Looping in R to sum for all times older than t -


i have series of net carbon uptake values (ncu) time. want create new series of net carbon release values (ncr) time through loop based on following:

  1. the ncr @ time t sum of c release during period of other times older time t.
  2. the c release during period @ time t can calculated difference of potential ncus @ time t , time t−1.
  3. ncu added @ beginning of each period.

the paper using base model off of states mathematical trick keeping track of decomposition @ various time intervals. equation ncrsubt = sum(ncusub[t] - ncusub[t-1]) t=1 t = t.

this have in r far: 

dt = 0.005          # time step in years  duration = 15       # simulation runs 15, 500 yr intervals  n = duration/dt + 1 # number of step including starting point  time = (0:(n-1))*dt # time in unit 500 yr intervals  ncr = numeric(n)  (i in 1:(n-1)){   ncr[i] = ncu[i] + (ncu[i] - ncu[i-1])   }

i can't figure out how accomplish making ncr[i] sum of loop above times less given time.

ncu has 2 variables, time(x) (in 500 year intervals) 1:15, , ncu (y).

edit

here sample values:

ncu values

ncu = c(52.02080416,55.0440176,77.09245546,80.12810245,71.14214209,60.14417294,36.10094125,66.21153828,64.23081522,61.24448865,54.23812349)

ncut - ncut-1 values

ncut_ncut_1 = c(-3.023213444,-22.04843786,-3.035646992,8.98596036,10.99796916,24.04323169,-30.11059703,1.980723063,2.986326567,7.006365164)

ncrt values

ncrt = c(10.77406468,13.79727813,35.84571598,38.88136298,29.89540262,18.89743346,-5.145798226,24.9647988,22.98407574,19.99774917)

excel screenshot of calculations:

excel screenshot of calculations

okay, let's quick answer this.

# load in data # includes data within screenshot (1:15) vs. (1:11) ncu = c(52.02080416,55.0440176,77.09245546,80.12810245,71.14214209,60.14417294,36.10094125,66.21153828,64.23081522,61.24448865,54.23812349, 65.31275,58.30238552, 51.28640117, 41.24673948)  # reverse difference e.g. -1*([t] - [t-1]) => [t-1]-[t]  dncu = -1*diff(ncu)  # here function use within `sapply()` # function provides sum x length of differenced # ncu data. calc_ncr = function(x, dncu, len_dncu){     sum(dncu[x:len_dncu]) }  # length of differenced ncu data len_dncu = length(dncu)  # vectorized loop speed.  # range given 1 length of differenced data.  sapply(1:len_dncu, fun = calc_ncr, dncu = ncut_ncut_1, len_dncu = len_dncu)

result (after using as.matrix() on sapply() make pretty):

           [,1]  [1,] 10.774065  [2,] 13.797278  [3,] 35.845716  [4,] 38.881363  [5,] 29.895403  [6,] 18.897433  [7,] -5.145798  [8,] 24.964799  [9,] 22.984076 [10,] 19.997749 [11,] 12.991384 [12,] 24.066011 [13,] 17.055646 [14,] 10.039662

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