Class: Matrix

new Matrix(rows, cols, value) → {Matrix}

creates a new Matrix. Entries are stored in a Float64Array.

Parameters:

Name Type Default Description

Name	Type	Default	Description
`rows`	number	null	The amount of rows of the matrix.
`cols`	number	null	The amount of columns of the matrix.
`value`	function \| string \| number	0	Can be a function with row and col as parameters, a number, or "zeros", "identity" or "I", or "center". function: for each entry the function gets called with the parameters for the actual row and column. string: allowed are "zero", creates a zero matrix. "identity" or "I", creates an identity matrix. "center", creates an center matrix. number: create a matrix filled with the given value.

rows

number

null

The amount of rows of the matrix.

cols

number

null

The amount of columns of the matrix.

value

function | string | number

Can be a function with row and col as parameters, a number, or "zeros", "identity" or "I", or "center".

function: for each entry the function gets called with the parameters for the actual row and column.
string: allowed are
- "zero", creates a zero matrix.
- "identity" or "I", creates an identity matrix.
- "center", creates an center matrix.
number: create a matrix filled with the given value.

Source: matrix/Matrix.js, line 9

Requires:

module:numerical/neumair_sum

Returns:

returns a rows times cols Matrix filled with value.

Type:: Matrix

Example

let A = new Matrix(10, 10, () => Math.random()); //creates a 10 times 10 random matrix.
let B = new Matrix(3, 3, "I"); // creates a 3 times 3 identity matrix.

Requires

module:numerical/neumair_sum

Members

asArray

Returns the Matrix as a Array of Arrays.

Source: matrix/Matrix.js, line 829

diag

Returns the diagonal of the Matrix.

Source: matrix/Matrix.js, line 841

mean

Returns the mean of all entries of the Matrix.

Source: matrix/Matrix.js, line 856

meanCols

Returns the mean of each column of the matrix.

Source: matrix/Matrix.js, line 902

meanRows

Returns the mean of each row of the matrix.

Source: matrix/Matrix.js, line 884

shape

Returns the number of rows and columns of the Matrix.

Source: matrix/Matrix.js, line 792

shape

Returns the matrix in the given shape with the given function which returns values for the entries of the matrix.

Source: matrix/Matrix.js, line 801

sum

Returns the sum oof all entries of the Matrix.

Source: matrix/Matrix.js, line 866

T

Returns a new transposed Matrix. Short-form of {@function transpose}.

Source: matrix/Matrix.js, line 271

to2dArray

Returns the Matrix as a Array of Float64Arrays.

Source: matrix/Matrix.js, line 817

values

Returns the entries of the Matrix.

Source: matrix/Matrix.js, line 875

Methods

(static) det(A) → {Number}

Computes the determinante of A, by using the LU decomposition of A.

Parameters:

Name	Type	Description
`A`	Matrix

Source: matrix/Matrix.js, line 1019

Returns:

det - Returns the determinate of the Matrix A.

Type:: Number

(static) from(A, typeopt) → {Matrix}

Creates a Matrix out of A.

Parameters:

Name	Type	Attributes	Default	Description
`A`	Matrix \| Array \| Float64Array \| number			The matrix, array, or number, which should converted to a Matrix.
`type`	"row" \| "col" \| "diag"	<optional>	"row"	If `A` is a Array or Float64Array, then type defines if it is a row- or a column vector.

Source: matrix/Matrix.js, line 91

Returns:

Type:: Matrix

Example

let A = Matrix.from([[1, 0], [0, 1]]); //creates a two by two identity matrix.
let S = Matrix.from([1, 2, 3], "diag"); // creates a 3 by 3 matrix with 1, 2, 3 on its diagonal. [[1, 0, 0], [0, 2, 0], [0, 0, 3]]

(static) LU(A) → {Object}

LU decomposition of the Matrix A. Creates two matrices, so that the dot product LU equals A.

Parameters:

Name	Type	Description
`A`	Matrix

Source: matrix/Matrix.js, line 986

Returns:

result - Returns the left triangle matrix L and the upper triangle matrix U.

Type:: Object

(static) solve(A, b) → {Matrix}

Solves the equation Ax = b. Returns the result x.

Parameters:

Name	Type	Description
`A`	Matrix	Matrix or LU Decomposition
`b`	Matrix	Matrix

Source: matrix/Matrix.js, line 957

Returns:

Type:: Matrix

(static) solve_CG(A, b, randomizeropt, tolopt) → {Matrix}

Solves the equation Ax = b using the conjugate gradient method. Returns the result x.

Parameters:

Name	Type	Attributes	Default	Description
`A`	Matrix			Matrix
`b`	Matrix			Matrix
`randomizer`	Randomizer	<optional>	null
`tol`	Number	<optional>	1e-3

Source: matrix/Matrix.js, line 925

Returns:

Type:: Matrix

(static) SVD(M, kopt) → {Object}

Computes the k components of the SVD decomposition of the matrix M

Parameters:

Name	Type	Attributes	Default	Description
`M`	Matrix
`k`	int	<optional>	2

Source: matrix/Matrix.js, line 1037

Returns:

Type:: Object

add(value, optionsopt) → {Matrix}

Entrywise addition with value.

