for (i in 2:100 )
{
count <- 0
for (j in i )
if( (i %% j ) == 0 )
count <- count + 1
if(count == 2 )
print(i)
}
I am trying to print print prime numbers in R. Could any one help me to resolve
Let us look at your code and show what went wrong. It's the inner loop that did not loop at all:
for (i in 2:100 )
{
count <- 0
for (j in 1:i ) # you forgot to provide a vector here
if( i %% j == 0 )
count <- count + 1
if(count == 2)
print(i)
}
The answer above tries to optimise the code some more and is a more efficient solution. For example does it only test odd numbers because even ones clearly aren't prime numbers.
The below code creates the function prime_numbers which returns prime numbers up to an inputted number.
prime_numbers <- function(n) {
if (n >= 2) {
x = seq(2, n)
prime_nums = c()
for (i in seq(2, n)) {
if (any(x == i)) {
prime_nums = c(prime_nums, i)
x = c(x[(x %% i) != 0], i)
}
}
return(prime_nums)
}
else {
stop("Input number should be at least 2.")
}
}
## return the answer to your question
prime_numbers(100)
If you wanted the range 3:100, after running the above code you could run something like this:
a<-prime_numbers(100)
a[a>3]
I hope this helps!
Related
I made a loop to generate a Markov Chain. If the proposal does not satisfy a condition, I want to restart the iteration with a new proposal? Is there a way to do this? My current code is shown below for reference. Currently, it sets the current chain's value to the previous one. But I don't want that. I want it to just restart the "i". So if i=2, and the condition in line 4 is not satisfied, I then want it to stay at i=2 until it is satisfied. Thanks in advance.
ABC_MCMC<-function(n){
for (i in 2:n){
prop<-rnorm(1,mean=chain[i-1],sd=1)
if (ABC(prop)==T & prop>=0){
h_ratio<-(dgamma(prop,shape=prior_alpha,rate=prior_beta)/dgamma(chain[i-1],shape=prior_alpha,rate=prior_beta))*
(dnorm(x=chain[i-1],mean=prop,sd=1)/dnorm(x=prop,mean=chain[i-1],sd=1))
u<-runif(1)
if (min(1,h_ratio)>u) {chain[i]=prop} else {chain[i]=chain[i-1]}
}
else{chain[i]=chain[i-1]}
}
return(chain<<-chain)
}
This is more of a comment than of an answer but to keep the code formatting I'm posting as an answer.
Replace the code inside the for loop for the code below.
while(TRUE) {
prop <- rnorm(1, mean = chain[i - 1L], sd = 1)
if (ABC(prop) && prop >= 0) {
h_ratio<-(dgamma(prop,shape=prior_alpha,rate=prior_beta)/dgamma(chain[i-1],shape=prior_alpha,rate=prior_beta))*
(dnorm(x=chain[i-1],mean=prop,sd=1)/dnorm(x=prop,mean=chain[i-1],sd=1))
u<-runif(1)
if (min(1,h_ratio)>u) {chain[i]=prop} else {chain[i]=chain[i-1]}
break
} else {chain[i] <- chain[i-1]}
}
Edit
The function below seems to be what is asked for.
ABC_MCMC <- function(n){
for (i in 2:n){
# loops until condition (ABC(prop) & prop >= 0) is met
while(TRUE) {
prop <- rnorm(1, mean = chain[i-1], sd = 1)
if (ABC(prop) & prop >= 0) {
h_ratio <- (dgamma(prop, shape = prior_alpha, rate = prior_beta)/dgamma(chain[i - 1L], shape = prior_alpha, rate = prior_beta)) *
(dnorm(chain[i - 1L], prop, 1)/dnorm(prop, chain[i - 1L], 1))
u <- runif(1)
if (min(1, h_ratio) > u) {
chain[i] <- prop
} else {
chain[i] <- chain[i - 1L]
}
break
}
}
}
# function return value
chain
}
Hi i just need some help understanding this line of code from a function to get prime numbers (see below for the whole function):
if (i == 2L || all(i %% 2L:ceiling(sqrt(i)) != 0))
What does i == 2L do as well as ceiling(sqrt(i)). This function basically just generates a vector of prime numbers or just returns the last prime number in the vector. I don't quite understand what those 2 sections are used for.
