diff --git a/src/Playground.ipynb b/src/Playground.ipynb
deleted file mode 100644
index bb41bef94ac418375086adb98852ec61fb94d83d..0000000000000000000000000000000000000000
--- a/src/Playground.ipynb
+++ /dev/null
@@ -1,165 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import pandas as pd\n",
- "import os\n",
- "import argparse\n",
- "import shutil\n",
- "import time\n",
- "import subprocess\n",
- "import re\n",
- "import numpy as np"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [],
- "source": [
- "# Function to extract the times of different stages from the program output\n",
- "def extract_times(program_output):\n",
- " # Dictionary to store timing values\n",
- " timing_values = {}\n",
- " \n",
- " # Regular expressions to match specific timing entries\n",
- " time_patterns = {\n",
- " 'Total time': r'Total time: (\\d+\\.\\d+)',\n",
- " 'Setup': r'Setup: (\\d+\\.\\d+)',\n",
- " 'Assembly Linear System': r'Assembly Linear System: (\\d+\\.\\d+)',\n",
- " 'Solving Linear System': r'Solving Linear System: (\\d+\\.\\d+)',\n",
- " 'Plotting': r'Plotting: (\\d+\\.\\d+)'\n",
- " }\n",
- " \n",
- " # Extract times using regex\n",
- " for key, pattern in time_patterns.items():\n",
- " match = re.search(pattern, program_output)\n",
- " if match:\n",
- " timing_values[key] = float(match.group(1))\n",
- " else:\n",
- " timing_values[key] = None\n",
- " \n",
- " return timing_values"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [],
- "source": [
- "# refinement level\n",
- "DEGREE_ELEVATIONS = 0\n",
- "H_REFINEMENTS = 1\n",
- "# Define the folder where the geometry is stored\n",
- "DataFolder = f'Data/H_REFINEMENTS_{H_REFINEMENTS}'"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [],
- "source": [
- "# path to gismo executable for numerical simulation\n",
- "stokes_executable = 'gismo/stokes_example'"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "# lets go for training data\n",
- "stage = 'train'\n",
- "df = pd.read_excel(f'{DataFolder}/{stage}/parameter_input.xlsx').transpose()\n",
- "N_FILES_STAGE = df.shape[1]\n",
- "\n",
- "# Just run the first geometry\n",
- "index_vec = [0, 1, 2, 3, 4]\n",
- "timings = []\n",
- "total_time = 0\n",
- "setup_time = 0\n",
- "assembly_linear_system_time = 0\n",
- "solving_linear_system_time = 0\n",
- "dict_entries = ['Total time', 'Setup', 'Assembly Linear System', 'Solving Linear System']\n",
- "property_entries = [total_time, setup_time, assembly_linear_system_time, solving_linear_system_time]\n",
- "for index in index_vec:\n",
- " # file for the geometry\n",
- " file = f'{DataFolder}/{stage}/microstructure/index_{index}.xml'\n",
- "\n",
- " # Run simulation\n",
- " program_output = subprocess.Popen(\n",
- " [f'./{stokes_executable}', f'-f {file}', '--export-xml', f'-e {DEGREE_ELEVATIONS}', f'-r {H_REFINEMENTS}', '--no-plot'],\n",
- " # shell=True, # do I need it?\n",
- " stdout=subprocess.PIPE,\n",
- " text=True\n",
- " ).communicate()[0]\n",
- " # print(program_output)\n",
- "\n",
- " timings.append(extract_times(program_output))\n",
- " total_time += timings[-1]['Total time']\n",
- " setup_time += timings[-1]['Setup']\n",
- " assembly_linear_system_time += timings[-1]['Assembly Linear System']\n",
- " solving_linear_system_time += timings[-1]['Solving Linear System']"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 21,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "total time: 2.417550374869\n",
