{ "cells": [ { "cell_type": "markdown", "id": "602bffa0", "metadata": { "papermill": { "duration": 0.005726, "end_time": "2024-07-23T19:30:56.673064", "exception": false, "start_time": "2024-07-23T19:30:56.667338", "status": "completed" }, "tags": [] }, "source": [ "# Service API Example on Hartmann6\n", "\n", "The Ax Service API is designed to allow the user to control scheduling of trials and data computation while having an easy to use interface with Ax.\n", "\n", "The user iteratively:\n", "- Queries Ax for candidates\n", "- Schedules / deploys them however they choose\n", "- Computes data and logs to Ax\n", "- Repeat" ] }, { "cell_type": "code", "execution_count": 1, "id": "a2caf294", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:30:56.685833Z", "iopub.status.busy": "2024-07-23T19:30:56.685362Z", "iopub.status.idle": "2024-07-23T19:31:00.477570Z", "shell.execute_reply": "2024-07-23T19:31:00.476813Z" }, "papermill": { "duration": 3.841268, "end_time": "2024-07-23T19:31:00.519542", "exception": false, "start_time": "2024-07-23T19:30:56.678274", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.utils.notebook.plotting: Please see\n", " (https://ax.dev/tutorials/visualizations.html#Fix-for-plots-that-are-not-rendering)\n", " if visualizations are not rendering.\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ax.service.ax_client import AxClient, ObjectiveProperties\n", "from ax.utils.measurement.synthetic_functions import hartmann6\n", "from ax.utils.notebook.plotting import init_notebook_plotting, render\n", "\n", "init_notebook_plotting()" ] }, { "cell_type": "markdown", "id": "1580c375", "metadata": { "papermill": { "duration": 0.038597, "end_time": "2024-07-23T19:31:00.595632", "exception": false, "start_time": "2024-07-23T19:31:00.557035", "status": "completed" }, "tags": [] }, "source": [ "## 1. Initialize client\n", "\n", "Create a client object to interface with Ax APIs. By default this runs locally without storage." ] }, { "cell_type": "code", "execution_count": 2, "id": "5f03ae21", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:31:00.676942Z", "iopub.status.busy": "2024-07-23T19:31:00.676445Z", "iopub.status.idle": "2024-07-23T19:31:00.680707Z", "shell.execute_reply": "2024-07-23T19:31:00.680016Z" }, "papermill": { "duration": 0.046527, "end_time": "2024-07-23T19:31:00.682085", "exception": false, "start_time": "2024-07-23T19:31:00.635558", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] 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" ] } ], "source": [ "ax_client = AxClient()" ] }, { "cell_type": "markdown", "id": "0f041693", "metadata": { "papermill": { "duration": 0.040222, "end_time": "2024-07-23T19:31:00.763753", "exception": false, "start_time": "2024-07-23T19:31:00.723531", "status": "completed" }, "tags": [] }, "source": [ "## 2. Set up experiment\n", "An experiment consists of a **search space** (parameters and parameter constraints) and **optimization configuration** (objectives and outcome constraints). Note that:\n", "- Only `parameters`, and `objectives` arguments are required.\n", "- Dictionaries in `parameters` have the following required keys: \"name\" - parameter name, \"type\" - parameter type (\"range\", \"choice\" or \"fixed\"), \"bounds\" for range parameters, \"values\" for choice parameters, and \"value\" for fixed parameters.\n", "- Dictionaries in `parameters` can optionally include \"value_type\" (\"int\", \"float\", \"bool\" or \"str\"), \"log_scale\" flag for range parameters, and \"is_ordered\" flag for choice parameters.\n", "- `parameter_constraints` should be a list of strings of form \"p1 >= p2\" or \"p1 + p2 <= some_bound\".\n", "- `outcome_constraints` should be a list of strings of form \"constrained_metric <= some_bound\"." ] }, { "cell_type": "code", "execution_count": 3, "id": "a8ae7543", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:31:00.846054Z", "iopub.status.busy": "2024-07-23T19:31:00.845550Z", "iopub.status.idle": "2024-07-23T19:31:00.861343Z", "shell.execute_reply": "2024-07-23T19:31:00.860739Z" }, "papermill": { "duration": 0.058878, "end_time": "2024-07-23T19:31:00.862678", "exception": false, "start_time": "2024-07-23T19:31:00.803800", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] 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=[ParameterConstraint(1.0*x1 + 1.0*x2 <= 2.0)]).\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR since there is at least one ordered parameter and there are no unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] 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 07-23 19:31:00] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=12\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=12\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.modelbridge.dispatch_utils: `verbose`, `disable_progbar`, and `jit_compile` are not yet supported when using `choose_generation_strategy` with ModularBoTorchModel, dropping these arguments.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:00] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 12 trials, BoTorch for subsequent trials]). Iterations after 12 will take longer to generate due to model-fitting.\n" ] } ], "source": [ "ax_client.create_experiment(\n", " name=\"hartmann_test_experiment\",\n", " parameters=[\n", " {\n", " \"name\": \"x1\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " \"value_type\": \"float\", # Optional, defaults to inference from type of \"bounds\".\n", " \"log_scale\": False, # Optional, defaults to False.\n", " },\n", " {\n", " \"name\": \"x2\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " },\n", " {\n", " \"name\": \"x3\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " },\n", " {\n", " \"name\": \"x4\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " },\n", " {\n", " \"name\": \"x5\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " },\n", " {\n", " \"name\": \"x6\",\n", " \"type\": \"range\",\n", " \"bounds\": [0.0, 1.0],\n", " },\n", " ],\n", " objectives={\"hartmann6\": ObjectiveProperties(minimize=True)},\n", " parameter_constraints=[\"x1 + x2 <= 2.0\"], # Optional.\n", " outcome_constraints=[\"l2norm <= 1.25\"], # Optional.\n", ")" ] }, { "cell_type": "markdown", "id": "04a3ee24", "metadata": { "papermill": { "duration": 0.040578, "end_time": "2024-07-23T19:31:00.944391", "exception": false, "start_time": "2024-07-23T19:31:00.903813", "status": "completed" }, "tags": [] }, "source": [ "## 3. Define how to evaluate trials\n", "When using Ax a service, evaluation of parameterizations suggested by Ax is done either locally or, more commonly, using an external scheduler. Below is a dummy evaluation function that outputs data for two metrics \"hartmann6\" and \"l2norm\". Note that all returned metrics correspond to either the `objectives` set on experiment creation or the metric names mentioned in `outcome_constraints`." ] }, { "cell_type": "code", "execution_count": 4, "id": "acac72da", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:31:01.027471Z", "iopub.status.busy": "2024-07-23T19:31:01.027194Z", "iopub.status.idle": "2024-07-23T19:31:01.031487Z", "shell.execute_reply": "2024-07-23T19:31:01.030808Z" }, "papermill": { "duration": 0.047711, "end_time": "2024-07-23T19:31:01.033097", "exception": false, "start_time": "2024-07-23T19:31:00.985386", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "\n", "\n", "def evaluate(parameterization):\n", " x = np.array([parameterization.get(f\"x{i+1}\") for i in range(6)])\n", " # In our case, standard error is 0, since we are computing a synthetic function.\n", " return {\"hartmann6\": (hartmann6(x), 0.0), \"l2norm\": (np.sqrt((x**2).sum()), 0.0)}" ] }, { "cell_type": "markdown", "id": "d6177dfa", "metadata": { "papermill": { "duration": 0.040542, "end_time": "2024-07-23T19:31:01.114881", "exception": false, "start_time": "2024-07-23T19:31:01.074339", "status": "completed" }, "tags": [] }, "source": [ "Result of the evaluation should generally be a mapping of the format: `{metric_name -> (mean, SEM)}`. If there is only one metric in the experiment – the objective – then evaluation function can return a single tuple of mean and SEM, in which case Ax will assume that evaluation corresponds to the objective. _It can also return only the mean as a float, in which case Ax will treat SEM as unknown and use a model that can infer it._ \n", "\n", "For more details on evaluation function, refer to the \"Trial Evaluation\" section in the Ax docs at [ax.dev](https://ax.dev/)" ] }, { "cell_type": "markdown", "id": "390b459b", "metadata": { "papermill": { "duration": 0.040664, "end_time": "2024-07-23T19:31:01.196127", "exception": false, "start_time": "2024-07-23T19:31:01.155463", "status": "completed" }, "tags": [] }, "source": [ "## 4. Run optimization loop\n", "With the experiment set up, we can start the optimization loop.\n", "\n", "At each step, the user queries the client for a new trial then submits the evaluation of that trial back to the client.\n", "\n", "Note that Ax auto-selects an appropriate optimization algorithm based on the search space. For more advance use cases that require a specific optimization algorithm, pass a `generation_strategy` argument into the `AxClient` constructor. Note that when Bayesian Optimization is used, generating new trials may take a few minutes." ] }, { "cell_type": "code", "execution_count": 5, "id": "27389154", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:31:01.278745Z", "iopub.status.busy": "2024-07-23T19:31:01.278161Z", "iopub.status.idle": "2024-07-23T19:32:44.676226Z", "shell.execute_reply": "2024-07-23T19:32:44.675561Z" }, "papermill": { "duration": 103.481089, "end_time": "2024-07-23T19:32:44.717701", "exception": false, "start_time": "2024-07-23T19:31:01.236612", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.733035, 'x2': 0.061008, 'x3': 0.085204, 'x4': 0.258361, 'x5': 0.114038, 'x6': 0.912911} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.402366, 0.0), 'l2norm': (1.208919, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.233727, 'x2': 0.841503, 'x3': 0.992144, 'x4': 0.91822, 'x5': 0.325854, 'x6': 0.309757} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.210452, 0.0), 'l2norm': (1.671036, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.456063, 'x2': 0.695674, 'x3': 0.762829, 'x4': 0.096171, 'x5': 0.281806, 'x6': 0.548972} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.485291, 0.0), 'l2norm': (1.289921, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.49945, 'x2': 0.156111, 'x3': 0.601239, 'x4': 0.157366, 'x5': 0.546349, 'x6': 0.805099} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.752704, 0.0), 'l2norm': (1.267579, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.326059, 'x2': 0.691856, 'x3': 0.229641, 'x4': 0.615605, 'x5': 0.919577, 'x6': 0.722951} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.014943, 0.0), 'l2norm': (1.544333, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.155288, 'x2': 0.887927, 'x3': 0.479935, 'x4': 0.805947, 'x5': 0.480473, 'x6': 0.114611} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.590213, 0.0), 'l2norm': (1.391548, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.247413, 'x2': 0.374861, 'x3': 0.069967, 'x4': 0.300832, 'x5': 0.543381, 'x6': 0.387147} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.47322, 0.0), 'l2norm': (0.861554, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.864984, 'x2': 0.079029, 'x3': 0.852291, 'x4': 0.765624, 'x5': 0.656406, 'x6': 0.724577} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.018271, 0.0), 'l2norm': (1.73865, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.254324, 'x2': 0.865416, 'x3': 0.799209, 'x4': 0.30456, 'x5': 0.899295, 'x6': 0.789859} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.04103, 0.0), 'l2norm': (1.725609, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.71055, 'x2': 0.782865, 'x3': 0.495047, 'x4': 0.153398, 'x5': 0.43716, 'x6': 0.706623} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.228334, 0.0), 'l2norm': (1.441107, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.600564, 'x2': 0.223024, 'x3': 0.091437, 'x4': 0.172231, 'x5': 0.313197, 'x6': 0.878329} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-1.063117, 0.0), 'l2norm': (1.14804, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/tmp.DL1QmpHQMI/Ax-main/ax/modelbridge/cross_validation.py:462: UserWarning:\n", "\n", "Encountered exception in computing model fit quality: RandomModelBridge does not support prediction.\n", "\n", "[INFO 07-23 19:31:01] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.364004, 'x2': 0.632958, 'x3': 0.24173, 'x4': 0.064652, 'x5': 0.511712, 'x6': 0.96865} using model Sobol.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:01] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.185426, 0.0), 'l2norm': (1.340104, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:10] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.541585, 'x2': 0.229734, 'x3': 0.15374, 'x4': 0.148959, 'x5': 0.385234, 'x6': 0.829596} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:10] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.230183, 0.0), 'l2norm': (1.1084, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:21] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.509567, 'x2': 0.207489, 'x3': 0.147193, 'x4': 0.070599, 'x5': 0.416679, 'x6': 0.785515} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:21] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.991403, 0.0), 'l2norm': (1.058307, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:27] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.518235, 'x2': 0.241577, 'x3': 0.200845, 'x4': 0.198987, 'x5': 0.417275, 'x6': 0.810633} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:27] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.390494, 0.0), 'l2norm': (1.112702, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:39] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.500609, 'x2': 0.26813, 'x3': 0.240861, 'x4': 0.247939, 'x5': 0.432561, 'x6': 0.838201} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:39] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.339179, 0.0), 'l2norm': (1.153985, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:47] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.550035, 'x2': 0.234856, 'x3': 0.206317, 'x4': 0.235548, 'x5': 0.442526, 'x6': 0.746864} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:47] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-1.404885, 0.0), 'l2norm': (1.099719, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:56] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.484511, 'x2': 0.22823, 'x3': 0.237, 'x4': 0.232679, 'x5': 0.384916, 'x6': 0.744099} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:31:56] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-1.988194, 0.0), 'l2norm': (1.048328, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:03] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.449918, 'x2': 0.214364, 'x3': 0.27629, 'x4': 0.271086, 'x5': 0.349526, 'x6': 0.70665} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:03] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.462304, 0.0), 'l2norm': (1.009814, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:10] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.414782, 'x2': 0.194756, 'x3': 0.314423, 'x4': 0.307907, 'x5': 0.311877, 'x6': 0.667367} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:10] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.754006, 0.0), 'l2norm': (0.972773, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:17] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.386351, 'x2': 0.212861, 'x3': 0.336375, 'x4': 0.311148, 'x5': 0.266056, 'x6': 0.632334} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:17] ax.service.ax_client: Completed trial 20 with data: {'hartmann6': (-2.746062, 0.0), 'l2norm': (0.935505, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:24] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.366382, 'x2': 0.146103, 'x3': 0.311708, 'x4': 0.335777, 'x5': 0.286141, 'x6': 0.655994} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:24] ax.service.ax_client: Completed trial 21 with data: {'hartmann6': (-2.843734, 0.0), 'l2norm': (0.936853, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:30] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.374518, 'x2': 0.096585, 'x3': 0.38366, 'x4': 0.296887, 'x5': 0.285061, 'x6': 0.65271} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:30] ax.service.ax_client: Completed trial 22 with data: {'hartmann6': (-2.924111, 0.0), 'l2norm': (0.944574, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:37] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.410246, 'x2': 0.054589, 'x3': 0.352164, 'x4': 0.310357, 'x5': 0.285893, 'x6': 0.592927} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:37] ax.service.ax_client: Completed trial 23 with data: {'hartmann6': (-2.619011, 0.0), 'l2norm': (0.908251, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:44] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.338156, 'x2': 0.123572, 'x3': 0.417111, 'x4': 0.301426, 'x5': 0.275234, 'x6': 0.697481} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:44] ax.service.ax_client: Completed trial 24 with data: {'hartmann6': (-3.002776, 0.0), 'l2norm': (0.978107, 0.0)}.\n" ] } ], "source": [ "for i in range(25):\n", " parameterization, trial_index = ax_client.get_next_trial()\n", " # Local evaluation here can be replaced with deployment to external system.\n", " ax_client.complete_trial(trial_index=trial_index, raw_data=evaluate(parameterization))" ] }, { "cell_type": "markdown", "id": "d5a69dd8", "metadata": { "papermill": { "duration": 0.043015, "end_time": "2024-07-23T19:32:44.803701", "exception": false, "start_time": "2024-07-23T19:32:44.760686", "status": "completed" }, "tags": [] }, "source": [ "### How many trials can run in parallel?\n", "By default, Ax restricts number of trials that can run in parallel for some optimization stages, in order to improve the optimization performance and reduce the number of trials that the optimization will require. To check the maximum parallelism for each optimization stage:" ] }, { "cell_type": "code", "execution_count": 6, "id": "c468b8c6", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:44.892013Z", "iopub.status.busy": "2024-07-23T19:32:44.891348Z", "iopub.status.idle": "2024-07-23T19:32:44.898246Z", "shell.execute_reply": "2024-07-23T19:32:44.897654Z" }, "papermill": { "duration": 0.052302, "end_time": "2024-07-23T19:32:44.899568", "exception": false, "start_time": "2024-07-23T19:32:44.847266", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[(12, 12), (-1, 3)]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.get_max_parallelism()" ] }, { "cell_type": "markdown", "id": "ab985c69", "metadata": { "papermill": { "duration": 0.042723, "end_time": "2024-07-23T19:32:44.985313", "exception": false, "start_time": "2024-07-23T19:32:44.942590", "status": "completed" }, "tags": [] }, "source": [ "The output of this function is a list of tuples of form (number of trials, max parallelism), so the example above means \"the max parallelism is 12 for the first 12 trials and 3 for all subsequent trials.\" This is because the first 12 trials are produced quasi-randomly and can all be evaluated at once, and subsequent trials are produced via Bayesian optimization, which converges on optimal point in fewer trials when parallelism is limited. `MaxParallelismReachedException` indicates that the parallelism limit has been reached –– refer to the 'Service API Exceptions Meaning and Handling' section at the end of the tutorial for handling." ] }, { "cell_type": "markdown", "id": "371bf6db", "metadata": { "papermill": { "duration": 0.042997, "end_time": "2024-07-23T19:32:45.071652", "exception": false, "start_time": "2024-07-23T19:32:45.028655", "status": "completed" }, "tags": [] }, "source": [ "### How to view all existing trials during optimization?" ] }, { "cell_type": "code", "execution_count": 7, "id": "9d981622", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:45.159234Z", "iopub.status.busy": "2024-07-23T19:32:45.158696Z", "iopub.status.idle": "2024-07-23T19:32:45.187870Z", "shell.execute_reply": "2024-07-23T19:32:45.187304Z" }, "papermill": { "duration": 0.074601, "end_time": "2024-07-23T19:32:45.189270", "exception": false, "start_time": "2024-07-23T19:32:45.114669", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:45] ax.modelbridge.generation_strategy: Note that parameter values in dataframe are rounded to 2 decimal points; the values in the dataframe are thus not the exact ones suggested by Ax in trials.\n" ] }, { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Generation StepGeneration Model(s)Trial IndexTrial StatusArm Parameterizations
0[GenerationStep_0][Sobol]0COMPLETED{'0_0': {'x1': 0.73, 'x2': 0.06, 'x3': 0.09, '...
1[GenerationStep_0][Sobol]1COMPLETED{'1_0': {'x1': 0.23, 'x2': 0.84, 'x3': 0.99, '...
2[GenerationStep_0][Sobol]2COMPLETED{'2_0': {'x1': 0.46, 'x2': 0.7, 'x3': 0.76, 'x...
3[GenerationStep_0][Sobol]3COMPLETED{'3_0': {'x1': 0.5, 'x2': 0.16, 'x3': 0.6, 'x4...
4[GenerationStep_0][Sobol]4COMPLETED{'4_0': {'x1': 0.33, 'x2': 0.69, 'x3': 0.23, '...
5[GenerationStep_0][Sobol]5COMPLETED{'5_0': {'x1': 0.16, 'x2': 0.89, 'x3': 0.48, '...
6[GenerationStep_0][Sobol]6COMPLETED{'6_0': {'x1': 0.25, 'x2': 0.37, 'x3': 0.07, '...
7[GenerationStep_0][Sobol]7COMPLETED{'7_0': {'x1': 0.86, 'x2': 0.08, 'x3': 0.85, '...
8[GenerationStep_0][Sobol]8COMPLETED{'8_0': {'x1': 0.25, 'x2': 0.87, 'x3': 0.8, 'x...
9[GenerationStep_0][Sobol]9COMPLETED{'9_0': {'x1': 0.71, 'x2': 0.78, 'x3': 0.5, 'x...
10[GenerationStep_0][Sobol]10COMPLETED{'10_0': {'x1': 0.6, 'x2': 0.22, 'x3': 0.09, '...
11[GenerationStep_0][Sobol]11COMPLETED{'11_0': {'x1': 0.36, 'x2': 0.63, 'x3': 0.24, ...
12[GenerationStep_1][BoTorch]12COMPLETED{'12_0': {'x1': 0.54, 'x2': 0.23, 'x3': 0.15, ...
13[GenerationStep_1][BoTorch]13COMPLETED{'13_0': {'x1': 0.51, 'x2': 0.21, 'x3': 0.15, ...
14[GenerationStep_1][BoTorch]14COMPLETED{'14_0': {'x1': 0.52, 'x2': 0.24, 'x3': 0.2, '...
15[GenerationStep_1][BoTorch]15COMPLETED{'15_0': {'x1': 0.5, 'x2': 0.27, 'x3': 0.24, '...
16[GenerationStep_1][BoTorch]16COMPLETED{'16_0': {'x1': 0.55, 'x2': 0.23, 'x3': 0.21, ...
17[GenerationStep_1][BoTorch]17COMPLETED{'17_0': {'x1': 0.48, 'x2': 0.23, 'x3': 0.24, ...
18[GenerationStep_1][BoTorch]18COMPLETED{'18_0': {'x1': 0.45, 'x2': 0.21, 'x3': 0.28, ...
19[GenerationStep_1][BoTorch]19COMPLETED{'19_0': {'x1': 0.41, 'x2': 0.19, 'x3': 0.31, ...
20[GenerationStep_1][BoTorch]20COMPLETED{'20_0': {'x1': 0.39, 'x2': 0.21, 'x3': 0.34, ...
21[GenerationStep_1][BoTorch]21COMPLETED{'21_0': {'x1': 0.37, 'x2': 0.15, 'x3': 0.31, ...
22[GenerationStep_1][BoTorch]22COMPLETED{'22_0': {'x1': 0.37, 'x2': 0.1, 'x3': 0.38, '...
23[GenerationStep_1][BoTorch]23COMPLETED{'23_0': {'x1': 0.41, 'x2': 0.05, 'x3': 0.35, ...
24[GenerationStep_1][BoTorch]24COMPLETED{'24_0': {'x1': 0.34, 'x2': 0.12, 'x3': 0.42, ...
\n", "
" ], "text/plain": [ " Generation Step Generation Model(s) Trial Index Trial Status \\\n", "0 [GenerationStep_0] [Sobol] 0 COMPLETED \n", "1 [GenerationStep_0] [Sobol] 1 COMPLETED \n", "2 [GenerationStep_0] [Sobol] 2 COMPLETED \n", "3 [GenerationStep_0] [Sobol] 3 COMPLETED \n", "4 [GenerationStep_0] [Sobol] 4 COMPLETED \n", "5 [GenerationStep_0] [Sobol] 5 COMPLETED \n", "6 [GenerationStep_0] [Sobol] 6 COMPLETED \n", "7 [GenerationStep_0] [Sobol] 7 COMPLETED \n", "8 [GenerationStep_0] [Sobol] 8 COMPLETED \n", "9 [GenerationStep_0] [Sobol] 9 COMPLETED \n", "10 [GenerationStep_0] [Sobol] 10 COMPLETED \n", "11 [GenerationStep_0] [Sobol] 11 COMPLETED \n", "12 [GenerationStep_1] [BoTorch] 12 COMPLETED \n", "13 [GenerationStep_1] [BoTorch] 13 COMPLETED \n", "14 [GenerationStep_1] [BoTorch] 14 COMPLETED \n", "15 [GenerationStep_1] [BoTorch] 15 COMPLETED \n", "16 [GenerationStep_1] [BoTorch] 16 COMPLETED \n", "17 [GenerationStep_1] [BoTorch] 17 COMPLETED \n", "18 [GenerationStep_1] [BoTorch] 18 COMPLETED \n", "19 [GenerationStep_1] [BoTorch] 19 COMPLETED \n", "20 [GenerationStep_1] [BoTorch] 20 COMPLETED \n", "21 [GenerationStep_1] [BoTorch] 21 COMPLETED \n", "22 [GenerationStep_1] [BoTorch] 22 COMPLETED \n", "23 [GenerationStep_1] [BoTorch] 23 COMPLETED \n", "24 [GenerationStep_1] [BoTorch] 24 COMPLETED \n", "\n", " Arm Parameterizations \n", "0 {'0_0': {'x1': 0.73, 'x2': 0.06, 'x3': 0.09, '... \n", "1 {'1_0': {'x1': 0.23, 'x2': 0.84, 'x3': 0.99, '... \n", "2 {'2_0': {'x1': 0.46, 'x2': 0.7, 'x3': 0.76, 'x... \n", "3 {'3_0': {'x1': 0.5, 'x2': 0.16, 'x3': 0.6, 'x4... \n", "4 {'4_0': {'x1': 0.33, 'x2': 0.69, 'x3': 0.23, '... \n", "5 {'5_0': {'x1': 0.16, 'x2': 0.89, 'x3': 0.48, '... \n", "6 {'6_0': {'x1': 0.25, 'x2': 0.37, 'x3': 0.07, '... \n", "7 {'7_0': {'x1': 0.86, 'x2': 0.08, 'x3': 0.85, '... \n", "8 {'8_0': {'x1': 0.25, 'x2': 0.87, 'x3': 0.8, 'x... \n", "9 {'9_0': {'x1': 0.71, 'x2': 0.78, 'x3': 0.5, 'x... \n", "10 {'10_0': {'x1': 0.6, 'x2': 0.22, 'x3': 0.09, '... \n", "11 {'11_0': {'x1': 0.36, 'x2': 0.63, 'x3': 0.24, ... \n", "12 {'12_0': {'x1': 0.54, 'x2': 0.23, 'x3': 0.15, ... \n", "13 {'13_0': {'x1': 0.51, 'x2': 0.21, 'x3': 0.15, ... \n", "14 {'14_0': {'x1': 0.52, 'x2': 0.24, 'x3': 0.2, '... \n", "15 {'15_0': {'x1': 0.5, 'x2': 0.27, 'x3': 0.24, '... \n", "16 {'16_0': {'x1': 0.55, 'x2': 0.23, 'x3': 0.21, ... \n", "17 {'17_0': {'x1': 0.48, 'x2': 0.23, 'x3': 0.24, ... \n", "18 {'18_0': {'x1': 0.45, 'x2': 0.21, 'x3': 0.28, ... \n", "19 {'19_0': {'x1': 0.41, 'x2': 0.19, 'x3': 0.31, ... \n", "20 {'20_0': {'x1': 0.39, 'x2': 0.21, 'x3': 0.34, ... \n", "21 {'21_0': {'x1': 0.37, 'x2': 0.15, 'x3': 0.31, ... \n", "22 {'22_0': {'x1': 0.37, 'x2': 0.1, 'x3': 0.38, '... \n", "23 {'23_0': {'x1': 0.41, 'x2': 0.05, 'x3': 0.35, ... \n", "24 {'24_0': {'x1': 0.34, 'x2': 0.12, 'x3': 0.42, ... " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.generation_strategy.trials_as_df" ] }, { "cell_type": "markdown", "id": "5a58452c", "metadata": { "papermill": { "duration": 0.04307, "end_time": "2024-07-23T19:32:45.276347", "exception": false, "start_time": "2024-07-23T19:32:45.233277", "status": "completed" }, "tags": [] }, "source": [ "## 5. Retrieve best parameters\n", "\n", "Once it's complete, we can access the best parameters found, as well as the corresponding metric values." ] }, { "cell_type": "code", "execution_count": 8, "id": "efd26279", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:45.365127Z", "iopub.status.busy": "2024-07-23T19:32:45.364604Z", "iopub.status.idle": "2024-07-23T19:32:45.702381Z", "shell.execute_reply": "2024-07-23T19:32:45.701668Z" }, "papermill": { "duration": 0.384048, "end_time": "2024-07-23T19:32:45.703879", "exception": false, "start_time": "2024-07-23T19:32:45.319831", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "{'x1': 0.33815614653423903,\n", " 'x2': 0.12357175858877631,\n", " 'x3': 0.4171113520719727,\n", " 'x4': 0.3014259064683609,\n", " 'x5': 0.2752337748246556,\n", " 'x6': 0.6974814384124463}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "best_parameters, values = ax_client.get_best_parameters()\n", "best_parameters" ] }, { "cell_type": "code", "execution_count": 9, "id": "1de80762", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:45.828705Z", "iopub.status.busy": "2024-07-23T19:32:45.828128Z", "iopub.status.idle": "2024-07-23T19:32:45.833051Z", "shell.execute_reply": "2024-07-23T19:32:45.832400Z" }, "papermill": { "duration": 0.063416, "end_time": "2024-07-23T19:32:45.834312", "exception": false, "start_time": "2024-07-23T19:32:45.770896", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "{'hartmann6': -3.0027733875921827, 'l2norm': 0.9781085008403068}" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "means, covariances = values\n", "means" ] }, { "cell_type": "markdown", "id": "94ea30a2", "metadata": { "papermill": { "duration": 0.044304, "end_time": "2024-07-23T19:32:45.923178", "exception": false, "start_time": "2024-07-23T19:32:45.878874", "status": "completed" }, "tags": [] }, "source": [ "For comparison, Hartmann6 minimum:" ] }, { "cell_type": "code", "execution_count": 10, "id": "55da8716", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:46.013279Z", "iopub.status.busy": "2024-07-23T19:32:46.012608Z", "iopub.status.idle": "2024-07-23T19:32:46.018038Z", "shell.execute_reply": "2024-07-23T19:32:46.017357Z" }, "papermill": { "duration": 0.052063, "end_time": "2024-07-23T19:32:46.019449", "exception": false, "start_time": "2024-07-23T19:32:45.967386", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "-3.32237" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hartmann6.fmin" ] }, { "cell_type": "markdown", "id": "bcd92f46", "metadata": { "papermill": { "duration": 0.044087, "end_time": "2024-07-23T19:32:46.109099", "exception": false, "start_time": "2024-07-23T19:32:46.065012", "status": "completed" }, "tags": [] }, "source": [ "## 6. Plot the response surface and optimization trace\n", "Here we arbitrarily select \"x1\" and \"x2\" as the two parameters to plot for both metrics, \"hartmann6\" and \"l2norm\"." ] }, { "cell_type": "code", "execution_count": 11, "id": "80391575", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:46.199049Z", "iopub.status.busy": "2024-07-23T19:32:46.198536Z", "iopub.status.idle": "2024-07-23T19:32:46.866986Z", "shell.execute_reply": "2024-07-23T19:32:46.866129Z" }, "papermill": { "duration": 0.719032, "end_time": "2024-07-23T19:32:46.872289", "exception": false, "start_time": "2024-07-23T19:32:46.153257", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:46] 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" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "xaxis": "x", "y": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "yaxis": "y", "z": [ [ -1.5891866384481468, -1.6456875092544574, -1.7019292311521494, -1.7575463041290935, -1.8121374027927672, -1.865266442720313, -1.916464717793401, -1.9652343191418384, -2.01105305216222, -2.053381058942045, -2.0916693212159707, -2.125370153713727, -2.153949688546562, -2.176902188901885, -2.193765811919551, -2.2041391765609166, -2.2076978134536116, -2.2042093351365626, -2.193546039573636, -2.175693716632779, -2.1507557005108278, -2.118951672430626, -2.0806112749421213, -2.036163127784374, -1.9861202298023706, -1.9310629410226041, -1.8716207712342134, -1.8084540993349059, -1.7422367622845134, -1.6736402266853758, -1.60331982139488, -1.531903289028904, -1.459981724065869, -1.388102815664864, -1.3167662079597988, -1.2464207272053778, -1.1774631971030067, -1.1102385621657989, -1.0450410552351086, -0.9821161716428803, -0.9216632432871352, -0.8638384371792264, -0.8087580325096106, -0.7565018567830605, -0.7071167846679477, -0.6606202229169179, -0.6170035213173687, -0.5762352634940509, -0.5382644029072277, -0.5030232189381021 ], [ -1.6021688569407715, -1.6597393909960751, -1.7171055631992325, -1.7738986078270313, -1.829712486830654, -1.8841047406377571, -1.936598408844095, -1.9866852433234747, -2.033830447229792, -2.0774791704158684, -2.1170649665146746, -2.1520203584235444, -2.1817895545845034, -2.205843196278665, -2.2236947896335573, -2.234918191833054, -2.2391652081404843, -2.2361820723650374, -2.2258234099357033, -2.208062303469293, -2.1829953441896057, -2.1508420375714565, -2.11193854108257, -2.0667263078067384, -2.0157366704220223, -1.9595726629111891, -1.8988894435200678, -1.83437459181429, -1.7667293560478663, -1.6966516710704274, -1.6248214909538699, -1.551888716874618, -1.4784637743130618, -1.4051107194542718, -1.3323426374364302, -1.2606190303890772, -1.1903448708102542, -1.1218710033858976, -1.0554956042545143, -0.9914664417324801, -0.9299837202034766, -0.8712033252852822, -0.8152403214329773, -0.7621725819779555, -0.7120444561418838, -0.6648703981050169, -0.6206385002248098, -0.5793138865145765, -0.5408419339987962, -0.5051512989996613 ], [ -1.6117722926405436, -1.6702129842221902, -1.7285001019314166, -1.7862628669649354, -1.843092025623651, -1.8985405005181382, -1.9521251047369734, -2.0033295503835244, -2.051608998216944, -2.0963963977463593, -2.1371108484636747, -2.173168161505153, -2.203993703012749, -2.229037441559874, -2.2477908923535557, -2.2598053532745372, -2.2647104881824816, -2.262231989145536, -2.2522068288542867, -2.234594592819388, -2.2094836205447512, -2.177091174509811, -2.1377574998297133, -2.0919342910547964, -2.040168613052681, -1.9830836552072557, -1.9213578199071635, -1.855703585053408, -1.786847380258359, -1.7155114271963954, -1.6423981673099537, -1.5681775824213298, -1.493477443050573, -1.4188763170104766, -1.344899042122722, -1.2720143035042482, -1.2006339423368664, -1.1311136422847827, -1.0637546769722246, -0.9988064463400854, -0.9364695743926912, -0.8768993820843742, -0.8202095852590439, -0.766476098286619, -0.7157408496412041, -0.6680155367328159, -0.6232852645153202, -0.5815120264023433, -0.5426379974112832, -0.5065886187158295 ], [ -1.6178575835342135, -1.6769537350463082, -1.7359417597081024, -1.7944500746747036, -1.8520676848997866, -1.9083446584136121, -1.9627936533851875, -2.014892734213575, -2.064089732656279, -2.109808417171918, -2.15145672072953, -2.1884372326448593, -2.220160068907856, -2.2460580821362672, -2.2656041442579635, -2.2783299315156285, -2.28384528482791, -2.281856864872938, -2.2721845599193613, -2.2547740377802272, -2.229704034743933, -2.1971874443363535, -2.1575659206680804, -2.111298404702964, -2.058944582460362, -2.001144704835667, -1.938597404147659, -1.8720371341916318, -1.8022126667743326, -1.729867750808244, -1.6557246492689754, -1.5804708850041922, -1.5047492031633047, -1.429150525190794, -1.3542095308599689, -1.2804024464846278, -1.2081466165274228, -1.1378014694460916, -1.0696705385537963, -1.0040042527428321, -0.9410032632507446, -0.8808221180832982, -0.8235731343364782, -0.7693303507221454, -0.7181334688395873, -0.6699917130289126, -0.624887555848888, -0.5827802701014458, -0.543609279521965, -0.5072972892970194 ], [ -1.6203184927945598, -1.6798429886398578, -1.7392982687524041, -1.7983130985302505, -1.8564761733866915, -1.9133364481137134, -1.968404504132998, -2.0211551948044244, -2.071031830054265, -2.1174521720252546, -2.159816504934988, -2.19751800326942, -2.229955538003197, -2.2565489141742203, -2.2767563108216207, -2.2900933926528033, -2.2961532007416805, -2.2946255593081335, -2.285314444163223, -2.268151648702897, -2.2432052341992583, -2.2106816742355564, -2.170921228996418, -2.1243867929992297, -2.071647126822163, -2.0133559128629535, -1.9502283973126397, -1.8830174527373447, -1.812490718578959, -1.7394101061067455, -1.6645144858450873, -1.5885059113533866, -1.5120393503316076, -1.4357156297993743, -1.3600771572818635, -1.28560593137869, -1.212723370734662, -1.1417915406871861, -1.073115420147212, -1.0069459146077162, -0.9434833782550844, -0.8828814568300944, -0.8252511031530944, -0.770664650004957, -0.719159851507172, -0.6707438253990307, -0.6253968456566512, -0.5830759485671332, -0.5437183263404022, -0.5072444911577051 ], [ -1.619084761506091, -1.678801266391373, -1.7384799422112658, -1.7977509917309502, -1.8562041771469557, -1.9133890381396939, -1.9688161324994367, -2.0219595397091306, -2.072260890120455, -2.1191351946343797, -2.1619787440780613, -2.2001793125068136, -2.233128819945084, -2.260238471206554, -2.2809561740373674, -2.2947857472212805, -2.3013070734763, -2.300195980255601, -2.291242324249958, -2.274364608989864, -2.2496195563102184, -2.2172054019934606, -2.1774582483913143, -2.1308414972523178, -2.077929110283783, -2.019384102313512, -1.9559341452940417, -1.8883463429129725, -1.8174030849233023, -1.7438804680672613, -1.6685302098846633, -1.5920654261465517, -1.5151501953948978, -1.4383925400566662, -1.3623403073985296, -1.2874794000220726, -1.2142338413258404, -1.1429672296077555, -1.0739852108005483, -1.0075386712575072, -0.9438274134548394, -0.883004128169016, -0.8251785176844135, -0.7704214574666766, -0.718769110030695, -0.6702269257415848, -0.624773482076455, -0.5823641262987915, -0.5429343972419464, -0.506403210509625 ], [ -1.6141241779157671, -1.6737906611655375, -1.7334424440713985, -1.7927121925609322, -1.8511920500357546, -1.9084337813263743, -1.9639499234130924, -2.0172161810300135, -2.0676753275313233, -2.114742884056144, -2.1578148454094954, -2.1962776884777564, -2.2295208246874694, -2.2569515265431006, -2.278012156125808, -2.2921992459571348, -2.2990836438380478, -2.298330574867533, -2.289718166047262, -2.273152805284359, -2.2486797345289675, -2.216487531194053, -2.1769055961960766, -2.1303944063159697, -2.0775290561474278, -2.0189774136342646, -1.9554748678912068, -1.8877979640459879, -1.8167391029705042, -1.7430840026774104, -1.6675929542075234, -1.59098625077332, -1.5139336566858905, -1.4370474630229932, -1.3608785353295143, -1.2859147448792856, -1.2125812331787158, -1.1412420456241292, -1.072202758141151, -1.0057137982359339, -0.9419742259502015, -0.881135791589124, -0.8233071279225933, -0.7685579670063682, -0.716923297616534, -0.668407399926063, -0.6229877105470836, -0.580618484255285, -0.541234229269787, -0.5047529014141496 ], [ -1.6054437672832513, -1.6648162352803868, -1.7241884290988458, -1.7831964450647648, -1.841436059319051, -1.8984628354491622, -1.9537932230590656, -2.0069068808731485, -2.0572504791785087, -2.1042432481063127, -2.147284533155958, -2.185763587485998, -2.2190717592566287, -2.2466171078763937, -2.2678412936860384, -2.28223832793901, -2.289374456759723, -2.288908119926007, -2.280608630719682, -2.2643720328097516, -2.2402325559907936, -2.2083682394319624, -2.169099631445446, -2.1228810337110073, -2.070284550748415, -2.0119781486286765, -1.9486997805909847, -1.881230103413059, -1.8103662292398472, -1.7368984136034107, -1.6615908091242513, -1.5851666621483114, -1.508297756754921, -1.4315975717674654, -1.3556174849866052, -1.2808453681884457, -1.2077059974269446, -1.1365628057488348, -1.0677206024324075, -1.0014289642027212, -0.9378860686454513, -0.8772427908142127, -0.8196069239160594, -0.7650474165569073, -0.7135985442430043, -0.6652639530408495, -0.6200205295141051, -0.5778220640659365, -0.5386026852454479, -0.5022800509327473 ], [ -1.5930900458382853, -1.6519263528153043, -1.7107679700058358, -1.7692553407055427, -1.8269890651502412, -1.8835300082048327, -1.9384003821654683, -1.991086031699131, -2.041040167187546, -2.087688802350317, -2.130438145156283, -2.168684158560377, -2.2018244383920944, -2.22927243802428, -2.250473894030518, -2.264925072291144, -2.2721921720984524, -2.2719309266552976, -2.263905166567793, -2.2480029151557894, -2.2242484941087772, -2.192809156493955, -2.1539949705613854, -2.1082511381467506, -2.0561427304430424, -1.9983328995910177, -1.9355566736677006, -1.8685930588262765, -1.7982381316039047, -1.725281201230652, -1.6504852510896582, -1.5745720280523332, -1.4982115244616407, -1.4220152467121294, -1.3465325472357603, -1.2722493297317703, -1.1995885393225207, -1.128911964970653, -1.060522984303483, -0.9946699634507412, -0.9315500881851289, -0.8713134517360819, -0.8140672630088921, -0.7598800694171457, -0.7087859130252918, -0.6607883584788853, -0.6158643471856301, -0.573967845105488, -0.535033261883227, -0.49897862738520526 ], [ -1.5771483257039278, -1.6352119297846226, -1.693277751287821, -1.7509914554095527, -1.8079596020999467, -1.8637497870788629, -1.9178917417911512, -1.9698796108979022, -2.0191756424603824, -2.0652155326608708, -2.107415657382959, -2.1451823890929127, -2.1779236297212723, -2.205062579221707, -2.2260535986354775, -2.2403998162127907, -2.2476718769201245, -2.247526973441383, -2.239727052131952, -2.2241548883025146, -2.2008265876724398, -2.1698990118441777, -2.1316707066410348, -2.0865752725263467, -2.0351669047168794, -1.978099009382553, -1.9160980156907386, -1.8499352495594321, -1.7803997312857112, -1.7082741119632816, -1.6343150157918158, -1.5592381470067933, -1.4837078587438417, -1.4083305249641305, -1.3336509546706146, -1.260151141585039, -1.1882507606539032, -1.118308946989957, -1.0506269979011065, -0.9854517198166242, -0.9229792030666601, -0.863358854080164, -0.8066975510283372, -0.7530638181505389, -0.7024919377374615, -0.6549859381327938, -0.6105234119286307, -0.5690591313774381, -0.530528438432604, -0.494850395196066 ], [ -1.5577411013745879, -1.6148046380557441, -1.6718590718628497, -1.7285561314889049, -1.7845094208278454, -1.8392946221177446, -1.892450640904297, -1.943481901341522, -1.9918620137360623, -2.037039039511421, -2.0784425661583326, -2.1154927691681706, -2.147611571629806, -2.174235908022803, -2.1948329527537846, -2.208916988213866, -2.2160673719856314, -2.215946836297414, -2.2083191346444386, -2.193064852950478, -2.1701940282728325, -2.1398540818201415, -2.1023315541448104, -2.058046407163319, -2.0075384240709333, -1.9514464751088898, -1.8904827359347378, -1.8254047817895414, -1.7569885117940112, -1.6860041934902723, -1.613196928761464, -1.539271895123143, -1.4648840341765978, -1.3906315025698308, -1.3170521114586546, -1.2446220490358169, -1.1737563086676257, -1.104810372828744, -1.0380828069263432, -0.9738184950383101, -0.9122123072250092, -0.8534130317674713, -0.7975274400691155, -0.7446243798491625, -0.6947388152465613, -0.6478757514768279, -0.6040139973709706, -0.5631097319772658, -0.525099851863856, -0.48990508421817647 ], [ -1.5350255889975144, -1.590874147293984, -1.646694756259758, -1.7021460224681448, -1.7568496294049476, -1.8103906261470444, -1.8623186391068054, -1.9121502038657305, -1.9593724240892052, -2.003448164206551, -2.0438229668358163, -2.079933848869936, -2.111220065608027, -2.1371358353592314, -2.157164885649328, -2.1708365195723935, -2.1777427157029097, -2.1775555795726302, -2.170044268845035, -2.1550903188372335, -2.1327000949684587, -2.1030129111788094, -2.0663032712856557, -2.022975912547303, -1.9735530689382932, -1.9186546125823774, -1.8589730791266033, -1.7952464567767379, -1.72823168149417, -1.6586811341451297, -1.5873234498691409, -1.5148489991380245, -1.4418997155523299, -1.369062592244648, -1.2968660861133954, -1.2257787433637928, -1.1562094897026103, -1.0885091543436616, -1.0229728968752052, -0.9598432794477303, -0.8993137803708535, -0.8415325858354721, -0.7866065287498258, -0.734605070245572, -0.6855642416551033, -0.6394904834290496, -0.5963643330371007, -0.5561439267741829, -0.5187682909499354, -0.48416040652437975 ], [ -1.5091905243596675, -1.5636245300296938, -1.6180051221107328, -1.6719985752125, -1.7252356398211424, -1.7773119340567904, -1.8277892374684201, -1.8761978712617586, -1.9220403558810994, -1.9647965331147386, -2.003930321429289, -2.0388982351996656, -2.0691597363054894, -2.0941893970216374, -2.113490735793058, -2.126611445639197, -2.1331595751948647, -2.132820051809398, -2.1253707570506486, -2.1106971715986425, -2.0888043925714115, -2.059825115281229, -2.024022065621976, -1.9817835691430672, -1.9336116489196145, -1.8801032357846563, -1.8219263721453387, -1.7597941466762217, -1.6944391859820505, -1.6265909335138244, -1.5569570093397016, -1.4862090266464418, -1.4149725736104002, -1.34382072223103, -1.2732703425007939, -1.2037805701508735, -1.135752899826318, -1.0695324946238443, -1.0054103965509922, -0.9436263905851874, -0.8843723245145888, -0.8277957243581747, -0.7740035753736298, -0.7230661639138223, -0.6750208968718316, -0.6298760337373601, -0.58761428172639, -0.5481962173424035, -0.5115635083851491, -0.47764191914884613 ], [ -1.480452352010893, -1.5332899856203739, -1.5860431870678213, -1.6383866643697869, -1.6899611716525462, -1.740374015612331, -1.7892004402256036, -1.8359860606586365, -1.8802505205772784, -1.9214925402189365, -1.9591965019126025, -1.992840681376828, -2.0219071737951184, -2.0458934814850114, -2.0643256253135003, -2.076772517739911, -2.0828611957631074, -2.0822923598933003, -2.074855498170985, -2.0604426843204395, -2.0390599238111404, -2.01083471302824, -1.9760183811465377, -1.9349819868701919, -1.8882052108383864, -1.836258782618055, -1.7797821662247644, -1.719459019523346, -1.6559930487739565, -1.5900863588688015, -1.5224215497986893, -1.453647958537513, -1.3843718143138348, -1.3151497377660746, -1.2464849242690803, -1.178825407997321, -1.112563913273346, -1.0480389078522983, -0.9855365583715185, -0.9252933505918102, -0.8674991825056676, -0.8123007731413865, -0.7598052581226589, -0.7100838669807932, -0.6631755978811098, -0.619090823258985, -0.5778147751067386, -0.5393108715242411, -0.5035238568813944, -0.4703827367992365 ], [ -1.4490509552013144, -1.5001300581361683, -1.55108931959542, -1.6016126175624648, -1.6513515903326497, -1.6999262636580479, -1.7469265293175835, -1.7919146321235393, -1.834428822663547, -1.873988323636861, -1.9100997353827283, -1.9422649681550903, -1.9699907325755641, -1.99279954446798, -2.010242106581029, -2.0219108195893187, -2.027454050338822, -2.0265906463660404, -2.0191240278290166, -2.0049550048133966, -1.9840922637098006, -1.9566592812198755, -1.922896361974109, -1.8831567138781384, -1.837896098924461, -1.7876565733143668, -1.7330458647676075, -1.6747146306066292, -1.6133339522937569, -1.5495749875335314, -1.4840919621928048, -1.4175089244845742, -1.3504101049475885, -1.2833334025701542, -1.2167664166318175, -1.1511444799796215, -1.0868502401559759, -1.024214428523751, -0.9635175336119642, -0.9049921512390291, -0.848825825451169, -0.795164226349433, -0.7441145371969915, -0.6957489458029089, -0.6501081549561714, -0.607204843977755, -0.5670270284248934, -0.5295412777598177, -0.4946957615600822, -0.462423103809364 ], [ -1.4152450840650783, -1.4644245309518442, -1.5134455455316844, -1.5620018764822894, -1.6097568629571584, -1.656344183263839, -1.7013694250345603, -1.7444126197797278, -1.7850318824292746, -1.8227682849528517, -1.8571520698980486, -1.8877102724432597, -1.913975766736536, -1.9354976833132946, -1.9518530597790194, -1.9626594878205266, -1.967588406424505, -1.9663785621800787, -1.958849008523707, -1.944910844315323, -1.9245767097518165, -1.8979669096555138, -1.8653110148224543, -1.8269440266472117, -1.783296760378101, -1.7348809437160664, -1.682270396916378, -1.6260802468367284, -1.5669462353904025, -1.5055058335278098, -1.4423822535818613, -1.3781717986731814, -1.3134344729871177, -1.2486874735028446, -1.184401072497246, -1.1209964132932384, -1.0588448098749161, -0.9982682180200128, -0.9395406109936293, -0.8828900427239819, -0.8285012188688696, -0.7765184255610168, -0.7270486900486527, -0.6801650686771051, -0.6359099764603451, -0.5942984891390549, -0.5553215632062424, -0.5189491319789152, -0.4851330465219579, -0.4538098392489417 ], [ -1.3793076383443725, -1.426468177996617, -1.4734297172043171, -1.5198965309623784, -1.5655444027099015, -1.6100214908987747, -1.6529499841180593, -1.6939286736287809, -1.7325365677180182, -1.7683376591936182, -1.8008869335891196, -1.8297376695126464, -1.8544500329111737, -1.8746009034375668, -1.8897947938399953, -1.8996756326639033, -1.9039390760625559, -1.9023448941738845, -1.894728838976222, -1.8810132460865467, -1.8612154701542551, -1.835453148626779, -1.8039453119857627, -1.767008602338672, -1.7250483720316758, -1.6785451410210093, -1.6280376018636056, -1.5741038387122437, -1.5173425233840083, -1.4583555786429119, -1.3977332976907828, -1.3360423632771743, -1.2738167649167036, -1.211551334914533, -1.1496975053695937, -1.0886608792889154, -1.0288002538978303, -0.9704277935031613, -0.9138101031498863, -0.8591699972865906, -0.8066887909764213, -0.7565089678573593, -0.7087371015517365, -0.6634469270106207, -0.6206824760102997, -0.5804612069088979, -0.5427770728647431, -0.5076034850389574, -0.4748961379169613, -0.444595672899193 ], [ -1.341520952123087, -1.3865655398154921, -1.4313697363792641, -1.4756489430369284, -1.5190920474294018, -1.5613624006348616, -1.6020995470381136, -1.6409218221640667, -1.677429927379003, -1.7112115761329303, -1.7418472825303473, -1.7689173281332016, -1.7920098961373343, -1.8107303030502493, -1.824711186686888, -1.8336234255350017, -1.8371874675758635, -1.835184635271466, -1.82746784787336, -1.8139710690916384, -1.7947166686048774, -1.76981982327568, -1.739489142439294, -1.704022944391646, -1.6638010570764967, -1.6192725982134966, -1.5709407574844143, -1.519345982269081, -1.4650490502726323, -1.408615303533358, -1.3506009223144082, -1.2915416742278283, -1.231944199171422, -1.1722796424219823, -1.1129793273535882, -1.0544321316220928, -0.9969832540804975, -0.9409341014943957, -0.8865430661927823, -0.8340270014787723, -0.7835632305096272, -0.7352919481497305, -0.6893188957586086, -0.645718207123062, -0.6045353403013677, -0.5657900251741764, -0.5294791699936376, -0.4955796821696181, -0.46405116894588705, -0.4348384925642981 ], [ -1.3021722131135667, -1.3450258738601877, -1.387597998981822, -1.4296156491591845, -1.470781382502415, -1.510774331484475, -1.549251994573268, -1.5858528443851403, -1.6201998465623775, -1.6519049685547569, -1.6805747337221706, -1.70581684258936, -1.7272478389438155, -1.744501743382397, -1.7572395106708996, -1.7651590896059222, -1.7680057745430617, -1.7655824364896202, -1.7577591114680864, -1.7444813144664744, -1.7257763608003094, -1.7017569508774302, -1.6726213575027464, -1.6386497868310483, -1.6001968662483748, -1.5576806842999218, -1.5115692538896597, -1.4623655649277412, -1.4105924592424408, -1.3567784031139793, -1.3014449259067908, -1.2450961407758738, -1.1882104544378238, -1.1312343563148843, -1.0745780592683472, -1.0186127229748743, -0.963668996213558, -0.9100366401557882, -0.85796502531875, -0.8076643230791712, -0.7593072368318667, -0.7130311385898522, -0.6689404950958935, -0.6271094841112039, -0.5875847168324718, -0.550387996452859, -0.5155190556867192, -0.48295822756128404, -0.4526690139127558, -0.42460052482925204 ], [ -1.26154912976527, -1.3021584049259742, -1.342446201026222, -1.3821516943747676, -1.4209915770652302, -1.4586612208765986, -1.494836515653919, -1.5291764712614173, -1.5613266634765217, -1.5909235886597768, -1.6175999685808795, -1.6409910145081732, -1.6607416179499803, -1.6765143838951784, -1.6879983608277471, -1.6949182500921092, -1.6970437956205524, -1.6941989651456153, -1.6862704406851445, -1.673214850659999, -1.6550641194341313, -1.6319283131944735, -1.6039954582491927, -1.5715280216911496, -1.5348560662498698, -1.494367468867011, -1.4504959394248096, -1.4037078028181853, -1.3544885605381873, -1.3033301305151128, -1.2507194294859592, -1.1971286861294925, -1.1430076227704626, -1.088777458182516, -1.034826572944686, -0.9815076293884083, -0.9291359293038408, -0.8779888047613018, -0.8283058574047842, -0.7802898825102359, -0.734108333453656, -0.689895199679521, -0.6477531871970793, -0.607756105463407, -0.5699513784328506, -0.5343626105706982, -0.500992150659658, -0.46982360716848615, -0.44082427873242536, -0.4139474718920697 ], [ -1.2199359375858974, -1.258267975492915, -1.2962406140516582, -1.3336055153488242, -1.3700938589652774, -1.4054175781436762, -1.4392712285715235, -1.4713345667831184, -1.501275905621297, -1.5287562983884917, -1.5534345803248766, -1.5749732651296626, -1.5930452548650105, -1.6073412734572317, -1.6175778770774145, -1.6235058292285043, -1.62491855543071, -1.6216603147574864, -1.6136336493035093, -1.6008056095957284, -1.5832122224163652, -1.5609606913204508, -1.534228922294171, -1.5032621584152945, -1.468366774544503, -1.4299015827287662, -1.3882672668763683, -1.3438947383984812, -1.2972332461782279, -1.2487389874265256, -1.1988647885913541, -1.1480512117607313, -1.0967192416221032, -1.0452645523288635, -0.9940532524214565, -0.9434189529224789, -0.8936609849596596, -0.8450435945840024, -0.7977959532769741, -0.7521128367690771, -0.7081558393627, -0.6660550050363035, -0.6259107700965579, -0.5877961251217014, -0.5517589164233943, -0.5178242191644074, -0.485996725465377, -0.45626310116991076, -0.42859427430098906, -0.4029476265688535 ], [ -1.1776098131909845, -1.2136511688164848, -1.249297906822132, -1.284314452327642, -1.3184467111161997, -1.3514233622486849, -1.38295774023536, -1.4127503723871608, -1.4404922268016143, -1.4658687105566832, -1.4885644353100544, -1.5082687380182083, -1.524681907497809, -1.5375220229062532, -1.5465322581074354, -1.5514884470471877, -1.5522066414440063, -1.5485503269332974, -1.5404369039882049, -1.5278429963835354, -1.5108081379376759, -1.4894364252661567, -1.4638958247139202, -1.434414988893244, -1.401277657437133, -1.3648149528311468, -1.3253960883165448, -1.2834181367527637, -1.239295542099582, -1.193449991508591, -1.1463011327243315, -1.0982584572614347, -1.049714511013451, -1.001039464873777, -0.9525769880865018, -0.9046413140033626, -0.8575153629838306, -0.8114497803973382, -0.7666627509787172, -0.7233404588750938, -0.6816380727704875, -0.6416811462300867, -0.6035673344101593, -0.5673683393559757, -0.5331320071193062, -0.5008845106947571, -0.4706325630990169, -0.44236561460659973, -0.4160579970546223, -0.3916709861348463 ], [ -1.1348377421082507, -1.1685929515411853, -1.201921559941864, -1.2346009354827239, -1.266391832177421, -1.297039722600532, -1.326276676393419, -1.3538238395632245, -1.3793945590250278, -1.4026981810817578, -1.4234445309420924, -1.4413490524668997, -1.4561385528556812, -1.467557455980697, -1.4753744210196793, -1.4793891310815872, -1.4794390019409895, -1.4754055078598127, -1.467219776376843, -1.4548670764614697, -1.4383898265898833, -1.4178887933658897, -1.39352224554514, -1.3655029717145692, -1.3340932480829348, -1.2995980283936202, -1.2623567864596128, -1.2227345424481364, -1.1811126300266557, -1.137879715147923, -1.0934234775714504, -1.0481232406490837, -1.0023437098834795, -0.9564298749251392, -0.9107030515014114, -0.8654579891978889, -0.8209609429025195, -0.7774485933627016, -0.7351276997349906, -0.6941753699776901, -0.6547398408897267, -0.6169416671896042, -0.5808752275979924, -0.5466104650783603, -0.5141947879311837, -0.4836550680633127, -0.454999682201054, -0.42822055083953403, -0.40329513812497175, -0.3801883835104515 ], [ -1.0918738653631619, -1.12336385862748, -1.1543988927632987, -1.1847693601959302, -1.2142508696422363, -1.2426056026315306, -1.2695841718268581, -1.294928026358212, -1.3183724386348945, -1.339650091667196, -1.3584952652903572, -1.3746485935104105, -1.3878623333877942, -1.3979060486852837, -1.4045725696682247, -1.4076840454313133, -1.4070978595135346, -1.4027121374791853, -1.3944705426469282, -1.382366041223504, -1.3664433298243557, -1.3467996649048442, -1.3235839191071095, -1.2969938106331607, -1.2672713956777706, -1.2346970594171442, -1.1995823630698275, -1.1622621816458998, -1.1230865878728502, -1.0824129043743005, -1.0405982718980562, -0.9979929857061898, -0.9549347543046114, -0.9117439486341861, -0.868719842939411, -0.8261378019352806, -0.7842473398389069, -0.7432709609684263, -0.703403684714979, -0.6648131565104363, -0.6276402488020764, -0.5920000607395096, -0.5579832315521481, -0.5256574899821683, -0.4950693702675072, -0.4662460336958305, -0.4391971433438504, -0.4139167479821455, -0.39038513902266025, -0.36857065164169633 ], [ -1.0489573111715467, -1.0782177223674176, -1.106998698468422, -1.1351036397087375, -1.1623229044966956, -1.1884351739705163, -1.213209274658491, -1.2364064955263179, -1.2577834249542492, -1.2770953182532565, -1.2940999868241398, -1.3085621757890622, -1.3202583679439865, -1.3289819186214618, -1.3345483894594836, -1.3368009108145893, -1.335615365296726, -1.3309051525524485, -1.322625273258463, -1.310775464688068, -1.2954021377656313, -1.2765989113660325, -1.25450561522152, -1.2293057338974467, -1.2012223799848083, -1.1705129986476193, -1.1374630998742759, -1.10237937421706, -1.0655825648273969, -1.0274004447758691, -0.988161193480062, -0.9481873933482328, -0.9077907913300576, -0.8672679005889166, -0.8268964609905431, -0.7869327352424103, -0.7476095890444692, -0.7091352858435308, -0.671692916861307, -0.6354403826304714, -0.6005108416594889, -0.567013543979991, -0.535034971514021, -0.5046402129237338, -0.4758745074325105, -0.448764899615964, -0.42332195495983604, -0.399541493720702, -0.3774063080232424, -0.3568878339809748 ], [ -1.0063105021835557, -1.0333899297476206, -1.0599694640119584, -1.085865402679335, -1.1108826440706823, -1.134816044915967, -1.157452193336009, -1.1785716252711995, -1.1979515020549028, -1.2153687525714816, -1.2306036652234054, -1.2434438926917577, -1.2536888064124196, -1.2611541083806053, -1.2656765764173257, -1.2671187871250291, -1.2653736310006694, -1.260368410081321, -1.2520682944756534, -1.2404789150987936, -1.2256478904757322, -1.207665128605744, -1.1866618104775906, -1.1628080454661618, -1.1363092815307516, -1.1074016425235842, -1.076346437932358, -1.0434241365255452, -1.0089281094655498, -0.9731584317383859, -0.9364159899465472, -0.8989970894152429, -0.8611886941691378, -0.823264377604036, -0.7854810144535187, -0.7480762077560426, -0.7112664175864556, -0.6752457397923636, -0.6401852710510413, -0.6062329896489356, -0.5735140783043853, -0.5421316152864655, -0.512167562430654, -0.48368398290897274, -0.4567244272904868, -0.4313154330433716, -0.4074680897224088, -0.38517962925394433, -0.3644350076532108, -0.34520845095797004 ], [ -0.9641379159150454, -0.9890961786147775, -1.0135381368795464, -1.0372927876304927, -1.0601792634762115, -1.0820081702487712, -1.1025832980622237, -1.1217037270427024, -1.1391663386635342, -1.1547687301855718, -1.1683125129044472, -1.1796069547896657, -1.1884729049812195, -1.1947469121616214, -1.1982854221824386, -1.1989689142041073, -1.1967058113743096, -1.1914359847592015, -1.1831336614034869, -1.1718095526953924, -1.1575120407308914, -1.1403272996539089, -1.1203782850231232, -1.0978225929711933, -1.0728492650255075, -1.0456746846468405, -1.0165377683653922, -0.9856946904847348, -0.9534133921552468, -0.9199681141475259, -0.8856341626596992, -0.8506830759255388, -0.8153783134563943, -0.7799715453481105, -0.7446995800180543, -0.7097819367048264, -0.6754190441746905, -0.6417910285644554, -0.6090570401114728, -0.5773550597444608, -0.5468021214250052, -0.5174948842114273, -0.48951048880511394, -0.46290763635809995, -0.4377278320444007, -0.4139967417749749, -0.3917256169398218, -0.3709127487332815, -0.3515449201049805, -0.333598829432037 ], [ -0.9226252662947563, -0.9455316929606435, -0.9679093901852459, -0.9895997757414204, -1.0104358256465948, -1.0302433795142978, -1.0488427794184108, -1.066050857230602, -1.0816832756561285, -1.095557215703405, -1.1074943880280153, -1.117324327630806, -1.1248879111605274, -1.1300410142994133, -1.1326582045270728, -1.1326363435635092, -1.129897956079051, -1.124394209357635, -1.1161073452863013, -1.1050524139677018, -1.091278179379792, -1.074867102444163, -1.0559343542396262, -1.0346258682389267, -1.011115499600097, -0.9856014147345804, -0.9583018787728369, -0.9294506369707356, -0.8992920961378261, -0.8680765045628815, -0.836055307065938, -0.8034768206648992, -0.7705823410784165, -0.7376027552134434, -0.704755702798618, -0.6722433028588892, -0.6402504381098937, -0.6089435723029154, -0.5784700616197421, -0.5489579110238593, -0.5205159197624012, -0.49323415676077487, -0.4671847061613197, -0.4424226252909782, -0.41898706133431174, -0.3969024783110007, -0.37617995200739107, -0.3568184967784518, -0.33880639423378045, -0.3221224994934768 ], [ -0.8819390674941249, -0.902870850918118, -0.9232653311322401, -0.9429759973987147, -0.9618492047100831, -0.979725436743778, -0.9964408643282876, -1.0118292090889633, -1.025723912796776, -1.0379606014819969, -1.0483798196248562, -1.0568299939059276, -1.0631705685364339, -1.067275235829069, -1.0690351674880172, -1.0683621355332609, -1.065191398617967, -1.059484221797449, -1.0512298976746988, -1.0404471461368165, -1.0271847897831226, -1.0115216326583527, -0.9935655095550044, -0.9734515188076045, -0.9513394986603267, -0.9274108507386023, -0.9018648489614267, -0.8749145947443551, -0.8467827879253271, -0.8176974780789443, -0.7878879452101268, -0.7575808357540352, -0.7269966530410804, -0.6963466740108966, -0.6658303380825431, -0.6356331308059994, -0.6059249645943889, -0.5768590414830401, -0.5485711684717747, -0.5211794846899785, -0.4947845515591265, -0.46946975241110955, -0.44530194652245403, -0.42233232383806296, -0.400597410158699, -0.3801201775336618, -0.36091122034568124, -0.3429699635315627, -0.326285875141786, -0.310839660751449 ], [ -0.8422265371044495, -0.8612671753533365, -0.8797655947602814, -0.8975869456821886, -0.9145904363565468, -0.9306305450317249, -0.9455584918937715, -0.9592239760192149, -0.9714771741110277, -0.9821709873905663, -0.9911635108109123, -0.9983206849831704, -1.0035190763325397, -1.0066487157382826, -1.0076159112444505, -1.0063459376133024, -1.0027854960173466, -0.9969048326447805, -0.9886994069899651, -0.9781910103694438, -0.9654282533743943, -0.9504863672409273, -0.9334662970466767, -0.9144931016256355, -0.893713712634127, -0.8712941394232612, -0.8474162337185727, -0.8222741460134965, -0.796070612953033, -0.769013212291726, -0.74131071102731, -0.7131696155461255, -0.6847910126664895, -0.6563677694804108, -0.6280821392928172, -0.6001038014553433, -0.5725883447575029, -0.5456761874439054, -0.5194919122088356, -0.49414398223508593, -0.4697247951096639, -0.44631102569007397, -0.4239642067448649, -0.40273149705414846, -0.38264658991502287, -0.3637307198142161, -0.3459937306197005, -0.3294351743836904, -0.3140454153207366, -0.29980671848861484 ], [ -0.8036157939122879, -0.8208536357723133, -0.83754776459614, -0.8535745307599911, -0.8688054210431615, -0.8831082132825945, -0.8963483575948078, -0.9083905857517544, -0.9191007425502338, -0.9283478237212812, -0.9360061942199795, -0.9419579488995586, -0.9460953650691013, -0.9483233839254087, -0.9485620462104474, -0.9467487977423547, -0.9428405739059107, -0.936815570010849, -0.9286746077603965, -0.9184420177263877, -0.9061659739688278, -0.8919182392964394, -0.8757933068238863, -0.8579069533213304, -0.8383942496773616, -0.8174071007357582, -0.7951114082624208, -0.7716839650682878, -0.7473091946482671, -0.7221758495052752, -0.6964737739246382, -0.6703908251441308, -0.6441100324303529, -0.617807057930756, -0.5916480071439195, -0.5657876207450053, -0.5403678633994213, -0.5155169093202333, -0.4913485092898846, -0.4679617106633578, -0.4454408915716839, -0.4238560639204604, -0.40326339701515346, -0.3837059143192467, -0.3652143191165309, -0.34780790971550546, -0.3314955504067222, -0.31627666999297244, -0.3021422649378216, -0.2890758888119138 ], [ -0.7662163055850439, -0.7817432111232059, -0.7967280636840158, -0.8110579122464615, -0.8246159104270006, -0.83728240870944, -0.8489362426228664, -0.859456215536557, -0.8687227677450533, -0.8766198152988007, -0.8830367327578856, -0.8878704439995244, -0.8910275748348782, -0.8924266110878971, -0.8919999967134902, -0.8896960993681307, -0.8854809665477674, -0.8793397949099603, -0.8712780394862243, -0.8613220986547447, -0.8495195250177424, -0.8359387311747254, -0.8206681816475032, -0.803815086190191, -0.785503633346379, -0.7658728242788823, -0.7450739837707541, -0.7232680366605642, -0.7006226434057493, -0.6773092883461379, -0.6535004095695086, -0.6293666513658468, -0.6050743103193891, -0.5807830349552727, -0.5566438268249666, -0.5327973778616131, -0.5093727645804462, -0.48648650443480046, -0.46424196421673525, -0.442729096241644, -0.42202446674256366, -0.4021915335538997, -0.3832811271092771, -0.3653320895166613, -0.3483720299770825, -0.33241815990911006, -0.31747817681691715, -0.30355117148510313, -0.29062853809554523, -0.2786948711773024 ], [ -0.73011954309668, -0.7440296654647758, -0.7574022629038998, -0.7701345512340263, -0.7821207134928592, -0.7932529263728272, -0.8034225546498246, -0.8125215100023293, -0.8204437643771321, -0.8270870008749269, -0.8323543771825932, -0.8361563681554536, -0.8384126456590855, -0.8390539457453285, -0.8380238662991524, -0.8352805331684322, -0.830798070217087, -0.8245678094073534, -0.8165991814474888, -0.8069202359987961, -0.795577752813863, -0.7826369209328958, -0.768180581210006, -0.7523080466195156, -0.7351335334376126, -0.7167842529574122, -0.6973982265894613, -0.6771218962177966, -0.6561076063127621, -0.6345110349215398, -0.612488648071598, -0.590195247299832, -0.5677816737704766, -0.5453927251436859, -0.5231653328342726, -0.5012270369993896, -0.479694784006795, -0.4586740563562055, -0.4382583291114367, -0.41852883173925315, -0.3995545819392812, -0.3813926501034691, -0.3640886098984768, -0.34767713149526014, -0.3321826779129148, -0.31762027041582497, -0.30399629477169154, -0.2913093257063035, -0.2795509517108009, -0.26870658636421485 ], [ -0.6953998013017532, -0.707788491924639, -0.7196467579525494, -0.7308814293347121, -0.7413970657725428, -0.7510969154214996, -0.7598840162820961, -0.7676624349747283, -0.7743386320862857, -0.7798229370689369, -0.7840311089443253, -0.7868859520917024, -0.7883189495418109, -0.7882718699151614, -0.7866982989623056, -0.7835650431527375, -0.7788533514788458, -0.7725599030769716, -0.7646975127549867, -0.7552955141609148, -0.7443997909432243, -0.732072439325464, -0.7183910602174153, -0.7034476942422262, -0.6873474276921864, -0.670206710311577, -0.6521514360546263, -0.6333148450748088, -0.6138353091196357, -0.5938540636191263, -0.5735129487509422, -0.5529522193903661, -0.5323084806320465, -0.5117128015319802, -0.4912890542887576, -0.47115251826814397, -0.4514087771926847, -0.4321529234041729, -0.41346906659563176, -0.39543012817217016, -0.37809788910720754, -0.36152325072685554, -0.3457466647984653, -0.3307986908116929, -0.3167006428775653, -0.30346529462014016, -0.29109761655081146, -0.2795955259513717, -0.26895063393137697, -0.25914897803370174 ], [ -0.6621151483505151, -0.6730779844836172, -0.6835197714084842, -0.6933563881524661, -0.7025021122751908, -0.7108705101447308, -0.7183754471926274, -0.7249322116240392, -0.7304587402556808, -0.7348769298492848, -0.7381140116804839, -0.7401039613823315, -0.7407889106508501, -0.7401205225814165, -0.7380612886480886, -0.7345857030850479, -0.7296812700933493, -0.7233493012089771, -0.715605464523827, -0.7064800542526284, -0.6960179581586314, -0.6842783111206182, -0.6713338349569126, -0.6572698766819253, -0.6421831687731142, -0.626180344967789, -0.6093762529953423, -0.5918921111980562, -0.5738535592775249, -0.5553886548291395, -0.5366258675089094, -0.5176921222284215, -0.4987109420260343, -0.47980073998768635, -0.46107330687008474, -0.442632535497701, -0.4245734132788147, -0.40698130004760824, -0.38993149127417825, -0.3734890493546076, -0.35770887146603336, -0.3426359536622209, -0.32830580806038423, -0.3147449920955042, -0.30197171403915213, -0.2899964854513819, -0.2788227976125933, -0.268447804530937, -0.258862999586851, -0.2500548762994437 ], [ -0.6303084703270444, -0.6399404015609738, -0.6490626415645829, -0.6575995487617674, -0.6654744618527126, -0.6726105220440116, -0.6789315950363588, -0.684363285436441, -0.6888340321150149, -0.692276268550615, -0.6946276275473846, -0.6958321651206808, -0.6958415740826952, -0.6946163542507381, -0.6921269035840847, -0.6883544932670841, -0.6832920900924108, -0.6769449916729258, -0.6693312441167368, -0.6604818177735761, -0.6504405242610641, -0.6392636667902442, -0.6270194252694091, -0.6137869871231656, -0.5996554435664047, -0.5847224786571654, -0.5690928844416016, -0.5528769397788463, -0.5361886931613794, -0.519144191453575, -0.5018596975344712, -0.48444994088105775, -0.46702644637375545, -0.4496959876326766, -0.43255921080068505, -0.41570947107881506, -0.3992319158090768, -0.3832028339939155, -0.36768927434730947, -0.35274891562290955, -0.3384301579090879, -0.3247723945116431, -0.3118064215485331, -0.2995549451730767, -0.288033152256957, -0.27724931734274716, -0.2672054252966056, -0.25789779464387785, -0.2493176908694732, -0.24145192212411604 ], [ -0.6000085813433661, -0.6084031898774152, -0.6163011649121671, -0.6236347767043863, -0.6303357774223622, -0.636336156599813, -0.6415689784809319, -0.6459692934507052, -0.6494751122075734, -0.652028427591815, -0.6535762651889913, -0.6540717401810997, -0.6534750946535689, -0.6517546869424098, -0.6488879028890662, -0.6448619583090665, -0.639674562777614, -0.633334417117137, -0.6258615207602216, -0.6172872703521776, -0.6076543373125353, -0.5970163192313496, -0.5854371674781206, -0.5729904007481935, -0.5597581209865297, -0.5458298538309252, -0.5313012401895001, -0.5162726088117328, -0.5008474619644991, -0.4851309080287153, -0.46922807654251086, -0.4532425534138592, -0.4372748768375999, -0.42142113733545306, -0.40577172687258145, -0.3904102800707637, -0.3754128430984306, -0.36084729215553313, -0.34677300518140675, -0.3332407712382658, -0.3202929063235125, -0.30796353515607866, -0.29627899634868116, -0.2852583317983889, -0.27491382766172345, -0.2652515816905804, -0.2562720785187451, -0.24797076002655138, -0.24033858205496594, -0.23336255166571684 ], [ -0.5712313731491877, -0.578480241445801, -0.585246964103979, -0.5914711635440237, -0.5970923725807896, -0.6020507250902497, -0.6062877128998885, -0.6097470008970207, -0.6123752893642732, -0.61412320946307, -0.6149462347348291, -0.6148055886466961, -0.6136691257691289, -0.6115121623431087, -0.6083182309778367, -0.6040797341940777, -0.5987984726245043, -0.5924860259627347, -0.5851639681903451, -0.5768639030798854, -0.56762731124596, -0.5575052057844043, -0.5465575994338168, -0.5348527918341199, -0.5224664905024472, -0.5094807833535457, -0.4959829838629016, -0.48206437239396316, -0.4678188590713631, -0.45334159533473517, -0.43872756348929365, -0.42407017662229507, -0.4094599252504706, -0.39498311136728337, -0.38072071359313375, -0.36674742653959025, -0.3531309109717945, -0.3399312779978455, -0.32720081197793716, -0.31498391716957896, -0.30331725704959034, -0.2922300460285968, -0.28174445147122673, -0.271876067853159, -0.2626344318825927, -0.2540235551293121, -0.2460424576379674, -0.23868569150534902, -0.2319438474069644, -0.22580403978939767 ], [ -0.5439809819861791, -0.5501731606521583, -0.5558988577858499, -0.5611045010262187, -0.5657367905801319, -0.569743327651659, -0.5730732954581713, -0.5756781848425268, -0.5775125540012717, -0.5785348093347776, -0.5787079920110844, -0.5780005526663841, -0.5763870949005924, -0.5738490670283978, -0.5703753810648028, -0.5659629382819701, -0.5606170419476023, -0.5543516800594162, -0.547189663967578, -0.539162612591433, -0.5303107762806638, -0.5206826989795974, -0.5103347219337654, -0.4993303364449728, -0.48773939689982837, -0.4756372083262972, -0.463103505064122, -0.45022133891878613, -0.4370758967223408, -0.423753269005093, -0.41033919400461905, -0.3969178049070168, -0.3835704130502874, -0.3703743651178263, -0.35740201643533376, -0.3447198628646976, -0.3323878680045296, -0.3204590094643429, -0.3089790495436723, -0.2979865159058602, -0.2875128617198951, -0.27758276562132644, -0.2682145302809352, -0.2594205425773809, -0.25120776560930536, -0.24357824063949773, -0.2365295840295255, -0.23005546967027934, -0.22414609130375918, -0.21878860171399495 ], [ -0.5182509538403852, -0.5234725221623914, -0.5282442128012879, -0.5325187283304619, -0.5362493463732657, -0.5393904887644874, -0.5418983315170106, -0.5437314477837369, -0.5448514739548469, -0.5452237870145658, -0.5448181794080476, -0.5436095160589498, -0.541578356959834, -0.5387115280543565, -0.535002623050307, -0.5304524194243232, -0.5250691932387253, -0.5188689194705667, -0.5118753472761538, -0.504119942844081, -0.4956416960387694, -0.48648679068272016, -0.47670814183810584, -0.4663648066176338, -0.455521277728138, -0.44424667106455606, -0.43261382028312734, -0.42069829258486524, -0.4085773412695196, -0.3963288124256391, -0.3840300258880964, -0.3717566546768596, -0.3595816324948935, -0.3475741247503563, -0.33579860325936073, -0.32431406576122823, -0.3131734361677938, -0.30242316907051014, -0.29210306409492226, -0.28224627638014255, -0.27287949367483155, -0.26402324163607904, -0.2556922774706418, -0.24789603630362844, -0.24063910188653048, -0.23392168106961142, -0.22774006836467953, -0.22208709229119816, -0.21695253899626554, -0.21232355111963264 ], [ -0.4940253923764856, -0.49835910378485593, -0.5022602629174067, -0.5056873367711597, -0.5085996164970172, -0.5109577305578433, -0.5127241885901925, -0.5138639484637988, -0.5143449973683871, -0.5141389361690345, -0.5132215548514959, -0.5115733857274709, -0.5091802202871608, -0.5060335752648464, -0.5021310936966112, -0.4974768675422553, -0.49208166982234025, -0.4859630861468467, -0.4791455378970634, -0.47166019203528, -0.4635447553914662, -0.4548431541282133, -0.4456051017352738, -0.43588556120484234, -0.4257441088985048, -0.41524420903242, -0.4044524087814506, -0.39343746495888565, -0.3822694144079737, -0.37101860207591064, -0.35975468367185803, -0.34854562413434664, -0.33745671875010763, -0.326549669873364, -0.3158817570802944, -0.30550513981647043, -0.2954663268086476, -0.28580583479989796, -0.2765580421316334, -0.2677512242999487, -0.2594077435187888, -0.2515443557449334, -0.24417259716151485, -0.23729921614865657, -0.23092662372672657, -0.22505334303704694, -0.21967444515868595, -0.21478196381690817, -0.2103652852619582, -0.2064115120179595 ], [ -0.4712800766528078, -0.4748050814283651, -0.4779153814042597, -0.4805747196342688, -0.48274786500361466, -0.4844010728361813, -0.4855025676123975, -0.4860230406838212, -0.4859361545404671, -0.4852190439619326, -0.4838528033406454, -0.48182294868590725, -0.479119842377687, -0.47573906870606664, -0.47168174865230095, -0.46695478326030726, -0.46157101629799213, -0.4555493086633733, -0.4489145190600966, -0.44169738772750744, -0.4339343223167921, -0.42566708720612645, -0.4169423995078203, -0.40781143663922514, -0.39832926156646076, -0.38855417272527093, -0.37854698631226347, -0.3683702593620447, -0.35808746311880935, -0.34776211807707746, -0.3374569050934013, -0.3272327713835794, -0.31714805584728756, -0.307257664170426, -0.2976123288891601, -0.28825799078677616, -0.2792353335205071, -0.270579492478047, -0.26231994306538686, -0.25448055655675217, -0.24707979754344522, -0.24013102887180604, -0.23364288839408387, -0.22761970546229182, -0.22206193155490517, -0.21696656659536562, -0.21232756898406602, -0.20813624247406493, -0.2043815966759457, -0.20105068037100926 ], [ -0.4499835382163875, -0.4527751759329949, -0.4551702975526559, -0.4571374576766821, -0.45864639654404615, -0.45966845163823233, -0.4601769841560286, -0.4601478136746515, -0.4595596533114138, -0.458394536750649, -0.45663822777998786, -0.45428060249578706, -0.4513159941635517, -0.44774349089842447, -0.4435671768896843, -0.4387963088318111, -0.4334454205143585, -0.4275343501026506, -0.42108818642170287, -0.4141371324237608, -0.4067162858511326, -0.3988653387789447, -0.3906281991362972, -0.38205253839838116, -0.3731892704135603, -0.3640919668501452, -0.3548162151745018, -0.34541892565088894, -0.33595759490731136, -0.3264895355041053, -0.3170710839985731, -0.30775680436407393, -0.29859870905614483, -0.28964552567358814, -0.2809420414850843, -0.2725285590458627, -0.26444049190303665, -0.25670811940814764, -0.24935650533525044, -0.24240556954502535, -0.23587028906937424, -0.2297609973679834, -0.22408374878521164, -0.21884071827267115, -0.21403061223370456, -0.20964907295671265, -0.20568906519719543, -0.2021412383807233, -0.19899426147863775, -0.19623512999247672 ], [ -0.43009808937785576, -0.43222774384471185, -0.4339792495802067, -0.435325533224344, -0.43624083012913517, -0.43670105053925157, -0.4366841545749647, -0.43617052983896965, -0.4351433646713687, -0.4335890094121553, -0.4314973175496051, -0.42886195838556085, -0.42568069287592014, -0.4219556046354418, -0.4176932787401063, -0.41290492190510975, -0.4076064188237841, -0.4018183208586179, -0.3955657647944055, -0.3888783208942964, -0.38178977093698097, -0.37433781816150213, -0.366563732034177, -0.3585119314498669, -0.3502295104134239, -0.3417657105105255, -0.3331713447390777, -0.3244981777755128, -0.3157982687945651, -0.3071232848640859, -0.29852379595450007, -0.2900485668008418, -0.28174386593334877, -0.27365281731376134, -0.2658148237613591, -0.2582650919675834, -0.2510342848982471, -0.24414831838469242, -0.2376283059896689, -0.23149064253981655, -0.22574720520944724, -0.2204056440169877, -0.21546973171672945, -0.21093974547138528, -0.20681285770900382, -0.2030835195126801, -0.19974382552830994, -0.19678385403812193, -0.19419197932955035, -0.19195515586556722 ], [ -0.41158079638928347, -0.41311580618811716, -0.4142910683979787, -0.41508346784313765, -0.4154712891208847, -0.4154345408936526, -0.4149552839684776, -0.4140179574863456, -0.41260969695324956, -0.4107206373892246, -0.40834419459278937, -0.4054773174527522, -0.4021207044156795, -0.3982789776508807, -0.3939608091434681, -0.38917899386845345, -0.3839504663111101, -0.37829625783780596, -0.37224139370712894, -0.3658147297549419, -0.3590487299015478, -0.35197918654048344, -0.34464488653046765, -0.33708722591863427, -0.3293497767214594, -0.3214778091879511, -0.3135177731399764, -0.30551674245834703, -0.2975218278306303, -0.2895795647635132, -0.2817352867759494, -0.2740324976208629, -0.2665122609883791, -0.2592126306214888, -0.252168146871534, -0.24540942596788984, -0.23896286451131454, -0.23285047370755496, -0.2270898467681779, -0.22169425099996398, -0.2166728259962094, -0.21203086297120066, -0.20777013828572422, -0.20388927598577244, -0.20038411838736092, -0.1972480889581305, -0.19447253686126476, -0.19204705688645318, -0.1899597818435148, -0.18819764685061435 ], [ -0.3943843929210611, -0.3953880110007617, -0.3960501884370706, -0.39635138028078554, -0.39627350470569667, -0.39580022886588706, -0.3949172544371291, -0.3936125976669934, -0.39187685833970276, -0.3897034717768437, -0.38708893787564924, -0.38403302125953853, -0.38053891689833663, -0.3766133760536169, -0.37226678810751723, -0.36751321471334486, -0.3623703737182056, -0.3568595713901398, -0.35100558256294034, -0.34483647931394923, -0.33838340964306235, -0.331680328269754, -0.3247636820830335, -0.3176720529794238, -0.3104457608678204, -0.30312642962265257, -0.295756518897043, -0.2883788251793825, -0.281035956524722, -0.2737697872298087, -0.26662090146854855, -0.2596280384935279, -0.25282755607080265, -0.24625293260691739, -0.2399343308709304, -0.23389824612100585, -0.22816725793826786, -0.22275989806519347, -0.21769063701890223, -0.21296998205901163, -0.20860467034581642, -0.20459793542848126, -0.20094982315709986, -0.19765753431691224, -0.19471577471061963, -0.19211709789045628, -0.18985223029452825, -0.18791037255158916, -0.18627947390038302, -0.18494647898169747 ], [ -0.378458130684049, -0.3789895268621909, -0.3791975832081781, -0.37906596283889593, -0.3785798315314698, -0.37772610847901633, -0.37649371341784077, -0.3748738054424622, -0.3728600085483401, -0.370448618794212, -0.3676387879804618, -0.36443267891525677, -0.3608355876953714, -0.35685602896166546, -0.3525057807836942, -0.3477998866531393, -0.34275661297629656, -0.33739736139450094, -0.33174653616378424, -0.32583136762643927, -0.3196816934509048, -0.3133296997640732, -0.3068096245410441, -0.3001574256781474, -0.2934104161256885, -0.286606868413982, -0.2797855910297179, -0.27298547958051733, -0.266245046721277, -0.2596019365682374, -0.2530924318588602, -0.24675096531238627, -0.24060965013581237, -0.23469784773602154, -0.2290417925385423, -0.2236642934399976, -0.21858452819657237, -0.21381794098284868, -0.2093762452706771, -0.20526752556377925, -0.20149642405567025, -0.19806439325579617, -0.19496999359805445, -0.19220921576993688, -0.1897758102121354, -0.18766160999720483, -0.1858568372743039, -0.18435038709435725, -0.1831300854059379, -0.18218292025014837 ], [ -0.36374856529647537, -0.3638628659127563, -0.3636716245249473, -0.3631613755744938, -0.36232017539959227, -0.36113782107529246, -0.35960606299349274, -0.3577188069723758, -0.355472301524116, -0.3528653058700425, -0.34989923439113624, -0.3465782734501178, -0.34290946692229884, -0.33890276731792623, -0.33457105004930876, -0.3299300891591539, -0.32499849363882594, -0.31979760427422366, -0.3143513517067189, -0.3086860770329062, -0.3028303167464569, -0.2968145541227333, -0.2906709392640745, -0.2844329799962766, -0.27813520570939765, -0.2718128061811088, -0.26550124755544036, -0.2592358681391177, -0.25305145768220816, -0.24698182544398906, -0.24105936462515942, -0.23531462352916577, -0.2297758967413429, -0.2244688521031245, -0.2194162105723848, -0.21463749547968747, -0.21014886476414718, -0.20596303456887677, -0.2020892957814575, -0.19853361789481738, -0.1952988282512711, -0.19238485035725628, -0.18978898300106373, -0.18750620225024273, -0.18552947049350066, -0.1838500397884526, -0.18245774019412897, -0.18134124699552312, -0.18048832346748345, -0.1798860379581022 ], [ -0.3502002765746369, -0.3499486359385189, -0.34940886539475613, -0.3485700587845132, -0.3474228339284682, -0.3459595225707883, -0.3441743520144839, -0.3420636146862882, -0.33962582180166934, -0.3368618373450686, -0.33377498874870426, -0.33037115095144864, -0.3266588009448508, -0.3226490404551966, -0.31835558504651107, -0.3137947186275085, -0.3089852130650216, -0.3039482133003977, -0.2987070889856923, -0.29328725415928114, -0.2877159568331449, -0.28202204055232916, -0.2762356800219383, -0.27038809281983744, -0.26451122909845204, -0.2586374411325191, -0.2527991347216091, -0.24702840494610878, -0.24135665972797027, -0.23581423613714048, -0.2304300163923796, -0.22523105287200562, -0.2202422138468061, -0.2154858635793706, -0.2109815913122557, -0.20674600294864254, -0.2027925866074114, -0.19913165880817596, -0.19577039237416138, -0.19271292115086025, -0.18996051134628322, -0.18751178552792913, -0.18536298347810298, -0.1835082441718443, -0.18193989470841498, -0.18064873453545238, -0.17962430619549918, -0.17885514665459556, -0.17832901575661264, -0.17803310034755393 ], [ -0.33775652335275796, -0.3371862220220566, -0.33634474749353116, -0.33522346512177736, -0.33381525197534334, -0.3321146607255425, -0.33011807367380364, -0.32782384357595373, -0.32523241792798074, -0.3223464434862009, -0.31917084801263407, -0.31571289656560586, -0.3119822200901039, -0.30799081458871025, -0.30375300974901753, -0.2992854065366286, -0.29460678389669737, -0.28973797530026757, -0.28470171638387753, -0.2795224653269287, -0.2742261978680095, -0.26884017897287227, -0.2633927131505447, -0.25791287531391793, -0.25243022396878734, -0.2469744984868174, -0.24157530238584546, -0.2362617750194531, -0.23106225495962174, -0.22600393968382915, -0.22111254790761037, -0.2164119928749456, -0.21192407683800818, -0.20766821841458616, -0.20366122504319417, -0.19991712196112355, -0.19644704680722636, -0.19325921521075995, -0.19035895802600145, -0.187748825923711, -0.18542875264237413, -0.1833962649820544, -0.1816467259425183, -0.18017359727428772, -0.17896870885693206, -0.1780225243206559, -0.17732439473938988, -0.17686279467019417, -0.17662553703333783, -0.17659996517471277 ] ], "zauto": true, "zmax": 2.3013070734763, "zmin": -2.3013070734763 }, { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 1, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(255,247,251)" ], [ 0.14285714285714285, "rgb(236,231,242)" ], [ 0.2857142857142857, "rgb(208,209,230)" ], [ 0.42857142857142855, "rgb(166,189,219)" ], [ 0.5714285714285714, "rgb(116,169,207)" ], [ 0.7142857142857143, "rgb(54,144,192)" ], [ 0.8571428571428571, "rgb(5,112,176)" ], [ 1.0, "rgb(3,78,123)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "xaxis": "x2", "y": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "yaxis": "y2", "z": [ [ 0.542630558955957, 0.5294754807366485, 0.5157269013672516, 0.5014209768258613, 0.48660538393667635, 0.47134048529259914, 0.4557004756201408, 0.439774478003411, 0.4236675488853323, 0.4075015367704526, 0.39141571805947717, 0.37556710005083366, 0.3601302303111389, 0.3452962782929663, 0.3312710591335478, 0.3182715646736244, 0.30652049379314905, 0.29623831375514165, 0.2876326517526462, 0.28088541291201763, 0.27613892896490566, 0.27348340143125044, 0.27294841118283636, 0.2745008187095799, 0.27804988604586833, 0.28345846449177986, 0.29055753304055304, 0.29916091491268665, 0.30907765951884303, 0.3201208289958871, 0.33211264221788966, 0.34488671706750257, 0.3582884410906008, 0.3721744201559052, 0.38641168978954704, 0.40087707558585983, 0.41545684480787, 0.43004663193332776, 0.4445515416239008, 0.458886312374793, 0.4729754391751618, 0.4867531843007432, 0.5001634386772572, 0.5131594248115574, 0.5257032531651348, 0.5377653568315707, 0.5493238356548258, 0.5603637421667632, 0.5708763395930173, 0.5808583580804443 ], [ 0.5388693397374698, 0.5254158499302447, 0.5113513351858748, 0.49671095774733603, 0.4815411701304598, 0.4659008219426321, 0.44986224955349674, 0.4335123266385708, 0.4169534499242305, 0.4003044282030086, 0.3837012306532272, 0.3672975271314608, 0.35126490990063997, 0.3357926122080475, 0.32108642412991795, 0.30736635024410947, 0.29486238531989234, 0.2838076847983196, 0.27442852682089913, 0.2669309903541573, 0.2614853128079177, 0.25821025455730273, 0.2571608818395396, 0.25832316365090835, 0.2616172289358188, 0.26690855006965303, 0.27402398323118515, 0.28276865644225074, 0.2929403745173565, 0.3043398241438142, 0.3167764811709197, 0.3300711568525124, 0.3440564652038701, 0.3585763483793584, 0.3734854316970219, 0.3886486005365053, 0.40394090377693875, 0.4192477190768008, 0.4344650459713019, 0.44949978979694394, 0.46426993081771, 0.4787045153001441, 0.4927434448632987, 0.5063370709200112, 0.5194456209812208, 0.5320384941525863, 0.5440934664784618, 0.5555958451708275, 0.5665376061748344, 0.5769165434826073 ], [ 0.5355478739361798, 0.5218440623373218, 0.5075156581609008, 0.49259683799312787, 0.47713273116149, 0.46118043255134955, 0.4448099917326582, 0.4281053654975437, 0.411165323880546, 0.39410430282807335, 0.3770531969213477, 0.36016007679670514, 0.34359078729612136, 0.32752931732133683, 0.3121777099993685, 0.2977550849504414, 0.2844950798769323, 0.27264075266210447, 0.26243588485999714, 0.2541119659446383, 0.2478711851936181, 0.24386750688400083, 0.24218975134600357, 0.242851382021236, 0.24579040092296367, 0.2508795773026081, 0.25794379776272425, 0.2667795232536918, 0.27717186142061967, 0.2889068033096293, 0.301778357402887, 0.3155917161928681, 0.3301640344972077, 0.3453241805888621, 0.36091233501362385, 0.37677983887168986, 0.3927893607679167, 0.4088152761818015, 0.42474409780807854, 0.4404748114423956, 0.45591901871869595, 0.47100083937162734, 0.48565656844784905, 0.49983411353840407, 0.5134922540617187, 0.5265997714359157, 0.539134498674238, 0.5510823332387756, 0.5624362500106176, 0.5731953434692292 ], [ 0.532683113812577, 0.5187785409051644, 0.5042399001622504, 0.489100420012309, 0.47340384779477673, 0.4572053358956701, 0.44057229014697796, 0.42358517581825506, 0.4063382866316856, 0.38894049566719435, 0.3715160213929857, 0.3542052511955699, 0.3371656563386607, 0.32057278515016613, 0.30462120471953813, 0.2895250403713678, 0.2755174160271764, 0.2628476626590472, 0.2517747918326317, 0.24255575528794718, 0.23542787775166704, 0.23058683615430817, 0.22816425368390122, 0.22821096882448838, 0.23069153838584194, 0.23549198185126735, 0.2424379148793754, 0.2513169720861657, 0.26189941545400636, 0.27395330102999077, 0.28725354068072095, 0.30158615878170736, 0.3167496705109354, 0.3325552223162049, 0.34882650808217175, 0.36539989321332006, 0.382124797073549, 0.39886420329010147, 0.4154951264626698, 0.43190889653621517, 0.44801118008187824, 0.46372171352202834, 0.47897376531593466, 0.4937133701112746, 0.507898390158032, 0.5214974615977398, 0.5344888791892415, 0.5468594654999299, 0.5586034616387594, 0.5697214675737271 ], [ 0.5302848775508368, 0.516229438547881, 0.5015345204744475, 0.486232454197573, 0.4703655721488305, 0.45398694065310935, 0.43716103450842875, 0.4199643565387362, 0.4024860221803885, 0.38482835323323156, 0.3671075540760848, 0.34945457211211534, 0.33201625890018527, 0.31495692519494467, 0.2984602837367773, 0.2827315476610043, 0.26799905207112146, 0.25451418689408806, 0.24254778479372066, 0.23238072866501427, 0.2242870088775238, 0.21850938697888544, 0.21523123280527104, 0.21455164613825844, 0.21647205159095345, 0.22089916401346732, 0.22766280082782162, 0.23654153444268922, 0.2472879396263707, 0.2596479548012757, 0.2733728853674541, 0.28822540856171425, 0.3039819103715428, 0.32043316397146, 0.33738457327091265, 0.354656494499457, 0.3720847051060745, 0.38952089501129505, 0.4068330213110414, 0.4239054093125858, 0.4406385448335214, 0.4569485571996355, 0.47276642979518896, 0.48803699533147693, 0.5027177799390835, 0.5167777581643598, 0.530196073734771, 0.5429607713271725, 0.5550675743685228, 0.5665187342285805 ], [ 0.5283559787275991, 0.5141988106441177, 0.49940063184633277, 0.48399292363358104, 0.46801658245047134, 0.45152247884140667, 0.4345719351784255, 0.4172371317973331, 0.3996014755562319, 0.3817599991765566, 0.3638199031342056, 0.3459013989917459, 0.3281390505975879, 0.3106838117059296, 0.2937058825583055, 0.27739829330071053, 0.26198070039197496, 0.24770221020652788, 0.23484117624561104, 0.2236991233661954, 0.21458584274646522, 0.20779417265894026, 0.20356667226059358, 0.2020615206229983, 0.20332848686507957, 0.20730397637195913, 0.21382654311762275, 0.2226656651966764, 0.23355290906849052, 0.2462071707194938, 0.2603510091288981, 0.27571926256435125, 0.2920627466993376, 0.3091495602596618, 0.32676556120364963, 0.34471469861324777, 0.3628193493025498, 0.3809205784594889, 0.3988782000348043, 0.4165705508581672, 0.4338939498757481, 0.4507618619818542, 0.46710381646714094, 0.48286414435414254, 0.49800060116998973, 0.512482936491943, 0.5262914624491563, 0.539415662739157, 0.5518528731637614, 0.5636070550755066 ], [ 0.526892671447314, 0.5126811755796403, 0.49783070142550034, 0.4823719144123095, 0.4663442556784594, 0.44979631718064644, 0.4327861118095951, 0.4153812551679339, 0.39765910665730186, 0.3797069612240236, 0.36162243909052727, 0.34351428395542666, 0.32550383703868613, 0.3077274784671946, 0.29034027449386723, 0.2735208746193718, 0.2574772884576006, 0.24245246885166302, 0.22872763048760775, 0.21662011028735126, 0.20647183949945405, 0.19862514990136754, 0.19338592917735745, 0.19098035589480816, 0.19151795208224154, 0.19497495814535792, 0.20120448018625461, 0.20996757224707208, 0.22097156989017003, 0.23390326568875733, 0.24845132743482942, 0.26431856468085463, 0.2812273847760014, 0.29892170972578497, 0.31716746076477115, 0.3357526041912482, 0.35448706532134683, 0.37320251274332433, 0.39175193682004733, 0.41000896651830715, 0.4278669140560295, 0.44523757594470564, 0.46204984293996376, 0.4782481812073112, 0.49379104665419554, 0.5086492879019051, 0.5228045838871953, 0.5362479516975737, 0.5489783502363199, 0.5610013963773351 ], [ 0.5258853697440937, 0.5116644105799065, 0.4968096614835244, 0.4813509863887863, 0.46532635041907827, 0.4487820107170296, 0.43177258167573074, 0.4143609989977493, 0.3966184440028701, 0.3786243412887592, 0.36046660884988224, 0.3422424148014415, 0.32405976514427626, 0.3060402858467323, 0.2883235261930045, 0.2710729364253028, 0.25448328407655413, 0.23878859241389738, 0.22426866508770124, 0.21125096091496726, 0.2001033244263065, 0.1912127368257246, 0.1849474451390848, 0.18160613392712344, 0.18136710852855895, 0.1842564312394355, 0.19014872313930234, 0.1987986906892297, 0.2098874274791332, 0.2230656458185766, 0.23798411856285975, 0.2543106991945543, 0.27173786785481946, 0.2899851273411408, 0.3087991696968419, 0.32795328000647317, 0.3472465214295728, 0.36650281350926067, 0.3855698753920686, 0.40431799548985525, 0.42263861917568163, 0.4404427772678049, 0.45765939821708, 0.47423355540170625, 0.49012470071432523, 0.5053049300548145, 0.5197573181005407, 0.533474350658041, 0.5464564741448488, 0.5587107739345931 ], [ 0.5253195739159205, 0.5111308961926863, 0.4963163185531062, 0.48090490139898284, 0.46493311677837557, 0.44844486479664164, 0.43149135021841245, 0.4141308527281688, 0.39642846651990993, 0.3784559428126796, 0.36029184175820494, 0.3420222820639483, 0.32374265301607874, 0.3055606977783382, 0.2876013472497678, 0.27001352384037086, 0.25297877709071886, 0.2367209883782103, 0.22151542796617069, 0.20769413467526057, 0.19564302448826756, 0.18578489332160936, 0.17854316611291324, 0.17428649953228412, 0.17326533099760963, 0.1755628038519952, 0.18108226738332162, 0.18957629306530438, 0.20070061827901448, 0.21406890457134867, 0.22929284873225805, 0.24600491029639157, 0.26386818816372876, 0.2825791228902774, 0.3018670296558582, 0.3214925550183762, 0.34124590001202076, 0.3609450417293319, 0.38043396060981693, 0.3995808338231425, 0.4182761707831559, 0.43643089372391974, 0.45397438668558454, 0.4708525468693583, 0.4870258748065972, 0.5024676368929263, 0.5171621279866593, 0.5311030547248189, 0.5442920531142051, 0.5567373474781816 ], [ 0.5251769184640964, 0.5110587995757789, 0.4963249196998437, 0.48100352750970005, 0.4651296008854007, 0.4487447084993511, 0.431896726340451, 0.4146394531665249, 0.39703221529293664, 0.37913961327086043, 0.3610316392583302, 0.3427844771912871, 0.3244823728005164, 0.30622100060271074, 0.28811272160627865, 0.2702939701100698, 0.2529346779185087, 0.23624908732031827, 0.22050646249395173, 0.20603900249435814, 0.19324262008019874, 0.1825644091519499, 0.17446987464647232, 0.16938648021512523, 0.16763114613642827, 0.16934511151861908, 0.17446599162895648, 0.18275087653401192, 0.1938357837080928, 0.20730163681406985, 0.2227245933132025, 0.23970498145048103, 0.2578796964914888, 0.27692517465770006, 0.29655617759755554, 0.3165231960207895, 0.3366096474409878, 0.3566292225858996, 0.37642341285351644, 0.39585916521346604, 0.4148266141767096, 0.433236866246756, 0.4510198358367025, 0.4681221465485716, 0.48450511835553284, 0.5001428618947746, 0.5150204981073899, 0.5291325166782954, 0.5424812813872936, 0.5550756853591173 ], [ 0.5254362490906264, 0.5114233780889216, 0.4968067244174484, 0.4816137260001404, 0.4658778981146627, 0.44963856807007313, 0.43294047002431113, 0.41583325574098123, 0.39837102650251854, 0.38061205552800637, 0.3626189463070756, 0.3444595518909676, 0.3262090470124671, 0.3079535729286362, 0.28979582905840234, 0.2718628259980247, 0.25431570367196227, 0.23736102337776654, 0.22126221905849683, 0.2063488420494485, 0.1930196816296977, 0.18173375786774176, 0.17298146992146982, 0.16722993673906786, 0.1648465062472668, 0.16602241010457375, 0.17073089086006996, 0.1787419211816285, 0.18968311236493765, 0.20311380676070925, 0.21858418935990068, 0.2356701483847707, 0.2539883848644683, 0.2731999553866704, 0.29300857482348813, 0.3131571804569038, 0.33342427455328394, 0.3536205346242352, 0.3735857570158607, 0.39318607086235186, 0.4123113484415987, 0.43087276193531704, 0.4488004630505817, 0.4660413810150043, 0.4825571450954687, 0.4983221418309399, 0.5133217168840541, 0.527550528713703, 0.5410110575251773, 0.5537122690554692 ], [ 0.5260746407621314, 0.5121981918487662, 0.49773144163122457, 0.4827010443623092, 0.46713913380357147, 0.45108296500967837, 0.4345744320969783, 0.417659530283624, 0.4003878814681303, 0.3828125063762477, 0.3649900987630657, 0.34698212864037536, 0.32885715495402346, 0.3106947385048922, 0.2925912821190314, 0.2746679555819705, 0.25708056292012227, 0.2400307621156589, 0.22377742119299462, 0.20864599042200146, 0.1950323782688046, 0.18339578174540674, 0.17423287125906986, 0.16802643253140087, 0.16516999605668767, 0.16588771817838052, 0.170184065190876, 0.1778500033464407, 0.18852038413745437, 0.20175031706311924, 0.21707930358793637, 0.23407067908471307, 0.2523295510910703, 0.27150755473845634, 0.29130135399282586, 0.3114489168939116, 0.33172540738139944, 0.35193934666552107, 0.37192917622939925, 0.3915601761627925, 0.41072165947934314, 0.4293243792477554, 0.4472981106237512, 0.4645893903659507, 0.4811594092730137, 0.49698205922250166, 0.5120421381187574, 0.5263337149258043, 0.5398586544773274, 0.5526252988626285 ], [ 0.5270682841489922, 0.5133561352808759, 0.4990684210471514, 0.48423107984789093, 0.46887500712154073, 0.45303564146968855, 0.4367524520884222, 0.4200684080176781, 0.40302956064311035, 0.3856849319201676, 0.36808696656106016, 0.35029286618463024, 0.3323671598851643, 0.3143858552702219, 0.2964424298373263, 0.278655740309017, 0.26117963209832573, 0.2442136153198997, 0.22801341560835436, 0.2128994187777198, 0.19925981592864925, 0.18754347049794118, 0.17823569970452774, 0.17181065715830254, 0.16866117043915624, 0.16902249701692082, 0.17292104368948902, 0.18017428581601902, 0.19044049909241312, 0.20329058977965966, 0.21827192499950196, 0.23494994625836516, 0.2529286778508322, 0.2718573944905496, 0.29143021037197697, 0.3113828280306535, 0.33148854657792287, 0.35155437070451856, 0.37141746364008177, 0.3909419537440996, 0.41001603880651444, 0.42854933129566763, 0.44647040511557207, 0.46372452181570395, 0.48027152629246983, 0.49608390856228923, 0.5111450305220149, 0.5254475163001915, 0.5389918031163592, 0.5517848473952183 ], [ 0.5283931909746347, 0.5148702292349393, 0.5007875307521408, 0.4861704355901159, 0.47104881084126693, 0.4554566183009249, 0.4394314158858728, 0.4230138841472014, 0.406247518383244, 0.38917868293755775, 0.37185728077376123, 0.35433833689165783, 0.3366848115901937, 0.3189719274276535, 0.30129318921016646, 0.28376808115296737, 0.26655113084197896, 0.24984163410942617, 0.23389282298564243, 0.219018561984452, 0.2055946402131922, 0.19405033129224225, 0.18484465686164797, 0.17842265946400834, 0.17515319978660954, 0.17526228608739608, 0.17878729113222797, 0.18557388861445612, 0.19531616691890297, 0.20761857454548566, 0.22205425833863035, 0.23820582391197914, 0.2556875044110953, 0.2741540434389494, 0.2933021022145676, 0.3128682212940324, 0.332625544316627, 0.3523803153842632, 0.37196853173653455, 0.3912528522329596, 0.41011975858227645, 0.42847694056617786, 0.44625087913058165, 0.4633846104824583, 0.4798356622303932, 0.4955741571775104, 0.5105810819635798, 0.5248467173442868, 0.5383692254413102, 0.551153387505249 ], [ 0.530025695982407, 0.5167141513444423, 0.5028597007646872, 0.48848725424260353, 0.47362592204127235, 0.4583085978602914, 0.4425715120751481, 0.4264538547358752, 0.4099976137263634, 0.39324782266452263, 0.3762534584271298, 0.35906925786822586, 0.3417587211788744, 0.3243985162130614, 0.3070843752094244, 0.28993836929229194, 0.2731171527619313, 0.2568203905755293, 0.24129811151266067, 0.22685512770759653, 0.2138498693022638, 0.20268406140172301, 0.19377917049095805, 0.1875369481203018, 0.18428669551400403, 0.1842309849108411, 0.18740892023818476, 0.19369278943184037, 0.2028187685770194, 0.21443657820409295, 0.22815886910791155, 0.24359832012176286, 0.2603899922483138, 0.2782020670726764, 0.2967393267025975, 0.3157428010393368, 0.3349876842362016, 0.35428061985864034, 0.37345686008932066, 0.3923775021179484, 0.41092686980157744, 0.42901005667808034, 0.4465506306569732, 0.46348849821816046, 0.479777926746973, 0.49538572412864673, 0.5102895741237201, 0.5244765245877397, 0.5379416237629946, 0.550686698068048 ], [ 0.5319427600280332, 0.5188625171151772, 0.5052571571454875, 0.4911513715900193, 0.4765738317492142, 0.46155681527761233, 0.44613583933041523, 0.43034940495542606, 0.4142389981132788, 0.397849533477893, 0.3812304600856222, 0.36443776138476197, 0.3475370613646868, 0.33060797666406955, 0.31374971697695325, 0.297087723690415, 0.28078084936743153, 0.2650282253416142, 0.25007454679428515, 0.2362120216969343, 0.22377669801841338, 0.21313645120714717, 0.20466808032121714, 0.1987227050323101, 0.1955829092625256, 0.19542109206896785, 0.19827239008859024, 0.20403244624606187, 0.21248017413879672, 0.2233154173665701, 0.23619818953281344, 0.250780248506835, 0.2667260527948738, 0.2837244522186125, 0.3014939448056658, 0.3197840837996082, 0.33837482371197825, 0.3570748670249073, 0.37571958129703775, 0.39416877243506826, 0.41230445216865497, 0.4300286665935703, 0.44726142004257546, 0.4639387135813652, 0.480010709776213, 0.49544003048743257, 0.5102001905930557, 0.5242741672592667, 0.5376531016084221, 0.5503351274453784 ], [ 0.5341221013930769, 0.5212909526433485, 0.5079534066580981, 0.49413417608728516, 0.479861834212757, 0.46516850449143626, 0.45008958992007414, 0.43466364779094496, 0.41893255003601404, 0.40294210077481757, 0.3867433028705181, 0.37039446326692443, 0.35396428936451296, 0.33753604202471693, 0.32121266397645526, 0.30512259083001847, 0.28942568016070047, 0.2743183760366507, 0.2600368828163528, 0.2468567843446212, 0.23508728232970358, 0.2250582194458393, 0.2170986732150049, 0.2115076752801642, 0.20852073824514755, 0.20827941552157597, 0.2108126652527, 0.21603604039745844, 0.22376829993203753, 0.23375888305084494, 0.24571758256865012, 0.2593399110445875, 0.2743254465895344, 0.290389398968121, 0.3072689705133009, 0.3247262314619457, 0.34254885957322295, 0.3605496471084903, 0.37856532762965717, 0.3964550455301419, 0.41409865506445187, 0.4313949589449871, 0.44825995382461625, 0.46462512535923667, 0.4804358203071104, 0.4956497128489734, 0.510235374915262, 0.5241709548287147, 0.5374429645466855, 0.5500451729353922 ], [ 0.5365421980547107, 0.5239760184723827, 0.5109230536214947, 0.49740828474869114, 0.4834605230383787, 0.4691121725390114, 0.4543990596760896, 0.43936043173760636, 0.4240392544709473, 0.40848296071573664, 0.39274481000349815, 0.3768860032709082, 0.3609786459985642, 0.34510955663610887, 0.3293847681544478, 0.31393436905159233, 0.29891708619656904, 0.2845237473061319, 0.27097851057187994, 0.25853656702546945, 0.24747699817373675, 0.23808976138614596, 0.23065659748668352, 0.2254271832730853, 0.22259392612831053, 0.22227060344888905, 0.22448026144232744, 0.2291555536566465, 0.23615077221466493, 0.24526135893961837, 0.25624549286173426, 0.2688434906094064, 0.28279290816630326, 0.29783907247825864, 0.31374176587554686, 0.3302790621390317, 0.3472492074255224, 0.36447121632175056, 0.3817846442802801, 0.3990488421393893, 0.4161418940893978, 0.43295937329709067, 0.449413006144769, 0.4654293073518905, 0.48094822843730123, 0.4959218478332154, 0.5103131206978665, 0.5240946990564971, 0.5372478276518081, 0.5497613172964156 ], [ 0.539182211047159, 0.526895051521637, 0.5141415371953633, 0.5009471502095789, 0.48734124154680325, 0.47335686834615975, 0.45903071591043176, 0.44440319977499215, 0.4295188638552182, 0.4144272032523453, 0.3991840375155878, 0.38385353334025796, 0.3685109158424384, 0.35324580739087236, 0.33816598965422356, 0.32340120284971385, 0.3091063916277602, 0.2954636080459979, 0.2826816320570557, 0.27099232997300626, 0.26064292369110686, 0.2518837870102902, 0.24495220074381552, 0.24005365477158008, 0.23734350719001418, 0.23691253270561158, 0.23877949468615028, 0.24289219401968973, 0.24913612431553386, 0.25734802456179373, 0.2673310573270258, 0.27886898705745333, 0.2917379163908366, 0.30571519472214714, 0.32058574717456173, 0.3361463158312783, 0.3522081164050088, 0.3685983315995413, 0.3851607652884113, 0.40175589919873134, 0.41826053125901713, 0.43456712871279357, 0.45058299486423936, 0.46622932237075015, 0.48144018608579925, 0.49616151321241825, 0.5103500570415679, 0.5239723921122653, 0.5370039426208447, 0.5494280517620522 ], [ 0.5420218783788298, 0.5300259888686477, 0.517584870229513, 0.504724700636652, 0.4914756126651979, 0.4778715975705417, 0.46395050253041814, 0.44975420605537236, 0.4353290706069475, 0.4207267758583498, 0.40600562457167017, 0.39123237863807286, 0.3764846188786144, 0.3618535246940673, 0.3474468396314044, 0.33339163539889755, 0.31983632934399275, 0.30695128066178906, 0.29492723276249255, 0.28397093746069774, 0.27429754756754443, 0.26611983827860564, 0.2596350011375422, 0.25501052925794515, 0.25237132626896885, 0.2517902954576655, 0.2532840793160798, 0.2568144280584851, 0.26229434528650686, 0.2695972571211969, 0.2785672733828174, 0.28902903100071814, 0.30079626374524726, 0.31367880575539697, 0.3274880769385611, 0.34204124141297776, 0.35716425801338686, 0.3726940235729578, 0.3884797816886147, 0.40438394422505136, 0.420282451120478, 0.43606477463868404, 0.45163365610941475, 0.4669046464077301, 0.48180550641436676, 0.4962755109345682, 0.5102646892376095, 0.523733027423214, 0.5366496519153251, 0.548992009109 ], [ 0.5450414216047414, 0.533347225612532, 0.5212294433235587, 0.5087150884581406, 0.4958352368204352, 0.48262498339628207, 0.46912349075906973, 0.4553742016377744, 0.44142529628701005, 0.4273304730970831, 0.41315011333692736, 0.398952852643835, 0.3848175187231658, 0.37083530565759154, 0.35711194455872086, 0.3437695099770866, 0.33094739281916824, 0.31880190439505496, 0.3075039907657783, 0.2972346706386327, 0.2881780906900091, 0.28051251467248023, 0.27440006661677285, 0.26997650340046386, 0.26734251733947145, 0.2665579087860638, 0.2676393981164504, 0.2705620403251505, 0.27526347570227505, 0.2816498698760713, 0.2896024387997359, 0.29898377862499126, 0.30964360310049543, 0.3214237715694993, 0.33416262705273797, 0.3476986972226129, 0.3618738015821579, 0.3765355961999258, 0.39153958672254363, 0.40675064869273797, 0.4220441044505751, 0.43730641291274525, 0.45243553048307494, 0.46734099886749375, 0.4819438103073658, 0.49617609437648497, 0.5099806642053554, 0.5233104544377154, 0.5361278785806918, 0.548404129603513 ], [ 0.5482214952619087, 0.536837542196279, 0.5250519342770898, 0.5128925917509889, 0.500391603032905, 0.48758521593856846, 0.4745139095307664, 0.46122260598210957, 0.4477610847268505, 0.43418465427073005, 0.42055511617820307, 0.406942017287486, 0.39342412817992595, 0.38009100977543, 0.36704444221989385, 0.3543994042422886, 0.34228422742447323, 0.3308395348363731, 0.32021563538308107, 0.31056820550921305, 0.3020523511715896, 0.29481547473676495, 0.2889897010568723, 0.2846848370035703, 0.2819828412101562, 0.28093451452101725, 0.28155864352841636, 0.283843304418584, 0.2877486616059453, 0.29321049955562994, 0.30014388847992696, 0.30844667112672064, 0.31800271334955454, 0.3286849952171971, 0.34035863031064484, 0.35288384203118645, 0.36611885715272513, 0.37992263474550375, 0.39415734117258827, 0.408690499861585, 0.4233967738372047, 0.43815936829812285, 0.4528710638224947, 0.46743490647428837, 0.4817645900582348, 0.4957845698337457, 0.509429947883358, 0.5226461693299899, 0.5353885665241523, 0.5476217856344885 ], [ 0.5515431954238715, 0.5404761177808538, 0.5290293381822182, 0.5172316795468844, 0.5051162165473881, 0.4927202801023783, 0.4800855243756343, 0.46725810220675107, 0.45428899419982177, 0.44123452708803707, 0.42815709549352354, 0.41512606570838434, 0.4022187905077576, 0.3895216034263674, 0.37713059707361235, 0.3651519358641848, 0.3537014267105583, 