diff --git a/docs/src/kerr_geodesic_summary.md b/docs/src/kerr_geodesic_summary.md index bcd1c43..1c1f29d 100644 --- a/docs/src/kerr_geodesic_summary.md +++ b/docs/src/kerr_geodesic_summary.md @@ -116,7 +116,10 @@ The Hamilton-Jacobi Equations then reduce to four first order differential equat \end{align} ``` where we have defined the Mino time by its relationship to the affine parameter; -$$d\tau=d\tilde\tau/\Sigma.$$ + +```math +d\tau=d\tilde\tau/\Sigma. +``` Equations (15)-(18) define a 'Kepler-like' problem for photons in the Kerr spacetime. The Mino time here acts similar to the Keplerian coordinate time in that problem, and can be expressed either in terms of $r$ or $\theta$ using equations (15) and (16); diff --git a/examples/coordinate-example.jl b/examples/coordinate-example.jl index 143a814..f29c177 100644 --- a/examples/coordinate-example.jl +++ b/examples/coordinate-example.jl @@ -25,7 +25,7 @@ curr_theme = Theme( set_theme!(merge!(curr_theme, theme_latexfonts())) # We will use a 0.99 spin Kerr black hole viewed by an asymptotic observer at an inclination angle of θo=π/4. -# A region spanned by radii between the horizon and 10M at varying inclinations will be raytraced onto the 20Mx20M +# A region spanned by radii between the horizon and 10M at varying inclinations will be raytraced onto the 15x15 # screen of the observer. @@ -47,7 +47,7 @@ axes_list = [ ] -# Initialize Camera and Pre-Allocate Memory for data to be plotted +# Initialize Camera and pre-allocate memory for data to be plotted coordinates = (zeros(sze, sze) for _ in 1:3) camera = Krang.SlowLightIntensityCamera(metric, θo, -ρmax, ρmax, -ρmax, ρmax, sze); colormaps = (:afmhot, :afmhot, :hsv) diff --git a/notebook_examples/coordinate-example.ipynb b/notebook_examples/coordinate-example.ipynb index 772c9eb..f879c9d 100644 --- a/notebook_examples/coordinate-example.ipynb +++ b/notebook_examples/coordinate-example.ipynb @@ -48,7 +48,7 @@ "cell_type": "markdown", "source": [ "We will use a 0.99 spin Kerr black hole viewed by an asymptotic observer at an inclination angle of θo=π/4.\n", - "A region spanned by radii between the horizon and 20M at varying inclinations will be raytraced onto the 20Mx20M\n", + "A region spanned by radii between the horizon and 10M at varying inclinations will be raytraced onto the 15x15\n", "screen of the observer." ], "metadata": {} @@ -110,7 +110,7 @@ { "cell_type": "markdown", "source": [ - "Initialize Camera and Pre-Allocate Memory for data to be plotted" + "Initialize Camera and pre-allocate memory for data to be plotted" ], "metadata": {} }, @@ -128,7 +128,7 @@ "cell_type": "code", "source": [ "coordinates = (zeros(sze, sze) for _ in 1:3)\n", - "camera = Krang.SlowLightIntensityCamera(metric, θo, -ρmax, ρmax, -ρmax, ρmax, sze, A=Matrix);\n", + "camera = Krang.SlowLightIntensityCamera(metric, θo, -ρmax, ρmax, -ρmax, ρmax, sze);\n", "colormaps = (:afmhot, :afmhot, :hsv)\n", "colorrange = ((-20, 20), (0, rmax), (0, 2π))" ], @@ -264,7 +264,7 @@ "```julia\n", "using CUDA\n", "\n", - "rendered_scene = coordinate_point.(CuArray(camera.screen.pixels), Ref(geometry))\n", + "rendered_scene = Array(coordinate_point.