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MathGroup Archive 2001

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Re: RE: inverting y axis in DensityPlot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27311] Re: [mg27278] RE: [mg27271] inverting y axis in DensityPlot
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Tue, 20 Feb 2001 03:05:20 -0500 (EST)
  • References: <96q2d1$mqc@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hartmut,
Here is a variant of your technique for modifying the option FrameTicks in
the last stage:

Block[{lst = {}, n = 1},
        Show[rg, opts /. (FrameTicks -> {bottom_, left_, up_, right_}) :>
        FrameTicks ->
            {bottom, left /. {y_, ylabel_ /; Element[ylabel, Reals], len_,
style_} /;                     (PrependTo[lst, y]; True) :> {lst[[n++]],
ylabel, len, style}, up, right}]
]


Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Wolf, Hartmut" <Hartmut.Wolf at t-systems.de> wrote in message
news:96q2d1$mqc at smc.vnet.net...
> A correction is to made, see below
>
>
> -----Original Message-----
> From: Matthias Hertel [mailto:wir95cgu at studserv.uni-leipzig.de]
To: mathgroup at smc.vnet.net
> Subject: [mg27311] [mg27271] inverting y axis in DensityPlot
>
>
> Hello,
>
> I would like to display the design matrix of a medium-sized general
> least-squares problem as a bitmap. (It's too large for StandardForm or
> MatrixForm to be useful, yet its structure is simple enough that one
> can tell if something has gone really wrong just by looking at a
> DensityPlot.)
>
>     ListDensityPlot[desmtx, Mesh->False]
>
> almost does what I want, but the matrix is displayed upside down
> (desmtx[[1,1]] is in the *bottom* left corner).
>
>     ListDensityPlot[Reverse@desmtx, Mesh->False]
>
> is closer, but now the frame tick marks are wrong (don't correspond to
> the row index). It would be perfect if there was something like
>
>     ListDensityPlot[desmtx, InvertY->True, Mesh->False]
>
> that's just like a normal ListDensityPlot but with the y axis flipped.
> But there isn't.
>
> So, how can I get a DensityPlot with (0, 0) in the top left corner and
> y increasing downwards?
>
> Thanks
> Matthias
>
> -----------------
>
>
> Matthias,
>
> let's make up an example:
>
> In[1]:=
> t = Table[Sin[x^2 - x y], {y, 0., 6, 6/50}, {x, 0., 6, 6/50}];
> In[2]:=
> g = ListDensityPlot[t, MeshRange -> {{-0.5, 50.5}, {-0.5, 50.5}},
>     Mesh -> False]
>
> We have 51 points in each direction, and we adjusted MeshRange a bit
> as to have the Tick marks point to the center of our raster "pixels"
> and not to their left lower corners. Now if we plot with the y-axes
> reversed
>
> In[4]:=
> gy = ListDensityPlot[Reverse@t,
>      MeshRange -> {{-0.5, 50.5}, {-0.5, 50.5}}, Mesh -> False]
>
> we get (of course) the same tick marks, corresponding to the indices
> of the reversed matrix. But you want to have them correspond to the
> indices of the original matrix.
>
> You can do that by either specifying the FrameTicks explicitly or with
> a hand-crafted tick function, yet the better idea seems to be: just take
> the automatically generated tick marks of the graphics and manipulate
> their labels a bit such that they'll come out "right".
>
> Now we can't get at the FrameTicks of a DensityGraphics by FullOptions
> (which does next to nothing here) nor by FullGraphics (which here does
> exactly nothing). The trick is to convert the DensityGraphics to a
> Graphics first:
>
> In[5]:=
> rg = Graphics[gy]
>
> and then get at the FullOptions
>
> In[6]:=
> opts = FullOptions[rg];
>
> Now we can do what we want, I did it this way:
>
> In[7]:=
> Block[{minlab = Infinity, maxlab = -Infinity},
>   Show[rg, opts /. (FrameTicks -> {bottom_, left_, up_, right_}) :>
>         FrameTicks -> {bottom,
>             left /. {y_, ylabel_?NumberQ, len_, style_}
>                     /; (If[ylabel > maxlab, maxlab = ylabel];
>                         If[ylabel < minlab, minlab = ylabel];
>                         True)
>                     :> {y, maxlab - ylabel + minlab, len, style},
>             up, right}]]
>
> This code deserves some explanation. As you see we manipulate the
> tick marks to the left. As generated by the automatic tick function the
> labels are numeric (not explicitly converted to strings) -- this is
> our luck. The intend of the conversion formula is clear, but how come
> the right values of maxlab and minlab (at the right time)?
> RuleDelayed does not evaluate it's rhs (it has the HoldRest attribute),
> but the lhs is evaluated and such is the condition on the pattern, which
> we just set to True, but misuse it as a hook to calculate the
> minimum and maximum for the labels on the fly.
>
> ---correction-----
>
> Reversing the _labels_ is not the right idea and will go wrong in general,
> instead just reverse all the frame ticks and leave the labels where they
> belong to (and we are not subjected to luck). So
>
> In[21]:=
> Block[{ymin = Infinity, ymax = -Infinity},
>   Show[rg, opts /. (FrameTicks -> {bottom_, left_, up_, right_}) :>
>         FrameTicks -> {bottom,
>             left /. {y_, ylabel_, len_, style_}
>                  /; (If[y > ymax, ymax = y]; If[y < ymin, ymin = y]; True)
>                  :> {ymax - y + ymin, ylabel, len, style},
>             up, right}]]
>
> -- Hartmut
>
>




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