0.34290309179193507, 0.3328865727353116, 0.32378335207913395, 0.3157219926069782, 0.30882282816059137, 0.30319272558227256, 0.29892060165285883, 0.2960742681192013, 0.2946988964135819, 0.29481702083108735, 0.296429667478873, 0.2995180320691547, 0.3040451850739481, 0.3099575089953725, 0.3171858503114054, 0.32564657650405626, 0.3352428013126358, 0.34586598669626967, 0.35739800413528977, 0.36971360584287744, 0.38268316265323415, 0.396175484891041, 0.4100605480609012, 0.4242119793439508, 0.43850920632621254, 0.45283921384357795, 0.4670978918763446, 0.4811909850496768, 0.49503467302303883, 0.5085558224613427, 0.5216919571244614, 0.5343909944220749, 0.5466107957695623 ], [ 0.5549881299467184, 0.5442426285698901, 0.5331391108911153, 0.5217072241649019, 0.5099809118495419, 0.4979984104920123, 0.4858022856816552, 0.47343954042227554, 0.4609618264079097, 0.44842577825678964, 0.4358934708783557, 0.423432970015098, 0.4111189067876858, 0.39903296286672896, 0.3872641113896306, 0.37590843123401185, 0.36506831243001897, 0.3548509114620534, 0.3453658047202136, 0.3367219227312744, 0.3290240065525089, 0.3223689722168905, 0.31684264908180665, 0.3125173277093402, 0.3094503943351354, 0.30768407051521224, 0.3072459948149855, 0.3081501789992528, 0.3103978251895534, 0.31397762383596167, 0.3188654126570142, 0.32502336185295055, 0.3323990568264939, 0.34092491476865844, 0.3505182954140403, 0.3610824980044011, 0.372508644190893, 0.3846782878554564, 0.3974664982725479, 0.41074513566876236, 0.42438606284516794, 0.43826409130815325, 0.4522595255530694, 0.4662602310377317, 0.4801632026338965, 0.4938756485096984, 0.5073156300182119, 0.5204123132201863, 0.5331058945452596, 0.5453472640685375 ], [ 0.558538541416276, 0.548117415660107, 0.5373594012150619, 0.5262948231195946, 0.5149582963309683, 0.5033886959676585, 0.4916291400917844, 0.47972700740565954, 0.46773400851888475, 0.4557063197860132, 0.4437047721606244, 0.43179506421620456, 0.4200479403814832, 0.40853924680949083, 0.39734975498207853, 0.38656463602674235, 0.37627248613415426, 0.36656385237618194, 0.3575292893574292, 0.34925708105150977, 0.3418308671118825, 0.3353274867299775, 0.32981536094838787, 0.3253536520809846, 0.32199226774744266, 0.3197725523901897, 0.3187282962490913, 0.3188865658047579, 0.32026787636999043, 0.32288539712724795, 0.32674315736192777, 0.3318335251416067, 0.3381344621492604, 0.3456071525273107, 0.35419454043799403, 0.3638211231595315, 0.374394100029921, 0.38580574401870005, 0.39793669466810916, 0.410659790369688, 0.42384405793693897, 0.43735853461940527, 0.45107568395949554, 0.46487425845224417, 0.47864154323075114, 0.4922749784311487, 0.5056832019478056, 0.5187865809706934, 0.5315173135523571, 0.5438191842911563 ], [ 0.5621774655597728, 0.5520816973776398, 0.5416693363905922, 0.5309711815430865, 0.5200222582521414, 0.5088617461226266, 0.49753289171958087, 0.48608291982547625, 0.4745629531497328, 0.46302794278031034, 0.45153659951691744, 0.44015130036470823, 0.42893792710154666, 0.4179655788600745, 0.4073060935373306, 0.3970333197748485, 0.3872221076272262, 0.37794703405464114, 0.36928094536657374, 0.3612934711294904, 0.35404972327987483, 0.347609415976928, 0.3420266040705906, 0.3373501306629459, 0.3336247071940187, 0.3308923566886666, 0.32919378476450434, 0.32856916074772924, 0.3290578352297009, 0.3306967010994345, 0.3335171921098174, 0.3375412391242297, 0.3427767826468556, 0.3492135916648097, 0.3568201185853913, 0.36554193520985695, 0.3753020016470317, 0.3860027025737761, 0.3975293229507466, 0.4097544780293618, 0.4225429707758354, 0.43575660218958895, 0.4492585690771832, 0.46291721227358174, 0.47660899829961256, 0.49022071361196407, 0.5036509180691552, 0.5168107449770541, 0.5296241543807582, 0.5420277502347457 ], [ 0.5658889034520438, 0.5561177965535326, 0.5460493212554927, 0.5357145031487426, 0.5251484720564643, 0.5143903352591029, 0.503483009181241, 0.4924730162195384, 0.48141025103026763, 0.4703477156730584, 0.4593412157404443, 0.44844900103655216, 0.4377313265936273, 0.4272499059784941, 0.4170672327941166, 0.4072457617328629, 0.39784696968106137, 0.3889303591709244, 0.3805525150726342, 0.37276636944936736, 0.36562085311369696, 0.359161098612993, 0.3534292953385051, 0.3484661807720796, 0.3443129952493768, 0.3410135598968084, 0.33861599965368594, 0.3371735700648055, 0.3367440941989111, 0.3373876907629266, 0.3391627623322566, 0.3421205650881501, 0.3462990200095085, 0.35171665872304664, 0.3583676497463649, 0.3662186943448018, 0.375208251856248, 0.3852481433846386, 0.39622720169940356, 0.40801637310397926, 0.42047457262490684, 0.4334546332843446, 0.4468088259100224, 0.4603936019048018, 0.4740733821790302, 0.4877233540444259, 0.5012313346244623, 0.5144988164416399, 0.5274413363711397, 0.5399883126449309 ], [ 0.5696579851034073, 0.560209353406011, 0.5504813134122388, 0.5405048421344768, 0.5303148422073979, 0.5199499528465925, 0.5094522949973233, 0.4988671527483458, 0.4882425923810887, 0.47762901863087226, 0.4670786653309757, 0.4566450156633421, 0.44638214746938226, 0.43634400370260773, 0.42658359942862123, 0.417152196406176, 0.40809850410160226, 0.3994679990766056, 0.39130248658186345, 0.38364004899193527, 0.3765155234954135, 0.36996161499228764, 0.3640106726545541, 0.3586970413851099, 0.35405975433478404, 0.3501451824396836, 0.3470091330579237, 0.34471782805404094, 0.34334722623816316, 0.3429803103032187, 0.34370223858433485, 0.3455936396787763, 0.34872273637348095, 0.353137323247636, 0.3588577799912005, 0.3658722050569461, 0.37413440345803345, 0.3835649487375532, 0.3940550095291207, 0.40547222812840655, 0.4176677443017424, 0.43048347425693645, 0.4437589233322619, 0.4573370497429347, 0.47106893467162286, 0.4848172074139536, 0.4984583071099177, 0.5118837379631053, 0.5250005053573129, 0.5377309205969215 ], [ 0.5734711043758478, 0.5643414986976933, 0.5549490429989371, 0.5453243779989536, 0.5355018406165695, 0.5255192089302381, 0.5154173603707297, 0.5052398425479301, 0.49503235735091156, 0.48484216032917266, 0.4747173794266321, 0.46470626081430916, 0.4548563560612831, 0.4452136754813035, 0.4358218481417453, 0.42672134973758524, 0.41794888371928285, 0.4095370249516488, 0.40151425266438684, 0.3939055025905531, 0.38673334850265784, 0.38001987383862373, 0.3737892114954865, 0.36807061661723856, 0.36290180269851924, 0.3583321321451725, 0.35442513192742137, 0.3512597324080874, 0.3489296363131945, 0.34754034848537657, 0.34720365899602706, 0.3480297693577442, 0.35011773480043656, 0.35354535929843284, 0.3583599788471823, 0.3645715688563909, 0.3721492617376184, 0.38102173649415844, 0.39108122821020475, 0.402190315086685, 0.41419032121812965, 0.42691015496634793, 0.44017461384173856, 0.4538115095105764, 0.4676572933138984, 0.48156112633011083, 0.4953875143201902, 0.5090177225661627, 0.5223502184192488, 0.5353003824556715 ], [ 0.5773160097686775, 0.5685009683989111, 0.55943815485283, 0.550157587759736, 0.5406927094397822, 0.5310800647442323, 0.5213588760540393, 0.511570512784477, 0.5017578569827328, 0.49196457091729157, 0.48223427846671363, 0.4726096802759128, 0.4631316337240707, 0.4538382431817617, 0.4447640237066803, 0.43593922115631906, 0.4273893912748572, 0.4191353557292867, 0.41119365907424443, 0.4035776412278345, 0.396299209536492, 0.3893713387234802, 0.38281124450292164, 0.3766440695414173, 0.37090679501208806, 0.36565195803143496, 0.3609506311406691, 0.3568940283334858, 0.353593075825433, 0.35117536646985575, 0.3497791473992225, 0.349544396068556, 0.35060159686599124, 0.35305943794946365, 0.35699312702779473, 0.36243517113723783, 0.36937014985997507, 0.3777342734723138, 0.38741957797662085, 0.39828177313937246, 0.4101502688803713, 0.42283883621365576, 0.4361556256572416, 0.44991170072077463, 0.46392768726065137, 0.4780384916687317, 0.492096268174527, 0.5059719290729884, 0.5195555222731087, 0.5327557808570548 ], [ 0.5811818414771605, 0.5726761489351743, 0.5639362611845096, 0.5549913034288118, 0.545873517971737, 0.5366178798254643, 0.5272615954956967, 0.5178434835051257, 0.5084032403454835, 0.49898060241894304, 0.4896144235465122, 0.4803416991358514, 0.4711965822673181, 0.46220945352627757, 0.4534061244916727, 0.44480727263616726, 0.43642822027616807, 0.42827917849927305, 0.42036607446995095, 0.41269206290542937, 0.4052597861872492, 0.3980743901504587, 0.39114722335621316, 0.3845000477048664, 0.3781694706201635, 0.37221117932488335, 0.3667034259620131, 0.3617490966367176, 0.3574756291636746, 0.35403207159597055, 0.3515827580931936, 0.3502974764431464, 0.35033862387144354, 0.3518466111844537, 0.35492547439011807, 0.35963100269790493, 0.3659634569499783, 0.3738661058798109, 0.3832295976565053, 0.39390103196761395, 0.4056958775995384, 0.4184107405269382, 0.4318353272368727, 0.4457625303016405, 0.45999615636440666, 0.47435627799476876, 0.4886824759505097, 0.5028353682127362, 0.5166968439021324, 0.530169380712809 ], [ 0.5850591113376657, 0.576857050072303, 0.5684329029654321, 0.559814655128726, 0.5510330776238616, 0.5421212850722072, 0.5331141674812315, 0.5240476959852565, 0.5149581089869711, 0.5058809941438706, 0.4968502930129169, 0.4878972689993728, 0.4790494952722021, 0.47032993674007867, 0.4617562176355789, 0.4533401816469573, 0.44508786215030405, 0.4369999827910694, 0.42907310023402684, 0.4213014784822638, 0.4136797455954465, 0.40620632759924447, 0.39888758027296933, 0.39174244713482764, 0.38480736136290505, 0.3781409815388696, 0.3718282101734826, 0.3659828023397984, 0.3607477575499098, 0.3562926532950361, 0.35280720151787653, 0.35049067861798955, 0.3495375505927859, 0.35012053730477094, 0.35237331492061336, 0.35637567252565316, 0.3621438457847414, 0.36962781266711187, 0.3787158121588538, 0.38924479726544087, 0.40101451358572404, 0.41380265925225657, 0.4273790157414336, 0.4415172114306461, 0.45600356124203006, 0.4706430176110615, 0.4852626158085523, 0.49971293765077723, 0.5138681219183692, 0.5276248825734902 ], [ 0.5889396280612134, 0.5810352096779208, 0.5729194270021891, 0.5646189107337778, 0.5561627312630419, 0.547581905209348, 0.5389087709728804, 0.53017623474253, 0.5214168965584091, 0.5126620765757993, 0.503940774688163, 0.4952786119264284, 0.48669681894139916, 0.478211354270817, 0.4698322513160341, 0.46156330582719146, 0.453402222707174, 0.44534133951938587, 0.43736903191157905, 0.42947188146879167, 0.42163764812549415, 0.4138590364715785, 0.4061381772944353, 0.39849166104258127, 0.39095585603406857, 0.3835921180732773, 0.3764913484813357, 0.3697771906559938, 0.3636069944302936, 0.35816957530644605, 0.35367884308745207, 0.350362692690231, 0.34844724530242055, 0.3481376004365344, 0.3495974960490162, 0.3529312213509251, 0.35817124831761893, 0.36527405258486817, 0.374124720892573, 0.3845489105720393, 0.39632932789407577, 0.4092235316466991, 0.4229804186347037, 0.43735375658670755, 0.45211213982847615, 0.4670454857943949, 0.4819686031365258, 0.4967225068081594, 0.5111741324435111, 0.5252149992084036 ], [ 0.5928163749612879, 0.5852035403613872, 0.5773887924503102, 0.5693972307115073, 0.5612560418964329, 0.5529939635290403, 0.5446406145914363, 0.536225696926855, 0.5277780801009294, 0.5193247941235558, 0.5108899684590926, 0.502493771711258, 0.49415142339916485, 0.48587236600195094, 0.47765970014975073, 0.4695099963632474, 0.461413600880566, 0.45335554883590296, 0.4453171838013118, 0.43727855749330724, 0.42922164678297825, 0.42113437659852127, 0.4130153757926557, 0.4048793160006932, 0.39676258628316985, 0.3887289324597963, 0.3808745334377023, 0.3733317975663398, 0.3662709570655936, 0.35989836775858897, 0.35445038389773, 0.35018192392741276, 0.34734953346892383, 0.34618995189881224, 0.3468967151206814, 0.349598656927803, 0.35434458380174955, 0.3610973962593492, 0.3697386903140134, 0.3800822835488105, 0.3918932536794449, 0.40490855901984746, 0.41885599689106306, 0.4334695448686239, 0.448500404496409, 0.4637239767277147, 0.4789434749750148, 0.4939910209362767, 0.5087270083057428, 0.5230383733916699 ], [ 0.5966833508628686, 0.5893561319938774, 0.5818353249941963, 0.574144361679754, 0.5663084107037575, 0.5583538066802674, 0.550307347583921, 0.5421954661988975, 0.5340432913313324, 0.5258736268431722, 0.5177058910792329, 0.5095550753483585, 0.5014307967663022, 0.4933365365288946, 0.4852691677707936, 0.4772188856189829, 0.4691696539913663, 0.4611002775875156, 0.4529861923863493, 0.44480204339201884, 0.43652508427113124, 0.42813938959005404, 0.41964081521109126, 0.4110425726166956, 0.4023811922294924, 0.3937225300282738, 0.38516731069910193, 0.37685549332467266, 0.3689685020290362, 0.3617281284799338, 0.3553907880759476, 0.3502359702470562, 0.34654837935226024, 0.34459455640919817, 0.34459657223720913, 0.34670712115125696, 0.3509911135785222, 0.35741792214248197, 0.36586584359049856, 0.3761371458724884, 0.38797969031766477, 0.4011104083432142, 0.41523674429451135, 0.4300737752742654, 0.4453562834269039, 0.46084614167353105, 0.4763359109421532, 0.4916496727658432, 0.5066420168464492, 0.5211959098449184 ], [ 0.6005353869089595, 0.5934880262614252, 0.5862544390801997, 0.5788562941947735, 0.5713166560233036, 0.563659388186453, 0.5559084289616919, 0.5480869465802767, 0.5402163927587629, 0.5323154855138381, 0.5243991668884266, 0.5164775970112978, 0.50855526182093, 0.5006302863449317, 0.4926940569313384, 0.48473126252120197, 0.4767204653761203, 0.46863530450824925, 0.46044641985461976, 0.4521241619573169, 0.4436421207080312, 0.4349814672972938, 0.4261360542359728, 0.4171181551422733, 0.40796464149288164, 0.3987432765851798, 0.38955864400907786, 0.3805570079213697, 0.3719291281233322, 0.3639097617035309, 0.3567723758837989, 0.35081766259236113, 0.3463550435840215, 0.3436777015645667, 0.34303370585361825, 0.3445979359022354, 0.3484506674851745, 0.3545678672105485, 0.3628253484092329, 0.373015150030901, 0.38486956842485864, 0.3980873392007666, 0.4123574333301152, 0.42737784472227286, 0.44286860536157413, 0.45857952471111063, 0.4742937432129572, 0.48982829782659265, 0.505032746880674, 0.5197866608701098 ], [ 0.6043679526057048, 0.5975949798267629, 0.5906423486600489, 0.5835299098061273, 0.5762785836239865, 0.5689097470166328, 0.5614444977478996, 0.5539028063091715, 0.5463025760409148, 0.5386586448804362, 0.5309817764254147, 0.5232777031982012, 0.5155462999414949, 0.5077809780498743, 0.4999684022620493, 0.4920886359654088, 0.4841158206303446, 0.4760194872005847, 0.4677665824735995, 0.45932427180571134, 0.4506635511263048, 0.4417636659055907, 0.432617290536854, 0.4232363641013991, 0.41365839952944156, 0.4039529703066226, 0.394227916213565, 0.3846345820564607, 0.3753711076584583, 0.3666824536242796, 0.3588555722688524, 0.35220811344337694, 0.34706958387875053, 0.34375523783338824, 0.34253517832506175, 0.34360361965458164, 0.3470548022947155, 0.35287140957355495, 0.3609282353241509, 0.3710095400621614, 0.3828350766962192, 0.39608859306983, 0.41044368147421234, 0.4255840355500359, 0.44121730325882, 0.45708314784374193, 0.4729567748310604, 0.48864927614103815, 0.5040059503965976, 0.5189034758896438 ], [ 0.6081769638461513, 0.601673231636418, 0.5949957852582537, 0.5881626399664328, 0.5811925751140284, 0.5741045127692778, 0.5669167809690836, 0.5596462736639969, 0.5523075299805682, 0.5449117678628885, 0.5374659209705425, 0.5299717421007631, 0.5224250502570055, 0.5148152104606647, 0.5071249440629328, 0.4993305713287637, 0.4914027864135057, 0.4833080569822818, 0.4750107265855248, 0.46647587780630956, 0.45767298839958087, 0.4485803807162113, 0.43919042461194957, 0.42951540105609387, 0.4195938592297664, 0.40949719089527664, 0.39933598498662987, 0.38926549510250674, 0.3794892452820854, 0.37025943919951576, 0.3618725158651102, 0.354658109056925, 0.3489601300210673, 0.34511003145351765, 0.34339460130737287, 0.34402333835838994, 0.34710230886417465, 0.3526209423812157, 0.3604550413102159, 0.37038460453184013, 0.3821211837711034, 0.39533807796988596, 0.40969776084507775, 0.4248733209634611, 0.4405630323906562, 0.45649873460902846, 0.472449398977725, 0.4882213480099114, 0.503656373775279, 0.5186286881672484 ], [ 0.6119586040889327, 0.6057192877592409, 0.5993117392773939, 0.5927521555487251, 0.5860572163625672, 0.5792434627052216, 0.572326568155462, 0.5653205171332991, 0.5582367141568554, 0.5510830602844473, 0.5438630460606252, 0.5365749237405129, 0.5292110342699182, 0.5217573752051285, 0.5141935031842434, 0.5064928675703099, 0.4986236696532489, 0.4905503339409301, 0.4822356646499973, 0.4736437418498453, 0.4647435880140346, 0.4555136064249817, 0.4459467557663577, 0.4360563754506332, 0.4258825050974998, 0.415498435802501, 0.4050170728011123, 0.39459646027585116, 0.38444350970288527, 0.3748146036616993, 0.3660114034449431, 0.35837006502332736, 0.35224247937414566, 0.3479694482138766, 0.34584800155565193, 0.3460978625108883, 0.3488340956446793, 0.35405271902658564, 0.3616329308451181, 0.3713547863392917, 0.3829270233379201, 0.3960181111057124, 0.4102846247159894, 0.4253935006940583, 0.44103718749488663, 0.45694236403922744, 0.4728736513976286, 0.4886338460949857, 0.5040619762154398, 0.5190301531136974 ], [ 0.6157091676443686, 0.6097297342654164, 0.6035872367766676, 0.5972961010814976, 0.590870982032726, 0.5843261487838332, 0.5776747725728894, 0.5709281321848265, 0.5640947623999726, 0.5571795822109886, 0.5501830519437427, 0.5431004208647232, 0.5359211383950249, 0.528628511543452, 0.5211996974836728, 0.5136061223564354, 0.5058144147089594, 0.49778793421687656, 0.48948896356638305, 0.4808816138829689, 0.4719354719508642, 0.46262998994442206, 0.45295958315052376, 0.44293935327033773, 0.4326112857844282, 0.42205066656800566, 0.41137230837760264, 0.40073595404641604, 0.39034992081441977, 0.380471688529085, 0.37140379569944754, 0.3634832775609942, 0.35706326378091285, 0.3524865914539972, 0.35005350974087734, 0.34998830092637523, 0.35241170534186655, 0.35732591865586955, 0.3646159824917492, 0.37406668182816416, 0.3853898844164192, 0.3982554836118719, 0.4123199810286077, 0.4272491223899371, 0.442733462968248, 0.45849744683084537, 0.47430338775957936, 0.4899518789640853, 0.5052799490618345, 0.5201579582051498 ], [ 0.6194249314411879, 0.6137010854241025, 0.6078191599504847, 0.6017918828907562, 0.5956319863543078, 0.5893516057034901, 0.5829615909536705, 0.5764707470306316, 0.5698850289942762, 0.563206729169387, 0.5564337046183107, 0.5495587047956966, 0.5425688696114548, 0.5354454764691312, 0.5281640201420796, 0.5206947107604585, 0.5130034721518233, 0.5050535150921373, 0.4968075477619863, 0.4882306690448954, 0.47929396916453565, 0.4699788356285769, 0.46028192806649953, 0.4502207384152014, 0.439839584764042, 0.42921578579155995, 0.4184656123894688, 0.4077493978430652, 0.3972749007593426, 0.38729767654881686, 0.37811690339282994, 0.3700650021831733, 0.36348976779196795, 0.3587289011098292, 0.35607890926401603, 0.3557629070111342, 0.3579037994952048, 0.36250928164673046, 0.36947242191083035, 0.37858722579889476, 0.3895745756887946, 0.40211210356811034, 0.4158622085606, 0.4304945932040183, 0.4457020412959889, 0.4612098556572561, 0.4767802209193982, 0.4922129498972479, 0.5073439047783896, 0.52204208608418 ], [ 0.6231020589889295, 0.6176296712425821, 0.6120041155810072, 0.6062365155830123, 0.6003378046010471, 0.5943181442751192, 0.5881862657194515, 0.5819487508287016, 0.5756092802878066, 0.569167884996081, 0.5626202482122816, 0.5559571160849937, 0.5491638834978557, 0.5422204294105616, 0.535101280231871, 0.5277761804923581, 0.5202111467128895, 0.5123700726936883, 0.5042169425027851, 0.4957186912747239, 0.48684873327891826, 0.47759115050345236, 0.46794550067658214, 0.457932156438413, 0.4475980195374041, 0.43702235437558795, 0.4263223402941703, 0.4156577388776601, 0.4052338080818404, 0.39530129288567273, 0.3861520601126424, 0.3781088838834232, 0.37150827562313865, 0.3666763497174171, 0.36389959874231786, 0.3633947353843457, 0.365283476341564, 0.36957811453095746, 0.37618139730126315, 0.3849003582327526, 0.3954701128585569, 0.40758181716639724, 0.4209093949092407, 0.4351314843674791, 0.44994718496894437, 0.46508580351452644, 0.48031167064449487, 0.49542535503924073, 0.5102624971957719, 0.5246912301394179 ], [ 0.6267365377426368, 0.6215115653550832, 0.6161383521431099, 0.6106265270508324, 0.6049853647523815, 0.59922322866656, 0.5933469470222893, 0.587361140150463, 0.5812675257607511, 0.5750642383447379, 0.5687452085293769, 0.5622996575267702, 0.5557117700091823, 0.548960614956489, 0.5420203874963766, 0.534861044844555, 0.5274494057221455, 0.5197507748743248, 0.5117311424848812, 0.5033599922895154, 0.49461373160424005, 0.4854797300815528, 0.4759609192159517, 0.46608085690953993, 0.4558890937586348, 0.44546658053899507, 0.43493071856668186, 0.42443946725252985, 0.41419368774875304, 0.40443664527192497, 0.39544939042573346, 0.3875407353374884, 0.3810309420541222, 0.3762292517874138, 0.37340703678807613, 0.37277030011799955, 0.37443667370293715, 0.378422013266549, 0.38463971920447265, 0.39291263126115605, 0.40299418683509547, 0.4145938355300065, 0.4274018752796295, 0.44111035167456497, 0.455428499038494, 0.4700926864348496, 0.48487169839735333, 0.4995684972636451, 0.514019580153506, 0.5280928464865462 ], [ 0.6303241488873791, 0.6253425516852469, 0.620217723211354, 0.6149579186590776, 0.6095709047522325, 0.6040634313951162, 0.5984406466266124, 0.5927054735419006, 0.5868579758375999, 0.5808947472552414, 0.5748083689680541, 0.5685869872658532, 0.5622140710352656, 0.5556684137678278, 0.5489244474615556, 0.5419529352376967, 0.5347221053698755, 0.5271992814845351, 0.5193530517996691, 0.5111560042035741, 0.5025880331586968, 0.4936401975317127, 0.4843190729932597, 0.474651494445886, 0.46468951692982685, 0.45451532979159154, 0.44424573040217963, 0.43403559556823973, 0.4240795871568977, 0.4146111233033125, 0.40589750843501216, 0.39823016817920204, 0.39190934549318085, 0.387223527329132, 0.38442527883905675, 0.3837067503554039, 0.3851792397175613, 0.38886110209526475, 0.39467667781002785, 0.40246622763764256, 0.41200423187285296, 0.4230218899540521, 0.43522963997980857, 0.44833662662114937, 0.4620655556226796, 0.47616267878782803, 0.49040348278710205, 0.5045950176227888, 0.5185758379451685, 0.5322143971871968 ], [ 0.6338604667981462, 0.6291181262669014, 0.6242376924743398, 0.6192261745939428, 0.6140899877430003, 0.6088344565257241, 0.6034632718179544, 0.5979779197118208, 0.5923771089180846, 0.5866562307731065, 0.580806893867724, 0.5748165826436489, 0.568668495448173, 0.5623416218355027, 0.555811120728851, 0.5490490598869876, 0.542025572561842, 0.5347104790221687, 0.5270754085301154, 0.5190964410600565, 0.5107572668602768, 0.5020528345372731, 0.49299342234706883, 0.48360901916920207, 0.47395383620688314, 0.46411068189393584, 0.4541948155950532, 0.4443567495876781, 0.4347833036348902, 0.4256960634709103, 0.417346317793196, 0.41000565048228405, 0.40395177147634675, 0.3994499743672593, 0.39673177265212883, 0.39597351764290295, 0.3972786334354899, 0.4006669775461818, 0.4060735300535326, 0.4133564887678829, 0.4223127252666197, 0.4326972494080484, 0.4442431803414364, 0.4566795043804742, 0.4697450857116672, 0.48319849848665747, 0.49682401055869796, 0.5104344347446225, 0.5238716618970279, 0.5370056198494984 ], [ 0.637340884145543, 0.6328335291584293, 0.628193374039133, 0.6234263125532542, 0.6185375656611567, 0.6135312193436747, 0.6084097251259662, 0.6031733822493787, 0.5978198271967229, 0.5923435633605175, 0.5867355706359549, 0.5809830411033697, 0.5750692921576173, 0.5689739118450651, 0.5626731922179429, 0.5561409047249365, 0.5493494666417923, 0.5422715390055667, 0.5348820841613945, 0.5271608944479496, 0.5190955820047086, 0.5106849918923404, 0.5019429645986906, 0.49290232654711763, 0.48361892460895706, 0.474175438886101, 0.4646846047665689, 0.4552913529485325, 0.44617324766728156, 0.43753849952695567, 0.4296208058950725, 0.4226704098635705, 0.41694115751364574, 0.4126740242475337, 0.41007851707010173, 0.40931431360316944, 0.4104760904178399, 0.41358434219535645, 0.4185839605507667, 0.42535069597101627, 0.433703960678007, 0.4434233426952694, 0.4542659761493413, 0.46598242958321695, 0.47832966682229566, 0.49108053096928495, 0.5040298736246781, 0.5169978360848965, 0.529830932313911, 0.5424015689136383 ], [ 0.6407606578096301, 0.6364838005140121, 0.632079600778118, 0.6275529669752873, 0.6229080805572819, 0.6181479697125546, 0.6132740545600135, 0.6082856826485816, 0.603179679663126, 0.5979499465701056, 0.5925871405791616, 0.5870784827757355, 0.5814077395674859, 0.5755554276420711, 0.5694992924411308, 0.5632151077614107, 0.5566778386197107, 0.5498632006387171, 0.5427496365912626, 0.5353207139265185, 0.527567925368079, 0.5194938468597575, 0.5111155715103585, 0.5024682924460057, 0.49360884899976964, 0.48461897731312437, 0.47560791817911435, 0.4667139368193843, 0.45810421553292513, 0.44997251937107463, 0.4425340535253019, 0.4360170899541138, 0.4306512987830046, 0.42665329839527244, 0.4242106724527165, 0.42346640902226645, 0.4245061196528906, 0.4273502354684723, 0.4319525720323617, 0.4382054031115706, 0.4459499029969182, 0.4549899364826316, 0.46510692027190886, 0.4760737964147684, 0.4876668052446122, 0.49967444840219843, 0.5119036023247057, 0.5241831053341535, 0.5363653105610943, 0.548326126424664 ], [ 0.6441149703952264, 0.6400638545245945, 0.6358910131550619, 0.6316004957415109, 0.6271955928157155, 0.6226784462354098, 0.6180496390771584, 0.613307783567847, 0.6084491309614358, 0.603467232870318, 0.5983526888894887, 0.5930930199728476, 0.5876727104559413, 0.5820734633773511, 0.5762747133612963, 0.570254438362529, 0.5639903056708974, 0.5574611783915812, 0.5506489958050304, 0.5435410241130368, 0.5361324524309463, 0.5284292815189933, 0.5204514183322833, 0.5122358464226432, 0.5038396890614241, 0.49534291810213577, 0.48685038890250387, 0.47849280664701993, 0.4704261665121763, 0.4628291844206593, 0.4558982833675539, 0.44983986593443903, 0.4448599220665651, 0.4411514937713858, 0.43888108183264746, 0.4381755908578885, 0.4391116712989655, 0.4417091591267064, 0.4459296924029411, 0.4516806434790726, 0.4588235356020512, 0.46718541460949065, 0.4765713925241756, 0.4867767560325252, 0.4975974852008896, 0.508838562559549, 0.5203199197695948, 0.5318801951231643, 0.5433786530501471, 0.5546956770907817 ], [ 0.6473990021479754, 0.6435685650284577, 0.639622161158705, 0.6355631016110898, 0.6313939259313924, 0.6271160490104773, 0.622729394898546, 0.6182320354037255, 0.6136198562242438, 0.6088862782643083, 0.6040220663401621, 0.59901526129831, 0.5938512742086438, 0.5885131823161968, 0.5829822654068123, 0.5772388177694148, 0.5712632646663136, 0.5650376028231121, 0.5585471715769083, 0.5517827445574462, 0.5447429105634177, 0.5374366858941957, 0.5298862679037072, 0.5221298000566479, 0.5142239717893436, 0.5062462226803659, 0.49829626291051154, 0.4904965679948192, 0.4829914687072619, 0.4759444579570642, 0.4695334028510764, 0.4639435114552301, 0.4593581784371907, 0.4559482116745361, 0.4538603661014068, 0.45320647306116574, 0.4540546164928175, 0.45642366080554314, 0.4602819592920505, 0.46555037066854427, 0.4721089838051773, 0.4798064058671864, 0.48847023537642825, 0.4979174248928333, 0.5079635439689467, 0.5184303487678666, 0.5291514362395368, 0.5399760420899754, 0.5507712148591656, 0.5614226768356452 ], [ 0.6506080083732475, 0.6469928570176144, 0.6432676125494066, 0.639434960403984, 0.6354968184766264, 0.6314540200021465, 0.627305989815339, 0.6230504311247713, 0.618683044256418, 0.6141973030572008, 0.6095843184798707, 0.6048328219386714, 0.5999293029371693, 0.5948583358232364, 0.5896031289310019, 0.5841463254629408, 0.5784710789167397, 0.5725624163627755, 0.5664088901167585, 0.5600045019768253, 0.553350863783262, 0.546459533119062, 0.5393544330061278, 0.5320742291660904, 0.5246744980983326, 0.517229475430268, 0.5098331304966817, 0.5025992771227424, 0.4956604138937955, 0.4891650064595804, 0.4832729995720351, 0.47814949580568533, 0.47395676860224356, 0.47084507390101676, 0.46894303892743416, 0.4683486584277394, 0.4691220243554482, 0.47128078482139457, 0.47479896525399945, 0.4796092640092449, 0.4856083921513198, 0.49266460656732003, 0.5006263809157522, 0.5093311844144668, 0.5186135386473717, 0.5283118084927116, 0.5382734712015571, 0.5483588422911647, 0.5584433958905384, 0.568418903094621 ] ] }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "text": [ "Arm 0_0
hartmann6: -0.402366 (SEM: 0)
x1: 0.733035
x2: 0.0610081
x3: 0.085204
x4: 0.258361
x5: 0.114038
x6: 0.912911", "Arm 1_0
hartmann6: -0.210452 (SEM: 0)
x1: 0.233727
x2: 0.841503
x3: 0.992144
x4: 0.91822
x5: 0.325854
x6: 0.309757", "Arm 2_0
hartmann6: -0.485291 (SEM: 0)
x1: 0.456063
x2: 0.695674
x3: 0.762829
x4: 0.0961709
x5: 0.281806
x6: 0.548972", "Arm 3_0
hartmann6: -0.752704 (SEM: 0)
x1: 0.49945
x2: 0.156111
x3: 0.601239
x4: 0.157366
x5: 0.546349
x6: 0.805099", "Arm 4_0
hartmann6: -0.0149427 (SEM: 0)
x1: 0.326059
x2: 0.691856
x3: 0.229641
x4: 0.615605
x5: 0.919577
x6: 0.722951", "Arm 5_0
hartmann6: -0.590213 (SEM: 0)
x1: 0.155288
x2: 0.887927
x3: 0.479935
x4: 0.805947
x5: 0.480473
x6: 0.114611", "Arm 6_0
hartmann6: -0.47322 (SEM: 0)
x1: 0.247413
x2: 0.374861
x3: 0.0699674
x4: 0.300832
x5: 0.543381
x6: 0.387147", "Arm 7_0
hartmann6: -0.018271 (SEM: 0)
x1: 0.864984
x2: 0.079029
x3: 0.852291
x4: 0.765624
x5: 0.656406
x6: 0.724577", "Arm 8_0
hartmann6: -0.0410299 (SEM: 0)
x1: 0.254324
x2: 0.865416
x3: 0.799209
x4: 0.30456
x5: 0.899295
x6: 0.789859", "Arm 9_0
hartmann6: -0.228334 (SEM: 0)
x1: 0.71055
x2: 0.782865
x3: 0.495047
x4: 0.153398
x5: 0.43716
x6: 0.706623", "Arm 10_0
hartmann6: -1.06312 (SEM: 0)
x1: 0.600564
x2: 0.223024
x3: 0.091437
x4: 0.172231
x5: 0.313197
x6: 0.878329", "Arm 11_0
hartmann6: -0.185426 (SEM: 0)
x1: 0.364004
x2: 0.632958
x3: 0.24173
x4: 0.0646517
x5: 0.511712
x6: 0.96865", "Arm 12_0
hartmann6: -1.23018 (SEM: 0)
x1: 0.541585
x2: 0.229734
x3: 0.15374
x4: 0.148959
x5: 0.385234
x6: 0.829596", "Arm 13_0
hartmann6: -0.991403 (SEM: 0)
x1: 0.509567
x2: 0.207489
x3: 0.147193
x4: 0.0705987
x5: 0.416679
x6: 0.785515", "Arm 14_0
hartmann6: -1.39049 (SEM: 0)
x1: 0.518235
x2: 0.241577
x3: 0.200845
x4: 0.198987
x5: 0.417275
x6: 0.810633", "Arm 15_0
hartmann6: -1.33918 (SEM: 0)
x1: 0.500609
x2: 0.26813
x3: 0.240861
x4: 0.247939
x5: 0.432561
x6: 0.838201", "Arm 16_0
hartmann6: -1.40488 (SEM: 0)
x1: 0.550035
x2: 0.234856
x3: 0.206317
x4: 0.235548
x5: 0.442526
x6: 0.746864", "Arm 17_0
hartmann6: -1.98819 (SEM: 0)
x1: 0.484511
x2: 0.22823
x3: 0.237
x4: 0.232679
x5: 0.384916
x6: 0.744099", "Arm 18_0
hartmann6: -2.4623 (SEM: 0)
x1: 0.449918
x2: 0.214364
x3: 0.27629
x4: 0.271086
x5: 0.349526
x6: 0.70665", "Arm 19_0
hartmann6: -2.75401 (SEM: 0)
x1: 0.414782
x2: 0.194756
x3: 0.314423
x4: 0.307907
x5: 0.311877
x6: 0.667367", "Arm 20_0
hartmann6: -2.74606 (SEM: 0)
x1: 0.386351
x2: 0.212861
x3: 0.336375
x4: 0.311148
x5: 0.266056
x6: 0.632334", "Arm 21_0
hartmann6: -2.84373 (SEM: 0)
x1: 0.366382
x2: 0.146103
x3: 0.311708
x4: 0.335777
x5: 0.286141
x6: 0.655994", "Arm 22_0
hartmann6: -2.92411 (SEM: 0)
x1: 0.374518
x2: 0.0965846
x3: 0.38366
x4: 0.296887
x5: 0.285061
x6: 0.65271", "Arm 23_0
hartmann6: -2.61901 (SEM: 0)
x1: 0.410246
x2: 0.0545891
x3: 0.352164
x4: 0.310357
x5: 0.285893
x6: 0.592927" ], "type": "scatter", "x": [ 0.7330349087715149, 0.233726822771132, 0.4560632612556219, 0.4994495641440153, 0.32605923898518085, 0.15528818685561419, 0.24741332605481148, 0.8649843530729413, 0.25432397425174713, 0.7105504367500544, 0.600564319640398, 0.364004491828382, 0.5415848197676835, 0.5095666068290555, 0.51823461918367, 0.5006089473312668, 0.5500353263563221, 0.48451098485418603, 0.4499176476637467, 0.41478153727762374, 0.3863509902382102, 0.36638225737028096, 0.3745182767069761, 0.4102456087040271 ], "xaxis": "x", "y": [ 0.06100805476307869, 0.8415030026808381, 0.6956740934401751, 0.15611135214567184, 0.6918562883511186, 0.8879265636205673, 0.3748607337474823, 0.07902895659208298, 0.8654162352904677, 0.7828654944896698, 0.22302412055432796, 0.6329575339332223, 0.22973441421901103, 0.20748873245947327, 0.24157697962290028, 0.26813013428499444, 0.23485606287129523, 0.2282301765187898, 0.21436412901899668, 0.19475629378241366, 0.212860591600044, 0.14610327237015194, 0.09658462471824511, 0.05458911567017346 ], "yaxis": "y" }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "showlegend": false, "text": [ "Arm 0_0
hartmann6: -0.402366 (SEM: 0)
x1: 0.733035
x2: 0.0610081
x3: 0.085204
x4: 0.258361
x5: 0.114038
x6: 0.912911", "Arm 1_0
hartmann6: -0.210452 (SEM: 0)
x1: 0.233727
x2: 0.841503
x3: 0.992144
x4: 0.91822
x5: 0.325854
x6: 0.309757", "Arm 2_0
hartmann6: -0.485291 (SEM: 0)
x1: 0.456063
x2: 0.695674
x3: 0.762829
x4: 0.0961709
x5: 0.281806
x6: 0.548972", "Arm 3_0
hartmann6: -0.752704 (SEM: 0)
x1: 0.49945
x2: 0.156111
x3: 0.601239
x4: 0.157366
x5: 0.546349
x6: 0.805099", "Arm 4_0
hartmann6: -0.0149427 (SEM: 0)
x1: 0.326059
x2: 0.691856
x3: 0.229641
x4: 0.615605
x5: 0.919577
x6: 0.722951", "Arm 5_0
hartmann6: -0.590213 (SEM: 0)
x1: 0.155288
x2: 0.887927
x3: 0.479935
x4: 0.805947
x5: 0.480473
x6: 0.114611", "Arm 6_0
hartmann6: -0.47322 (SEM: 0)
x1: 0.247413
x2: 0.374861
x3: 0.0699674
x4: 0.300832
x5: 0.543381
x6: 0.387147", "Arm 7_0
hartmann6: -0.018271 (SEM: 0)
x1: 0.864984
x2: 0.079029
x3: 0.852291
x4: 0.765624
x5: 0.656406
x6: 0.724577", "Arm 8_0
hartmann6: -0.0410299 (SEM: 0)
x1: 0.254324
x2: 0.865416
x3: 0.799209
x4: 0.30456
x5: 0.899295
x6: 0.789859", "Arm 9_0
hartmann6: -0.228334 (SEM: 0)
x1: 0.71055
x2: 0.782865
x3: 0.495047
x4: 0.153398
x5: 0.43716
x6: 0.706623", "Arm 10_0
hartmann6: -1.06312 (SEM: 0)
x1: 0.600564
x2: 0.223024
x3: 0.091437
x4: 0.172231
x5: 0.313197
x6: 0.878329", "Arm 11_0
hartmann6: -0.185426 (SEM: 0)
x1: 0.364004
x2: 0.632958
x3: 0.24173
x4: 0.0646517
x5: 0.511712
x6: 0.96865", "Arm 12_0
hartmann6: -1.23018 (SEM: 0)
x1: 0.541585
x2: 0.229734
x3: 0.15374
x4: 0.148959
x5: 0.385234
x6: 0.829596", "Arm 13_0
hartmann6: -0.991403 (SEM: 0)
x1: 0.509567
x2: 0.207489
x3: 0.147193
x4: 0.0705987
x5: 0.416679
x6: 0.785515", "Arm 14_0
hartmann6: -1.39049 (SEM: 0)
x1: 0.518235
x2: 0.241577
x3: 0.200845
x4: 0.198987
x5: 0.417275
x6: 0.810633", "Arm 15_0
hartmann6: -1.33918 (SEM: 0)
x1: 0.500609
x2: 0.26813
x3: 0.240861
x4: 0.247939
x5: 0.432561
x6: 0.838201", "Arm 16_0
hartmann6: -1.40488 (SEM: 0)
x1: 0.550035
x2: 0.234856
x3: 0.206317
x4: 0.235548
x5: 0.442526
x6: 0.746864", "Arm 17_0
hartmann6: -1.98819 (SEM: 0)
x1: 0.484511
x2: 0.22823
x3: 0.237
x4: 0.232679
x5: 0.384916
x6: 0.744099", "Arm 18_0
hartmann6: -2.4623 (SEM: 0)
x1: 0.449918
x2: 0.214364
x3: 0.27629
x4: 0.271086
x5: 0.349526
x6: 0.70665", "Arm 19_0
hartmann6: -2.75401 (SEM: 0)
x1: 0.414782
x2: 0.194756
x3: 0.314423
x4: 0.307907
x5: 0.311877
x6: 0.667367", "Arm 20_0
hartmann6: -2.74606 (SEM: 0)
x1: 0.386351
x2: 0.212861
x3: 0.336375
x4: 0.311148
x5: 0.266056
x6: 0.632334", "Arm 21_0
hartmann6: -2.84373 (SEM: 0)
x1: 0.366382
x2: 0.146103
x3: 0.311708
x4: 0.335777
x5: 0.286141
x6: 0.655994", "Arm 22_0
hartmann6: -2.92411 (SEM: 0)
x1: 0.374518
x2: 0.0965846
x3: 0.38366
x4: 0.296887
x5: 0.285061
x6: 0.65271", "Arm 23_0
hartmann6: -2.61901 (SEM: 0)
x1: 0.410246
x2: 0.0545891
x3: 0.352164
x4: 0.310357
x5: 0.285893