(CuArray(camera.screen.pixels), Ref(geometry)))\n", "```" ], "metadata": {} diff --git a/notebook_examples/custom-material-example.ipynb b/notebook_examples/custom-material-example.ipynb index e8e1a7b..4410910 100644 --- a/notebook_examples/custom-material-example.ipynb +++ b/notebook_examples/custom-material-example.ipynb @@ -115,7 +115,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "(Krang.Mesh{Krang.ConeGeometry{Float64, Nothing}, Main.var\"##131077\".ZAMORedshifts{Float64}}(Krang.ConeGeometry{Float64, Nothing}(1.3089969389957472, nothing), Main.var\"##131077\".ZAMORedshifts{Float64}(1, 1.141067359796659, 10.0)),)" + "text/plain": "(Krang.Mesh{Krang.ConeGeometry{Float64, Nothing}, Main.var\"##131431\".ZAMORedshifts{Float64}}(Krang.ConeGeometry{Float64, Nothing}(1.3089969389957472, nothing), Main.var\"##131431\".ZAMORedshifts{Float64}(1, 1.141067359796659, 10.0)),)" }, "metadata": {}, "execution_count": 5 diff --git a/notebook_examples/mino-time-example.ipynb b/notebook_examples/mino-time-example.ipynb index b20167c..3228877 100644 --- a/notebook_examples/mino-time-example.ipynb +++ b/notebook_examples/mino-time-example.ipynb @@ -11,29 +11,36 @@ "cell_type": "markdown", "source": [ "In this example, we will raytrace the region around a Kerr black hole as seen by an observer stationed at infinity.\n", - "We will show the emission coordinates of the n=0 (direct) and n=1 (indirect) photons as they are emitted from the\n", - "source, at a fixed inclination angle from the black hole's spin axis.\n", + "We will return the coordinates associated with a ray by marching along the ray's Mino time parameter from the assymptotic observer.\n", "\n", "First, let's import Krang and CairoMakie for plotting." ], "metadata": {} }, { - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": "true" - }, - "metadata": {}, - "execution_count": 1 - } - ], + "outputs": [], "cell_type": "code", "source": [ "using Krang\n", "import GLMakie as GLMk\n", - "GLMk.Makie.inline!(true)" + "GLMk.Makie.inline!(true)\n", + "\n", + "curr_theme = GLMk.Theme(# Makie theme\n", + " fontsize=20,\n", + " Axis=(\n", + " xticksvisible=false,\n", + " xticklabelsvisible=false,\n", + " yticksvisible=false,\n", + " yticklabelsvisible=false,\n", + " leftspinevisible=false,\n", + " rightspinevisible=false,\n", + " topspinevisible=false,\n", + " bottomspinevisible=false,\n", + " titlefontsize=30,\n", + " ),\n", + ")\n", + "\n", + "GLMk.set_theme!(GLMk.merge(curr_theme, GLMk.theme_latexfonts()))" ], "metadata": {}, "execution_count": 1 @@ -41,9 +48,7 @@ { "cell_type": "markdown", "source": [ - "We will use a 0.99 spin Kerr black hole viewed by an asymptotic observer at an inclination angle of θo=π/4.\n", - "A region spanned by radii between the horizon and 20M at varying inclinations will be raytraced onto the 20Mx20M\n", - "screen of the observer." + "We will use a 0.99 spin Kerr black hole viewed by an asymptotic observer at an inclination angle of θo=π/4." ], "metadata": {} }, @@ -54,8 +59,6 @@ "metric = Krang.Kerr(0.99); # Kerr spacetime with 0.99 spin\n", "θo = 85 * π / 180; # Observer inclination angle with respect to spin axis\n", "sze = 200; # Number of pixels along each axis of the screen\n", - "rmin = Krang.horizon(metric); # Minimal radius to raytrace\n", - "rmax = 10; # Maximal radius to raytrace\n", "ρmax = 5; # Size of the screen" ], "metadata": {}, @@ -66,7 +69,7 @@ "source": [ "We will define a camera with the above parameters.\n", "The SlowLightIntensityCamera pre-calculates information about the spacetime and the observer's screen to speed up the\n", - "raytracing for slowlight applications." + "raytracing for slow light applications." ], "metadata": {} }, @@ -82,7 +85,7 @@ { "cell_type": "markdown", "source": [ - "Let us now create a figure to plot the emission coordinates on," + "Let us now create a figure to plot the emission coordinates on." ], "metadata": {} }, @@ -99,23 +102,6 @@ ], "cell_type": "code", "source": [ - "curr_theme = GLMk.Theme(# Makie theme\n", - " fontsize=20,\n", - " Axis=(\n", - " xticksvisible=false,\n", - " xticklabelsvisible=false,\n", - " yticksvisible=false,\n", - " yticklabelsvisible=false,\n", - " leftspinevisible=false,\n", - " rightspinevisible=false,\n", - " topspinevisible=false,\n", - " bottomspinevisible=false,\n", - " titlefontsize=30,\n", - " ),\n", - ")\n", - "\n", - "GLMk.set_theme!