Combining two consecutive density plots

Question

I would like to combine two density plots using Show[ ] with different consecutive x-values so that the color scheme and legends match. For example,

plot01 = DensityPlot[2 Sin[x y], {x, 0, 1}, {y, 0, 3}, 
  ColorFunction -> "M10DefaultDensityGradient", 
  PlotLegends -> Automatic]

plot02 = DensityPlot[2 Sin[x y], {x, 1, 3}, {y, 0, 3}, 
  ColorFunction -> "M10DefaultDensityGradient", 
PlotLegends -> Automatic]

As such, plot01 has a scheme based on the range {0.0, 2.0} while plot02 has one based on the range {-2.0, 2.0}. I would like both of them to have a color scheme and legend based on {-2.0, 2.0} so that when they are combined, the colors match smoothly. How do I make this happen?

Answer 1

If you have to use Show with two separate plots (rather than a single one with {x, 0, 3}), you can specify the range for color scheme as {-2,2} in both plots and add the option ColorFunctionScaling -> False:

plot01 = DensityPlot[2 Sin[x y], {x, 0, 1}, {y, 0, 3}, 
   ColorFunction -> ColorData[{"M10DefaultDensityGradient", {-2, 2}}], 
   ColorFunctionScaling -> False];
plot02 = DensityPlot[2 Sin[x y], {x, 1, 3}, {y, 0, 3}, 
   ColorFunction -> ColorData[ {"M10DefaultDensityGradient", {-2, 2}}], 
   ColorFunctionScaling -> False];
Legended[Show[plot01, plot02, PlotRange -> All], 
 BarLegend[{"M10DefaultDensityGradient", {-2, 2}}]]