x6: 0.592927" ], "type": "scatter", "x": [ 0.7330349087715149, 0.233726822771132, 0.4560632612556219, 0.4994495641440153, 0.32605923898518085, 0.15528818685561419, 0.24741332605481148, 0.8649843530729413, 0.25432397425174713, 0.7105504367500544, 0.600564319640398, 0.364004491828382, 0.5415848197676835, 0.5095666068290555, 0.51823461918367, 0.5006089473312668, 0.5500353263563221, 0.48451098485418603, 0.4499176476637467, 0.41478153727762374, 0.3863509902382102, 0.36638225737028096, 0.3745182767069761, 0.4102456087040271 ], "xaxis": "x2", "y": [ 0.06100805476307869, 0.8415030026808381, 0.6956740934401751, 0.15611135214567184, 0.6918562883511186, 0.8879265636205673, 0.3748607337474823, 0.07902895659208298, 0.8654162352904677, 0.7828654944896698, 0.22302412055432796, 0.6329575339332223, 0.22973441421901103, 0.20748873245947327, 0.24157697962290028, 0.26813013428499444, 0.23485606287129523, 0.2282301765187898, 0.21436412901899668, 0.19475629378241366, 0.212860591600044, 0.14610327237015194, 0.09658462471824511, 0.05458911567017346 ], "yaxis": "y2" } ], "layout": { "annotations": [ { "font": { "size": 14 }, "showarrow": false, "text": "Mean", "x": 0.25, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" }, { "font": { "size": 14 }, "showarrow": false, "text": "Standard Error", "x": 0.8, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" } ], "autosize": false, "height": 450, "hovermode": "closest", "legend": { "orientation": "h", "x": 0, "y": -0.25 }, "margin": { "b": 100, "l": 35, "pad": 0, "r": 35, "t": 35 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "sequentialminus": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "hartmann6" }, "width": 950, "xaxis": { "anchor": "y", "autorange": false, "domain": [ 0.05, 0.45 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x1" }, "type": "linear" }, "xaxis2": { "anchor": "y2", "autorange": false, "domain": [ 0.6, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x1" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x2" }, "type": "linear" }, "yaxis2": { "anchor": "x2", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(ax_client.get_contour_plot())" ] }, { "cell_type": "markdown", "id": "56941d81", "metadata": { "papermill": { "duration": 0.05776, "end_time": "2024-07-23T19:32:46.989896", "exception": false, "start_time": "2024-07-23T19:32:46.932136", "status": "completed" }, "tags": [] }, "source": [ "We can also retrieve a contour plot for the other metric, \"l2norm\" –– say, we are interested in seeing the response surface for parameters \"x3\" and \"x4\" for this one." ] }, { "cell_type": "code", "execution_count": 12, "id": "df715c15", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:47.108256Z", "iopub.status.busy": "2024-07-23T19:32:47.107765Z", "iopub.status.idle": "2024-07-23T19:32:47.735315Z", "shell.execute_reply": "2024-07-23T19:32:47.734569Z" }, "papermill": { "duration": 0.691496, "end_time": "2024-07-23T19:32:47.739942", "exception": false, "start_time": "2024-07-23T19:32:47.048446", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:47] ax.service.ax_client: Retrieving contour plot with parameter 'x3' on X-axis and 'x4' on Y-axis, for metric 'l2norm'. Remaining parameters are affixed to the middle of their range.\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "xaxis": "x", "y": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "yaxis": "y", "z": [ [ 1.0048055865520427, 1.0047550199520734, 1.00512662179346, 1.0059256701526103, 1.0071558811971333, 1.0088193857729588, 1.0109167432847093, 1.013446993369067, 1.0164077406860519, 1.0197952624406041, 1.023604623649035, 1.0278297835462422, 1.0324636790614536, 1.0374982776472774, 1.0429246000151395, 1.0487327208098671, 1.0549117596917033, 1.061449875787628, 1.0683342756242458, 1.0755512400047753, 1.083086170534204, 1.090923652853036, 1.0990475316350516, 1.1074409919529544, 1.1160866422815434, 1.1249665956602926, 1.1340625469265155, 1.1433558451584782, 1.1528275613922812, 1.1624585522656716, 1.172229520535273, 1.1821210734786558, 1.192113780103474, 1.2021882279076983, 1.212325079720141, 1.2225051309347887, 1.2327093672565461, 1.2429190229088865, 1.25311563911406, 1.263281122540227, 1.2733978033106654, 1.2834484920863924, 1.2934165356645468, 1.3032858704847297, 1.3130410734078781, 1.3226674091319186, 1.332150873635726, 1.341478233098758, 1.3506370578226958, 1.3596157507794107 ], [ 1.0032957600225405, 1.0032924517056758, 1.0037166730289642, 1.0045737148545408, 1.0058672813935532, 1.007599474604522, 1.009770819263472, 1.0123803283427029, 1.0154256020058727, 1.0189029467055615, 1.0228074957506432, 1.0271333116946162, 1.0318734553254147, 1.0370200151257167, 1.042564101914735, 1.0484958222401501, 1.0548042481834619, 1.0614773999148719, 1.0685022519847163, 1.0758647674210597, 1.0835499575247831, 1.0915419612059527, 1.0998241361129426, 1.1083791542148576, 1.1171890961143427, 1.1262355404196116, 1.1354996464324623, 1.1449622299148816, 1.1546038326908532, 1.1644047873663144, 1.1743452786119282, 1.184405402367261, 1.1945652240942295, 1.2048048369130429, 1.2151044201528705, 1.225444298577234, 1.2358050023180034, 1.2461673273740037, 1.2565123963941118, 1.2668217193593734, 1.2770772536939596, 1.287261463265165, 1.2973573756761685, 1.3073486372154846, 1.317219564807952, 1.3269551943185678, 1.3365413245944857, 1.3459645566917673, 1.355212327818393, 1.3642729396279896 ], [ 1.0022035277030887, 1.0022512658146312, 1.0027315004740143, 1.0036495190662196, 1.0050090030445136, 1.0068120224577752, 1.0090590747938601, 1.0117491664868645, 1.0148799276745488, 1.0184477426857808, 1.0224478731980777, 1.026874551093316, 1.0317210252096578, 1.0369795588929218, 1.0426413891706732, 1.048696668433384, 1.0551344124392095, 1.061942474195484, 1.0691075544743889, 1.0766152500725445, 1.0844501334029197, 1.092595853007746, 1.1010352439834084, 1.1097504390849748, 1.1187229741714053, 1.12793388463452, 1.1373637919046602, 1.14699298080662, 1.1568014694737108, 1.1667690738700878, 1.1768754689091598, 1.1871002478573358, 1.1974229813060702, 1.207823276570614, 1.2182808379857846, 1.2287755282477604, 1.2392874307046564, 1.2497969123218744, 1.260284686926294, 1.2707318782483599, 1.2811200822184619, 1.2914314279242285, 1.3016486365955389, 1.3117550779574743, 1.321734823282282, 1.331572694485912, 1.3412543086550202, 1.350766117457156, 1.360095440976576, 1.3692304956254664 ], [ 1.0015372461869934, 1.0016397399176744, 1.0021792905929798, 1.0031611707262083, 1.0045890343870276, 1.0064649242034092, 1.008789326463698, 1.011561270868432, 1.0147784619891005, 1.018437419936172, 1.0225336019627633, 1.0270614785957166, 1.0320145488482508, 1.0373852964100598, 1.0431651061495406, 1.049344171061753, 1.055911420338351, 1.0628544905965436, 1.0701597490199921, 1.0778123644759945, 1.08579641417765, 1.0940950102538607, 1.1026904317649509, 1.1115642514214241, 1.120697450723731, 1.130070521194017, 1.1396635522235674, 1.149456307729799, 1.159428294507519, 1.1695588251710771, 1.1798270782004023, 1.1902121570389017, 1.2006931495887425, 1.2112491888940047, 1.2218595153387377, 1.232503540332195, 1.2431609112037156, 1.2538115768691138, 1.2644358537348077, 1.2750144912515176, 1.285528736495591, 1.2959603971315168, 1.3062919020898174, 1.3165063592829338, 1.3265876096843476, 1.3365202771186036, 1.3462898131568206, 1.3558825365836795, 1.365285666995785, 1.3744873522015966 ], [ 1.0013038706040833, 1.001464713799754, 1.0020667603198357, 1.0031152635317724, 1.0046138542555292, 1.0065645624235815, 1.0089678905087158, 1.011822932890325, 1.015127523830423, 1.0188783856189092, 1.0230712427323319, 1.0277008723331307, 1.032761077418748, 1.0382445919874408, 1.0441429488162064, 1.0504463511160744, 1.0571435857945362, 1.0642220013179786, 1.0716675543887835, 1.0794649139146901, 1.0875976020484597, 1.0960481507337814, 1.1047982560777299, 1.1138289191037911, 1.123120567649811, 1.1326531589968645, 1.1424062658257228, 1.1523591494859777, 1.162490824783126, 1.1727801200153136, 1.1832057351985095, 1.1937463005535962, 1.2043804365295818, 1.2150868159691985, 1.2258442285091349, 1.236631646943253, 1.247428295045646, 1.2582137162227307, 1.268967842307376, 1.279671061792971, 1.2903042868070576, 1.3008490181290053, 1.3112874075596463, 1.3216023169563347, 1.3317773732612888, 1.3417970188823274, 1.3516465568373754, 1.3613121901499614, 1.3707810550792785, 1.380041247881009 ], [ 1.0015090510578268, 1.0017317045506862, 1.0023992922695237, 1.0035170533394242, 1.005088610509223, 1.0071160082555883, 1.0095998057990152, 1.0125392161903457, 1.0159322689292887, 1.019775960920031, 1.0240663553507245, 1.0287985961641535, 1.0339668280971965, 1.0395640420457741, 1.0455818904858445, 1.052010526861717, 1.0588385131038025, 1.0660528167376169, 1.0736388939998023, 1.081580837056014, 1.0898615557507019, 1.0984629662025893, 1.1073661661548027, 1.1165515862003375, 1.1259991139589154, 1.1356881936866117, 1.1455979065899367, 1.1557070378810723, 1.165994136114933, 1.1764375692467925, 1.1870155805883953, 1.1977063466704414, 1.208488038048601, 1.2193388833465078, 1.2302372363011602, 1.2411616452351908, 1.2520909241913736, 1.2630042248875002, 1.2738811086445718, 1.2847016174727963, 1.2954463435413426, 1.3060964962945387, 1.3166339665050018, 1.327041386577236, 1.3373021864420203, 1.3474006444210174, 1.357321932498686, 1.367052155517288, 1.3765783839088457, 1.3858886796911953 ], [ 1.0021572795448712, 1.0024450802419564, 1.0031811370809665, 1.0043706905566039, 1.0060173830566927, 1.0081233145158275, 1.010689155056028, 1.0137143021082342, 1.0171970535862518, 1.0211347546916334, 1.02552387181124, 1.0303599597000392, 1.0356375180073103, 1.0413497704249701, 1.0474884279394012, 1.054043503478374, 1.0610032268457055, 1.0683540764136619, 1.0760809124332313, 1.0841671769751147, 1.0925951205709334, 1.1013460222676996, 1.1104003820360053, 1.1197380769008123, 1.1293384816098837, 1.1391805601629572, 1.1492429366051449, 1.1595039532539533, 1.1699417230875246, 1.1805341811894405, 1.1912591384015, 1.202094338894472, 1.213017522277086, 1.2240064900975882, 1.2350391760963233, 1.2460937192847812, 1.2571485388042831, 1.2681824095059613, 1.2791745372483345, 1.2901046329913664, 1.3009529848488937, 1.311700527330684, 1.3223289070573259, 1.3328205442716339, 1.3431586895088268, 1.3533274748344033, 1.3633119591204284, 1.373098166911901, 1.382673120533273, 1.3920248651978409 ], [ 1.003252068107676, 1.0036082698559867, 1.0044156573013512, 1.0056794993025933, 1.0074034983199067, 1.0095898637083918, 1.0122394423742882, 1.0153518900122336, 1.0189258482042294, 1.0229590778088846, 1.0274484968346735, 1.0323900893783953, 1.037778690527546, 1.0436076969558123, 1.0498687832496345, 1.0565517041635264, 1.0636442335361562, 1.071132247165556, 1.078999919163234, 1.0872299815850937, 1.095803996892971, 1.1047026057019869, 1.1139057297981911, 1.123392725975292, 1.1331424966499073, 1.1431335681788632, 1.1533441486259786, 1.163752175135304, 1.1743353585080398, 1.1850712299794182, 1.1959371930040426, 1.2069105812157095, 1.2179687225939868, 1.2290890091462106, 1.2402489709989646, 1.2514263536019712, 1.262599196712825, 1.2737459138966238, 1.2848453713936243, 1.295876965342613, 1.3068206964715439, 1.3176572414673362, 1.3283680203115977, 1.3389352589259667, 1.3493420465199937, 1.359572387088043, 1.3696112445669881, 1.3794445812482483, 1.389059389135786, 1.3984437140525345 ], [ 1.0047961289809948, 1.0052239746102118, 1.0061055715487228, 1.0074462549115197, 1.009249838883155, 1.0115187063545252, 1.0142539539768431, 1.0174555711062878, 1.0211226116686056, 1.0252533030496902, 1.029845036685805, 1.0348942098444227, 1.0403959351045668, 1.0463436858107873, 1.0527289764416459, 1.0595411689910637, 1.0667674540524166, 1.0743930004262385, 1.0824012242967505, 1.090774111480777, 1.0994925326727853, 1.1085365119719048, 1.1178854320759857, 1.1275181777879748, 1.1374132300982465, 1.1475487267919677, 1.157902504573539, 1.1684521344766439, 1.179174958570416, 1.190048132642582, 1.2010486769998336, 1.2121535357827715, 1.2233396441018392, 1.2345840016853489, 1.245863751442751, 1.257156261274912, 1.2684392075311466, 1.2796906586612762, 1.290889157794484, 1.3020138031608723, 1.3130443254328859, 1.3239611611918487, 1.334745521820417, 1.345379457192998, 1.3558459135954446, 1.366128785364493, 1.3762129598054806, 1.3860843550290451, 1.395729950443915, 1.4051378097514071 ], [ 1.0067915214944578, 1.0072943380186319, 1.0082531477027108, 1.0096733987982853, 1.0115590766513607, 1.01391280664873, 1.016736007824367, 1.0200290706681683, 1.0237915125572614, 1.0280220503205397, 1.0327185337692861, 1.03787771557417, 1.0434948878556494, 1.0495634728178456, 1.0560746835514239, 1.063017353411436, 1.0703779763141017, 1.078140934748855, 1.0862888463477718, 1.0948029465599372, 1.1036634396208693, 1.1128497784863798, 1.1223408628514921, 1.1321151645748007, 1.1421507997719564, 1.1524255685441525, 1.1629169801591484, 1.1736022765027059, 1.1844584616955163, 1.1954623418261983, 1.206590575988903, 1.2178197380845648, 1.2291263878819012, 1.2404871493844416, 1.2518787944230072, 1.2632783294596366, 1.2746630837657114, 1.2860107973681674, 1.2972997074014898, 1.3085086317312806, 1.3196170489084158, 1.3306051736644682, 1.341454027271828, 1.3521455021758497, 1.3626624203739102, 1.3729885850805426, 1.3831088252880674, 1.3930090329138367, 1.4026761923200024, 1.4120984020965832 ], [ 1.0092397313951151, 1.009821032986668, 1.0108602948925245, 1.0123631308423355, 1.0143337592054666, 1.0167751142649286, 1.019689000364963, 1.0230762577947405, 1.0269368895859523, 1.0312700867795654, 1.036074098598025, 1.0413459318291127, 1.0470809247578063, 1.0532723003223619, 1.0599108277123026, 1.0669846932390075, 1.074479612582922, 1.0823791423371572, 1.0906651017795288, 1.0993180083550667, 1.1083174539852454, 1.1176423858420046, 1.1272712883253126, 1.1371822841648733, 1.1473531809834734, 1.157761488836394, 1.1683844286889897, 1.1791989450431632, 1.1901817299787263, 1.201309261486141, 1.2125578561312944, 1.223903734484119, 1.2353230969767606, 1.2467922076123477, 1.2582874829983899, 1.2697855843889494, 1.2812635107039472, 1.2926986908010467, 1.3040690735726508, 1.3153532147047755, 1.3265303591534239, 1.3375805185642924, 1.3484845429884484, 1.3592241863404204, 1.369782165120573, 1.3801422099917773, 1.3902891098727708, 1.400208748291828, 1.4098881318367087, 1.4193154106386232 ], [ 1.0121416574629691, 1.0128052359777449, 1.0139285189792566, 1.015517338322795, 1.0175762027349824, 1.0201084105650846, 1.023116194781453, 1.0266008652071312, 1.0305628950247399, 1.0350018905012286, 1.0399163967534997, 1.0453035353183562, 1.0511585333218338, 1.057474262149049, 1.0642409216994526, 1.0714459679430923, 1.0790743029380057, 1.0871086668153895, 1.095530125326949, 1.1043185456986424, 1.113452985882892, 1.1229119659716018, 1.1326736271658586, 1.1427158048648498, 1.153016048677232, 1.1635516185505101, 1.1742994782959242, 1.1852362994766634, 1.1963384818872917, 1.2075821922117582, 1.2189434196734528, 1.2303980460845783, 1.2419219271746382, 1.2534909820542173, 1.265081287904386, 1.2766691773295777, 1.2882313361939992, 1.2997449001346766, 1.311187548284986, 1.3225375930343755, 1.3337740648881888, 1.344876791675201, 1.3558264714880266, 1.3666047388437563, 1.3771942236338053, 1.3875786025043, 1.3977426423823136, 1.4076722359443339, 1.417354428913443, 1.4267774391700465 ], [ 1.0154974966603334, 1.0162474793494207, 1.017458733197561, 1.0191373547171731, 1.021288188040696, 1.0239149309211035, 1.0270202601766891, 1.0306059391061486, 1.0346728544053987, 1.0392209265503076, 1.0442488563138477, 1.0497537160803454, 1.0557304579325695, 1.0621714635966788, 1.0690662717372708, 1.0764015718205966, 1.0841614696493709, 1.0923279484398347, 1.100881406331354, 1.1098011567770039, 1.1190658179467616, 1.1286535664023136, 1.138542269049706, 1.148709527654906, 1.159132673960334, 1.1697887471431105, 1.1806544753694934, 1.1917062736620616, 1.2029202630321971, 1.2142723111204041, 1.225738091975668, 1.2372931614455558, 1.2489130443689909, 1.2605733299527455, 1.2722497721129846, 1.2839183920324309, 1.2955555806484265, 1.3071381992144946, 1.3186436764513525, 1.3300501011156813, 1.3413363090658845, 1.3524819640974524, 1.3634676319659196, 1.3742748471246062, 1.384886171791326, 1.3952852470348394, 1.4054568356476078, 1.4153868566527277, 1.4250624113810824, 1.4344718011504125 ], [ 1.0193065387408327, 1.0201473980666318, 1.0214509474492317, 1.0232235816479147, 1.0254705056690712, 1.0281958253124879, 1.0314026433098529, 1.035093122989874, 1.039268470354875, 1.043928786823604, 1.049072767602194, 1.0546972671808368, 1.060796812365318, 1.067363188229111, 1.0743852245223067, 1.0818488588307908, 1.0897374679353127, 1.0980323800734397, 1.106713442304421, 1.1157595281907193, 1.1251489157352974, 1.1348595177672265, 1.1448689862531205, 1.1551547307734304, 1.1656938927528038, 1.1764633084937983, 1.1874394825197638, 1.1985985823819723, 1.2099164585678257, 1.2213686885090855, 1.2329306412931913, 1.244577558769684, 1.2562846486898427, 1.2680271858906935, 1.2797806180737623, 1.2915206732961546, 1.3032234668222185, 1.3148656054514198, 1.3264242878350254, 1.3378773996199889, 1.3492036025174194, 1.3603824165927318, 1.3713942952259015, 1.3822206923052303, 1.3928441213103995, 1.4032482060211824, 1.4134177226666598, 1.4233386334115732, 1.4329981111638477, 1.4423845557801296 ], [ 1.023566898870607, 1.0245034087714395, 1.0259038863300418, 1.0277750392494482, 1.0301224339843786, 1.032950562814599, 1.0362629030073303, 1.040061931509897, 1.044349052011183, 1.0491243972664346, 1.0543864948754118, 1.0601318292164463, 1.0663543838059146, 1.0730452832974995, 1.0801926487162574, 1.0877817264258076, 1.0957952702011426, 1.1042140831576386, 1.1130175934653315, 1.122184352853564, 1.1316923938805892, 1.141519434664506, 1.1516429580411542, 1.1620402090130735, 1.172688153740082, 1.1835634332505987, 1.194642332594893, 1.2059007754359663, 1.2173143465370393, 1.2288583401274333, 1.2405078299531147, 1.252237756120703, 1.264023023970397, 1.2758386107268938, 1.287659676320443, 1.2994616754094284, 1.3112204682133122, 1.3229124282602913, 1.3345145455661633, 1.3460045240947156, 1.3573608726136623, 1.368562988264249, 1.3795912323183777, 1.3904269977177304, 1.4010527680867515, 1.4114521679966252, 1.4216100043390387, 1.431512298751752, 1.4411463111250937, 1.4505005543097682 ], [ 1.0282752275387255, 1.0293123711684493, 1.0308145988065465, 1.0327889231524234, 1.03524124574709, 1.0381763943794542, 1.0415981408260448, 1.0455091658579914, 1.049910936230517, 1.054803468243934, 1.0601849786142727, 1.066051463701696, 1.0723962905971651, 1.0792099080164597, 1.086479772844209, 1.094190536005844, 1.1023244573498023, 1.1108619554222228, 1.119782171605291, 1.1290634457036361, 1.1386836464849723, 1.1486203513172206, 1.1588509049515445, 1.1693524024470654, 1.1801016393122403, 1.1910750611690457, 1.2022487325460955, 1.213598333716264, 1.22509918712267, 1.236726310660931, 1.248454493097016, 1.2602583863575691, 1.272112609676832, 1.2839918611887178, 1.2958710332609746, 1.3077253285531691, 1.3195303743866438, 1.3312623335269966, 1.342898009900431, 1.3544149481032666, 1.3657915258303968, 1.3770070385555715, 1.388041775956361, 1.3988770897025478, 1.4094954523296175, 1.419880507009407, 1.430017108115598, 1.4398913525671921, 1.449490602021163, 1.4588034960756908 ], [ 1.0334264384668825, 1.0345692811275928, 1.0361781185720815, 1.03826023723892, 1.0408218222321386, 1.0438679615172621, 1.04740262154521, 1.0514285662862421, 1.0559471932497067, 1.0609582724855795, 1.0664595998554516, 1.0724466104725399, 1.0789120310191493, 1.0858456643744288, 1.0932343831745839, 1.101062359914197, 1.1093114964623878, 1.1179619623496833, 1.1269927312901746, 1.1363820241010267, 1.1461076097246483, 1.1561469625613476, 1.166477306876684, 1.1770755921351805, 1.187918440587052, 1.198982097772984, 1.2102424042807327, 1.221674796777588, 1.2332543392698394, 1.2449557814705519, 1.2567536393021843, 1.268622292103827, 1.280536091416875, 1.2924694768668525, 1.304397095395718, 1.3162939208039057, 1.3281353711804273, 1.3398974223190545, 1.3515567156428585, 1.3630906594990115, 1.374477522953669, 1.3856965214268508, 1.39672789367137, 1.4075529697313123, 1.4181542296245055, 1.428515352589804, 1.4386212568299828, 1.4484581297702162, 1.4580134489416157, 1.467275993689574 ], [ 1.0390134881672042, 1.040267033624218, 1.0419872169702247, 1.044181546348215, 1.0468564189069904, 1.0500170912152045, 1.0536676156493114, 1.0578107207057368, 1.062447617677189, 1.0675777297131939, 1.0731983623193384, 1.0793043625540915, 1.0858878378472623, 1.0929380119558672, 1.100441276016638, 1.1083814483722685, 1.1167402022843673, 1.1254975776354113, 1.1346324788310038, 1.1441230796372137, 1.153947094747138, 1.1640819189291616, 1.174504663255025, 1.1851921293231353, 1.1961207598695733, 1.207266594260181, 1.2186052458828316, 1.230111908797888, 1.2417613943247627, 1.2535281943679966, 1.2653865665089772, 1.277310635450991, 1.289274505706092, 1.3012523810480412, 1.313218686986468, 1.3251481932189342, 1.3370161336350124, 1.3487983219653055, 1.3604712615915484, 1.3720122483736403, 1.3833994656184803, 1.3946120705285647, 1.4056302716371767, 1.416435396874501, 1.427009952024712, 1.437337669436756, 1.4474035469473994, 1.4571938770682453, 1.4666962665807541, 1.475899646774543 ], [ 1.0450272284843856, 1.0463962766190478, 1.0482322674400704, 1.050542863042181, 1.0533345884392693, 1.0566127703838017, 1.0603814402035021, 1.0646431848046554, 1.0693989363291014, 1.0746477044413583, 1.0803862750749922, 1.0866089212675158, 1.0933071874241045, 1.100469808775082, 1.1080828073276359, 1.116129767003925, 1.1245922461726072, 1.1334502525269161, 1.1426826963858971, 1.152267755867699, 1.1621831211202647, 1.1724061198544438, 1.1829137510004617, 1.193682663269227, 1.2046891133048205, 1.2159089294248413, 1.2273174966648397, 1.2388897700216828, 1.250600316570768, 1.262423383443441, 1.2743329869044948, 1.2863030172940793, 1.2983073548447868, 1.3103199919715536, 1.3223151583269097, 1.3342674455918508, 1.3461519295753814, 1.3579442877062007, 1.369620910418394, 1.3811590052715463, 1.3925366929154597, 1.4037330942262616, 1.4147284081148555, 1.4255039796529174, 1.4360423582846538, 1.4463273460024921, 1.4563440354671058, 1.4660788381505114, 1.4755195026766785, 1.4846551236276155 ], [ 1.0514563399554655, 1.0529453598570713, 1.0549012193083493, 1.0573316573069755, 1.060243237832924, 1.0636412613977515, 1.067529641726549, 1.0719107375507808, 1.0767851366832544, 1.0821514019917449, 1.0880058051358132, 1.0943420898688934, 1.101151315999228, 1.1084218313340448, 1.1161393990592101, 1.1242874754206669, 1.132847597363373, 1.141799814932179, 1.1511230981918994, 1.160795663989061, 1.1707951961083198, 1.1810989614971066, 1.19168384588484, 1.2025263408191185, 1.2136025127017425, 1.2248879771569823, 1.236357893167182, 1.2479869835495303, 1.2597495826400766, 1.2716197085500005, 1.2835711556155742, 1.2955776021124825, 1.307612728458486, 1.3196503416338283, 1.3316645021824685, 1.3436296507930205, 1.3555207320348692, 1.367313313319298, 1.378983697566189, 1.39050902839183, 1.401867386904361, 1.4130378794132052, 1.4240007155393835, 1.4347372763647295, 1.4452301723893566, 1.455463291184481, 1.4654218347371826, 1.4750923465878305, 1.4844627289612442, 1.4935222501890566 ], [ 1.058287342449392, 1.0599003694422806, 1.0619796642715698, 1.0645329630240798, 1.0675667821776627, 1.0710863085128142, 1.0750952576178725, 1.0795956959989117, 1.0845878290407767, 1.0900697678685232, 1.096037300810081, 1.1024837061045099, 1.1093996469721528, 1.1167731839284358, 1.1245899209982102, 1.132833275774006, 1.1414848360991863, 1.150524748118757, 1.1599320780735436, 1.1696851036354872, 1.1797615135941302, 1.1901385183546371, 1.200792890775372, 1.2117009644564758, 1.2228386158627274, 1.2341812508981365, 1.245703809094164, 1.257380791731907, 1.2691863150639944, 1.2810941865036085, 1.2930779999019075, 1.305111245389742, 1.3171674292960012, 1.329220200055342, 1.34124347657054, 1.3532115760733403, 1.3650993390669357, 1.3768822494051471, 1.3885365479618028, 1.4000393386736765, 1.4113686860117096, 1.4225037031583778, 1.43342463035602, 1.4441129030498376, 1.4545512095890696, 1.4647235383762378, 1.4746152144715428, 1.4842129257705328, 1.4935047389786567, 1.5024801057064232 ], [ 1.065504672064917, 1.067245231613567, 1.069450972354678, 1.0721295505225426, 1.075287356494204, 1.0789293891680896, 1.0830591039047728, 1.0876782330513213, 1.092786584772778, 1.098381834807465, 1.1044593351342218, 1.1110119704942212, 1.1180300948246495, 1.1255015723226047, 1.1334119318800318, 1.1417446222807572, 1.1504813350462864, 1.1596023490382392, 1.1690868502742249, 1.1789131916263018, 1.1890590754335078, 1.1995016609259506, 1.2102176122705806, 1.2211831096332417, 1.2323738455694742, 1.2437650246827752, 1.2553313784319242, 1.2670472011525562, 1.2788864087858174, 1.2908226187376646, 1.3028292475576708, 1.314879622385934, 1.3269471020273298, 1.3390052037940428, 1.3510277327145195, 1.3629889102161838, 1.3748634998815914, 1.38662692832019, 1.3982553995798779, 1.409726001844563, 1.42101680543427, 1.4321069513506854, 1.4429767298038612, 1.4536076483229206, 1.4639824892022264, 1.4740853561696596, 1.4839017102895502, 1.4934183952308901, 1.5026236521432002, 1.5115071244869034 ], [ 1.0730908098591811, 1.0749618669914336, 1.0772964740890456, 1.080102137626031, 1.0833850545250054, 1.0871499768862174, 1.091400055960865, 1.096136667330614, 1.1013592250835995, 1.1070649997549573, 1.1132489613844319, 1.1199036729975969, 1.1270192587919754, 1.1345834638264418, 1.1425818085011388, 1.1509978244133519, 1.1598133429658462, 1.1690087992269749, 1.1785635138826454, 1.1884559252464062, 1.1986637576991352, 1.209164127767011, 1.2199336002586971, 1.230948212556887, 1.242183485588982, 1.253614436843345, 1.2652156060207433, 1.276961099080577, 1.2888246524626312, 1.3007797164564472, 1.3127995549942464, 1.324857358324603, 1.3369263648131284, 1.3489799882759335, 1.360991947605948, 1.3729363958830847, 1.3847880465967146, 1.3965222950156553, 1.4081153331015532, 1.4195442566730514, 1.4307871637951497, 1.4418232435967966, 1.4526328549179608, 1.4631975943625863, 1.4735003534911362, 1.4835253650310904, 1.4932582381182073, 1.5026859827075054, 1.511797023411157, 1.5205812031301844 ], [ 1.0810264478023248, 1.083030378098636, 1.0854956695356892, 1.0884296184806648, 1.0918381737258531, 1.0957257967509817, 1.1000953069758674, 1.1049477159187802, 1.1102820589886955, 1.1160952388696221, 1.1223818988107863, 1.1291343459647272, 1.1363425426819944, 1.1439941766483217, 1.1520748096464002, 1.1605680918842889, 1.169456017702346, 1.1787191923968445, 1.1883370807333664, 1.198288214998773, 1.2085503515925113, 1.2191005766979337, 1.2299153705243027, 1.2409706444509518, 1.2522417661902823, 1.2637035859268986, 1.275330472731016, 1.2870963666244999, 1.298974848285149, 1.310939225853622, 1.3229626366835412, 1.3350181610056042, 1.347078944159438, 1.3591183240899845, 1.3711099610554986, 1.3830279668422834, 1.3948470311583083, 1.4065425432430434, 1.4180907070659727, 1.429468648783571, 1.4406545153859622, 1.4516275636935485, 1.4623682390668817, 1.4728582433751378, 1.4830805919347794, 1.4930196592836966, 1.502661213799606, 1.5119924413058783, 1.521001957933103, 1.5296798126203892 ], [ 1.089290679157246, 1.0914292563559784, 1.0940264500941406, 1.0970892968986314, 1.1006234553305299, 1.1046330660065322, 1.1091206019570057, 1.1140867143622522, 1.1195300825079426, 1.1254472805446303, 1.1318326763022648, 1.138678377827373, 1.1459742405300697, 1.1537079415854135, 1.1618651193118268, 1.1704295655089638, 1.1793834506715075, 1.18870755788462, 1.1983815022219608, 1.2083839181739764, 1.2186926061801133, 1.2292846382383165, 1.2401364296515363, 1.2512237880536323, 1.262521951851272, 1.2740056288367447, 1.2856490430031648, 1.2974259944823654, 1.3093099346915453, 1.3212740565568921, 1.3332913981644885, 1.345334957300237, 1.35737781394032, 1.369393257694014, 1.3813549173516249, 1.3932368899556642, 1.4050138671264967, 1.4166612566938341, 1.4281552979905836, 1.4394731694455891, 1.4505930873646904, 1.461494395017368, 1.4721576413520203, 1.4825646488515745, 1.4926985702152757, 1.5025439337151223, 1.512086677227922, 1.5213141710865543, 1.5302152300267813, 1.5387801146272682 ], [ 1.097861203113784, 1.1001355985490386, 1.1028653240449906, 1.1060571170789968, 1.1097163153283827, 1.1138467196497874, 1.1184504520615393, 1.1235278142587353, 1.1290771550683076, 1.1350947578021346, 1.1415747599142307, 1.148509116918374, 1.1558876196267023, 1.163697968428657, 1.1719259012829373, 1.1805553647787554, 1.189568711813194, 1.1989469066685585, 1.208669719287457, 1.218715894963354, 1.2290632921639775, 1.239688988024453, 1.2505693566189109, 1.2616801285235533, 1.272996441264781, 1.2844928894412213, 1.296143581338655, 1.3079222064395295, 1.3198021159072582, 1.3317564162139899, 1.343758074695534, 1.3557800349408193, 1.367795339467976, 1.3797772569939217, 1.391699411666994, 1.4035359118182702, 1.4152614760366602, 1.4268515546457783, 1.4382824449326488, 1.449531398738132, 1.4605767212606469, 1.471397860148806, 1.4819754841659516, 1.4922915509031287, 1.502329363198223, 1.5120736140903006, 1.5215104202989864, 1.53062734436992, 1.539413405767342, 1.5478590813225677 ], [ 1.1067145361427173, 1.1091253260609133, 1.1119876406097549, 1.115307888686386, 1.1190910662100668, 1.1233406242925714, 1.1280583362727727, 1.1332441691778057, 1.1388961672678233, 1.1450103569582546, 1.1515806830282604, 1.158598985097718, 1.1660550206019484, 1.173936536046718, 1.1822293828316, 1.1909176684697347, 1.1999839298601305, 1.2094093134169421, 1.2191737477801239, 1.2292560982213385, 1.2396342967756953, 1.2502854473295637, 1.2611859092512117, 1.2723113659570189, 1.2836368858837306, 1.295136982938935, 1.3067856821183446, 1.3185565941377744, 1.3304230010607092, 1.342357953286688, 1.3543343770303413, 1.3663251905849885, 1.3783034271801409, 1.3902423620334092, 1.402115641184622, 1.4138974098146155, 1.4255624379397434, 1.43708624159853, 1.4484451978846509, 1.4596166524172685, 1.4705790180681284, 1.4813118639828722, 1.4917959941410095, 1.5020135148958091, 1.511947891123065, 1.521583990786061, 1.5309081178933708, 1.5399080339851976, 1.5485729684313507, 1.5568936179582382 ], [ 1.1158262247345827, 1.1183734026049441, 1.121367809789758, 1.1248155055003333, 1.1287211309648575, 1.1330877841957718, 1.1379168966642914, 1.1432081171812658, 1.148959209745452, 1.1551659730880055, 1.1618221897176895, 1.1689196111323983, 1.1764479833851798, 1.1843951135643094, 1.1927469735011649, 1.2014878329601584, 1.2106004115688827, 1.2200660375043098, 1.2298648017381808, 1.2399756992247217, 1.2503767521174638, 1.261045114053491, 1.2719571579315418, 1.2830885519007045, 1.294414329289971, 1.3059089580828094, 1.3175464145985516, 1.3293002646665575, 1.3411437541025426, 1.353049908954726, 1.364991644908505, 1.3769418844629948, 1.388873680003039, 1.4007603406384876, 1.4125755606099712, 1.4242935471134626, 1.4358891455288, 1.4473379602171592, 1.4586164692556802, 1.4697021316899874, 1.4805734860985706, 1.4912102394730473, 1.5015933456230324, 1.5117050725132257, 1.521529058132634, 1.5310503546808976, 1.5402554610334855, 1.5491323436139917, 1.5576704459565383, 1.5658606873816228 ], [ 1.1251710558077548, 1.1278540477632772, 1.130979516571635, 1.1345531576857606, 1.13857925090071, 1.1430605424648226, 1.1479981313838177, 1.153391364782535, 1.1592377481619054, 1.1655328768862132, 1.1722703949869955, 1.17944198618567, 1.1870373998871493, 1.1950445119777602, 1.2034494169996006, 1.2122365452580688, 1.2213887962627, 1.230887679062583, 1.240713450685655, 1.2508452458428179, 1.2612611938398708, 1.2719385216346282, 1.28285364460108, 1.2939822484132715, 1.3052993663773211, 1.3167794565826676, 1.3283964826244854, 1.3401240006374446, 1.3519352542302838, 1.3638032778134732, 1.3757010078870082, 1.387601401153491, 1.399477557846019, 1.4113028483841297, 1.423051041354398, 1.4346964308148344, 1.446213961006068, 1.45757934669042, 1.468769187509632, 1.479761074939919, 1.4905336906200861, 1.501066895028722, 1.51134180568762, 1.5213408642674857, 1.5310478921681543, 1.5404481343357674, 1.5495282912628747, 1.5582765392908564, 1.5666825394954607, 1.5747374355827233 ], [ 1.134723262151425, 1.1375409445211226, 1.1407959286140077, 1.1444935377373073, 1.148637688178262, 1.153230778914903, 1.1582735871483198, 1.1637651740071389, 1.1697028053838596, 1.1760818930440189, 1.182895960725497, 1.1901366388127355, 1.1977936893519041, 1.2058550608482799, 1.2143069697900868, 1.2231340036014708, 1.2323192381666057, 1.2418443624946964, 1.251689803613095, 1.2618348462447417, 1.2722577439110891, 1.2829358203658265, 1.293845562289857, 1.3049627056610895, 1.3162623190136897, 1.3277188869403524, 1.33930639679998, 1.350998430860536, 1.3627682652206337, 1.3745889759674808, 1.3864335522477378, 1.3982750153051235, 1.410086542090713, 1.4218415917668807, 1.4335140332796168, 1.4450782721366706, 1.456509374572303, 1.4677831873799683, 1.4788764518329085, 1.4897669102768445, 1.500433404158878, 1.5108559624467677, 1.5210158795884057, 1.5308957823594658, 1.5404796851452982, 1.549753033397904, 1.5587027351977985, 1.5673171810302877, 1.575586252053228, 1.5835013172855892 ], [ 1.1444567209388001, 1.147407439411014, 1.1507898966029586, 1.1546090397739697, 1.1588684230551074, 1.163570104673139, 1.1687145510816748, 1.17430055181921, 1.1803251492609925, 1.1867835874115846, 1.193669283384408, 1.2009738241855337, 1.2086869899064872, 1.2167968025919231, 1.2252895981382652, 1.2341501169078701, 1.243361607606057, 1.2529059385713488, 1.2627637110324494, 1.2729143699861818, 1.2833363099099193, 1.2940069742305467, 1.304902949029437, 1.3160000526414588, 1.3272734234896757, 1.3386976086815627, 1.3502466556579173, 1.3618942086611978, 1.373613611113785, 1.3853780142883145, 1.3971604920008507, 1.4089341605140675, 1.4206723024258854, 1.4323484930376646, 1.4439367275320218, 1.455411547224297, 1.466748163161994, 1.4779225754151573, 1.4889116865115253, 1.499693407611994, 1.5102467561853214, 1.520551944120041, 1.530590455400907, 1.54034511267336, 1.5498001322183297, 1.5589411670578177, 1.5677553381052274, 1.5762312534593947, 1.5843590161144823, 1.592130220515314 ], [ 1.154345143746084, 1.1574267340531734, 1.1609341463468414, 1.1648719514143406, 1.1692433450491975, 1.1740500524812019, 1.1792922403689707, 1.1849684396657454, 1.191075482834994, 1.197608458751821, 1.2045606881114632, 1.2119237212608927, 1.2196873591272381, 1.2278396964681524, 1.23636718520709, 1.2452547143646555, 1.254485702261064, 1.2640421963825057, 1.2739049766120765, 1.2840536583464648, 1.2944667931831788, 1.3051219661500681, 1.3159958896418809, 1.3270644951581563, 1.338303024507924, 1.3496861223428718, 1.3611879317491091, 1.3727821942555447, 1.384442355103272, 1.3961416740580466, 1.4078533415088883, 1.4195505991278397, 1.4312068639937214, 1.442795854813884, 1.4542917187058757, 1.4656691569151699, 1.4769035478301733, 1.4879710656978156, 1.4988487935299788, 1.5095148288120683, 1.5199483807730063, 1.5301298581436347, 1.5400409465130995, 1.5496646745860643, 1.5589854688420064, 1.5679891962983128, 1.5766631952757701, 1.5849962942548352, 1.5929788190886593, 1.6006025890012188 ], [ 1.1643622567621765, 1.1675720669462253, 1.1712014615437796, 1.1752546371149146, 1.179734436691699, 1.1846422609791416, 1.1899779874455019, 1.19573990014726, 1.201924633178927, 1.2085271304330862, 1.2155406238633555, 1.2229566316643043, 1.2307649767705036, 1.238953824937783, 1.2475097405479634, 1.2564177573351376, 1.2656614606101275, 1.2752230773534026, 1.2850835707764892, 1.2952227365603715, 1.3056192988455255, 1.316251005015021, 1.3270947192224536, 1.3381265153439412, 1.3493217705017422, 1.3606552604947455, 1.3721012584044785, 1.383633637381664, 1.395225978228834, 1.4068516819489316, 1.4184840869863509, 1.4300965904869285, 1.4416627725720108, 1.4531565223699134, 1.4645521643759165, 