I tried norm, but I think it gives the wrong result. (the norm of c(1, 2, 3) is sqrt(1*1+2*2+3*3), but it returns 6..
x1 <- 1:3 norm(x1) # Error in norm(x1) : 'A' must be a numeric matrix norm(as.matrix(x1)) # [1] 6 as.matrix(x1) # [,1] # [1,] 1 # [2,] 2 # [3,] 3 norm(as.matrix(x1)) # [1] 6 Does anyone know what's the function to calculate the norm of a vector in R?
This is a trivial function to write yourself:
norm_vec <- function(x) sqrt(sum(x^2)) norm(c(1,1), type="2") # 1.414214 norm(c(1, 1, 1), type="2") # 1.732051 norm(x, type = c("O", "I", "F", "M", "2")) The default is "O".
"O", "o" or "1" specifies the one norm, (maximum absolute column sum);
"F" or "f" specifies the Frobenius norm (the Euclidean norm of x treated as if it were a vector);
norm(as.matrix(x1),"o") The result is 6, same as norm(as.matrix(x1))
norm(as.matrix(x1),"f") The result is sqrt(1*1+2*2+3*3)
So, norm(as.matrix(x1),"f") is answer.
I was surprised that nobody had tried profiling the results for the above suggested methods, so I did that. I've used a random uniform function to generate a list and used that for repetition (Just a simple back of the envelop type of benchmark):
> uut <- lapply(1:100000, function(x) {runif(1000, min=-10^10, max=10^10)}) > norm_vec <- function(x) sqrt(sum(x^2)) > norm_vec2 <- function(x){sqrt(crossprod(x))} > > system.time(lapply(uut, norm_vec)) user system elapsed 0.58 0.00 0.58 > system.time(lapply(uut, norm_vec2)) user system elapsed 0.35 0.00 0.34 > system.time(lapply(uut, norm, type="2")) user system elapsed 6.75 0.00 6.78 > system.time(lapply(lapply(uut, as.matrix), norm)) user system elapsed 2.70 0.00 2.73 It seems that taking the power and then sqrt manually is faster than the builtin norm for real values vectors at least. This is probably because norm internally does an SVD:
> norm function (x, type = c("O", "I", "F", "M", "2")) { if (identical("2", type)) { svd(x, nu = 0L, nv = 0L)$d[1L] } else .Internal(La_dlange(x, type)) } and the SVD function internally converts the vector into a matrix, and does more complicated stuff:
> svd function (x, nu = min(n, p), nv = min(n, p), LINPACK = FALSE) { x <- as.matrix(x) ... We can also find the norm as :
Result<-sum(abs(x)^2)^(1/2) OR Even You can also try as:
Result<-sqrt(t(x)%*%x) Both will give the same answer
I'mma throw this out there too as an equivalent R expression
norm_vec(x) <- function(x){sqrt(crossprod(x))} Don't confuse R's crossprod with a similarly named vector/cross product. That naming is known to cause confusion especially for those with a physics/mechanics background.
If you have a data.frame or a data.table 'DT', and want to compute the Euclidian norm (norm 2) across each row, the apply function can be used.
apply(X = DT, MARGIN = 1, FUN = norm, '2') Example:
>DT accx accy accz 1: 9.576807 -0.1629486 -0.2587167 2: 9.576807 -0.1722938 -0.2681506 3: 9.576807 -0.1634264 -0.2681506 4: 9.576807 -0.1545590 -0.2681506 5: 9.576807 -0.1621254 -0.2681506 6: 9.576807 -0.1723825 -0.2682434 7: 9.576807 -0.1723825 -0.2728810 8: 9.576807 -0.1723825 -0.2775187 > apply(X = DT, MARGIN = 1, FUN = norm, '2') [1] 9.581687 9.582109 9.581954 9.581807 9.581932 9.582114 9.582245 9.582378 Create your matrix as column vise using cbind then the norm function works well with Frobenius norm (the Euclidean norm) as an argument.
x1<-cbind(1:3)
norm(x1,"f")
[1] 3.741657
sqrt(1*1+2*2+3*3)
[1] 3.741657