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"source": [
"# Sensitivity analysis for the Ishigama function using PCE\n",
"\n",
"Run an EasyVVUQ campaign to analyze the sensitivity for the Ishigami function\n",
"\n",
"This is done with PCE."
]
},
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"source": [
"# Run an EasyVVUQ campaign to analyze the sensitivity for the Ishigami function\n",
"# This is done with PCE.\n",
"%matplotlib inline\n",
"import os\n",
"import easyvvuq as uq\n",
"import chaospy as cp\n",
"import pickle\n",
"import numpy as np\n",
"import matplotlib.pylab as plt\n",
"import time\n",
"import pandas as pd"
]
},
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"'1.26.4'"
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"source": [
"# Define the Ishigami function\n",
"def ishigamiSA(a,b):\n",
" '''Exact sensitivity indices of the Ishigami function for given a and b.\n",
" From https://openturns.github.io/openturns/master/examples/meta_modeling/chaos_ishigami.html\n",
" '''\n",
" var = 1.0/2 + a**2/8 + b*np.pi**4/5 + b**2*np.pi**8/18\n",
" S1 = (1.0/2 + b*np.pi**4/5+b**2*np.pi**8/50)/var\n",
" S2 = (a**2/8)/var\n",
" S3 = 0\n",
" S13 = b**2*np.pi**8/2*(1.0/9-1.0/25)/var\n",
" exact = {\n",
" 'expectation' : a/2,\n",
" 'variance' : var,\n",
" 'S1' : (1.0/2 + b*np.pi**4/5+b**2*np.pi**8.0/50)/var,\n",
" 'S2' : (a**2/8)/var,\n",
" 'S3' : 0,\n",
" 'S12' : 0,\n",
" 'S23' : 0,\n",
" 'S13' : S13,\n",
" 'S123' : 0,\n",
" 'ST1' : S1 + S13,\n",
" 'ST2' : S2,\n",
" 'ST3' : S3 + S13\n",
" }\n",
" return exact\n",
"\n",
"Ishigami_a = 7.0\n",
"Ishigami_b = 0.1\n",
"exact = ishigamiSA(Ishigami_a, Ishigami_b)"
]
},
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"source": [
"# define a model to run the Ishigami code directly from python, expecting a dictionary and returning a dictionary\n",
"def run_ishigami_model(input):\n",
" import Ishigami\n",
" qois = [\"Ishigami\"]\n",
" del input['out_file']\n",
" return {qois[0]: Ishigami.evaluate(**input)}"
]
},
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"source": [
"# Define parameter space\n",
"def define_params():\n",
" return {\n",
" \"x1\": {\"type\": \"float\", \"min\": -np.pi, \"max\": np.pi, \"default\": 0.0},\n",
" \"x2\": {\"type\": \"float\", \"min\": -np.pi, \"max\": np.pi, \"default\": 0.0},\n",
" \"x3\": {\"type\": \"float\", \"min\": -np.pi, \"max\": np.pi, \"default\": 0.0},\n",
" \"a\": {\"type\": \"float\", \"min\": Ishigami_a, \"max\": Ishigami_a, \"default\": Ishigami_a},\n",
" \"b\": {\"type\": \"float\", \"min\": Ishigami_b, \"max\": Ishigami_b, \"default\": Ishigami_b},\n",
" \"out_file\": {\"type\": \"string\", \"default\": \"output.csv\"}\n",
" }"
]
},
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"source": [
"# Define parameter space\n",
"def define_vary():\n",
" return {\n",
" \"x1\": cp.Uniform(-np.pi, np.pi),\n",
" \"x2\": cp.Uniform(-np.pi, np.pi),\n",
" \"x3\": cp.Uniform(-np.pi, np.pi)\n",
" }"
]
},
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"execution_count": 7,
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"source": [
"# Set up and run a campaign\n",
"def run_campaign(pce_order=2, use_files=False):\n",
"\n",
" times = np.zeros(7)\n",
"\n",
" time_start = time.time()\n",
" time_start_whole = time_start\n",
"\n",
" # Set up a fresh campaign called \"Ishigami_pce.\"\n",
" my_campaign = uq.Campaign(name='Ishigami_pce.')\n",
"\n",
" # Create an encoder and decoder for PCE test app\n",
" if use_files:\n",
" encoder = uq.encoders.GenericEncoder(template_fname='Ishigami.template',\n",
" delimiter='$',\n",
" target_filename='Ishigami_in.json')\n",
"\n",
" decoder = uq.decoders.SimpleCSV(target_filename=\"output.csv\",\n",
