mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 23:10:14 +08:00
Gudni Karl Rosenkjaer
191 lines
6.1 KiB
Plaintext
191 lines
6.1 KiB
Plaintext
{
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"metadata": {
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"name": "",
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"signature": "sha256:4f51688cd2ee8a11dad3df1928925d3c9cad0da43a3f6a3c3c840024caae5fe1"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Issues with padding cells and high frequencies in the analytic MT layered earth."
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"import SimPEG as simpeg\n",
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"elev = 300\n",
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"# 3D mesh and model\n",
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"M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,5),(100,5,1.5)],[(100,5,-1.5),(100.,5),(100,5,1.5)],[(100,10,-1.5),(100.,10),(100,10,1.5)]], x0=['C','C','C'])\n",
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"conds = [1,1e-2]\n",
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"sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-10000,-10000,-200],[10000,10000,0],conds)\n",
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"sig[M.gridCC[:,2]>elev] = 1e-8\n",
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"sig[M.gridCC[:,2]<-600] = 1e-1\n",
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"# Make the 1D mesh and model\n",
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"mesh1d = simpeg.Mesh.TensorMesh([M.hz],np.array([M.x0[2]]))\n",
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"sig1D = M.r(sig,'CC','CC','M')[0,0,:]"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"Efficiency Warning: Interpolation will be slow, use setup.py!\n",
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"\n",
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" python setup.py build_ext --inplace\n",
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" \n"
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]
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}
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],
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"prompt_number": 1
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# Run for high frequency\n",
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"freq = 1e4"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 3
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"# Run the analytic problem\n",
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"import simpegMT as simpegmt\n",
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"anaEd, anaEu, anaHd, anaHu = simpegmt.Utils.MT1Danalytic.getEHfields(mesh1d,sig1D,freq,np.array([300]))\n",
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"anaE = anaEd+anaEu\n",
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"anaH = anaHd+anaHu\n",
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"anaZ = anaE/anaH\n"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 4
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"anaZ"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 5,
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"text": [
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"array([ nan+nanj])"
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]
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}
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],
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"prompt_number": 5
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Returns nan because in the analytic solution the propagation of the fields in the layer \"blows\" up."
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"sig = 10\n",
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"sig0 = 20\n",
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"mu = 4*np.pi*1e-7\n",
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"eps = 8.85*1e-12\n",
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"for h in [10000,5000,1000,500,100,50,10]:\n",
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" w = 2*np.pi*freq\n",
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" k0 = np.sqrt(eps*mu*w**2-1j*mu*sig0*w)\n",
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" k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)\n",
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" zp = (w*mu)/k\n",
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" yp1 = k0/(w*mu)\n",
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" # Convert fields to down/up going components in layer below current layer\n",
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" Pj1 = np.array([[1,1],[yp1,-yp1]])\n",
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" # Convert fields to down/up going components in current layer\n",
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" Pjinv = 1./2*np.array([[1,zp],[1,-zp]])\n",
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" # Propagate down and up components through the current layer\n",
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" elamh = np.array([[np.exp(-1j*k*h),0],[0,np.exp(1j*k*h)]])\n",
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" UD = elamh.dot(Pjinv.dot(Pj1)).dot([1,0])\n",
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" print h, w, k \n",
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" print elamh\n",
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" #print Pj1, Pjinv, elamh\n",
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" print UD"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"10000 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 0. -0.j 0. +0.j]\n",
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" [ 0. +0.j inf+infj]]\n",
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"[ 0. +0.j nan+nanj]\n",
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"5000 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 0. -0.j 0. +0.j]\n",
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" [ 0. +0.j inf+infj]]\n",
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"[ 0. +0.j nan+nanj]\n",
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"1000 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 1.33271357e-273 -2.32814399e-278j 0.00000000e+000 +0.00000000e+000j]\n",
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" [ 0.00000000e+000 +0.00000000e+000j 7.50348781e+272 +1.31079930e+268j]]\n",
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"[ 1.60872758e-273 -2.81162844e-278j -1.55402321e+272 -2.70737840e+267j]\n",
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"500 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 3.65063497e-137 -3.18868363e-142j 0.00000000e+000 +0.00000000e+000j]\n",
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" [ 0.00000000e+000 +0.00000000e+000j 2.73924950e+136 +2.39262488e+131j]]\n",
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"[ 4.40670622e-137 -3.85267017e-142j -5.67317146e+135 -4.92836188e+130j]\n",
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"100 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 5.15790907e-28 -9.01045454e-34j 0.00000000e+00 +0.00000000e+00j]\n",
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" [ 0.00000000e+00 +0.00000000e+00j 1.93877012e+27 +3.38687631e+21j]]\n",
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"[ 6.22614702e-28 -1.09272824e-33j -4.01532439e+26 -6.82387175e+20j]\n",
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"50 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 2.27110305e-14 -1.98371768e-20j 0.00000000e+00 +0.00000000e+00j]\n",
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" [ 0.00000000e+00 +0.00000000e+00j 4.40314674e+13 +3.84597256e+07j]]\n",
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"[ 2.74146389e-14 -2.41688373e-20j -9.11921548e+12 -7.53244599e+06j]\n",
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"10 62831.8530718 (0.628318548187-0.628318513249j)\n",
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"[[ 1.86744306e-03 -3.26227365e-10j 0.00000000e+00 +0.00000000e+00j]\n",
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" [ 0.00000000e+00 +0.00000000e+00j 5.35491562e+02 +9.35460925e-05j]]\n",
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"[ 2.25420318e-03 -4.12148003e-10j -1.10903934e+02 -1.41102131e-05j]\n"
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]
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}
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],
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"prompt_number": 11
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},
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{
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"cell_type": "heading",
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"level": 3,
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"metadata": {},
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"source": [
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"Is there a smart way to \"fix\" this so that the 1D layering can be used for the analytic solution?"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [],
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"language": "python",
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"metadata": {},
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"outputs": []
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}
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],
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"metadata": {}
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}
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]
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} |