![]() ![]() In R, function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization. In Python NumPy arrays implement the flatten method, while in R the desired effect can be achieved via the c() or as.vector() functions. GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. In Matlab/ GNU Octave a matrix A can be vectorized by A(:). Programming languages that implement matrices may have easy means for vectorization. ![]() There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice versa called, respectively, the duplication matrix and the elimination matrix. MATLAB supports (and encourages) vectorized operations on vectors and matrices.įor example, suppose we have A and B, two n-by- m matrices and we want C to be the element-wise product of the corresponding elements (i.e., C(i,j) = A(i,j)*B(i,j)).Vec ( A ) = T. implicit array expansion (opens new window). ![]() A comparison between the speed of computing using bsxfun vs.NumPy's Broadcasting 1 (opens new window), 2 (opens new window).MATLAB documentation on " Compatible Array Sizes for Basic Operations (opens new window)".If such a concern does not exist, MATLAB R2016 release notes (opens new window) encourage users to switch from bsxfun:Ĭompared to using bsxfun, implicit expansion offers faster speed of execution, better memory usage, and improved readability of code. Therefore, the explicit invocation of bsxfun 1 (opens new window), 2 (opens new window) (which achieves the same effect) should be used if code needs to run on older MATLAB versions. N-D arrays that have the right amount of singleton dimensions but they're in the wrong order (#2).Ĭode relying on this convention is NOT backward-compatible with any older versions of MATLAB. N-D arrays that have the right amount of singleton dimensions but they're in the wrong order (#1). Vectors where a dimension is a multiple of the same dimension in the other array.Īrrays with dimensions that are multiples of each other. # Examples of incompatible sizes: Description In other words - dimensions that appear in one array and do not appear in the other, are implicitly fit for automatic expansion.įor example, in MATLAB versions before R2016b this would happen:Īns = 9 3 9 4 7 10 5 11 5 # Examples of compatible sizes: Description Note that trailing singleton (that is, of size 1) dimensions are omitted by MATLAB, even though there's theoretically an infinite amount of them. Sizes are considered "compatible" when each dimension in one array is either exactly equal to the same dimension in the other array, or is equal to 1. The aforementioned binary operations are allowed between arrays, as long as they have "compatible sizes". Elementary math functions: max, min, mod, rem, hypot, atan2, atan2d.Bit-wise functions: bitand, bitor, bitxor.Element-wise arithmetic operators: +,.The operators that support implicit expansion are 1 (opens new window): MATLAB R2016b featured a generalization of its scalar expansion 1 (opens new window), 2 (opens new window) mechanism, to also support certain element-wise operations between arrays of different sizes, as long as their dimension are compatible. # Implicit array expansion (broadcasting) Internally, bsxfun does not replicate the array and executes an efficient loop. The function, must be a binary function meaning it must take exactly two inputs. In other languages, this is commonly referred to as broadcasting and happens automatically in Python (numpy) and Octave. All conditions are met and B will be replicated to match the 3rd dimension of A. Secondly, A has K layers while B has implicitly only 1, hence it is a singleton. Firstly, their first two dimensions have corresponding sizes. After the expansion, a binary function is applied elementwise on the two arrays.įor example, let A be an M-by- N-by K array and B is an M-by- N array. ![]() Then the array with the singleton dimension will be expanded to match the dimension of the other array. has a size of 1) in either of the two arrays
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