1.4758245836138268, 1.4869493480385112, 1.4979028266401775, 1.5086623017775778, 1.5192060743704539, 1.5295135607151464, 1.5395653798440756, 1.54934343052562, 1.558830957189977, 1.568012604264463, 1.5768744586027945, 1.5854040798926838, 1.5935905191192503, 1.601424325343428, 1.6088975412208337 ], [ 1.1744819700588978, 1.1778168844201258, 1.1815648560841323, 1.185729711669582, 1.190313948275369, 1.1953186509567, 1.2007434181752294, 1.206586297656483, 1.2128437350558747, 1.219510537602743, 1.2265798544402622, 1.2340431747197869, 1.241890343688431, 1.2501095961132067, 1.2586876055212393, 1.2676095470197428, 1.2768591709921246, 1.2864188848103295, 1.2962698398709047, 1.306392021710578, 1.3167643415994865, 1.3273647287340198, 1.3381702228427692, 1.3491570675835205, 1.360300805486452, 1.3715763753665764, 1.3829582130996443, 1.3944203564678253, 1.405936554484627, 1.4174803812548884, 1.429025354061112, 1.440545055027218, 1.4520132554183962, 1.463404041403728, 1.474691939940881, 1.4858520433378761, 1.4968601310002778, 1.507692786877712, 1.5183275111729537, 1.5287428249651787, 1.5389183665189552, 1.5488349781978341, 1.5584747830697725, 1.5678212504766649, 1.5768592500360963, 1.58557509374497, 1.5939565660559065, 1.6019929419931127, 1.6096749935594041, 1.6169949848555163 ], [ 1.1846785349607911, 1.188134999755593, 1.191997734776198, 1.1962702025508964, 1.2009545619779514, 1.2060515915661811, 1.2115606205623708, 1.2174794700421085, 1.2238044059634139, 1.2305301059464717, 1.2376496411411224, 1.245154473991206, 1.253034472043142, 1.2612779372411704, 1.2698716494832758, 1.2788009226646573, 1.2880496710789051, 1.2976004839246664, 1.3074347057837286, 1.317532521264005, 1.3278730424748013, 1.3384343985412446, 1.3491938268868213, 1.360127766447072, 1.3712119532756497, 1.3824215191464524, 1.3937310937463439, 1.4051149109163652, 1.4165469191706062, 1.4280008964391295, 1.4394505686810255, 1.4508697317243533, 1.4622323754328923, 1.4735128090883893, 1.4846857867174097, 1.4957266309858352, 1.5066113542294457, 1.517316775182177, 1.5278206300003223, 1.5381016762560142, 1.54813978868227, 1.5579160455897063, 1.5674128050366791, 1.5766137700150034, 1.5855040421070303, 1.5940701632704346, 1.6023001456094068, 1.6101834891882465, 1.6177111881308015, 1.6248757254212247 ], [ 1.194926688732844, 1.1985007396146858, 1.2024740415010573, 1.206849699892283, 1.211629543889831, 1.2168140547051982, 1.2224023018515402, 1.2283918887911656, 1.234778909710601, 1.2415579188690413, 1.2487219136153669, 1.2562623317095796, 1.2641690630508997, 1.2724304753585574, 1.2810334528315752, 1.2899634463913412, 1.2992045338350129, 1.3087394881283503, 1.3185498521463137, 1.3286160184064693, 1.3389173126872818, 1.3494320808228648, 1.3601377783570487, 1.3710110630691608, 1.3820278906157102, 1.3931636136468166, 1.4043930847551045, 1.4156907635116085, 1.427030827663784, 1.4383872883418463, 1.449734108870357, 1.4610453265353325, 1.472295176431733, 1.4834582163249335, 1.4945094513099708, 1.505424456947626, 1.516179499496987, 1.5267516518492557, 1.5371189037936719, 1.5472602653112515, 1.5571558616911485, 1.5667870193938795, 1.5761363417409227, 1.5851877736858317, 1.5939266551126328, 1.6023397623066997, 1.6104153374453658, 1.6181431061537785, 1.6255142833604967, 1.6325215678612888 ], [ 1.2052017859989381, 1.2088890771104743, 1.212968393990529, 1.2174424931241519, 1.222312882738182, 1.2275797561135755, 1.2332419323016761, 1.2392968057621536, 1.245740306328869, 1.2525668707020359, 1.259769426363004, 1.2673393884279052, 1.2752666695265074, 1.2835397023521464, 1.2921454741218035, 1.301069571856445, 1.3102962371751035, 1.319808429212523, 1.3295878943208337, 1.3396152413837024, 1.3498700218229072, 1.3603308136706678, 1.370975309370705, 1.3817804072182953, 1.39272230652476, 1.4037766066803417, 1.4149184102878622, 1.4261224304581956, 1.437363102213412, 1.448614697755419, 1.4598514451485278, 1.4710476497526765, 1.4821778175456983, 1.4932167793005124, 1.5041398144434077, 1.5149227733183606, 1.525542196521081, 1.5359754299456492, 1.546200734205548, 1.5561973871469523, 1.5659457782630881, 1.5754274939406594, 1.5846253926182245, 1.593523669107467, 1.6021079075155398, 1.6103651224041329, 1.6182837880220111, 1.6258538556462225, 1.6330667592567376, 1.6399154099445568 ], [ 1.2154799165099432, 1.2192757510556926, 1.2234562046539952, 1.2280236935451303, 1.2329794144216892, 1.2383232821195869, 1.244053874390548, 1.2501683850605547, 1.256662586766453, 1.2635308042761626, 1.270765899140411, 1.2783592661104703, 1.2863008414095198, 1.2945791225950662, 1.3031811994294848, 1.3120927949168806, 1.3212983154916758, 1.3307809092721166, 1.3405225313201665, 1.3505040149656056, 1.360705148431855, 1.3711047562133276, 1.3816807848657475, 1.3924103930524705, 1.4032700458187133, 1.4142356131290834, 1.4252824726983593, 1.4363856170764218, 1.4475197648272737, 1.4586594754841655, 1.4697792677843968, 1.4808537405038114, 1.4918576950358289, 1.5027662587037076, 1.5135550076656015, 1.5242000881750246, 1.534678334898298, 1.5449673849661931, 1.5550457864503597, 1.5648931000046151, 1.5744899924952214, 1.5838183215598278, 1.5928612101779955, 1.6016031105024597, 1.610029856383922, 1.6181287042169346, 1.6258883619340783, 1.6332990061732744, 1.6403522878325238, 1.6470413264023325 ], [ 1.2257380090895091, 1.2296373711538378, 1.233913787130156, 1.238569342398433, 1.2436049318086728, 1.2490202013687859, 1.2548134966702917, 1.26098181917911, 1.2675207914113396, 1.274424631848785, 1.281686140231252, 1.28929669360438, 1.2972462532214384, 1.3055233821179364, 1.3141152729236925, 1.3230077852711013, 1.332185492018719, 1.341631733445051, 1.351328678579238, 1.3612573929127076, 1.371397911861457, 1.3817293194992286, 1.392229832233221, 1.4028768872237056, 1.4136472354397618, 1.4245170392845523, 1.4354619747116526, 1.44645733769169, 1.4574781547839841, 1.4684992974319195, 1.4794955994462968, 1.4904419769795763, 1.5013135501382646, 1.5120857652388762, 1.522734516593579, 1.533236266619989, 1.5435681630095384, 1.5537081516629652, 1.5636350841108366, 1.573328818181278, 1.5827703107555684, 1.591941701561793, 1.600826387094838, 1.6094090839122785, 1.6176758807355476, 1.6256142789773156, 1.6332132215134694, 1.6404631097140479, 1.6473558089364921, 1.653884642859941 ], [ 1.2359539217882416, 1.239951509117713, 1.2443184484879402, 1.2490565043070836, 1.2541662795779056, 1.2596471612430025, 1.2654972719187945, 1.271713428998665, 1.27829111200619, 1.2852244389353589, 1.2925061521314376, 1.3001276140533324, 1.3080788130313745, 1.3163483789098858, 1.3249236082608078, 1.3337904986891784, 1.3429337916365367, 1.35233702303051, 1.3619825811280113, 1.3718517709479683, 1.3819248847740084, 1.3921812783114338, 1.402599452187406, 1.4131571385725012, 1.4238313927612916, 1.434598689571677, 1.4454350244033798, 1.4563160187365356, 1.4672170297579792, 1.4781132636826246, 1.4889798922009865, 1.4997921713406415, 1.5105255618892066, 1.5211558503975087, 1.5316592696711102, 1.5420126175721254, 1.552193372895203, 1.5621798070553004, 1.5719510903313043, 1.5814873914502767, 1.5907699693702324, 1.59978125622432, 1.608504930521826, 1.6169259798582516, 1.625030752562111, 1.632806997894084, 1.6402438946087785, 1.6473320678830046, 1.6540635948020548, 1.660431998770042 ], [ 1.24610651846485, 1.250196775906499, 1.2546485672319867, 1.2594633461832334, 1.2646414341773837, 1.270181969009608, 1.2760828596008424, 1.2823407476491218, 1.288950976953174, 1.295907571052657, 1.3032032196751766, 1.3108292743055472, 1.3187757530077229, 1.3270313544490624, 1.3355834809127916, 1.3444182699501284, 1.3535206342279191, 1.3628743090749278, 1.372461907219736, 1.382264980240036, 1.3922640862967843, 1.4024388637948226, 1.412768110680428, 1.423229869143234, 1.4338015155245896, 1.444459855239924, 1.4551812224957588, 1.4659415845235215, 1.4767166499657243, 1.4874819809416873, 1.498213108197291, 1.5088856486140116, 1.519475424225515, 1.529958581771567, 1.5403117117170382, 1.550511965582441, 1.5605371703772242, 1.5703659389009053, 1.5799777746819756, 1.5893531703620418, 1.5984736984019683, 1.6073220930869008, 1.6158823229349433, 1.6241396527662415, 1.6320806948600328, 1.6396934488113857, 1.646967329890058, 1.65389318589519, 1.660463302684582, 1.6666713987306703 ], [ 1.256175732179709, 1.2603528854562924, 1.2648836574725721, 1.2697692019552484, 1.2750095692309382, 1.2806036580228595, 1.286549172960629, 1.2928425885610055, 1.299479120357228, 1.3064527037477993, 1.3137559810066184, 1.321380296751962, 1.329315702021306, 1.3375509669519388, 1.346073601934395, 1.3548698869955484, 1.3639249090870813, 1.3732226069067135, 1.3827458228624736, 1.3924763618011264, 1.4023950561520608, 1.4124818371791938, 1.4227158120745083, 1.4330753466588302, 1.44353815346987, 1.4540813850093455, 1.4646817318869654, 1.4753155255400412, 1.4859588451252046, 1.4965876280790797, 1.5071777837319864, 1.5177053092412347, 1.52814640699376, 1.538477602518914, 1.5486758618571184, 1.5587187072541846, 1.568584329998352, 1.5782516991919802, 1.5877006652536303, 1.5969120569815256, 1.6058677710750788, 1.6145508531072108, 1.6229455690634493, 1.6310374667107321, 1.6388134262251877, 1.6462616996875066, 1.653371939241556, 1.6601352138993004, 1.6665440151576814, 1.6725922517642258 ], [ 1.2661426159286322, 1.2704007054349409, 1.275004419792265, 1.2799546236471204, 1.2852511069327823, 1.2908925395279913, 1.2968764313133856, 1.3031990982994153, 1.3098556354292765, 1.3168398965689752, 1.3241444820888468, 1.331760734321493, 1.3396787410579383, 1.3478873471236015, 1.3563741739669637, 1.365125647102256, 1.3741270311780982, 1.3833624723989186, 1.3928150480043955, 1.40246682251051, 1.412298910429049, 1.4222915452025908, 1.4324241541120613, 1.4426754389263936, 1.4530234620620655, 1.4634457380008457, 1.473919329673783, 1.4844209494590355, 1.494927064362038, 1.5054140048523967, 1.5158580767278433, 1.5262356752664563, 1.5365234008204491, 1.5466981749038866, 1.5567373557379491, 1.566618852145971, 1.5763212346411521, 1.5858238425253133, 1.5951068858208557, 1.6041515408912113, 1.6129400386678412, 1.621455744494073, 1.6296832287145742, 1.6376083272815052, 1.6452181918096627, 1.6525013286873573, 1.659447627032259, 1.6660483754649178, 1.672296267851759, 1.6781853983380879 ], [ 1.2759893813600829, 1.28032229567832, 1.284992779480175, 1.2900014194965612, 1.295347756134905, 1.301030240796184, 1.3070461982925625, 1.313391794969626, 1.32006201307563, 1.3270506318425472, 1.3343502156535503, 1.341952109572582, 1.3498464424104832, 1.358022137403383, 1.3664669304891286, 1.37516739609078, 1.3841089802561424, 1.3932760409597653, 1.402651895349303, 1.4122188737073382, 1.4219583799000275, 1.4318509580883916, 1.4418763654820794, 1.4520136509124077, 1.462241238987401, 1.472537019562573, 1.482878442215825, 1.4932426153527163, 1.5036064094912631, 1.5139465641857421, 1.5242397979512614, 1.5344629204488145, 1.5445929460901677, 1.5546072081274684, 1.5644834722096619, 1.5742000483208651, 1.5837358999691686, 1.593070749471473, 1.6021851781835283, 1.6110607205557697, 1.6196799509561473, 1.6280265622889663, 1.6360854355534642, 1.6438426996227888, 1.6512857806800643, 1.6584034409175925, 1.6651858062825662, 1.671624383231742, 1.6777120646326908, 1.683443125114783 ], [ 1.2856994262083539, 1.2901009350621395, 1.2948319129102528, 1.2998926799123445, 1.305282537955404, 1.3109997304494418, 1.31704140694613, 1.3234035931257626, 1.3300811666444752, 1.3370678392678648, 1.3443561456414652, 1.3519374389666847, 1.3598018937668093, 1.3679385158462845, 1.376335159471337, 1.3849785517349926, 1.3938543240167016, 1.4029470504071067, 1.4122402929412126, 1.4217166534663623, 1.4313578319615812, 1.4411446911177317, 1.4510573269793685, 1.46107514543458, 1.4711769443150817, 1.4813410008324783, 1.4915451640269362, 1.5017669518409456, 1.5119836523549903, 1.5221724286359781, 1.5323104265562542, 1.5423748848452772, 1.5523432465416338, 1.5621932709245583, 1.5719031449265488, 1.581451592965699, 1.5908179840926795, 1.5999824353258372, 1.6089259100514937, 1.6176303103968928, 1.6260785625410543, 1.6342546940135088, 1.6421439021407223, 1.6497326129322567, 1.657008529849085, 1.6639606720604116, 1.670579401967231, 1.6768564419449232, 1.682784880428093, 1.688359167622715 ], [ 1.2952573512390206, 1.299721137632282, 1.304506262914402, 1.3096127921517, 1.3150397998207235, 1.3207853319235678, 1.3268463726679869, 1.3332188162081748, 1.3398974438958933, 1.3468759074361878, 1.3541467182780935, 1.3617012435029086, 1.369529708402609, 1.3776212058732193, 1.3859637126847757, 1.3945441126337095, 1.4033482265366133, 1.4123608489868968, 1.4215657917670683, 1.4309459337878807, 1.4404832774083975, 1.450159010975053, 1.4599535773999848, 1.4698467485751383, 1.4798177053872088, 1.489845123056287, 1.4999072614679692, 1.5099820601040554, 1.5200472371021032, 1.5300803918909454, 1.5400591107605157, 1.5499610746336514, 1.5597641682183279, 1.5694465896356962, 1.5789869595462307, 1.588364428737176, 1.5975587830937243, 1.6065505448560211, 1.6153210690683575, 1.6238526341559902, 1.6321285256204403, 1.6401331119256104, 1.6478519117523458, 1.6552716519261486, 1.6623803154677073, 1.6691671793737037, 1.6756228419018462, 1.681739239302544, 1.6875096521058537, 1.692928701230221 ], [ 1.304648967543856, 1.3091686588606313, 1.3140015440482968, 1.3191474446482232, 1.3246052189072681, 1.330372726071523, 1.3364467950054446, 1.3428231975902627, 1.3494966273158449, 1.3564606834331319, 1.363707860980859, 1.3712295469433253, 1.3790160227377777, 1.3870564731728243, 1.395339001965709, 1.4038506538580802, 1.412577443327506, 1.421504389856868, 1.4306155596938244, 1.4398941140079087, 1.4493223633300594, 1.4588818281371365, 1.4685533054186861, 1.4783169410332244, 1.488152307623516, 1.4980384878143307, 1.507954162360017, 1.5178777028441548, 1.5277872684594516, 1.5376609063155746, 1.5474766546373493, 1.5572126481295052, 1.5668472246996992, 1.5763590326532086, 1.585727137403703, 1.5949311266893058, 1.6039512132445801, 1.6127683338607461, 1.6213642437706304, 1.629721605323029, 1.6378240699646252, 1.6456563526252248, 1.6532042977034431, 1.6604549359716039, 1.667396531857739, 1.6740186207147012, 1.6803120358463843, 1.6862689252243124, 1.691882757988476, 1.6971483209802805 ], [ 1.3138612950430526, 1.318430492915006, 1.3233047386707968, 1.3284836219448994, 1.3339657959722364, 1.339748943934018, 1.345829749407608, 1.352203871338148, 1.3588659239159357, 1.3658094617035101, 1.3730269703115283, 1.3805098628747556, 1.3882484825304062, 1.3962321110529092, 1.404448983753029, 1.4128863107071155, 1.4215303043439824, 1.4303662133831718, 1.4393783630885255, 1.4485502017734606, 1.4578643534681, 1.4673026766311172, 1.47684632875878, 1.4864758367084248, 1.4961711725119349, 1.5059118344051288, 1.5156769327414648, 1.525445280392748, 1.5351954871666311, 1.5449060576925002, 1.5545554921453755, 1.5641223890951772, 1.5735855496885485, 1.5829240822963397, 1.5921175066949766, 1.6011458567978836, 1.6099897809173624, 1.6186306385201976, 1.627050592444991, 1.6352326955763734, 1.6431609710226063, 1.6508204849173551, 1.6581974110633964, 1.6652790867523604, 1.6720540592280306, 1.6785121224063844, 1.6846443436196175, 1.6904430803084225, 1.6959019867422063, 1.7010160109960348 ], [ 1.3228825530555852, 1.3274948618351803, 1.332404084760771, 1.3376095911894752, 1.3431098405655533, 1.3489023507048958, 1.3549836699788522, 1.3613493537840478, 1.3679939456560213, 1.374910963350613, 1.3820928901790976, 1.3895311718428514, 1.397216218971682, 1.4051374155289702, 1.4132831332066467, 1.4216407518958463, 1.4301966862839517, 1.438936418596667, 1.4478445374737245, 1.456904782937773, 1.4661000973870046, 1.4754126825112315, 1.4848240619969857, 1.494315149848432, 1.5038663241059407, 1.5134575056925648, 1.5230682420598631, 1.5326777952389794, 1.5422652338311866, 1.5518095283961437, 1.561289649617209, 1.570684668544681, 1.5799738581414886, 1.5891367952859325, 1.5981534623247526, 1.6070043472211182, 1.615670541308504, 1.6241338336461157, 1.6323768009761501, 1.640382892309762, 1.6481365072177185, 1.6556230669726806, 1.662829077782764, 1.6697421854669405, 1.6763512210505196, 1.6826462368981612, 1.6886185331495847, 1.6942606743740274, 1.6995664965092114, 1.7045311042947249 ], [ 1.3317021437875187, 1.3363511974945552, 1.3412890563820459, 1.3465148811347956, 1.3520269485986252, 1.3578226219009186, 1.3638983242812208, 1.3702495169915865, 1.3768706816017087, 1.3837553070148925, 1.3908958814692098, 1.3982838897636118, 1.4059098159136048, 1.4137631514055737, 1.421832409183878, 1.4301051434713774, 1.438567975491899, 1.4472066251322673, 1.4560059485516568, 1.4649499817160792, 1.4740219898047622, 1.4832045224019756, 1.4924794743510787, 1.501828152106121, 1.5112313453695352, 1.5206694037512412, 1.530122318125421, 1.5395698062959464, 1.5489914025113778, 1.5583665502965351, 1.5676746979920044, 1.5768953963176253, 1.5860083972037842, 1.5949937530678673, 1.6038319156556364, 1.6125038335215438, 1.6209910471907092, 1.6292757810313074, 1.637341030871085, 1.6451706464175158, 1.6527494075878693, 1.6600630939235352, 1.6670985463509826, 1.673843720657564, 1.6802877321720349, 1.686420891272541, 1.6922347294860125, 1.697722016087487, 1.702876765251719, 1.7076942339484749 ] ], "zauto": true, "zmax": 1.7076942339484749, "zmin": -1.7076942339484749 }, { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 1, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(255,247,251)" ], [ 0.14285714285714285, "rgb(236,231,242)" ], [ 0.2857142857142857, "rgb(208,209,230)" ], [ 0.42857142857142855, "rgb(166,189,219)" ], [ 0.5714285714285714, "rgb(116,169,207)" ], [ 0.7142857142857143, "rgb(54,144,192)" ], [ 0.8571428571428571, "rgb(5,112,176)" ], [ 1.0, "rgb(3,78,123)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "xaxis": "x2", "y": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "yaxis": "y2", "z": [ [ 0.04778837988822157, 0.04506376534586057, 0.04259056823973424, 0.040400074705921094, 0.038522282014150026, 0.03698310733059093, 0.03580098740992917, 0.03498347045005608, 0.03452469322449219, 0.034404603978218866, 0.03459032328495163, 0.035039324528323035, 0.035703562089395756, 0.036533559683341855, 0.03748175292599293, 0.03850480516408843, 0.039564954514741665, 0.04063061889461696, 0.04167651493040228, 0.042683502168416765, 0.04363829837584303, 0.0445331520992256, 0.04536551368390332, 0.04613771523418788, 0.04685665022528246, 0.047533431472952636, 0.048182999815288355, 0.048823654238549744, 0.049476477301185574, 0.05016463810111738, 0.050912569120596454, 0.05174503265384041, 0.05268611518249147, 0.05375821008844994, 0.05498106507826147, 0.056370975220604615, 0.05794019227785237, 0.059696596718326285, 0.06164364547231464, 0.0637805740246563, 0.06610280369514128, 0.06860248909488624, 0.07126913789128202, 0.07409024276264166, 0.07705187948538623, 0.0801392410835802, 0.08333709259475917, 0.08663014247777588, 0.09000333452097507, 0.09344206866094373 ], [ 0.04672908000930987, 0.04393735866633678, 0.041385005153540225, 0.03910313427360783, 0.037122628319234706, 0.0354715879850463, 0.034171949934943865, 0.03323575090972222, 0.03266192767940901, 0.03243469064691046, 0.032524163141510284, 0.03288921946681011, 0.03348170698253546, 0.034250929593956515, 0.035147480723507034, 0.03612598658370898, 0.037146749586305886, 0.03817652029604425, 0.03918868728750934, 0.040163134079823366, 0.04108593861789102, 0.04194902055547905, 0.042749787679951905, 0.04349079564808235, 0.044179411115729074, 0.044827453550494355, 0.045450782982990975, 0.0460687986176609, 0.046703816730439066, 0.04738030643075094, 0.04812397930544451, 0.04896075313348813, 0.04991563798438823, 0.051011619663620084, 0.0522686333642308, 0.05370272264899968, 0.05532546209680297, 0.057143688398282565, 0.05915954231216703, 0.061370783456443576, 0.06377131084419238, 0.06635180922562467, 0.0691004440674356, 0.07200354184617068, 0.0750462113203631, 0.07821288044156588, 0.08148773932796044, 0.08485509096582017, 0.08829961814443858, 0.09180657843068779 ], [ 0.04588360745642943, 0.043032584853400904, 0.04040800535147015, 0.038040215371222354, 0.03596031288276901, 0.034197959232478856, 0.032778190978468104, 0.03171753712370725, 0.031020234989796384, 0.030675683451061458, 0.030658135102548424, 0.030928917273495154, 0.031440549867587785, 0.03214156140013189, 0.03298086109068031, 0.033911007399044714, 0.03489024250487136, 0.035883498238168623, 0.036862693659894946, 0.03780661869171632, 0.03870061811457133, 0.039536207471511486, 0.04031068682025178, 0.04102677243918234, 0.04169223671907658, 0.0423195280602678, 0.04292533249811675, 0.04353003567048647, 0.0441570478416513, 0.04483196708407604, 0.04558157721712032, 0.04643270684651303, 0.04741100994479092, 0.04853975950082141, 0.049838764389354, 0.05132351755643339, 0.05300465800219477, 0.05488778478621977, 0.056973609969316705, 0.0592583927249179, 0.061734569077551524, 0.06439148433777445, 0.0672161451703712, 0.07019392843796016, 0.07330920720179315, 0.07654587515036931, 0.07988776652161238, 0.08331897875592495, 0.08682411046729903, 0.09038842916583921 ], [ 0.04522966511214799, 0.04232622535705811, 0.03963591890403987, 0.037187845842110476, 0.03501271818674779, 0.03314111160637052, 0.031600625465531, 0.030412054266035632, 0.02958518217375154, 0.029115332464833103, 0.02898193891445058, 0.029149862754461933, 0.029573153515796105, 0.030200083245890675, 0.03097808348411975, 0.03185763937496933, 0.032794822162110236, 0.03375260635290224, 0.03470131616485872, 0.035618549441551524, 0.036488843727044064, 0.0373032512655401, 0.038058908785793474, 0.03875863056025406, 0.039410515846949476, 0.04002753896542918, 0.040627077863959506, 0.04123033329856852, 0.041861595859298065, 0.04254733332183946, 0.04331509703912124, 0.04419228187565022, 0.045204814116292576, 0.04637587620678346, 0.04772479446504821, 0.04926620706345193, 0.05100959333605272, 0.05295919035073063, 0.05511426424186183, 0.057469657961416, 0.06001651372056181, 0.06274306845728747, 0.06563543806806241, 0.0686783318647038, 0.07185566473648278, 0.0751510558009807, 0.07854821704363922, 0.08203124391225697, 0.08558482346234476, 0.08919437607951328 ], [ 0.044744748268028725, 0.04179457251878484, 0.039044270537248744, 0.03652136567589077, 0.03425570155632738, 0.03227816750256757, 0.030618318045873155, 0.029300788859632408, 0.028340879044468206, 0.027740306777080965, 0.027484573055564416, 0.027543113326791296, 0.02787241031878409, 0.028421073686536857, 0.029135329835973313, 0.029963632830084002, 0.030859808005086767, 0.031784765221540716, 0.03270713866800521, 0.033603264049590874, 0.0344568217768389, 0.035258358626927576, 0.03600479956620882, 0.036698989112721604, 0.03734925486144325, 0.037968957795563314, 0.0385759793325322, 0.03919209111768851, 0.03984216035599124, 0.04055316225254625, 0.041353002541725886, 0.042269194711166226, 0.043327481078906126, 0.044550522371442976, 0.04595679358604839, 0.04755980608223988, 0.04936772856416525, 0.05138341559438754, 0.0536047903992508, 0.05602548567968407, 0.05863562983717401, 0.061422674247800194, 0.06437218112771334, 0.06746852084440098, 0.07069545435442798, 0.07403659669087725, 0.07747577023975519, 0.08099726303944388, 0.08458600933930369, 0.08822770893233095 ], [ 0.04440817867688268, 0.041415709354584974, 0.03861026765878783, 0.036017620239867494, 0.03366640232643586, 0.03158730892034227, 0.0298112331589326, 0.028366080628032694, 0.027272363683514274, 0.026538354672201826, 0.026156264561641992, 0.02610103491569562, 0.026332500772540523, 0.026800284268411172, 0.027449771309093027, 0.028227505554880097, 0.02908505336444599, 0.029981202195322368, 0.03088284129996606, 0.03176500562593903, 0.03261049014953153, 0.03340930431461329, 0.03415811036544962, 0.03485969834942569, 0.03552249259419292, 0.0361600508509125, 0.036790500656525754, 0.03743585403714952, 0.03812115090553463, 0.03887340435591803, 0.039720357477228484, 0.040689107480922235, 0.0418046995643795, 0.043088826169272586, 0.04455877342018078, 0.04622672877268327, 0.04809950749466008, 0.05017868697206036, 0.052461077495655054, 0.05493942162083218, 0.057603206214597726, 0.06043948660214684, 0.0634336502355511, 0.06657007763402625, 0.06983268401884857, 0.07320534315333704, 0.07667220546953059, 0.08021792722494327, 0.08382782817087583, 0.08748799375083878 ], [ 0.04420279017181974, 0.041171419449736235, 0.038314932764694234, 0.03565729371094147, 0.033225728671633835, 0.03105034290140676, 0.029162786564745913, 0.02759356988753219, 0.02636787865069318, 0.025500372369086335, 0.024990315553750773, 0.024818919602019648, 0.024950278778139264, 0.025335795453103167, 0.025920507425724854, 0.02664928587442168, 0.027471516315649654, 0.028343871433114884, 0.02923148432299258, 0.030108076002309202, 0.03095553706826948, 0.03176330214818767, 0.03252769952903562, 0.033251344862121245, 0.03394257696225721, 0.034614894254733096, 0.03528633235928483, 0.03597872120369465, 0.03671677242499475, 0.03752697476809876, 0.03843631547854969, 0.03947089382685347, 0.04065453792425501, 0.04200756340248096, 0.04354580988341407, 0.045280054859016344, 0.0472158435086383, 0.04935370557368014, 0.05168967647784276, 0.05421601195898368, 0.05692198505612488, 0.05979467399789874, 0.06281967851765449, 0.06598173094927194, 0.06926519151031128, 0.07265443260344505, 0.0761341254244156, 0.07968944543087053, 0.08330621320655215, 0.086970985496194 ], [ 0.044116076878820513, 0.041048493007332945, 0.03814457311592441, 0.03542653680573265, 0.032920119860476896, 0.030654552060501307, 0.02866171745276093, 0.026974017360233565, 0.025620577688210636, 0.024621963475691577, 0.023984504450516295, 0.02369622677136142, 0.02372635148642, 0.024028936195818407, 0.024549332911710044, 0.02523114050659463, 0.026021763828127122, 0.02687584554186602, 0.027756790442297466, 0.028637002214883384, 0.02949743569410669, 0.030326883336543424, 0.031121223789017455, 0.03188272105451097, 0.032619377436208435, 0.033344297928911415, 0.034075004735331774, 0.03483264044326605, 0.0356410140809874, 0.036525474482465514, 0.03751163728796015, 0.03862403845966806, 0.039884826738473315, 0.04131262652787676, 0.042921691690137403, 0.04472142969282727, 0.04671631569310508, 0.04890615560237902, 0.05128661282835428, 0.05384989408951758, 0.056585494382073914, 0.059480921931979736, 0.06252235098018205, 0.06569517572537684, 0.06898445842680348, 0.0723752774613378, 0.07585298790828517, 0.07940340965723362, 0.08301295775850039, 0.08666872806718774 ], [ 0.04414072060571207, 0.041039323737173075, 0.03809145318484292, 0.035317717057270444, 0.03274236829801255, 0.03039356897523621, 0.028302980734486095, 0.026504171749427742, 0.025029333835505155, 0.023904175975073837, 0.02314176303305123, 0.022737218244229175, 0.0226656821089264, 0.022884853797250006, 0.023341269959705344, 0.0239778647424383, 0.024740414515295236, 0.025581701524153302, 0.026463458230098273, 0.027356754812182114, 0.02824153878209392, 0.029105834860293407, 0.029944886230448418, 0.030760350350857658, 0.03155956111454558, 0.03235481704814839, 0.03316263533896726, 0.03400291327152886, 0.03489795697331543, 0.035871369033210004, 0.03694682705775732, 0.03814682666874348, 0.03949149381739611, 0.04099758165248597, 0.04267775058027852, 0.04454018949282636, 0.046588583019944535, 0.0488223796542079, 0.05123728158947948, 0.05382586462338457, 0.05657824321185495, 0.059482714625098784, 0.06252633918036078, 0.06569543469944353, 0.06897597952146496, 0.07235392890604252, 0.0758154552733917, 0.07934712479619303, 0.08293602271640584, 0.08656983845652085 ], [ 0.04427451597143038, 0.04114181754284824, 0.03815368974366927, 0.03532930463239315, 0.0326914998081107, 0.03026725063188918, 0.02808760867441485, 0.026186607769025726, 0.024598551163046142, 0.02335330824296209, 0.022470022963587938, 0.021950897956486422, 0.021777655905983174, 0.02191270900243761, 0.022304871814847537, 0.022897262228508332, 0.02363455805231866, 0.02446794174228922, 0.025357545943105717, 0.026273056132563116, 0.02719327474532344, 0.02810525042608322, 0.029003315797268846, 0.0298881789728155, 0.03076609451574212, 0.03164807943568305, 0.032549118102812524, 0.03348730270330178, 0.03448287523925336, 0.03555716781413279, 0.036731474256786696, 0.03802592020719499, 0.039458421467157896, 0.0410438240148115, 0.04279330087640223, 0.04471404533758169, 0.04680925691046944, 0.049078377983837435, 0.05151751414910688, 0.0541199630270441, 0.05687678267599129, 0.05977734581653293, 0.06280984424748758, 0.06596172453490348, 0.06922004900351739, 0.07257178469405945, 0.07600402780029854, 0.07950417314051987, 0.08306003844116318, 0.08665995241986266 ], [ 0.04451979173648115, 0.04135873246733796, 0.038334510800946776, 0.03546505514601678, 0.03277188939716257, 0.030280738527615415, 0.0280217265669622, 0.026028709088322007, 0.024337135853295912, 0.02297991387233737, 0.021981331976608447, 0.021350330498475567, 0.021075667627365312, 0.021125547830849963, 0.021452345426972802, 0.022000455766559842, 0.0227141823098643, 0.02354346877274355, 0.02444693444036535, 0.02539278292805827, 0.026358454215611872, 0.027329719258873196, 0.02829963271307313, 0.02926753079311587, 0.030238120850534667, 0.031220638553477134, 0.03222802299152447, 0.03327606186848606, 0.03438247734003573, 0.035565950745441714, 0.03684511500036954, 0.038237569839074774, 0.03975899063583124, 0.04142240147408963, 0.04323766686752663, 0.04521122833885476, 0.04734607971139698, 0.04964194681614486, 0.05209561928880198, 0.054701376160255465, 0.05745145129446405, 0.0603364955909996, 0.06334600616181425, 0.06646870527702242, 0.06969286199114028, 0.07300655645942426, 0.07639789127432527, 0.0798551563044694, 0.08336695418155805, 0.0869222933399105 ], [ 0.04488247565144199, 0.04169662769946406, 0.03864109008178548, 0.0357327370227204, 0.03299189536670132, 0.030443018607419117, 0.028115059956857417, 0.026041144892193866, 0.024256969742511618, 0.022797320752136925, 0.021690503297806262, 0.020951533116634998, 0.020576354161209624, 0.02053991373788053, 0.020799510604901737, 0.021302111818041192, 0.02199256499874576, 0.022820053467365885, 0.023741800348888866, 0.02472439669326512, 0.025743633616846267, 0.026783622957573864, 0.027835702433240843, 0.028897365068287353, 0.02997128835853332, 0.03106445383103176, 0.032187315379515045, 0.03335297339495822, 0.03457632726728822, 0.035873202289508806, 0.03725947163866277, 0.03875021420981265, 0.04035895998390624, 0.04209707370167699, 0.04397331526474433, 0.04599359493736013, 0.04816091849336622, 0.05047549745974242, 0.05293498641243018, 0.05553480421797881, 0.05826849820825381, 0.06112811717309644, 0.06410456810972763, 0.06718794071569904, 0.07036779130740284, 0.07363338362485565, 0.07697388784471368, 0.08037854137552863, 0.08383677606684456, 0.0873383167239622 ], [ 0.04537096674485131, 0.04216461602573355, 0.03908318546916777, 0.0361426686076429, 0.033362314867108896, 0.03076532047863688, 0.028379304013540826, 0.026236231902754023, 0.02437128263069417, 0.022820038140099183, 0.021613611779139272, 0.020772156436166006, 0.020298569472278347, 0.020175186285539423, 0.02036549723615174, 0.020820426519456325, 0.02148645053747994, 0.02231261034885963, 0.023254922377116075, 0.02427824477654253, 0.02535640682448804, 0.026471443060355634, 0.02761251024416213, 0.02877478921943726, 0.029958484213354678, 0.03116792969589013, 0.03241077285744181, 0.033697192982862854, 0.03503913041407289, 0.0364495167614797, 0.03794151770382273, 0.03952781537235155, 0.04121996578777839, 0.04302786670052171, 0.044959363081928154, 0.04702000388259721, 0.04921294806790413, 0.05153900391689892, 0.053996775691878704, 0.05658288711368116, 0.05929225124958953, 0.06211836014387183, 0.06505357318414569, 0.06808938935915972, 0.07121669421133814, 0.07442597687875539, 0.07770751599700906, 0.08105153548072302, 0.08444833253670951, 0.08788838091690855 ], [ 0.04599496775719385, 0.04277309535127692, 0.03967178143065496, 0.03670629016975413, 0.03389491064808585, 0.031259628040222205, 0.028826645234395498, 0.02662648326349849, 0.02469322528072274, 0.023062335063942382, 0.021766568034216265, 0.020830088393449776, 0.020262103835255795, 0.020052512303714787, 0.0201719411880711, 0.020576574947789802, 0.021215698093197694, 0.0220389814314406, 0.02300155543529841, 0.02406650883359821, 0.025205443408273874, 0.026397931980429157, 0.027630527645139683, 0.02889569310093053, 0.030190807009316305, 0.03151728240965596, 0.03287977777284529, 0.034285467127056, 0.035743342013771544, 0.03726353262407496, 0.03885665119018838, 0.04053317339275041, 0.042302880876406906, 0.044174389110608135, 0.0461547803069135, 0.04824935254279541, 0.05046148592017237, 0.05279261679645285, 0.05524230361559458, 0.05780836352712086, 0.060487057839459554, 0.06327330580539725, 0.06616090937369927, 0.06914277544665969, 0.07221112612636958, 0.07535769093711606, 0.07857387784484327, 0.08185092200759114, 0.08518001264771839, 0.08855239935558137 ], [ 0.04676439969478857, 0.043532592773592456, 0.04041787887634099, 0.03743492159898691, 0.03460116335625546, 0.03193745450900226, 0.029468581695478092, 0.02722347929380367, 0.025234764832396693, 0.02353709698781066, 0.022163853212669334, 0.021142012669416826, 0.020486089524779476, 0.020193160599031063, 0.020241412454903344, 0.02059330124745759, 0.02120206924796707, 0.02201892313992095, 0.022998612415902172, 0.024102589654773052, 0.025300103530294396, 0.026568000677618237, 0.02788992247024658, 0.029255327202489675, 0.030658543897552935, 0.03209792391706423, 0.033575088224066414, 0.03509424490713137, 0.036661551793071435, 0.03828450904577269, 0.039971378925111344, 0.041730640317340126, 0.04357049227800911, 0.04549842300803186, 0.047520858744256156, 0.049642902031362686, 0.051868162198782077, 0.05419867408508336, 0.05663489534772005, 0.05917576880688893, 0.06181883442156368, 0.06456037548431863, 0.06739558499337643, 0.0703187403740537, 0.0733233772810493, 0.07640245573862692, 0.07954851412630759, 0.08275380837453362, 0.08601043517060972, 0.08931043902033622 ], [ 0.04768848040909369, 0.04445280360391527, 0.041331511536132313, 0.03833877667928893, 0.03549130620557286, 0.03280891838844865, 0.03031505294822169, 0.028037044529278035, 0.026005867382831598, 0.024254924044956307, 0.022817399971199612, 0.02172194004860898, 0.020987124835490388, 0.02061630590426543, 0.02059502716707639, 0.02089255016159554, 0.021467030021236153, 0.022272173112679226, 0.02326304961525871, 0.024399846056406046, 0.025649558598843564, 0.026986244802670672, 0.02839050526488351, 0.029848668746685764, 0.031351935908393726, 0.032895584620344975, 0.034478257942479, 0.036101322193529975, 0.037768275426509464, 0.03948419156899122, 0.0412551942241846, 0.04308796241184979, 0.04498927637939204, 0.04696561434970159, 0.04902281080668472, 0.05116578427772524, 0.053398338462969576, 0.055723035955767206, 0.05814113954255358, 0.060652612753958016, 0.06325616925150564, 0.06594935979241114, 0.06872868573814034, 0.07158972907555583, 0.0745272903950749, 0.07753552794522876, 0.08060809254839076, 0.08373825468070661, 0.08691902131604874, 0.09014324118325329 ], [ 0.04877500931376416, 0.04554186062986705, 0.04242101324877987, 0.03942624282049527, 0.0365736307139777, 0.03388208501614522, 0.031373818725625176, 0.02907464877584, 0.027013878507042725, 0.025223405490854837, 0.023735625683692953, 0.022579837712432976, 0.021777375129807486, 0.021336596467696606, 0.021249624186933467, 0.02149248892804268, 0.02202885963276525, 0.022815833316993515, 0.023809644357677226, 0.024969832262352075, 0.026261514722178234, 0.027656151982560225, 0.029131394683125228, 