#### 7.45 bug in densityplot in MapleV.5 and patch (6.10.98)

I noticed in the Unix version R5 that density plot interchanges the roles of the independent
variables. For example,

densityplot(x^2 -y,x=-3..3,y=-3..3);

yields a density plot of

` y^2-x`

and

densityplot(x^2-y,y=-3..3,x=-3..3);

yields the correct density plot but with the axes labeled incorrectly.

Is there a patch for this error?

It is corrected with Maple 6.01. (U. Klein)

Just got MAPLEVR5 (win95). I thought I would run an example from A. Heck’s book
(Introduction to MAPLE, Springer Verlag, 2ed page 428):

> restart;
> with(plots):
> phi:=ln(sqrt((x+ 1)^2 + y^2)) - ln(sqrt((x-1)^2 + y^2));
> densityplot(phi,x=-2..2,y=-1..1,grid=[80,80],axes=box,style=patchnogrid,
colorstyle=HUE);

Release 4 does the plot correctly (like in Heck’s book). Release 5 confuses the
axes!!!!!!

This problem is not seen for contourplot or gradplot however. The problem appears to be
endemic to densityplot

Bummer.

It is as if the arguments of the function are permuted or something like that within
densityplot. Anybody else notice this problem? Is there a work-around?

The quality of the output from densityplot is better though, if one is prepared to ignore this
minor detail.

Also, it appears that R5 renders the plot about 2-3 times faster in `1/2`

memory than
R4.

As several people have noticed, densityplot in Release 5 has a bug which causes \(x\) and \(y\) to be
"interchanged". Actually the result of

densityplot(f(x,y), x = a .. b, y = c .. d)

is what should be obtained from

densityplot(f(a + (b-a)*(y-c)/(d-c), c + (d-c)*(x-a)/(b-a)), x = a .. b, y = c .. d)

So a work-around is to use

> dplot:= proc(f, r1, r2)
local x, y, a, b, c, d, g;
if not typematch(r1, x::name = a::anything .. b::anything) then
ERROR("incorrect second argument") fi;
if not typematch(r2, y::name = c::anything .. d::anything) then
ERROR("incorrect third argument") fi;
g:= unapply(f, x, y);
densityplot(g(a+(b-a)*(y-c)/(d-c), c + (d-c)*(x-a)/(b-a)), args[2..-1]);
end;

The bug seems to be related to the use of hfarrays in densityplot.