[R] calculations on diagonals of a matrix

[Griffith Feeney]

Given an nxm matrix A I want to compute the nxm matrix B whose ij-th 
element is the sum of the elements of A lying on the diagonal that ends 
with element ij, i.e.,

     b_ij = a_ij + a_(i-1)(j-1) + a_(i-2)(j-2) + ...

In APL (which I no longer use), I would use the 'rotate' operator to derive 
an array whose columns are diagonals of the given array and then cumulate 
down columns. Is there a similar operator in R, or is there another/better way?

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