" output_columns=[\"Ishigami\"])\n",
"\n",
" execute = uq.actions.ExecuteLocal('python3 %s/Ishigami.py Ishigami_in.json' % (os.getcwd()))\n",
"\n",
" actions = uq.actions.Actions(uq.actions.CreateRunDirectory('/tmp'), \n",
" uq.actions.Encode(encoder), execute, uq.actions.Decode(decoder))\n",
" else:\n",
" actions = uq.actions.Actions(uq.actions.ExecutePython(run_ishigami_model))\n",
"\n",
" # Add the app (automatically set as current app)\n",
" my_campaign.add_app(name=\"Ishigami\", params=define_params(), actions=actions)\n",
"\n",
" # Create the sampler\n",
" time_end = time.time()\n",
" times[1] = time_end-time_start\n",
" print('Time for phase 1 = %.3f' % (times[1]))\n",
"\n",
" time_start = time.time()\n",
" # Associate a sampler with the campaign\n",
" my_campaign.set_sampler(uq.sampling.PCESampler(vary=define_vary(), polynomial_order=pce_order))\n",
"\n",
" # Will draw all (of the finite set of samples)\n",
" my_campaign.draw_samples()\n",
" print('Number of samples = %s' % my_campaign.get_active_sampler().count)\n",
"\n",
" time_end = time.time()\n",
" times[2] = time_end-time_start\n",
" print('Time for phase 2 = %.3f' % (times[2]))\n",
"\n",
" time_start = time.time()\n",
" # Run the cases\n",
" my_campaign.execute(sequential=True).collate(progress_bar=True)\n",
"\n",
" time_end = time.time()\n",
" times[3] = time_end-time_start\n",
" print('Time for phase 3 = %.3f' % (times[3]))\n",
"\n",
" time_start = time.time()\n",
" # Get the results\n",
" results_df = my_campaign.get_collation_result()\n",
"\n",
" time_end = time.time()\n",
" times[4] = time_end-time_start\n",
" print('Time for phase 4 = %.3f' % (times[4]))\n",
"\n",
" time_start = time.time()\n",
" # Post-processing analysis\n",
" results = my_campaign.analyse(qoi_cols=[\"Ishigami\"])\n",
" \n",
" time_end = time.time()\n",
" times[5] = time_end-time_start\n",
" print('Time for phase 5 = %.3f' % (times[5]))\n",
"\n",
" time_start = time.time()\n",
" # Save the results\n",
" pickle.dump(results, open('Ishigami_results.pickle','bw'))\n",
" time_end = time.time()\n",
" times[6] = time_end-time_start\n",
" print('Time for phase 6 = %.3f' % (times[6]))\n",
"\n",
" times[0] = time_end - time_start_whole\n",
"\n",
" return results_df, results, times, pce_order, my_campaign.get_active_sampler().count"
]
},
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"scrolled": true
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 1 = 0.035\n",
"Number of samples = 8\n",
"Time for phase 2 = 0.042\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████████████████████████████| 8/8 [00:00<00:00, 2215.40it/s]\n",
"Traceback (most recent call last):\n",
" File \"/Volumes/UserData/dpc/GIT/EasyVVUQ/env_3.12/lib/python3.12/site-packages/easyvvuq/analysis/pce_analysis.py\", line 495, in analyse\n",
" dY_hat = build_surrogate_der(fit, verbose=False)\n",
" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
" File \"/Volumes/UserData/dpc/GIT/EasyVVUQ/env_3.12/lib/python3.12/site-packages/easyvvuq/analysis/pce_analysis.py\", line 347, in build_surrogate_der\n",
" assert(sum(sum(np.array(Y_hat[t].exponents))) == 0)\n",
" ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
"AssertionError\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.023\n",
"Time for phase 4 = 0.003\n",
"Time for phase 5 = 0.031\n",
"Time for phase 6 = 0.002\n",
"Time for phase 1 = 0.010\n",
"Number of samples = 27\n",
"Time for phase 2 = 0.059\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████████| 27/27 [00:00<00:00, 5205.29it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.010\n",
"Time for phase 4 = 0.002\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 5 = 0.102\n",
