{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"originalKey": "e23719d9-8a24-4208-8439-34e7b8270c79"
},
"source": [
"# Visualizations\n",
"\n",
"This tutorial illustrates the core visualization utilities available in Ax."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2023-08-11T15:49:12.547363Z",
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"iopub.status.idle": "2023-08-11T15:49:40.470870Z",
"shell.execute_reply": "2023-08-11T15:49:40.469918Z"
},
"executionStartTime": 1627652821316,
"executionStopTime": 1627652822868,
"hidden_ranges": [],
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"outputs": [
{
"data": {
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:39] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n"
]
},
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from ax.service.ax_client import AxClient, ObjectiveProperties\n",
"\n",
"from ax.modelbridge.cross_validation import cross_validate\n",
"from ax.plot.contour import interact_contour\n",
"from ax.plot.diagnostic import interact_cross_validation\n",
"from ax.plot.scatter import (\n",
" interact_fitted,\n",
" plot_objective_vs_constraints,\n",
" tile_fitted,\n",
")\n",
"from ax.plot.slice import plot_slice\n",
"from ax.utils.measurement.synthetic_functions import hartmann6\n",
"from ax.utils.notebook.plotting import render, init_notebook_plotting\n",
"\n",
"init_notebook_plotting()"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"hidden_ranges": [],
"originalKey": "8449378f-890e-4e76-8d73-ce2aa4120a69",
"showInput": true
},
"source": [
"## 1. Create experiment and run optimization\n",
"\n",
"The vizualizations require an experiment object and a model fit on the evaluated data. The routine below is a copy of the Service API tutorial, so the explanation here is omitted. Retrieving the experiment and model objects for each API paradigm is shown in the respective tutorials"
]
},
{
"cell_type": "markdown",
"metadata": {
"originalKey": "f7544e06-6c6a-4841-b659-3be6a198a948"
},
"source": [
"#### 1a. Define search space and evaluation function"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2023-08-11T15:49:40.602558Z",
"iopub.status.busy": "2023-08-11T15:49:40.602267Z",
"iopub.status.idle": "2023-08-11T15:49:40.606808Z",
"shell.execute_reply": "2023-08-11T15:49:40.606240Z"
},
"executionStartTime": 1627652824829,
"executionStopTime": 1627652824877,
"hidden_ranges": [],
"originalKey": "28f6cb76-828f-445d-bdda-ba057c87dcd0",
"requestMsgId": "7495e7e2-1025-4292-b3aa-e953739cef3e"
},
"outputs": [],
"source": [
"noise_sd = 0.1\n",
"param_names = [f\"x{i+1}\" for i in range(6)] # x1, x2, ..., x6\n",
"\n",
"\n",
"def noisy_hartmann_evaluation_function(parameterization):\n",
" x = np.array([parameterization.get(p_name) for p_name in param_names])\n",
" noise1, noise2 = np.random.normal(0, noise_sd, 2)\n",
"\n",
" return {\n",
" \"hartmann6\": (hartmann6(x) + noise1, noise_sd),\n",
" \"l2norm\": (np.sqrt((x**2).sum()) + noise2, noise_sd),\n",
" }"
]
},
{
"cell_type": "markdown",
"metadata": {
"originalKey": "17a51543-298e-47d4-bcd9-33459fe1169e"
},
"source": [
"#### 1b. Create Experiment"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2023-08-11T15:49:40.609703Z",
"iopub.status.busy": "2023-08-11T15:49:40.609460Z",
"iopub.status.idle": "2023-08-11T15:49:40.620448Z",
"shell.execute_reply": "2023-08-11T15:49:40.619742Z"
},
"executionStartTime": 1627654956712,
"executionStopTime": 1627654956823,
"hidden_ranges": [],
"originalKey": "6fca889c-a4ff-42ef-a669-6eb8803de89c",
"requestMsgId": "905eff52-e649-4bd5-abf0-ff69c1549852"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 6 decimal points.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x1. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x1', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x2', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x3', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x4', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x5', parameter_type=FLOAT, range=[0.0, 1.0]), RangeParameter(name='x6', parameter_type=FLOAT, range=[0.0, 1.0])], parameter_constraints=[]).\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.modelbridge.dispatch_utils: Using Models.GPEI since there are more ordered parameters than there are categories for the unordered categorical parameters.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=6 num_trials=None use_batch_trials=False\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 12 trials, GPEI for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.\n"
]
}
],
"source": [
"ax_client = AxClient()\n",
