{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using LinearAlgebra\n",
"using Plots\n",
"import JSON\n",
"# using Quaternions\n",
"using StaticArrays, Rotations\n",
"using Distributed\n",
"using StaticArrays, BenchmarkTools\n",
"using Base.Threads\n",
"using CUDAnative\n",
"using CuArrays,CUDAdrv \n",
"using Test\n",
"import Base: +, * , -, ^"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Todo\n",
"- create struct for material and get for each edge its properties\n",
"- implement getTimestep (done)\n",
"- implement on single voxel (done)\n",
"- get reat E and L (done)\n",
"- compare to Frame3dd"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"struct Vector3\n",
" x::Float64\n",
" y::Float64\n",
" z::Float64\n",
" function Vector3()\n",
" x=0.0\n",
" y=0.0\n",
" z=0.0\n",
" new(x,y,z)\n",
" end\n",
" function Vector3(x,y,z)\n",
" new(x,y,z)\n",
" end\n",
"end\n",
"struct Quaternion\n",
" x::Float64\n",
" y::Float64\n",
" z::Float64\n",
" w::Float64\n",
" function Quaternion()\n",
" x=0.0\n",
" y=0.0\n",
" z=0.0\n",
" w=1.0\n",
" new(x,y,z,w)\n",
" end\n",
" function Quaternion(x,y,z,w)\n",
" new(x,y,z,w)\n",
" end\n",
"end\n",
"struct RotationMatrix\n",
" te1::Float64\n",
" te2::Float64\n",
" te3::Float64\n",
" te4::Float64\n",
" te5::Float64\n",
" te6::Float64\n",
" te7::Float64\n",
" te8::Float64\n",
" te9::Float64\n",
" te10::Float64\n",
" te11::Float64\n",
" te12::Float64\n",
" te13::Float64\n",
" te14::Float64\n",
" te15::Float64\n",
" te16::Float64\n",
" function RotationMatrix()\n",
" te1 =0.0\n",
" te2 =0.0\n",
" te3 =0.0\n",
" te4 =0.0\n",
" te5 =0.0\n",
" te6 =0.0\n",
" te7 =0.0\n",
" te8 =0.0\n",
" te9 =0.0\n",
" te10=0.0\n",
" te11=0.0\n",
" te12=0.0\n",
" te13=0.0\n",
" te14=0.0\n",
" te15=0.0\n",
" te16=0.0\n",
" new(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
" end\n",
" function RotationMatrix(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
" new(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
" end\n",
"end\n",
"\n",
"+(f::Vector3, g::Vector3)=Vector3(f.x+g.x , f.y+g.y,f.z+g.z )\n",
"-(f::Vector3, g::Vector3)=Vector3(f.x-g.x , f.y-g.y,f.z-g.z )\n",
"*(f::Vector3, g::Vector3)=Vector3(f.x*g.x , f.y*g.y,f.z*g.z )\n",
"\n",
"+(f::Vector3, g::Number)=Vector3(f.x+g , f.y+g,f.z+g )\n",
"-(f::Vector3, g::Number)=Vector3(f.x-g , f.y-g,f.z-g )\n",
"*(f::Vector3, g::Number)=Vector3(f.x*g , f.y*g,f.z*g )\n",
"\n",
"+(g::Vector3, f::Number)=Vector3(f.x+g , f.y+g,f.z+g )\n",
"-(g::Vector3, f::Number)=Vector3(g-f.x , g-f.y,g-f.z )\n",
"*(g::Vector3, f::Number)=Vector3(f.x*g , f.y*g,f.z*g )\n",
"\n",
"addX(f::Vector3, g::Number)=Vector3(f.x+g , f.y,f.z)\n",
"addY(f::Vector3, g::Number)=Vector3(f.x , f.y+g,f.z )\n",
"addZ(f::Vector3, g::Number)=Vector3(f.x , f.y,f.z+g )\n",
"\n",
"function normalizeVector3(f::Vector3)\n",
" leng=sqrt((f.x * f.x) + (f.y * f.y) + (f.z * f.z))\n",
" return Vector3(f.x/leng,f.y/leng,f.z/leng)\n",
" \n",
"end\n",
"function normalizeQuaternion(f::Quaternion)\n",
" l = sqrt((f.x * f.x) + (f.y * f.y) + (f.z * f.z)+ (f.w * f.w))\n",
" if l === 0 \n",
" qx = 0\n",
" qy = 0\n",
" qz = 0\n",
" qw = 1\n",
" else \n",
" l = 1 / l\n",
" qx = f.x * l\n",
" qy = f.y * l\n",
" qz = f.z * l\n",
" qw = f.w * l\n",
" end\n",
" return Quaternion(qx,qy,qz,qw)\n",
"end\n",
"\n",
"function normalizeQuaternion1!(fx::Float64,fy::Float64,fz::Float64,fw::Float64)\n",
" l = sqrt((fx * fx) + (fy * fy) + (fz * fz)+ (fw * fw))\n",
" if l === 0 \n",
" qx = 0.0\n",
" qy = 0.0\n",
" qz = 0.0\n",
" qw = 1.0\n",
" else \n",
" l = 1.0 / l\n",
" qx = fx * l\n",
" qy = fy * l\n",
" qz = fz * l\n",
" qw = fw * l\n",
" end\n",
" return qx,qy,qz,qw\n",
"end\n",
"\n",
"\n",
"function dotVector3(f::Vector3, g::Vector3)\n",
" return (f.x * g.x) + (f.y * g.y) + (f.z * g.z)\n",
"end\n",
"\n",
"function Base.show(io::IO, v::Vector3)\n",
" print(io, \"x:$(v.x), y:$(v.y), z:$(v.z)\")\n",
"end\n",
"\n",
"function Base.show(io::IO, v::Quaternion)\n",
" print(io, \"x:$(v.x), y:$(v.y), z:$(v.z), w:$(v.z)\")\n",
"end\n",
"\n",
"Base.Broadcast.broadcastable(q::Vector3) = Ref(q)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"simulateParallel (generic function with 2 methods)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function simulateParallel(numTimeSteps,dt)\n",
" # initialize(setup)\n",
" \n",
" for i in 1:numTimeSteps\n",
" #println(\"Timestep:\",i)\n",
" doTimeStep(dt,i)\n",
" end\n",
"end\n",
"\n",
"function simulateParallel(metavoxel,numTimeSteps,dt)\n",
" # initialize(setup)\n",
" \n",
" for i in 1:numTimeSteps\n",
" #println(\"Timestep:\",i)\n",
" doTimeStep(metavoxel,dt,i)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"initialize (generic function with 1 method)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function initialize(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
"\n",
" i=1\n",
" # pre-calculate current position\n",
" for node in nodes\n",
" # element=parse(Int,node[\"id\"][2:end])\n",
" N_position[i]=Vector3(node[\"position\"][\"x\"]/100.0,node[\"position\"][\"y\"]/100.0,node[\"position\"][\"z\"]/100.0)\n",
" N_restrained[i]=node[\"restrained_degrees_of_freedom\"][1] ## todo later consider other degrees of freedom\n",
" N_displacement[i]=Vector3(node[\"displacement\"][\"x\"],node[\"displacement\"][\"y\"],node[\"displacement\"][\"z\"])\n",
" N_angle[i]=Vector3(node[\"angle\"][\"x\"],node[\"angle\"][\"y\"],node[\"angle\"][\"z\"])\n",
" N_force[i]=Vector3(node[\"force\"][\"x\"]/1,node[\"force\"][\"y\"]/1,node[\"force\"][\"z\"]/1)\n",
" N_currPosition[i]=Vector3(node[\"position\"][\"x\"]/100.0,node[\"position\"][\"y\"]/100.0,node[\"position\"][\"z\"]/100.0)\n",
"\n",
" # for dynamic simulations\n",
" # append!(N_posTimeSteps,[[]])\n",
" # append!(N_angTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
"\n",
" i=1\n",
" # pre-calculate the axis\n",
" for edge in edges\n",
" # element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
"\n",
" node1 = [fromNode[\"position\"][\"x\"]/100.0 fromNode[\"position\"][\"y\"]/100.0 fromNode[\"position\"][\"z\"]/100.0]\n",
" node2 = [toNode[\"position\"][\"x\"]/100.0 toNode[\"position\"][\"y\"]/100.0 toNode[\"position\"][\"z\"]/100.0]\n",
"\n",
" length=norm(node2-node1)\n",
" axis=normalize(collect(Iterators.flatten(node2-node1)))\n",
"\n",
" E_source[i]=edge[\"source\"]+1\n",
" E_target[i]=edge[\"target\"]+1\n",
" E_area[i]=edge[\"area\"]\n",
" E_density[i]=edge[\"density\"]\n",
" E_stiffness[i]=edge[\"stiffness\"]\n",
" E_axis[i]=Vector3(axis[1],axis[2],axis[3])\n",
" E_currentRestLength[i]=length #?????????? todo change\n",
"# E_currentRestLength[i]=75/sqrt(2)\n",
"\n",
" N_edgeID[E_source[i],N_currEdge[E_source[i]]]=i\n",
" N_edgeFirst[E_source[i],N_currEdge[E_source[i]]]=true\n",
" N_currEdge[E_source[i]]+=1\n",
"\n",
" N_edgeID[E_target[i],N_currEdge[E_target[i]]]=i\n",
" N_edgeFirst[E_target[i],N_currEdge[E_target[i]]]=false\n",
" N_currEdge[E_target[i]]+=1\n",
"\n",
"\n",
" # for dynamic simulations\n",
" # append!(E_stressTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"doTimeStep! (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function doTimeStep(dt,currentTimeStep)\n",
" # update forces: go through edges, get currentposition from nodes, calc pos2 and update stresses and interior forces of nodes\n",
" run_updateEdges!(\n",
" E_sourceGPU, \n",
" E_targetGPU,\n",
" E_areaGPU,\n",
" E_densityGPU,\n",
" E_stiffnessGPU,\n",
" E_stressGPU,\n",
" E_axisGPU,\n",
" E_currentRestLengthGPU,\n",
" E_pos2GPU,\n",
" E_angle1vGPU,\n",
" E_angle2vGPU,\n",
" E_angle1GPU,\n",
" E_angle2GPU,\n",
" E_intForce1GPU,\n",
" E_intMoment1GPU,\n",
" E_intForce2GPU,\n",
" E_intMoment2GPU,\n",
" E_dampGPU,\n",
" N_currPositionGPU,\n",
" N_orientGPU)\n",
" \n",
" # update forces: go through nodes and update interior force (according to int forces from edges), integrate and update currpos\n",
" run_updateNodes!(dt,currentTimeStep,\n",
" N_positionGPU, \n",
" N_restrainedGPU,\n",
" N_displacementGPU,\n",
" N_angleGPU,\n",
" N_currPositionGPU,\n",
" N_linMomGPU,\n",
" N_angMomGPU,\n",
" N_intForceGPU,\n",
" N_intMomentGPU,\n",
" N_forceGPU,\n",
" N_momentGPU,\n",
" N_orientGPU,\n",
" N_edgeIDGPU, \n",
" N_edgeFirstGPU, \n",
" E_intForce1GPU,\n",
" E_intMoment1GPU,\n",
" E_intForce2GPU,\n",
" E_intMoment2GPU)\n",
" \n",
"end\n",
"\n",
"function doTimeStep!(metavoxel,dt,currentTimeStep)\n",
" # update forces: go through edges, get currentposition from nodes, calc pos2 and update stresses and interior forces of nodes\n",
" run_updateEdges!(\n",
" metavoxel[\"E_sourceGPU\"], \n",
" metavoxel[\"E_targetGPU\"],\n",
" metavoxel[\"E_areaGPU\"],\n",
" metavoxel[\"E_densityGPU\"],\n",
" metavoxel[\"E_stiffnessGPU\"],\n",
" metavoxel[\"E_stressGPU\"],\n",
" metavoxel[\"E_axisGPU\"],\n",
" metavoxel[\"E_currentRestLengthGPU\"],\n",
" metavoxel[\"E_pos2GPU\"],\n",
" metavoxel[\"E_angle1vGPU\"],\n",
" metavoxel[\"E_angle2vGPU\"],\n",
" metavoxel[\"E_angle1GPU\"],\n",
" metavoxel[\"E_angle2GPU\"],\n",
" metavoxel[\"E_intForce1GPU\"],\n",
" metavoxel[\"E_intMoment1GPU\"],\n",
" metavoxel[\"E_intForce2GPU\"],\n",
" metavoxel[\"E_intMoment2GPU\"],\n",
" metavoxel[\"E_dampGPU\"],\n",
" metavoxel[\"N_currPositionGPU\"],\n",
" metavoxel[\"N_orientGPU\"])\n",
" \n",
" # update forces: go through nodes and update interior force (according to int forces from edges), integrate and update currpos\n",
" run_updateNodes!(dt,currentTimeStep,\n",
" metavoxel[\"N_positionGPU\"], \n",
" metavoxel[\"N_restrainedGPU\"],\n",
" metavoxel[\"N_displacementGPU\"],\n",
" metavoxel[\"N_angleGPU\"],\n",
" metavoxel[\"N_currPositionGPU\"],\n",
" metavoxel[\"N_linMomGPU\"],\n",
" metavoxel[\"N_angMomGPU\"],\n",
" metavoxel[\"N_intForceGPU\"],\n",
" metavoxel[\"N_intMomentGPU\"],\n",
" metavoxel[\"N_forceGPU\"],\n",
" metavoxel[\"N_momentGPU\"],\n",
" metavoxel[\"N_orientGPU\"],\n",
" metavoxel[\"N_edgeIDGPU\"], \n",
" metavoxel[\"N_edgeFirstGPU\"], \n",
" metavoxel[\"E_intForce1GPU\"],\n",
" metavoxel[\"E_intMoment1GPU\"],\n",
" metavoxel[\"E_intForce2GPU\"],\n",
" metavoxel[\"E_intMoment2GPU\"])\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"run_updateEdges! (generic function with 1 method)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateEdges!(E_source,E_target,E_area,E_density,E_stiffness,E_stress,E_axis,\n",
" E_currentRestLength,E_pos2,E_angle1v,E_angle2v,\n",
" E_angle1,E_angle2,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2,E_damp,\n",
" N_currPosition,N_orient)\n",
"\n",
" index = (blockIdx().x - 1) * blockDim().x + threadIdx().x\n",
" stride = blockDim().x * gridDim().x\n",
" ## @cuprintln(\"thread $index, block $stride\")\n",
" N=length(E_source)\n",
" for i = index:stride:N\n",
" \n",
" @inbounds pVNeg=N_currPosition[E_source[i]]\n",
" @inbounds pVPos=N_currPosition[E_target[i]]\n",
" \n",
" @inbounds oVNeg=N_orient[E_source[i]]\n",
" @inbounds oVPos=N_orient[E_target[i]]\n",
" \n",
" @inbounds oldPos2=Vector3(E_pos2[i].x,E_pos2[i].y,E_pos2[i].z) #?copy?\n",
" @inbounds oldAngle1v = Vector3(E_angle1v[i].x,E_angle1v[i].y,E_angle1v[i].z)\n",
" @inbounds oldAngle2v = Vector3(E_angle2v[i].x,E_angle2v[i].y,E_angle2v[i].z)# remember the positions/angles from last timestep to calculate velocity\n",
" \n",
" \n",
" @inbounds E_pos2[i],E_angle1v[i],E_angle2v[i],E_angle1[i],E_angle2[i],totalRot= orientLink!(E_currentRestLength[i],pVNeg,pVPos,oVNeg,oVPos,E_axis[i])\n",
" \n",
" @inbounds dPos2 = Vector3(0.5,0.5,0.5) * (E_pos2[i]-oldPos2) #deltas for local damping. velocity at center is half the total velocity\n",
" @inbounds dAngle1 = Vector3(0.5,0.5,0.5) *(E_angle1v[i]-oldAngle1v)\n",
" @inbounds dAngle2 = Vector3(0.5,0.5,0.5) *(E_angle2v[i]-oldAngle2v)\n",
" \n",
" \n",
" @inbounds strain=(E_pos2[i].x/E_currentRestLength[i])\n",
" \n",
" positiveEnd=true\n",
" if axialStrain( positiveEnd,strain)>100.0\n",
" diverged=true\n",
" @cuprintln(\"DIVERGED!!!!!!!!!!\")\n",
" return \n",
" end\n",
" \n",
" @inbounds E = E_stiffness[i]\n",
" \n",
" \n",
" \n",
" @inbounds l = E_currentRestLength[i]\n",
" \n",
" \n",
" nu=0\n",
"# L = 5.0 #?? change!!!!!!\n",
" L=l\n",
" a1 = E*L # EA/L : Units of N/m\n",
" a2 = E * L*L*L / (12.0*(1+nu)) # GJ/L : Units of N-m\n",
" b1 = E*L # 12EI/L^3 : Units of N/m\n",
" b2 = E*L*L/2.0 # 6EI/L^2 : Units of N (or N-m/m: torque related to linear distance)\n",
" b3 = E*L*L*L/6.0 # 2EI/L : Units of N-m\n",
" \n",
" nu=0.35\n",
" W = 75\n",
"# L = W/sqrt(2)\n",
" l=L\n",
" n_min = 1\n",
" n_max = 7\n",
" # Cross Section inputs, must be floats\n",
" mass=125000 #before for voxel\n",
" mass=1\n",
" E = 2000e9 # MPa\n",
" G = E * 1 / 3 # MPa\n",
" h = 2.38/100.0 # mm\n",
" b = 2.38/100.0 # mm\n",
" rho = 7.85e-9 / 3 # kg/mm^3\n",
" S = h * b\n",
" Sy = (S * (6 + 12 * nu + 6 * nu^2)/ (7 + 12 * nu + 4 * nu^2))\n",
" # For solid rectangular cross section (width=b, depth=d & ( b < d )):\n",
" Q = 1 / 3 - 0.2244 / (min(h / b, b / h) + 0.1607)\n",
" Jxx = Q * min(h * b^3, b * h^3)\n",
" s=b\n",
" \n",
" MaxFreq2=E*s/mass\n",
" dt= 1/(6.283185*sqrt(MaxFreq2))\n",
"\n",
"\n",
" ##if voxels\n",
" #nu=0\n",
" #L=l\n",
" #a1 = E*L # EA/L : Units of N/m\n",
" #a2 = E * L*L*L / (12.0*(1+nu)) # GJ/L : Units of N-m\n",
" #b1 = E*L # 12EI/L^3 : Units of N/m\n",
" #b2 = E*L*L/2.0 # 6EI/L^2 : Units of N (or N-m/m: torque related to linear distance)\n",
" #b3 = E*L*L*L/6.0 # 2EI/L : Units of N-m\n",
"\n",
" I= b*h^3/12\n",
" J=b*h*(b*b+h*h)/12\n",
" a1=E*b*h/L\n",
" a2=G*J/L\n",
" b1=12*E*I/(L^3)\n",
" b2=6*E*I/(L^2)\n",
" b3=2*E*I/(L)\n",
" \n",
" \n",
"\n",
" \n",
" #inbounds currentTransverseArea=25.0 #?? change!!!!!! E_area[i]\n",
" @inbounds currentTransverseArea= b*h\n",
" @inbounds _stress=updateStrain(strain,E)\n",
" \n",
" #@inbounds currentTransverseArea= E_area[i]\n",
" #@inbounds _stress=updateStrain(strain,E_stiffness[i])\n",
" \n",
" @inbounds E_stress[i]=_stress\n",
" \n",
" #@cuprintln(\"_stress $_stress\")\n",
" x=(_stress*currentTransverseArea)\n",
" @inbounds y=(b1*E_pos2[i].y-b2*(E_angle1v[i].z + E_angle2v[i].z))\n",
" @inbounds z=(b1*E_pos2[i].z + b2*(E_angle1v[i].y + E_angle2v[i].y))\n",
" \n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" # Use Curstress instead of -a1*Pos2.x to account for non-linear deformation \n",
" forceNeg = Vector3(x,y,z)\n",
" \n",
" forcePos = Vector3(-x,-y,-z)\n",
" \n",
" @inbounds x= (a2*(E_angle2v[i].x-E_angle1v[i].x))\n",
" @inbounds y= (-b2*E_pos2[i].z-b3*(2.0*E_angle1v[i].y+E_angle2v[i].y))\n",
" @inbounds z=(b2*E_pos2[i].y - b3*(2.0*E_angle1v[i].z + E_angle2v[i].z)) \n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" momentNeg = Vector3(x,y,z)\n",
" \n",
"\n",
" @inbounds x= (a2*(E_angle1v[i].x-E_angle2v[i].x))\n",
" @inbounds y= (-b2*E_pos2[i].z- b3*(E_angle1v[i].y+2.0*E_angle2v[i].y))\n",
" @inbounds z=(b2*E_pos2[i].y - b3*(E_angle1v[i].z + 2.0*E_angle2v[i].z))\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" momentPos = Vector3(x,y,z)\n",
" \n",
" \n",
" ### damping\n",
" @inbounds if E_damp[i] #first pass no damping\n",
" sqA1=CUDAnative.sqrt(a1) \n",
" sqA2xIp=CUDAnative.sqrt(a2*L*L/6.0) \n",
" sqB1=CUDAnative.sqrt(b1) \n",
" sqB2xFMp=CUDAnative.sqrt(b2*L/2) \n",
" sqB3xIp=CUDAnative.sqrt(b3*L*L/6.0)\n",
" \n",
" dampingMultiplier=Vector3(28099.3,28099.3,28099.3) # 2*mat->_sqrtMass*mat->zetaInternal/previousDt;?? todo link to material\n",
" \n",
" zeta=1\n",
" dampingM= 2*sqrt(mass)*zeta/dt\n",
" dampingMultiplier=Vector3(dampingM,dampingM,dampingM)\n",
" \n",
" posCalc=Vector3(sqA1*dPos2.x, sqB1*dPos2.y - sqB2xFMp*(dAngle1.z+dAngle2.z),sqB1*dPos2.z + sqB2xFMp*(dAngle1.y+dAngle2.y))\n",
" \n",
" \n",
" forceNeg =forceNeg + (dampingMultiplier*posCalc);\n",
" forcePos =forcePos - (dampingMultiplier*posCalc);\n",
"\n",
" momentNeg -= Vector3(0.5,0.5,0.5)*dampingMultiplier*Vector3(-sqA2xIp*(dAngle2.x - dAngle1.x),\n",
" sqB2xFMp*dPos2.z + sqB3xIp*(2*dAngle1.y + dAngle2.y),\n",
" -sqB2xFMp*dPos2.y + sqB3xIp*(2*dAngle1.z + dAngle2.z));\n",
" momentPos -= Vector3(0.5,0.5,0.5)*dampingMultiplier*Vector3(sqA2xIp*(dAngle2.x - dAngle1.x),\n",
" sqB2xFMp*dPos2.z + sqB3xIp*(dAngle1.y + 2*dAngle2.y),\n",
" -sqB2xFMp*dPos2.y + sqB3xIp*(dAngle1.z + 2*dAngle2.z));\n",
"\n",
" else\n",
" @inbounds E_damp[i]=true \n",
" end\n",
"\n",
" smallAngle=true\n",
" if !smallAngle # ?? check\n",
" @inbounds forceNeg = RotateVec3DInv(E_angle1[i],forceNeg)\n",
" @inbounds momentNeg = RotateVec3DInv(E_angle1[i],momentNeg)\n",
" end\n",
" \n",
" @inbounds forcePos = RotateVec3DInv(E_angle2[i],forcePos)\n",
" @inbounds momentPos = RotateVec3DInv(E_angle2[i],momentPos)\n",
"\n",
" @inbounds forceNeg =toAxisOriginalVector3(forceNeg,E_axis[i])\n",
" @inbounds forcePos =toAxisOriginalVector3(forcePos,E_axis[i])\n",
"\n",
" @inbounds momentNeg=toAxisOriginalQuat(momentNeg,E_axis[i])# TODOO CHECKKKKKK\n",
" @inbounds momentPos=toAxisOriginalQuat(momentPos,E_axis[i])\n",
"\n",
"\n",
" @inbounds E_intForce1[i] =forceNeg\n",
" @inbounds E_intForce2[i] =forcePos\n",
" \n",
"\n",
"\n",
" @inbounds x= momentNeg.x\n",
" @inbounds y= momentNeg.y\n",
" @inbounds z= momentNeg.z \n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" @inbounds E_intMoment1[i]=Vector3(x,y,z)\n",
"\n",
" @inbounds x= momentNeg.x\n",
" @inbounds y= momentNeg.y\n",
" @inbounds z= momentNeg.z\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" @inbounds E_intMoment2[i]=Vector3(x,y,z)\n",
" \n",
" #x=E_pos2[i].x*10000000000\n",
" #y=E_pos2[i].y*10000000000\n",
" #z=E_pos2[i].z*10000000000\n",
" #@cuprintln(\"pos2 x $x, y $y, z $z \")\n",
" ##x=E_intMoment2[i].x*10000000000\n",
" #y=E_intMoment2[i].y*10000000000\n",
" #z=E_intMoment2[i].z*10000000000\n",
" #@cuprintln(\"E_intMoment2 x $x, y $y, z $z \")\n",
"\n",
" \n",
" \n",
" end\n",
" return\n",
"end\n",
"\n",
"function run_updateEdges!(E_source,E_target,E_area,E_density,E_stiffness,\n",
" E_stress,E_axis,E_currentRestLength,E_pos2,E_angle1v,E_angle2v,\n",
" E_angle1,E_angle2,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2,\n",
" E_damp,N_currPosition,N_orient)\n",
" N=length(E_source)\n",
" numblocks = ceil(Int, N/256)\n",
" CuArrays.@sync begin\n",
" @cuda threads=256 blocks=numblocks updateEdges!(E_source,E_target,E_area,E_density,\n",
" E_stiffness,E_stress,E_axis,E_currentRestLength,E_pos2,E_angle1v,\n",
" E_angle2v,E_angle1,E_angle2,E_intForce1,E_intMoment1,E_intForce2,\n",
" E_intMoment2,E_damp,N_currPosition,N_orient)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"run_updateNodes! (generic function with 1 method)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateNodes!(dt,currentTimeStep,N_position, N_restrained,N_displacement,N_angle,N_currPosition,N_linMom,N_angMom,N_intForce,N_intMoment,N_force,N_moment,N_orient,N_edgeID,N_edgeFirst,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2)\n",
"\n",
" index = (blockIdx().x - 1) * blockDim().x + threadIdx().x\n",
" stride = blockDim().x * gridDim().x\n",
" ## @cuprintln(\"thread $index, block $stride\")\n",
" N,M=size(N_edgeID)\n",
" for i = index:stride:N\n",
" @inbounds if N_restrained[i]\n",
" return\n",
" else\n",
" for j in 1:M\n",
" temp=N_edgeID[i,j]\n",
" @inbounds if (N_edgeID[i,j]!=-1)\n",
" #@cuprintln(\"i $i, j $j, N_edgeID[i,j] $temp\")\n",
" @inbounds N_intForce[i]=ifelse(N_edgeFirst[i,j], N_intForce[i]+E_intForce1[N_edgeID[i,j]], N_intForce[i]+E_intForce2[N_edgeID[i,j]] )\n",
" @inbounds N_intMoment[i]=ifelse(N_edgeFirst[i,j], N_intMoment[i]+E_intMoment1[N_edgeID[i,j]], N_intMoment[i]+E_intMoment2[N_edgeID[i,j]] )\n",
" end\n",
" end\n",
" @inbounds curForce = force(N_intForce[i],N_orient[i],N_force[i],true,currentTimeStep)\n",
" \n",
" #@inbounds N_force[i]=Vector3(0,0,0) ##????\n",
" \n",
" @inbounds N_intForce[i]=Vector3(0,0,0)\n",
" \n",
" #x=curForce.x\n",
" #y=curForce.y\n",
" #z=curForce.z\n",
" #@cuprintln(\"curForce x $x, y $y, z $z \")\n",
" \n",
" #x=N_linMom[i].x*10000000000\n",
" #y=N_linMom[i].y*10000000000\n",
" #z=N_linMom[i].z*10000000000\n",
" #@cuprintln(\"N_linMom[i] x $x, y $y, z $z \")\n",
" \n",
" \n",
" @inbounds N_linMom[i]=N_linMom[i]+curForce*Vector3(dt,dt,dt) #todo make sure right\n",
" massInverse=8e-6 # todo ?? later change //8e-6\n",
" mass=1\n",
" massInverse=1.0/mass #\n",
" @inbounds translate=N_linMom[i]*Vector3((dt*massInverse),(dt*massInverse),(dt*massInverse)) # ??massInverse\n",
" \n",
" #x=translate.x*10000000000\n",
" #y=translate.y*10000000000\n",
" #z=translate.z*10000000000\n",
" #@cuprintln(\"translate x $x, y $y, z $z \")\n",
" \n",
" @inbounds N_currPosition[i]=N_currPosition[i]+translate\n",
" @inbounds N_displacement[i]=N_displacement[i]+translate\n",
" \n",
" \n",
" \n",
" # Rotation\n",
" @inbounds curMoment = moment(N_intMoment[i],N_orient[i],N_moment[i]) \n",
" \n",
" \n",
" \n",
" @inbounds N_intMoment[i]=Vector3(0,0,0) # do i really need it?\n",
" \n",
" @inbounds N_angMom[i]=N_angMom[i]+curMoment*Vector3(dt,dt,dt)\n",
" \n",
" \n",
" \n",
" \n",
" momentInertiaInverse=1.92e-6 # todo ?? later change 1/Inertia (1/(kg*m^2))\n",
" \n",
" \n",
" @inbounds temp=FromRotationVector(N_angMom[i]*Vector3((dt*momentInertiaInverse),(dt*momentInertiaInverse),(dt*momentInertiaInverse)))\n",
" \n",
" \n",
" #x=temp.x*10000000000\n",
" #y=temp.y*10000000000\n",
" #z=temp.z*10000000000\n",
" #@cuprintln(\"temp x $x, y $y, z $z \")\n",
" \n",
" @inbounds N_orient[i]=multiplyQuaternions(temp,N_orient[i])\n",
" \n",
" #@inbounds x= N_orient[i].x*temp.x\n",
" #@inbounds y= N_orient[i].y*temp.y\n",
" #@inbounds z= N_orient[i].z*temp.z\n",
" #@inbounds w= N_orient[i].w*temp.w\n",
" #x=convert(Float64,x)\n",
" #y=convert(Float64,y)\n",
" #z=convert(Float64,z)\n",
" #w=convert(Float64,w)\n",
" \n",
" #@inbounds N_orient[i]=Quaternion(x,y,z,w)\n",
" \n",
" #x=N_orient[i].x*10000000000\n",
" #y=N_orient[i].y*10000000000\n",
" #z=N_orient[i].z*10000000000\n",
" #w=N_orient[i].w\n",
" #@cuprintln(\"N_orient x $x, y $y, z $z, w $w \")\n",
" \n",
" \n",
" end\n",
" end\n",
" return\n",
"end\n",
"\n",
"\n",
"function run_updateNodes!(dt,currentTimeStep,N_position, N_restrained,N_displacement, N_angle,N_currPosition,N_linMom,N_angMom,N_intForce,N_intMoment,N_force,N_moment,N_orient,N_edgeID,N_edgeFirst,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2)\n",
" N=length(N_intForce)\n",
" numblocks = ceil(Int, N/256)\n",
" CuArrays.@sync begin\n",
" @cuda threads=256 blocks=numblocks updateNodes!(dt,currentTimeStep,N_position, N_restrained,N_displacement, N_angle,N_currPosition,N_linMom,N_angMom,N_intForce,N_intMoment,N_force,N_moment,N_orient,N_edgeID,N_edgeFirst,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"orientLink! (generic function with 1 method)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function orientLink!(currentRestLength,pVNeg,pVPos,oVNeg,oVPos,axis) # updates pos2, angle1, angle2, and smallAngle //Quat3D<double> /*double restLength*/\n",
" \n",
" pos2 = toAxisXVector3(pVPos-pVNeg,axis) # digit truncation happens here...\n",
" angle1 = toAxisXQuat(oVNeg,axis)\n",
" angle2 = toAxisXQuat(oVPos,axis)\n",
" \n",
" #x=pos2.x*10000000000\n",
" #y=pos2.y*10000000000\n",
" #z=pos2.z*10000000000\n",
" #@cuprintln(\"pos2 x $x, y $y, z $z \")\n",
" \n",
" #x=angle1.x*10000000000\n",
" #y=angle1.y*10000000000\n",
" #z=angle1.z*10000000000\n",
" #@cuprintln(\"angle1 x $x, y $y, z $z \")\n",
" #x=oVNeg.x*10000000000\n",
" #y=oVNeg.y*10000000000\n",
" #z=oVNeg.z*10000000000\n",
" #@cuprintln(\"oVNeg x $x, y $y, z $z \")\n",
" \n",
" \n",
" \n",
" totalRot = conjugate(angle1) #keep track of the total rotation of this bond (after toAxisX()) # Quat3D<double>\n",
" pos2 = RotateVec3D(totalRot,pos2)\n",
" \n",
" #x=pos2.x*10000000000\n",
" #y=pos2.y*10000000000\n",
" #z=pos2.z*10000000000\n",
" #@cuprintln(\"pos2 2 x $x, y $y, z $z \")\n",
" \n",
" \n",
" #x=totalRot.x*10000000000\n",
" #y=totalRot.y*10000000000\n",
" #z=totalRot.z*10000000000\n",
" #@cuprintln(\"totalRot x $x, y $y, z $z \")\n",
" \n",
" \n",
"# x=pos2.x*10000000000\n",
"# y=pos2.y*10000000000\n",
"# z=pos2.z*10000000000\n",
"# @cuprintln(\"pos2 x $x, y $y, z $z \")\n",
" \n",
" angle2 = Quaternion(angle2.x*totalRot.x,angle2.y*totalRot.y,angle2.z*totalRot.z,angle2.w*totalRot.w)\n",
" angle1 = Quaternion(0.0,0.0,0.0,1.0)#new THREE.Quaternion() #zero for now...\n",
"\n",
" smallAngle=true #todo later remove\n",
" \n",
" \n",
" if (smallAngle)\t #Align so Angle1 is all zeros\n",
" #pos2[1] =pos2[1]- currentRestLength #only valid for small angles\n",
" pos2=Vector3(pos2.x-currentRestLength,pos2.y,pos2.z)\n",
" else #Large angle. Align so that Pos2.y, Pos2.z are zero.\n",
" # FromAngleToPosX(angle1,pos2) #get the angle to align Pos2 with the X axis\n",
" # totalRot = angle1.clone().multiply(totalRot) #update our total rotation to reflect this\n",
" # angle2 = angle1.clone().multiply( angle2) #rotate angle2\n",
" # pos2 = new THREE.Vector3(pos2.length() - currentRestLength, 0, 0);\n",
" end\n",
" \n",
" angle1v = ToRotationVector(angle1)\n",
" angle2v = ToRotationVector(angle2)\n",
" \n",
" \n",
" \n",
" \n",
"# pos2,angle1v,angle2v,angle1,angle2,\n",
" return pos2,angle1v,angle2v,angle1,angle2,totalRot\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"toAxisOriginalQuat (generic function with 1 method)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function toAxisXVector3(pV::Vector3,axis::Vector3) #TODO CHANGE\n",
"\n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
" q=setFromUnitVectors(vector,xaxis)\n",
" \n",
" \n",
" \n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
" \n",
" \n",
"# v= applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" \n",
" return Vector3(v.x,v.y,v.z)\n",
"end\n",
"\n",
"function toAxisOriginalVector3(pV::Vector3,axis::Vector3)\n",
" \n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
"\n",
" q=setFromUnitVectors(xaxis,vector)\n",
" \n",
"\n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
"\n",
"# v= applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" \n",
" return Vector3(v.x,v.y,v.z)\n",
"end\n",
"\n",
"function toAxisXQuat(pQ::Quaternion,axis::Vector3)\n",
" \n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
"\n",
"\n",
" q=setFromUnitVectors(vector,xaxis)\n",
" \n",
" #d=17\n",
" #qw=round(q[1], digits=d)\n",
" #qx=round(q[2], digits=d)\n",
" #qy=round(q[3], digits=d)\n",
" #qz=round(q[4], digits=d)\n",
" #\n",
"\n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
" \n",
" pV=Vector3(pQ.x,pQ.y,pQ.z)\n",
" \n",
"# v=applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" return Quaternion(v.x,v.y,v.z,1.0)\n",
" \n",
" # return [1.0 v[1] v[2] v[3]]\n",
"end\n",
"\n",
"function toAxisOriginalQuat(pQ::Vector3,axis::Vector3)\n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
" \n",
" q=setFromUnitVectors(xaxis,vector)\n",
" \n",
"\n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
" \n",
" pV=Vector3(pQ.x,pQ.y,pQ.z)\n",
"# v=applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" return Quaternion(v.x,v.y,v.z,1.0)\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"applyQuaternion1 (generic function with 1 method)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function setFromUnitVectors(vFrom::Vector3, vTo::Vector3)\n",
" # assumes direction vectors vFrom and vTo are normalized\n",
" EPS = 0.000000001;\n",
" r= dotVector3(vFrom,vTo)+1.0\n",
" # r = dot(vFrom,vTo)+1\n",
"\n",
" if r < EPS\n",
" r = 0;\n",
" if abs( vFrom.x ) > abs( vFrom.z ) \n",
" qx = - vFrom.y\n",
" qy = vFrom.x\n",
" qz = 0.0\n",
" qw = r\n",
" else \n",
" qx = 0.0\n",
" qy = -(vFrom.z)\n",
" qz = vFrom.y\n",
" qw = r\n",
" end\n",
" else \n",
" # crossVectors( vFrom, vTo ); // inlined to avoid cyclic dependency on Vector3\n",
" qx = vFrom.y * vTo.z - vFrom.z * vTo.y\n",
" qy = vFrom.z * vTo.x - vFrom.x * vTo.z\n",
" qz = vFrom.x * vTo.y - vFrom.y * vTo.x\n",
" qw = r\n",
"\n",
" end\n",
" qx= (qx==-0.0) ? 0.0 : qx\n",
" qy= (qy==-0.0) ? 0.0 : qy\n",
" qz= (qz==-0.0) ? 0.0 : qz\n",
" qw= (qw==-0.0) ? 0.0 : qw\n",
" \n",
" \n",
" mx=qx*qx\n",
" my=qy*qy\n",
" mz=qz*qz\n",
" mw=qw*qw\n",
" mm=mx+my\n",
" mm=mm+mz\n",
" mm=mm+mw\n",
" mm=convert(Float64,mm)#??????????????????? todo check later\n",
" \n",
" l=CUDAnative.sqrt(mm)\n",
" \n",
" #l = sqrt((qx * qx) + (qy * qy) + (qz * qz)+ (qw * qw))\n",
" if l === 0 \n",
" qx = 0.0\n",
" qy = 0.0\n",
" qz = 0.0\n",
" qw = 1.0\n",
" else \n",
" l = 1.0 / l\n",
" qx = qx * l\n",
" qy = qy * l\n",
" qz = qz * l\n",
" qw = qw * l\n",
" end\n",
" \n",
" \n",
"\n",
" # return qx,qy,qz,qw\n",
" return Quaternion(qx,qy,qz,qw)\n",
" \n",
" # return normalizeQ(Quat(qw,qx,qy,qz))\n",
" # return Quat(nn[1], nn[2], nn[3], nn[4])\n",
"\n",
"end\n",
"\n",
"function quatToMatrix( quaternion::Quaternion)\n",
"\n",
" #te = RotationMatrix()\n",
" \n",
" x = quaternion.x\n",
" y = quaternion.y\n",
" z = quaternion.z\n",
" w = quaternion.w\n",
" \n",
" x2 = x + x\n",
" y2 = y + y\n",
" z2 = z + z\n",
" xx = x * x2\n",
" xy = x * y2\n",
" xz = x * z2\n",
" yy = y * y2\n",
" yz = y * z2\n",
" zz = z * z2\n",
" wx = w * x2\n",
" wy = w * y2\n",
" wz = w * z2\n",
"\n",
" sx = 1.0\n",
" sy = 1.0\n",
" sz = 1.0\n",
"\n",
" te1 = ( 1.0 - ( yy + zz ) ) * sx\n",
" te2 = ( xy + wz ) * sx\n",
" te3 = ( xz - wy ) * sx\n",
" te4 = 0.0\n",
"\n",
" te5 = ( xy - wz ) * sy\n",
" te6 = ( 1.0 - ( xx + zz ) ) * sy\n",
" te7 = ( yz + wx ) * sy\n",
" te8 = 0.0\n",
"\n",
" te9 = ( xz + wy ) * sz\n",
" te10 = ( yz - wx ) * sz\n",
" te11 = ( 1.0 - ( xx + yy ) ) * sz\n",
" te12 = 0.0\n",
"\n",
" te13 = 0.0 #position.x;\n",
" te14 = 0.0 #position.y;\n",
" te15 = 0.0 #position.z;\n",
" te16 = 1.0\n",
" \n",
" \n",
" te= RotationMatrix(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
"\n",
" return te\n",
"\n",
"end\n",
"\n",
"function setFromRotationMatrix(m::RotationMatrix)\n",
" #te = m\n",
" #m11 = (te[ 1 ]== -0.0) ? 0.0 : te[ 1 ]\n",
" #m12 = (te[ 5 ]== -0.0) ? 0.0 : te[ 5 ]\n",
" #m13 = (te[ 9 ]== -0.0) ? 0.0 : te[ 9 ]\n",
" #m21 = (te[ 2 ]== -0.0) ? 0.0 : te[ 2 ]\n",
" #m22 = (te[ 6 ]== -0.0) ? 0.0 : te[ 6 ]\n",
" #m23 = (te[ 10]== -0.0) ? 0.0 : te[ 10]\n",
" #m31 = (te[ 3 ]== -0.0) ? 0.0 : te[ 3 ]\n",
" #m32 = (te[ 7 ]== -0.0) ? 0.0 : te[ 7 ]\n",
" #m33 = (te[ 11]== -0.0) ? 0.0 : te[ 11]\n",
"\n",
" m11 = convert(Float64,m.te1 )\n",
" m12 = convert(Float64,m.te5 )\n",
" m13 = convert(Float64,m.te9 )\n",
" m21 = convert(Float64,m.te2 )\n",
" m22 = convert(Float64,m.te6 )\n",
" m23 = convert(Float64,m.te10)\n",
" m31 = convert(Float64,m.te3 )\n",
" m32 = convert(Float64,m.te7 )\n",
" m33 = convert(Float64,m.te11)\n",
" \n",
"\n",
" y = CUDAnative.asin( clamp( m13, -1.0, 1.0 ) ) ##check if has to be changed to cuda\n",
