Applying function to lists R

Question

I have a function like this

f(x) = a0 + 2/n * (a1 cos(x) + b1 sin(x) +  a2 cos(2*x) + b2 sin(2*x) + a3 cos(3*x) + b3 sin(3*x))

where x is a vector. I have two list one (xlist) containing the values of different x and the other the corresponding coefficients (the two lists have then the same length).

I would like to apply the f function to all the elements of xlist with the corresponding coefficients. Should I use lapply? How?

Here is an example of my data

head(list)

$`1`
 [1] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
[26] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
[51] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

$`2`
 [1] "6.69999980926514" "7.5"              "8.80000019073485" "8.52499973773958"
 [5] "7.96666669845581" "6.69999980926514" "8"                "8.35000002384187"
 [9] "6.86666663487752" NA                 NA                 "6.5"             
[13] "6.83749985694886" "9.25"             "7.5"              "6.90000003576279"
[17] "6.86666655540466" "6.80000003178914" NA                 "6.5"             
[21] "9.24999999999998" "7"                NA                 NA                
[25] "12.1999998092651" NA                 NA                 NA                
[29] NA                 "10.6000003814697" NA                 NA                
[33] NA                 NA                 "10.8000001907349" "10.3000001907349"
[37] NA                 "10"               NA                 NA                
[41] "9.69999980926514" NA                 "11"               "10.8000001907349"
[45] NA                 NA                 NA                 NA                
[49] NA                 NA                 NA                 "9.80000019073486"
[53] NA                 NA                 NA                 "8.80000019073486"
[57] NA                 "9.34999990463257" "9.19999980926513" "11.3666664759318"
[61] NA                 "9.23333326975504" "9.89999961853028" "9.98333326975507"
[65] "10.1000003814697" "9.89999961853028" "10.2000002861023" "10.1333335240682"
[69] "8.69999980926514" "8.10000014305114" "7.80000019073486" NA                
[73] "7.17499995231629"

$`3`
 [1] "19.2916666666667" "20.810000038147"  "20.0652381896973" "18.8437498807907"
 [5] "20.1949997901917" "20.483333407508"  "18.183333211475"  "17.5416665077209"
 [9] "17.0666666939145" "17.3499999364217" "17.7023808706374" "19.1339998626709"
[13] "18.8966665267944" "17.7916667461395" "19.3999999046326" "15.0499997933705"
[17] "15.7500001192093" "16.4111108779907" "15.1766667683919" "16.2199998378754"
[21] "13.9375"          "15.2999999523163" "15.4000000953674" "13.3000001907349"
[25] "18.6124999523163" "19.2916664282481" "16.9500002861023" "15.4666668574015"
[29] "20.3133335749308" "15.0708334048589" "18.3250002861023" "15.9000000953674"
[33] "15.5500001907349" "16.0249998569488" "19.0500001907349" "15.4000002543132"
[37] "18.4583331743876" "15.7250001430512" "18.7388887405396" "17.8388888041178"
[41] "13.0416667461396" "14.8777777883742" "18.1946297892818" "17.1666669580672"
[45] "18.5020833015442" "14.4916666348775" "14.875"           "17.1666666666667"
[49] "15.6708332697551" "19.1062924618624" "15.9388887087504" "14.6312497854233"
[53] "15.3333334128062" "17.5484848022461" "15.8914288157509" "17.9214814786558"
[57] "15.3875000476837" "18.739999961853"  "15.3555357796805" "18.3854166666667"
[61] "19.3625001907349" "19.6166665395101" "18.7305555873447" "19.2566665331522"
[65] "19.1083335876465" "17.6285716465541" "18.8063492396521" "16.6624999046326"
[69] "18.3625003099441" "18.8749999523163" "18.389999961853"  "17.3500001430512"
[73] "15.0333334604899"

head(coefflist)

$`1`
[1] -0.99816132  0.94322618  1.20707782  0.18038590  0.40502377 -0.06045413
[7]  0.16397336

$`2`
[1] -1.03218220  0.86101832  1.22405685  0.17861695  0.48982884 -0.00870947
[7]  0.07130413

