Creating a matrix in R - r

Imagine that I have two observed variables, interest and M2, both with length 1000.
I am trying to apply a function taking each observation of interest and M2 to generate a matrix of values called PCoCo. The matrix will have a 1000x1000 length.
The purpose is to generate a 3D surface plot with x = interest, y = M2, z = PCoCo.
I have the following code:
#Creating a matrix from 2 variables; interest, M2, and a function CoCo.Price.
interest = seq(0,0.1, length = 1000)
M2 = seq(0,10, length = 1000)
#PCoCo = price of the coco, should be a matrix
PCoCo = matrix(nrow=length(interest), ncol=(M2))
f = function(interest, M2){
for(i in 1:length(interest)){
for(j in 1:length(M2)){
PCoCo[j,i] = CoCo.Price(C.p, c.r, m, N, q, interest[i], S, S.Trigger,
sigma, M2[j])
}
}
}
z = outer(interest, M2, f)
I used to get the following error before assigning PCoCo as a matrix before running f:
Error in PCoCo[j, i] <- matrix(CoCo.Price(C.p, c.r, m, N, q, interest[i], :
incorrect number of subscripts on matrix
Now, I do not, however R is taking ages to compute the matrix.
I have tried reducing the dimensions to 100x100 but it is still taking very long.
The issue might be with the CoCo.Price function as it is about a 100 line function, which also has some foor loops in it.
Any advice?
Thanks.

Related

Hand calculated Variogram in R

I am trying to calculate a variogram in R by "hand" to create a vector of several values at different lags, k.
Essentially I am trying to calculate this:
Gk = Var (yt+k − yt)/ Var (yt+1 − yt), k = 1, 2, … , 12
Where the time series observations are represented by yt.
My attempt below (where diff.df is a vector of differenced data length 72.
k <- seq(1,12,1)
x <- seq(1,length(diff.df)-length(k),1)
vario <- var(diff.df[x+k,]-diff.df[x,])/ var(diff.df[x+1,]-dif[x])
is producing an error of "incorrect number of dimensions"
I'm unsure what I am doing wrong here. any help would be appreciated.
Thanks.
I realized that I was acting as if the vector was a data frame ([x,] as opposed to simply looking up index of x, [x])
for (i in 1:70){
x <- seq(1,71-i,1)
vario[i] <- var(diff2.df[x+i]-diff2.df[x])/ var(diff2.df[x+1]-diff2.df[x])
}
vario
plot(vario,type = 'l',xlab = 'Lag', ylab = 'Variogram')
is the final working code for anyone that cares.

How can I simulate m random samples of size n from a given distribution with R?

I know how to generate a random sample of size n from a standard statistical distribution, say exponential. But if I want to generate m such random samples of size n (i.e. m vectors of dimension n) how can I do it?
To create a n by m matrix containing m samples of size n you can use:
x <- replicate(m, rnorm(n, ...))
Obviously substituting rnorm with other distributions if desired. If you then want to store these in separate individual vectors then you can use
v <- x[ , i]
This puts the ith column of x into v, which corresponds to the ith sample. It may be easier/quicker to just use a simple for loop altogether though:
for(i in 1:m){
name <- paste("V", i, sep = "")
assign(name, rnorm(n, ...))
}
This generates a random sample at each iteration, and for stage i, names the sample Vi. By the end of it you'll have m random samples named V1, V2, ..., Vm.

Pointwise multiplication and right matrix division

I'm currently trying to recreate this Matlab function in R:
function X = uniform_sphere_points(n,d)
% X = uniform_sphere_points(n,d)
%
%function generates n points unformly within the unit sphere in d dimensions
z= randn(n,d);
r1 = sqrt(sum(z.^2,2));
X=z./repmat(r1,1,d);
r=rand(n,1).^(1/d);
X = X.*repmat(r,1,d);
Regarding the the right matrix division I installed the pracma package. My R code right now is:
uniform_sphere_points <- function(n,d){
# function generates n points uniformly within the unit sphere in d dimensions
z = rnorm(n, d)
r1 = sqrt(sum(z^2,2))
X = mrdivide(z, repmat(r1,1,d))
r = rnorm(1)^(1/d)
X = X * matrix(r,1,d)
return(X)
}
But it is not really working since I always end with a non-conformable arrays error in R.
This operation for sampling n random points from the d-dimensional unit sphere could be stated in words as:
Construct a n x d matrix with entries drawn from the standard normal distribution
Normalize each row so it has (2-norm) magnitude 1
For each row, compute a random value by taking a draw from the uniform distribution (between 0 and 1) and raise that value to the 1/d power. Multiply all elements in the row by that value.
The following R code does these operations:
unif.samp <- function(n, d) {
z <- matrix(rnorm(n*d), nrow=n, ncol=d)
z * (runif(n)^(1/d) / sqrt(rowSums(z^2)))
}
Note that in the second line of code I have taken advantage of the fact that multiplying a n x d matrix in R by a vector of length n will multiply each row by the corresponding value in that vector. This saves us the work of using repmat to construct matrices of exactly the same size as our original matrix for these sorts of row-specific operations.

