entrywise
Computes a vector or matrix from a homogeneous list of vectors or matrices by applying a number list function to each entry.
Syntax
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entrywise(L, f)-
Lis a homogeneous list of vectors or matrices -
fis a number-valued number list function
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Description
If L is a list of vectors or matrices of the same format and f a function that accepts a list of numbers and returns a number, then entrywise(L, f) returns the vector or matrix with the format of the elements of L whose entries are the images under f of the entrywise lists of numbers obtained from L.
In other words, if L is
L = '(A1, A2, ..., An),
where the elements Ak are either all vectors of dimension k or all matrices of size k×m, then entrywise(L, f) is, if the Ak’s are vectors, the vector A of dimension k with components
A[i] = f('(A1[i], A2[i], ..., An[i])), ∀i ∈ [1, k] ∩ ℤ
or, if the Ak’s are matrices, the matrix A with size k×m with entries
A[i, j] = f('(A1[i, j], A2[i, j], ..., An[i, j])), ∀(i, j) ∈ [1, k]×[1, m] ∩ ℤ².
Examples
L ≔ compute(RandomIntMatrix(2, 1, 10), n, 1, 4)
⎛8 3⎞ ⎛9 6⎞ ⎛1 3⎞ ⎛7 4⎞ ⎝6 6⎠ ⎝1 4⎠ ⎝6 8⎠ ⎝4 6⎠
entrywise(L, HarmonicMean)
⎛2.90071942446 3.69230769231⎞ ⎝2.52631578947 5.64705882353⎠
inv(∑(L@inv)/4)
⎛−20.8980582524 −4.36893203883⎞ ⎝ 6.04368932039 6.69902912621⎠