Multiplying vector combinations

Question

Normal R vector multiplication, only multiplies vectors once, or recycles the shorter vector. IE:

> c(2,3,4) * c(1,2)
[1] 2 6 4
Warning message:
In c(2, 3, 4) * c(1, 2) :
  longer object length is not a multiple of shorter object length

What I would like to do is to multiply every combination of two vectors. In this specific case, I'm calculating the maximum speed in MPH that an electric bicycle motor can spin:*

d <- c(20,26,29) #bicycle wheel diameter possibilities in inches
rpm <- c(150,350) #maximum motor RPM. Choices depends on motor winding.
cir <- pi * d #circumference
mph <- cir * rpm / 63360 * 60 #max speed in mph for each wheel diameter and RPM combination
mph

What I would like is for mph to contain every maximum speed combination of the given wheel diameters with the given max motor RPM.

* Please note that it will be generating zero torque at this speed because of back EMF.

Answer 1

You are probably looking for outer() or it's alias binary operator %o%:

> c(2,3,4) %o% c(1,2)
     [,1] [,2]
[1,]    2    4
[2,]    3    6
[3,]    4    8
> outer(c(2,3,4), c(1,2))
     [,1] [,2]
[1,]    2    4
[2,]    3    6
[3,]    4    8

In your case, outer() offers the flexibility to specify a function that is applied to the combinations; %o% only applies the * multiplication function. For your example and data

mph <- function(d, rpm) {
    cir <- pi * d
    cir * rpm / 63360 * 60
}

> outer(c(20,26,29), c(150,350), FUN = mph)
          [,1]     [,2]
[1,]  8.924979 20.82495
[2,] 11.602473 27.07244
[3,] 12.941220 30.19618

Answer 2

I believe the function you're looking for is outer

> outer(cir, rpm, function(X, Y) X * Y / 63360 * 60)
          [,1]     [,2]
[1,]  8.924979 20.82495
[2,] 11.602473 27.07244
[3,] 12.941220 30.19618

In this case you could clean up the notation a bit:

outer(cir, rpm / 63360 * 60)