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 > >