I have a math problem that I have solved analytically. I now want to generate a number of graphs based on different parameter values. My problem is threefold:
- It takes a couple of minutes to produce a single graph.
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I am wasting time waiting until one graph is finished so that I can start the next one for different parameter values, or one for e.g. different domain and range of the plot.
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My code seems generally badly designed.
What I’d like is:
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Make the computation much more efficient, and maybe less messy in terms of code.
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More importantly: Make it so that I can generate an arbitrary amount of graphs for different settings very easily, and wait until the computer finishes them all. An make it so that after the computation is done, I can easily change the range and domain of the graph, and its design, without the computer having to redo the underlying computations.
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Generally improve the design of the code.
Here is the mathematical problem (the code is given below):
The heaviest part of the computation seems to be in finding $ t$ .
I have taken as a first example, $ $ A(i)= \begin{cases} 0 &\text { if } i<a\ tech\cdot(i-a) &\text { if } i\geq a\end{cases}$ $ For some real number $ tech$ .
I use the following code to compute this problem:
ClearAll[x, A, i, L, K, phi, t, intA] A[i_, tech_] := If[i > a, tech*(i - a), 0]; intA[t_?NumericQ, tech_] := NIntegrate[A[i, tech]^(phi/(1 - phi)), {i, Max[a, t], 1}]; t[LK_, tech_] := t[LK, tech] = x /. FindRoot[A[x, tech] - ((LK/x)*intA[x, tech])^(1 - phi), {x, (a + 1)/2}] L = 5; K = 5; phi = -0.5; a = 0.5; tech = 20; cL[L_, K_, tech_] := L/t[L/K, tech]; cK[L_, K_, tech_] := K/intA[t[L/K, tech], tech]; Lab[i_, L_, K_, tech_] := If[i > t[L/K, tech], 0, cL[L, K, tech]]; Kap[i_, L_, K_, tech_] := If[i > t[L/K, tech], (cK[L, K, tech])*(A[i, tech])^(phi/(1 - phi)), 0]; Plot[{Lab[i, L, K, tech], Kap[i, L, K, tech]*A[i, tech], A[i, tech]}, {i, 0, 1}, PlotRange -> All] tildeF[L_, K_, tech_] := tildeF[L, K, tech] = NIntegrate[(Lab[i, L, K, tech] + A[i, tech]*Kap[i, L, K, tech])^ phi, {i, 0, 1}]; F[L_, K_, tech_] := tildeF[L, K, tech]^(1/phi); F[5, 5, 30] Plot3D[{F[L, K, tech]}, {L, 0, 10}, {K, 0, 10}] It is especially the Plot3D that is taking most of the computation time.
