I have data frame 'df' which has 8*8 rows and columns.
here i am getting the answer directly the 5th multiplication, i want all the intermediate multiplications answers.
And i also want the code in loop for 15 times, so there will be 15 intermediate multiplication outputs.
Code:
p <- eigen(df)$vector
d <- eigen(df)$values
n <- 5
p %*% diag(d^n) %*% solve(p)
expected output will: if i am multiplying n = 15 times, then there should be 15 matrices for each intermediate multiplication.
please help.
Assuming that you mean power (X^n) can do the following:
mat <- matrix(1:9, nrow=3)
n <- 5
pows <- list()
pows[[1]] <- mat
for (i in 2:n) {
pows[[i]] <- pows[[i - 1]] %*% pows[[1]]
}
p <- eigen(mat)$vector
d <- eigen(mat)$values
res <- p %*% diag(d^n) %*% solve(p)
all(res - pows[[n]] < 1e-6)
Can also use:
library(expm)
mat %^% n
Related
n <- c(12,24)
mu<-c(6.573,6.5)
sigma<-sqrt(0.25)
Diseased.Data<-round(rnorm(n[1], mu[1], sigma), 4)
Healthy.Data<-round(rnorm(n[2], mu[2], sigma), 4)
g <- c(2,3,4)
for(i in 1:3){
pool.dis.data <- matrix(NA,n[1]/g[i],n[1]/g[i])
for(j in n[1]/g[i]){
pool.dis.data <- replicate(n[1]/g[i],mean(sample(Diseased.Data,g[i])))
}
}
When I run the code above, I get only the answer from the last element of g. What I need is each column in the matrix to have an element from g. For example, the matrix should look like:
m <- cbind(a1,a2,a3,a4,a5,a6)
m1 <- cbind(b1,b2,b3,b4)
m2 <- cbind(c1,c2,c3)
I am trying to implement the Regularized Latent Semantic Indexing (RLSI) algorithm on R.
The original paper can be found here:
http://research.microsoft.com/en-us/people/hangli/sigirfp372-wang.pdf
Below is my code.
Here, I generate a matrix D from two matrices U and V. Each column of U correspond to a topic vector, and it is made to be sparse. After that, I apply RLSI on the D matrix to see if I can factorize it into two matrices, one of which has sparse vectors like U.
However, the resulting U is far from being sparse. Actually, every element of it is filled with numbers.
Is there something wrong with my code?
Thank you very much in advance.
library(magrittr)
# functions
updateU <- function(D,U,V){
S <- V %*% t(V)
R <- D %*% t(V)
for(m in 1:M){
u_m <- rep(0, K)
u_previous <- u_m
diff_u <- 100
while(diff_u > 0.1){
for(k in 1:K){
w_mk <- R[m,k] - S[k,-k] %*% U[m,-k]
in_hinge <- (abs(w_mk) - 0.5 * lambda_1)
u_m[k] <- (ifelse(in_hinge > 0, in_hinge, 0) * ifelse(w_mk >= 0, 1, -1)) / S[k,k]
}
diff_u <- sum(u_m - u_previous)
u_previous <- u_m
}
U[m,] <- u_m
}
return(U)
}
updateV <- function(D,U,V){
Sigma <- solve(t(U) %*% U + lambda_2 * diag(K))
Phi <- t(U) %*% D
V <- Sigma %*% Phi
return(V)
}
# Set constants
M <- 5000
N <- 1000
K <- 30
lambda_1 <- 1
lambda_2 <- 0.5
# Create D
originalU <- c(rpois(50000, lambda = 10), rep(0, 100000)) %>% sample(., 150000) %>% matrix(., M, K)
originalV <- rpois(30000, lambda = 5) %>% sample(., 30000) %>% matrix(., K, N)
D <- originalU %*% originalV
# Initialize U and V
V <- matrix(rpois(30000, lambda = 5), K, N)
U <- matrix(0, M, K)
# Run RLSI (iterate 100 times for now)
for(t in 1:100){
cat(t,":")
U <- updateU(D,U,V)
V <- updateV(D,U,V)
loss <- sum((D - U %*% V) ^ 2)
cat(loss, "\n")
}
I've got it. Each row in U has to be set to a zero vector each time updateU function is run.
