I want to generate a random matrix which should be symmetric.
I have tried this:
matrix(sample(0:1, 25, TRUE), 5, 5)
but it is not necessarily symmetric.
How can I do that?
Another quite interesting opportunity is based on the following mathematical fact: if A is some matrix, then A multiplied by its transpose is always symmetric.
> A <- matrix(runif(25), 5, 5)
> A %*% t(A)
[,1] [,2] [,3] [,4] [,5]
[1,] 1.727769 1.0337816 1.2195505 1.4661507 1.1041355
[2,] 1.033782 1.0037048 0.7368944 0.9073632 0.7643080
[3,] 1.219551 0.7368944 1.8383986 1.3309980 0.9867812
[4,] 1.466151 0.9073632 1.3309980 1.3845322 1.0034140
[5,] 1.104135 0.7643080 0.9867812 1.0034140 0.9376534
Try this from the Matrix package
library(Matrix)
x<-Matrix(rnorm(9),3)
x
3 x 3 Matrix of class "dgeMatrix"
[,1] [,2] [,3]
[1,] -0.9873338 0.8965887 -0.6041742
[2,] -0.3729662 -0.5882091 -0.2383262
[3,] 2.1263985 -0.3550972 0.1067264
X<-forceSymmetric(x)
X
3 x 3 Matrix of class "dsyMatrix"
[,1] [,2] [,3]
[1,] -0.9873338 0.8965887 -0.6041742
[2,] 0.8965887 -0.5882091 -0.2383262
[3,] -0.6041742 -0.2383262 0.1067264
If you don't want to use a package:
n=3
x <- matrix(rnorm(n*n), n)
ind <- lower.tri(x)
x[ind] <- t(x)[ind]
x
I like this one:
n <- 3
aux <- matrix(NA, nrow = n, ncol = n)
for(i in c(1:n)){
for(j in c(i:n)){
aux[i,j] <- sample(c(1:n), 1)
aux[j,i] <- aux[i,j]
}
}
Related
I have a list of matrices (size n*n), and I need to create a new matrix giving the minimum value observed for each cell, based on my list.
For instance, with the following matrices list:
> a = list(matrix(rexp(9), 3), matrix(rexp(9), 3), matrix(rexp(9), 3))
> a
[[1]]
[,1] [,2] [,3]
[1,] 0.5220069 0.39643016 0.04255687
[2,] 0.4464044 0.66029350 0.34116609
[3,] 2.2495949 0.01705576 0.08861866
[[2]]
[,1] [,2] [,3]
[1,] 0.3823704 0.271399 0.7388449
[2,] 0.1227819 1.160775 1.2131681
[3,] 0.1914548 1.004209 0.7628437
[[3]]
[,1] [,2] [,3]
[1,] 0.2125612 0.45379057 1.5987420
[2,] 0.3242311 0.02736743 0.4372894
[3,] 0.6634098 1.15401347 0.9008529
The output should be:
[,1] [,2] [,3]
[1,] 0.2125612 0.271399 0.04255687
[2,] 0.1227819 0.02736743 0.34116609
[3,] 0.1914548 0.01705576 0.08861866
I tried using apply loop with the following code (using melt and dcast from reshape2 library):
library(reshape2)
all = melt(a)
allComps = unique(all[,c(1:2)])
allComps$min=apply(allComps, 1, function(x){
g1 = x[1]
g2 = x[2]
b = unlist(lapply(a, function(y){
return(y[g1,g2])
}))
return(b[which(b==min(b))])
})
dcast(allComps, Var1~Var2)
It works but it is taking a very long time to run when applied on large matrices (6000*6000). I am looking for a faster way to do this.
Use Reduce with pmin :
Reduce(pmin, a)
# [,1] [,2] [,3]
#[1,] 0.02915345 0.03157736 0.3142273
#[2,] 0.57661027 0.05621098 0.1452668
#[3,] 0.48021473 0.18828404 0.4787604
data
set.seed(123)
a = list(matrix(rexp(9), 3), matrix(rexp(9), 3), matrix(rexp(9), 3))
Maybe it should be considered to store the matrices in an array instead of a list. This can be done with simplify2array. In an array the minimum over specific dimensions can be found using min in apply.
A <- simplify2array(a)
apply(A, 1:2, min)
We can use
apply(array(unlist(a), c(3, 3, 3)), 1:2, min)
I am sorry in advance if that's a silly question, but I am a bit new to it.
I would like to write a for loop where the input is a time sequence. Based on the time conditions I would like to select either mat1, mat2, or mat3 to substitute the "mat" parameter and multiply it by 2.
output <- mat*2 #general function
For each time point, I need to have an output.
time=seq(0,10, by=1)
mat1 <- matrix(data = rexp(9, rate = 10), nrow = 3, ncol = 3)
mat2 <- matrix(data = rexp(9, rate = 10), nrow = 3, ncol = 3)
mat3 <- matrix(data = rexp(9, rate = 10), nrow = 3, ncol = 3)
I would like when the time <= 3 the "mat1" to be selected
when the time>3 & time<=6 the "mat2" to be selected
and when the time >6 the "mat3" to be selected and then multiplied by 2.
I know that all this is a bit sketchy but any help would be highly appreciated.
By the way, if you want a list of consecutive integers you can simply use time <- 0:10
Here is one method
lapply(as.character(cut(time,c(-1,3.1,6.1,10),labels=c('mat1','mat2','mat3'))), function(x) get(x)*2)
[[1]]
[,1] [,2] [,3]
[1,] 0.4013379 1.2690301 0.142831401
[2,] 0.1536697 0.1132762 0.040964909
[3,] 0.1412248 0.2209273 0.007446217
[[2]]
[,1] [,2] [,3]
[1,] 0.4013379 1.2690301 0.142831401
[2,] 0.1536697 0.1132762 0.040964909
[3,] 0.1412248 0.2209273 0.007446217
...
