How to make a generalized function update the value of a vector? - r

Question

I have been trying to write a generalized function that multiplies each value in each row of a matrix by the corresponding value of a vector in terms of their position (i.e. matrix[1,1]*vector[1], matrix[1,2]*vector[2], etc) and then sum them together. It is important to note that the lengths of the vector and the rows of the matrix are always the same, which means that in each row the first value of the vector is multiplied with the first value of the matrix row. Also important to note, I think, is that the rows and columns of the matrix are of equal length. The end sum for each row should be assigned to different existing vector, the length of which is equal to the number of rows.
This is the matrix and vector:
a <- c(4, -9, 2, -1)
b <- c(-1, 3, -8, 2)
c <- c(5, 2, 6, 3)
d <- c(7, 9, -2, 5)
matrix <- cbind(a,b,c,d)
a b c d
[1,] 4 -1 5 7
[2,] -9 3 2 9
[3,] 2 -8 6 -2
[4,] -1 2 3 5
vector <- c(1, 2, 3, 4)
These are the basic functions that I have to generalize for the rows and columns of matrix and a vector of lenghts "n":
f.1 <- function() {
(matrix[1,1]*vector[1]
+ matrix[1,2]*vector[2]
+ matrix[1,3]*vector[3]
+ matrix[1,4]*vector[4])
}
f.2 <- function() {
(matrix[2,1]*vector[1]
+ matrix[2,2]*vector[2]
+ matrix[2,3]*vector[3]
+ matrix[2,4]*vector[4])
}
and so on...
This is the function I have written:
ncells = 4
f = function(x) {
i = x
result = 0
for(j in 1:ncells) {
result = result + vector[j] * matrix[i][j]
}
return(result)
}
Calling the function:
result.cell = function() {
for(i in 1:ncells) {
new.vector[i] = f(i)
}
}
The vector to which this result should be assigned (i.e. new.vector) has been defined beforehand:
new.vector <- c()
I expected that the end sum for each row will be assigned to the vector in a corresponding manner (e.g. if the sums for all rows were 1, 2, 3, 4, etc. then new.vector(1, 2, 3, 4, etc) but it did not happen.
(Edit) When I do this with the basic functions, the assignment works:
new.vector[1] <- f.1()
new.vector[2] <- f.2()
This does not however work with the generalized function:
new.vector[1:ncells] <- result cell[1:ncells]
(End Edit)
I have also tried setting the length for the the new.vector to be equal to ncells but I don't think it did any good:
length(new.vector) = ncells
My question is how can I make the new vector take the resulting sums of the multiplied elements of a row of a matrix by the corresponding value of a vector.
I hope I have been clear and thanks in advance!

Answer 1

There is no need for a loop here, we can use R's power of matrix multiplication and then sum the rows with rowSums. Note that m and v are used as names for matrix and vector to avoid conflict with those function names.
nr <- nrow(m)
rowSums(m * matrix(rep(v, nr), nr, byrow = TRUE))
# [1] 45 39 -4 32
However, if the vector v is always going to be the column number, we can simply use the col function as our multiplier.
rowSums(m * col(m))
# [1] 45 39 -4 32
Data:
a <- c(4, -9, 2, -1)
b <- c(-1, 3, -8, 2)
c <- c(5, 2, 6, 3)
d <- c(7, 9, -2, 5)
m <- cbind(a, b, c, d)
v <- 1:4