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I have implemented a numeric Laplace Solver in C++ and am trying to graphically represent the validity of my method. I have outputted the grid from C++ and imported it into Mathematica to get the following MatrixPlot:

Matrix Plot

And I wish to compare this directly to:

Density Plot

However; I am not sure how I can rearrange the axes. I wish for the MatrixPlot axes to be {0.0,0.2,0.4,0.8,1.0} like the contour plot (however, I cannot just use FrameTick as I wish to do larger matrices ($20\times 20$, $100\times 100$ and $1000\times 1000$, where it would be impractical to write each tick out by hand), and I also wish for the plot to be reoriented so it has the same orientation as the contour plot. How can I achieve this?

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  • $\begingroup$ @Karsten7. But then Mathematica interpolates over the points for me (which I don't want) and it still has axes going up to 7 instead of 1? $\endgroup$ – Thomas Russell Dec 28 '14 at 19:15
  • $\begingroup$ @Karsten7. Thank you, that's useful; but how do I rescale the axes now? $\endgroup$ – Thomas Russell Dec 28 '14 at 19:21
  • $\begingroup$ @Karsten7. Thank you so much, you've saved me a lot of time!! $\endgroup$ – Thomas Russell Dec 28 '14 at 19:23
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Some data

m = Table[i*j, {i, 7}, {j, 7}];

Its

MatrixPlot[m]

matrix

and a ListDensityPlot of the same data, without interpolation and rescaled axes:

ListDensityPlot[m, DataRange -> {{0, 1}, {0, 1}}, InterpolationOrder -> 0]

density

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