{ "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 08-10 23:15:40] 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 08-10 23:15:40] 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": [ "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 08-10 23:15:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x2. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x3. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x4. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x5. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x6. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.modelbridge.dispatch_utils: Using GPEI (Bayesian optimization) since there are more continuous parameters than there are categories for the unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] 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 08-10 23:15:40] ax.service.ax_client: Generated new trial 0 with parameters {'x1': 0.51, 'x2': 0.81, 'x3': 0.95, 'x4': 0.2, 'x5': 0.64, 'x6': 0.03}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Completed trial 0 with data: {'hartmann6': (-0.59, 0.0), 'l2norm': (1.51, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Generated new trial 1 with parameters {'x1': 0.35, 'x2': 0.49, 'x3': 0.01, 'x4': 0.06, 'x5': 0.13, 'x6': 0.2}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Completed trial 1 with data: {'hartmann6': (-0.14, 0.0), 'l2norm': (0.65, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Generated new trial 2 with parameters {'x1': 0.84, 'x2': 0.27, 'x3': 0.86, 'x4': 0.76, 'x5': 0.95, 'x6': 0.67}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Completed trial 2 with data: {'hartmann6': (-0.0, 0.0), 'l2norm': (1.85, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Generated new trial 3 with parameters {'x1': 0.38, 'x2': 0.39, 'x3': 0.97, 'x4': 0.66, 'x5': 0.16, 'x6': 0.77}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Completed trial 3 with data: {'hartmann6': (-0.58, 0.0), 'l2norm': (1.52, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Generated new trial 4 with parameters {'x1': 0.0, 'x2': 0.7, 'x3': 0.32, 'x4': 0.31, 'x5': 0.46, 'x6': 0.21}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Completed trial 4 with data: {'hartmann6': (-0.19, 0.0), 'l2norm': (0.97, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Generated new trial 5 with parameters {'x1': 0.14, 'x2': 0.86, 'x3': 0.78, 'x4': 0.23, 'x5': 0.05, 'x6': 0.34}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:40] ax.service.ax_client: Completed trial 5 with data: {'hartmann6': (-0.16, 0.0), 'l2norm': (1.24, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:46] ax.service.ax_client: Generated new trial 6 with parameters {'x1': 0.43, 'x2': 0.75, 'x3': 0.64, 'x4': 0.16, 'x5': 0.59, 'x6': 0.04}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:46] ax.service.ax_client: Completed trial 6 with data: {'hartmann6': (-0.48, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:53] ax.service.ax_client: Generated new trial 7 with parameters {'x1': 0.6, 'x2': 0.9, 'x3': 0.59, 'x4': 0.17, 'x5': 0.7, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:53] ax.service.ax_client: Completed trial 7 with data: {'hartmann6': (-0.31, 0.0), 'l2norm': (1.42, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:59] ax.service.ax_client: Generated new trial 8 with parameters {'x1': 0.35, 'x2': 0.62, 'x3': 0.8, 'x4': 0.13, 'x5': 0.54, 'x6': 0.05}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:15:59] ax.service.ax_client: Completed trial 8 with data: {'hartmann6': (-0.27, 0.0), 'l2norm': (1.21, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:06] ax.service.ax_client: Generated new trial 9 with parameters {'x1': 0.34, 'x2': 0.84, 'x3': 0.72, 'x4': 0.16, 'x5': 0.54, 'x6': 0.1}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:06] ax.service.ax_client: Completed trial 9 with data: {'hartmann6': (-0.51, 0.0), 'l2norm': (1.29, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:12] ax.service.ax_client: Generated new trial 10 with parameters {'x1': 0.46, 'x2': 0.79, 'x3': 0.68, 'x4': 0.15, 'x5': 0.47, 'x6': 0.04}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:12] ax.service.ax_client: Completed trial 10 with data: {'hartmann6': (-0.46, 0.0), 'l2norm': (1.24, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:19] ax.service.ax_client: Generated new trial 11 with parameters {'x1': 0.39, 'x2': 0.78, 'x3': 0.67, 'x4': 0.05, 'x5': 0.6, 'x6': 0.15}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:19] ax.service.ax_client: Completed trial 11 with data: {'hartmann6': (-0.18, 0.0), 'l2norm': (1.26, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:25] ax.service.ax_client: Generated new trial 12 with parameters {'x1': 0.37, 'x2': 0.77, 'x3': 0.64, 'x4': 0.21, 'x5': 0.53, 'x6': 0.03}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:25] ax.service.ax_client: Completed trial 12 with data: {'hartmann6': (-0.77, 0.0), 'l2norm': (1.21, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:31] ax.service.ax_client: Generated new trial 13 with parameters {'x1': 0.38, 'x2': 0.78, 'x3': 0.64, 'x4': 0.25, 'x5': 0.51, 'x6': 0.01}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:31] ax.service.ax_client: Completed trial 13 with data: {'hartmann6': (-0.99, 0.0), 'l2norm': (1.22, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:37] ax.service.ax_client: Generated new trial 14 with parameters {'x1': 0.4, 'x2': 0.79, 'x3': 0.64, 'x4': 0.29, 'x5': 0.48, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:37] ax.service.ax_client: Completed trial 14 with data: {'hartmann6': (-1.33, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:43] ax.service.ax_client: Generated new trial 15 with parameters {'x1': 0.41, 'x2': 0.8, 'x3': 0.63, 'x4': 0.35, 'x5': 0.43, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:43] ax.service.ax_client: Completed trial 15 with data: {'hartmann6': (-1.79, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:49] ax.service.ax_client: Generated new trial 16 with parameters {'x1': 0.42, 'x2': 0.8, 'x3': 0.58, 'x4': 0.43, 'x5': 0.38, 'x6': 0.01}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:49] ax.service.ax_client: Completed trial 16 with data: {'hartmann6': (-2.39, 0.0), 'l2norm': (1.22, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:55] ax.service.ax_client: Generated new trial 17 with parameters {'x1': 0.43, 'x2': 0.79, 'x3': 0.53, 'x4': 0.53, 'x5': 0.33, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:16:55] ax.service.ax_client: Completed trial 17 with data: {'hartmann6': (-2.8, 0.0), 'l2norm': (1.22, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:01] ax.service.ax_client: Generated new trial 18 with parameters {'x1': 0.45, 'x2': 0.79, 'x3': 0.53, 'x4': 0.58, 'x5': 0.29, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:01] ax.service.ax_client: Completed trial 18 with data: {'hartmann6': (-2.81, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:07] ax.service.ax_client: Generated new trial 19 with parameters {'x1': 0.41, 'x2': 0.81, 'x3': 0.46, 'x4': 0.57, 'x5': 0.38, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:07] ax.service.ax_client: Completed trial 19 with data: {'hartmann6': (-2.98, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:13] ax.service.ax_client: Generated new trial 20 with parameters {'x1': 0.43, 'x2': 0.78, 'x3': 0.36, 'x4': 0.6, 'x5': 0.44, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:13] ax.service.ax_client: Completed trial 20 with data: {'hartmann6': (-2.76, 0.0), 'l2norm': (1.22, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:19] ax.service.ax_client: Generated new trial 21 with parameters {'x1': 0.37, 'x2': 0.85, 'x3': 0.45, 'x4': 0.59, 'x5': 0.34, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:19] ax.service.ax_client: Completed trial 21 with data: {'hartmann6': (-3.0, 0.0), 'l2norm': (1.24, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:25] ax.service.ax_client: Generated new trial 22 with parameters {'x1': 0.41, 'x2': 0.88, 'x3': 0.39, 'x4': 0.56, 'x5': 0.32, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:25] ax.service.ax_client: Completed trial 22 with data: {'hartmann6': (-3.09, 0.0), 'l2norm': (1.23, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:30] ax.service.ax_client: Generated new trial 23 with parameters {'x1': 0.42, 'x2': 0.89, 'x3': 0.4, 'x4': 0.56, 'x5': 0.33, 'x6': 0.0}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:30] ax.service.ax_client: Completed trial 23 with data: {'hartmann6': (-3.08, 0.0), 'l2norm': (1.24, 0.0)}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:34] ax.service.ax_client: Generated new trial 24 with parameters {'x1': 0.4, 'x2': 0.88, 'x3': 0.38, 'x4': 0.57, 'x5': 0.3, 'x6': 0.08}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:34] ax.service.ax_client: Completed trial 24 with data: {'hartmann6': (-3.08, 0.0), 'l2norm': (1.23, 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 08-10 23:17:34] 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': 0.51, 'x2': 0.81, 'x3': 0.95, '...
10Sobol1COMPLETED{'1_0': {'x1': 0.35, 'x2': 0.49, 'x3': 0.01, '...
20Sobol2COMPLETED{'2_0': {'x1': 0.84, 'x2': 0.27, 'x3': 0.86, '...
30Sobol3COMPLETED{'3_0': {'x1': 0.38, 'x2': 0.39, 'x3': 0.97, '...
40Sobol4COMPLETED{'4_0': {'x1': 0.0, 'x2': 0.7, 'x3': 0.32, 'x4...
50Sobol5COMPLETED{'5_0': {'x1': 0.14, 'x2': 0.86, 'x3': 0.78, '...
61GPEI6COMPLETED{'6_0': {'x1': 0.43, 'x2': 0.75, 'x3': 0.64, '...
71GPEI7COMPLETED{'7_0': {'x1': 0.6, 'x2': 0.9, 'x3': 0.59, 'x4...
81GPEI8COMPLETED{'8_0': {'x1': 0.35, 'x2': 0.62, 'x3': 0.8, 'x...
91GPEI9COMPLETED{'9_0': {'x1': 0.34, 'x2': 0.84, 'x3': 0.72, '...
101GPEI10COMPLETED{'10_0': {'x1': 0.46, 'x2': 0.79, 'x3': 0.68, ...
111GPEI11COMPLETED{'11_0': {'x1': 0.39, 'x2': 0.78, 'x3': 0.67, ...
121GPEI12COMPLETED{'12_0': {'x1': 0.37, 'x2': 0.77, 'x3': 0.64, ...
131GPEI13COMPLETED{'13_0': {'x1': 0.38, 'x2': 0.78, 'x3': 0.64, ...
141GPEI14COMPLETED{'14_0': {'x1': 0.4, 'x2': 0.79, 'x3': 0.64, '...
151GPEI15COMPLETED{'15_0': {'x1': 0.41, 'x2': 0.8, 'x3': 0.63, '...
161GPEI16COMPLETED{'16_0': {'x1': 0.42, 'x2': 0.8, 'x3': 0.58, '...
171GPEI17COMPLETED{'17_0': {'x1': 0.43, 'x2': 0.79, 'x3': 0.53, ...
181GPEI18COMPLETED{'18_0': {'x1': 0.45, 'x2': 0.79, 'x3': 0.53, ...
191GPEI19COMPLETED{'19_0': {'x1': 0.41, 'x2': 0.81, 'x3': 0.46, ...
201GPEI20COMPLETED{'20_0': {'x1': 0.43, 'x2': 0.78, 'x3': 0.36, ...
211GPEI21COMPLETED{'21_0': {'x1': 0.37, 'x2': 0.85, 'x3': 0.45, ...
221GPEI22COMPLETED{'22_0': {'x1': 0.41, 'x2': 0.88, 'x3': 0.39, ...
231GPEI23COMPLETED{'23_0': {'x1': 0.42, 'x2': 0.89, 'x3': 0.4, '...
241GPEI24COMPLETED{'24_0': {'x1': 0.4, 'x2': 0.88, 'x3': 0.38, '...
