Create a Triangular Matrix from a Vector performing sequential operations - r

Question

I have been trying to solve the following problem.
Suppose I have the following vector:
aux1<-c(0,0,0,4,5,0,7,0,0,10,11,12) where the numbers represent the number of the row.
I want to calculate the distance between the differents elements of this vector fixing the first component, then the second and so on.
If the element is zero, I do not want to count it, so I put a NA instead. The output I want should look like this:
NA NA NA NA NA
NA NA NA NA NA
NA NA NA NA NA
NA NA NA NA NA
1 NA NA NA NA
NA NA NA NA NA
3 2 NA NA NA
NA NA NA NA NA
NA NA NA NA NA
6 5 3 NA NA
7 6 4 1
8 7 5 2 1
In the first column, I have the difference between the first element different from zero and all other elements, i.e., Matrix[5,1]=5-4=1 and Matrix[12,1]=12-4=8. Also, Matrix[7,2]=7-5=2, where 5 is the second element in the vector non-equal to zero. Notice that Matrix[10,3]=10-7=3, where 7 is third element non-equal to zero, but the seventh element in my vector.
I have tried to do this in a loop. My current code looks like this:
M=matrix(nrow=N-1, ncol=N-1))
for (i in 1:N-1){
for (j in 1:N-1){
if(j<=i)
next
else
if(aux1[j]>0)
M[j,i]=aux1[j]-aux1[i]
else
M[j,i]=0
}
}
Unfortunately. I have not been able to solve my problem. Any help would be greatly appreciated.

Answer 1

You could try something like the following (with generous help from #thela)
res <- outer(aux1, head(aux1[aux1 > 0], -1), `-`)
is.na(res) <- res <= 0
# [,1] [,2] [,3] [,4] [,5]
# [1,] NA NA NA NA NA
# [2,] NA NA NA NA NA
# [3,] NA NA NA NA NA
# [4,] NA NA NA NA NA
# [5,] 1 NA NA NA NA
# [6,] NA NA NA NA NA
# [7,] 3 2 NA NA NA
# [8,] NA NA NA NA NA
# [9,] NA NA NA NA NA
# [10,] 6 5 3 NA NA
# [11,] 7 6 4 1 NA
# [12,] 8 7 5 2 1

Answer 2

Using sapply and ifelse :
sapply(head(vv[vv>0],-1),function(y)ifelse(vv-y>0,vv-y,NA))
You loop over the positive values (you should also remove the last element), then you extract each value from the original vector. I used ifelse to replace negative values.
# [,1] [,2] [,3] [,4] [,5]
# [1,] NA NA NA NA NA
# [2,] NA NA NA NA NA
# [3,] NA NA NA NA NA
# [4,] NA NA NA NA NA
# [5,] 1 NA NA NA NA
# [6,] NA NA NA NA NA
# [7,] 3 2 NA NA NA
# [8,] NA NA NA NA NA
# [9,] NA NA NA NA NA
# [10,] 6 5 3 NA NA
# [11,] 7 6 4 1 NA
# [12,] 8 7 5 2 1