"ax_client.create_experiment(\n",
" name=\"test_visualizations\",\n",
" parameters=[\n",
" {\n",
" \"name\": p_name,\n",
" \"type\": \"range\",\n",
" \"bounds\": [0.0, 1.0],\n",
" }\n",
" for p_name in param_names\n",
" ],\n",
" objectives={\"hartmann6\": ObjectiveProperties(minimize=True)},\n",
" outcome_constraints=[\"l2norm <= 1.25\"],\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {
"code_folding": [],
"hidden_ranges": [],
"originalKey": "ab892f7c-4830-4c1d-b476-ec1078ec3faf",
"showInput": false
},
"source": [
"#### 1c. Run the optimization and fit a GP on all data"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2023-08-11T15:49:40.626214Z",
"iopub.status.busy": "2023-08-11T15:49:40.625969Z",
"iopub.status.idle": "2023-08-11T15:51:49.754722Z",
"shell.execute_reply": "2023-08-11T15:51:49.753929Z"
},
"executionStartTime": 1627654642967,
"executionStopTime": 1627654862819,
"hidden_ranges": [],
"originalKey": "7269a5ba-45c8-4acf-ac83-a5ea8a52d6c1",
"requestMsgId": "c7a4dea8-fd6d-4e1a-84de-ad973ede0cd7"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.959061, 'x2': 0.421097, 'x3': 0.693045, 'x4': 0.394199, 'x5': 0.937822, 'x6': 0.651645}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (0.040888, 0.1), 'l2norm': (1.849496, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.442236, 'x2': 0.450873, 'x3': 0.061154, 'x4': 0.802372, 'x5': 0.223707, 'x6': 0.536141}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.055425, 0.1), 'l2norm': (1.12866, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.921714, 'x2': 0.006742, 'x3': 0.18159, 'x4': 0.41122, 'x5': 0.030623, 'x6': 0.600647}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.241457, 0.1), 'l2norm': (1.189034, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.404707, 'x2': 0.802856, 'x3': 0.487908, 'x4': 0.594826, 'x5': 0.447605, 'x6': 0.076676}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-2.941819, 0.1), 'l2norm': (1.283768, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.295047, 'x2': 0.488927, 'x3': 0.894945, 'x4': 0.382528, 'x5': 0.480947, 'x6': 0.079408}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.453999, 0.1), 'l2norm': (1.266909, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.3332, 'x2': 0.885637, 'x3': 0.073471, 'x4': 0.077522, 'x5': 0.867887, 'x6': 0.965997}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (0.014857, 0.1), 'l2norm': (1.672911, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.695888, 'x2': 0.819337, 'x3': 0.838895, 'x4': 0.155663, 'x5': 0.83838, 'x6': 0.954818}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (0.082659, 0.1), 'l2norm': (1.96107, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.258997, 'x2': 0.964524, 'x3': 0.560169, 'x4': 0.060604, 'x5': 0.905849, 'x6': 0.262307}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.292789, 0.1), 'l2norm': (1.485219, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.539608, 'x2': 0.013607, 'x3': 0.39022, 'x4': 0.540406, 'x5': 0.894388, 'x6': 0.614211}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.007765, 0.1), 'l2norm': (1.32753, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.15475, 'x2': 0.417481, 'x3': 0.271358, 'x4': 0.50263, 'x5': 0.94393, 'x6': 0.379732}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.376055, 0.1), 'l2norm': (1.170875, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.531038, 'x2': 0.995568, 'x3': 0.926524, 'x4': 0.966679, 'x5': 0.272159, 'x6': 0.307865}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.311272, 0.1), 'l2norm': (1.893716, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.86786, 'x2': 0.608454, 'x3': 0.655593, 'x4': 0.127577, 'x5': 0.611836, 'x6': 0.9546}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:40] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.098855, 0.1), 'l2norm': (1.673908, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:50] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.319713, 'x2': 0.677944, 'x3': 0.445753, 'x4': 0.553277, 'x5': 0.490442, 'x6': 0.112938}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:49:50] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.7292, 0.1), 'l2norm': (1.085585, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:50:13] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.331355, 'x2': 0.778461, 'x3': 0.43235, 'x4': 0.543415, 'x5': 0.480897, 'x6': 0.091974}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:50:13] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-2.481291, 0.1), 'l2norm': (1.288739, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:50:34] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.441385, 