://img.shields.io/david/dstructs/matrix.svg
[dependencies-url]: https://david-dm.org/dstructs/matrix
[dev-dependencies-image]: http://img.shields.io/david/dev/dstructs/matrix.svg
[dev-dependencies-url]: https://david-dm.org/dev/dstructs/matrix
[github-issues-image]: http://img.shields.io/github/issues/dstructs/matrix.svg
[github-issues-url]: https://github.com/dstructs/matrix/issues
[matrix]: https://en.wikipedia.org/wiki/Matrix_(mathematics)
[browserify]: https://github.com/substack/node-browserify
[cast-arrays]: https://github.com/compute-io/cast-arrays
[array-length]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/length
[indexspace]: https://github.com/compute-io/indexspace
[array-string]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/toString
[json]: http://www.json.org/
[json-stringify]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/stringify
[json-parse]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/parse
[row-major-order]: https://en.wikipedia.org/wiki/Row-major_order
[zeros]: https://github.com/compute-io/zeros
[mocha]: http://mochajs.org/
[chai]: http://chaijs.com
[istanbul]: https://github.com/gotwarlost/istanbul
[mit-license]: http://opensource.org/licenses/MIT
[compute-io]: https://github.com/compute-io