{ "cells": [ { "cell_type": "markdown", "metadata": {}, "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, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.utils.notebook.plotting: Injecting Plotly library into cell. Do not overwrite or delete cell.\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from ax.service.ax_client import AxClient\n", "from ax.utils.measurement.synthetic_functions import hartmann6\n", "from ax.utils.notebook.plotting import render, init_notebook_plotting\n", "\n", "init_notebook_plotting()" ] }, { "cell_type": "markdown", "metadata": {}, "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, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] 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 2 decimal points.\n" ] } ], "source": [ "ax_client = AxClient()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Set up experiment\n", "An experiment consists of a **search space** (parameters and parameter constraints) and **optimization configuration** (objective name, minimization setting, and outcome constraints). Note that:\n", "- Only `name`, `parameters`, and `objective_name` 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, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 6 trials, GPEI for subsequent trials]). Iterations after 6 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", " objective_name=\"hartmann6\",\n", " minimize=True, # Optional, defaults to False.\n", " parameter_constraints=[\"x1 + x2 <= 2.0\"], # Optional.\n", " outcome_constraints=[\"l2norm <= 1.25\"], # Optional.\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "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 `objective_name` set on experiment creation or the metric names mentioned in `outcome_constraints`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "def evaluate(parameters):\n", " x = np.array([parameters.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", "metadata": {}, "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", "metadata": {}, "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, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.27, 'x2': 0.49, 'x3': 0.72, 'x4': 0.49, 'x5': 0.02, 'x6': 0.03}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.64, 0.0), 'l2norm': (1.04, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.21, 'x2': 0.72, 'x3': 0.92, 'x4': 0.14, 'x5': 0.28, 'x6': 0.35}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.27, 0.0), 'l2norm': (1.28, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.43, 'x2': 0.1, 'x3': 0.49, 'x4': 0.46, 'x5': 0.67, 'x6': 0.97}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:15] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.15, 0.0), 'l2norm': (1.43, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:16] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.18, 'x2': 0.53, 'x3': 0.19, 'x4': 0.6, 'x5': 0.94, 'x6': 0.92}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:16] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.01, 0.0), 'l2norm': (1.56, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:16] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.71, 'x2': 0.63, 'x3': 0.95, 'x4': 0.69, 'x5': 0.09, 'x6': 0.39}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:16] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.08, 0.0), 'l2norm': (1.56, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:16] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.82, 'x2': 0.16, 'x3': 0.77, 'x4': 0.33, 'x5': 0.69, 'x6': 0.9}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:16] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.07, 0.0), 'l2norm': (1.64, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:20] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.19, 'x2': 0.45, 'x3': 0.66, 'x4': 0.39, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:20] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.25, 0.0), 'l2norm': (0.91, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:24] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.3, 'x2': 0.51, 'x3': 0.75, 'x4': 0.54, 'x5': 0.02, 'x6': 0.02}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:24] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.84, 0.0), 'l2norm': (1.1, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:28] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.33, 'x2': 0.53, 'x3': 0.79, 'x4': 0.61, 'x5': 0.02, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:29] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-1.03, 0.0), 'l2norm': (1.18, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:32] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.34, 'x2': 0.54, 'x3': 0.81, 'x4': 0.66, 'x5': 0.02, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:32] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-1.09, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:37] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.29, 'x2': 0.51, 'x3': 0.89, 'x4': 0.68, 'x5': 0.01, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:37] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.76, 0.0), 'l2norm': (1.27, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:41] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.38, 'x2': 0.56, 'x3': 0.75, 'x4': 0.64, 'x5': 0.03, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:41] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-1.32, 0.0), 'l2norm': (1.21, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:45] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.44, 'x2': 0.59, 'x3': 0.69, 'x4': 0.64, 'x5': 0.06, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:45] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-1.47, 0.0), 'l2norm': (1.2, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:50] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.47, 'x2': 0.64, 'x3': 0.63, 'x4': 0.63, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:50] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-1.78, 0.0), 'l2norm': (1.19, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:55] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.47, 'x2': 0.73, 'x3': 0.58, 'x4': 0.6, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:45:55] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-2.36, 0.0), 'l2norm': (1.2, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:00] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.45, 'x2': 0.8, 'x3': 0.55, 'x4': 0.55, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:00] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-2.83, 0.0), 'l2norm': (1.2, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:04] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.43, 'x2': 0.88, 'x3': 0.52, 'x4': 0.51, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:04] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.97, 0.0), 'l2norm': (1.22, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:08] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.34, 'x2': 0.86, 'x3': 0.51, 'x4': 0.57, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:08] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.86, 0.0), 'l2norm': (1.2, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:13] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.4, 'x2': 0.86, 'x3': 0.61, 'x4': 0.44, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:13] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.62, 0.0), 'l2norm': (1.21, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:17] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.45, 'x2': 0.87, 'x3': 0.45, 'x4': 0.57, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:17] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-3.01, 0.0), 'l2norm': (1.22, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:22] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.44, 'x2': 0.88, 'x3': 0.51, 'x4': 0.57, 'x5': 0.0, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:22] ax.service.ax_client: Completed trial 20 with data: {'hartmann6': (-3.05, 0.0), 'l2norm': (1.24, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:24] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.44, 'x2': 0.89, 'x3': 0.5, 'x4': 0.58, 'x5': 0.09, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:24] ax.service.ax_client: Completed trial 21 with data: {'hartmann6': (-3.06, 0.0), 'l2norm': (1.26, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:28] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.42, 'x2': 0.87, 'x3': 0.49, 'x4': 0.57, 'x5': 0.04, 'x6': 0.05}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:28] ax.service.ax_client: Completed trial 22 with data: {'hartmann6': (-3.15, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:32] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.42, 'x2': 0.89, 'x3': 0.48, 'x4': 0.58, 'x5': 0.04, 'x6': 0.08}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:32] ax.service.ax_client: Completed trial 23 with data: {'hartmann6': (-3.09, 0.0), 'l2norm': (1.24, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:36] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.43, 'x2': 0.88, 'x3': 0.51, 'x4': 0.58, 'x5': 0.05, 'x6': 0.04}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:36] ax.service.ax_client: Completed trial 24 with data: {'hartmann6': (-3.15, 0.0), 'l2norm': (1.25, 0.0)}.\n" ] } ], "source": [ "for i in range(25):\n", " parameters, trial_index = ax_client.get_next_trial()\n", " # Local evaluation here can be replaced with deployment to external system.\n", " ax_client.complete_trial(trial_index=trial_index, raw_data=evaluate(parameters))" ] }, { "cell_type": "markdown", "metadata": {}, "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, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(6, 6), (-1, 3)]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.get_max_parallelism()" ] }, { "cell_type": "markdown", "metadata": {}, "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 6 for the first 6 trials and 3 for all subsequent trials.\" This is because the first 6 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", "metadata": {}, "source": [ "### How to view all existing trials during optimization?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:36] 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 ModelTrial IndexTrial StatusArm Parameterizations
00Sobol0COMPLETED{'0_0': {'x1': 0.27, 'x2': 0.49, 'x3': 0.72, '...
10Sobol1COMPLETED{'1_0': {'x1': 0.21, 'x2': 0.72, 'x3': 0.92, '...
20Sobol2COMPLETED{'2_0': {'x1': 0.43, 'x2': 0.1, 'x3': 0.49, 'x...
30Sobol3COMPLETED{'3_0': {'x1': 0.18, 'x2': 0.53, 'x3': 0.19, '...
40Sobol4COMPLETED{'4_0': {'x1': 0.71, 'x2': 0.63, 'x3': 0.95, '...
50Sobol5COMPLETED{'5_0': {'x1': 0.82, 'x2': 0.16, 'x3': 0.77, '...
61GPEI6COMPLETED{'6_0': {'x1': 0.19, 'x2': 0.45, 'x3': 0.66, '...
71GPEI7COMPLETED{'7_0': {'x1': 0.3, 'x2': 0.51, 'x3': 0.75, 'x...
81GPEI8COMPLETED{'8_0': {'x1': 0.33, 'x2': 0.53, 'x3': 0.79, '...
91GPEI9COMPLETED{'9_0': {'x1': 0.34, 'x2': 0.54, 'x3': 0.81, '...
101GPEI10COMPLETED{'10_0': {'x1': 0.29, 'x2': 0.51, 'x3': 0.89, ...
111GPEI11COMPLETED{'11_0': {'x1': 0.38, 'x2': 0.56, 'x3': 0.75, ...
121GPEI12COMPLETED{'12_0': {'x1': 0.44, 'x2': 0.59, 'x3': 0.69, ...
131GPEI13COMPLETED{'13_0': {'x1': 0.47, 'x2': 0.64, 'x3': 0.63, ...
141GPEI14COMPLETED{'14_0': {'x1': 0.47, 'x2': 0.73, 'x3': 0.58, ...
151GPEI15COMPLETED{'15_0': {'x1': 0.45, 'x2': 0.8, 'x3': 0.55, '...
161GPEI16COMPLETED{'16_0': {'x1': 0.43, 'x2': 0.88, 'x3': 0.52, ...
171GPEI17COMPLETED{'17_0': {'x1': 0.34, 'x2': 0.86, 'x3': 0.51, ...
181GPEI18COMPLETED{'18_0': {'x1': 0.4, 'x2': 0.86, 'x3': 0.61, '...
191GPEI19COMPLETED{'19_0': {'x1': 0.45, 'x2': 0.87, 'x3': 0.45, ...
201GPEI20COMPLETED{'20_0': {'x1': 0.44, 'x2': 0.88, 'x3': 0.51, ...
211GPEI21COMPLETED{'21_0': {'x1': 0.44, 'x2': 0.89, 'x3': 0.5, '...
221GPEI22COMPLETED{'22_0': {'x1': 0.42, 'x2': 0.87, 'x3': 0.49, ...
231GPEI23COMPLETED{'23_0': {'x1': 0.42, 'x2': 0.89, 'x3': 0.48, ...
241GPEI24COMPLETED{'24_0': {'x1': 0.43, 'x2': 0.88, 'x3': 0.51, ...
\n", "
" ], "text/plain": [ " Generation Step Generation Model Trial Index Trial Status \\\n", "0 0 Sobol 0 COMPLETED \n", "1 0 Sobol 1 COMPLETED \n", "2 0 Sobol 2 COMPLETED \n", "3 0 Sobol 3 COMPLETED \n", "4 0 Sobol 4 COMPLETED \n", "5 0 Sobol 5 COMPLETED \n", "6 1 GPEI 6 COMPLETED \n", "7 1 GPEI 7 COMPLETED \n", "8 1 GPEI 8 COMPLETED \n", "9 1 GPEI 9 COMPLETED \n", "10 1 GPEI 10 COMPLETED \n", "11 1 GPEI 11 COMPLETED \n", "12 1 GPEI 12 COMPLETED \n", "13 1 GPEI 13 COMPLETED \n", "14 1 GPEI 14 COMPLETED \n", "15 1 GPEI 15 COMPLETED \n", "16 1 GPEI 16 COMPLETED \n", "17 1 GPEI 17 COMPLETED \n", "18 1 GPEI 18 COMPLETED \n", "19 1 GPEI 19 COMPLETED \n", "20 1 GPEI 20 COMPLETED \n", "21 1 GPEI 21 COMPLETED \n", "22 1 GPEI 22 COMPLETED \n", "23 1 GPEI 23 COMPLETED \n", "24 1 GPEI 24 COMPLETED \n", "\n", " Arm Parameterizations \n", "0 {'0_0': {'x1': 0.27, 'x2': 0.49, 'x3': 0.72, '... \n", "1 {'1_0': {'x1': 0.21, 'x2': 0.72, 'x3': 0.92, '... \n", "2 {'2_0': {'x1': 0.43, 'x2': 0.1, 'x3': 0.49, 'x... \n", "3 {'3_0': {'x1': 0.18, 'x2': 0.53, 'x3': 0.19, '... \n", "4 {'4_0': {'x1': 0.71, 'x2': 0.63, 'x3': 0.95, '... \n", "5 {'5_0': {'x1': 0.82, 'x2': 0.16, 'x3': 0.77, '... \n", "6 {'6_0': {'x1': 0.19, 'x2': 0.45, 'x3': 0.66, '... \n", "7 {'7_0': {'x1': 0.3, 'x2': 0.51, 'x3': 0.75, 'x... \n", "8 {'8_0': {'x1': 0.33, 'x2': 0.53, 'x3': 0.79, '... \n", "9 {'9_0': {'x1': 0.34, 'x2': 0.54, 'x3': 0.81, '... \n", "10 {'10_0': {'x1': 0.29, 'x2': 0.51, 'x3': 0.89, ... \n", "11 {'11_0': {'x1': 0.38, 'x2': 0.56, 'x3': 0.75, ... \n", "12 {'12_0': {'x1': 0.44, 'x2': 0.59, 'x3': 0.69, ... \n", "13 {'13_0': {'x1': 0.47, 'x2': 0.64, 'x3': 0.63, ... \n", "14 {'14_0': {'x1': 0.47, 'x2': 0.73, 'x3': 0.58, ... \n", "15 {'15_0': {'x1': 0.45, 'x2': 0.8, 'x3': 0.55, '... \n", "16 {'16_0': {'x1': 0.43, 'x2': 0.88, 'x3': 0.52, ... \n", "17 {'17_0': {'x1': 0.34, 'x2': 0.86, 'x3': 0.51, ... \n", "18 {'18_0': {'x1': 0.4, 'x2': 0.86, 'x3': 0.61, '... \n", "19 {'19_0': {'x1': 0.45, 'x2': 0.87, 'x3': 0.45, ... \n", "20 {'20_0': {'x1': 0.44, 'x2': 0.88, 'x3': 0.51, ... \n", "21 {'21_0': {'x1': 0.44, 'x2': 0.89, 'x3': 0.5, '... \n", "22 {'22_0': {'x1': 0.42, 'x2': 0.87, 'x3': 0.49, ... \n", "23 {'23_0': {'x1': 0.42, 'x2': 0.89, 'x3': 0.48, ... \n", "24 {'24_0': {'x1': 0.43, 'x2': 0.88, 'x3': 0.51, ... " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.generation_strategy.trials_as_df" ] }, { "cell_type": "markdown", "metadata": {}, "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, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "{'x1': 0.42261693595076183,\n", " 'x2': 0.8743919010098683,\n", " 'x3': 0.4854770307718386,\n", " 'x4': 0.5674793100350288,\n", " 'x5': 0.0425719770072076,\n", " 'x6': 0.04825437095562463}" ] }, "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, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "{'hartmann6': -3.153334467033569, 'l2norm': 1.2267962566391677}" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "means, covariances = values\n", "means " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison, Hartmann6 minimum:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [ { "data": { "text/plain": [ "-3.32237" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hartmann6.fmin" ] }, { "cell_type": "markdown", "metadata": {}, "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, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:36] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Ramaining 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": [ [ -0.1106536332134751, -0.10676272802530096, -0.10343010300721, -0.10069217071736203, -0.09857945276408997, -0.09711563930858502, -0.09631675518676786, -0.09619047380015622, -0.09673561802411723, -0.09794188288168915, -0.09978980756193656, -0.10225101468398079, -0.10528872293153824, -0.10885852596555567, -0.11290941673000932, -0.11738502290526842, -0.12222500738548447, -0.1273665782476927, -0.13274604655017708, -0.13830036798289536, -0.14396860609365314, -0.14969326036613406, -0.15542141132509268, -0.16110564630276802, -0.1667047425441821, -0.17218409790688027, -0.17751591250576726, -0.18267913638362954, -0.18765920797553082, -0.19244761534926336, -0.19704131676875658, -0.20144205909865076, -0.20565563219464278, -0.20969109508908246, -0.21356000594673308, -0.21727568291691868, -0.22085251760974334, -0.22430535738552804, -0.22764896730334505, -0.23089757767916508, -0.23406451892597713, -0.2371619417833417, -0.24020061822333827, -0.24318981622698677, -0.24613724020633287, -0.24904902802574203, -0.251929795261681, -0.2547827174401254, -0.2576096414117699, -0.26041121768300024 ], [ -0.10005206557098978, -0.09598803869707795, -0.09252740787908786, -0.08971031609791802, -0.0875704068547496, -0.0861337365983923, -0.08541780314255698, -0.0854307392760072, -0.0861707191102794, -0.08762561985484107, -0.08977297350805857, -0.09258023154315564, -0.09600535151766443, -0.09999769843754347, -0.1044992367448212, -0.10944597225172803, -0.11476958857286368, -0.12039921089338645, -0.1262632223170459, -0.13229105526684082, -0.13841488272184854, -0.14457114124354686, -0.1507018290983253, -0.15675553727714542, -0.1626881875674, -0.16846346867968998, -0.17405297747100668, -0.17943608642959163, -0.18459956997499605, -0.18953703029336366, -0.19424816822145607, -0.19873794625992858, -0.20301568951908577, -0.20709416681761117, -0.21098868888436173, -0.2147162542812342, -0.21829476685060367, -0.22174234168655627, -0.22507671022405984, -0.22831472930933283, -0.23147199423084608, -0.23456255173147267, -0.23759870599494515, -0.24059090845374165, -0.24354772091365962, -0.24647584082350105, -0.24938017741773622, -0.2522639678072178, -0.2551289227760303, -0.2579753929603248 ], [ -0.08965809506901223, -0.08543404215780637, -0.08186109080127824, -0.07898341636033912, -0.07683804047521736, -0.07545357525678575, -0.0748490924319718, -0.07503317613874905, -0.07600321687401523, -0.07774499898972609, -0.08023262483705218, -0.08342880526681995, -0.08728552922310184, -0.0917451055693359, -0.09674154941091118, -0.10220226465687299, -0.10804995615157709, -0.1142046900836482, -0.12058601193800289, -0.1271150279271458, -0.13371635895621936, -0.1403198854394705, -0.14686221578920056, -0.15328782975586397, -0.15954986832213924, -0.16561056276369523, -0.1714413151168832, -0.17702245925357674, -0.18234274507057968, -0.18739859742074483, -0.19219320625164227, -0.1967355052605433, -0.2010390937922153, -0.20512115144662868, -0.20900138774515686, -0.2127010610268738, -0.21624209222439972, -0.2196462908869763, -0.22293470321618858, -0.22612708524812652, -0.22924149881625921, -0.2322940236098756, -0.2352985754706498, -0.23826681894908708, -0.2412081609435368, -0.24412981181741888, -0.24703690058282302, -0.2499326314040069, -0.25281846967943244, -0.25569434718867545 ], [ -0.0795971486157736, -0.07523130020956237, -0.07156683552265553, -0.06865226618773579, -0.06652825037521604, -0.06522614530879944, -0.06476669280858882, -0.06515890768228938, -0.06639923837079587, -0.06847106406664283, -0.0713445821123937, -0.07497712385324729, -0.07931391681465372, -0.08428928723605789, -0.089828271288374, -0.09584857781536527, -0.1022628224401565, -0.10898093456813163, -0.11591262703721683, -0.1229698141475506, -0.13006886798735118, -0.13713261494753293, -0.14409199286939245, -0.15088731255066845, -0.15746909311461432, -0.1637984667010759, -0.16984717192853815, -0.17559717587351664, -0.18103997974593034, -0.1861756734429516, -0.1910118087531596, -0.19556216065070564, -0.19984544169954854, -0.2038840271053466, -0.20770273848239884, -0.21132772395638333, -0.21478546166958568, -0.21810190377579652, -0.22130176908918808, -0.2244079849784535, -0.22744127300462003, -0.2304198681888221, -0.23335935857322965, -0.2362726297507156, -0.23916989810147582, -0.24205881639101712, -0.2449446359617835, -0.24783041081367796, -0.2507172302607781, -0.2536044684409977 ], [ -0.07001050460134084, -0.06552712070678379, -0.06179793985798887, -0.05887610827850498, -0.0568061744825088, -0.05562242443138121, -0.05534735627707299, -0.05599037746155977, -0.057546807731119864, -0.05999726663027971, -0.06330751255482925, -0.06742878231820426, -0.07229865597568708, -0.07784244268598983, -0.08397505173734987, -0.09060328117096961, -0.09762842764543667, -0.10494909819387566, -0.1124640897711846, -0.12007519761301078, -0.1276898190179736, -0.13522323465799313, -0.14260047328411485, -0.1497576952565518, -0.15664306273291917, -0.16321709656040495, -0.1694525491922061, -0.17533384713800504, -0.18085617418510536, -0.18602427733671956, -0.19085108130486006, -0.195356195264192, -0.1995643886184124, -0.20350410213951764, -0.20720604841162804, -0.2107019423078511, -0.21402338929241194, -0.21720094744764973, -0.22026336878552533, -0.2232370168871154, -0.22614545129521013, -0.2290091642917802, -0.2318454525527347, -0.23466840445845438, -0.2374889832977365, -0.24031518698379384, -0.24315226596862916, -0.24600298258826636, -0.24886789691849542, -0.2517456662227875 ], [ -0.061055763263005325, -0.05648612626187477, -0.05272598149052654, -0.04983339265855946, -0.04785703882735581, -0.046834304434296925, -0.04678951317013347, -0.0477324034267228, -0.04965694559471512, -0.05254059709859704, -0.05634407863772495, -0.061011734265587814, -0.06647250919264613, -0.07264154407034207, -0.0794223455443821, -0.08670945341342695, -0.09439148862174074, -0.1023544373596379, -0.11048500799446304, -0.11867389160457065, -0.126818764325501, -0.13482688977728952, -0.14261721031874663, -0.15012185345543916, -0.1572870204886727, -0.16407326445458037, -0.170455200050724, -0.17642071692290973, -0.18196978780102824, -0.18711297404819915, -0.19186973371778193, -0.19626663243600717, -0.20033554703442902, -0.20411193770955594, -0.20763324838232444, -0.21093747842641997, -0.21406195325523303, -0.21704230725958618, -0.21991168078220769, -0.2227001234115471, -0.22543418886139066, -0.2281367018946483, -0.23082667487524655, -0.23351935026825688, -0.23622634542525955, -0.23895587697581533, -0.24171304381754144, -0.24450014981597357, -0.24731704969493018, -0.2501615040611058 ], [ -0.05290703079828463, -0.048290535510081556, -0.04454119650855737, -0.04172224987894846, -0.03988672001168525, -0.03907523493784315, -0.03931398655084939, -0.040612950517907365, -0.042964485765952576, -0.04634243022095075, -0.05070179641012573, -0.05597914684037941, -0.062093695112901415, -0.06894913623946208, -0.07643616168056577, -0.084435565484275, -0.0928218025358527, -0.10146682336222623, -0.1102439865171223, -0.11903184226218166, -0.1277175911184878, -0.13620004685498155, -0.14439197261889603, -0.15222170674278712, -0.1596340460562944, -0.16659040407271286, -0.17306830471036272, -0.17906030597790146, -0.18457247051942982, -0.1896225107798195, -0.19423773677272926, -0.19845292587613828, -0.20230821909926044, -0.20584712933055793, -0.2091147264689166, -0.2121560439489063, -0.21501473240102742, -0.21773196994565436, -0.22034562536941937, -0.22288966027961754, -0.22539374912115062, -0.22788309135041773, -0.2303783876834753, -0.23289595173661248, -0.23544792913672752, -0.2380425979184022, -0.24068472641815064, -0.24337596765700686, -0.24611527215716955, -0.24889930410399574 ], [ -0.04575473595679003, -0.041140070799706496, -0.03745248019977199, -0.03476058383923242, -0.033121925732261026, -0.032580484031797585, -0.033164322426595394, -0.03488351723548955, -0.03772850286038465, -0.0416689770502896, -0.04665349419220588, -0.05260984826180137, -0.059446307232926765, -0.06705370951182266, -0.0753083740474687, -0.08407571454061968, -0.0932143910796035, -0.10258078622735334, -0.11203356290336863, -0.12143805235390026, -0.1306702335342096, -0.13962009892966254, -0.14819425216638948, -0.15631764369417933, -0.16393441538864684, -0.1710078862696378, -0.17751976391802105, -0.18346870560963757, -0.1888683777483673, -0.19374517192314955, -0.19813573250005923, -0.20208443682874178, -0.20564094813386546, -0.20885793621235416, -0.21178903501888646, -0.21448708134240402, -0.21700265661584806, -0.2193829353632597, -0.2216708292233931, -0.22390440482706087, -0.22611654669616343, -0.2283348322670835, -0.23058158454830413, -0.23287406823743795, -0.23522479682971942, -0.23764192090393, -0.24012967100602944, -0.24268883207526004, -0.24531722995074068, -0.24801021399610734 ], [ -0.03980498822652856, -0.0352513947503601, -0.03168690644506067, -0.02918567514256254, -0.027809879538367888, -0.027606898071655284, -0.028606614549784748, -0.03081901213052407, -0.03423222449575958, -0.038811214927878535, -0.04449724134948019, -0.051208236086556, -0.05884018277496983, -0.06726951133307124, -0.07635645967119631, -0.08594927453266843, -0.0958890519190907, -0.1060149587705701, -0.11616953980272737, -0.12620380210543058, -0.1359817872804776, -0.1453843846270253, -0.15431220365991027, -0.16268740193226927, -0.1704544453973713, -0.17757985439475044, -0.18405105145354184, -0.1898744726741819, -0.19507313052168773, -0.1996838231114486, -0.20375417619763803, -0.20733968303562178, -0.2105008784824065, -0.2133007513057743, -0.21580246620385735, -0.21806743709686227, -0.22015376750141646, -0.22211505304781576, -0.22399952559211034, -0.22584950757680433, -0.2277011386909351, -0.22958433372616316, -0.23152293005747349, -0.233534984685708, -0.23563318365024255, -0.23782533034684206, -0.24011488346919396, -0.24250151963001354, -0.2449816999883614, -0.24754922425968506 ], [ -0.03527837890236496, -0.030856968121468986, -0.027488649874193305, -0.025253171605831515, -0.024217379770480996, -0.02443202480186324, -0.025928683148692677, -0.028716975555056035, -0.0327822801021771, -0.03808414491368883, -0.04455559446714652, -0.05210349189491481, -0.060610066317156264, -0.06993564084891779, -0.07992250856217598, -0.0903998087336022, -0.10118916498146713, -0.11211077210174913, -0.12298957016709244, -0.13366113022684045, -0.14397689851648932, -0.15380850286041992, -0.1630509084086691, -0.17162430894884761, -0.17947474227218563, -0.18657351164042413, -0.19291557099596912, -0.19851708349482267, -0.20341238944080686, -0.2076506224513348, -0.21129219590845416, -0.21440535104686864, -0.21706291929462962, -0.2193394100380197, -0.2213084950611115, -0.223040925435132, -0.224602887256371, -0.22605477994465928, -0.2274503846183651, -0.2288363796564059, -0.23025215498282203, -0.23172987483277296, -0.23329473980027782, -0.23496540196740812, -0.2367544911652597, -0.23866921536174512, -0.24071200339345644, -0.2428811634566712, -0.24517153573884065, -0.24757512217054667 ], [ -0.032408121773547016, -0.02820321439013962, -0.025117185312495405, -0.023235330330122927, -0.022629087939516124, -0.02335244705879158, -0.025438448050358664, -0.02889598155325368, -0.03370711678726179, -0.03982520367961184, -0.047173985440435606, -0.055647925261895104, -0.06511389023015379, -0.07541424855806822, -0.08637132859505092, -0.09779307004955662, -0.10947958340143327, -0.12123023813530343, -0.1328508385737852, -0.1441604280153559, -0.15499729146945085, -0.16522380101993495, -0.17472985544334274, -0.18343479215049108, -0.19128777802670593, -0.19826680082477655, -0.20437647267303483, -0.2096449154048261, -0.2141200225516493, -0.21786538826572666, -0.2209561655292609, -0.22347507258610566, -0.2255087153727473, -0.22714434149446827, -0.2284670929608421, -0.2295577835968956, -0.23049119426064957, -0.23133485490424643, -0.23214826641335518, -0.23298250584966906, -0.23388015481649682, -0.23487549080406445, -0.23599488433560634, -0.2372573495239092, -0.2386752014748057, -0.24025478025483626, -0.24199720746011444, -0.2438991474998442, -0.2459535513617408, -0.2481503657508033 ], [ -0.03143743084055295, -0.027547874434703745, -0.024844634131156562, -0.02341836779294848, -0.02334489086313951, -0.02468116054157443, -0.027461320386646504, -0.031693036424479626, -0.037354392767177114, -0.044391635920861594, -0.052718054538583026, -0.0622142484396675, -0.07272997305003459, -0.08408764326699414, -0.09608745025511856, -0.1085138983256162, -0.12114342470007577, -0.13375264324338687, -0.14612667370768118, -0.15806699486501818, -0.16939829859576183, -0.17997391777905825, -0.1896795395878521, -0.19843507707336094, -0.20619473320173043, -0.2129454324848108, -0.2187039013162979, -0.223512741670572, -0.22743586381825298, -0.23055362790418998, -0.23295800103318332, -0.23474797665525493, -0.23602543663805498, -0.23689157162738783, -0.23744391778098906, -0.2377740208628898, -0.23796570305178344, -0.23809388316829105, -0.23822388595524724, -0.23841116871594958, -0.23870139213156572, -0.2391307647119636, -0.23972659564069265, -0.24050799762548514, -0.24148668892729952, -0.24266785143199665, -0.2440510090621799, -0.24563089776362879, -0.24739830460372136, -0.24934085912245485 ], [ -0.03261604077705149, -0.029156440435134767, -0.02695212981468398, -0.026098773813407528, -0.026676176827074682, -0.028743821718701712, -0.032336426550899855, -0.03745977731293171, -0.04408714363718036, -0.05215661672686389, -0.061569714228262074, -0.07219156596018395, -0.08385292043295256, -0.09635409345673596, -0.10947082296333122, -0.12296181328807498, -0.13657757031106654, -0.15006997337107775, -0.16320192732140804, -0.175756408180046, -0.1875442662854503, -0.19841027524107568, -0.20823709383159206, -0.21694701363342084, -0.2245015669814454, -0.23089924179190557, -0.23617167322413235, -0.240378749335044, -0.2436030806311893, -0.24594425113933926, -0.24751320488635287, -0.24842704101458524, -0.24880440605328547, -0.2487615928771758, -0.24840938876323082, -0.24785066253521082, -0.24717864331476602, -0.24647581942357877, -0.24581337315592844, -0.2452510628480924, -0.24483746543826435, -0.24461049843752503, -0.2445981482675923, -0.24481934105288938, -0.24528490134771186, -0.24599855339333043, -0.24695792801207062, -0.24815554598072476, -0.24957975560808854, -0.25121560825431666 ], [ -0.036195794559101824, -0.033297574756271375, -0.031725089015528285, -0.031578455959124785, -0.03294087314946692, -0.035873695303669795, -0.040411477819241926, -0.04655727069895721, -0.05427851067956091, -0.06350390548479745, -0.0741217207881788, -0.08597985466171787, -0.09888800558963129, -0.11262210423410668, -0.1269309913516372, -0.14154510174218182, -0.1561866855174583, -0.1705808994007314, -0.1844669683823852, -0.19760857918240138, -0.20980273259990456, -0.22088644318733852, -0.2307409051260907, -0.23929300467841785, -0.24651431162338477, -0.2524178901995777, -0.2570534119081713, -0.26050112014667626, -0.26286519530894115, -0.26426701336674463, -0.26483870026973544, -0.2647172780457898, -0.26403959236173447, -0.26293811681331003, -0.26153765263209827, -0.25995288584481124, -0.2582867261698063, -0.2566293302798579, -0.25505770296027896, -0.2536357696221845, -0.2524148195104341, -0.2514342283248223, -0.2507223800500271, -0.250297719334001, -0.25016987698907034, -0.2503408216662302, -0.25080600024774635, -0.25155543793144, -0.25257477634036274, -0.253846234325491 ], [ -0.042425254667292744, -0.04023745072609608, -0.03944730380534689, -0.04015860786954484, -0.04245711620879811, -0.04640515073336382, -0.052036115220207124, -0.059349223210053204, -0.0683048298733735, -0.07882082012686231, -0.09077053680901992, -0.103982715685901, -0.11824381328504208, -0.13330296047299628, -0.14887955253765162, -0.1646732144374201, -0.18037559348830223, -0.1956831785319204, -0.210310173701171, -0.2240004042023711, -0.23653731663230593, -0.24775134533031795, -0.2575242125281536, -0.26579006184847986, -0.2725336378864409, -0.27778597465794763, -0.28161821564642286, -0.2841342511357432, -0.2854628350792052, -0.2857497560721409, -0.28515051175645234, -0.28382379833291926, -0.2819259964316374, -0.27960672394065655, -0.2770054413056302, -0.27424903579485904, -0.27145027536827215, -0.26870700550636917, -0.2661019586777902, -0.26370305152924467, -0.2615640556928309, -0.2597255415955957, -0.2582160089638037, -0.2570531316810212, -0.2562450576380122, -0.255791715905594, -0.25568609387996566, -0.25591545602320753, -0.25646248353276113, -0.2573063208256072 ], [ -0.05154334203629851, -0.05023300126040797, -0.050393820120733235, -0.0521322434136966, -0.05553547153965277, -0.06066560084232964, -0.06755359962850571, -0.07619345401673372, -0.08653691385427753, -0.0984893515747336, -0.11190729725430204, -0.12659820942190736, -0.14232296216159668, -0.15880136002119327, -0.1757207325282919, -0.19274732990605203, -0.20953988453587824, -0.22576438078333094, -0.2411088555135159, -0.25529698546398527, -0.26809932758771327, -0.2793413483598788, -0.28890775772807875, -0.29674308269191774, -0.30284880247133295, -0.30727766474038987, -0.3101259785966928, -0.31152473059752683, -0.31163031402191854, -0.31061553102514283, -0.3086613588708427, -0.30594979706683145, -0.30265795523881645, -0.2989534151148858, -0.2949908084156674, -0.29090949382462794, -0.2868321850549511, -0.28286437152771526, -0.2790943767389471, -0.2755939114835517, -0.27241899553226934, -0.2696111392464742, -0.2671986941722506, -0.2651982979029184, -0.2636163530082134, -0.2624504925049962, -0.2616909952708122, -0.2613221241369452, -0.2613233673159059, -0.2616705704801745 ], [ -0.06377207187780942, -0.0635241306528549, -0.06482264018640893, -0.06777541356932715, -0.07246969738428688, -0.07896585117175547, -0.0872907906101037, -0.09743154915700325, -0.10932942741632501, -0.12287530416008297, -0.13790675612456704, -0.154207648457233, -0.1715107854481408, -0.18950402890333407, -0.20783999205855275, -0.22614901992655723, -0.24405472481851676, -0.26119093859256326, -0.2772186604471836, -0.2918414930131201, -0.30481820087467604, -0.3159713726269344, -0.3251916518696245, -0.3324375295692208, -0.3377311649827468, -0.3411510522108012, -0.34282253768889737, -0.3429072215092688, -0.3415921729633389, -0.33907970463234727, -0.33557822821067007, -0.33129449907491915, -0.32642737192603843, -0.3211630493000772, -0.3156717099669095, -0.31010534972255743, -0.3045966439830472, -0.29925864049173634, -0.2941851030459133, -0.28945134696071295, -0.28511542948621327, -0.2812195807284359, -0.2777917812393689, -0.27484741066325724, -0.27239090753054795, -0.27041739363959194, -0.26891422774000984, -0.26786246272610814, -0.2672381885260575, -0.26701374954500845 ], [ -0.07930853693313078, -0.08032503481862996, -0.08296538453592839, -0.08733722752104378, -0.09352615500662775, -0.10158894186689471, -0.11154647289805819, -0.12337673376409053, -0.13700837194585302, -0.15231546129058438, -0.16911420318253811, -0.18716233580761577, -0.20616196344197912, -0.22576632636041816, -0.2455906919836348, -0.2652270758447255, -0.28426195822748634, -0.3022956512131212, -0.3189616105438233, -0.33394387555845784, -0.3469910011060071, -0.3579252885399222, -0.3666467365117563, -0.37313179000344365, -0.37742754349021834, -0.3796424599277024, -0.379934860294473, -0.3785004284531557, -0.37555981054530796, -0.37134713201488223, -0.3660999719877387, -0.36005107273798376, -0.3534218501803523, -0.3464176202139806, -0.3392243624448763, -0.33200679698511393, -0.32490753872594147, -0.3180471044211355, -0.31152457111123866, -0.30541871267095844, -0.29978946994845446, -0.2946796365037059, -0.29011666520299273, -0.28611452065279575, -0.2826755189145824, -0.2797921095934903, -0.277448566729247, -0.27562256436749477, -0.2742866205918024, -0.27340940039808337 ], [ -0.09831638271178833, -0.10081488250984671, -0.10501716977157494, -0.11102893277947046, -0.11893211403136394, -0.12877771900798773, -0.14057825205215502, -0.15430016629608234, -0.16985686557855795, -0.1871029486292295, -0.20583051385767326, -0.22576840990138258, -0.24658527644968142, -0.26789702485288847, -0.2892790283932145, -0.3102827379850175, -0.3304557803481656, -0.3493639609007462, -0.3666131391960319, -0.38186880282069646, -0.39487139450518915, -0.4054460082083753, -0.413505840528964, -0.41904959728255875, -0.42215375031480273, -0.42296100283133464, -0.4216665083903035, -0.41850332270551216, -0.4137283191734793, -0.4076094573040232, -0.4004149388284668, -0.39240447635382747, -0.38382266339873694, -0.3748942784036595, -0.3658212694770928, -0.3567811346889207, -0.34792641702210836, -0.3393850584190605, -0.3312613922867078, -0.32363759077401855, -0.3165754177263995, -0.3101181684043559, -0.3042927022960116, -0.29911149597241815, -0.29457465963197116, -0.2906718745372132, -0.2873842196629497, -0.2846858650976618, -0.282545617463156, -0.28092830910023103 ], [ -0.12091711781649073, -0.1251282261666422, -0.13112609315717805, -0.1390124634891663, -0.1488633746746988, -0.16072156398195436, -0.17458844878977287, -0.1904160802430943, -0.20809963754367633, -0.22747120590542935, -0.2482957388262086, -0.27027020380804534, -0.29302689440808294, -0.31614169856768615, -0.33914769619070384, -0.361553817700182, -0.3828675068165641, -0.402619553380166, -0.4203886971213866, -0.4358234249502182, -0.44865867079893174, -0.45872582876819323, -0.4659554471657672, -0.4703729662902858, -0.4720886901092365, -0.47128370121600405, -0.46819359403050553, -0.4630917568163946, -0.45627358032167065, -0.4480425280016813, -0.43869857044383376, -0.42852912950860733, -0.4178024229688051, -0.40676294642948774, -0.39562875791451857, -0.3845902178031999, -0.37380986015573714, -0.36342311293291796, -0.35353963177399716, -0.3442450573453679, -0.3356030460529773, -0.32765745688365633, -0.3204346035491219, -0.31394550191685977, -0.3081880591051642, -0.3031491636976995, -0.2988066471831805, -0.2951310955869533, -0.2920874977489545, -0.28963672306416344 ], [ -0.14718169315918517, -0.15334562206268298, -0.16138284898851363, -0.1713890249446901, -0.1834318139963378, -0.19754292154340036, -0.2137096593803003, -0.23186646027815438, -0.25188693674096907, -0.2735772758178199, -0.29667194822843324, -0.3208328413539483, -0.34565293727575575, -0.37066547093538205, -0.39535905221165146, -0.41919850485819055, -0.4416502469575718, -0.4622101021705154, -0.4804307415900042, -0.4959457362952231, -0.5084875538014793, -0.5178976962160105, -0.5241283497396272, -0.5272361173675466, -0.5273693782548143, -0.5247513875709473, -0.5196613557440581, -0.5124154977672877, -0.5033495633120393, -0.4928038006020672, -0.481110793063098, -0.4685862076621172, -0.4555222286732661, -0.44218330771498104, -0.42880381125147826, -0.4155871582275201, -0.4027060855508202, -0.39030373761476533, -0.3784953351695812, -0.36737023171307204, -0.35699420943471405, -0.3474119014206305, -0.3386492534683627, -0.33071595913496665, -0.3236078172163932, -0.3173089731278582, -0.31179401566371223, -0.3070299090479456, -0.3029777474462303, -0.29959432540063746 ], [ -0.17712285096928726, -0.1854850261898271, -0.1958111118757797, -0.20818841960285717, -0.22267363092912884, -0.23928446763038247, -0.2579908837995295, -0.2787062073451949, -0.3012788526743697, -0.32548544247667777, -0.351026389114806, -0.3775251486804687, -0.40453240053946327, -0.43153622801010827, -0.45797889281242465, -0.48327997585327576, -0.506864584733878, -0.5281942266805837, -0.5467971227471531, -0.5622944746967016, -0.5744196229663341, -0.5830280804149726, -0.5880978386404201, -0.589720774760401, -0.5880871112261112, -0.583465493922841, -0.5761813158469253, -0.5665955348348759, -0.5550856055520443, -0.5420294630545288, -0.5277929004735862, -0.5127202482102755, -0.49712799685852227, -0.48130088374768665, -0.4654899418386773, -0.44991204915061145, -0.43475058501918107, -0.42015687477118036, -0.40625217439946093, -0.393130005796378, -0.3808586996503014, -0.3694840382758042, -0.359031916576392, -0.3495109584072955, -0.3409150399357943, -0.33322568283702414, -0.32641428945213224, -0.32044420006062313, -0.3152725595306114, -0.3108519869359887 ], [ -0.21068877138035758, -0.22149457369753822, -0.2343593819719334, -0.2493599027843587, -0.2665391753860893, -0.2858979005221678, -0.3073853012686576, -0.33088996228669565, -0.3562312985392422, -0.38315253649049374, -0.4113163255770713, -0.4403042871008458, -0.4696218717296501, -0.4987097265607736, -0.5269622587495313, -0.5537531765938388, -0.5784665765607957, -0.6005308785431187, -0.6194519546501294, -0.6348414869620573, -0.6464370947438988, -0.6541120119898723, -0.6578737667772169, -0.6578529896330388, -0.6542847594152733, -0.6474855376422073, -0.637828717199126, -0.6257212768523858, -0.6115832396765011, -0.5958308210952672, -0.5788634825628405, -0.5610546478308798, -0.5427455850182332, -0.5242418646707454, -0.5058118164734255, -0.4876864766947788, -0.47006060951232187, -0.4530944761474551, -0.43691610486021615, -0.42162387817294245, -0.4072893013932135, -0.3939598509693416, -0.38166182558084305, -0.37040314019488174, -0.36017601612824524, -0.35095953027698634, -0.3427219952878209, -0.3354231501827223, -0.3290161480666838, -0.32344933407138776 ], [ -0.24775851760123868, -0.2612473273120335, -0.27689497219443604, -0.29476535244158586, -0.31488525852967864, -0.33723537113384605, -0.3617408301119447, -0.3882618437393266, -0.416585022865678, -0.4464163693148857, -0.47737709963274155, -0.5090036943056404, -0.5407536427534545, -0.5720181844365835, -0.6021427997275266, -0.6304552176888595, -0.6562993674516396, -0.6790722829225673, -0.6982598887691921, -0.7134672432441168, -0.7244393968734475, -0.731070463863366, -0.7334004397350385, -0.7316012250359698, -0.7259547495272762, -0.7168267479405045, -0.7046396040984367, -0.689846970728217, -0.6729119051077216, -0.6542893217693044, -0.6344128296895646, -0.6136855512357859, -0.5924742883958678, -0.5711063445354378, -0.5498683585900819, -0.5290066078070392, -0.5087283474788646, -0.4892038601447384, -0.47056897275927856, -0.45292786609045255, -0.4363560479913393, -0.4209033949175027, -0.4065971882299175, -0.3934450870917521, -0.38143799097250786, -0.37055275385976727, -0.3607547203906307, -0.3520000617855912, -0.34423789681931294, -0.3374121899924569 ], [ -0.2881396944376844, -0.3045384846857353, -0.32320071329380284, -0.3441754256397389, -0.3674707239841217, -0.393044448094114, -0.4207944891355524, -0.45054923992627693, -0.48205890583676836, -0.5149886548241303, -0.5489148479075721, -0.5833258107874422, -0.6176286919676355, -0.6511637723503014, -0.6832270077594848, -0.7131005267125349, -0.7400893572336817, -0.7635611139727223, -0.7829841900186086, -0.7979596102482803, -0.8082423615113763, -0.8137496428662131, -0.8145556750555593, -0.8108748780231705, -0.803036801376125, -0.7914568472682928, -0.7766065656718392, -0.7589864090624993, -0.7391026947978298, -0.7174494689966456, -0.6944951819224413, -0.6706736157204769, -0.646378303025289, -0.621959656129376, -0.597724110602853, -0.573934713818347, -0.5508127194265457, -0.5285398632674201, -0.5072610867587848, -0.4870875402183017, -0.46809974441343005, -0.4503508188874359, -0.43386970523734103, -0.418664326680132, -0.4047246349979192, -0.39202550426849303, -0.38052943871438205, -0.3701890699220518, -0.36094942655450013, -0.3527499672579162 ], [ -0.33156859456514076, -0.35108537097508075, -0.37297476282785724, -0.3972691557281325, -0.423955809809599, -0.45296723008590445, -0.4841712600612056, -0.5173614410467817, -0.552248407626676, -0.5884533503304716, -0.6255048439255056, -0.6628405589475319, -0.6998154495773049, -0.7357178073970108, -0.7697939452819789, -0.8012811536009804, -0.8294470398798762, -0.8536317287270935, -0.8732881351778731, -0.8880151138775524, -0.8975790136362871, -0.9019209660719119, -0.9011496686521606, -0.8955218118541965, -0.8854139975373695, -0.8712906341565222, -0.8536719056323744, -0.8331048413133606, -0.8101392195258882, -0.7853088850344232, -0.7591182415228833, -0.7320332204214544, -0.7044758567049528, -0.6768216199347603, -0.6493987645703779, -0.6224891131432592, -0.5963298308748861, -0.5711158721152563, -0.5470028718604167, -0.5241103212252631, -0.5025249092226567, -0.4823039406575864, -0.46347875706952646, -0.4460580989845653, -0.43003135644921, -0.4153716628163666, -0.40203879493743044, -0.38998185147388487, -0.37914168975881135, -0.3694531101188776 ], [ -0.3777129296536199, -0.400530331952746, -0.4258336535821057, -0.45363714767673624, -0.4839054816224799, -0.5165438083574989, -0.5513876737183472, -0.5881933482898551, -0.6266294060648878, -0.6662706359800717, -0.7065956375592608, -0.7469896601805928, -0.7867542982821685, -0.8251254159605621, -0.861300003661723, -0.8944714961234025, -0.9238714954560537, -0.948814154889052, -0.9687381717967207, -0.9832409202635114, -0.9921000404142372, -0.9952797419394631, -0.9929217047568537, -0.9853230287300565, -0.9729054760211061, -0.9561808652325122, -0.9357169712640063, -0.912107064667405, -0.8859448013769091, -0.857804945785657, -0.828229567125126, -0.7977189006140597, -0.7667259214620049, -0.7356537270445466, -0.7048549629673719, -0.6746326955824787, -0.6452422886651007, -0.616893968215514, -0.5897558527718412, -0.5639572905162427, -0.5395923852954407, -0.5167236185248265, -0.49538548904651325, -0.475588103138586, -0.4573206552080804, -0.4405547480142533, -0.4252475102564581, -0.41134447900517457, -0.39878222435562094, -0.3874907033087618 ], [ -0.4261770553057842, -0.45244641793745455, -0.48131844807029056, -0.5127882081942641, -0.5467965353341147, -0.5832198293984407, -0.6218598084299974, -0.6624338699148394, -0.7045669357177121, -0.7477859216559313, -0.7915182292268036, -0.8350958447568234, -0.8777666501800928, -0.9187142667388619, -0.9570870361848458, -0.992035532246871, -1.0227563836933018, -1.048538485223896, -1.068806356406348, -1.0831549992479217, -1.0913714396546155, -1.0934401780211989, -1.0895325354404257, -1.0799825765996947, -1.0652541471206265, -1.0459041606047363, -1.0225466819615148, -0.9958210270468116, -0.9663655861078388, -0.9347977971714178, -0.9016998341519176, -0.8676091311656893, -0.8330127373903171, -0.7983445623551367, -0.763984727446986, -0.7302604170120248, -0.6974477834957918, -0.665774589303348, -0.6354233608407859, -0.6065348921276468, -0.5792119739623531, -0.5535232476455982, -0.5295070963140145, -0.5071754968622681, -0.486517764313507, -0.46750412990943624, -0.4500891046020923, -0.4342145908166717, -0.41981271675694165, -0.4068083784985965 ], [ -0.4765094286325773, -0.5063455473043741, -0.538903627316879, -0.5741589655798753, -0.6120279360199494, -0.6523575179253776, -0.6949149336585765, -0.739378087190174, -0.7853277360900879, -0.8322425892039186, -0.8794987644810991, -0.9263752014574386, -0.9720666010268549, -1.0157051347427806, -1.056391407325939, -1.0932339208138604, -1.1253946771947185, -1.1521368675048913, -1.1728693001830377, -1.1871818330561381, -1.194866937572788, -1.1959246123656948, -1.1905506901906824, -1.1791113416438368, -1.1621084758147786, -1.1401413377542502, -1.1138689831205992, -1.0839769368425434, -1.0511497842745836, -1.0160501274309914, -0.9793034567957962, -0.9414880369848493, -0.9031287766046877, -0.8646941217778727, -0.8265951734452341, -0.7891864099257465, -0.7527675591551096, -0.7175862933370852, -0.683841510455832, -0.6516870276294231, -0.621235548803085, -0.592562791928021, -0.5657116752524021, -0.540696473433437, -0.5175068647452115, -0.49611180205016137, -0.47646315267550854, -0.45849906549483843, -0.44214703667860844, -0.4273266580356061 ], [ -0.5282119093625017, -0.5616886917686803, -0.5980081751720505, -0.6371258454019256, -0.6789336475798778, -0.7232492851961577, -0.7698057746438111, -0.8182419966450624, -0.8680952276535816, -0.9187968867198774, -0.969672957206718, -1.0199506713067994, -1.0687729810759592, -1.1152219647433765, -1.1583515259792958, -1.1972285017259843, -1.2309797055438652, -1.2588407869218516, -1.2802015337356465, -1.2946418809180753, -1.3019537547487707, -1.3021459594449856, -1.2954321307274963, -1.2822045468756478, -1.262998510738155, -1.2384526549035857, -1.2092699400316893, -1.176182764019209, -1.1399240396095192, -1.1012047609208315, -1.060697666555722, -1.0190261250380908, -0.9767572180426314, -0.9343980522098908, -0.892394483708079, -0.8511316175247371, -0.8109356045391198, -0.7720763866070106, -0.734771131044114, -0.699188156577674, -0.6654511913328109, -0.633643827847437, -0.6038140570093218, -0.5759787767106237, -0.5501281845505814, -0.5262299782092283, -0.5042333022521341, -0.48407239560687576, -0.46566990904493344, -0.44893987599073326 ], [ -0.5807504432155637, -0.6178975508697041, -0.6580082450085727, -0.7010186985122949, -0.746797149478249, -0.7951330093719947, -0.8457263674089492, -0.8981786760042241, -0.9519856415760334, -1.006533587392405, -1.061100758649625, -1.1148651372191762, -1.1669202309898976, -1.2162998925149382, -1.2620124126089394, -1.3030829041234429, -1.3386014455388104, -1.3677728677999632, -1.3899628652292841, -1.404734760679011, -1.4118720842581665, -1.4113841257194888, -1.403494357998185, -1.3886143547828556, -1.3673077760720966, -1.3402497249161438, -1.308186310828783, -1.2718979943338204, -1.2321687659296852, -1.189761861703622, -1.145401758420865, -1.0997616538914294, -1.0534554409134942, -1.0070332050707025, -0.9609794095349768, -0.915713096655316, -0.8715895919774104, -0.8289033221020069, -0.7878914500330254, -0.7487380951637139, -0.7115789475049459, -0.6765061147921323, -0.643573062825008, -0.6127995279800778, -0.584176298671476, -0.5576697805931883, -0.5332262788736091, -0.5107759483044165, -0.4902363798771143, -0.471515807318452 ], [ -0.6335666502382525, -0.6743671788828253, -0.7182508100330348, -0.765135420015763, -0.8148669187860635, -0.8672082119853154, -0.9218286856954224, -0.9782950315399651, -1.036064464228691, -1.0944816140260643, -1.152780559818353, -1.2100935382925235, -1.2654677331499633, -1.3178911176340384, -1.3663275156960701, -1.4097598486559024, -1.447239049087451, -1.477934607240061, -1.5011815584987223, -1.5165183567723628, -1.5237108197260998, -1.5227591883928455, -1.5138879378050119, -1.497520629574142, -1.4742440949328643, -1.4447671184999797, -1.4098785196689216, -1.3704084259878244, -1.32719508619603, -1.28105820827292, -1.232778782272824, -1.1830847271210294, -1.1326414283061406, -1.082046200429288, -1.0318258065876553, -0.9824363142543293, -0.9342647153964024, -0.887631863870144, -0.8427963794493991, -0.7999592379779569, -0.7592688173822845, -0.7208262062647405, -0.6846906109776345, -0.6508847222563738, -0.619399925879433, -0.5902012643707217, -0.563232078556203, -0.5384182784447566, -0.5156722118705126, -0.4948961160966747 ], [ -0.6860898696139273, -0.7304790768403656, -0.778067776751386, -0.8287570156755194, -0.8823723268035573, -0.9386525957459279, -0.9972395529979062, -1.0576687300136873, -1.119362942352487, -1.1816295806071544, -1.2436631547496857, -1.3045545868867672, -1.3633085997627952, -1.418870116114186, -1.4701597994481816, -1.5161177217414026, -1.5557527337782922, -1.5881936692616279, -1.6127373859425072, -1.628888230985618, -1.6363841112958575, -1.6352059956220268, -1.6255700743781636, -1.6079043711670598, -1.582813675004691, -1.5510377635300536, -1.5134078866567648, -1.4708055987573305, -1.4241266868425497, -1.3742515686583354, -1.3220224211859026, -1.2682265650570783, -1.2135852534753964, -1.1587469028611375, -1.1042838505332662, -1.0506918462079842, -0.9983916230736737, -0.9477320215173369, -0.8989942433346071, -0.8523968958613719, -0.8081015479263399, -0.7662185680525886, -0.7268130546224248, -0.689910701258349, -0.6555034706640046, -0.6235549777193075, -0.5940055080631257, -0.5667766215992891, -0.5417753110196042, -0.5188977032525048 ], [ -0.7377492678889168, -0.7856143397322414, -0.836790147417126, -0.8911627160806228, -0.9485395915057594, -1.0086386615364318, -1.0710776804993425, -1.135365336752816, -1.2008949202251398, -1.2669418506642316, -1.3326664774427468, -1.397123599457834, -1.4592800050261217, -1.518040918553837, -1.5722855031479823, -1.6209104979025268, -1.6628797466041352, -1.6972759985489008, -1.7233502388348902, -1.7405632907079551, -1.7486148168280393, -1.7474562199800865, -1.7372861058549243, -1.718529446894347, -1.6918037744747876, -1.657877113595413, -1.617622720047538, -1.5719750789553026, -1.5218904190034495, -1.4683136112866984, -1.4121520976255568, -1.3542566110938559, -1.2954079379738273, -1.236308756104139, -1.1775795679882446, -1.1197578363269594, -1.0632995599311785, -1.0085826613620177, -0.9559116763224711, -0.9055233333241658, -0.8575926914137478, -0.8122395672788155, -0.7695350348140962, -0.7295078235739024, -0.6921504798761344, -0.6574251871362556, -0.6252691710430135, -0.595599640713532, -0.568318239017827, -0.5433149938190767 ], [ -0.7879856802547976, -0.8391665281173276, -0.8937619163783244, -0.9516448617767862, -1.0126075778534802, -1.0763503053751418, -1.142470890737131, -1.2104559399513488, -1.2796745807380505, -1.3493760561869115, -1.4186925130211487, -1.4866483829234949, -1.5521776209256792, -1.6141496909378814, -1.6714045199127716, -1.7227956655317325, -1.767239717936515, -1.8037686426284354, -1.8315806271631374, -1.850084335938306, -1.8589315961658608, -1.8580345854108868, -1.847565480902421, -1.8279389117658478, -1.7997798882741696, -1.7638816131237673, -1.7211583399111716, -1.6725981797360703, -1.6192197188359414, -1.5620349134859595, -1.5020193710462935, -1.4400900634388674, -1.3770898369128717, -1.313777741021891, -1.2508241053178555, -1.1888093454558764, -1.1282256041680936, -1.0694804772132602, -1.012902212924514, -0.9587458947054517, -0.9072002160589021, -0.8583945392044297, -0.812405994415244, -0.7692664313539002, -0.7289690787768615, -0.6914748070714544, -0.656717920513655, -0.6246114336743258, -0.5950518095096085, -0.5679231556467357 ], [ -0.8362629092054956, -0.8905539947092824, -0.9483534522029837, -1.0095233530734165, -1.0738433085447452, -1.1409993613044724, -1.2105736390929458, -1.282035570701627, -1.354735656753179, -1.427902966695736, -1.50064766684151, -1.5719699261531777, -1.6407764395498616, -1.7059054907759117, -1.766160895389845, -1.8203542965920396, -1.867354166620878, -1.9061386096659694, -1.935847875472352, -1.9558316562653195, -1.9656860504579325, -1.965275756234682, -1.9547386457952847, -1.9344721475623878, -1.9051033588894593, -1.8674469294168394, -1.8224559863472953, -1.7711714979916637, -1.7146746321510755, -1.654045261674087, -1.5903282594891075, -1.5245079518501503, -1.4574902179434992, -1.3900912357227122, -1.323031691340861, -1.2569352847608397, -1.1923304845519125, -1.12965464603695, -1.0692597706385105, -1.0114193316341935, -0.9563357159282353, -0.9041479329015744, -0.8549393229362279, -0.8087450636624145, -0.7655593248994442, -0.7253419664711486, -0.6880247086037516, -0.6535167338372737, -0.6217097032229083, -0.5924821886892941 ], [ -0.8820782433608241, -0.9392314308692812, -0.9999741424936925, -1.0641594664322551, -1.1315570288012395, -1.20184199631363, -1.2745848270423146, -1.3492425305530484, -1.42515237721822, -1.501529165110343, -1.5774672840969322, -1.6519488721486444, -1.7238592894844786, -1.7920108865681341, -1.8551755592960089, -1.9121258342730925, -1.9616832141085716, -2.002771307435583, -2.0344700268299274, -2.056066105340079, -2.0670946647854938, -2.0673668591474916, -2.056979879892552, -2.0363077642688463, -2.005974100420191, -1.96681024427433, -1.9198044022562613, -1.866047491862149, -1.80668108263874, -1.7428513180579857, -1.675671045058505, -1.606190871835091, -1.535378774222799, -1.4641072206070394, -1.3931465079480434, -1.3231629781427505, -1.254720903799944, -1.1882870139983208, -1.1242368229724249, -1.062862101324999, -1.0043789796426101, -0.9489362967773416, -0.8966239024420467, -0.8474807005635566, -0.8015022804312305, -0.7586480307463109, -0.7188476700196325, -0.6820071573951231, -0.6480139723066211, -0.6167417704180478 ], [ -0.9249719810640359, -0.9847004070700216, -1.0480840666317708, -1.1149687957749552, -1.1851165785915203, -1.2581947076069382, -1.333765656010495, -1.4112783754766665, -1.4900618987662075, -1.5693222860839695, -1.6481440864979389, -1.725497559467385, -1.800252875516644, -1.8712023392670953, -1.9370912980930575, -1.9966577673137267, -2.0486798939899304, -2.092029222899854, -2.1257264291018205, -2.1489949561629964, -2.1613071620095403, -2.162417481892767, -2.152378050002036, -2.131534226420653, -2.1005002515380373, -2.060118153376565, -2.0114052867982215, -1.9554969027422011, -1.8935897979491734, -1.8268917151273136, -1.7565793299399166, -1.6837659161997622, -1.6094784520174419, -1.534643110435855, -1.4600777025896856, -1.3864895787689198, -1.3144776126150401, -1.2445370963589721, -1.1770665966962852, -1.1123760270922838, -1.0506953684169484, -0.9921836128851187, -0.9369376191925642, -0.8850006545485533, -0.8363704672689883, -0.7910067862651515, -0.7488381847140138, -0.7097682770716185, -0.673681243289237, -0.6404466929802393 ], [ -0.9645357543268022, -1.026518675426916, -1.0922044297164153, -1.1614330069234975, -1.233960701542501, -1.3094494740860751, -1.3874569727208652, -1.4674278770925606, -1.5486873795687832, -1.630437771926879, -1.7117592413498282, -1.791616074126937, -1.8688694843000748, -1.9422981816826703, -2.0106275122441573, -2.072567481679404, -2.126859158479075, -2.1723278344183927, -2.2079399681886342, -2.2328595433975527, -2.246498358075729, -2.2485543327999427, -2.2390325425854423, -2.218245501386394, -2.186792053898726, -2.1455174433441373, -2.0954598576056584, -2.0377902450125793, -1.9737521364770978, -1.9046068841956085, -1.831587757308259, -1.7558643653433779, -1.678517330611871, -1.6005221454990837, -1.5227406767299467, -1.4459186746315686, -1.3706877622345652, -1.2975705996731899, -1.2269881673396492, -1.159268344478367, -1.0946551598980656, -1.0333182538380257, -0.9753622175145498, -0.9208355750913407, -0.8697392477983996, -0.8220343970159518, -0.7776495866283492, -0.7364872380662238, -0.698429376552022, -0.6633426858464186 ], [ -1.0004194580901338, -1.0643079957516774, -1.1319264603002261, -1.2031100281542872, -1.2776108063228733, -1.3550874348121087, -1.4350952904193648, -1.5170779013639668, -1.6003603251496992, -1.6841453896697491, -1.7675138383842834, -1.8494295358852075, -1.928750951374583, -2.004250101230498, -2.0746399374070883, -2.138610740554768, -2.194875339737284, -2.2422218920617567, -2.2795715587532244, -2.3060368908401694, -2.320975422052136, -2.3240322874652692, -2.315166041867133, -2.294653461378199, -2.263071875998718, -2.2212609762584683, -2.1702691712850117, -2.1112915222645223, -2.0456065457489854, -1.9745179552525376, -1.899305347977947, -1.8211856852353079, -1.7412856689006837, -1.6606239776486063, -1.5801017570863858, -1.500499608536717, -1.4224794279240405, -1.3465896771287584, -1.2732729377177552, -1.2028748519325325, -1.1356537759082457, -1.0717906492348366, -1.0113987255136179, -0.954532916360122, -0.9011985829318344, -0.8513596704867432, -0.8049461275755366, -0.7618605859746553, -0.7219843031418439, -0.6851823878342569 ], [ -1.032336607169372, -1.0977602534854873, -1.166918465714428, -1.23964226857021, -1.3156806338837228, -1.3946903627107483, -1.4762265098876017, -1.5597339110637383, -1.6445405065697098, -1.7298533005278636, -1.8147579399269, -1.8982230329532985, -1.9791104236675432, -2.0561926590874493, -2.128178760237522, -2.1937490533955293, -2.2515991361828074, -2.300491981060807, -2.339315747250672, -2.3671432702826065, -2.3832877807729886, -2.3873486015528176, -2.3792407514290277, -2.3592037541307986, -2.3277875103450603, -2.2858164879274243, -2.234336898242475, -2.17455389840263, -2.107766484427426, -2.0353066713357975, -1.9584874647772414, -1.8785618370749395, -1.7966930181049279, -1.713935141422195, -1.6312226264398113, -1.549366477576453, -1.4690557674799902, -1.3908628012290394, -1.3152507354802196, -1.242582695497482, -1.1731316677509553, -1.1070906381792067, -1.0445825977388075, -0.9856701531782511, -0.930364568831544, -0.8786341309590587, -0.8304117750505354, -0.785601952676852, -0.7440867410337677, -0.7057312175477287 ], [ -1.0600679757822054, -1.1266416685233334, -1.196930766125627, -1.2707624783684526, -1.3478832993935157, -1.4279492079848635, -1.510516358143412, -1.5950327759982204, -1.6808317066766536, -1.7671273964371617, -1.8530142466676611, -1.937470426374711, -2.01936715580391, -2.097484933758316, -2.1705379060587036, -2.2372072651355532, -2.296183921176221, -2.3462196171157803, -2.386184206083759, -2.415125184396791, -2.43232416016497, -2.437344150929492, -2.4300617127416637, -2.410679024643038, -2.379713262480592, -2.3379637941776306, -2.286461268623857, -2.2264054082894917, -2.1590993110099435, -2.085887211508249, -2.0081006058644206, -1.9270152879750229, -1.8438198421252947, -1.7595947647925052, -1.6753006484704687, -1.5917736048473738, -1.509726158234239, -1.429752055087759, -1.3523337097897121, -1.2778512802331135, -1.2065926093943804, -1.138763470335744, -1.0744977119830654, -1.0138670264866738, -0.9568901525091555, -0.903541398761683, -0.8537584239994392, -0.8074492478643005, -0.7644984947795587, -0.7247728930624884 ], [ -1.0834634251433382, -1.1507949522348546, -1.2217982969715426, -1.2962969473852706, -1.3740352787982786, -1.4546691123013595, -1.5377567235377387, -1.6227507807358141, -1.708991813345564, -1.7957039525005623, -1.8819938392226083, -1.9668537565869433, -2.0491701860562612, -2.127739072781145, -2.2012890371060054, -2.268513485746229, -2.3281119386636075, -2.3788398179390264, -2.4195644896091335, -2.4493237564792416, -2.4673816855838377, -2.473275998961199, -2.4668513886583923, -2.448274001149751, -2.4180240984177868, -2.376866732731533, -2.3258037762127026, -2.2660136509053506, -2.198786450684985, -2.125461550702622, -2.047372876696483, -1.9658046730005099, -1.8819585649470858, -1.7969312766964505, -1.711701557609535, -1.627124555933076, -1.543931887748772, -1.4627358350396884, -1.3840363651626268, -1.3082299312733379, -1.235619256080299, -1.1664235062790227, -1.1007884301200068, -1.0387961594226942, -0.9804744757613694, -0.9258054145661735, -0.8747331359136933, -0.8271710312796082, -0.7830080649865514, -0.7421143701650738 ], [ -1.1024418914742222, -1.170139352965236, -1.2414407742628935, -1.316165872885267, -1.394057084928772, -1.4747705243787521, -1.5578673685523905, -1.6428061187963308, -1.7289363038448526, -1.8154943310324951, -1.901602345975686, -1.9862711255207957, -2.0684081793596722, -2.146832328171194, -2.220295985269934, -2.2875160881009937, -2.3472139884873338, -2.398163545787943, -2.439245242823504, -2.469502640408725, -2.488196336316345, -2.4948501296646297, -2.4892842933482533, -2.4716315351080707, -2.442332532683853, -2.4021103041140566, -2.3519259889164075, -2.292921737305569, -2.2263580278037485, -2.1535524182335495, -2.0758250146799972, -1.9944537200798782, -1.9106403135785146, -1.8254869557796543, -1.7399818566260816, -1.6549924693343288, -1.571264529253253, -1.4894254006372523, -1.409990424362562, -1.3333712102064226, -1.2598850523149343, -1.1897648495373145, -1.123169078934668, -1.0601915028378377, -1.0008703919702457, -0.9451971247483971, -0.8931240810073593, -0.8445717914201221, -0.7994353353002196, -0.7575900020403048 ], [ -1.116989584140146, -1.1846686293199187, -1.2558604456023277, -1.3303808956475012, -1.4079705997517582, -1.488286341207353, -1.570892891121068, -1.6552556786841166, -1.7407348473788786, -1.8265813721706183, -1.911936065272758, -1.9958324589918686, -2.0772046998837252, -2.1549016731003974, -2.2277085239760854, -2.2943764522092986, -2.3536610146247545, -2.404368132279445, -2.4454056474374277, -2.4758369122732966, -2.49493193489064, -2.502211324799296, -2.497478538967506, -2.480836445343799, -2.452685153547859, -2.4136999997254582, -2.364791576190803, -2.307052749088217, -2.2416993844219726, -2.1700114564348048, -2.0932797611628495, -2.0127614326134604, -1.9296455526595646, -1.8450287133514982, -1.759899502615815, -1.6751304564911562, -1.591475917549549, -1.5095743319067096, -1.429953708347995, -1.3530391874783563, -1.2791618882465678, -1.2085683945343808, -1.1414304086319318, -1.077854231086401, -1.017889830736003, -0.9615393491222437, -0.9087649444136463, -0.8594959255258602, -0.8136351606855727, -0.7710647689905296 ], [ -1.1271565232301506, -1.1944470935995761, -1.2651375843344987, -1.3390399801512638, -1.4158932623890301, -1.4953553068718273, -1.5769952116931816, -1.6602864631076832, -1.7446014580040479, -1.8292080308395655, -1.9132687783601023, -1.9958441258873012, -2.0759002093767482, -2.15232271152038, -2.2239377151671245, -2.289540328599533, -2.3479312038943045, -2.397960081924439, -2.438574265193965, -2.468868733000463, -2.488133845660403, -2.4958964271471444, -2.4919502852615487, -2.4763726313551224, -2.4495235587582425, -2.4120273239077306, -2.364736794126165, -2.308685232417262, -2.2450313737772527, -2.1750039255625357, -2.0998504809747303, -2.020794076728853, -1.938998888043757, -1.8555451899794406, -1.7714128219409992, -1.6874719197010668, -1.6044795169992805, -1.5230806549781388, -1.443812782498175, -1.367112420870575, -1.2933232635873877, -1.2227050637269876, -1.1554428191896164, -1.0916558962632683, -1.0314068366160787, -0.9747096748256485, -0.9215376566957224, -0.8718302964536974, -0.8254997466182578, -0.782436480498258 ], [ -1.1330516188950623, -1.199603962275188, -1.2694240072199718, -1.3423199750819088, -1.4180295219416412, -1.4962121741063303, -1.5764422188636609, -1.6582024443164567, -1.740879227145065, -1.823759588932161, -1.906030975718278, -1.9867846490529857, -2.0650236838094234, -2.1396766031828314, -2.209617577713911, -2.2736937916884807, -2.3307599679267748, -2.379719135221385, -2.419567640448837, -2.449441411009641, -2.4686598647368165, -2.4767637679009793, -2.4735435792752045, -2.4590551546433135, -2.433620273370297, -2.3978107808961364, -2.3524173579358587, -2.298406365995811, -2.2368698798447983, -2.168974351626092, -2.0959125157698795, -2.0188616925736764, -1.9389501269273233, -1.8572317430601055, -1.7746688267984112, -1.6921216448951673, -1.6103437958810223, -1.529982066390276, -1.4515796617319587, -1.3755818309374241, -1.3023430757878915, -1.2321352973369988, -1.1651563802879652, -1.1015388405696434, -1.0413582641429682, -0.9846413472549226, -0.9313734127875027, -0.8815053269801882, -0.8349597784074573, -0.7916369090870076 ], [ -1.1348365534750626, -1.200326325730071, -1.2689349927572255, -1.340467314407668, -1.4146601226714093, -1.4911753353139214, -1.5695934611796243, -1.6494079780431672, -1.7300210621466094, -1.8107412601340076, -1.890783812903269, -1.9692744528386656, -2.045257574585273, -2.117709682592415, -2.1855588877585936, -2.247710895840802, -2.303081355733883, -2.35063363064163, -2.389420136090823, -2.418624572953784, -2.4376018968968545, -2.445912783917095, -2.4433495388335746, -2.4299506990679225, -2.4060021398763904, -2.3720236401959047, -2.328741704615522, -2.277051463122525, -2.2179719243556564, -2.152599273918329, -2.0820623465665364, -2.0074832597843684, -1.929944916676032, -1.8504659699571064, -1.7699830191093582, -1.689339300450648, -1.6092788731384768, -1.5304452317577926, -1.4533833213964056, -1.3785440413052295, -1.3062904612688597, -1.236905116979409, -1.170597883441531, -1.1075140421425376, -1.0477422562221475, -0.991322248559926, -0.9382520422643694, -0.8884946737193121, -0.8419843274125048, -0.7986318713621224 ], [ -1.132718766608817, -1.1968510986277872, -1.2639400385515656, -1.333787394994021, -1.4061298814797067, -1.4806327406611823, -1.5568839029655872, -1.634389047168249, -1.7125680202627878, -1.7907531730579849, -1.8681902687440528, -1.94404270932168, -2.017399873830575, -2.087290334903295, -2.1527005682268454, -2.2125994450282676, -2.2659682747139294, -2.311835470329271, -2.349314148048192, -2.3776403125499166, -2.396208883013042, -2.4046047288103063, -2.402626026901476, -2.3902975474408428, -2.3678720199024847, -2.335818743942964, -2.2948001101437225, -2.245638327416695, -2.189275869631458, -2.126733589176213, -2.059070099042993, -1.9873451662320594, -1.912588822445452, -1.8357769390481908, -1.7578132658826913, -1.679517431059913, -1.6016181152434545, -1.5247504986436577, -1.449457078756823, -1.3761910265379265, -1.305321354134321, -1.2371392852570966, -1.1718653352177006, -1.1096567135464788, -1.050614754246744, -0.9947921561830751, -0.9421998794973442, -0.8928135947278257, -0.8465796212166792, -0.80342032218553 ], [ -1.1269438608144833, -1.1894563324772927, -1.2547529189500795, -1.3226331911506712, -1.3928346415268202, -1.4650269403393836, -1.5388067705051633, -1.6136935932725398, -1.6891267770574587, -1.7644646066856842, -1.8389857717094882, -1.9118939954574, -1.982326487640384, -2.049366850512644, -2.112062904322202, -2.1694495892651293, -2.2205766376629437, -2.2645401240265297, -2.3005163793571564, -2.327796225228791, -2.3458171545484032, -2.3541909974803468, -2.3527247253795025, -2.341432334751399, -2.320536284762115, -2.2904578472125348, -2.2517969448523503, -2.2053033441631147, -2.1518420546832324, -2.0923561998472073, -2.0278304348127785, -1.9592573646563958, -1.887608603234929, -1.8138113145269235, -1.7387304184939494, -1.6631561691413281, -1.587796517911759, -1.5132735288611754, -1.4401230734972477, -1.3687970656392205, -1.2996675702684528, -1.2330322132302605, -1.1691204161547613, -1.1081000741022855, -1.0500843773370074, -0.9951385511988863, -0.9432863489316677, -0.8945161821881932, -0.8487868139301584, -0.8060325699108432 ] ], "zauto": true, "zmax": 2.502211324799296, "zmin": -2.502211324799296 }, { "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": [ [ 0.719176210827855, 0.7173592108172676, 0.7156441070095164, 0.7140503866346992, 0.7125963622099276, 0.7112987142396288, 0.7101720670299172, 0.7092286155970006, 0.7084778198174039, 0.7079261792101031, 0.7075770982286033, 0.7074308478759208, 0.7074846250501242, 0.7077327064986189, 0.7081666898271073, 0.7087758099072421, 0.7095473155017471, 0.7104668882258042, 0.711519084313504, 0.7126877792219338, 0.7139565959485201, 0.715309300000745, 0.7167301470534442, 0.7182041731602581, 0.71971742158596, 0.7212571045114721, 0.722811701683733, 0.7243710012642312, 0.7259260904993662, 0.7274693053257942, 0.7289941486639975, 0.7304951870480261, 0.7319679345413509, 0.7334087317718256, 0.7348146265544842, 0.7361832611116736, 0.7375127694686245, 0.7388016872881424, 0.7400488752671596, 0.7412534562784087, 0.7424147657081611, 0.7435323139055513, 0.744605759300332, 0.7456348905388279, 0.7466196159057685, 0.7475599583170034, 0.7484560542614056, 0.7493081552189998, 0.7501166302686862, 0.7508819688077495 ], [ 0.7140189273909304, 0.7119223640512592, 0.7099389269136779, 0.7080914928693485, 0.7064016735375263, 0.70488926640677, 0.7035717401944309, 0.7024637764726194, 0.7015768877533214, 0.7009191292297976, 0.7004949174130024, 0.7003049641862567, 0.7003463295446092, 0.700612590713158, 0.701094119702831, 0.7017784559600732, 0.702650755948369, 0.7036942976481847, 0.704891015447473, 0.7062220400058764, 0.7076682185522452, 0.7092105936628953, 0.7108308226103214, 0.7125115244426173, 0.7142365475231751, 0.7159911557784083, 0.7177621368772613, 0.719537839628366, 0.7213081508086582, 0.7230644233658163, 0.724799368535142, 0.7265069240477041, 0.7281821095067702, 0.7298208784186875, 0.731419974514646, 0.7329767980890762, 0.7344892862608916, 0.7359558094391019, 0.737375084903572, 0.7387461073171028, 0.7400680951614618, 0.741340451514363, 0.742562737223749, 0.7437346543534842, 0.7448560377348328, 0.7459268525280957, 0.7469471958499538, 0.7479173007301847, 0.7488375409062242, 0.7497084352286214 ], [ 0.708377260755272, 0.7059643384931521, 0.7036760934173111, 0.7015393021752563, 0.6995794077610538, 0.6978198635196856, 0.6962815105892619, 0.6949820156085901, 0.6939353938124142, 0.693151639556268, 0.6926364820209933, 0.6923912785242521, 0.6924130516965915, 0.6926946699677513, 0.6932251636243056, 0.6939901615211058, 0.694972426861929, 0.6961524649087236, 0.6975091716410773, 0.6990204907624192, 0.700664047300662, 0.7024177293336108, 0.7042601947188369, 0.7061712864976744, 0.7081323480970473, 0.7101264367765767, 0.7121384402711799, 0.7141551067605453, 0.7161650018853828, 0.7181584084797552, 0.720127185138089, 0.7220645989514298, 0.7239651460625367, 0.7258243714462305, 0.7276386968311367, 0.7294052631950041, 0.7311217919724572, 0.7327864671272343, 0.7343978386167669, 0.7359547465248405, 0.7374562642351162, 0.7389016584224074, 0.7402903632992915, 0.7416219664216944, 0.742896203381315, 0.7441129588544088, 0.7452722717015531, 0.746374342094004, 0.7474195389567133, 0.7484084063477863 ], [ 0.7022387505600894, 0.69946927890335, 0.6968360805877714, 0.6943703937616074, 0.6921020908954261, 0.690058898691789, 0.6882656477042609, 0.6867435839756524, 0.6855097737337632, 0.6845766293036365, 0.6839515800239631, 0.6836369061926246, 0.6836297469966719, 0.6839222851276356, 0.6845021015994796, 0.6853526846549264, 0.6864540673094672, 0.6877835599878209, 0.6893165388501333, 0.6910272476153089, 0.6928895714288124, 0.6948777455583982, 0.6969669688931004, 0.6991339014278691, 0.7013570349847565, 0.7036169361977459, 0.7058963693025155, 0.7081803128593174, 0.7104558888790385, 0.7127122249248814, 0.7149402698824154, 0.7171325826460054, 0.7192831104440158, 0.7213869703935858, 0.7234402445497093, 0.7254397955113474, 0.7273831067861899, 0.7292681497173827, 0.7310932768836587, 0.7328571404850296, 0.7345586332690699, 0.7361968489688299, 0.7377710589388091, 0.7392807016207146, 0.7407253815857469, 0.7421048751356172, 0.7434191397614328, 0.7446683251277739, 0.7458527836449748, 0.7469730790969257 ], [ 0.6955980517770479, 0.6924285085674508, 0.6894065090856291, 0.6865683622895898, 0.6839490345141284, 0.6815812275029526, 0.6794944780300719, 0.677714317494308, 0.6762615294703146, 0.6751515410109606, 0.6743939795297734, 0.6739924212731024, 0.6739443495818829, 0.6742413312656579, 0.6748694076428422, 0.6758096837487495, 0.6770390859867499, 0.6785312466058541, 0.6802574644581093, 0.6821876868957517, 0.6842914581847077, 0.686538785406516, 0.688900882660752, 0.6913507670233047, 0.693863693431645, 0.6964174287766388, 0.6989923766283427, 0.7015715723445418, 0.7041405734633401, 0.7066872723822367, 0.709201657827988, 0.7116755491658184, 0.714102323880535, 0.7164766542353633, 0.7187942647123231, 0.7210517177516911, 0.7232462317822176, 0.7253755326843235, 0.7274377376715877, 0.7294312690591571, 0.7313547944202581, 0.7332071891078371, 0.7349875169338634, 0.736695024862683, 0.7383291478125309, 0.7398895200134161, 0.7413759897973227, 0.7427886351664658, 0.7441277779735542, 0.7453939950359482 ], [ 0.6884586366243505, 0.6848423653212323, 0.6813841007120219, 0.678125870711568, 0.6751084628364596, 0.6723703427499871, 0.669946579983798, 0.6678678255959583, 0.6661593876419968, 0.664840449629636, 0.6639234744172525, 0.6634138308874047, 0.6633096726052952, 0.6636020860709474, 0.664275511060664, 0.6653084176865348, 0.6666742058642252, 0.6683422752867925, 0.6702792004148602, 0.6724499376587323, 0.6748189920964134, 0.6773514786788397, 0.6800140265848907, 0.6827754929607175, 0.6856074710974468, 0.6884845957256565, 0.6913846626658814, 0.6942885904798152, 0.6971802577062122, 0.7000462510709234, 0.7028755584947468, 0.7056592367569328, 0.7083900782963114, 0.711062295720489, 0.7136712368288862, 0.7162131378026172, 0.7186849179331015, 0.7210840159416835, 0.7234082655502844, 0.7256558063866343, 0.7278250253983498, 0.729914523553283, 0.731923102578424, 0.733849766719949, 0.7356937349037687, 0.737454459175068, 0.73913164585253, 0.7407252764177855, 0.7422356257513933, 0.7436632759062841 ], [ 0.6808346004782453, 0.676722182276961, 0.67277682000904, 0.6690469324917069, 0.6655799097029546, 0.6624208560285079, 0.6596113175644636, 0.657188044334789, 0.6551818418293903, 0.6536165682713921, 0.6525083339809673, 0.6518649561042137, 0.6516857144414584, 0.6519614408689135, 0.6526749554171812, 0.6538018373748576, 0.6553114924042668, 0.6571684504865063, 0.6593338088913367, 0.6617667229348245, 0.664425847008532, 0.6672706390465145, 0.6702624610447793, 0.6733654329316249, 0.6765470230500785, 0.6797783822213886, 0.6830344472744588, 0.6862938527388861, 0.6895386959467051, 0.6927542017853843, 0.6959283300366791, 0.6990513620652551, 0.702115495969468, 0.705114471328658, 0.7080432372241744, 0.7108976708053019, 0.7136743485660223, 0.71637036872549, 0.7189832205475727, 0.7215106948940205, 0.7239508295545685, 0.7263018827182172, 0.728562328158222, 0.7307308661558635, 0.7328064447830053, 0.7347882868335174, 0.7366759183969055, 0.738469195778228, 0.7401683281694258, 0.7417738941547894 ], [ 0.6727525089799807, 0.6680923566936108, 0.663606155107139, 0.6593493864111611, 0.6553768614471998, 0.6517412761149971, 0.648491717072004, 0.6456721723843025, 0.6433201099893648, 0.6414651933678257, 0.6401282087084945, 0.63932027906576, 0.6390424357605137, 0.6392856028593672, 0.6400310256005741, 0.6412511391966674, 0.6429108345240898, 0.6449690381156095, 0.6473804926670197, 0.6500976068069938, 0.6530722421651441, 0.6562573212719107, 0.6596081678568078, 0.6630835260854804, 0.6666462412066099, 0.6702636159015465, 0.6739074809814769, 0.67755403450558, 0.6811835101028897, 0.6847797346340283, 0.688329629296754, 0.6918226989612828, 0.6952505438078681, 0.6986064167182922, 0.7018848403624719, 0.7050812900904365, 0.7081919427850385, 0.7112134876770245, 0.7141429925279799, 0.7169778172264188, 0.7197155663868985, 0.7223540726969137, 0.7248914032865916, 0.7273258821325558, 0.7296561223394092, 0.7318810630057144, 0.7340000062426144, 0.7360126507561865, 0.7379191192200562, 0.7397199774441932 ], [ 0.6642531946916455, 0.6589924201389344, 0.6539094593628606, 0.6490674974147063, 0.6445295941479169, 0.640357050054931, 0.6366076716447938, 0.6333339938473064, 0.6305815293270624, 0.6283871282699944, 0.6267775455077114, 0.6257683211259567, 0.6253630807667322, 0.6255533474259538, 0.6263189245799724, 0.6276288620841227, 0.6294429576860217, 0.6317136884179845, 0.6343884190731788, 0.6374117087706035, 0.640727535761855, 0.644281283791203, 0.6480213742667406, 0.6519004783529725, 0.6558762928447772, 0.6599119061719239, 0.6639758118133685, 0.6680416443895123, 0.672087719695469, 0.6760964563503508, 0.6800537465960075, 0.6839483300709585, 0.687771209636802, 0.6915151344089279, 0.6951741632116758, 0.6987433122956758, 0.7022182843982417, 0.7055952718474204, 0.7088708239779226, 0.7120417681537096, 0.7151051737141478, 0.7180583487921135, 0.7208988609054208, 0.7236245733062967, 0.726233690177155, 0.7287248048325524, 0.7310969461104775, 0.7333496191108111, 0.735482837367839, 0.7374971444255732 ], [ 0.6553933770593485, 0.6494789852377286, 0.6437422354655257, 0.6382545766733341, 0.6330881148592711, 0.6283137972258664, 0.623999427658239, 0.6202075673092712, 0.6169933934153529, 0.6144026138465614, 0.6124695618163862, 0.6112156184997485, 0.6106481218579891, 0.6107599080680775, 0.6115295913503208, 0.6129226196093367, 0.6148930568352238, 0.6173859552787139, 0.6203401097042354, 0.6236909473639095, 0.6273733072396801, 0.6313238975279963, 0.6354832807309008, 0.6397973069916648, 0.6442179850247658, 0.6487038362278532, 0.6532198161101593, 0.6577369071697222, 0.6622314911053911, 0.6666845997943432, 0.6710811283250716, 0.6754090736924548, 0.6796588428175008, 0.6838226556030883, 0.6878940540481114, 0.6918675174693387, 0.6957381764803134, 0.6995016140355895, 0.7031537398785103, 0.7066907244231093, 0.7101089788294184, 0.7134051693068229, 0.7165762551633144, 0.7196195416072069, 0.7225327397059661, 0.7253140271886566, 0.7279621049559267, 0.7304762452583463, 0.7328563285395695, 0.735102866922443 ], [ 0.6462469402326434, 0.6396273991711565, 0.6331801938480076, 0.6269854612890333, 0.6211250630692745, 0.6156806152811855, 0.6107312602100421, 0.6063512204924142, 0.6026072045529377, 0.5995557717660612, 0.5972408138056023, 0.5956913552480702, 0.5949199061100509, 0.5949215944145811, 0.5956742561120195, 0.5971395627572439, 0.599265139343369, 0.6019874926118217, 0.6052354643425396, 0.6089338679820223, 0.6130069696624262, 0.617381529735745, 0.6219892105136621, 0.6267682577757349, 0.6316644579672224, 0.6366314465027678, 0.6416304893987763, 0.6466298810836181, 0.651604100291221, 0.6565328498817851, 0.661400081805188, 0.6661930808113479, 0.6709016540476815, 0.6755174509741687, 0.6800334203334091, 0.6844433984518778, 0.6887418154214452, 0.6929235018192994, 0.696983577531934, 0.7009174049677929, 0.7047205906546237, 0.708389021322511, 0.7119189226922509, 0.7153069311265996, 0.7185501699982862, 0.7216463241033809, 0.7245937067565277, 0.7273913154026369, 0.7300388727080835, 0.7325368511697357 ], [ 0.636905662395685, 0.6295328836815551, 0.6223208580754804, 0.6153586278475968, 0.6087383579491106, 0.6025532650230787, 0.5968951755199576, 0.5918517263955203, 0.5875032595854841, 0.5839195217568747, 0.581156360209224, 0.579252689496547, 0.5782280658244783, 0.5780812177653856, 0.5787898201077816, 0.5803116603120199, 0.5825871573631428, 0.5855429945556958, 0.5890964700986239, 0.5931600891636567, 0.5976459305453885, 0.602469407417693, 0.6075521746932786, 0.6128240805590276, 0.6182241881559691, 0.6237009877846259, 0.6292119748714813, 0.6347227875361906, 0.6402060882527427, 0.6456403466960593, 0.6510086445984793, 0.6562975855952771, 0.661496358620954, 0.6665959752798367, 0.6715886808340719, 0.6764675248135502, 0.68122606972255, 0.6858582134675194, 0.690358101465655, 0.6947201065856901, 0.6989388580839552, 0.7030093038254572, 0.7069267929232357, 0.7106871683327953, 0.7142868609069862, 0.717722978040726, 0.7209933814296701, 0.7240967497322855, 0.7270326231251839, 0.7298014279017598 ], [ 0.6274791532953531, 0.6193108904882217, 0.6112844248112389, 0.603497635616577, 0.5960532875157051, 0.589056944432602, 0.5826143785203306, 0.5768284395421815, 0.571795397038972, 0.5676008540571778, 0.564315455202553, 0.5619907524422858, 0.5606557089591497, 0.5603143641999135, 0.5609451118686243, 0.5625018488863978, 0.5649169727023575, 0.568105907410231, 0.5719726054268678, 0.576415358535083, 0.5813322759154376, 0.5866259222138842, 0.5922068056833627, 0.5979956115280644, 0.6039242480800494, 0.6099358920527646, 0.6159842803075315, 0.6220325077032531, 0.6280515675720147, 0.6340188277562663, 0.6399165834119107, 0.6457307771028323, 0.6514499328915964, 0.6570643170542617, 0.662565314350669, 0.6679449945587806, 0.6731958374361616, 0.67831058326394, 0.6832821785882445, 0.6881037909669232, 0.6927688711856367, 0.697271245736141, 0.7016052259724249, 0.7057657232030242, 0.709748361151431, 0.7135495789130724, 0.7171667189520782, 0.720598095966213, 0.7238430436938694, 0.7269019379724623 ], [ 0.6180937327605645, 0.6090963587906706, 0.6002135229620654, 0.591551510366028, 0.5832236300224176, 0.5753482382923002, 0.5680461071853553, 0.5614370277826042, 0.5556355906813681, 0.5507462020577961, 0.5468575782669836, 0.5440371866736654, 0.5423263040173689, 0.541736463403385, 0.5422479858747761, 0.5438110220158887, 0.546349115807223, 0.5497648600600947, 0.5539468682812031, 0.5587771313098965, 0.5641378778656324, 0.5699172694292702, 0.5760135495471811, 0.5823375545177911, 0.5888137204160939, 0.5953798663175661, 0.6019860970956763, 0.6085931680459915, 0.6151706097741411, 0.6216948459267503, 0.6281474647152724, 0.6345137388908414, 0.6407814342603788, 0.6469399065851875, 0.6529794606153833, 0.6588909311590636, 0.6646654416242289, 0.6702942973448208, 0.6757689764318138, 0.6810811876794715, 0.686222971705514, 0.6911868271764187, 0.6959658483674381, 0.700553863500924, 0.7049455655652734, 0.7091366289700777, 0.7131238067365383, 0.7169050041674, 0.7204793262009149, 0.7238470969558897 ], [ 0.6088899853581509, 0.5990415424420313, 0.5892714704261235, 0.5796936019157435, 0.570431285740527, 0.5616156837353112, 0.5533832588174041, 0.5458722354420447, 0.5392178607342174, 0.5335464416210407, 0.528968394183112, 0.5255708849646943, 0.5234109805926144, 0.5225104198299386, 0.5228530582646017, 0.5243856646087709, 0.5270221444228045, 0.5306506108127081, 0.5351422172463884, 0.5403604539374935, 0.5461697073442935, 0.5524422082206301, 0.5590629148622811, 0.5659322738487587, 0.5729670959967696, 0.58009995624114, 0.5872775848361139, 0.5944586933431925, 0.6016116052370518, 0.6087119657117196, 0.6157407088518216, 0.6226823756252231, 0.6295238097417434, 0.6362532121650062, 0.6428595075627795, 0.6493319638796955, 0.6556600052963256, 0.6618331648806831, 0.6678411326196357, 0.6736738645371745, 0.6793217275628123, 0.6847756618987934, 0.690027347718846, 0.6950693664090283, 0.6998953487223698, 0.7045001036709526, 0.708879723136675, 0.7130316583184672, 0.7169547653787018, 0.7206493190179057 ], [ 0.60001877142306, 0.5893120987014109, 0.5786386207137816, 0.5681184019888763, 0.5578838017803885, 0.5480782419279988, 0.5388540277192431, 0.5303688565637922, 0.522780675223655, 0.516240716261071, 0.5108848945843583, 0.5068242471823733, 0.5041356307517826, 0.5028542499971901, 0.5029695674843238, 0.5044256499064935, 0.5071261373283182, 0.5109430591246314, 0.5157279877212925, 0.5213237330780356, 0.5275749565896657, 0.5343365772492609, 0.5414794461625239, 0.5488933018884209, 0.5564873931653519, 0.5641893490459076, 0.5719429193840043, 0.5797051494530946, 0.5874434382303455, 0.5951327972497124, 0.6027535005906826, 0.6102892107837714, 0.6177255864394616, 0.6250493258099727, 0.6322475730953656, 0.6393076058344159, 0.6462167261818723, 0.6529622906161179, 0.6595318270419956, 0.6659132021307623, 0.6720948132390139, 0.6780657877028369, 0.6838161778685286, 0.6893371435188669, 0.6946211151657684, 0.6996619327315082, 0.704454954979085, 0.7089971360085231, 0.7132870663411314, 0.71732497754929 ], [ 0.5916355796120784, 0.5800812223278051, 0.5685064569562766, 0.557035831475358, 0.5458091352761578, 0.5349808532377108, 0.5247185741048631, 0.5151998068771335, 0.506606638545701, 0.4991178406370199, 0.4928984746542844, 0.4880877465475274, 0.48478666263857273, 0.4830476458362753, 0.48286834678215007, 0.48419124728530105, 0.4869094285317893, 0.4908774841033367, 0.49592550470004176, 0.5018736760436121, 0.508545326266244, 0.5157769916888831, 0.52342491744422, 0.5313681222355534, 0.5395086184818018, 0.5477695872160682, 0.5560923195679159, 0.5644326273491161, 0.5727572583465493, 0.5810406734408232, 0.5892623812679211, 0.5974048968875046, 0.605452299130091, 0.6133893056091559, 0.6212007592143345, 0.6288714174729859, 0.6363859482398099, 0.6437290543633994, 0.6508856705784716, 0.6578411941660773, 0.6645817250666687, 0.6710943007539331, 0.6773671168775628, 0.6833897275291013, 0.6891532201270042, 0.6946503603335287, 0.6998757027921213, 0.7048256641831666, 0.7094985562485389, 0.7138945779578071 ], [ 0.5838932828207778, 0.5715217902572921, 0.5590692621393853, 0.5466626465180048, 0.5344470835294459, 0.5225862506717042, 0.5112616283193778, 0.5006699335988478, 0.49101787268026914, 0.4825135080597021, 0.47535405877322134, 0.4697108768172879, 0.4657134960588182, 0.46343561711425646, 0.462886154460636, 0.464007698070271, 0.46668306236911034, 0.47074862227482034, 0.4760116427961763, 0.48226829398094434, 0.4893195069741362, 0.4969828824904686, 0.5051000265729578, 0.5135396153289268, 0.5221970464996347, 0.530991746871188, 0.5398631691104352, 0.5487663358826597, 0.5576675569781075, 0.5665407122979796, 0.5753642920638149, 0.5841192307960715, 0.5927874672210972, 0.6013511043560381, 0.6097920238480196, 0.6180918152199196, 0.6262319029565203, 0.6341937829042474, 0.6419593073507828, 0.6495109812729687, 0.6568322489262723, 0.6639077603437971, 0.6707236126426732, 0.6772675629496476, 0.6835292098489228, 0.6895001397804746, 0.695174034589659, 0.7005467368386844, 0.7056162705947273, 0.710382817050963 ], [ 0.5769336060296234, 0.5637967625569651, 0.5505134977479426, 0.5372109192333847, 0.5240370889547782, 0.5111624185019251, 0.49878003331395826, 0.48710414254962975, 0.4763652435748629, 0.46680106669343197, 0.4586427307832492, 0.452096732945472, 0.44732496433188457, 0.44442639570255665, 0.4434246510461576, 0.4442648203735812, 0.4468206465700683, 0.4509105033320395, 0.4563185033889456, 0.4628163846085679, 0.47018250366730696, 0.4782157353128427, 0.48674362991533343, 0.495625359799216, 0.5047506394015474, 0.5140360054018994, 0.5234197420219162, 0.5328564787714661, 0.5423121785460646, 0.5517599384222329, 0.5611767789927319, 0.5705414157729387, 0.5798328898465427, 0.5890298772501897, 0.5981104848412488, 0.6070523594714307, 0.6158329726874069, 0.6244299830382837, 0.6328216142437699, 0.6409870156060747, 0.6489065899165056, 0.6565622846513081, 0.663937846541563, 0.6710190400061737, 0.6777938285545881, 0.684252516638945, 0.6903878484794724, 0.6961950604675958, 0.7016718848321531, 0.7068185040616651 ], [ 0.5708779065368333, 0.5570484470120217, 0.543005455781113, 0.5288740446312713, 0.5148026634890787, 0.5009656218587146, 0.487564712800342, 0.47482878322746125, 0.4630097529436503, 0.4523735482424374, 0.44318497087559705, 0.4356868676301146, 0.4300759747867966, 0.42647985082110035, 0.4249403436070328, 0.4254081751919216, 0.42775044512980875, 0.43176924909893344, 0.4372267931292967, 0.4438714440740787, 0.45146008487252687, 0.45977410025048226, 0.46862833174325474, 0.47787380395932433, 0.48739578222312996, 0.4971089030993545, 0.5069509390868643, 0.5168764058565536, 0.5268508232968736, 0.5368460754488955, 0.5468370177738755, 0.5567992683497746, 0.5667079921106497, 0.5765374328256562, 0.5862609482245172, 0.5958513392350487, 0.6052813159313498, 0.6145239958798842, 0.623553375770434, 0.6323447502152112, 0.6408750719881553, 0.6491232578119331, 0.657070446233258, 0.6647002123726472, 0.6719987410401757, 0.6789549566853211, 0.6855606068684501, 0.6918102956915321, 0.6977014647292044, 0.7032343210335775 ], [ 0.5658181505864885, 0.5513876202116089, 0.5366782575751684, 0.5218113731717596, 0.5069334698067455, 0.492219856979129, 0.4778775676201963, 0.46414626905907136, 0.45129537952023735, 0.43961542141814375, 0.42940212851280796, 0.4209332883279671, 0.4144407083405594, 0.4100823596732695, 0.40792137013344987, 0.4079178278448354, 0.409936075760557, 0.4137656276468607, 0.41915015386054033, 0.4258176987698095, 0.4335064420847013, 0.44198279360858234, 0.4510511259475004, 0.4605562273171092, 0.4703804304348812, 0.48043753591519434, 0.49066538458302744, 0.5010184782675954, 0.5114615557653773, 0.5219645861367699, 0.5324992889690278, 0.5430370473172517, 0.5535479413334258, 0.5640005829067904, 0.5743624494270326, 0.5846004711731894, 0.5946816978815731, 0.6045739380679968, 0.6142463192907067, 0.6236697548805974, 0.6328173235943131, 0.6416645767020784, 0.6501897866689599, 0.6583741469929967, 0.6662019271330423, 0.673660581829822, 0.6807408114588617, 0.6874365694996716, 0.6937450143934941, 0.6996664053824854 ], [ 0.5618091683351584, 0.5468838095247299, 0.531619740043767, 0.5161332395708443, 0.5005670212636213, 0.48509479061074995, 0.4699253341846835, 0.4553047339452334, 0.4415147008026033, 0.4288646946606301, 0.4176758709614821, 0.40825638558189664, 0.40087028092922705, 0.3957053990800345, 0.39284801845861506, 0.3922715173189293, 0.39384277576058435, 0.39734462610083826, 0.4025080725721928, 0.4090462535185069, 0.4166833890207094, 0.4251749043732477, 0.43431793375897243, 0.4439535207624567, 0.45396284592063985, 0.4642599737622019, 0.47478327435085915, 0.4854871194348626, 0.4963348600306894, 0.5072935617287253, 0.518330558723689, 0.5294116082010878, 0.5405002795712762, 0.5515581759493676, 0.5625456252160145, 0.5734225597858035, 0.5841493977451074, 0.5946878223195141, 0.605001420588238, 0.6150561831149677, 0.624820886360114, 0.6342673847816392, 0.6433708354055876, 0.6521098695396675, 0.660466717953998, 0.6684272894545763, 0.6759811992017928, 0.6831217423141228, 0.6898458096368777, 0.696153745224036 ], [ 0.5588633001012515, 0.5435581602549756, 0.5278630318657939, 0.5118886346861304, 0.4957727449530371, 0.47968545262468176, 0.4638341561506998, 0.44846685253769747, 0.43387159660463404, 0.42036956006812093, 0.4082993702166938, 0.3979918424785031, 0.3897370313421172, 0.38374911930379957, 0.38013746143530797, 0.3788921431808327, 0.37988879331776304, 0.3829114257548471, 0.3876867008151326, 0.39392069614377795, 0.4013304785779785, 0.4096660277622774, 0.41872150268102104, 0.4283372900415136, 0.43839546308861127, 0.44881148260318415, 0.4595245905763959, 0.4704887055048435, 0.48166493438055485, 0.49301619239566924, 0.5045039352299172, 0.51608668964262, 0.5277199121218631, 0.5393566830104813, 0.5509488109856125, 0.5624480345392407, 0.5738071258876624, 0.5849808041719734, 0.5959264375594714, 0.6066045567087288, 0.61697922002281, 0.6270182718185099, 0.6366935256562126, 0.6459808928301102, 0.6548604646244619, 0.6633165486545304, 0.6713376551293955, 0.678916427855456, 