'x2': 0.749986, 'x3': 0.411011, 'x4': 0.626722, 'x5': 0.450572, 'x6': 0.085772}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:50:34] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-2.497182, 0.1), 'l2norm': (1.267041, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:50:55] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.323854, 'x2': 0.766789, 'x3': 0.525732, 'x4': 0.613687, 'x5': 0.439902, 'x6': 0.068391}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:50:55] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-2.528026, 0.1), 'l2norm': (1.048959, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:14] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.354954, 'x2': 0.82938, 'x3': 0.486524, 'x4': 0.612547, 'x5': 0.445268, 'x6': 0.020166}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:14] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.897653, 0.1), 'l2norm': (1.033244, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:24] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.399697, 'x2': 0.85098, 'x3': 0.479693, 'x4': 0.593301, 'x5': 0.410735, 'x6': 0.040845}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:24] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-3.136699, 0.1), 'l2norm': (1.140757, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:36] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.44363, 'x2': 0.88217, 'x3': 0.520244, 'x4': 0.578702, 'x5': 0.449428, 'x6': 0.02675}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:36] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.861125, 0.1), 'l2norm': (1.419748, 0.1)}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:49] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.376834, 'x2': 0.864701, 'x3': 0.449668, 'x4': 0.6294, 'x5': 0.38359, 'x6': 0.074089}.\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:49] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.967483, 0.1), 'l2norm': (1.262153, 0.1)}.\n"
]
}
],
"source": [
"for i in range(20):\n",
" parameters, trial_index = ax_client.get_next_trial()\n",
" # Local evaluation here can be replaced with deployment to external system.\n",
" ax_client.complete_trial(\n",
" trial_index=trial_index, raw_data=noisy_hartmann_evaluation_function(parameters)\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {
"originalKey": "72f4d3e7-fa04-43d0-8451-ded292e705df"
},
"source": [
"## 2. Contour plots\n",
"\n",
"The plot below shows the response surface for `hartmann6` metric as a function of the `x1`, `x2` parameters.\n",
"\n",
"The other parameters are fixed in the middle of their respective ranges, which in this example is 0.5 for all of them."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"code_folding": [],
"execution": {
"iopub.execute_input": "2023-08-11T15:51:49.758619Z",
"iopub.status.busy": "2023-08-11T15:51:49.758339Z",
"iopub.status.idle": "2023-08-11T15:51:51.732145Z",
"shell.execute_reply": "2023-08-11T15:51:51.731263Z"
},
"executionStartTime": 1627654870209,
"executionStopTime": 1627654871972,
"hidden_ranges": [],
"originalKey": "843df85c-965d-4a83-9fe1-696225d81c0f",
"requestMsgId": "4a643541-867c-46b6-868d-64337920c2a3"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[INFO 08-11 11:51:49] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n"
]
},
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hartmann6: 0.0408881 (SEM: 0.1)
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hartmann6: -0.0988553 (SEM: 0.1)
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hartmann6: -2.48129 (SEM: 0.1)
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hartmann6: -2.49718 (SEM: 0.1)
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hartmann6: -2.52803 (SEM: 0.1)
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hartmann6: -2.89765 (SEM: 0.1)
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hartmann6: -3.1367 (SEM: 0.1)
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hartmann6: -2.86112 (SEM: 0.1)
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hartmann6: -0.0554249 (SEM: 0.1)
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hartmann6: -0.241457 (SEM: 0.1)
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hartmann6: -2.94182 (SEM: 0.1)
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x4: 0.594826
x5: 0.447605
x6: 0.0766765",
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hartmann6: -0.453999 (SEM: 0.1)
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x6: 0.0794081",
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hartmann6: 0.0148572 (SEM: 0.1)