- "setup time: 0.03952433483208\n",
- "assembly linear system time: 0.32472395699010004\n",
- "solving linear system time: 2.053302083049\n"
- ]
- }
- ],
- "source": [
- "print(f'total time: {total_time}')\n",
- "print(f'setup time: {setup_time}')\n",
- "print(f'assembly linear system time: {assembly_linear_system_time}')\n",
- "print(f'solving linear system time: {solving_linear_system_time}')"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "POD",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.12.7"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/src/Visualizations/HighestError.zip b/src/Visualizations/HighestError.zip
new file mode 100644
index 0000000000000000000000000000000000000000..b86d91da4f04716b612abf628faaf7c114022a39
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diff --git a/src/Visualizations/HighestError/Pressure_RBFCubic_R16_i59_Error.png b/src/Visualizations/HighestError/Pressure_RBFCubic_R16_i59_Error.png
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diff --git a/src/Visualizations/HighestError/VelocityX_RBFCubic_R16_i63_Error.png b/src/Visualizations/HighestError/VelocityX_RBFCubic_R16_i63_Error.png
new file mode 100644
index 0000000000000000000000000000000000000000..48f149921ff1bea779b4bc45ccfc9e9482840c0e
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diff --git a/src/Visualizations/HighestError/VelocityX_RBFCubic_R16_i63_Predicted.png b/src/Visualizations/HighestError/VelocityX_RBFCubic_R16_i63_Predicted.png
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diff --git a/src/Visualizations/HighestError/VelocityX_RBFCubic_R16_i63_True.png b/src/Visualizations/HighestError/VelocityX_RBFCubic_R16_i63_True.png
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diff --git a/src/Visualizations/HighestError/VelocityY_RBFCubic_R16_i55_Error.png b/src/Visualizations/HighestError/VelocityY_RBFCubic_R16_i55_Error.png
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new file mode 100644
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diff --git a/src/Visualizations/HighestError/VelocityY_RBFCubic_R16_i55_True.png b/src/Visualizations/HighestError/VelocityY_RBFCubic_R16_i55_True.png
new file mode 100644
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diff --git a/src/f2_EvaluationError_POD.py b/src/f2_EvaluationError_POD.py
index 03889624f0a0ec2556a864f7bff840a747e8f9b2..27045e9b47c18703ad5bf32e4b678af6e67d160b 100755
--- a/src/f2_EvaluationError_POD.py
+++ b/src/f2_EvaluationError_POD.py
@@ -115,17 +115,7 @@ for R_ in tqdm(R):
ms_v.show()
# Compute errors
- # norms = list(norm_funcs.keys())
- # error_values = []
- # # Pressure
- # for norm in norms:
- # error_value = compute_integral_error(
- # multipatch=microstructure,
- # fields_original=pressure_data,
- # fields_recreated=pressure_rec_data,
- # norm=norm
- # )
- # error_values.append(error_value)
+ # Pressure
error_values = compute_integral_error(
multipatch=microstructure,
fields_original=pressure_data,
@@ -138,15 +128,6 @@ for R_ in tqdm(R):
L2_rel_p_s.append(error_values[3])
# Velocity
- # error_values = []
- # for norm in norms:
- # error_value = compute_integral_error(
- # multipatch=ms_vel,
- # fields_original=velocity_data,
- # fields_recreated=velocity_rec_data,
- # norm=norm
- # )
- # error_values.append(error_value)
error_values = compute_integral_error(
multipatch=ms_vel,
fields_original=velocity_data,