\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': 0.51, 'x2': 0.81, 'x3': 0.95, '... \n", "1 {'1_0': {'x1': 0.35, 'x2': 0.49, 'x3': 0.01, '... \n", "2 {'2_0': {'x1': 0.84, 'x2': 0.27, 'x3': 0.86, '... \n", "3 {'3_0': {'x1': 0.38, 'x2': 0.39, 'x3': 0.97, '... \n", "4 {'4_0': {'x1': 0.0, 'x2': 0.7, 'x3': 0.32, 'x4... \n", "5 {'5_0': {'x1': 0.14, 'x2': 0.86, 'x3': 0.78, '... \n", "6 {'6_0': {'x1': 0.43, 'x2': 0.75, 'x3': 0.64, '... \n", "7 {'7_0': {'x1': 0.6, 'x2': 0.9, 'x3': 0.59, 'x4... \n", "8 {'8_0': {'x1': 0.35, 'x2': 0.62, 'x3': 0.8, 'x... \n", "9 {'9_0': {'x1': 0.34, 'x2': 0.84, 'x3': 0.72, '... \n", "10 {'10_0': {'x1': 0.46, 'x2': 0.79, 'x3': 0.68, ... \n", "11 {'11_0': {'x1': 0.39, 'x2': 0.78, 'x3': 0.67, ... \n", "12 {'12_0': {'x1': 0.37, 'x2': 0.77, 'x3': 0.64, ... \n", "13 {'13_0': {'x1': 0.38, 'x2': 0.78, 'x3': 0.64, ... \n", "14 {'14_0': {'x1': 0.4, 'x2': 0.79, 'x3': 0.64, '... \n", "15 {'15_0': {'x1': 0.41, 'x2': 0.8, 'x3': 0.63, '... \n", "16 {'16_0': {'x1': 0.42, 'x2': 0.8, 'x3': 0.58, '... \n", "17 {'17_0': {'x1': 0.43, 'x2': 0.79, 'x3': 0.53, ... \n", "18 {'18_0': {'x1': 0.45, 'x2': 0.79, 'x3': 0.53, ... \n", "19 {'19_0': {'x1': 0.41, 'x2': 0.81, 'x3': 0.46, ... \n", "20 {'20_0': {'x1': 0.43, 'x2': 0.78, 'x3': 0.36, ... \n", "21 {'21_0': {'x1': 0.37, 'x2': 0.85, 'x3': 0.45, ... \n", "22 {'22_0': {'x1': 0.41, 'x2': 0.88, 'x3': 0.39, ... \n", "23 {'23_0': {'x1': 0.42, 'x2': 0.89, 'x3': 0.4, '... \n", "24 {'24_0': {'x1': 0.4, 'x2': 0.88, 'x3': 0.38, '... " ] }, "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': 0.40720578843023586,\n", " 'x2': 0.8804264767498129,\n", " 'x3': 0.39488582944328565,\n", " 'x4': 0.5594486009641354,\n", " 'x5': 0.32181171640762957,\n", " 'x6': 0.0}" ] }, "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": [ "{'l2norm': 1.230222949620768, 'hartmann6': -3.085343556421985}" ] }, "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 08-10 23:17:34] ax.service.ax_client: Retrieving contour plot with parameter 'x1' on X-axis and 'x2' on Y-axis, for metric 'hartmann6'. Remaining parameters are affixed to the middle of their range.\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "xaxis": "x", "y": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "yaxis": "y", "z": [ [ -0.2483095447632584, -0.2534126042372733, -0.25921179703325925, -0.26565504043903987, -0.27267749757407045, -0.2802023406701726, -0.2881418492483605, -0.29639881976595683, -0.30486825296486697, -0.3134392766312972, -0.3219972549241704, -0.3304260307892163, -0.3386102450446067, -0.3464376742233345, -0.35380152891005723, -0.36060265491366705, -0.3667515810961317, -0.37217036011038207, -0.37679415189994137, -0.3805725048812213, -0.3834702965668839, -0.3854683041936616, -0.38656338669169443, -0.38676827180913953, -0.38611095584222, -0.3846337374321963, -0.3823919203499925, -0.3794522321470687, -0.3758910151706176, -0.3717922531021346, -0.3672454995482509, -0.3623437752621832, -0.35718149755227424, -0.35185249980568567, -0.34644819142352423, -0.3410558994864814, -0.33575742379069173, -0.3306278270860895, -0.32573447288423873, -0.3211363144359508, -0.31688343065268176, -0.3130167980041061, -0.30956828183306784, -0.30656082609665947, -0.3040088172398434, -0.30191859568264756, -0.3002890871867536, -0.2991125260840988, -0.29837524291164996, -0.2980584903037098 ], [ -0.2445700873914065, -0.2502123196119621, -0.25661156972753374, -0.2637113876065986, -0.27144123741136306, -0.2797173211844457, -0.28844377700680424, -0.29751422578777187, -0.3068136291110033, -0.3162204110397231, -0.3256087895177686, -0.33485125788891246, -0.3438211538254382, -0.352395251258396, -0.3604563104021834, -0.36789552143358795, -0.37461477875426674, -0.3805287251631121, -0.3855665089919652, -0.38967320272122596, -0.39281083919607107, -0.394959031578731, -0.39611515561309274, -0.3962940873192514, -0.3955275051966287, -0.39386278241474504, -0.39136151015609666, -0.38809770707918045, -0.3841557807792819, -0.3796283144156166, -0.37461375498836325, -0.3692140791114594, -0.36353250789866465, -0.3576713353768475, -0.3517299254297157, -0.34580292147260816, -0.3399787016428747, -0.33433810093722205, -0.32895341097615605, -0.32388765831614463, -0.3191941537098453, -0.31491629756013184, -0.311087621057087, -0.3077320380953308, -0.3048642799670631, -0.30249048291751235, -0.30060889782668365, -0.29921069143233714, -0.2982808095190401, -0.2977988742466362 ], [ -0.24088796392977896, -0.24711278548755566, -0.25416041863646943, -0.26196975291329094, -0.27046412885948046, -0.2795522248181843, -0.2891293624251672, -0.2990792020889279, -0.3092757866913707, -0.31958588113862985, -0.3298715473677398, -0.33999288880566336, -0.34981089472539806, -0.3591903130123597, -0.36800247914071305, -0.3761280294003958, -0.3834594275628612, -0.38990323642215186, -0.3953820694116307, -0.3998361633221237, -0.4032245215719352, -0.40552558886979806, -0.4067374325020624, -0.40687742246532, -0.40598142140132865, -0.40410251454294455, -0.40130932820907306, -0.3976840013556695, -0.39331988707438126, -0.38831906888580514, -0.38278977982469187, -0.376843810760881, -0.37059398865345894, -0.36415179630384087, -0.357625193627382, -0.35111668750732206, -0.3447216838656574, -0.3385271424748483, -0.332610542854195, -0.32703915876668876, -0.3218696296007676, -0.31714780938604203, -0.31290886833832743, -0.3091776175708192, -0.30596902481229304, -0.3032888874897721, -0.30113462920718104, -0.29949618633096065, -0.2983569529325374, -0.2976947545927964 ], [ -0.2372816505049935, -0.24413483443190942, -0.2518818637369571, -0.2604566671980404, -0.26977601827724307, -0.2797404878045988, -0.29023586433913406, -0.3011350104548409, -0.3123001085730408, -0.32358523820357765, -0.33483921764493774, -0.3459086370773945, -0.3566410060954177, -0.36688793651913354, -0.37650828031709727, -0.385371142366866, -0.3933586885543032, -0.40036867165455026, -0.40631660110808754, -0.411137488930547, -0.4147871132891875, -0.41724275423078083, -0.4185033727196419, -0.4185892240457837, -0.41754091871756394, -0.41541796661741726, -0.41229686167439716, -0.4082687828200684, -0.40343700106374947, -0.39791409116648657, -0.39181904922947, -0.3852744147528475, -0.37840348807350566, -0.3713277226056704, -0.36416435720610396, -0.35702433849842574, -0.35001056723642476, -0.34321648768636603, -0.3367250252509085, -0.33060786558949273, -0.3249250585455842, -0.3197249223255345, -0.31504421751407286, -0.31090855650106297, -0.30733301153100223, -0.30432288365632454, -0.3018745951653403, -0.2999766693698689, -0.2986107637940876, -0.29775272563767263 ], [ -0.23377095724109775, -0.241300619118493, -0.24980074132169672, -0.2591999859714684, -0.26940809869006355, -0.28031692953859166, -0.29180197590390544, -0.303724412217103, -0.3159335550626099, -0.328269699256463, -0.3405672508581148, -0.3526580764608963, -0.3643749838721294, -0.37555524676338514, -0.3860440844660199, -0.3956980074751639, -0.4043879394261254, -0.4120020277287125, -0.4184480584394161, -0.4236553972771977, -0.4275763888871189, -0.4301871611791792, -0.43148780092195926, -0.4315018901406992, -0.43027541890450627, -0.42787511684323964, -0.42438627096081083, -0.4199101188159554, -0.41456092213205764, -0.4084628352370878, -0.4017466850540621, -0.39454677502951396, -0.38699781536925204, -0.37923206760223027, -0.3713767743418077, -0.36355192665896574, -0.35586840305260603, -0.34842649666224956, -0.3413148318812743, -0.3346096583613831, -0.3283744997564576, -0.32266012643407016, -0.31750481563381183, -0.3129348589307954, -0.3089652750832006, -0.3056006861126275, -0.3028363155079572, -0.30065906950947263, -0.29904866530057617, -0.2979787734168071 ], [ -0.2303770442066604, -0.23863360300176417, -0.24794316701330632, -0.25822882282072834, -0.26939281215131583, -0.2813176230386627, -0.2938676629293546, -0.3068914748924563, -0.3202244399356379, -0.33369189418865686, -0.3471125793092933, -0.3603023373708897, -0.3730779569086805, -0.38526107388947317, -0.39668202943309094, -0.40718358478862426, -0.41662439343146607, -0.42488213076378567, -0.43185618476927634, -0.4374698173488698, -0.44167171718326215, -0.44443688169492856, -0.4457667881810199, -0.4456888416999689, -0.4442551181146953, -0.4415404523688584, -0.43763995177993564, -0.4326660391580849, -0.4267451487366233, -0.4200142079180119, -0.41261703937037164, -0.40470081164136595, -0.3964126534900345, -0.38789652931501495, -0.3792904522770518, -0.37072408979345484, -0.36231679458933963, -0.35417607464189416, -0.3463964979869404, -0.33905901394350835, -0.3322306610124257, -0.32596462343561095, -0.3203005929128572, -0.3152653889127581, -0.31087378999630566, -0.30712952921190895, -0.3040264085674045, -0.3015494905324143, -0.29967632821251877, -0.298378200047418 ], [ -0.22712243037256696, -0.23615854030353933, -0.2463364836988966, -0.2575734626878121, -0.26976372633636014, -0.28277973349934427, -0.2964739637851024, -0.310681333641339, -0.3252221544754821, -0.33990555420508484, -0.3545332724861129, -0.36890373234947915, -0.3828162860584752, -0.3960755296360623, -0.40849557787562996, -0.4199041893426442, -0.4301466290574889, -0.4390891559886593, -0.4466220244907322, -0.452661895030526, -0.45715356157095266, -0.46007092197114985, -0.4614171439582795, -0.4612240116935534, -0.459550474538564, -0.45648045722615305, -0.4521200257090673, -0.4465940321333689, -0.4400423830408774, -0.4326160855479092, -0.42447322663080933, -0.41577503166241336, -0.40668213172531964, -0.3973511472017749, -0.3879316700550257, -0.37856370126476935, -0.3693755748937373, -0.360482377623468, -0.3519848532060773, -0.34396876559569023, -0.33650468263801514, -0.32964813391919956, -0.3234400913291171, -0.3179077186010071, -0.31306533603913556, -0.3089155483509256, -0.30545048652233286, -0.3026531186459138, -0.3004985892273353, -0.29895555151388464 ], [ -0.22403099487813538, -0.23390144442757377, -0.2450091932161229, -0.2572652534539559, -0.2705553832901535, -0.28474132223524595, -0.2996627474586888, -0.3151399033312996, -0.3309768344514954, -0.34696513563429654, -0.3628881205526773, -0.3785253028773037, -0.3936570785377619, -0.40806949383154134, -0.4215589805602562, -0.4339369357457806, -0.445034020041998, -0.454704046736771, -0.4628273339355802, -0.46931339825519824, -0.4741028812343907, -0.47716862119951886, -0.47851581387168074, -0.4781812434076125, -0.4762316091082258, -0.4727610177781265, -0.4678877532163229, -0.4617504683832081, -0.4545039692504437, -0.4463147705024665, -0.43735660201934734, -0.42780603273461404, -0.417838357331657, -0.4076238641428871, -0.39732457244205954, -0.38709149669472964, -0.3770624663863973, -0.36736050432663225, -0.35809274478277553, -0.34934985585021805, -0.3412059181072091, -0.3337187035018101, -0.32693029404393636, -0.32086797859333105, -0.31554536719177406, -0.31096366537614806, -0.30711305519539667, -0.3039741348007521, -0.30151937413808727, -0.29971455017699733 ], [ -0.221127969850192, -0.2318895439191042, -0.24399087066754155, -0.2573364743463493, -0.2718031183597214, -0.2872411134409918, -0.30347642647243456, -0.3203135370964635, -0.3375389650412879, -0.35492537317905626, -0.3722361390718698, -0.3892302797417023, -0.40566760892429543, -0.4213140015422454, -0.43594663540765766, -0.44935907478815784, -0.4613660548576938, -0.4718078215535332, -0.4805538801682583, -0.48750601085288825, -0.49260042282115424, -0.495808943420065, -0.4971391739002946, -0.49663358925369283, -0.4943676114429052, -0.4904467387480893, -0.48500286317210095, -0.478189947680436, -0.4701792616712337, -0.46115438457167435, -0.4513061839750281, -0.44082795812935316, -0.4299109059002455, -0.41874005412508286, -0.40749073610632425, -0.39632567897406235, -0.38539272423897897, -0.37482317676052246, -0.36473075355094053, -0.3552110856730032, -0.34634171381708423, -0.33818251045632675, -0.33077645805221767, -0.32415071279890717, -0.3183178860348228, -0.3132774799673377, -0.30901742011297273, -0.30551563334039145, -0.30274162722513287, -0.3006580332972826 ], [ -0.218439923933768, -0.2301512250693425, -0.24331206028905505, -0.25782017979132377, -0.2735428475000772, -0.29031822138630514, -0.30795762158228057, -0.32624862750881345, -0.3449589189155372, -0.36384075686726325, -0.3826359882331928, -0.40108144925963096, -0.41891463816169405, -0.4358795214026394, -0.45173233209631103, -0.46624721130619695, -0.4792215345289249, -0.4904807580897895, -0.49988261634470743, -0.5073205039774588, -0.5127258918296713, -0.5160696522336056, -0.5173622115081694, -0.5166525013779255, -0.5140257432308654, -0.5096001630156927, -0.503522793083551, -0.4959645639256324, -0.4871149189119296, -0.4771761966967655, -0.4663580194193302, -0.4548719028119248, -0.44292627080679114, -0.4307220167032466, -0.41844870974569415, -0.40628150375578165, -0.3943787660547704, -0.3828804121562147, -0.3719069055758596, -0.36155886282623073, -0.3519171908997911, -0.3430436775675413, -0.33498195267466735, -0.32775874026415086, -0.3213853257935705, -0.31585916902951294, -0.31116560065386545, -0.3072795486104778, -0.3041672483249942, -0.3017878988446514 ], [ -0.21599473555972382, -0.22871596022011165, -0.24300415184193835, -0.2587500174666588, -0.27581082134859924, -0.29401183593943414, -0.3131487755098388, -0.3329911468424257, -0.3532864230878492, -0.3737649273455569, -0.3941453002184955, -0.4141404179667929, -0.43346362219098267, -0.4518351158329289, -0.4689883721327177, -0.48467639256992745, -0.49867763759469486, -0.5108014423539685, -0.5208927221875701, -0.5288357738607253, -0.5345569928644637, -0.5380263581192498, -0.5392575841815989, -0.5383069054543274, -0.5352705314352129, -0.5302808886586577, -0.5235018346845779, -0.5151230841815597, -0.5053541212367023, -0.4944178832262056, -0.4825444909341474, -0.46996527074632555, -0.45690727285013955, -0.44358844007749687, -0.43021353058468537, -0.41697084828613706, -0.40402979099826763, -0.39153918957177436, -0.3796263828101155, -0.3683969527429729, -0.3579350322621614, -0.3483040912286455, -0.33954810669018365, -0.33169302651811605, -0.3247484423525173, -0.318709396163807, -0.3135582541216617, -0.30926659114141186, -0.3057970389850899, -0.30310505981805536 ], [ -0.213821554777192, -0.2276142207351297, -0.2430992365228304, -0.2601600194460174, -0.2786433447160048, -0.29836086467136247, -0.3190917134132083, -0.34058612344512385, -0.3625699507237412, -0.3847499847819109, -0.4068199089681247, -0.4284667689921262, -0.44937780238923897, -0.4692474743380747, -0.48778455469912196, -0.5047190567739784, -0.5198088412646706, -0.5328456720622364, -0.5436604982554669, -0.5521277347566486, -0.5581683280424331, -0.5617514282735763, -0.5628945461150422, -0.5616621493709227, -0.558162744130448, -0.5525445772397389, -0.5449901801351827, -0.5357100382807617, -0.5249357088728136, -0.5129127197152176, -0.49989356604575697, -0.486131084605642, -0.47187243210766616, -0.45735383551287734, -0.4427962204977446, -0.4284017671936835, -0.414351392202158, -0.4008031150677883, -0.3878912366147015, -0.3757262356240548, -0.36439527835255026, -0.3539632310195001, -0.34447406706248707, -0.3359525670925355, -0.3284062185977513, -0.3218272332886686, -0.3161946115441625, -0.31147619496219314, -0.30763065904193265, -0.3046094082176751 ], [ -0.21195075219511028, -0.22687737345248538, -0.24362994137734972, -0.26208436547037284, -0.2820764604385404, -0.30340353024292854, -0.3258271483975951, -0.34907705195947136, -0.3728560349408365, -0.39684570756461224, -0.42071297757847526, -0.44411710431498974, -0.4667171709457393, -0.4881798119708254, -0.5081870193927774, -0.5264438319168552, -0.5426856884196285, -0.55668520334671, -0.5682581031441921, -0.5772680563701251, -0.5836301432696767, -0.587312749359841, -0.5883377343131156, -0.5867788191290234, -0.5827582424800178, -0.5764418481381193, -0.5680328649789466, -0.5577647165232044, -0.5458932401324875, -0.5326887043983223, -0.5184279899012371, -0.5033872501810378, -0.48783530513146245, -0.4720279468663081, -0.4562032659712353, -0.4405780397121051, -0.42534516702350933, -0.41067208997778626, -0.39670010850521364, -0.3835444738640881, -0.37129513544737947, -0.36001801320723836, -0.34975667233459784, -0.34053428592433255, -0.3323557834437756, -0.32521009643988197, -0.31907242692990745, -0.31390647750915934, -0.30966659485280057, -0.30629978969779525 ], [ -0.21041385318406935, -0.22653755919413587, -0.24462924113874318, -0.2645571175086048, -0.28614559686712027, -0.3091769223188454, -0.33339413111892513, -0.35850523608679863, -0.3841885027626668, -0.4100986782610375, -0.43587401994242936, -0.46114396853840545, -0.48553730574578724, -0.508690626437056, -0.53025693828206, -0.5499141765556183, -0.5673733911931703, -0.5823863310588492, -0.594752123651687, -0.6043227359084035, -0.6110069129383338, -0.6147723344060488, -0.6156458062758176, -0.6137114152457677, -0.6091067034168107, -0.6020170548638066, -0.5926686052313797, -0.581320074278768, -0.5682539695612162, -0.5537676148486668, -0.5381644240080589, -0.5217457791350102, -0.504803791897401, -0.4876151401803308, -0.4704360871946769, -0.45349871375740947, -0.4370083305231479, -0.4211419874546949, -0.4060479629989896, -0.39184609429757, -0.3786288005148368, -0.366462651772302, -0.35539034383999724, -0.3454329513534311, -0.33659234785131553, -0.32885369768799355, -0.322187941593544, -0.3165542134571582, -0.3119021402655964, -0.30817398978066013 ], [ -0.20924345495996532, -0.22662755155652703, -0.246130246269749, -0.26761192486305063, -0.29088517862384, -0.31571650388635786, -0.34182944345441124, -0.3689090637924439, -0.39660762885793366, -0.4245513159990817, -0.4523478151232432, -0.4795946518084483, -0.5058880713790678, -0.530832309351083, -0.5540490516597222, -0.5751868557613098, -0.5939302635723515, -0.6100082944705241, -0.6232019693888321, -0.6333504962642164, -0.6403557549245088, -0.6441847664214265, -0.6448699227950176, -0.6425068843629497, -0.6372502090677826, -0.6293069408427291, -0.6189285275869404, -0.6064015439777422, -0.5920377480250811, -0.5761640010400848, -0.5591125353773715, -0.5412119753446629, -0.5227794184152097, -0.5041137796641529, -0.4854905027750285, -0.4671576533105566, -0.4493333383943934, -0.43220434315118017, -0.4159258379494787, -0.40062199011527433, -0.38638730693985757, -0.3732885406763996, -0.36136699790124693, -0.35064111237845064, -0.34110916003908853, -0.3327520149697645, -0.3255358649960127, -0.3194148236220855, -0.31433339122858084, -0.3102287323307569 ], [ -0.20847312347644564, -0.22718059371148724, -0.24816596573518934, -0.2712816991117668, -0.2963282006186667, -0.3230555725772368, -0.3511669373158324, -0.38032321633797705, -0.41014921055573716, -0.44024081662784265, -0.47017321542336066, -0.4995098721821708, -0.5278121856762874, -0.5546496099615923, -0.5796100446306528, -0.6023102482381858, -0.6224059779352067, -0.6396015024879307, -0.653658085479539, -0.6644010038822793, -0.6717246697349797, -0.6755954732326394, -0.6760520713216177, -0.6732030027209058, -0.6672217009575363, -0.6583391741973621, -0.6468347938086084, -0.6330257570721034, -0.6172558487475801, -0.59988412009014, -0.5812740423988022, -0.561783591952121, -0.5417566026246067, -0.521515597914682, -0.5013561978930938, -0.48154309666503115, -0.4623075264582732, -0.4438460665741957, -0.4263206182445092, -0.409859347621096, -0.39455839556847827, -0.38048416114324324, -0.367675982146104, -0.35614905772062777, -0.3458974819292945, -0.33689728143455766, -0.32910937333114576, -0.3224823798622124, -0.31695525472207353, -0.3124596907776651 ], [ -0.2081372661673575, -0.228230210279587, -0.25076904264464606, -0.27559825813154815, -0.3025057656696273, -0.33122467839265246, -0.36143682097019936, -0.39277781432225345, -0.4248435679244924, -0.4571980047763434, -0.4893818522722142, -0.5209223412205443, -0.5513436548557034, -0.580177953435078, -0.6069767654178467, -0.6313224842051562, -0.6528396439038859, -0.6712055757512958, -0.6861599800523102, -0.6975129027512373, -0.7051506004142793, -0.7090388307221067, -0.7092232279971704, -0.7058266107709228, -0.6990432996374838, -0.6891307636628055, -0.6763991229772899, -0.6611991811460375, -0.6439097258559562, -0.6249248204269916, -0.6046417261093906, -0.5834499683992429, -0.5617219131481549, -0.5398050699309347, -0.5180162051596947, -0.49663723426936834, -0.4759127747528157, -0.4560491803215976, -0.4372148391949354, -0.4195415032610057, -0.4031264156350026, -0.3880350177033698, -0.3743040389569102, -0.36194480006450036, -0.3509465886397737, -0.3412799956535909, -0.3329001268265589, -0.3257496266427494, -0.319761472439979, -0.31486151233546744 ], [ -0.20827097548040063, -0.22980999047156914, -0.2539714603515988, -0.2805919382874178, -0.30944658638823697, -0.34025100010001796, -0.3726648967133813, -0.4062975060419608, -0.4407144754828338, -0.47544610533107035, -0.5099967480124491, -0.5438552209886548, -0.5765060850900773, -0.6074416206943192, -0.6361742912190023, -0.6622494184982264, -0.6852577125698605, -0.7048472074322115, -0.7207340674116952, -0.7327116649146612, -0.7406573135792531, -0.7445360952533242, -0.744401359933162, -0.7403917016047761, -0.732724493728727, -0.7216863610660659, -0.7076212185108567, -0.6909166805146254, -0.6719897150532197, -0.6512723860315305, -0.6291984182296374, -0.6061911591870014, -0.5826533326472075, -0.5589588023357928, -0.5354464089622674, -0.5124158161050721, -0.49012520514801194, -0.4687905950350334, -0.4485865263238281, -0.42964783653643634, -0.4120722601527478, -0.3959236066467765, -0.3812352988708849, -0.3680140875843191, -0.3562437925406685, -0.34588895372890927, -0.33689830641442853, -0.3292080196254822, -0.322744659363454, -0.3174278552030012 ], [ -0.20890983681878916, -0.23195333760985815, -0.2578042158537672, -0.28629117358314904, -0.3171764522589804, -0.35015768349801724, -0.3848717554149276, -0.42090050595745876, -0.4577780354111023, -0.49499944595513456, -0.5320308465006908, -0.5683204861079671, -0.6033108842469252, -0.6364518030610724, -0.6672138538299706, -0.6951024497000272, -0.7196717153176461, -0.7405378504395673, -0.7573913333606554, -0.770007263159913, -0.7782531069234296, -0.7820931707944373, -0.7815892738373322, -0.7768973702226405, -0.7682602065626947, -0.7559964598629936, -0.7404871108025928, -0.7221600124466105, -0.7014736896514019, -0.678901354797027, -0.6549159804470748, -0.6299770688719397, -0.6045195399236681, -0.5789449512179708, -0.553615085692063, -0.5288477997548445, -0.5049149222799394, -0.4820419284536429, -0.4604090785535251, -0.44015370448790936, -0.4213733402573835, -0.40412942031450483, -0.3884513064546159, -0.3743404445224173, -0.36177449302702913, -0.35071130396883454, -0.3410926700686051, -0.3328477813063567, -0.32589635705628484, -0.32015143844541594 ], [ -0.21008969296742386, -0.23469317884038832, -0.2622969564041244, -0.2927220401326276, -0.3257176630461557, -0.36096314572181554, -0.39807193531273544, -0.43659759387899166, -0.4760415059697868, -0.5158621071129307, -0.5554854812242582, -0.5943172111249237, -0.6317553748536396, -0.6672045527377101, -0.700090645306973, -0.7298762042108343, -0.7560758544407542, -0.7782712464192483, -0.796124836433891, -0.8093916784117212, -0.817928354988049, -0.8216982223224352, -0.8207723228182972, -0.8153256360955756, -0.8056287537823862, -0.7920355041792418, -0.7749674310644961, -0.7548962756521149, -0.7323256894361464, -0.7077733289565029, -0.6817542929461765, -0.6547666108867393, -0.6272792275055351, -0.5997226841102353, -0.5724824938637932, -0.5458950514899698, -0.5202458083707341, -0.4957693773843501, -0.47265120193945953, -0.45103042336874044, -0.4310036027662949, -0.41262899032586786, -0.3959310807752896, -0.38090524215208965, -0.36752225271922456, -0.3557326243695865, -0.3454706287019924, -0.3366579733541064, -0.3292071011777865, -0.3230241039610484 ], [ -0.21184635536547392, -0.2380616273554459, -0.2674775741313462, -0.29990776374618044, -0.3350884298094481, -0.3726803507850974, -0.41227305448063767, -0.4533910886614103, -0.49550210320094235, -0.538026541644468, -0.5803488063874788, -0.6218298112891064, -0.6618208480919842, -0.6996786596339668, -0.7347815338828336, -0.7665461143203034, -0.7944444728233462, -0.8180208217214211, -0.8369070681356536, -0.8508362631436772, -0.8596529132073631, -0.863319154745258, -0.8619159903413207, -0.8556391581666192, -0.8447897115609835, -0.8297599287498278, -0.8110156375848425, -0.7890763329627599, -0.7644945447350354, -0.7378357999791401, -0.709660274114245, -0.6805069111281825, -0.6508804742076658, -0.6212417037728041, -0.5920005297241142, -0.5635121137757065, -0.536075383127438, -0.5099336516650758, -0.48527690107332555, -0.4622453028904473, -0.44093359483328354, -0.4213959723643059, -0.40365121207303467, -0.3876878009299257, -0.373468900289913, -0.36093702266105077, -0.35001834107780083, -0.3406265849081417, -0.33266650236113104, -0.32603688963449007 ], [ -0.2142152507924049, -0.24208958784924306, -0.2733717522490491, -0.3078681877809908, -0.3453022449386396, -0.3853160626492308, -0.4274749286186452, -0.4712738136908218, -0.5161457988447855, -0.561472192197315, -0.6065942240869475, -0.6508262738382686, -0.6934705988421181, -0.7338334962759337, -0.7712427323313744, -0.8050659317430711, -0.8347294424438194, -0.8597369877417553, -0.8796872069917987, -0.8942889931449636, -0.90337341048547, -0.9069009860471758, -0.9049633790473965, -0.8977788695270117, -0.8856817226311957, -0.8691061572061402, -0.8485662222148864, -0.8246332362711641, -0.7979125236769363, -0.769021015345751, -0.7385669576795678, -0.707132580849695, -0.6752601950063899, -0.6434418535775133, -0.6121124654104638, -0.5816460534808401, -0.5523547403194909, -0.524489979224461, -0.49824553502360447, -0.473761737971901, -0.4511305790084973, -0.4304012745157091, -0.41158599559587006, -0.39466552401840893, -0.37959465953315585, -0.3663072581446618, -0.3547208267173537, -0.34474063568311464, -0.33626333925121277, -0.3291801124763142 ], [ -0.2172309903272165, -0.2468062943714886, -0.28000245523866374, -0.3166191977948185, -0.35636722281494004, -0.3988700833234038, -0.4436686882316663, -0.4902280752192453, -0.5379461426528636, -0.5861641416341355, -0.6341788491100964, -0.6812564269031379, -0.7266479933413991, -0.7696068854508459, -0.8094074750025606, -0.845365232859967, -0.8768575265473493, -0.9033443979895865, -0.924388315622134, -0.9396716535268332, -0.9490104730967421, -0.952363154851189, -0.9498326426496799, -0.9416615686404457, -0.9282202762230123, -0.9099885944335839, -0.8875329325844378, -0.861480688862815, -0.8324940369945427, -0.801244920178444, -0.768392658220323, -0.7345650871538654, -0.7003436934131966, -0.6662528262830187, -0.6327527879618607, -0.6002364056841057, -0.5690285727370282, -0.5393881910673267, -0.5115119441455515, -0.48553936222719707, -0.46155870123549647, -0.4396132303558009, -0.4197076027864962, -0.4018140616414657, -0.38587830364359044, -0.3718248839817212, -0.3595620952957048, -0.34898629231054046, -0.33998566214745796, -0.3324434602604843 ], [ -0.2209268460979512, -0.2522387684879466, -0.2873893544564192, -0.3261720991710828, -0.36828541313169505, -0.4133344849347238, -0.4608359118932368, -0.5102246785904548, -0.5608631427655111, -0.6120518386481089, -0.6630420617470568, -0.7130503038243118, -0.7612746335506405, -0.8069130595433498, -0.8491837756167774, -0.8873469889626239, -0.9207277880591043, -0.9487392320224002, -0.9709045472974426, -0.9868770211188956, -0.9964559376984576, -0.9995968162430247, -0.9964144115118669, -0.9871775152895703, -0.9722955084033105, -0.952297658341525, -0.9278070544195999, -0.899511588340712, -0.8681344418650184, -0.834406212792251, -0.7990402609419334, -0.7627122531893458, -0.726044344242546, -0.6895939997120365, -0.6538471583640014, -0.6192152281766158, -0.5860352969314574, -0.554572894361233, -0.5250266532207145, -0.497534266445516, -0.472179213309853, -0.44899781700995, -0.42798628910978886, -0.4091075049302467, -0.3922973329726084, -0.37747040799371223, -0.3645252905178954, -0.3533489959378362, -0.3438209053635467, -0.3358160899032234 ], [ -0.22533412077891546, -0.25841118510075245, -0.2955481803100344, -0.33653294407490775, -0.38105208981764094, -0.428692846527013, -0.4789477951827599, -0.5312220115148041, -0.5848422433148953, -0.6390679478683661, -0.6931042078110161, -0.7461166714343859, -0.7972486951997901, -0.8456407955843687, -0.8904523550564729, -0.930885293703382, -0.9662091368899245, -0.9957865968771491, -1.0190984485382102, -1.0357661244146135, -1.045570128749455, -1.0484621955790485, -1.0445692768757797, -1.0341880925040012, -1.0177700813488992, -0.9958979075089086, -0.9692558085331864, -0.9385967024909877, -0.9047089942072952, -0.8683855597875272, -0.8303966767273516, -0.7914679238452212, -0.7522634370559593, -0.7133744241069049, -0.675312510166848, -0.6385072814273195, -0.6033072883272412, -0.5699837406891212, -0.5387361551254765, -0.5096992840204893, -0.4829507500748075, -0.45851891725929184, -0.43639063679019385, -0.4165186070381446, -0.3988281737903512, -0.38322346942898267, -0.3695928459783645, -0.357813598715932, -0.3477560061121522, -0.3392867305922731 ], [ -0.23048139561911696, -0.26534413400611423, -0.3044899930165834, -0.347701805327177, -0.39465502027437815, -0.4449195087907377, -0.4979643781119858, -0.5531652276778972, -0.6098134436025366, -0.6671273802137154, -0.7242655131209746, -0.7803418008429773, -0.8344435287385942, -0.8856518248225873, -0.9330648458072338, -0.975823359787919, -1.0131381304787612, -1.044318159285028, -1.0687984668790589, -1.0861656837610512, -1.0961792955256116, -1.0987860880751015, -1.0941254151099722, -1.0825236107555585, -1.0644772139804333, -1.0406263340148934, -1.0117209287472517, -0.9785835407401928, -0.9420720075251954, -0.9030450231757958, -0.8623325085113894, -0.8207118360609721, -0.7788902123793868, -0.7374929865174014, -0.697057306848313, -0.6580303477528043, -0.6207712358565767, -0.5855557948885668, -0.5525832775356798, -0.5219843436587852, -0.4938296601384239, -0.4681386234539351, -0.4448878296075547, -0.4240190283739209, -0.4054463948291003, -0.38906302855401464, -0.37474665004397645, -0.36236450645561313, -0.3517775274611884, -0.3428437894849964 ], [ -0.23639364580150812, -0.27305376805895487, -0.31422036671714526, -0.3596719976768976, -0.4090737227525023, -0.46197886329457993, -0.5178338575022762, -0.5759855679555402, -0.6356906076844976, -0.6961265645058675, -0.7564052861179744, -0.8155885673353429, -0.8727066226918205, -0.9267796286228255, -0.9768423957811211, -1.0219719161640652, -1.0613171638437808, -1.0941301456629113, -1.119796797148886, -1.13786585800539, -1.148073325912956, -1.1503596121756183, -1.144876451930232, -1.1319813479646332, -1.1122189524974146, -1.0862909056603338, -1.055017500396972, -1.0192954953574667, -0.980056285684711, -0.9382277589832271, -0.8947019796958555, -0.8503097354869262, -0.8058021237066938, -0.761838777184137, -0.7189819757868708, -0.6776957015481472, -0.6383486230953013, -0.601220007657167, -0.5665076330220418, -0.53433688773445, -0.50477038717931, -0.47781757954161386, -0.453443955708988, -0.43157960185163613, -0.41212693764554487, -0.3949675653681056, -0.3799682163888769, -0.3669858244377632, -0.3558717827043012, -0.3464754576589172 ], [ -0.2430912181378999, -0.28155083464954256, -0.32473848728299837, -0.3724292522651008, -0.4242787247062292, -0.4798246974043092, -0.5384920149001305, -0.5995998601453975, -0.6623710164924466, -0.7259430246208378, -0.789381486003717, -0.8516959707890929, -0.9118590355240126, -0.9688287417020163, -1.0215748067845614, -1.0691081532638864, -1.1105132054131195, -1.1449818698001857, -1.1718477241220702, -1.1906184484261404, -1.20100387783031, -1.2029363470438645, -1.1965796876513892, -1.1823239389044926, -1.160764788263153, -1.132669459177516, -1.0989331543643028, -1.060531339204681, -1.0184729066658413, -0.9737580533856457, -0.9273431791284519, -0.880113782670131, -0.8328653579082719, -0.7862916811913525, -0.7409795342068954, -0.6974087395298061, -0.6559563398766933, -0.6169037922252677, -0.5804461502767018, -0.5467023523823709, -0.5157258970012614, -0.4875153559731943, -0.462024333176683, -0.439170613126303, -0.4188443561506451, -0.4009152832484788, -0.3852388564717367, -0.3716615031432873, -0.3600249583568367, -0.3501698139301248 ], [ -0.25058867658582074, -0.29083959714367214, -0.33603617345807146, -0.3859508585718555, -0.44023084240232513, -0.4983996221771755, -0.5598617951871834, -0.6239102411097721, -0.6897352161643492, -0.7564353269118593, -0.8230307336905933, -0.8884791680607032, -0.9516954031781273, -1.0115746867995432, -1.0670203491144976, -1.1169753742178146, -1.160457249965705, -1.19659496765844, -1.2246666421987393, -1.2441357353157332, -1.2546830941220075, -1.2562310093296394, -1.2489548289725807, -1.2332782513936738, -1.2098507530380167, -1.179509066417868, -1.1432277288836505, -1.1020651803390438, -1.0571114437753562, -1.0094417680087446, -0.9600786794195433, -0.9099632915854425, -0.8599356444611324, -0.8107232153068421, -0.7629364185282596, -0.7170697758742096, -0.6735074244681091, -0.6325317018781653, -0.5943336811698762, -0.5590247028939147, -0.5266481434655221, -0.49719085066821445, -0.470593851906455, -0.44676208992590327, -0.42557306006099305, -0.4068843129416758, -0.3905398500092415, -0.3763754805441426, -0.36422323294348935, -0.3539149241636278 ], [ -0.258893536761603, -0.3009166679046069, -0.3480968448113094, -0.40020480036108497, -0.45688051218078285, -0.5176346181037329, -0.5818530758059934, -0.6488041471090766, -0.7176472154325227, -0.787443459475805, -0.8571688378980612, -0.925730102741413, -0.9919846231684863, -1.0547646594784785, -1.1129063906723975, -1.1652835108302815, -1.2108446663748467, -1.2486535313522786, -1.2779299513373028, -1.298090145740632, -1.308783093029965, -1.309918852617527, -1.301683402046416, -1.2845349156620272, -1.2591791487191346, -1.226526019209983, -1.1876335303254961, -1.1436469873330606, -1.0957407190082322, -1.045067269503627, -0.9927165851035751, -0.9396858404036696, -0.8868593793360677, -0.8349976245303804, -0.7847335229738964, -0.7365750018183533, -0.6909119316125892, -0.6480262010037595, -0.6081036749486086, -0.5712470152861775, -0.5374885643649701, -0.5068027076987361, -0.4791173242716873, -0.4543240938638773, -0.4322875565696076, -0.4128529120628994, -0.39585260938952416, -0.38111181758628243, -0.368452888797843, -0.3576989337929185 ], [ -0.2680049318185074, -0.31176979478786326, -0.36089447846558387, -0.4151489280081859, -0.4741672162660321, -0.53744874214932, -0.604362670893975, -0.6741546182551066, -0.745955081067221, -0.8187896973757269, -0.8915918981588684, -0.9632188045748451, -1.032471301170116, -1.098119065970847, -1.158930963881128, -1.213710650927365, -1.2613366113840137, -1.3008053361915648, -1.3312760398467771, -1.3521149715468594, -1.3629364544347973, -1.3636360063942612, -1.354409057702034, -1.335748708994512, -1.3084191010480233, -1.2734066050994177, -1.2318563435218153, -1.1850038111063523, -1.1341101884453744, -1.0804069183036042, -1.0250520631020479, -0.9690987879726438, -0.9134750818231784, -0.858973245099725, -0.8062474459268625, -0.7558176027159217, -0.7080779161427179, -0.6633085177717735, -0.6216889072982643, -0.5833120921995884, -0.548198596332633, -0.5163097439843981, -0.4875598361577469, -0.4618270075864712, -0.43896268426784757, -0.4187996551830121, -0.4011588340107717, -0.3858548236138585, -0.37270041425690037, -0.36151015144932774 ], [ -0.2779122777322578, -0.3233766675562306, -0.37439261862027917, -0.43073022790775417, -0.49201905965610504, -0.5577490479199948, -0.627274617535665, -0.6998209605748636, -0.7744919728694978, -0.8502799957415453, -0.9260780300120702, -1.0006954104110923, -1.0728780220736969, -1.141333990039586, -1.2047653650209869, -1.2619056957881805, -1.3115626576009227, -1.3526643415249022, -1.3843075656459791, -1.4058063733981114, -1.4167379528543114, -1.4169810120082935, -1.4067390243518014, -1.3865400405028017, -1.357208162930695, -1.3198088730587039, -1.2755773588953172, -1.2258418362675338, -1.1719520590447892, -1.1152191854342925, -1.056869398583042, -0.9980112186066525, -0.9396151915140956, -0.8825041303420349, -0.8273519333813686, -0.774689017843826, -0.7249125156600518, -0.6782995617312222, -0.6350222483981421, -0.5951630987220352, -0.5587301961501945, -0.5256713732072332, -0.495887089345849, -0.4692418098456467, -0.4455738333202769, -0.42470360970467613, -0.4064406507425893, -0.39058916874405303, -0.3769525939107009, -0.3653371218765946 ], [ -0.28859403303951736, -0.3357038364038307, -0.3885435254924636, -0.4468842675987077, -0.5103525668782886, -0.5784307768910105, -0.6504607912693988, -0.7256498031349866, -0.803077648021874, -0.8817059356578836, -0.960389735561639, -1.0378929315012129, -1.112908475402242, -1.184084627722667, -1.2500578389450188, -1.309492222212362, -1.361124742069656, -1.4038146144465025, -1.4365952346165687, -1.4587269174363764, -1.469747821279594, -1.4695178607041375, -1.4582470155192904, -1.4364978266698307, -1.4051552274996364, -1.365365609331237, -1.3184561918250126, -1.2658493924660899, -1.2089842261102588, -1.1492514517386478, -1.087944602994806, -1.0262263215610365, -0.9651081977501766, -0.9054419228142772, -0.8479194981057572, -0.7930803197285163, -0.74132310926696, -0.6929208848536977, -0.6480374507860356, -0.6067442015629658, -0.5690363545160425, -0.5348480154824548, -0.5040657259963242, -0.4765403311538945, -0.4520971461430412, -0.4305444930801423, -0.4116807371049984, -0.39529998060779326, -0.38119658495869624, -0.36916868666943303 ], [ -0.30001667068839066, -0.3487058561067997, -0.4032875682699285, -0.4635349082757726, -0.5290727746018734, -0.5993778797286821, -0.6737818930740092, -0.7514765770163322, -0.8315204484411416, -0.91284722624674, -0.9942769158007906, -1.0745307597900338, -1.1522514271337356, -1.2260296846314618, -1.2944383509809212, -1.356073566272821, -1.4096024820198179, -1.4538157729370684, -1.4876832427782847, -1.5104108899225916, -1.521496858396613, -1.520780884404652, -1.5084779452110735, -1.4851840835257113, -1.451845030405053, -1.4096887470537136, -1.3601351598679283, -1.3047010370878334, -1.2449140964328937, -1.182243518090833, -1.118048576347574, -1.0535441894977644, -0.9897810751395888, -0.927637941003018, -0.867823181316134, -0.8108836809212107, -0.7572185230129902, -0.7070956602586081, -0.6606699351324082, -0.6180011934612943, -0.5790715876310332, -0.5438014811905777, -0.5120636262153788, -0.4836954831255791, -0.45850969339307857, -0.4363028075169406, -0.4168624243450768, -0.39997292342118584, -0.3854199782241883, -0.37299403181901136 ], [ -0.31213399015999066, -0.36232477871805757, -0.41855297324277385, -0.4805943788854259, -0.5480736940033022, -0.6204639199120257, -0.6970888386080367, -0.7771274269355105, -0.8596197642259533, -0.9434747411328046, -1.0274804910720547, -1.1103188708539204, -1.1905854896373804, -1.2668166839643604, -1.3375243935451624, -1.4012390820393112, -1.4565598319247384, -1.5022099713173254, -1.5370964894735546, -1.5603716047544076, -1.5714936910827473, -1.5702818632759141, -1.5569548131471218, -1.5321405561468935, -1.4968445007889204, -1.4523754010103438, -1.4002449429567552, -1.3420627766336966, -1.2794433189170007, -1.2139318158639243, -1.1469507920396502, -1.079764992531078, -1.0134619768921256, -0.9489454322682428, -0.8869384115661461, -0.8279938877323343, -0.7725102471887724, -0.7207496495147505, -0.6728575502726404, -0.6288820840628904, -0.5887923920374145, -0.5524953178957904, -0.5198501704499677, -0.49068145547290654, -0.46478962095184917, -0.4419599491528283, -0.4219697783555224, -0.4045942580327978, -0.3896108429719042, -0.3768027215587155 ], [ -0.3248868888453128, -0.3764901078840309, -0.4342560271055992, -0.49796379307796634, -0.5672392019472801, -0.6415533950677003, -0.7202245615695924, -0.802421544957181, -0.8871689419977131, -0.973354039719228, -1.0597365644173469, -1.1449626455251964, -1.2275846018688952, -1.306088089559141, -1.3789277251708558, -1.444571468659171, -1.5015529804708838, -1.548530357676148, -1.5843495657102942, -1.6081108205180077, -1.6192344163840506, -1.6175196287581242, -1.603188031614246, -1.5768976127374927, -1.5397111276337914, -1.493015629074106, -1.4384116673208485, -1.3775984182094907, -1.3122733794056665, -1.2440542535266887, -1.1744234304120675, -1.1046924523834898, -1.0359831141646145, -0.9692219270726257, -0.9051449043541304, -0.8443098533708918, -0.7871136265791218, -0.733812127537864, -0.6845412834129536, -0.6393376389780054, -0.5981576491411794, -0.5608951105217815, -0.5273964597744709, -0.4974738759070515, -0.47091626477158943, -0.44749828973818095, -0.42698765729993493, -0.40915088238003405, -0.39375775533963464, -0.3805847185614284 ], [ -0.33820367892881065, -0.39111929509655896, -0.4503018035422358, -0.515534159958718, -0.5864443915526633, -0.6625034845917697, -0.7430262172448338, -0.8271738900352823, -0.9139585802148569, -1.0022492949165316, -1.0907810309857116, -1.1781681977167722, -1.2629240950879232, -1.3434881099686544, -1.418261899453759, -1.4856550121466081, -1.5441393188558992, -1.5923108245445943, -1.628957354221622, -1.6531301566455017, -1.6642145783573221, -1.6619921572467544, -1.646687197927763, -1.618985398259196, -1.5800033131246531, -1.5312018583486307, -1.474265318004477, -1.4109769326025496, -1.343111930420892, -1.2723555702226916, -1.200245839623198, -1.12813750749466, -1.0571837266793365, -0.9883316147168825, -0.9223285370736412, -0.8597360782808493, -0.8009489830081837, -0.7462167341801635, -0.6956658976081999, -0.6493218504911316, -0.607128967835491, -0.5689687269452441, -0.5346754889950428, -0.5040499298642951, -0.47687023190477595, -0.4529012301014894, -0.43190174584785723, -0.413630352648958, -0.39784981090381843, -0.3843303911194186 ], [ -0.35200098275832803, -0.40611880553932267, -0.46658543166098565, -0.5331878948331017, -0.6055573733814282, -0.6831661978543251, -0.7653277419938362, -0.8511982292345412, -0.9397801263911792, -1.029927520939866, -1.1203545065187543, -1.209648063222764, -1.2962871847696875, -1.3786700151220477, -1.4551504091044687, -1.5240845551243163, -1.5838872604636638, -1.6330967618183339, -1.6704468433120936, -1.6949440042121031, -1.7059429176148768, -1.7032106076763451, -1.686974841246414, -1.6579468638290698, -1.6172923881929362, -1.566539680846069, -1.5074492037879328, -1.4418805738967957, -1.3716796270390113, -1.2985929970628876, -1.2242091546988247, -1.149922028756202, -1.0769130306806551, -1.006147650043087, -0.9383831289430085, -0.8741840042513395, -0.8139426306139937, -0.7579022239986544, -0.7061804765839516, -0.6587923264998606, -0.6156709566064514, -0.5766865038463476, -0.5416622698313058, -0.5103884389583797, -0.48263344768804917, -0.4581532260299812, -0.43669856702573384, -0.41802088632279344, -0.4018766226144652, -0.3880305085110505 ], [ -0.3661851763419811, -0.42138571890952525, -0.48299386698638425, -0.5508007849455685, -0.624441474790069, -0.7033908606449332, -0.7869626935352052, -0.8743104095332319, -0.9644296660866717, -1.0561629695245645, -1.148207420548598, -1.23912707339247, -1.3273716947997003, -1.4113037605179888, -1.489235235167177, -1.55947497618876, -1.6203866534879323, -1.6704564317984294, -1.7083695291114676, -1.73309298259056, -1.7439557096503258, -1.740714113179678, -1.7236011290802837, -1.6933518594751433, -1.6511756263474016, -1.5986594583240468, -1.5376299989046873, -1.47001335756565, -1.3977171419929448, -1.3225419623514754, -1.2461208652722928, -1.169882422087329, -1.0950330183184502, -1.0225542961450025, -0.9532120558530797, -0.8875732119103414, -0.8260277486813562, -0.7688130905395267, -0.7160388617307913, -0.6677105886124356, -0.6237514203107669, -0.5840213708837865, -0.5483339041096507, -0.5164698992380079, -0.48818917080252666, -0.46323978859107284, -0.4413654737921118, -0.4223113491718564, -0.4058283060158794, -0.39167622629262144 ], [ -0.38065429176156673, -0.43680977289555056, -0.49940807227103245, -0.5682443181706746, -0.6429577452268151, -0.7230268447879571, -0.8077672700915354, -0.8963317465950743, -0.9877117732965937, -1.0807415426043854, -1.1741050969463047, -1.2663482090862732, -1.3558967835355709, -1.4410836681905237, -1.52018553852126, -1.5914709073860756, -1.6532594855519482, -1.7039925580263942, -1.742313739990692, -1.7671568826069564, -1.77783030987765, -1.7740838963750027, -1.7561582587862605, -1.724811199279154, -1.6812893213321805, -1.6272279472559565, -1.5645077140942258, -1.4951093805217741, -1.420991956916577, -1.344001531430206, -1.265809098102272, -1.18787294363563, -1.1114209810020106, -1.0374488118571716, -0.9667296365904323, -0.8998324188481204, -0.837145084559818, -0.7789000486216411, -0.7251999723890254, -0.6760422756669376, -0.6313414812148468, -0.5909489148163585, -0.5546696097280822, -0.5222764825478694, -0.49352197965956257, -0.4681474622557331, -0.44589062347290476, -0.4264912290259105, -0.4096954542736375, -0.3952590637163751 ], [ -0.3953002477838544, -0.4522757164130776, -0.5157054776408297, -0.5853882491394967, -0.6609676468512767, -0.7419264226221497, -0.8275833878873224, -0.9170924019526261, -1.009443278977277, -1.103465056463201, -1.197832628196711, -1.2910782065960034, -1.3816094046571876, -1.4677358581003515, -1.5477061527035239, -1.619756324523956, -1.6821705040019064, -1.7333537474557517, -1.7719164796380116, -1.796766610752143, -1.8071972729299213, -1.8029558999042925, -1.7842935583571728, -1.751989631101477, -1.7073208920751384, -1.6519590359832876, -1.5878248567563313, -1.5169404065939915, -1.4413044935993131, -1.3627992580269663, -1.2831263793713796, -1.203768560094882, -1.1259716402159543, -1.050743005506805, -0.9788622397249649, -0.9109002475616528, -0.8472434697227558, -0.7881203670200065, -0.7336280078662852, -0.6837572548089744, -0.6384156285059744, -0.5974473887750097, -0.5606507048960263, -0.5277920063730216, -0.4986177351289264, -0.47286378535915063, -0.4502629390685654, -0.4305505998219439, -0.413469106012764, -0.3987708758359918 ], [ -0.41001126016929157, -0.46766582249432553, -0.5317625733046067, -0.6021032624157576, -0.6783357969638096, -0.7599476176078752, -0.846261688730622, -0.9364346147516108, -1.0294568108396676, -1.1241551888206136, -1.219199343380961, -1.313112673161026, -1.4042902066030045, -1.4910250692584373, -1.571545446929885, -1.64406351731899, -1.7068372419380968, -1.7582453358785008, -1.7968746730873801, -1.8216154365804482, -1.8317515353127627, -1.8270320957129527, -1.807720872772782, -1.774616869786701, -1.729019056795539, -1.6726227178787774, -1.6073740622693673, -1.5353221635644583, -1.4584931736846345, -1.378795149894863, -1.2979526679499152, -1.2174672119839054, -1.1385987928476513, -1.0623643974738917, -0.9895490786265637, -0.920725747608842, -0.8562801443819494, -0.7964380537599158, -0.7412925372598331, -0.6908296480950635, -0.6449517048777874, -0.6034976751558678, -0.5662605585570346, -0.5330018793006656, -0.5034635258960909, -0.47737723834688894, -0.4544720620973772, -0.4344800798839791, -0.41714070930024716, -0.40220382309210656 ], [ -0.4246742878845986, -0.48286241571537825, -0.5474574924405954, -0.6182635957592173, -0.6949326314699207, -0.7769569250760205, -0.8636643529832705, -0.9542156592269202, -1.0476039641760415, -1.142656947956287, -1.2380426766560049, -1.332280471889836, -1.4237585652517737, -1.5107604789714515, -1.591502061412718, -1.6641808291046065, -1.7270387649219479, -1.7784390238203516, -1.816955462091406, -1.8414696377327378, -1.8512630110661323, -1.8460905926760707, -1.8262298828398178, -1.7924960127402358, -1.7462013081333487, -1.689051598429447, -1.6230036195187383, -1.5501189067108203, -1.472438078860947, -1.3918845168428586, -1.3101975028322448, -1.2288913796764842, -1.1492364119511849, -1.0722569612554584, -0.9987426835399213, -0.9292686730457482, -0.8642208988122353, -0.8038239057934959, -0.7481684902135047, -0.6972377877213575, -0.6509308424715606, -0.6090832132072322, -0.5714845167190459, -0.5378930304841039, -0.508047603583574, -0.4816771858202399, -0.45850830200818393, -0.4382707886259589, -0.42070208524836705, -0.4055503412536797 ], [ -0.4391773921137033, -0.4977502898895084, -0.5626724613872871, -0.6337495038772009, -0.710636873830467, -0.7928317909488847, -0.8796676067857985, -0.9703104136533787, -1.0637579801814412, -1.158841522506179, -1.2542312653980436, -1.348447160023343, -1.4398764675453977, -1.5268001450260957, -1.6074300168361029, -1.679958518806805, -1.7426223316072529, -1.7937803471056457, -1.832004457038333, -1.8561773224767228, -1.865585345697759, -1.8599934415387356, -1.8396925053887208, -1.8055086883798954, -1.7587581682275977, -1.7011445069171502, -1.6346205426299503, -1.5612459784059785, -1.483063012698034, -1.4019995644584218, -1.3198011786697736, -1.2379889048754413, -1.1578391835261814, -1.0803814423225766, -1.0064090615160586, -0.9364995321667642, -0.8710400509868301, -0.810255442906521, -0.7542360673352714, -0.7029641167794297, -0.6563373629813978, -0.6141899040186535, -0.5763098154383728, -0.5424538321010898, -0.5123593151044262, -0.4857538185502781, -0.462362587240464, -0.4419143058472462, -0.4241453946570186, -0.4088031145146833 ], [ -0.4534119135305593, -0.512218920510573, -0.5772960217471679, -0.6484494683744131, -0.7253377169625606, -0.8074627576287258, -0.8941638333760591, -0.9846134487548678, -1.0778158336382442, -1.1726084011965061, -1.2676671452624515, -1.3615173124974234, -1.4525510245353404, -1.5390537720761688, -1.619241792780963, -1.6913121978218497, -1.753507226683639, -1.8041929477760184, -1.8419504580235841, -1.8656734131492299, -1.8746606038349762, -1.8686903319192987, -1.8480653060357153, -1.8136164414039437, -1.7666540104019681, -1.7088670994621078, -1.6421911058734953, -1.5686702966791315, -1.4903359151948963, -1.409109705412515, -1.3267349413507055, -1.2447330759625952, -1.1643824994027547, -1.0867152817547419, -1.0125275741178963, -0.9423994395105728, -0.8767202886794254, -0.8157167511924573, -0.7594805923872527, -0.7079950544139865, -0.6611586577787143, -0.61880600607663, -0.5807254912976043, -0.5466740236808483, -0.5163890394848729, -0.48959810134808746, -0.46602642271551775, -0.4454026375055974, -0.4274631108507968, -0.41195505431129154 ], [ -0.467274402936361, -0.5261644063774119, -0.5912249581989233, -0.6622620873522134, -0.7389366517346105, -0.8207552114132225, -0.90706322369652, -0.9970405709209588, -1.0896996636205831, -1.1838866911118378, -1.2782869604107783, -1.371435631099517, -1.461735485956335, -1.5474836331591137, -1.626909148422801, -1.6982235331572502, -1.7596853292481374, -1.80967899369152, -1.8468056777799315, -1.8699795241871513, -1.878518581703136, -1.8722171961077516, -1.8513874491988678, -1.8168582959622885, -1.769924593239384, -1.712249643572597, -1.6457390057684353, -1.5724088973888757, -1.494267724037699, -1.4132206634903457, -1.3310002682622482, -1.2491220356049453, -1.1688619597866876, -1.0912521934032033, -1.0170905764630878, -0.9469598082331868, -0.8812524086880038, -0.8201982635967772, -0.7638923290859114, -0.7123208441381584, -0.6653850633314445, -0.6229220337542817, -0.5847222993500603, -0.5505446463221323, -0.5201281356018174, -0.49320173196960815, -0.4694918579215467, -0.4487281913185406, -0.43064800141262527, -0.41499928604248815 ], [ -0.48066826677306007, -0.5394911016909535, -0.6043658925556578, -0.675097604377425, -0.751348901487622, -0.8326306915881162, -0.9182949283639696, -1.0075297853207932, -1.0993575160624325, -1.192635607358689, -1.2860621656259656, -1.3781868195155005, -1.467428740401713, -1.5521036356500661, -1.630461682725568, -1.7007382233362227, -1.7612184286306696, -1.8103157640984664, -1.8466615283154533, -1.8691989284462296, -1.8772710994622788, -1.8706901564309235, -1.8497746474368968, -1.8153449804660033, -1.7686717866680512, -1.7113824144936922, -1.6453415034430174, -1.5725258037763252, -1.4949098899227302, -1.4143725277054806, -1.3326273546531398, -1.2511776062383049, -1.1712924620189982, -1.0940014564459075, -1.020102867726913, -0.9501819233809593, -0.8846349858187363, -0.8236965036833919, -0.7674662833708369, -0.715935401880546, -0.6690097450536436, -0.6265306691297124, -0.5882926467527076, -0.5540579933084184, -0.5235689059906623, -0.49655711514816825, -0.4727514688508181, -0.4518837647945513, -0.4336931208981293, -0.417929145369784 ], [ -0.49350511031693356, -0.5521129217741316, -0.6166365268963494, -0.6868790592186246, -0.7625044452148998, -0.8430277455183699, -0.9278076991424984, -1.0160416735339095, -1.1067634024192508, -1.1988441517149007, -1.2909982560828905, -1.3817942849267577, -1.469673396479099, -1.5529766759829127, -1.6299833468019278, -1.698961552920092, -1.7582327208250135, -1.8062490185981188, -1.841680857307714, -1.863507807661503, -1.8711026530321742, -1.8642961261284956, -1.8434101884307714, -1.809250669071111, -1.7630561865605396, -1.7064092782155373, -1.6411240125954947, -1.5691275884643965, -1.4923508248045974, -1.4126369660158336, -1.3316729624124348, -1.2509436500076898, -1.1717069627753265, -1.0949869888886319, -1.0215810025866812, -0.9520764335487077, -0.88687400011045, -0.8262138143151039, -0.7702020077004768, -0.7188361764331196, -0.6720285993032796, -0.6296266946085138, -0.5914305478571651, -0.5572075815905484, -0.5267045802014128, -0.49965735447388226, -0.4757983559259643, -0.45486254738304677, -0.43659181587369655, -0.4207381851707386 ], [ -0.5057057773210737, -0.5639543221689453, -0.6279665359936011, -0.6975430611183517, -0.7723486316179371, -0.8519023352682031, -0.9355700316247799, -1.0225592074602707, -1.1119167112654202, -1.202530038687755, -1.2931331134065291, -1.3823177967546696, -1.468552633613296, -1.5502105514187692, -1.6256072838703695, -1.6930520422996287, -1.7509111863842373, -1.7976840873019393, -1.832087848734374, -1.8531442429331708, -1.8602589737145445, -1.8532815063449266, -1.8325342454889073, -1.7988031968657086, -1.753288380920288, -1.6975200809263025, -1.6332536356018619, -1.562358026615804, -1.4867115903175467, -1.4081138289390394, -1.3282177999995917, -1.2484840846895864, -1.1701550001883785, -1.0942462631016177, -1.0215525066006144, -0.9526627911598908, -0.8879824435999573, -0.8277580863027421, -0.7721034180634356, -0.7210240299289822, -0.6744401790058101, -0.6322069503091894, -0.5941316036403771, -0.5599881462507514, -0.5295293192683848, -0.5024962632907735, -0.4786261588014822, -0.4576581374227774, -0.43933774280702786, -0.4234201935639236 ], [ -0.5172010962020236, -0.5749509628492916, -0.6382981222070089, -0.7070401995687047, -0.7808424019905909, -0.8592278188842646, -0.9415698407961031, -1.0270870443916047, -1.1148410371232242, -1.2037379608293683, -1.2925345981102598, -1.3798502849164693, -1.4641860752252436, -1.5439527743760026, -1.6175094613029786, -1.683213804865969, -1.7394846378095714, -1.7848756644563313, -1.8181567490298498, -1.8383962160980647, -1.8450347726320193, -1.8379401679167104, -1.8174325081429896, -1.784273612737942, -1.7396195775966339, -1.6849424299914157, -1.6219321276706447, -1.5523922255754403, -1.4781411258856374, -1.4009273676292002, -1.3223635960506315, -1.243880669436719, -1.166701053294724, -1.0918291146044554, -1.0200550285489183, -0.9519686621306365, -0.8879799193187026, -0.8283424945161681, -0.7731786279192304, -0.7225031405389672, -0.6762456438731007, -0.6342703164711779, -0.5963930053429924, -0.5623956576194905, -0.5320382408846609, -0.5050683941902018, -0.4812290876437948, -0.46026457353493877, -0.44192489850663585, -0.4259692227529013 ] ], "zauto": true, "zmax": 1.878518581703136, "zmin": -1.878518581703136 }, { "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": [ [ 0.7047599719974037, 0.7023573889015742, 0.6999334888177914, 0.6974880942289218, 0.695023988272043, 0.6925480162564233, 0.6900720070001652, 0.6876134046818739, 0.6851955185725928, 0.6828473259355271, 0.680602800518302, 0.6784997821236523, 0.6765784473870676, 0.6748794830837951, 0.6734420958730877, 0.6723020118168617, 0.6714896221785197, 0.6710284179949688, 0.6709338263991907, 0.6712125208203796, 0.6718622309579912, 0.6728720333831927, 0.6742230656119101, 0.6758895795237532, 0.6778402356517286, 0.6800395373682021, 0.6824493108495552, 0.6850301496163164, 0.687742758205358, 0.6905491456383959, 0.6934136342840321, 0.6963036628518042, 0.6991903736196605, 0.7020489838890456, 0.7048589504049917, 0.7076039432360456, 0.7102716523365389, 0.7128534555001371, 0.7153439803681498, 0.7177405953085079, 0.7200428641638419, 0.7222519980668999, 0.7243703338990805, 0.726400863845048, 0.7283468343213896, 0.7302114258535548, 0.7319975187837093, 0.7337075435138953, 0.7353434087367838, 0.7369064970698822 ], [ 0.7000403341453342, 0.6974619315878609, 0.6948641111728602, 0.6922451567365475, 0.6896064749182174, 0.6869539125230643, 0.6842988796164664, 0.681659147752304, 0.6790592114514197, 0.6765301332744926, 0.6741088362252291, 0.6718368579393673, 0.6697586340530004, 0.6679194273100911, 0.666363058130787, 0.6651296159339061, 0.6642533345953637, 0.6637607987962006, 0.6636696126739905, 0.6639876132854543, 0.66471265631815, 0.665832948398272, 0.6673278563787213, 0.6691690938769136, 0.6713221706493638, 0.6737479897624548, 0.6764044875043749, 0.6792482273140801, 0.68223587773479, 0.6853255226621401, 0.6884777684009963, 0.691656625860114, 0.6948301579113219, 0.6979708920945363, 0.701056007948052, 0.7040673164977711, 0.7069910567615723, 0.7098175402096207, 0.7125406785743361, 0.7151574328732849, 0.7176672217829224, 0.7200713255638526, 0.7223723177784042, 0.7245735514317331, 0.7266787194178833, 0.7286915018476944, 0.7306153055718987, 0.7324530945345833, 0.7342073039411673, 0.7358798269050975 ], [ 0.6949513539973394, 0.6921899065139882, 0.6894119522328058, 0.686613872413134, 0.6837953104494982, 0.6809607423915695, 0.6781208394167834, 0.6752934664690334, 0.6725041822707595, 0.6697861430988811, 0.6671793633706307, 0.6647293457547226, 0.662485156217945, 0.6604970780304089, 0.6588140257728673, 0.6574809289616963, 0.6565363001417653, 0.6560101825384932, 0.655922629990217, 0.6562828132569497, 0.6570887811412695, 0.658327842280066, 0.6599774827267764, 0.6620067010870155, 0.6643776284771925, 0.667047302698181, 0.6699694800515119, 0.6730963886827718, 0.6763803494106568, 0.6797752104557077, 0.6832375598475614, 0.6867276935016733, 0.6902103287478901, 0.6936550633790098, 0.697036589737003, 0.7003346822036541, 0.7035339845317081, 0.7066236302922368, 0.7095967347899338, 0.712449799658149, 0.7151820717317248, 0.7177948956963482, 0.7202910956615939, 0.7226744146412245, 0.7249490335330812, 0.7271191832286567, 0.7291888556046091, 0.7311616119434026, 0.7330404812669069, 0.734827936460279 ], [ 0.6894716938943195, 0.6865203778384961, 0.683556708394022, 0.6805747439105495, 0.6775719114489585, 0.674550873544223, 0.6715211738418776, 0.6685004760637703, 0.6655152343139646, 0.6626006756314554, 0.6598000347830494, 0.6571630513971529, 0.6547438136808267, 0.6525981027434294, 0.6507804479447985, 0.6493411382885835, 0.6483234415430245, 0.6477612592633916, 0.6476773950247626, 0.6480825428073566, 0.6489750241160475, 0.6503412286636763, 0.6521566550414303, 0.6543874112246676, 0.6569920212316667, 0.6599233902854638, 0.6631308000516711, 0.6665618309117448, 0.6701641339827716, 0.6738869981580519, 0.677682675585286, 0.6815074432019534, 0.6853223895190272, 0.6890939261198683, 0.6927940331773397, 0.6964002578987877, 0.6998954938438814, 0.7032675768650164, 0.7065087392750455, 0.7096149671802864, 0.7125853064261698, 0.7154211602983963, 0.7181256173038617, 0.7207028405515001, 0.7231575421395894, 0.7254945572709766, 0.7277185242803537, 0.7298336690001067, 0.7318436854059959, 0.7337516995925277 ], [ 0.6835797790325894, 0.6804322712154408, 0.6772780734965889, 0.6741084385492043, 0.6709180495261555, 0.6677072327382363, 0.664483937295903, 0.6612652610574851, 0.658078328689459, 0.6549603771455886, 0.6519579727398043, 0.6491253662423394, 0.6465220799622802, 0.6442099037277227, 0.6422495442301367, 0.6406972140677036, 0.6396014552604667, 0.6390004640120329, 0.6389201223507455, 0.6393728577134521, 0.6403573579288073, 0.6418590821506197, 0.6438514412730246, 0.6462974817759836, 0.6491518954939265, 0.6523631892620185, 0.6558758741959615, 0.6596325655628906, 0.6635759138834958, 0.6676503123048995, 0.6718033436531516, 0.6759869442009074, 0.680158272146688, 0.6842802789334045, 0.6883219918588259, 0.6922585270504515, 0.6960708621865845, 0.6997454073899195, 0.7032734195433601, 0.7066503091710749, 0.7098748896558539, 0.7129486159844939, 0.7158748548234379, 0.7186582201716645, 0.7213039999041331, 0.7238176890371895, 0.7262046363033842, 0.7284698022902255, 0.7306176204862073, 0.7326519474092543 ], [ 0.6772539776821445, 0.6739045562900536, 0.6705559276012081, 0.6671959871014318, 0.6638160632442048, 0.6604135332301474, 0.656994195557857, 0.6535741373010391, 0.6501808638786831, 0.6468535162548219, 0.643642080718673, 0.6406055927532988, 0.6378094396511127, 0.6353219649587314, 0.6332106586465113, 0.631538267510512, 0.6303591709651764, 0.6297163340111437, 0.6296390755783425, 0.6301417886695202, 0.6312236368034165, 0.632869148880002, 0.6350495579861629, 0.637724687553666, 0.6408451804690324, 0.6443548855977882, 0.6481932502500102, 0.6522976050739618, 0.6566052615781413, 0.6610553681756042, 0.6655904884144441, 0.6701578773488849, 0.6747104418905074, 0.6792073808675192, 0.6836145115421829, 0.6879043013545735, 0.6920556356658336, 0.6960533629089013, 0.6998876665681949, 0.7035533179461614, 0.7070488643890643, 0.7103758046827787, 0.7135377972280502, 0.7165399381582445, 0.7193881366921822, 0.7220886046532591, 0.7246474670879862, 0.7270704919911641, 0.7293629298116389, 0.7315294479839104 ], [ 0.6704728218762175, 0.666916467371561, 0.6633705616514151, 0.6598190162181408, 0.6562491015204633, 0.6526545315938648, 0.6490382976239314, 0.6454149396449685, 0.6418119793285799, 0.6382703029372856, 0.6348433768961865, 0.6315952911230571, 0.6285977465498589, 0.6259262198176261, 0.6236556346468398, 0.6218559305103295, 0.620587932645457, 0.6198998876371646, 0.6198249401403475, 0.6203797036639108, 0.6215639443749297, 0.6233612763304444, 0.6257406793967576, 0.628658607369712, 0.6320614518154012, 0.635888155956583, 0.6400728172718576, 0.6445471631469439, 0.6492428215067367, 0.6540933344207845, 0.6590358786625844, 0.6640126671716537, 0.6689720136524139, 0.6738690521715536, 0.6786661157034394, 0.6833327915494016, 0.6878456858204959, 0.6921879418338256, 0.6963485667249115, 0.7003216258235184, 0.7041053650655131, 0.7077013182102695, 0.7111134486322317, 0.7143473659428475, 0.717409646754691, 0.7203072775686301, 0.723047226967393, 0.7256361447705, 0.7280801780646284, 0.7303848883611072 ], [ 0.6632152755513805, 0.659447768708074, 0.6557029437523817, 0.6519600194096752, 0.6482014024789252, 0.6444163168861522, 0.6406041768494075, 0.6367773360006831, 0.632962882768271, 0.6292032289606777, 0.6255553471522171, 0.6220886440123204, 0.618881598998757, 0.6160174355223544, 0.613579206766267, 0.6116447520923408, 0.6102819968253614, 0.6095450207167826, 0.609471213437875, 0.610079687450446, 0.6113709580967818, 0.6133277588764889, 0.6159167613083165, 0.6190909248373897, 0.6227922090498347, 0.6269544224569823, 0.6315060391061663, 0.6363728685462587, 0.6414805055886108, 0.6467565112884696, 0.6521322891417344, 0.6575446268995516, 0.662936880537668, 0.6682597864136148, 0.67347190139821, 0.6785396874916577, 0.6834372746907998, 0.6881459510851583, 0.692653440314182, 0.6969530324989294, 0.7010426353571012, 0.7049238079382734, 0.7086008312704812, 0.7120798594165962, 0.7153681822628584, 0.7184736189663631, 0.7214040493522265, 0.7241670804229342, 0.7267698370222518, 0.7292188598397428 ], [ 0.6554610582179876, 0.6514790718333183, 0.6475350337410145, 0.6436026722896989, 0.6396586123434322, 0.6356866355010311, 0.6316816833941904, 0.6276531684196632, 0.6236272005150976, 0.6196474276837046, 0.6157743143890165, 0.6120828351823503, 0.6086587273556513, 0.6055936086337452, 0.6029794028423877, 0.6009026053826463, 0.5994389415243457, 0.5986489138800635, 0.5985746062725924, 0.5992379323555226, 0.6006403248303176, 0.6027636942473861, 0.6055723756857574, 0.6090157397159393, 0.6130311636801618, 0.6175471186480308, 0.6224861998077614, 0.6277679916186297, 0.6333117021394089, 0.639038522692397, 0.6448736759767174, 0.6507481170842137, 0.6565998553371466, 0.6623748746029151, 0.6680276460825231, 0.6735212481232065, 0.6788271287863136, 0.6839245652745399, 0.6887998874359847, 0.6934455392397489, 0.6978590523529513, 0.7020420005928742, 0.7059989944240674, 0.7097367623401838, 0.7132633523859846, 0.7165874735195551, 0.7197179840125236, 0.7226635233777684, 0.7254322758610389, 0.7280318475377412 ], [ 0.6471910334810296, 0.6429922136455448, 0.6388501538066556, 0.6347321987159711, 0.6306081496766281, 0.6264552555177592, 0.6222629501523956, 0.6180368216839139, 0.6138013495818999, 0.609601050438221, 0.6054998198948546, 0.6015784364597384, 0.5979303869888333, 0.5946563641482, 0.5918579487182243, 0.5896310966460394, 0.5880600773793323, 0.5872124424713729, 0.5871354473434388, 0.5878541326384874, 0.5893710404240546, 0.5916673444238194, 0.5947050502555534, 0.5984298851407724, 0.6027745344208454, 0.6076619640661824, 0.613008659301255, 0.6187276826463824, 0.6247314979370904, 0.6309345222873929, 0.6372553664231608, 0.6436187183151483, 0.6499568254504756, 0.6562105418013174, 0.6623299258387838, 0.6682744017693509, 0.6740125224280687, 0.6795213944801979, 0.684785841868668, 0.6897973906733249, 0.6945531580685161, 0.6990547212015858, 0.7033070303617724, 0.7073174166410149, 0.7110947291048748, 0.7146486216882323, 0.7179889966531193, 0.7211256002005795, 0.7240677571107899, 0.7268242252247991 ], [ 0.6383876731126009, 0.6339707052207569, 0.6296334241551824, 0.6253357955225346, 0.6210396210988357, 0.6167143748948805, 0.6123427945741585, 0.6079256197831808, 0.6034849299220879, 0.5990656558632746, 0.5947350113012243, 0.5905797959579664, 0.5867017483227015, 0.583211348600304, 0.5802206650236545, 0.5778359654613725, 0.5761508497737772, 0.5752405779317781, 0.5751580800654561, 0.5759318722579998, 0.5775658239567798, 0.5800404926677134, 0.5833156060134677, 0.5873332449211475, 0.5920213450174913, 0.5972972441987354, 0.6030711172657253, 0.6092492209758789, 0.6157369130768343, 0.6224414136320882, 0.6292742632346707, 0.6361534183858023, 0.6430049215588279, 0.6497640964633855, 0.6563762451971074, 0.6627968569589654, 0.6689913707128651, 0.674934560972198, 0.6806096334539257, 0.6860071248296976, 0.6911236990928609, 0.6959609241350785, 0.7005240983482826, 0.7048211807207854, 0.7088618609179262, 0.7126567897143954, 0.7162169759121982, 0.7195533441684409, 0.7226764392698621, 0.7255962563576803 ], [ 0.6290356088898104, 0.6244002628518759, 0.6198722740911252, 0.6154031247349181, 0.6109452955657386, 0.6064590784996945, 0.6019191590759724, 0.5973202505683326, 0.5926811346770368, 0.5880466077033344, 0.5834870304431125, 0.579095418872496, 0.5749822735173309, 0.5712686053171165, 0.5680778430694169, 0.5655274623239495, 0.5637212179040685, 0.5627427666181574, 0.5626512380965704, 0.5634789932129373, 0.565231474921634, 0.5678887863479691, 0.5714084838998124, 0.5757290638854089, 0.5807737193929796, 0.5864540921889693, 0.5926738829772231, 0.5993322737427494, 0.6063271481813253, 0.6135580844242122, 0.6209290637874425, 0.6283508140296455, 0.6357427000656425, 0.6430340924171004, 0.6501651784077324, 0.6570872236409117, 0.6637623320692799, 0.6701627850126408, 0.676270059304287, 0.6820736319562366, 0.6875696750795772, 0.6927597331072772, 0.6976494577016055, 0.7022474568298047, 0.7065642955295341, 0.7106116684015767, 0.7144017488362209, 0.7179467079162877, 0.7212583870085659, 0.7243481021646895 ], [ 0.6191222860291116, 0.6142694344235375, 0.6095570404076098, 0.604926883480734, 0.6003206453337258, 0.5956878496832066, 0.5909935930881641, 0.586225218833075, 0.5813971758562507, 0.5765534757526098, 0.5717673932083452, 0.567138330552823, 0.5627860673656218, 0.5588429175991381, 0.5554445841850151, 0.5527206869860687, 0.5507859935517989, 0.5497332687996717, 0.5496283828097736, 0.5505079286959083, 0.5523791990426993, 0.5552220530797238, 0.5589920502481681, 0.5636242430903864, 0.5690371681029878, 0.575136768237891, 