[R] data transformation

[ronggui]

i have data fame da:
> da
    x y
1   1 a
2   2 a
3   3 a
4   4 a
5   5 a
6   6 b
7   7 b
8   8 b
9   9 b
10 10 b
> str(da)
`data.frame':   10 obs. of  2 variables:
 $ x: num  1 2 3 4 5 6 7 8 9 10
 $ y: Factor w/ 2 levels "a","b": 1 1 1 1 1 2 2 2 2 2

and i want to generate new variable da$z,when y=="a",da$z=da$x-mean(x[y=="a"])  ,when   y=="b",da$z=da$x-mean(x[y=="b"]).

this data frame is simple and i can do it by hand,if the y has many levels and i have x1,x2....
can i do it quickly?