"\n",
" if ( abs( m13 ) < 0.9999999999 ) \n",
" \n",
" x = CUDAnative.atan2( - m23, m33 )\n",
" z = CUDAnative.atan2( - m12, m11 )#-m12, m11\n",
" # if(m23==0.0)\n",
" # x = atan( m23, m33 )\n",
" # end\n",
" # if(m12==0.0)\n",
" # z = atan( m12, m11 )\n",
" # end\n",
"\n",
" else\n",
"\n",
" x = CUDAnative.atan2( m32, m22 )\n",
" z = 0.0;\n",
"\n",
" end\n",
" \n",
" \n",
" return Vector3(x,y,z)\n",
" \n",
"end\n",
"\n",
"function setQuaternionFromEuler(euler::Vector3)\n",
" x=euler.x\n",
" y=euler.y\n",
" z=euler.z\n",
" \n",
" \n",
" c1 = CUDAnative.cos( x / 2.0 )\n",
" c2 = CUDAnative.cos( y / 2.0 )\n",
" c3 = CUDAnative.cos( z / 2.0 )\n",
"\n",
" s1 = CUDAnative.sin( x / 2.0 )\n",
" s2 = CUDAnative.sin( y / 2.0 )\n",
" s3 = CUDAnative.sin( z / 2.0 )\n",
" \n",
" \n",
" x = s1 * c2 * c3 + c1 * s2 * s3\n",
" y = c1 * s2 * c3 - s1 * c2 * s3\n",
" z = c1 * c2 * s3 + s1 * s2 * c3\n",
" w = c1 * c2 * c3 - s1 * s2 * s3\n",
" \n",
" return Quaternion(x,y,z,w)\n",
"end\n",
"\n",
"function applyQuaternion1(e::Vector3,q2::Quaternion)\n",
" x = e.x\n",
" y = e.y\n",
" z = e.z\n",
"\n",
" qx = q2.x\n",
" qy = q2.y\n",
" qz = q2.z\n",
" qw = q2.w\n",
"\n",
" # calculate quat * vector\n",
"\n",
" ix = qw * x + qy * z - qz * y\n",
" iy = qw * y + qz * x - qx * z\n",
" iz = qw * z + qx * y - qy * x\n",
" iw = - qx * x - qy * y - qz * z\n",
"\n",
" # calculate result * inverse quat\n",
"\n",
" xx = ix * qw + iw * - qx + iy * - qz - iz * - qy\n",
" yy = iy * qw + iw * - qy + iz * - qx - ix * - qz\n",
" zz = iz * qw + iw * - qz + ix * - qy - iy * - qx\n",
" \n",
" d=15\n",
"\n",
" return Vector3(xx,yy,zz)\n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"multiplyQuaternions (generic function with 1 method)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function conjugate(q::Quaternion)\n",
" x= (-q.x==-0) ? 0.0 : -q.x\n",
" y= (-q.y==-0) ? 0.0 : -q.y\n",
" z= (-q.z==-0) ? 0.0 : -q.z\n",
" w=q.w\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" w=convert(Float64,w)\n",
" return Quaternion(x,y,z,w)\n",
"end\n",
"\n",
"function RotateVec3D(a::Quaternion, f::Vector3) \n",
" fx= (f.x==-0) ? 0 : f.x\n",
" fy= (f.y==-0) ? 0 : f.y\n",
" fz= (f.z==-0) ? 0 : f.z\n",
" # fx= f.x\n",
" # fy= f.y\n",
" # fz= f.z\n",
" tw = fx*a.x + fy*a.y + fz*a.z\n",
" tx = fx*a.w - fy*a.z + fz*a.y\n",
" ty = fx*a.z + fy*a.w - fz*a.x\n",
" tz = -fx*a.y + fy*a.x + fz*a.w\n",
"\n",
" return Vector3((a.w*tx+a.x*tw+a.y*tz-a.z*ty),(a.w*ty-a.x*tz+a.y*tw+a.z*tx),(a.w*tz+a.x*ty-a.y*tx+a.z*tw))\n",
"end\n",
"#!< Returns a vector representing the specified vector \"f\" rotated by this quaternion. @param[in] f The vector to transform.\n",
"\n",
"function RotateVec3DInv(a::Quaternion, f::Vector3) \n",
" fx=f.x\n",
" fy=f.y\n",
" fz=f.z\n",
" tw = a.x*fx + a.y*fy + a.z*fz\n",
" tx = a.w*fx - a.y*fz + a.z*fy\n",
" ty = a.w*fy + a.x*fz - a.z*fx\n",
" tz = a.w*fz - a.x*fy + a.y*fx\n",
" return Vector3((tw*a.x + tx*a.w + ty*a.z - tz*a.y),(tw*a.y - tx*a.z + ty*a.w + tz*a.x),(tw*a.z + tx*a.y - ty*a.x + tz*a.w))\n",
"end\n",
"#!< Returns a vector representing the specified vector \"f\" rotated by the inverse of this quaternion. This is the opposite of RotateVec3D. @param[in] f The vector to transform.\n",
"\n",
"function ToRotationVector(a::Quaternion) \n",
" if (a.w >= 1.0 || a.w <= -1.0) \n",
" return Vector3(0.0,0.0,0.0)\n",
" end\n",
" squareLength = 1.0-a.w*a.w; # because x*x + y*y + z*z + w*w = 1.0, but more susceptible to w noise (when \n",
" SLTHRESH_ACOS2SQRT= 2.4e-3; # SquareLength threshhold for when we can use square root optimization for acos. From SquareLength = 1-w*w. (calculate according to 1.0-W_THRESH_ACOS2SQRT*W_THRESH_ACOS2SQRT\n",
"\n",
" if (squareLength < SLTHRESH_ACOS2SQRT) # ???????\n",
" x=a.x*(2.0*CUDAnative.sqrt((2-2*a.w)/squareLength))\n",
" y=a.y*(2.0*CUDAnative.sqrt((2-2*a.w)/squareLength))\n",
" z=a.z*(2.0*CUDAnative.sqrt((2-2*a.w)/squareLength))\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" return Vector3(x,y,z) ; # acos(w) = sqrt(2*(1-x)) for w close to 1. for w=0.001, error is 1.317e-6\n",
" else \n",
" x=a.x*(2.0*CUDAnative.acos(a.w)/CUDAnative.sqrt(squareLength))\n",
" y=a.y*(2.0*CUDAnative.acos(a.w)/CUDAnative.sqrt(squareLength))\n",
" z=a.z*(2.0*CUDAnative.acos(a.w)/CUDAnative.sqrt(squareLength))\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
"\n",
" return Vector3(x,y,z)\n",
" end \n",
"end \n",
"# !< Returns a rotation vector representing this quaternion rotation. Adapted from http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/\n",
"\n",
"function FromRotationVector(VecIn::Vector3)\n",
" theta=VecIn*Vector3(0.5,0.5,0.5)\n",
" ntheta=CUDAnative.sqrt((theta.x * theta.x) + (theta.y * theta.y) + (theta.z * theta.z))\n",
" thetaMag2=ntheta*ntheta\n",
" \n",
" DBL_EPSILONx24 =5.328e-15\n",
" if thetaMag2*thetaMag2 < DBL_EPSILONx24\n",
" qw=1.0 - 0.5*thetaMag2\n",
"\t\ts=1.0 - thetaMag2 / 6.0\n",
" else\n",
" thetaMag = CUDAnative.sqrt(thetaMag2)\n",
"\t\tqw=CUDAnative.cos(thetaMag)\n",
"\t\ts=CUDAnative.sin(thetaMag) / thetaMag\n",
" end\n",
" qx=theta.x*s\n",
" qy=theta.y*s\n",
" qz=theta.z*s\n",
" \n",
" qx=convert(Float64,qx)\n",
" qy=convert(Float64,qy)\n",
" qz=convert(Float64,qz)\n",
" qw=convert(Float64,qw)\n",
" \n",
" return Quaternion(qx,qy,qz,qw)\n",
"end\n",
"\n",
"function multiplyQuaternions(q::Quaternion,f::Quaternion)\n",
" x=q.x\n",
" y=q.y\n",
" z=q.z\n",
" w=q.w\n",
" x1=w*f.x + x*f.w + y*f.z - z*f.y \n",
" y1=w*f.y - x*f.z + y*f.w + z*f.x\n",
" z1=w*f.z + x*f.y - y*f.x + z*f.w\n",
" w1=w*f.w - x*f.x - y*f.y - z*f.z\n",
"# x1=convert(Float64,x1)\n",
"# y1=convert(Float64,y1)\n",
"# z1=convert(Float64,z1)\n",
"# w1=convert(Float64,w1)\n",
"\treturn Quaternion(x1,y1,z1,w1 ); #!< overload quaternion multiplication.\n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"axialStrain (generic function with 1 method)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateStrain( axialStrain,E) # ?from where strain\n",
" strain = axialStrain # redundant?\n",
" currentTransverseStrainSum=0.0 # ??? todo\n",
" linear=true\n",
" maxStrain=1000000000000000;# ?? todo later change\n",
" if linear\n",
" if axialStrain > maxStrain\n",
" maxStrain = axialStrain # remember this maximum for easy reference\n",
" end\n",
" return stress(axialStrain,E)\n",
" else \n",
" if (axialStrain > maxStrain) # if new territory on the stress/strain curve\n",
" maxStrain = axialStrain # remember this maximum for easy reference\n",
" returnStress = stress(axialStrain,E) # ??currentTransverseStrainSum\n",
" if (nu != 0.0) \n",
" strainOffset = maxStrain-stress(axialStrain,E)/(_eHat*(1.0-nu)) # precalculate strain offset for when we back off\n",
" else \n",
" strainOffset = maxStrain-returnStress/E # precalculate strain offset for when we back off\n",
" end\n",
" else # backed off a non-linear material, therefore in linear region.\n",
" relativeStrain = axialStrain-strainOffset # treat the material as linear with a strain offset according to the maximum plastic deformation\n",
" if (nu != 0.0) \n",
" returnStress = stress(relativeStrain,E)\n",
" else \n",
" returnStress = E*relativeStrain\n",
" end\n",
" end\n",
" return returnStress\n",
" end\n",
"end\n",
"\n",
"function stress( strain , E ) #end,transverseStrainSum, forceLinear){\n",
" # reference: http://www.colorado.edu/engineering/CAS/courses.d/Structures.d/IAST.Lect05.d/IAST.Lect05.pdf page 10\n",
" # if (isFailed(strain)) return 0.0f; //if a failure point is set and exceeded, we've broken!\n",
" # var E =setup.edges[0].stiffness; //todo change later to material ??\n",
" # var E=1000000;//todo change later to material ??\n",
" # var scaleFactor=1;\n",
" return E*strain;\n",
"\n",
" # # if (strain <= strainData[1] || linear || forceLinear){ //for compression/first segment and linear materials (forced or otherwise), simple calculation\n",
"\n",
" # if (nu==0.0) return E*strain;\n",
" # else return _eHat*((1-nu)*strain + nu*transverseStrainSum); \n",
" # else return eHat()*((1-nu)*strain + nu*transverseStrainSum); \n",
" # # }\n",
"\n",
" #//the non-linear feature with non-zero poissons ratio is currently experimental\n",
" #int DataCount = modelDataPoints();\n",
" #for (int i=2; i<DataCount; i++){ //go through each segment in the material model (skipping the first segment because it has already been handled.\n",
" # if (strain <= strainData[i] || i==DataCount-1){ //if in the segment ending with this point (or if this is the last point extrapolate out) \n",
" # float Perc = (strain-strainData[i-1])/(strainData[i]-strainData[i-1]);\n",
" # float basicStress = stressData[i-1] + Perc*(stressData[i]-stressData[i-1]);\n",
" # if (nu==0.0f) return basicStress;\n",
" # else { //accounting for volumetric effects\n",
" # float modulus = (stressData[i]-stressData[i-1])/(strainData[i]-strainData[i-1]);\n",
" # float modulusHat = modulus/((1-2*nu)*(1+nu));\n",
" # float effectiveStrain = basicStress/modulus; //this is the strain at which a simple linear stress strain line would hit this point at the definied modulus\n",
" # float effectiveTransverseStrainSum = transverseStrainSum*(effectiveStrain/strain);\n",
" # return modulusHat*((1-nu)*effectiveStrain + nu*effectiveTransverseStrainSum);\n",
" # }\n",
" # }\n",
" #}\n",
"\n",
" # assert(false); //should never reach this point\n",
" # return 0.0f;\n",
"end \n",
"\n",
"function axialStrain( positiveEnd,strain)\n",
"\t#strainRatio = pVPos->material()->E/pVNeg->material()->E;\n",
"\tstrainRatio=1.0;\n",
"\treturn positiveEnd ? 2.0 *strain*strainRatio/(1.0+strainRatio) : 2.0*strain/(1.0+strainRatio)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"moment (generic function with 1 method)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function force(N_intForce,N_orient,N_force,static,currentTimeStep) \n",
" # forces from internal bonds\n",
" totalForce=Vector3(0,0,0)\n",
" # new THREE.Vector3(node.force.x,node.force.y,node.force.z);\n",
" # todo \n",
"\n",
"\n",
" totalForce=totalForce+N_intForce\n",
"\n",
" # for (int i=0; i<6; i++){ \n",
" # \tif (links[i]) totalForce += links[i]->force(isNegative((linkDirection)i)); # total force in LCS\n",
" # }\n",
" totalForce = RotateVec3D(N_orient,totalForce); # from local to global coordinates\n",
"\n",
"\n",
" # assert(!(totalForce.x != totalForce.x) || !(totalForce.y != totalForce.y) || !(totalForce.z != totalForce.z)); //assert non QNAN\n",
"\n",
" # other forces\n",
" if(static)\n",
" totalForce=totalForce+N_force\n",
" # }else if(currentTimeStep<50){\n",
" # \ttotalForce.add(new THREE.Vector3(node.force.x,node.force.y,node.force.z));\n",
" else\n",
" # var ex=0.1;\n",
" # if(node.force.y!=0){\n",
" # \tvar f=400*Math.sin(currentTimeStep*ex);\n",
" # \ttotalForce.add(new THREE.Vector3(0,f,0));\n",
"\n",
" # }\n",
" #x=N_position[node][3]\n",
" #t=currentTimeStep\n",
" #wave=getForce(x,t)\n",
" #totalForce=totalForce+[0 wave 0]\n",
" end\n",
"\n",
"\n",
" # if (externalExists()) totalForce += external()->force(); //external forces\n",
" # totalForce -= velocity()*mat->globalDampingTranslateC(); //global damping f-cv\n",
" # totalForce.z += mat->gravityForce(); //gravity, according to f=mg\n",
"\n",
" # if (isCollisionsEnabled()){\n",
" # \tfor (std::vector<CVX_Collision*>::iterator it=colWatch->begin(); it!=colWatch->end(); it++){\n",
" # \t\ttotalForce -= (*it)->contactForce(this);\n",
" # \t}\n",
" # }\n",
" # todo make internal forces 0 again\n",
" # N_intForce[node]=[0 0 0] # do i really need it?\n",
"\n",
" # node.force.x=0;\n",
" # node.force.y=0;\n",
" # node.force.z=0;\n",
"\n",
"\n",
" return totalForce\n",
"end\n",
"\n",
"\n",
"function moment(intMoment,orient,moment) \n",
" #moments from internal bonds\n",
" totalMoment=Vector3(0,0,0)\n",
" # for (int i=0; i<6; i++){ \n",
" # \tif (links[i]) totalMoment += links[i]->moment(isNegative((linkDirection)i)); //total force in LCS\n",
" # }\n",
"\n",
" totalMoment=totalMoment+intMoment\n",
" \n",
" \n",
"\n",
" totalMoment = RotateVec3D(orient,totalMoment);\n",
" \n",
" \n",
"\n",
" totalMoment=totalMoment+moment\n",
"\n",
"\n",
" #other moments\n",
" # if (externalExists()) totalMoment += external()->moment(); //external moments\n",
" # totalMoment -= angularVelocity()*mat->globalDampingRotateC(); //global damping\n",
"\n",
" return totalMoment\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"updateDataAndSave! (generic function with 1 method)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateDataAndSave!(metavoxel,setup,fileName)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" \n",
" setup[\"animation\"][\"showDisplacement\"]=false\n",
" voxCount=size(nodes)[1]\n",
" linkCount=size(edges)[1]\n",
" \n",
" N_displacement=Array(metavoxel[\"N_displacementGPU\"])\n",
" N_angle=Array(metavoxel[\"N_angleGPU\"])\n",
" E_stress=Array(metavoxel[\"E_stressGPU\"])\n",
" \n",
" setup[\"viz\"][\"maxStress\"]=maximum(E_stress)\n",
" setup[\"viz\"][\"minStress\"]=minimum(E_stress) \n",
"\n",
"\n",
" i=1\n",
"\tfor edge in edges\n",
" edge[\"stress\"]=E_stress[i]\n",
" i=i+1\n",
"\n",
" end\n",
" \n",
" \n",
" i=1 \n",
"\tfor node in nodes\n",
" node[\"displacement\"][\"x\"]=N_displacement[i].x*100\n",
" node[\"displacement\"][\"y\"]=N_displacement[i].y*100\n",
" node[\"displacement\"][\"z\"]=N_displacement[i].z*100\n",
" \n",
" node[\"angle\"][\"x\"]=N_angle[i].x\n",
" node[\"angle\"][\"y\"]=N_angle[i].y\n",
" node[\"angle\"][\"z\"]=N_angle[i].z\n",
" i=i+1\n",
"\n",
" end\n",
" \n",
" # pass data as a json string (how it shall be displayed in a file)\n",
" stringdata = JSON.json(setup)\n",
"\n",
" # write the file with the stringdata variable information\n",
" open(fileName, \"w\") do f\n",
" write(f, stringdata)\n",
" end\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"runMetavoxelGPU! (generic function with 1 method)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function runMetavoxelGPU!(setup,numTimeSteps,latticeSize,displacements,returnEvery,save)\n",
" function initialize!(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
"\n",
" i=1\n",
" # pre-calculate current position\n",
" for node in nodes\n",
" # element=parse(Int,node[\"id\"][2:end])\n",
" N_position[i]=Vector3(node[\"position\"][\"x\"]/100.0,node[\"position\"][\"y\"]/100.0,node[\"position\"][\"z\"]/100.0)\n",
" N_restrained[i]=node[\"restrained_degrees_of_freedom\"][1] ## todo later consider other degrees of freedom\n",
" N_displacement[i]=Vector3(node[\"displacement\"][\"x\"],node[\"displacement\"][\"y\"],node[\"displacement\"][\"z\"])\n",
" N_angle[i]=Vector3(node[\"angle\"][\"x\"],node[\"angle\"][\"y\"],node[\"angle\"][\"z\"])\n",
" N_force[i]=Vector3(node[\"force\"][\"x\"],node[\"force\"][\"y\"]/1,node[\"force\"][\"z\"])\n",
" N_currPosition[i]=Vector3(node[\"position\"][\"x\"]/100.0,node[\"position\"][\"y\"]/100.0,node[\"position\"][\"z\"]/100.0)\n",
"\n",
" # for dynamic simulations\n",
" # append!(N_posTimeSteps,[[]])\n",
" # append!(N_angTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
"\n",
" i=1\n",
" # pre-calculate the axis\n",
" for edge in edges\n",
" # element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
"\n",
" node1 = [fromNode[\"position\"][\"x\"]/100.0 fromNode[\"position\"][\"y\"]/100.0 fromNode[\"position\"][\"z\"]/100.0]\n",
" node2 = [toNode[\"position\"][\"x\"]/100.0 toNode[\"position\"][\"y\"]/100.0 toNode[\"position\"][\"z\"]/100.0]\n",
"\n",
" length=norm(node2-node1)\n",
" axis=normalize(collect(Iterators.flatten(node2-node1)))\n",
"\n",
" E_source[i]=edge[\"source\"]+1\n",
" E_target[i]=edge[\"target\"]+1\n",
" E_area[i]=edge[\"area\"]\n",
" E_density[i]=edge[\"density\"]\n",
" E_stiffness[i]=edge[\"stiffness\"]\n",
" E_axis[i]=Vector3(axis[1],axis[2],axis[3])\n",
" E_currentRestLength[i]=length #?????? todo change\n",
"# E_currentRestLength[i]=75/sqrt(2)\n",
" \n",
"\n",
" N_edgeID[E_source[i],N_currEdge[E_source[i]]]=i\n",
" N_edgeFirst[E_source[i],N_currEdge[E_source[i]]]=true\n",
" N_currEdge[E_source[i]]+=1\n",
"\n",
" N_edgeID[E_target[i],N_currEdge[E_target[i]]]=i\n",
" N_edgeFirst[E_target[i],N_currEdge[E_target[i]]]=false\n",
" N_currEdge[E_target[i]]+=1\n",
"\n",
"\n",
" # for dynamic simulations\n",
" # append!(E_stressTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
" end\n",
" function simulateParallel!(metavoxel,numTimeSteps,dt,returnEvery)\n",
" # initialize(setup)\n",
"\n",
" for i in 1:numTimeSteps\n",
" #println(\"Timestep:\",i)\n",
" doTimeStep!(metavoxel,dt,i)\n",
" if(mod(i,returnEvery)==0)\n",
" append!(displacements,[Array(metavoxel[\"N_displacementGPU\"])])\n",
" end\n",
" end\n",
" end\n",
" \n",
" ########\n",
" voxCount=0\n",
" linkCount=0\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" voxCount=size(nodes)[1]\n",
" linkCount=size(edges)[1]\n",
" strain =0 #todooo moveeee\n",
" maxNumEdges=10\n",
"\n",
" ########\n",
" voxCount=0\n",
" linkCount=0\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" voxCount=size(nodes)[1]\n",
" linkCount=size(edges)[1]\n",
" strain =0 #todooo moveeee\n",
"\n",
" ############# nodes\n",
" N_position=fill(Vector3(),voxCount)\n",
" N_restrained=zeros(Bool, voxCount)\n",
" N_displacement=fill(Vector3(),voxCount)\n",
" N_angle=fill(Vector3(),voxCount)\n",
" N_currPosition=fill(Vector3(),voxCount)\n",
" N_linMom=fill(Vector3(),voxCount)\n",
" N_angMom=fill(Vector3(),voxCount)\n",
" N_intForce=fill(Vector3(),voxCount)\n",
" N_intMoment=fill(Vector3(),voxCount)\n",
" N_moment=fill(Vector3(),voxCount)\n",
" # N_posTimeSteps=[]\n",
" # N_angTimeSteps=[]\n",
" N_force=fill(Vector3(),voxCount)\n",
" N_orient=fill(Quaternion(),voxCount)\n",
" N_edgeID=fill(-1,(voxCount,maxNumEdges))\n",
" N_edgeFirst=fill(true,(voxCount,maxNumEdges))\n",
" N_currEdge=fill(1,voxCount)\n",
"\n",
" ############# edges\n",
" E_source=fill(0,linkCount)\n",
" E_target=fill(0,linkCount)\n",
" E_area=fill(0.0f0,linkCount)\n",
" E_density=fill(0.0f0,linkCount)\n",
" E_stiffness=fill(0.0f0,linkCount)\n",
" E_stress=fill(0.0f0,linkCount)\n",
" E_axis=fill(Vector3(1.0,0.0,0.0),linkCount)\n",
" E_currentRestLength=fill(0.0f0,linkCount)\n",
" E_pos2=fill(Vector3(),linkCount)\n",
" E_angle1v=fill(Vector3(),linkCount)\n",
" E_angle2v=fill(Vector3(),linkCount)\n",
" E_angle1=fill(Quaternion(),linkCount)\n",
" E_angle2=fill(Quaternion(),linkCount)\n",
"\n",
" E_intForce1=fill(Vector3(),linkCount)\n",
" E_intMoment1=fill(Vector3(),linkCount) \n",
"\n",
" E_intForce2=fill(Vector3(),linkCount)\n",
" E_intMoment2=fill(Vector3(),linkCount)\n",
" E_damp=fill(false,linkCount)\n",
"\n",
" E_currentTransverseStrainSum=fill(0.0f0,linkCount)# TODO remove ot incorporate\n",
" # E_stressTimeSteps=[]\n",
"\n",
"\n",
" #################################################################\n",
" initialize!(setup)\n",
" #################################################################\n",
"\n",
" ########################## turn to cuda arrays\n",
" ############# nodes\n",
" N_positionGPU= CuArray(N_position) \n",
" N_restrainedGPU= CuArray(N_restrained) \n",
" N_displacementGPU=CuArray(N_displacement) \n",
" N_angleGPU= CuArray(N_angle) \n",
" N_currPositionGPU=CuArray(N_currPosition) \n",
" N_linMomGPU= CuArray(N_linMom) \n",
" N_angMomGPU= CuArray(N_angMom) \n",
" N_intForceGPU= CuArray(N_intForce) \n",
" N_intMomentGPU= CuArray(N_intMoment) \n",
" N_momentGPU= CuArray(N_moment) \n",
" N_forceGPU= CuArray(N_force) \n",
" N_orientGPU= CuArray(N_orient) \n",
" N_edgeIDGPU= CuArray(N_edgeID) \n",
" N_edgeFirstGPU= CuArray(N_edgeFirst) \n",
"\n",
"\n",
" ############# edges\n",
" E_sourceGPU= CuArray(E_source) \n",
" E_targetGPU= CuArray(E_target)\n",
" E_areaGPU= CuArray(E_area) \n",
" E_densityGPU= CuArray(E_density)\n",
" E_stiffnessGPU= CuArray(E_stiffness)\n",
" E_stressGPU= CuArray(E_stress)\n",
" E_axisGPU= CuArray(E_axis) \n",
" E_currentRestLengthGPU= CuArray(E_currentRestLength)\n",
" E_pos2GPU= CuArray(E_pos2)\n",
" E_angle1vGPU= CuArray(E_angle1v)\n",
" E_angle2vGPU= CuArray(E_angle2v)\n",
" E_angle1GPU= CuArray(E_angle1)\n",
" E_angle2GPU= CuArray(E_angle2)\n",
" E_currentTransverseStrainSumGPU=CuArray(E_currentTransverseStrainSum)\n",
" E_intForce1GPU= CuArray(E_intForce1) \n",
" E_intMoment1GPU= CuArray(E_intMoment1) \n",
" E_intForce2GPU= CuArray(E_intForce2) \n",
" E_intMoment2GPU= CuArray(E_intMoment2)\n",
" E_dampGPU= CuArray(E_damp) \n",
" # E_stressTimeSteps=[]\n",
"\n",
"\n",
" #########################################\n",
" metavoxel = Dict(\n",
" \"N_positionGPU\" => N_positionGPU, \n",
" \"N_restrainedGPU\" => N_restrainedGPU, \n",
" \"N_displacementGPU\" => N_displacementGPU,\n",
" \"N_angleGPU\" => N_angleGPU, \n",
" \"N_currPositionGPU\" => N_currPositionGPU,\n",
" \"N_linMomGPU\" => N_linMomGPU, \n",
" \"N_angMomGPU\" => N_angMomGPU, \n",
" \"N_intForceGPU\" => N_intForceGPU, \n",
" \"N_intMomentGPU\" => N_intMomentGPU, \n",
" \"N_momentGPU\" => N_momentGPU, \n",
" \"N_forceGPU\" => N_forceGPU, \n",
" \"N_orientGPU\" => N_orientGPU, \n",
" \"N_edgeIDGPU\" => N_edgeIDGPU, \n",
" \"N_edgeFirstGPU\" => N_edgeFirstGPU,\n",
" \"E_sourceGPU\" =>E_sourceGPU, \n",
" \"E_targetGPU\" =>E_targetGPU, \n",
" \"E_areaGPU\" =>E_areaGPU, \n",
" \"E_densityGPU\" =>E_densityGPU, \n",
" \"E_stiffnessGPU\" =>E_stiffnessGPU, \n",
" \"E_stressGPU\" =>E_stressGPU, \n",
" \"E_axisGPU\" =>E_axisGPU, \n",
" \"E_currentRestLengthGPU\" =>E_currentRestLengthGPU, \n",
" \"E_pos2GPU\" =>E_pos2GPU, \n",
" \"E_angle1vGPU\" =>E_angle1vGPU, \n",
" \"E_angle2vGPU\" =>E_angle2vGPU, \n",
" \"E_angle1GPU\" =>E_angle1GPU, \n",
" \"E_angle2GPU\" =>E_angle2GPU, \n",
" \"E_currentTransverseStrainSumGPU\" =>E_currentTransverseStrainSumGPU,\n",
" \"E_intForce1GPU\" =>E_intForce1GPU, \n",
" \"E_intMoment1GPU\" =>E_intMoment1GPU, \n",
" \"E_intForce2GPU\" =>E_intForce2GPU, \n",
" \"E_intMoment2GPU\" =>E_intMoment2GPU, \n",
" \"E_dampGPU\" =>E_dampGPU \n",
" )\n",
"\n",
" #########################################\n",
" \n",
"\n",
" dt=0.0251646\n",
" E = 2000e9 # MPa\n",
" s=2.38/100.0\n",
" mass=1 \n",
" \n",
" \n",
" \n",
" MaxFreq2=E*s/mass\n",
" dt= 1/(6.283185*sqrt(MaxFreq2))\n",
"# dt=0.0001646\n",
" println(\"dt: $dt\")\n",
" \n",
" append!(displacements,[Array(metavoxel[\"N_displacementGPU\"])])\n",
" \n",
" t=@timed doTimeStep!(metavoxel,dt,0)\n",
" append!(displacements,[Array(metavoxel[\"N_displacementGPU\"])])\n",
" time=t[2]\n",
" println(\"first timestep took $time seconds\")\n",
" t=@timed simulateParallel!(metavoxel,numTimeSteps-1,dt,returnEvery)\n",
" time=t[2]\n",
" \n",
" if save\n",
" updateDataAndSave!(metavoxel,setup,\"../json/trialJuliaParallelGPU.json\")\n",
" end\n",
" println(\"ran latticeSize $latticeSize with $voxCount voxels and $linkCount edges for $numTimeSteps time steps took $time seconds\")\n",
" return\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"fea (generic function with 1 method)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function fea(setup)\n",
" #######################################################\n",
" function points(element, properties)\n",
" elements = properties[\"elements\"]\n",
" nodes = properties[\"nodes\"]\n",
" degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = elements[element][1]\n",
" toNode = elements[element][2]\n",
"\n",
" # the coordinates for each node\n",
" fromPoint = nodes[fromNode]\n",
" toPoint = nodes[toNode]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = degrees_of_freedom[fromNode]\n",
" dofs=vcat(dofs,degrees_of_freedom[toNode])\n",
"\n",
" return fromPoint, toPoint, dofs\n",
" end\n",
"\n",
" function direction_cosine(vec1, vec2)\n",
" return dot(vec1,vec2) / (norm(vec1) * norm(vec2))\n",
" end\n",
"\n",
" function rotation_matrix(element_vector, x_axis, y_axis,z_axis)\n",
" # find the direction cosines\n",
" x_proj = direction_cosine(element_vector, x_axis)\n",
" y_proj = direction_cosine(element_vector, y_axis)\n",
" z_proj = direction_cosine(element_vector, z_axis);\n",
" return [[x_proj y_proj z_proj 0 0 0];[0 0 0 x_proj y_proj z_proj]]\n",
" end\n",
"\n",
" function rotation_matrix(element_vector, x_axis, y_axis,z_axis)\n",
" # find the direction cosines\n",
" L=norm(element_vector)\n",
" l = (element_vector[1])/L\n",
" m = (element_vector[2])/L\n",
" n = (element_vector[3])/L\n",
" D = ( l^2+ m^2+n^2)^0.5\n",
"\n",
" transMatrix=[[l m n 0 0 0 0 0 0 0 0 0];[-m/D l/D 0 0 0 0 0 0 0 0 0 0];[ -l*n/D -m*n/D D 0 0 0 0 0 0 0 0 0];[ 0 0 0 l m n 0 0 0 0 0 0];[ 0 0 0 -m/D l/D 0 0 0 0 0 0 0];[ 0 0 0 -l*n/D -m*n/D D 0 0 0 0 0 0];[ 0 0 0 0 0 0 l m n 0 0 0];[ 0 0 0 0 0 0 -m/D l/D 0 0 0 0];[ 0 0 0 0 0 0 -l*n/D -m*n/D D 0 0 0];[ 0 0 0 0 0 0 0 0 0 l m n];[ 0 0 0 0 0 0 0 0 0 -m/D l/D 0];[ 0 0 0 0 0 0 0 0 0 -l*n/D -m*n/D D]]\n",
"\n",
" return transMatrix\n",
" end\n",
" \n",
" #######################################################\n",
" function get_matrices(setup)\n",
"\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" ndofs = length(nodes)*6\n",
"\n",
" x_axis = [1 0 0]\n",
" y_axis = [0 1 0]\n",
" z_axis = [0 0 1]\n",
"\n",
" M = zeros((ndofs,ndofs))\n",
" K = zeros((ndofs,ndofs))\n",
" \n",
" \n",
" for edge in edges\n",
" #degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
" \n",
"\n",
" # the coordinates for each node\n",
" fromPoint = [fromNode[\"position\"][\"x\"]/100.0 fromNode[\"position\"][\"y\"]/100.0 fromNode[\"position\"][\"z\"]/100.0]\n",
" toPoint = [toNode[\"position\"][\"x\"]/100.0 toNode[\"position\"][\"y\"]/100.0 toNode[\"position\"][\"z\"]/100.0]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = convert(Array{Int}, fromNode[\"degrees_of_freedom\"])\n",
" dofs=vcat(dofs,convert(Array{Int}, toNode[\"degrees_of_freedom\"]))\n",
"\n",
" element_vector=toPoint-fromPoint\n",
"\n",
" # find element mass and stifness matrices\n",
" length = norm(element_vector)\n",
" rho = edge[\"density\"]\n",
" area = edge[\"area\"]\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
"\n",
" A = edge[\"area\"]\n",
" G=1.0#todo shear_modulus\n",
" ixx = 1.0#todo section ixx\n",
" iyy = 1.0#todo section.iyy#\n",
" l0=length\n",
" j=1.0;#todo check\n",
" l02 = l0 * l0\n",
" l03 = l0 * l0 * l0\n",
" \n",
" ################################\n",
" mass=1\n",
" nu=0.35\n",
" W = 75\n",
" L = W/sqrt(2)\n",
" L=length\n",
" n_min = 1\n",
" n_max = 7\n",
" # Cross Section inputs, must be floats\n",
" E = 2000e9 # MPa\n",
" G = E * 1 / 3 # MPa\n",
" h = 2.38/100.0 # mm\n",
" b = 2.38/100.0 # mm\n",
" rho = 7.85e-9 / 3 # kg/mm^3\n",
" S = h * b\n",
" Sy = (S * (6 + 12 * nu + 6 * nu^2)/ (7 + 12 * nu + 4 * nu^2))\n",
" # For solid rectangular cross section (width=b, depth=d & ( b < d )):\n",
" Q = 1 / 3 - 0.2244 / (min(h / b, b / h) + 0.1607)\n",
" J = Q * min(h * b^3, b * h^3)\n",
" \n",
" \n",
" ##if voxels\n",
" #nu=0\n",
" #L=l\n",
" #a1 = E*L # EA/L : Units of N/m\n",
" #a2 = E * L*L*L / (12.0*(1+nu)) # GJ/L : Units of N-m\n",
" #b1 = E*L # 12EI/L^3 : Units of N/m\n",
" #b2 = E*L*L/2.0 # 6EI/L^2 : Units of N (or N-m/m: torque related to linear distance)\n",
" #b3 = E*L*L*L/6.0 # 2EI/L : Units of N-m\n",
" \n",
" I= b*h^3/12\n",
"# J=b*h*(b*b+h*h)/12\n",
" a1=E*b*h/L\n",
" a2=G*J/L\n",
" b1=12*E*I/(L^3)\n",
" b2=6*E*I/(L^2)\n",
" b3=2*E*I/(L)\n",
" \n",
" # Cm = rho * area * length /6.0\n",
" # Ck= E * area / length \n",
"\n",
" # m = [[2 1];[1 2]]\n",
" # k = [[1 -1];[-1 1]]\n",
" \n",
"\n",
" k = [[E*A/l0 0 0 0 0 0 -E*A/l0 0 0 0 0 0];[0 12*E*ixx/l03 0 0 0 6*E*ixx/l02 0 -12*E*ixx/l03 0 0 0 6*E*ixx/l02];[0 0 12*E*iyy/l03 0 -6*E*iyy/l02 0 0 0 -12*E*iyy/l03 0 -6*E*iyy/l02 0];[0 0 0 G*j/l0 0 0 0 0 0 -G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 4*E*iyy/l0 0 0 0 6*E*iyy/l02 0 2*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 4*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 2*E*ixx/l0];[-E*A/l0 0 0 0 0 0 E*A/l0 0 0 0 0 0];[0 -12*E*ixx/l03 0 0 0 -6*E*ixx/l02 0 12*E*ixx/l03 0 0 0 -6*E*ixx/l02];[0 0 -12*E*iyy/l03 0 6*E*iyy/l02 0 0 0 12*E*iyy/l03 0 6*E*iyy/l02 0];[0 0 0 -G*j/l0 0 0 0 0 0 G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 2*E*iyy/l0 0 0 0 6*E*iyy/l02 0 4*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 2*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 4*E*ixx/l0]]\n",
" k= [[ a1 0 0 0 0 0 -a1 0 0 0 0 0 ];\n",
" [ 0 b1 0 0 0 b2 0 -b1 0 0 0 b2 ];\n",
" [ 0 0 b1 0 -b2 0 0 0 -b1 0 -b2 0 ];\n",
" [ 0 0 0 a2 0 0 0 0 0 -a2 0 0 ];\n",
" [ 0 0 0 0 2b3 0 0 0 b2 0 b3 0 ];\n",
" [ 0 0 0 0 0 2b3 0 -b2 0 0 0 b3 ];\n",
" [ 0 0 0 0 0 0 a1 0 0 0 0 0 ];\n",
" [ 0 0 0 0 0 0 0 b1 0 0 0 -b2 ];\n",
" [ 0 0 0 0 0 0 0 0 b1 0 b2 0 ];\n",
" [ 0 0 0 0 0 0 0 0 0 a2 0 0 ];\n",
" [ 0 0 0 0 0 0 0 0 0 0 2b3 0 ];\n",
" [ 0 0 0 0 0 0 0 0 0 0 0 2b3 ]]\n",
" # find rotated mass and stifness matrices\n",
" tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis)\n",
"\n",
" # m_r=transpose(tau)*m*tau\n",
" k_r=transpose(tau)*k*tau\n",
"\n",
" # change from element to global coordinate\n",
" index= dofs.+1\n",
"\n",
" B=zeros((12,ndofs))\n",
" for i in 1:12\n",
" B[i,index[i]]=1.0\n",
" end\n",
"\n",
"\n",
" # M_rG= transpose(B)*m_r*B\n",
" K_rG= transpose(B)*k_r*B\n",
"\n",
" # M += Cm .* M_rG\n",
" # K += Ck .* K_rG\n",
" K += K_rG\n",
"\n",
" end\n",
" \n",
" \n",
" # construct the force vector\n",
" F=zeros(ndofs)\n",
" remove_indices=[];\n",
" for node in nodes\n",
" #insert!(F,i, value);\n",
" #F=vcat(F,value)\n",
" \n",
" \n",
" i=parse(Int,node[\"id\"][2:end])\n",
" f=node[\"force\"]\n",
" \n",
" # println(f)\n",
" F[(i)*6+1]=f[\"x\"]/1.0\n",
" F[(i)*6+2]=f[\"y\"]/1.0\n",
" F[(i)*6+3]=f[\"z\"]/1.0\n",
" F[(i)*6+4]=0\n",
" F[(i)*6+5]=0\n",
" F[(i)*6+6]=0\n",
" Load+=f[\"y\"]/1.0\n",
" if (F[(i)*6+2]!=0)\n",
" append!(topNodesIndices,i)\n",
" end\n",
" \n",
" dofs = convert(Array{Int}, node[\"degrees_of_freedom\"]).+1\n",
" restrained_dofs=node[\"restrained_degrees_of_freedom\"]\n",
" for (index, value) in enumerate(dofs)\n",
" if restrained_dofs[index]\n",
" append!( remove_indices, value)\n",
" end\n",
" end\n",
" \n",
" end\n",
"\n",
" #println(remove_indices)\n",
" #print(K)\n",
" #print(F)\n",
" \n",
"\n",
" #M = M[setdiff(1:end, remove_indices), :]\n",
" K = K[setdiff(1:end, remove_indices), :]\n",
"\n",
" #M = M[:,setdiff(1:end, remove_indices)]\n",
" K = K[:,setdiff(1:end, remove_indices)]\n",
"\n",
" F = F[setdiff(1:end, remove_indices)]\n",
" U=zeros(ndofs)\n",
" \n",
" return M,K,F,U,remove_indices\n",
" end\n",
"\n",
" \n",
" function updateDisplacement(setup, X)\n",
" nodes= setup[\"nodes\"]\n",
" i=0\n",
" for node in nodes\n",
" \n",
"# if !node[\"restrained_degrees_of_freedom\"][2]\n",
" #i=parse(Int,node[\"id\"][2:end])\n",
