Several people have complained about this on StackExchange since M11 was released. You will find my analysis of the problem here:

http://mathematica.stackexchange.com/q/123943/12

Another thread: http://mathematica.stackexchange.com/q/125127/12

Hi Sander,

by the way, why is this:

pdftanemura[x_] := 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;
Plot[pdftanemura[y], {y, 0.01, 100}, 
PlotRange -> {{0.01, 100}, {10^-4, 10}}, 
ScalingFunctions -> {"Log", "Log"}, Mesh -> All,Meshstyle->Red]

Meshpoints do not coincide with the curve... Precision-issue? Cannot fix it with WorkingPrecision.

Cheers,

M.

Hi,

just executed the code in the codex. Runs on MMA11 on OSX10.11.6. Same result for Mathematica Online and Development Platform.

Because those point would be 'negative' y values (with the right axes)

yes, I know. that's exactly my problem. This is why I was thinking of a WorkingPrcision problem. For example:

pdftanemura[x_] := 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;
Plot[pdftanemura[y], {y, 0.01, 100}, 
 PlotRange -> {{0.01, 100}, {10^-4, 10}}, 
 ScalingFunctions -> {"Log", "Log"}, Mesh -> All, MeshStyle -> Red, 
 WorkingPrecision -> 1]

gives warnings, and this figure:

Not quite what I would expect, but I think it points at a precision problem mostly because of the error message:

Cheers,

Marco

What might happen internally is that they do a replacement y -> Exp[y] and f -> Log[f], now they can feed in 'linear values' of y, and get the vertical values out. But the replacement might not work on the symbol (because it is HoldFirst for the plot). So it remains untouched somehow? Terrible behavior in my opinion... very confusing, even for the more experienced. I just stumbled upon it because my 'old' code now gave a completely different plot...

It took me way more time than it should to find the mistake, here is the 'distilled' version haha. I'm considering sending this in as a bug, as I can imagine lots of people will trip over this new behavior, especially beginners (which I am apparently)...

Some of the transformation stuff is happening here:

f = x^2
tr = Trace[LogLogPlot[f, {x, -3, 3}]];
Column[tr[[5, 2, 2, 3, 3, {14, 29, 31}]], Frame -> All]

But it is near impossible to compare it with the 10.4.1 implementation without the actual source code.

--SH

Hi Marco,

Thanks for verifying and brainstorming! I've send it to them. Might be solved in future 11.1...

I thought this was already fixed in 11.0.1.

Hi Sander,

yes, I unfortunately see the same behaviour.

Cheers,

Marco

Dear Sander,

I think you are absolutely right. This is weird, and potentially a serious and hidden problem.

See also:

pdftanemura[x_] := 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;
LogLinearPlot[pdftanemura[y], {y, 0.01, 100}, 
 PlotRange -> {{0.01, 100}, {10^-4, 10}}]
LogLinearPlot[Evaluate[pdftanemura[y]], {y, 0.01, 100}, 
 PlotRange -> {{0.01, 100}, {10^-4, 10}}]

and

pdftanemura[x_] := 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;
Plot[pdftanemura[y], {y, 0.01, 100}, 
 PlotRange -> {{0.01, 100}, {10^-4, 10}}, 
 ScalingFunctions -> {"Log", "Linear"}]
Plot[Evaluate[pdftanemura[y]], {y, 0.01, 100}, 
 PlotRange -> {{0.01, 100}, {10^-4, 10}}, 
 ScalingFunctions -> {"Log", "Linear"}]

which will, of course, all be the same problem.

Cheers,

Marco

I can verify that problem, too! (11.0.0 for Linux x86 (64-bit) (July 28, 2016))

Yes, strange! But is your definition

pdftanemura[x_] := 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;

supposed to be like so? Should not it read:

pdftanemura[y_] := 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;

Because then it seems to work.

Regard -- Henrik

Dear Henrik,

yes, you are right! I overlooked this from Sander's reply to my post, but I am still confused. In the original post it reads:

pdftanemura = 15.344341419321385` E^(-3.04011` y^1.078`) y^2.315`;

so no proper function is defined. The expression is just substituted in the plot. The definition of the function was only introduced when Sander replied to my first post.

I am not really sure what is going on here. I think that the explicit dependence on x in the later definition does/should not matter. A bit like here:

g[x_] := Sin[y];
g[5]
(*Sin[y]*) 

If I try to plot

Plot[g[x], {x, -6, 6}]

this gives

whereas

Plot[g[x], {y, 0, 6}]

gives

If I define

pdftanemura[x_] := 15.344341419321385 E^(-3.04011  y^1.078) y^2.315;

I get:

 pdftanemura
(*15.3443 E^(-3.04011 y^1.078) y^2.315*)

So basically if I define pdftanemura as above and plot

GraphicsRow[{Plot[pdftanemura[x], {y, 0, 6}], Plot[pdftanemura[y], {y, 0, 6}]}]

I get

Which is, sort of, what I expect. In this case it should not matter whether I define the dependance on x or y, or should it?

Cheers, Marco

Dear Marco, dear Sander, yes, the original problem of course remains! Thanks for spotting and bringing this up! My post was just meant as minor remark ...

Regards -- Henrik