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Broadcast array shapes to a single shape.
import broadcastShapes from 'https://cdn.jsdelivr.net/gh/stdlib-js/ndarray-base-broadcast-shapes@deno/mod.js';Broadcasts array shapes to a single shape.
var sh1 = [ 8, 1, 6, 1 ];
var sh2 = [ 7, 1, 5 ];
var sh = broadcastShapes( [ sh1, sh2 ] );
// returns [ 8, 7, 6, 5 ]-
When operating on two arrays, the function compares their shapes element-wise, beginning with the trailing (i.e., rightmost) dimension. The following are examples of compatible shapes and their corresponding broadcasted shape:
A (4d array): 8 x 1 x 6 x 1 B (3d array): 7 x 1 x 5 --------------------------------- Result (4d array): 8 x 7 x 6 x 5 A (2d array): 5 x 4 B (1d array): 1 ------------------------- Result (2d array): 5 x 4 A (2d array): 5 x 4 B (1d array): 4 ------------------------- Result (2d array): 5 x 4 A (3d array): 15 x 3 x 5 B (3d array): 15 x 1 x 5 ------------------------------ Result (3d array): 15 x 3 x 5 A (3d array): 15 x 3 x 5 B (2d array): 3 x 5 ------------------------------ Result (3d array): 15 x 3 x 5 A (3d array): 15 x 3 x 5 B (2d array): 3 x 1 ------------------------------ Result (3d array): 15 x 3 x 5 A (5d array): 8 x 1 x 1 x 6 x 1 B (4d array): 1 x 7 x 1 x 5 C (5d array): 8 x 4 x 1 x 6 x 5 ------------------------------------- Result (5d array): 8 x 4 x 7 x 6 x 5 A (5d array): 8 x 1 x 1 x 6 x 1 B (1d array): 0 ------------------------------------- Result (5d array): 8 x 1 x 1 x 6 x 0 A (5d array): 8 x 0 x 1 x 6 x 1 B (2d array): 6 x 5 ------------------------------------- Result (5d array): 8 x 0 x 1 x 6 x 5 A (5d array): 8 x 1 x 1 x 6 x 1 B (5d array): 8 x 0 x 1 x 6 x 1 ------------------------------------- Result (5d array): 8 x 0 x 1 x 6 x 1 A (3d array): 3 x 2 x 1 B (0d array): ----------------------------- Result (3d array): 3 x 2 x 1 A (0d array): B (3d array): 3 x 2 x 1 ----------------------------- Result (3d array): 3 x 2 x 1As demonstrated above, arrays are not required to have the same number of dimensions in order to be broadcast compatible. Array shapes with fewer dimensions are implicitly prepended with singleton dimensions (i.e., dimensions equal to
1). Accordingly, the following exampleA (2d array): 5 x 4 B (1d array): 4 ------------------------- Result (2d array): 5 x 4is equivalent to
A (2d array): 5 x 4 B (2d array): 1 x 4 ------------------------- Result (2d array): 5 x 4Similarly, a zero-dimensional array is expanded (by prepending singleton dimensions) from
A (3d array): 3 x 2 x 1 B (0d array): ----------------------------- Result (3d array): 3 x 2 x 1to
A (3d array): 3 x 2 x 1 B (3d array): 1 x 1 x 1 ----------------------------- Result (3d array): 3 x 2 x 1Stated otherwise, every array has implicit leading dimensions of size
1. During broadcasting, a3 x 4matrix is the same as a3 x 4 x 1 x 1 x 1multidimensional array. -
Two respective dimensions in two shape arrays are compatible if
- the dimensions are equal.
- one dimension is
1.
The two aforementioned rules apply to empty arrays or arrays that have a dimension of size
0. For unequal dimensions, the size of the dimension which is not1determines the size of the output shape dimension.Accordingly, dimensions of size
0must be paired with a dimension of size0or1. In such cases, by the rules above, the size of the corresponding output shape dimension is0. -
The function returns
nullif provided incompatible shapes (i.e., shapes which cannot be broadcast with one another).var sh1 = [ 3, 2 ]; var sh2 = [ 2, 3 ]; var sh = broadcastShapes( [ sh1, sh2 ] ); // returns null
The following are examples of array shapes which are not compatible and do not broadcast:
A (1d array): 3 B (1d array): 4 # dimension does not match A (2d array): 2 x 1 B (3d array): 8 x 4 x 3 # second dimension does not match A (3d array): 15 x 3 x 5 B (2d array): 15 x 3 # singleton dimensions can only be prepended, not appended A (5d array): 8 x 8 x 1 x 6 x 1 B (5d array): 8 x 0 x 1 x 6 x 1 # second dimension does not match
import lpad from 'https://cdn.jsdelivr.net/gh/stdlib-js/string-left-pad@deno/mod.js';
import broadcastShapes from 'https://cdn.jsdelivr.net/gh/stdlib-js/ndarray-base-broadcast-shapes@deno/mod.js';
var shapes;
var out;
var sh;
var i;
var j;
function shape2string( shape ) {
return lpad( shape.join( ' x ' ), 20, ' ' );
}
shapes = [
[ [ 1, 2 ], [ 2 ] ],
[ [ 1, 1 ], [ 3, 4 ] ],
[ [ 6, 7 ], [ 5, 6, 1 ], [ 7 ], [ 5, 1, 7 ] ],
[ [ 1, 3 ], [ 3, 1 ] ],
[ [ 1 ], [ 3 ] ],
[ [ 2 ], [ 3, 2 ] ],
[ [ 2, 3 ], [ 2, 3 ], [ 2, 3 ], [ 2, 3 ] ],
[ [ 1, 2 ], [ 1, 2 ] ]
];
for ( i = 0; i < shapes.length; i++ ) {
sh = shapes[ i ];
for ( j = 0; j < sh.length; j++ ) {
console.log( shape2string( sh[ j ] ) );
}
console.log( lpad( '', 20, '-' ) );
out = broadcastShapes( sh );
console.log( shape2string( out )+'\n' );
}This package is part of stdlib, a standard library 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.
See LICENSE.
Copyright © 2016-2025. The Stdlib Authors.
