Skip to content

diagonal

Directory actions

More options

Directory actions

More options

Latest commit

 

History

History

diagonal

Folders and files

NameName
Last commit message
Last commit date

parent directory

..
benchmark
benchmark
 
 
docs
docs
 
 
examples
examples
 
 
lib
lib
 
 
test
test
 
 
README.md
README.md
 
 
package.json
package.json
 
 

README.md

diagonal

Return a read-only 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} ].

Usage

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

diagonal( x[, options] )

Returns a read-only view of the diagonal of a matrix (or stack of matrices).

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 );
// returns <ndarray>[ 1.0, 5.0, 9.0 ]

The function accepts the following arguments:

  • x: input ndarray.
  • options: function options.

The function accepts the following options:

  • k: diagonal offset. The diagonal offset 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. Default: 0.
  • dims: dimension indices defining the plane from which to extract the diagonal. Must contain exactly two unique dimension indices. The first element specifies the row-like dimension. The second element specifies the column-like dimension. If a dimension index is provided as an integer less than zero, the dimension index is resolved relative to the last dimension, with the last dimension corresponding to the value -1. Default: [-2, -1].

Notes

  • The order of the dimension indices contained in options.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].

Examples

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

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

// Extract the main diagonals from the stack:
var y = diagonal( x );
console.log( ndarray2array( y ) );

// Extract super-diagonals from the stack:
y = diagonal( x, {
    'k': 1
});
console.log( ndarray2array( y ) );

// Extract sub-diagonals from the stack:
y = diagonal( x, {
    'k': -1
});
console.log( ndarray2array( y ) );