Workletize the logistic map.
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@ -13,51 +13,90 @@
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#include <vector>
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#include <vtkm/cont/DataSetBuilderUniform.h>
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#include <vtkm/io/ImageWriterPNG.h>
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#include <vtkm/worklet/WorkletMapField.h>
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// The logistic map is xᵢ₊₁ = rxᵢ(1-xᵢ).
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// If we start this iteration out at (say) x₀ = 0.5, the map has "transients",
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// which we must iterate away to produce the final image.
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struct LogisticBurnIn : public vtkm::worklet::WorkletMapField
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{
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using ControlSignature = void(WholeArrayOut);
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using ExecutionSignature = void(_1, WorkIndex);
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template <typename OutputArrayPortalType>
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VTKM_EXEC void operator()(OutputArrayPortalType& outputArrayPortal, vtkm::Id workIndex) const
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{
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vtkm::Id width = outputArrayPortal.GetNumberOfValues();
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double rmin = 2.9;
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double r = rmin + (4.0 - rmin) * workIndex / (width - 1);
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double x = 0.5;
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// 2048 should be enough iterations to get rid of the transients:
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int n = 0;
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while (n++ < 2048)
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{
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x = r * x * (1 - x);
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}
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outputArrayPortal.Set(workIndex, x);
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}
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};
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// After burn-in, the iteration is periodic but in general not convergent,
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// i.e., for large enough i, there exists an integer p > 0 such that
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// xᵢ₊ₚ = xᵢ for all i.
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// So color the pixels corresponding to xᵢ, xᵢ₊₁, .. xᵢ₊ₚ.
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struct LogisticLimitPoints : public vtkm::worklet::WorkletMapField
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{
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using ControlSignature = void(WholeArrayIn, WholeArrayOut);
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using ExecutionSignature = void(_1, _2, WorkIndex);
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template <typename InputArrayPortalType, typename OutputArrayPortalType>
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VTKM_EXEC void operator()(const InputArrayPortalType& inputArrayPortal,
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OutputArrayPortalType& outputArrayPortal,
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vtkm::Id workIndex) const
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{
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vtkm::Id width = inputArrayPortal.GetNumberOfValues();
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double x = inputArrayPortal.Get(workIndex);
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double rmin = 2.9;
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double r = rmin + (4.0 - rmin) * workIndex / (width - 1);
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vtkm::Vec4f orange(1.0, 0.5, 0.0, 0.0);
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// We can't display need more limit points than pixels of height:
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vtkm::Id limit_points = 0;
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vtkm::Id height = 1800;
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while (limit_points++ < height)
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{
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vtkm::Id j = vtkm::Round(x * (height - 1));
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outputArrayPortal.Set(j * width + workIndex, orange);
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x = r * x * (1 - x);
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}
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}
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};
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int main()
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{
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size_t height = 1800;
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size_t width = height * 1.618;
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vtkm::Id height = 1800;
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vtkm::Id width = height * 1.618;
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vtkm::cont::DataSetBuilderUniform dsb;
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vtkm::cont::DataSet ds = dsb.Create(vtkm::Id2(width, height));
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std::vector<double> x(width, 0.5);
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vtkm::cont::ArrayHandle<double> x;
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x.Allocate(width);
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vtkm::cont::Invoker invoke;
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invoke(LogisticBurnIn{}, x);
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double rmin = 2.9;
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for (size_t i = 0; i < width; ++i)
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vtkm::cont::ArrayHandle<vtkm::Vec4f> pixels;
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pixels.Allocate(width * height);
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auto wp = pixels.WritePortal();
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for (vtkm::Id i = 0; i < pixels.GetNumberOfValues(); ++i)
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{
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double r = rmin + (4.0 - rmin) * i / (width - 1);
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int n = 0;
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// 2048 should be enough iterations to be "converged";
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// though of course the iterations actually don't all converge but cycle or are chaotic.
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while (n++ < 2048)
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{
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x[i] = r * x[i] * (1 - x[i]);
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}
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}
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vtkm::Vec4f v(1.0, 0.5, 0.0, 0.0);
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std::vector<vtkm::Vec4f> pixelValues(width * height, vtkm::Vec4f(0, 0, 0, 0));
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size_t iterates = 0;
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// We don't need more iterates than pixels of height,
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// by the pigeonhole principle.
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while (iterates++ < height)
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{
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for (size_t i = 0; i < width; ++i)
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{
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double r = rmin + (4.0 - rmin) * i / (width - 1);
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double y = x[i];
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assert(y >= 0 && y <= 1);
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size_t j = std::round(y * (height - 1));
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pixelValues[j * width + i] = v;
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x[i] = r * x[i] * (1 - x[i]);
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}
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wp.Set(i, vtkm::Vec4f(0, 0, 0, 0));
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}
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invoke(LogisticLimitPoints{}, x, pixels);
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std::string colorFieldName = "pixels";
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ds.AddPointField(colorFieldName, pixelValues);
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ds.AddPointField(colorFieldName, pixels);
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std::string filename = "logistic.png";
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vtkm::io::ImageWriterPNG writer(filename);
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writer.WriteDataSet(ds, colorFieldName);
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