Parameters:

Name Type Attributes Description

value Matrix | Array | Number

options

Object

Properties

Name	Type	Attributes	Default	Description
`inline`	Boolean	<optional>	false	If true, applies addition to the element, otherwise it creates first a copy and applies the addition on the copy.

Source: matrix/Matrix.js, line 764

Returns:

Type:: Matrix

Example

let A = Matrix.from([[1, 2], [3, 4]]); // a 2 by 2 matrix.
let B = A.clone(); // B == A;

A.add(2); // [[3, 4], [5, 6]];
A.add(B); // [[2, 4], [6, 8]];

add_entry(row, col, value) → {Matrix}

Adds a given value to the col^th entry from the row^th row of the Matrix.

Parameters:

Name	Type	Description
`row`	int
`col`	int
`value`	float64

Source: matrix/Matrix.js, line 241

Returns:

Type:: Matrix

clone() → {Matrix}

Clones the Matrix.

Source: matrix/Matrix.js, line 704

Returns:

Type:: Matrix

col(col) → {Array}

Returns the col^th column from the Matrix.

Parameters:

Name	Type	Description
`col`	Number

Source: matrix/Matrix.js, line 204

Returns:

Type:: Array

concat(B, typeopt) → {Matrix}

Appends matrix B to the matrix.

Parameters:

Name	Type	Attributes	Default	Description
`B`	Matrix			matrix to append.
`type`	"horizontal" \| "vertical" \| "diag"	<optional>	"horizontal"	type of concatenation.

Source: matrix/Matrix.js, line 503

Returns:

Type:: Matrix

Example

let A = Matrix.from([[1, 1], [1, 1]]); // 2 by 2 matrix filled with ones.
let B = Matrix.from([[2, 2], [2, 2]]); // 2 by 2 matrix filled with twos.

A.concat(B, "horizontal"); // 2 by 4 matrix. [[1, 1, 2, 2], [1, 1, 2, 2]]
A.concat(B, "vertical"); // 4 by 2 matrix. [[1, 1], [1, 1], [2, 2], [2, 2]]
A.concat(B, "diag"); // 4 by 4 matrix. [[1, 1, 0, 0], [1, 1, 0, 0], [0, 0, 2, 2], [0, 0, 2, 2]]

divide(value, optionsopt) → {Matrix}

Entrywise division with value.

Parameters:

Name Type Attributes Description

value Matrix | Array | Number

options

Object

Properties

Name	Type	Attributes	Default	Description
`inline`	Boolean	<optional>	false	If true, applies division to the element, otherwise it creates first a copy and applies the division on the copy.

Source: matrix/Matrix.js, line 745

Returns:

Type:: Matrix

Example

let A = Matrix.from([[1, 2], [3, 4]]); // a 2 by 2 matrix.
let B = A.clone(); // B == A;

A.divide(2); // [[0.5, 1], [1.5, 2]];
A.divide(B); // [[1, 1], [1, 1]];

dot(B) → {Matrix|Array}

Returns the dot product. If B is an Array or Float64Array then an Array gets returned. If B is a Matrix then a Matrix gets returned.

Parameters:

Name	Type	Description
`B`	Matrix \| Array \| Float64Array	the right side

Source: matrix/Matrix.js, line 345

Returns:

Type:: Matrix | Array

dotTrans(B) → {Matrix|Array}

Returns the dot product with the transposed version of B. If B is an Array or Float64Array then an Array gets returned. If B is a Matrix then a Matrix gets returned.

Parameters:

Name	Type	Description
`B`	Matrix \| Array \| Float64Array	the right side

Source: matrix/Matrix.js, line 430

Returns:

Type:: Matrix | Array

entry(row, col) → {float64}

Returns the col^th entry from the row^th row of the Matrix.

Parameters:

Name	Type	Description
`row`	int
`col`	int

Source: matrix/Matrix.js, line 218

Returns:

Type:: float64

gather(row_indices, col_indices) → {Matrix}

Returns a new array gathering entries defined by the indices given by argument.

Parameters:

Name	Type	Description
`row_indices`	Array.<Number>	Array consists of indices of rows for gathering entries of this matrix
`col_indices`	Array.<Number>	Array consists of indices of cols for gathering entries of this matrix

Source: matrix/Matrix.js, line 594

Returns:

Type:: Matrix

get_block(start_row, start_col, end_rowopt, end_colopt) → {Matrix}

Extracts the entries from the start_row^th row to the end_row^th row, the start_col^th column to the end_col^th column of the matrix. If end_row or end_col is empty, the respective value is set to this.rows or this.cols.

