Need help implementing a function in R

Question

I'm trying to code in such a way as to take advantage of scripting, as I regularly get output in this format and having to copy/paste it in Excel one by one is a real chore. However, I'm stuck when it comes to implementing the functions.

So, my data is in the following form:

Condition Sample1 Sample2 .... Sample n
T1        6.99    5.80    ....  n_1      
T2        2.05    3.04    ....  n_1      
T3        4.50    4.69    ....  n_1      
T4        4.71    5.22    ....  n_1      
T5        5.66    3.65    ....  n_1      
T6        9.76    2.89    ....  n_1      

I need to apply the following equation: , where x is the individual entry and n is a coefficient, such that the full equation looks something like this:

.

Basically, per column, I need to consider each element in sequence and multiply it by a sequential coefficient (odd numbers from 1: length Condition) to get the answer S, for each Sample. The size of my dataset will not change - it will always be T1:T6, what will change is Sample 1...n. Ideally the value of S will be appended at the bottom of the column, or saved in a separate dataset with reference to the sample that it belongs to.

I've tried a number of solutions, including transposing, but can't seem to wrap my head around it.

My current attempt at implementing a simpler function on a portion of the dataset yielded no success.

 for (i in 2:8){dT[7,i] <-
     ((1*dT[1,i])+(3*dT[2,i])+(5*dT[3,i])+(7*dT[4,i])+(9*dT[5,i]))+(11*dT[6,i])
 }

I think the right solution involves some kind of *apply but I'm completely clueless as to how to use those properly.

EDIT: Adding a reproducible example:

N   Condition   Sample A    Sample B    Sample C    Sample D

1   T1          91.323      78.758      70.298      66.765
3   T2          -3.737      -1.5        -7.744      -9.247
5   T3          5.205       4.533       2.284       2.178
7   T4          -0.486      -0.068      -1.386      -0.927
9   T5          0.337       -0.139      0.087       0.055
    S        -0.046296296   -0.123654391    0.394039047 0.445258425

Answer 1

Does this, what you want to do?

per_row <- function(row){
  l <- length(row)
  exp <- 2*(1:l)-1  # all the exponents
  each <- row*(-1)^exp  # compute all of these at once
  return(sum(each)) # return sum
}

#some sample data
datafr <- data.frame(a = sample(1:6), b = 1:6)

#apply per column
apply(datafr, 2, per_row)

Answer 2

What about this? It should be agnostic to the number of SampleN columns you have. Note that it is specifically designed for your 6 condition case with only 6 odd number multipliers, but you said that would not change so it should be alright.

suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(tidyr))

samples <- tribble(
  ~Sample1, ~Sample2, ~Sample3,
  6.99, 5.80, 2.5,  
  2.05, 3.04, 3.4,    
  4.50, 4.69, 8.7,     
  4.71, 5.22, 8.6,     
  5.66, 3.65, 3.4,     
  9.76, 2.89, 5.6 
)

samples 
#> # A tibble: 6 x 3
#>   Sample1 Sample2 Sample3
#>     <dbl>   <dbl>   <dbl>
#> 1    6.99    5.80    2.50
#> 2    2.05    3.04    3.40
#> 3    4.50    4.69    8.70
#> 4    4.71    5.22    8.60
#> 5    5.66    3.65    3.40
#> 6    9.76    2.89    5.60

samples_modified <- samples %>%
  # Add the multipliers as a column
  mutate(multiplier = c(1,3,5,7,9,11)) %>%

  # Gather all the samples. Make it 'tidy'
  gather(key = "sample", value = "x", -multiplier) %>%

  # Perform the multiplication on each element, we will sum later
  mutate(x_modified = x * (-1) ^ ((multiplier - 1) / 2))

# Now we want to sum the x_modified column for each sample group
samples_modified %>%
  group_by(sample) %>%
  summarise(S = sum(x_modified))
#> # A tibble: 3 x 2
#>   sample       S
#>   <chr>    <dbl>
#> 1 Sample1  0.630
#> 2 Sample2  2.99 
#> 3 Sample3 -3.00

Answer 3

Seems simple. Since R is vectorized use vectors' multiplication. And then sum.

zirconium <- function(x){
    n <- 2*seq_along(x) - 1
    sum(x * (-1)^((n - 1)/2))
}

sapply(dT[-1], zirconium)
#Sample1 Sample2 
#   0.63    2.99

DATA.

dT <-
structure(list(Condition = structure(1:6, .Label = c("T1", "T2", 
"T3", "T4", "T5", "T6"), class = "factor"), Sample1 = c(6.99, 
2.05, 4.5, 4.71, 5.66, 9.76), Sample2 = c(5.8, 3.04, 4.69, 5.22, 
3.65, 2.89)), .Names = c("Condition", "Sample1", "Sample2"), class = "data.frame", row.names = c(NA, 
-6L))