"Time for phase 6 = 0.001\n",
"Time for phase 1 = 0.006\n",
"Number of samples = 64\n",
"Time for phase 2 = 0.091\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████████| 64/64 [00:00<00:00, 5930.44it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.016\n",
"Time for phase 4 = 0.002\n",
"Time for phase 5 = 0.167\n",
"Time for phase 6 = 0.001\n",
"Time for phase 1 = 0.006\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of samples = 125\n",
"Time for phase 2 = 0.147\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████████████████████████| 125/125 [00:00<00:00, 6213.12it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.027\n",
"Time for phase 4 = 0.003\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 5 = 0.305\n",
"Time for phase 6 = 0.001\n",
"Time for phase 1 = 0.006\n",
"Number of samples = 216\n",
"Time for phase 2 = 0.192\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████████████████████████| 216/216 [00:00<00:00, 6028.10it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.046\n",
"Time for phase 4 = 0.006\n",
"Time for phase 5 = 0.485\n",
"Time for phase 6 = 0.001\n",
"Time for phase 1 = 0.006\n",
"Number of samples = 343\n",
"Time for phase 2 = 0.240\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████████████████████████| 343/343 [00:00<00:00, 2419.45it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.154\n",
"Time for phase 4 = 0.006\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 5 = 0.766\n",
"Time for phase 6 = 0.001\n",
"Time for phase 1 = 0.006\n",
"Number of samples = 512\n",
"Time for phase 2 = 0.319\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████████████████████████| 512/512 [00:00<00:00, 6729.86it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.093\n",
"Time for phase 4 = 0.007\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 5 = 1.293\n",
"Time for phase 6 = 0.004\n",
"Time for phase 1 = 0.007\n",
"Number of samples = 729\n",
"Time for phase 2 = 0.414\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|███████████████████████████████████████| 729/729 [00:00<00:00, 6692.38it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.131\n",
"Time for phase 4 = 0.009\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 5 = 2.202\n",
"Time for phase 6 = 0.001\n",
"Time for phase 1 = 0.007\n",
"Number of samples = 1000\n",
"Time for phase 2 = 0.561\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 1000/1000 [00:00<00:00, 6859.50it/s]"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.172\n",
"Time for phase 4 = 0.011\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 5 = 3.796\n",
"Time for phase 6 = 0.002\n",
"Time for phase 1 = 0.025\n",
"Number of samples = 1331\n",
"Time for phase 2 = 0.813\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 1331/1331 [00:00<00:00, 6505.47it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.240\n",
"Time for phase 4 = 0.015\n",
"Time for phase 5 = 6.412\n",
"Time for phase 6 = 0.002\n",
"Time for phase 1 = 0.008\n",
"Number of samples = 1728\n",
"Time for phase 2 = 0.850\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 1728/1728 [00:00<00:00, 6791.62it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.299\n",
"Time for phase 4 = 0.094\n",
"Time for phase 5 = 10.218\n",
"Time for phase 6 = 0.009\n",
"Time for phase 1 = 0.015\n",
"Number of samples = 2197\n",
"Time for phase 2 = 1.097\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 2197/2197 [00:00<00:00, 6577.30it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.396\n",
"Time for phase 4 = 0.140\n",
"Time for phase 5 = 17.613\n",
"Time for phase 6 = 0.016\n",
"Time for phase 1 = 0.011\n",
"Number of samples = 2744\n",