" node[\"displacement\"][\"x\"]=X[(i)*6+1]/15\n",
" node[\"displacement\"][\"y\"]=X[(i)*6+2]/15\n",
" node[\"displacement\"][\"z\"]=X[(i)*6+3]/15\n",
" node[\"angle\"][\"x\"]=X[(i)*6+4]\n",
" node[\"angle\"][\"y\"]=X[(i)*6+5]\n",
" node[\"angle\"][\"z\"]=X[(i)*6+6]\n",
" append!(displacementFEA,[Vector3(X[(i)*6+1],X[(i)*6+2],X[(i)*6+3])])\n",
" i=i+1\n",
"# else\n",
"# append!(displacementFEA,[Vector3(0,0,0)])\n",
"# end\n",
" end\n",
" end\n",
" \n",
" #######################################################\n",
"\n",
" function get_stresses(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" ndofs = length(nodes)*6\n",
"\n",
" x_axis = [1 0 0]\n",
" y_axis = [0 1 0]\n",
" z_axis = [0 0 1]\n",
"\n",
" # find the stresses in each member\n",
" stresses=zeros(length(edges))\n",
" max11=-10e6\n",
" min11=10e6\n",
" for edge in edges\n",
" #degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
" # the coordinates for each node\n",
" fromPoint = [fromNode[\"position\"][\"x\"]/100.0 fromNode[\"position\"][\"y\"]/100.0 fromNode[\"position\"][\"z\"]/100.0]\n",
" toPoint = [toNode[\"position\"][\"x\"]/100.0 toNode[\"position\"][\"y\"]/100.0 toNode[\"position\"][\"z\"]/100.0]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = convert(Array{Int}, fromNode[\"degrees_of_freedom\"])\n",
" dofs=vcat(dofs,convert(Array{Int}, toNode[\"degrees_of_freedom\"]))\n",
"\n",
" element_vector=toPoint-fromPoint\n",
"\n",
"\n",
" # find rotated mass and stifness matrices\n",
" tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis)\n",
"\n",
" # i1=parse(Int,fromNode[\"id\"][2:end])\n",
" # i2=parse(Int,toNode[\"id\"][2:end])\n",
"\n",
" # global_displacements=[X[(i1)*6+1] X[(i1)*6+2] X[(i1)*6+3] X[(i1)*6+4] X[(i1)*6+5] X[(i1)*6+6] X[(i2)*6+1] X[(i2)*6+2] X[(i2)*6+3] X[(i2)*6+4] X[(i2)*6+5] X[(i2)*6+6]] # todo change\n",
" global_displacements=[fromNode[\"displacement\"][\"x\"] fromNode[\"displacement\"][\"y\"] fromNode[\"displacement\"][\"z\"] fromNode[\"angle\"][\"x\"] fromNode[\"angle\"][\"y\"] fromNode[\"angle\"][\"z\"] toNode[\"displacement\"][\"x\"] toNode[\"displacement\"][\"y\"] toNode[\"displacement\"][\"z\"] toNode[\"angle\"][\"x\"] toNode[\"angle\"][\"y\"] toNode[\"angle\"][\"z\"]] # todo change\n",
"\n",
" # nodal displacement\n",
"\n",
" q=tau*transpose(global_displacements)\n",
" # println(q)\n",
" # calculate the strain and stresses\n",
" strain =(q[7]-q[1])/norm(element_vector)\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
" stress=E.*strain\n",
" edge[\"stress\"]=stress\n",
" if stress>max11\n",
" max11=stress\n",
" end\n",
" if stress<min11\n",
" min11=stress\n",
" end\n",
" # println(element)\n",
" # println(stress)\n",
" end\n",
"\n",
"\n",
"\n",
" setup[\"viz\"][\"minStress\"]=min11\n",
" setup[\"viz\"][\"maxStress\"]=max11\n",
" return stresses\n",
" end\n",
" \n",
" function initialize(setup)\n",
" nodes = setup[\"nodes\"]\n",
" ndofs = length(nodes)*6\n",
" \n",
" i=0\n",
" for node in nodes\n",
" dg=[]\n",
" for ii in 0:5\n",
" append!(dg,i+ii) \n",
" end\n",
" i+=6\n",
" node[\"degrees_of_freedom\"]=dg\n",
" end\n",
" end\n",
"\n",
" #######################################################\n",
" function solveFea(setup)\n",
" // # determine the global matrices\n",
" initialize(setup)\n",
" M,K,F,U,ind=get_matrices(setup)\n",
" \n",
" #println(M)\n",
" #println(K)\n",
" #println(F)\n",
"\n",
" #evals=eigvals(K,M)\n",
" #evecs=eigvecs(K,M)\n",
" #frequencies=sqrt.(evals)\n",
" X=inv(K)*F\n",
" U[setdiff(1:end, ind)]=X\n",
"\n",
" updateDisplacement(setup, U)\n",
"\n",
" # determine the stresses in each element\n",
" stresses=get_stresses(setup)\n",
" end\n",
" #######################################################\n",
" displacementFEA=[]\n",
" Load=0\n",
" topNodesIndices=[]\n",
" solveFea(setup)\n",
" return displacementFEA,Load,topNodesIndices\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"recommendedTimeStep (generic function with 1 method)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function recommendedTimeStep()\n",
" \n",
" \n",
"# #find the largest natural frequency (sqrt(k/m)) that anything in the simulation will experience, then multiply by 2*pi and invert to get the optimally largest timestep that should retain stability\n",
"# MaxFreq2 = 0.0; #maximum frequency in the simulation in rad/sec\n",
" \n",
"# for e in 1:length(edges) #for each edge\n",
"# CVX_Link* pL = (*it);\n",
"# #axial\n",
"# m1 = mass(), m2 = mass()\n",
"# thisMaxFreq2 = axialStiffness()/(m1<m2?m1:m2)\n",
"# if (thisMaxFreq2 > MaxFreq2) \n",
"# MaxFreq2 = thisMaxFreq2;\n",
"# end\n",
"\n",
"# #rotational will always be less than or equal\n",
"# end\n",
" \n",
"\n",
"# if (MaxFreq2 <= 0.0) #didn't find anything (i.e no links) check for individual voxelss\n",
"# for n in 1:length(nodes) #for each node\n",
"# thisMaxFreq2 = youngsModulus*nomSize/mass;\n",
"# #thisMaxFreq2 = (*it)->mat->youngsModulus()*(*it)->mat->nomSize/(*it)->mat->mass();\n",
"# if (thisMaxFreq2 > MaxFreq2) \n",
"# MaxFreq2 = thisMaxFreq2;\n",
"# end\n",
"# end\n",
"# end\n",
"\n",
"# if (MaxFreq2 <= 0.0) \n",
"# return 0.0\n",
"# else \n",
"# return 1.0/(6.283185*sqrt(MaxFreq2)) #the optimal timestep is to advance one radian of the highest natural frequency\n",
"# end\n",
" MaxFreq2=E*size/mass\n",
" return 1/(6.283185*sqrt(MaxFreq2))\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"getSetup (generic function with 1 method)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function getSetup(latticeSize)\n",
" setup = Dict()\n",
" name=string(\"../json/setupTestUni$latticeSize\",\".json\")\n",
"# open(\"../json/setupValid2.json\", \"r\") do f\n",
"# open(\"../json/setupTest.json\", \"r\") do f\n",
" # open(\"../json/trialJulia.json\", \"r\") do f\n",
"# open(\"../json/setupTestUni4.json\", \"r\") do f\n",
" # open(\"../json/setupChiral.json\", \"r\") do f\n",
"# open(\"../json/setupTestCubeUni10.json\", \"r\") do f\n",
" open(name, \"r\") do f\n",
"# global setup\n",
" dicttxt = String(read(f)) # file information to string\n",
" setup=JSON.parse(dicttxt) # parse and transform data\n",
" end\n",
"\n",
" setup=setup[\"setup\"]\n",
" return setup\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4-element Array{Any,1}:\n",
" 4\n",
" 7\n",
" 8\n",
" 9"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"latticeSize=1\n",
"setup=getSetup(latticeSize)\n",
"displacementFEA,Load,topNodesIndices=fea(setup)\n",
"topNodesIndices"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5-element Array{Float64,1}:\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"DDisplacements=[[],[],[],[],[]]\n",
"DDisplacementsFEA=[[],[],[],[],[]]\n",
"EsFEA=[0.0,0,0,0,0]\n",
"Es=[0.0,0,0,0,0]"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [],
"source": [
"latticeSize=5\n",
"setup=getSetup(latticeSize)\n",
"displacementFEA,Load,topNodesIndices=fea(setup);"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dt: 7.294855212986817e-7\n",
"first timestep took 0.0006283 seconds\n",
"ran latticeSize 5 with 540 voxels and 1800 edges for 2000 time steps took 0.8313075 seconds\n",
"EsFEA:[4.516432560172212, 7.389712166701619, 9.998185539814536, 12.509610413282042, 14.980612218071958]\n",
"Es:[-1.7207658256817755, -1.7187653726043761, -1.8909709475438676, -2.125645742684135, -2.322015017271702]\n",
"FEA displacement= -8.696319301969073e-10,converged displacement= 3.0929663544073403e-9\n"
]
},
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 361.293, 1000.76)\" x=\"361.293\" y=\"1000.76\">7</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 230.056, 822.641)\" x=\"230.056\" y=\"822.641\">2×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 338.454, 795.231)\" x=\"338.454\" y=\"795.231\">-</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 361.293, 795.231)\" x=\"361.293\" y=\"795.231\">7</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 230.056, 617.109)\" x=\"230.056\" y=\"617.109\">3×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 338.454, 589.699)\" x=\"338.454\" y=\"589.699\">-</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 361.293, 589.699)\" x=\"361.293\" y=\"589.699\">7</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 230.056, 411.577)\" x=\"230.056\" y=\"411.577\">4×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 338.454, 384.167)\" x=\"338.454\" y=\"384.167\">-</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 361.293, 384.167)\" x=\"361.293\" y=\"384.167\">7</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 230.056, 206.045)\" x=\"230.056\" y=\"206.045\">5×10</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 338.454, 178.634)\" x=\"338.454\" y=\"178.634\">-</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:38px; text-anchor:start;\" transform=\"rotate(0, 361.293, 178.634)\" x=\"361.293\" y=\"178.634\">7</text>\n",
"</g>\n",
"<g clip-path=\"url(#clip0800)\">\n",
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"</g>\n",
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:66px; text-anchor:middle;\" transform=\"rotate(0, 1379.9, 1559.48)\" x=\"1379.9\" y=\"1559.48\">timestep</text>\n",
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" 829.222,450.927 830.139,453.928 831.057,456.985 831.975,460.096 832.893,463.26 833.811,466.473 834.728,469.733 835.646,473.038 836.564,476.386 837.482,479.774 \n",
" 838.4,483.2 839.317,486.662 840.235,490.156 841.153,493.682 842.071,497.235 842.989,500.815 843.906,504.418 844.824,508.043 845.742,511.686 846.66,515.346 \n",
" 847.577,519.02 848.495,522.706 849.413,526.401 850.331,530.103 851.249,533.81 852.166,537.519 853.084,541.229 854.002,544.936 854.92,548.638 855.838,552.334 \n",
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" 865.933,591.909 866.851,595.354 867.769,598.764 868.687,602.138 869.604,605.473 870.522,608.769 871.44,612.022 872.358,615.232 873.276,618.397 874.193,621.514 \n",
" 875.111,624.582 876.029,627.6 876.947,630.566 877.865,633.477 878.782,636.334 879.7,639.134 880.618,641.875 881.536,644.557 882.454,647.178 883.371,649.736 \n",
" 884.289,652.231 885.207,654.661 886.125,657.025 887.043,659.322 887.96,661.551 888.878,663.711 889.796,665.8 890.714,667.818 891.631,669.764 892.549,671.637 \n",
" 893.467,673.436 894.385,675.161 895.303,676.81 896.22,678.384 897.138,679.881 898.056,681.302 898.974,682.645 899.892,683.91 900.809,685.097 901.727,686.205 \n",
" 902.645,687.235 903.563,688.185 904.481,689.056 905.398,689.848 906.316,690.561 907.234,691.193 908.152,691.747 909.07,692.221 909.987,692.616 910.905,692.932 \n",
" 911.823,693.169 912.741,693.328 913.658,693.408 914.576,693.411 915.494,693.336 916.412,693.184 917.33,692.956 918.247,692.653 919.165,692.274 920.083,691.821 \n",
" 921.001,691.293 921.919,690.693 922.836,690.021 923.754,689.277 924.672,688.463 925.59,687.579 926.508,686.627 927.425,685.607 928.343,684.521 929.261,683.369 \n",
" 930.179,682.152 931.097,680.873 932.014,679.532 932.932,678.129 933.85,676.668 934.768,675.148 935.685,673.571 936.603,671.939 937.521,670.252 938.439,668.513 \n",
" 939.357,666.722 940.274,664.882 941.192,662.993 942.11,661.057 943.028,659.076 943.946,657.052 944.863,654.984 945.781,652.877 946.699,650.73 947.617,648.546 \n",
" 948.535,646.326 949.452,644.072 950.37,641.785 951.288,639.468 952.206,637.122 953.124,634.748 954.041,632.348 954.959,629.925 955.877,627.479 956.795,625.013 \n",
" 957.712,622.527 958.63,620.025 959.548,617.507 960.466,614.976 961.384,612.432 962.301,609.878 963.219,607.316 964.137,604.747 965.055,602.173 965.973,599.595 \n",
" 966.89,597.015 967.808,594.436 968.726,591.858 969.644,589.283 970.562,586.713 971.479,584.15 972.397,581.595 973.315,579.05 974.233,576.515 975.151,573.994 \n",
" 976.068,571.487 976.986,568.997 977.904,566.523 978.822,564.069 979.739,561.635 980.657,559.223 981.575,556.834 982.493,554.47 983.411,552.132 984.328,549.821 \n",
" 985.246,547.539 986.164,545.287 987.082,543.067 988,540.879 988.917,538.724 989.835,536.605 990.753,534.522 991.671,532.475 992.589,530.468 993.506,528.499 \n",
" 994.424,526.571 995.342,524.684 996.26,522.839 997.178,521.038 998.095,519.281 999.013,517.569 999.931,515.902 1000.85,514.283 1001.77,512.71 1002.68,511.186 \n",
" 1003.6,509.71 1004.52,508.284 1005.44,506.908 1006.36,505.583 1007.27,504.308 1008.19,503.086 1009.11,501.915 1010.03,500.797 1010.94,499.732 1011.86,498.72 \n",
" 1012.78,497.762 1013.7,496.858 1014.62,496.008 1015.53,495.213 1016.45,494.472 1017.37,493.786 1018.29,493.154 1019.2,492.578 1020.12,492.056 1021.04,491.59 \n",
" 1021.96,491.178 1022.88,490.821 1023.79,490.519 1024.71,490.272 1025.63,490.079 1026.55,489.94 1027.46,489.855 1028.38,489.824 1029.3,489.846 1030.22,489.922 \n",
" 1031.14,490.05 1032.05,490.23 1032.97,490.463 1033.89,490.747 1034.81,491.081 1035.72,491.467 1036.64,491.902 1037.56,492.386 1038.48,492.919 1039.4,493.5 \n",
" 1040.31,494.129 1041.23,494.804 1042.15,495.525 1043.07,496.292 1043.98,497.103 1044.9,497.957 1045.82,498.855 1046.74,499.795 1047.66,500.776 1048.57,501.797 \n",
" 1049.49,502.858 1050.41,503.957 1051.33,505.094 1052.25,506.268 1053.16,507.478 1054.08,508.722 1055,510 1055.92,511.31 1056.83,512.652 1057.75,514.025 \n",
" 1058.67,515.428 1059.59,516.859 1060.51,518.317 1061.42,519.802 1062.34,521.311 1063.26,522.845 1064.18,524.402 1065.09,525.981 1066.01,527.581 1066.93,529.2 \n",
" 1067.85,530.837 1068.77,532.492 1069.68,534.162 1070.6,535.848 1071.52,537.547 1072.44,539.259 1073.35,540.983 1074.27,542.716 1075.19,544.459 1076.11,546.21 \n",
" 1077.03,547.967 1077.94,549.73 1078.86,551.497 1079.78,553.268 1080.7,555.041 1081.61,556.814 1082.53,558.588 1083.45,560.36 1084.37,562.13 1085.29,563.896 \n",
" 1086.2,565.657 1087.12,567.413 1088.04,569.162 1088.96,570.902 1089.87,572.634 1090.79,574.356 1091.71,576.067 1092.63,577.765 1093.55,579.45 1094.46,581.121 \n",
" 1095.38,582.777 1096.3,584.417 1097.22,586.04 1098.13,587.645 1099.05,589.23 1099.97,590.796 1100.89,592.342 1101.81,593.865 1102.72,595.366 1103.64,596.844 \n",
" 1104.56,598.298 1105.48,599.727 1106.39,601.13 1107.31,602.507 1108.23,603.856 1109.15,605.178 1110.07,606.471 1110.98,607.736 1111.9,608.97 1112.82,610.174 \n",
" 1113.74,611.347 1114.65,612.488 1115.57,613.597 1116.49,614.673 1117.41,615.717 1118.33,616.726 1119.24,617.702 1120.16,618.643 1121.08,619.549 1122,620.42 \n",
" 1122.91,621.255 1123.83,622.055 1124.75,622.818 1125.67,623.544 1126.59,624.234 1127.5,624.887 1128.42,625.502 1129.34,626.08 1130.26,626.621 1131.18,627.124 \n",
" 1132.09,627.589 1133.01,628.017 1133.93,628.406 1134.85,628.758 1135.76,629.071 1136.68,629.347 1137.6,629.585 1138.52,629.786 1139.44,629.948 1140.35,630.073 \n",
" 1141.27,630.161 1142.19,630.211 1143.11,630.225 1144.02,630.201 1144.94,630.141 1145.86,630.045 1146.78,629.912 1147.7,629.744 1148.61,629.541 1149.53,629.302 \n",
" 1150.45,629.028 1151.37,628.72 1152.28,628.379 1153.2,628.003 1154.12,627.595 1155.04,627.154 1155.96,626.68 1156.87,626.175 1157.79,625.639 1158.71,625.073 \n",
" 1159.63,624.476 1160.54,623.85 1161.46,623.194 1162.38,622.511 1163.3,621.8 1164.22,621.061 1165.13,620.296 1166.05,619.506 1166.97,618.69 1167.89,617.849 \n",
" 1168.8,616.985 1169.72,616.098 1170.64,615.188 1171.56,614.257 1172.48,613.304 1173.39,612.332 1174.31,611.34 1175.23,610.329 1176.15,609.3 1177.06,608.254 \n",
" 1177.98,607.192 1178.9,606.113 1179.82,605.021 1180.74,603.914 1181.65,602.793 1182.57,601.66 1183.49,600.516 1184.41,599.361 1185.32,598.195 1186.24,597.021 \n",
" 1187.16,595.837 1188.08,594.647 1189,593.449 1189.91,592.245 1190.83,591.037 1191.75,589.823 1192.67,588.606 1193.58,587.387 1194.5,586.165 1195.42,584.942 \n",
" 1196.34,583.719 1197.26,582.496 1198.17,581.274 1199.09,580.054 1200.01,578.837 1200.93,577.623 1201.85,576.414 1202.76,575.209 1203.68,574.01 1204.6,572.818 \n",
" 1205.52,571.632 1206.43,570.455 1207.35,569.286 1208.27,568.127 1209.19,566.977 1210.11,565.839 1211.02,564.711 1211.94,563.595 1212.86,562.493 1213.78,561.403 \n",
" 1214.69,560.327 1215.61,559.266 1216.53,558.22 1217.45,557.189 1218.37,556.175 1219.28,555.177 1220.2,554.197 1221.12,553.235 1222.04,552.291 1222.95,551.366 \n",
" 1223.87,550.46 1224.79,549.574 1225.71,548.708 1226.63,547.863 1227.54,547.039 1228.46,546.236 1229.38,545.456 1230.3,544.698 1231.21,543.962 1232.13,543.249 \n",
" 1233.05,542.56 1233.97,541.894 1234.89,541.252 1235.8,540.634 1236.72,540.04 1237.64,539.471 1238.56,538.927 1239.47,538.408 1240.39,537.914 1241.31,537.446 \n",
" 1242.23,537.003 1243.15,536.586 1244.06,536.194 1244.98,535.829 1245.9,535.489 1246.82,535.176 1247.73,534.888 1248.65,534.627 1249.57,534.391 1250.49,534.182 \n",
" 1251.41,533.999 1252.32,533.842 1253.24,533.711 1254.16,533.606 1255.08,533.527 1255.99,533.473 1256.91,533.445 1257.83,533.443 1258.75,533.466 1259.67,533.514 \n",
" 1260.58,533.587 1261.5,533.685 1262.42,533.807 1263.34,533.954 1264.25,534.125 1265.17,534.32 1266.09,534.538 1267.01,534.78 1267.93,535.045 1268.84,535.332 \n",
" 1269.76,535.642 1270.68,535.974 1271.6,536.327 1272.52,536.702 1273.43,537.098 1274.35,537.515 1275.27,537.952 1276.19,538.409 1277.1,538.885 1278.02,539.38 \n",
" 1278.94,539.893 1279.86,540.425 1280.78,540.975 1281.69,541.541 1282.61,542.125 1283.53,542.725 1284.45,543.34 1285.36,543.971 1286.28,544.617 1287.2,545.277 \n",
" 1288.12,545.951 1289.04,546.638 1289.95,547.338 1290.87,548.05 1291.79,548.774 1292.71,549.509 1293.62,550.254 1294.54,551.01 1295.46,551.775 1296.38,552.55 \n",
" 1297.3,553.333 1298.21,554.123 1299.13,554.921 1300.05,555.726 1300.97,556.538 1301.88,557.354 1302.8,558.176 1303.72,559.003 1304.64,559.834 1305.56,560.668 \n",
" 1306.47,561.504 1307.39,562.344 1308.31,563.185 1309.23,564.027 1310.14,564.87 1311.06,565.713 1311.98,566.556 1312.9,567.398 1313.82,568.239 1314.73,569.077 \n",
" 1315.65,569.913 1316.57,570.746 1317.49,571.575 1318.4,572.4 1319.32,573.221 1320.24,574.037 1321.16,574.847 1322.08,575.651 1322.99,576.448 1323.91,577.239 \n",
" 1324.83,578.022 1325.75,578.797 1326.66,579.564 1327.58,580.322 1328.5,581.071 1329.42,581.81 1330.34,582.539 1331.25,583.257 1332.17,583.965 1333.09,584.661 \n",
" 1334.01,585.345 1334.92,586.018 1335.84,586.678 1336.76,587.326 1337.68,587.96 1338.6,588.581 1339.51,589.188 1340.43,589.781 1341.35,590.36 1342.27,590.924 \n",
" 1343.18,591.474 1344.1,592.008 1345.02,592.527 1345.94,593.03 1346.86,593.517 1347.77,593.988 1348.69,594.443 1349.61,594.881 1350.53,595.303 1351.45,595.708 \n",
" 1352.36,596.096 1353.28,596.466 1354.2,596.82 1355.12,597.156 1356.03,597.474 1356.95,597.775 1357.87,598.058 1358.79,598.323 1359.71,598.57 1360.62,598.8 \n",
" 1361.54,599.011 1362.46,599.205 1363.38,599.38 1364.29,599.538 1365.21,599.677 1366.13,599.799 1367.05,599.903 1367.97,599.988 1368.88,600.056 1369.8,600.106 \n",
" 1370.72,600.138 1371.64,600.153 1372.55,600.15 1373.47,600.13 1374.39,600.092 1375.31,600.037 1376.23,599.966 1377.14,599.877 1378.06,599.771 1378.98,599.649 \n",
" 1379.9,599.511 1380.81,599.356 1381.73,599.185 1382.65,598.998 1383.57,598.796 1384.49,598.579 1385.4,598.346 1386.32,598.098 1387.24,597.836 1388.16,597.559 \n",
" 1389.07,597.268 1389.99,596.964 1390.91,596.645 1391.83,596.314 1392.75,595.969 1393.66,595.612 1394.58,595.242 1395.5,594.86 1396.42,594.466 1397.33,594.061 \n",
" 1398.25,593.645 1399.17,593.217 1400.09,592.78 1401.01,592.332 1401.92,591.875 1402.84,591.408 1403.76,590.932 1404.68,590.447 1405.59,589.954 1406.51,589.453 \n",
" 1407.43,588.944 1408.35,588.428 1409.27,587.906 1410.18,587.376 1411.1,586.841 1412.02,586.3 1412.94,585.753 1413.85,585.202 1414.77,584.646 1415.69,584.086 \n",
" 1416.61,583.522 1417.53,582.954 1418.44,582.384 1419.36,581.811 1420.28,581.235 1421.2,580.658 1422.12,580.079 1423.03,579.499 1423.95,578.918 1424.87,578.337 \n",
" 1425.79,577.756 1426.7,577.175 1427.62,576.595 1428.54,576.016 1429.46,575.438 1430.38,574.862 1431.29,574.289 1432.21,573.718 1433.13,573.15 1434.05,572.585 \n",
" 1434.96,572.024 1435.88,571.466 1436.8,570.913 1437.72,570.365 1438.64,569.821 1439.55,569.283 1440.47,568.75 1441.39,568.223 1442.31,567.702 1443.22,567.188 \n",
" 1444.14,566.68 1445.06,566.18 1445.98,565.686 1446.9,565.201 1447.81,564.723 1448.73,564.253 1449.65,563.792 1450.57,563.339 1451.48,562.895 1452.4,562.46 \n",
" 1453.32,562.034 1454.24,561.618 1455.16,561.212 1456.07,560.816 1456.99,560.429 1457.91,560.053 1458.83,559.688 1459.74,559.333 1460.66,558.989 1461.58,558.656 \n",
" 1462.5,558.334 1463.42,558.024 1464.33,557.725 1465.25,557.437 1466.17,557.161 1467.09,556.897 1468,556.644 1468.92,556.404 1469.84,556.176 1470.76,555.959 \n",
" 1471.68,555.755 1472.59,555.563 1473.51,555.384 1474.43,555.216 1475.35,555.061 1476.26,554.919 1477.18,554.789 1478.1,554.671 1479.02,554.566 1479.94,554.473 \n",
" 1480.85,554.392 1481.77,554.324 1482.69,554.268 1483.61,554.225 1484.52,554.193 1485.44,554.174 1486.36,554.167 1487.28,554.172 1488.2,554.189 1489.11,554.219 \n",
" 1490.03,554.259 1490.95,554.312 1491.87,554.376 1492.79,554.452 1493.7,554.539 1494.62,554.638 1495.54,554.747 1496.46,554.868 1497.37,554.999 1498.29,555.141 \n",
" 1499.21,555.294 1500.13,555.457 1501.05,555.63 1501.96,555.814 1502.88,556.007 1503.8,556.21 1504.72,556.423 1505.63,556.645 1506.55,556.876 1507.47,557.115 \n",
" 1508.39,557.364 1509.31,557.621 1510.22,557.887 1511.14,558.16 1512.06,558.441 1512.98,558.73 1513.89,559.027 1514.81,559.33 1515.73,559.641 1516.65,559.958 \n",
" 1517.57,560.281 1518.48,560.611 1519.4,560.947 1520.32,561.288 1521.24,561.635 1522.15,561.987 1523.07,562.343 1523.99,562.705 1524.91,563.071 1525.83,563.441 \n",
" 1526.74,563.815 1527.66,564.193 1528.58,564.574 1529.5,564.958 1530.41,565.345 1531.33,565.734 1532.25,566.126 1533.17,566.52 1534.09,566.915 1535,567.312 \n",
" 1535.92,567.71 1536.84,568.11 1537.76,568.51 1538.67,568.91 1539.59,569.311 1540.51,569.711 1541.43,570.112 1542.35,570.511 1543.26,570.91 1544.18,571.308 \n",
" 1545.1,571.705 1546.02,572.1 1546.93,572.493 1547.85,572.884 1548.77,573.272 1549.69,573.659 1550.61,574.042 1551.52,574.423 1552.44,574.8 1553.36,575.174 \n",
" 1554.28,575.544 1555.19,575.91 1556.11,576.272 1557.03,576.63 1557.95,576.983 1558.87,577.332 1559.78,577.676 1560.7,578.015 1561.62,578.348 1562.54,578.676 \n",
" 1563.46,578.998 1564.37,579.315 1565.29,579.625 1566.21,579.93 1567.13,580.228 1568.04,580.52 1568.96,580.805 1569.88,581.083 1570.8,581.354 1571.72,581.619 \n",
" 1572.63,581.876 1573.55,582.126 1574.47,582.369 1575.39,582.604 1576.3,582.832 1577.22,583.051 1578.14,583.263 1579.06,583.468 1579.98,583.664 1580.89,583.852 \n",
" 1581.81,584.032 1582.73,584.204 1583.65,584.367 1584.56,584.523 1585.48,584.67 1586.4,584.808 1587.32,584.938 1588.24,585.06 1589.15,585.173 1590.07,585.277 \n",
" 1590.99,585.374 1591.91,585.461 1592.82,585.54 1593.74,585.61 1594.66,585.672 1595.58,585.726 1596.5,585.77 1597.41,585.807 1598.33,585.834 1599.25,585.854 \n",
" 1600.17,585.865 1601.08,585.867 1602,585.862 1602.92,585.848 1603.84,585.826 1604.76,585.795 1605.67,585.757 1606.59,585.711 1607.51,585.656 1608.43,585.594 \n",
" 1609.34,585.524 1610.26,585.447 1611.18,585.362 1612.1,585.269 1613.02,585.169 1613.93,585.062 1614.85,584.948 1615.77,584.827 1616.69,584.698 1617.6,584.563 \n",
" 1618.52,584.422 1619.44,584.274 1620.36,584.119 1621.28,583.958 1622.19,583.791 1623.11,583.618 1624.03,583.44 1624.95,583.255 1625.86,583.065 1626.78,582.87 \n",
" 1627.7,582.669 1628.62,582.464 1629.54,582.253 1630.45,582.038 1631.37,581.819 1632.29,581.594 1633.21,581.366 1634.12,581.134 1635.04,580.897 1635.96,580.657 \n",
" 1636.88,580.414 1637.8,580.167 1638.71,579.917 1639.63,579.664 1640.55,579.408 1641.47,579.15 1642.39,578.889 1643.3,578.626 1644.22,578.36 1645.14,578.093 \n",
" 1646.06,577.824 1646.97,577.554 1647.89,577.282 1648.81,577.009 1649.73,576.735 1650.65,576.461 1651.56,576.185 1652.48,575.909 1653.4,575.633 1654.32,575.357 \n",
" 1655.23,575.081 1656.15,574.805 1657.07,574.53 1657.99,574.255 1658.91,573.981 1659.82,573.708 1660.74,573.436 1661.66,573.165 1662.58,572.896 1663.49,572.629 \n",
" 1664.41,572.363 1665.33,572.099 1666.25,571.838 1667.17,571.578 1668.08,571.321 1669,571.067 1669.92,570.815 1670.84,570.566 1671.75,570.32 1672.67,570.077 \n",
" 1673.59,569.838 1674.51,569.602 1675.43,569.369 1676.34,569.14 1677.26,568.915 1678.18,568.694 1679.1,568.477 1680.01,568.264 1680.93,568.055 1681.85,567.851 \n",
" 1682.77,567.651 1683.69,567.456 1684.6,567.265 1685.52,567.079 1686.44,566.898 1687.36,566.722 1688.27,566.551 1689.19,566.385 1690.11,566.225 1691.03,566.069 \n",
" 1691.95,565.919 1692.86,565.774 1693.78,565.635 1694.7,565.501 1695.62,565.373 1696.53,565.25 1697.45,565.133 1698.37,565.022 1699.29,564.917 1700.21,564.817 \n",
" 1701.12,564.723 1702.04,564.635 1702.96,564.552 1703.88,564.476 1704.79,564.405 1705.71,564.341 1706.63,564.282 1707.55,564.229 1708.47,564.182 1709.38,564.141 \n",
" 1710.3,564.106 1711.22,564.077 1712.14,564.053 1713.06,564.035 1713.97,564.024 1714.89,564.017 1715.81,564.017 1716.73,564.023 1717.64,564.034 1718.56,564.05 \n",
" 1719.48,564.073 1720.4,564.101 1721.32,564.134 1722.23,564.173 1723.15,564.217 1724.07,564.267 1724.99,564.321 1725.9,564.381 1726.82,564.447 1727.74,564.517 \n",
" 1728.66,564.592 1729.58,564.672 1730.49,564.757 1731.41,564.846 1732.33,564.941 1733.25,565.04 1734.16,565.143 1735.08,565.251 1736,565.362 1736.92,565.479 \n",
" 1737.84,565.599 1738.75,565.723 1739.67,565.851 1740.59,565.983 1741.51,566.119 1742.42,566.258 1743.34,566.401 1744.26,566.546 1745.18,566.696 1746.1,566.848 \n",
" 1747.01,567.003 1747.93,567.161 1748.85,567.322 1749.77,567.486 1750.68,567.652 1751.6,567.82 1752.52,567.991 1753.44,568.164 1754.36,568.339 1755.27,568.516 \n",
" 1756.19,568.694 1757.11,568.875 1758.03,569.056 1758.94,569.24 1759.86,569.424 1760.78,569.61 1761.7,569.796 1762.62,569.984 1763.53,570.172 1764.45,570.361 \n",
" 1765.37,570.551 1766.29,570.741 1767.2,570.931 1768.12,571.121 1769.04,571.312 1769.96,571.502 1770.88,571.692 1771.79,571.882 1772.71,572.071 1773.63,572.26 \n",
" 1774.55,572.448 1775.46,572.635 1776.38,572.821 1777.3,573.007 1778.22,573.191 1779.14,573.374 1780.05,573.555 1780.97,573.735 1781.89,573.913 1782.81,574.09 \n",
" 1783.73,574.265 1784.64,574.438 1785.56,574.609 1786.48,574.778 1787.4,574.945 1788.31,575.109 1789.23,575.272 1790.15,575.431 1791.07,575.588 1791.99,575.743 \n",
" 1792.9,575.894 1793.82,576.043 1794.74,576.189 1795.66,576.333 1796.57,576.473 1797.49,576.61 1798.41,576.743 1799.33,576.874 1800.25,577.001 1801.16,577.125 \n",
" 1802.08,577.246 1803,577.363 1803.92,577.476 1804.83,577.586 1805.75,577.692 1806.67,577.795 1807.59,577.893 1808.51,577.988 1809.42,578.08 1810.34,578.167 \n",
" 1811.26,578.251 1812.18,578.33 1813.09,578.406 1814.01,578.478 1814.93,578.545 1815.85,578.609 1816.77,578.669 1817.68,578.724 1818.6,578.776 1819.52,578.824 \n",
" 1820.44,578.867 1821.35,578.907 1822.27,578.942 1823.19,578.973 1824.11,579.001 1825.03,579.024 1825.94,579.043 1826.86,579.058 1827.78,579.069 1828.7,579.077 \n",
" 1829.61,579.08 1830.53,579.079 1831.45,579.074 1832.37,579.065 1833.29,579.053 1834.2,579.037 1835.12,579.016 1836.04,578.992 1836.96,578.965 1837.87,578.933 \n",
" 1838.79,578.898 1839.71,578.859 1840.63,578.817 1841.55,578.771 1842.46,578.722 1843.38,578.669 1844.3,578.613 1845.22,578.554 1846.13,578.491 1847.05,578.426 \n",
" 1847.97,578.357 1848.89,578.285 1849.81,578.21 1850.72,578.132 1851.64,578.051 1852.56,577.967 1853.48,577.881 1854.39,577.792 1855.31,577.7 1856.23,577.606 \n",
" 1857.15,577.51 1858.07,577.411 1858.98,577.31 1859.9,577.206 1860.82,577.101 1861.74,576.993 1862.66,576.884 1863.57,576.772 1864.49,576.659 1865.41,576.544 \n",
" 1866.33,576.428 1867.24,576.31 1868.16,576.19 1869.08,576.069 1870,575.947 1870.92,575.823 1871.83,575.699 1872.75,575.573 1873.67,575.447 1874.59,575.319 \n",
" 1875.5,575.191 1876.42,575.062 1877.34,574.933 1878.26,574.803 1879.18,574.673 1880.09,574.542 1881.01,574.411 1881.93,574.28 1882.85,574.149 1883.76,574.017 \n",
" 1884.68,573.886 1885.6,573.755 1886.52,573.625 1887.44,573.494 1888.35,573.364 1889.27,573.235 1890.19,573.106 1891.11,572.978 1892.02,572.85 1892.94,572.724 \n",
" 1893.86,572.598 1894.78,572.473 1895.7,572.349 1896.61,572.226 1897.53,572.105 1898.45,571.985 1899.37,571.866 1900.28,571.748 1901.2,571.632 1902.12,571.518 \n",
" 1903.04,571.405 1903.96,571.293 1904.87,571.184 1905.79,571.076 1906.71,570.97 1907.63,570.866 1908.54,570.764 1909.46,570.664 1910.38,570.566 1911.3,570.47 \n",
" 1912.22,570.376 1913.13,570.284 1914.05,570.195 1914.97,570.108 1915.89,570.023 1916.8,569.94 1917.72,569.86 1918.64,569.783 1919.56,569.708 1920.48,569.635 \n",
" 1921.39,569.565 1922.31,569.498 1923.23,569.433 1924.15,569.371 1925.06,569.311 1925.98,569.254 1926.9,569.2 1927.82,569.149 1928.74,569.1 1929.65,569.054 \n",
" 1930.57,569.011 1931.49,568.97 1932.41,568.933 1933.33,568.898 1934.24,568.866 1935.16,568.837 1936.08,568.81 1937,568.786 1937.91,568.766 1938.83,568.747 \n",
" 1939.75,568.732 1940.67,568.72 1941.59,568.71 1942.5,568.703 1943.42,568.699 1944.34,568.697 1945.26,568.699 1946.17,568.703 1947.09,568.709 1948.01,568.719 \n",
" 1948.93,568.731 1949.85,568.745 1950.76,568.763 1951.68,568.782 1952.6,568.805 1953.52,568.829 1954.43,568.857 1955.35,568.887 1956.27,568.919 1957.19,568.953 \n",
" 1958.11,568.99 1959.02,569.03 1959.94,569.071 1960.86,569.115 1961.78,569.161 1962.69,569.209 1963.61,569.259 1964.53,569.311 1965.45,569.366 1966.37,569.422 \n",
" 1967.28,569.48 1968.2,569.54 1969.12,569.602 1970.04,569.665 1970.95,569.731 1971.87,569.798 1972.79,569.866 1973.71,569.936 1974.63,570.008 1975.54,570.081 \n",
" 1976.46,570.156 1977.38,570.231 1978.3,570.309 1979.21,570.387 1980.13,570.466 1981.05,570.547 1981.97,570.629 1982.89,570.711 1983.8,570.795 1984.72,570.879 \n",
" 1985.64,570.965 1986.56,571.051 1987.47,571.138 1988.39,571.225 1989.31,571.313 1990.23,571.401 1991.15,571.49 1992.06,571.58 1992.98,571.669 1993.9,571.759 \n",
" 1994.82,571.849 1995.73,571.94 1996.65,572.03 1997.57,572.121 1998.49,572.211 1999.41,572.301 2000.32,572.392 2001.24,572.482 2002.16,572.572 2003.08,572.661 \n",
" 2004,572.75 2004.91,572.839 2005.83,572.927 2006.75,573.015 2007.67,573.102 2008.58,573.189 2009.5,573.275 2010.42,573.36 2011.34,573.444 2012.26,573.528 \n",
" 2013.17,573.61 2014.09,573.692 2015.01,573.773 2015.93,573.853 2016.84,573.931 2017.76,574.009 2018.68,574.085 2019.6,574.16 2020.52,574.234 2021.43,574.307 \n",
