510720ce-67f1-4e23-bae9-a668078e8571 9 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Inversing a function in discrete mode

x f x 2 π * / 2 π * x / tanh * sqrt :

t0 1 time :

In Mathematics, an InverseFunction is the solution of this function. f(x) is the model of difficulty, documented in Mathematica 4.0. _____________________________ Note: the function starts existing around 'x = 0.02, f(0.02) = 0.0564' our choice to solve is wise , down to lower possible limit. The upper limit 0.99 is practical. In fact, at 1, the solution is infinite. From educated practice, we know in advance that the upper limit of inversion is 1. By looking at the plot of the function, its value 1± ? is around x~25. Plug this value 25 as the upper limit of the bracketed solve block ... success ! ______________________________ Inversing a data set is not possible in Smath 5346. Under the hood of 'solve' there is a derivative component that does NOT works from linterp, ainterp, cinterp. The only alternative is via some sort of model to fake the data set. Piece wise is a valid approach if no model will fit.

f L H N Inverse dx H L - N / : i 1 N range ω i el L dx - (dx i * + : for j 1 ω rows range sol j el x f ω j el - 0 ≡ x 0.02 25 solve eval : for ω sol augment 51 line :

25 f 0.989679

Sol f 0.06 0.995 100 Inverse :

1 time t0 - 26 sec *

50 x f * Sol 2 1 sys x f 0.02 0.0564 + 12 red 1 5 mat 2 1 sys