Matrix computation with for loop

I am newcomer to R, migrated from GAUSS because of the license verification issues.
I want to speed-up the following code which creates n×k matrix A. Given the n×1 vector x and vectors of parameters mu, sig (both of them k dimensional), A is created as A[i,j]=dnorm(x[i], mu[j], sigma[j]). Following code works ok for small numbers n=40, k=4, but slows down significantly when n is around 10^6 and k is about the same size as n^{1/3}.
I am doing simulation experiment to verify the bootstrap validity, so I need to repeatedly compute matrix A for #ofsimulation × #bootstrap times, and it becomes little time comsuming as I want to experiment with many different values of n,k. I vectorized the code as much as I could (thanks to vector argument of dnorm), but can I ask more speed up?
Preemptive thanks for any help.
x = rnorm(40)
mu = c(-1,0,4,5)
sig = c(2^2,0.5^2,2^2,3^2)
n = length(x)
k = length(mu)
A = matrix(NA,n,k)
for(j in 1:k){
A[,j]=dnorm(x,mu[j],sig[j])
}
Your method can be put into a function like this
A.fill <- function(x,mu,sig) {
k <- length(mu)
n <- length(x)
A <- matrix(NA,n,k)
for(j in 1:k) A[,j] <- dnorm(x,mu[j],sig[j])
A
}
and it's clear that you are filling the matrix A column by column.
R stores the entries of a matrix columnwise (just like Fortran).
This means that the matrix can be filled with a single call of dnorm using suitable repetitions of x, mu, and sig. The vector z will have the columns of the desired matrix stacked. and then the matrix to be returned can be formed from that vector just by specifying the number of rows an columns. See the following function
B.fill <- function(x,mu,sig) {
k <- length(mu)
n <- length(x)
z <- dnorm(rep(x,times=k),rep(mu,each=n),rep(sig,each=n))
B <- matrix(z,nrow=n,ncol=k)
B
}
Let's make an example with your data and test this as follows:
N <- 40
set.seed(11)
x <- rnorm(N)
mu <- c(-1,0,4,5)
sig <- c(2^2,0.5^2,2^2,3^2)
A <- A.fill(x,mu,sig)
B <- B.fill(x,mu,sig)
all.equal(A,B)
# [1] TRUE
I'm assuming that n is an integer multiple of k.
Addition
As noted in the comments B.fill is quite slow for large values of n.
The reason lies in the construct rep(...,each=...).
So is there a way to speed A.fill.
I tested this function:
C.fill <- function(x,mu,sig) {
k <- length(mu)
n <- length(x)
sapply(1:k,function(j) dnorm(x,mu[j],sig[j]), simplify=TRUE)
}
This function is about 20% faster than A.fill.

compute samples variance without loops

Here is what I want to do:
I have a time series data frame with let us say 100 time-series of
length 600 - each in one column of the data frame.
I want to pick up 10 of the time-series randomly and then assign them
random weights that sum up to one. Using those I want to compute the
variance of the sum of the 10 weighted time series variables (e.g.
convex combination).
The df is in the form
v1,v2,v2.....v100
1,5,6,.......9
2,4,6,.......10
3,5,8,.......6
2,2,8,.......2
etc
i can compute it inside a loop but r is vector oriented and it is not efficient.
ntrials = 10000
ts.sd = NULL
for (x in 1:ntrials))
{
temp = t(weights[,x]) %*% cov(df[, samples[, x]]) %*% weights[, x]
ts.sd = cbind(ts.sd, temp)
}
Not sure what type of "random" you want for your weights... so I'll use a normal distribution scaled s.t. it sums to one:
x=as.data.frame(matrix(sample(1:20, 100*600, replace=TRUE), ncol=100))
myfun <- function(inc, DF=x) {
w = runif(10)
w = w / sum(w)
t(w) %*% cov(DF[, sample(seq_along(DF), 10)]) %*% w
}
lapply(1:ntrials, myfun)
However, this isn't really avoiding loops per say since lapply is just an efficient looping construct. That said, for loops in R aren't explicitly bad or inefficient. Growing a data structure, like you're doing with cbind, however, is.
But in this case since you're only growing it by appending a single element it really wont change things much. The "correct" version would be to pre-allocate your vector ts.sd using ntrials.
ts.sd = vector(mode='numeric', length=ntrials)
The in your loop assign into it using i:
for (x in 1:ntrials))
{
temp = t(weights[,x]) %*% cov(df[, samples[, x]]) %*% weights[, x]
ts.sd[i] = temp
}

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