" 2022.35,574.379 2023.27,574.449 2024.19,574.517 2025.1,574.585 2026.02,574.65 2026.94,574.715 2027.86,574.777 2028.78,574.839 2029.69,574.898 2030.61,574.956 \n",
" 2031.53,575.013 2032.45,575.067 2033.36,575.12 2034.28,575.172 2035.2,575.221 2036.12,575.269 2037.04,575.315 2037.95,575.359 2038.87,575.402 2039.79,575.442 \n",
" 2040.71,575.481 2041.62,575.518 2042.54,575.553 2043.46,575.586 2044.38,575.617 2045.3,575.647 2046.21,575.674 2047.13,575.699 2048.05,575.723 2048.97,575.745 \n",
" 2049.88,575.764 2050.8,575.782 2051.72,575.798 2052.64,575.812 2053.56,575.824 2054.47,575.834 2055.39,575.842 2056.31,575.848 2057.23,575.852 2058.14,575.855 \n",
" 2059.06,575.855 2059.98,575.854 2060.9,575.851 2061.82,575.846 2062.73,575.839 2063.65,575.83 2064.57,575.819 2065.49,575.807 2066.4,575.793 2067.32,575.777 \n",
" 2068.24,575.76 2069.16,575.74 2070.08,575.719 2070.99,575.697 2071.91,575.672 2072.83,575.647 2073.75,575.619 2074.67,575.59 2075.58,575.56 2076.5,575.528 \n",
" 2077.42,575.494 2078.34,575.459 2079.25,575.423 2080.17,575.385 2081.09,575.346 2082.01,575.305 2082.93,575.264 2083.84,575.221 2084.76,575.177 2085.68,575.131 \n",
" 2086.6,575.085 2087.51,575.037 2088.43,574.989 2089.35,574.939 2090.27,574.888 2091.19,574.837 2092.1,574.784 2093.02,574.731 2093.94,574.677 2094.86,574.622 \n",
" 2095.77,574.566 2096.69,574.51 2097.61,574.452 2098.53,574.395 2099.45,574.336 2100.36,574.277 2101.28,574.218 2102.2,574.158 2103.12,574.098 2104.03,574.037 \n",
" 2104.95,573.976 2105.87,573.914 2106.79,573.853 2107.71,573.791 2108.62,573.729 2109.54,573.667 2110.46,573.605 2111.38,573.542 2112.29,573.48 2113.21,573.417 \n",
" 2114.13,573.355 2115.05,573.293 2115.97,573.231 2116.88,573.169 2117.8,573.108 2118.72,573.046 2119.64,572.985 2120.55,572.924 2121.47,572.864 2122.39,572.804 \n",
" 2123.31,572.744 2124.23,572.685 2125.14,572.627 2126.06,572.569 2126.98,572.511 2127.9,572.455 2128.81,572.398 2129.73,572.343 2130.65,572.288 2131.57,572.234 \n",
" 2132.49,572.181 2133.4,572.128 2134.32,572.077 2135.24,572.026 2136.16,571.976 2137.07,571.927 2137.99,571.879 2138.91,571.832 2139.83,571.786 2140.75,571.741 \n",
" 2141.66,571.697 2142.58,571.654 2143.5,571.612 2144.42,571.571 2145.33,571.531 2146.25,571.493 2147.17,571.455 2148.09,571.419 2149.01,571.384 2149.92,571.35 \n",
" 2150.84,571.318 2151.76,571.286 2152.68,571.256 2153.6,571.227 2154.51,571.2 2155.43,571.173 2156.35,571.148 2157.27,571.124 2158.18,571.102 2159.1,571.081 \n",
" 2160.02,571.061 2160.94,571.042 2161.86,571.025 2162.77,571.009 2163.69,570.995 2164.61,570.982 2165.53,570.97 2166.44,570.959 2167.36,570.95 2168.28,570.942 \n",
" 2169.2,570.936 2170.12,570.93 2171.03,570.926 2171.95,570.924 2172.87,570.922 2173.79,570.922 2174.7,570.924 2175.62,570.926 2176.54,570.93 2177.46,570.935 \n",
" 2178.38,570.942 2179.29,570.949 2180.21,570.958 2181.13,570.968 2182.05,570.979 2182.96,570.992 2183.88,571.005 2184.8,571.02 2185.72,571.036 2186.64,571.053 \n",
" 2187.55,571.071 2188.47,571.09 2189.39,571.111 2190.31,571.132 2191.22,571.154 2192.14,571.178 2193.06,571.202 2193.98,571.227 2194.9,571.254 2195.81,571.281 \n",
" 2196.73,571.309 2197.65,571.338 2198.57,571.368 2199.48,571.398 2200.4,571.43 2201.32,571.462 2202.24,571.495 2203.16,571.529 2204.07,571.563 2204.99,571.598 \n",
" 2205.91,571.634 2206.83,571.67 2207.74,571.707 2208.66,571.745 2209.58,571.783 2210.5,571.821 2211.42,571.861 2212.33,571.9 2213.25,571.94 2214.17,571.98 \n",
" 2215.09,572.021 2216,572.062 2216.92,572.104 2217.84,572.145 2218.76,572.187 2219.68,572.229 2220.59,572.272 2221.51,572.314 2222.43,572.357 2223.35,572.4 \n",
" 2224.27,572.443 2225.18,572.486 2226.1,572.528 2227.02,572.571 2227.94,572.614 2228.85,572.657 2229.77,572.7 2230.69,572.743 2231.61,572.786 2232.53,572.828 \n",
" 2233.44,572.87 2234.36,572.912 2235.28,572.954 2236.2,572.996 2237.11,573.037 2238.03,573.078 2238.95,573.119 2239.87,573.159 2240.79,573.199 2241.7,573.238 \n",
" 2242.62,573.277 2243.54,573.316 2244.46,573.354 2245.37,573.392 2246.29,573.429 2247.21,573.465 2248.13,573.501 2249.05,573.537 2249.96,573.572 2250.88,573.606 \n",
" 2251.8,573.64 2252.72,573.672 2253.63,573.705 2254.55,573.736 2255.47,573.767 2256.39,573.797 2257.31,573.827 2258.22,573.856 2259.14,573.884 2260.06,573.911 \n",
" 2260.98,573.937 2261.89,573.963 2262.81,573.987 2263.73,574.011 2264.65,574.035 2265.57,574.057 2266.48,574.078 2267.4,574.099 2268.32,574.118 2269.24,574.137 \n",
" 2270.15,574.155 2271.07,574.172 2271.99,574.188 2272.91,574.204 2273.83,574.218 2274.74,574.232 2275.66,574.244 2276.58,574.256 2277.5,574.266 2278.41,574.276 \n",
" 2279.33,574.285 2280.25,574.293 2281.17,574.3 2282.09,574.306 2283,574.311 2283.92,574.316 2284.84,574.319 2285.76,574.322 2286.67,574.323 2287.59,574.324 \n",
" 2288.51,574.324 2289.43,574.323 2290.35,574.321 2291.26,574.318 2292.18,574.314 2293.1,574.309 2294.02,574.304 2294.94,574.298 2295.85,574.29 2296.77,574.283 \n",
" 2297.69,574.274 \n",
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" 911.823,1388.71 912.741,1388.71 913.658,1388.71 914.576,1388.71 915.494,1388.71 916.412,1388.71 917.33,1388.71 918.247,1388.71 919.165,1388.71 920.083,1388.71 \n",
" 921.001,1388.71 921.919,1388.71 922.836,1388.71 923.754,1388.71 924.672,1388.71 925.59,1388.71 926.508,1388.71 927.425,1388.71 928.343,1388.71 929.261,1388.71 \n",
" 930.179,1388.71 931.097,1388.71 932.014,1388.71 932.932,1388.71 933.85,1388.71 934.768,1388.71 935.685,1388.71 936.603,1388.71 937.521,1388.71 938.439,1388.71 \n",
" 939.357,1388.71 940.274,1388.71 941.192,1388.71 942.11,1388.71 943.028,1388.71 943.946,1388.71 944.863,1388.71 945.781,1388.71 946.699,1388.71 947.617,1388.71 \n",
" 948.535,1388.71 949.452,1388.71 950.37,1388.71 951.288,1388.71 952.206,1388.71 953.124,1388.71 954.041,1388.71 954.959,1388.71 955.877,1388.71 956.795,1388.71 \n",
" 957.712,1388.71 958.63,1388.71 959.548,1388.71 960.466,1388.71 961.384,1388.71 962.301,1388.71 963.219,1388.71 964.137,1388.71 965.055,1388.71 965.973,1388.71 \n",
" 966.89,1388.71 967.808,1388.71 968.726,1388.71 969.644,1388.71 970.562,1388.71 971.479,1388.71 972.397,1388.71 973.315,1388.71 974.233,1388.71 975.151,1388.71 \n",
" 976.068,1388.71 976.986,1388.71 977.904,1388.71 978.822,1388.71 979.739,1388.71 980.657,1388.71 981.575,1388.71 982.493,1388.71 983.411,1388.71 984.328,1388.71 \n",
" 985.246,1388.71 986.164,1388.71 987.082,1388.71 988,1388.71 988.917,1388.71 989.835,1388.71 990.753,1388.71 991.671,1388.71 992.589,1388.71 993.506,1388.71 \n",
" 994.424,1388.71 995.342,1388.71 996.26,1388.71 997.178,1388.71 998.095,1388.71 999.013,1388.71 999.931,1388.71 1000.85,1388.71 1001.77,1388.71 1002.68,1388.71 \n",
" 1003.6,1388.71 1004.52,1388.71 1005.44,1388.71 1006.36,1388.71 1007.27,1388.71 1008.19,1388.71 1009.11,1388.71 1010.03,1388.71 1010.94,1388.71 1011.86,1388.71 \n",
" 1012.78,1388.71 1013.7,1388.71 1014.62,1388.71 1015.53,1388.71 1016.45,1388.71 1017.37,1388.71 1018.29,1388.71 1019.2,1388.71 1020.12,1388.71 1021.04,1388.71 \n",
" 1021.96,1388.71 1022.88,1388.71 1023.79,1388.71 1024.71,1388.71 1025.63,1388.71 1026.55,1388.71 1027.46,1388.71 1028.38,1388.71 1029.3,1388.71 1030.22,1388.71 \n",
" 1031.14,1388.71 1032.05,1388.71 1032.97,1388.71 1033.89,1388.71 1034.81,1388.71 1035.72,1388.71 1036.64,1388.71 1037.56,1388.71 1038.48,1388.71 1039.4,1388.71 \n",
" 1040.31,1388.71 1041.23,1388.71 1042.15,1388.71 1043.07,1388.71 1043.98,1388.71 1044.9,1388.71 1045.82,1388.71 1046.74,1388.71 1047.66,1388.71 1048.57,1388.71 \n",
" 1049.49,1388.71 1050.41,1388.71 1051.33,1388.71 1052.25,1388.71 1053.16,1388.71 1054.08,1388.71 1055,1388.71 1055.92,1388.71 1056.83,1388.71 1057.75,1388.71 \n",
" 1058.67,1388.71 1059.59,1388.71 1060.51,1388.71 1061.42,1388.71 1062.34,1388.71 1063.26,1388.71 1064.18,1388.71 1065.09,1388.71 1066.01,1388.71 1066.93,1388.71 \n",
" 1067.85,1388.71 1068.77,1388.71 1069.68,1388.71 1070.6,1388.71 1071.52,1388.71 1072.44,1388.71 1073.35,1388.71 1074.27,1388.71 1075.19,1388.71 1076.11,1388.71 \n",
" 1077.03,1388.71 1077.94,1388.71 1078.86,1388.71 1079.78,1388.71 1080.7,1388.71 1081.61,1388.71 1082.53,1388.71 1083.45,1388.71 1084.37,1388.71 1085.29,1388.71 \n",
" 1086.2,1388.71 1087.12,1388.71 1088.04,1388.71 1088.96,1388.71 1089.87,1388.71 1090.79,1388.71 1091.71,1388.71 1092.63,1388.71 1093.55,1388.71 1094.46,1388.71 \n",
" 1095.38,1388.71 1096.3,1388.71 1097.22,1388.71 1098.13,1388.71 1099.05,1388.71 1099.97,1388.71 1100.89,1388.71 1101.81,1388.71 1102.72,1388.71 1103.64,1388.71 \n",
" 1104.56,1388.71 1105.48,1388.71 1106.39,1388.71 1107.31,1388.71 1108.23,1388.71 1109.15,1388.71 1110.07,1388.71 1110.98,1388.71 1111.9,1388.71 1112.82,1388.71 \n",
" 1113.74,1388.71 1114.65,1388.71 1115.57,1388.71 1116.49,1388.71 1117.41,1388.71 1118.33,1388.71 1119.24,1388.71 1120.16,1388.71 1121.08,1388.71 1122,1388.71 \n",
" 1122.91,1388.71 1123.83,1388.71 1124.75,1388.71 1125.67,1388.71 1126.59,1388.71 1127.5,1388.71 1128.42,1388.71 1129.34,1388.71 1130.26,1388.71 1131.18,1388.71 \n",
" 1132.09,1388.71 1133.01,1388.71 1133.93,1388.71 1134.85,1388.71 1135.76,1388.71 1136.68,1388.71 1137.6,1388.71 1138.52,1388.71 1139.44,1388.71 1140.35,1388.71 \n",
" 1141.27,1388.71 1142.19,1388.71 1143.11,1388.71 1144.02,1388.71 1144.94,1388.71 1145.86,1388.71 1146.78,1388.71 1147.7,1388.71 1148.61,1388.71 1149.53,1388.71 \n",
" 1150.45,1388.71 1151.37,1388.71 1152.28,1388.71 1153.2,1388.71 1154.12,1388.71 1155.04,1388.71 1155.96,1388.71 1156.87,1388.71 1157.79,1388.71 1158.71,1388.71 \n",
" 1159.63,1388.71 1160.54,1388.71 1161.46,1388.71 1162.38,1388.71 1163.3,1388.71 1164.22,1388.71 1165.13,1388.71 1166.05,1388.71 1166.97,1388.71 1167.89,1388.71 \n",
" 1168.8,1388.71 1169.72,1388.71 1170.64,1388.71 1171.56,1388.71 1172.48,1388.71 1173.39,1388.71 1174.31,1388.71 1175.23,1388.71 1176.15,1388.71 1177.06,1388.71 \n",
" 1177.98,1388.71 1178.9,1388.71 1179.82,1388.71 1180.74,1388.71 1181.65,1388.71 1182.57,1388.71 1183.49,1388.71 1184.41,1388.71 1185.32,1388.71 1186.24,1388.71 \n",
" 1187.16,1388.71 1188.08,1388.71 1189,1388.71 1189.91,1388.71 1190.83,1388.71 1191.75,1388.71 1192.67,1388.71 1193.58,1388.71 1194.5,1388.71 1195.42,1388.71 \n",
" 1196.34,1388.71 1197.26,1388.71 1198.17,1388.71 1199.09,1388.71 1200.01,1388.71 1200.93,1388.71 1201.85,1388.71 1202.76,1388.71 1203.68,1388.71 1204.6,1388.71 \n",
" 1205.52,1388.71 1206.43,1388.71 1207.35,1388.71 1208.27,1388.71 1209.19,1388.71 1210.11,1388.71 1211.02,1388.71 1211.94,1388.71 1212.86,1388.71 1213.78,1388.71 \n",
" 1214.69,1388.71 1215.61,1388.71 1216.53,1388.71 1217.45,1388.71 1218.37,1388.71 1219.28,1388.71 1220.2,1388.71 1221.12,1388.71 1222.04,1388.71 1222.95,1388.71 \n",
" 1223.87,1388.71 1224.79,1388.71 1225.71,1388.71 1226.63,1388.71 1227.54,1388.71 1228.46,1388.71 1229.38,1388.71 1230.3,1388.71 1231.21,1388.71 1232.13,1388.71 \n",
" 1233.05,1388.71 1233.97,1388.71 1234.89,1388.71 1235.8,1388.71 1236.72,1388.71 1237.64,1388.71 1238.56,1388.71 1239.47,1388.71 1240.39,1388.71 1241.31,1388.71 \n",
" 1242.23,1388.71 1243.15,1388.71 1244.06,1388.71 1244.98,1388.71 1245.9,1388.71 1246.82,1388.71 1247.73,1388.71 1248.65,1388.71 1249.57,1388.71 1250.49,1388.71 \n",
" 1251.41,1388.71 1252.32,1388.71 1253.24,1388.71 1254.16,1388.71 1255.08,1388.71 1255.99,1388.71 1256.91,1388.71 1257.83,1388.71 1258.75,1388.71 1259.67,1388.71 \n",
" 1260.58,1388.71 1261.5,1388.71 1262.42,1388.71 1263.34,1388.71 1264.25,1388.71 1265.17,1388.71 1266.09,1388.71 1267.01,1388.71 1267.93,1388.71 1268.84,1388.71 \n",
" 1269.76,1388.71 1270.68,1388.71 1271.6,1388.71 1272.52,1388.71 1273.43,1388.71 1274.35,1388.71 1275.27,1388.71 1276.19,1388.71 1277.1,1388.71 1278.02,1388.71 \n",
" 1278.94,1388.71 1279.86,1388.71 1280.78,1388.71 1281.69,1388.71 1282.61,1388.71 1283.53,1388.71 1284.45,1388.71 1285.36,1388.71 1286.28,1388.71 1287.2,1388.71 \n",
" 1288.12,1388.71 1289.04,1388.71 1289.95,1388.71 1290.87,1388.71 1291.79,1388.71 1292.71,1388.71 1293.62,1388.71 1294.54,1388.71 1295.46,1388.71 1296.38,1388.71 \n",
" 1297.3,1388.71 1298.21,1388.71 1299.13,1388.71 1300.05,1388.71 1300.97,1388.71 1301.88,1388.71 1302.8,1388.71 1303.72,1388.71 1304.64,1388.71 1305.56,1388.71 \n",
" 1306.47,1388.71 1307.39,1388.71 1308.31,1388.71 1309.23,1388.71 1310.14,1388.71 1311.06,1388.71 1311.98,1388.71 1312.9,1388.71 1313.82,1388.71 1314.73,1388.71 \n",
" 1315.65,1388.71 1316.57,1388.71 1317.49,1388.71 1318.4,1388.71 1319.32,1388.71 1320.24,1388.71 1321.16,1388.71 1322.08,1388.71 1322.99,1388.71 1323.91,1388.71 \n",
" 1324.83,1388.71 1325.75,1388.71 1326.66,1388.71 1327.58,1388.71 1328.5,1388.71 1329.42,1388.71 1330.34,1388.71 1331.25,1388.71 1332.17,1388.71 1333.09,1388.71 \n",
" 1334.01,1388.71 1334.92,1388.71 1335.84,1388.71 1336.76,1388.71 1337.68,1388.71 1338.6,1388.71 1339.51,1388.71 1340.43,1388.71 1341.35,1388.71 1342.27,1388.71 \n",
" 1343.18,1388.71 1344.1,1388.71 1345.02,1388.71 1345.94,1388.71 1346.86,1388.71 1347.77,1388.71 1348.69,1388.71 1349.61,1388.71 1350.53,1388.71 1351.45,1388.71 \n",
" 1352.36,1388.71 1353.28,1388.71 1354.2,1388.71 1355.12,1388.71 1356.03,1388.71 1356.95,1388.71 1357.87,1388.71 1358.79,1388.71 1359.71,1388.71 1360.62,1388.71 \n",
" 1361.54,1388.71 1362.46,1388.71 1363.38,1388.71 1364.29,1388.71 1365.21,1388.71 1366.13,1388.71 1367.05,1388.71 1367.97,1388.71 1368.88,1388.71 1369.8,1388.71 \n",
" 1370.72,1388.71 1371.64,1388.71 1372.55,1388.71 1373.47,1388.71 1374.39,1388.71 1375.31,1388.71 1376.23,1388.71 1377.14,1388.71 1378.06,1388.71 1378.98,1388.71 \n",
" 1379.9,1388.71 1380.81,1388.71 1381.73,1388.71 1382.65,1388.71 1383.57,1388.71 1384.49,1388.71 1385.4,1388.71 1386.32,1388.71 1387.24,1388.71 1388.16,1388.71 \n",
" 1389.07,1388.71 1389.99,1388.71 1390.91,1388.71 1391.83,1388.71 1392.75,1388.71 1393.66,1388.71 1394.58,1388.71 1395.5,1388.71 1396.42,1388.71 1397.33,1388.71 \n",
" 1398.25,1388.71 1399.17,1388.71 1400.09,1388.71 1401.01,1388.71 1401.92,1388.71 1402.84,1388.71 1403.76,1388.71 1404.68,1388.71 1405.59,1388.71 1406.51,1388.71 \n",
" 1407.43,1388.71 1408.35,1388.71 1409.27,1388.71 1410.18,1388.71 1411.1,1388.71 1412.02,1388.71 1412.94,1388.71 1413.85,1388.71 1414.77,1388.71 1415.69,1388.71 \n",
" 1416.61,1388.71 1417.53,1388.71 1418.44,1388.71 1419.36,1388.71 1420.28,1388.71 1421.2,1388.71 1422.12,1388.71 1423.03,1388.71 1423.95,1388.71 1424.87,1388.71 \n",
" 1425.79,1388.71 1426.7,1388.71 1427.62,1388.71 1428.54,1388.71 1429.46,1388.71 1430.38,1388.71 1431.29,1388.71 1432.21,1388.71 1433.13,1388.71 1434.05,1388.71 \n",
" 1434.96,1388.71 1435.88,1388.71 1436.8,1388.71 1437.72,1388.71 1438.64,1388.71 1439.55,1388.71 1440.47,1388.71 1441.39,1388.71 1442.31,1388.71 1443.22,1388.71 \n",
" 1444.14,1388.71 1445.06,1388.71 1445.98,1388.71 1446.9,1388.71 1447.81,1388.71 1448.73,1388.71 1449.65,1388.71 1450.57,1388.71 1451.48,1388.71 1452.4,1388.71 \n",
" 1453.32,1388.71 1454.24,1388.71 1455.16,1388.71 1456.07,1388.71 1456.99,1388.71 1457.91,1388.71 1458.83,1388.71 1459.74,1388.71 1460.66,1388.71 1461.58,1388.71 \n",
" 1462.5,1388.71 1463.42,1388.71 1464.33,1388.71 1465.25,1388.71 1466.17,1388.71 1467.09,1388.71 1468,1388.71 1468.92,1388.71 1469.84,1388.71 1470.76,1388.71 \n",
" 1471.68,1388.71 1472.59,1388.71 1473.51,1388.71 1474.43,1388.71 1475.35,1388.71 1476.26,1388.71 1477.18,1388.71 1478.1,1388.71 1479.02,1388.71 1479.94,1388.71 \n",
" 1480.85,1388.71 1481.77,1388.71 1482.69,1388.71 1483.61,1388.71 1484.52,1388.71 1485.44,1388.71 1486.36,1388.71 1487.28,1388.71 1488.2,1388.71 1489.11,1388.71 \n",
" 1490.03,1388.71 1490.95,1388.71 1491.87,1388.71 1492.79,1388.71 1493.7,1388.71 1494.62,1388.71 1495.54,1388.71 1496.46,1388.71 1497.37,1388.71 1498.29,1388.71 \n",
" 1499.21,1388.71 1500.13,1388.71 1501.05,1388.71 1501.96,1388.71 1502.88,1388.71 1503.8,1388.71 1504.72,1388.71 1505.63,1388.71 1506.55,1388.71 1507.47,1388.71 \n",
" 1508.39,1388.71 1509.31,1388.71 1510.22,1388.71 1511.14,1388.71 1512.06,1388.71 1512.98,1388.71 1513.89,1388.71 1514.81,1388.71 1515.73,1388.71 1516.65,1388.71 \n",
" 1517.57,1388.71 1518.48,1388.71 1519.4,1388.71 1520.32,1388.71 1521.24,1388.71 1522.15,1388.71 1523.07,1388.71 1523.99,1388.71 1524.91,1388.71 1525.83,1388.71 \n",
" 1526.74,1388.71 1527.66,1388.71 1528.58,1388.71 1529.5,1388.71 1530.41,1388.71 1531.33,1388.71 1532.25,1388.71 1533.17,1388.71 1534.09,1388.71 1535,1388.71 \n",
" 1535.92,1388.71 1536.84,1388.71 1537.76,1388.71 1538.67,1388.71 1539.59,1388.71 1540.51,1388.71 1541.43,1388.71 1542.35,1388.71 1543.26,1388.71 1544.18,1388.71 \n",
" 1545.1,1388.71 1546.02,1388.71 1546.93,1388.71 1547.85,1388.71 1548.77,1388.71 1549.69,1388.71 1550.61,1388.71 1551.52,1388.71 1552.44,1388.71 1553.36,1388.71 \n",
" 1554.28,1388.71 1555.19,1388.71 1556.11,1388.71 1557.03,1388.71 1557.95,1388.71 1558.87,1388.71 1559.78,1388.71 1560.7,1388.71 1561.62,1388.71 1562.54,1388.71 \n",
" 1563.46,1388.71 1564.37,1388.71 1565.29,1388.71 1566.21,1388.71 1567.13,1388.71 1568.04,1388.71 1568.96,1388.71 1569.88,1388.71 1570.8,1388.71 1571.72,1388.71 \n",
" 1572.63,1388.71 1573.55,1388.71 1574.47,1388.71 1575.39,1388.71 1576.3,1388.71 1577.22,1388.71 1578.14,1388.71 1579.06,1388.71 1579.98,1388.71 1580.89,1388.71 \n",
" 1581.81,1388.71 1582.73,1388.71 1583.65,1388.71 1584.56,1388.71 1585.48,1388.71 1586.4,1388.71 1587.32,1388.71 1588.24,1388.71 1589.15,1388.71 1590.07,1388.71 \n",
" 1590.99,1388.71 1591.91,1388.71 1592.82,1388.71 1593.74,1388.71 1594.66,1388.71 1595.58,1388.71 1596.5,1388.71 1597.41,1388.71 1598.33,1388.71 1599.25,1388.71 \n",
" 1600.17,1388.71 1601.08,1388.71 1602,1388.71 1602.92,1388.71 1603.84,1388.71 1604.76,1388.71 1605.67,1388.71 1606.59,1388.71 1607.51,1388.71 1608.43,1388.71 \n",
" 1609.34,1388.71 1610.26,1388.71 1611.18,1388.71 1612.1,1388.71 1613.02,1388.71 1613.93,1388.71 1614.85,1388.71 1615.77,1388.71 1616.69,1388.71 1617.6,1388.71 \n",
" 1618.52,1388.71 1619.44,1388.71 1620.36,1388.71 1621.28,1388.71 1622.19,1388.71 1623.11,1388.71 1624.03,1388.71 1624.95,1388.71 1625.86,1388.71 1626.78,1388.71 \n",
" 1627.7,1388.71 1628.62,1388.71 1629.54,1388.71 1630.45,1388.71 1631.37,1388.71 1632.29,1388.71 1633.21,1388.71 1634.12,1388.71 1635.04,1388.71 1635.96,1388.71 \n",
" 1636.88,1388.71 1637.8,1388.71 1638.71,1388.71 1639.63,1388.71 1640.55,1388.71 1641.47,1388.71 1642.39,1388.71 1643.3,1388.71 1644.22,1388.71 1645.14,1388.71 \n",
" 1646.06,1388.71 1646.97,1388.71 1647.89,1388.71 1648.81,1388.71 1649.73,1388.71 1650.65,1388.71 1651.56,1388.71 1652.48,1388.71 1653.4,1388.71 1654.32,1388.71 \n",
" 1655.23,1388.71 1656.15,1388.71 1657.07,1388.71 1657.99,1388.71 1658.91,1388.71 1659.82,1388.71 1660.74,1388.71 1661.66,1388.71 1662.58,1388.71 1663.49,1388.71 \n",
" 1664.41,1388.71 1665.33,1388.71 1666.25,1388.71 1667.17,1388.71 1668.08,1388.71 1669,1388.71 1669.92,1388.71 1670.84,1388.71 1671.75,1388.71 1672.67,1388.71 \n",
" 1673.59,1388.71 1674.51,1388.71 1675.43,1388.71 1676.34,1388.71 1677.26,1388.71 1678.18,1388.71 1679.1,1388.71 1680.01,1388.71 1680.93,1388.71 1681.85,1388.71 \n",
" 1682.77,1388.71 1683.69,1388.71 1684.6,1388.71 1685.52,1388.71 1686.44,1388.71 1687.36,1388.71 1688.27,1388.71 1689.19,1388.71 1690.11,1388.71 1691.03,1388.71 \n",
" 1691.95,1388.71 1692.86,1388.71 1693.78,1388.71 1694.7,1388.71 1695.62,1388.71 1696.53,1388.71 1697.45,1388.71 1698.37,1388.71 1699.29,1388.71 1700.21,1388.71 \n",
" 1701.12,1388.71 1702.04,1388.71 1702.96,1388.71 1703.88,1388.71 1704.79,1388.71 1705.71,1388.71 1706.63,1388.71 1707.55,1388.71 1708.47,1388.71 1709.38,1388.71 \n",
" 1710.3,1388.71 1711.22,1388.71 1712.14,1388.71 1713.06,1388.71 1713.97,1388.71 1714.89,1388.71 1715.81,1388.71 1716.73,1388.71 1717.64,1388.71 1718.56,1388.71 \n",
" 1719.48,1388.71 1720.4,1388.71 1721.32,1388.71 1722.23,1388.71 1723.15,1388.71 1724.07,1388.71 1724.99,1388.71 1725.9,1388.71 1726.82,1388.71 1727.74,1388.71 \n",
" 1728.66,1388.71 1729.58,1388.71 1730.49,1388.71 1731.41,1388.71 1732.33,1388.71 1733.25,1388.71 1734.16,1388.71 1735.08,1388.71 1736,1388.71 1736.92,1388.71 \n",
" 1737.84,1388.71 1738.75,1388.71 1739.67,1388.71 1740.59,1388.71 1741.51,1388.71 1742.42,1388.71 1743.34,1388.71 1744.26,1388.71 1745.18,1388.71 1746.1,1388.71 \n",
" 1747.01,1388.71 1747.93,1388.71 1748.85,1388.71 1749.77,1388.71 1750.68,1388.71 1751.6,1388.71 1752.52,1388.71 1753.44,1388.71 1754.36,1388.71 1755.27,1388.71 \n",
" 1756.19,1388.71 1757.11,1388.71 1758.03,1388.71 1758.94,1388.71 1759.86,1388.71 1760.78,1388.71 1761.7,1388.71 1762.62,1388.71 1763.53,1388.71 1764.45,1388.71 \n",
" 1765.37,1388.71 1766.29,1388.71 1767.2,1388.71 1768.12,1388.71 1769.04,1388.71 1769.96,1388.71 1770.88,1388.71 1771.79,1388.71 1772.71,1388.71 1773.63,1388.71 \n",
" 1774.55,1388.71 1775.46,1388.71 1776.38,1388.71 1777.3,1388.71 1778.22,1388.71 1779.14,1388.71 1780.05,1388.71 1780.97,1388.71 1781.89,1388.71 1782.81,1388.71 \n",
" 1783.73,1388.71 1784.64,1388.71 1785.56,1388.71 1786.48,1388.71 1787.4,1388.71 1788.31,1388.71 1789.23,1388.71 1790.15,1388.71 1791.07,1388.71 1791.99,1388.71 \n",
" 1792.9,1388.71 1793.82,1388.71 1794.74,1388.71 1795.66,1388.71 1796.57,1388.71 1797.49,1388.71 1798.41,1388.71 1799.33,1388.71 1800.25,1388.71 1801.16,1388.71 \n",
" 1802.08,1388.71 1803,1388.71 1803.92,1388.71 1804.83,1388.71 1805.75,1388.71 1806.67,1388.71 1807.59,1388.71 1808.51,1388.71 1809.42,1388.71 1810.34,1388.71 \n",
" 1811.26,1388.71 1812.18,1388.71 1813.09,1388.71 1814.01,1388.71 1814.93,1388.71 1815.85,1388.71 1816.77,1388.71 1817.68,1388.71 1818.6,1388.71 1819.52,1388.71 \n",
" 1820.44,1388.71 1821.35,1388.71 1822.27,1388.71 1823.19,1388.71 1824.11,1388.71 1825.03,1388.71 1825.94,1388.71 1826.86,1388.71 1827.78,1388.71 1828.7,1388.71 \n",
" 1829.61,1388.71 1830.53,1388.71 1831.45,1388.71 1832.37,1388.71 1833.29,1388.71 1834.2,1388.71 1835.12,1388.71 1836.04,1388.71 1836.96,1388.71 1837.87,1388.71 \n",
" 1838.79,1388.71 1839.71,1388.71 1840.63,1388.71 1841.55,1388.71 1842.46,1388.71 1843.38,1388.71 1844.3,1388.71 1845.22,1388.71 1846.13,1388.71 1847.05,1388.71 \n",
" 1847.97,1388.71 1848.89,1388.71 1849.81,1388.71 1850.72,1388.71 1851.64,1388.71 1852.56,1388.71 1853.48,1388.71 1854.39,1388.71 1855.31,1388.71 1856.23,1388.71 \n",
" 1857.15,1388.71 1858.07,1388.71 1858.98,1388.71 1859.9,1388.71 1860.82,1388.71 1861.74,1388.71 1862.66,1388.71 1863.57,1388.71 1864.49,1388.71 1865.41,1388.71 \n",
" 1866.33,1388.71 1867.24,1388.71 1868.16,1388.71 1869.08,1388.71 1870,1388.71 1870.92,1388.71 1871.83,1388.71 1872.75,1388.71 1873.67,1388.71 1874.59,1388.71 \n",
" 1875.5,1388.71 1876.42,1388.71 1877.34,1388.71 1878.26,1388.71 1879.18,1388.71 1880.09,1388.71 1881.01,1388.71 1881.93,1388.71 1882.85,1388.71 1883.76,1388.71 \n",
" 1884.68,1388.71 1885.6,1388.71 1886.52,1388.71 1887.44,1388.71 1888.35,1388.71 1889.27,1388.71 1890.19,1388.71 1891.11,1388.71 1892.02,1388.71 1892.94,1388.71 \n",
" 1893.86,1388.71 1894.78,1388.71 1895.7,1388.71 1896.61,1388.71 1897.53,1388.71 1898.45,1388.71 1899.37,1388.71 1900.28,1388.71 1901.2,1388.71 1902.12,1388.71 \n",
" 1903.04,1388.71 1903.96,1388.71 1904.87,1388.71 1905.79,1388.71 1906.71,1388.71 1907.63,1388.71 1908.54,1388.71 1909.46,1388.71 1910.38,1388.71 1911.3,1388.71 \n",
" 1912.22,1388.71 1913.13,1388.71 1914.05,1388.71 1914.97,1388.71 1915.89,1388.71 1916.8,1388.71 1917.72,1388.71 1918.64,1388.71 1919.56,1388.71 1920.48,1388.71 \n",
" 1921.39,1388.71 1922.31,1388.71 1923.23,1388.71 1924.15,1388.71 1925.06,1388.71 1925.98,1388.71 1926.9,1388.71 1927.82,1388.71 1928.74,1388.71 1929.65,1388.71 \n",
" 1930.57,1388.71 1931.49,1388.71 1932.41,1388.71 1933.33,1388.71 1934.24,1388.71 1935.16,1388.71 1936.08,1388.71 1937,1388.71 1937.91,1388.71 1938.83,1388.71 \n",
" 1939.75,1388.71 1940.67,1388.71 1941.59,1388.71 1942.5,1388.71 1943.42,1388.71 1944.34,1388.71 1945.26,1388.71 1946.17,1388.71 1947.09,1388.71 1948.01,1388.71 \n",
" 1948.93,1388.71 1949.85,1388.71 1950.76,1388.71 1951.68,1388.71 1952.6,1388.71 1953.52,1388.71 1954.43,1388.71 1955.35,1388.71 1956.27,1388.71 1957.19,1388.71 \n",
" 1958.11,1388.71 1959.02,1388.71 1959.94,1388.71 1960.86,1388.71 1961.78,1388.71 1962.69,1388.71 1963.61,1388.71 1964.53,1388.71 1965.45,1388.71 1966.37,1388.71 \n",
" 1967.28,1388.71 1968.2,1388.71 1969.12,1388.71 1970.04,1388.71 1970.95,1388.71 1971.87,1388.71 1972.79,1388.71 1973.71,1388.71 1974.63,1388.71 1975.54,1388.71 \n",
" 1976.46,1388.71 1977.38,1388.71 1978.3,1388.71 1979.21,1388.71 1980.13,1388.71 1981.05,1388.71 1981.97,1388.71 1982.89,1388.71 1983.8,1388.71 1984.72,1388.71 \n",
" 1985.64,1388.71 1986.56,1388.71 1987.47,1388.71 1988.39,1388.71 1989.31,1388.71 1990.23,1388.71 1991.15,1388.71 1992.06,1388.71 1992.98,1388.71 1993.9,1388.71 \n",
" 1994.82,1388.71 1995.73,1388.71 1996.65,1388.71 1997.57,1388.71 1998.49,1388.71 1999.41,1388.71 2000.32,1388.71 2001.24,1388.71 2002.16,1388.71 2003.08,1388.71 \n",
" 2004,1388.71 2004.91,1388.71 2005.83,1388.71 2006.75,1388.71 2007.67,1388.71 2008.58,1388.71 2009.5,1388.71 2010.42,1388.71 2011.34,1388.71 2012.26,1388.71 \n",
" 2013.17,1388.71 2014.09,1388.71 2015.01,1388.71 2015.93,1388.71 2016.84,1388.71 2017.76,1388.71 2018.68,1388.71 2019.6,1388.71 2020.52,1388.71 2021.43,1388.71 \n",
" 2022.35,1388.71 2023.27,1388.71 2024.19,1388.71 2025.1,1388.71 2026.02,1388.71 2026.94,1388.71 2027.86,1388.71 2028.78,1388.71 2029.69,1388.71 2030.61,1388.71 \n",
" 2031.53,1388.71 2032.45,1388.71 2033.36,1388.71 2034.28,1388.71 2035.2,1388.71 2036.12,1388.71 2037.04,1388.71 2037.95,1388.71 2038.87,1388.71 2039.79,1388.71 \n",
" 2040.71,1388.71 2041.62,1388.71 2042.54,1388.71 2043.46,1388.71 2044.38,1388.71 2045.3,1388.71 2046.21,1388.71 2047.13,1388.71 2048.05,1388.71 2048.97,1388.71 \n",
" 2049.88,1388.71 2050.8,1388.71 2051.72,1388.71 2052.64,1388.71 2053.56,1388.71 2054.47,1388.71 2055.39,1388.71 2056.31,1388.71 2057.23,1388.71 2058.14,1388.71 \n",
" 2059.06,1388.71 2059.98,1388.71 2060.9,1388.71 2061.82,1388.71 2062.73,1388.71 2063.65,1388.71 2064.57,1388.71 2065.49,1388.71 2066.4,1388.71 2067.32,1388.71 \n",
" 2068.24,1388.71 2069.16,1388.71 2070.08,1388.71 2070.99,1388.71 2071.91,1388.71 2072.83,1388.71 2073.75,1388.71 2074.67,1388.71 2075.58,1388.71 2076.5,1388.71 \n",
" 2077.42,1388.71 2078.34,1388.71 2079.25,1388.71 2080.17,1388.71 2081.09,1388.71 2082.01,1388.71 2082.93,1388.71 2083.84,1388.71 2084.76,1388.71 2085.68,1388.71 \n",
" 2086.6,1388.71 2087.51,1388.71 2088.43,1388.71 2089.35,1388.71 2090.27,1388.71 2091.19,1388.71 2092.1,1388.71 2093.02,1388.71 2093.94,1388.71 2094.86,1388.71 \n",
" 2095.77,1388.71 2096.69,1388.71 2097.61,1388.71 2098.53,1388.71 2099.45,1388.71 2100.36,1388.71 2101.28,1388.71 2102.2,1388.71 2103.12,1388.71 2104.03,1388.71 \n",
" 2104.95,1388.71 2105.87,1388.71 2106.79,1388.71 2107.71,1388.71 2108.62,1388.71 2109.54,1388.71 2110.46,1388.71 2111.38,1388.71 2112.29,1388.71 2113.21,1388.71 \n",
" 2114.13,1388.71 2115.05,1388.71 2115.97,1388.71 2116.88,1388.71 2117.8,1388.71 2118.72,1388.71 2119.64,1388.71 2120.55,1388.71 2121.47,1388.71 2122.39,1388.71 \n",
" 2123.31,1388.71 2124.23,1388.71 2125.14,1388.71 2126.06,1388.71 2126.98,1388.71 2127.9,1388.71 2128.81,1388.71 2129.73,1388.71 2130.65,1388.71 2131.57,1388.71 \n",
" 2132.49,1388.71 2133.4,1388.71 2134.32,1388.71 2135.24,1388.71 2136.16,1388.71 2137.07,1388.71 2137.99,1388.71 2138.91,1388.71 2139.83,1388.71 2140.75,1388.71 \n",
" 2141.66,1388.71 2142.58,1388.71 2143.5,1388.71 2144.42,1388.71 2145.33,1388.71 2146.25,1388.71 2147.17,1388.71 2148.09,1388.71 2149.01,1388.71 2149.92,1388.71 \n",
" 2150.84,1388.71 2151.76,1388.71 2152.68,1388.71 2153.6,1388.71 2154.51,1388.71 2155.43,1388.71 2156.35,1388.71 2157.27,1388.71 2158.18,1388.71 2159.1,1388.71 \n",
" 2160.02,1388.71 2160.94,1388.71 2161.86,1388.71 2162.77,1388.71 2163.69,1388.71 2164.61,1388.71 2165.53,1388.71 2166.44,1388.71 2167.36,1388.71 2168.28,1388.71 \n",
" 2169.2,1388.71 2170.12,1388.71 2171.03,1388.71 2171.95,1388.71 2172.87,1388.71 2173.79,1388.71 2174.7,1388.71 2175.62,1388.71 2176.54,1388.71 2177.46,1388.71 \n",
" 2178.38,1388.71 2179.29,1388.71 2180.21,1388.71 2181.13,1388.71 2182.05,1388.71 2182.96,1388.71 2183.88,1388.71 2184.8,1388.71 2185.72,1388.71 2186.64,1388.71 \n",
" 2187.55,1388.71 2188.47,1388.71 2189.39,1388.71 2190.31,1388.71 2191.22,1388.71 2192.14,1388.71 2193.06,1388.71 2193.98,1388.71 2194.9,1388.71 2195.81,1388.71 \n",
" 2196.73,1388.71 2197.65,1388.71 2198.57,1388.71 2199.48,1388.71 2200.4,1388.71 2201.32,1388.71 2202.24,1388.71 2203.16,1388.71 2204.07,1388.71 2204.99,1388.71 \n",
" 2205.91,1388.71 2206.83,1388.71 2207.74,1388.71 2208.66,1388.71 2209.58,1388.71 2210.5,1388.71 2211.42,1388.71 2212.33,1388.71 2213.25,1388.71 2214.17,1388.71 \n",
" 2215.09,1388.71 2216,1388.71 2216.92,1388.71 2217.84,1388.71 2218.76,1388.71 2219.68,1388.71 2220.59,1388.71 2221.51,1388.71 2222.43,1388.71 2223.35,1388.71 \n",
" 2224.27,1388.71 2225.18,1388.71 2226.1,1388.71 2227.02,1388.71 2227.94,1388.71 2228.85,1388.71 2229.77,1388.71 2230.69,1388.71 2231.61,1388.71 2232.53,1388.71 \n",
" 2233.44,1388.71 2234.36,1388.71 2235.28,1388.71 2236.2,1388.71 2237.11,1388.71 2238.03,1388.71 2238.95,1388.71 2239.87,1388.71 2240.79,1388.71 2241.7,1388.71 \n",
" 2242.62,1388.71 2243.54,1388.71 2244.46,1388.71 2245.37,1388.71 2246.29,1388.71 2247.21,1388.71 2248.13,1388.71 2249.05,1388.71 2249.96,1388.71 2250.88,1388.71 \n",
" 2251.8,1388.71 2252.72,1388.71 2253.63,1388.71 2254.55,1388.71 2255.47,1388.71 2256.39,1388.71 2257.31,1388.71 2258.22,1388.71 2259.14,1388.71 2260.06,1388.71 \n",
" 2260.98,1388.71 2261.89,1388.71 2262.81,1388.71 2263.73,1388.71 2264.65,1388.71 2265.57,1388.71 2266.48,1388.71 2267.4,1388.71 2268.32,1388.71 2269.24,1388.71 \n",
" 2270.15,1388.71 2271.07,1388.71 2271.99,1388.71 2272.91,1388.71 2273.83,1388.71 2274.74,1388.71 2275.66,1388.71 2276.58,1388.71 2277.5,1388.71 2278.41,1388.71 \n",
" 2279.33,1388.71 2280.25,1388.71 2281.17,1388.71 2282.09,1388.71 2283,1388.71 2283.92,1388.71 2284.84,1388.71 2285.76,1388.71 2286.67,1388.71 2287.59,1388.71 \n",
" 2288.51,1388.71 2289.43,1388.71 2290.35,1388.71 2291.26,1388.71 2292.18,1388.71 2293.1,1388.71 2294.02,1388.71 2294.94,1388.71 2295.85,1388.71 2296.77,1388.71 \n",
" 2297.69,1388.71 \n",
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]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"latticeSize=5\n",
"setup=getSetup(latticeSize)\n",
"numTimeSteps=2000\n",
"displacements=[]\n",
"save=true\n",
"returnEvery=1\n",
"runMetavoxelGPU!(setup,numTimeSteps,latticeSize,displacements,returnEvery,true)\n",
"\n",
"numTimeStepsRecorded=length(displacements)\n",
"d=[]\n",
"dFEA=[]\n",
"j=length(displacements[end])\n",
