﻿ entrywise – Algosim documentation
Algosim documentation: entrywise

# entrywise

Computes a vector or matrix from a homogeneous list of vectors or matrices by applying a number list function to each entry.

## Syntax

• `entrywise(L, f)`

• `L` is a homogeneous list of vectors or matrices

• `f` is a number-valued number list function

## 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⎠
```