"Time for phase 2 = 1.335\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 2744/2744 [00:00<00:00, 6627.28it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.602\n",
"Time for phase 4 = 0.028\n",
"Time for phase 5 = 25.524\n",
"Time for phase 6 = 0.012\n",
"Time for phase 1 = 0.022\n",
"Number of samples = 3375\n",
"Time for phase 2 = 1.766\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 3375/3375 [00:00<00:00, 6642.32it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.594\n",
"Time for phase 4 = 0.099\n",
"Time for phase 5 = 38.722\n",
"Time for phase 6 = 0.005\n",
"Time for phase 1 = 0.014\n",
"Number of samples = 4096\n",
"Time for phase 2 = 2.180\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 4096/4096 [00:00<00:00, 6635.85it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.727\n",
"Time for phase 4 = 0.043\n",
"Time for phase 5 = 58.738\n",
"Time for phase 6 = 0.006\n",
"Time for phase 1 = 0.012\n",
"Number of samples = 4913\n",
"Time for phase 2 = 2.675\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 4913/4913 [00:00<00:00, 6714.53it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 0.942\n",
"Time for phase 4 = 0.047\n",
"Time for phase 5 = 85.127\n",
"Time for phase 6 = 0.005\n",
"Time for phase 1 = 0.018\n",
"Number of samples = 5832\n",
"Time for phase 2 = 3.358\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 5832/5832 [00:00<00:00, 6390.76it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 1.097\n",
"Time for phase 4 = 0.133\n",
"Time for phase 5 = 121.527\n",
"Time for phase 6 = 0.007\n",
"Time for phase 1 = 0.013\n",
"Number of samples = 6859\n",
"Time for phase 2 = 3.828\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 6859/6859 [00:01<00:00, 6721.68it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 1.287\n",
"Time for phase 4 = 0.070\n",
"Time for phase 5 = 172.143\n",
"Time for phase 6 = 0.017\n",
"Time for phase 1 = 0.033\n",
"Number of samples = 8000\n",
"Time for phase 2 = 4.975\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 8000/8000 [00:01<00:00, 6451.04it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 1.556\n",
"Time for phase 4 = 0.085\n",
"Time for phase 5 = 250.738\n",
"Time for phase 6 = 0.012\n",
"Time for phase 1 = 0.034\n",
"Number of samples = 9261\n",
"Time for phase 2 = 6.199\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████████████████████████████████| 9261/9261 [00:01<00:00, 6093.26it/s]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time for phase 3 = 1.871\n",
"Time for phase 4 = 0.099\n",
"Time for phase 5 = 340.794\n",
"Time for phase 6 = 0.015\n"
]
}
],
"source": [
"# Calculate the polynomial chaos expansion for a range of orders\n",
"\n",
"R = {}\n",
"for pce_order in range(1, 21):\n",
" R[pce_order] = {}\n",
" (R[pce_order]['results_df'], \n",
" R[pce_order]['results'], \n",
" R[pce_order]['times'], \n",
" R[pce_order]['order'], \n",
" R[pce_order]['number_of_samples']) = run_campaign(pce_order=pce_order, use_files=False)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2021-06-07T15:00:53.741252Z",
"start_time": "2021-06-07T15:00:53.565998Z"
},
"code_folding": [
0
],
"execution": {
"iopub.execute_input": "2025-07-18T11:53:51.803988Z",
"iopub.status.busy": "2025-07-18T11:53:51.803600Z",
"iopub.status.idle": "2025-07-18T11:53:51.919314Z",
"shell.execute_reply": "2025-07-18T11:53:51.918997Z",
"shell.execute_reply.started": "2025-07-18T11:53:51.803972Z"
}
},
"outputs": [],
"source": [
"# save the results\n",
"\n",
"pickle.dump(R, open('collected_results.pickle','bw'))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2021-06-07T15:00:53.767105Z",
"start_time": "2021-06-07T15:00:53.742000Z"