Parameters:

Name	Type	Attributes	Default
`start_row`	Number
`start_col`	Number
`end_row`	Number	<optional>	null
`end_col`	Number	<optional>	null

Source: matrix/Matrix.js, line 568

Returns:

Returns a end_row - start_row times end_col - start_col matrix, with respective entries from the matrix.

Type:: Matrix

Example

let A = Matrix.from([[1, 2, 3], [4, 5, 6], [7, 8, 9]]); // a 3 by 3 matrix.

A.get_block(1, 1); // [[5, 6], [8, 9]]
A.get_block(0, 0, 1, 1); // [[1]]
A.get_block(1, 1, 2, 2); // [[5]]
A.get_block(0, 0, 2, 2); // [[1, 2], [4, 5]]

inverse() → {Matrix}

Returns the inverse of the Matrix.

Source: matrix/Matrix.js, line 279

Returns:

Type:: Matrix

(generator) iterate_rows() → {Float64Array}

Returns an generator yielding each row of the Matrix.

Source: matrix/Matrix.js, line 140

Yields:

Type:: Float64Array

mult(value, optionsopt) → {Matrix}

Entrywise multiplication with value.

Parameters:

Name Type Attributes Description

value Matrix | Array | Number

options

Object

Properties

Name	Type	Attributes	Default	Description
`inline`	Boolean	<optional>	false	If true, applies multiplication to the element, otherwise it creates first a copy and applies the multiplication on the copy.

Source: matrix/Matrix.js, line 726

Returns:

Type:: Matrix

Example

let A = Matrix.from([[1, 2], [3, 4]]); // a 2 by 2 matrix.
let B = A.clone(); // B == A;

A.mult(2); // [[2, 4], [6, 8]];
A.mult(B); // [[1, 4], [9, 16]];

outer(B) → {Matrix}

Computes the outer product from this and B.

Parameters:

Name	Type	Description
`B`	Matrix

Source: matrix/Matrix.js, line 469

Returns:

Type:: Matrix

row(row) → {Float64Array}

Returns the row^th row from the Matrix.

Parameters:

Name	Type	Description
`row`	Number

Source: matrix/Matrix.js, line 130

Returns:

Type:: Float64Array

set_block(offset_row, offset_col, B) → {Matrix}

Writes the entries of B in A at an offset position given by offset_row and offset_col.

Parameters:

Name	Type	Description
`offset_row`	int
`offset_col`	int
`B`	Matrix

Source: matrix/Matrix.js, line 540

Returns:

Type:: Matrix

set_entry(row, col, value) → {Matrix}

Sets the col^th entry from the row^th row of the Matrix to the given value.

Parameters:

Name	Type	Description
`row`	int
`col`	int
`value`	float64

Source: matrix/Matrix.js, line 229

Returns:

Type:: Matrix

set_row(row, values) → {Matrix}

Sets the entries of row^th row from the Matrix to the entries from values.

Parameters:

Name	Type	Description
`row`	Number
`values`	Array

Source: matrix/Matrix.js, line 165

Returns:

Type:: Matrix

sub(value, optionsopt) → {Matrix}

Entrywise subtraction with value.

Parameters:

Name Type Attributes Description

value Matrix | Array | Number

options

Object

Properties

Name	Type	Attributes	Default	Description
`inline`	Boolean	<optional>	false	If true, applies subtraction to the element, otherwise it creates first a copy and applies the subtraction on the copy.

Source: matrix/Matrix.js, line 783

Returns:

Type:: Matrix

Example

let A = Matrix.from([[1, 2], [3, 4]]); // a 2 by 2 matrix.
let B = A.clone(); // B == A;

A.sub(2); // [[-1, 0], [1, 2]];
A.sub(B); // [[0, 0], [0, 0]];

sub_entry(row, col, value) → {Matrix}

Subtracts a given value from the col^th entry from the row^th row of the Matrix.

Parameters:

Name	Type	Description
`row`	int
`col`	int
`value`	float64

Source: matrix/Matrix.js, line 253

Returns:

Type:: Matrix

swap_rows(row1, row2) → {Matrix}

Swaps the rows row1 and row2 of the Matrix.

Parameters:

Name	Type	Description
`row1`	Number
`row2`	Number

Source: matrix/Matrix.js, line 189

Returns:

Type:: Matrix

transDot(B) → {Matrix|Array}

Transposes the current matrix and returns the dot product with B. If B is an Array or Float64Array then an Array gets returned. If B is a Matrix then a Matrix gets returned.

Parameters:

Name	Type	Description
`B`	Matrix \| Array \| Float64Array	the right side

Source: matrix/Matrix.js, line 387

Returns:

Type:: Matrix | Array

transpose() → {Matrix}

Returns a new transposed Matrix.

Source: matrix/Matrix.js, line 262

Returns:

Type:: Matrix