diff --git a/src/i6_VisualizeDifferentErrorFields.py b/src/i6_VisualizeDifferentErrorFields.py
index 5713002952868585cda808a7bcb536e4c0e9f9cd..892ecb6b4ddca0a3572109d4f6300f03803ed2c4 100644
--- a/src/i6_VisualizeDifferentErrorFields.py
+++ b/src/i6_VisualizeDifferentErrorFields.py
@@ -27,7 +27,7 @@ ModelFolder = f'{DataFolder}/TrainedModels/RBF_cubic'
PatchesFolder = f'{DataFolder}/Patches'
R_ = 21
-sample = 14#!0
+sample = 14
GEOMETRY_FILE = f'{DataFolder}/test/microstructure/index_{sample}.xml'
PRESSURE_FILE = f'{PatchesFolder}/POD_{int(R_)}/pressure_field_patches_{sample}.xml'
diff --git a/src/i8_IdentifyWorstPrediction.ipynb b/src/i8_IdentifyWorstPrediction.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..6f66293f6bc99924e7b9c3c732f42987e9c4b1ac
--- /dev/null
+++ b/src/i8_IdentifyWorstPrediction.ipynb
@@ -0,0 +1,359 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "541bec77",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import argparse\n",
+ "import os\n",
+ "from tqdm import tqdm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "7a7f470c",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from miscellaneous.error_evaluation import get_solution_vectors, load_geometry, compute_integral_error, show_multipatch_field"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "21199ef3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Define refinement\n",
+ "DEGREE_ELEVATIONS = 1\n",
+ "H_REFINEMENTS = [0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "33201cad",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Take the 99 percent cutoff\n",
+ "# As the velocity cutoff is later than the pressure cutoff we take the velocity cutoff\n",
+ "R = 16\n",
+ "models = {\n",
+ " # 'POD'\n",
+ " # 'LinearRegression',\n",
+ " # 'GP_RationalQuadratic',\n",
+ " # 'RBF_Linear',\n",
+ " # 'RBF_thinplatespline',\n",
+ " 'RBF_cubic',\n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "de6d2dd0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "DataFolder = [f'Data/H_REFINEMENTS_{H_REFINEMENT}' for H_REFINEMENT in H_REFINEMENTS]\n",
+ "# Load test input \n",
+ "df = [pd.read_excel(f'{DataFolder_}/test/parameter_input.xlsx').transpose() for DataFolder_ in DataFolder]\n",
+ "SAMPLES_TEST = [df_.shape[1] for df_ in df]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "a38a3424",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ " 0%| | 0/1 [00:00<?, ?it/s]"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Evaluating model RBF_cubic with R=16 for H_REFINEMENT=0\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "100%|██████████| 64/64 [00:36<00:00, 1.77it/s]\n",
+ "100%|██████████| 1/1 [00:36<00:00, 36.16s/it]\n"
+ ]
+ }
+ ],
+ "source": [
+ "L1_rel_p, L2_rel_p = [], []\n",
+ "L1_rel_vx, L2_rel_vx = [], []\n",
+ "L1_rel_vy, L2_rel_vy = [], []\n",
+ "\n",
+ "# Loop over H_REFINEMENTS\n",
+ "for h_ref_idx, H_REFINEMENT in enumerate(H_REFINEMENTS):\n",
+ " L1_rel_p_h, L2_rel_p_h = [], []\n",
+ " L1_rel_vx_h, L2_rel_vx_h = [], []\n",
+ " L1_rel_vy_h, L2_rel_vy_h = [], []\n",
+ " \n",
+ " DataFolder = f'Data/H_REFINEMENTS_{H_REFINEMENT}'\n",
+ " \n",
+ " for model_name in tqdm(models):\n",
+ " print(f'Evaluating model {model_name} with R={R} for H_REFINEMENT={H_REFINEMENT}')\n",
+ " ModelFolder = f'{DataFolder}/TrainedModels/{model_name}'\n",
+ " PatchesFolder = f'{DataFolder}/Patches'\n",
+ " # Solution vector\n",