(GLMk.merge(curr_theme, GLMk.theme_latexfonts()))\n", - "\n", "fig = GLMk.Figure(resolution=(500, 600));" ], "metadata": {}, @@ -124,8 +110,7 @@ { "cell_type": "markdown", "source": [ - "and use this figure make an animation by looping over the inclination angle θs.\n", - "This loop will plot the emission coordinates for each θs." + "We will create a loop to plot the emission coordinates for each θs." ], "metadata": {} }, @@ -155,7 +140,7 @@ " data = (time, radius, inclination, azimuth)\n", " titles = (GLMk.L\"\\text{Regularized Time }(t_s)\", GLMk.L\"\\text{Radius }(r_s)\", GLMk.L\"\\text{Inclination }(\\theta_s)\", GLMk.L\"\\text{Azimuth } (\\phi_s)\")\n", " colormaps = (:afmhot, :afmhot, :afmhot, :hsv)\n", - " colorrange = ((-20, 20), (0, rmax), (0,π), (0, 2π))\n", + " colorrange = ((-20, 20), (0, 10.0), (0,π), (0, 2π))\n", " indices = ((1,1), ())\n", "\n", " for i in 1:4\n", diff --git a/notebook_examples/neural-net-example.ipynb b/notebook_examples/neural-net-example.ipynb index 582a2a0..e24de1a 100644 --- a/notebook_examples/neural-net-example.ipynb +++ b/notebook_examples/neural-net-example.ipynb @@ -214,7 +214,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "WARNING: using ComponentArrays.Axis in module ##131080 conflicts with an existing identifier.\n" + "WARNING: using ComponentArrays.Axis in module ##131434 conflicts with an existing identifier.\n" ] } ], diff --git a/notebook_examples/raytracing-mesh-example.ipynb b/notebook_examples/raytracing-mesh-example.ipynb index e4fdf7b..9636002 100644 --- a/notebook_examples/raytracing-mesh-example.ipynb +++ b/notebook_examples/raytracing-mesh-example.ipynb @@ -12,7 +12,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "Krang.SlowLightIntensityCamera{Float64, Matrix{Krang.SlowLightIntensityPixel{Float64}}}(Krang.Kerr{Float64}(1.0, 0.99), Krang.SlowLightIntensityScreen{Float64, Matrix{Krang.SlowLightIntensityPixel{Float64}}}((-12.0, 12.0), (-12.0, 12.0), Krang.SlowLightIntensityPixel{Float64}[Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, -12.0), (-17.811393086775468 - 3.6622313808008166e-17im, 0.3222351305493678 + 1.2554506945771609e-15im, 1.5419781346644301 - 1.2759301128716357e-15im, 15.947179821561672 + 5.7101732102483e-17im), 0.10027124075812203, 3.1948265198800945, 7.300113474580925, -2.1933076951002244, -13.17634564256269, -0.2458426263266534, -0.14259682643912724, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, 12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, -11.757575757575758), (-17.638476027306 - 2.5119566969130612e-17im, 0.31478822909250326 + 8.454330522229745e-16im, 1.5466851612338912 - 8.596354078342111e-16im, 15.777002636979606 + 3.932192258036724e-17im), 0.101372414125879, 3.16735588607714, 7.200050727203687, -2.1843464618842914, -13.041084896738482, -0.24555855578357275, -0.1430989095121752, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, 12.0) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, 11.757575757575758), (-17.638476027306 - 2.5119566969130612e-17im, 0.31478822909250326 + 8.454330522229745e-16im, 1.5466851612338912 - 8.596354078342111e-16im, 15.777002636979606 + 3.932192258036724e-17im), 0.101372414125879, 3.16735588607714, 7.200050727203687, -2.1843464618842914, -13.041084896738482, -0.24555855578357275, -0.1430989095121752, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, 12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, 