Apply vector exponents to columns of matrix

Question

In the cmprsk package one of the tests to call crr shows the following:

crr(ftime,fstatus,cov,cbind(cov[,1],cov[,1]),function(Uft) cbind(Uft,Uft^2))

It's the final inline function function(Uft) cbind(Uft,Uft^2) which I am interested in generalizing. This example call to crr above has cov1 as cov and cov2 as cbind(cov[,1],cov[,1]), essentially hardcoding the number of covariates. Hence the hardcoding of the function function(Uft) cbind(Uft,Uft^2) is sufficient.

I am working on some benchmarking code where I would like the number of covariates to be variable. So I generate a matrix cov2 which is has nobs rows and ncovs columns (rather than ncovs being pre-defined as 2 above).

My question is - how do I modify the inline function function(Uft) cbind(Uft,Uft^2) to take in a single column vector of length nobs and return a matrix of size nobs x ncovs where each column is simply the input vector raised to the column index?

Minimal reproducible example below. My call to z2 <- crr(...) is incorrect:

#!/usr/bin/env Rscript

library(cmprsk)

for(seed in c(1, 2)) {
    for(Nobs in c(10, 20)) {
        for(Ncovs in c(2, 3)) {
            set.seed(seed);
            ftime <- rexp(Nobs);
            fstatus <- sample(0:Ncovs,Nobs,replace=TRUE);
            cov1 <- matrix(runif(Nobs*Ncovs),nrow=Nobs);
            cov2 <- matrix(runif(Nobs*Ncovs),nrow=Nobs);
            df <- data.frame(ftime=ftime, fstatus=fstatus, cov1=cov1);

            z1 <- crr(ftime, fstatus, cov1, );
            z2 <- crr(ftime, fstatus, cov1, cov2, function(Uft) Uft^cbind(1:Ncovs));
        }   
    }   
}

user_18104806 · Answer

You can use sapply :

Uft <- 1:5
Ncovs <- 6
sapply(1:Ncovs, function(i) Uft^i)
#>      [,1] [,2] [,3] [,4] [,5]  [,6]
#> [1,]    1    1    1    1    1     1
#> [2,]    2    4    8   16   32    64
#> [3,]    3    9   27   81  243   729
#> [4,]    4   16   64  256 1024  4096
#> [5,]    5   25  125  625 3125 15625

In your code :

function(Uft) sapply(1:Ncovs, function(i) Uft^i)

A better alternative using outer :

function(Uft) outer(Uft, 1:Ncovs, "^")

user_12148402 · Answer

vec <- 1:4
ncovs <- 5
matrix(unlist(Reduce("*", rep(list(vec), ncovs), accumulate= TRUE)), ncol = ncovs)

gives:

     [,1] [,2] [,3] [,4] [,5]
[1,]    1    1    1    1    1
[2,]    2    4    8   16   32
[3,]    3    9   27   81  243
[4,]    4   16   64  256 1024

Apply vector exponents to columns of matrix

2 Answers