+ " L1_rel_p_s, L2_rel_p_s = [], []\n",
+ " L1_rel_vx_s, L2_rel_vx_s = [], []\n",
+ " L1_rel_vy_s, L2_rel_vy_s = [], []\n",
+ "\n",
+ " # iterate over the test samples\n",
+ " for sample in tqdm(range(SAMPLES_TEST[h_ref_idx])):\n",
+ " # Collect input files for evaluation\n",
+ " GEOMETRY_FILE = f'{DataFolder}/test/microstructure/index_{sample}.xml'\n",
+ " PRESSURE_FILE = f'{PatchesFolder}/{model_name}_{int(R)}/pressure_field_patches_{sample}.xml'\n",
+ " VELOCITY_FILE = f'{PatchesFolder}/{model_name}_{int(R)}/velocity_field_patches_{sample}.xml'\n",
+ " PRESSURE_REC_FILE = f'{PatchesFolder}/{model_name}_{int(R)}/pressure_field_rec_patches_{sample}.xml'\n",
+ " VELOCITY_REC_FILE = f'{PatchesFolder}/{model_name}_{int(R)}/velocity_field_rec_patches_{sample}.xml'\n",
+ "\n",
+ " # Get solution vector for pressure and velocity\n",
+ " pressure_data = get_solution_vectors(file_path=PRESSURE_FILE)\n",
+ " velocity_data = get_solution_vectors(file_path=VELOCITY_FILE, two_dimensional=True)\n",
+ " pressure_rec_data = get_solution_vectors(file_path=PRESSURE_REC_FILE)\n",
+ " velocity_rec_data = get_solution_vectors(file_path=VELOCITY_REC_FILE, two_dimensional=True)\n",
+ "\n",
+ " # Load the geometry\n",
+ " microstructure, ms_vel = load_geometry(GEOMETRY_FILE, degree_elevations=DEGREE_ELEVATIONS, h_refinements=H_REFINEMENTS[h_ref_idx])\n",
+ "\n",
+ " # Compute the error\n",
+ " # Pressure\n",
+ " error_values = compute_integral_error(\n",
+ " multipatch=microstructure,\n",
+ " fields_original=pressure_data,\n",
+ " fields_recreated=pressure_rec_data,\n",
+ " )\n",
+ " L1_rel_p_s.append(error_values[2])\n",
+ " L2_rel_p_s.append(error_values[3])\n",
+ " # Velocity\n",
+ " error_values = compute_integral_error(\n",
+ " multipatch=ms_vel,\n",
+ " fields_original=velocity_data,\n",
+ " fields_recreated=velocity_rec_data,\n",
+ " )\n",
+ "\n",
+ " # Append the error values\n",
+ " L1_rel_vx_s.append(error_values[2][0])\n",
+ " L2_rel_vx_s.append(error_values[3][0])\n",
+ " L1_rel_vy_s.append(error_values[2][1])\n",
+ " L2_rel_vy_s.append(error_values[3][1])\n",
+ "\n",
+ " # Append the error values for this model\n",
+ " L1_rel_p_h.append(L1_rel_p_s)\n",
+ " L2_rel_p_h.append(L2_rel_p_s)\n",
+ " L1_rel_vx_h.append(L1_rel_vx_s)\n",
+ " L2_rel_vx_h.append(L2_rel_vx_s)\n",
+ " L1_rel_vy_h.append(L1_rel_vy_s)\n",
+ " L2_rel_vy_h.append(L2_rel_vy_s)\n",
+ " \n",
+ " # Append results for this h-refinement level\n",
+ " L1_rel_p.append(L1_rel_p_h)\n",
+ " L2_rel_p.append(L2_rel_p_h)\n",
+ " L1_rel_vx.append(L1_rel_vx_h)\n",
+ " L2_rel_vx.append(L2_rel_vx_h)\n",
+ " L1_rel_vy.append(L1_rel_vy_h)\n",
+ " L2_rel_vy.append(L2_rel_vy_h)\n",
+ "\n",
+ "# Save the error values\n",
+ "np.savez(\n",
+ " f'Data/error_evaluation_99Cutoff.npz',\n",
+ " L1_rel_p=L1_rel_p, L2_rel_p=L2_rel_p,\n",
+ " L1_rel_vx=L1_rel_vx, L2_rel_vx=L2_rel_vx,\n",
+ " L1_rel_vy=L1_rel_vy, L2_rel_vy=L2_rel_vy,\n",
+ " h_refinements=H_REFINEMENTS\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "c8e0eca1",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "((1, 64), (1, 64), (1, 64))"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "L2_rel_p = np.array(L2_rel_p).reshape(len(models), SAMPLES_TEST[0])\n",
+ "L2_rel_vx = np.array(L2_rel_vx).reshape(len(models), SAMPLES_TEST[0])\n",
+ "L2_rel_vy = np.array(L2_rel_vy).reshape(len(models), SAMPLES_TEST[0])\n",