0.6860495163504192, 0.6927373884979002 ], [ 0.5569483573408097, 0.5413801464707358, 0.5253815231672929, 0.5090578039417687, 0.49254142709200827, 0.4759976011081301, 0.4596298363778361, 0.4436839311269806, 0.42844826892596427, 0.4142477804411788, 0.4014290735189322, 0.39033555929609165, 0.38127415845810786, 0.37447887439588157, 0.3700796430336889, 0.368085347931943, 0.3683865536975207, 0.3707774186993265, 0.3749903676130152, 0.38073424414789125, 0.38772756646897966, 0.39572181914623933, 0.4045134253122164, 0.4139457899511853, 0.42390420931706063, 0.43430674594433916, 0.4450937932568456, 0.4562183522047937, 0.4676382534161982, 0.47931083424214144, 0.49119001418811464, 0.5032253483396102, 0.5153624741494149, 0.5275443637865124, 0.5397128947088216, 0.5518103972465117, 0.5637809843101693, 0.5755715872285048, 0.5871327022458332, 0.5984188955571319, 0.609389128855355, 0.620006962394427, 0.6302406779978416, 0.6400633475036596, 0.649452857425384, 0.6583918903424896, 0.6668678581494605, 0.6748727811064074, 0.6824031084342711, 0.6894594796718135 ], [ 0.555989416968057, 0.5402689129288522, 0.5240894049041228, 0.5075515008403902, 0.49078253644271697, 0.4739422907076707, 0.457228645041748, 0.44088180983530867, 0.42518505222167163, 0.41045935740860423, 0.3970495587266704, 0.3853006666677418, 0.37552568913253737, 0.36796977322279223, 0.3627786493001253, 0.3599801595436915, 0.3594848196343604, 0.3611056248824308, 0.3645913674565525, 0.36966443720346037, 0.37605449409091374, 0.3835224583352582, 0.39187301181754125, 0.4009567610279295, 0.410664849845151, 0.4209192825597771, 0.4316619119387104, 0.442844324336924, 0.45441998209199286, 0.4663391552088552, 0.47854652039819745, 0.49098089212684165, 0.5035763786562105, 0.5162642766636025, 0.5289751569333927, 0.5416407780947325, 0.5541956410314393, 0.5665781327520101, 0.5787312954386752, 0.5906032984501874, 0.6021476996190404, 0.6133235702512233, 0.6240955371165606, 0.634433772592225, 0.6443139458578441, 0.6537171357124585, 0.6626296992837504, 0.6710430895572596, 0.6789536167093342, 0.686362152111398 ], [ 0.5558744232598835, 0.5400993433215593, 0.5238480804772307, 0.5072175345526954, 0.490330587898711, 0.47334158824206235, 0.45644174951280136, 0.43986317726799845, 0.42387960293742055, 0.40880146952809754, 0.39496311572546616, 0.3827008776003225, 0.37232320525724294, 0.3640770544880878, 0.3581177135688159, 0.3544901638822567, 0.35312782288514094, 0.35386950362549124, 0.3564898630760606, 0.3607351307786179, 0.3663557756922926, 0.37313031564399574, 0.38087799828214625, 0.38946110372144754, 0.3987794706725004, 0.40876053870699997, 0.41934802883823685, 0.4304916862867552, 0.44213957331628806, 0.45423346778133383, 0.4667071751225561, 0.4794870952378786, 0.49249420814842754, 0.5056466916901765, 0.5188625670672247, 0.5320619945464521, 0.5451690478172877, 0.5581129483751861, 0.5708288330026965, 0.5832581663135447, 0.5953489117195894, 0.607055554075151, 0.6183390388068429, 0.629166664584553, 0.6395119445547351, 0.6493544366730044, 0.6586795364197179, 0.6674782236602055, 0.675746757700645, 0.683486318858338 ], [ 0.5564630147540072, 0.5407122073796498, 0.5244777575582115, 0.5078539168612755, 0.49095992411428613, 0.47394501080535345, 0.4569932318641359, 0.44032693419261937, 0.42420715032987333, 0.40892885936859324, 0.3948091968344156, 0.3821676557515807, 0.37129927511837857, 0.36244448286328057, 0.3557617263046957, 0.3513099214448859, 0.3490460406903863, 0.34883904040775504, 0.35049648041390846, 0.3537968118453291, 0.3585197104439092, 0.364468734436803, 0.37148366753875767, 0.37944282239185206, 0.38825757814984246, 0.3978623515388915, 0.40820321417264627, 0.4192277378587196, 0.43087767162385276, 0.44308502311949877, 0.4557712735427617, 0.46884893540213457, 0.48222448222569014, 0.49580176274970705, 0.5094852436310321, 0.5231826962983208, 0.5368071811844316, 0.5502783511004558, 0.5635231901638177, 0.5764763384732087, 0.5890801453331296, 0.6012845644136977, 0.6130469677527646, 0.624331921738253, 0.6351109422084862, 0.6453622290723674, 0.65507037258959, 0.6642260217065742, 0.672825507326431, 0.6808704180073819 ], [ 0.5575975576588122, 0.5419271399629236, 0.525772695438643, 0.5092267483522002, 0.49240565614597465, 0.4754539657964149, 0.45854846481885775, 0.4419008628886837, 0.42575762609668144, 0.4103952506219029, 0.39610944885222554, 0.38319757622018435, 0.37193525323887644, 0.36255028912841036, 0.3551989749297843, 0.34995055550427145, 0.34678440413086786, 0.3456011908513733, 0.34624534849977184, 0.3485331106761513, 0.3522795076431209, 0.3573189759568629, 0.3635167539663018, 0.3707708934381403, 0.37900676582539805, 0.3881670753092168, 0.3982006052879922, 0.4090523895883568, 0.42065700027635494, 0.4329355237499696, 0.4457958615331059, 0.45913542258645806, 0.4728450966342968, 0.48681352204889733, 0.5009309474329529, 0.515092305353216, 0.5291993857440923, 0.5431621790746947, 0.5568995546956572, 0.5703394663156829, 0.5834188587535276, 0.5960834103223878, 0.6082872000970678, 0.6199923492394065, 0.6311686554690206, 0.6417932207268808, 0.6518500627760787, 0.6613296994837138, 0.6702286971689574, 0.678549179337574 ], [ 0.5591151431677248, 0.5435568889788052, 0.5275181302467477, 0.5110903281882527, 0.4943875500450607, 0.4775500837104757, 0.460747607019415, 0.4441809832261677, 0.42808145090971106, 0.4127058462017021, 0.39832672164095634, 0.3852169776200239, 0.37362994131774707, 0.3637774966154869, 0.35581034360753394, 0.34980500331795494, 0.3457612011123941, 0.34361079240717096, 0.34323625798245627, 0.34449424775030574, 0.34723866539182374, 0.35133854103050877, 0.35668788239181237, 0.3632070065673375, 0.3708368545137737, 0.37952907025399746, 0.38923502199964205, 0.3998965075929552, 0.4114398790096532, 0.4237741237810273, 0.436792424755542, 0.450376110354116, 0.4643997430555821, 0.47873626685991094, 0.493261479270262, 0.5078574617530415, 0.5224149015990261, 0.5368344317393513, 0.551027207901279, 0.5649149592286403, 0.5784297185935279, 0.5915133877612733, 0.6041172384723305, 0.6162014040608685, 0.6277343821119885, 0.6386925473928424, 0.6490596639984232, 0.6588263834141138, 0.6679897179937196, 0.6765524845980614 ], [ 0.5608593141261978, 0.5454212728959519, 0.5295068941467251, 0.5132069455506381, 0.49663358436605826, 0.47992321192112714, 0.46323875534517767, 0.44677058811850484, 0.4307350979407746, 0.4153698684175206, 0.40092469242985374, 0.3876482847072496, 0.3757716077344247, 0.3654899786300403, 0.3569471792733788, 0.35022512541943757, 0.34534186961361274, 0.342258843253239, 0.34089584883828233, 0.3411502776683771, 0.3429160935479702, 0.34609852494738774, 0.3506218597474548, 0.35642968421798243, 0.3634787840971471, 0.3717292707403325, 0.38113401626313065, 0.39163012427712685, 0.4031341474651154, 0.41554150338339263, 0.4287294617312625, 0.44256244779414655, 0.4568982726215951, 0.47159413382769, 0.4865116391831005, 0.5015205211477564, 0.5165010344992792, 0.5313452282557547, 0.5459573686829671, 0.5602537939482929, 0.5741624373352133, 0.5876221930458194, 0.6005822356222958, 0.6130013515648587, 0.6248473039660931, 0.6360962277966387, 0.6467320423913488, 0.6567458653163603, 0.666135414798866, 0.6749043934805324 ], [ 0.5626904811549002, 0.5473595497328391, 0.531554097966767, 0.5153642931285227, 0.4989005662752202, 0.4822957502605533, 0.46570654232675357, 0.44931363906737887, 0.4333197727399464, 0.4179449037000585, 0.40341808438095067, 0.38996606334112094, 0.3777995143419072, 0.3670986915316032, 0.3580010261991628, 0.35059333443100477, 0.34491064850748554, 0.3409422586867246, 0.3386437532672386, 0.3379522842886139, 0.3388014995251327, 0.34113279383586204, 0.34490062500194335, 0.35007126400560246, 0.35661605721988604, 0.36450160063841314, 0.37367978881747377, 0.38408036845197313, 0.3956075883207501, 0.4081412301419364, 0.42154119835133974, 0.4356542358218208, 0.4503212574677371, 0.46538410229016913, 0.48069097775439756, 0.49610032665439224, 0.5114831850708703, 0.526724294721632, 0.5417223044386086, 0.5563893825120002, 0.5706505028890471, 0.5844425936568025, 0.5977136651897815, 0.6104219778778874, 0.6225352688154292, 0.6340300323542617, 0.6448908379422569, 0.6551096663888292, 0.6646852490124378, 0.6736224000853376 ], [ 0.5644942870852209, 0.5492402984122121, 0.5335087851460106, 0.5173891761788271, 0.5009901981307483, 0.48444138640428064, 0.46789384651951016, 0.4515197383331026, 0.43550990370794335, 0.42006913250043293, 0.40540882030147374, 0.39173723848869796, 0.3792482673200365, 0.3681100952373655, 0.35845583668763364, 0.3503780231674135, 0.343928332209409, 0.33912280008064305, 0.3359514141332542, 0.3343898277758946, 0.33441035947683734, 0.3359896084482403, 0.3391109047688627, 0.34376119275718736, 0.3499234647460974, 0.35756707000489774, 0.36663871523242303, 0.37705658032488537, 0.38870888135291826, 0.4014568810478117, 0.41514126825805875, 0.42959029530999765, 0.4446280895570031, 0.46008195642289007, 0.4757880246812485, 0.4915950645363187, 0.5073666432593158, 0.522981958662563, 0.538335738926502, 0.5533375635749103, 0.5679108860039235, 0.5819919530006081, 0.5955287394516768, 0.6084799557494596, 0.6208141434934401, 0.6325088502791778, 0.643549863077643, 0.6539304778368273, 0.6636507867129802, 0.6727169707413548 ], [ 0.5661874972920196, 0.5509683295784997, 0.5352620133432117, 0.5191569186139136, 0.5027599563304195, 0.48619758073385, 0.4696159941970774, 0.4531801350148548, 0.43707102708573153, 0.4214811778268909, 0.4066079614357208, 0.39264532048890427, 0.3797746048523962, 0.3681558195368059, 0.3579207988268664, 0.3491696971408087, 0.34197161533265885, 0.3363692542279552, 0.33238645507468234, 0.33003667024547073, 0.3293300716638665, 0.3302772724260809, 0.3328884768318389, 0.3371681104977076, 0.3431063004329185, 0.3506695582480149, 0.35979329111036357, 0.37037819386330556, 0.382291390943275, 0.3953718846393355, 0.4094389073005113, 0.4243014125710398, 0.4397671268648057, 0.45565008896049297, 0.47177618156447154, 0.4879866322327977, 0.5041397631024149, 0.520111405981659, 0.5357944143600826, 0.551097646380383, 0.5659447037740026, 0.5802726191024744, 0.594030603226331, 0.6071789035611992, 0.6196877822788209, 0.6315365997078058, 0.6427129778156725, 0.6532120175640018, 0.6630355483277899, 0.6721913944655546 ], [ 0.5677212717867302, 0.5524884927785413, 0.536751262080314, 0.5205964279056854, 0.5041288544226218, 0.4874720468296697, 0.4707679533034207, 0.4541756125909793, 0.43786835106369154, 0.4220293625927322, 0.4068457467466956, 0.3925014224269781, 0.3791697140907715, 0.3670067134347959, 0.35614660896315115, 0.3466999321616359, 0.3387550695974878, 0.3323825543894655, 0.3276408219437974, 0.3245815743623495, 0.32325285176241275, 0.32369841792145976, 0.32595303852783963, 0.33003443346300204, 0.33593377981637557, 0.34360724782180385, 0.35297089652446456, 0.3639003536426118, 0.37623539855694277, 0.3897883670276348, 0.40435460274585355, 0.41972311094127535, 0.4356859726357634, 0.45204568722704563, 0.4686201915585268, 0.4852457259048819, 0.5017779518645266, 0.5180918049249502, 0.5340805376820026, 0.5496543276933427, 0.5647387234232357, 0.579273105700039, 0.5932092625065271, 0.6065101160108841, 0.6191486020060833, 0.6311066802672072, 0.6423744456246143, 0.6529493095996038, 0.6628352276024723, 0.6720419540974577 ], [ 0.5690818849561915, 0.5537864958402302, 0.5379613584168578, 0.5216912240576812, 0.5050785590752936, 0.4882439234561821, 0.47132551901718134, 0.4544776442975879, 0.4378678542203863, 0.42167276707691215, 0.4060726973155148, 0.39124559729469194, 0.3773610987282111, 0.3645756459752194, 0.35302968120399036, 0.3428474832873792, 0.3341395868890354, 0.32700686840275767, 0.32154465712753966, 0.3178449177771468, 0.315994857261183, 0.31607123497581957, 0.31813097074775026, 0.3221999380290431, 0.32826263692429863, 0.3362554231636989, 0.3460650903291031, 0.35753319098189246, 0.3704650829345469, 0.3846417824850664, 0.3998324938419564, 0.41580604821269945, 0.4323401433496422, 0.44922794765064156, 0.4662821523553588, 0.48333686794199227, 0.5002478902277693, 0.5168918625327639, 0.5331647877593895, 0.5489802409399588, 0.5642675264996639, 0.5789699307534856, 0.5930431459737886, 0.6064538891875915, 0.6191787049068935, 0.6312029228229293, 0.6425197350844305, 0.6531293592333318, 0.6630382588381173, 0.6722584017414505 ], [ 0.5702891007927918, 0.5548870061860521, 0.538922273754643, 0.5224768976824032, 0.5056504724063765, 0.48856044445128605, 0.47134154128669004, 0.4541441655393354, 0.43713162109599624, 0.4204761928445509, 0.40435433561066697, 0.38894151178873715, 0.3744074806976845, 0.3609129737843858, 0.3486085602368876, 0.33763602845914986, 0.3281318035535882, 0.3202309794701365, 0.3140698129263522, 0.3097844031649351, 0.30750403749056915, 0.30733926775016845, 0.30936672908521967, 0.3136142381600603, 0.32005007032319166, 0.3285792563357294, 0.33904770772356196, 0.35125288654910364, 0.3649584001308609, 0.37990962636900655, 0.39584803327453505, 0.41252278151376676, 0.4296990882704394, 0.44716347565997616, 0.46472639075167327, 0.4822228226443469, 0.4995115347756898, 0.5164734461642229, 0.5330095806533522, 0.5490388864923135, 0.5644961244872223, 0.5793299379823963, 0.593501153759927, 0.6069813184784569, 0.619751447867502, 0.6318009521477214, 0.6431266974575012, 0.653732166042706, 0.6636266847106338, 0.6728246992988405 ], [ 0.5713925022600762, 0.5558493909511423, 0.5397042188324629, 0.5230355089602122, 0.5059393943140496, 0.48852984163063873, 0.4709380727829844, 0.45331100930470436, 0.4358086556604, 0.4186005005921149, 0.4018612522581236, 0.38576650032039544, 0.3704891411874391, 0.35619749033395653, 0.3430557953618248, 0.3312272499768985, 0.3208786119635288, 0.3121843747179211, 0.3053275873367335, 0.3004944427693901, 0.2978610997866744, 0.297573804726908, 0.2997263781076706, 0.3043410593185932, 0.3113582902260826, 0.32063821283163996, 0.3319728677937007, 0.3451052196144824, 0.35975027336456383, 0.37561444181824105, 0.3924109845817487, 0.4098708768859514, 0.42774946420411836, 0.44582971830702717, 0.4639230045727416, 0.4818681778887625, 0.4995296651382461, 0.516795027991778, 0.533572355359148, 0.54978771678506, 0.5653828154914314, 0.5803129098671006, 0.5945450219565032, 0.608056417978952, 0.6208333262144106, 0.6328698487793761, 0.644167022985984, 0.6547319924254322, 0.6645772553042881, 0.6737199660306309 ], [ 0.5724661348701655, 0.5567615065529353, 0.5404105006087673, 0.52348744523334, 0.5060843356985377, 0.48831110183103626, 0.470295104535609, 0.4521797149593587, 0.4341219283139086, 0.4162891361201757, 0.3988554244304964, 0.3819980486707548, 0.3658949776773149, 0.35072446569052385, 0.3366673323480087, 0.3239118650636786, 0.31265999801435, 0.30313192262190664, 0.29556514853683186, 0.2902041396454427, 0.2872787826249453, 0.2869741003978942, 0.2893983258966556, 0.2945589892294911, 0.3023548386861224, 0.3125856892220718, 0.3249759551607008, 0.33920416504029854, 0.3549311983110034, 0.37182280993075034, 0.3895650639304241, 0.40787332756251177, 0.4264963282991652, 0.44521684012258883, 0.46385028099596726, 0.4822421491031042, 0.5002649228544866, 0.5178148266700079, 0.5348087103066269, 0.55118118453942, 0.5668820840523211, 0.581874278739499, 0.5961318209589568, 0.6096383949189792, 0.6223860228202948, 0.6343739785357646, 0.6456078614990879, 0.6560987891895961, 0.665862674419485, 0.6749195621256028 ], [ 0.5736018743702737, 0.5577319952026537, 0.5411686422988552, 0.5239812739620033, 0.5062570409065867, 0.4881011381948186, 0.46963642612922785, 0.4510021967290853, 0.43235206791662095, 0.4138511682305651, 0.39567303096959133, 0.3779969158324936, 0.36100653325035903, 0.3448912103633474, 0.329850202057367, 0.3160999153426051, 0.3038822134917955, 0.29346995481858945, 0.2851642776418273, 0.2792781976795142, 0.27610425151836815, 0.2758704435684981, 0.2786961855588469, 0.2845633187197392, 0.29331286269719675, 0.3046676078027775, 0.3182708750030649, 0.33372843823413945, 0.35064376808320075, 0.36864242019927135, 0.38738590996267414, 0.40657756581326854, 0.4259631711064149, 0.44532865381787107, 0.46449635131255584, 0.4833207722723962, 0.5016843677289695, 0.5194935749719956, 0.5366752574151313, 0.5531735854935683, 0.5689473594861533, 0.5839677489055672, 0.5982164070997246, 0.611683910607053, 0.6243684691144692, 0.6362748526258771, 0.6474134867032865, 0.6577996733210122, 0.6674529028748653, 0.6763962312112916 ], [ 0.5749019752706278, 0.5588815987188728, 0.5421203253176249, 0.524682186746647, 0.5066488325330398, 0.4881199770877446, 0.4692131606585153, 0.4500627222618153, 0.4308179954571974, 0.4116409293989673, 0.39270361074445786, 0.3741864861718223, 0.3562783717899836, 0.33917941569223153, 0.3231078034830343, 0.308309883869601, 0.2950713725548837, 0.28372457186514244, 0.27464407154526466, 0.2682231400747874, 0.26482747487125263, 0.2647330479374981, 0.26806653074862324, 0.27477135571698647, 0.284613351108187, 0.29722173454945494, 0.3121472295952092, 0.3289175680915139, 0.34707860200828056, 0.36621854592942643, 0.3859784904751246, 0.40605393317195854, 0.4261914133074631, 0.44618301250915776, 0.4658603083506608, 0.48508857110269143, 0.5037615327116945, 0.5217968222202327, 0.5391320562031747, 0.5557215318367513, 0.5715334575127553, 0.5865476536941354, 0.6007536577735284, 0.6141491689543391, 0.6267387725117962, 0.6385328874992923, 0.6495468881107291, 0.6598003562152531, 0.6693164305242717, 0.6781212258244467 ], [ 0.5764712988125502, 0.5603340566286177, 0.5434107870938257, 0.5257597277676038, 0.5074565147873156, 0.48859471109969665, 0.46928569518332425, 0.44965783025589745, 0.4298549551128021, 0.4100344423201112, 0.39036536350194534, 0.371027657304201, 0.3522135230530508, 0.3341323777914504, 0.3170203207201237, 0.3011537708375357, 0.28686445888311357, 0.2745493262851172, 0.26466517217303764, 0.2576968728274901, 0.25409390906693874, 0.2541850772414605, 0.2580996109281443, 0.26572905091778937, 0.27674719796585956, 0.2906759107907693, 0.3069661134359123, 0.32506670418861067, 0.34446927815696277, 0.3647297697421418, 0.38547391037346884, 0.406393608458362, 0.42723935382386985, 0.4478116192963126, 0.4679527061374496, 0.48753958546585674, 0.5064778392328035, 0.5246966163556734, 0.5421444633245578, 0.5587858887808542, 0.5745985399227207, 0.589570888503387, 0.6037003402931463, 0.6169916938454831, 0.629455883601024, 0.6411089502449691, 0.6519711887858988, 0.6620664324604087, 0.6714214382687914, 0.6800653474480918 ], [ 0.5784097449366284, 0.5622072004885504, 0.5451783807276381, 0.527375609168029, 0.5088682297938538, 0.48974318808775885, 0.4701050186299931, 0.45007518271879604, 0.42979082998094204, 0.4094032767125068, 0.3890768099434628, 0.3689888159928017, 0.3493326062862772, 0.3303244767017557, 0.3122161539384571, 0.29531237606221916, 0.2799904098804017, 0.2667136391901041, 0.25602599516807295, 0.24851160862066263, 0.24471134452018595, 0.24500969571904568, 0.24953325350991876, 0.2581099838612842, 0.2703094763097343, 0.28553920090495266, 0.3031500978730536, 0.32251701747675643, 0.34308407344053266, 0.36438141165127524, 0.3860245086088636, 0.40770517538314327, 0.42917995403922304, 0.4502587818225089, 0.47079507123486547, 0.4906774633789277, 0.5098231273811841, 0.5281723575292209, 0.5456842167721705, 0.5623330140586534, 0.5781054482070385, 0.5929982891382659, 0.6070164954573569, 0.6201716870030932, 0.6324809047439872, 0.6439656007021948, 0.654650809139611, 0.6645644580043947, 0.673736786997167, 0.682199845595087 ], [ 0.5808054072672838, 0.5646048665563714, 0.5475450382449719, 0.5296724909805519, 0.5110502938862832, 0.49175861979759017, 0.4718948011173291, 0.4515728072493571, 0.4309222527468795, 0.4100872775384821, 0.38922597648400925, 0.36851147448878063, 0.3481361589895125, 0.3283207950128567, 0.3093298953663375, 0.2914932341956994, 0.2752300596203366, 0.261066868021365, 0.24963237611107333, 0.2416090242453888, 0.2376286319521917, 0.238129319664925, 0.24323018169996227, 0.25269023686238823, 0.2659732827364924, 0.2823768939064421, 0.30116116910233187, 0.32163744065499394, 0.34321155808780685, 0.3653945488940633, 0.38779569628246807, 0.4101086781080325, 0.4320965978242618, 0.4535784705390565, 0.47441794942875837, 0.4945142629652627, 0.5137950370635676, 0.5322106235433225, 0.549729600146018, 0.5663351769263346, 0.5820223091623414, 0.5967953682932783, 0.6106662592350883, 0.623652897621775, 0.6357779776373254, 0.6470679732018996, 0.657552324553213, 0.6672627700703759, 0.6762327902118227, 0.6844971369270968 ], [ 0.5837289189251142, 0.567610202013608, 0.5506083446018878, 0.5327645936377646, 0.5141360757150488, 0.49479640089567356, 0.47483576834185276, 0.4543605707071147, 0.43349264329049697, 0.4123685465120797, 0.39113961854254525, 0.3699739700028422, 0.34906203075710857, 0.3286275017269137, 0.30894523465021045, 0.2903660339235557, 0.27334476634859184, 0.2584616533385636, 0.24641774977658792, 0.23797940683440327, 0.2338554268977464, 0.2345272723890856, 0.24010336742440297, 0.2502800143777607, 0.26443017915114914, 0.2817612187343749, 0.30146167230933973, 0.32279467768713616, 0.3451380177834827, 0.3679891933836072, 0.3909534710820648, 0.4137263593591928, 0.4360762206909196, 0.45782923143602067, 0.47885716268225925, 0.49906773483806444, 0.5183970816515409, 0.5368038595141664, 0.5542646142277219, 0.5707701066767268, 0.5863223764864776, 0.600932382179087, 0.6146180986391933, 0.6274029815740902, 0.6393147281202259, 0.6503842761850219, 0.6606449949758683, 0.6701320270421155, 0.6788817489354296, 0.6869313236934139 ], [ 0.5872293537751887, 0.5712808235373433, 0.5544358026987133, 0.5367308801544434, 0.518217855576579, 0.4989643378733544, 0.47905390227782135, 0.4585858336358326, 0.4376746394065022, 0.4164497633003014, 0.39505627966189777, 0.3736577793245792, 0.35244308610336356, 0.33163867273758885, 0.3115282957646708, 0.2924797898849607, 0.2749751900130947, 0.2596333882506719, 0.24720476661407748, 0.2385100483432415, 0.2343051437645245, 0.23509502129715049, 0.24097699093553573, 0.2516050395595588, 0.2662946154209121, 0.2841976160941426, 0.3044590346146633, 0.32631235216826765, 0.34911736568474616, 0.37236204653368027, 0.3956478449018216, 0.4186702062555577, 0.4411998763484407, 0.46306699916190985, 0.48414831833417943, 0.5043571306125887, 0.5236354649435678, 0.5419479859645003, 0.5592772105730819, 0.57561972299111, 0.5909831559833444, 0.6053837686399965, 0.6188444960573545, 0.6313933772099234, 0.6430622883238848, 0.6538859235174065, 0.6639009748781829, 0.6731454721848238, 0.6816582491600365, 0.6894785090016102 ], [ 0.5913318984719985, 0.5756461060219216, 0.5590616522772708, 0.5416112877725471, 0.5233423076076789, 0.5043171547805588, 0.48461364998216766, 0.46432490788500774, 0.4435591594402294, 0.4224399444113133, 0.40110747390592694, 0.37972236364366213, 0.35847331788086556, 0.3375905048718062, 0.3173659332649771, 0.29818047715675283, 0.2805333657877285, 0.265063011633865, 0.25253850740665285, 0.2437945387786291, 0.23959295174013462, 0.24043591551783197, 0.24641163912175057, 0.25716240584877165, 0.27199187516556855, 0.2900408760669404, 0.3104441438197685, 0.33242587397620416, 0.35533786685035773, 0.3786616809241723, 0.4019940925134771, 0.42502761137691736, 0.4475316619417069, 0.4693364792983693, 0.49032007076435824, 0.51039792241132, 0.5295149449477089, 0.5476391694441679, 0.5647567861744561, 0.5808682117392556, 0.5959849491867264, 0.6101270675903266, 0.6233211725859722, 0.635598771018802, 0.6469949547127518, 0.6575473435731406, 0.6672952391490873, 0.6762789480798626, 0.6845392415823861, 0.6921169229077045 ], [ 0.5960373341534655, 0.5807066574778312, 0.5644863272527894, 0.5474061405832694, 0.5295098130124443, 0.5108556080495408, 0.491516672128606, 0.47158116704623215, 0.4511524501236025, 0.4303497851081926, 0.4093103726896423, 0.388193835128978, 0.367190581293903, 0.34653552004166877, 0.32652802348919124, 0.30755728306290103, 0.29012844544014543, 0.2748785001833875, 0.2625627018993777, 0.25398782950168536, 0.2498800588615591, 0.25071299885724735, 0.2565685657987678, 0.26710836063523846, 0.2816700837913059, 0.2994281180949398, 0.31954079612747954, 0.34124419130851036, 0.36389291718928496, 0.38696594978708443, 0.4100550895958706, 0.4328474341832523, 0.45510763927874226, 0.47666229861773723, 0.49738703023666314, 0.5171961126255161, 0.5360342682175291, 0.5538701651231396, 0.5706912631532512, 0.5864997050751255, 0.6013090237387814, 0.615141492227205, 0.628025986845067, 0.6399962636586306, 0.6510895712283278, 0.6613455377458043, 0.6708052820995203, 0.6795107069780822, 0.6875039390015294, 0.6948268866716278 ], [ 0.601323190342413, 0.5864358109154494, 0.5706783473501044, 0.5540785034580481, 0.5366773338729817, 0.5185299239933734, 0.4997058615477698, 0.48028961983172036, 0.46038112346426957, 0.44009697830413397, 0.41957310811807363, 0.3989698095045207, 0.3784804139877506, 0.35834464076086786, 0.3388670099796448, 0.3204388764197827, 0.30355915400867994, 0.2888433723847557, 0.2770046243689998, 0.2687881905941408, 0.2648533427082523, 0.26562662123521974, 0.27118552498921267, 0.2812329717632166, 0.2951747531675356, 0.312254351162577, 0.3316831499879906, 0.3527296271538404, 0.37476341287649295, 0.3972668145418028, 0.4198284014980607, 0.4421291027411088, 0.46392669141478055, 0.48504137039654704, 0.5053434129667776, 0.5247429706720615, 0.5431818214658966, 0.5606267361815264, 0.5770641512138635, 0.5924958818580197, 0.6069356635038566, 0.6204063547550608, 0.6329376740744176, 0.644564370009415, 0.6553247460301092, 0.6652594763804693, 0.6744106607639181, 0.6828210744462432, 0.6905335773799448, 0.6975906518276558 ], [ 0.6071462861588367, 0.5927827752478245, 0.5775781966748748, 0.5615589218369408, 0.5447641634829178, 0.5272467250796719, 0.509073628234756, 0.49032675836743517, 0.4711038056202913, 0.4515199575958267, 0.43171100500193993, 0.41183870129702804, 0.3920992721145415, 0.37273572321032655, 0.3540537739935792, 0.3364394875806073, 0.32037365190152906, 0.30643380911459495, 0.29527101774314646, 0.28754897161065573, 0.28384390593343045, 0.2845265839049071, 0.2896704603758135, 0.2990292668481173, 0.3120939553496241, 0.32819834054612024, 0.3466279806826607, 0.3667014536892605, 0.38781625557904364, 0.4094661744213611, 0.4312409215610464, 0.45281693335341583, 0.4739450084819653, 0.49443779471433796, 0.5141584639611725, 0.5330110059704436, 0.5509321381432808, 0.5678846550979485, 0.5838519951968381, 0.5988338107601714, 0.6128423581872553, 0.6258995570605516, 0.6380345967508028, 0.6492819930689172, 0.6596800162399452, 0.6692694258183992, 0.6780924591916928, 0.6861920289770513, 0.6936110916369149, 0.7003921555268436 ], [ 0.6134462770630282, 0.5996769653225816, 0.5851035869656457, 0.5697517927346174, 0.5536596088921258, 0.5368782642481108, 0.5194729739702647, 0.50152382985222, 0.48312706368179675, 0.46439709225670933, 0.44546989539742027, 0.4265083693509561, 0.4077102422165901, 0.3893187855005417, 0.3716357012373332, 0.35503398582177703, 0.3399661732278795, 0.32696051097972156, 0.31659573195221974, 0.30944701750904174, 0.30600475762590046, 0.3065834444992537, 0.3112518541537334, 0.3198138662877508, 0.33184767762457096, 0.34678441105306645, 0.36399495219349065, 0.38286067587913236, 0.40281862711521177, 0.42338331256875106, 0.44415203687642396, 0.46480070934154577, 0.4850751743996146, 0.5047811465638963, 0.5237743773310842, 0.5419517819874516, 0.5592437598235891, 0.5756076978776138, 0.5910225451779956, 0.605484313209738, 0.6190023604815598, 0.6315963343935221, 0.643293662212949, 0.6541275005349575, 0.6641350676291042, 0.6733562953816534, 0.6818327475000582, 0.6896067587625027, 0.696720756842342, 0.7032167339813126 ] ] }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "text": [ "0_0", "1_0", "2_0", "3_0", "4_0", "5_0", "6_0", "7_0", "8_0", "9_0", "10_0", "11_0", "12_0", "13_0", "14_0", "15_0", "16_0", "17_0", "18_0", "19_0", "20_0", "21_0", "22_0", "23_0" ], "type": "scatter", "x": [ 0.27277045603841543, 0.21175731625407934, 0.4312838092446327, 0.1797152440994978, 0.7082942668348551, 0.8214593231678009, 0.19429569731792892, 0.3009712127031631, 0.32808789348660206, 0.3419170482789374, 0.2929502941842078, 0.3849430696971001, 0.43858922561682445, 0.4699073759964763, 0.4744394363561025, 0.4494999041662254, 0.42568580536559575, 0.33636774088297955, 0.3966745696372959, 0.44747582204470726, 0.4376736851484068, 0.43718880792229775, 0.42261693595076183, 0.41847060485928145 ], "xaxis": "x", "y": [ 0.4860017206519842, 0.7150549702346325, 0.10096925031393766, 0.5281501533463597, 0.6264908136799932, 0.16045302338898182, 0.44698952479583787, 0.5051994955367584, 0.5283450808523815, 0.5443598765345412, 0.5120116843839567, 0.5639405274924641, 0.5877443281650403, 0.6427206306874169, 0.7273556997401969, 0.7984077383760276, 0.8788709285290766, 0.8583064561640562, 0.8560335644002842, 0.8696804343008991, 0.8775640248817276, 0.8893671401352032, 0.8743919010098683, 0.887410548304023 ], "yaxis": "y" }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "showlegend": false, "text": [ "0_0", "1_0", "2_0", "3_0", "4_0", "5_0", "6_0", "7_0", "8_0", "9_0", "10_0", "11_0", "12_0", "13_0", "14_0", "15_0", "16_0", "17_0", "18_0", "19_0", "20_0", "21_0", "22_0", "23_0" ], "type": "scatter", "x": [ 0.27277045603841543, 0.21175731625407934, 0.4312838092446327, 0.1797152440994978, 0.7082942668348551, 0.8214593231678009, 0.19429569731792892, 0.3009712127031631, 0.32808789348660206, 0.3419170482789374, 0.2929502941842078, 0.3849430696971001, 0.43858922561682445, 0.4699073759964763, 0.4744394363561025, 0.4494999041662254, 0.42568580536559575, 0.33636774088297955, 0.3966745696372959, 0.44747582204470726, 0.4376736851484068, 0.43718880792229775, 0.42261693595076183, 0.41847060485928145 ], "xaxis": "x2", "y": [ 0.4860017206519842, 0.7150549702346325, 0.10096925031393766, 0.5281501533463597, 0.6264908136799932, 0.16045302338898182, 0.44698952479583787, 0.5051994955367584, 0.5283450808523815, 0.5443598765345412, 0.5120116843839567, 0.5639405274924641, 0.5877443281650403, 0.6427206306874169, 0.7273556997401969, 0.7984077383760276, 0.8788709285290766, 0.8583064561640562, 0.8560335644002842, 0.8696804343008991, 0.8775640248817276, 0.8893671401352032, 0.8743919010098683, 0.887410548304023 ], "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 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 } }, "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": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "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": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "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 } } }, "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", "metadata": {}, "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, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:37] ax.service.ax_client: Retrieving contour plot with