0.030670499013585917, 0.03226160416265618, 0.03389701392817664, 0.0355725320266791, 0.037286856273677345, 0.03904102133673936, 0.040837878754184265, 0.04268160765664897, 0.04457725549756947, 0.04653031287257284, 0.04854632930456155, 0.050630577561430426, 0.052787772962743805, 0.05502185176042227, 0.057335809667340754, 0.059731598534843555, 0.06221007649694911, 0.0647710048883104, 0.06741308401938725, 0.07013401943156744, 0.07293061043935942, 0.0757988534305527, 0.0787340533644443, 0.08173093802601597, 0.08478377073570671, 0.08788645829172706, 0.09103265187972354 ], [ 0.05002986761477404, 0.04680583378871895, 0.04369252466173617, 0.040703401065268645, 0.03785402370901262, 0.03516252027923835, 0.03265002348717711, 0.030340968416447366, 0.02826305360304545, 0.02644656706738985, 0.02492270638489469, 0.0237205969490438, 0.02286308993664724, 0.022362136875376127, 0.022215260516612368, 0.022404697121392536, 0.022899784799210836, 0.023661684372815815, 0.024648660742304696, 0.025820411458707275, 0.027140806012801118, 0.02857915855806356, 0.03011048801566449, 0.03171521719245072, 0.03337862639428835, 0.03509023780393406, 0.03684321054004157, 0.03863377293578866, 0.04046069457670613, 0.0423247931076444, 0.04422847108166263, 0.04617528120579793, 0.04816952167380755, 0.05021586569014556, 0.05231903038597002, 0.05448349014220243, 0.05671323813348154, 0.059011598058829474, 0.06138108590828806, 0.06382331955682846, 0.06633897221849078, 0.06892776448042519, 0.071588488822414, 0.0743190601969757, 0.07711658633224386, 0.07997745183226368, 0.0828974107866461, 0.08587168336832003, 0.0888950527135165, 0.09196195917873859 ], [ 0.05145672065187638, 0.04824843917136994, 0.0451497105263718, 0.04217375098122263, 0.03933569652113828, 0.03665301871136416, 0.03414591744402126, 0.031837595929077804, 0.029754253698473603, 0.02792454814856967, 0.026378212479860438, 0.02514356488541222, 0.02424392009139743, 0.023693465568568554, 0.023493782291648585, 0.02363238004691175, 0.024083991936241163, 0.024814196792285286, 0.0257840361451634, 0.026954232358400512, 0.028288208985319748, 0.029753794959562856, 0.03132389405584521, 0.03297649765050272, 0.03469434965905593, 0.03646446207664062, 0.03827758822822974, 0.040127702501527536, 0.04201150410514748, 0.04392794849265817, 0.045877805660612114, 0.047863244526140616, 0.04988744415442974, 0.0519542342574879, 0.054067768455182484, 0.0562322340707864, 0.05845160177351545, 0.06072941735478192, 0.0630686365560619, 0.0654715023729895, 0.06793946282895548, 0.07047312597943697, 0.073072247962346, 0.07573574928860115, 0.07846175427014841, 0.08124764847892021, 0.0840901493695701, 0.08698538562091464, 0.08992898129404805, 0.09291614151144936 ], [ 0.05305689570500319, 0.04987092628442695, 0.04679365391855712, 0.04383810733042373, 0.04101907840919634, 0.03835348887634723, 0.0358607336229048, 0.03356291771600563, 0.03148484674140424, 0.02965356216452813, 0.02809716501530788, 0.02684270753025702, 0.02591314094826545, 0.025323726251039264, 0.02507880811936841, 0.025170075392002705, 0.02557706291665761, 0.02626978395532052, 0.027212571170974007, 0.028367959087688393, 0.029699774274485165, 0.031175138626519317, 0.03276549481706056, 0.03444693012075127, 0.036200072787836136, 0.038009763628136455, 0.03986462860933926, 0.04175662081734649, 0.043680564524916046, 0.04563371496888341, 0.04761533860289383, 0.04962631544061585, 0.051668764677632595, 0.05374569536828014, 0.055860684631341175, 0.05801758624647665, 0.06022027244553426, 0.0624724112174616, 0.06477728063005705, 0.0671376206509012, 0.06955552185104755, 0.07203234931053183, 0.07456869910337696, 0.07716438398527029, 0.07981844437523646, 0.08252918042548973, 0.08529420090040336, 0.08811048470996564, 0.0909744512263168, 0.09388203591101608 ], [ 0.054829402689694724, 0.0516721095295099, 0.0486228943792379, 0.045694639884919334, 0.042901853804499866, 0.040260987368395014, 0.037790725724297584, 0.03551217590467888, 0.03344883123293358, 0.03162613902022983, 0.030070465302215982, 0.028807284490588884, 0.027858584362045753, 0.027239792545388483, 0.02695690783375103, 0.027004722651025336, 0.027366812995231825, 0.028017364039252462, 0.02892423908451207, 0.030052384764416823, 0.031366802017804826, 0.032834693168599466, 0.03442675196371414, 0.03611776298023838, 0.037886728650778315, 0.03971671182286306, 0.041594526324869506, 0.043510357527823174, 0.045457358799825334, 0.04743124740221442, 0.04942991103985348, 0.05145303025660686, 0.053501719419314385, 0.0555781883770072, 0.057685426954022956, 0.0598269146506753, 0.062006357997009875, 0.06422745782505819, 0.06649370828452437, 0.06880822877100098, 0.07117362913446332, 0.0735919076665247, 0.07606438050384873, 0.0785916402992707, 0.0811735413553061, 0.08380920792387261, 0.08649706206991904, 0.08923486737629252, 0.09201978481778361, 0.0948484373281064 ], [ 0.056771064066091455, 0.053648510415239443, 0.050633578754129424, 0.04773902964150336, 0.0449791228986967, 0.04236988771431651, 0.03992935771702339, 0.03767770337573761, 0.03563715727130857, 0.03383158987340025, 0.03228557430415101, 0.031022813373980385, 0.03006393177138894, 0.02942387344855143, 0.02910942371709231, 0.02911753872233993, 0.02943504538309975, 0.030039859063654046, 0.030903362372742948, 0.031993279244787454, 0.03327639126627624, 0.03472068383111297, 0.036296792491031994, 0.03797881732053262, 0.039744658125404425, 0.04157602858919201, 0.04345827594145447, 0.04538009385547406, 0.04733318362123979, 0.04931189564018175, 0.051312868849824056, 0.05333467744502871, 0.05537749000587055, 0.057442744217351, 0.05953283966884597, 0.06165085106650572, 0.06380026418572071, 0.06598473682366353, 0.06820788679049386, 0.0704731085782069, 0.07278341978470612, 0.07514133768909205, 0.07754878562558885, 0.08000702804746146, 0.08251663246556012, 0.08507745583844516, 0.08768865251975921, 0.09034870055559414, 0.09305544297623357, 0.09580614073436126 ], [ 0.058876722098536685, 0.055794579178901856, 0.05281969506428162, 0.04996471415192, 0.04724366052650767, 0.04467215973113672, 0.04226761757883841, 0.04004929485665978, 0.03803818864790327, 0.03625660516927594, 0.03472730130004327, 0.03347210739135249, 0.032510048329105604, 0.031855157133683365, 0.03151437778311909, 0.03148607542074866, 0.03175960162132858, 0.03231608128617543, 0.03313021912511549, 0.03417265695842571, 0.03541236180721042, 0.03681865943731641, 0.03836273323040828, 0.04001858072240333, 0.0417635175657272, 0.04357834903803921, 0.04544731963299151, 0.0473579260773998, 0.049300652872040863, 0.05126866827224125, 0.0532575037195842, 0.055264730202280524, 0.05728963940106552, 0.05933293443359841, 0.06139643352523968, 0.06348278930593708, 0.06559522620797177, 0.06773729834044144, 0.06991267008552057, 0.07212492141790591, 0.07437737956328469, 0.07667297808914997, 0.07901414389043661, 0.08140271183671544, 0.08383986613915538, 0.08632610682641027, 0.08886123913642563, 0.09144438317231574, 0.09407400085774494, 0.09674793706804061 ], [ 0.0611394951002358, 0.058102967569360925, 0.05517336146283315, 0.05236319393589783, 0.04968624397853054, 0.04715772635149097, 0.044794415234025095, 0.04261466304258369, 0.04063823936217454, 0.03888589895007575, 0.03737858856147252, 0.036136237104824845, 0.03517615765867491, 0.034511221620212376, 0.03414810922786417, 0.03408602643687548, 0.03431623372111192, 0.034822542351261754, 0.03558267078736708, 0.03657014048818534, 0.03775631495961569, 0.03911224983549127, 0.04061015978324427, 0.04222444549164715, 0.043932318035933025, 0.045714101823476204, 0.04755330457127382, 0.04943653071351266, 0.05135329628369401, 0.053295785813125794, 0.05525857794327306, 0.05723835665389349, 0.05923361862652361, 0.06124438339783853, 0.06327191078855185, 0.06531842898130019, 0.06738687610728565, 0.06948065797647726, 0.07160342444974115, 0.073758866780754, 0.07595053798399169, 0.07818169788534327, 0.08045518398702305, 0.08277330865403036, 0.08513778244611636, 0.08754966272640946, 0.09000932602593086, 0.09251646207733388, 0.09507008698625154, 0.09766857270564276 ], [ 0.06355105871305748, 0.06056482834125836, 0.05768514491535583, 0.05492437278836141, 0.05229601927318174, 0.04981486228914195, 0.047497021975249756, 0.0453599285793098, 0.043422124850000604, 0.04170283279754808, 0.04022122118189114, 0.038995342767658224, 0.038040777486536434, 0.037369114769845974, 0.03698650919051375, 0.03689260159731476, 0.037080067552779886, 0.037534925472071816, 0.03823755185752766, 0.039164188090047174, 0.04028864595623038, 0.041583940687683035, 0.04302366691115091, 0.04458303502149892, 0.04623956696491099, 0.047973498168581624, 0.04976795026971572, 0.05160893796189299, 0.05348526277503079, 0.055388333750730954, 0.05731194332716215, 0.05925201762520052, 0.06120635382875954, 0.06317435305405202, 0.06515675444888312, 0.06715537473952372, 0.06917285663773923, 0.0712124291253203, 0.07327768243122122, 0.07537236035785932, 0.07750017240388504, 0.07966462781729412, 0.08186889327508753, 0.08411567533071186, 0.0864071281255482, 0.08874478616763747, 0.09112952128872567, 0.0935615222484096, 0.096040294904857, 0.09856468044712587 ], [ 0.06610193306044425, 0.06317012134864755, 0.06034438790002256, 0.05763690774503617, 0.05506087799705972, 0.05263060196742954, 0.050361513623530134, 0.04827010166114549, 0.046373683598992084, 0.04468997750216864, 0.04323642874890663, 0.042029278759336056, 0.04108241556230173, 0.04040611705374528, 0.04000586754304984, 0.039881466066788364, 0.04002662254227422, 0.04042914864563669, 0.041071720791251994, 0.04193307160478441, 0.04298939760142056, 0.04421576968964962, 0.04558738387796142, 0.04708056128764519, 0.048673472002499996, 0.05034660231500589, 0.052083007899298144, 0.05386840158297261, 0.055691120583496054, 0.05754200995914816, 0.0594142501822175, 0.06130314898071958, 0.06320591155138576, 0.06512139891886778, 0.0670498813277845, 0.06899279175244673, 0.07095248356437797, 0.07293199583460809, 0.07493482945371752, 0.07696473706898317, 0.0790255296536504, 0.08112090226535561, 0.08325428118035982, 0.08542869409680874, 0.08764666449749096, 0.08991013058286793, 0.09222038847276286, 0.09457805867977402, 0.09698307422676579, 0.099434688254912 ], [ 0.06878176133495086, 0.0659079106876011, 0.0631395258603713, 0.06048854902764968, 0.05796782201502482, 0.05559113075581371, 0.053373188729665025, 0.05132952548425591, 0.04947624151323141, 0.047829591744802384, 0.04640537117055946, 0.04521810185145381, 0.0442800617794105, 0.043600247468672165, 0.04318340976921336, 0.043029326221175945, 0.043132455802903945, 0.04348205959182031, 0.04406278014260326, 0.04485558400265681, 0.045838915097947706, 0.04698989519261156, 0.04828543507201778, 0.049703168219114226, 0.05122216842421963, 0.052823451593595326, 0.05449028584446246, 0.05620834442689276, 0.057965737189974706, 0.059752952367172416, 0.06156273451743453, 0.06338991843235751, 0.06523123364677179, 0.06708509018383545, 0.06895135329547608, 0.070831113040785, 0.0727264533492818, 0.0746402245223078, 0.0765758227442107, 0.07853697995248274, 0.08052756723449306, 0.08255141469431741, 0.08461215041285888, 0.08671306068311244, 0.08885697314106634, 0.09104616375307732, 0.09328228790134645, 0.0955663350775377, 0.09789860600085741, 0.10027871036668833 ], [ 0.07157956970511146, 0.06876664175007538, 0.06605838281747667, 0.06346645554589303, 0.06100329965161476, 0.05868214144255188, 0.056516943060050714, 0.05452226399139677, 0.05271300552757588, 0.051104012167748285, 0.04970951541127777, 0.04854242711116252, 0.047613521252889236, 0.04693057989400687, 0.04649761110857314, 0.04631426112317039, 0.046375528759258704, 0.04667184608559445, 0.047189525352357736, 0.0479115082382925, 0.04881830861565252, 0.04988902500497488, 0.05110231208876739, 0.052437231687749705, 0.05387393973513594, 0.05539419724635653, 0.056981715330064825, 0.058622356492923966, 0.06030421887491593, 0.06201762936346944, 0.06375506821411693, 0.06551104358963554, 0.06728193035499917, 0.06906578403235107, 0.07086213818417762, 0.07267179161751383, 0.07449659055983726, 0.07633921019246742, 0.07820293948498115, 0.0800914730175414, 0.08200871329258844, 0.08395858683496843, 0.08594487709748622, 0.08797107679164802, 0.0900402617404149, 0.09215498771355851, 0.0943172109883932, 0.09652823262309691, 0.09878866568725779, 0.10109842401398698 ], [ 0.07448400213355788, 0.07173439100313563, 0.0690884369467567, 0.06655747665781396, 0.06415350310970072, 0.06188914533667299, 0.05977759045252615, 0.057832426298339096, 0.05606738328367973, 0.05449595856813457, 0.05313091650331203, 0.05198367716761865, 0.0510636288685412, 0.05037742669287858, 0.04992836054762905, 0.0497158842521917, 0.049735385713237885, 0.049978246395423344, 0.050432193061853446, 0.05108189847721586, 0.05190975321373516, 0.052896715709977456, 0.05402315272528392, 0.055269601632699956, 0.05661741142421272, 0.05804924367543474, 0.05954943369171266, 0.06110422424688385, 0.06270189039453879, 0.06433277539368738, 0.06598925658214393, 0.06766565747503057, 0.06935811944032087, 0.07106444358065486, 0.0727839112025172, 0.0745170895542742, 0.07626562832693543, 0.07803205164274972, 0.0798195497933036, 0.08163177471683176, 0.08347264302017758, 0.08534615016709128, 0.08725619920521531, 0.08920644704553317, 0.09120017082113754, 0.0932401562408857, 0.09532860914239942, 0.09746709067830571, 0.09965647578903046, 0.10189693387678456 ], [ 0.07748352669577721, 0.07479908460879005, 0.07221705170165711, 0.06974839533442402, 0.06740462216248531, 0.06519773353908563, 0.06314012700000031, 0.06124442734776003, 0.05952323232735417, 0.05798876294856104, 0.05665241815743666, 0.05552424801055423, 0.05461237753080851, 0.05392243187226637, 0.05345702741329442, 0.053215397535160296, 0.05319321232871686, 0.05338262824978164, 0.053772571395969235, 0.054349224586321625, 0.055096662185613356, 0.05599756323574111, 0.05703393403853064, 0.05818778290072328, 0.05944170719409907, 0.060779371148759954, 0.062185868325012175, 0.06364797383728706, 0.06515429802109077, 0.06669535614320943, 0.06826356908396188, 0.06985320873847574, 0.07146030002378309, 0.07308248939877517, 0.07471888802593309, 0.07636989627359159, 0.07803701520667221, 0.079722650004488, 0.08142990980314219, 0.08316240819878143, 0.0849240684777868, 0.08671893747947827, 0.08855101177978712, 0.09042407956262187, 0.0923415810937289, 0.09430649012651648, 0.09632121786904399, 0.09838754036220262, 0.10050654930921729, 0.10267862560906292 ], [ 0.08056661228219276, 0.07794868458522478, 0.07543167106343879, 0.07302613138383035, 0.07074305321642216, 0.0685937884606281, 0.06658994029308464, 0.06474318890520098, 0.06306504601096304, 0.06156653323644313, 0.0602577878303907, 0.059147610585602896, 0.058242984225720815, 0.05754860336953392, 0.05706646616854004, 0.056795579378016124, 0.056731820750732256, 0.056867985468671375, 0.05719401996680465, 0.05769742216739604, 0.05836376737296902, 0.059177307800167764, 0.06012159216771035, 0.06118005839244594, 0.06233656416695127, 0.06357583354678883, 0.06488380993153223, 0.06624791540486748, 0.06765722282180289, 0.0691025505756343, 0.07057649130520242, 0.07207338565898945, 0.0735892512723937, 0.07512167582837292, 0.07666968178237164, 0.07823356922130427, 0.07981474246855351, 0.08141552544810687, 0.0830389704415006, 0.08468866464852479, 0.08636853882337785, 0.08808268212975756, 0.08983516717724967, 0.09162988891767157, 0.09347042066377338, 0.09535988993490627, 0.0973008761482239, 0.09929533139144936, 0.10134452468100134, 0.10344900928071742 ], [ 0.08372187622485429, 0.08117134310967396, 0.07871997970174013, 0.07637790593185739, 0.0741555656851387, 0.07206364867830985, 0.07011296839384186, 0.0683142875248368, 0.06667808492827962, 0.06521426277276757, 0.0639317995570322, 0.06283836360931548, 0.06193991148295946, 0.06124030452337247, 0.060740982493831155, 0.06044073332790052, 0.060335591562056236, 0.060418885142132464, 0.06068143324688844, 0.061111879981720185, 0.061697133944305906, 0.06242287449176255, 0.06327408309768522, 0.06423556178593598, 0.06529240837122656, 0.06643042782643195, 0.06763646852143466, 0.06889867999867577, 0.07020669476056289, 0.07155174022264334, 0.07292668887019006, 0.07432605522639668, 0.07574594797960087, 0.07718398492510635, 0.07863917754691556, 0.08011179128195584, 0.08160318687404415, 0.08311564776990708, 0.08465219822283554, 0.08621641660954854, 0.08781224837479018, 0.08944382293323813, 0.09111527871927828, 0.09283060033308178, 0.09459347135289363, 0.09640714585564757, 0.09827434101932665, 0.10019715239947712, 0.10217699262332484, 0.10421455338236585 ], [ 0.08693820451408985, 0.08445552686073662, 0.08207003032364736, 0.07979137002875275, 0.07762942939532894, 0.07559423197268422, 0.07369581473360695, 0.07194405715375364, 0.07034846300484551, 0.06891789597310005, 0.06766027595300045, 0.06658224974313856, 0.0656888569897956, 0.06498321824650424, 0.06446627538293481, 0.0641366139100962, 0.0639903913976835, 0.06402138641679252, 0.06422116986055514, 0.0645793873929321, 0.06508413061515939, 0.06572236721867698, 0.06648039776233869, 0.06734430848628771, 0.06830039461883336, 0.06933553543103216, 0.07043750940731551, 0.07159524426157776, 0.07279900154284583, 0.07404049907346431, 0.07531297657278223, 0.07661121082840337, 0.07793148701784662, 0.07927153256446477, 0.08063041947832371, 0.08200844065900191, 0.0834069652284458, 0.08482827766746583, 0.08627540535496447, 0.08775193902997465, 0.08926185066830399, 0.09080931323430694, 0.09239852667860844, 0.09403355435628241, 0.09571817370270987, 0.09745574450927419, 0.09924909749341007, 0.10110044508214659, 0.10301131546813853, 0.10498251010636626 ], [ 0.09020484696751895, 0.0877901141014553, 0.08547034139200366, 0.08325470121389553, 0.0811525076877069, 0.07917312219252584, 0.07732582564534417, 0.07561965412159305, 0.07406319687070742, 0.07266435939703603, 0.07143009890297188, 0.07036614462033058, 0.06947672066815781, 0.06876429309856197, 0.06822936467613326, 0.06787033982629871, 0.06768347772539565, 0.06766294404247938, 0.06780096245798618, 0.06808805735276575, 0.06851337064947845, 0.06906503001129487, 0.06973054311568568, 0.0704971934382236, 0.07135241622465778, 0.07228413810731411, 0.07328106912160745, 0.07433294088372937, 0.0754306888800437, 0.07656657996766043, 0.07773428830033985, 0.0789289241269475, 0.0801470204791278, 0.08138648289586906, 0.08264650722082964, 0.08392747030421768, 0.0852307982445536, 0.08655881667242107, 0.08791458752439409, 0.08930173676797483, 0.09072427758322132, 0.09218643353749328, 0.09369246625550894, 0.09524651194132056, 0.09685243081599648, 0.0985136730761642, 0.10023316435531739, 0.10201321290458937, 0.10385543984307825, 0.10576073291458672 ], [ 0.09351149008354583, 0.0911644676234789, 0.08890996883875164, 0.08675667229407122, 0.08471332120588133, 0.08278862573893277, 0.08099113710855053, 0.07932909177045827, 0.0778102262409329, 0.07644156614102315, 0.0752291967320973, 0.07417802614098856, 0.07329155609936516, 0.07257167764680202, 0.0720185101686799, 0.07163030083454136, 0.0714033978058823, 0.07133230480650966, 0.07140981757013022, 0.071627235386447, 0.07197463459660083, 0.07244118635607764, 0.0730154987789081, 0.0736859637063507, 0.07444109040180709, 0.07526981181288593, 0.07616175295703904, 0.0771074548695194, 0.07809855097323484, 0.0791278954606057, 0.0801896452621321, 0.08127929848118036, 0.08239369293374342, 0.08353096880291701, 0.08469049955020766, 0.0858727952424367, 0.08707938244312599, 0.08831266483430368, 0.08957576880011411, 0.09087237831123476, 0.09220656357234713, 0.09358260799281722, 0.09500483806677942, 0.09647746065749498, 0.09800441193621663, 0.09958922180658927, 0.1012348970507013, 0.10294382568190216, 0.10471770412148258, 0.10655748788581021 ], [ 0.09684831044051838, 0.09456848680722428, 0.09237855550992652, 0.09028669663259276, 0.08830108728168952, 0.08642980318912992, 0.08468069677230255, 0.08306125119529653, 0.08157841197108863, 0.08023840016885357, 0.07904651416873505, 0.07800692982802353, 0.07712251145788106, 0.07639464766364606, 0.07582312641000394, 0.07540606232052567, 0.07513988615493578, 0.07501940189273724, 0.0750379114553192, 0.0751874015798718, 0.07545878250424169, 0.07584216457115125, 0.07632715697546553, 0.07690317270025286, 0.07755972497432702, 0.07828670291072992, 0.07907461686423088, 0.07991480702898705, 0.08079961154626644, 0.08172249269939957, 0.08267812155806978, 0.08366242271097603, 0.08467258157177676, 0.0857070172639584, 0.08676532439589715, 0.08784818722500577, 0.08895726985420863, 0.09009508625327034, 0.09126485407331371, 0.09247033642280712, 0.0937156759750781, 0.09500522594449132, 0.09634338255686968, 0.09773442360533303, 0.09918235748872882, 0.10069078675320477, 0.10226278959430544, 0.10390082204439563, 0.1056066427057131, 0.10738126094664564 ], [ 0.1002060114621228, 0.09799264198786246, 0.09586636196047603, 0.09383485403749138, 0.09190573948457569, 0.0900864810708803, 0.08838426662077312, 0.08680587366943635, 0.08535751738844673, 0.0840446860028672, 0.08287197014908161, 0.0818428947680865, 0.08095976386869326, 0.08022352948091792, 0.07963369604770824, 0.07918827019060894, 0.07888376323681195, 0.07871525033313483, 0.07867648581404806, 0.07876007027405685, 0.07895766106894077, 0.07926021518522734, 0.0796582518385625, 0.08014212183927122, 0.08070227155180913, 0.08132949089405367, 0.08201513693414947, 0.08275132692161868, 0.08353109677416276, 0.08434852295674357, 0.0851988072487478, 0.08607832508575447, 0.08698463902372726, 0.08791647947446656, 0.08887369528054272, 0.08985717701027228, 0.09086875611856013, 0.09191108337889076, 0.09298749026439919, 0.09410183724058407, 0.09525835320872511, 0.09646147057396474, 0.09771566056264686, 0.09902527343692925, 0.10039438811279344, 0.10182667535594908, 0.10332527820190601, 0.1048927125364676, 0.10653078991655919, 0.10824056376198071 ], [ 0.1035758462158989, 0.10142799412107892, 0.09936428195396943, 0.09739190097856636, 0.09551793142270777, 0.09374924817843973, 0.09209241088096282, 0.090553539434647, 0.08913817750584511, 0.08785114815304998, 0.08669640746890273, 0.08567690366311513, 0.08479445017939348, 0.08404962197063033, 0.0834416837585139, 0.08296855787592106, 0.08262683716768343, 0.08241184558992969, 0.08231774591060671, 0.08233769065935637, 0.0824640095923312, 0.08268842474515613, 0.0830022828396419, 0.0833967944342459, 0.08386326967696904, 0.08439334164556532, 0.08497916980885474, 0.08561361787913323, 0.08629040204998242, 0.08700420718396115, 0.08775076985002302, 0.08852692818554289, 0.08933063938940151, 0.0901609662836779, 0.09101803486781841, 0.09190296518613508, 0.09281777818491553, 0.09376528158173636, 0.09474893812329525, 0.09577271996649106, 0.09684095326210863, 0.09795815731857295, 0.0991288829340855, 0.10035755456544916, 0.10164832091271088, 0.10300491821346598, 0.1044305500502948, 0.10592778679112012, 0.10749848693904708, 0.10914374171758974 ], [ 0.10694962868871892, 0.1048662024688705, 0.10286384567859345, 0.1009492684302192, 0.09912902834671963, 0.09740944017430732, 0.0957964730222106, 0.09429563670151163, 0.09291185984108721, 0.09164936376790764, 0.09051153742724705, 0.08950081972634921, 0.08861859643587187, 0.08786511900957739, 0.08723945225978479, 0.0867394567041037, 0.08636180962551324, 0.08610206661157449, 0.08595476279218989, 0.08591355045860637, 0.0859713674967092, 0.0861206293328777, 0.08635343601310783, 0.08666178565623815, 0.08703778578656024, 0.08747385483394704, 0.08796290722710982, 0.08849851682696593, 0.08907505480286279, 0.08968779933125164, 0.09033301562463969, 0.09100800574842778, 0.09171112845899017, 0.09244178992363869, 0.09320040670121005, 0.09398834281166529, 0.09480782314099265, 0.09566182583952781, 0.0965539567896752, 0.09748830963904902, 0.09846931529871411, 0.09950158516136405, 0.10058975256085657, 0.10173831712871977, 0.10295149666573908, 0.10423309090851125, 0.10558636112047502, 0.10701392878328676, 0.10851769583905548, 0.11009878798750361 ], [ 0.11031973572353454, 0.10829952271409164, 0.10635721331306404, 0.10449905018151802, 0.10273108956732588, 0.10105911559902213, 0.09948854500420184, 0.0980243239638405, 0.09667081980263864, 0.09543171124196602, 0.09430988190342447, 0.09330732252453108, 0.0924250478046561, 0.0916630338248699, 0.09102018150287827, 0.09049431053437812, 0.0900821867858153, 0.08977958426105746, 0.08958138074235074, 0.08948168420852254, 0.08947398536201284, 0.08955133021456899, 0.08970650579408984, 0.08993223167535459, 0.09022135017178234, 0.09056700856888585, 0.09096282761659236, 0.09140305150411081, 0.09188267560490844, 0.09239754931286273, 0.09294445223512586, 0.09352114283445799, 0.09412637932087553, 0.09475991319486146, 0.09542245636926933, 0.0961156232744633, 0.09684184980906788, 0.0976042914564992, 0.0984067033536007, 0.09925330556649437, 0.10014863728138901, 0.10109740402253724, 0.10210432232605589, 0.10317396648277895, 0.10431062197531193, 0.1055181500431866, 0.10679986740101793, 0.10815844451438486, 0.10959582503530063, 0.11111316806278874 ], [ 0.11367910152960231, 0.11172079759111399, 0.10983716119654025, 0.10803398401098287, 0.10631684418894775, 0.10469102584277913, 0.10316143131577217, 0.10173248808997347, 0.10040805295946503, 0.09919131689540046, 0.09808471473615707, 0.09708984436065436, 0.09620740025242394, 0.09543712625920431, 0.09477779185233999, 0.09422719529034587, 0.09378219584089062, 0.0934387757126277, 0.09319213072692277, 0.09303678717147176, 0.09296674086973453, 0.09297561339139337, 0.09305681959665674, 0.09320374037773287, 0.09340989451325853, 0.0936691039269695, 0.09397564725831017, 0.0943243974203226, 0.09471093965498792, 0.09513166743056553, 0.09558385431189798, 0.0960657006482559, 0.09657635455808258, 0.09711590725552897, 0.09768536327850799, 0.09828658666488505, 0.09892222460307021, 0.09959561057060509, 0.1003106494740892, 0.10107168780906066, 0.10188337234946389, 0.10275050132154884, 0.10367787237657841, 0.10467013190648024, 0.10573163030486141, 0.10686628763026614, 0.10807747376191033, 0.10936790655426096, 0.11073957072099096, 0.1121936592585536 ], [ 0.11702120641043481, 0.1151234418083557, 0.11329706249582287, 0.11154742771163119, 0.10987966220081657, 0.10829858113108767, 0.1068086098168676, 0.105413700112757, 0.10411724597948074, 0.10292200133449908, 0.10183000381012511, 0.10084250838326081, 0.0999599349463856, 0.0991818337082229, 0.09850687181937014, 0.09793284382147852, 0.09745670746333304, 0.0970746451920741, 0.09678215031594442, 0.09657413556002206, 0.09644506060638038, 0.09638907431325433, 0.096400166700499, 0.09647232549226503, 0.0965996920087898, 0.09677671145637773, 0.09699827311932124, 0.09725983654406821, 0.09755754046163627, 0.09788829186751055, 0.09824983333126178, 0.09864078722015004, 0.09906067608548089, 0.09950991898321157, 0.09998980399484897, 0.10050243769779986, 0.10105067282216444, 0.10163801583395694, 0.10226851670567765, 0.10294664366510728, 0.10367714623245848, 0.10446491033301435, 0.10531480966748376, 0.10623155779134644, 0.10721956545508354, 0.10828280765524376, 0.10942470452232858, 0.11064801962607668, 0.11195477853449363, 0.11334620956437054 ], [ 0.12034006110108562, 0.1185014227484541, 0.11673086393349176, 0.11503333158298297, 0.1134135225631105, 0.11187581414559247, 0.11042419094940524, 0.10906217019107999, 0.10779272758444766, 0.10661822669090044, 0.10554035488153352, 0.10456006927961202, 0.10367755605912096, 0.10289220624940944, 0.10220261072519768, 0.10160657635875707, 0.1011011644169199, 0.10068275126320471, 0.10034711035453132, 0.10008951348863245, 0.09990484834289798, 0.09978774861328661, 0.0997327325555662, 0.09973434546675695, 0.09978730161371185, 0.0998866212891206, 0.10002775901050912, 0.10020671932672225, 0.10042015721245848, 0.10066546057485512, 0.1009408129381506, 0.10124523489583064, 0.10157860341875005, 0.10194164858628882, 0.10233592777574184, 0.10276377781581464, 0.10322824609559797, 0.10373300212851118, 0.10428223160166988, 0.10488051548571159, 0.10553269731776305, 0.10624374227013723, 0.10701859204026723, 0.10786201989922427, 0.10877849037430432, 0.10977202798007614, 0.11084609913039963, 0.11200351085879907, 0.11324632926580548, 0.11457581974075448 ], [ 0.1236301878755062, 0.12184923817050615, 0.12013305984813602, 0.1184862086851229, 0.11691297957973838, 0.1154173425383604, 0.11400287651236386, 0.11267270284877719, 0.11142942051592376, 0.11027504560756447, 0.10921095787491855, 0.10823785714619258, 0.10735573243493976, 0.10656384629131721, 0.10586073651001016, 0.10524423669068647, 0.10471151638621734, 0.10425914072177776, 0.103883148486485, 0.1035791468538131, 0.10334242013850738, 0.10316804939477808, 0.1030510392351859, 0.10298644801464558, 0.10296951747357577, 0.10299579804787463, 0.10306126630005194, 0.10316243127002912, 0.10329642695112089, 0.1034610885363376, 0.10365501053043713, 0.1038775852705811, 0.10412902083847059, 0.10441033778238715, 0.10472334450643693, 0.10507059163691834, 0.1054553061515198, 0.10588130656171817, 0.10635290097102283, 0.10687477038165986, 0.10745184016958524, 0.10808914316197928, 0.10879167819425972, 0.10956426835156735, 0.11041142327000475, 0.11133720984918168, 0.1123451354865397, 0.11343804748019606, 0.1146180515771404, 0.11588645180530713 ], [ 0.12688659937925134, 0.12516189190900798, 0.12349866460447807, 0.12190110387558689, 0.12037312855885429, 0.11891833129773471, 0.11753991889432834, 0.11624065330047299, 0.11502279522412998, 0.11388805257651345, 0.1128375361451679, 0.11187172491914757, 0.11099044339219322, 0.11019285291602829, 0.10947745876976357, 0.10884213406846464, 0.1082841609843821, 0.1078002890392669, 0.10738680949484103, 0.10703964417054176, 0.10675444639987305, 0.10652671133559286, 0.1063518924538823, 0.10622552089873755, 0.10614332424604282, 0.10610134133770154, 0.10609603001673612, 0.10612436485849283, 0.10618392231484133, 0.10627295104502679, 0.10639042558180942, 0.10653608186453621, 0.10671043355868202, 0.10691476847645268, 0.10715112482198937, 0.10742224741597031, 0.10773152451528734, 0.10808290633833091, 0.1084808069327571, 0.1089299915702456, 0.1094354524017053, 0.11000227562718257, 0.11063550388991077, 0.11133999795117769, 0.11212030189947207, 0.11298051615707612, 0.11392418234490462, 0.11495418364457412, 0.1160726636681972, 0.1172809660458253 ], [ 0.1301047759635338, 0.12843486836607826, 0.1268231841557545, 0.12527356242004542, 0.12378957152230415, 0.12237445567920376, 0.12103108141318424, 0.11976188543765551, 0.11856882576767241, 0.11745333802613324, 0.11641629901084179, 0.11545799958024038, 0.11457812878985876, 0.1137757709611068, 0.1130494169929479, 0.11239699074998404, 0.11181589080353081, 0.11130304719851539, 0.1108549923072436, 0.11046794425013064, 0.11013790084883135, 0.10986074165693797, 0.10963233530631063, 0.1094486492207554, 0.10930585868108314, 0.1092004522655663, 0.10912933082106031, 0.10908989732290504, 0.10908013523687059, 0.1090986732870703, 0.10914483484718031, 0.10921867050124721, 0.1093209726626841, 0.10945327149810304, 0.10961781178229285, 0.10981751071869894, 0.11005589720259329, 0.11033703348422838, 0.110665420704072, 0.11104589031114957, 0.11148348391912577, 0.11198332467495233, 0.11255048367532498, 0.11318984532601013, 0.11390597575657153, 0.11470299844168394, 0.11558448101413893, 0.1165533368741311, 0.11761174461442943, 0.11876108752230713 ], [ 0.13328064214308008, 0.13166410642593515, 0.13010258738076874, 0.12859959877819968, 0.1271583835298594, 0.12578186521800822, 0.12447260021913635, 0.12323273186197098, 0.122063948236746, 0.1209674453938915, 0.11994389771811224, 0.11899343722290501, 0.1181156433710644, 0.1173095447857273, 0.11657363387953275, 0.1159058950103732, 0.11530384629255856, 0.11476459467942476, 0.11428490341792352, 0.11386127048803282, 0.11349001620736444, 0.11316737782586306, 0.11288960867127286, 0.11265307923955434, 0.11245437755393117, 0.1122904061343125, 0.11215847301282827, 0.11205637438709648, 0.1119824667058436, 0.11193572621940018, 0.1119157942909181, 0.11192300704790298, 0.11195840825656289, 0.11202374462629393, 0.11212144310324038, 0.1122545700964087, 0.11242677300217098, 0.11264220485533263, 0.11290543343359336, 0.11322133666724672, 0.11359498673848495, 0.11403152576783275, 0.11453603644443217, 0.11511341132291944, 0.11576822474211262, 0.11650461138361985, 0.1173261553555715, 0.11823579334637344, 0.11923573485295168, 0.12032740177424667 ], [ 0.1364105426705722, 0.13484597328069953, 0.13333327766967298, 0.13187566601215348, 0.13047608002720598, 0.12913714918403676, 0.12786114806503948, 0.12664995620770533, 0.12550502187668133, 0.12442733129563621, 0.12341738488161925, 0.12247518196169292, 0.12160021530629915, 0.12079147658588307, 0.1200474735526459, 0.11936625938061163, 0.1187454741826162, 0.11818239828459874, 0.11767401640025534, 0.11721709143642348, 0.11680824629314668, 0.11644405171913394, 0.11612111805430825, 0.11583618854176576, 0.11558623182053142, 0.11536853121274364, 0.11518076848513015, 0.11502109988421795, 0.11488822240697129, 0.1147814284644501, 0.11470064731860778, 0.11464647191849577, 0.11462017003132918, 0.11462367885894119, 0.11465958265567464, 0.11473107322488756, 0.11484189357221879, 0.11499626543573979, 0.11519880189259407, 0.11545440674861639, 0.11576816293401099, 0.11614521262885914, 0.1165906322945385, 0.11710930615343623, 0.11770580190131538, 0.11838425251917631, 0.1191482479481186, 0.12000074008889694, 0.12094396409215852, 0.12197937823893977 ], [ 0.1394912186124876, 0.13797723854142316, 0.13651206511195527, 0.13509862614069815, 0.13373958550221574, 0.1324373037170598, 0.1311938001300533, 0.13001071788380147, 0.1288892929851231, 0.12783032880774556, 0.1268341773627725, 0.1259007285915991, 0.12502940879041013, 0.1242191890622666, 0.12346860441822045, 0.12277578382410183, 0.12213849112980076, 0.12155417644143943, 0.12102003712318131, 0.12053308726371066, 0.12009023412950237, 0.1196883598661838, 0.11932440650950032, 0.11899546223276919, 0.11869884668792141, 0.11843219328830255, 0.11819352632673402, 0.11798133091412835, 0.11779461385424765, 0.11763295373257161, 0.11749653868681535, 0.11738619054139593, 0.1173033742286436, 0.1172501916882758, 0.1172293597380408, 0.11724417174691439, 0.11729844332126067, 0.11739644263467154, 0.11754280649008711, 0.11774244368841333, 0.11800042777464487, 0.11832188171636632, 0.11871185750973642, 0.11917521406971299, 0.11971649700747986, 0.12033982399550362, 0.12104877934318593, 0.12184632114044013, 0.12273470387474401, 0.123715418809575 ], [ 0.1425197837221755, 0.14105504891449816, 0.1396361395431217, 0.1382657216646291, 0.1369462036364118, 0.135679700785508, 0.13446800199215575, 0.1333125392812193, 0.13221436157822067, 0.1311741138077019, 0.1301920224824008, 0.129267888846852, 0.12840109049691883, 0.1275905921991408, 0.1268349663868077, 0.12613242352295212, 0.1254808522071565, 0.12487786857779316, 0.12432087424022532, 0.12380712164962347, 0.12333378560778528, 0.12289803930750062, 0.12249713318242139, 0.1221284746988379, 0.12178970715793493, 0.12147878556061803, 0.12119404761663523, 0.12093427805020807, 0.12069876445970465, 0.12048734312460456, 0.12030043331575678, 0.12013905885382212, 0.12000485587667277, 0.1199000660221386, 0.11982751451168065, 0.11979057293737182, 0.11979310691173602, 0.1198394091377935, 0.11993411889138857, 0.1200821293699465, 0.12028848483593531, 0.1205582699465604, 0.12089649408557472, 0.12130797386535587, 0.12179721721342474, 0.12236831256553908, 0.12302482663220532, 0.123769713973056, 0.1246052412045359, 0.12553292809747896 ] ] }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "text": [ "Arm 0_0
l2norm: 1.20892 (SEM: 0)
x1: 0.733035
