RCPP and R discrepancy - r

Question

I'm new to C++ programming and apologize if my solution is in plain sight. I am attempting to use RCPP to speed up a slow R function. I think I've narrowed down the issue to a nested for loop. I've simplified the function and provided one R and one RCPP version for comparison. Will someone please explain why my RCPP function yields different results? Thanks!
## Data ##
set.seed(666)
input <- rmultinom(10,2,c(.4,.5,.6)) + 1
## R ##
testR <- \(input){
M1 <- matrix(c(0.5,0.4,0.0,0.3,0.5,0.0,0.2,0.1,1.0),3,3)
M2 <- matrix(c(0.75,0.0,0.0,0.0,0.6,0.0,0.25,0.4,1.0),3,3)
Mrows <- nrow(M1)
tmsteps <- ncol(input)
N <- nrow(input)
alphas <- NULL; tmp <- NULL; out <- NULL
for(i in 1:N){
alphas = c(0,-1e6,-1e6)
for(j in 1:tmsteps){
for(k in 1:Mrows){
tmp[k] = sum(alphas + M1[,k] + M2[k, input[i,j] ])
}
alphas <- tmp
}
out[i] <- sum(alphas)
}
sum(out)
}
## RCPP ##
cppFunction('double testRCPP(IntegerMatrix input){
NumericVector v1 = {0.5,0.4,0.0,0.3,0.5,0.0,0.2,0.1,1.0};
v1.attr("dim") = Dimension(3, 3);
NumericMatrix M1 = as<NumericMatrix>(v1);
NumericVector v2 = {0.75,0.0,0.0,0.0,0.6,0.0,0.25,0.4,1.0};
v2.attr("dim") = Dimension(3, 3);
NumericMatrix M2 = as<NumericMatrix>(v2);
int Mrows = M1.nrow();
int tmsteps = input.ncol();
int N = input.nrow();
NumericVector alphas(3);
NumericVector tmp(3);
NumericVector out(N);
for(int i=0; i<N; i++){
alphas = {0,-1e6,-1e6};
for(int j=0; j<tmsteps; j++){
for(int k=0; k<Mrows; k++){
tmp[k] = sum(alphas + M1(_,k) + M2(k, (input(i,j) - 1) ));
}
alphas = tmp;
}
out += alphas;
}
return(sum(out));
}')
> testRCPP(input)
[1] -2.273726e+14
> testR(input)
[1] -354293536945

Answer 1

I have figured out how to get the Rcpp to behave like the R function. I think my issue has to do with C++ variable scoping.
I had previously been initializing the tmp variable outside the nested for loop.
NumericVector tmp(3);
for(int i=0; i<N; i++){
alphas = {0,-1e6,-1e6};
...
All is good when I declare the tmp variable inside the loop, although I don't understand why yet.
for(int i=0; i<N; i++){
alphas = {0,-1e6,-1e6};
for(int j=0; j<tmsteps; j++){
NumericVector tmp(3);
for(int k=0; k<Mrows; k++){
tmp[k] = sum(alphas + M1(_,k) + M2(k, (input(i,j) - 1) ));
}
alphas = tmp;
}
...