7a50f4ee-d741-4a1c-9eab-8bd36a003da6 12 6 5 auto

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

Solving for a vectorised function

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. The seeded solve scanner is of no gain versus the direct "Sol". The 'roots' can't be applied wrt the derivative that does not take discrete vector of values. In lieu, the 'solve' block concludes pretty well.. a bit slow. _____________________________ 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. Pushing a bit more, 'solve' cries to murder.

Design a discrete function inverser  in the L, H span , N points 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 20 solve : for ω sol augment 51 line :

Sol f 0.06 0.99 100 Inverse :

1 time t0 - 28 sec *

Magnify the function to see

50 x f * Sol 2 1 sys

The native function

x f

This exercise is purely didactic/demo. No further exploration will be applied. It aims at setting up the solver wisely. The f(x) does not plot part of the low region, this default is due to Smath too granular in this region.

The other way around Maple "root"

x f x 2 π * / 2 π * x / tanh * sqrt :

w sol t f w - t root : w 2 sqrt * π sqrt * - t 2 π * t / tanh * sqrt + 2 sqrt π sqrt * / t root

Maple expression var root ≡ is live in Smath 5346 but undocumented ≡

For solving, we equate the Maple 'root' to 0 and include in the Smath solve block c/w the 'roots' range. Indirectly, Mathcad/Mathsoft "tracking" implements a version of Maple "root" [or similar to Maple], but active by clicking in the curve for quick coordinates.

The symmetric solver within the range above

w t Sol w 2 sqrt * π sqrt * - t 2 π * t / tanh * sqrt + 2 sqrt π sqrt * / 0 ≡ t 20 - 20 solve :

w 0.875 :

w 0.95 ≤

w t Sol 6.3582 - 6.3582 21 mat

up dn locate line j 1 up range v j el j dn + : u j el locate j 0 * + : 21 line for u v augment 21 line :

Neg 21 - w t Sol 1 el line :

Pos 21 - w t Sol 2 el line :

Curve tracking Mathcad/Mathsoft style

x f w Neg Pos 4 1 sys

jmGiraud: 2015_08_23

w w t Sol 12 mat 78 / 6.358 - 6.358 21 mat 12 mat