Normally i would just check for a prime number like this all(i %% 2:(i-1) !=0) So why are those two elements changed in the code?
get_prime <- function(n, all = TRUE, i = 1, primes = c()){
if ( n <= 0) {
stop("Not a valid number")
}
if (length(primes) < n) {
if (i == 2L || all(i %% 2L:ceiling(sqrt(i)) != 0)) {
get_prime(n, all = all, i = i + 1, primes = c(primes, i))
} else {
get_prime(n, all = all, i = i + 1, primes = primes)
}
} else {
if (all) {
return(primes)
} else {
return(tail(primes, 1))
}
}
}
Imagine you had to check if q=1,000,001 was a prime number.
The simplest way to do this is to check if any integer in [2, 1000000] is a factor of q.
Suppose a factor, f, of q does exist and it is not in [2, ceiling(sqrt(q))].
So f > ceiling(sqrt(q)) and q/f <= q/sqrt(q) = sqrt(q)
So whatever q/f is, it lies in [2, ceiling(sqrt(q))].
That's why you only need to check up to ceiling(sqrt(q))
i've been trying for a while now to write a function that has two arguments. The one an integer = n and the other a logical argument. How would i write a function that would return either the first n prime numbers in a vector if the logical argument is true or the n th prime number if the logical argument is false?
This is as far as i have gotten.
getprime <- function(n=0 , all=TRUE) {
if (n<=0) {
print("Not a valid number")
} else if (n>0) {
for (primen in 1:n) {
while (n %% 2:(n-1) == 0) {
n=n+1
print(n)
}
}
}
print(n)
}
The results that have to be displayed are shown below.
> genprime(7, all=TRUE)
[1] 2 3 5 7 11 13 17
> genprime(7, all=FALSE)
[1] 17
You could write a recursive function (a function that calls itself). In addition to the two arguments n and all, it would also take a counter i and a (empty) vector of prime numbers primes.
As long as the number of prime numbers found is less than n, the function calls itself and with each time it calls itself, it would increase the counter variable i. If i is a prime number, it gets added to the primes vector.
get_prime <- function(n, all = TRUE, i = 1, primes = c()){
if ( n <= 0) {
stop("Not a valid number")
}
if (length(primes) < n) {
if (i == 2L || all(i %% 2L:ceiling(sqrt(i)) != 0)) {
get_prime(n, all = all, i = i + 1, primes = c(primes, i))
} else {
get_prime(n, all = all, i = i + 1, primes = primes)
}
} else {
if (all) {
return(primes)
} else {
return(tail(primes, 1))
}
}
}
The results are:
get_prime(7, TRUE)
[1] 2 3 5 7 11 13 17
get_prime(7, FALSE)
[1] 17
I am learning how to use while and for loops, and am having difficulty executing a for loop within a while loop. I am trying to recurse a simple procedure over a vector, and have the while loop set the conditionals for which parts of the vector are operated upon. This is really just meant as an exercise to understand how to use for and while loops in conjunction.
data <- c(1:200)
n=0
while(n < 100){
for(x in data){
n=x+1
if(x >= 10 & x < 100){
print("double digit")
} else {
print("single digit")
}}}
I want to stop the while loop when the procedure hits x=100 of the vector that runs from 1:200. But instead, the for loop runs through every element within the vector, from 1:200, failing to stop executing when n hits 100.
Would appreciate any advice to help out a new coder, thanks.
I have also tried
for(x in data){
n=x+1
while(n < 100){
if(x >= 10 & x < 100){
print("double digit")
} else {
print("single digit")
}}}
But the code does not stop executing.
