Solve simple equation with the floor function.

S and P are known element in the equation. I want to find x

S = 10;
P = 13;
S = floor(P*(1-x))

I do not know how to deal with the floor functions.

Answer 1

[Matt J]

It is the same as solving

S+delta=P*(1-x)

where 0<=delta<1 is arbitrary. The solution is then,

x=1-(S+delta)/P

It's important to keep in mind if you are solving this numerically that delta=0 will be a numerically unstable choice because the resulting x will take you close to the discontinuity of the floor function.

Let's test with delta=0.5:

S = 10;
P = 13;
delta=0.5;

x=1-(S+delta)/P

x = 0.1923

S == floor(P*(1-x)) %check

ans = logical
   1

[NA]

Thank you for your time