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x6: 0.965997",
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hartmann6: 0.0826586 (SEM: 0.1)
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x3: 0.838895
x4: 0.155663
x5: 0.83838
x6: 0.954818",
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hartmann6: -0.292789 (SEM: 0.1)
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x3: 0.560169
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x5: 0.905849
x6: 0.262307",
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hartmann6: -0.0077648 (SEM: 0.1)
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x2: 0.0136075
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x4: 0.540406
x5: 0.894388
x6: 0.614211",
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hartmann6: -0.376055 (SEM: 0.1)
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x2: 0.417481
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hartmann6: 0.0408881 (SEM: 0.1)
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hartmann6: -2.48129 (SEM: 0.1)
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hartmann6: -2.89765 (SEM: 0.1)
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hartmann6: -3.1367 (SEM: 0.1)
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x2: 0.85098
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x6: 0.0408445",
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hartmann6: -2.86112 (SEM: 0.1)
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x4: 0.578702
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x6: 0.0267496",
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hartmann6: -0.0554249 (SEM: 0.1)
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hartmann6: -0.241457 (SEM: 0.1)
x1: 0.921714
x2: 0.00674208
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x4: 0.41122
x5: 0.0306228
x6: 0.600647",
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hartmann6: -2.94182 (SEM: 0.1)
x1: 0.404707
x2: 0.802856
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x4: 0.594826
x5: 0.447605
x6: 0.0766765",
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hartmann6: -0.453999 (SEM: 0.1)
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x2: 0.488927
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x6: 0.0794081",
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hartmann6: 0.0148572 (SEM: 0.1)
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"# this could alternately be done with `ax.plot.contour.plot_contour`\n",
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},
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"Arm 0_0
hartmann6: 0.0408881 (SEM: 0.1)
x1: 0.959061
x2: 0.421097
x3: 0.693045
x4: 0.394199
x5: 0.937822
x6: 0.651645",
"Arm 10_0
hartmann6: -0.311272 (SEM: 0.1)
x1: 0.531038
x2: 0.995568
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hartmann6: 0.0408881 (SEM: 0.1)
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hartmann6: 0.0148572 (SEM: 0.1)
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hartmann6: 0.0408881 (SEM: 0.1)
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"Arm 0_0
hartmann6: 0.0408881 (SEM: 0.1)
x1: 0.959061
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x6: 0.307865",
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x6: 0.9546",
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hartmann6: -1.7292 (SEM: 0.1)
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hartmann6: -2.48129 (SEM: 0.1)
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x6: 0.0857722",
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hartmann6: -2.52803 (SEM: 0.1)
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hartmann6: -2.89765 (SEM: 0.1)
x1: 0.354954
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x5: 0.445268
x6: 0.0201658",
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hartmann6: -3.1367 (SEM: 0.1)
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x6: 0.0408445",
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hartmann6: -2.86112 (SEM: 0.1)
x1: 0.44363
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x5: 0.449428
x6: 0.0267496",
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hartmann6: -0.0554249 (SEM: 0.1)
x1: 0.442236
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x5: 0.223707
x6: 0.536141",
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hartmann6: 0.0408881 (SEM: 0.1)
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hartmann6: 0.0408881 (SEM: 0.1)
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hartmann6: -2.94182 (SEM: 0.1)
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