## The magic empty bracket

I have been working with R for some time now, but once in a while, basic functions catch my eye that I was not aware of…
For some project I wanted to transform a correlation matrix into a covariance matrix. Now, since `cor2cov` does not exist, I thought about “reversing” the `cov2cor` function (`stats:::cov2cor`).
Inside the code of this function, a specific line jumped into my retina:

```r[] <- Is * V * rep(Is, each = p)
```

What’s this [ ]?

Well, it stands for every element $E_{ij}$ of matrix $E$. Consider this:

```mat <- matrix(NA, nrow = 5, ncol = 5)
```
```> mat
[,1] [,2] [,3] [,4] [,5]
[1,]   NA   NA   NA   NA   NA
[2,]   NA   NA   NA   NA   NA
[3,]   NA   NA   NA   NA   NA
[4,]   NA   NA   NA   NA   NA
[5,]   NA   NA   NA   NA   NA```

With the empty bracket, we can now substitute ALL values by a new value:

```mat[] <- 1
```
```> mat
[,1] [,2] [,3] [,4] [,5]
[1,]    1    1    1    1    1
[2,]    1    1    1    1    1
[3,]    1    1    1    1    1
[4,]    1    1    1    1    1
[5,]    1    1    1    1    1```

Interestingly, this also works with lists:

```L <- list(a = 1, b = 2, c = 3)

>L
\$a
[1] 1
\$b
[1] 2
\$c
[1] 3
L[] <- 5

> L
\$a
[1] 5

\$b
[1] 5

\$c
[1] 5

Cheers,
Andrej

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This entry was posted  on Wednesday, January 30th, 2013 at 3:42 pm and is filed under R Internals.					You can follow any responses to this entry through the RSS 2.0 feed.

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### 13 Responses to The magic empty bracket

1. Michael Folkes says:

awesome thanks! one good turn deserves another.
In case you didn’t resolve cor2cov, here’s an eg:

#__________________
# this code shows how to build correlated series, which in this case have lognormal error
# the example represents four time series (so the matrices are 4×4)
require(MASS)

sd<-log(1.2)
cov.mat<-matrix(c(sd^2,0,0,0,
0,sd^2,0,0,
0,0,sd^2,0,
0,0,0,sd^2),
ncol=4,byrow=T)

# correlation of 50% between series
cor.mat<- matrix(c(1,0.5,0.5,0.5,
0.5,1,0.5,0.5,
0.5,0.5,1,0.5,
0.5,0.5,0.5,1),ncol=4)

# next two lines are cor2cov():
d <- sqrt(diag(cov.mat))
cov.mat2 <- outer(d, d)*cor.mat

cov.mat2

#demonstrating the math is correct:
cov2cor(cov.mat2)

junk<-mvrnorm(100000,mu=rep(log(1e4),4),cov.mat2)
junk2<-exp(junk)

# demonstrating the sampled results have desired correlation:
cor(junk2)
acf(junk2)

• anspiess says:

Thanks for the code, works like charm!

2. eran says:

Great tip, will come in handy (a.s.)

Maybe drop a line to Norman S. Matloff, he can add it to the next addition of “the art of R programming”.

• anspiess says:

Hmm, can’t imagine it isn’t in there yet…
I will have a look. Thanks for the suggestion!

3. carlwitthoft says:

To make this post complete, you might want to discuss what happens to “r” when you type
> r r[] <- something

• anspiess says:

Hmm, dunno what you mean… Is your code line correct?
Cheers,
Andrej

• carlwitthoft says:

Sorry — something fouled up there. I wanted to compare
> r[ ] r <- something
in both the case where "r" previously existed and where it did not.

4. carlwitthoft says:

OK, let me try that again. WordPress is destroying lines of text near the character “>” so pretend the prompt is “%”
% r <- something
vs
% r[] <- something

• anspiess says:

Ok!
r[] <- 5 will fill each element of an existing object with 5 while r <- something, if r already exists, will results in a new object r with a single value 5.
What would be really nice as a syntax:
r[] <- 5 * r[]
doing an element-wise function as a loop instead of lapply.
Should be possible, since lists are stored internally as C objects, not?

Cheers.

5. Ken Butler says:

Isnâ€™t this just the same thing as r[,]<-5, which (to my mind) more transparently sets all the elements in all the rows and all the columns to 5?

• anspiess says:

Yes, you’re right. The version r[] <- 5 works on matrices, data.frames and lists though…
Greets,
Andrej

• carlwitthoft says:

True – except that if you screw up and type r[,,,]<- 42 but r happens to be of rank !=4 , it'll throw an error. using r[ ] avoids this risk.

6. Reblogged this on Stats in the Wild and commented:
I didn’t know this either!