I am trying to get a function that is the opposite of diff()
I want to add the values of adjacent columns in a matrix for each column in the matrix.
I do NOT need the sum of the entire column or row.
For example:
If I had:
[ 1 2 4;
3 5 8 ]
I would end up with:
[ 3 6;
8 13 ]
Of course for just one or two columns this is simple as I can just do x[,1]+x[,2], but these matrices are quite large.
I'm surprised that I cannot seem to find an efficient way to do this.
m <- matrix(c(1,3,2,5,4,8), nrow=2)
m[,-1] + m[,-ncol(m)]
[,1] [,2]
[1,] 3 6
[2,] 8 13
Or, just for the fun of it:
n <- ncol(m)
x <- suppressWarnings(matrix(c(1, 1, rep(0, n-1)),
nrow = n, ncol = n-1))
m %*% x
[,1] [,2]
[1,] 3 6
[2,] 8 13
Dummy data
mat <- matrix(sample(0:9, 100, replace = TRUE), nrow = 10)
Solution:
sum.mat <- lapply(1:(ncol(mat)-1), function(i) mat[,i] + mat[,i+1])
sum.mat <- matrix(unlist(sum.mat), byrow = FALSE, nrow = nrow(mat))
You could use:
m <- matrix(c(1,2,4,3,5,8), nrow=2, byrow=T)
sapply(2:ncol(m), function(x) m[,x] + m[,(x-1)])
Related
I have two matrices, call them A (n x 2) and B (q x 2). I'd like to get an n x q x 2 array C, such that C[1,5,] represents the difference between the first row of A and the fifth row of B, taking the subtraction of the first element in the first row of A with the first element in the fifth row of B and the second element similarly subtracted.
I'm trying to perform this function via the outer function, but it also gives me the "non-diagonal" subtractions; i.e. it will also subtract A[1,1] - B[5,2] and A[1,2] - B[5,1] which I am not interested in. Does anyone have a fast, easy way to do this?
Current code
>diffs <- outer(A,B,FUN ='-')
>diffs[1,,5,]
[,1] [,2]
[1,] **-0.3808701** 0.7591052
[2,] 0.2629293 **1.4029046**
I've added the stars to indicate what I actually want.
Thanks for any help in advance
(EDIT)
Here's a simpler case for illustrative purposes
> A <- matrix(1:10, nrow = 5, ncol = 2)
> B <- matrix(4:9, nrow = 3, ncol = 2)
> A
[,1] [,2]
[1,] 1 6
[2,] 2 7
[3,] 3 8
[4,] 4 9
[5,] 5 10
> B
[,1] [,2]
[1,] 4 7
[2,] 5 8
[3,] 6 9
>diffs <- outer(A,B,FUN ='-')
>diffs[1,,3,] == (A[1,] - B[3,])
[,1] [,2]
[1,] TRUE FALSE
[2,] FALSE TRUE
>diffs[1,,3,]
[,1] [,2]
[1,] -5 -8
[2,] 0 -3
Before worrying about the shape of the output I think we should make sure we're getting the correct values.
A <- matrix(1:10, nrow=5, ncol=2)
B <- matrix(4:9, nrow=3, ncol=2)
# long-winded method
dia_long <- c(
c(A[1,] - B[1,]),
c(A[1,] - B[2,]),
c(A[1,] - B[3,]),
c(A[2,] - B[1,]),
c(A[2,] - B[2,]),
c(A[2,] - B[3,]),
c(A[3,] - B[1,]),
c(A[3,] - B[2,]),
c(A[3,] - B[3,]),
c(A[4,] - B[1,]),
c(A[4,] - B[2,]),
c(A[4,] - B[3,]),
c(A[5,] - B[1,]),
c(A[5,] - B[2,]),
c(A[5,] - B[3,]))
# loop method
comb <- expand.grid(1:nrow(A), 1:nrow(B))
dia_loop <- list()
for (i in 1:nrow(comb)) {
dia_loop[[i]] <- A[comb[i, 1], ] - B[comb[i, 2], ]
}
dia_loop <- unlist(dia_loop)
# outer/apply method
dia_outer <- apply(outer(A, B, FUN='-'), c(3, 1), diag)
# they all return the same values
all.identical <- function(l) {
all(sapply(2:length(l), FUN=function(x) identical(l[1], l[x])))
}
all.identical(lapply(list(dia_long, dia_loop, dia_outer), sort))
# TRUE
table(dia_long)
# dia_long
# -5 -4 -3 -2 -1 0 1 2 3
# 1 2 4 5 6 5 4 2 1
Are these the values you are looking for?
My solution: use nested lapply and sapply functions to extract the diagonals. I then needed to do some post-processing (not related to this specific problem), before I then turned it into an array. Should be noted that this is a q x 2 x n array, which turned out to be better for my purposes - this could be permuted with aperm from here though to solve the original question.
A <- matrix(1:10, nrow = 5, ncol = 2)
B <- matrix(4:9, nrow = 3, ncol = 2)
diffs <- outer(A,B, FUN = '-')
diffs <- lapply(X = 1:nrow(A),FUN = function(y){
t(sapply(1:ncol(B), FUN = function(x) diag(diffs[y,,x,])))})
diffs <- array(unlist(lapply(diffs, FUN = t)), dim = c(nrow(B),2,nrow(A)))
I would like to compute the standard deviation of the nearest neighbors (3*3 moving window) of each element in a matrix. I wrote some code in R to implement it:
library(FNN)
df <- matrix(1:10000, nrow = 100, ncol = 100, byrow = TRUE)
df_ <- reshape2::melt(df)
df_index <- df_[, c(1,2)]
df_query <- df_index
neighbor_index <- knnx.index(df_index, df_query, k = 9, algorithm = 'kd_tree')
neighbor_coor<- apply(neighbor_index, 1, function(x) df_query[x, ])
neighbor_sd <- lapply(neighbor_coor, function(x) sd(df[x[, 1], x[, 2]]))
sd <- do.call(rbind, neighbor_sd)
But the speed is too slow. Would you give me some advice to speed up? Are there other ways to implement it?
