New answers tagged code-review
2
Use an association to avoid indexing e.g.
ops = AssociationThread[{"Add", "Subtract"}, {plus, minus}];
Manipulate[ops[op][x, y],
{{op, "Add", "operation type"}, Keys@ops, ControlType -> PopupMenu},
{x, 1, 10}, {y, 1, 10}]
2
All credit to @Roman who deserves the accept for discovering 7095816 was the target number. With this number pinned down I tried to solve this myself with Mathematica, but it was still too slow:
variables = Array[x, 16];
matrix = ArrayReshape[variables, {4, 4}];
target = 7095816;
uniqueConstraint = (And @@ (Unequal @@@ Subsets[variables, {2}]));
...
4
There are only seven (six unique) solutions up to row/column sums of $10^8$ (of course there are 1152 equivalent squares by permutation/transposition for each one):
$$
\left(
\begin{array}{cccc}
2 & 16 & 108 & 180 \\
24 & 192 & 9 & 15 \\
144 & 18 & 150 & 90 \\
160 & 20 & 135 & 81 \\
\end{array}
\right),\...
4
Abs makes this integrand hard to evaluate for the system and it is more straightforward to obtain a numerical integral. Defining first
iLT[t_, x_] = InverseLaplaceTransform[1/(1 + s L (s c + (1/R3))), s, t - x]//FullSimplify
one can see that it takes vary small values in the interesting region and in order to avoid false numerical integration we specify ...
3
When Plot is too slow, I fall back on a Table and a ListLinePlot which means you can control how many points to plot:
u = 230*Sqrt[2];
ω = 2*Pi*50;
Φ = Pi/46;
L = 45*10^(-7);
c = 59*10^(-6);
R3 = 1/10;
ilt = InverseLaplaceTransform[1/(1 + s*L*(s*c + (1/R3))), s, τ];
intg[t_?NumericQ] :=
NIntegrate[Abs[u*Sin[ω*x + Φ]]*(ilt /. {τ -> t - x}), {x, 0, t}];
...
4
it is having hard time with exact integral. Replace with numerical.
Clear["Global`*"];
u = 230*Sqrt[2];
ω = 2*Pi*50;
Φ = Pi/46;
L = 45*10^(-7);
c = 59*10^(-6);
R3 = 1/10;
tmp = InverseLaplaceTransform[1/(1 + s*L*(s*c + (1/R3))), s, t - x];
Integrand = Abs[u*Sin[ω*x + Φ]]*tmp;
f[t_?NumericQ] := NIntegrate[Integrand, {x, 0, t}]
...
1
The transformation can be calculated once outside (before) the plot. Replace InverseLaplaceTransform with its result and use NIntegrate instead of Integrate.
Then the plot will be done in a few seconds.
Andreas
1
The numeric integration confirms the former
f = 10^5;u = 1;m = (R1 + R3)/(c*R1*R3);R1 = 100;R3 = 100;n = 100;k = c*R1;c = 100*10^(-9);
g[t_?NumericQ] := (NIntegrate[(((((u*Sin[2*Pi*f*x])*
Sign[u*Sin[2*Pi*f*x]])/2) + ((u*Sin[2*Pi*f*x])/
2)))*((Exp[-m*(t - x)])/k), {x, 0, t}])^2/n;
f*NIntegrate[g[t], {t, 0, 1/f}]
(*0.000187112*)
in view of
N[...
3
You can use a RadioButtonBar to pick the 10 combinations of equations. Use Subsets[equations, {3}] instead of Permutations because this avoids all the choices where you have a repeated equation.
It's a bit clunky and I didn't know how to represent this very well with the UI elements, but I've also added a CheckboxBar so you can select the equations from the ...
7
I think it might be helpful to evaluate the arguments on their own and see what happens.
The first argument
r^# & /@ Range[0, n]
outputs (for a specific choice of n)
With[{n = 3}, r^# & /@ Range[0, n]]
(* {1, r, r^2, r^3} *)
which generates a list that you could also get by the following
Table[r^i, {i, 0, n}]
The FullForm of the first argument ...
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