Phdaml Phdaml - 2 months ago 6
R Question

add a vector to all rows of a matrix

I am maximizing a likelihood function and trying to reduce the loop.
I want to add the vector(parameters to be estimated) to all rows of a matrix (data). The length of vector equals to the column of matrix.

a+b
would give the wrong results because the recycle rule of R is by column not row.

a<-c(1,2,0,0,0) # parameters to be optimized
b<-matrix(1,ncol=5,nrow=6) # data
t(a+t(b)) # my code would work, anything more intuitive?


Desired output

[,1] [,2] [,3] [,4] [,5]
[1,] 2 3 1 1 1
[2,] 2 3 1 1 1
[3,] 2 3 1 1 1
[4,] 2 3 1 1 1
[5,] 2 3 1 1 1
[6,] 2 3 1 1 1


The wrong output

a+b
[,1] [,2] [,3] [,4] [,5]
[1,] 2 3 1 1 1
[2,] 3 1 1 1 2
[3,] 1 1 1 2 3
[4,] 1 1 2 3 1
[5,] 1 2 3 1 1
[6,] 2 3 1 1 1

Answer

We can use col to replicate the 'a' elements

b + a[col(b)]
#     [,1] [,2] [,3] [,4] [,5]
#[1,]    2    3    1    1    1
#[2,]    2    3    1    1    1
#[3,]    2    3    1    1    1
#[4,]    2    3    1    1    1
#[5,]    2    3    1    1    1
#[6,]    2    3    1    1    1

Or a faster option would be to use rep

b + rep(a, each = nrow(b))

Or use sweep

sweep(b, 2, a, "+")

Benchmarks

set.seed(24)
b <- matrix(sample(0:9, 8000*5000, replace=TRUE), ncol=5000)
a <- sample(0:3, 5000, replace=TRUE)
system.time(b + a[col(b)])
#  user  system elapsed 
#  1.08    0.06    1.14 
system.time(b + rep(a, each = nrow(b)))
#   user  system elapsed 
#   0.83    0.03    0.86 

system.time(t(a+t(b)))
#   user  system elapsed 
#   1.14    0.03    1.17 

system.time(sweep(b, 2, a, "+"))
#  user  system elapsed 
#  0.62    0.06    0.69