},
"code_folding": [
0
],
"execution": {
"iopub.execute_input": "2025-07-18T11:53:51.920136Z",
"iopub.status.busy": "2025-07-18T11:53:51.920044Z",
"iopub.status.idle": "2025-07-18T11:53:51.968542Z",
"shell.execute_reply": "2025-07-18T11:53:51.968312Z",
"shell.execute_reply.started": "2025-07-18T11:53:51.920127Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Total | \n",
" Phase 1 | \n",
" Phase 2 | \n",
" Phase 3 | \n",
" Phase 4 | \n",
" Phase 5 | \n",
" Phase 6 | \n",
"
\n",
" \n",
" \n",
" \n",
" | 1 | \n",
" 0.136015 | \n",
" 0.035234 | \n",
" 0.042051 | \n",
" 0.022817 | \n",
" 0.002804 | \n",
" 0.031306 | \n",
" 0.001599 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.183633 | \n",
" 0.009532 | \n",
" 0.059000 | \n",
" 0.009928 | \n",
" 0.002095 | \n",
" 0.102321 | \n",
" 0.000598 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.283654 | \n",
" 0.006476 | \n",
" 0.091341 | \n",
" 0.015623 | \n",
" 0.002103 | \n",
" 0.167288 | \n",
" 0.000655 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.489075 | \n",
" 0.006287 | \n",
" 0.146644 | \n",
" 0.027074 | \n",
" 0.003282 | \n",
" 0.304970 | \n",
" 0.000645 | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.734818 | \n",
" 0.006247 | \n",
" 0.191741 | \n",
" 0.045707 | \n",
" 0.005522 | \n",
" 0.484538 | \n",
" 0.000784 | \n",
"
\n",
" \n",
" | 6 | \n",
" 1.172222 | \n",
" 0.005645 | \n",
" 0.240188 | \n",
" 0.153843 | \n",
" 0.005686 | \n",
" 0.765923 | \n",
" 0.000756 | \n",
"
\n",
" \n",
" | 7 | \n",
" 1.722358 | \n",
" 0.005779 | \n",
" 0.319212 | \n",
" 0.092979 | \n",
" 0.007243 | \n",
" 1.292582 | \n",
" 0.004394 | \n",
"
\n",
" \n",
" | 8 | \n",
" 2.764593 | \n",
" 0.006714 | \n",
" 0.413856 | \n",
" 0.130983 | \n",
" 0.009136 | \n",
" 2.202459 | \n",
" 0.001216 | \n",
"
\n",
" \n",
" | 9 | \n",
" 4.548368 | \n",
" 0.007211 | \n",
" 0.560690 | \n",
" 0.171505 | \n",
" 0.010738 | \n",
" 3.795933 | \n",
" 0.001979 | \n",
"
\n",
" \n",
" | 10 | \n",
" 7.508641 | \n",
" 0.025425 | \n",
" 0.813369 | \n",
" 0.240470 | \n",
" 0.015083 | \n",
" 6.411912 | \n",
" 0.002048 | \n",
"
\n",
" \n",
" | 11 | \n",
" 11.479659 | \n",
" 0.008179 | \n",
" 0.849865 | \n",
" 0.299316 | \n",
" 0.093911 | \n",
" 10.218461 | \n",
" 0.009438 | \n",
"
\n",
" \n",
" | 12 | \n",
" 19.279597 | \n",
" 0.014593 | \n",
" 1.096601 | \n",
" 0.395720 | \n",
" 0.139500 | \n",
" 17.612834 | \n",
" 0.016208 | \n",
"
\n",
" \n",
" | 13 | \n",
" 27.512393 | \n",
" 0.011029 | \n",
" 1.335461 | \n",
" 0.601954 | \n",
" 0.027602 | \n",
" 25.524038 | \n",
" 0.011818 | \n",
"
\n",
" \n",
" | 14 | \n",
" 41.208407 | \n",
" 0.021860 | \n",
" 1.766254 | \n",
" 0.594309 | \n",
" 0.098854 | \n",
" 38.721792 | \n",
" 0.004774 | \n",
"
\n",
" \n",
" | 15 | \n",
" 61.707634 | \n",
" 0.014210 | \n",
" 2.179576 | \n",
" 0.727041 | \n",
" 0.042867 | \n",
" 58.737626 | \n",
" 0.005689 | \n",
"
\n",
" \n",
" | 16 | \n",
" 88.810914 | \n",
" 0.011573 | \n",
" 2.674999 | \n",
" 0.942351 | \n",
" 0.047150 | \n",
" 85.127170 | \n",
" 0.005375 | \n",
"
\n",
" \n",
" | 17 | \n",
" 126.140729 | \n",
" 0.018024 | \n",
" 3.357794 | \n",
" 1.096967 | \n",
" 0.133123 | \n",
" 121.527227 | \n",
" 0.007013 | \n",
"
\n",
" \n",
" | 18 | \n",
" 177.369814 | \n",
" 0.012838 | \n",
" 3.828274 | \n",
" 1.286765 | \n",
" 0.070440 | \n",
" 172.143392 | \n",
" 0.016534 | \n",
"
\n",
" \n",
" | 19 | \n",
" 257.401974 | \n",
" 0.032902 | \n",
" 4.975153 | \n",
" 1.555708 | \n",
" 0.084697 | \n",
" 250.738268 | \n",
" 0.012211 | \n",
"
\n",
" \n",
" | 20 | \n",
" 349.016879 | \n",
" 0.033758 | \n",
" 6.199063 | \n",
" 1.871499 | \n",
" 0.098941 | \n",
" 340.793901 | \n",
" 0.014523 | \n",
"
\n",
" \n",
"
\n",
"