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broadcastShapes
Broadcast array shapes to a single shape.
Installation
npm install @stdlib/ndarray-base-broadcast-shapesAlternatively,
- To load the package in a website via a
scripttag without installation and bundlers, use the ES Module available on theesmbranch. - If you are using Deno, visit the
denobranch. - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umdbranch.
The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
Usage
var broadcastShapes = require( '@stdlib/ndarray-base-broadcast-shapes' );broadcastShapes( shapes )
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 ]Notes
-
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
Examples
var lpad = require( '@stdlib/string-left-pad' );
var broadcastShapes = require( '@stdlib/ndarray-base-broadcast-shapes' );
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' );
}C APIs
Usage
#include "stdlib/ndarray/base/broadcast_shapes.h"stdlib_ndarray_broadcast_shapes( M, **shapes, *ndims, *out )
Broadcasts array shapes to a single shape.
#include "stdlib/ndarray/base/broadcast_shapes.h"
#include <stdint.h>
int64_t N1 = 4;
int64_t sh1[] = { 8, 1, 6, 1 };
int64_t N2 = 3;
int64_t sh2[] = { 7, 1, 5 };
int64_t ndims[] = { N1, N2 };
int64_t *shapes[] = { sh1, sh2 };
int64_t out[] = { 0, 0, 0, 0 };
int8_t status = stdlib_ndarray_broadcast_shapes( 2, shapes, ndims, out );
if ( status != 0 ) {
// Handle error...
}The function accepts the following arguments:
- M:
[in] int64_tnumber of shape arrays. - shapes:
[in] int64_t**array of shape arrays (dimensions). - ndims:
[in] int64_t*number of dimensions for each respective shape array. - out:
[out] int64_t*output shape array.
int8_t stdlib_ndarray_broadcast_shapes( int64_t M, int64_t *shapes[], int64_t ndims[], int64_t *out );If successful, the function returns 0; otherwise, the function returns -1 (e.g., due to incompatible shapes).
Notes
- Even if the function is unsuccessful, the function may still overwrite elements in the output array before returning. In other words, do not assume that providing incompatible shapes is a no-op with regard to the output array.
Examples
#include "stdlib/ndarray/base/broadcast_shapes.h"
#include <stdint.h>
#include <stdio.h>
#include <inttypes.h>
int main( void ) {
int64_t N1 = 4;
int64_t sh1[] = { 8, 1, 6, 1 };
int64_t N2 = 3;
int64_t sh2[] = { 7, 1, 5 };
int64_t ndims[] = { N1, N2 };
int64_t *shapes[] = { sh1, sh2 };
int64_t out[] = { 0, 0, 0, 0 };
int8_t status = stdlib_ndarray_broadcast_shapes( 2, shapes, ndims, out );
if ( status != 0 ) {
printf( "incompatible shapes\n" );
return 1;
}
int64_t i;
printf( "shape = ( " );
for ( i = 0; i < N1; i++ ) {
printf( "%"PRId64"", out[ i ] );
if ( i < N1-1 ) {
printf( ", " );
}
}
printf( " )\n" );
return 0;
}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
License
See LICENSE.
Copyright
Copyright © 2016-2023. The Stdlib Authors.
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