[[10]]
[,1] [,2] [,3]
[1,] 0.16712782 0.06451693 0.06554605
[2,] 0.03614116 0.18526124 0.46443236
[3,] 0.53055007 0.01203971 0.16585931
[[11]]
[,1] [,2] [,3]
[1,] 0.16712782 0.06451693 0.06554605
[2,] 0.03614116 0.18526124 0.46443236
[3,] 0.53055007 0.01203971 0.16585931
In R I have two matrices X and Z and I would like a
matrix W such that the row (i) of W contains row (i) of X interacted with row (i) of Z.
W(i) = X(i1)Z(i1) ... X(iJ)Z(i1) ... X(i1)Z(iK) ... X(iJ)Z(iK)
Here is an example in small scale doing what I want:
set.seed(1)
n <- 3
K <- 2
J <- 3
X <- matrix(rnorm(J*n),ncol=J)
Z <- matrix(rnorm(K*n),ncol=K)
W <- matrix(NA,nrow=n,ncol=K*J)
for (i in 1:n)
{
for (k in 1:K)
{
for (j in 1:J)
{
W[i,j + J*(k-1)] <- X[i,j] * Z[i,k]
}
}
}
Is there a clever way to do that?
I ended up doing
X[,sort(rep(1:J,K))] * Z[,rep(1:K,J)]
For this example, you can do
cbind(X * Z[, 1], X * Z[, 2])
# [,1] [,2] [,3] [,4] [,5] [,6]
#[1,] 0.1913117 -0.4871802 -0.1488552 0.3891785 -0.9910532 -0.3028107
#[2,] 0.2776285 0.4981436 1.1161854 -0.4067148 -0.7297608 -1.6351676
#[3,] -0.3257642 -0.3198541 0.2244645 -0.9400245 -0.9229703 0.6477142
Or more generally we can use apply for many more columns.
W[] <- apply(Z, 2, function(x) X * x)
which gives the same output as W which we get after running your loop.
W
# [,1] [,2] [,3] [,4] [,5] [,6]
#[1,] 0.1913117 -0.4871802 -0.1488552 0.3891785 -0.9910532 -0.3028107
#[2,] 0.2776285 0.4981436 1.1161854 -0.4067148 -0.7297608 -1.6351676
#[3,] -0.3257642 -0.3198541 0.2244645 -0.9400245 -0.9229703 0.6477142
How do I get actual matrix using Singular value decomposition(SVD)
efficiently in R ,
cause A=svd$u %*% svd$d %*% t(svd$v) This is not an efficient way to get matrix A
Try svd(A)$u%*%diag(svd(A)$d)%*%t(svd(A)$v).
set.seed(12345)
A <- matrix(data=runif(n=9, min=1, max=9), nrow=3)
A
[,1] [,2] [,3]
[1,] 6.767231 8.088997 3.600763
[2,] 8.006186 4.651848 5.073795
[3,] 7.087859 2.330974 6.821642
s <- svd(A)
D <- diag(s$d)
s$u %*% D %*% t(s$v)
[,1] [,2] [,3]
[1,] 6.767231 8.088997 3.600763
[2,] 8.006186 4.651848 5.073795
[3,] 7.087859 2.330974 6.821642
Improving upon the answer by #MYaseen208
(s$u) %*% (t(s$v)*s$d)
This has one less matrix multiplication (which is an O(n^3) operation).
I am using the choleski decomposition to compute the inverse of a matrix that is positive semidefinite. However, when my matrix becomes extremely large and has zeros in it I have that my matrix is no longer (numerically from the computers point of view) positive definite. So to get around this problem I use the pivot = TRUE option in the choleski command in R. However, (as you will see below) the two return the same output but with the rows and columns or the matrix rearranged. I am trying to figure out is there a way (or transformation) to make them the same. Here is my code:
X = matrix(rnorm(9),nrow=3)
A = X%*%t(X)
inv1 = function(A){
Q = chol(A)
L = t(Q)
inverse = solve(Q)%*%solve(L)
return(inverse)
}
inv2 = function(A){
Q = chol(A,pivot=TRUE)
L = t(Q)
inverse = solve(Q)%*%solve(L)
return(inverse)
}
Which when run results in:
> inv1(A)
[,1] [,2] [,3]
[1,] 9.956119 -8.187262 -4.320911
[2,] -8.187262 7.469862 3.756087
[3,] -4.320911 3.756087 3.813175
>
> inv2(A)
[,1] [,2] [,3]
[1,] 7.469862 3.756087 -8.187262
[2,] 3.756087 3.813175 -4.320911
[3,] -8.187262 -4.320911 9.956119
Is there a way to get the two answers to match? I want inv2() to return the answer from inv1().
That is explained in ?chol: the column permutation is returned as an attribute.
inv2 <- function(A){
Q <- chol(A,pivot=TRUE)
Q <- Q[, order(attr(Q,"pivot"))]
Qi <- solve(Q)
Qi %*% t(Qi)
}
inv2(A)
solve(A) # Identical
Typically
M = matrix(rnorm(9),3)
M
[,1] [,2] [,3]
[1,] 1.2109251 -0.58668426 -0.4311855
[2,] -0.8574944 0.07003322 -0.6112794
[3,] 0.4660271 -0.47364400 -1.6554356
library(Matrix)
pm1 <- as(as.integer(c(2,3,1)), "pMatrix")
M %*% pm1
[,1] [,2] [,3]
[1,] -0.4311855 1.2109251 -0.58668426
[2,] -0.6112794 -0.8574944 0.07003322
[3,] -1.6554356 0.4660271 -0.47364400