"step=1\n",
"for i in 1:step:numTimeStepsRecorded\n",
" append!(d,displacements[i][j].y)\n",
" append!(dFEA,displacementFEA[j].y)\n",
"end\n",
"\n",
"DDisplacements[latticeSize]=d*100\n",
"DDisplacementsFEA[latticeSize]=dFEA*100\n",
"\n",
"E1=getYoungsModulus(latticeSize,5,displacementFEA,Load,topNodesIndices)/1000\n",
"E2=getYoungsModulus(latticeSize,5,displacements[end],Load,topNodesIndices)/1000\n",
"\n",
"EsFEA[latticeSize]=E1\n",
"Es[latticeSize]=E2\n",
"\n",
"print(\"EsFEA:\" )\n",
"println(EsFEA)\n",
"print(\"Es:\" )\n",
"println(Es)\n",
"\n",
"println(\"FEA displacement= $(displacementFEA[j].y),converged displacement= $(displacements[numTimeStepsRecorded][j].y)\")\n",
"plot(1:step:numTimeStepsRecorded,d*100,label=\"Dynamic\",xlabel=\"timestep\",ylabel=\"displacement\",title=\"$latticeSize Voxel Convergence Study\")\n",
"plot!(1:step:numTimeStepsRecorded,dFEA*100,label=\"FEA\")\n",
"# savefig(\"5_voxel_convergence\")"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
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" \"/>\n",
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2045.56, 283.175)\" x=\"2045.56\" y=\"283.175\">Dyanmic</text>\n",
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"<g clip-path=\"url(#clip5200)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2045.56, 343.655)\" x=\"2045.56\" y=\"343.655\">FEA</text>\n",
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]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n=[]\n",
"nFEA=[]\n",
"j=length(displacements[end])\n",
"for i in 1:j\n",
" append!(n,displacements[end][i].y)\n",
" append!(nFEA,displacementFEA[i].y)\n",
"end\n",
"scatter(1:j,n,label=\"Dyanmic\",xlabel=\"Node ID\",ylabel=\"displacement\",title=\"Node Displacement\")\n",
"scatter!(1:j,nFEA,label=\"FEA\")\n",
"# savefig(\"node_displacement_one_voxel\")"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"ename": "UndefVarError",
"evalue": "UndefVarError: E1 not defined",
"output_type": "error",
"traceback": [
"UndefVarError: E1 not defined",
"",
"Stacktrace:",
" [1] top-level scope at In[28]:15"
]
}
],
"source": [
"function getYoungsModulus(latticeSize,voxelSize,disp,Load,topNodesIndices)\n",
" F=-Load\n",
" l0=voxelSize*sqrt(2)/100.0*latticeSize\n",
" A=(voxelSize*sqrt(2)/100.0)^2*latticeSize^2\n",
"\n",
" δl1=-mean( x.y for x in disp[topNodesIndices])\n",
"\n",
" stresses=F/A\n",
" strain=δl1/l0\n",
"\n",
" E=stresses/strain *1e-9\n",
"\n",
" return E\n",
"end\n",
"\n",
"# F=-Load\n",
"# l0=5*sqrt(2)/100.0*latticeSize\n",
"# A=(5*sqrt(2)/100.0)^2*latticeSize^2\n",
"\n",
"# δl1=-mean( x.y for x in displacementFEA[topNodesIndices])\n",
"# δl2=-mean( x.y for x in displacements[end][topNodesIndices])\n",
"\n",
"# stresses=F/A\n",
"# strain1=δl1/l0\n",
"# strain2=δl2/l0\n",
"\n",
"# # DDisplacements[latticeSize]=[displacements[end][end].y]\n",
"# # DDisplacementsFEA[latticeSize]=[displacementFEA[end].y]\n",
"\n",
"# E1=getYoungsModulus(latticeSize,5,displacementFEA,Load,topNodesIndices)/1000\n",
"# E2=getYoungsModulus(latticeSize,5,displacements[end],Load,topNodesIndices)/1000\n",
"# EsFEA[latticeSize]=E1\n",
"# Es[latticeSize]=E2\n",
"\n",
"println(\"E FEA= $E1,E dynamic= $E2\")\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"# Es1=[0.060884503402759034, 0.028613329550419765,0.04290673059936012,0.05720947849175027,0.07151182744350526 ]\n",
"# Es2=[4.476556777767441 ,2.4245859780625727, 2.450108731865717,2.4714994633266203,2.464207835015529]\n",
"\n",
"# EsFEA=[9.777375254441967, 4.997590597979953, 7.496951555575914,9.995905987397883,12.494879504999625 ] #FEA\n",
"# Es=[4.476556777767441 ,2.4245859780625727, 2.450108731865717,2.4714994633266203,2.464207835015529] #DYNAMIC"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:middle;\" transform=\"rotate(0, 1297.64, 1479.62)\" x=\"1297.64\" y=\"1479.62\">3</text>\n",
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"<circle clip-path=\"url(#clip3402)\" cx=\"1795.33\" cy=\"1388.71\" r=\"14\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"none\"/>\n",
"<circle clip-path=\"url(#clip3402)\" cx=\"2293.03\" cy=\"1388.71\" r=\"14\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" stroke=\"none\"/>\n",
"<path clip-path=\"url(#clip3400)\" d=\"\n",
"M1853.56 386.635 L2280.76 386.635 L2280.76 205.195 L1853.56 205.195 Z\n",
" \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
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" \"/>\n",
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" 1877.56,265.675 2021.56,265.675 \n",
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"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 2045.56, 283.175)\" x=\"2045.56\" y=\"283.175\">Dyanmic</text>\n",
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" 1877.56,326.155 2021.56,326.155 \n",
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},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(1:5,Es,label=\"Dyanmic\",xlabel=\"lattice size\",ylabel=\"E\",title=\"Young's Modulus\")\n",
"plot!(1:5,EsFEA,label=\"FEA\")\n",
"scatter!(1:5,Es,color=\"black\",label=\"\")\n",
"scatter!(1:5,EsFEA,color=\"black\",label=\"\")\n",
"# savefig(\"youngs_modulus\")"
]
},
{
"cell_type": "code",
"execution_count": 885,
"metadata": {},
"outputs": [
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" 1288.17,243.863 1289.06,243.863 1289.96,243.863 1290.85,243.863 1291.75,243.863 1292.64,243.863 1293.54,243.863 1294.43,243.863 1295.33,243.863 1296.22,243.863 \n",
" 1297.12,243.863 1298.01,243.863 1298.9,243.863 1299.8,243.863 1300.69,243.863 1301.59,243.863 1302.48,243.863 1303.38,243.863 1304.27,243.863 1305.17,243.863 \n",
" 1306.06,243.863 1306.96,243.863 1307.85,243.863 1308.75,243.863 1309.64,243.863 1310.53,243.863 1311.43,243.863 1312.32,243.863 1313.22,243.863 1314.11,243.863 \n",
" 1315.01,243.863 1315.9,243.863 1316.8,243.863 1317.69,243.863 1318.59,243.863 1319.48,243.863 1320.38,243.863 1321.27,243.863 1322.16,243.863 1323.06,243.863 \n",
" 1323.95,243.863 1324.85,243.863 1325.74,243.863 1326.64,243.863 1327.53,243.863 1328.43,243.863 1329.32,243.863 1330.22,243.863 1331.11,243.863 1332.01,243.863 \n",
" 1332.9,243.863 1333.79,243.863 1334.69,243.863 1335.58,243.863 1336.48,243.863 1337.37,243.863 1338.27,243.863 1339.16,243.863 1340.06,243.863 1340.95,243.863 \n",
" 1341.85,243.863 1342.74,243.863 1343.64,243.863 1344.53,243.863 1345.42,243.863 1346.32,243.863 1347.21,243.863 1348.11,243.863 1349,243.863 1349.9,243.863 \n",
" 1350.79,243.863 1351.69,243.863 1352.58,243.863 1353.48,243.863 1354.37,243.863 1355.27,243.863 1356.16,243.863 1357.05,243.863 1357.95,243.863 1358.84,243.863 \n",
" 1359.74,243.863 1360.63,243.863 1361.53,243.863 1362.42,243.863 1363.32,243.863 1364.21,243.863 1365.11,243.863 1366,243.863 1366.9,243.863 1367.79,243.863 \n",
" 1368.68,243.863 1369.58,243.863 1370.47,243.863 1371.37,243.863 1372.26,243.863 1373.16,243.863 1374.05,243.863 1374.95,243.863 1375.84,243.863 1376.74,243.863 \n",
" 1377.63,243.863 1378.53,243.863 1379.42,243.863 1380.31,243.863 1381.21,243.863 1382.1,243.863 1383,243.863 1383.89,243.863 1384.79,243.863 1385.68,243.863 \n",
" 1386.58,243.863 1387.47,243.863 1388.37,243.863 1389.26,243.863 1390.16,243.863 1391.05,243.863 1391.94,243.863 1392.84,243.863 1393.73,243.863 1394.63,243.863 \n",
" 1395.52,243.863 1396.42,243.863 1397.31,243.863 1398.21,243.863 1399.1,243.863 1400,243.863 1400.89,243.863 1401.79,243.863 1402.68,243.863 1403.57,243.863 \n",
" 1404.47,243.863 1405.36,243.863 1406.26,243.863 1407.15,243.863 1408.05,243.863 1408.94,243.863 1409.84,243.863 1410.73,243.863 1411.63,243.863 1412.52,243.863 \n",
" 1413.42,243.863 1414.31,243.863 1415.2,243.863 1416.1,243.863 1416.99,243.863 1417.89,243.863 1418.78,243.863 1419.68,243.863 1420.57,243.863 1421.47,243.863 \n",
" 1422.36,243.863 1423.26,243.863 1424.15,243.863 1425.04,243.863 1425.94,243.863 1426.83,243.863 1427.73,243.863 1428.62,243.863 1429.52,243.863 1430.41,243.863 \n",
" 1431.31,243.863 1432.2,243.863 1433.1,243.863 1433.99,243.863 1434.89,243.863 1435.78,243.863 1436.67,243.863 1437.57,243.863 1438.46,243.863 1439.36,243.863 \n",
" 1440.25,243.863 1441.15,243.863 1442.04,243.863 1442.94,243.863 1443.83,243.863 1444.73,243.863 1445.62,243.863 1446.52,243.863 1447.41,243.863 1448.3,243.863 \n",
" 1449.2,243.863 1450.09,243.863 1450.99,243.863 1451.88,243.863 1452.78,243.863 1453.67,243.863 1454.57,243.863 1455.46,243.863 1456.36,243.863 1457.25,243.863 \n",
" 1458.15,243.863 1459.04,243.863 1459.93,243.863 1460.83,243.863 1461.72,243.863 1462.62,243.863 1463.51,243.863 1464.41,243.863 1465.3,243.863 1466.2,243.863 \n",
" 1467.09,243.863 1467.99,243.863 1468.88,243.863 1469.78,243.863 1470.67,243.863 1471.56,243.863 1472.46,243.863 1473.35,243.863 1474.25,243.863 1475.14,243.863 \n",
" 1476.04,243.863 1476.93,243.863 1477.83,243.863 1478.72,243.863 1479.62,243.863 1480.51,243.863 1481.41,243.863 1482.3,243.863 1483.19,243.863 1484.09,243.863 \n",
" 1484.98,243.863 1485.88,243.863 1486.77,243.863 1487.67,243.863 1488.56,243.863 1489.46,243.863 1490.35,243.863 1491.25,243.863 1492.14,243.863 1493.04,243.863 \n",
" 1493.93,243.863 1494.82,243.863 1495.72,243.863 1496.61,243.863 1497.51,243.863 1498.4,243.863 1499.3,243.863 1500.19,243.863 1501.09,243.863 1501.98,243.863 \n",
" 1502.88,243.863 1503.77,243.863 1504.67,243.863 1505.56,243.863 1506.45,243.863 1507.35,243.863 1508.24,243.863 1509.14,243.863 1510.03,243.863 1510.93,243.863 \n",
" 1511.82,243.863 1512.72,243.863 1513.61,243.863 1514.51,243.863 1515.4,243.863 1516.3,243.863 1517.19,243.863 1518.08,243.863 1518.98,243.863 1519.87,243.863 \n",
" 1520.77,243.863 1521.66,243.863 1522.56,243.863 1523.45,243.863 1524.35,243.863 1525.24,243.863 1526.14,243.863 1527.03,243.863 1527.93,243.863 1528.82,243.863 \n",
" 1529.71,243.863 1530.61,243.863 1531.5,243.863 1532.4,243.863 1533.29,243.863 1534.19,243.863 1535.08,243.863 1535.98,243.863 1536.87,243.863 1537.77,243.863 \n",
" 1538.66,243.863 1539.56,243.863 1540.45,243.863 1541.34,243.863 1542.24,243.863 1543.13,243.863 1544.03,243.863 1544.92,243.863 1545.82,243.863 1546.71,243.863 \n",
" 1547.61,243.863 1548.5,243.863 1549.4,243.863 1550.29,243.863 1551.19,243.863 1552.08,243.863 1552.97,243.863 1553.87,243.863 1554.76,243.863 1555.66,243.863 \n",
" 1556.55,243.863 1557.45,243.863 1558.34,243.863 1559.24,243.863 1560.13,243.863 1561.03,243.863 1561.92,243.863 1562.81,243.863 1563.71,243.863 1564.6,243.863 \n",
" 1565.5,243.863 1566.39,243.863 1567.29,243.863 1568.18,243.863 1569.08,243.863 1569.97,243.863 1570.87,243.863 1571.76,243.863 1572.66,243.863 1573.55,243.863 \n",
" 1574.44,243.863 1575.34,243.863 1576.23,243.863 1577.13,243.863 1578.02,243.863 1578.92,243.863 1579.81,243.863 1580.71,243.863 1581.6,243.863 1582.5,243.863 \n",
" 1583.39,243.863 1584.29,243.863 1585.18,243.863 1586.07,243.863 1586.97,243.863 1587.86,243.863 1588.76,243.863 1589.65,243.863 1590.55,243.863 1591.44,243.863 \n",
" 1592.34,243.863 1593.23,243.863 1594.13,243.863 1595.02,243.863 1595.92,243.863 1596.81,243.863 1597.7,243.863 1598.6,243.863 1599.49,243.863 1600.39,243.863 \n",
" 1601.28,243.863 1602.18,243.863 1603.07,243.863 1603.97,243.863 1604.86,243.863 1605.76,243.863 1606.65,243.863 1607.55,243.863 1608.44,243.863 1609.33,243.863 \n",
" 1610.23,243.863 1611.12,243.863 1612.02,243.863 1612.91,243.863 1613.81,243.863 1614.7,243.863 1615.6,243.863 1616.49,243.863 1617.39,243.863 1618.28,243.863 \n",
" 1619.18,243.863 1620.07,243.863 1620.96,243.863 1621.86,243.863 1622.75,243.863 1623.65,243.863 1624.54,243.863 1625.44,243.863 1626.33,243.863 1627.23,243.863 \n",
" 1628.12,243.863 1629.02,243.863 1629.91,243.863 1630.81,243.863 1631.7,243.863 1632.59,243.863 1633.49,243.863 1634.38,243.863 1635.28,243.863 1636.17,243.863 \n",
" 1637.07,243.863 1637.96,243.863 1638.86,243.863 1639.75,243.863 1640.65,243.863 1641.54,243.863 1642.44,243.863 1643.33,243.863 1644.22,243.863 1645.12,243.863 \n",
" 1646.01,243.863 1646.91,243.863 1647.8,243.863 1648.7,243.863 1649.59,243.863 1650.49,243.863 1651.38,243.863 1652.28,243.863 1653.17,243.863 1654.07,243.863 \n",
" 1654.96,243.863 1655.85,243.863 1656.75,243.863 1657.64,243.863 1658.54,243.863 1659.43,243.863 1660.33,243.863 1661.22,243.863 1662.12,243.863 1663.01,243.863 \n",
" 1663.91,243.863 1664.8,243.863 1665.7,243.863 1666.59,243.863 1667.48,243.863 1668.38,243.863 1669.27,243.863 1670.17,243.863 1671.06,243.863 1671.96,243.863 \n",
" 1672.85,243.863 1673.75,243.863 1674.64,243.863 1675.54,243.863 1676.43,243.863 1677.33,243.863 1678.22,243.863 1679.11,243.863 1680.01,243.863 1680.9,243.863 \n",
" 1681.8,243.863 1682.69,243.863 1683.59,243.863 1684.48,243.863 1685.38,243.863 1686.27,243.863 1687.17,243.863 1688.06,243.863 1688.96,243.863 1689.85,243.863 \n",
" 1690.74,243.863 1691.64,243.863 1692.53,243.863 1693.43,243.863 1694.32,243.863 1695.22,243.863 1696.11,243.863 1697.01,243.863 1697.9,243.863 1698.8,243.863 \n",
" 1699.69,243.863 1700.58,243.863 1701.48,243.863 1702.37,243.863 1703.27,243.863 1704.16,243.863 1705.06,243.863 1705.95,243.863 1706.85,243.863 1707.74,243.863 \n",
" 1708.64,243.863 1709.53,243.863 1710.43,243.863 1711.32,243.863 1712.21,243.863 1713.11,243.863 1714,243.863 1714.9,243.863 1715.79,243.863 1716.69,243.863 \n",
" 1717.58,243.863 1718.48,243.863 1719.37,243.863 1720.27,243.863 1721.16,243.863 1722.06,243.863 1722.95,243.863 1723.84,243.863 1724.74,243.863 1725.63,243.863 \n",
" 1726.53,243.863 1727.42,243.863 1728.32,243.863 1729.21,243.863 1730.11,243.863 1731,243.863 1731.9,243.863 1732.79,243.863 1733.69,243.863 1734.58,243.863 \n",
" 1735.47,243.863 1736.37,243.863 1737.26,243.863 1738.16,243.863 1739.05,243.863 1739.95,243.863 1740.84,243.863 1741.74,243.863 1742.63,243.863 1743.53,243.863 \n",
" 1744.42,243.863 1745.32,243.863 1746.21,243.863 1747.1,243.863 1748,243.863 1748.89,243.863 1749.79,243.863 1750.68,243.863 1751.58,243.863 1752.47,243.863 \n",
" 1753.37,243.863 1754.26,243.863 1755.16,243.863 1756.05,243.863 1756.95,243.863 1757.84,243.863 1758.73,243.863 1759.63,243.863 1760.52,243.863 1761.42,243.863 \n",
" 1762.31,243.863 1763.21,243.863 1764.1,243.863 1765,243.863 1765.89,243.863 1766.79,243.863 1767.68,243.863 1768.58,243.863 1769.47,243.863 1770.36,243.863 \n",
" 1771.26,243.863 1772.15,243.863 1773.05,243.863 1773.94,243.863 1774.84,243.863 1775.73,243.863 1776.63,243.863 1777.52,243.863 1778.42,243.863 1779.31,243.863 \n",
" 1780.21,243.863 1781.1,243.863 1781.99,243.863 1782.89,243.863 1783.78,243.863 1784.68,243.863 1785.57,243.863 1786.47,243.863 1787.36,243.863 1788.26,243.863 \n",
" 1789.15,243.863 1790.05,243.863 1790.94,243.863 1791.84,243.863 1792.73,243.863 1793.62,243.863 1794.52,243.863 1795.41,243.863 1796.31,243.863 1797.2,243.863 \n",
" 1798.1,243.863 1798.99,243.863 1799.89,243.863 1800.78,243.863 1801.68,243.863 1802.57,243.863 1803.47,243.863 1804.36,243.863 1805.25,243.863 1806.15,243.863 \n",
" 1807.04,243.863 1807.94,243.863 1808.83,243.863 1809.73,243.863 1810.62,243.863 1811.52,243.863 1812.41,243.863 1813.31,243.863 1814.2,243.863 1815.1,243.863 \n",
" 1815.99,243.863 1816.88,243.863 1817.78,243.863 1818.67,243.863 1819.57,243.863 1820.46,243.863 1821.36,243.863 1822.25,243.863 1823.15,243.863 1824.04,243.863 \n",
" 1824.94,243.863 1825.83,243.863 1826.73,243.863 1827.62,243.863 1828.51,243.863 1829.41,243.863 1830.3,243.863 1831.2,243.863 1832.09,243.863 1832.99,243.863 \n",
" 1833.88,243.863 1834.78,243.863 1835.67,243.863 1836.57,243.863 1837.46,243.863 1838.35,243.863 1839.25,243.863 1840.14,243.863 1841.04,243.863 1841.93,243.863 \n",
" 1842.83,243.863 1843.72,243.863 1844.62,243.863 1845.51,243.863 1846.41,243.863 1847.3,243.863 1848.2,243.863 1849.09,243.863 1849.98,243.863 1850.88,243.863 \n",
" 1851.77,243.863 1852.67,243.863 1853.56,243.863 1854.46,243.863 1855.35,243.863 1856.25,243.863 1857.14,243.863 1858.04,243.863 1858.93,243.863 1859.83,243.863 \n",
" 1860.72,243.863 1861.61,243.863 1862.51,243.863 1863.4,243.863 1864.3,243.863 1865.19,243.863 1866.09,243.863 1866.98,243.863 1867.88,243.863 1868.77,243.863 \n",
" 1869.67,243.863 1870.56,243.863 1871.46,243.863 1872.35,243.863 1873.24,243.863 1874.14,243.863 1875.03,243.863 1875.93,243.863 1876.82,243.863 1877.72,243.863 \n",
" 1878.61,243.863 1879.51,243.863 1880.4,243.863 1881.3,243.863 1882.19,243.863 1883.09,243.863 1883.98,243.863 1884.87,243.863 1885.77,243.863 1886.66,243.863 \n",
" 1887.56,243.863 1888.45,243.863 1889.35,243.863 1890.24,243.863 1891.14,243.863 1892.03,243.863 1892.93,243.863 1893.82,243.863 1894.72,243.863 1895.61,243.863 \n",
" 1896.5,243.863 1897.4,243.863 1898.29,243.863 1899.19,243.863 1900.08,243.863 1900.98,243.863 1901.87,243.863 1902.77,243.863 1903.66,243.863 1904.56,243.863 \n",
" 1905.45,243.863 1906.35,243.863 1907.24,243.863 1908.13,243.863 1909.03,243.863 1909.92,243.863 1910.82,243.863 1911.71,243.863 1912.61,243.863 1913.5,243.863 \n",
" 1914.4,243.863 1915.29,243.863 1916.19,243.863 1917.08,243.863 1917.98,243.863 1918.87,243.863 1919.76,243.863 1920.66,243.863 1921.55,243.863 1922.45,243.863 \n",
" 1923.34,243.863 1924.24,243.863 1925.13,243.863 1926.03,243.863 1926.92,243.863 1927.82,243.863 1928.71,243.863 1929.61,243.863 1930.5,243.863 1931.39,243.863 \n",
" 1932.29,243.863 1933.18,243.863 1934.08,243.863 1934.97,243.863 1935.87,243.863 1936.76,243.863 1937.66,243.863 1938.55,243.863 1939.45,243.863 1940.34,243.863 \n",
" 1941.24,243.863 1942.13,243.863 1943.02,243.863 1943.92,243.863 1944.81,243.863 1945.71,243.863 1946.6,243.863 1947.5,243.863 1948.39,243.863 1949.29,243.863 \n",
" 1950.18,243.863 1951.08,243.863 1951.97,243.863 1952.87,243.863 1953.76,243.863 1954.65,243.863 1955.55,243.863 1956.44,243.863 1957.34,243.863 1958.23,243.863 \n",
" 1959.13,243.863 1960.02,243.863 1960.92,243.863 1961.81,243.863 1962.71,243.863 1963.6,243.863 1964.5,243.863 1965.39,243.863 1966.28,243.863 1967.18,243.863 \n",
" 1968.07,243.863 1968.97,243.863 1969.86,243.863 1970.76,243.863 1971.65,243.863 1972.55,243.863 1973.44,243.863 1974.34,243.863 1975.23,243.863 1976.12,243.863 \n",
" 1977.02,243.863 1977.91,243.863 1978.81,243.864 1979.7,243.864 1980.6,243.864 1981.49,243.864 1982.39,243.864 1983.28,243.864 1984.18,243.864 1985.07,243.864 \n",
" 1985.97,243.864 1986.86,243.864 1987.75,243.864 1988.65,243.864 1989.54,243.864 1990.44,243.864 1991.33,243.864 1992.23,243.864 1993.12,243.864 1994.02,243.864 \n",
" 1994.91,243.864 1995.81,243.864 1996.7,243.864 1997.6,243.864 1998.49,243.864 1999.38,243.864 2000.28,243.864 2001.17,243.864 2002.07,243.864 2002.96,243.864 \n",
" 2003.86,243.864 2004.75,243.864 2005.65,243.864 2006.54,243.864 2007.44,243.864 2008.33,243.864 2009.23,243.864 2010.12,243.864 2011.01,243.864 2011.91,243.864 \n",
" 2012.8,243.864 2013.7,243.864 2014.59,243.864 2015.49,243.864 2016.38,243.864 2017.28,243.864 2018.17,243.864 2019.07,243.864 2019.96,243.864 2020.86,243.864 \n",
" 2021.75,243.864 2022.64,243.864 2023.54,243.864 2024.43,243.864 2025.33,243.864 2026.22,243.864 2027.12,243.864 2028.01,243.864 2028.91,243.864 2029.8,243.864 \n",
" 2030.7,243.864 2031.59,243.864 2032.49,243.864 2033.38,243.864 2034.27,243.864 2035.17,243.864 2036.06,243.864 2036.96,243.864 2037.85,243.864 2038.75,243.864 \n",
" 2039.64,243.864 2040.54,243.864 2041.43,243.864 2042.33,243.864 2043.22,243.864 2044.12,243.864 2045.01,243.864 2045.9,243.864 2046.8,243.864 2047.69,243.864 \n",
" 2048.59,243.864 2049.48,243.864 2050.38,243.864 2051.27,243.864 2052.17,243.864 2053.06,243.864 2053.96,243.864 2054.85,243.864 2055.75,243.864 2056.64,243.864 \n",
" 2057.53,243.864 2058.43,243.864 2059.32,243.864 2060.22,243.864 2061.11,243.864 2062.01,243.864 2062.9,243.864 2063.8,243.864 2064.69,243.864 2065.59,243.864 \n",
" 2066.48,243.864 2067.38,243.864 2068.27,243.864 2069.16,243.864 2070.06,243.864 2070.95,243.864 2071.85,243.864 2072.74,243.864 2073.64,243.864 2074.53,243.864 \n",
" 2075.43,243.864 2076.32,243.864 2077.22,243.864 2078.11,243.864 2079.01,243.864 2079.9,243.864 2080.79,243.864 2081.69,243.864 2082.58,243.864 2083.48,243.864 \n",
" 2084.37,243.864 2085.27,243.864 2086.16,243.864 2087.06,243.864 2087.95,243.864 2088.85,243.864 2089.74,243.864 2090.64,243.864 2091.53,243.864 2092.42,243.864 \n",
" 2093.32,243.864 2094.21,243.864 2095.11,243.864 2096,243.864 2096.9,243.864 2097.79,243.864 2098.69,243.864 2099.58,243.864 2100.48,243.864 2101.37,243.864 \n",
" 2102.27,243.864 2103.16,243.864 2104.05,243.864 2104.95,243.864 2105.84,243.864 2106.74,243.864 2107.63,243.864 2108.53,243.864 2109.42,243.864 2110.32,243.864 \n",
" 2111.21,243.864 2112.11,243.864 2113,243.864 2113.89,243.864 2114.79,243.864 2115.68,243.864 2116.58,243.864 2117.47,243.864 2118.37,243.864 2119.26,243.864 \n",
" 2120.16,243.864 2121.05,243.864 2121.95,243.864 2122.84,243.864 2123.74,243.864 2124.63,243.864 2125.52,243.864 2126.42,243.864 2127.31,243.864 2128.21,243.864 \n",
" 2129.1,243.864 2130,243.864 2130.89,243.864 2131.79,243.864 2132.68,243.864 2133.58,243.864 2134.47,243.864 2135.37,243.864 2136.26,243.864 2137.15,243.864 \n",
" 2138.05,243.864 2138.94,243.864 2139.84,243.864 2140.73,243.864 2141.63,243.864 2142.52,243.864 2143.42,243.864 2144.31,243.864 2145.21,243.864 2146.1,243.864 \n",
" 2147,243.864 2147.89,243.864 2148.78,243.864 2149.68,243.864 2150.57,243.864 2151.47,243.864 2152.36,243.864 2153.26,243.864 2154.15,243.864 2155.05,243.864 \n",
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" 1171.87,473.504 1172.76,473.504 1173.66,473.505 1174.55,473.505 1175.45,473.505 1176.34,473.505 1177.24,473.505 1178.13,473.506 1179.03,473.506 1179.92,473.506 \n",
" 1180.82,473.506 1181.71,473.506 1182.61,473.506 1183.5,473.506 1184.39,473.506 1185.29,473.506 1186.18,473.506 1187.08,473.507 1187.97,473.507 1188.87,473.507 \n",
" 1189.76,473.507 1190.66,473.506 1191.55,473.506 1192.45,473.506 1193.34,473.506 1194.24,473.506 1195.13,473.506 1196.02,473.506 1196.92,473.506 1197.81,473.506 \n",
" 1198.71,473.506 1199.6,473.506 1200.5,473.506 1201.39,473.505 1202.29,473.505 1203.18,473.505 1204.08,473.505 1204.97,473.505 1205.87,473.505 1206.76,473.505 \n",
" 1207.65,473.504 1208.55,473.504 1209.44,473.504 1210.34,473.504 1211.23,473.504 1212.13,473.504 1213.02,473.503 1213.92,473.503 1214.81,473.503 1215.71,473.503 \n",
" 1216.6,473.503 1217.5,473.503 1218.39,473.503 1219.28,473.502 1220.18,473.502 1221.07,473.502 1221.97,473.502 1222.86,473.502 1223.76,473.502 1224.65,473.502 \n",
" 1225.55,473.502 1226.44,473.501 1227.34,473.501 1228.23,473.501 1229.13,473.501 1230.02,473.501 1230.91,473.501 1231.81,473.501 1232.7,473.501 1233.6,473.501 \n",
" 1234.49,473.501 1235.39,473.501 1236.28,473.501 1237.18,473.501 1238.07,473.501 1238.97,473.501 1239.86,473.501 1240.76,473.501 1241.65,473.501 1242.54,473.501 \n",
" 1243.44,473.501 1244.33,473.501 1245.23,473.501 1246.12,473.501 1247.02,473.501 1247.91,473.501 1248.81,473.501 1249.7,473.501 1250.6,473.501 1251.49,473.501 \n",
" 1252.39,473.501 1253.28,473.501 1254.17,473.501 1255.07,473.501 1255.96,473.501 1256.86,473.501 1257.75,473.502 1258.65,473.502 1259.54,473.502 1260.44,473.502 \n",
" 1261.33,473.502 1262.23,473.502 1263.12,473.502 1264.02,473.502 1264.91,473.502 1265.8,473.502 1266.7,473.502 1267.59,473.502 1268.49,473.502 1269.38,473.502 \n",
" 1270.28,473.502 1271.17,473.502 1272.07,473.503 1272.96,473.503 1273.86,473.503 1274.75,473.503 1275.65,473.503 1276.54,473.503 1277.43,473.503 1278.33,473.503 \n",
" 1279.22,473.503 1280.12,473.503 1281.01,473.503 1281.91,473.503 1282.8,473.503 1283.7,473.503 1284.59,473.503 1285.49,473.503 1286.38,473.503 1287.27,473.503 \n",
" 1288.17,473.503 1289.06,473.503 1289.96,473.503 1290.85,473.503 1291.75,473.503 1292.64,473.503 1293.54,473.503 1294.43,473.503 1295.33,473.503 1296.22,473.503 \n",
" 1297.12,473.503 1298.01,473.503 1298.9,473.503 1299.8,473.503 1300.69,473.503 1301.59,473.503 1302.48,473.503 1303.38,473.503 1304.27,473.503 1305.17,473.503 \n",
" 1306.06,473.503 1306.96,473.503 1307.85,473.503 1308.75,473.503 1309.64,473.503 1310.53,473.503 1311.43,473.503 1312.32,473.503 1313.22,473.503 1314.11,473.503 \n",
" 1315.01,473.503 1315.9,473.503 1316.8,473.503 1317.69,473.503 1318.59,473.503 1319.48,473.503 1320.38,473.503 1321.27,473.503 1322.16,473.503 1323.06,473.502 \n",
" 1323.95,473.502 1324.85,473.502 1325.74,473.502 1326.64,473.502 1327.53,473.502 1328.43,473.502 1329.32,473.502 1330.22,473.502 1331.11,473.502 1332.01,473.502 \n",
" 1332.9,473.502 1333.79,473.502 1334.69,473.502 1335.58,473.502 1336.48,473.502 1337.37,473.502 1338.27,473.502 1339.16,473.502 1340.06,473.502 1340.95,473.502 \n",
" 1341.85,473.502 1342.74,473.502 1343.64,473.502 1344.53,473.502 1345.42,473.502 1346.32,473.502 1347.21,473.502 1348.11,473.502 1349,473.502 1349.9,473.502 \n",
" 1350.79,473.502 1351.69,473.502 1352.58,473.502 1353.48,473.502 1354.37,473.502 1355.27,473.502 1356.16,473.502 1357.05,473.502 1357.95,473.502 1358.84,473.502 \n",
" 1359.74,473.502 1360.63,473.502 1361.53,473.502 1362.42,473.502 1363.32,473.502 1364.21,473.502 1365.11,473.502 1366,473.502 1366.9,473.502 1367.79,473.502 \n",
" 1368.68,473.502 1369.58,473.502 1370.47,473.502 1371.37,473.502 1372.26,473.502 1373.16,473.502 1374.05,473.502 1374.95,473.502 1375.84,473.503 1376.74,473.503 \n",
" 1377.63,473.503 1378.53,473.503 1379.42,473.503 1380.31,473.503 1381.21,473.503 1382.1,473.503 1383,473.503 1383.89,473.503 1384.79,473.503 1385.68,473.503 \n",
" 1386.58,473.503 1387.47,473.503 1388.37,473.503 1389.26,473.503 1390.16,473.503 1391.05,473.503 1391.94,473.503 1392.84,473.503 1393.73,473.503 1394.63,473.503 \n",
" 1395.52,473.503 1396.42,473.503 1397.31,473.503 1398.21,473.503 1399.1,473.503 1400,473.503 1400.89,473.503 1401.79,473.503 1402.68,473.503 1403.57,473.503 \n",
" 1404.47,473.503 1405.36,473.503 1406.26,473.503 1407.15,473.503 1408.05,473.503 1408.94,473.503 1409.84,473.503 1410.73,473.503 1411.63,473.503 1412.52,473.503 \n",
" 1413.42,473.503 1414.31,473.503 1415.2,473.503 1416.1,473.503 1416.99,473.503 1417.89,473.503 1418.78,473.503 1419.68,473.503 1420.57,473.503 1421.47,473.503 \n",
" 1422.36,473.503 1423.26,473.503 1424.15,473.503 1425.04,473.503 1425.94,473.503 1426.83,473.503 1427.73,473.503 1428.62,473.503 1429.52,473.503 1430.41,473.503 \n",
" 1431.31,473.502 1432.2,473.502 1433.1,473.502 1433.99,473.502 1434.89,473.502 1435.78,473.502 1436.67,473.502 1437.57,473.502 1438.46,473.502 1439.36,473.502 \n",
" 1440.25,473.502 1441.15,473.502 1442.04,473.502 1442.94,473.502 1443.83,473.502 1444.73,473.502 1445.62,473.502 1446.52,473.502 1447.41,473.502 1448.3,473.502 \n",
" 1449.2,473.502 1450.09,473.502 1450.99,473.502 1451.88,473.502 1452.78,473.502 1453.67,473.502 1454.57,473.502 1455.46,473.502 1456.36,473.502 1457.25,473.502 \n",
" 1458.15,473.502 1459.04,473.502 1459.93,473.502 1460.83,473.502 1461.72,473.502 1462.62,473.502 1463.51,473.502 1464.41,473.502 1465.3,473.502 1466.2,473.502 \n",
" 1467.09,473.502 1467.99,473.502 1468.88,473.503 1469.78,473.503 1470.67,473.503 1471.56,473.503 1472.46,473.503 1473.35,473.503 1474.25,473.503 1475.14,473.503 \n",
" 1476.04,473.503 1476.93,473.503 1477.83,473.503 1478.72,473.503 1479.62,473.503 1480.51,473.503 1481.41,473.503 1482.3,473.503 1483.19,473.503 1484.09,473.503 \n",
" 1484.98,473.503 1485.88,473.503 1486.77,473.503 1487.67,473.503 1488.56,473.503 1489.46,473.503 1490.35,473.503 1491.25,473.503 1492.14,473.503 1493.04,473.503 \n",
" 1493.93,473.503 1494.82,473.503 1495.72,473.503 1496.61,473.503 1497.51,473.503 1498.4,473.503 1499.3,473.503 1500.19,473.503 1501.09,473.503 1501.98,473.503 \n",
" 1502.88,473.503 1503.77,473.503 1504.67,473.503 1505.56,473.503 1506.45,473.503 1507.35,473.503 1508.24,473.503 1509.14,473.503 1510.03,473.503 1510.93,473.503 \n",
" 1511.82,473.503 1512.72,473.503 1513.61,473.503 1514.51,473.503 1515.4,473.503 1516.3,473.503 1517.19,473.503 1518.08,473.503 1518.98,473.503 1519.87,473.503 \n",
" 1520.77,473.503 1521.66,473.503 1522.56,473.503 1523.45,473.503 1524.35,473.503 1525.24,473.503 1526.14,473.503 1527.03,473.503 1527.93,473.503 1528.82,473.503 \n",
" 1529.71,473.503 1530.61,473.503 1531.5,473.503 1532.4,473.503 1533.29,473.503 1534.19,473.503 1535.08,473.503 1535.98,473.503 1536.87,473.503 1537.77,473.503 \n",
" 1538.66,473.503 1539.56,473.503 1540.45,473.503 1541.34,473.503 1542.24,473.503 1543.13,473.503 1544.03,473.503 1544.92,473.503 1545.82,473.503 1546.71,473.503 \n",
" 1547.61,473.503 1548.5,473.503 1549.4,473.503 1550.29,473.503 1551.19,473.503 1552.08,473.503 1552.97,473.503 1553.87,473.503 1554.76,473.503 1555.66,473.503 \n",
" 1556.55,473.503 1557.45,473.503 1558.34,473.503 1559.24,473.503 1560.13,473.503 1561.03,473.503 1561.92,473.503 1562.81,473.503 1563.71,473.503 1564.6,473.503 \n",
" 1565.5,473.503 1566.39,473.503 1567.29,473.503 1568.18,473.503 1569.08,473.503 1569.97,473.503 1570.87,473.503 1571.76,473.503 1572.66,473.503 1573.55,473.503 \n",
" 1574.44,473.503 1575.34,473.503 1576.23,473.503 1577.13,473.503 1578.02,473.503 1578.92,473.503 1579.81,473.503 1580.71,473.503 1581.6,473.503 1582.5,473.503 \n",
" 1583.39,473.503 1584.29,473.503 1585.18,473.503 1586.07,473.503 1586.97,473.503 1587.86,473.503 1588.76,473.503 1589.65,473.503 1590.55,473.503 1591.44,473.503 \n",
" 1592.34,473.503 1593.23,473.503 1594.13,473.503 1595.02,473.503 1595.92,473.503 1596.81,473.503 1597.7,473.503 1598.6,473.503 1599.49,473.503 1600.39,473.503 \n",
" 1601.28,473.503 1602.18,473.503 1603.07,473.503 1603.97,473.503 1604.86,473.503 1605.76,473.503 1606.65,473.503 1607.55,473.503 1608.44,473.503 1609.33,473.503 \n",
" 1610.23,473.503 1611.12,473.503 1612.02,473.503 1612.91,473.503 1613.81,473.503 1614.7,473.503 1615.6,473.503 1616.49,473.503 1617.39,473.503 1618.28,473.503 \n",
" 1619.18,473.503 1620.07,473.503 1620.96,473.503 1621.86,473.503 1622.75,473.503 1623.65,473.503 1624.54,473.503 1625.44,473.503 1626.33,473.503 1627.23,473.503 \n",
" 1628.12,473.503 1629.02,473.503 1629.91,473.503 1630.81,473.503 1631.7,473.503 1632.59,473.503 1633.49,473.503 1634.38,473.503 1635.28,473.503 1636.17,473.503 \n",
" 1637.07,473.503 1637.96,473.503 1638.86,473.503 1639.75,473.503 1640.65,473.503 1641.54,473.503 1642.44,473.503 1643.33,473.503 1644.22,473.503 1645.12,473.503 \n",
" 1646.01,473.503 1646.91,473.503 1647.8,473.503 1648.7,473.503 1649.59,473.503 1650.49,473.503 1651.38,473.503 1652.28,473.503 1653.17,473.503 1654.07,473.503 \n",
" 1654.96,473.503 1655.85,473.503 1656.75,473.503 1657.64,473.503 1658.54,473.503 1659.43,473.503 1660.33,473.503 1661.22,473.503 1662.12,473.503 1663.01,473.503 \n",