+ "L2_rel_p.shape, L2_rel_vx.shape, L2_rel_vy.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "ebf09da1",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Identify for each model the index with the highest L2 error\n",
+ "identifier_p = np.where(\n",
+ " L2_rel_p == np.max(L2_rel_p),\n",
+ " True,\n",
+ " False,\n",
+ ")\n",
+ "identifier_vx = np.where(\n",
+ " L2_rel_vx == np.max(L2_rel_vx),\n",
+ " True,\n",
+ " False,\n",
+ ")\n",
+ "identifier_vy = np.where(\n",
+ " L2_rel_vy == np.max(L2_rel_vy),\n",
+ " True,\n",
+ " False,\n",
+ ")\n",
+ "# print('Pressure')\n",
+ "# print(f'Max Pressure Error: {L2_rel_p[identifier_p == True]}')\n",
+ "# print(f'Identifier pressure {identifier_p}')\n",
+ "# print(f'---------' * 20)\n",
+ "# print('Velocity X')\n",
+ "# print(f'Max Velocity X Error: {L2_rel_vx[identifier_vx == True]}')\n",
+ "# print(f'Identifier velocity x {identifier_vx}')\n",
+ "# print(f'---------' * 20)\n",
+ "# print('Velocity Y')\n",
+ "# print(f'Max Velocity Y Error: {L2_rel_vy[identifier_vy == True]}')\n",
+ "# print(f'Identifier velocity y {identifier_vy}')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "5b6e6c8f",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "((array([0]), array([59])),\n",
+ " (array([0]), array([63])),\n",
+ " (array([0]), array([55])))"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "idx_p = np.where(identifier_p == True)\n",
+ "idx_vx = np.where(identifier_vx == True)\n",
+ "idx_vy = np.where(identifier_vy == True)\n",
+ "idx_p, idx_vx, idx_vy"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "bd27750b",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Pressure\n",
+ "Pressure\n",
+ "Model with maximum relative L2 error: RBF_cubic\n",
+ "Test sample for the maximum error: 59\n",
+ "Max Pressure Error: [0.0580657]\n",
+ "------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
+ "Velocity X\n",
+ "Model with maximum relative L2 error: RBF_cubic\n",
+ "Test sample for the maximum error: 63\n",
+ "Max Velocity X Error: [0.03785187]\n",
+ "------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
+ "Velocity Y\n",
+ "Model with maximum relative L2 error: RBF_cubic\n",
+ "Test sample for the maximum error: 55\n",
+ "Max Velocity Y Error: [0.06116032]\n",
+ "------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_81308/1771942688.py:9: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
+ " print(f'Model with maximum relative L2 error: {model_list[int(idx[0])]}')\n",
+ "/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_81308/1771942688.py:10: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
+ " print(f'Test sample for the maximum error: {int(idx[1])}')\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(f'Pressure')\n",
+ "model_list = list(models)\n",
+ "for field_name, idx, L2_rel in [\n",
+ " (\"Pressure\", idx_p, L2_rel_p), \n",
+ " (\"Velocity X\", idx_vx, L2_rel_vx), \n",
+ " (\"Velocity Y\", idx_vy, L2_rel_vy)\n",
+ "]:\n",
+ " print(f'{field_name}')\n",
+ " print(f'Model with maximum relative L2 error: {model_list[int(idx[0])]}')\n",
+ " print(f'Test sample for the maximum error: {int(idx[1])}')\n",
+ " print(f'Max {field_name} Error: {L2_rel[idx]}')\n",
+ " print(f'---------' * 20)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "0f4e9bf4",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "POD",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.12.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}