First let's try a for loop. Each time through it n will be set to the loop counter plus 1. If this result is between 10 and 100, print a message, if not print something else. Note that no loop depends on n .
data <- c(1:200)
n = 0
for (x in data) {
n = x + 1
if (n < 100) {
if (x >= 10 && x < 100) {
print("double digit")
} else {
print("single digit")
}
}
}
x
#[1] 200
n
#[1] 201
Now for a while loop. I believe it is much simpler, it only envolves one variable, n.
n <- 0
while (n < 100) {
n = n + 1
if (n < 100) {
if (n >= 10) {
print("double digit")
} else {
print("single digit")
}
}
}
n
#[1] 100
I was asked to implement function that calculates n-dimensional matrix determinant using Laplace expansion. This involves recursion. I developed this:
minor<-function(A,i,j) {
return(A[c(1:(i-1),(i+1):dim(A)[1]),c(1:(j-1),(j+1):dim(A)[2])])
}
determinantRec<-function(X,k) {
if (dim(X)[1] == 1 && dim(X)[2] == 1) return(X[1][1])
else {
s = 0
for (i in 1:dim(X)[2]) {
s = s + X[k][i]*(-1)^(k+i)*determinantRec(minor(X,k,i),k)
}
return(s)
}
}
where k in determinantRec(X,k) function indicates which row I want to use Laplace expansion along of.
My problem is when I run determinantRec(matrix(c(1,2,3,4),nrow = 2,ncol = 2),1) this error appears:
C stack usage 7970628 is too close to the limit
What is wrong with my code?
#julia, there is one simple type in your code. Just remove the '*' at the end of the definition of 's'. And don't indent the recursion.
determinantRek<-function(X,k) {
if (dim(X)[1] == 1 && dim(X)[2] == 1)
return(X[1,1])
if (dim(X)[1] == 2 && dim(X)[2] == 2)
return(X[1,1]*X[2,2]-X[1,2]*X[2,1])
else
s = 0
for (i in 1:dim(X)[2]) {
s = s + X[k,i]*(-1)^(k+i)
determinantRek(X[-k,-i],k)
}
return(s)
}
I did this way and works just fine, although it is super slow, compared to the det function in base R
laplace_expansion <- function(mat){
det1 <- function(mat){
mat[1]*mat[4]-mat[2]*mat[3]
}
determinant <- 0
for(j in 1:ncol(mat)){
mat1 <- mat[-1,-j]
if(nrow(mat1) == 2){
determinant <- determinant+mat[1,j]*(-1)^(1+j)*det1(mat1)
}else{
val <- mat[1,j]*(-1)^(1+j)
if(val != 0){
determinant <- determinant+val*laplace_expansion(mat1)
}
}
}
return(determinant)
}
This is my approach, I think it's cleaner.
deter <- function(X) {
stopifnot(is.matrix(X))
stopifnot(identical(ncol(X), nrow(X)))
if (all(dim(X) == c(1, 1))) return(as.numeric(X))
i <- 1:nrow(X)
out <- purrr::map_dbl(i, function(i){
X[i, 1] * (-1)^(i + 1) * deter(X[-i, -1, drop = FALSE])
})
return(sum(out))
}
Thank you #ArtemSokolov and #MrFlick for pointing the problem cause, it was it. I also discovered that this code does not calculate properly the determinant of 2x2 matrix. After all it looks like that:
determinantRek<-function(X,k) {
if (dim(X)[1] == 1 && dim(X)[2] == 1)
return(X[1,1])
if (dim(X)[1] == 2 && dim(X)[2] == 2)
return(X[1,1]*X[2,2]-X[1,2]*X[2,1])
else
s = 0
for (i in 1:dim(X)[2]) {
s = s + X[k,i]*(-1)^(k+i)*
determinantRek(X[-k,-i],k)
}
return(s)
}
Debuging with browser() was also helpful :)