0.5818201486879298, 0.5889791629668452, 0.5965038434862588, 0.6042856546785362, 0.6122204938869121, 0.6202113270326088, 0.6281703389377769, 0.6360205029786709, 0.6436965216071914, 0.6511451442944324, 0.6583249200530477, 0.6652054795952751, 0.6717664639465155, 0.6779962224658784, 0.6838903966646696, 0.6894504908954032, 0.6946825107880514, 0.6995957284717803, 0.7042016125127386, 0.7085129416598648, 0.7125431057712523, 0.7163055850325765, 0.7198135897640648, 0.7230798375017422 ], [ 0.6086387337138358, 0.6035703359336653, 0.598681666583177, 0.5939034632168428, 0.5891649628659272, 0.5844031428927274, 0.5795717801970839, 0.5746493281025967, 0.5696447225282528, 0.5646004339024766, 0.5595923523656767, 0.5547264100794153, 0.5501321881241614, 0.5459541033362276, 0.542341084179668, 0.5394358678590768, 0.5373651191017772, 0.5362314372405462, 0.5361079826812186, 0.5370359822706047, 0.5390248857856834, 0.5420545755756615, 0.5460788690586229, 0.5510296107055058, 0.5568208595515747, 0.5633529324616442, 0.5705162641158807, 0.5781951398322482, 0.5862713492985885, 0.5946277385654398, 0.6031515558826275, 0.6117374341071814, 0.6202898460835786, 0.6287249061786323, 0.636971454832609, 0.6449714340042089, 0.6526796236797288, 0.6600628537169682, 0.6670988283093547, 0.6737747042258128, 0.6800855532715647, 0.6860328194332234, 0.6916228567366913, 0.6968656086891108, 0.7017734668127712, 0.706360325659621, 0.7106408354620806, 0.7146298413260572, 0.7183419893701316, 0.7217914750427767 ], [ 0.5975804698237765, 0.5922995146702573, 0.5872445179088059, 0.5823337113179528, 0.5774820640648947, 0.5726120246062465, 0.5676641142770231, 0.5626061915036554, 0.5574403483790552, 0.5522066487305504, 0.5469832335476049, 0.5418826814438905, 0.537044902510298, 0.5326272426887029, 0.528792842313527, 0.5256985601191532, 0.5234838613605809, 0.5222619116361445, 0.5221137114584942, 0.5230855314217365, 0.5251893181920844, 0.5284053087369258, 0.5326859278883578, 0.5379601587007495, 0.5441378691993048, 0.5511139070425843, 0.5587720098131549, 0.5669886651154057, 0.5756370073150835, 0.5845907194119245, 0.5937277903065638, 0.6029339093614704, 0.6121052787852732, 0.6211506794627253, 0.6299927122863402, 0.6385682281128237, 0.6468280352384093, 0.6547360235142077, 0.6622678672793345, 0.6694094692583453, 0.6761552911536771, 0.6825066908263949, 0.6884703565420645, 0.6940568999487388, 0.6992796438085469, 0.7041536192690567, 0.7086947709679667, 0.7129193562937524, 0.7168435171699001, 0.7204829981739215 ], [ 0.5859485583578716, 0.5804589570896698, 0.5752493291656444, 0.570223809377791, 0.5652810892400643, 0.5603268905766644, 0.5552863289095075, 0.550114772242139, 0.5448059854547231, 0.5393966518814235, 0.5339667342363347, 0.5286355489310012, 0.5235538683560831, 0.5188928193938778, 0.5148307726971106, 0.5115397382695297, 0.5091728954761424, 0.5078547026895993, 0.5076745394738543, 0.5086841315399983, 0.5108982938042239, 0.5142980212164248, 0.5188348034691033, 0.5244352353334159, 0.5310054002592481, 0.5384349239676265, 0.5466008676198473, 0.5553716949800047, 0.5646114422647531, 0.5741840370485757, 0.5839575496904835, 0.5938080774899552, 0.6036229719541641, 0.6133032015298323, 0.6227647586598933, 0.6319391356050079, 0.6407729842044088, 0.6492271303823267, 0.6572751354106061, 0.6649015898313885, 0.6721003019441218, 0.6788725097489597, 0.6852252101110283, 0.691169666206439, 0.6967201264776521, 0.7018927662543392, 0.706704846789115, 0.7111740750949773, 0.7153181408316001, 0.7191544027365097 ], [ 0.573750838901297, 0.568057260558917, 0.5627063026024759, 0.5575862835385532, 0.5525774139267786, 0.5475662678203858, 0.5424601846362528, 0.5371999543711808, 0.5317693810817113, 0.5262006897684609, 0.5205751760090004, 0.5150189637947158, 0.5096942288840262, 0.5047867565682433, 0.5004911960386762, 0.49699575851018146, 0.494468252448402, 0.4930451384989013, 0.4928246912368253, 0.4938644953007014, 0.4961826346934371, 0.49976134342625084, 0.5045517534236673, 0.5104786841221134, 0.5174449703102377, 0.5253353555853864, 0.5340202871306852, 0.543359971703918, 0.5532088632557496, 0.5634204862140593, 0.5738522824696307, 0.584370074932455, 0.5948517721030475, 0.6051900582049977, 0.6152939687295441, 0.625089395962502, 0.6345186756141579, 0.6435394650606776, 0.6521231403135412, 0.6602529238840069, 0.6679219219444784, 0.6751312076132076, 0.6818880457015125, 0.6882043175752185, 0.6940951750180941, 0.6995779294967883, 0.7046711673522442, 0.7093940710793895, 0.7137659208287935, 0.7178057475118884 ], [ 0.5610033473549284, 0.5551109883904752, 0.5496333743267022, 0.5444411624223288, 0.5393936817405663, 0.5343557096973021, 0.5292142184824288, 0.5238931445851346, 0.5183645553572215, 0.5126550450086591, 0.5068467017212449, 0.5010725112411831, 0.4955066048474384, 0.4903503302973854, 0.48581569198507496, 0.48210816829083986, 0.47941110533397024, 0.47787364714295544, 0.4776034434035615, 0.47866432331251807, 0.48107806568414796, 0.48482870533541533, 0.48986772212960883, 0.4961189218497355, 0.503482560067313, 0.5118389267290864, 0.521051948111032, 0.5309733192971445, 0.5414473739985401, 0.5523165240415988, 0.5634268239048116, 0.5746331151873537, 0.5858032729539195, 0.5968212484633094, 0.6075888068924361, 0.6180260369136122, 0.628070831133315, 0.6376775966551134, 0.6468154632921653, 0.6554662297820584, 0.6636222424005455, 0.6712843488657524, 0.6784600220981886, 0.6851617078600017, 0.6914054190654757, 0.6972095772291478, 0.702594086727219, 0.7075796186300765, 0.7121870762604899, 0.7164372130646538 ], [ 0.547731945271569, 0.5416462263289883, 0.5360576661936056, 0.5308172972135672, 0.5257609703626958, 0.5207287913759931, 0.5155845593905832, 0.5102329055189283, 0.5046322571627657, 0.498802325590391, 0.4928254120251285, 0.4868414105479278, 0.48103697552859476, 0.47562994970596995, 0.47085079799603813, 0.4669233460560869, 0.46404737454387446, 0.46238535417849425, 0.4620547415858605, 0.46312596594341765, 0.46562494371283253, 0.4695381511588277, 0.4748182524187346, 0.4813889515165223, 0.48914872343679106, 0.4979739093112665, 0.5077220200703387, 0.5182359443305469, 0.5293492906534796, 0.5408925836822874, 0.552699689725459, 0.5646137532399429, 0.5764920475712907, 0.5882093859916749, 0.5996600028992205, 0.6107580303593788, 0.6214368310986671, 0.6316475057223705, 0.6413568869790417, 0.6505452905434763, 0.6592042310863735, 0.6673342497481426, 0.6749429437671772, 0.6820432450400695, 0.6886519624023021, 0.6947885810086418, 0.7004742991384456, 0.7057312757664961, 0.7105820593752944, 0.7150491682642626 ], [ 0.5339741703701597, 0.5277003547731881, 0.5220171368731218, 0.5167538552461461, 0.5117200987308468, 0.5067282103078777, 0.5016158112201019, 0.49626562013019404, 0.4906204172139765, 0.4846917200876351, 0.4785614398465806, 0.4723764272966728, 0.4663364474840409, 0.46067680150178203, 0.4556475509180601, 0.45149196479660775, 0.44842714310761345, 0.4466294837201895, 0.44622662370131855, 0.4472959046943164, 0.4498678289780855, 0.45393202502890834, 0.4594433010067587, 0.46632631143271586, 0.47447866211053125, 0.48377330311026917, 0.4940614216512362, 0.5051767425040457, 0.516941465305831, 0.529173389807981, 0.5416933667113495, 0.5543321427292293, 0.5669358709206489, 0.5793698911042976, 0.5915207198576392, 0.6032964438728776, 0.6146258561065456, 0.6254567208970904, 0.6357535300454873, 0.6454950479145408, 0.6546718656411624, 0.6632841098584765, 0.6713393891155139, 0.6788510145705468, 0.6858364997774528, 0.6923163248225195, 0.6983129394918876, 0.7038499756067789, 0.7089516378298014, 0.7136422434919485 ], [ 0.519781311362913, 0.5133240428894306, 0.5075624384904763, 0.5023019917437364, 0.4973230773975906, 0.4924069910962156, 0.4873620010564292, 0.48204618467003923, 0.4763845968976632, 0.4703792201463521, 0.46411096725725226, 0.4577337054606978, 0.45146092150246847, 0.4455463710090872, 0.4402608832982547, 0.4358682899857127, 0.4326038900135286, 0.43065856854285595, 0.43017045329977943, 0.43122405584033957, 0.43385490132000437, 0.43805653285666163, 0.4437869648998919, 0.45097296910352863, 0.45951227340448564, 0.469275009868234, 0.4801060839737128, 0.49182961138455195, 0.5042556118962946, 0.5171882700487753, 0.5304345927353437, 0.5438122781315768, 0.5571559259343931, 0.5703211675529072, 0.5831867107513186, 0.5956545856288735, 0.6076490273111365, 0.6191144591265243, 0.6300129895467398, 0.6403217470036606, 0.6500302792546347, 0.6591381568365535, 0.6676528518280067, 0.6755879151156579, 0.6829614451244681, 0.6897948243532221, 0.6961116927568932, 0.7019371254139801, 0.7072969833571223, 0.7122174092147343 ], [ 0.5052206935167092, 0.49858345593579406, 0.49275897183935496, 0.48752669218095057, 0.48263469315694235, 0.4778297849982521, 0.47288758370558326, 0.4676387237474555, 0.4619884310255861, 0.4559278146173743, 0.4495361963574481, 0.4429745384247847, 0.4364706836675563, 0.4302978708949722, 0.4247489087741682, 0.4201093469107659, 0.4166335751150821, 0.4145274997522696, 0.4139399900648307, 0.41496292067619195, 0.4176372442270666, 0.4219612016156268, 0.42789713898321907, 0.4353751783911908, 0.44429418677979354, 0.4545220116347057, 0.4658972233740714, 0.47823376916279764, 0.4913286297447164, 0.5049714543797572, 0.5189546170007613, 0.5330822130621322, 0.547176985714684, 0.5610847589669987, 0.57467646037131, 0.5878481415116136, 0.6005195455233153, 0.6126317703922275, 0.6241444920727963, 0.6350330925508841, 0.6452859194337639, 0.6549018044295046, 0.6638878950306321, 0.672257805993212, 0.6800300700689063, 0.6872268550039907, 0.6938729106163279, 0.6999947115457391, 0.7056197651493411, 0.7107760582758175 ], [ 0.49037813363795923, 0.48356264200503046, 0.4776891104222063, 0.47250875727654934, 0.46773420111462743, 0.4630742394209604, 0.45826848204150966, 0.45311731402400485, 0.44750406034191365, 0.4414076624046198, 0.43490529370281766, 0.4281651113313652, 0.4214299651954567, 0.41499363283721896, 0.40917215957624015, 0.40427402464746354, 0.40057364330540624, 0.39829248096336684, 0.39759035752337146, 0.3985666365551546, 0.4012680447689652, 0.4056982787058677, 0.4118251417624733, 0.4195833306025263, 0.42887381229670307, 0.43956256824032264, 0.4514816298375907, 0.46443407805280523, 0.47820291757769906, 0.49256235219602645, 0.5072894295405199, 0.52217424504211, 0.5370275646590454, 0.5516854805169248, 0.5660113108217621, 0.5798953045290262, 0.5932528304689227, 0.6060216888075918, 0.6181590555590264, 0.6296384182641263, 0.6404467206435954, 0.6505818240220252, 0.6600503176912879, 0.6688656651693653, 0.6770466511260398, 0.6846160867893961, 0.6915997333236612, 0.6980254081915237, 0.703922245871388, 0.7093200899162978 ], [ 0.47536047933663217, 0.4683660240892642, 0.46245452702153533, 0.45734687009511793, 0.4527170693306966, 0.44823238982374697, 0.44359312558869346, 0.4385666918165237, 0.43301254453881843, 0.4268962522310906, 0.4202923352283407, 0.41337626103544384, 0.4064065363037963, 0.39969854473247646, 0.39359287289257217, 0.3884222228926103, 0.38448205802759, 0.382009995298123, 0.38117700986491493, 0.3820900210777568, 0.3848017906473595, 0.3893221408175213, 0.3956253666100168, 0.40365184433115964, 0.4133054327625523, 0.4244504525044028, 0.4369119775773964, 0.45048136899243946, 0.4649266683024224, 0.4800057945548242, 0.49547994783668625, 0.5111250570928325, 0.5267400323434375, 0.5421515231057313, 0.5572155707301364, 0.5718168985425393, 0.5858666631245399, 0.5992993930985968, 0.6120696642654693, 0.6241488708874939, 0.6355222915094574, 0.6461865293640662, 0.6561473321622578, 0.6654177560584839, 0.6740166233881096, 0.6819672236174384, 0.6892962141782926, 0.6960326873182457, 0.7022073778286175, 0.7078519932141737 ], [ 0.460298081141624, 0.45312086156121734, 0.4471785004174261, 0.4421596353111014, 0.43769667924041206, 0.4334119926611842, 0.42896342436471513, 0.42408290279995764, 0.4186042372574204, 0.4124785555325076, 0.40577728360329135, 0.3986833119693621, 0.39147141882986514, 0.38447964340540575, 0.37807445815845253, 0.37261419031390725, 0.3684165218434127, 0.365735943527537, 0.3647548488576484, 0.36558774688947293, 0.3682935843885413, 0.37288881297515375, 0.37935503915329033, 0.38763915446582475, 0.3976483800147206, 0.40924524486714536, 0.4222471634539669, 0.43643276163531325, 0.45155413192383415, 0.46735222723558906, 0.48357214812833055, 0.49997580769985284, 0.516350686224978, 0.5325145301118406, 0.5483166109891247, 0.5636365006320431, 0.578381335770383, 0.5924823805499989, 0.6058914599078465, 0.6185776106475047, 0.6305241168862568, 0.6417259736152188, 0.6521877510356238, 0.6619218006179123, 0.6709467377650761, 0.6792861438226767, 0.6869674434508638, 0.6940209267589788, 0.7004788964144204, 0.7063749273118906 ], [ 0.44534695053613194, 0.4379794547949979, 0.432007997759333, 0.4270874090407294, 0.4228058252607554, 0.41873767059237915, 0.41449557963971906, 0.40977382756210545, 0.4043790895191956, 0.3982471715958624, 0.39144602980572524, 0.3841660527775296, 0.376698816098702, 0.36940599475295033, 0.3626813082878093, 0.3569102428941214, 0.35243408893051686, 0.34952516319611715, 0.34837769388533546, 0.3491138332479606, 0.3517987369926171, 0.35645573243886103, 0.36307418640661393, 0.3716078768893902, 0.3819673440151059, 0.39401271122496523, 0.40755267718190935, 0.4223519704796948, 0.43814583145137914, 0.45465783945730376, 0.4716171301554041, 0.4887721634547025, 0.5058997828554652, 0.5228096504644676, 0.5393449531801912, 0.5553805689641869, 0.5708198160534983, 0.5855906592988388, 0.5996419520093996, 0.6129400292794761, 0.6254657743138727, 0.6372121568588597, 0.648182180465609, 0.6583871552498366, 0.667845217961144, 0.6765800380526201, 0.6846196679655089, 