" 1663.91,473.503 1664.8,473.503 1665.7,473.503 1666.59,473.503 1667.48,473.503 1668.38,473.503 1669.27,473.503 1670.17,473.503 1671.06,473.503 1671.96,473.503 \n",
" 1672.85,473.503 1673.75,473.503 1674.64,473.503 1675.54,473.503 1676.43,473.503 1677.33,473.503 1678.22,473.503 1679.11,473.503 1680.01,473.503 1680.9,473.503 \n",
" 1681.8,473.503 1682.69,473.503 1683.59,473.503 1684.48,473.503 1685.38,473.503 1686.27,473.503 1687.17,473.503 1688.06,473.503 1688.96,473.503 1689.85,473.503 \n",
" 1690.74,473.503 1691.64,473.503 1692.53,473.503 1693.43,473.503 1694.32,473.503 1695.22,473.503 1696.11,473.503 1697.01,473.503 1697.9,473.503 1698.8,473.503 \n",
" 1699.69,473.503 1700.58,473.503 1701.48,473.503 1702.37,473.503 1703.27,473.503 1704.16,473.503 1705.06,473.503 1705.95,473.503 1706.85,473.503 1707.74,473.503 \n",
" 1708.64,473.503 1709.53,473.503 1710.43,473.503 1711.32,473.503 1712.21,473.503 1713.11,473.503 1714,473.503 1714.9,473.503 1715.79,473.503 1716.69,473.503 \n",
" 1717.58,473.503 1718.48,473.503 1719.37,473.503 1720.27,473.503 1721.16,473.503 1722.06,473.503 1722.95,473.503 1723.84,473.503 1724.74,473.503 1725.63,473.503 \n",
" 1726.53,473.503 1727.42,473.503 1728.32,473.503 1729.21,473.503 1730.11,473.503 1731,473.503 1731.9,473.503 1732.79,473.503 1733.69,473.503 1734.58,473.503 \n",
" 1735.47,473.503 1736.37,473.503 1737.26,473.503 1738.16,473.503 1739.05,473.503 1739.95,473.503 1740.84,473.503 1741.74,473.503 1742.63,473.503 1743.53,473.503 \n",
" 1744.42,473.503 1745.32,473.503 1746.21,473.503 1747.1,473.503 1748,473.503 1748.89,473.503 1749.79,473.503 1750.68,473.503 1751.58,473.503 1752.47,473.503 \n",
" 1753.37,473.503 1754.26,473.503 1755.16,473.503 1756.05,473.503 1756.95,473.503 1757.84,473.503 1758.73,473.503 1759.63,473.503 1760.52,473.503 1761.42,473.503 \n",
" 1762.31,473.503 1763.21,473.503 1764.1,473.503 1765,473.503 1765.89,473.503 1766.79,473.503 1767.68,473.503 1768.58,473.503 1769.47,473.503 1770.36,473.503 \n",
" 1771.26,473.503 1772.15,473.503 1773.05,473.503 1773.94,473.503 1774.84,473.503 1775.73,473.503 1776.63,473.503 1777.52,473.503 1778.42,473.503 1779.31,473.503 \n",
" 1780.21,473.503 1781.1,473.503 1781.99,473.503 1782.89,473.503 1783.78,473.503 1784.68,473.503 1785.57,473.503 1786.47,473.503 1787.36,473.503 1788.26,473.503 \n",
" 1789.15,473.503 1790.05,473.503 1790.94,473.503 1791.84,473.503 1792.73,473.503 1793.62,473.503 1794.52,473.503 1795.41,473.503 1796.31,473.503 1797.2,473.503 \n",
" 1798.1,473.503 1798.99,473.503 1799.89,473.503 1800.78,473.503 1801.68,473.503 1802.57,473.503 1803.47,473.503 1804.36,473.503 1805.25,473.503 1806.15,473.503 \n",
" 1807.04,473.503 1807.94,473.503 1808.83,473.503 1809.73,473.503 1810.62,473.503 1811.52,473.503 1812.41,473.503 1813.31,473.503 1814.2,473.503 1815.1,473.503 \n",
" 1815.99,473.503 1816.88,473.503 1817.78,473.503 1818.67,473.503 1819.57,473.503 1820.46,473.503 1821.36,473.503 1822.25,473.503 1823.15,473.503 1824.04,473.503 \n",
" 1824.94,473.503 1825.83,473.503 1826.73,473.503 1827.62,473.503 1828.51,473.503 1829.41,473.503 1830.3,473.503 1831.2,473.503 1832.09,473.503 1832.99,473.503 \n",
" 1833.88,473.503 1834.78,473.503 1835.67,473.503 1836.57,473.503 1837.46,473.503 1838.35,473.503 1839.25,473.503 1840.14,473.503 1841.04,473.503 1841.93,473.503 \n",
" 1842.83,473.503 1843.72,473.503 1844.62,473.503 1845.51,473.503 1846.41,473.503 1847.3,473.503 1848.2,473.503 1849.09,473.503 1849.98,473.503 1850.88,473.503 \n",
" 1851.77,473.503 1852.67,473.503 1853.56,473.503 1854.46,473.503 1855.35,473.503 1856.25,473.503 1857.14,473.503 1858.04,473.503 1858.93,473.503 1859.83,473.503 \n",
" 1860.72,473.503 1861.61,473.503 1862.51,473.503 1863.4,473.503 1864.3,473.503 1865.19,473.503 1866.09,473.503 1866.98,473.503 1867.88,473.503 1868.77,473.503 \n",
" 1869.67,473.503 1870.56,473.503 1871.46,473.503 1872.35,473.503 1873.24,473.503 1874.14,473.503 1875.03,473.503 1875.93,473.503 1876.82,473.503 1877.72,473.503 \n",
" 1878.61,473.503 1879.51,473.503 1880.4,473.503 1881.3,473.503 1882.19,473.503 1883.09,473.503 1883.98,473.503 1884.87,473.503 1885.77,473.503 1886.66,473.503 \n",
" 1887.56,473.503 1888.45,473.503 1889.35,473.503 1890.24,473.503 1891.14,473.503 1892.03,473.503 1892.93,473.503 1893.82,473.503 1894.72,473.503 1895.61,473.503 \n",
" 1896.5,473.503 1897.4,473.503 1898.29,473.503 1899.19,473.503 1900.08,473.503 1900.98,473.503 1901.87,473.503 1902.77,473.503 1903.66,473.503 1904.56,473.503 \n",
" 1905.45,473.503 1906.35,473.503 1907.24,473.503 1908.13,473.503 1909.03,473.503 1909.92,473.503 1910.82,473.503 1911.71,473.503 1912.61,473.503 1913.5,473.503 \n",
" 1914.4,473.503 1915.29,473.503 1916.19,473.503 1917.08,473.503 1917.98,473.503 1918.87,473.503 1919.76,473.503 1920.66,473.503 1921.55,473.503 1922.45,473.503 \n",
" 1923.34,473.503 1924.24,473.503 1925.13,473.503 1926.03,473.503 1926.92,473.503 1927.82,473.503 1928.71,473.503 1929.61,473.503 1930.5,473.503 1931.39,473.503 \n",
" 1932.29,473.503 1933.18,473.503 1934.08,473.503 1934.97,473.503 1935.87,473.503 1936.76,473.503 1937.66,473.503 1938.55,473.503 1939.45,473.503 1940.34,473.503 \n",
" 1941.24,473.503 1942.13,473.503 1943.02,473.503 1943.92,473.503 1944.81,473.503 1945.71,473.503 1946.6,473.503 1947.5,473.503 1948.39,473.503 1949.29,473.503 \n",
" 1950.18,473.503 1951.08,473.503 1951.97,473.503 1952.87,473.503 1953.76,473.503 1954.65,473.503 1955.55,473.503 1956.44,473.503 1957.34,473.503 1958.23,473.503 \n",
" 1959.13,473.503 1960.02,473.503 1960.92,473.503 1961.81,473.503 1962.71,473.503 1963.6,473.503 1964.5,473.503 1965.39,473.503 1966.28,473.503 1967.18,473.503 \n",
" 1968.07,473.503 1968.97,473.503 1969.86,473.503 1970.76,473.503 1971.65,473.503 1972.55,473.503 1973.44,473.503 1974.34,473.503 1975.23,473.503 1976.12,473.503 \n",
" 1977.02,473.503 1977.91,473.503 1978.81,473.503 1979.7,473.503 1980.6,473.503 1981.49,473.503 1982.39,473.503 1983.28,473.503 1984.18,473.503 1985.07,473.503 \n",
" 1985.97,473.503 1986.86,473.503 1987.75,473.503 1988.65,473.503 1989.54,473.503 1990.44,473.503 1991.33,473.503 1992.23,473.503 1993.12,473.503 1994.02,473.503 \n",
" 1994.91,473.503 1995.81,473.503 1996.7,473.503 1997.6,473.503 1998.49,473.503 1999.38,473.503 2000.28,473.503 2001.17,473.503 2002.07,473.503 2002.96,473.503 \n",
" 2003.86,473.503 2004.75,473.503 2005.65,473.503 2006.54,473.503 2007.44,473.503 2008.33,473.503 2009.23,473.503 2010.12,473.503 2011.01,473.503 2011.91,473.503 \n",
" 2012.8,473.503 2013.7,473.503 2014.59,473.503 2015.49,473.503 2016.38,473.503 2017.28,473.503 2018.17,473.503 2019.07,473.503 2019.96,473.503 2020.86,473.503 \n",
" 2021.75,473.503 2022.64,473.503 2023.54,473.503 2024.43,473.503 2025.33,473.503 2026.22,473.503 2027.12,473.503 2028.01,473.503 2028.91,473.503 2029.8,473.503 \n",
" 2030.7,473.503 2031.59,473.503 2032.49,473.503 2033.38,473.503 2034.27,473.503 2035.17,473.503 2036.06,473.503 2036.96,473.503 2037.85,473.503 2038.75,473.503 \n",
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" 1046.62,627.644 1047.52,627.445 1048.41,627.246 1049.31,627.048 1050.2,626.852 1051.1,626.657 1051.99,626.465 1052.89,626.275 1053.78,626.087 1054.68,625.902 \n",
" 1055.57,625.721 1056.47,625.542 1057.36,625.368 1058.25,625.197 1059.15,625.03 1060.04,624.867 1060.94,624.709 1061.83,624.555 1062.73,624.406 1063.62,624.262 \n",
" 1064.52,624.122 1065.41,623.989 1066.31,623.86 1067.2,623.737 1068.1,623.62 1068.99,623.508 1069.88,623.402 1070.78,623.302 1071.67,623.208 1072.57,623.12 \n",
" 1073.46,623.038 1074.36,622.962 1075.25,622.892 1076.15,622.828 1077.04,622.77 1077.94,622.719 1078.83,622.674 1079.73,622.634 1080.62,622.601 1081.51,622.574 \n",
" 1082.41,622.553 1083.3,622.538 1084.2,622.529 1085.09,622.526 1085.99,622.528 1086.88,622.536 1087.78,622.55 1088.67,622.569 1089.57,622.593 1090.46,622.622 \n",
" 1091.36,622.657 1092.25,622.697 1093.14,622.741 1094.04,622.79 1094.93,622.844 1095.83,622.902 1096.72,622.965 1097.62,623.031 1098.51,623.101 1099.41,623.175 \n",
" 1100.3,623.253 1101.2,623.334 1102.09,623.418 1102.99,623.506 1103.88,623.596 1104.77,623.689 1105.67,623.784 1106.56,623.881 1107.46,623.981 1108.35,624.083 \n",
" 1109.25,624.186 1110.14,624.291 1111.04,624.397 1111.93,624.505 1112.83,624.613 1113.72,624.722 1114.62,624.832 1115.51,624.942 1116.4,625.053 1117.3,625.163 \n",
" 1118.19,625.274 1119.09,625.384 1119.98,625.494 1120.88,625.603 1121.77,625.711 1122.67,625.818 1123.56,625.925 1124.46,626.03 1125.35,626.133 1126.25,626.236 \n",
" 1127.14,626.336 1128.03,626.435 1128.93,626.532 1129.82,626.626 1130.72,626.719 1131.61,626.809 1132.51,626.897 1133.4,626.982 1134.3,627.065 1135.19,627.145 \n",
" 1136.09,627.222 1136.98,627.296 1137.88,627.368 1138.77,627.436 1139.66,627.502 1140.56,627.564 1141.45,627.623 1142.35,627.679 1143.24,627.731 1144.14,627.781 \n",
" 1145.03,627.827 1145.93,627.869 1146.82,627.908 1147.72,627.944 1148.61,627.977 1149.5,628.006 1150.4,628.031 1151.29,628.054 1152.19,628.073 1153.08,628.088 \n",
" 1153.98,628.101 1154.87,628.11 1155.77,628.115 1156.66,628.118 1157.56,628.117 1158.45,628.113 1159.35,628.107 1160.24,628.097 1161.13,628.084 1162.03,628.068 \n",
" 1162.92,628.05 1163.82,628.028 1164.71,628.004 1165.61,627.978 1166.5,627.949 1167.4,627.917 1168.29,627.883 1169.19,627.847 1170.08,627.809 1170.98,627.769 \n",
" 1171.87,627.726 1172.76,627.682 1173.66,627.636 1174.55,627.588 1175.45,627.539 1176.34,627.488 1177.24,627.436 1178.13,627.382 1179.03,627.328 1179.92,627.272 \n",
" 1180.82,627.215 1181.71,627.157 1182.61,627.099 1183.5,627.04 1184.39,626.98 1185.29,626.92 1186.18,626.86 1187.08,626.799 1187.97,626.738 1188.87,626.677 \n",
" 1189.76,626.616 1190.66,626.556 1191.55,626.495 1192.45,626.435 1193.34,626.375 1194.24,626.316 1195.13,626.257 1196.02,626.199 1196.92,626.142 1197.81,626.085 \n",
" 1198.71,626.03 1199.6,625.975 1200.5,625.922 1201.39,625.869 1202.29,625.818 1203.18,625.768 1204.08,625.719 1204.97,625.672 1205.87,625.626 1206.76,625.582 \n",
" 1207.65,625.539 1208.55,625.497 1209.44,625.458 1210.34,625.42 1211.23,625.383 1212.13,625.349 1213.02,625.316 1213.92,625.285 1214.81,625.255 1215.71,625.228 \n",
" 1216.6,625.202 1217.5,625.178 1218.39,625.156 1219.28,625.136 1220.18,625.118 1221.07,625.101 1221.97,625.087 1222.86,625.074 1223.76,625.063 1224.65,625.054 \n",
" 1225.55,625.047 1226.44,625.042 1227.34,625.038 1228.23,625.036 1229.13,625.036 1230.02,625.038 1230.91,625.041 1231.81,625.047 1232.7,625.053 1233.6,625.062 \n",
" 1234.49,625.071 1235.39,625.083 1236.28,625.096 1237.18,625.11 1238.07,625.126 1238.97,625.143 1239.86,625.161 1240.76,625.181 1241.65,625.202 1242.54,625.224 \n",
" 1243.44,625.247 1244.33,625.271 1245.23,625.296 1246.12,625.322 1247.02,625.349 1247.91,625.377 1248.81,625.406 1249.7,625.435 1250.6,625.465 1251.49,625.496 \n",
" 1252.39,625.527 1253.28,625.559 1254.17,625.591 1255.07,625.623 1255.96,625.656 1256.86,625.689 1257.75,625.722 1258.65,625.756 1259.54,625.789 1260.44,625.823 \n",
" 1261.33,625.857 1262.23,625.89 1263.12,625.923 1264.02,625.957 1264.91,625.99 1265.8,626.022 1266.7,626.055 1267.59,626.087 1268.49,626.119 1269.38,626.15 \n",
" 1270.28,626.181 1271.17,626.211 1272.07,626.24 1272.96,626.269 1273.86,626.298 1274.75,626.325 1275.65,626.352 1276.54,626.379 1277.43,626.404 1278.33,626.429 \n",
" 1279.22,626.453 1280.12,626.476 1281.01,626.498 1281.91,626.519 1282.8,626.539 1283.7,626.558 1284.59,626.577 1285.49,626.594 1286.38,626.61 1287.27,626.626 \n",
" 1288.17,626.64 1289.06,626.654 1289.96,626.666 1290.85,626.677 1291.75,626.688 1292.64,626.697 1293.54,626.705 1294.43,626.712 1295.33,626.718 1296.22,626.724 \n",
" 1297.12,626.728 1298.01,626.731 1298.9,626.733 1299.8,626.734 1300.69,626.734 1301.59,626.734 1302.48,626.732 1303.38,626.729 1304.27,626.726 1305.17,626.722 \n",
" 1306.06,626.716 1306.96,626.71 1307.85,626.703 1308.75,626.696 1309.64,626.687 1310.53,626.678 1311.43,626.668 1312.32,626.657 1313.22,626.646 1314.11,626.634 \n",
" 1315.01,626.621 1315.9,626.608 1316.8,626.594 1317.69,626.58 1318.59,626.565 1319.48,626.55 1320.38,626.534 1321.27,626.518 1322.16,626.502 1323.06,626.485 \n",
" 1323.95,626.468 1324.85,626.45 1325.74,626.433 1326.64,626.415 1327.53,626.397 1328.43,626.379 1329.32,626.36 1330.22,626.342 1331.11,626.323 1332.01,626.305 \n",
" 1332.9,626.286 1333.79,626.268 1334.69,626.249 1335.58,626.231 1336.48,626.213 1337.37,626.195 1338.27,626.177 1339.16,626.159 1340.06,626.142 1340.95,626.124 \n",
" 1341.85,626.107 1342.74,626.091 1343.64,626.074 1344.53,626.058 1345.42,626.043 1346.32,626.027 1347.21,626.012 1348.11,625.998 1349,625.984 1349.9,625.97 \n",
" 1350.79,625.957 1351.69,625.944 1352.58,625.932 1353.48,625.92 1354.37,625.909 1355.27,625.898 1356.16,625.888 1357.05,625.878 1357.95,625.869 1358.84,625.86 \n",
" 1359.74,625.852 1360.63,625.845 1361.53,625.838 1362.42,625.831 1363.32,625.826 1364.21,625.82 1365.11,625.816 1366,625.812 1366.9,625.808 1367.79,625.805 \n",
" 1368.68,625.803 1369.58,625.801 1370.47,625.8 1371.37,625.799 1372.26,625.799 1373.16,625.799 1374.05,625.8 1374.95,625.801 1375.84,625.803 1376.74,625.805 \n",
" 1377.63,625.808 1378.53,625.811 1379.42,625.815 1380.31,625.819 1381.21,625.824 1382.1,625.829 1383,625.834 1383.89,625.84 1384.79,625.846 1385.68,625.853 \n",
" 1386.58,625.86 1387.47,625.867 1388.37,625.874 1389.26,625.882 1390.16,625.89 1391.05,625.899 1391.94,625.907 1392.84,625.916 1393.73,625.925 1394.63,625.934 \n",
" 1395.52,625.944 1396.42,625.953 1397.31,625.963 1398.21,625.973 1399.1,625.983 1400,625.993 1400.89,626.003 1401.79,626.013 1402.68,626.023 1403.57,626.033 \n",
" 1404.47,626.044 1405.36,626.054 1406.26,626.064 1407.15,626.074 1408.05,626.084 1408.94,626.094 1409.84,626.104 1410.73,626.114 1411.63,626.123 1412.52,626.133 \n",
" 1413.42,626.142 1414.31,626.152 1415.2,626.161 1416.1,626.169 1416.99,626.178 1417.89,626.187 1418.78,626.195 1419.68,626.203 1420.57,626.211 1421.47,626.218 \n",
" 1422.36,626.226 1423.26,626.233 1424.15,626.24 1425.04,626.246 1425.94,626.253 1426.83,626.259 1427.73,626.264 1428.62,626.27 1429.52,626.275 1430.41,626.28 \n",
" 1431.31,626.284 1432.2,626.288 1433.1,626.292 1433.99,626.296 1434.89,626.299 1435.78,626.302 1436.67,626.304 1437.57,626.307 1438.46,626.309 1439.36,626.311 \n",
" 1440.25,626.312 1441.15,626.313 1442.04,626.314 1442.94,626.314 1443.83,626.314 1444.73,626.314 1445.62,626.314 1446.52,626.313 1447.41,626.312 1448.3,626.311 \n",
" 1449.2,626.31 1450.09,626.308 1450.99,626.306 1451.88,626.304 1452.78,626.301 1453.67,626.298 1454.57,626.295 1455.46,626.292 1456.36,626.289 1457.25,626.285 \n",
" 1458.15,626.282 1459.04,626.278 1459.93,626.274 1460.83,626.269 1461.72,626.265 1462.62,626.26 1463.51,626.256 1464.41,626.251 1465.3,626.246 1466.2,626.241 \n",
" 1467.09,626.236 1467.99,626.23 1468.88,626.225 1469.78,626.22 1470.67,626.214 1471.56,626.209 1472.46,626.203 1473.35,626.198 1474.25,626.192 1475.14,626.186 \n",
" 1476.04,626.181 1476.93,626.175 1477.83,626.17 1478.72,626.164 1479.62,626.158 1480.51,626.153 1481.41,626.147 1482.3,626.142 1483.19,626.137 1484.09,626.131 \n",
" 1484.98,626.126 1485.88,626.121 1486.77,626.116 1487.67,626.111 1488.56,626.106 1489.46,626.102 1490.35,626.097 1491.25,626.093 1492.14,626.088 1493.04,626.084 \n",
" 1493.93,626.08 1494.82,626.076 1495.72,626.072 1496.61,626.069 1497.51,626.065 1498.4,626.062 1499.3,626.059 1500.19,626.056 1501.09,626.053 1501.98,626.05 \n",
" 1502.88,626.048 1503.77,626.045 1504.67,626.043 1505.56,626.041 1506.45,626.039 1507.35,626.038 1508.24,626.036 1509.14,626.035 1510.03,626.034 1510.93,626.033 \n",
" 1511.82,626.032 1512.72,626.031 1513.61,626.031 1514.51,626.03 1515.4,626.03 1516.3,626.03 1517.19,626.03 1518.08,626.031 1518.98,626.031 1519.87,626.032 \n",
" 1520.77,626.033 1521.66,626.034 1522.56,626.035 1523.45,626.036 1524.35,626.037 1525.24,626.039 1526.14,626.04 1527.03,626.042 1527.93,626.044 1528.82,626.046 \n",
" 1529.71,626.048 1530.61,626.05 1531.5,626.052 1532.4,626.055 1533.29,626.057 1534.19,626.06 1535.08,626.062 1535.98,626.065 1536.87,626.068 1537.77,626.07 \n",
" 1538.66,626.073 1539.56,626.076 1540.45,626.079 1541.34,626.082 1542.24,626.085 1543.13,626.088 1544.03,626.091 1544.92,626.094 1545.82,626.097 1546.71,626.1 \n",
" 1547.61,626.103 1548.5,626.106 1549.4,626.11 1550.29,626.113 1551.19,626.116 1552.08,626.119 1552.97,626.122 1553.87,626.125 1554.76,626.128 1555.66,626.131 \n",
" 1556.55,626.133 1557.45,626.136 1558.34,626.139 1559.24,626.142 1560.13,626.144 1561.03,626.147 1561.92,626.15 1562.81,626.152 1563.71,626.155 1564.6,626.157 \n",
" 1565.5,626.159 1566.39,626.161 1567.29,626.163 1568.18,626.165 1569.08,626.167 1569.97,626.169 1570.87,626.171 1571.76,626.173 1572.66,626.174 1573.55,626.176 \n",
" 1574.44,626.177 1575.34,626.178 1576.23,626.18 1577.13,626.181 1578.02,626.182 1578.92,626.183 1579.81,626.184 1580.71,626.184 1581.6,626.185 1582.5,626.186 \n",
" 1583.39,626.186 1584.29,626.186 1585.18,626.187 1586.07,626.187 1586.97,626.187 1587.86,626.187 1588.76,626.187 1589.65,626.187 1590.55,626.186 1591.44,626.186 \n",
" 1592.34,626.186 1593.23,626.185 1594.13,626.185 1595.02,626.184 1595.92,626.183 1596.81,626.182 1597.7,626.182 1598.6,626.181 1599.49,626.18 1600.39,626.179 \n",
" 1601.28,626.177 1602.18,626.176 1603.07,626.175 1603.97,626.174 1604.86,626.173 1605.76,626.171 1606.65,626.17 1607.55,626.168 1608.44,626.167 1609.33,626.165 \n",
" 1610.23,626.164 1611.12,626.162 1612.02,626.161 1612.91,626.159 1613.81,626.157 1614.7,626.156 1615.6,626.154 1616.49,626.152 1617.39,626.151 1618.28,626.149 \n",
" 1619.18,626.147 1620.07,626.145 1620.96,626.144 1621.86,626.142 1622.75,626.14 1623.65,626.139 1624.54,626.137 1625.44,626.135 1626.33,626.134 1627.23,626.132 \n",
" 1628.12,626.13 1629.02,626.129 1629.91,626.127 1630.81,626.126 1631.7,626.124 1632.59,626.123 1633.49,626.122 1634.38,626.12 1635.28,626.119 1636.17,626.118 \n",
" 1637.07,626.116 1637.96,626.115 1638.86,626.114 1639.75,626.113 1640.65,626.112 1641.54,626.111 1642.44,626.11 1643.33,626.109 1644.22,626.108 1645.12,626.107 \n",
" 1646.01,626.106 1646.91,626.106 1647.8,626.105 1648.7,626.104 1649.59,626.104 1650.49,626.103 1651.38,626.103 1652.28,626.102 1653.17,626.102 1654.07,626.102 \n",
" 1654.96,626.101 1655.85,626.101 1656.75,626.101 1657.64,626.101 1658.54,626.101 1659.43,626.101 1660.33,626.101 1661.22,626.101 1662.12,626.101 1663.01,626.101 \n",
" 1663.91,626.101 1664.8,626.102 1665.7,626.102 1666.59,626.102 1667.48,626.103 1668.38,626.103 1669.27,626.104 1670.17,626.104 1671.06,626.105 1671.96,626.105 \n",
" 1672.85,626.106 1673.75,626.106 1674.64,626.107 1675.54,626.108 1676.43,626.109 1677.33,626.109 1678.22,626.11 1679.11,626.111 1680.01,626.112 1680.9,626.113 \n",
" 1681.8,626.113 1682.69,626.114 1683.59,626.115 1684.48,626.116 1685.38,626.117 1686.27,626.118 1687.17,626.119 1688.06,626.12 1688.96,626.121 1689.85,626.122 \n",
" 1690.74,626.123 1691.64,626.123 1692.53,626.124 1693.43,626.125 1694.32,626.126 1695.22,626.127 1696.11,626.128 1697.01,626.129 1697.9,626.13 1698.8,626.131 \n",
" 1699.69,626.132 1700.58,626.133 1701.48,626.133 1702.37,626.134 1703.27,626.135 1704.16,626.136 1705.06,626.137 1705.95,626.137 1706.85,626.138 1707.74,626.139 \n",
" 1708.64,626.14 1709.53,626.14 1710.43,626.141 1711.32,626.142 1712.21,626.142 1713.11,626.143 1714,626.143 1714.9,626.144 1715.79,626.144 1716.69,626.145 \n",
" 1717.58,626.145 1718.48,626.146 1719.37,626.146 1720.27,626.146 1721.16,626.147 1722.06,626.147 1722.95,626.147 1723.84,626.147 1724.74,626.148 1725.63,626.148 \n",
" 1726.53,626.148 1727.42,626.148 1728.32,626.148 1729.21,626.148 1730.11,626.148 1731,626.148 1731.9,626.148 1732.79,626.148 1733.69,626.148 1734.58,626.148 \n",
" 1735.47,626.148 1736.37,626.148 1737.26,626.148 1738.16,626.148 1739.05,626.147 1739.95,626.147 1740.84,626.147 1741.74,626.147 1742.63,626.146 1743.53,626.146 \n",
" 1744.42,626.146 1745.32,626.145 1746.21,626.145 1747.1,626.145 1748,626.144 1748.89,626.144 1749.79,626.143 1750.68,626.143 1751.58,626.142 1752.47,626.142 \n",
" 1753.37,626.141 1754.26,626.141 1755.16,626.141 1756.05,626.14 1756.95,626.14 1757.84,626.139 1758.73,626.139 1759.63,626.138 1760.52,626.137 1761.42,626.137 \n",
" 1762.31,626.136 1763.21,626.136 1764.1,626.135 1765,626.135 1765.89,626.134 1766.79,626.134 1767.68,626.133 1768.58,626.133 1769.47,626.132 1770.36,626.132 \n",
" 1771.26,626.131 1772.15,626.131 1773.05,626.13 1773.94,626.13 1774.84,626.13 1775.73,626.129 1776.63,626.129 1777.52,626.128 1778.42,626.128 1779.31,626.127 \n",
" 1780.21,626.127 1781.1,626.127 1781.99,626.126 1782.89,626.126 1783.78,626.126 1784.68,626.125 1785.57,626.125 1786.47,626.125 1787.36,626.124 1788.26,626.124 \n",
" 1789.15,626.124 1790.05,626.124 1790.94,626.124 1791.84,626.123 1792.73,626.123 1793.62,626.123 1794.52,626.123 1795.41,626.123 1796.31,626.123 1797.2,626.122 \n",
" 1798.1,626.122 1798.99,626.122 1799.89,626.122 1800.78,626.122 1801.68,626.122 1802.57,626.122 1803.47,626.122 1804.36,626.122 1805.25,626.122 1806.15,626.122 \n",
" 1807.04,626.122 1807.94,626.122 1808.83,626.123 1809.73,626.123 1810.62,626.123 1811.52,626.123 1812.41,626.123 1813.31,626.123 1814.2,626.123 1815.1,626.123 \n",
" 1815.99,626.124 1816.88,626.124 1817.78,626.124 1818.67,626.124 1819.57,626.124 1820.46,626.125 1821.36,626.125 1822.25,626.125 1823.15,626.125 1824.04,626.126 \n",
" 1824.94,626.126 1825.83,626.126 1826.73,626.126 1827.62,626.127 1828.51,626.127 1829.41,626.127 1830.3,626.128 1831.2,626.128 1832.09,626.128 1832.99,626.128 \n",
" 1833.88,626.129 1834.78,626.129 1835.67,626.129 1836.57,626.13 1837.46,626.13 1838.35,626.13 1839.25,626.13 1840.14,626.131 1841.04,626.131 1841.93,626.131 \n",
" 1842.83,626.132 1843.72,626.132 1844.62,626.132 1845.51,626.132 1846.41,626.133 1847.3,626.133 1848.2,626.133 1849.09,626.133 1849.98,626.133 1850.88,626.134 \n",
" 1851.77,626.134 1852.67,626.134 1853.56,626.134 1854.46,626.135 1855.35,626.135 1856.25,626.135 1857.14,626.135 1858.04,626.135 1858.93,626.135 1859.83,626.136 \n",
" 1860.72,626.136 1861.61,626.136 1862.51,626.136 1863.4,626.136 1864.3,626.136 1865.19,626.136 1866.09,626.136 1866.98,626.136 1867.88,626.136 1868.77,626.137 \n",
" 1869.67,626.137 1870.56,626.137 1871.46,626.137 1872.35,626.137 1873.24,626.137 1874.14,626.137 1875.03,626.137 1875.93,626.137 1876.82,626.137 1877.72,626.137 \n",
" 1878.61,626.137 1879.51,626.137 1880.4,626.137 1881.3,626.136 1882.19,626.136 1883.09,626.136 1883.98,626.136 1884.87,626.136 1885.77,626.136 1886.66,626.136 \n",
" 1887.56,626.136 1888.45,626.136 1889.35,626.136 1890.24,626.136 1891.14,626.135 1892.03,626.135 1892.93,626.135 1893.82,626.135 1894.72,626.135 1895.61,626.135 \n",
" 1896.5,626.135 1897.4,626.135 1898.29,626.134 1899.19,626.134 1900.08,626.134 1900.98,626.134 1901.87,626.134 1902.77,626.134 1903.66,626.133 1904.56,626.133 \n",
" 1905.45,626.133 1906.35,626.133 1907.24,626.133 1908.13,626.133 1909.03,626.133 1909.92,626.132 1910.82,626.132 1911.71,626.132 1912.61,626.132 1913.5,626.132 \n",
" 1914.4,626.132 1915.29,626.131 1916.19,626.131 1917.08,626.131 1917.98,626.131 1918.87,626.131 1919.76,626.131 1920.66,626.131 1921.55,626.131 1922.45,626.13 \n",
" 1923.34,626.13 1924.24,626.13 1925.13,626.13 1926.03,626.13 1926.92,626.13 1927.82,626.13 1928.71,626.13 1929.61,626.13 1930.5,626.13 1931.39,626.129 \n",
" 1932.29,626.129 1933.18,626.129 1934.08,626.129 1934.97,626.129 1935.87,626.129 1936.76,626.129 1937.66,626.129 1938.55,626.129 1939.45,626.129 1940.34,626.129 \n",
" 1941.24,626.129 1942.13,626.129 1943.02,626.129 1943.92,626.129 1944.81,626.129 1945.71,626.129 1946.6,626.129 1947.5,626.129 1948.39,626.129 1949.29,626.129 \n",
" 1950.18,626.129 1951.08,626.129 1951.97,626.129 1952.87,626.129 1953.76,626.129 1954.65,626.129 1955.55,626.129 1956.44,626.129 1957.34,626.129 1958.23,626.129 \n",
" 1959.13,626.129 1960.02,626.129 1960.92,626.129 1961.81,626.129 1962.71,626.129 1963.6,626.13 1964.5,626.13 1965.39,626.13 1966.28,626.13 1967.18,626.13 \n",
" 1968.07,626.13 1968.97,626.13 1969.86,626.13 1970.76,626.13 1971.65,626.13 1972.55,626.13 1973.44,626.13 1974.34,626.131 1975.23,626.131 1976.12,626.131 \n",
" 1977.02,626.131 1977.91,626.131 1978.81,626.131 1979.7,626.131 1980.6,626.131 1981.49,626.131 1982.39,626.131 1983.28,626.131 1984.18,626.131 1985.07,626.132 \n",
" 1985.97,626.132 1986.86,626.132 1987.75,626.132 1988.65,626.132 1989.54,626.132 1990.44,626.132 1991.33,626.132 1992.23,626.132 1993.12,626.132 1994.02,626.132 \n",
" 1994.91,626.132 1995.81,626.132 1996.7,626.133 1997.6,626.133 1998.49,626.133 1999.38,626.133 2000.28,626.133 2001.17,626.133 2002.07,626.133 2002.96,626.133 \n",
" 2003.86,626.133 2004.75,626.133 2005.65,626.133 2006.54,626.133 2007.44,626.133 2008.33,626.133 2009.23,626.133 2010.12,626.133 2011.01,626.133 2011.91,626.133 \n",
" 2012.8,626.133 2013.7,626.133 2014.59,626.133 2015.49,626.133 2016.38,626.133 2017.28,626.133 2018.17,626.133 2019.07,626.133 2019.96,626.133 2020.86,626.133 \n",
" 2021.75,626.133 2022.64,626.133 2023.54,626.133 2024.43,626.133 2025.33,626.133 2026.22,626.133 2027.12,626.133 2028.01,626.133 2028.91,626.133 2029.8,626.133 \n",
" 2030.7,626.133 2031.59,626.133 2032.49,626.133 2033.38,626.133 2034.27,626.133 2035.17,626.133 2036.06,626.133 2036.96,626.133 2037.85,626.133 2038.75,626.133 \n",
" 2039.64,626.133 2040.54,626.133 2041.43,626.133 2042.33,626.133 2043.22,626.133 2044.12,626.132 2045.01,626.132 2045.9,626.132 2046.8,626.132 2047.69,626.132 \n",
" 2048.59,626.132 2049.48,626.132 2050.38,626.132 2051.27,626.132 2052.17,626.132 2053.06,626.132 2053.96,626.132 2054.85,626.132 2055.75,626.132 2056.64,626.132 \n",
" 2057.53,626.132 2058.43,626.132 2059.32,626.132 2060.22,626.132 2061.11,626.132 2062.01,626.132 2062.9,626.132 2063.8,626.131 2064.69,626.131 2065.59,626.131 \n",
" 2066.48,626.131 2067.38,626.131 2068.27,626.131 2069.16,626.131 2070.06,626.131 2070.95,626.131 2071.85,626.131 2072.74,626.131 2073.64,626.131 2074.53,626.131 \n",
" 2075.43,626.131 2076.32,626.131 2077.22,626.131 2078.11,626.131 2079.01,626.131 2079.9,626.131 2080.79,626.131 2081.69,626.131 2082.58,626.131 2083.48,626.131 \n",
" 2084.37,626.131 2085.27,626.131 2086.16,626.131 2087.06,626.131 2087.95,626.131 2088.85,626.131 2089.74,626.131 2090.64,626.131 2091.53,626.131 2092.42,626.131 \n",
" 2093.32,626.131 2094.21,626.131 2095.11,626.131 2096,626.131 2096.9,626.131 2097.79,626.131 2098.69,626.131 2099.58,626.131 2100.48,626.131 2101.37,626.131 \n",
" 2102.27,626.131 2103.16,626.131 2104.05,626.131 2104.95,626.131 2105.84,626.131 2106.74,626.131 2107.63,626.131 2108.53,626.131 2109.42,626.131 2110.32,626.131 \n",
" 2111.21,626.131 2112.11,626.131 2113,626.131 2113.89,626.131 2114.79,626.131 2115.68,626.131 2116.58,626.131 2117.47,626.131 2118.37,626.131 2119.26,626.131 \n",
" 2120.16,626.132 2121.05,626.132 2121.95,626.132 2122.84,626.132 2123.74,626.132 2124.63,626.132 2125.52,626.132 2126.42,626.132 2127.31,626.132 2128.21,626.132 \n",
" 2129.1,626.132 2130,626.132 2130.89,626.132 2131.79,626.132 2132.68,626.132 2133.58,626.132 2134.47,626.132 2135.37,626.132 2136.26,626.132 2137.15,626.132 \n",
" 2138.05,626.132 2138.94,626.132 2139.84,626.132 2140.73,626.132 2141.63,626.132 2142.52,626.132 2143.42,626.132 2144.31,626.132 2145.21,626.132 2146.1,626.132 \n",
" 2147,626.132 2147.89,626.132 2148.78,626.132 2149.68,626.132 2150.57,626.132 2151.47,626.132 2152.36,626.132 2153.26,626.132 2154.15,626.132 2155.05,626.132 \n",
" 2155.94,626.132 2156.84,626.132 2157.73,626.132 2158.63,626.132 2159.52,626.132 2160.41,626.132 2161.31,626.132 2162.2,626.132 2163.1,626.132 2163.99,626.132 \n",
" 2164.89,626.132 2165.78,626.132 2166.68,626.132 2167.57,626.132 2168.47,626.132 2169.36,626.132 2170.26,626.132 2171.15,626.132 2172.04,626.132 2172.94,626.132 \n",
" 2173.83,626.132 2174.73,626.132 2175.62,626.132 2176.52,626.132 2177.41,626.132 2178.31,626.132 2179.2,626.132 2180.1,626.132 2180.99,626.132 2181.89,626.132 \n",
" 2182.78,626.132 2183.67,626.132 2184.57,626.132 2185.46,626.132 2186.36,626.132 2187.25,626.132 2188.15,626.132 2189.04,626.132 2189.94,626.132 2190.83,626.132 \n",
" 2191.73,626.132 2192.62,626.132 2193.52,626.132 2194.41,626.132 2195.3,626.132 2196.2,626.132 2197.09,626.132 2197.99,626.132 2198.88,626.132 2199.78,626.132 \n",
" 2200.67,626.132 2201.57,626.132 2202.46,626.132 2203.36,626.132 2204.25,626.132 2205.15,626.132 2206.04,626.132 2206.93,626.132 2207.83,626.132 2208.72,626.132 \n",
" 2209.62,626.132 2210.51,626.132 2211.41,626.132 2212.3,626.132 2213.2,626.132 2214.09,626.132 2214.99,626.132 2215.88,626.132 2216.78,626.132 2217.67,626.132 \n",
" 2218.56,626.132 2219.46,626.132 2220.35,626.132 2221.25,626.132 2222.14,626.132 2223.04,626.132 2223.93,626.132 2224.83,626.132 2225.72,626.132 2226.62,626.132 \n",
" 2227.51,626.132 2228.41,626.132 2229.3,626.132 2230.19,626.132 2231.09,626.132 2231.98,626.132 2232.88,626.132 2233.77,626.132 2234.67,626.132 2235.56,626.132 \n",
" 2236.46,626.132 2237.35,626.132 2238.25,626.132 2239.14,626.132 2240.04,626.132 2240.93,626.132 2241.82,626.132 2242.72,626.132 2243.61,626.132 2244.51,626.132 \n",
" 2245.4,626.132 2246.3,626.132 2247.19,626.132 2248.09,626.132 2248.98,626.132 2249.88,626.132 2250.77,626.132 2251.66,626.132 2252.56,626.132 2253.45,626.132 \n",
" 2254.35,626.132 2255.24,626.132 2256.14,626.132 2257.03,626.132 2257.93,626.132 2258.82,626.132 2259.72,626.132 2260.61,626.132 2261.51,626.132 2262.4,626.132 \n",
" 2263.29,626.132 2264.19,626.132 2265.08,626.132 2265.98,626.132 2266.87,626.132 2267.77,626.132 2268.66,626.132 2269.56,626.132 2270.45,626.132 2271.35,626.132 \n",
" 2272.24,626.132 2273.14,626.132 2274.03,626.132 2274.92,626.132 2275.82,626.132 2276.71,626.132 2277.61,626.132 2278.5,626.132 2279.4,626.132 2280.29,626.132 \n",
" 2281.19,626.132 2282.08,626.132 2282.98,626.132 2283.87,626.132 2284.77,626.132 2285.66,626.132 2286.55,626.132 2287.45,626.132 2288.34,626.132 2289.24,626.132 \n",
" 2290.13,626.132 2291.03,626.132 2291.92,626.132 2292.82,626.132 2293.71,626.132 2294.61,626.132 2295.5,626.132 2296.4,626.132 2297.29,626.132 2298.18,626.132 \n",
" 2299.08,626.132 \n",
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" 912.433,742.854 913.328,745.032 914.222,747.225 915.117,749.431 916.012,751.646 916.906,753.868 917.801,756.097 918.695,758.328 919.59,760.561 920.485,762.793 \n",