12.0), (-17.811393086775468 - 3.6622313808008166e-17im, 0.3222351305493678 + 1.2554506945771609e-15im, 1.5419781346644301 - 1.2759301128716357e-15im, 15.947179821561672 + 5.7101732102483e-17im), 0.10027124075812203, 3.1948265198800945, 7.300113474580925, -2.1933076951002244, -13.17634564256269, -0.2458426263266534, -0.14259682643912724, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, 12.0); Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, -12.0), (-17.640437321470174 - 2.4530065262927946e-17im, 0.3305713202666105 + 8.45498564627043e-16im, 1.534155704198172 - 8.593965268063113e-16im, 15.775710297005391 + 3.842802744219619e-17im), 0.1013823110504783, 3.2477381116067705, 7.025903203700722, -2.182974372020287, -13.040840967779726, -0.2535489935759499, -0.14584785744144382, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, 11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, -11.757575757575758), (-17.465724293757646 - 2.5252190636852947e-17im, 0.32306161221907637 + 8.542281192425115e-16im, 1.5388774673628065 - 8.68697217553463e-16im, 15.603785214175762 + 3.9721288947804355e-17im), 0.10251985582662307, 3.2192884868709597, 6.92595757190612, -2.173824128209073, -12.904166251891354, -0.2532463985867103, -0.14637960398006838, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, 11.757575757575758) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, 11.757575757575758), (-17.465724293757646 - 2.5252190636852947e-17im, 0.32306161221907637 + 8.542281192425115e-16im, 1.5388774673628065 - 8.68697217553463e-16im, 15.603785214175762 + 3.9721288947804355e-17im), 0.10251985582662307, 3.2192884868709597, 6.92595757190612, -2.173824128209073, -12.904166251891354, -0.2532463985867103, -0.14637960398006838, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, 11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, 12.0), (-17.640437321470174 - 2.4530065262927946e-17im, 0.3305713202666105 + 8.45498564627043e-16im, 1.534155704198172 - 8.593965268063113e-16im, 15.775710297005391 + 3.842802744219619e-17im), 0.1013823110504783, 3.2477381116067705, 7.025903203700722, -2.182974372020287, -13.040840967779726, -0.2535489935759499, -0.14584785744144382, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, 11.757575757575758); … ; Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, -12.0), (-17.781479386402786 - 4.969222631444887e-17im, 0.26163540322435885 + 1.2663858277683034e-15im, 1.9482024385129888 - 1.3015057232471788e-15im, 15.57164154466544 + 8.48121217933244e-17im), 0.103156828843341, -1.7925822533610245, 23.940178550610657, -2.206246964058812, -12.98400431167325, -0.12329863072332145, -0.090263065858183, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, -11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, -11.757575757575758), (-17.609506000215994 - 3.408011043629016e-17im, 0.25504723925106276 + 8.529391086302426e-16im, 1.959574258655218 - 8.774316195876013e-16im, 15.394884502309713 + 5.857262139364886e-17im), 0.10437921921156745, -1.7722671921105388, 23.738179537197063, -2.1976301247423478, -12.845399511775305, -0.12290682708752478, -0.09028812494436153, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, -11.757575757575758) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, 11.757575757575758), (-17.609506000215994 - 3.408011043629016e-17im, 0.25504723925106276 + 8.529391086302426e-16im, 1.959574258655218 - 8.774316195876013e-16im, 15.394884502309713 + 5.857262139364886e-17im), 0.10437921921156745, -1.7722671921105388, 23.738179537197063, -2.1976301247423478, -12.845399511775305, -0.12290682708752478, -0.09028812494436153, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, -11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, 