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Having looked here, what should I do differently to get the progress indicator working properly?
Monitor[Plot[{Pause[0.1];
LogIntegral[x] - Sum[2 N[Re[ExpIntegralEi[ZetaZero[n] Log[x]]]], {n, 1, 500}] - Log[2],
Sum[PrimePi[x^(1/n)]/n, {n, 1, Floor[Log[x]]}]},
{x, 2, 1000}], Row[{ProgressIndicator[x, {2, 1000}], x}, " "]]
This is a quick and dirty way to watch whats going on..
Monitor[list = {{0, 0}};
Plot[{y = LogIntegral[x] -
Sum[2 N[Re[ExpIntegralEi[ZetaZero[n] Log[x]]]], {n, 1, 500}] - Log[2],
Sum[PrimePi[x^(1/n)]/n, {n, 1, Floor[Log[x]]}]}, {x, 2, 1000},
EvaluationMonitor :> AppendTo[list, {x, y}] ],
ListPlot[list, Epilog -> {PointSize[.05], Red, Point[list[[-1]]]},
PlotRange -> {{0, 1000}, {0, 200}}]]
What you see is the function globally smooth but locally jagged so the recursion keeps going and going. ( you likely want to set MaxRecursion to something reasonable.. )
MaxRecursion -> 0, PlotPoints -> 200 is really what I was after
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ListPlot with ListLinePlot, is there any way to (a) stop the tracing from max back to zero (b) replace each subsequent tracing with the new one?
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The problem is with the speed of your first sum. I did the following and things worked fine.
(zzero[#] = N@ZetaZero[#]) & /@ Range[600];
sum[x_?NumericQ] := Sum[2 Re[ExpIntegralEi[zzero[n] Log[x]]], {n, 1, 500}]
Monitor[Plot[{
LogIntegral[x] - sum[x] - Log[2],
Sum[PrimePi[x^(1/n)]/n, {n, 1, Floor[Log[x]]}]}, {x, 2, 1000}
],
Row[{ProgressIndicator[x, {2, 1000}], x}, " "]
]
Here's the progress bar in action:
Pause for a purpose), but the fact that the progress indicator starts anew multiple times.
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Jul 21, 2014 at 20:11
Sum[2 N[Re[ExpIntegralEi[ZetaZero[n] Log[x]]]]. If you remove that, things work fine. $\endgroup$ProgressIndicatorseems to go through each sum, rather than indicate the progress of the entire calculation. $\endgroup$Plotadaptively evaluatesxin a non sequential order. Without knowing a priori how many evaluations will be needed I see no sensible way to make the progress indicator work $\endgroup$MaxRecursion -> 0, PlotPoints -> 200$\endgroup$Monitor[Sum[Pause[0.1]; x, {x, 1, 100}], Row[{ProgressIndicator[x, {1, 100}], x}, " "]]$\endgroup$