parameter 'x3' on X-axis and 'x4' on Y-axis, for metric 'l2norm'. Ramaining 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": [ [ 1.07202698887374, 1.0655662445715628, 1.059326092775075, 1.0533306162052751, 1.0476043520969451, 1.04217217706096, 1.0370591768618918, 1.0322905008477519, 1.0278912010283352, 1.0238860561130085, 1.0202993811892171, 1.0171548241484942, 1.0144751504420297, 1.0122820182641266, 1.0105957468053646, 1.009435080768644, 1.0088169548769836, 1.0087562625921793, 1.0092656336767367, 1.0103552255329609, 1.0120325334095954, 1.0143022245472912, 1.017166001116563, 1.0206224963710517, 1.024667207793436, 1.0292924701629302, 1.0344874704484466, 1.0402383052701847, 1.0465280804270662, 1.0533370507188586, 1.0606427970669106, 1.0684204368235004, 1.0766428622205728, 1.085281001199624, 1.0943040944270441, 1.1036799821575596, 1.1133753947650165, 1.123356241194275, 1.1335878902580003, 1.14403544054568, 1.1546639756555521, 1.1654388024230713, 1.1763256707274587, 1.1872909742468414, 1.1983019321584352, 1.2093267522206113, 1.2203347759302643, 1.2312966065430506, 1.2421842207144091, 1.2529710644108445 ], [ 1.0688837811749772, 1.0623377978226354, 1.0560149193656545, 1.0499398094251415, 1.0441376253311418, 1.0386339013687327, 1.0334544160511747, 1.0286250430370159, 1.024171585572844, 1.0201195946696022, 1.0164941716113405, 1.0133197558502984, 1.0106198998577844, 1.00841703306767, 1.0067322176544613, 1.0055848995100642, 1.004992658396342, 1.0049709618209066, 1.005532927674341, 1.006689101037236, 1.00844725077469, 1.0108121915472144, 1.0137856366504423, 1.017366086632784, 1.0215487579264353, 1.026325554775086, 1.031685086581822, 1.0376127314804209, 1.0440907455140542, 1.0510984153611442, 1.058612251157597, 1.0666062147086433, 1.0750519773374738, 1.0839192008467617, 1.0931758346208, 1.1027884217963622, 1.1127224076791675, 1.1229424441512845, 1.1334126846480208, 1.1440970653019207, 1.1549595689654768, 1.1659644699363059, 1.1770765582308593, 1.1882613431132303, 1.199485236239002, 1.2107157152004118, 1.2219214684698565, 1.2330725227655428, 1.2441403537570064, 1.2550979808462388 ], [ 1.0660074683305127, 1.0593822220493792, 1.052982478094535, 1.046833466710611, 1.0409609521521275, 1.0353911146099208, 1.0301504152720784, 1.0252654440026545, 1.020762749388722, 1.0166686512425005, 1.0130090360544042, 1.0098091363772197, 1.0070932956778478, 1.0048847208142626, 1.0032052249664583, 1.002074964550618, 1.0015121743451894, 1.001532905719836, 1.0021507734392583, 1.0033767169664287, 1.0052187824644987, 1.0076819317481518, 1.0107678842258327, 1.0144749973790685, 1.0187981905368502, 1.0237289156343048, 1.0292551773307537, 1.0353616033580453, 1.0420295643498305, 1.049237340753991, 1.0569603328486288, 1.065171308463092, 1.0738406818398207, 1.0829368162359891, 1.0924263424115277, 1.1022744851103154, 1.1124453900087097, 1.1229024443414197, 1.133608585446466, 1.1445265926995702, 1.155619359620842, 1.166850144215313, 1.1781827967519385, 1.1895819651126844, 1.201013278508122, 1.2124435107476883, 1.22384072439279, 1.2351743970576494, 1.2464155309214133, 1.2575367462458131 ], [ 1.0634107407478055, 1.0567127041313606, 1.0502424500961025, 1.044025758422469, 1.038088984098264, 1.0324589382485345, 1.0271627513114914, 1.0222277177968866, 1.0176811222295723, 1.013550046223959, 1.0098611570603362, 1.0066404786457286, 1.0039131463390747, 1.0017031477971867, 1.0000330527398718, 0.998923735317788, 0.9983940935631478, 0.9984607711699436, 0.9991378875367818, 1.0004367825555924, 1.0023657829853159, 1.0049299973534431, 1.0081311461347595, 1.0119674334307875, 1.01643346550499, 1.0215202203289984, 1.0272150708047572, 1.0335018626109833, 1.0403610457688828, 1.0477698571363125, 1.0557025492361627, 1.0641306592191573, 1.0730233104604394, 1.0823475383838363, 1.0920686316608372, 1.1021504799732278, 1.112555920047704, 1.123247072614277, 1.1341856642137307, 1.1453333292577188, 1.1566518892865119, 1.1681036078340885, 1.1796514205766677, 1.1912591414236993, 1.2028916458648589, 1.2145150332142451, 1.2260967694321794, 1.2376058120243154, 1.2490127181995994, 1.2602897370990722 ], [ 1.0611059146532593, 1.0543420596928283, 1.0478081491387456, 1.0415304923047444, 1.0355360155556774, 1.0298521425868232, 1.0245066560750484, 1.0195275398778891, 1.0149428012191526, 1.0107802726450843, 1.0070673939737214, 1.0038309749961198, 1.0010969403257328, 0.9988900585248739, 0.9972336584536192, 0.9961493366637052, 0.995656660563558, 0.9957728729652804, 0.9965126044326611, 0.9978876005156803, 0.9999064714108656, 1.002574471759849, 1.0058933181301524, 1.009861051170373, 1.0144719484770632, 1.019716492865102, 1.0255813990414941, 1.0320496997214972, 1.0391008901018135, 1.0467111274438003, 1.0548534804595364, 1.0634982213728894, 1.072613152075223, 1.0821639548180828, 1.0921145574561646, 1.1024275034055049, 1.1130643171937766, 1.1239858576801705, 1.1351526525890523, 1.146525209776173, 1.1580643024521062, 1.1697312272553875, 1.1814880354579977, 1.193297738605833, 1.2051244905104657, 1.2169337477342355, 1.2286924106118828, 1.2403689465210754, 1.2519334966569748, 1.263357967083441 ], [ 1.059104852180358, 1.052282650107961, 1.0456924356503325, 1.0393610246590625, 1.033315892233497, 1.0275850527140173, 1.022196920197636, 1.0171801485798473, 1.0125634503806011, 1.0083753939566082, 1.0046441791489615, 1.0013973919728185, 0.9986617396310731, 0.9964627679228593, 0.9948245640114644, 0.9937694484913286, 0.9933176617152272, 0.993487050359855, 0.9942927611565646, 0.99574694951661, 0.9978585113543492, 1.0006328466718912, 1.004071663340711, 1.0081728289425818, 1.0129302774875357, 1.018333976318262, 1.0243699565901423, 1.0310204084731658, 1.0382638397836477, 1.0460752942716312, 1.054426623431262, 1.0632868036334135, 1.0726222887563481, 1.0823973874384356, 1.0925746536819612, 1.1031152798325254, 1.1139794819130346, 1.1251268688082687, 1.13651678871795, 1.148108648420919, 1.1598622030020729, 1.1717378155816744, 1.1836966880936648, 1.1957010651893665, 1.2077144138737594, 1.2197015815576375, 1.2316289349258107, 1.2434644815049916, 1.2551779751942176, 1.2667410064152322 ], [ 1.0574188785085477, 1.0505462961943743, 1.043907627062217, 1.0375301674663826, 1.0314419152213006, 1.0256714496855743, 1.0202477915550352, 1.015200241186078, 1.010558194511256, 1.0063509359471783, 1.0026074081445924, 0.9993559590056589, 0.9966240671020883, 0.9944380474720445, 0.9928227407457919, 0.9918011896287381, 0.9913943079196494, 0.9916205484065805, 0.9924955770909886, 0.9940319621534368, 0.996238886792039, 0.9991218954355886, 1.0026826827628654, 1.0069189343745588, 1.0118242268262025, 1.017387993043478, 1.023595556961673, 1.0304282386647812, 1.0378635284973783, 1.0458753257687063, 1.0544342349633307, 1.0635079100202687, 1.0730614354262362, 1.0830577317401846, 1.0934579728262874, 1.1042220025531848, 1.115308739974882, 1.1266765639136698, 1.1382836702147623, 1.15008839748009, 1.1620495195420104, 1.1741265050603484, 1.1862797462346875, 1.1984707596240742, 1.2106623624589261, 1.2228188276961953, 1.2349060205486138, 1.2468915184750526, 1.2587447158126375, 1.270436913496188 ], [ 1.0560586965367627, 1.0491441890659212, 1.0424654049246938, 1.0360500918859419, 1.029926741030224, 1.024124467302123, 1.0186728690105042, 1.0136018649026692, 1.0089415076651587, 1.0047217730296782, 1.0009723241100974, 0.9977222511822917, 0.9949997878565394, 0.9928320054879856, 0.9912444887211459, 0.990260996250734, 0.9899031121669661, 0.9901898945809349, 0.9911375295141356, 0.992758999184363, 0.9950637747103652, 0.9980575437657777, 1.00174198372221, 1.0061145902370745, 1.0111685700092388, 1.0168928045429584, 1.0232718892890622, 1.0302862495951746, 1.0379123316748096, 1.046122863519878, 1.054887177575797, 1.0641715843184005, 1.0739397838382794, 1.0841533013330302, 1.0947719321467453, 1.1057541827138664, 1.1170576953968487, 1.1286396475846385, 1.1404571182811907, 1.152467418434161, 1.1646283840959464, 1.1768986338753316, 1.1892377938219831, 1.2016066938020584, 1.2139675396062304, 1.2262840646158786, 1.2385216640330619, 1.2506475136670103, 1.2626306742565727, 1.2744421814441114 ], [ 1.055034299673499, 1.0480867987190454, 1.0413767193539154, 1.0349322286702771, 1.028782278129041, 1.0229564849657486, 1.017484991835468, 1.0123983031295323, 1.0077270965963776, 1.0035020092063878, 0.9997533966384805, 0.9965110663560934, 0.9938039850002881, 0.9916599617705638, 0.9901053105903088, 0.9891644951499163, 0.9888597623511108, 0.9892107711805591, 0.9902342255312664, 0.9919435208515721, 0.9943484155949862, 0.9974547391219162, 1.0012641478201036, 1.0057739406437063, 1.0109769439464675, 1.0168614733893095, 1.0234113779040968, 1.0306061673353923, 1.0384212216771347, 1.0468280760374677, 1.0557947718977974, 1.0652862621760173, 1.0752648553272648, 1.0856906824332029, 1.0965221710804975, 1.107716510844119, 1.1192300972837221, 1.131018944311481, 1.1430390582619858, 1.1552467705786247, 1.1675990293056264, 1.1800536521860665, 1.1925695458843983, 1.2051068966104082, 1.2176273373065205, 1.2300940957761093, 1.2424721269418868, 1.2547282310983157, 1.2668311587872199, 1.2787517019413956 ], [ 1.0543548834315208, 1.0473837810396374, 1.0406516914886383, 1.0341871661581652, 1.0280195806121808, 1.0221790172172847, 1.016696125366811, 1.011601957543664, 1.0069277796257794, 1.00270485412112, 0.9989641954400132, 0.9957362968980605, 0.9930508299175047, 0.9909363168770056, 0.9894197802581768, 0.9885263721423985, 0.9882789896925419, 0.9886978839489595, 0.9898002709831282, 0.9915999560554901, 0.9941069827561119, 0.9973273199898045, 1.0012625999219613, 1.0059099194739982, 1.0112617165453428, 1.0173057298168109, 1.024025047826459, 1.0313982491700227, 1.0393996314197804, 1.0479995219993985, 1.0571646601542184, 1.0668586356716985, 1.077042367458164, 1.087674603721819, 1.0987124255092373, 1.1101117367269122, 1.1218277264321106, 1.133815292814598, 1.1460294224848517, 1.1584255229166875, 1.1709597096428752, 1.1835890526479125, 1.1962717880946863, 1.2089675020271675, 1.2216372921695995, 1.2342439126900326, 1.2467519051655234, 1.2591277173091067, 1.2713398095568516, 1.2833587485288185 ], [ 1.0540287566275348, 1.0470438840389393, 1.0402995147652745, 1.0338245466443785, 1.027648739778678, 1.0218026007030883, 1.0163172436078831, 1.011224226650336, 1.0065553615266323, 1.0023424947274344, 0.9986172592965263, 0.9954107964838548, 0.992753447463478, 0.9906744162996146, 0.9892014066066793, 0.9883602358608508, 0.9881744330549715, 0.9886648272850853, 0.9898491368146058, 0.9917415700374131, 0.9943524513690118, 0.997687886223637, 1.0017494796665347, 1.0065341228693325, 1.012033860007161, 1.018235845672279, 1.0251223993122043, 1.032671158820179, 1.0408553305182608, 1.0496440277624874, 1.0590026856954662, 1.0688935357019296, 1.079276120272839, 1.0901078275596976, 1.1013444250906241, 1.112940573956975, 1.1248503081066499, 1.1370274678354948, 1.1494260816077615, 1.1620006953088995, 1.1747066522974836, 1.187500330676782, 1.200339345789832, 1.2131827260738424, 1.2259910693519684, 1.2387266848092284, 1.2513537237512995, 1.2638383001851141, 1.2761486005773846, 1.288254980999379 ], [ 1.0540632531051133, 1.0470748542566342, 1.040328355960252, 1.0338529620758528, 1.027678774560359, 1.0218366794851632, 1.016358209648975, 1.011275381625708, 1.0066205051869095, 1.0024259632528805, 0.998723960889657, 0.995546242417652, 0.9929237764705647, 0.9908864098751031, 0.9894624925393085, 0.9886784771491136, 0.9885584993594951, 0.9891239462732261, 0.9903930232200342, 0.9923803310260975, 0.9950964678862269, 0.998547671370423, 1.0027355167467897, 1.0076566874406967, 1.01330283189666, 1.0196605182928573, 1.026711294547531, 1.0344318560712173, 1.0427943181188624, 1.0517665838432304, 1.0613127937615907, 1.0713938378334202, 1.0819679081683058, 1.0929910689019724, 1.1044178202149335, 1.1162016358536861, 1.1282954576458548, 1.1406521359192043, 1.1532248107537693, 1.165967234801173, 1.1788340432087776, 1.191780979399981, 1.2047650868240747, 1.217744876399722, 1.23068047763385, 1.2435337788688865, 1.256268559376265, 1.2688506135529958, 1.2812478656004003, 1.2934304719051792 ], [ 1.0544646450191375, 1.0474833444037315, 1.040745257098044, 1.034279850187275, 1.0281175219139917, 1.0222894897959933, 1.0168276549781967, 1.0117644404732022, 1.0071326010033659, 1.0029650023292112, 0.9992943682710367, 0.9961529941459828, 0.9935724260973349, 0.9915831068309178, 0.9902139896329984, 0.9894921242455317, 0.9894422202104314, 0.9900861956142897, 0.9914427216632873, 0.9935267760241229, 0.9963492201442599, 0.9999164175208841, 1.0042299108056159, 1.0092861754063145, 1.0150764656486866, 1.021586766481369, 1.0287978592139755, 1.0366855041186047, 1.045220736326763, 1.0543702648678441, 1.0640969585384468, 1.0743603971761306, 1.085117463380046, 1.0963229482008283, 1.107930145068296, 1.1198914092672796, 1.1321586653496156, 1.144683851409342, 1.157419296287475, 1.1703180324991425, 1.1833340530291305, 1.1964225234397914, 1.209539961732109, 1.2226443973137593, 1.2356955178371045, 1.2486548093233234, 1.2614856916098136, 1.27415364829737, 1.286626348348363, 1.2988737553889158 ], [ 1.0552380588394326, 1.048274823454864, 1.0415560394780854, 1.0351113923624213, 1.0289715284831942, 1.0231679455468812, 1.0177328589754242, 1.0126990417484045, 1.0080996352004181, 1.0039679283948015, 1.0003371039693592, 0.9972399488219372, 0.9947085287274544, 0.9927738270079691, 0.9914653487641156, 0.990810693954014, 0.9908351047813309, 0.9915609953869345, 0.9930074746256745, 0.9951898755703339, 0.9981193080549705, 1.0018022527122274, 1.0062402161941344, 1.0114294672199782, 1.0173608714731726, 1.0240198400210323, 1.0313864009134743, 1.0394353972142634, 1.0481368074319897, 1.057456176806102, 1.0673551409004087, 1.0777920171860231, 1.0887224363980048, 1.1000999839189607, 1.111876822574146, 1.1240042720379277, 1.1364333262293238, 1.1491150978963713, 1.1620011879888048, 1.1750439851430754, 1.1881969064916365, 1.2014145942813945, 1.2146530832377533, 1.2278699516260536, 1.2410244653475775, 1.2540777201322824, 1.2669927828304437, 1.2797348295744977, 1.2922712764815483, 1.3045718976203629 ], [ 1.0563873953448222, 1.0494534905333441, 1.0427652112297796, 1.0363524146865337, 1.0302459450384736, 1.0244775261246974, 1.0190796301299427, 1.0140853193742847, 1.0095280585484725, 1.0054414947653965, 1.0018592030184983, 0.9988143950583245, 0.996339590379125, 0.9944662490141507, 0.9932243672352146, 0.9926420390894283, 0.9927449890078077, 0.9935560834598067, 0.995094832708959, 0.9973768969593536, 1.0004136142812383, 1.0042115702802419, 1.008772231079606, 1.0140916613649398, 1.0201603476220105, 1.0269631430772759, 1.0344793452692511, 1.042682909962533, 1.0515427968531181, 1.0610234339858509, 1.0710852798832375, 1.0816854559198241, 1.0927784172107262, 1.1043166287851203, 1.1162512154177835, 1.128532558209609, 1.14111081844158, 1.1539363784947574, 1.1669601994172523, 1.1801341034958228, 1.1934109965641273, 1.2067450478775907, 1.2200918450789475, 1.233408538675299, 1.246653985637844, 1.2597888964414594, 1.2727759851149023, 1.2855801183329865, 1.2981684575032029, 1.3105105871105744 ], [ 1.0579152549814712, 1.0510221940576834, 1.0443758799548983, 1.0380062938326535, 1.0319444254111387, 1.0262221682497492, 1.0208721907912663, 1.0159277803669815, 1.011422657281553, 1.0073907561162447, 1.0038659715517637, 1.0008818663722783, 0.9984713399387835, 0.9966662563887775, 0.9954970332073947, 0.9949921926931493, 0.9951778812507819, 0.996077364377645, 0.9977105085831162, 1.0000932651025003, 1.0032371738232106, 1.0071489088960406, 1.0118298895311781, 1.0172759799318634, 1.0234773007310964, 1.0304181703999422, 1.0380771889121396, 1.0464274678501846, 1.0554370018113688, 1.0650691663473353, 1.0752833187715325, 1.0860354709878601, 1.0972789988822, 1.108965351415807, 1.121044724734733, 1.1334666723622977, 1.1461806313842897, 1.1591363553984928, 1.1722842562809874, 1.185575666668753, 1.1989630418262722, 1.2124001222958203, 1.225842077426173, 1.2392456454262972, 1.2525692794321703, 1.2657733027061273, 1.2788200706905717, 1.2916741338854005, 1.3043023935820959, 1.3166742421721687 ], [ 1.0598228700436985, 1.0529823577266568, 1.046389672153279, 1.040074869592992, 1.0340690318394405, 1.0284041639085415, 1.0231130675438476, 1.0182291876154812, 1.013786428378109, 1.0098189365206105, 1.0063608480418076, 1.0034459962818285, 1.001107579001763, 0.9993777833203144, 0.9982873686781006, 0.9978652098966718, 0.9981378048944667, 0.9991287547317281, 1.0008582273120132, 1.0033424200812542, 1.006593041101695, 1.0106168314495836, 1.0154151543831658, 1.0209836774992074, 1.0273121725693344, 1.0343844535716862, 1.0421784666109024, 1.0506665363679992, 1.0598157632537537, 1.0695885546482484, 1.0799432636959234, 1.0908349012357013, 1.1022158815386347, 1.114036761307358, 1.1262469342546813, 1.1387952505002854, 1.1516305404134957, 1.1647020351029571, 1.1779596885880506, 1.191354417570038, 1.2048382817393164, 1.2183646296904316, 1.2318882329545469, 1.2453654246540646, 1.2587542516604437, 1.2720146416871922, 1.285108580782119, 1.2980002928442436, 1.3106564111316559, 1.3230461319006168 ], [ 1.0621100451940477, 1.0553339150031893, 1.0488066612397222, 1.0425583660123527, 1.036620148831234, 1.0310240666053991, 1.025802989576447, 1.0209904501918199, 1.0166204617588557, 1.0127273036372937, 1.009345269768659, 1.006508377568012, 1.004250034695716, 1.002602662078622, 1.0015972728680211, 1.0012630089142847, 1.0016266388941375, 1.002712025487913, 1.0045395729240443, 1.0071256706072091, 1.0104821530736356, 1.014615800633782, 1.0195279080713047, 1.0252139498988595, 1.0316633692299237, 1.038859512869576, 1.0467797277283202, 1.0553956235984119, 1.0646734956555415, 1.0745748880431196, 1.0850572689644313, 1.09607477915336, 1.1075790104832537, 1.119519770559414, 1.1318457928227574, 1.144505359908146, 1.157446820041726, 1.1706189906104003, 1.1839714574177644, 1.1974547899586239, 1.2110207001124447, 1.2246221729346927, 1.238213594155142, 1.2517508912579962, 1.265191695875316, 1.278495526749834, 1.2916239861110401, 1.3045409585318013, 1.3172128000862406, 1.329608506396559 ], [ 1.0647751078638128, 1.0580752538047857, 1.051625306036281, 1.0454553231922157, 1.0395964078003967, 1.0340806083792615, 1.0289407976758291, 1.024210523992389, 1.0199238323507502, 1.0161150521119227, 1.0128185476515263, 1.0100684288499655, 1.007898218573609, 1.0063404751015097, 1.005426368711415, 1.0051852135055999, 1.0056439581477044, 1.006826642565329, 1.0087538318315554, 1.011442043205869, 1.0149031873305532, 1.0191440492549586, 1.024165838508281, 1.029963838964326, 1.0365271879067879, 1.0438388089607464, 1.0518755153472477, 1.0606082887864454, 1.070002726437485, 1.0800196350254805, 1.0906157393879283, 1.1017444635480527, 1.113356737245575, 1.1254017804029748, 1.137827822650807, 1.1505827246525233, 1.1636144817162304, 1.176871606289473, 1.1903034017659988, 1.2038601526004633, 1.217493262592692, 1.2311553733573684, 1.2448004892060058, 1.2583841251063297, 1.2718634837470413, 1.285197658353734, 1.2983478512036306, 1.311277594222998, 1.323952957334969, 1.3363427316659975 ], [ 1.0678148700569514, 1.0612031731098444, 1.0548424016516031, 1.0487625418940127, 1.042994624835599, 1.0375706301840761, 1.032523366687917, 1.0278863257961035, 1.0236935053352956, 1.0199791997211216, 1.0167777531489937, 1.014123272302927, 1.0120492954630946, 1.010588415592471, 1.009771856171393, 1.0096290003717001, 1.0101868767598456, 1.011469608192837, 1.0134978349333503, 1.016288128117108, 1.0198524151911026, 1.0241974441742192, 1.029324317690915, 1.0352281296598609, 1.0418977363009132, 1.0493156880864496, 1.0574583403129256, 1.066296147728501, 1.0757941344279462, 1.0859125157726763, 1.0966074362727127, 1.1078317778226017, 1.1195359876356008, 1.1316688754270394, 1.1441783351610821, 1.1570119577679183, 1.1701175166659257, 1.1834433256682317, 1.1969384859223053, 1.2105530515721525, 1.2242381502045674, 1.2379460929323711, 1.251630501332681, 1.2652464670784749, 1.2787507480924085, 1.2921019949370738, 1.3052609943382791, 1.3181909135141063, 1.3308575288768119, 1.3432294248362098 ], [ 1.0712246030114727, 1.0647128531345353, 1.0584530446244074, 1.052475043063749, 1.0468097539904269, 1.0414890283088334, 1.036545544427177, 1.032012664037579, 1.0279242582018366, 1.0243145001982485, 1.0212176214669921, 1.0186676270249757, 1.016697966991553, 1.0153411614869903, 1.0146283772764817, 1.0145889562960804, 1.0152498987776928, 1.0166353072219363, 1.018765801994748, 1.0216579247286572, 1.02532355162931, 1.0297693445535325, 1.0349962723632393, 1.0409992373974686, 1.0477668407989356, 1.0552813150867189, 1.0635186426497867, 1.0724488654642699, 1.0820365758287436, 1.0922415623039867, 1.1030195714590683, 1.114323136273925, 1.1261024173848784, 1.138306004464319, 1.1508816320643975, 1.1637767768468574, 1.176939120098968, 1.1903168785480613, 1.2038590244390286, 1.2175154289860752, 1.2312369688924187, 1.244975632900888, 1.2586846558675595, 1.2723186948015346, 1.2858340481477737, 1.299188908944, 1.31234363568405, 1.3252610219060263, 1.337906546055437, 1.35024858606799 ], [ 1.074998026046359, 1.0685978406149337, 1.0624506141000267, 1.0565860443104016, 1.051034858421839, 1.0458287194906577, 1.0410001100448254, 1.0365821896921148, 1.0326086234135088, 1.0291133769762209, 1.0261304757444916, 1.0236937231492322, 1.0218363752831323, 1.020590768633511, 1.019987898996954, 1.020056951314367, 1.0208247827086616, 1.022315364563752, 1.0245491941315947, 1.027542691805399, 1.031307606497688, 1.0358504578113852, 1.0411720488309453, 1.047267086077575, 1.0541239421593311, 1.061724590975562, 1.0700447348373023, 1.0790541283625918, 1.088717087256423, 1.0989931534346744, 1.1098378738027366, 1.1212036403172465, 1.133040534993597, 1.1452971257999276, 1.1579211678425734, 1.1708601782939465, 1.1840618717754774, 1.1974744629479104, 1.2110468613859056, 1.2247287966261196, 1.2384709158145264, 1.2522248921136816, 1.2659435709202116, 1.279581166529814, 1.2930935078508963, 1.306438320773781, 1.3195755280858514, 1.3324675454026642, 1.3450795527191424, 1.357379724796729 ], [ 1.079127310734476, 1.072850050537638, 1.0668267706175683, 1.061086955185274, 1.0556611015325204, 1.0505806272266311, 1.0458777547563354, 1.0415853706131646, 1.0377368555117161, 1.034365882200722, 1.0315061771330825, 1.0291912422052703, 1.0274540329288753, 1.0263265898757277, 1.0258396211951406, 1.0260220356239065, 1.026900427901448, 1.0284985220544798, 1.0308365827393797, 1.033930810667821, 1.037792744751386, 1.042428700259437, 1.0478392778557095, 1.054018981417792, 1.0609559815825713, 1.0686320559405011, 1.0770227255230738, 1.0860975916299456, 1.0958208591433958, 1.1061520149537134, 1.117046615663237, 1.1284571294593453, 1.140333774139408, 1.1526252970232438, 1.1652796525081603, 1.1782445483857216, 1.1914678511608576, 1.2048978609466598, 1.2184834845422101, 1.2321743472955273, 1.2459208876945775, 1.2596744730282872, 1.2733875621353512, 1.2870139259349755, 1.3005089218397503, 1.3138298069125258, 1.3269360679357027, 1.339789744413972, 1.3523557221761442, 1.364601979545957 ], [ 1.0836031012919447, 1.0774597853958323, 1.0715714738050548, 1.065967392819054, 1.060677759977507, 1.0557336914983164, 1.0511670875509638, 1.0470104924142531, 1.0432969262842833, 1.0400596852383746, 1.0373321056602052, 1.0351472893462386, 1.033537785625146, 1.0325352272469008, 1.0321699176899812, 1.0324703690876107, 1.0334627924057915, 1.0351705450293474, 1.0376135456668352, 1.0408076724422413, 1.0447641668733139, 1.0494890734049152, 1.0549827500665958, 1.0612394890962824, 1.0682472854005873, 1.0759877843289414, 1.0844364282021828, 1.0935628044230594, 1.1033311790948857, 1.113701181903287, 1.1246285935625768, 1.1360661786301147, 1.147964505032831, 1.160272697181653, 1.1729390812165121, 1.185911697369411, 1.199138673821007, 1.2125684762278037, 1.2261500640444827, 1.2398329954712823, 1.2535675250231497, 1.2673047312463321, 1.2809966992350976, 1.2945967669313536, 1.3080598293087364, 1.3213426830230575, 1.334404387226775, 1.3472066141474708, 1.3597139650583616, 1.3718942322594376 ], [ 1.0884145517640005, 1.082415772708482, 1.0766730199113104, 1.0712152190758257, 1.066072259971205, 1.061274903675849, 1.0568546680427575, 1.0528436885175492, 1.0492745511614112, 1.0461800944718802, 1.0435931763882726, 1.0415464027694419, 1.0400718137179616, 1.0392005245114309, 1.0389623187424317, 1.0393851927603956, 1.0404948528787612, 1.042314170287379, 1.0448626033540886, 1.0481556030047559, 1.0522040238258135, 1.0570135706868173, 1.0625843167797626, 1.0689103323577622, 1.0759794623922747, 1.0837732845796877, 1.092267266386151, 1.1014311223234239, 1.111229352955522, 1.1216219286003088, 1.1325650665848026, 1.1440120435841814, 1.1559139849448965, 1.1682205804824246, 1.1808806895919832, 1.1938428156936154, 1.2070554489423841, 1.220467294421188, 1.2340274180210535, 1.247685351230515, 1.261391197297501, 1.2750957746374552, 1.2887508208122613, 1.3023092649942583, 1.3157255618140835, 1.3289560674668124, 1.3419594315045187, 1.35469697539444, 1.3671330312107783, 1.379235219540263 ], [ 1.0935493802244873, 1.087705221135462, 1.0821180996530189, 1.0768165998845654, 1.071830237781382, 1.0671893677667308, 1.062925067969547, 1.0590690012905586, 1.055653249260635, 1.0527101154011353, 1.0502718945958278, 1.0483706048841162, 1.0470376781629431, 1.0463036066508393, 1.0461975427745527, 1.0467468515831486, 1.047976617107383, 1.0499091074986031, 1.0525632084766239, 1.055953840598006, 1.0600913828236254, 1.0649811320612763, 1.070622834496774, 1.077010327880355, 1.0841313326823292, 1.091967422834323, 1.1004941934148054, 1.1096816244509295, 1.1194946197998012, 1.1298936815041696, 1.1408356666233979, 1.152274567747578, 1.1641622609347935, 1.176449174669433, 1.1890848484234233, 1.2020183668870676, 1.2151986735162927, 1.2285747827507398, 1.242095922414818, 1.255711644882252, 1.269371946397418, 1.283027428236122, 1.2966295221588835, 1.3101307880119233, 1.3234852761571256, 1.3366489344667143, 1.3495800311175976, 1.3622395614966245, 1.374591609996409, 1.3866036440127603 ], [ 1.0989939398016833, 1.0933138950632757, 1.0878918763371723, 1.0827560868234478, 1.0779356246373684, 1.073460388434171, 1.0693609620179734, 1.0656684752701624, 1.062414438483081, 1.0596305469520875, 1.0573484524952423, 1.0555994984829296, 1.0544144150445296, 1.0538229714832987, 1.0538535837228538, 1.054532876022063, 1.0558851984585345, 1.0579321050293233, 1.0606918018287388, 1.0641785806502808, 1.068402260225497, 1.0733676643976302, 1.0790741725282158, 1.0855153805912803, 1.0926789098643666, 1.1005463925195713, 1.109093649575651, 1.1182910580478789, 1.128104083745658, 1.1384939379368122, 1.1494183037675427, 1.1608320743762506, 1.1726880495602534, 1.1849375500733337, 1.1975309251044586, 1.210417945771846, 1.223548092845167, 1.2368707590124746, 1.2503353945839706, 1.263891630578973, 1.277489414233092, 1.2910791882646295, 1.3046121363110592, 1.3180405035631761, 1.331317986069711, 1.3444001677567585, 1.3572449741174384, 1.3698131077498186, 1.3820684335628977, 1.3939782889767038 ], [ 1.104733305913694, 1.0992262070439234, 1.0939780836549728, 1.0890167203855445, 1.08437075553872, 1.0800695853615983, 1.0761432476836013, 1.0726222823683895, 1.0695375658071051, 1.0669201164730273, 1.0648008683994474, 1.0632104093814174, 1.0621786808089084, 1.061734636419079, 1.0619058580514047, 1.0627181278887317, 1.0641949588907114, 1.0663570884001687, 1.0692219443978754, 1.0728030996035678, 1.0771097352696375, 1.0821461433291837, 1.0879113012398431, 1.0943985566581105, 1.1015954571421025, 1.1094837520905594, 1.1180395799713745, 1.1272338351397935, 1.1370326883689656, 1.1473982177105582, 1.1582890953561056, 1.1696612742668457, 1.181468625725063, 1.1936634934670822, 1.2061971477495959, 1.2190201392522027, 1.2320825651146063, 1.2453342670746392, 1.258724986161003, 1.2722045015890697, 1.2857227836967173, 1.2992301901599281, 1.3126777289026037, 1.3260173991225095, 1.339202605534677, 1.3521886244218126, 1.3649330879395514, 1.3773964483224077, 1.3895423865313503, 1.4013381385503443 ], [ 1.1107513786610497, 1.1054253269657401, 1.1003591419599263, 1.0955801536785157, 1.09111650066667, 1.0869970326301137, 1.0832511928189352, 1.0799088777289703, 1.077000271505129, 1.0745556522544872, 1.0726051673532244, 1.0711785748066378, 1.0703049478646778, 1.0700123405072057, 1.070327412230374, 1.0712750119656536, 1.0728777231546176, 1.0751553751957532, 1.0781245308264353, 1.0817979644929305, 1.0861841530811729, 1.0912868067737322, 1.0971044729834944, 1.1036302485903162, 1.110851633300369, 1.1187505486259106, 1.1273035327267118, 1.1364821028203362, 1.1462532573163702, 1.1565800734350857, 1.1674223467675011, 1.1787372194561814, 1.1904797534161928, 1.2026034215387431, 1.215060508326951, 1.2278024267168177, 1.240779966675905, 1.2539434939260312, 1.267243117395267, 1.2806288457050095, 1.2940507570633066, 1.3074592102635088, 1.320805122222195, 1.3340403268115708, 1.3471180122056423, 1.3599932148711362, 1.3726233338566858, 1.3849686231883755, 1.3969926234718055, 1.4086625037955305 ], [ 1.1170309989041733, 1.1118933063460734, 1.1070162912728998, 1.1024267946448079, 1.0981524173206152, 1.0942214208614456, 1.0906626084493738, 1.0875051836436482, 1.0847785845288058, 1.082512290669144, 1.0807356002019601, 1.0794773744228732, 1.0787657474074175, 1.078627798669463, 1.0790891877088917, 1.0801737507133056, 1.0819030618422398, 1.084295964625457, 1.0873680831727293, 1.0911313280847974, 1.0955934178430746, 1.1007574422883402, 1.1066214993384282, 1.113178437727207, 1.1204157356263937, 1.128315536441514, 1.1368548489532042, 1.1460059010242194, 1.1557366175809594, 1.1660111786470997, 1.1767906057272697, 1.1880333271270456, 1.1996956845849518, 1.2117323616542937, 1.2240967330629309, 1.2367411478810237, 1.2496171643444944, 1.2626757520251148, 1.2758674733683515, 1.2891426573515694, 1.3024515845211198, 1.3157447102730524, 1.3289729545395106, 1.3420880763804857, 1.355043132854338, 1.367792999638964, 1.380294914046699, 1.3925089943246491, 1.4043986929831984, 1.4159311533095553 ], [ 1.1235540761709653, 1.1186112156888257, 1.1139297387328007, 1.1095359642732336, 1.1054569195776633, 1.1017202390241765, 1.0983540434263561, 1.0953867977399645, 1.0928471448882364, 1.0907637133440073, 1.0891648960724325, 1.0880785985118886, 1.087531953517729, 1.0875510017039338, 1.0881603365129842, 1.0893827147742896, 1.0912386356463242, 1.093745893835743, 1.0969191169375576, 1.1007693015738296, 1.1053033683745472, 1.110523761003851, 1.1164281182139284, 1.123009048816256, 1.1302540360214393, 1.138145488897466, 1.1466609449615275, 1.1557734109072875, 1.1654518113771835, 1.1756615025134918, 1.186364801454941, 1.1975214871056696, 1.2090892408676768, 1.221024014976166, 1.2332803345257517, 