x2: 0.0610081
x3: 0.085204
x4: 0.258361
x5: 0.114038
x6: 0.912911", "Arm 1_0
l2norm: 1.67104 (SEM: 0)
x1: 0.233727
x2: 0.841503
x3: 0.992144
x4: 0.91822
x5: 0.325854
x6: 0.309757", "Arm 2_0
l2norm: 1.28992 (SEM: 0)
x1: 0.456063
x2: 0.695674
x3: 0.762829
x4: 0.0961709
x5: 0.281806
x6: 0.548972", "Arm 3_0
l2norm: 1.26758 (SEM: 0)
x1: 0.49945
x2: 0.156111
x3: 0.601239
x4: 0.157366
x5: 0.546349
x6: 0.805099", "Arm 4_0
l2norm: 1.54433 (SEM: 0)
x1: 0.326059
x2: 0.691856
x3: 0.229641
x4: 0.615605
x5: 0.919577
x6: 0.722951", "Arm 5_0
l2norm: 1.39155 (SEM: 0)
x1: 0.155288
x2: 0.887927
x3: 0.479935
x4: 0.805947
x5: 0.480473
x6: 0.114611", "Arm 6_0
l2norm: 0.861554 (SEM: 0)
x1: 0.247413
x2: 0.374861
x3: 0.0699674
x4: 0.300832
x5: 0.543381
x6: 0.387147", "Arm 7_0
l2norm: 1.73865 (SEM: 0)
x1: 0.864984
x2: 0.079029
x3: 0.852291
x4: 0.765624
x5: 0.656406
x6: 0.724577", "Arm 8_0
l2norm: 1.72561 (SEM: 0)
x1: 0.254324
x2: 0.865416
x3: 0.799209
x4: 0.30456
x5: 0.899295
x6: 0.789859", "Arm 9_0
l2norm: 1.44111 (SEM: 0)
x1: 0.71055
x2: 0.782865
x3: 0.495047
x4: 0.153398
x5: 0.43716
x6: 0.706623", "Arm 10_0
l2norm: 1.14804 (SEM: 0)
x1: 0.600564
x2: 0.223024
x3: 0.091437
x4: 0.172231
x5: 0.313197
x6: 0.878329", "Arm 11_0
l2norm: 1.3401 (SEM: 0)
x1: 0.364004
x2: 0.632958
x3: 0.24173
x4: 0.0646517
x5: 0.511712
x6: 0.96865", "Arm 12_0
l2norm: 1.1084 (SEM: 0)
x1: 0.541585
x2: 0.229734
x3: 0.15374
x4: 0.148959
x5: 0.385234
x6: 0.829596", "Arm 13_0
l2norm: 1.05831 (SEM: 0)
x1: 0.509567
x2: 0.207489
x3: 0.147193
x4: 0.0705987
x5: 0.416679
x6: 0.785515", "Arm 14_0
l2norm: 1.1127 (SEM: 0)
x1: 0.518235
x2: 0.241577
x3: 0.200845
x4: 0.198987
x5: 0.417275
x6: 0.810633", "Arm 15_0
l2norm: 1.15398 (SEM: 0)
x1: 0.500609
x2: 0.26813
x3: 0.240861
x4: 0.247939
x5: 0.432561
x6: 0.838201", "Arm 16_0
l2norm: 1.09972 (SEM: 0)
x1: 0.550035
x2: 0.234856
x3: 0.206317
x4: 0.235548
x5: 0.442526
x6: 0.746864", "Arm 17_0
l2norm: 1.04833 (SEM: 0)
x1: 0.484511
x2: 0.22823
x3: 0.237
x4: 0.232679
x5: 0.384916
x6: 0.744099", "Arm 18_0
l2norm: 1.00981 (SEM: 0)
x1: 0.449918
x2: 0.214364
x3: 0.27629
x4: 0.271086
x5: 0.349526
x6: 0.70665", "Arm 19_0
l2norm: 0.972773 (SEM: 0)
x1: 0.414782
x2: 0.194756
x3: 0.314423
x4: 0.307907
x5: 0.311877
x6: 0.667367", "Arm 20_0
l2norm: 0.935505 (SEM: 0)
x1: 0.386351
x2: 0.212861
x3: 0.336375
x4: 0.311148
x5: 0.266056
x6: 0.632334", "Arm 21_0
l2norm: 0.936853 (SEM: 0)
x1: 0.366382
x2: 0.146103
x3: 0.311708
x4: 0.335777
x5: 0.286141
x6: 0.655994", "Arm 22_0
l2norm: 0.944574 (SEM: 0)
x1: 0.374518
x2: 0.0965846
x3: 0.38366
x4: 0.296887
x5: 0.285061
x6: 0.65271", "Arm 23_0
l2norm: 0.908251 (SEM: 0)
x1: 0.410246
x2: 0.0545891
x3: 0.352164
x4: 0.310357
x5: 0.285893
x6: 0.592927" ], "type": "scatter", "x": [ 0.08520395308732986, 0.9921442000195384, 0.7628285074606538, 0.6012392016127706, 0.22964108362793922, 0.4799351133406162, 0.06996737327426672, 0.8522909376770258, 0.7992090051993728, 0.49504704121500254, 0.09143701009452343, 0.24173001665621996, 0.15374043186441474, 0.14719315645869904, 0.2008447325317255, 0.24086089115113105, 0.2063165257341789, 0.23699963310767794, 0.27629014558919923, 0.314423056342953, 0.336374608096881, 0.311707618051601, 0.38366040002196883, 0.3521642064355677 ], "xaxis": "x", "y": [ 0.25836071372032166, 0.918219524435699, 0.09617094416171312, 0.15736639499664307, 0.615604704245925, 0.8059473633766174, 0.30083159543573856, 0.7656241683289409, 0.3045598091557622, 0.1533977249637246, 0.17223140317946672, 0.06465172953903675, 0.14895908172003156, 0.07059872784562918, 0.1989866615030246, 0.24793923958243091, 0.23554818504724517, 0.2326785528202722, 0.27108602737444704, 0.30790695943829866, 0.3111478319917405, 0.3357773333014482, 0.2968873266334985, 0.3103569476094648 ], "yaxis": "y" }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "showlegend": false, "text": [ "Arm 0_0
l2norm: 1.20892 (SEM: 0)
x1: 0.733035
x2: 0.0610081
x3: 0.085204
x4: 0.258361
x5: 0.114038
x6: 0.912911", "Arm 1_0
l2norm: 1.67104 (SEM: 0)
x1: 0.233727
x2: 0.841503
x3: 0.992144
x4: 0.91822
x5: 0.325854
x6: 0.309757", "Arm 2_0
l2norm: 1.28992 (SEM: 0)
x1: 0.456063
x2: 0.695674
x3: 0.762829
x4: 0.0961709
x5: 0.281806
x6: 0.548972", "Arm 3_0
l2norm: 1.26758 (SEM: 0)
x1: 0.49945
x2: 0.156111
x3: 0.601239
x4: 0.157366
x5: 0.546349
x6: 0.805099", "Arm 4_0
l2norm: 1.54433 (SEM: 0)
x1: 0.326059
x2: 0.691856
x3: 0.229641
x4: 0.615605
x5: 0.919577
x6: 0.722951", "Arm 5_0
l2norm: 1.39155 (SEM: 0)
x1: 0.155288
x2: 0.887927
x3: 0.479935
x4: 0.805947
x5: 0.480473
x6: 0.114611", "Arm 6_0
l2norm: 0.861554 (SEM: 0)
x1: 0.247413
x2: 0.374861
x3: 0.0699674
x4: 0.300832
x5: 0.543381
x6: 0.387147", "Arm 7_0
l2norm: 1.73865 (SEM: 0)
x1: 0.864984
x2: 0.079029
x3: 0.852291
x4: 0.765624
x5: 0.656406
x6: 0.724577", "Arm 8_0
l2norm: 1.72561 (SEM: 0)
x1: 0.254324
x2: 0.865416
x3: 0.799209
x4: 0.30456
x5: 0.899295
x6: 0.789859", "Arm 9_0
l2norm: 1.44111 (SEM: 0)
x1: 0.71055
x2: 0.782865
x3: 0.495047
x4: 0.153398
x5: 0.43716
x6: 0.706623", "Arm 10_0
l2norm: 1.14804 (SEM: 0)
x1: 0.600564
x2: 0.223024
x3: 0.091437
x4: 0.172231
x5: 0.313197
x6: 0.878329", "Arm 11_0
l2norm: 1.3401 (SEM: 0)
x1: 0.364004
x2: 0.632958
x3: 0.24173
x4: 0.0646517
x5: 0.511712
x6: 0.96865", "Arm 12_0
l2norm: 1.1084 (SEM: 0)
x1: 0.541585
x2: 0.229734
x3: 0.15374
x4: 0.148959
x5: 0.385234
x6: 0.829596", "Arm 13_0
l2norm: 1.05831 (SEM: 0)
x1: 0.509567
x2: 0.207489
x3: 0.147193
x4: 0.0705987
x5: 0.416679
x6: 0.785515", "Arm 14_0
l2norm: 1.1127 (SEM: 0)
x1: 0.518235
x2: 0.241577
x3: 0.200845
x4: 0.198987
x5: 0.417275
x6: 0.810633", "Arm 15_0
l2norm: 1.15398 (SEM: 0)
x1: 0.500609
x2: 0.26813
x3: 0.240861
x4: 0.247939
x5: 0.432561
x6: 0.838201", "Arm 16_0
l2norm: 1.09972 (SEM: 0)
x1: 0.550035
x2: 0.234856
x3: 0.206317
x4: 0.235548
x5: 0.442526
x6: 0.746864", "Arm 17_0
l2norm: 1.04833 (SEM: 0)
x1: 0.484511
x2: 0.22823
x3: 0.237
x4: 0.232679
x5: 0.384916
x6: 0.744099", "Arm 18_0
l2norm: 1.00981 (SEM: 0)
x1: 0.449918
x2: 0.214364
x3: 0.27629
x4: 0.271086
x5: 0.349526
x6: 0.70665", "Arm 19_0
l2norm: 0.972773 (SEM: 0)
x1: 0.414782
x2: 0.194756
x3: 0.314423
x4: 0.307907
x5: 0.311877
x6: 0.667367", "Arm 20_0
l2norm: 0.935505 (SEM: 0)
x1: 0.386351
x2: 0.212861
x3: 0.336375
x4: 0.311148
x5: 0.266056
x6: 0.632334", "Arm 21_0
l2norm: 0.936853 (SEM: 0)
x1: 0.366382
x2: 0.146103
x3: 0.311708
x4: 0.335777
x5: 0.286141
x6: 0.655994", "Arm 22_0
l2norm: 0.944574 (SEM: 0)
x1: 0.374518
x2: 0.0965846
x3: 0.38366
x4: 0.296887
x5: 0.285061
x6: 0.65271", "Arm 23_0
l2norm: 0.908251 (SEM: 0)
x1: 0.410246
x2: 0.0545891
x3: 0.352164
x4: 0.310357
x5: 0.285893
x6: 0.592927" ], "type": "scatter", "x": [ 0.08520395308732986, 0.9921442000195384, 0.7628285074606538, 0.6012392016127706, 0.22964108362793922, 0.4799351133406162, 0.06996737327426672, 0.8522909376770258, 0.7992090051993728, 0.49504704121500254, 0.09143701009452343, 0.24173001665621996, 0.15374043186441474, 0.14719315645869904, 0.2008447325317255, 0.24086089115113105, 0.2063165257341789, 0.23699963310767794, 0.27629014558919923, 0.314423056342953, 0.336374608096881, 0.311707618051601, 0.38366040002196883, 0.3521642064355677 ], "xaxis": "x2", "y": [ 0.25836071372032166, 0.918219524435699, 0.09617094416171312, 0.15736639499664307, 0.615604704245925, 0.8059473633766174, 0.30083159543573856, 0.7656241683289409, 0.3045598091557622, 0.1533977249637246, 0.17223140317946672, 0.06465172953903675, 0.14895908172003156, 0.07059872784562918, 0.1989866615030246, 0.24793923958243091, 0.23554818504724517, 0.2326785528202722, 0.27108602737444704, 0.30790695943829866, 0.3111478319917405, 0.3357773333014482, 0.2968873266334985, 0.3103569476094648 ], "yaxis": "y2" } ], "layout": { "annotations": [ { "font": { "size": 14 }, "showarrow": false, "text": "Mean", "x": 0.25, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" }, { "font": { "size": 14 }, "showarrow": false, "text": "Standard Error", "x": 0.8, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" } ], "autosize": false, "height": 450, "hovermode": "closest", "legend": { "orientation": "h", "x": 0, "y": -0.25 }, "margin": { "b": 100, "l": 35, "pad": 0, "r": 35, "t": 35 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "sequentialminus": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "l2norm" }, "width": 950, "xaxis": { "anchor": "y", "autorange": false, "domain": [ 0.05, 0.45 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x3" }, "type": "linear" }, "xaxis2": { "anchor": "y2", "autorange": false, "domain": [ 0.6, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x3" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "title": { "text": "x4" }, "type": "linear" }, "yaxis2": { "anchor": "x2", "autorange": false, "domain": [ 0, 1 ], "exponentformat": "e", "range": [ 0.0, 1.0 ], "tickfont": { "size": 11 }, "tickmode": "auto", "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(ax_client.get_contour_plot(param_x=\"x3\", param_y=\"x4\", metric_name=\"l2norm\"))" ] }, { "cell_type": "markdown", "id": "1c94392e", "metadata": { "papermill": { "duration": 0.072054, "end_time": "2024-07-23T19:32:47.886633", "exception": false, "start_time": "2024-07-23T19:32:47.814579", "status": "completed" }, "tags": [] }, "source": [ "Here we plot the optimization trace, showing the progression of finding the point with the optimal objective:" ] }, { "cell_type": "code", "execution_count": 13, "id": "ba950338", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:48.033247Z", "iopub.status.busy": "2024-07-23T19:32:48.032568Z", "iopub.status.idle": "2024-07-23T19:32:48.093103Z", "shell.execute_reply": "2024-07-23T19:32:48.092384Z" }, "papermill": { "duration": 0.136078, "end_time": "2024-07-23T19:32:48.094882", "exception": false, "start_time": "2024-07-23T19:32:47.958804", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "hoverinfo": "none", "legendgroup": "", "line": { "width": 0 }, "mode": "lines", "showlegend": false, "type": "scatter", "x": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ], "y": [ -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.47321995777363224, -0.47321995777363224, -0.47321995777363224, -0.47321995777363224, -1.0631174550427627, -1.0631174550427627, -1.230183226696405, -1.230183226696405, -1.3904935872884185, -1.3904935872884185, -1.4048846168682736, -1.9881940486934668, -2.4623035295567637, -2.754005575889331, -2.754005575889331, -2.843734354086443, -2.92411121049959, -2.92411121049959, -3.002776294780392 ] }, { "fill": "tonexty", "fillcolor": "rgba(128,177,211,0.3)", "legendgroup": "objective value", "line": { "color": "rgba(128,177,211,1)" }, "mode": "lines", "name": "objective value", "text": [ "
Parameterization:
x1: 0.7330349087715149
x2: 0.06100805476307869
x3: 0.08520395308732986
x4: 0.25836071372032166
x5: 0.11403815448284149
x6: 0.9129114151000977", "
Parameterization:
x1: 0.233726822771132
x2: 0.8415030026808381
x3: 0.9921442000195384
x4: 0.918219524435699
x5: 0.32585372496396303
x6: 0.30975723545998335", "
Parameterization:
x1: 0.4560632612556219
x2: 0.6956740934401751
x3: 0.7628285074606538
x4: 0.09617094416171312
x5: 0.2818061150610447
x6: 0.5489717852324247", "
Parameterization:
x1: 0.4994495641440153
x2: 0.15611135214567184
x3: 0.6012392016127706
x4: 0.15736639499664307
x5: 0.5463494751602411
x6: 0.8050991520285606", "
Parameterization:
x1: 0.32605923898518085
x2: 0.6918562883511186
x3: 0.22964108362793922
x4: 0.615604704245925
x5: 0.9195767743512988
x6: 0.7229511104524136", "
Parameterization:
x1: 0.15528818685561419
x2: 0.8879265636205673
x3: 0.4799351133406162
x4: 0.8059473633766174
x5: 0.48047301918268204
x6: 0.1146114207804203", "
Parameterization:
x1: 0.24741332605481148
x2: 0.3748607337474823
x3: 0.06996737327426672
x4: 0.30083159543573856
x5: 0.5433813789859414
x6: 0.38714681193232536", "
Parameterization:
x1: 0.8649843530729413
x2: 0.07902895659208298
x3: 0.8522909376770258
x4: 0.7656241683289409
x5: 0.6564057199284434
x6: 0.7245773272588849", "
Parameterization:
x1: 0.25432397425174713
x2: 0.8654162352904677
x3: 0.7992090051993728
x4: 0.3045598091557622
x5: 0.8992946818470955
x6: 0.7898592324927449", "
Parameterization:
x1: 0.7105504367500544
x2: 0.7828654944896698
x3: 0.49504704121500254
x4: 0.1533977249637246
x5: 0.43716037832200527
x6: 0.7066231714561582", "
Parameterization:
x1: 0.600564319640398
x2: 0.22302412055432796
x3: 0.09143701009452343
x4: 0.17223140317946672
x5: 0.3131968714296818
x6: 0.8783289324492216", "
Parameterization:
x1: 0.364004491828382
x2: 0.6329575339332223
x3: 0.24173001665621996
x4: 0.06465172953903675
x5: 0.5117117082700133
x6: 0.9686502488330007", "
Parameterization:
x1: 0.5415848197676835
x2: 0.22973441421901103
x3: 0.15374043186441474
x4: 0.14895908172003156
x5: 0.38523428198119164
x6: 0.8295957422999123", "
Parameterization:
x1: 0.5095666068290555
x2: 0.20748873245947327
x3: 0.14719315645869904
x4: 0.07059872784562918
x5: 0.41667892971867865
x6: 0.7855147018452772", "
Parameterization:
x1: 0.51823461918367
x2: 0.24157697962290028
x3: 0.2008447325317255
x4: 0.1989866615030246
x5: 0.41727542268258766
x6: 0.8106330626026472", "
Parameterization:
x1: 0.5006089473312668
x2: 0.26813013428499444
x3: 0.24086089115113105
x4: 0.24793923958243091
x5: 0.43256106420060975
x6: 0.8382009361590881", "
Parameterization:
x1: 0.5500353263563221
x2: 0.23485606287129523
x3: 0.2063165257341789
x4: 0.23554818504724517
x5: 0.4425264156626228
x6: 0.746863910083577", "
Parameterization:
x1: 0.48451098485418603
x2: 0.2282301765187898
x3: 0.23699963310767794
x4: 0.2326785528202722
x5: 0.3849155621059659
x6: 0.744098703991238", "
Parameterization:
x1: 0.4499176476637467
x2: 0.21436412901899668
x3: 0.27629014558919923
x4: 0.27108602737444704
x5: 0.34952558849401766
x6: 0.7066503415230804", "
Parameterization:
x1: 0.41478153727762374
x2: 0.19475629378241366
x3: 0.314423056342953
x4: 0.30790695943829866
x5: 0.3118772944049488
x6: 0.6673668377595394", "
Parameterization:
x1: 0.3863509902382102
x2: 0.212860591600044
x3: 0.336374608096881
x4: 0.3111478319917405
x5: 0.26605592592513
x6: 0.6323343617032745", "
Parameterization:
x1: 0.36638225737028096
x2: 0.14610327237015194
x3: 0.311707618051601
x4: 0.3357773333014482
x5: 0.28614071883969966
x6: 0.6559936589380183", "
Parameterization:
x1: 0.3745182767069761
x2: 0.09658462471824511
x3: 0.38366040002196883
x4: 0.2968873266334985
x5: 0.2850605424571068
x6: 0.6527101299330064", "
Parameterization:
x1: 0.4102456087040271
x2: 0.05458911567017346
x3: 0.3521642064355677
x4: 0.3103569476094648
x5: 0.285892531662494
x6: 0.5929273675939716", "
Parameterization:
x1: 0.33815614653423903
x2: 0.12357175858877631
x3: 0.4171113520719727
x4: 0.3014259064683609
x5: 0.2752337748246556
x6: 0.6974814384124463" ], "type": "scatter", "x": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ], "y": [ -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.47321995777363224, -0.47321995777363224, -0.47321995777363224, -0.47321995777363224, -1.0631174550427627, -1.0631174550427627, -1.230183226696405, -1.230183226696405, -1.3904935872884185, -1.3904935872884185, -1.4048846168682736, -1.9881940486934668, -2.4623035295567637, -2.754005575889331, -2.754005575889331, -2.843734354086443, -2.92411121049959, -2.92411121049959, -3.002776294780392 ] }, { "fill": "tonexty", "fillcolor": "rgba(128,177,211,0.3)", "hoverinfo": "none", "legendgroup": "", "line": { "width": 0 }, "mode": "lines", "showlegend": false, "type": "scatter", "x": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 ], "y": [ -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.4023662708347658, -0.47321995777363224, -0.47321995777363224, -0.47321995777363224, -0.47321995777363224, -1.0631174550427627, -1.0631174550427627, -1.230183226696405, -1.230183226696405, -1.3904935872884185, -1.3904935872884185, -1.4048846168682736, -1.9881940486934668, -2.4623035295567637, -2.754005575889331, -2.754005575889331, -2.843734354086443, -2.92411121049959, -2.92411121049959, -3.002776294780392 ] }, { "line": { "color": "rgba(253,180,98,1)", "dash": "dash" }, "mode": "lines", "name": "Optimum", "type": "scatter", "x": [ 1, 25 ], "y": [ -3.32237, -3.32237 ] } ], "layout": { "showlegend": true, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "fillpattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 }, "type": "scatter" } ], "scatter3d": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatter3d" } ], "scattercarpet": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattercarpet" } ], "scattergeo": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergeo" } ], "scattergl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattergl" } ], "scattermapbox": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scattermapbox" } ], "scatterpolar": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolar" } ], "scatterpolargl": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterpolargl" } ], "scatterternary": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "scatterternary" } ], "surface": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "surface" } ], "table": [ { "cells": { "fill": { "color": "#EBF0F8" }, "line": { "color": "white" } }, "header": { "fill": { "color": "#C8D4E3" }, "line": { "color": "white" } }, "type": "table" } ] }, "layout": { "annotationdefaults": { "arrowcolor": "#2a3f5f", "arrowhead": 0, "arrowwidth": 1 }, "autotypenumbers": "strict", "coloraxis": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "colorscale": { "diverging": [ [ 0, "#8e0152" ], [ 0.1, "#c51b7d" ], [ 0.2, "#de77ae" ], [ 0.3, "#f1b6da" ], [ 0.4, "#fde0ef" ], [ 0.5, "#f7f7f7" ], [ 0.6, "#e6f5d0" ], [ 0.7, "#b8e186" ], [ 0.8, "#7fbc41" ], [ 0.9, "#4d9221" ], [ 1, "#276419" ] ], "sequential": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "sequentialminus": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ] }, "colorway": [ "#636efa", "#EF553B", "#00cc96", "#ab63fa", "#FFA15A", "#19d3f3", "#FF6692", "#B6E880", "#FF97FF", "#FECB52" ], "font": { "color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Best objective found vs. # of iterations" }, "xaxis": { "title": { "text": "Iteration" } }, "yaxis": { "title": { "text": "Hartmann6" } } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(\n", " ax_client.get_optimization_trace(objective_optimum=hartmann6.fmin)\n", ") # Objective_optimum is optional." ] }, { "cell_type": "markdown", "id": "2af23a7d", "metadata": { "papermill": { "duration": 0.074984, "end_time": "2024-07-23T19:32:48.246552", "exception": false, "start_time": "2024-07-23T19:32:48.171568", "status": "completed" }, "tags": [] }, "source": [ "## 7. Save / reload optimization to JSON / SQL\n", "We can serialize the state of optimization to JSON and save it to a `.json` file or save it to the SQL backend. For the former:" ] }, { "cell_type": "code", "execution_count": 14, "id": "e561bc03", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:48.398370Z", "iopub.status.busy": "2024-07-23T19:32:48.398080Z", "iopub.status.idle": "2024-07-23T19:32:48.428682Z", "shell.execute_reply": "2024-07-23T19:32:48.428105Z" }, "papermill": { "duration": 0.108152, "end_time": "2024-07-23T19:32:48.430038", "exception": false, "start_time": "2024-07-23T19:32:48.321886", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:48] ax.service.ax_client: Saved JSON-serialized state of optimization to `ax_client_snapshot.json`.\n" ] } ], "source": [ "ax_client.save_to_json_file() # For custom filepath, pass `filepath` argument." ] }, { "cell_type": "code", "execution_count": 15, "id": "f64df513", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:48.582691Z", "iopub.status.busy": "2024-07-23T19:32:48.582184Z", "iopub.status.idle": "2024-07-23T19:32:48.699365Z", "shell.execute_reply": "2024-07-23T19:32:48.698663Z" }, "papermill": { "duration": 0.195834, "end_time": "2024-07-23T19:32:48.701091", "exception": false, "start_time": "2024-07-23T19:32:48.505257", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:48] 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" ] } ], "source": [ "restored_ax_client = (\n", " AxClient.load_from_json_file()\n", ") # For custom filepath, pass `filepath` argument." ] }, { "cell_type": "markdown", "id": "e8f78797", "metadata": { "papermill": { "duration": 0.074802, "end_time": "2024-07-23T19:32:48.851728", "exception": false, "start_time": "2024-07-23T19:32:48.776926", "status": "completed" }, "tags": [] }, "source": [ "To store state of optimization to an SQL backend, first follow [setup instructions](https://ax.dev/docs/storage.html#sql) on Ax website." ] }, { "cell_type": "markdown", "id": "350c6257", "metadata": { "papermill": { "duration": 0.075198, "end_time": "2024-07-23T19:32:49.009146", "exception": false, "start_time": "2024-07-23T19:32:48.933948", "status": "completed" }, "tags": [] }, "source": [ "Having set up the SQL backend, pass `DBSettings` to `AxClient` on instantiation (note that `SQLAlchemy` dependency will have to be installed – for installation, refer to [optional dependencies](https://ax.dev/docs/installation.html#optional-dependencies) on Ax website):" ] }, { "cell_type": "code", "execution_count": 16, "id": "4dd15b04", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:49.161661Z", "iopub.status.busy": "2024-07-23T19:32:49.161051Z", "iopub.status.idle": "2024-07-23T19:32:49.171959Z", "shell.execute_reply": "2024-07-23T19:32:49.171384Z" }, "papermill": { "duration": 0.088528, "end_time": "2024-07-23T19:32:49.173288", "exception": false, "start_time": "2024-07-23T19:32:49.084760", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:49] 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" ] } ], "source": [ "from ax.storage.sqa_store.structs import DBSettings\n", "\n", "# URL is of the form \"dialect+driver://username:password@host:port/database\".\n", "db_settings = DBSettings(url=\"sqlite:///foo.db\")\n", "# Instead of URL, can provide a `creator function`; can specify custom encoders/decoders if necessary.\n", "new_ax = AxClient(db_settings=db_settings)" ] }, { "cell_type": "markdown", "id": "4971b8e4", "metadata": { "papermill": { "duration": 0.075156, "end_time": "2024-07-23T19:32:49.325245", "exception": false, "start_time": "2024-07-23T19:32:49.250089", "status": "completed" }, "tags": [] }, "source": [ "When valid `DBSettings` are passed into `AxClient`, a unique experiment name is a required argument (`name`) to `ax_client.create_experiment`. The **state of the optimization is auto-saved** any time it changes (i.e. a new trial is added or completed, etc). \n", "\n", "To reload an optimization state later, instantiate `AxClient` with the same `DBSettings` and use `ax_client.load_experiment_from_database(experiment_name=\"my_experiment\")`." ] }, { "cell_type": "markdown", "id": "4898a66a", "metadata": { "papermill": { "duration": 0.075367, "end_time": "2024-07-23T19:32:49.476254", "exception": false, "start_time": "2024-07-23T19:32:49.400887", "status": "completed" }, "tags": [] }, "source": [ "# Special Cases" ] }, { "cell_type": "markdown", "id": "2646caf9", "metadata": { "papermill": { "duration": 0.075338, "end_time": "2024-07-23T19:32:49.628185", "exception": false, "start_time": "2024-07-23T19:32:49.552847", "status": "completed" }, "tags": [] }, "source": [ "**Evaluation failure**: should any optimization iterations fail during evaluation, `log_trial_failure` will ensure that the same trial is not proposed again." ] }, { "cell_type": "code", "execution_count": 17, "id": "6282c547", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:49.781167Z", "iopub.status.busy": "2024-07-23T19:32:49.780709Z", "iopub.status.idle": "2024-07-23T19:32:57.259635Z", "shell.execute_reply": "2024-07-23T19:32:57.258955Z" }, "papermill": { "duration": 7.557422, "end_time": "2024-07-23T19:32:57.261272", "exception": false, "start_time": "2024-07-23T19:32:49.703850", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:57] ax.service.ax_client: Generated new trial 25 with parameters {'x1': 0.273544, 'x2': 0.127601, 'x3': 0.421919, 'x4': 0.283195, 'x5': 0.297826, 'x6': 0.674414} using model BoTorch.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:57] ax.service.ax_client: Registered failure of trial 25.\n" ] } ], "source": [ "_, trial_index = ax_client.get_next_trial()\n", "ax_client.log_trial_failure(trial_index=trial_index)" ] }, { "cell_type": "markdown", "id": "3e5f6fda", "metadata": { "papermill": { "duration": 0.074833, "end_time": "2024-07-23T19:32:57.411678", "exception": false, "start_time": "2024-07-23T19:32:57.336845", "status": "completed" }, "tags": [] }, "source": [ "**Adding custom trials**: should there be need to evaluate a specific parameterization, `attach_trial` will add it to the experiment." ] }, { "cell_type": "code", "execution_count": 18, "id": "f0a65029", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:57.563243Z", "iopub.status.busy": "2024-07-23T19:32:57.562735Z", "iopub.status.idle": "2024-07-23T19:32:57.569010Z", "shell.execute_reply": "2024-07-23T19:32:57.568329Z" }, "papermill": { "duration": 0.083411, "end_time": "2024-07-23T19:32:57.570436", "exception": false, "start_time": "2024-07-23T19:32:57.487025", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:57] ax.core.experiment: Attached custom parameterizations [{'x1': 0.9, 'x2': 0.9, 'x3': 0.9, 'x4': 0.9, 'x5': 0.9, 'x6': 0.9}] as trial 26.\n" ] }, { "data": { "text/plain": [ "({'x1': 0.9, 'x2': 0.9, 'x3': 0.9, 'x4': 0.9, 'x5': 0.9, 'x6': 0.9}, 26)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.attach_trial(\n", " parameters={\"x1\": 0.9, \"x2\": 0.9, \"x3\": 0.9, \"x4\": 0.9, \"x5\": 0.9, \"x6\": 0.9}\n", ")" ] }, { "cell_type": "markdown", "id": "ad4d20ee", "metadata": { "papermill": { "duration": 0.075787, "end_time": "2024-07-23T19:32:57.722237", "exception": false, "start_time": "2024-07-23T19:32:57.646450", "status": "completed" }, "tags": [] }, "source": [ "**Need to run many trials in parallel**: for optimal results and optimization efficiency, we strongly recommend sequential optimization (generating a few trials, then waiting for them to be completed with evaluation data). However, if your use case needs to dispatch many trials in parallel before they are updated with data and you are running into the *\"All trials for current model have been generated, but not enough data has been observed to fit next model\"* error, instantiate `AxClient` as `AxClient(enforce_sequential_optimization=False)`." ] }, { "cell_type": "code", "execution_count": null, "id": "b9f2bcf7", "metadata": { "papermill": { "duration": 0.07504, "end_time": "2024-07-23T19:32:57.872840", "exception": false, "start_time": "2024-07-23T19:32:57.797800", "status": "completed" }, "tags": [] }, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "c06476cb", "metadata": { "papermill": { "duration": 0.07524, "end_time": "2024-07-23T19:32:58.023741", "exception": false, "start_time": "2024-07-23T19:32:57.948501", "status": "completed" }, "tags": [] }, "source": [ "**Nonlinear parameter constraints and/or constraints on non-Range parameters:** Ax parameter constraints can currently only support linear inequalities ([discussion](https://github.com/facebook/Ax/issues/153)). Users may be able to simulate this functionality, however, by substituting the following `evaluate` function for that defined in section 3 above." ] }, { "cell_type": "code", "execution_count": 19, "id": "06ef8f68", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:58.177263Z", "iopub.status.busy": "2024-07-23T19:32:58.176954Z", "iopub.status.idle": "2024-07-23T19:32:58.181607Z", "shell.execute_reply": "2024-07-23T19:32:58.181014Z" }, "papermill": { "duration": 0.082065, "end_time": "2024-07-23T19:32:58.182957", "exception": false, "start_time": "2024-07-23T19:32:58.100892", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "def evaluate(parameterization):\n", " x = np.array([parameterization.get(f\"x{i+1}\") for i in range(6)])\n", " # First calculate the nonlinear quantity to be constrained.\n", " l2norm = np.sqrt((x**2).sum())\n", " # Then define a constraint consistent with an outcome constraint on this experiment.\n", " if l2norm > 1.25:\n", " return {\"l2norm\": (l2norm, 0.0)}\n", " return {\"hartmann6\": (hartmann6(x), 0.0), \"l2norm\": (l2norm, 0.0)}" ] }, { "cell_type": "markdown", "id": "1d2543ba", "metadata": { "papermill": { "duration": 0.075248, "end_time": "2024-07-23T19:32:58.333922", "exception": false, "start_time": "2024-07-23T19:32:58.258674", "status": "completed" }, "tags": [] }, "source": [ "For this to work, the constraint quantity (`l2norm` in this case) should have a corresponding outcome constraint on the experiment. See the outcome_constraint arg to ax_client.create_experiment in section 2 above for how to specify outcome constraints.\n", "\n", "This setup accomplishes the following:\n", "1. Allows computation of an arbitrarily complex constraint value.\n", "2. Skips objective computation when the constraint is violated, useful when the objective is relatively expensive to compute.\n", "3. Constraint metric values are returned even when there is a violation. This helps the model understand + avoid constraint violations." ] }, { "cell_type": "markdown", "id": "ef699a44", "metadata": { "papermill": { "duration": 0.075654, "end_time": "2024-07-23T19:32:58.485310", "exception": false, "start_time": "2024-07-23T19:32:58.409656", "status": "completed" }, "tags": [] }, "source": [ "# Service API Exceptions Meaning and Handling\n", "[**`DataRequiredError`**](https://ax.dev/api/exceptions.html#ax.exceptions.core.DataRequiredError): Ax generation strategy needs to be updated with more data to proceed to the next optimization model. When the optimization moves from initialization stage to the Bayesian optimization stage, the underlying BayesOpt model needs sufficient data to train. For optimal results and optimization efficiency (finding the optimal point in the least number of trials), we recommend sequential optimization (generating a few trials, then waiting for them to be completed with evaluation data). Therefore, the correct way to handle this exception is to wait until more trial evaluations complete and log their data via `ax_client.complete_trial(...)`. \n", "\n", "However, if there is strong need to generate more trials before more data is available, instantiate `AxClient` as `AxClient(enforce_sequential_optimization=False)`. With this setting, as many trials will be generated from the initialization stage as requested, and the optimization will move to the BayesOpt stage whenever enough trials are completed." ] }, { "cell_type": "markdown", "id": "0bb617f2", "metadata": { "papermill": { "duration": 0.075748, "end_time": "2024-07-23T19:32:58.637624", "exception": false, "start_time": "2024-07-23T19:32:58.561876", "status": "completed" }, "tags": [] }, "source": [ "[**`MaxParallelismReachedException`**](https://ax.dev/api/modelbridge.html#ax.modelbridge.generation_strategy.MaxParallelismReachedException): generation strategy restricts the number of trials that can be ran simultaneously (to encourage sequential optimization), and the parallelism limit has been reached. The correct way to handle this exception is the same as `DataRequiredError` – to wait until more trial evluations complete and log their data via `ax_client.complete_trial(...)`.\n", " \n", "In some cases higher parallelism is important, so `enforce_sequential_optimization=False` kwarg to AxClient allows to suppress limiting of parallelism. It's also possible to override the default parallelism setting for all stages of the optimization by passing `choose_generation_strategy_kwargs` to `ax_client.create_experiment`:" ] }, { "cell_type": "code", "execution_count": 20, "id": "a065d5a9", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:58.791237Z", "iopub.status.busy": "2024-07-23T19:32:58.790742Z", "iopub.status.idle": "2024-07-23T19:32:58.802247Z", "shell.execute_reply": "2024-07-23T19:32:58.801598Z" }, "papermill": { "duration": 0.08949, "end_time": "2024-07-23T19:32:58.803700", "exception": false, "start_time": "2024-07-23T19:32:58.714210", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] 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 07-23 19:32:58] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter y. If that is not the expected value type, you can explicitly specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.service.utils.instantiation: Created search space: SearchSpace(parameters=[RangeParameter(name='x', parameter_type=FLOAT, range=[-5.0, 10.0]), RangeParameter(name='y', parameter_type=FLOAT, range=[0.0, 15.0])], parameter_constraints=[]).\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.modelbridge.dispatch_utils: Using Models.BOTORCH_MODULAR since there is at least one ordered parameter and there are no unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.modelbridge.dispatch_utils: Calculating the number of remaining initialization trials based on num_initialization_trials=None max_initialization_trials=None num_tunable_parameters=2 num_trials=None use_batch_trials=False\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.modelbridge.dispatch_utils: calculated num_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.modelbridge.dispatch_utils: num_completed_initialization_trials=0 num_remaining_initialization_trials=5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.modelbridge.dispatch_utils: `verbose`, `disable_progbar`, and `jit_compile` are not yet supported when using `choose_generation_strategy` with ModularBoTorchModel, dropping these arguments.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 07-23 19:32:58] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+BoTorch', steps=[Sobol for 5 trials, BoTorch for subsequent trials]). Iterations after 5 will take longer to generate due to model-fitting.\n" ] } ], "source": [ "ax_client = AxClient()\n", "ax_client.create_experiment(\n", " parameters=[\n", " {\"name\": \"x\", \"type\": \"range\", \"bounds\": [-5.0, 10.0]},\n", " {\"name\": \"y\", \"type\": \"range\", \"bounds\": [0.0, 15.0]},\n", " ],\n", " # Sets max parallelism to 10 for all steps of the generation strategy.\n", " choose_generation_strategy_kwargs={\"max_parallelism_override\": 10},\n", ")" ] }, { "cell_type": "code", "execution_count": 21, "id": "59331037", "metadata": { "execution": { "iopub.execute_input": "2024-07-23T19:32:58.958417Z", "iopub.status.busy": "2024-07-23T19:32:58.957907Z", "iopub.status.idle": "2024-07-23T19:32:58.962619Z", "shell.execute_reply": "2024-07-23T19:32:58.961968Z" }, "papermill": { "duration": 0.082673, "end_time": "2024-07-23T19:32:58.964007", "exception": false, "start_time": "2024-07-23T19:32:58.881334", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[(5, 10), (-1, 10)]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.get_max_parallelism() # Max parallelism is now 10 for all stages of the optimization." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.14" }, "papermill": { "default_parameters": {}, "duration": 126.359246, "end_time": "2024-07-23T19:33:02.071710", "environment_variables": {}, "exception": null, "input_path": "/tmp/tmp.DL1QmpHQMI/Ax-main/tutorials/gpei_hartmann_service.ipynb", "output_path": "/tmp/tmp.DL1QmpHQMI/Ax-main/tutorials/gpei_hartmann_service.ipynb", "parameters": {}, "start_time": "2024-07-23T19:30:55.712464", "version": "2.6.0" } }, "nbformat": 4, "nbformat_minor": 5 }