Taking vector norm from a data matrix in R

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I am trying to achieve some set of calculations using R for calculating the norm of a point with a given coordinate and then take the maximum and then take the square out of it.

I have tried the following:

a <- c(-0.5,1)
b <- c(-1,-1.5)
c <- c(-1.5,1.5)
d <- c(1.5,-0.5)
e <- c(0.5,-0.5)
df <- data.frame(a,b,c,d,e)

In a more detailed way, this is what I want to perform:

task

I tried using the norm and using the Frobenius but I want to put everything into a function to be used later. Because manually when I create vectors for these tasks it becomes too tedious to calculate every point. Looking for an efficient/simpler way to perform this.

r function
1 Answers

We loop across the columns, get the square of the elements, sum it, return with square root, get the max and square it

library(dplyr)
df %>%
   summarise(across(everything(), ~ sqrt(sum(.^2)))) %>% 
   max %>%
   .^2
#[1] 4.5

In base R, we can use

max(sqrt(colSums(df^2)))^2
#[1] 4.5

If we want to print with all the digits, specify the digits in print

print(max(sqrt(colSums(df^2)))^2, digits = 16)
#[1] 4.499999999999999
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