1.24581155082238, 1.2585700649879017, 1.271507534209483, 1.284575066164914, 1.2977234075182142, 1.3109031415220473, 1.3240649214083815, 1.337159770627281, 1.3501394719214843, 1.362957046344038, 1.3755672987392884, 1.3879273873098221, 1.3999973674958723, 1.4117406649239355, 1.423124444980535 ], [ 1.1303017262156625, 1.1255592924702318, 1.1210788177662037, 1.1168860677484025, 1.1130074622533688, 1.1094699720673151, 1.1063009966165864, 1.1035282206177368, 1.101179447618527, 1.099282408307423, 1.0978645414862473, 1.096952745732782, 1.0965731000881622, 1.09675055267371, 1.097508577083205, 1.0988687978436846, 1.1008505883353767, 1.1034706474345877, 1.1067425648431215, 1.1106763894875846, 1.1152782201437337, 1.1205498418465263, 1.1264884345950048, 1.1330863810136524, 1.1403311957192992, 1.1482055904523252, 1.1566876759264395, 1.1657512855889158, 1.1753663911211503, 1.1854995682926621, 1.1961144681156755, 1.2071722539740617, 1.218631979744504, 1.2304509030042066, 1.2425847448722638, 1.2549879173099052, 1.2676137367186757, 1.2804146327651629, 1.2933423523875553, 1.3063481595000863, 1.3193830424511914, 1.3323979561429855, 1.345344132298488, 1.3581734824377312, 1.37083909563083, 1.3832958063397265, 1.3955007872445346, 1.4074141142335503, 1.418999255975937, 1.4302234544929373 ], [ 1.1372544158016729, 1.1327170970260618, 1.1284421559087996, 1.1244547750841887, 1.1207807352705228, 1.1174463099882639, 1.114478141665922, 1.111903097326762, 1.1097481019933746, 1.1080399479406924, 1.1068050779993024, 1.1060693413032434, 1.1058577202479902, 1.1061940280529616, 1.1071005773079317, 1.1085978213391208, 1.1107039722755148, 1.1134346024199733, 1.116802238942289, 1.1208159658715955, 1.1254810514923215, 1.1307986228551967, 1.1367654112120098, 1.1433735916044367, 1.1506107355369928, 1.1584598871437, 1.1668997610042176, 1.1759050455034168, 1.185446782211633, 1.195492782602994, 1.2060080415517287, 1.21695511395582, 1.228294435513561, 1.2399845871159338, 1.251982518180711, 1.2642437512183018, 1.2767225853833402, 1.2893723047866097, 1.3021453874907674, 1.3149937123014765, 1.3278687737656871, 1.3407219325721578, 1.353504736214708, 1.366169335649519, 1.3786690000206536, 1.3909587034460218, 1.4029957366514467, 1.4147402885308424, 1.426155948573954, 1.4372100959685095 ], [ 1.144392112121351, 1.1400636734282432, 1.1359978479967148, 1.1322192075375672, 1.1287528642506555, 1.1256243635999907, 1.1228595589751227, 1.1204844666068372, 1.118525099090327, 1.117007275910559, 1.1159564094907832, 1.1153972655376827, 1.115353696888941, 1.1158483507527095, 1.116902350247995, 1.1185349526067654, 1.120763188370247, 1.123601488458584, 1.1270613090857604, 1.131150767958548, 1.135874308654118, 1.1412324128745446, 1.1472213815498986, 1.1538332045248918, 1.1610555339959656, 1.168871768676788, 1.1772612444474488, 1.1861995146500284, 1.1956586918266383, 1.205607815576751, 1.2160132109198671, 1.2268388092146258, 1.2380464180699582, 1.2495959438036472, 1.261445583834172, 1.2735520111787042, 1.285870567034985, 1.2983554647575228, 1.3109599989751248, 1.3236367556357787, 1.3363378329243512, 1.3490151002443176, 1.3616205300762723, 1.374106627991756, 1.3864269619630039, 1.398536763728259, 1.4103935537780843, 1.4219577341058274, 1.4331930991646649, 1.4440672307744253 ], [ 1.1516944342014832, 1.1475777123679427, 1.143723631366828, 1.1401561260112125, 1.1368996130461384, 1.1339788821560486, 1.1314189694083947, 1.1292450116846235, 1.1274820806763384, 1.1261549951137886, 1.1252881100737302, 1.1249050825231033, 1.1250286127430462, 1.1256801620068013, 1.1268796479261682, 1.1286451203087962, 1.1309924222435044, 1.1339348434719851, 1.1374827758515178, 1.1416433836678508, 1.146420304343058, 1.1518133971132756, 1.157818557771522, 1.1644276157846511, 1.171628325398877, 1.1794044546386315, 1.1877359660438698, 1.1965992721442884, 1.205967539348809, 1.2158110087245237, 1.226097303163865, 1.2367916984310308, 1.247857349133998, 1.2592554759661823, 1.2709455321305168, 1.2828853697736275, 1.2950314203182194, 1.30733889045042, 1.319761967145606, 1.3322540280029014, 1.3447678671970453, 1.357255963684319, 1.3696708249169314, 1.3819654293501278, 1.3940937671849212, 1.4060114511520387, 1.4176763487113715, 1.4290491801198262, 1.4400940333026904, 1.4507787617241503 ], [ 1.1591408036753776, 1.1552377131051115, 1.1515970597625833, 1.1482421177293651, 1.1451965840297949, 1.1424844681202377, 1.1401299644214749, 1.1381573066356307, 1.1365906026564931, 1.1354536490170046, 1.134769724048272, 1.134561359284873, 1.1348500891864548, 1.1356561800070328, 1.1369983396887784, 1.1388934120389949, 1.1413560602012653, 1.1443984465435428, 1.1480299184671656, 1.1522567120818514, 1.157081687832232, 1.1625041134807061, 1.1685195097195524, 1.1751195714837903, 1.1822921733585934, 1.1900214603699402, 1.1982880166220766, 1.2070690951384713, 1.2163388848823289, 1.2260687874336866, 1.2362276778251846, 1.2467821319674095, 1.2576966154185376, 1.2689336414430683, 1.2804539156135404, 1.292216485676374, 1.3041789085286013, 1.31629743545769, 1.3285272101423762, 1.3408224774489375, 1.3531368140992497, 1.3654234066203175, 1.3776354069447396, 1.3897263857312128, 1.4016508806631691, 1.4133650109915177, 1.4248271105403394, 1.4359983251153647, 1.4468431266563098, 1.457329711239964 ], [ 1.166710592425777, 1.1630221416953475, 1.1595956728264507, 1.156453777697413, 1.1536194122366172, 1.1511157847095161, 1.1489662277163286, 1.147194052836937, 1.1458223869659279, 1.1448739895582252, 1.1443710502814826, 1.1443349669751768, 1.1447861043866259, 1.1457435349335239, 1.1472247637719586, 1.1492454417624292, 1.1518190715334309, 1.1549567137050019, 1.1586667023446602, 1.1629543806712512, 1.1678218695650466, 1.1732678821367881, 1.1792875969459176, 1.1858725999829645, 1.1930109010043348, 1.2006870233981135, 1.2088821591833097, 1.2175743732943454, 1.2267388356785143, 1.236348057669726, 1.2463721118056101, 1.2567788217982008, 1.2675339202180196, 1.2786011824693622, 1.2899425528845385, 1.3015182792557307, 1.3132870659274805, 1.3252062468228873, 1.3372319749906327, 1.3493194291292596, 1.3614230489393715, 1.3734968228370406, 1.385494654552725, 1.3973708247051226, 1.4090805422413044, 1.420580556947369, 1.4318297870092809, 1.4427899100463728, 1.4534258721314424, 1.4637062832011396 ], [ 1.17438326480561, 1.1709095829493328, 1.1676971583543625, 1.1647678818108336, 1.162143949880857, 1.159847752356383, 1.1579017441558732, 1.1563283007941654, 1.1551495567017325, 1.1543872258854968, 1.1540624047368875, 1.1541953572301291, 1.154805283346339, 1.1559100723387263, 1.1575260434481034, 1.1596676779022148, 1.162347347474143, 1.165575046479442, 1.169358135735054, 1.1737011084800417, 1.1786053892679722, 1.1840691770109941, 1.1900873422915366, 1.1966513864447934, 1.2037494656524512, 1.2113664776254416, 1.2194842020886598, 1.2280814803444715, 1.237134415088802, 1.246616570729146, 1.256499157537411, 1.2667511898961454, 1.2773396181860635, 1.288229442829824, 1.299383824528018, 1.3107642046807737, 1.322330444848132, 1.3340409874369044, 1.345853036732081, 1.3577227632435473, 1.3696055437089418, 1.381456257890416, 1.3932296643225335, 1.404880866832913, 1.4163658644521293, 1.4276421563298256, 1.4386693581146868, 1.449409781450154, 1.4598289338538868, 1.469895908987711 ], [ 1.1821385124124213, 1.178878883898946, 1.175879504867559, 1.1731615489317704, 1.1707464383119726, 1.1686557308823409, 1.1669109924426246, 1.165533653546254, 1.164544850389693, 1.163965249516348, 1.1638148564313704, 1.1641128086834738, 1.1648771545707908, 1.166124619390622, 1.1678703620932869, 1.1701277263164256, 1.1729079910409936, 1.1762201274529944, 1.1800705698902028, 1.1844630098073115, 1.1893982222464288, 1.1948739340520902, 1.2008847417298065, 1.2074220842181018, 1.2144742719288677, 1.2220265685099123, 1.2300613165484597, 1.2385580938327083, 1.2474938839478016, 1.2568432449090388, 1.266578462747708, 1.276669683137511, 1.2870850219251018, 1.2977906625914708, 1.3087509528433106, 1.3199285123154885, 1.3312843594291432, 1.3427780607289066, 1.3543679043354457, 1.3660111026746165, 1.3776640368779196, 1.38928256126406, 1.4008223855827655, 1.4122395426931436, 1.4234909323165097, 1.4345349133162435, 1.4453319039286894, 1.455844945304925, 1.4660401887701566, 1.4758872786362989 ], [ 1.1899563797077362, 1.1869092869164903, 1.1841211424956126, 1.1816123897690085, 1.1794036650833097, 1.1775156848939463, 1.1759691189142296, 1.17478444885167, 1.1739818124564414, 1.1735808328805237, 1.173600433709661, 1.1740586405010947, 1.1749723702546973, 1.176357210975928, 1.1782271943591367, 1.1805945656154218, 1.183469555550101, 1.1868601610844132, 1.190771941389709, 1.1952078374872075, 1.2001680233444962, 1.2056497959391894, 1.211647510257092, 1.2181525626459266, 1.2251534224318779, 1.2326357075465704, 1.240582295695717, 1.248973459134149, 1.2577870092767474, 1.266998437893091, 1.276581044785032, 1.2865060472197354, 1.2967426727921467, 1.307258243057453, 1.318018258463421, 1.3289864949609993, 1.340125119907394, 1.3513948317871622, 1.3627550275726457, 1.374164004517249, 1.3855792083650116, 1.3969575435246688, 1.4082557586291538, 1.4194309114132346, 1.4304409019956361, 1.4412450481982724, 1.451804665563436, 1.4620836113674294, 1.4720487563757632, 1.481670358151102 ], [ 1.197817379117431, 1.1949805510351308, 1.1924010706334884, 1.190098640943968, 1.1880931044450918, 1.1864043306557002, 1.18505209067255, 1.184055918362028, 1.1834349581375032, 1.1832077995456767, 1.1833922992600168, 1.184005391549635, 1.1850628888675978, 1.1865792748874189, 1.1885674931045496, 1.1910387349862313, 1.1940022325519857, 1.1974650611175137, 1.201431958622448, 1.205905168335044, 1.210884311611052, 1.2163662966055409, 1.2223452672677302, 1.2288125945584345, 1.2357569087423617, 1.2431641681420678, 1.25101775641394, 1.259298597875631, 1.26798527934844, 1.2770541678730944, 1.2864795166217906, 1.296233555925763, 1.3062865715567993, 1.3166069768839503, 1.3271613880375561, 1.3379147112585976, 1.3488302498664404, 1.3598698364437352, 1.3709939957350046, 1.3821621460510611, 1.3933328503481717, 1.4044641297093934, 1.4155138488213415, 1.4264401742164206, 1.4372020932842233, 1.4477599691224876, 1.4580760972132993, 1.4681152271873037, 1.4778450168022128, 1.4872363939955144 ], [ 1.2057025946042428, 1.2030730604287792, 1.2006989713083072, 1.1985992831702872, 1.196793040200265, 1.1952992634139235, 1.1941368270872876, 1.1933243229295938, 1.1928799121201874, 1.192821165633184, 1.1931648936504, 1.193926965322082, 1.1951221206802918, 1.1967637771378201, 1.1988638337030386, 1.201432476776715, 1.204477992120635, 1.208006588221312, 1.2120222367123974, 1.2165265356396926, 1.2215186010170755, 1.2269949912104576, 1.2329496671281865, 1.23937398901142, 1.246256747956684, 1.25358422746658, 1.2613402877538529, 1.2695064637415574, 1.2780620672022112, 1.2869842845841488, 1.2962482647815312, 1.3058271949915976, 1.315692367047015, 1.325813240189649, 1.336157508313319, 1.3466911799832608, 1.3573786786040956, 1.3681829691554246, 1.379065718103518, 1.3899874946851638, 1.4009080236233507, 1.4117864993565972, 1.4225819680936933, 1.4332537759389918, 1.4437620704690644, 1.454068332441771, 1.464135906898349, 1.4739305007602417, 1.4834206173476783, 1.492577905737298 ], [ 1.213593773052699, 1.2111679194078864, 1.2089953076452833, 1.2070941429904072, 1.205482670446437, 1.2041790648065258, 1.203201309458488, 1.2025670640270532, 1.202293521145228, 1.2023972529514664, 1.2028940482800554, 1.2037987419502632, 1.205125038066002, 1.2068853298013207, 1.2090905187501682, 1.21174983752641, 1.2148706798611193, 1.2184584428864842, 1.222516386529882, 1.2270455148651347, 1.2320444837809654, 1.237509538350684, 1.2434344817959426, 1.2498106759850682, 1.256627071152178, 1.263870260240675, 1.2715245513303188, 1.279572050407027, 1.2879927466350771, 1.296764593488332, 1.305863581521892, 1.3152638018366776, 1.32493750275226, 1.334855145107022, 1.344985463368096, 1.3552955402250346, 1.3657509019903014, 1.3763156417395273, 1.3869525773815488, 1.3976234527667908, 1.4082891906115256, 1.4189102049371303, 1.4294467766338192, 1.4398594884902094, 1.4501097068564024, 1.4601600883288244, 1.46997508384885, 1.4795214109293122, 1.4887684675704158, 1.497688667794469 ], [ 1.2214734031359664, 1.2192470336585604, 1.2172714072388404, 1.215563977978832, 1.2141421942468766, 1.2130233905694012, 1.2122246692565586, 1.2117627719514716, 1.2116539415425285, 1.2119137751798827, 1.212557069493645, 1.213597659522116, 1.2150482533176785, 1.2169202646937278, 1.2192236470842437, 1.2219667319743122, 1.2251560757744029, 1.2287963192902234, 1.2328900640085254, 1.2374377691972331, 1.2424376732365314, 1.247885741611245, 1.2537756426096036, 1.260098750062616, 1.2668441705794782, 1.2739987909270551, 1.281547339764387, 1.289472457185907, 1.2977547656990047, 1.306372937470276, 1.3153037548198834, 1.3245221636950588, 1.334001322703688, 1.3437126526901202, 1.3536258933928682, 1.3637091743688432, 1.3739291074007658, 1.3842509075274552, 1.394638550021396, 1.405054970970876, 1.4154623188998807, 1.4258222630511221, 1.4360963597954803, 1.446246472163563, 1.456235229791668, 1.466026509411437, 1.4755859112043914, 1.484881205065004, 1.4938827232466505, 1.5025636812469527 ], [ 1.2293247816327988, 1.2272931777836587, 1.22550953060094, 1.2239905457238716, 1.222752880712737, 1.221813039226507, 1.221187255870095, 1.2208913720276617, 1.2209407032458488, 1.2213498990232443, 1.2221327961984958, 1.2233022675066199, 1.224870067282444, 1.2268466767156192, 1.2292411514796178, 1.2320609749321332, 1.2353119203713485, 1.2389979259766672, 1.243120986002505, 1.2476810614715663, 1.2526760129834598, 1.2581015572982124, 1.2639512480974358, 1.2702164798527984, 1.2768865121882749, 1.283948510715026, 1.2913875992836323, 1.299186918170597, 1.3073276830625604, 1.3157892408738074, 1.324549120317505, 1.3335830774745618, 1.3428651389755197, 1.3523676474329562, 1.3620613151610717, 1.3719152929495335, 1.381897260907448, 1.3919735484531242, 1.4021092905631611, 1.4122686272492575, 1.4224149523764782, 1.432511215696147, 1.4425202779108546, 1.4524053128933634, 1.4621302447369238, 1.4716602014904137, 1.480961963596756, 1.4900043840995898, 1.4987587597565017, 1.5071991367288602 ], [ 1.2371320674232846, 1.23529004948871, 1.2336929251665867, 1.2323566572309947, 1.2312971213315898, 1.230530002822404, 1.2300706851779992, 1.2299341304209583, 1.2301347522256696, 1.2306862826409826, 1.2316016336856337, 1.2328927554105984, 1.2345704923793315, 1.2366444408745771, 1.2391228094732505, 1.2420122859072606, 1.2453179133068824, 1.2490429789594197, 1.2531889185616276, 1.25775523855887, 1.2627394585212488, 1.2681370746071912, 1.2739415440483388, 1.280144289339572, 1.2867347195690417, 1.293700265244727, 1.3010264222556496, 1.3086968004170167, 1.31669317250113, 1.3249955207634017, 1.333582079625307, 1.3424293751496712, 1.3515122639393184, 1.360803975817335, 1.370276165908257, 1.3798989824912322, 1.3896411573382588, 1.3994701253313517, 1.40935218001961, 1.419252671265199, 1.4291362498581706, 1.4389671615322035, 1.4487095889820099, 1.458328035509933, 1.4677877385522984, 1.4770550966074187, 1.4860980900387664, 1.4948866755296177, 1.5033931357341006, 1.5115923694776103 ], [ 1.2448803236103052, 1.2432223109886158, 1.2418058655831143, 1.2406462156488063, 1.2397584666434756, 1.2391575010258995, 1.2388578705299063, 1.2388736814266839, 1.2392184735180813, 1.239905093862649, 1.2409455665198665, 1.2423509598987752, 1.244131253602563, 1.24629520695343, 1.248850231638452, 1.2518022711073906, 1.2551556894438138, 1.2589131723833986, 1.2630756429341763, 1.2676421936345619, 1.272610036856701, 1.2779744737369503, 1.2837288813395618, 1.2898647166141082, 1.2963715347098235, 1.3032370183997704, 1.3104470148925225, 1.3179855762901216, 1.325835000461014, 1.3339758701264277, 1.3423870894075114, 1.3510459187673791, 1.3599280109782488, 1.3690074522312592, 1.3782568136359767, 1.3876472190776197, 1.3971484357508215, 1.4067289937235838, 1.4163563405888118, 1.4259970364857588, 1.4356169932611453, 1.4451817590453475, 1.4546568459823537, 1.4640080945405711, 1.4732020633508678, 1.4822064296802608, 1.4909903832297984, 1.4995249954465086, 1.5077835480496042, 1.5157418076676605 ], [ 1.2525555483884863, 1.2510756183926797, 1.2498336811960074, 1.248844241406253, 1.24812164855036, 1.2476800001095956, 1.2475330378803473, 1.247694038242427, 1.2481756971334053, 1.248990010765363, 1.2501481533743664, 1.251660353554318, 1.2535357709823431, 1.255782375576276, 1.2584068313132546, 1.2614143870569055, 1.2648087767598057, 1.2685921312998019, 1.2727649039481579, 1.2773258110392207, 1.2822717888151798, 1.2875979666775599, 1.2932976562363667, 1.2993623546853428, 1.3057817602457429, 1.3125437968269282, 1.3196346447605516, 1.327038774564863, 1.334738981229313, 1.342716417456839, 1.3509506255730153, 1.359419569261113, 1.3680996677328732, 1.3769658362296717, 1.3859915377464447, 1.3951488515256438, 1.4044085641742883, 1.4137402892154947, 1.4231126204507412, 1.432493323561038, 1.441849568747966, 1.4511482047836313, 1.4603560716312163, 1.4694403450800817, 1.4783689031083425, 1.4871107005679196, 1.4956361368661737, 1.5039174009708085, 1.5119287793551053, 1.5196469151849867 ], [ 1.2601446954144258, 1.2588366399579978, 1.2577627717737496, 1.2569368849727705, 1.2563725896567108, 1.2560832184054864, 1.2560817268937274, 1.2563805892696296, 1.256991689130264, 1.2579262071425352, 1.2591945065825392, 1.2608060182890273, 1.2627691267357142, 1.2650910591072968, 1.2677777793940488, 1.2708338895796067, 1.2742625399613308, 1.2780653504922181, 1.282242344751022, 1.286791897726625, 1.291710698051068, 1.296993724659635, 1.3026342371423576, 1.308623778347902, 1.3149521871915903, 1.3216076191956652, 1.3285765721366285, 1.3358439143536642, 1.34339291380697, 1.3512052668397403, 1.359261126714862, 1.3675391332483136, 1.3760164461063864, 1.3846687854411668, 1.393470484405736, 1.402394558656714, 1.411412798185443, 1.4204958866924242, 1.429613553177756, 1.438734759373848, 1.4478279249969288, 1.4568611904941402, 1.4658027140934615, 1.474620996771694, 1.483285225649674, 1.4917656237863157, 1.5000337928170207, 1.508063034647144, 1.515828639515393, 1.5233081299974178 ], [ 1.2676356845243537, 1.266493064188375, 1.2655806125931175, 1.2649114285197818, 1.2644984010888158, 1.2643541198640336, 1.2644907798363074, 1.264920081955699, 1.2656531300635996, 1.2667003252682127, 1.2680712590004042, 1.2697746061733817, 1.2718180200368434, 1.274208030449022, 1.2769499473719415, 1.2800477714076486, 1.2835041131182685, 1.2873201226955147, 1.2914954312563667, 1.2960281046406588, 1.3009146100860043, 1.3061497955837513, 1.3117268811207934, 1.3176374604454495, 1.3238715115316404, 1.3304174136258022, 1.3372619687095932, 1.3443904254411654, 1.3517865041587624, 1.3594324223156342, 1.3673089206966804, 1.3753952918485606, 1.3836694132237062, 1.392107788487009, 1.4006856011734952, 1.4093767853529204, 1.418154118108534, 1.426989338431314, 1.435853296515888, 1.4447161363573242, 1.4535475129390145, 1.4623168431750804, 1.4709935872290163, 1.479547554100123, 1.487949222781377, 1.49617006822372, 1.5041828801263606, 1.5119620624210437, 1.519483902263636, 1.5267267992441176 ] ], "zauto": true, "zmax": 1.5267267992441176, "zmin": -1.5267267992441176 }, { "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": [ [ 0.1349979671295245, 0.13286491800243, 0.13071897538338664, 0.12856424053049267, 0.12640495501998208, 0.12424546829496197, 0.1220902006544017, 0.11994360193283633, 0.11781010634881088, 0.1156940842745296, 0.11359979199813895, 0.11153132090572082, 0.10949254788784164, 0.10748708915238013, 0.10551825996973921, 0.10358904314865974, 0.1017020691945769, 0.09985961108995406, 0.09806359641272289, 0.09631563904127566, 0.09461709196728961, 0.09296912176043759, 0.09137280404039169, 0.08982923797780415, 0.08833967645645197, 0.08690566718423472, 0.08552919883951103, 0.08421284536205957, 0.0829599007961606, 0.08177449668436955, 0.08066169388352688, 0.07962754080668992, 0.07867909047667074, 0.07782436944147621, 0.07707229264603155, 0.07643251994338976, 0.07591525227058749, 0.07553096879895105, 0.075290110670984, 0.07520272210596123, 0.07527806523041496, 0.0755242301733156, 0.07594776572955371, 0.07655335719781618, 0.07734357609037883, 0.07831872112496062, 0.07947676180940194, 0.08081338625087445, 0.08232214516750395, 0.08399467601257393 ], [ 0.1332185416655659, 0.13101764616783695, 0.12880356072660837, 0.12658060572690455, 0.12435325717002797, 0.12212611290120495, 0.11990385374703642, 0.1176911997400766, 0.11549286184322023, 0.11331348987744992, 0.1111576177031249, 0.10902960710150571, 0.1069335922363148, 0.10487342702161818, 0.102852638148173, 0.1008743868804653, 0.09894144297671954, 0.09705617414482501, 0.09522055427046064, 0.09343619319247612, 0.09170439002752372, 0.09002621096364663, 0.0884025910895844, 0.08683445827840479, 0.08532287550806854, 0.08386919640349091, 0.08247522735101356, 0.08114338837380268, 0.07987686413571131, 0.07867973598654095, 0.07755708585776491, 0.07651506302753577, 0.07556090527021044, 0.07470290670964767, 0.0739503259062426, 0.07331322951246053, 0.07280226947789732, 0.07242839550531231, 0.07220250935182881, 0.07213507345936296, 0.07223569272443343, 0.07251269401573103, 0.07297273207928405, 0.07362045151201961, 0.0744582317112547, 0.07548603504500377, 0.07670136876253002, 0.07809935996575573, 0.07967293223405102, 0.08141306400767322 ], [ 0.1314395786522416, 0.12917039020668186, 0.12688769653221169, 0.1245960420889663, 0.12230014351623239, 0.12000485470200063, 0.11771512622673727, 0.1154359592728078, 0.11317235432982797, 0.11092925532949792, 0.10871149021421737, 0.10652370937938654, 0.10437032391859832, 0.1022554461217394, 0.10018283519278062, 0.0981558516169062, 0.09617742395261185, 0.09425003198128941, 0.09237571004072899, 0.0905560739346574, 0.08879237400457277, 0.08708557576355701, 0.08543646795997085, 0.08384579614572266, 0.08231441789620002, 0.08084347392334779, 0.07943456760164898, 0.07808994403076001, 0.07681265878496941, 0.07560672598640687, 0.07447723526738835, 0.07343042750377513, 0.0724737198566827, 0.0716156716575886, 0.07086588411002749, 0.0702348288684407, 0.06973360358053006, 0.06937361672170266, 0.06916620962732942, 0.06912223032462833, 0.06925158089416282, 0.06956276647840944, 0.07006247822085102, 0.0707552429510782, 0.07164316846825838, 0.07272580491244693, 0.07400013113331842, 0.07546066219177001, 0.07709966246687763, 0.07890744022639552 ], [ 0.12966488113953387, 0.12732708949115507, 0.1249754561259677, 0.12261475353413978, 0.12024994414879549, 0.11788614444453488, 0.11552858288027255, 0.11318255168043727, 0.11085335268590973, 0.10854623781620067, 0.10626634507412074, 0.10401863149483508, 0.10180780498528373, 0.09963825759762136, 0.09751400339607842, 0.09543862465675515, 0.09341523061304043, 0.09144643323926181, 0.0895343445591113, 0.08768059958610806, 0.0858864081851976, 0.08415263786123281, 0.08247992775877028, 0.08086883208798847, 0.07931998892207515, 0.07783430803381611, 0.07641316936048317, 0.07505862199366486, 0.07377357241854438, 0.07256195013397086, 0.07142883875230466, 0.0703805611348584, 0.06942470798859508, 0.06857010061221543, 0.06782668022718442, 0.06720531879065564, 0.06671754969464508, 0.06637522163223157, 0.06619008528665797, 0.06617333009279422, 0.0663350962793137, 0.06668399429720527, 0.06722666782206359, 0.06796743619374451, 0.06890804659495947, 0.07004755584773849, 0.07138234807892685, 0.07290628020067083, 0.07461093482759179, 0.07648595192901131 ], [ 0.1278984543823064, 0.12549189826677828, 0.12307114067324493, 0.1206411849674157, 0.11820724332178156, 0.11577470004885745, 0.11334906826663378, 0.11093593978362647, 0.10854092832106833, 0.10616960650003977, 0.10382743742299201, 0.10151970217829392, 0.09925142519086018, 0.09702730001599205, 0.0948516188936219, 0.09272821009076795, 0.09066038768204546, 0.08865091885107028, 0.08670201392517371, 0.08481534406796193, 0.08299209075444391, 0.08123302978994494, 0.07953865071920711, 0.07790931009662788, 0.07634541442229635, 0.07484762582419513, 0.07341708104675136, 0.07205561223656932, 0.07076595658300093, 0.069551941164956, 0.06841862936397283, 0.06737241583801144, 0.06642105820205556, 0.0655736351796917, 0.06484042315518342, 0.0642326860145591, 0.06376237729035905, 0.06344175928096747, 0.06328295112497326, 0.06329742639276706, 0.06349548953933759, 0.06388576780976876, 0.06447475885360653, 0.06526647265675174, 0.0662621987450011, 0.06746041676159537, 0.06885685273182132, 0.0704446676837747, 0.07221475274969648, 0.07415609738922202 ], [ 0.12614450106401257, 0.12366918134271755, 0.12117927546803275, 0.11868001931860926, 0.1161768774036092, 0.11367550564768637, 0.1111817070265844, 0.1087013798282538, 0.10624045853115921, 0.10380484759422541, 0.10140034885731719, 0.09903258376966079, 0.09670691230038232, 0.09442835113113503, 0.09220149455666433, 0.09003044237030028, 0.08791873980315708, 0.08586933520387773, 0.08388456145238812, 0.08196614695063055, 0.08011526129424805, 0.07833259931520195, 0.07661850508317737, 0.07497313474825339, 0.0733966539872663, 0.07188946256002571, 0.070452435417917, 0.06908716725930723, 0.06779620564825514, 0.06658325694363672, 0.06545334932901625, 0.06441293808443999, 0.06346993975514972, 0.06263368396046355, 0.06191477431112709, 0.06132485352445015, 0.06087627275350619, 0.06058167176937506, 0.06045348504002942, 0.06050339840055592, 0.06074179054641635, 0.06117720090695579, 0.06181586822394275, 0.06266138058394782, 0.06371446734108913, 0.06497294775056175, 0.0664318332088943, 0.0680835634071177, 0.0699183445690918, 0.07192455197189265 ], [ 0.12440741484338526, 0.1218635080173879, 0.11930460437769104, 0.11673617267017052, 0.11416393087525388, 0.11159380866322206, 0.109031902261765, 0.10648442139680876, 0.10395762816503004, 0.10145776798316537, 0.09899099315604955, 0.09656328013096427, 0.09418034217289846, 0.09184754000318031, 0.08956979387143288, 0.08735150152754097, 0.08519646753942615, 0.08310785023773755, 0.08108813309840954, 0.07913912741654508, 0.07726201250392604, 0.07545741822360005, 0.07372555240751333, 0.07206637265370121, 0.0704797983703925, 0.06896595505202625, 0.0675254390446973, 0.0661595879043741, 0.06487073921821478, 0.06366245965421939, 0.06253972606219378, 0.06150904155448524, 0.06057847146447693, 0.059757586781475754, 0.05905730612779865, 0.0584896318428022, 0.0580672817040641, 0.05780322564050605, 0.057710146475540514, 0.05779985451398103, 0.05808269591998025, 0.058567001811234684, 0.059258626205770146, 0.06016061470703264, 0.06127303224103515, 0.06259295954479759, 0.06411464828512752, 0.06582980779180102, 0.06772798548938777, 0.06979699938993017 ], [ 0.12269177211525281, 0.12007964410960228, 0.11745208228831108, 0.11481478729047655, 0.11217373015686655, 0.10953511466399025, 0.10690533168698398, 0.10429090514260966, 0.10169842923617399, 0.0991344969983423, 0.09660562047519478, 0.09411814345303299, 0.09167814828039171, 0.0892913592038698, 0.08696304565219103, 0.08469793004272065, 0.08250010586261329, 0.08037297285857255, 0.07831919697099307, 0.07634070294858437, 0.07443870714880282, 0.07261379667217079, 0.07086605858842289, 0.06919525962189399, 0.06760107247717712, 0.06608334037824398, 0.06464236686350631, 0.0632792139633887, 0.06199598905515282, 0.060796099246737394, 0.05968445217356427, 0.05866758348549606, 0.05775369383315888, 0.056952581649220436, 0.05627546246171705, 0.0557346711318109, 0.05534325071802783, 0.055114440985782526, 0.05506109074278822, 0.05519503008572402, 0.055526449081510894, 0.056063335413064824, 0.05681102231005706, 0.05777188828968062, 0.05894523282688028, 0.06032733041819635, 0.06191164431626615, 0.06368916492739805, 0.06564882918235786, 0.06777797647412169 ], [ 0.12100232188097793, 0.11832254196978056, 0.11562686539883764, 0.11292122238832254, 0.11021183503974556, 0.10750517973383851, 0.10480794123828516, 0.10212695797740347, 0.09946915805930003, 0.0968414858858982, 0.09425081951701954, 0.09170387945385786, 0.08920713018151953, 0.08676667668872211, 0.08438815927063834, 0.08207665119123046, 0.0798365651598391, 0.07767157592751216, 0.07558456742954953, 0.07357761353084578, 0.07165200127882825, 0.06980830436363301, 0.0680465120432483, 0.06636621508796459, 0.06476684552281574, 0.0632479615144339, 0.06180956325902481, 0.060452420862986286, 0.059178391594309966, 0.05799070196078239, 0.05689417000960245, 0.055895344946349096, 0.05500254438356659, 0.05422577401075673, 0.053576520183244276, 0.05306741309349704, 0.05271176722705667, 0.05252301696216366, 0.05251407801412039, 0.05269667837644217, 0.05308071267675764, 0.05367367803368908, 0.054480244796154376, 0.055502001262484404, 0.05673738979136884, 0.05818182727655078, 0.05982798128427214, 0.06166615865669898, 0.06368475798813168, 0.06587074032833785 ], [ 0.11934397362694832, 0.1165973283491483, 0.11383429921520478, 0.1110610424057828, 0.10828402749838305, 0.10551000007653813, 0.10274593580046462, 0.09999898530952409, 0.09727640943893913, 0.09458550442471589, 0.09193351707368155, 0.08932755032817351, 0.08677446029905846, 0.08428074671476474, 0.08185243986212899, 0.07949498847050203, 0.07721315455704526, 0.07501092288101667, 0.07289143413534765, 0.07085695203809635, 0.06890887471688378, 0.0670477998435261, 0.06527365058823383, 0.06358586551095392, 0.061983650137896334, 0.06046628162614657, 0.059033451303302203, 0.05768562383487723, 0.05642438714824596, 0.05525276465141062, 0.054175461022618256, 0.05319901486382108, 0.05233183552990155, 0.051584107169523656, 0.050967550340902064, 0.05049504068478705, 0.050180095377068475, 0.05003625148290135, 0.05007637503376175, 0.05031195342712689, 0.05075243312460593, 0.05140466581289019, 0.052272516732318766, 0.053356669183903034, 0.05465463307350423, 0.05616093878667325, 0.05786747678558579, 0.059763931986745115, 0.06183826089837153, 0.06407716655702737 ], [ 0.11772178310955392, 0.11490929000581414, 0.11207990409712354, 0.10924000266734211, 0.10639629765550854, 0.10355579857218966, 0.10072576670102347, 0.09791365989827838, 0.09512706738462887, 0.09237363407323526, 0.0896609742292896, 0.08699657465062867, 0.08438768814747885, 0.0818412189349512, 0.07936360268019418, 0.0769606853870121, 0.07463760702486943, 0.0723986977093875, 0.07024739610758982, 0.06818620124898628, 0.06621666964991137, 0.06433946913607794, 0.06255449856203497, 0.0608610785387439, 0.05925821235543791, 0.05774490896070634, 0.056320551956510506, 0.05498529110623164, 0.05374042694308021, 0.05258875555760281, 0.0515348400212634, 0.050585177207420055, 0.049748233725177234, 0.049034331934907895, 0.04845537639550005, 0.04802442270439113, 0.047755104697511194, 0.047660952060495594, 0.0477546470735821, 0.04804728340424535, 0.04854769733734174, 0.0492619386231218, 