Produce a matrix from every row (tidyverse) - r

Question

I am trying to implement analyses across a posterior of matrices. What I start with is a tibble of k^2 columns, where k is the dimensions of the matrix. The ith row forms the matrix of the ith iteration.
So, for example for a 3x3 matrix, this is:
set.seed(12)
n <- 1000
z1z1 <- rnorm(n, 5, 1)
z2z2 <- rnorm(n, 5, 1)
z3z3 <- rnorm(n, 5, 1)
z1z2 <- rnorm(n, 0, 1)
z1z3 <- rnorm(n, 0, 1)
z2z3 <- rnorm(n, 0, 1)
post3 <- as_tibble(matrix(c(z1z1, z1z2, z1z3,
z1z2, z2z2, z2z3,
z1z3, z2z3, z3z3),
ncol = 9))
post3
Giving:
# A tibble: 1,000 x 9
V1 V2 V3 V4 V5 V6 V7 V8 V9
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 3.52 -0.618 2.96 -0.618 2.48 -0.634 2.96 -0.634 5.98
2 6.58 -0.827 0.0909 -0.827 5.52 -1.84 0.0909 -1.84 6.20
3 4.04 1.48 -1.66 1.48 6.58 0.166 -1.66 0.166 5.58
4 4.08 -1.01 0.809 -1.01 5.49 0.607 0.809 0.607 6.55
5 3.00 0.582 -0.485 0.582 6.20 0.0765 -0.485 0.0765 6.38
6 4.73 0.718 1.97 0.718 4.00 -0.147 1.97 -0.147 4.35
7 4.68 -0.372 0.572 -0.372 4.65 -1.68 0.572 -1.68 3.83
8 4.37 -0.809 0.883 -0.809 3.96 0.985 0.883 0.985 4.97
9 4.89 0.405 0.686 0.405 6.02 0.252 0.686 0.252 6.29
10 5.43 0.124 0.199 0.124 5.75 0.354 0.199 0.354 4.20
# ... with 990 more rows
Where this is the matrix in the first iteration:
k <- sqrt(length(post3))
matrix(post3[1,], nrow = k)
[,1] [,2] [,3]
[1,] 3.519432 -0.618137 2.962622
[2,] -0.618137 2.479522 -0.6338298
[3,] 2.962622 -0.6338298 5.977552
I am then working along this posterior to calculate the dominance of the first eigenvector:
post3 %>%
rowwise %>%
mutate(
pre_eig = list(eigen(matrix(c(V1, V2, V3, V4, V5, V6, V7, V8, V9), nrow = k))),
dom = pre_eig[[1]][1] / sum(pre_eig[[1]][1:k])) %>%
select('dom')
Giving:
# A tibble: 1,000 x 1
dom
<dbl>
1 0.676
2 0.437
3 0.462
4 0.427
5 0.414
6 0.504
7 0.474
8 0.429
9 0.394
10 0.383
# ... with 990 more rows
What I would like to do is make this script versatile so that it can take posteriors for any value of k. The issue I am having is in how to define the matrix without having to hand write all the column names - when applying this to 2000x2000 matrices I don't want to write out V1, V2, V3... V4000000!
I tried a few things (including ...eigen(matrix(c(paste0('V', 1:(k^2))), nrow = k)))..., which I think is not working because it wants V1, V2... rather than "V1", "V2"...) and I all out of ideas. How do I get it to automatically take the column names from the posterior tibble?
I would then be able to use the exact same piece of script for example on post3 <- as_tibble(matrix(c(z1z1, z1z2, z1z2, z2z2), ncol = 4))...

Answer 1

You can avoid naming all the columns explicitly if you gather each row's values into key-value pairs:
library(tidyr)
post3 %>%
# add row ID (so that results can be sorted back into original order)
mutate(row.id = seq(1, n())) %>%
# convert each row to long format, with values sorted from 1st to k^2th column
gather(position, value, -row.id) %>%
mutate(position = as.numeric(gsub("^V", "", position))) %>%
arrange(row.id, position) %>%
select(-position) %>%
# group by row ID & calculate
group_by(row.id) %>%
summarise(pre_eig = list(eigen(matrix(value, nrow = k))[["values"]]),
dom = pre_eig[[1]][1] / sum(pre_eig[[1]][1:k])) %>%
ungroup() %>%
# sort results in original order
arrange(row.id) %>%
select(dom)
The results should be the same as before:
# A tibble: 1,000 x 1
dom
<dbl>
1 0.676
2 0.437
3 0.462
4 0.427
5 0.414
6 0.504
7 0.474
8 0.429
9 0.394
10 0.383
# ... with 990 more rows