Masi - 2 months ago 13

R Question

I want to do a simple column (Nx1) times row (1xM) multiplication, resulting in (NxM) matrix.

Code where I create a row by sequence, and column by transposing a similar sequence

`row1 <- seq(1:6)`

col1 <- t(seq(1:6))

col1 * row1

Output which indicates that R thinks matrices more like columns

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

[1,] 1 4 9 16 25 36

Expected output: NxM matrix.

OS: Debian 8.5

Linux kernel: 4.6 backports

Hardware: Asus Zenbook UX303UA

Answer

In this case using `outer`

would be a more natural choice

```
outer(1:6, 1:6)
```

In general for two **numerical vectors** `x`

and `y`

, the matrix rank-1 operation can be computed as

```
outer(x, y)
```

If you want to resort to real matrix multiplication routines, use `tcrossprod`

:

```
tcrossprod(x, y)
```

If either of your `x`

and `y`

is a matrix with dimension, use `as.numeric`

to cast it as a vector first.

It is highly not recommended to use general matrix multiplication operation `"%*%"`

for this. But if you want, make sure you get the dimension comformable, so that `x`

is a single-column matrix and `y`

is a single-row matrix: `x %*% y`

.

Can you say anything about efficiency?

Matrix rank-1 operation is known to be memory-bound. So make sure we use `gc()`

for garbage collection to tell R to release memory from heap after every replicate (otherwise your system will stall):

```
x <- runif(500)
y <- runif(500)
xx <- matrix(x, ncol = 1)
yy <- matrix(y, nrow = 1)
system.time(replicate(200, {outer(x,y); gc();}))
# user system elapsed
# 4.484 0.324 4.837
system.time(replicate(200, {tcrossprod(x,y); gc();}))
# user system elapsed
# 4.320 0.324 4.653
system.time(replicate(200, {xx %*% yy; gc();}))
# user system elapsed
# 4.372 0.324 4.708
```

In terms of performance, they are all very alike.