0.050192932542466734, 0.05134035892999615, 0.0527007434967452, 0.054267729240126024, 0.05603247718714295, 0.05798413898182706, 0.06011034790444267, 0.06239768621576531 ], [ 0.11614093594106015, 0.11326385692365186, 0.11036935820813977, 0.1074640322014274, 0.10455482666992139, 0.10164900799448373, 0.09875411560226839, 0.0958779068610707, 0.09302829177657139, 0.09021325694181363, 0.0874407783821835, 0.08471872326171434, 0.08205474092426142, 0.0794561445026494, 0.07692978540819236, 0.07448192446340321, 0.0721181052698986, 0.06984303753968785, 0.06766050037164549, 0.06557327749049527, 0.06358313780249658, 0.061690874680777566, 0.059896415602092315, 0.05819900970748949, 0.05659749447941023, 0.05509063441306519, 0.053677515199457494, 0.05235796779494458, 0.0511329892128773, 0.050005122129283076, 0.04897875418751614, 0.04806030040847016, 0.04725823812365816, 0.04658297295523473, 0.046046526311718086, 0.04566204961089965, 0.04544318786249229, 0.045403334465973784, 0.04555483771979638, 0.04590823347289738, 0.046471582593253076, 0.04724998267462098, 0.04824530036676054, 0.04945613828396271, 0.050878016558757407, 0.05250372217881389, 0.05432376485459235, 0.056326877331851925, 0.058500507785820235, 0.06083126723320519 ], [ 0.11460672886150242, 0.11166658301151529, 0.10870847771230911, 0.1057392135440585, 0.10276596631044657, 0.09979625058915262, 0.09683787440836517, 0.09389888434267944, 0.09098750035794344, 0.08811203980818366, 0.08528083012497377, 0.08250210998161525, 0.07978391912007092, 0.07713397767421885, 0.0745595567976587, 0.072067343793385, 0.06966330680017481, 0.06735256639615339, 0.06513928408758113, 0.06302658023909773, 0.06101649605096486, 0.05911001501090177, 0.05730715809154069, 0.05560716319988319, 0.05400875273563765, 0.0525104838631932, 0.05111116517900919, 0.04981031234649338, 0.04860860572217266, 0.0475083066184044, 0.04651358674594393, 0.04563072798533255, 0.04486815680263146, 0.0442362889369198, 0.04374717507748828, 0.043413956854968044, 0.043250164018293825, 0.04326890645301596, 0.043482035127614144, 0.04389935876128286, 0.0445280023854906, 0.045371976922144494, 0.04643199731013987, 0.047705547838429015, 0.04918715732475235, 0.050868822461038445, 0.052740509179298095, 0.054790667916533475, 0.05700671404705412, 0.05937544341076054 ], [ 0.11312454856691487, 0.11012312413563942, 0.10710319404691665, 0.10407175932162366, 0.10103621496744418, 0.09800431370141303, 0.09498412078792168, 0.091983959330658, 0.08901234538661976, 0.0860779123197421, 0.08318932389949742, 0.08035517581055268, 0.07758388552843645, 0.0748835710141048, 0.07226191949242967, 0.06972604882502263, 0.06728236577256123, 0.064936427813373, 0.06269281806695395, 0.06055504599040259, 0.05852548934715249, 0.056605394711775094, 0.054794953530121926, 0.0530934676007939, 0.051499611217714264, 0.05001178718893826, 0.04862856142532506, 0.047349147461344776, 0.046173900289493766, 0.04510477039232283, 0.044145665446251675, 0.04330266963995215, 0.04258407892595705, 0.04200022440029647, 0.04156307487693437, 0.04128563299196097, 0.04118116557975809, 0.04126233573929869, 0.04154032582164879, 0.042024050772626886, 0.04271955394177163, 0.04362965096860222, 0.04475384657780236, 0.04608850459621503, 0.04762721525539618, 0.049361284263171115, 0.05128026706173152, 0.05337248499535421, 0.0556254806853266, 0.05802639100053086 ], [ 0.11169984794443549, 0.10863921331726506, 0.10555952807982331, 0.1024679853896753, 0.09937218983456582, 0.09628012112251541, 0.09320008889399241, 0.09014067807654585, 0.0871106842412425, 0.08411903846232119, 0.0811747212353123, 0.0782866650972714, 0.07546364576128034, 0.07271416190298444, 0.07004630433295163, 0.06746761630229232, 0.06498494827968805, 0.06260431283371783, 0.060330748275857105, 0.05816820328407668, 0.056119458352315875, 0.05418610276712692, 0.05236858677674942, 0.050666366480292616, 0.04907815278301351, 0.04760226528031515, 0.04623707790537535, 0.04498152743498131, 0.043835641099624116, 0.042801028359952996, 0.04188127665901828, 0.041082192950606757, 0.04041184235949308, 0.03988035209874223, 0.03949947207060563, 0.039281912322210864, 0.03924050948717477, 0.039387305095174886, 0.0397326411678817, 0.04028438471180815, 0.04104737684731841, 0.042023165070227124, 0.043210027214984105, 0.04460324700399241, 0.04619556681827948, 0.047977730425642975, 0.04993903565641962, 0.05206783739954587, 0.05435196613776377, 0.05677904969119394 ], [ 0.11033811954235925, 0.10722063290242548, 0.10408356093339173, 0.10093428027801372, 0.09778059496805311, 0.09463069980217557, 0.09149313484180766, 0.08837673056023175, 0.08529054324699449, 0.08224378032671115, 0.07924571529455392, 0.07630559200722781, 0.07343251812661275, 0.07063534765655138, 0.06792255285170994, 0.06530208647466312, 0.06278123664104772, 0.06036647853676008, 0.058063330258226784, 0.0558762238703982, 0.05380840712193432, 0.05186189528770865, 0.050037495062046425, 0.048334921768782416, 0.046753025976467, 0.04529013517027454, 0.043944500882007013, 0.04271482347753775, 0.04160080868577002, 0.040603695448658786, 0.03972668690272058, 0.03897521731336527, 0.038356998349786744, 0.03788180798520806, 0.03756101362718823, 0.037406856057553325, 0.03743155885450569, 0.037646362792445744, 0.03806060711771018, 0.038680980221143066, 0.039511036235552896, 0.04055102544216665, 0.0417980281027069, 0.04324633047510175, 0.04488795172537498, 0.046713225642725786, 0.0487113568274723, 0.050870897694579024, 0.053180120584764096, 0.055627282061484595 ], [ 0.10904486608204192, 0.10587318348544116, 0.10268140122846496, 0.09947707066232621, 0.09626818490158581, 0.0930631415472718, 0.08987069648260779, 0.08669990841713722, 0.08356007396984988, 0.08046065317999726, 0.07741118539765272, 0.07442119552260057, 0.07150009053456938, 0.06865704622860987, 0.06590088412860699, 0.06323993886335305, 0.06068191709454376, 0.058233750680455866, 0.05590144942273199, 0.053689962610638464, 0.051603063453542326, 0.04964327567007308, 0.04781186565974821, 0.046108924989235314, 0.04453356444054779, 0.043084231208066946, 0.041759144908512555, 0.040556827577382035, 0.039476681159869784, 0.038519547518732954, 0.037688174874403964, 0.03698751390681454, 0.03642477793501058, 0.036009224654928104, 0.03575165067728321, 0.03566363190461401, 0.0357565874168371, 0.036040783263571345, 0.03652441393190151, 0.037212892989814075, 0.0381084473154941, 0.039210049434858264, 0.04051365735979373, 0.04201268043576434, 0.04369856562345184, 0.04556140254582584, 0.04759046935393837, 0.04977467323998043, 0.05210286928500157, 0.05456406364669293 ], [ 0.10782556780507734, 0.10460264934862346, 0.10135914847828582, 0.09810278255636612, 0.09484172346823967, 0.0915845593040316, 0.0883402469958599, 0.08511805574217612, 0.08192750123363057, 0.07877827086208644, 0.07568014021416916, 0.07264288118936958, 0.06967616201571032, 0.06678943926649138, 0.06399184176742022, 0.061292046166785054, 0.05869814417439376, 0.056217502418190624, 0.05385661793936415, 0.051620975894845114, 0.049514921124034564, 0.04754156137879976, 0.045702725958822604, 0.04399900719946111, 0.042429911242633456, 0.040994136603178785, 0.039689983335700424, 0.03851587334344057, 0.03747093710477499, 0.03655559901628573, 0.03577207814300422, 0.035124717789095684, 0.03462006837865162, 0.034266674068501556, 0.034074552830647684, 0.034054408684418454, 0.03421666613337168, 0.03457045928838228, 0.035122727833695425, 0.03587755810728507, 0.036835859267426434, 0.037995394352139555, 0.039351115873427114, 0.04089570651584857, 0.042620208339350096, 0.044514636247568524, 0.046568502044232796, 0.04877121095486079, 0.0511123232612732, 0.05358169506830538 ], [ 0.10668564645173846, 0.1034147601774957, 0.10012285235387042, 0.09681779790678963, 0.09350793746895729, 0.09020203761301739, 0.08690924182439641, 0.08363901220360263, 0.08040106215688506, 0.0772052805979882, 0.0740616483984705, 0.07098014793426774, 0.06797066652427122, 0.06504289430210704, 0.062206216612101434, 0.05946960047179586, 0.05684147422809052, 0.05432959964709166, 0.05194093685765496, 0.049681505389827615, 0.047556249396642526, 0.045568921882081025, 0.043722010364270134, 0.042016732795955566, 0.040453134792099534, 0.0390303142068739, 0.03774678488698366, 0.036600968378481875, 0.03559177384301543, 0.03471919833786909, 0.03398485883886852, 0.03339235997393826, 0.032947411179596334, 0.03265763496428198, 0.032532052464676275, 0.032580288537588466, 0.03281159682123241, 0.03323385131181052, 0.03385266892017093, 0.03467080617338544, 0.03568791456209365, 0.03690066011780574, 0.038303139301201786, 0.039887477103955044, 0.04164448298813848, 0.04356426010081105, 0.04563669920355687, 0.047851826902372975, 0.05020000878907879, 0.0526720284031936 ], [ 0.1056304256953185, 0.10231514883510125, 0.09897846756266243, 0.09562840629075445, 0.0922734648456651, 0.08892257685115157, 0.08558505851629625, 0.08227054796438794, 0.078988935609308, 0.07575028647077472, 0.07256475566696144, 0.06944249855691921, 0.06639357703487397, 0.06342786321319208, 0.06055494111424622, 0.05778400605123165, 0.05512376029132862, 0.05258230274841821, 0.05016701046684973, 0.047884411318319366, 0.045740051382561375, 0.043738367239315346, 0.041882582280353124, 0.04017465526300846, 0.03861531543981501, 0.037204217771844864, 0.03594024066928882, 0.0348219264369667, 0.03384803376144282, 0.03301813838198174, 0.032333190867041006, 0.031795927230452596, 0.031411034645721723, 0.031185002949231377, 0.031125641295219858, 0.031241302080256605, 0.031539919362744306, 0.032028019315336664, 0.032709877311159034, 0.033586968841788425, 0.03465779408284797, 0.03591806989358523, 0.03736120726810901, 0.0389789490408528, 0.04076203833780659, 0.04270081407995851, 0.04478566992153585, 0.047007352877754656, 0.04935710890775991, 0.051826702113793435 ], [ 0.10466508792252709, 0.10130930504396098, 0.09793180414696857, 0.09454075148209916, 0.09114479708755949, 0.08775303095631394, 0.08437492913946515, 0.08102029004638127, 0.07769916168032495, 0.07442176107313718, 0.07119838769430414, 0.06803933301739844, 0.06495478860730046, 0.06195475490309956, 0.05904895218459701, 0.05624673396376393, 0.05355700132412517, 0.05098811487144284, 0.048547799602453215, 0.04624303809614574, 0.044079950076225366, 0.042063662438461304, 0.04019818331607005, 0.03848630525948848, 0.036929572939444294, 0.035528355325244364, 0.03428205631304895, 0.033189478496087256, 0.03224932332562818, 0.031460773172188, 0.030824066211694666, 0.030340953959345034, 0.03001493186786858, 0.02985115975967568, 0.029856039904674492, 0.03003648925714862, 0.030399014755982477, 0.030948756473100532, 0.031688681684420544, 0.03261908178445462, 0.03373744993767125, 0.03503872547590099, 0.03651581314620056, 0.038160244131953805, 0.03996284588166138, 0.04191431803591525, 0.044005654785801415, 0.04622839511910879, 0.0485747134742014, 0.05103738219671528 ], [ 0.1037946273622484, 0.10040252494239482, 0.09698847313334649, 0.09356077278493774, 0.09012821574399131, 0.08670003849383702, 0.08328586512927201, 0.07989564001562863, 0.0765395510708863, 0.07322794528534043, 0.06997123879396781, 0.06677982444011907, 0.06366398016545545, 0.0606337815395834, 0.057699021098092725, 0.054869135726180934, 0.052153141076883215, 0.049559569174007646, 0.04709640252273402, 0.04477099627774897, 0.04258998068978194, 0.0405591405683748, 0.03868327764993059, 0.0369660749108096, 0.03540999627580781, 0.03401626593831496, 0.03278497259229158, 0.03171533030588007, 0.030806098337414895, 0.03005612134649136, 0.029464909021651466, 0.029033142724085654, 0.02876298782754589, 0.028658111074208622, 0.02872335303675182, 0.02896407943492297, 0.029385315575440357, 0.029990832026213447, 0.030782372375789877, 0.03175918210934473, 0.032917919008427415, 0.03425292829139131, 0.035756784828888735, 0.037420963946004346, 0.03923650504188643, 0.04119456553866197, 0.04328680791591376, 0.04550560482822658, 0.04784407872859071, 0.05029601128209232 ], [ 0.1030237997307277, 0.09959985666304215, 0.09615382766185278, 0.09269414125019396, 0.08922972315750628, 0.08576994719552655, 0.08232457474499925, 0.07890368324767938, 0.07551758479677764, 0.07217673674808935, 0.06889164717713361, 0.06567277887687711, 0.06253045625632017, 0.059474779728647786, 0.05651555169031555, 0.05366221671866774, 0.05092381598931576, 0.04830895221740768, 0.04582575715474069, 0.04348184987180788, 0.04128427231376515, 0.03923939083440135, 0.03735276017425526, 0.03562896003245637, 0.03407143215001794, 0.03268236305596331, 0.031462667412218905, 0.03041212198717273, 0.02952967630890587, 0.028813924623860485, 0.02826367383315605, 0.027878498000426268, 0.027659147315972066, 0.027607689654812546, 0.027727309914997007, 0.028021769772822294, 0.028494620493718936, 0.029148336529725923, 0.029983568860886208, 0.03099868794735339, 0.032189704666229696, 0.03355055493096238, 0.035073648274039894, 0.03675053814896102, 0.03857257521434969, 0.040531439985227596, 0.042619498207730394, 0.04482996577733338, 0.04715690226820883, 0.049595071567442944 ], [ 0.10235706878230585, 0.09890604232919536, 0.095432900001271, 0.0919461912007523, 0.08845496787915026, 0.08496873249725684, 0.08149737376718193, 0.0780510905710323, 0.07464030524899445, 0.07127556842694369, 0.0679674586611085, 0.06472648130787216, 0.06156297199819068, 0.05848701064006269, 0.05550835164603359, 0.052636374710722855, 0.04988005763804239, 0.04724796835147778, 0.044748267650499066, 0.04238870846122939, 0.04017661295025749, 0.03811880818994106, 0.0362215064211778, 0.03449012884782474, 0.03292909175703519, 0.031541596907119995, 0.030329487482668584, 0.029293237310266847, 0.02843212636730413, 0.027744617222597565, 0.02722889108495319, 0.026883443724523053, 0.0267076006123499, 0.026701805133768155, 0.026867572936091582, 0.02720708528617737, 0.027722495334469893, 0.028415111202563622, 0.029284663848424933, 0.03032884468750136, 0.031543215011857285, 0.03292148049290794, 0.03445603223400439, 0.03613860945207891, 0.03796094141933932, 0.03991526223228717, 0.04199464036110638, 0.04419310986280683, 0.046505623777270876, 0.048927870857378084 ], [ 0.10179855042572256, 0.09832545717432518, 0.09483033520931529, 0.09132184789224358, 0.08780916568441895, 0.08430191112189024, 0.08081009066679301, 0.07734401378557239, 0.07391420048924909, 0.07053127968427261, 0.06720588198564983, 0.06394853203611742, 0.060769546668331856, 0.0576789461488001, 0.05468638585506933, 0.051801114594256924, 0.04903196292564663, 0.046387360039654366, 0.04387537111653038, 0.04150373944744511, 0.03927991060080618, 0.03721101203858598, 0.03530376376946524, 0.03356430643168266, 0.031997953549433335, 0.030608902417398408, 0.0293999667636996, 0.028372413683764367, 0.027525985551105508, 0.02685915652448853, 0.026369614205729013, 0.02605488401627382, 0.025912951148232034, 0.025942708434895028, 0.026144085304249443, 0.026517793159299568, 0.027064735569653806, 0.02778523986062033, 0.028678327596149192, 0.029741227902041107, 0.03096925468338539, 0.03235605345824294, 0.033894123500547525, 0.03557546857603898, 0.03739222937551172, 0.03933718645560661, 0.04140407202449924, 0.04358767564840037, 0.0458837646626168, 0.04828886264013211 ], [ 0.10135195537241781, 0.09786204684608088, 0.0943503226084804, 0.09082555261045787, 0.08729701765246238, 0.08377445137802085, 0.0802679681930941, 0.07678797737895923, 0.07334508462253797, 0.06994998342011065, 0.06661334029222629, 0.06334567938767752, 0.0601572736658446, 0.057058051121384505, 0.05405752501422364, 0.051164756245496615, 0.04838835330877942, 0.045736510215066084, 0.0432170753891433, 0.04083763538007291, 0.03860558785678148, 0.036528171321270016, 0.034612417603945976, 0.03286500096130584, 0.03129197684913838, 0.0298984338277866, 0.028688118670963176, 0.02766312713142391, 0.02682376619606288, 0.02616867394879327, 0.02569522507270928, 0.025400164340297515, 0.025280324461836437, 0.025333233084288854, 0.025557423638714837, 0.025952342273779586, 0.026517867664969504, 0.027253588755331237, 0.028158066627432365, 0.029228306006804435, 0.030459581157477763, 0.03184563914887945, 0.03337919370034574, 0.0350525621185031, 0.0368582928894534, 0.038789665715764365, 0.04084099615959326, 0.04300772606904653, 0.04528631960705238, 0.04767401007269659 ], [ 0.10102053160190572, 0.09751926433102784, 0.09399652668680465, 0.09046118701656607, 0.08692262736067623, 0.08339068252228961, 0.079875564100978, 0.07638776964549399, 0.0729379780931123, 0.06953693399416701, 0.06619532465809602, 0.06292365622133168, 0.05973213654603464, 0.0566305744962764, 0.05362830603550635, 0.050734157139253, 0.04795645104961489, 0.04530306233743238, 0.04278151235000123, 0.040399090326609335, 0.03816297313600131, 0.03608030673433287, 0.03415820760192635, 0.032403646673245697, 0.030823195221935436, 0.029422643238860086, 0.02820654306380447, 0.02717777479799099, 0.026337258780617313, 0.02568393477305101, 0.025215074838887384, 0.024926902694764535, 0.02481538480781497, 0.024876980388569083, 0.02510912662155371, 0.025510306121838824, 0.026079676796671277, 0.02681639231032685, 0.02771884507239251, 0.028784079612016924, 0.030007548854635212, 0.03138325870715333, 0.03290422561474152, 0.03456310020067475, 0.036352797805013215, 0.03826700790262021, 0.04030050528671564, 0.042449237882603186, 0.04471020875577523, 0.04708119908795839 ], [ 0.10080700822898424, 0.09730000829281586, 0.09377201945373685, 0.0902319990438815, 0.08668941981781737, 0.08315420618749614, 0.07963665447948651, 0.0761473372390806, 0.07269699265965836, 0.0692964016263086, 0.06595625663072349, 0.0626870288713914, 0.059498842025478955, 0.0564013631474598, 0.0534037224260558, 0.050514473461671976, 0.04774160356163717, 0.04509259859617364, 0.042574558827058503, 0.04019435105715742, 0.03795876965972366, 0.03587466693201386, 0.03394900537587981, 0.03218878538736787, 0.030600815899322235, 0.02919132568979198, 0.027965458265223533, 0.026926745326776257, 0.026076695837495615, 0.02541464652670288, 0.02493797605026948, 0.024642688033780374, 0.02452424446521697, 0.02457842832138619, 0.024801980683107707, 0.025192816199026687, 0.025749757104655414, 0.026471890822439486, 0.027357783536235653, 0.028404818929077605, 0.029608865925600705, 0.030964349114393868, 0.03246466283287217, 0.03410278435969692, 0.035871918712981905, 0.03776603365690586, 0.03978019469977944, 0.04191066582080731, 0.04415478988453201, 0.046510696986021456 ], [ 0.1007135426023123, 0.09720656491034975, 0.09367921663022047, 0.09014053305927415, 0.08660006523166715, 0.08306781341500015, 0.07955414373662847, 0.07606968782770929, 0.07262522645667739, 0.06923155959594429, 0.06589936723839301, 0.06263906749649105, 0.05946068091043225, 0.05637371214482527, 0.05338706186375202, 0.05050898185619448, 0.047747084629365645, 0.04510841391550055, 0.04259957434545676, 0.04022690703689691, 0.03799668409125117, 0.03591528127688825, 0.033989278062200784, 0.032225432256174046, 0.030630487771195564, 0.02921080235531147, 0.027971827956846065, 0.026917533134056742, 0.026049908242417645, 0.02536871524701182, 0.0248716110888796, 0.02455467963293653, 0.0244132749972856, 0.024442957743004215, 0.02464024942025248, 0.025002972580719443, 0.025530075502487797, 0.026221017066520292, 0.027074937793284726, 0.028089905020689344, 0.029262470670573873, 0.030587650234000147, 0.03205928618235895, 0.03367065567299208, 0.035415144622275456, 0.037286828803027805, 0.039280853926641254, 0.04139356803136151, 0.043622415108526866, 0.04596563970452712 ], [ 0.10074167261747455, 0.09724055548862293, 0.09371982027370025, 0.09018856726032941, 0.08665641099937146, 0.083133411147867, 0.07962998562252838, 0.07615680582210352, 0.0727246747817055, 0.0693443906408892, 0.06602659976130655, 0.06278164617081518, 0.059619426579829785, 0.0565492626956097, 0.05357980444115889, 0.05071897826015397, 0.04797399311173362, 0.04535141219062309, 0.04285729027150071, 0.04049736488910951, 0.03827727529460028, 0.03620276846581106, 0.03427983989593367, 0.03251475305812289, 0.03091389047103319, 0.029483415541575592, 0.028228769103622237, 0.02715408249434388, 0.02626164495148373, 0.025551592520318092, 0.02502196279453239, 0.02466917342084228, 0.02448884990347225, 0.024476796262213923, 0.024629827039467207, 0.024946200447862117, 0.02542551273971088, 0.026068094425517104, 0.026874120699349118, 0.027842739420981335, 0.028971492841118288, 0.030256184225987904, 0.031691181878840735, 0.0332700274116634, 0.034986157277373586, 0.036833554609236964, 0.03880719976579378, 0.04090325661850482, 0.04311899690937376, 0.04545251400532432 ], [ 0.10089227625894925, 0.09740289215445064, 0.0938947704845742, 0.09037706132659945, 0.08685942534773651, 0.08335196205555433, 0.07986511963428686, 0.07640958601435029, 0.07299616194289028, 0.06963561837716017, 0.06633854253695741, 0.0631151793855316, 0.05997527800494124, 0.056927954975731616, 0.05398158894687112, 0.051143761370803065, 0.04842125701355313, 0.04582013346507178, 0.043345860857625346, 0.04100352132658865, 0.038798043337236694, 0.036734430987463686, 0.034817936212270945, 0.0330541169984216, 0.031448732322502525, 0.03000744892291229, 0.028735377707194212, 0.02763651398136591, 0.026713211939453904, 0.02596585697725081, 0.025392884221596825, 0.02499121489698249, 0.02475705628991332, 0.024686876700212107, 0.024778277903893375, 0.02503048785127069, 0.025444298666707693, 0.026021452660899638, 0.026763668524370614, 0.027671622637262614, 0.028744202376857132, 0.0299782335225068, 0.03136871206109786, 0.032909417760463515, 0.034593702696218774, 0.03641524155929322, 0.03836858174943063, 0.04044940936974453, 0.042654524897091935, 0.0449815814176671 ], [ 0.10116554027404427, 0.09769374381687075, 0.09420420867935239, 0.09070611714189962, 0.0872091557924243, 0.08372344122067255, 0.08025942668691322, 0.07682778933048715, 0.07343929861800409, 0.07010466831161674, 0.06683439629487135, 0.06363859908794685, 0.0605268506609438, 0.057508037896111024, 0.05459024723931098, 0.0517806979939453, 0.04908573647716343, 0.04651090101167107, 0.044061059857465563, 0.041740612676348356, 0.039553731884388155, 0.03750460539281713, 0.03559763013001431, 0.03383750076719253, 0.03222914504412313, 0.030777480043519836, 0.02948700394837234, 0.02836129087740835, 0.027402509735105565, 0.026611120930154684, 0.02598589438736228, 0.02552432517574113, 0.025223407693356042, 0.025080599081871158, 0.0250947055828592, 0.025266406260087398, 0.02559820940430844, 0.0260938053968679, 0.026756982557251494, 0.027590428264965657, 0.028594775180958466, 0.02976815457773522, 0.031106335320051987, 0.0326033419473093, 0.034252327410920755, 0.03604645013839365, 0.037979555193145616, 0.040046549040643656, 0.04224345042913582, 0.04456717134049458 ], [ 0.10156093962248167, 0.09811251426102888, 0.09464745454027451, 0.09117495494742338, 0.08770470502337697, 0.08424681252205837, 0.08081170706310639, 0.07741002379968127, 0.07405246777128696, 0.07074966121254529, 0.06751197817276124, 0.06434937332684866, 0.061271214668354355, 0.05828613254968747, 0.055401899753383665, 0.052625358221790236, 0.04996240688402239, 0.04741806085747, 0.04499658459495444, 0.04270169032062887, 0.040536779295614056, 0.03850518918169492, 0.036610399310308996, 0.03485614119890043, 0.03324636861136648, 0.03178506332200029, 0.030475890237543306, 0.029321764261343163, 0.02832443975890739, 0.02748426354532839, 0.02680022410684944, 0.02627037119908972, 0.025892576419240754, 0.025665483064018824, 0.025589393335128267, 0.025666805204008093, 0.025902369685446715, 0.026302193675066875, 0.02687262426683233, 0.02761883846432933, 0.0285436410489137, 0.029646800888239924, 0.030925065010193528, 0.03237276913091351, 0.03398280367600782, 0.03574764196342191, 0.03766018370322713, 0.03971426974456383, 0.04190483527633912, 0.04422775500248821 ], [ 0.1020772289497701, 0.09865783377062914, 0.09522299818220965, 0.09178190660043768, 0.08834422599737914, 0.0849200265495726, 0.0815196824461806, 0.07815375237946348, 0.07483284040320771, 0.07156743946074152, 0.0683677619796828, 0.06524356445834652, 0.06220397576566432, 0.05925734161727571, 0.05641109985666373, 0.05367170205469681, 0.051044595716594136, 0.04853427726190027, 0.046144418417112545, 0.04387805782761334, 0.0417378365555719, 0.03972624278100616, 0.03784582063495196, 0.03609929457845533, 0.034489568045176854, 0.03301957601972841, 0.031692005920715687, 0.03050894507885123, 0.029471555804296612, 0.028579904895308934, 0.02783306681520177, 0.027229568315303265, 0.0267681502925373, 0.026448710040328265, 0.026273186988050725, 0.02624610632467009, 0.026374531644387175, 0.026667314378861474, 0.027133740178221736, 0.02778188901349957, 0.028617149791374367, 0.02964129304059927, 0.03085231528286887, 0.032245012975596114, 0.03381203528188378, 0.03554507708140907, 0.03743591116102102, 0.039477073767644685, 0.04166214951214404, 0.04398570552627775 ], [ 0.10271244682951755, 0.09932756507411306, 0.09592850836233541, 0.09252442676148682, 0.08912493700637827, 0.0857400406872531, 0.08238002242761698, 0.0790553276232193, 0.07577642049218411, 0.07255362481161856, 0.06939695180664698, 0.06631592215796937, 0.06331939183131345, 0.060415394076324895, 0.05761101198030804, 0.05491229670866001, 0.05232424523863323, 0.04985084727892784, 0.047495203753512544, 0.04525970890178579, 0.043146275765411815, 0.041156572668957114, 0.039292229270685305, 0.037554968435422935, 0.035946627967466116, 0.034469056282119714, 0.033123897879381956, 0.03191232343667242, 0.03083479606796308, 0.029890986557823615, 0.029079942525482835, 0.028400570942262775, 0.02785241204039048, 0.027436580109576423, 0.027156649316589506, 0.027019204708928036, 0.027033795595839606, 0.027212144572029914, 0.027566671865114092, 0.028108632409309563, 0.028846332078194006, 0.029783897268151047, 0.030920896559230377, 0.032252829614455095, 0.033772237451831576, 0.035470055023747796, 0.03733684657095168, 0.03936368782970342, 0.04154261188530852, 0.04386665942839481 ], [ 0.1034639329511184, 0.10011882373666, 0.09676085676375976, 0.09339912189927958, 0.09004315639880636, 0.08670286073596921, 0.08338839442953787, 0.08011005153629244, 0.07687811667130802, 0.07370270404399114, 0.0705935840659858, 0.06756000452862469, 0.06461051597995014, 0.06175281342087169, 0.05899360828392887, 0.05633854520464712, 0.053792176627104095, 0.051358004176036906, 0.04903858867627646, 0.046835720992373216, 0.044750634601813756, 0.042784230021838426, 0.04093727368897896, 0.039210532821549154, 0.03760481600994358, 0.03612090826551153, 0.03475941801034305, 0.0335205875020715, 0.032404149139782325, 0.03140932690976832, 0.030535073864321177, 0.029780596005421375, 0.029146141108408456, 0.028633938537548413, 0.02824908353023121, 0.02800009605485731, 0.02789888481529928, 0.027959941084433476, 0.02819877945292797, 0.028629889952555734, 0.029264673601175562, 0.03010989206668913, 0.031167017577218285, 0.032432573525964126, 0.03389924726517499, 0.035557370442991836, 0.03739635169156386, 0.03940576953082489, 0.041576003840458425, 0.043898429382297766 ], [ 0.10432835784448415, 0.10102801243587452, 0.09771615758769969, 0.09440179608173732, 0.09109435557731195, 0.08780360225603033, 0.08453953466025572, 0.08131225753444761, 0.07813183668382355, 0.07500813748205105, 0.0719506516845766, 0.06896831955549805, 0.06606935680106203, 0.06326109808751917, 0.06054987052015696, 0.05794091076688931, 0.05543833788205257, 0.053045189803788216, 0.05076352477522547, 0.04859457995662246, 0.04653896938164051, 0.044596894090302264, 0.04276833129333715, 0.0410531695367146, 0.03945126530245472, 0.03796241420832716, 0.03658625559048484, 0.03532215847158478, 0.034169162479906756, 0.03312606003319121, 0.03219169718405872, 0.03136553431717591, 0.030648444630401853, 0.030043645753594247, 0.029557573918765775, 0.029200445315744655, 0.02898623740601328, 0.028931895765320563, 0.029055743790155377, 0.029375316079400794, 0.029905069253412606, 0.03065453162379067, 0.03162735369961545, 0.03282143597914614, 0.034229968732553795, 0.0358429789385453, 0.03764892691069034, 0.039636004146356464, 0.04179296408817306, 0.04410948198591529 ], [ 0.10530176418287246, 0.10205086792506163, 0.09878982096499278, 0.09552751170426718, 0.09227322798646201, 0.08903656881730629, 0.08582733666701879, 0.08265541034244928, 0.07953059962720295, 0.07646248448238697, 0.07346024356039321, 0.07053247901479069, 0.0676870468900349, 0.0649309044153194, 0.062269986848490305, 0.059709126565908446, 0.057252025317946605, 0.05490128655781524, 0.05265850843131309, 0.05052442984598542, 0.04849911314553549, 0.04658213908935472, 0.04477278533617426, 0.04307016075832232, 0.041473276397570764, 0.03998105013295012, 0.03859226458536278, 0.03730552244721263, 0.036119264075391115, 0.03503192132217536, 0.03404227215808349, 0.03315002817887915, 0.03235663154188382, 0.031666164960435984, 0.031086200579448924, 0.030628351076186243, 0.030308266974399884, 0.03014487848123038, 0.030158827745062306, 0.03037026462064192, 0.030796420031948313, 0.031449516721178475, 0.03233552921397204, 0.03345405208381482, 0.03479918541902788, 0.036361063906204374, 0.03812755449102698, 0.04008572731615148, 0.04222288136133331, 0.04452708389464752 ], [ 0.10637961823283204, 0.10318251895738488, 0.09997661810879135, 0.0967706626636827, 0.09357377111874868, 0.09039534363680266, 0.0872449533527148, 0.08413221903290259, 0.08106666048837756, 0.07805753969705027, 0.07511369246326331, 0.07224335752479517, 0.0694540121038551, 0.06675222466995047, 0.06414353671291453, 0.06163238512484634, 0.05922207489768869, 0.05691480795942832, 0.05471176812627473, 0.05261325485603131, 0.05061885083868506, 0.04872760207856926, 0.0469381859547205, 0.045249044662902735, 0.04365846969577995, 0.0421646376451241, 0.040765616935207825, 0.039459385517020454, 0.03824391579916514, 0.037117389076311985, 0.036078591870873145, 0.03512751741619804, 0.034266146893208345, 0.033499321405189006, 0.03283554697339296, 0.0322875176188852, 0.03187211937167181, 0.031609718166458196, 0.031522657975310286, 0.03163309795780591, 0.03196054957606958, 0.03251964121754991, 0.03331863721559175, 0.03435903390791679, 0.03563622392752711, 0.03714091529703094, 0.03886084463657348, 0.04078236246148878, 0.04289162622209439, 0.0451753168455025 ], [ 0.10755686966004595, 0.10441755305439288, 0.10127075571773189, 0.09812505706252397, 0.09498937815074378, 0.09187289070119982, 0.08878490801231621, 0.08573475821600525, 0.08273164146827298, 0.07978447418223776, 0.07690172517273376, 0.07409125049252223, 0.07136013559240448, 0.06871455492867175, 0.06615965988598546, 0.06369950546131602, 0.06133702419503431, 0.0590740521418064, 0.05691140636176457, 0.05484900702617379, 0.052886030796531376, 0.05102107708760491, 0.049252326796592014, 0.04757767554122456, 0.04599483124649383, 0.044501378811973205, 0.04309483090517057, 0.04177270046954644, 0.04053264290255403, 0.0393727191451495, 0.03829182076701982, 