Calculate cumulative sum of vector and matrix by rows up to diagonal

Question

I have a matrix (x)

x<-c(6,3,2,0,4,8,0,0,5)
x<-matrix(x, nrow = 3, ncol = 3)
       [ ,1][ ,2][ ,3]
[1, ]   6    0    0 
[2, ]   3    4    0 
[3, ]   2    8    5 

and a vector (y):

y<-c(0.5,1.2,4.8)
y
[1] 0.5 1.2 4.8

I want to calculate cumulative sum by rows up to matrix diagonal with elements of the vector y. What I need:

        [ ,1]             [ ,1][ ,2][ ,3]              [ ,1] 
   [1, ] 0.5          [1, ]  6    0    0          [1, ]  3  
(y)[2, ] 1.2   *  (x) [2, ]  3    4    0    = (w) [2, ]  6,3
   [3, ] 4.8          [3, ]  2    8    5          [3, ]  34,6

Where:

         [ ,1]
   [1, ]  3         0.5*6
(w)[2, ]  6,3   =   0.5*3 + 1.2*4
   [3, ]  34,6      0.5*2 + 1.2*8 + 4.8*5

As a result I need this vector (w). cumsum(y*x) – calculates all elements of columns in numerical order. I’ve got a vector:

[1]  3.0  6.6 16.2 16.2 21.0 59.4 59.4 59.4 83.4

cumsum(y*t(x))
[1]  3.0  3.0  3.0  4.5  9.3  9.3 10.3 19.9 43.9

I need, that zeros would be not calculated. Is it possible? Thank You in advance!

Answer 1

A for loop can be used to obtain w cumulative values:

w=integer()

for(i in 1:ncol(x)){

  w[i]=sum(x[i,1:i]*y[1:i])

 }

w

Answer 2

You can try with colSums, i.e.

colSums(y *t(x))
#[1]  3.0  6.3 34.6