Suppose I have a 10 x 10 matrix. I want to randomly choose 2 numbers from each column and take the square of the difference of these numbers. I wrote the R code for that and I get 10 values, but I wish to repeat this, say, 100 times, in which case I need to get 100*10=1000 numbers. How could I do that?
x <- rnorm(100)
m <- 10
n <- 10
X <- matrix(x,m,n)
for (i in 1:m ) {
y <- sample(X[,i],2,rep=F)
q2[i] <- (y[1]-y[2])^2
}
Or as #Davide Passaretti and #nrussell mentioned in the comments, you can use replicate
f1 <- function(x, m){
q2 <- vector(mode='numeric', length= m)
for(i in 1:m){
y <- sample(x[,i], 2, rep=FALSE)
q2[i] <- (y[1]-y[2])^2
}
q2
}
n <- 100
res <- replicate(100, f1(X, m))
prod(dim(res))
#[1] 1000
As of now I am computing some features from a large matrix and doing it all in a for-loop. As expected it's very slow. I have been able to vectorize part of the code, but I'm stuck on one part.
I would greatly appreciate some advice/help!
s1 <- MyMatrix #dim = c(5167,256)
fr <- MyVector #vector of length 256
tw <- 5
fw <- 6
# For each point S(t,f) we need the sub-matrix of points S_hat(i,j),
# i in [t - tw, t + tw], j in [f - fw, f + fw] for the feature vector.
# To avoid edge effects, I pad the original matrix with zeros,
# resulting in a matrix of size nobs+2*tw x nfreqs+2*fw
nobs <- dim(s1)[1] #note: this is 5167
nf <- dim(s1)[2] #note: this is 256
sp <- matrix(0, nobs+2*tw, nf+2*fw)
t1 <- tw+1; tn <- nobs+tw
f1 <- fw+1; fn <- nf+fw
sp[t1:tn, f1:fn] <- s1 # embed the actual matrix into the padding
nfeatures <- 1 + (2*tw+1)*(2*fw+1) + 1
fsp <- array(NaN, c(dim(sp),nfeatures))
for (t in t1:tn){
for (f in f1:fn){
fsp[t,f,1] <- fr[(f - f1 + 1)] #this part I can vectorize
fsp[t,f,2:(nfeatures-1)] <- as.vector(sp[(t-tw):(t+tw),(f-fw):(f+fw)]) #this line is the problem
fsp[t,f,nfeatures] <- var(fsp[t,f,2:(nfeatures-1)])
}
}
fspec[t1:tn, f1:fn, 1] <- t(matrix(rep(fr,(tn-t1+1)),ncol=(tn-t1+1)))
#vectorized version of the first feature ^
return(fsp[t1:tn, f1:fn, ]) #this is the returned matrix
I assume that the var feature will be easy to vectorize after the 2nd feature is vectorized
I have the following code in R:
z <- scale(x) / sqrt(n-1) # standardized matrix x such that z'z=correlation matrix
R <- t(z) %*% z # correlation matrix
I <- diag(py - 1) # identity matrix(py defined before)
df <- rep(0, length(k)) # k=seq(0,5,0.001)
for (i in seq(0,5,0.001)) {
H <- z %*% solve(R+(i*I)) %*% t(z)
tr <- sum(diag(H))
df <- c(df,tr) ## problem here
}
The last line in the code is not good, as what I want is a vector (df) that reads each number from tr for each i, so that df returns a vector containing all tr.
Any help is appreciated.
Thanks
Separate the points that you want to solve at from the loop index.
solve_points <- seq(0,5,0.001)
for(i in seq_along(solve_points))
{
H=z%*%solve(R+(solve_points*I))%*%t(z)
tr=sum(diag(H))
df[i] <- tr
You want to fill in the vector df, not concatenate it all the time. That will slow R down a lot as it has to copy the object each iteration of the loop.
I think you probably want something like this:
for (i in seq_along(k)) { ## loop over 1:length(k)
H <- z %*% solve(R+(k[i]*I)) %*% t(z) ## use i to index into k
tr <- sum(diag(H))
df[i] <- tr ## add `tr` to the ith element of df
}
but a reproducible example would have helped. For example, you might not need to index k, depends on what your code is really doing and you don;t provide all the objects to check.