0.03729027185003328, 0.036370580094957694, 0.03553825472484643, 0.03480254954011068, 0.03417693946349946, 0.03367911752593122, 0.03333032969414158, 0.033153966702731304, 0.033173506060573496, 0.033410108113734426, 0.03388033951541983, 0.03459453176468424, 0.035556131418353655, 0.0367621077445537, 0.038204182298686246, 0.03987046512073657, 0.041747076124601025, 0.043819455272838724, 0.046073234290596066 ], [ 0.1088280176701916, 0.10575008977253751, 0.10266595692028405, 0.09958400633761906, 0.09651293567999378, 0.09346166140878559, 0.09043920999564377, 0.08745459259752175, 0.08451666500397532, 0.08163397608561394, 0.07881460960930609, 0.07606602600883525, 0.07339491230882676, 0.07080704961426082, 0.068307208058293, 0.06589907849644282, 0.06358524826360176, 0.06136722486471641, 0.0592455067295258, 0.05721969467464643, 0.05528863241973281, 0.05345056063539296, 0.051703267892545306, 0.050044224649111686, 0.048470693569172565, 0.04697982059382578, 0.04556872466859415, 0.04423461710442998, 0.04297499056117483, 0.04178791867852512, 0.040672497062739295, 0.03962943269603981, 0.03866175209657722, 0.03777555185902973, 0.03698066532753949, 0.036291077253467564, 0.03572490018259515, 0.035303750925792896, 0.03505144928526842, 0.03499210704623117, 0.035147857644322926, 0.035536634967259735, 0.036170463749375784, 0.037054620954502064, 0.03818778875147891, 0.039563044152279965, 0.04116933734878155, 0.04299306556285493, 0.045019434317558116, 0.04723344392570117 ], [ 0.11018718136893588, 0.10717385805163375, 0.1041555460209843, 0.10114041773439507, 0.09813692414066909, 0.095153702978253, 0.09219947095005147, 0.08928290063303396, 0.08641248409830046, 0.08359638655702897, 0.08084229484367574, 0.07815726707471346, 0.07554759118851524, 0.07301866102611068, 0.07057487886181692, 0.06821959255439512, 0.06595507356067584, 0.0637825389015305, 0.06170221601501609, 0.05971344480411151, 0.05781480691848507, 0.05600426944158866, 0.0542793297451618, 0.052637151132811685, 0.05107468528818112, 0.049588786930098196, 0.04817633697283032, 0.04683440051755867, 0.04556045217715389, 0.04435270046525247, 0.04321053269339792, 0.042135080643725877, 0.04112987566506257, 0.040201522608860125, 0.03936028094873746, 0.03862040772189758, 0.038000103318237624, 0.0375209225795423, 0.037206583157444253, 0.037081223302466215, 0.03716731356247505, 0.03748356493455452, 0.03804323628201979, 0.03885317813042945, 0.03991376410243846, 0.041219625504629674, 0.042760917152573, 0.04452477054302063, 0.046496636317798386, 0.04866133279063471 ], [ 0.11162817225533228, 0.10868227530409746, 0.10573253444359787, 0.10278688725937316, 0.0998535177824925, 0.09694076529366556, 0.09405701815288822, 0.09121059371187959, 0.08840960642822702, 0.08566182754030952, 0.08297454100879532, 0.08035440176056435, 0.07780730340720089, 0.07533826332953904, 0.07295133307835491, 0.070649541218921, 0.06843487390990872, 0.06630829567759741, 0.06426980926731171, 0.06231854961871947, 0.06045290364092923, 0.058670645410140394, 0.05696907649454928, 0.05534516389089027, 0.053795673611219924, 0.052317305694539254, 0.05090684499714657, 0.04956134953307051, 0.048278401977315026, 0.0470564477957955, 0.045895233417268116, 0.04479633903781746, 0.04376377368997514, 0.04280456772195235, 0.04192926477554059, 0.041152189322805725, 0.040491356949449685, 0.03996791436313842, 0.039605054197433105, 0.039426447745526116, 0.03945436258264084, 0.03970774687682306, 0.040200619542788564, 0.040941065583554655, 0.041930996828687644, 0.043166647004435704, 0.04463960187661611, 0.046338080616599164, 0.048248198083595796, 0.05035501970982355 ], [ 0.11314456689881182, 0.11026852609647375, 0.10738970552880629, 0.10451579058975047, 0.1016546815418741, 0.09881440340972715, 0.09600300211711524, 0.09322842809855834, 0.0904984096105134, 0.08782031910026769, 0.08520103718506834, 0.08264681993348814, 0.08016317606463048, 0.0777547611969714, 0.07542529618905794, 0.07317751575443705, 0.07101315182479179, 0.06893295364048581, 0.06693674351371484, 0.0650235040807199, 0.06319149024504775, 0.06143835759617049, 0.059761299480081166, 0.0581571874669249, 0.05662271465194899, 0.05515454743926415, 0.053749498014087356, 0.05240473494121277, 0.05111805130742111, 0.04988820670109291, 0.04871534972044131, 0.04760151114269693, 0.046551135166996986, 0.04557158966526353, 0.04467357040125042, 0.04387129494596753, 0.043182377489102544, 0.04262729454019069, 0.04222840037912874, 0.042008530515558605, 0.041989330130282054, 0.042189536579484946, 0.04262349464420096, 0.04330015974154428, 0.04422274269250117, 0.04538900047743495, 0.04679203530063151, 0.04842137898237684, 0.05026413077656772, 0.05230596921777955 ], [ 0.11472977806603882, 0.11192563855195206, 0.10911969619274875, 0.10631936984929478, 0.10353226265424624, 0.10076607355616393, 0.09802849636263435, 0.09532710765467917, 0.0926692458657489, 0.09006188483877156, 0.0875115062199829, 0.0850239760088818, 0.08260443131799489, 0.08025718374330543, 0.07798564554935289, 0.07579228401521128, 0.07367860773293643, 0.07164518648604612, 0.06969170379996467, 0.06781703873842046, 0.06601937152185348, 0.06429630659939296, 0.06264500735975308, 0.06106233893534492, 0.05954501940058995, 0.05808978451329942, 0.05669357597959377, 0.055353766672949535, 0.0540684367900702, 0.05283671118863883, 0.05165915917993831, 0.05053824367145601, 0.049478787664052434, 0.048488404900785174, 0.047577821579944585, 0.046761002555713374, 0.046054994516682976, 0.04547941654078658, 0.045055569606618606, 0.04480520054865079, 0.044749033503451954, 0.04490525381685487, 0.04528816963600241, 0.04590726253619627, 0.046766765221820474, 0.04786579115695339, 0.049198926133179464, 0.05075711357760925, 0.05252864355266088, 0.0545000846230541 ], [ 0.11637712283244551, 0.1136465569305645, 0.1109150738471171, 0.10818981462575311, 0.10547807539714996, 0.1027872210939513, 0.10012458792603074, 0.09749737609692208, 0.09491253508395986, 0.09237664471246715, 0.08989579615706825, 0.0874754778010991, 0.08512047145595149, 0.08283476465418593, 0.08062148446271773, 0.07848285743707055, 0.07642019894976565, 0.07443393327523933, 0.07252364371981336, 0.07068815007997659, 0.06892560920095638, 0.0672336337967181, 0.06560942529309174, 0.06404991837572027, 0.06255193797804903, 0.061112373101030446, 0.05972837525431822, 0.05839759134842283, 0.057118440375899304, 0.055890439179304176, 0.05471457440507473, 0.05359370544089622, 0.052532967664709905, 0.051540128670879946, 0.050625835355321905, 0.04980368090413697, 0.04909002252306779, 0.04850349761265517, 0.04806422072613956, 0.0477926948026197, 0.04770853044864669, 0.0478291221172241, 0.04816846128656013, 0.048736258201266806, 0.04953749099543635, 0.050572416592158165, 0.0518369878240239, 0.05332355393902354, 0.05502169430944258, 0.05691904791908263 ], [ 0.11807988650771732, 0.11542420919099089, 0.11276840738500718, 0.11011933606638682, 0.10748397787110026, 0.10486935944397424, 0.10228245778911693, 0.09973009817719446, 0.09721884592567764, 0.09475489516686748, 0.09234395848891903, 0.08999116198867778, 0.08770095070896262, 0.08547700954067242, 0.08332220436276266, 0.0812385474213176, 0.07922718972997429, 0.07728844170963306, 0.07542182157216357, 0.07362612936618591, 0.07189954346323482, 0.07023973587171303, 0.0686440033314478, 0.06710941269522239, 0.06563296143926281, 0.06421175678851213, 0.0628432191809724, 0.061525316755500575, 0.06025683634232905, 0.05903769234418132, 0.05786926756565816, 0.056754769690272426, 0.05569957464592368, 0.05471151528340689, 0.053801063171014914, 0.05298134609139326, 0.05226794750170548, 0.05167844982142034, 0.05123171239028661, 0.05094691567119279, 0.05084244974317866, 0.05093476671555651, 0.051237340205622074, 0.05175986935751662, 0.05250782678166433, 0.0534823873896716, 0.05468070610298658, 0.05609645697376696, 0.05772051831337617, 0.05954169067515614 ], [ 0.11983138150184172, 0.11725156867873858, 0.11467233142159218, 0.11210023331517295, 0.10954194018975973, 0.10700413950252093, 0.10449345091739803, 0.10201632968267113, 0.09957896508472604, 0.09718717695198513, 0.09484631383341842, 0.09256115700479108, 0.0903358347773372, 0.0881737516146239, 0.08607753623969301, 0.08404901220950356, 0.08208919337677825, 0.08019830534920015, 0.07837583266187668, 0.07662059012550472, 0.07493081594716647, 0.07330428396127982, 0.07173843278544653, 0.07023051091123322, 0.06877773844636331, 0.0673774880319044, 0.06602748878433408, 0.06472605727988985, 0.06347235795104196, 0.06226669131419573, 0.06111080203104034, 0.06000819022906083, 0.05896439965262342, 0.05798724659038243, 0.057086946211546974, 0.05627609043147763, 0.05556943625197082, 0.05498347767511212, 0.05453579837748156, 0.054244234603813134, 0.05412591334605375, 0.054196261964419824, 0.054468102693969025, 0.05495094136641738, 0.055650531934418206, 0.05656875240108768, 0.0577037754997614, 0.059050473085510945, 0.06060096739013154, 0.06234523855042041 ], [ 0.12162500054069941, 0.11912170940068094, 0.11661960332486086, 0.11412495192861576, 0.11164410384502732, 0.10918340946370288, 0.10674913600521324, 0.10434737654481009, 0.10198395520042028, 0.09966433129990614, 0.09739350588653768, 0.09517593434448934, 0.09301544915792656, 0.09091519679434841, 0.08887759238025328, 0.08690429520448062, 0.08499620717730215, 0.08315349528241742, 0.08137563792645221, 0.07966149409587014, 0.07800939356080977, 0.07641724617290897, 0.07488266866352594, 0.07340312821265634, 0.07197610323090523, 0.07059926293155162, 0.06927066790219844, 0.06798899350005913, 0.06675377601966423, 0.06556567790691072, 0.06442676278879346, 0.06334076410976638, 0.06231332352202657, 0.061352168143419906, 0.06046719104370609, 0.059670398740211385, 0.05897569487542116, 0.05839848184952383, 0.05795508206320444, 0.05766200588248158, 0.05753512060153179, 0.05758879776719016, 0.05783512872793398, 0.05828329503453108, 0.058939159913618165, 0.05980511311386331, 0.06088016210316753, 0.062160227718566344, 0.06363857989658368, 0.06530634244670093 ], [ 0.12345426389466412, 0.1210278546227723, 0.11860315286769728, 0.11618613421714005, 0.11378283232984447, 0.11139926528445429, 0.10904135532795269, 0.1067148436269881, 0.10442520215318217, 0.10217754534691172, 0.09997654465525954, 0.0978263493743611, 0.09573051738802893, 0.09369195933542117, 0.09171289943096246, 0.08979485559914423, 0.08793864081349223, 0.08614438662235822, 0.08441158892165991, 0.08273917523611568, 0.08112559223401662, 0.07956891203023181, 0.07806695606331522, 0.07661743590262428, 0.0752181110742037, 0.07386696460427343, 0.07256239710409912, 0.07130343947536412, 0.07008998237464432, 0.06892301726075262, 0.06780487921853051, 0.06673947617638264, 0.06573248333200771, 0.06479147662803598, 0.06392597629320518, 0.06314737219461558, 0.062468708272213125, 0.06190431435887049, 0.06146928999029427, 0.06117886481485716, 0.06104768087636683, 0.06108905911507337, 0.0613143213564808, 0.06173223637393452, 0.06234864344011754, 0.0631662816634401, 0.06418482387924744, 0.0654010867656734, 0.06680936998798938, 0.06840186949374596 ] ] }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "text": [ "0_0", "1_0", "2_0", "3_0", "4_0", "5_0", "6_0", "7_0", "8_0", "9_0", "10_0", "11_0", "12_0", "13_0", "14_0", "15_0", "16_0", "17_0", "18_0", "19_0", "20_0", "21_0", "22_0", "23_0" ], "type": "scatter", "x": [ 0.7245777016505599, 0.9210068788379431, 0.4902732791379094, 0.18550697807222605, 0.9477102681994438, 0.7721278304234147, 0.6640654237952077, 0.7549303681670096, 0.7903788558980334, 0.8100541161892053, 0.8943502586659912, 0.7544410620076232, 0.6894892798604945, 0.6265551165213862, 0.577605048638068, 0.550753852628226, 0.5230489239382824, 0.5122936123522853, 0.6130380393456225, 0.4508900016528717, 0.5075227206552099, 0.5025878609009615, 0.4854770307718386, 0.4848857242527197 ], "xaxis": "x", "y": [ 0.4896725546568632, 0.1411228971555829, 0.46095985267311335, 0.6044925963506103, 0.6915651960298419, 0.33214059565216303, 0.3939260532285253, 0.5407279090104576, 0.6098283551821468, 0.6587780717916488, 0.6778688796331444, 0.6449240347401863, 0.6419712980599209, 0.6281956615704509, 0.5982145369969085, 0.5539255242521771, 0.5113153412825011, 0.5713282501836204, 0.4443768367568401, 0.5699695946747757, 0.5746448123097645, 0.5789541060518526, 0.5674793100350288, 0.5807341214462963 ], "yaxis": "y" }, { "hoverinfo": "text", "legendgroup": "In-sample", "marker": { "color": "black", "opacity": 0.5, "symbol": 1 }, "mode": "markers", "name": "In-sample", "showlegend": false, "text": [ "0_0", "1_0", "2_0", "3_0", "4_0", "5_0", "6_0", "7_0", "8_0", "9_0", "10_0", "11_0", "12_0", "13_0", "14_0", "15_0", "16_0", "17_0", "18_0", "19_0", "20_0", "21_0", "22_0", "23_0" ], "type": "scatter", "x": [ 0.7245777016505599, 0.9210068788379431, 0.4902732791379094, 0.18550697807222605, 0.9477102681994438, 0.7721278304234147, 0.6640654237952077, 0.7549303681670096, 0.7903788558980334, 0.8100541161892053, 0.8943502586659912, 0.7544410620076232, 0.6894892798604945, 0.6265551165213862, 0.577605048638068, 0.550753852628226, 0.5230489239382824, 0.5122936123522853, 0.6130380393456225, 0.4508900016528717, 0.5075227206552099, 0.5025878609009615, 0.4854770307718386, 0.4848857242527197 ], "xaxis": "x2", "y": [ 0.4896725546568632, 0.1411228971555829, 0.46095985267311335, 0.6044925963506103, 0.6915651960298419, 0.33214059565216303, 0.3939260532285253, 0.5407279090104576, 0.6098283551821468, 0.6587780717916488, 0.6778688796331444, 0.6449240347401863, 0.6419712980599209, 0.6281956615704509, 0.5982145369969085, 0.5539255242521771, 0.5113153412825011, 0.5713282501836204, 0.4443768367568401, 0.5699695946747757, 0.5746448123097645, 0.5789541060518526, 0.5674793100350288, 0.5807341214462963 ], "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 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 } }, "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": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "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": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "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 } } }, "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", "metadata": {}, "source": [ "Here we plot the optimization trace, showing the progression of finding the point with the optimal objective:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "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": [ -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.8443522317069964, -1.0288318983634899, -1.0938747876390158, -1.0938747876390158, -1.315707654184007, -1.4652106326934136, -1.7817418189631244, -2.3550330931944945, -2.834990998734847, -2.9711655440024836, -2.9711655440024836, -2.9711655440024836, -3.0058879383673323, -3.054942325823102, -3.0597312775268293, -3.1533383413653775, -3.1533383413653775, -3.153972487560694 ] }, { "fill": "tonexty", "fillcolor": "rgba(128,177,211,0.3)", "legendgroup": "mean", "line": { "color": "rgba(128,177,211,1)" }, "mode": "lines", "name": "mean", "text": [ "
Parameterization:
x1: 0.27277045603841543
x2: 0.4860017206519842
x3: 0.7245777016505599
x4: 0.4896725546568632
x5: 0.016776829957962036
x6: 0.025310590863227844", "
Parameterization:
x1: 0.21175731625407934
x2: 0.7150549702346325
x3: 0.9210068788379431
x4: 0.1411228971555829
x5: 0.2786991214379668
x6: 0.35350997373461723", "
Parameterization:
x1: 0.4312838092446327
x2: 0.10096925031393766
x3: 0.4902732791379094
x4: 0.46095985267311335
x5: 0.6712788958102465
x6: 0.971739524975419", "
Parameterization:
x1: 0.1797152440994978
x2: 0.5281501533463597
x3: 0.18550697807222605
x4: 0.6044925963506103
x5: 0.9359499057754874
x6: 0.9218545891344547", "
Parameterization:
x1: 0.7082942668348551
x2: 0.6264908136799932
x3: 0.9477102681994438
x4: 0.6915651960298419
x5: 0.08570482302457094
x6: 0.389578377828002", "
Parameterization:
x1: 0.8214593231678009
x2: 0.16045302338898182
x3: 0.7721278304234147
x4: 0.33214059565216303
x5: 0.6924089286476374
x6: 0.900620374828577", "
Parameterization:
x1: 0.19429569731792892
x2: 0.44698952479583787
x3: 0.6640654237952077
x4: 0.3939260532285253
x5: 6.384689399226754e-17
x6: 1.934267444203101e-16", "
Parameterization:
x1: 0.3009712127031631
x2: 0.5051994955367584
x3: 0.7549303681670096
x4: 0.5407279090104576
x5: 0.019009931183155717
x6: 0.01627616845494311", "
Parameterization:
x1: 0.32808789348660206
x2: 0.5283450808523815
x3: 0.7903788558980334
x4: 0.6098283551821468
x5: 0.019758928639687746
x6: 6.84946188768533e-18", "
Parameterization:
x1: 0.3419170482789374
x2: 0.5443598765345412
x3: 0.8100541161892053
x4: 0.6587780717916488
x5: 0.020105409694201895
x6: 1.4468724852270396e-13", "
Parameterization:
x1: 0.2929502941842078
x2: 0.5120116843839567
x3: 0.8943502586659912
x4: 0.6778688796331444
x5: 0.006329562718949968
x6: 3.3538128502420383e-18", "
Parameterization:
x1: 0.3849430696971001
x2: 0.5639405274924641
x3: 0.7544410620076232
x4: 0.6449240347401863
x5: 0.03289929995219823
x6: 7.94762758167772e-15", "
Parameterization:
x1: 0.43858922561682445
x2: 0.5877443281650403
x3: 0.6894892798604945
x4: 0.6419712980599209
x5: 0.058411339246201
x6: 0.0", "
Parameterization:
x1: 0.4699073759964763
x2: 0.6427206306874169
x3: 0.6265551165213862
x4: 0.6281956615704509
x5: 2.107324319485517e-15
x6: 2.66727146069383e-15", "
Parameterization:
x1: 0.4744394363561025
x2: 0.7273556997401969
x3: 0.577605048638068
x4: 0.5982145369969085
x5: 0.0
x6: 0.0", "
Parameterization:
x1: 0.4494999041662254
x2: 0.7984077383760276
x3: 0.550753852628226
x4: 0.5539255242521771
x5: 1.0302128280740713e-12
x6: 1.136201712390764e-12", "
Parameterization:
x1: 0.42568580536559575
x2: 0.8788709285290766
x3: 0.5230489239382824
x4: 0.5113153412825011
x5: 1.7536587352672373e-08
x6: 4.609350256115356e-10", "
Parameterization:
x1: 0.33636774088297955
x2: 0.8583064561640562
x3: 0.5122936123522853
x4: 0.5713282501836204
x5: 7.688412403359396e-16
x6: 1.8822895737348175e-15", "
Parameterization:
x1: 0.3966745696372959
x2: 0.8560335644002842
x3: 0.6130380393456225
x4: 0.4443768367568401
x5: 6.223230745144125e-15
x6: 5.156240401209584e-15", "
Parameterization:
x1: 0.44747582204470726
x2: 0.8696804343008991
x3: 0.4508900016528717
x4: 0.5699695946747757
x5: 0.0
x6: 0.0", "
Parameterization:
x1: 0.4376736851484068
x2: 0.8775640248817276
x3: 0.5075227206552099
x4: 0.5746448123097645
x5: 3.873917825276913e-17
x6: 4.569912702457492e-17", "
Parameterization:
x1: 0.43718880792229775
x2: 0.8893671401352032
x3: 0.5025878609009615
x4: 0.5789541060518526
x5: 0.09169833601659122
x6: 0.0", "
Parameterization:
x1: 0.42261693595076183
x2: 0.8743919010098683
x3: 0.4854770307718386
x4: 0.5674793100350288
x5: 0.0425719770072076
x6: 0.04825437095562463", "
Parameterization:
x1: 0.41847060485928145
x2: 0.887410548304023
x3: 0.4848857242527197
x4: 0.5807341214462963
x5: 0.04189703001587689
x6: 0.0810309472623818", "
Parameterization:
x1: 0.42651509505001167
x2: 0.8812934413145114
x3: 0.507173281563125
x4: 0.5772004405796546
x5: 0.04631206291508088
x6: 0.0424943672709597" ], "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": [ -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.8443522317069964, -1.0288318983634899, -1.0938747876390158, -1.0938747876390158, -1.315707654184007, -1.4652106326934136, -1.7817418189631244, -2.3550330931944945, -2.834990998734847, -2.9711655440024836, -2.9711655440024836, -2.9711655440024836, -3.0058879383673323, -3.054942325823102, -3.0597312775268293, -3.1533383413653775, -3.1533383413653775, -3.153972487560694 ] }, { "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": [ -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.640188177317451, -0.8443522317069964, -1.0288318983634899, -1.0938747876390158, -1.0938747876390158, -1.315707654184007, -1.4652106326934136, -1.7817418189631244, -2.3550330931944945, -2.834990998734847, -2.9711655440024836, -2.9711655440024836, -2.9711655440024836, -3.0058879383673323, -3.054942325823102, -3.0597312775268293, -3.1533383413653775, -3.1533383413653775, -3.153972487560694 ] }, { "line": { "color": "rgba(253,180,98,1)", "dash": "dash" }, "mode": "lines", "name": "Optimum", "type": "scatter", "x": [ 1, 25 ], "y": [ -3.32237, -3.32237 ] }, { "line": { "color": "rgba(141,211,199,1)", "dash": "dash" }, "mode": "lines", "name": "model change", "type": "scatter", "x": [ 6, 6 ], "y": [ -3.32237, -0.640188177317451 ] } ], "layout": { "showlegend": true, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 } }, "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": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "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": [ { "marker": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "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": "Model performance vs. # of iterations" }, "xaxis": { "title": { "text": "Iteration" } }, "yaxis": { "title": { "text": "Hartmann6" } } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "render(ax_client.get_optimization_trace(objective_optimum=hartmann6.fmin)) # Objective_optimum is optional." ] }, { "cell_type": "markdown", "metadata": {}, "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, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:39] 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, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 12-08 18:46:40] ax.service.ax_client: Starting optimization with verbose logging. To disable logging, set the `verbose_logging` argument to `False`. Note that float values in the logs are rounded to 2 decimal points.\n" ] } ], "source": [ "restored_ax_client = AxClient.load_from_json_file() # For custom filepath, pass `filepath` argument." ] }, { "cell_type": "markdown", "metadata": {}, "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", "metadata": {}, "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, "metadata": { "collapsed": true }, "outputs": [ { "ename": "ModuleNotFoundError", "evalue": "No module named 'psycopg2'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mdb_settings\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDBSettings\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"postgresql+psycopg2://sarah:c82i94d@ocalhost:5432/foobar\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;31m# Instead of URL, can provide a `creator function`; can specify custom encoders/decoders if necessary.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mnew_ax\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mAxClient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdb_settings\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdb_settings\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m~/build/facebook/Ax/ax/service/ax_client.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, generation_strategy, db_settings, enforce_sequential_optimization, random_seed, verbose_logging, suppress_storage_errors)\u001b[0m\n\u001b[1;32m 132\u001b[0m \u001b[0msuppress_storage_errors\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mbool\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 133\u001b[0m ) -> None:\n\u001b[0;32m--> 134\u001b[0;31m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdb_settings\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdb_settings\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 135\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mverbose_logging\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 136\u001b[0m \u001b[0mlogger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetLevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlogging\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mWARNING\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# pragma: no cover\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/build/facebook/Ax/ax/service/utils/with_db_settings_base.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, db_settings, logging_level)\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdb_settings_set\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 68\u001b[0m init_engine_and_session_factory(\n\u001b[0;32m---> 69\u001b[0;31m \u001b[0mcreator\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdb_settings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcreator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdb_settings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 70\u001b[0m )\n\u001b[1;32m 71\u001b[0m \u001b[0mlogger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetLevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlogging_level\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/build/facebook/Ax/ax/storage/sqa_store/db.py\u001b[0m in \u001b[0;36minit_engine_and_session_factory\u001b[0;34m(url, creator, echo, force_init, **kwargs)\u001b[0m\n\u001b[1;32m 338\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;31m# pragma: no cover\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 339\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0murl\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 340\u001b[0;31m \u001b[0mengine\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcreate_mysql_engine_from_url\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mecho\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mecho\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 341\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mcreator\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 342\u001b[0m \u001b[0mengine\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcreate_mysql_engine_from_creator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcreator\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcreator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mecho\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mecho\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/build/facebook/Ax/ax/storage/sqa_store/db.py\u001b[0m in \u001b[0;36mcreate_mysql_engine_from_url\u001b[0;34m(url, echo, pool_recycle, **kwargs)\u001b[0m\n\u001b[1;32m 279\u001b[0m \"\"\"\n\u001b[1;32m 280\u001b[0m return create_engine(\n\u001b[0;32m--> 281\u001b[0;31m \u001b[0mname_or_url\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpool_recycle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mpool_recycle\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mecho\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mecho\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 282\u001b[0m )\n\u001b[1;32m 283\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/virtualenv/python3.7.1/lib/python3.7/site-packages/sqlalchemy/engine/__init__.py\u001b[0m in \u001b[0;36mcreate_engine\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 498\u001b[0m \u001b[0mstrategy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"strategy\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdefault_strategy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 499\u001b[0m \u001b[0mstrategy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstrategies\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstrategies\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mstrategy\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 500\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mstrategy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcreate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 501\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/virtualenv/python3.7.1/lib/python3.7/site-packages/sqlalchemy/engine/strategies.py\u001b[0m in \u001b[0;36mcreate\u001b[0;34m(self, name_or_url, **kwargs)\u001b[0m\n\u001b[1;32m 85\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[0mdbapi_args\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpop_kwarg\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m \u001b[0mdbapi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdialect_cls\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdbapi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mdbapi_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 89\u001b[0m \u001b[0mdialect_args\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"dbapi\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbapi\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/virtualenv/python3.7.1/lib/python3.7/site-packages/sqlalchemy/dialects/postgresql/psycopg2.py\u001b[0m in \u001b[0;36mdbapi\u001b[0;34m(cls)\u001b[0m\n\u001b[1;32m 776\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mclassmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 777\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdbapi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 778\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mpsycopg2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 779\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 780\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mpsycopg2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'psycopg2'" ] } ], "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=\"postgresql+psycopg2://sarah:c82i94d@ocalhost:5432/foobar\")\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", "metadata": {}, "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", "metadata": {}, "source": [ "# Special Cases" ] }, { "cell_type": "markdown", "metadata": {}, "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": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "_, trial_index = ax_client.get_next_trial()\n", "ax_client.log_trial_failure(trial_index=trial_index)" ] }, { "cell_type": "markdown", "metadata": {}, "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": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ax_client.attach_trial(parameters={\"x1\": 0.9, \"x2\": 0.9, \"x3\": 0.9, \"x4\": 0.9, \"x5\": 0.9, \"x6\": 0.9})" ] }, { "cell_type": "markdown", "metadata": {}, "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": "markdown", "metadata": {}, "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", "metadata": {}, "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": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 04-16 10:14:20] 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 2 decimal points.\n", "[INFO 04-16 10:14:20] ax.modelbridge.dispatch_utils: Using Bayesian Optimization generation strategy: GenerationStrategy(name='Sobol+GPEI', steps=[Sobol for 5 trials, GPEI 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": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(5, 10), (-1, 10)]" ] }, "execution_count": 5, "metadata": { "bento_obj_id": "140609783487456" }, "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": "python3", "language": "python", "name": "python3" } }, "nbformat": 4, "nbformat_minor": 2 }