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https://github.com/not-an-aardvark/node-matrices

A simple and lightweight matrix library for Node.js
https://github.com/not-an-aardvark/node-matrices

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A simple and lightweight matrix library for Node.js

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# node-matrices [![Build Status](https://travis-ci.org/not-an-aardvark/node-matrices.svg?branch=master)](https://travis-ci.org/not-an-aardvark/node-matrices)



node-matrices is a simple, lightweight matrix manipulation library supporting many common matrix operations.

## Installation

```bash

npm install node-matrices

```

```javascript

var Matrix = require('node-matrices');

```

## Documentation

General notes:



* All Matrix objects are immutable.

* All indices are zero-based.



---

### Basic manipulation

`.constructor(...rows)`

* Each parameter to the constructor should be an array of integers corresponding to a single row of the matrix. All of the rows should have the same length.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6],

  [7, 8, 9]

);

// -> Matrix { data: [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ] }

```

---

* `#numRows()` - Returns the number of rows in the matrix.

* `#numColumns()` - Returns the number of columns in the matrix.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6]

);

m.numRows()

// -> 2

m.numColumns()

// -> 3

```

---

* `#get(rowIndex, columnIndex)` - Returns the value at a specific location. This will return `undefined` if either index is out of range.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6]

);

m.get(0, 1)

// -> 2

m.get(1, 2)

// -> 6

m.get(500, 0)

// -> undefined

```

---

* `#getRow(rowIndex)` - Returns a new matrix containing only the row at the specified index.

* `#getColumn(columnIndex)` - Returns a new matrix containing only the column at the specified index.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6],

  [7, 8, 9]

);

m.getRow(1)

// -> Matrix { data: [ [ 4, 5, 6 ] ] }

m.getColumn(2)

// -> Matrix { data: [ [ 3 ], [ 6 ], [ 9 ] ] }

```

---

* `#sliceRows(startIndex[, endIndex])`

* `#sliceColumns(startIndex[, endIndex])`

* `#sliceBlock(startRowIndex, endRowIndex, startColumnIndex, endColumnIndex)`

* Returns a new matrix containing only the rows between `startIndex` and `endIndex - 1`, inclusive. If `endIndex` is not provided, the rows/columns will be sliced until the end of the matrix.

```javascript

var m = new Matrix(

  [1, 2, 3, 4],

  [5, 6, 7, 8],

  [9, 10, 11, 12],

  [13, 14, 15, 16]

);

m.sliceRows(1, 3)

// -> Matrix { data: [ [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ] }

m.sliceColumns(0, 2)

// -> Matrix { data: [ [ 1, 2 ], [ 5, 6 ], [ 9, 10 ], [ 13, 14 ] ] }

m.sliceBlock(0, 3, 1, 3)

// -> Matrix { data: [ [ 2, 3 ], [ 6, 7 ], [ 10, 11 ] ] }

```

---

* `#omitRow(rowIndex)`

* `#omitColumn(columnIndex)`

* Returns a new matrix with the specified row or column omitted.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6],

  [7, 8, 9]

);

m.omitRow(0)

// -> Matrix { data: [ [ 4, 5, 6 ], [ 7, 8, 9 ] ] }

m.omitColumn(1)

// -> Matrix { data: [ [ 1, 3 ], [ 4, 6 ], [ 7, 9 ] ] }

```

---

* `#combineHorizontal(otherMatrix)`

* `#combineVertical(otherMatrix)`

* Combines two matrices as blocks. An error will be thrown if the matrices have a different number of rows (for `combineHorizontal`) or a different number of columns (for `combineVertical`).

```javascript

var m1 = new Matrix(

  [1, 2],

  [3, 4]

);

var m2 = new Matrix(

  [5, 6],

  [7, 8]

);

m1.combineHorizontal(m2)

// -> Matrix { data: [ [ 1, 2, 5, 6 ], [ 3, 4, 7, 8 ] ] }

m1.combineVertical(m2)

// -> Matrix { data: [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 7, 8 ] ] }

```

---

* `#replace(rowIndex, columnIndex, value)`

* Returns a new matrix where the which is exactly the same as the old matrix, except that the value at `rowIndex` and `columnIndex` is `value`.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6],

  [7, 8, 9]

);

m.replace(1, 2, Infinity)

// -> Matrix { data: [ [ 1, 2, 3 ], [ 4, 5, Infinity ], [ 7, 8, 9 ] ] }

```

---

### Matrix operations

* `#transpose()`

* Returns the transpose of this matrix.

```javascript

var m = new Matrix(

  [1, 2, 3],

  [4, 5, 6],

);

m.transpose()

// -> Matrix { data: [ [ 1, 4 ], [ 2, 5 ], [ 3, 6 ] ] }

```

---

* `#determinant()`

* Returns the determinant of this matrix. An error will be thrown if this matrix is not square.

```javascript

var m = new Matrix(

  [1, 2],

  [3, 4]

);

m.determinant()

// -> -2

```

---

* `#adjugate()`

* Returns the [adjugate](https://en.wikipedia.org/wiki/Adjugate_matrix) of this matrix. An error will be thrown if this matrix is not square.

```javascript

var m = new Matrix(

  [1, 2],

  [3, 4]

);

m.adjugate()

// -> Matrix { data: [ [ 4, -2 ], [ -3, 1 ] ] }

```

---

* `#inverse()`

* Returns the inverse of this matrix. An error will be thrown if this matrix is not square, or if this matrix is singular.

```javascript

var m = new Matrix(

  [1, 2],

  [3, 4]

);

m.inverse()

// -> Matrix { data: [ [ -2, 1 ], [ 1.5, -0.5 ] ] }