" 921.379,765.022 922.274,767.245 923.169,769.462 924.063,771.668 924.958,773.864 925.852,776.046 926.747,778.213 927.642,780.363 928.536,782.493 929.431,784.603 \n",
" 930.325,786.69 931.22,788.752 932.115,790.787 933.009,792.795 933.904,794.772 934.798,796.719 935.693,798.632 936.588,800.511 937.482,802.354 938.377,804.159 \n",
" 939.272,805.926 940.166,807.652 941.061,809.337 941.955,810.979 942.85,812.577 943.745,814.13 944.639,815.637 945.534,817.097 946.428,818.509 947.323,819.871 \n",
" 948.218,821.184 949.112,822.446 950.007,823.656 950.901,824.815 951.796,825.92 952.691,826.972 953.585,827.97 954.48,828.913 955.375,829.802 956.269,830.636 \n",
" 957.164,831.413 958.058,832.136 958.953,832.802 959.848,833.412 960.742,833.966 961.637,834.463 962.531,834.905 963.426,835.29 964.321,835.62 965.215,835.893 \n",
" 966.11,836.111 967.004,836.274 967.899,836.381 968.794,836.435 969.688,836.434 970.583,836.379 971.478,836.271 972.372,836.111 973.267,835.898 974.161,835.635 \n",
" 975.056,835.321 975.951,834.957 976.845,834.544 977.74,834.083 978.634,833.575 979.529,833.02 980.424,832.42 981.318,831.775 982.213,831.087 983.107,830.356 \n",
" 984.002,829.584 984.897,828.772 985.791,827.92 986.686,827.031 987.58,826.105 988.475,825.143 989.37,824.147 990.264,823.118 991.159,822.058 992.054,820.966 \n",
" 992.948,819.846 993.843,818.698 994.737,817.523 995.632,816.323 996.527,815.1 997.421,813.854 998.316,812.587 999.21,811.3 1000.11,809.995 1001,808.674 \n",
" 1001.89,807.337 1002.79,805.986 1003.68,804.623 1004.58,803.249 1005.47,801.865 1006.37,800.472 1007.26,799.073 1008.16,797.668 1009.05,796.259 1009.95,794.848 \n",
" 1010.84,793.435 1011.73,792.022 1012.63,790.611 1013.52,789.202 1014.42,787.797 1015.31,786.398 1016.21,785.005 1017.1,783.62 1018,782.245 1018.89,780.879 \n",
" 1019.79,779.526 1020.68,778.185 1021.58,776.858 1022.47,775.546 1023.36,774.251 1024.26,772.973 1025.15,771.713 1026.05,770.473 1026.94,769.253 1027.84,768.055 \n",
" 1028.73,766.879 1029.63,765.726 1030.52,764.598 1031.42,763.494 1032.31,762.417 1033.21,761.366 1034.1,760.343 1034.99,759.348 1035.89,758.382 1036.78,757.445 \n",
" 1037.68,756.539 1038.57,755.663 1039.47,754.819 1040.36,754.007 1041.26,753.227 1042.15,752.48 1043.05,751.766 1043.94,751.086 1044.84,750.44 1045.73,749.828 \n",
" 1046.62,749.251 1047.52,748.709 1048.41,748.202 1049.31,747.73 1050.2,747.293 1051.1,746.892 1051.99,746.527 1052.89,746.197 1053.78,745.902 1054.68,745.643 \n",
" 1055.57,745.42 1056.47,745.232 1057.36,745.079 1058.25,744.961 1059.15,744.878 1060.04,744.83 1060.94,744.816 1061.83,744.836 1062.73,744.89 1063.62,744.978 \n",
" 1064.52,745.098 1065.41,745.251 1066.31,745.436 1067.2,745.653 1068.1,745.901 1068.99,746.18 1069.88,746.489 1070.78,746.828 1071.67,747.195 1072.57,747.591 \n",
" 1073.46,748.015 1074.36,748.466 1075.25,748.943 1076.15,749.447 1077.04,749.975 1077.94,750.527 1078.83,751.103 1079.73,751.702 1080.62,752.323 1081.51,752.966 \n",
" 1082.41,753.628 1083.3,754.311 1084.2,755.012 1085.09,755.731 1085.99,756.467 1086.88,757.219 1087.78,757.987 1088.67,758.77 1089.57,759.566 1090.46,760.375 \n",
" 1091.36,761.195 1092.25,762.027 1093.14,762.869 1094.04,763.72 1094.93,764.579 1095.83,765.446 1096.72,766.319 1097.62,767.198 1098.51,768.082 1099.41,768.969 \n",
" 1100.3,769.859 1101.2,770.752 1102.09,771.646 1102.99,772.54 1103.88,773.433 1104.77,774.325 1105.67,775.215 1106.56,776.102 1107.46,776.985 1108.35,777.864 \n",
" 1109.25,778.737 1110.14,779.604 1111.04,780.463 1111.93,781.315 1112.83,782.159 1113.72,782.993 1114.62,783.817 1115.51,784.63 1116.4,785.432 1117.3,786.223 \n",
" 1118.19,787 1119.09,787.764 1119.98,788.514 1120.88,789.25 1121.77,789.971 1122.67,790.676 1123.56,791.365 1124.46,792.037 1125.35,792.692 1126.25,793.329 \n",
" 1127.14,793.948 1128.03,794.549 1128.93,795.13 1129.82,795.693 1130.72,796.236 1131.61,796.758 1132.51,797.26 1133.4,797.742 1134.3,798.203 1135.19,798.642 \n",
" 1136.09,799.06 1136.98,799.457 1137.88,799.831 1138.77,800.184 1139.66,800.514 1140.56,800.822 1141.45,801.108 1142.35,801.372 1143.24,801.613 1144.14,801.831 \n",
" 1145.03,802.027 1145.93,802.2 1146.82,802.351 1147.72,802.48 1148.61,802.586 1149.5,802.67 1150.4,802.732 1151.29,802.772 1152.19,802.79 1153.08,802.786 \n",
" 1153.98,802.761 1154.87,802.715 1155.77,802.648 1156.66,802.56 1157.56,802.451 1158.45,802.323 1159.35,802.174 1160.24,802.006 1161.13,801.819 1162.03,801.612 \n",
" 1162.92,801.388 1163.82,801.145 1164.71,800.884 1165.61,800.606 1166.5,800.311 1167.4,799.999 1168.29,799.672 1169.19,799.329 1170.08,798.971 1170.98,798.598 \n",
" 1171.87,798.211 1172.76,797.81 1173.66,797.396 1174.55,796.97 1175.45,796.531 1176.34,796.081 1177.24,795.62 1178.13,795.148 1179.03,794.666 1179.92,794.175 \n",
" 1180.82,793.675 1181.71,793.166 1182.61,792.65 1183.5,792.127 1184.39,791.597 1185.29,791.061 1186.18,790.519 1187.08,789.973 1187.97,789.422 1188.87,788.867 \n",
" 1189.76,788.309 1190.66,787.749 1191.55,787.186 1192.45,786.622 1193.34,786.057 1194.24,785.491 1195.13,784.926 1196.02,784.361 1196.92,783.797 1197.81,783.235 \n",
" 1198.71,782.675 1199.6,782.118 1200.5,781.564 1201.39,781.014 1202.29,780.468 1203.18,779.926 1204.08,779.39 1204.97,778.86 1205.87,778.336 1206.76,777.818 \n",
" 1207.65,777.308 1208.55,776.804 1209.44,776.309 1210.34,775.822 1211.23,775.343 1212.13,774.874 1213.02,774.414 1213.92,773.963 1214.81,773.523 1215.71,773.093 \n",
" 1216.6,772.674 1217.5,772.266 1218.39,771.869 1219.28,771.484 1220.18,771.111 1221.07,770.75 1221.97,770.401 1222.86,770.065 1223.76,769.742 1224.65,769.431 \n",
" 1225.55,769.134 1226.44,768.85 1227.34,768.58 1228.23,768.323 1229.13,768.08 1230.02,767.851 1230.91,767.636 1231.81,767.435 1232.7,767.248 1233.6,767.076 \n",
" 1234.49,766.917 1235.39,766.773 1236.28,766.643 1237.18,766.527 1238.07,766.425 1238.97,766.338 1239.86,766.265 1240.76,766.205 1241.65,766.16 1242.54,766.129 \n",
" 1243.44,766.112 1244.33,766.108 1245.23,766.118 1246.12,766.142 1247.02,766.179 1247.91,766.229 1248.81,766.292 1249.7,766.368 1250.6,766.457 1251.49,766.558 \n",
" 1252.39,766.671 1253.28,766.797 1254.17,766.934 1255.07,767.083 1255.96,767.243 1256.86,767.414 1257.75,767.596 1258.65,767.789 1259.54,767.992 1260.44,768.205 \n",
" 1261.33,768.427 1262.23,768.659 1263.12,768.9 1264.02,769.15 1264.91,769.409 1265.8,769.675 1266.7,769.949 1267.59,770.231 1268.49,770.52 1269.38,770.816 \n",
" 1270.28,771.118 1271.17,771.426 1272.07,771.74 1272.96,772.06 1273.86,772.384 1274.75,772.713 1275.65,773.047 1276.54,773.385 1277.43,773.726 1278.33,774.07 \n",
" 1279.22,774.418 1280.12,774.768 1281.01,775.12 1281.91,775.474 1282.8,775.829 1283.7,776.186 1284.59,776.543 1285.49,776.901 1286.38,777.259 1287.27,777.617 \n",
" 1288.17,777.974 1289.06,778.33 1289.96,778.685 1290.85,779.038 1291.75,779.39 1292.64,779.739 1293.54,780.086 1294.43,780.429 1295.33,780.77 1296.22,781.107 \n",
" 1297.12,781.441 1298.01,781.77 1298.9,782.095 1299.8,782.415 1300.69,782.731 1301.59,783.042 1302.48,783.347 1303.38,783.646 1304.27,783.94 1305.17,784.227 \n",
" 1306.06,784.509 1306.96,784.784 1307.85,785.052 1308.75,785.313 1309.64,785.567 1310.53,785.814 1311.43,786.053 1312.32,786.285 1313.22,786.509 1314.11,786.725 \n",
" 1315.01,786.933 1315.9,787.133 1316.8,787.325 1317.69,787.508 1318.59,787.683 1319.48,787.849 1320.38,788.006 1321.27,788.155 1322.16,788.295 1323.06,788.426 \n",
" 1323.95,788.548 1324.85,788.661 1325.74,788.765 1326.64,788.86 1327.53,788.947 1328.43,789.024 1329.32,789.092 1330.22,789.151 1331.11,789.201 1332.01,789.242 \n",
" 1332.9,789.275 1333.79,789.298 1334.69,789.313 1335.58,789.319 1336.48,789.316 1337.37,789.305 1338.27,789.285 1339.16,789.257 1340.06,789.221 1340.95,789.176 \n",
" 1341.85,789.123 1342.74,789.063 1343.64,788.994 1344.53,788.918 1345.42,788.835 1346.32,788.744 1347.21,788.645 1348.11,788.54 1349,788.428 1349.9,788.308 \n",
" 1350.79,788.183 1351.69,788.051 1352.58,787.913 1353.48,787.768 1354.37,787.618 1355.27,787.462 1356.16,787.301 1357.05,787.135 1357.95,786.963 1358.84,786.787 \n",
" 1359.74,786.606 1360.63,786.421 1361.53,786.231 1362.42,786.038 1363.32,785.841 1364.21,785.64 1365.11,785.436 1366,785.229 1366.9,785.019 1367.79,784.806 \n",
" 1368.68,784.591 1369.58,784.374 1370.47,784.155 1371.37,783.935 1372.26,783.712 1373.16,783.489 1374.05,783.264 1374.95,783.039 1375.84,782.813 1376.74,782.587 \n",
" 1377.63,782.36 1378.53,782.134 1379.42,781.907 1380.31,781.682 1381.21,781.457 1382.1,781.233 1383,781.01 1383.89,780.788 1384.79,780.568 1385.68,780.35 \n",
" 1386.58,780.134 1387.47,779.919 1388.37,779.707 1389.26,779.498 1390.16,779.291 1391.05,779.087 1391.94,778.886 1392.84,778.688 1393.73,778.494 1394.63,778.303 \n",
" 1395.52,778.115 1396.42,777.931 1397.31,777.752 1398.21,777.576 1399.1,777.405 1400,777.237 1400.89,777.075 1401.79,776.917 1402.68,776.763 1403.57,776.614 \n",
" 1404.47,776.47 1405.36,776.332 1406.26,776.198 1407.15,776.069 1408.05,775.946 1408.94,775.827 1409.84,775.714 1410.73,775.607 1411.63,775.505 1412.52,775.409 \n",
" 1413.42,775.318 1414.31,775.232 1415.2,775.153 1416.1,775.079 1416.99,775.01 1417.89,774.948 1418.78,774.891 1419.68,774.84 1420.57,774.794 1421.47,774.754 \n",
" 1422.36,774.72 1423.26,774.691 1424.15,774.669 1425.04,774.651 1425.94,774.64 1426.83,774.633 1427.73,774.633 1428.62,774.638 1429.52,774.648 1430.41,774.663 \n",
" 1431.31,774.684 1432.2,774.71 1433.1,774.741 1433.99,774.778 1434.89,774.819 1435.78,774.865 1436.67,774.916 1437.57,774.971 1438.46,775.032 1439.36,775.097 \n",
" 1440.25,775.166 1441.15,775.239 1442.04,775.317 1442.94,775.399 1443.83,775.485 1444.73,775.574 1445.62,775.668 1446.52,775.765 1447.41,775.865 1448.3,775.969 \n",
" 1449.2,776.076 1450.09,776.187 1450.99,776.3 1451.88,776.416 1452.78,776.535 1453.67,776.656 1454.57,776.78 1455.46,776.906 1456.36,777.034 1457.25,777.164 \n",
" 1458.15,777.296 1459.04,777.43 1459.93,777.566 1460.83,777.702 1461.72,777.84 1462.62,777.98 1463.51,778.12 1464.41,778.261 1465.3,778.403 1466.2,778.545 \n",
" 1467.09,778.688 1467.99,778.831 1468.88,778.975 1469.78,779.118 1470.67,779.261 1471.56,779.404 1472.46,779.546 1473.35,779.689 1474.25,779.83 1475.14,779.97 \n",
" 1476.04,780.11 1476.93,780.249 1477.83,780.386 1478.72,780.522 1479.62,780.657 1480.51,780.79 1481.41,780.922 1482.3,781.052 1483.19,781.18 1484.09,781.306 \n",
" 1484.98,781.43 1485.88,781.552 1486.77,781.671 1487.67,781.789 1488.56,781.903 1489.46,782.016 1490.35,782.125 1491.25,782.232 1492.14,782.336 1493.04,782.438 \n",
" 1493.93,782.536 1494.82,782.632 1495.72,782.724 1496.61,782.813 1497.51,782.899 1498.4,782.982 1499.3,783.062 1500.19,783.138 1501.09,783.211 1501.98,783.28 \n",
" 1502.88,783.346 1503.77,783.409 1504.67,783.468 1505.56,783.523 1506.45,783.575 1507.35,783.624 1508.24,783.668 1509.14,783.709 1510.03,783.747 1510.93,783.781 \n",
" 1511.82,783.811 1512.72,783.838 1513.61,783.861 1514.51,783.881 1515.4,783.897 1516.3,783.909 1517.19,783.918 1518.08,783.924 1518.98,783.925 1519.87,783.924 \n",
" 1520.77,783.919 1521.66,783.911 1522.56,783.899 1523.45,783.884 1524.35,783.865 1525.24,783.844 1526.14,783.819 1527.03,783.791 1527.93,783.76 1528.82,783.726 \n",
" 1529.71,783.69 1530.61,783.65 1531.5,783.607 1532.4,783.562 1533.29,783.514 1534.19,783.463 1535.08,783.41 1535.98,783.354 1536.87,783.296 1537.77,783.236 \n",
" 1538.66,783.173 1539.56,783.108 1540.45,783.041 1541.34,782.972 1542.24,782.901 1543.13,782.829 1544.03,782.754 1544.92,782.678 1545.82,782.6 1546.71,782.521 \n",
" 1547.61,782.441 1548.5,782.359 1549.4,782.276 1550.29,782.192 1551.19,782.106 1552.08,782.02 1552.97,781.933 1553.87,781.845 1554.76,781.757 1555.66,781.668 \n",
" 1556.55,781.578 1557.45,781.488 1558.34,781.398 1559.24,781.308 1560.13,781.217 1561.03,781.126 1561.92,781.036 1562.81,780.945 1563.71,780.855 1564.6,780.765 \n",
" 1565.5,780.675 1566.39,780.586 1567.29,780.497 1568.18,780.409 1569.08,780.322 1569.97,780.236 1570.87,780.15 1571.76,780.065 1572.66,779.981 1573.55,779.899 \n",
" 1574.44,779.817 1575.34,779.737 1576.23,779.658 1577.13,779.58 1578.02,779.504 1578.92,779.429 1579.81,779.356 1580.71,779.284 1581.6,779.214 1582.5,779.146 \n",
" 1583.39,779.079 1584.29,779.014 1585.18,778.951 1586.07,778.89 1586.97,778.831 1587.86,778.773 1588.76,778.718 1589.65,778.665 1590.55,778.613 1591.44,778.564 \n",
" 1592.34,778.517 1593.23,778.472 1594.13,778.43 1595.02,778.389 1595.92,778.351 1596.81,778.315 1597.7,778.281 1598.6,778.249 1599.49,778.22 1600.39,778.193 \n",
" 1601.28,778.168 1602.18,778.146 1603.07,778.126 1603.97,778.108 1604.86,778.092 1605.76,778.079 1606.65,778.068 1607.55,778.059 1608.44,778.052 1609.33,778.048 \n",
" 1610.23,778.046 1611.12,778.046 1612.02,778.048 1612.91,778.053 1613.81,778.059 1614.7,778.068 1615.6,778.078 1616.49,778.091 1617.39,778.106 1618.28,778.123 \n",
" 1619.18,778.141 1620.07,778.162 1620.96,778.185 1621.86,778.209 1622.75,778.235 1623.65,778.263 1624.54,778.293 1625.44,778.324 1626.33,778.357 1627.23,778.392 \n",
" 1628.12,778.428 1629.02,778.466 1629.91,778.505 1630.81,778.545 1631.7,778.587 1632.59,778.63 1633.49,778.674 1634.38,778.72 1635.28,778.766 1636.17,778.814 \n",
" 1637.07,778.863 1637.96,778.913 1638.86,778.963 1639.75,779.015 1640.65,779.067 1641.54,779.12 1642.44,779.174 1643.33,779.228 1644.22,779.283 1645.12,779.338 \n",
" 1646.01,779.394 1646.91,779.45 1647.8,779.507 1648.7,779.563 1649.59,779.62 1650.49,779.678 1651.38,779.735 1652.28,779.792 1653.17,779.85 1654.07,779.907 \n",
" 1654.96,779.964 1655.85,780.021 1656.75,780.078 1657.64,780.135 1658.54,780.191 1659.43,780.247 1660.33,780.302 1661.22,780.357 1662.12,780.412 1663.01,780.465 \n",
" 1663.91,780.519 1664.8,780.571 1665.7,780.623 1666.59,780.674 1667.48,780.725 1668.38,780.774 1669.27,780.823 1670.17,780.871 1671.06,780.917 1671.96,780.963 \n",
" 1672.85,781.008 1673.75,781.052 1674.64,781.094 1675.54,781.136 1676.43,781.176 1677.33,781.216 1678.22,781.254 1679.11,781.29 1680.01,781.326 1680.9,781.36 \n",
" 1681.8,781.393 1682.69,781.425 1683.59,781.455 1684.48,781.484 1685.38,781.512 1686.27,781.538 1687.17,781.563 1688.06,781.586 1688.96,781.608 1689.85,781.629 \n",
" 1690.74,781.648 1691.64,781.666 1692.53,781.682 1693.43,781.697 1694.32,781.71 1695.22,781.722 1696.11,781.733 1697.01,781.742 1697.9,781.749 1698.8,781.756 \n",
" 1699.69,781.76 1700.58,781.764 1701.48,781.766 1702.37,781.766 1703.27,781.765 1704.16,781.763 1705.06,781.76 1705.95,781.755 1706.85,781.749 1707.74,781.741 \n",
" 1708.64,781.732 1709.53,781.722 1710.43,781.711 1711.32,781.698 1712.21,781.684 1713.11,781.67 1714,781.653 1714.9,781.636 1715.79,781.618 1716.69,781.599 \n",
" 1717.58,781.578 1718.48,781.557 1719.37,781.534 1720.27,781.511 1721.16,781.486 1722.06,781.461 1722.95,781.435 1723.84,781.408 1724.74,781.381 1725.63,781.352 \n",
" 1726.53,781.323 1727.42,781.293 1728.32,781.262 1729.21,781.231 1730.11,781.199 1731,781.167 1731.9,781.134 1732.79,781.101 1733.69,781.067 1734.58,781.033 \n",
" 1735.47,780.998 1736.37,780.964 1737.26,780.928 1738.16,780.893 1739.05,780.857 1739.95,780.821 1740.84,780.785 1741.74,780.749 1742.63,780.713 1743.53,780.677 \n",
" 1744.42,780.64 1745.32,780.604 1746.21,780.568 1747.1,780.532 1748,780.496 1748.89,780.46 1749.79,780.424 1750.68,780.389 1751.58,780.353 1752.47,780.319 \n",
" 1753.37,780.284 1754.26,780.25 1755.16,780.216 1756.05,780.182 1756.95,780.149 1757.84,780.117 1758.73,780.085 1759.63,780.053 1760.52,780.022 1761.42,779.992 \n",
" 1762.31,779.962 1763.21,779.933 1764.1,779.904 1765,779.876 1765.89,779.849 1766.79,779.822 1767.68,779.796 1768.58,779.771 1769.47,779.747 1770.36,779.723 \n",
" 1771.26,779.7 1772.15,779.678 1773.05,779.657 1773.94,779.637 1774.84,779.617 1775.73,779.598 1776.63,779.581 1777.52,779.564 1778.42,779.547 1779.31,779.532 \n",
" 1780.21,779.518 1781.1,779.505 1781.99,779.492 1782.89,779.48 1783.78,779.47 1784.68,779.46 1785.57,779.451 1786.47,779.443 1787.36,779.436 1788.26,779.43 \n",
" 1789.15,779.425 1790.05,779.421 1790.94,779.417 1791.84,779.415 1792.73,779.413 1793.62,779.412 1794.52,779.412 1795.41,779.413 1796.31,779.415 1797.2,779.418 \n",
" 1798.1,779.422 1798.99,779.426 1799.89,779.431 1800.78,779.437 1801.68,779.444 1802.57,779.452 1803.47,779.46 1804.36,779.469 1805.25,779.479 1806.15,779.49 \n",
" 1807.04,779.501 1807.94,779.513 1808.83,779.526 1809.73,779.539 1810.62,779.553 1811.52,779.567 1812.41,779.583 1813.31,779.598 1814.2,779.615 1815.1,779.631 \n",
" 1815.99,779.649 1816.88,779.667 1817.78,779.685 1818.67,779.704 1819.57,779.723 1820.46,779.742 1821.36,779.762 1822.25,779.783 1823.15,779.803 1824.04,779.824 \n",
" 1824.94,779.845 1825.83,779.867 1826.73,779.889 1827.62,779.911 1828.51,779.933 1829.41,779.955 1830.3,779.978 1831.2,780 1832.09,780.023 1832.99,780.046 \n",
" 1833.88,780.069 1834.78,780.092 1835.67,780.115 1836.57,780.138 1837.46,780.161 1838.35,780.184 1839.25,780.207 1840.14,780.229 1841.04,780.252 1841.93,780.274 \n",
" 1842.83,780.297 1843.72,780.319 1844.62,780.341 1845.51,780.363 1846.41,780.384 1847.3,780.405 1848.2,780.426 1849.09,780.447 1849.98,780.468 1850.88,780.488 \n",
" 1851.77,780.508 1852.67,780.527 1853.56,780.546 1854.46,780.565 1855.35,780.583 1856.25,780.601 1857.14,780.618 1858.04,780.635 1858.93,780.652 1859.83,780.668 \n",
" 1860.72,780.684 1861.61,780.699 1862.51,780.713 1863.4,780.728 1864.3,780.741 1865.19,780.754 1866.09,780.767 1866.98,780.779 1867.88,780.791 1868.77,780.802 \n",
" 1869.67,780.812 1870.56,780.822 1871.46,780.831 1872.35,780.84 1873.24,780.848 1874.14,780.856 1875.03,780.863 1875.93,780.869 1876.82,780.875 1877.72,780.88 \n",
" 1878.61,780.885 1879.51,780.889 1880.4,780.893 1881.3,780.896 1882.19,780.898 1883.09,780.9 1883.98,780.901 1884.87,780.902 1885.77,780.902 1886.66,780.901 \n",
" 1887.56,780.901 1888.45,780.899 1889.35,780.897 1890.24,780.894 1891.14,780.891 1892.03,780.888 1892.93,780.884 1893.82,780.879 1894.72,780.874 1895.61,780.868 \n",
" 1896.5,780.862 1897.4,780.856 1898.29,780.849 1899.19,780.841 1900.08,780.834 1900.98,780.825 1901.87,780.817 1902.77,780.808 1903.66,780.798 1904.56,780.788 \n",
" 1905.45,780.778 1906.35,780.768 1907.24,780.757 1908.13,780.746 1909.03,780.734 1909.92,780.723 1910.82,780.711 1911.71,780.698 1912.61,780.686 1913.5,780.673 \n",
" 1914.4,780.66 1915.29,780.647 1916.19,780.634 1917.08,780.62 1917.98,780.606 1918.87,780.593 1919.76,780.579 1920.66,780.564 1921.55,780.55 1922.45,780.536 \n",
" 1923.34,780.522 1924.24,780.507 1925.13,780.493 1926.03,780.478 1926.92,780.464 1927.82,780.449 1928.71,780.435 1929.61,780.42 1930.5,780.406 1931.39,780.391 \n",
" 1932.29,780.377 1933.18,780.363 1934.08,780.348 1934.97,780.334 1935.87,780.32 1936.76,780.307 1937.66,780.293 1938.55,780.279 1939.45,780.266 1940.34,780.253 \n",
" 1941.24,780.24 1942.13,780.227 1943.02,780.214 1943.92,780.202 1944.81,780.19 1945.71,780.178 1946.6,780.166 1947.5,780.155 1948.39,780.144 1949.29,780.133 \n",
" 1950.18,780.122 1951.08,780.112 1951.97,780.102 1952.87,780.092 1953.76,780.083 1954.65,780.074 1955.55,780.065 1956.44,780.056 1957.34,780.048 1958.23,780.04 \n",
" 1959.13,780.033 1960.02,780.026 1960.92,780.019 1961.81,780.013 1962.71,780.007 1963.6,780.001 1964.5,779.996 1965.39,779.991 1966.28,779.986 1967.18,779.982 \n",
" 1968.07,779.978 1968.97,779.975 1969.86,779.972 1970.76,779.969 1971.65,779.966 1972.55,779.964 1973.44,779.963 1974.34,779.961 1975.23,779.96 1976.12,779.96 \n",
" 1977.02,779.96 1977.91,779.96 1978.81,779.96 1979.7,779.961 1980.6,779.962 1981.49,779.964 1982.39,779.965 1983.28,779.968 1984.18,779.97 1985.07,779.973 \n",
" 1985.97,779.976 1986.86,779.979 1987.75,779.983 1988.65,779.987 1989.54,779.991 1990.44,779.996 1991.33,780.001 1992.23,780.006 1993.12,780.011 1994.02,780.017 \n",
" 1994.91,780.023 1995.81,780.029 1996.7,780.035 1997.6,780.042 1998.49,780.048 1999.38,780.055 2000.28,780.062 2001.17,780.07 2002.07,780.077 2002.96,780.085 \n",
" 2003.86,780.093 2004.75,780.101 2005.65,780.109 2006.54,780.117 2007.44,780.126 2008.33,780.134 2009.23,780.143 2010.12,780.152 2011.01,780.16 2011.91,780.169 \n",
" 2012.8,780.178 2013.7,780.187 2014.59,780.196 2015.49,780.206 2016.38,780.215 2017.28,780.224 2018.17,780.233 2019.07,780.242 2019.96,780.251 2020.86,780.261 \n",
" 2021.75,780.27 2022.64,780.279 2023.54,780.288 2024.43,780.297 2025.33,780.306 2026.22,780.315 2027.12,780.324 2028.01,780.333 2028.91,780.341 2029.8,780.35 \n",
" 2030.7,780.358 2031.59,780.367 2032.49,780.375 2033.38,780.383 2034.27,780.391 2035.17,780.399 2036.06,780.407 2036.96,780.415 2037.85,780.422 2038.75,780.429 \n",
" 2039.64,780.437 2040.54,780.444 2041.43,780.45 2042.33,780.457 2043.22,780.463 2044.12,780.47 2045.01,780.476 2045.9,780.481 2046.8,780.487 2047.69,780.493 \n",
" 2048.59,780.498 2049.48,780.503 2050.38,780.508 2051.27,780.512 2052.17,780.517 2053.06,780.521 2053.96,780.525 2054.85,780.528 2055.75,780.532 2056.64,780.535 \n",
" 2057.53,780.538 2058.43,780.541 2059.32,780.543 2060.22,780.546 2061.11,780.548 2062.01,780.55 2062.9,780.551 2063.8,780.553 2064.69,780.554 2065.59,780.555 \n",
" 2066.48,780.555 2067.38,780.556 2068.27,780.556 2069.16,780.556 2070.06,780.556 2070.95,780.555 2071.85,780.555 2072.74,780.554 2073.64,780.553 2074.53,780.552 \n",
" 2075.43,780.55 2076.32,780.549 2077.22,780.547 2078.11,780.545 2079.01,780.542 2079.9,780.54 2080.79,780.537 2081.69,780.534 2082.58,780.531 2083.48,780.528 \n",
" 2084.37,780.525 2085.27,780.521 2086.16,780.518 2087.06,780.514 2087.95,780.51 2088.85,780.506 2089.74,780.502 2090.64,780.497 2091.53,780.493 2092.42,780.488 \n",
" 2093.32,780.484 2094.21,780.479 2095.11,780.474 2096,780.469 2096.9,780.464 2097.79,780.459 2098.69,780.453 2099.58,780.448 2100.48,780.442 2101.37,780.437 \n",
" 2102.27,780.431 2103.16,780.426 2104.05,780.42 2104.95,780.414 2105.84,780.409 2106.74,780.403 2107.63,780.397 2108.53,780.391 2109.42,780.386 2110.32,780.38 \n",
" 2111.21,780.374 2112.11,780.368 2113,780.362 2113.89,780.357 2114.79,780.351 2115.68,780.345 2116.58,780.339 2117.47,780.334 2118.37,780.328 2119.26,780.323 \n",
" 2120.16,780.317 2121.05,780.312 2121.95,780.306 2122.84,780.301 2123.74,780.295 2124.63,780.29 2125.52,780.285 2126.42,780.28 2127.31,780.275 2128.21,780.27 \n",
" 2129.1,780.266 2130,780.261 2130.89,780.256 2131.79,780.252 2132.68,780.248 2133.58,780.243 2134.47,780.239 2135.37,780.235 2136.26,780.231 2137.15,780.228 \n",
" 2138.05,780.224 2138.94,780.221 2139.84,780.217 2140.73,780.214 2141.63,780.211 2142.52,780.208 2143.42,780.205 2144.31,780.202 2145.21,780.2 2146.1,780.197 \n",
" 2147,780.195 2147.89,780.193 2148.78,780.191 2149.68,780.189 2150.57,780.188 2151.47,780.186 2152.36,780.185 2153.26,780.184 2154.15,780.182 2155.05,780.181 \n",
" 2155.94,780.181 2156.84,780.18 2157.73,780.18 2158.63,780.179 2159.52,780.179 2160.41,780.179 2161.31,780.179 2162.2,780.179 2163.1,780.18 2163.99,780.18 \n",
" 2164.89,780.181 2165.78,780.181 2166.68,780.182 2167.57,780.183 2168.47,780.184 2169.36,780.186 2170.26,780.187 2171.15,780.189 2172.04,780.19 2172.94,780.192 \n",
" 2173.83,780.194 2174.73,780.196 2175.62,780.198 2176.52,780.2 2177.41,780.202 2178.31,780.205 2179.2,780.207 2180.1,780.21 2180.99,780.212 2181.89,780.215 \n",
" 2182.78,780.218 2183.67,780.221 2184.57,780.224 2185.46,780.227 2186.36,780.23 2187.25,780.233 2188.15,780.236 2189.04,780.239 2189.94,780.243 2190.83,780.246 \n",
" 2191.73,780.249 2192.62,780.253 2193.52,780.256 2194.41,780.26 2195.3,780.263 2196.2,780.267 2197.09,780.271 2197.99,780.274 2198.88,780.278 2199.78,780.282 \n",
" 2200.67,780.285 2201.57,780.289 2202.46,780.293 2203.36,780.296 2204.25,780.3 2205.15,780.304 2206.04,780.307 2206.93,780.311 2207.83,780.315 2208.72,780.318 \n",
" 2209.62,780.322 2210.51,780.325 2211.41,780.329 2212.3,780.332 2213.2,780.336 2214.09,780.339 2214.99,780.343 2215.88,780.346 2216.78,780.349 2217.67,780.352 \n",
" 2218.56,780.355 2219.46,780.359 2220.35,780.362 2221.25,780.365 2222.14,780.368 2223.04,780.37 2223.93,780.373 2224.83,780.376 2225.72,780.378 2226.62,780.381 \n",
" 2227.51,780.384 2228.41,780.386 2229.3,780.388 2230.19,780.391 2231.09,780.393 2231.98,780.395 2232.88,780.397 2233.77,780.399 2234.67,780.4 2235.56,780.402 \n",
" 2236.46,780.404 2237.35,780.405 2238.25,780.407 2239.14,780.408 2240.04,780.41 2240.93,780.411 2241.82,780.412 2242.72,780.413 2243.61,780.414 2244.51,780.415 \n",
" 2245.4,780.415 2246.3,780.416 2247.19,780.416 2248.09,780.417 2248.98,780.417 2249.88,780.418 2250.77,780.418 2251.66,780.418 2252.56,780.418 2253.45,780.418 \n",
" 2254.35,780.418 2255.24,780.417 2256.14,780.417 2257.03,780.417 2257.93,780.416 2258.82,780.415 2259.72,780.415 2260.61,780.414 2261.51,780.413 2262.4,780.412 \n",
" 2263.29,780.411 2264.19,780.41 2265.08,780.409 2265.98,780.408 2266.87,780.407 2267.77,780.405 2268.66,780.404 2269.56,780.402 2270.45,780.401 2271.35,780.399 \n",
" 2272.24,780.398 2273.14,780.396 2274.03,780.394 2274.92,780.392 2275.82,780.39 2276.71,780.389 2277.61,780.387 2278.5,780.385 2279.4,780.383 2280.29,780.381 \n",
" 2281.19,780.379 2282.08,780.376 2282.98,780.374 2283.87,780.372 2284.77,780.37 2285.66,780.368 2286.55,780.365 2287.45,780.363 2288.34,780.361 2289.24,780.359 \n",
" 2290.13,780.356 2291.03,780.354 2291.92,780.352 2292.82,780.349 2293.71,780.347 2294.61,780.345 2295.5,780.342 2296.4,780.34 2297.29,780.338 2298.18,780.335 \n",
" 2299.08,780.333 \n",
" \"/>\n",
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" 518.805,201.243 519.699,208.575 520.594,216.323 521.488,224.459 522.383,232.96 523.278,241.802 524.172,250.963 525.067,260.423 525.962,270.166 526.856,280.175 \n",
" 527.751,290.435 528.645,300.934 529.54,311.662 530.435,322.608 531.329,333.766 532.224,345.127 533.118,356.686 534.013,368.439 534.908,380.382 535.802,392.512 \n",
" 536.697,404.826 537.591,417.322 538.486,429.998 539.381,442.853 540.275,455.884 541.17,469.09 542.065,482.467 542.959,496.014 543.854,509.726 544.748,523.601 \n",
" 545.643,537.633 546.538,551.818 547.432,566.149 548.327,580.62 549.221,595.224 550.116,609.953 551.011,624.797 551.905,639.748 552.8,654.795 553.694,669.928 \n",
" 554.589,685.135 555.484,700.405 556.378,715.726 557.273,731.085 558.168,746.468 559.062,761.864 559.957,777.259 560.851,792.639 561.746,807.992 562.641,823.303 \n",
" 563.535,838.56 564.43,853.749 565.324,868.857 566.219,883.873 567.114,898.783 568.008,913.576 568.903,928.24 569.797,942.763 570.692,957.136 571.587,971.348 \n",
" 572.481,985.389 573.376,999.251 574.271,1012.92 575.165,1026.4 576.06,1039.67 576.954,1052.73 577.849,1065.58 578.744,1078.2 579.638,1090.59 580.533,1102.74 \n",
" 581.427,1114.66 582.322,1126.34 583.217,1137.77 584.111,1148.95 585.006,1159.89 585.9,1170.56 586.795,1180.99 587.69,1191.15 588.584,1201.06 589.479,1210.71 \n",
" 590.373,1220.1 591.268,1229.23 592.163,1238.11 593.057,1246.72 593.952,1255.07 594.847,1263.16 595.741,1271 596.636,1278.57 597.53,1285.89 598.425,1292.96 \n",
" 599.32,1299.76 600.214,1306.31 601.109,1312.61 602.003,1318.65 602.898,1324.44 603.793,1329.98 604.687,1335.27 605.582,1340.3 606.476,1345.09 607.371,1349.62 \n",
" 608.266,1353.91 609.16,1357.94 610.055,1361.73 610.95,1365.27 611.844,1368.56 612.739,1371.6 613.633,1374.4 614.528,1376.94 615.423,1379.24 616.317,1381.29 \n",
" 617.212,1383.09 618.106,1384.64 619.001,1385.94 619.896,1387 620.79,1387.8 621.685,1388.36 622.579,1388.66 623.474,1388.71 624.369,1388.52 625.263,1388.07 \n",
" 626.158,1387.37 627.053,1386.43 627.947,1385.23 628.842,1383.78 629.736,1382.08 630.631,1380.13 631.526,1377.94 632.42,1375.49 633.315,1372.8 634.209,1369.86 \n",
" 635.104,1366.67 635.999,1363.24 636.893,1359.56 637.788,1355.65 638.682,1351.49 639.577,1347.1 640.472,1342.47 641.366,1337.61 642.261,1332.51 643.156,1327.19 \n",
" 644.05,1321.64 644.945,1315.87 645.839,1309.88 646.734,1303.68 647.629,1297.26 648.523,1290.64 649.418,1283.81 650.312,1276.79 651.207,1269.57 652.102,1262.16 \n",
" 652.996,1254.56 653.891,1246.78 654.785,1238.83 655.68,1230.71 656.575,1222.43 657.469,1213.99 658.364,1205.4 659.258,1196.66 660.153,1187.79 661.048,1178.78 \n",
" 661.942,1169.65 662.837,1160.39 663.732,1151.03 664.626,1141.55 665.521,1131.98 666.415,1122.32 667.31,1112.57 668.205,1102.75 669.099,1092.86 669.994,1082.9 \n",
" 670.888,1072.89 671.783,1062.83 672.678,1052.73 673.572,1042.6 674.467,1032.44 675.361,1022.27 676.256,1012.09 677.151,1001.9 678.045,991.717 678.94,981.548 \n",
" 679.835,971.398 680.729,961.275 681.624,951.186 682.518,941.139 683.413,931.14 684.308,921.197 685.202,911.316 686.097,901.505 686.991,891.77 687.886,882.118 \n",
" 688.781,872.556 689.675,863.089 690.57,853.724 691.464,844.468 692.359,835.327 693.254,826.305 694.148,817.41 695.043,808.647 695.938,800.02 696.832,791.537 \n",
" 697.727,783.201 698.621,775.017 699.516,766.991 700.411,759.127 701.305,751.43 702.2,743.904 703.094,736.554 703.989,729.382 704.884,722.393 705.778,715.591 \n",
" 706.673,708.979 707.567,702.561 708.462,696.339 709.357,690.316 710.251,684.496 711.146,678.88 712.041,673.471 712.935,668.272 713.83,663.284 714.724,658.509 \n",
" 715.619,653.949 716.514,649.606 717.408,645.48 718.303,641.574 719.197,637.887 720.092,634.422 720.987,631.177 721.881,628.155 722.776,625.355 723.67,622.777 \n",
" 724.565,620.422 725.46,618.29 726.354,616.379 727.249,614.691 728.143,613.223 729.038,611.976 729.933,610.948 730.827,610.139 731.722,609.547 732.617,609.171 \n",
" 733.511,609.01 734.406,609.062 735.3,609.325 736.195,609.798 737.09,610.479 737.984,611.366 738.879,612.456 739.773,613.747 740.668,615.238 741.563,616.925 \n",
" 742.457,618.805 743.352,620.877 744.246,623.138 745.141,625.584 746.036,628.213 746.93,631.022 747.825,634.006 748.72,637.165 749.614,640.493 750.509,643.988 \n",
" 751.403,647.646 752.298,651.464 753.193,655.438 754.087,659.564 754.982,663.84 755.876,668.26 756.771,672.821 757.666,677.52 758.56,682.353 759.455,687.314 \n",
" 760.349,692.401 761.244,697.61 762.139,702.936 763.033,708.375 763.928,713.923 764.823,719.576 765.717,725.329 766.612,731.179 767.506,737.121 768.401,743.15 \n",
" 769.296,749.263 770.19,755.455 771.085,761.721 771.979,768.058 772.874,774.461 773.769,780.925 774.663,787.447 775.558,794.021 776.452,800.643 777.347,807.309 \n",
" 778.242,814.015 779.136,820.756 780.031,827.527 780.926,834.325 781.82,841.145 782.715,847.983 783.609,854.834 784.504,861.693 785.399,868.558 786.293,875.423 \n",
" 787.188,882.284 788.082,889.137 788.977,895.977 789.872,902.802 790.766,909.605 791.661,916.385 792.555,923.135 793.45,929.853 794.345,936.534 795.239,943.174 \n",