12.0), (-17.781479386402786 - 4.969222631444887e-17im, 0.26163540322435885 + 1.2663858277683034e-15im, 1.9482024385129888 - 1.3015057232471788e-15im, 15.57164154466544 + 8.48121217933244e-17im), 0.103156828843341, -1.7925822533610245, 23.940178550610657, -2.206246964058812, -12.98400431167325, -0.12329863072332145, -0.090263065858183, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, -11.757575757575758); Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, -12.0), (-17.952668704272526 - 3.2765377669138564e-17im, 0.25561836422800255 + 8.357723444881215e-16im, 1.9534780245174446 - 8.5861149839102065e-16im, 15.743572315527079 + 5.560453157203775e-17im), 0.10200223134145532, -1.7809590013311702, 24.074212683041594, -2.2160995622595325, -13.12017807786004, -0.12114996795799929, -0.08885191284558384, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, -12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, -11.757575757575758), (-17.7824416240653 - 5.053263097256706e-17im, 0.24910086974177226 + 1.2662896490723065e-15im, 1.9646605627738465 - 1.3020934455761203e-15im, 15.568680191549678 + 8.63364274763809e-17im), 0.1031843291537721, -1.7612081103544948, 23.875316012316453, -2.207649485347096, -12.98305147895367, -0.12077580730248855, -0.08887616558388427, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, -12.0) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, 11.757575757575758), (-17.7824416240653 - 5.053263097256706e-17im, 0.24910086974177226 + 1.2662896490723065e-15im, 1.9646605627738465 - 1.3020934455761203e-15im, 15.568680191549678 + 8.63364274763809e-17im), 0.1031843291537721, -1.7612081103544948, 23.875316012316453, -2.207649485347096, -12.98305147895367, -0.12077580730248855, -0.08887616558388427, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, -12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, 12.0), (-17.952668704272526 - 3.2765377669138564e-17im, 0.25561836422800255 + 8.357723444881215e-16im, 1.9534780245174446 - 8.5861149839102065e-16im, 15.743572315527079 + 5.560453157203775e-17im), 0.10200223134145532, -1.7809590013311702, 24.074212683041594, -2.2160995622595325, -13.12017807786004, -0.12114996795799929, -0.08885191284558384, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, -12.0)]), (Inf, 1.5707963267948966))" + "text/plain": "Krang.SlowLightIntensityCamera{Float64, Matrix{Krang.SlowLightIntensityPixel{Float64}}}(Krang.Kerr{Float64}(1.0, 0.99), Krang.SlowLightIntensityScreen{Float64, Matrix{Krang.SlowLightIntensityPixel{Float64}}}((-12.0, 12.0), (-12.0, 12.0), Krang.SlowLightIntensityPixel{Float64}[Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, -12.0), (-17.811393086775468 - 3.6622313808008166e-17im, 0.3222351305493678 + 1.2554506945771609e-15im, 1.5419781346644301 - 1.2759301128716357e-15im, 15.947179821561672 + 5.7101732102483e-17im), 0.10027124075812203, 0.20054248151624407, 3.1948265198800945, 7.300113474580925, -2.1933076951002244, -13.17634564256269, -0.2458426263266534, -0.14259682643912724, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, 12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, -11.757575757575758), (-17.638476027306 - 2.5119566969130612e-17im, 0.31478822909250326 + 8.454330522229745e-16im, 1.5466851612338912 - 8.596354078342111e-16im, 15.777002636979606 + 3.932192258036724e-17im), 0.101372414125879, 0.202744828251758, 3.16735588607714, 7.200050727203687, -2.1843464618842914, -13.041084896738482, -0.24555855578357275, -0.1430989095121752, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, 12.0) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, 