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visits member for 2 years, 7 months
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May
29
comment NDSolve: methods and step size choosing
@Albert: Certainly not. But how many people will have read through the books by Hairer et al. - of which I spot at least three? ;-)
May
29
comment NDSolve: methods and step size choosing
Have you had a look at the complete tutorial Advanced Numerical Differential Equation Solving in Mathematica? I believe your questions are being answered there albeit it may take some reading time.
May
27
comment Inverting a Spline-Function (Bezier or BSpline)
For completeness: Surprisingly using InverseFunction with an InterpolatedFunction turns out to be slower than the indicated FindRoot- solution. But since there should be some symmetry here, I simply switched the $(x,y)$ pairs for the reference points to be $(y,x)$ pairs before letting Interpolation with Order 2 and Spline-Method find a solution. Using the thus obtained InterpolationFunction is as fast as can be wished for.
May
27
accepted Inverting a Spline-Function (Bezier or BSpline)
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
I just tested the FindRoot-Solution vs. using InverseFunctionon an interpolated Function as suggested in the solution on 10000 random values. It surprised me quite a bit to find the FindRoot-solution turning out faster (4.7 secs vs. 6.9 secs).
May
24
revised How can i get the solution of complicated equation?
Added the code-wrapper.
May
24
comment How can i get the solution of complicated equation?
Justed added the code using OCR.
May
24
suggested suggested edit on How can i get the solution of complicated equation?
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
That is a reasonable suggestion but since I am a bit "clueless" about which functional form to use - and what the implication of it would be - I thought "that is exactly what splines were invented for"?
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
My problem is, that besides the point $(\alpha,\beta)$ where both parameters are to be estimated, and the points $(0,0)$ and $(x_\text{max},y_\text{max})$ I do not know anything else. Interpolation[] will give a function passing through the points. I find it very hard to keep it within plausible ranges?
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
Great, thanks. You said "if you absolutely must use B-splines" -- well I need to 'calibrate' a transformation where I do not know the mapping (function) to use. From some reasonable assumptions (all values within $[0,\infty($, the function probably not beeing s-shaped etc., I found a spline to be the best way to define a smooth function with just two parameters (next to one for scaling the maximum value). What else to use/do?
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
That is interesting and a bit weird at the same time. I had tried defining a pure function (e.g. g = Last[#]&) and then using Composition[g,f][t] in the equation definition but that did not work out. I am not quite getting why the delayed function does help here?
May
24
revised Inverting a Spline-Function (Bezier or BSpline)
I got confused with x and y, so I had to edit the equation for the equation solving.
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
@BoLe Uups, you are right, I should have used Last instead of First in my post here and so you are correct. But that still does not change the principle problem with equation solving. Thanks for pointing out the error, I will edit my question.
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
I tried FindRoot (e.g. FindRoot[First@f[t]==0.6,{t,0.5}]) but I still get the wrong result doing so?
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
Thanks for that answer, but I was aware of this possibility already and have accordingly changed my question. Why does "regular" equation solving with the Spline Function not work?
May
24
revised Inverting a Spline-Function (Bezier or BSpline)
Giving a more precise question since I am aware of using an approximation to the spline which can then be easily inverted. I still cannot see any reason for regular equation solving not working here?
May
24
comment Inverting a Spline-Function (Bezier or BSpline)
Thank you, Sjoerd, I should have mentioned that solution - whiich is what I am doing now: using a grid with Interpolation[] where I have gotten the best results using InterpolationOrder->2. But that still is not perfect and still wonder why equation solving won't work here.
May
24
asked Inverting a Spline-Function (Bezier or BSpline)
May
19
comment Why don't these styling rules work when viewed in TableForm?
As a matter of taste I would rewrite the replacement rule as m /. l_List /; Last[l] > 0 :> ... . This formulation already hints at what is the problem with Style being applied to a list.