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diagonal

Return a view of the diagonal of a matrix (or stack of matrices).

For an M-by-N matrix A, the k-th diagonal is defined as

$$D_k = \{\, A_{i,j} : j - i = k \,\}$$

where k = 0 corresponds to the main diagonal, k > 0 corresponds to the super-diagonals (above the main diagonal), and k < 0 corresponds to the sub-diagonals (below the main diagonal). For example, given the matrix

$$A = \begin{bmatrix} a_{0,0} & a_{0,1} & a_{0,2} \\ a_{1,0} & a_{1,1} & a_{1,2} \\ a_{2,0} & a_{2,1} & a_{2,2} \end{bmatrix}$$

the main diagonal is [ a_{0,0}, a_{1,1}, a_{2,2} ], the super-diagonal k = 1 is [ a_{0,1}, a_{1,2} ], and the sub-diagonal k = -1 is [ a_{1,0}, a_{2,1} ].

Installation

npm install @stdlib/ndarray-base-diagonal

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var diagonal = require( '@stdlib/ndarray-base-diagonal' );

diagonal( x, dims, k, writable )

Returns a view of the diagonal of a matrix (or stack of matrices) x.

var array = require( '@stdlib/ndarray-array' );

var x = array( [ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ] );
// returns <ndarray>[ [ 1.0, 2.0, 3.0 ], [ 4.0, 5.0, 6.0 ], [ 7.0, 8.0, 9.0 ] ]

var y = diagonal( x, [ 0, 1 ], 0, false );
// returns <ndarray>[ 1.0, 5.0, 9.0 ]

The function accepts the following arguments:

• x: input ndarray.
• dims: dimension indices defining the plane from which to extract the diagonal.
• k: diagonal offset.
• writable: boolean indicating whether the returned ndarray should be writable.

Notes

• The order of the dimension indices contained in dims matters. The first element specifies the row-like dimension. The second element specifies the column-like dimension.
• Each provided dimension index must reside on the interval [-ndims, ndims-1].
• The diagonal offset k is interpreted as column - row. Accordingly, when k = 0, the function returns the main diagonal; when k > 0, the function returns the diagonal above the main diagonal; and when k < 0, the function returns the diagonal below the main diagonal.
• The returned ndarray is a view of the input ndarray. Accordingly, writing to the original ndarray will mutate the returned ndarray and vice versa.
• The writable parameter only applies to ndarray constructors supporting read-only instances.

Examples

var uniform = require( '@stdlib/random-uniform' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var diagonal = require( '@stdlib/ndarray-base-diagonal' );

// Create a stack of matrices:
var x = uniform( [ 2, 3, 3 ], -10.0, 10.0, {
    'dtype': 'float64'
});
console.log( ndarray2array( x ) );

// Extract the main diagonals from the stack:
var y = diagonal( x, [ 1, 2 ], 0, false );
console.log( ndarray2array( y ) );

// Extract super-diagonals from the stack:
y = diagonal( x, [ 1, 2 ], 1, false );
console.log( ndarray2array( y ) );

// Extract sub-diagonals from the stack:
y = diagonal( x, [ 1, 2 ], -1, false );
console.log( ndarray2array( y ) );

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.