" 796.134,949.77 797.028,956.318 797.923,962.813 798.818,969.253 799.712,975.633 800.607,981.95 801.502,988.2 802.396,994.38 803.291,1000.49 804.185,1006.51 \n",
" 805.08,1012.46 805.975,1018.33 806.869,1024.11 807.764,1029.79 808.658,1035.39 809.553,1040.89 810.448,1046.29 811.342,1051.59 812.237,1056.78 813.131,1061.87 \n",
" 814.026,1066.84 814.921,1071.71 815.815,1076.45 816.71,1081.09 817.605,1085.6 818.499,1089.99 819.394,1094.26 820.288,1098.4 821.183,1102.41 822.078,1106.29 \n",
" 822.972,1110.05 823.867,1113.66 824.761,1117.15 825.656,1120.5 826.551,1123.71 827.445,1126.78 828.34,1129.71 829.234,1132.51 830.129,1135.15 831.024,1137.66 \n",
" 831.918,1140.02 832.813,1142.24 833.708,1144.31 834.602,1146.24 835.497,1148.02 836.391,1149.66 837.286,1151.15 838.181,1152.49 839.075,1153.68 839.97,1154.73 \n",
" 840.864,1155.63 841.759,1156.38 842.654,1156.99 843.548,1157.45 844.443,1157.77 845.337,1157.94 846.232,1157.97 847.127,1157.86 848.021,1157.6 848.916,1157.2 \n",
" 849.81,1156.66 850.705,1155.98 851.6,1155.17 852.494,1154.21 853.389,1153.13 854.284,1151.9 855.178,1150.55 856.073,1149.06 856.967,1147.45 857.862,1145.71 \n",
" 858.757,1143.84 859.651,1141.85 860.546,1139.74 861.44,1137.51 862.335,1135.16 863.23,1132.7 864.124,1130.12 865.019,1127.43 865.913,1124.64 866.808,1121.74 \n",
" 867.703,1118.73 868.597,1115.63 869.492,1112.42 870.387,1109.13 871.281,1105.73 872.176,1102.25 873.07,1098.68 873.965,1095.03 874.86,1091.3 875.754,1087.48 \n",
" 876.649,1083.59 877.543,1079.63 878.438,1075.6 879.333,1071.5 880.227,1067.34 881.122,1063.11 882.016,1058.83 882.911,1054.5 883.806,1050.11 884.7,1045.68 \n",
" 885.595,1041.2 886.49,1036.68 887.384,1032.12 888.279,1027.52 889.173,1022.89 890.068,1018.24 890.963,1013.55 891.857,1008.85 892.752,1004.12 893.646,999.381 \n",
" 894.541,994.626 895.436,989.861 896.33,985.089 897.225,980.314 898.119,975.538 899.014,970.764 899.909,965.996 900.803,961.236 901.698,956.488 902.593,951.755 \n",
" 903.487,947.039 904.382,942.344 905.276,937.672 906.171,933.026 907.066,928.409 907.96,923.825 908.855,919.275 909.749,914.762 910.644,910.29 911.539,905.86 \n",
" 912.433,901.475 913.328,897.139 914.222,892.853 915.117,888.619 916.012,884.441 916.906,880.321 917.801,876.26 918.695,872.262 919.59,868.328 920.485,864.46 \n",
" 921.379,860.661 922.274,856.933 923.169,853.277 924.063,849.696 924.958,846.191 925.852,842.764 926.747,839.417 927.642,836.151 928.536,832.968 929.431,829.871 \n",
" 930.325,826.859 931.22,823.935 932.115,821.099 933.009,818.354 933.904,815.7 934.798,813.139 935.693,810.671 936.588,808.298 937.482,806.02 938.377,803.838 \n",
" 939.272,801.754 940.166,799.768 941.061,797.881 941.955,796.093 942.85,794.404 943.745,792.816 944.639,791.329 945.534,789.942 946.428,788.657 947.323,787.474 \n",
" 948.218,786.392 949.112,785.412 950.007,784.533 950.901,783.756 951.796,783.081 952.691,782.507 953.585,782.035 954.48,781.663 955.375,781.391 956.269,781.22 \n",
" 957.164,781.148 958.058,781.175 958.953,781.301 959.848,781.524 960.742,781.844 961.637,782.261 962.531,782.773 963.426,783.379 964.321,784.078 965.215,784.87 \n",
" 966.11,785.754 967.004,786.728 967.899,787.791 968.794,788.942 969.688,790.179 970.583,791.502 971.478,792.909 972.372,794.398 973.267,795.969 974.161,797.619 \n",
" 975.056,799.348 975.951,801.153 976.845,803.033 977.74,804.986 978.634,807.011 979.529,809.105 980.424,811.268 981.318,813.497 982.213,815.791 983.107,818.148 \n",
" 984.002,820.565 984.897,823.041 985.791,825.574 986.686,828.162 987.58,830.803 988.475,833.495 989.37,836.236 990.264,839.024 991.159,841.857 992.054,844.733 \n",
" 992.948,847.65 993.843,850.605 994.737,853.596 995.632,856.622 996.527,859.681 997.421,862.769 998.316,865.885 999.21,869.027 1000.11,872.193 1001,875.38 \n",
" 1001.89,878.586 1002.79,881.809 1003.68,885.048 1004.58,888.299 1005.47,891.561 1006.37,894.831 1007.26,898.108 1008.16,901.388 1009.05,904.671 1009.95,907.954 \n",
" 1010.84,911.235 1011.73,914.511 1012.63,917.781 1013.52,921.043 1014.42,924.294 1015.31,927.533 1016.21,930.758 1017.1,933.966 1018,937.156 1018.89,940.326 \n",
" 1019.79,943.473 1020.68,946.596 1021.58,949.693 1022.47,952.763 1023.36,955.803 1024.26,958.811 1025.15,961.787 1026.05,964.727 1026.94,967.631 1027.84,970.497 \n",
" 1028.73,973.324 1029.63,976.109 1030.52,978.851 1031.42,981.548 1032.31,984.2 1033.21,986.805 1034.1,989.361 1034.99,991.867 1035.89,994.321 1036.78,996.723 \n",
" 1037.68,999.071 1038.57,1001.36 1039.47,1003.6 1040.36,1005.78 1041.26,1007.9 1042.15,1009.96 1043.05,1011.97 1043.94,1013.91 1044.84,1015.78 1045.73,1017.6 \n",
" 1046.62,1019.35 1047.52,1021.04 1048.41,1022.66 1049.31,1024.22 1050.2,1025.71 1051.1,1027.13 1051.99,1028.48 1052.89,1029.77 1053.78,1030.99 1054.68,1032.14 \n",
" 1055.57,1033.22 1056.47,1034.23 1057.36,1035.17 1058.25,1036.05 1059.15,1036.85 1060.04,1037.58 1060.94,1038.24 1061.83,1038.83 1062.73,1039.35 1063.62,1039.8 \n",
" 1064.52,1040.19 1065.41,1040.5 1066.31,1040.74 1067.2,1040.91 1068.1,1041.02 1068.99,1041.05 1069.88,1041.02 1070.78,1040.92 1071.67,1040.75 1072.57,1040.51 \n",
" 1073.46,1040.21 1074.36,1039.84 1075.25,1039.41 1076.15,1038.92 1077.04,1038.35 1077.94,1037.73 1078.83,1037.05 1079.73,1036.3 1080.62,1035.49 1081.51,1034.62 \n",
" 1082.41,1033.7 1083.3,1032.71 1084.2,1031.67 1085.09,1030.58 1085.99,1029.43 1086.88,1028.22 1087.78,1026.96 1088.67,1025.65 1089.57,1024.3 1090.46,1022.89 \n",
" 1091.36,1021.43 1092.25,1019.93 1093.14,1018.38 1094.04,1016.78 1094.93,1015.15 1095.83,1013.47 1096.72,1011.75 1097.62,1009.99 1098.51,1008.2 1099.41,1006.37 \n",
" 1100.3,1004.5 1101.2,1002.6 1102.09,1000.67 1102.99,998.709 1103.88,996.718 1104.77,994.699 1105.67,992.653 1106.56,990.583 1107.46,988.489 1108.35,986.374 \n",
" 1109.25,984.238 1110.14,982.084 1111.04,979.911 1111.93,977.724 1112.83,975.521 1113.72,973.306 1114.62,971.08 1115.51,968.843 1116.4,966.598 1117.3,964.347 \n",
" 1118.19,962.089 1119.09,959.828 1119.98,957.565 1120.88,955.3 1121.77,953.036 1122.67,950.774 1123.56,948.515 1124.46,946.261 1125.35,944.013 1126.25,941.773 \n",
" 1127.14,939.541 1128.03,937.32 1128.93,935.111 1129.82,932.915 1130.72,930.733 1131.61,928.567 1132.51,926.418 1133.4,924.288 1134.3,922.177 1135.19,920.086 \n",
" 1136.09,918.018 1136.98,915.973 1137.88,913.952 1138.77,911.957 1139.66,909.988 1140.56,908.047 1141.45,906.135 1142.35,904.253 1143.24,902.402 1144.14,900.582 \n",
" 1145.03,898.796 1145.93,897.043 1146.82,895.325 1147.72,893.643 1148.61,891.998 1149.5,890.389 1150.4,888.819 1151.29,887.288 1152.19,885.796 1153.08,884.345 \n",
" 1153.98,882.935 1154.87,881.567 1155.77,880.241 1156.66,878.959 1157.56,877.719 1158.45,876.524 1159.35,875.374 1160.24,874.268 1161.13,873.208 1162.03,872.194 \n",
" 1162.92,871.227 1163.82,870.305 1164.71,869.431 1165.61,868.604 1166.5,867.825 1167.4,867.093 1168.29,866.409 1169.19,865.774 1170.08,865.186 1170.98,864.647 \n",
" 1171.87,864.156 1172.76,863.713 1173.66,863.318 1174.55,862.972 1175.45,862.675 1176.34,862.425 1177.24,862.223 1178.13,862.069 1179.03,861.963 1179.92,861.904 \n",
" 1180.82,861.893 1181.71,861.928 1182.61,862.01 1183.5,862.139 1184.39,862.313 1185.29,862.533 1186.18,862.798 1187.08,863.108 1187.97,863.462 1188.87,863.859 \n",
" 1189.76,864.3 1190.66,864.784 1191.55,865.31 1192.45,865.877 1193.34,866.486 1194.24,867.134 1195.13,867.823 1196.02,868.55 1196.92,869.316 1197.81,870.119 \n",
" 1198.71,870.959 1199.6,871.835 1200.5,872.746 1201.39,873.692 1202.29,874.671 1203.18,875.683 1204.08,876.728 1204.97,877.803 1205.87,878.909 1206.76,880.044 \n",
" 1207.65,881.208 1208.55,882.399 1209.44,883.617 1210.34,884.86 1211.23,886.129 1212.13,887.421 1213.02,888.736 1213.92,890.072 1214.81,891.43 1215.71,892.807 \n",
" 1216.6,894.204 1217.5,895.618 1218.39,897.049 1219.28,898.496 1220.18,899.957 1221.07,901.433 1221.97,902.921 1222.86,904.421 1223.76,905.931 1224.65,907.452 \n",
" 1225.55,908.98 1226.44,910.517 1227.34,912.06 1228.23,913.608 1229.13,915.161 1230.02,916.718 1230.91,918.277 1231.81,919.837 1232.7,921.398 1233.6,922.958 \n",
" 1234.49,924.517 1235.39,926.073 1236.28,927.626 1237.18,929.174 1238.07,930.717 1238.97,932.253 1239.86,933.782 1240.76,935.302 1241.65,936.814 1242.54,938.315 \n",
" 1243.44,939.805 1244.33,941.283 1245.23,942.748 1246.12,944.2 1247.02,945.637 1247.91,947.059 1248.81,948.465 1249.7,949.853 1250.6,951.224 1251.49,952.576 \n",
" 1252.39,953.909 1253.28,955.222 1254.17,956.514 1255.07,957.784 1255.96,959.033 1256.86,960.258 1257.75,961.46 1258.65,962.638 1259.54,963.791 1260.44,964.919 \n",
" 1261.33,966.021 1262.23,967.097 1263.12,968.145 1264.02,969.166 1264.91,970.16 1265.8,971.124 1266.7,972.06 1267.59,972.966 1268.49,973.843 1269.38,974.689 \n",
" 1270.28,975.505 1271.17,976.29 1272.07,977.045 1272.96,977.767 1273.86,978.458 1274.75,979.117 1275.65,979.743 1276.54,980.338 1277.43,980.899 1278.33,981.428 \n",
" 1279.22,981.924 1280.12,982.387 1281.01,982.817 1281.91,983.213 1282.8,983.576 1283.7,983.906 1284.59,984.203 1285.49,984.466 1286.38,984.696 1287.27,984.893 \n",
" 1288.17,985.056 1289.06,985.187 1289.96,985.284 1290.85,985.349 1291.75,985.381 1292.64,985.38 1293.54,985.348 1294.43,985.283 1295.33,985.186 1296.22,985.058 \n",
" 1297.12,984.898 1298.01,984.707 1298.9,984.486 1299.8,984.234 1300.69,983.952 1301.59,983.64 1302.48,983.299 1303.38,982.929 1304.27,982.53 1305.17,982.104 \n",
" 1306.06,981.649 1306.96,981.168 1307.85,980.659 1308.75,980.125 1309.64,979.565 1310.53,978.979 1311.43,978.369 1312.32,977.734 1313.22,977.076 1314.11,976.395 \n",
" 1315.01,975.691 1315.9,974.966 1316.8,974.219 1317.69,973.451 1318.59,972.663 1319.48,971.856 1320.38,971.03 1321.27,970.186 1322.16,969.324 1323.06,968.446 \n",
" 1323.95,967.551 1324.85,966.64 1325.74,965.715 1326.64,964.775 1327.53,963.822 1328.43,962.857 1329.32,961.879 1330.22,960.889 1331.11,959.889 1332.01,958.879 \n",
" 1332.9,957.859 1333.79,956.831 1334.69,955.796 1335.58,954.752 1336.48,953.703 1337.37,952.648 1338.27,951.587 1339.16,950.523 1340.06,949.454 1340.95,948.383 \n",
" 1341.85,947.309 1342.74,946.235 1343.64,945.159 1344.53,944.083 1345.42,943.007 1346.32,941.933 1347.21,940.861 1348.11,939.792 1349,938.725 1349.9,937.663 \n",
" 1350.79,936.606 1351.69,935.553 1352.58,934.507 1353.48,933.467 1354.37,932.434 1355.27,931.409 1356.16,930.392 1357.05,929.384 1357.95,928.386 1358.84,927.398 \n",
" 1359.74,926.421 1360.63,925.455 1361.53,924.501 1362.42,923.56 1363.32,922.631 1364.21,921.716 1365.11,920.815 1366,919.928 1366.9,919.056 1367.79,918.2 \n",
" 1368.68,917.359 1369.58,916.535 1370.47,915.727 1371.37,914.937 1372.26,914.164 1373.16,913.409 1374.05,912.673 1374.95,911.955 1375.84,911.256 1376.74,910.577 \n",
" 1377.63,909.917 1378.53,909.277 1379.42,908.658 1380.31,908.059 1381.21,907.481 1382.1,906.924 1383,906.388 1383.89,905.874 1384.79,905.382 1385.68,904.911 \n",
" 1386.58,904.463 1387.47,904.037 1388.37,903.633 1389.26,903.252 1390.16,902.893 1391.05,902.557 1391.94,902.244 1392.84,901.954 1393.73,901.687 1394.63,901.442 \n",
" 1395.52,901.221 1396.42,901.022 1397.31,900.847 1398.21,900.694 1399.1,900.565 1400,900.458 1400.89,900.374 1401.79,900.312 1402.68,900.274 1403.57,900.258 \n",
" 1404.47,900.264 1405.36,900.292 1406.26,900.343 1407.15,900.415 1408.05,900.509 1408.94,900.625 1409.84,900.762 1410.73,900.92 1411.63,901.099 1412.52,901.299 \n",
" 1413.42,901.519 1414.31,901.759 1415.2,902.02 1416.1,902.299 1416.99,902.598 1417.89,902.917 1418.78,903.253 1419.68,903.608 1420.57,903.982 1421.47,904.372 \n",
" 1422.36,904.78 1423.26,905.205 1424.15,905.647 1425.04,906.105 1425.94,906.579 1426.83,907.068 1427.73,907.572 1428.62,908.09 1429.52,908.623 1430.41,909.17 \n",
" 1431.31,909.729 1432.2,910.302 1433.1,910.887 1433.99,911.484 1434.89,912.093 1435.78,912.713 1436.67,913.343 1437.57,913.983 1438.46,914.633 1439.36,915.293 \n",
" 1440.25,915.961 1441.15,916.637 1442.04,917.321 1442.94,918.012 1443.83,918.71 1444.73,919.414 1445.62,920.125 1446.52,920.84 1447.41,921.56 1448.3,922.285 \n",
" 1449.2,923.013 1450.09,923.745 1450.99,924.48 1451.88,925.217 1452.78,925.955 1453.67,926.696 1454.57,927.437 1455.46,928.179 1456.36,928.92 1457.25,929.661 \n",
" 1458.15,930.401 1459.04,931.14 1459.93,931.877 1460.83,932.611 1461.72,933.342 1462.62,934.071 1463.51,934.795 1464.41,935.515 1465.3,936.231 1466.2,936.942 \n",
" 1467.09,937.647 1467.99,938.346 1468.88,939.039 1469.78,939.725 1470.67,940.404 1471.56,941.076 1472.46,941.739 1473.35,942.395 1474.25,943.042 1475.14,943.679 \n",
" 1476.04,944.308 1476.93,944.927 1477.83,945.535 1478.72,946.133 1479.62,946.721 1480.51,947.298 1481.41,947.863 1482.3,948.416 1483.19,948.958 1484.09,949.488 \n",
" 1484.98,950.005 1485.88,950.509 1486.77,951.001 1487.67,951.479 1488.56,951.944 1489.46,952.395 1490.35,952.832 1491.25,953.255 1492.14,953.665 1493.04,954.059 \n",
" 1493.93,954.439 1494.82,954.805 1495.72,955.155 1496.61,955.491 1497.51,955.811 1498.4,956.116 1499.3,956.406 1500.19,956.68 1501.09,956.939 1501.98,957.182 \n",
" 1502.88,957.41 1503.77,957.621 1504.67,957.817 1505.56,957.997 1506.45,958.162 1507.35,958.31 1508.24,958.443 1509.14,958.56 1510.03,958.661 1510.93,958.746 \n",
" 1511.82,958.816 1512.72,958.869 1513.61,958.908 1514.51,958.93 1515.4,958.937 1516.3,958.929 1517.19,958.906 1518.08,958.867 1518.98,958.813 1519.87,958.744 \n",
" 1520.77,958.661 1521.66,958.562 1522.56,958.45 1523.45,958.322 1524.35,958.181 1525.24,958.026 1526.14,957.856 1527.03,957.673 1527.93,957.477 1528.82,957.267 \n",
" 1529.71,957.045 1530.61,956.809 1531.5,956.561 1532.4,956.301 1533.29,956.028 1534.19,955.744 1535.08,955.448 1535.98,955.141 1536.87,954.822 1537.77,954.493 \n",
" 1538.66,954.153 1539.56,953.803 1540.45,953.443 1541.34,953.073 1542.24,952.694 1543.13,952.306 1544.03,951.909 1544.92,951.503 1545.82,951.09 1546.71,950.668 \n",
" 1547.61,950.239 1548.5,949.803 1549.4,949.359 1550.29,948.91 1551.19,948.454 1552.08,947.992 1552.97,947.524 1553.87,947.051 1554.76,946.573 1555.66,946.091 \n",
" 1556.55,945.605 1557.45,945.114 1558.34,944.62 1559.24,944.123 1560.13,943.623 1561.03,943.12 1561.92,942.615 1562.81,942.108 1563.71,941.6 1564.6,941.09 \n",
" 1565.5,940.58 1566.39,940.069 1567.29,939.557 1568.18,939.046 1569.08,938.535 1569.97,938.026 1570.87,937.517 1571.76,937.009 1572.66,936.504 1573.55,936 \n",
" 1574.44,935.499 1575.34,935 1576.23,934.504 1577.13,934.012 1578.02,933.523 1578.92,933.038 1579.81,932.557 1580.71,932.081 1581.6,931.609 1582.5,931.142 \n",
" 1583.39,930.68 1584.29,930.224 1585.18,929.774 1586.07,929.33 1586.97,928.892 1587.86,928.461 1588.76,928.036 1589.65,927.618 1590.55,927.208 1591.44,926.805 \n",
" 1592.34,926.409 1593.23,926.022 1594.13,925.642 1595.02,925.271 1595.92,924.908 1596.81,924.554 1597.7,924.209 1598.6,923.872 1599.49,923.545 1600.39,923.227 \n",
" 1601.28,922.918 1602.18,922.619 1603.07,922.33 1603.97,922.051 1604.86,921.781 1605.76,921.522 1606.65,921.273 1607.55,921.034 1608.44,920.805 1609.33,920.587 \n",
" 1610.23,920.38 1611.12,920.183 1612.02,919.996 1612.91,919.821 1613.81,919.656 1614.7,919.502 1615.6,919.359 1616.49,919.227 1617.39,919.105 1618.28,918.995 \n",
" 1619.18,918.895 1620.07,918.807 1620.96,918.729 1621.86,918.662 1622.75,918.606 1623.65,918.561 1624.54,918.527 1625.44,918.503 1626.33,918.491 1627.23,918.488 \n",
" 1628.12,918.497 1629.02,918.516 1629.91,918.545 1630.81,918.585 1631.7,918.635 1632.59,918.695 1633.49,918.766 1634.38,918.846 1635.28,918.936 1636.17,919.036 \n",
" 1637.07,919.146 1637.96,919.265 1638.86,919.394 1639.75,919.531 1640.65,919.678 1641.54,919.834 1642.44,919.999 1643.33,920.172 1644.22,920.354 1645.12,920.544 \n",
" 1646.01,920.742 1646.91,920.948 1647.8,921.162 1648.7,921.383 1649.59,921.612 1650.49,921.848 1651.38,922.091 1652.28,922.341 1653.17,922.598 1654.07,922.861 \n",
" 1654.96,923.13 1655.85,923.405 1656.75,923.686 1657.64,923.973 1658.54,924.265 1659.43,924.562 1660.33,924.864 1661.22,925.171 1662.12,925.482 1663.01,925.797 \n",
" 1663.91,926.117 1664.8,926.44 1665.7,926.767 1666.59,927.097 1667.48,927.43 1668.38,927.767 1669.27,928.105 1670.17,928.446 1671.06,928.79 1671.96,929.135 \n",
" 1672.85,929.482 1673.75,929.83 1674.64,930.18 1675.54,930.531 1676.43,930.882 1677.33,931.234 1678.22,931.587 1679.11,931.939 1680.01,932.291 1680.9,932.643 \n",
" 1681.8,932.995 1682.69,933.345 1683.59,933.695 1684.48,934.043 1685.38,934.39 1686.27,934.735 1687.17,935.078 1688.06,935.419 1688.96,935.758 1689.85,936.094 \n",
" 1690.74,936.428 1691.64,936.759 1692.53,937.086 1693.43,937.411 1694.32,937.731 1695.22,938.049 1696.11,938.362 1697.01,938.671 1697.9,938.976 1698.8,939.277 \n",
" 1699.69,939.573 1700.58,939.865 1701.48,940.151 1702.37,940.433 1703.27,940.71 1704.16,940.981 1705.06,941.246 1705.95,941.507 1706.85,941.761 1707.74,942.009 \n",
" 1708.64,942.252 1709.53,942.489 1710.43,942.719 1711.32,942.943 1712.21,943.16 1713.11,943.371 1714,943.576 1714.9,943.773 1715.79,943.964 1716.69,944.148 \n",
" 1717.58,944.325 1718.48,944.495 1719.37,944.658 1720.27,944.813 1721.16,944.962 1722.06,945.103 1722.95,945.237 1723.84,945.363 1724.74,945.482 1725.63,945.594 \n",
" 1726.53,945.698 1727.42,945.795 1728.32,945.884 1729.21,945.966 1730.11,946.04 1731,946.107 1731.9,946.166 1732.79,946.217 1733.69,946.262 1734.58,946.298 \n",
" 1735.47,946.327 1736.37,946.349 1737.26,946.363 1738.16,946.37 1739.05,946.37 1739.95,946.362 1740.84,946.347 1741.74,946.325 1742.63,946.296 1743.53,946.259 \n",
" 1744.42,946.216 1745.32,946.166 1746.21,946.108 1747.1,946.045 1748,945.974 1748.89,945.897 1749.79,945.813 1750.68,945.723 1751.58,945.626 1752.47,945.523 \n",
" 1753.37,945.414 1754.26,945.299 1755.16,945.178 1756.05,945.051 1756.95,944.919 1757.84,944.781 1758.73,944.637 1759.63,944.489 1760.52,944.335 1761.42,944.176 \n",
" 1762.31,944.012 1763.21,943.843 1764.1,943.669 1765,943.491 1765.89,943.309 1766.79,943.122 1767.68,942.931 1768.58,942.737 1769.47,942.538 1770.36,942.336 \n",
" 1771.26,942.13 1772.15,941.921 1773.05,941.709 1773.94,941.494 1774.84,941.275 1775.73,941.054 1776.63,940.831 1777.52,940.605 1778.42,940.377 1779.31,940.147 \n",
" 1780.21,939.914 1781.1,939.681 1781.99,939.445 1782.89,939.208 1783.78,938.97 1784.68,938.73 1785.57,938.49 1786.47,938.248 1787.36,938.007 1788.26,937.764 \n",
" 1789.15,937.522 1790.05,937.279 1790.94,937.036 1791.84,936.793 1792.73,936.55 1793.62,936.308 1794.52,936.067 1795.41,935.826 1796.31,935.586 1797.2,935.348 \n",
" 1798.1,935.11 1798.99,934.874 1799.89,934.639 1800.78,934.406 1801.68,934.175 1802.57,933.945 1803.47,933.718 1804.36,933.493 1805.25,933.27 1806.15,933.049 \n",
" 1807.04,932.831 1807.94,932.616 1808.83,932.403 1809.73,932.194 1810.62,931.987 1811.52,931.784 1812.41,931.584 1813.31,931.387 1814.2,931.194 1815.1,931.004 \n",
" 1815.99,930.818 1816.88,930.636 1817.78,930.458 1818.67,930.284 1819.57,930.113 1820.46,929.947 1821.36,929.785 1822.25,929.628 1823.15,929.475 1824.04,929.326 \n",
" 1824.94,929.182 1825.83,929.042 1826.73,928.907 1827.62,928.777 1828.51,928.651 1829.41,928.53 1830.3,928.414 1831.2,928.303 1832.09,928.197 1832.99,928.096 \n",
" 1833.88,928 1834.78,927.909 1835.67,927.824 1836.57,927.743 1837.46,927.667 1838.35,927.597 1839.25,927.531 1840.14,927.471 1841.04,927.416 1841.93,927.367 \n",
" 1842.83,927.322 1843.72,927.283 1844.62,927.248 1845.51,927.219 1846.41,927.195 1847.3,927.177 1848.2,927.163 1849.09,927.155 1849.98,927.151 1850.88,927.153 \n",
" 1851.77,927.159 1852.67,927.171 1853.56,927.187 1854.46,927.209 1855.35,927.235 1856.25,927.266 1857.14,927.302 1858.04,927.343 1858.93,927.388 1859.83,927.438 \n",
" 1860.72,927.493 1861.61,927.552 1862.51,927.615 1863.4,927.683 1864.3,927.755 1865.19,927.831 1866.09,927.911 1866.98,927.996 1867.88,928.084 1868.77,928.176 \n",
" 1869.67,928.272 1870.56,928.372 1871.46,928.476 1872.35,928.583 1873.24,928.694 1874.14,928.807 1875.03,928.925 1875.93,929.045 1876.82,929.169 1877.72,929.295 \n",
" 1878.61,929.425 1879.51,929.557 1880.4,929.692 1881.3,929.829 1882.19,929.969 1883.09,930.112 1883.98,930.256 1884.87,930.403 1885.77,930.552 1886.66,930.703 \n",
" 1887.56,930.856 1888.45,931.01 1889.35,931.166 1890.24,931.324 1891.14,931.483 1892.03,931.644 1892.93,931.805 1893.82,931.968 1894.72,932.131 1895.61,932.296 \n",
" 1896.5,932.461 1897.4,932.627 1898.29,932.794 1899.19,932.96 1900.08,933.128 1900.98,933.295 1901.87,933.462 1902.77,933.63 1903.66,933.797 1904.56,933.964 \n",
" 1905.45,934.131 1906.35,934.297 1907.24,934.463 1908.13,934.628 1909.03,934.793 1909.92,934.956 1910.82,935.119 1911.71,935.28 1912.61,935.441 1913.5,935.6 \n",
" 1914.4,935.758 1915.29,935.914 1916.19,936.069 1917.08,936.222 1917.98,936.374 1918.87,936.523 1919.76,936.671 1920.66,936.817 1921.55,936.961 1922.45,937.103 \n",
" 1923.34,937.242 1924.24,937.38 1925.13,937.515 1926.03,937.647 1926.92,937.777 1927.82,937.905 1928.71,938.03 1929.61,938.152 1930.5,938.271 1931.39,938.388 \n",
" 1932.29,938.502 1933.18,938.613 1934.08,938.721 1934.97,938.825 1935.87,938.927 1936.76,939.026 1937.66,939.121 1938.55,939.213 1939.45,939.302 1940.34,939.388 \n",
" 1941.24,939.47 1942.13,939.549 1943.02,939.625 1943.92,939.697 1944.81,939.766 1945.71,939.831 1946.6,939.893 1947.5,939.951 1948.39,940.006 1949.29,940.057 \n",
" 1950.18,940.105 1951.08,940.149 1951.97,940.189 1952.87,940.226 1953.76,940.26 1954.65,940.29 1955.55,940.316 1956.44,940.338 1957.34,940.358 1958.23,940.373 \n",
" 1959.13,940.385 1960.02,940.394 1960.92,940.399 1961.81,940.4 1962.71,940.398 1963.6,940.393 1964.5,940.384 1965.39,940.371 1966.28,940.356 1967.18,940.337 \n",
" 1968.07,940.314 1968.97,940.289 1969.86,940.26 1970.76,940.228 1971.65,940.193 1972.55,940.154 1973.44,940.113 1974.34,940.068 1975.23,940.021 1976.12,939.971 \n",
" 1977.02,939.917 1977.91,939.861 1978.81,939.802 1979.7,939.741 1980.6,939.676 1981.49,939.609 1982.39,939.54 1983.28,939.468 1984.18,939.393 1985.07,939.317 \n",
" 1985.97,939.238 1986.86,939.156 1987.75,939.073 1988.65,938.987 1989.54,938.899 1990.44,938.809 1991.33,938.718 1992.23,938.624 1993.12,938.529 1994.02,938.432 \n",
" 1994.91,938.333 1995.81,938.233 1996.7,938.132 1997.6,938.029 1998.49,937.924 1999.38,937.819 2000.28,937.712 2001.17,937.604 2002.07,937.495 2002.96,937.385 \n",
" 2003.86,937.274 2004.75,937.163 2005.65,937.051 2006.54,936.938 2007.44,936.824 2008.33,936.71 2009.23,936.596 2010.12,936.481 2011.01,936.366 2011.91,936.25 \n",
" 2012.8,936.135 2013.7,936.02 2014.59,935.904 2015.49,935.789 2016.38,935.674 2017.28,935.559 2018.17,935.444 2019.07,935.33 2019.96,935.217 2020.86,935.103 \n",
" 2021.75,934.991 2022.64,934.879 2023.54,934.768 2024.43,934.657 2025.33,934.548 2026.22,934.439 2027.12,934.332 2028.01,934.225 2028.91,934.12 2029.8,934.016 \n",
" 2030.7,933.913 2031.59,933.811 2032.49,933.711 2033.38,933.612 2034.27,933.515 2035.17,933.419 2036.06,933.325 2036.96,933.232 2037.85,933.141 2038.75,933.052 \n",
" 2039.64,932.965 2040.54,932.879 2041.43,932.796 2042.33,932.714 2043.22,932.634 2044.12,932.556 2045.01,932.48 2045.9,932.406 2046.8,932.335 2047.69,932.265 \n",
" 2048.59,932.198 2049.48,932.132 2050.38,932.069 2051.27,932.009 2052.17,931.95 2053.06,931.894 2053.96,931.84 2054.85,931.789 2055.75,931.74 2056.64,931.693 \n",
" 2057.53,931.648 2058.43,931.606 2059.32,931.567 2060.22,931.53 2061.11,931.495 2062.01,931.463 2062.9,931.433 2063.8,931.406 2064.69,931.381 2065.59,931.359 \n",
" 2066.48,931.339 2067.38,931.321 2068.27,931.306 2069.16,931.294 2070.06,931.284 2070.95,931.276 2071.85,931.271 2072.74,931.268 2073.64,931.268 2074.53,931.27 \n",
" 2075.43,931.274 2076.32,931.281 2077.22,931.29 2078.11,931.301 2079.01,931.315 2079.9,931.331 2080.79,931.349 2081.69,931.37 2082.58,931.392 2083.48,931.417 \n",
" 2084.37,931.444 2085.27,931.473 2086.16,931.505 2087.06,931.538 2087.95,931.573 2088.85,931.61 2089.74,931.65 2090.64,931.691 2091.53,931.734 2092.42,931.778 \n",
" 2093.32,931.825 2094.21,931.873 2095.11,931.924 2096,931.975 2096.9,932.029 2097.79,932.084 2098.69,932.14 2099.58,932.198 2100.48,932.258 2101.37,932.318 \n",
" 2102.27,932.381 2103.16,932.444 2104.05,932.509 2104.95,932.575 2105.84,932.642 2106.74,932.71 2107.63,932.779 2108.53,932.85 2109.42,932.921 2110.32,932.993 \n",
" 2111.21,933.066 2112.11,933.14 2113,933.215 2113.89,933.29 2114.79,933.366 2115.68,933.442 2116.58,933.519 2117.47,933.597 2118.37,933.675 2119.26,933.753 \n",
" 2120.16,933.832 2121.05,933.911 2121.95,933.99 2122.84,934.069 2123.74,934.149 2124.63,934.229 2125.52,934.308 2126.42,934.388 2127.31,934.467 2128.21,934.546 \n",
" 2129.1,934.626 2130,934.704 2130.89,934.783 2131.79,934.861 2132.68,934.939 2133.58,935.017 2134.47,935.094 2135.37,935.17 2136.26,935.246 2137.15,935.321 \n",
" 2138.05,935.396 2138.94,935.47 2139.84,935.543 2140.73,935.616 2141.63,935.687 2142.52,935.758 2143.42,935.828 2144.31,935.897 2145.21,935.964 2146.1,936.031 \n",
" 2147,936.097 2147.89,936.162 2148.78,936.225 2149.68,936.288 2150.57,936.349 2151.47,936.409 2152.36,936.467 2153.26,936.525 2154.15,936.581 2155.05,936.636 \n",
" 2155.94,936.689 2156.84,936.741 2157.73,936.791 2158.63,936.84 2159.52,936.888 2160.41,936.934 2161.31,936.979 2162.2,937.022 2163.1,937.063 2163.99,937.103 \n",
" 2164.89,937.141 2165.78,937.178 2166.68,937.213 2167.57,937.246 2168.47,937.278 2169.36,937.308 2170.26,937.337 2171.15,937.364 2172.04,937.389 2172.94,937.412 \n",
" 2173.83,937.434 2174.73,937.454 2175.62,937.473 2176.52,937.489 2177.41,937.504 2178.31,937.517 2179.2,937.529 2180.1,937.539 2180.99,937.547 2181.89,937.554 \n",
" 2182.78,937.558 2183.67,937.562 2184.57,937.563 2185.46,937.563 2186.36,937.561 2187.25,937.558 2188.15,937.553 2189.04,937.546 2189.94,937.538 2190.83,937.528 \n",
" 2191.73,937.516 2192.62,937.503 2193.52,937.489 2194.41,937.473 2195.3,937.455 2196.2,937.436 2197.09,937.416 2197.99,937.394 2198.88,937.371 2199.78,937.346 \n",
" 2200.67,937.32 2201.57,937.293 2202.46,937.264 2203.36,937.234 2204.25,937.203 2205.15,937.171 2206.04,937.137 2206.93,937.102 2207.83,937.066 2208.72,937.029 \n",
" 2209.62,936.991 2210.51,936.952 2211.41,936.911 2212.3,936.87 2213.2,936.828 2214.09,936.785 2214.99,936.741 2215.88,936.696 2216.78,936.65 2217.67,936.604 \n",
" 2218.56,936.557 2219.46,936.509 2220.35,936.46 2221.25,936.411 2222.14,936.361 2223.04,936.31 2223.93,936.259 2224.83,936.208 2225.72,936.156 2226.62,936.103 \n",
" 2227.51,936.051 2228.41,935.997 2229.3,935.944 2230.19,935.89 2231.09,935.836 2231.98,935.782 2232.88,935.727 2233.77,935.673 2234.67,935.618 2235.56,935.563 \n",
" 2236.46,935.508 2237.35,935.453 2238.25,935.399 2239.14,935.344 2240.04,935.289 2240.93,935.235 2241.82,935.18 2242.72,935.126 2243.61,935.072 2244.51,935.019 \n",
" 2245.4,934.965 2246.3,934.912 2247.19,934.86 2248.09,934.808 2248.98,934.756 2249.88,934.704 2250.77,934.654 2251.66,934.603 2252.56,934.554 2253.45,934.504 \n",
" 2254.35,934.456 2255.24,934.408 2256.14,934.361 2257.03,934.314 2257.93,934.268 2258.82,934.223 2259.72,934.179 2260.61,934.135 2261.51,934.092 2262.4,934.05 \n",
" 2263.29,934.009 2264.19,933.969 2265.08,933.93 2265.98,933.891 2266.87,933.854 2267.77,933.817 2268.66,933.782 2269.56,933.747 2270.45,933.714 2271.35,933.681 \n",
" 2272.24,933.65 2273.14,933.619 2274.03,933.59 2274.92,933.561 2275.82,933.534 2276.71,933.508 2277.61,933.483 2278.5,933.459 2279.4,933.437 2280.29,933.415 \n",
" 2281.19,933.394 2282.08,933.375 2282.98,933.357 2283.87,933.34 2284.77,933.324 2285.66,933.309 2286.55,933.296 2287.45,933.283 2288.34,933.272 2289.24,933.262 \n",
" 2290.13,933.253 2291.03,933.246 2291.92,933.239 2292.82,933.234 2293.71,933.23 2294.61,933.227 2295.5,933.225 2296.4,933.224 2297.29,933.224 2298.18,933.226 \n",
" 2299.08,933.229 \n",
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" 1746.47,568.075 2280.76,568.075 2280.76,205.195 1746.47,205.195 1746.47,568.075 \n",
" \"/>\n",
"<polyline clip-path=\"url(#clip7600)\" style=\"stroke:#009af9; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1770.47,265.675 1914.47,265.675 \n",
" \"/>\n",
"<g clip-path=\"url(#clip7600)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1938.47, 283.175)\" x=\"1938.47\" y=\"283.175\">Lattice size: 1</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip7600)\" style=\"stroke:#e26f46; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1770.47,326.155 1914.47,326.155 \n",
" \"/>\n",
"<g clip-path=\"url(#clip7600)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1938.47, 343.655)\" x=\"1938.47\" y=\"343.655\">Lattice size: 2</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip7600)\" style=\"stroke:#3da44d; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1770.47,386.635 1914.47,386.635 \n",
" \"/>\n",
"<g clip-path=\"url(#clip7600)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1938.47, 404.135)\" x=\"1938.47\" y=\"404.135\">Lattice size: 3</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip7600)\" style=\"stroke:#c271d2; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1770.47,447.115 1914.47,447.115 \n",
" \"/>\n",
"<g clip-path=\"url(#clip7600)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1938.47, 464.615)\" x=\"1938.47\" y=\"464.615\">Lattice size: 4</text>\n",
"</g>\n",
"<polyline clip-path=\"url(#clip7600)\" style=\"stroke:#ac8d18; stroke-width:4; stroke-opacity:1; fill:none\" points=\"\n",
" 1770.47,507.595 1914.47,507.595 \n",
" \"/>\n",
"<g clip-path=\"url(#clip7600)\">\n",
"<text style=\"fill:#000000; fill-opacity:1; font-family:Arial,Helvetica Neue,Helvetica,sans-serif; font-size:48px; text-anchor:start;\" transform=\"rotate(0, 1938.47, 525.095)\" x=\"1938.47\" y=\"525.095\">Lattice size: 5</text>\n",
"</g>\n",
"</svg>\n"
]
},
"execution_count": 885,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot()\n",
"for i in 1:5\n",
" plot!(1:step:numTimeStepsRecorded,DDisplacements[i],label=\"Lattice size: $i\",xlabel=\"timestep\",ylabel=\"displacement\",title=\"Dynamic Model Convergence\")\n",
"\n",
"end\n",
"plot!()\n",
"# savefig(\"dynamic_convergence\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
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},
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"display_name": "Julia 1.2.0",
"language": "julia",
"name": "julia-1.2"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.2.0"
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"nbformat": 4,
"nbformat_minor": 4
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