CODEWITHSUNDEEP
rmatrix-multiplication
Matt
Matt

Reputation: 13

Matrix multiplication in a for loop

When the following code is run in R, an error message pops up:

"Error in Xt[i, ] <- F * Xt[i - 1, ] + V : number of items to replace is not a multiple of replacement length"

Appreciate your help.

X=matrix(rnorm(6),100,6)
n = nrow(X)

F =  diag(1,6,6); F[1,4] = F[2,5] = F[3,6] = 1

#create process & measurement noises (standard deviation)
W = diag(rnorm(1,0,0.01),6,6) 
V = diag(rnorm(1,0,0.02),6,6) 

#create and init Xt and Yt matrices
Xt = matrix(NA, nrow=n+1, ncol=6)
Yt = matrix(NA, nrow=n, ncol=6)
Xt[1,] = X[1,]

#test: 
F * Xt[1,] + V #this is fine!!!

#before entering the loop:
for (i in 2:3)
{
  Xt[i,] = F * Xt[i-1,] + V #BUT this is not!!!
  Yt[i,] = Xt[i,] + W
}

Upvotes: 1

Views: 157

Answers (1)

Martin Gal
Martin Gal

Reputation: 16998

Take a look at the dimensions: You define 

Xt[1,] = X[1,]

which gives you a 6x1-matrix. Your next step is calculating

F * Xt[1,] + V

Since F and V are of dimension 6x6 this yields a new 6x6-matrix. Check with 

dim(as.matrix(X[t,1]))
dim(F)
dim(V)

Now Xt itself is of dim 101x6, therefore Xt[n,], which is a little bit unintuitively, gives a transposed 6x1 object. So, inside your loop you tried to assign an object

F * Xt[i-1,] + V
dim(F * Xt[i-1,] + V)   # this gives 6x6

to

Xt[i,]
dim(as.matrix(Xt[i,]))  # this gives 6x1

So your dimensions don't fit. I hope this answers your question.

I have one annotation:

F * Xt[1,] + V

The multiplication F*Xt[1,] is an element-wise multiplication not the classical matrix-vector-multiplication. If you want to perform an A*b multiplication with mxn-matrix A and nx1-vector b you have to use %*% instead. In this case, V has to be of dimension mx1.

Upvotes: 1

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