As #romanlustrik proposed in his comment, we can use a raster::focal() for this problem.
library(raster)
df <- matrix(1:10000, nrow = 100, ncol = 100, byrow = TRUE)
dfR <- raster(df)
dfSD <- as.matrix(focal(dfR, w = matrix(1,3,3), fun = sd))
where, w is the a matrix representing the nearest neighbors and their weighting within fun (in this case 3x3 which is the cell itself and it 8 neighbors). Thus, any neighborhood pattern is imaginable as long as it it can be represented by a matrix.
matrix(1,3,3)
# [,1] [,2] [,3]
# [1,] 1 1 1
# [2,] 1 1 1
# [3,] 1 1 1
An example with only the 4 neighbors (excluding diagonals and the cell itself):
matrix(c(0,1,0,1,0,1,0,1,0), 3, 3)
# [,1] [,2] [,3]
# [1,] 0 1 0
# [2,] 1 0 1
# [3,] 0 1 0
I would like to add each coefficient of a vector to each different column of a matrix. For example, if I have a vector and a matrix:
x <- c(1,2,3)
M <- matrix(c(5,6,7), nrow = 3, ncol = 3)
I would like to in my new matrix M1 1+5 in the first column, 2+6 in the second and 3+7 in the last one.
Is there any function in R that does this task?
try this:
M + rep(x, each = nrow(M))
or this:
apply(M, 1, `+`, x)
result:
[,1] [,2] [,3]
[1,] 6 7 8
[2,] 7 8 9
[3,] 8 9 10
EDIT:
akrun commented on two other great solutions:
M + x[col(M)]
and
sweep(M, 2, x, "+")
Does anyone know a fast way to create a matrix
like the following one in R.
[,1] [,2] [,3] [,4]
[1,] 1 1 1 1
[2,] 1 2 2 2
[3,] 1 2 3 3
[4,] 1 2 3 4
The matrix above is 4x4 and I want to create something like 10000x10000.
You can do:
N <- 4
m <- matrix(nrow = N, ncol = N)
m[] <- pmin.int(col(m), row(m))
or a shorter version as suggested by #dickoa:
m <- outer(1:N, 1:N, pmin.int)
These also work and are both faster:
m <- pmin.int(matrix(1:N, nrow = N, byrow = TRUE),
matrix(1:N, nrow = N, byrow = FALSE))
m <- matrix(pmin.int(rep(1:N, each = N), 1:N), nrow = N)
Finally, here is a cute one using a matrix product but it is rather slow:
x <- matrix(1, N, N)
m <- lower.tri(x, diag = TRUE) %*% upper.tri(x, diag = TRUE)
Note that a 10k-by-10k matrix for R seems big, I hope you don't run out of memory.
I have 2 matrices.
The first one:
[1,2,3]
and the second one:
[3,1,2
2,1,3
3,2,1]
I'm looking for a way to multiply them.
The result is supposed to be: [11, 13, 10]
In R, mat1%*%mat2 don't work.
You need the transpose of the second matrix to get the result you wanted:
> v1 <- c(1,2,3)
> v2 <- matrix(c(3,1,2,2,1,3,3,2,1), ncol = 3, byrow = TRUE)
> v1 %*% t(v2)
[,1] [,2] [,3]
[1,] 11 13 10
Or potentially quicker (see ?crossprod) if the real problem is larger:
> tcrossprod(v1, v2)
[,1] [,2] [,3]
[1,] 11 13 10
mat1%%mat2 Actuall y works , this gives [ 16 9 11 ]
but you want mat1 %% t(mat2). This means transpose of second matrix, then u can get [11 13 10 ]
Rcode:
mat1 = matrix(c(1,2,3),nrow=1,ncol=3,byrow=TRUE)
mat2 = matrix(c(3,1,2,2,1,3,3,2,1), nrow=3,ncol=3,byrow=TRUE)
print(mat1)
print(mat2 )
#matrix Multiplication
print(mat1 %*% mat2 )
# matrix multiply with second matrix with transpose
# Note of using function t()
print(mat1 %*% t(mat2 ))
It's difficult to say what the best answer here is because the notation in the question isn't in R, it's in matlab. It's hard to tell if the questioner wants to multiple a vector, 1 row matrix, or 1 column matrix given the mixed notation.
An alternate answer to this question is simply switch the order of the multiplication.
v1 <- c(1,2,3)
v2 <- matrix(c(3,1,2,2,1,3,3,2,1), ncol = 3, byrow = TRUE)
v2 %*% v1
This yields an answer that's a single column rather than a single row matrix.
try this one
x<-c()
y<-c()
for(i in 1:9)
{
x[i]<-as.integer(readline("Enter number for 1st matrix"))
}
for(i in 1:9)
{
y[i]<-as.integer(readline("Enter number for 2nd matrix"))
}
M1 <- matrix(x, nrow=3,ncol = 3, byrow=TRUE)
M2 <- matrix(y, nrow=3,ncol = 3, byrow=TRUE)
print(M1%*%M2)