annotate EquidistantGrid.jl @ 51:614b56a017b9

Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 11 Jan 2019 11:55:13 +0100
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children 8c6db1f6d8e0
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614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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1 # EquidistantGrid is a grid with equidistant grid spacing per coordinat
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
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2 # direction. The domain is defined through the two points P1 = x̄₁, P2 = x̄₂
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3 # by the exterior product of the vectors obtained by projecting (x̄₂-x̄₁) onto
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4 # the coordinate directions. E.g for a 2D grid with x̄₁=(-1,0) and x̄₂=(1,2)
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5 # the domain is defined as (-1,1)x(0,2).
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6 struct EquidistantGrid <: AbstractGrid
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7 numberOfPointsPerDim::Tuple # First coordinate direction stored first, then
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8 # second, then third.
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9 limits::NTuple{2,Tuple} # Stores the two points which defines the range of
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10 # the e.g (-1,0) and (1,2) for a domain of size
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11 # (-1,1)x(0,2)
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12
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13 # General constructor
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14 function EquidistantGrid(nPointsPerDim::Tuple, lims::NTuple{2,Tuple})
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15 @assert length(nPointsPerDim) > 0
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16 @assert count(x -> x > 0, nPointsPerDim) == length(nPointsPerDim)
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17 @assert length(lims[1]) == length(nPointsPerDim)
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18 @assert length(lims[2]) == length(nPointsPerDim)
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19 # TODO: Assert that the same values are not passed in both lims[1] and lims[2]
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20 # i.e the domain length is positive for all dimensions
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21 return new(nPointsPerDim, lims)
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22 end
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23 # 1D constructor which can be called as EquidistantGrid(m, (xl,xr))
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24 function EquidistantGrid(nPointsPerDim::Integer, lims::NTuple{2,Real})
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25 return EquidistantGrid((nPointsPerDim,), ((lims[1],),(lims[2],)))
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26 end
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27
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28 end
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29
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30 # Returns the number of dimensions of an EquidistantGrid.
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31 #
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32 # @Input: grid - an EquidistantGrid
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33 # @Return: numberOfPoints - The number of dimensions
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34 function numberOfDimensions(grid::EquidistantGrid)
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35 return length(grid.numberOfPointsPerDim)
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36 end
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37
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38 # Computes the total number of points of an EquidistantGrid.
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39 #
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40 # @Input: grid - an EquidistantGrid
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41 # @Return: numberOfPoints - The total number of points
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42 function numberOfPoints(grid::EquidistantGrid)
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43 numberOfPoints = grid.numberOfPointsPerDim[1];
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44 for i = 2:length(grid.numberOfPointsPerDim);
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45 numberOfPoints = numberOfPoints*grid.numberOfPointsPerDim[i]
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46 end
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47 return numberOfPoints
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48 end
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49
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50 # Computes the grid spacing of an EquidistantGrid, i.e the unsigned distance
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51 # between two points for each coordinate direction.
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52 #
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53 # @Input: grid - an EquidistantGrid
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54 # @Return: h̄ - Grid spacing for each coordinate direction stored in a tuple.
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55 function spacings(grid::EquidistantGrid)
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56 h̄ = Vector{Real}(undef, numberOfDimensions(grid))
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57 for i ∈ eachindex(h̄)
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58 h̄[i] = abs(grid.limits[2][i]-grid.limits[1][i])/(grid.numberOfPointsPerDim[i]-1)
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59 end
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60 return Tuple(h̄)
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61 end
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62
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63 # Computes the points of an EquidistantGrid as a vector of tuples. The vector is ordered
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64 # such that points in the first coordinate direction varies first, then the second
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65 # and lastely the third (if applicable)
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66 #
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67 # @Input: grid - an EquidistantGrid
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68 # @Return: points - the points of the grid.
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69 function points(grid::EquidistantGrid)
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70 # Compute signed grid spacings
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71 dx̄ = Vector{Real}(undef, numberOfDimensions(grid))
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72 for i ∈ eachindex(dx̄)
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73 dx̄[i] = (grid.limits[2][i]-grid.limits[1][i])/(grid.numberOfPointsPerDim[i]-1)
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74 end
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75 dx̄ = Tuple(dx̄)
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76
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77 points = Vector{NTuple{numberOfDimensions(grid),Real}}(undef, numberOfPoints(grid))
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78 # Compute the points based on their Cartesian indices and the signed
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79 # grid spacings
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80 cartesianIndices = CartesianIndices(grid.numberOfPointsPerDim)
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81 for i ∈ 1:numberOfPoints(grid)
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82 ci = Tuple(cartesianIndices[i]) .-1
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83 points[i] = grid.limits[1] .+ dx̄.*ci
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84 end
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85 # TBD: Keep? this? How do we want to represent points in 1D?
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86 if numberOfDimensions(grid) == 1
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87 points = broadcast(x -> x[1], points)
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88 end
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89 return points
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90 end
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91
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92 function pointsalongdim(grid::EquidistantGrid, dim::Integer)
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93 @assert dim<=numberOfDimensions(grid)
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94 @assert dim>0
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95 points = range(grid.limits[1][dim],stop=grid.limits[2][dim],length=grid.numberOfPointsPerDim[dim])
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96 end
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97
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98 using PyPlot, PyCall
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99 # using Plots; pyplot()
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100
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101 function plotgridfunction(grid::EquidistantGrid, gridfunction)
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102 if numberOfDimensions(grid) == 1
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103 plot(pointsalongdim(grid,1), gridfunction, linewidth=2.0)
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104 elseif numberOfDimensions(grid) == 2
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105 mx = grid.numberOfPointsPerDim[1];
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106 my = grid.numberOfPointsPerDim[2];
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107 x = pointsalongdim(grid,1)
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108 X = repeat(x,1,my)
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109 y = pointsalongdim(grid,2)
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110 Y = repeat(y,1,mx)
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111 # plot_surface(X,Y,reshape(gridfunction,mx,my))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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112 fig = figure()
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
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113 ax = fig[:add_subplot](1,1,1, projection = "3d")
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
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114 ax[:plot_surface](X,Y,reshape(gridfunction,mx,my))
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
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115 plt[:show]()
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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116 else
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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117 error(string("Plot not implemented for dimension ", string(numberOfDimensions(grid))))
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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118 end
614b56a017b9 Split grid.jl into AbstractGrid.jl and EquidistantGrid.jl
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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119 end