Is it possible to have function object as an element

Question

Short answer: yes, see the accepted reply.

---

I have the two data.table below.

stocks = data.table(Ticker = c('xx','xx','yy','yy'), Date = c(as.IDate("2000-01-01"), as.IDate("2000-01-02")), t = c(1.8, 3.5))
   Ticker       Date   t
1:     xx 2000-01-01 1.8
2:     xx 2000-01-02 3.5
3:     yy 2000-01-01 1.8
4:     yy 2000-01-02 3.5
tt = data.table(Date = c(as.IDate("2000-01-01"), as.IDate("2000-01-02")), t0 = c(1,2), t1 = c(2,3), t2 = c(3,4), y0 = c(10, 20), y1 = c(-20, -30), y2 = c(33,44))
         Date t0 t1 t2 y0  y1 y2
1: 2000-01-01  1  2  3 10 -20 33
2: 2000-01-02  2  3  4 20 -30 44

For each row in stocks, I want to find the approximate y given t, based on linear interpolation of values in tt.

zz = tt[stocks, on = 'Date']
zz[, y.approx := approx(c(t0,t1,t2), c(y0,y1,y2), t)$y, by = 'Date,Ticker']
         Date t0 t1 t2 y0  y1 y2 Ticker   t y.approx
1: 2000-01-01  1  2  3 10 -20 33     xx 1.8      -14
2: 2000-01-02  2  3  4 20 -30 44     xx 3.5        7
3: 2000-01-01  1  2  3 10 -20 33     yy 1.8      -14
4: 2000-01-02  2  3  4 20 -30 44     yy 3.5        7

The problem is that doing this way has lots of duplicate calculation. Ideally I want to define an approxfun for each day and apply it to each row in stocks. But datatable cannot take function objects as its element.

tt[, ff := approxfun(c(t0,t1,t2), c(y0,y1,y2)), by = Date]
Error in `[.data.table`(tt, , `:=`(ff, approxfun(c(t0, t1, t2), c(y0,  : 
  j evaluates to type 'closure'. Must evaluate to atomic vector or list.

My question is:

1. Is there a better way than doing approx on each row (and being slow)?
2. Is it possible for datatable to have function objects as its element?

Answer 1

It's pretty easy to store functions in a data.table - you just need to put them in a list:

tt[, ff := .(list(approxfun(c(t0,t1,t2), c(y0,y1,y2)))), by = Date]
#         Date t0 t1 t2 y0  y1 y2         ff
#1: 2000-01-01  1  2  3 10 -20 33 <function>
#2: 2000-01-02  2  3  4 20 -30 44 <function>

stocks[tt, y.approx := ff[[1]](t), on = 'Date', by = .EACHI]
stocks
#   Ticker       Date   t y.approx
#1:     xx 2000-01-01 1.8      -14
#2:     xx 2000-01-02 3.5        7
#3:     yy 2000-01-01 1.8      -14
#4:     yy 2000-01-02 3.5        7

Answer 2

How about something like:

> zz
         Date t0 t1 t2 y0  y1 y2 Ticker   t
1: 2000-01-01  1  2  3 10 -20 33     xx 1.8
2: 2000-01-02  2  3  4 20 -30 44     xx 3.5
3: 2000-01-01  1  2  3 10 -20 33     yy 1.8
4: 2000-01-02  2  3  4 20 -30 44     yy 3.5

> zz[t0<=t & t<=t1, y.approx:={a=(t-t0)/(t1-t0); y0+a*(y1-y0)}]
> zz
         Date t0 t1 t2 y0  y1 y2 Ticker   t y.approx
1: 2000-01-01  1  2  3 10 -20 33     xx 1.8      -14
2: 2000-01-02  2  3  4 20 -30 44     xx 3.5       NA
3: 2000-01-01  1  2  3 10 -20 33     yy 1.8      -14
4: 2000-01-02  2  3  4 20 -30 44     yy 3.5       NA

> zz[t1<=t & t<=t2, y.approx:={a=(t-t1)/(t2-t1); y1+a*(y2-y1)}]
> zz
         Date t0 t1 t2 y0  y1 y2 Ticker   t y.approx
1: 2000-01-01  1  2  3 10 -20 33     xx 1.8      -14
2: 2000-01-02  2  3  4 20 -30 44     xx 3.5        7
3: 2000-01-01  1  2  3 10 -20 33     yy 1.8      -14
4: 2000-01-02  2  3  4 20 -30 44     yy 3.5        7
> 

Don't know how general you need it to be (how many columns you really have). But worth trying to vectorize like this to save the function call overhead by row. Several iterations of a for loop for number of time deltas (2 in this case) should be faster than looping by row (let us know if you go that way and need to generate the query dynamically for each time delta).

Answer 3

We can hack it with a global list of functions and the superassignment operator:

x <- list();
invisible(tt[,{ x[[as.character(Date)]] <<- approxfun(c(t0,t1,t2),c(y0,y1,y2)); 0; },Date]);
x;
## $`2000-01-01`
## function (v)
## .approxfun(x, y, v, method, yleft, yright, f)
## <bytecode: 0x602762000>
## <environment: 0x603118610>
##
## $`2000-01-02`
## function (v)
## .approxfun(x, y, v, method, yleft, yright, f)
## <bytecode: 0x602762000>
## <environment: 0x60312c9d0>
##
stocks[,y.approx:=x[[as.character(Date)]](t),Date];
##    Ticker       Date   t y.approx
## 1:     xx 2000-01-01 1.8      -14
## 2:     xx 2000-01-02 3.5        7
## 3:     yy 2000-01-01 1.8      -14
## 4:     yy 2000-01-02 3.5        7