How to find when a value is reached given a function?
If I run this:
```
Y = c(10000, 20000, 40000, 80000, 160000, 320000, 640000, 1280000)
X = 0:7
plot(Y~X, log='y')
model <- lm(log10(Y) ~ X)
abline(model)
predict(model, data.frame(Y=log10(1000000)))
```
I get a funny answer:
```
1 2 3 4 5 6 7 8
4.00000 4.30103 4.60206 4.90309 5.20412 5.50515 5.80618 6.10721
Warning message:
'newdata' had 1 row but variables found have 8 rows
```
but:
```
data.frame(Y=log10(1000000))
Y 1 6 ``` What is the correct use? Thank you
On Mon, Jan 25, 2021 at 3:20 PM Luigi Marongiu <marongiu.luigi at gmail.com> wrote:
Thanks, I'll check it out. I ran the simulation and I got:
```
t = 1, N = 20,000
t = 2, N = 40,000
t = 3, N = 80,000
t = 4, N = 160,000
t = 5, N = 320,000
t = 6, N = 640,000
t = 7, N = 1,280,000
```
Hence the answer is t=6.{...} but the problem is to get that
fractional value. Would be possible to use some kind of interpolation?
I have the known Xs (the t values), the known Ys (the Nt), I need to
get x when y is 10?
On Sun, Jan 24, 2021 at 9:40 PM Duncan Murdoch <murdoch.duncan at gmail.com> wrote:
On 24/01/2021 2:57 p.m., Luigi Marongiu wrote:
Hello
I am trying to simulate a PCR by running a logistic equation. So I set
the function:
```
PCR <- function(initCopy, dupRate, Carry) {
ROI_T = initCopy
A = array()
for (i in 1:45) {
ROI_TplusOne <- ROI_T * dupRate * (1 - ROI_T/Carry)
A[i] <- ROI_TplusOne
ROI_T <- ROI_TplusOne
}
return(A)
}
```
Which returns an array that follows the logistic shape, for instance
```
d <- 2
K <- 10^13
A_0 <- 10000
PCR_array <- PCR(A_0, d, K)
plot(PCR_array)
```
Given the formula `ROI_TplusOne <- ROI_T * dupRate * (1 -
ROI_T/Carry)`, is it possible to determine at what time point `i` a
given threshold is reached? For instance, what fractional value of i
returns 1000 000 copies?
There are two answers: The brute force answer is just to try it and count how far you need to go. This is really simple, but really inefficient. The faster and more elegant way is to solve the recursive relation for an explicit solution. You've got a quadratic recurrence relation; there's no general solution to those, but there are solutions in special cases. See https://math.stackexchange.com/q/3179834 and links therein for some hints. Duncan Murdoch
-- Best regards, Luigi
Best regards, Luigi