```

---

* `#add(otherMatrix)`

* `#subtract(otherMatrix)`

* Returns the sum or difference of this matrix and another matrix. An error will be thrown if the two matrices have different dimensions.

```javascript

var m1 = new Matrix(

  [1, 2],

  [3, 4]

);

var m2 = new Matrix(

  [5, 5],

  [5, 5]

);

m1.add(m2)

// -> Matrix { data: [ [ 6, 7 ], [ 8, 9 ] ] }

m1.subtract(m2)

// -> Matrix { data: [ [ -4, -3 ], [ -2, -1 ] ] }

```

---

* `#multiply(otherMatrix)`

* Returns the product of this matrix and another matrix. An error will be thrown if the matrices do not have compatible sizes.

* To multiply a matrix by a scalar, use `#scale()`.

```javascript

var m1 = new Matrix(

  [1, 2, 3],

  [4, 5, 6]

);

var m2 = new Matrix(

  [7, 8],

  [9, 10],

  [11, 12]

);

m1.multiply(m2)

// -> Matrix { data: [ [ 58, 64 ], [ 139, 154 ] ] }

m1.multiply(m1)

// (throws an error)

```

---

* `#scale(scalar)`

* Returns the scalar product of this matrix and `scalar`.

```javascript

var m1 = new Matrix(

  [1, 2],

  [3, 4]

);

m1.scale(3)

// -> Matrix { data: [ [ 3, 6 ], [ 9, 12 ] ] }

```

---

* `#pow(exponent)`

* Raises this matrix to the `exponent` power. An error will be thrown if this matrix is not square, or if `exponent` is not an integer.

```javascript

var m1 = new Matrix(

  [1, 2],

  [3, 4]

);

m1.pow(5)

// -> Matrix { data: [ [ 37, 54 ], [ 81, 118 ] ] }

```

---

### Value-checking

* `#equals(otherMatrix)`

* Returns `true` if `this` and `otherMatrix` are equivalent, and `false` otherwise. Equivalent matrices contain all of the same values in the same locations.

```javascript

var m1 = new Matrix([1, 2, 3]);

var m2 = new Matrix([1, 2, 3]);

var m3 = new Matrix([1, 2, 4]);

m1.equals(m2)

// -> true

m1.equals(m3)

// -> false

```

---

* `#isSquare()`

* Returns `true` if this matrix is square (i.e. has the same number of rows and columns), and `false` otherwise.

```javascript

var m1 = new Matrix(

  [1, 2],

  [3, 4]

);

var m2 = new Matrix(

  [1, 2, 3],

  [4, 5, 6]

);

m1.isSquare()

// -> true

m2.isSquare()

// -> false

```

---

* `#isSymmetric()`

* `#isSkewSymmetric()`

* Returns `true` if this matrix is symmetric (for `isSymmetric`) or skew-symmetric (for `isSkewSymmetric`). Otherwise, returns `false`.

```javascript

var m1 = new Matrix(

  [1, 2],

  [2, 4]

);

var m2 = new Matrix(

  [0, 2],

  [-2, 0]

);

m1.isSymmetric()

// -> true

m1.isSkewSymmetric()

// -> false

m2.isSymmetric()

// -> false

m2.isSkewSymmetric()

// -> true

```

---

* `#isUpperTriangular()`

* `#isLowerTriangular()`

* `#isDiagonal()`

* Returns `true` if this matrix is upper triangular, lower triangular, or diagonal, respectively; otherwise, returns `false`.

```javascript

var m1 = new Matrix(

  [1, 2],

  [0, 5]

);

var m2 = new Matrix(

  [1, 0],

  [0, 5]

);

m1.isUpperTriangular()

// -> true

m1.isLowerTriangular()

// -> false

m1.isDiagonal()

// -> false

m2.isUpperTriangular()

// -> true

m2.isLowerTriangular()

// -> true

m2.isDiagonal()

// -> true

```

---

* `#isIdentity()`

* Returns `true` if this matrix is an identity matrix, otherwise `false`.

```javascript

var m1 = new Matrix(

  [1, 0],

  [0, 1]

);

var m2 = new Matrix(

  [1, 1],

  [0, 1]

);

m1.isIdentity()

// -> true

m2.isIdentity()

// -> false

```

---

* `#isNonZero()`

* Returns `true` if this matrix contains any nonzero values. Otherwise, returns `false`.

```javascript

var m1 = new Matrix(

  [0, 0],

  [0, 0]

);

var m2 = new Matrix(

  [0, 1],

  [0, 0]

);

m1.isNonZero()

// -> false

m2.isNonZero()

// -> true

```

---

* `#isSingular()`

* Returns `true` if this matrix is singular, otherwise `false`. An error will be thrown if this matrix is not square.

```javascript

var m1 = new Matrix(

  [1, 2],

  [3, 4]

);

var m2 = new Matrix(

  [1, 2],

  [2, 4]

);

m1.isSingular()

// -> false

m2.isSingular()

// -> true

```

---

### Static methods

* `.identity(size)`

* Returns an identity matrix of the specified size.

```javascript

Matrix.identity(3)

// -> Matrix { data: [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] }

```

---

* `.zeros(numRows, numColumns)`

* Returns a matrix of the specified dimensions which only contains zeros.

```javascript

Matrix.zeros(2, 3)

// -> Matrix { data: [ [ 0, 0, 0 ], [ 0, 0, 0 ] ] }

```