11.757575757575758), (-17.638476027306 - 2.5119566969130612e-17im, 0.31478822909250326 + 8.454330522229745e-16im, 1.5466851612338912 - 8.596354078342111e-16im, 15.777002636979606 + 3.932192258036724e-17im), 0.101372414125879, 0.202744828251758, 3.16735588607714, 7.200050727203687, -2.1843464618842914, -13.041084896738482, -0.24555855578357275, -0.1430989095121752, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, 12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-12.0, 12.0), (-17.811393086775468 - 3.6622313808008166e-17im, 0.3222351305493678 + 1.2554506945771609e-15im, 1.5419781346644301 - 1.2759301128716357e-15im, 15.947179821561672 + 5.7101732102483e-17im), 0.10027124075812203, 0.20054248151624407, 3.1948265198800945, 7.300113474580925, -2.1933076951002244, -13.17634564256269, -0.2458426263266534, -0.14259682643912724, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, 12.0); Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, -12.0), (-17.640437321470174 - 2.4530065262927946e-17im, 0.3305713202666105 + 8.45498564627043e-16im, 1.534155704198172 - 8.593965268063113e-16im, 15.775710297005391 + 3.842802744219619e-17im), 0.1013823110504783, 0.2027646221009566, 3.2477381116067705, 7.025903203700722, -2.182974372020287, -13.040840967779726, -0.2535489935759499, -0.14584785744144382, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, 11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, -11.757575757575758), (-17.465724293757646 - 2.5252190636852947e-17im, 0.32306161221907637 + 8.542281192425115e-16im, 1.5388774673628065 - 8.68697217553463e-16im, 15.603785214175762 + 3.9721288947804355e-17im), 0.10251985582662307, 0.20503971165324614, 3.2192884868709597, 6.92595757190612, -2.173824128209073, -12.904166251891354, -0.2532463985867103, -0.14637960398006838, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, 11.757575757575758) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, 11.757575757575758), (-17.465724293757646 - 2.5252190636852947e-17im, 0.32306161221907637 + 8.542281192425115e-16im, 1.5388774673628065 - 8.68697217553463e-16im, 15.603785214175762 + 3.9721288947804355e-17im), 0.10251985582662307, 0.20503971165324614, 3.2192884868709597, 6.92595757190612, -2.173824128209073, -12.904166251891354, -0.2532463985867103, -0.14637960398006838, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, 11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (-11.757575757575758, 12.0), (-17.640437321470174 - 2.4530065262927946e-17im, 0.3305713202666105 + 8.45498564627043e-16im, 1.534155704198172 - 8.593965268063113e-16im, 15.775710297005391 + 3.842802744219619e-17im), 0.1013823110504783, 0.2027646221009566, 3.2477381116067705, 7.025903203700722, -2.182974372020287, -13.040840967779726, -0.2535489935759499, -0.14584785744144382, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, 11.757575757575758); … ; Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, -12.0), (-17.781479386402786 - 4.969222631444887e-17im, 0.26163540322435885 + 1.2663858277683034e-15im, 1.9482024385129888 - 1.3015057232471788e-15im, 15.57164154466544 + 8.48121217933244e-17im), 0.103156828843341, 0.206313657686682, -1.7925822533610245, 23.940178550610657, -2.206246964058812, -12.98400431167325, -0.12329863072332145, -0.090263065858183, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, -11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, -11.757575757575758), (-17.609506000215994 - 3.408011043629016e-17im, 0.25504723925106276 + 8.529391086302426e-16im, 1.959574258655218 - 8.774316195876013e-16im, 15.394884502309713 + 5.857262139364886e-17im), 0.10437921921156745, 