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I need to write a cumulative summation function in R but I've been hitting a brick wall. The function has the following structure:
a*x1
a*x2 + a^2*x1
a*x3 + a^2*x2 + a^3*x1
a*x4 + a^2*x3 + a^3*x2 + a^4*x1
And so on. cumsum doesn't seem to work for this type of function. Is there any way this could be implemented in R?
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Recursion is a method in C++ which calls itself directly or indirectly until a suitable condition is met. In this method, we repeatedly call the function within the same function, and it has a base case and a recursive condition.
The classic example of recursive programming involves computing factorials. The factorial of a number is computed as that number times all of the numbers below it up to and including 1. For example, factorial(5) is the same as 5*4*3*2*1 , and factorial(3) is 3*2*1 .
Recursion means “solving a problem using the solution of smaller subproblems (smaller version of the same problem)” or “defining a problem in terms of itself”. This is a widely used idea in data structures and algorithms to solve complex problems by breaking them down into simpler ones.
Since your recursion is
u[n+1] = a * ( x[n+1] + u[n] )
i.e.,
u[n+1]/a = x[n+1] + a * u[n]/a,
you can use filter:
x <- 1:5
a <- 2
a*filter(1:5, a, method="recursive")
# Compare with the expected values
a*x[1]
a*x[2] + a^2*x[1]
a*x[3] + a^2*x[2] + a^3*x[1]
a*x[4] + a^2*x[3] + a^3*x[2] + a^4*x[1]
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