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Apr
23
comment Why timing of FindRoot is almost the same even if the function is speedup significantly
@Sander I found adding _?NumericQ brings things to normal. see my update. Though I still don't know what has FindRoot done to func1 without NumericQ to make it unexpectedly fast. As you said, we'd better just accept this. Thank you very much for the considerable time you have spent on my post
Apr
23
revised Why timing of FindRoot is almost the same even if the function is speedup significantly
added 506 characters in body
Apr
22
comment Why timing of FindRoot is almost the same even if the function is speedup significantly
I update my post again, have a look again : )
Apr
22
revised Why timing of FindRoot is almost the same even if the function is speedup significantly
added 2496 characters in body
Apr
22
comment Why timing of FindRoot is almost the same even if the function is speedup significantly
@Sander I updated my post, have a look
Apr
22
revised Why timing of FindRoot is almost the same even if the function is speedup significantly
added 686 characters in body
Apr
22
comment Why timing of FindRoot is almost the same even if the function is speedup significantly
@DanielLichtblau Hi, DanielLichtblau. I see many upvotes on ciao's comment and also Sander's, but I just still don't get the point. The stepmonitor shows the same for func1 and func2, now func2 is 25 times faster than func1. But the speed of whole process is not that different. What did FindRoot spend its time on?
Apr
22
revised Why timing of FindRoot is almost the same even if the function is speedup significantly
added 13 characters in body
Apr
22
comment Why timing of FindRoot is almost the same even if the function is speedup significantly
Hi, Sander, thank you very much for the answer. But my point in my post is that "why speed up func has no effect on speed of FindRoot even though the internal steps are exactly the same?" It seems that you havn't explained this in your answer
Apr
22
revised Why timing of FindRoot is almost the same even if the function is speedup significantly
added 14 characters in body
Apr
22
comment Why timing of FindRoot is almost the same even if the function is speedup significantly
@ciao Hi, ciao. I don't quite understand your claim. The three func versions produced the same result. Why will there be any difference in internal steps? As I tested, the internal processes are exactly the same. FindRoot[func[u] - num == 0, {u, -100, 100}, StepMonitor :> Print["Step to u = ", u]] for all three func version. On the other hand, the most time cosuming part in finding root is calculate the function values at different point, Why shouldn't we expect a linear relationship??
Apr
21
asked Why timing of FindRoot is almost the same even if the function is speedup significantly
Apr
21
accepted best way for finding approximate root of monotonic sawtooth like function
Apr
21
comment best way for finding approximate root of monotonic sawtooth like function
I was googling secant before I post this. Somehow I didn't find how to do it in mathematica.... I should have read the doc more carefully. Thank you very much for quick response : )
Apr
21
comment 1D ImplictRegion can not be plotted with RegionPlot
@JasonB While I can confirm on 10.4, both of them fail...
Apr
21
asked best way for finding approximate root of monotonic sawtooth like function
Apr
21
comment How to form a block-diagonal Matrix from a list of matrices?
Oops, I am wrong. It is working for SparseArray, while not working for SymmetrizedArray type. Check it again : )
Apr
21
comment How to form a block-diagonal Matrix from a list of matrices?
Hi, kglr. It fails for sparse block. For a fix, diagF = SparseArray[Band[{1, 1}] -> Normal /@ {##}] &
Apr
21
answered 1D ImplictRegion can not be plotted with RegionPlot
Apr
20
comment 1D ImplictRegion can not be plotted with RegionPlot
@JasonB Don't know whether other version works well or not.