0.2087584384231349, -1.7722671921105388, 23.738179537197063, -2.1976301247423478, -12.845399511775305, -0.12290682708752478, -0.09028812494436153, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, -11.757575757575758) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, 11.757575757575758), (-17.609506000215994 - 3.408011043629016e-17im, 0.25504723925106276 + 8.529391086302426e-16im, 1.959574258655218 - 8.774316195876013e-16im, 15.394884502309713 + 5.857262139364886e-17im), 0.10437921921156745, 0.2087584384231349, -1.7722671921105388, 23.738179537197063, -2.1976301247423478, -12.845399511775305, -0.12290682708752478, -0.09028812494436153, (0.0, 0.1890203905949582), (5.207905202559685e-18, 0.2675319714243842), (1.4665239682731889e-15, 0.047328338742640384), 1.5707963267948966, 138.24058769513314, -11.757575757575758) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (11.757575757575758, 12.0), (-17.781479386402786 - 4.969222631444887e-17im, 0.26163540322435885 + 1.2663858277683034e-15im, 1.9482024385129888 - 1.3015057232471788e-15im, 15.57164154466544 + 8.48121217933244e-17im), 0.103156828843341, 0.206313657686682, -1.7925822533610245, 23.940178550610657, -2.206246964058812, -12.98400431167325, -0.12329863072332145, -0.090263065858183, (0.0, 0.18707522107719277), (5.102694996447354e-18, 0.26752176320486787), (1.4669344203343482e-15, 0.047793721890844104), 1.5707963267948966, 144.0, -11.757575757575758); Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, -12.0), (-17.952668704272526 - 3.2765377669138564e-17im, 0.25561836422800255 + 8.357723444881215e-16im, 1.9534780245174446 - 8.5861149839102065e-16im, 15.743572315527079 + 5.560453157203775e-17im), 0.10200223134145532, 0.20400446268291064, -1.7809590013311702, 24.074212683041594, -2.2160995622595325, -13.12017807786004, -0.12114996795799929, -0.08885191284558384, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, -12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, -11.757575757575758), (-17.7824416240653 - 5.053263097256706e-17im, 0.24910086974177226 + 1.2662896490723065e-15im, 1.9646605627738465 - 1.3020934455761203e-15im, 15.568680191549678 + 8.63364274763809e-17im), 0.1031843291537721, 0.2063686583075442, -1.7612081103544948, 23.875316012316453, -2.207649485347096, -12.98305147895367, -0.12077580730248855, -0.08887616558388427, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, -12.0) … Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, 11.757575757575758), (-17.7824416240653 - 5.053263097256706e-17im, 0.24910086974177226 + 1.2662896490723065e-15im, 1.9646605627738465 - 1.3020934455761203e-15im, 15.568680191549678 + 8.63364274763809e-17im), 0.1031843291537721, 0.2063686583075442, -1.7612081103544948, 23.875316012316453, -2.207649485347096, -12.98305147895367, -0.12077580730248855, -0.08887616558388427, (0.0, 0.18708517002259337), (5.207905202559688e-18, 0.26212388077819737), (1.497074218783015e-15, 0.04588827118022064), 1.5707963267948966, 138.24058769513314, -12.0) Krang.SlowLightIntensityPixel{Float64}(Krang.Kerr{Float64}(1.0, 0.99), (12.0, 12.0), (-17.952668704272526 - 3.2765377669138564e-17im, 0.25561836422800255 + 8.357723444881215e-16im, 1.9534780245174446 - 8.5861149839102065e-16im, 15.743572315527079 + 5.560453157203775e-17im), 0.10200223134145532, 0.20400446268291064, -1.7809590013311702, 24.074212683041594, -2.2160995622595325, -13.12017807786004, -0.12114996795799929, -0.08885191284558384, (0.0, 0.18519854383797518), (5.102694996447269e-18, 0.2621141790545372), (1.4968675014460734e-15, 0.04636852782576966), 1.5707963267948966, 144.0, -12.0)]), (Inf, 1.5707963267948966))" }, "metadata": {}, "execution_count": 1