$`3`
[1] -0.76477491  0.81255792  1.06977327  0.08542454  0.48862804  0.10553910
[7]  0.16869875


length(list)
73
head(coefflist)
73

Many thanks

Please can you provide an example of your data. As the question is currently written, it is difficult to see what form your data takes. See this question stackoverflow.com/q/5963269/134830 for how to provide your data to us. — Richie Cotton
– Richie Cotton, Commented Feb 17, 2014 at 16:46

rawr · Accepted Answer · 2014-02-17 17:29:25Z

3

I don't use mapply much, so here is an example I walked through myself:

set.seed(1618)
coeflist <- list(a = rnorm(5),
                 b = runif(5),
                 x = rnorm(5),
                 n = seq(1, 500, length = 5),
                 x.all = rnorm(100))


mapply(function(a, b, x, n) a + (2 / n) * (a * cos(x) + b * sin(x) +
                                             a * cos(2 * x) + b * sin(2 * x) + 
                                             a * cos(3 * x) + b * sin(3 * x)),
       coeflist[['a']], coeflist[['b']], coeflist[['x']], coeflist[['n']])

# [1] -1.0978364 -0.4403969 -0.5748082  0.5659216 -1.7714444

Below is the long way to get mapply results

# super long way (take the first element in each list and apply the function);
# repeat for each of n elements in list:
sapply(1:5, function(qq)

  coeflist[['a']][qq] + (2 / coeflist[['n']][qq]) * 
    (coeflist[['a']][qq] * cos(coeflist[['x']][qq]) +
       coeflist[['b']][qq] * sin(coeflist[['x']][qq]) +
       coeflist[['a']][qq] * cos(2 * coeflist[['x']][qq]) + 
       coeflist[['b']][qq] * sin(2 * coeflist[['x']][qq]) +
       coeflist[['a']][qq] * cos(3 * coeflist[['x']][qq]) +
       coeflist[['b']][qq] * sin(3 * coeflist[['x']][qq]))
)
# results are same as above but with much more work:
# [1] -1.0978364 -0.4403969 -0.5748082  0.5659216 -1.7714444

And this is if you have a lot of x's and want to run each one for each set of coefficients

 sapply(coeflist[['x.all']], function(x) 
   mapply(function(a, b, x, n) a + (2 / n) * (a * cos(x) + b * sin(x) +
                                                a * cos(2 * x) + b * sin(2 * x) +
                                                a * cos(3 * x) + b * sin(3 * x)),
          coeflist[['a']], coeflist[['b']], x, coeflist[['n']])
 )

#           [,1]         [,2]       [,3]       [,4]       [,5]       [,6]       [,7]
# [1,]  3.5548544 -0.08107256 -0.5391973  0.4732270 -3.7242500 -5.9636420 -5.9918891
# [2,] -0.3915859 -0.40732538 -0.4114718 -0.4048558 -0.4259481 -0.4343241 -0.4344591
# [3,] -0.5550217 -0.56512808 -0.5565757 -0.5639058 -0.5623012 -0.5745126 -0.5745335
# [4,]  0.5654853  0.57204328  0.5618304  0.5714012  0.5640612  0.5748265  0.5748127
# [5,] -1.7533459 -1.76927445 -1.7559892 -1.7673417 -1.7650747 -1.7842027 -1.7842367

etc, etc. I have 100 results, one for each x in x.all in my list, and for each of those 100, there are 5 calculations, one for each combination of coefficients: a, b, n, and x.

answered Feb 17, 2014 at 17:29

rawr

20.9k4 gold badges49 silver badges80 bronze badges

Sign up to request clarification or add additional context in comments.

3 Comments

user3036416 Over a year ago

Hi, thanks for your answer but what I was looking for is a method to associate the i element of xlist (xlist[[i]]) with the set of coefficient (coeflist[[i]]) and than calulate f[i].

rawr Over a year ago

R keeps things in order and is vectorized.. so just stick [i] on mapply such as mapply(...)[i] to get the calculation for a[i], b[i], n[i], and x[i].

rawr Over a year ago

And since n is a constant, change the arg list from coeflist[['n']] to n = 5

Baumann · Accepted Answer · 2014-02-17 18:29:37Z

Working with your data:

list = structure(list(`1` = structure(list(V1 = c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), .Names = "V1", class = "data.frame", row.names = c(NA, -73L)), `2` = structure(list(V1 = c(6.69999980926514, 7.5, 8.80000019073485, 8.52499973773958, 7.96666669845581, 6.69999980926514, 8, 8.35000002384187, 6.86666663487752, NA, NA, 6.5, 6.83749985694886, 9.25, 7.5, 6.90000003576279, 6.86666655540466, 6.80000003178914, NA, 6.5, 9.24999999999998, 7, NA, NA, 12.1999998092651, NA, NA, NA, NA, 10.6000003814697, NA, NA, NA, NA, 10.8000001907349, 10.3000001907349, NA, 10, NA, NA, 9.69999980926514, NA, 11, 10.8000001907349, NA, NA, NA, NA, NA, NA, NA, 9.80000019073486, NA, NA, NA, 8.80000019073486, NA, 9.34999990463257, 9.19999980926513, 11.3666664759318, NA, 9.23333326975504, 9.89999961853028, 9.98333326975507, 10.1000003814697, 9.89999961853028, 10.2000002861023, 10.1333335240682, 8.69999980926514, 8.10000014305114, 7.80000019073486, NA, 7.17499995231629)), .Names = "V1", class = "data.frame", row.names = c(NA, -73L)), `3` = structure(list(V1 = c(19.2916666666667, 20.810000038147, 20.0652381896973, 18.8437498807907, 20.1949997901917, 20.483333407508, 18.183333211475, 17.5416665077209, 17.0666666939145, 17.3499999364217, 17.7023808706374, 19.1339998626709, 18.8966665267944, 17.7916667461395, 19.3999999046326, 15.0499997933705, 15.7500001192093, 16.4111108779907, 15.1766667683919, 16.2199998378754, 13.9375, 15.2999999523163, 15.4000000953674, 13.3000001907349, 18.6124999523163, 19.2916664282481, 16.9500002861023, 15.4666668574015, 20.3133335749308, 15.0708334048589, 18.3250002861023, 15.9000000953674, 15.5500001907349, 16.0249998569488, 19.0500001907349, 15.4000002543132, 18.4583331743876, 15.7250001430512, 18.7388887405396, 17.8388888041178, 13.0416667461396, 14.8777777883742, 18.1946297892818, 17.1666669580672, 18.5020833015442, 14.4916666348775, 14.875, 17.1666666666667, 15.6708332697551, 19.1062924618624, 15.9388887087504, 14.6312497854233, 15.3333334128062, 17.5484848022461, 15.8914288157509, 17.9214814786558, 15.3875000476837, 18.739999961853, 15.3555357796805, 18.3854166666667, 19.3625001907349, 19.6166665395101, 18.7305555873447, 19.2566665331522, 19.1083335876465, 17.6285716465541, 18.8063492396521, 16.6624999046326, 18.3625003099441, 18.8749999523163, 18.389999961853, 17.3500001430512, 15.0333334604899)), .Names = "V1", class = "data.frame", row.names = c(NA, -73L))), .Names = c("1", "2", "3"))
coefflist = structure(list(`1` = structure(list(V1 = c(-0.99816132, 0.94322618, 1.20707782, 0.1803859, 0.40502377, -0.06045413, 0.16397336)), .Names = "V1", class = "data.frame", row.names = c(NA, -7L)), `2` = structure(list(V1 = c(-1.0321822, 0.86101832, 1.22405685, 0.17861695, 0.48982884, -0.00870947, 0.07130413)), .Names = "V1", class = "data.frame", row.names = c(NA, -7L)), `3` = structure(list(V1 = c(-0.76477491, 0.81255792, 1.06977327, 0.08542454, 0.48862804, 0.1055391, 0.16869875)), .Names = "V1", class = "data.frame", row.names = c(NA, -7L))), .Names = c("1", "2", "3"))

f <- function(x, coef, n) {
  coef=coef$V1
  x=x$V1
  a0 = coef[1]
  a1 = coef[2]
  a2 = coef[3]
  a3 = coef[4]
  b1 = coef[5]
  b2 = coef[6]
  b3 = coef[7]  
  a0 + 2/n * (a1*cos(x) + b1*sin(x) +  a2*cos(2*x) + b2*sin(2*x) + a3*cos(3*x) + b3*sin(3*x))
}
y = mapply(f, x=list, coef=coefflist, n=1)
head(y)

#       1          2         3
# [1,] NA  2.8195891  3.010415
# [2,] NA -1.7689234 -2.123251
# [3,] NA -0.8235252 -1.080907
# [4,] NA -1.4899560  3.156538
# [5,] NA -2.6507462 -1.653132
# [6,] NA  2.8195891 -2.340157

Collectives™ on Stack Overflow

Applying function to lists R

2 Answers 2

3 Comments

Comments

Your Answer

Linked

Hot Network Questions

Collectives™ on Stack Overflow

2 Answers 2

3 Comments

Comments

Your Answer

Sign up or log in

Post as a guest

Linked

Related