0.6919955128815393, 0.6987414075795969, 0.7048927955154202 ], [ 0.4306902275367594, 0.42312074200424615, 0.41711521453159006, 0.41229363942166997, 0.4081977763215924, 0.4043516783081287, 0.4003205867229844, 0.3957594839253086, 0.39044682584130747, 0.3843024497003347, 0.37739052218170044, 0.36990891508980417, 0.362166360576187, 0.35454900233845565, 0.34747913582226075, 0.34137107871661765, 0.33659141189216124, 0.33343158322783456, 0.332098356040994, 0.33272168728301654, 0.33537284511330984, 0.34008192621353545, 0.3468459482225366, 0.3556252410079556, 0.36633287059438707, 0.3788252885437842, 0.3929010046072888, 0.4083095847865549, 0.42476871504284014, 0.44198461399521805, 0.4596711072954861, 0.47756427334566875, 0.4954315323883203, 0.5130755764871806, 0.5303343604909646, 0.5470785854704894, 0.5632079325881791, 0.5786469640660203, 0.5933412499819817, 0.6072539857728506, 0.6203631630491759, 0.63265924083384, 0.6441432157632041, 0.6548249848131505, 0.664721912340856, 0.6738575397728755, 0.682260401891893, 0.6899629337815366, 0.6970004657091342, 0.7034103101011662 ], [ 0.4165384207438797, 0.4087507789386362, 0.4026981087854329, 0.3979653133869014, 0.3940465612185771, 0.3904140200563915, 0.3865842281059927, 0.38217196603944853, 0.3769269072749125, 0.37075254948887887, 0.3637089859895417, 0.35600139719418245, 0.3479557631358673, 0.33998327264743916, 0.3325360091831452, 0.3260589098646301, 0.32094588103351945, 0.31750929501157066, 0.3159696013562029, 0.31646496523114115, 0.31907259186349574, 0.32382880179794105, 0.33073738470172553, 0.3397638962105455, 0.35082210905300515, 0.3637627020012731, 0.378372061881595, 0.3943833072243995, 0.41149622771702354, 0.429400287722975, 0.44779531969305947, 0.4664066902999346, 0.48499406748295765, 0.5033545800565972, 0.5213219444097278, 0.5387632244336645, 0.5555745899539344, 0.5716769996418909, 0.5870123179412672, 0.6015400580861079, 0.6152347418673036, 0.6280837657194046, 0.6400856333632065, 0.6512484286098864, 0.6615884346818232, 0.6711288427665089, 0.6798985236445355, 0.6879308584845468, 0.6952626379874544, 0.7019330444809426 ], [ 0.4031277104769576, 0.39510141554929606, 0.38897930218949733, 0.38431196471258094, 0.3805460278670499, 0.3771015656442389, 0.3734462935545957, 0.36915483436862784, 0.36394815880261644, 0.35771336724801134, 0.35050620177687036, 0.34253873710657273, 0.3341539056326405, 0.3257881214578769, 0.31792422328322306, 0.31103959946259707, 0.3055578945071409, 0.3018148162084074, 0.3000462974193007, 0.3003995433197091, 0.3029575357987006, 0.30776177488729656, 0.3148209521120158, 0.32410320904843015, 0.3355198731205235, 0.3489127341514296, 0.36405365392458444, 0.38065813429235473, 0.3984082882784845, 0.4169782176504443, 0.4360558760627396, 0.45535825378896116, 0.47463940458576703, 0.4936925653777514, 0.512348302939803, 0.530470558493274, 0.5479520197882034, 0.5647097142374423, 0.5806812505100429, 0.595821806183168, 0.6101017690630164, 0.6235048613600039, 0.6360265712132902, 0.6476727505777155, 0.6584582865706783, 0.668405799105483, 0.6775443531724265, 0.685908197250392, 0.6935355511093682, 0.7004674692724685 ], [ 0.3907154717676013, 0.382426333587845, 0.37620257548753444, 0.3715625738173466, 0.3679071285720409, 0.36460573884789144, 0.36107870976261514, 0.3568617277002405, 0.3516478990428408, 0.34530821355504016, 0.3378937611920458, 0.3296227790860381, 0.3208543463481, 0.31204972404445736, 0.3037230529788807, 0.2963859103267355, 0.2904944291451548, 0.2864107744686448, 0.2843890105341008, 0.28458688071340643, 0.28709315945830793, 0.29195297079341026, 0.2991768311421583, 0.30873117194827376, 0.32052007485290956, 0.33437215859689795, 0.35004194396993626, 0.36722646018762606, 0.3855911615829574, 0.4047971560573397, 0.4245235396684574, 0.44448195602776136, 0.4644234217380362, 0.48413915981913913, 0.5034577064086321, 0.522240311713713, 0.5403760713439021, 0.5577776007299775, 0.5743775635984705, 0.5901260377064161, 0.6049885345267806, 0.6189444423613302, 0.631985687302382, 0.6441154641685576, 0.6553469529505563, 0.6657019902354048, 0.675209703405874, 0.683905137794947, 0.6918279160858348, 0.6990209688289144 ], [ 0.379572171759016, 0.3709935728936762, 0.36462613671644534, 0.35995964369339556, 0.35635284755095387, 0.3531283255121558, 0.34966223937463037, 0.34545394299459903, 0.34017037685433055, 0.33366708191107247, 0.3259901567893895, 0.31736289629803704, 0.30815910548377934, 0.29886378976699063, 0.29002230184083855, 0.28218183274883196, 0.2758339536006168, 0.27137113333364543, 0.26906924645040237, 0.2690990139888107, 0.27155543049960434, 0.2764852312151455, 0.2838962871713409, 0.2937470333125876, 0.30592757331877146, 0.32024783236028254, 0.33644190901717164, 0.3541880832467095, 0.3731372217801326, 0.39294094799474416, 0.41327348382536233, 0.43384482158857707, 0.4544058806131301, 0.4747478640879267, 0.49469834379593214, 0.51411616421789, 0.5328865387373394, 0.5509170174963586, 0.5681344882074972, 0.5844830624080222, 0.5999225694901511, 0.6144273731432577, 0.6279852835623673, 0.6405964206499714, 0.6522719611840053, 0.6630327631313732, 0.6729078992823636, 0.6819331521360055, 0.6901495269406142, 0.6976018349233324 ], [ 0.36996905928490553, 0.3610738847396009, 0.3545120062793146, 0.3497498666625676, 0.3461102874658975, 0.34287502086669697, 0.3393814529403228, 0.3350967442204259, 0.3296643071227093, 0.32292530879707554, 0.31492049606035155, 0.3058767370986867, 0.2961804713847494, 0.2863384833676055, 0.2769263735968041, 0.26852775926761663, 0.26167252980524336, 0.2567879107714636, 0.2541763939051237, 0.25402533063637023, 0.2564370705034021, 0.26145761800743866, 0.2690862036742092, 0.2792647137465773, 0.2918604323852062, 0.3066579017253598, 0.3233677324996892, 0.3416500869143379, 0.36114460605074006, 0.38149817251023443, 0.40238504921626816, 0.4235178332489994, 0.4446505189018035, 0.46557627755849806, 0.48612263443037085, 0.5061461035511856, 0.5255275126443646, 0.5441685117479006, 0.5619892477038305, 0.5789269152605325, 0.5949348147408418, 0.6099815855238178, 0.624050379953619, 0.6371378480126435, 0.6492528931024472, 0.6604152230668254, 0.6706537576836741, 0.6800049688898238, 0.6885112293371767, 0.696219234589184 ], [ 0.36216172634498267, 0.3529248524524473, 0.3461113794762252, 0.34117121703435205, 0.3373997553282442, 0.3340465684960848, 0.33041783003805714, 0.32595424632059417, 0.3202793275830672, 0.31322140952446836, 0.3048155739889203, 0.29529046769565, 0.28504243189019446, 0.27459713387855567, 0.26455836800126953, 0.255546015273087, 0.24813067805760736, 0.24277908565652623, 0.23982621328995107, 0.23948109896922123, 0.24185559425488007, 0.2469924906305851, 0.2548748143776102, 0.26541695537747045, 0.27845247604312195, 0.2937329985855125, 0.31094304143069246, 0.3297265502761904, 0.3497167565064554, 0.3705617513306361, 0.39194153531326303, 0.41357593201351683, 0.43522522959434756, 0.4566864017701644, 0.47778759564482554, 0.49838280376713967, 0.5183477312374233, 0.537577117188542, 0.5559832900655425, 0.5734955213374858, 0.5900597231839572, 0.6056381280808538, 0.6202087214766396, 0.6337643265397963, 0.646311339051602, 0.6578681745197356, 0.6684635218742385, 0.6781345062555141, 0.6869248556541575, 0.6948831496102076 ], [ 0.35637071489711486, 0.3467717744851505, 0.33964676699779206, 0.3344370831573469, 0.3304212904848102, 0.3268277797150163, 0.3229411401956696, 0.3181829015745145, 0.31216129300295287, 0.3046939029451026, 0.29581001464175755, 0.285738112543392, 0.2748812129077721, 0.2637800900995359, 0.2530634536987726, 0.2433859405871525, 0.2353602220828601, 0.22949701574307188, 0.22617036071352714, 0.2256174160118035, 0.22796289596630048, 0.23324395754647137, 0.24141838498411083, 0.2523598957785374, 0.26585582464072677, 0.2816171679706766, 0.2993008218904145, 0.31853801158592293, 0.33896183570088007, 0.36022854049671155, 0.38203004662690687, 0.40409810273134095, 0.4262023235099694, 0.448145003417455, 0.4697552358571385, 0.4908839941850675, 0.5114008890740094, 0.5311925850141279, 0.550162436975123, 0.5682307687531781, 0.5853352681534323, 0.6014311238744096, 0.6164906995144361, 0.6305026866726203, 0.6434707831117737, 0.6554120022585611, 0.6663547447256549, 0.6763367616814228, 0.6854031237745559, 0.6936042858482805 ], [ 0.3527616655730427, 0.3427876510525756, 0.33529295851689556, 0.3297191086240908, 0.3253399093426523, 0.3213753367882009, 0.3170996835354805, 0.311923899312207, 0.30544649809707514, 0.297477033586925, 0.2880392274611194, 0.2773595766498653, 0.26584433230147453, 0.254044934149003, 0.2426105265577915, 0.23222735932345465, 0.22354986224198511, 0.21713614084168473, 0.21340584771523408, 0.21263163647613278, 0.2149555609548344, 0.22040690654219047, 0.22890803037266655, 0.24027728026092907, 0.25424275196664053, 0.27046806158341563, 0.2885827431579442, 0.3082105611169091, 0.32899197547330417, 0.3505988972398102, 0.37274138732206935, 0.3951675256756654, 0.4176588390215244, 0.44002398714523533, 0.46209291497042343, 0.4837127567906937, 0.504745844622469, 0.5250694939724042, 0.5445769024685895, 0.5631784501425919, 0.5808028256337956, 0.5973976117071289, 0.6129291687364227, 0.6273818153925199, 0.6407564096746624, 0.6530684858324319, 0.6643461162212545, 0.6746276553531176, 0.6839594978885366, 0.6923939515026357 ], [ 0.35142855447762356, 0.34107577391815147, 0.3331599952110114, 0.3271314304581028, 0.3222716805583681, 0.3178059344370482, 0.31301045504299646, 0.30729513979974943, 0.3002551691847061, 0.2916954743709821, 0.2816350434444246, 0.2702970067244748, 0.25808759659144015, 0.2455642042789365, 0.23339097550857787, 0.22228090823474203, 0.21292763910842627, 0.2059379406219677, 0.20178235503526784, 0.20077624669998861, 0.20308392647832257, 0.20872468597710309, 0.21757485440975177, 0.22938277078875266, 0.24380572628340205, 0.2604556819640118, 0.2789375072222279, 0.2988743861163973, 0.3199222809306809, 0.3417761745331189, 0.36416995320872075, 0.3868717282329749, 0.4096768189348181, 0.43240068967816014, 0.4548735820437341, 0.4769376665920233, 0.49844664931985705, 0.5192671733382063, 0.5392811267336359, 0.5583880296013071, 0.5765068974714207, 0.5935772466166038, 0.6095591422358134, 0.6244323592274178, 0.6381948235720549, 0.6508605426364606, 0.662457232507656, 0.673023826195527, 0.6826080109328843, 0.6912639044990397 ], [ 0.3523836913921617, 0.3416587148037062, 0.3332817528750474, 0.3267194713466368, 0.3212732098414614, 0.31618674082723086, 0.31075067070891216, 0.30438376518277127, 0.29668484153259006, 0.28745833462362697, 0.276720111875605, 0.26468934221050705, 0.25176963299164684, 0.23851988134874783, 0.225613348907409, 0.21378342519562327, 0.20375782538210918, 0.19619006147214882, 0.19160384140678927, 0.19036235104265212, 0.19265598769670905, 0.19849170164182728, 0.20769016528601958, 0.21991787886738312, 0.23475401615962188, 0.25175876459409613, 0.270517771047228, 0.29066155423549944, 0.31186946976814073, 0.3338660426039573, 0.35641351094238233, 0.37930261285404127, 0.40234342296685943, 0.42535796462085634, 0.44817576812968146, 0.470632666761206, 0.4925723067753482, 0.513849364857598, 0.5343333675924914, 0.5539121921454339, 0.5724946447404625, 0.5900118383908234, 0.6064173510355368, 0.6216863154091764, 0.6358136790962301, 0.6488118974829954, 0.6607083061053634, 0.6715423810282146, 0.6813630498780484, 0.6902261704864578 ], [ 0.35555696833549083, 0.34447646794671777, 0.3356129348742996, 0.3284559115638545, 0.32233683261509466, 0.3165300782895827, 0.3103521561152605, 0.30324038775841894, 0.29480445762232127, 0.2848530573896612, 0.2734014305769534, 0.26066523200844577, 0.24704390405623866, 0.23309425504198747, 0.21949301080092765, 0.20698668374529614, 0.1963294451232011, 0.18821555977236276, 0.18321920901910702, 0.18175168726284593, 0.1840298143552909, 0.1900451034225476, 0.19955614400486796, 0.21214241284558294, 0.22730509057747347, 0.24455793020341138, 0.2634752518587898, 0.2837028391240674, 0.30494999816661017, 0.3269754805740828, 0.34957268959494897, 0.372556176598346, 0.3957506937976165, 0.41898388944820947, 0.4420831867166847, 0.46487655557459995, 0.48719616422924517, 0.5088835491362326, 0.5297949954265319, 0.54980613807255, 0.5688152066092726, 0.586744713115244, 0.6035416598642519, 0.6191765077823422, 0.6336412175526753, 0.6469466801582231, 0.6591198197598994, 0.6702005997981585, 0.6802391068734144, 0.6892928343242396 ], [ 0.3608046187375048, 0.34939430297492985, 0.34003531967329903, 0.33224490286347297, 0.32539268893676476, 0.31879350764433273, 0.3117997153334637, 0.3038760257791317, 0.2946500760581706, 0.28393998213616595, 0.27176368843083415, 0.2583349104768904, 0.2440486980934496, 0.2294574790911317, 0.21523670405734882, 0.20213862151839715, 0.19093428855602396, 0.1823483778705372, 0.17699623919003935, 0.175329928206652, 0.17758689377308376, 0.18373903753167722, 0.19348244361232023, 0.20631494965240227, 0.22166974385937677, 0.23902525794854423, 0.2579539103453107, 0.2781234991303531, 0.2992775291051053, 0.3212112399442827, 0.3437499562393044, 0.36673168931351025, 0.3899947586957454, 0.41337090396852866, 0.43668378423814985, 0.459751961720901, 0.4823948444683462, 0.5044398718599888, 0.5257294488827092, 0.54612659633432, 0.5655187909767797, 0.5838198923779861, 0.6009703392377547, 0.6169359507388703, 0.6317057183385636, 0.6452889566616118, 0.6577121296943653, 0.6690156023380883, 0.6792505011889569, 0.6884758094072148 ], [ 0.36792537859309576, 0.3562184082549279, 0.34637175112803803, 0.33793354240023016, 0.33031723276248753, 0.3228853201698621, 0.3150338192507912, 0.3062623109955945, 0.2962228994010813, 0.2847483799498694, 0.271863315410097, 0.25778203416247947, 0.24289623556380752, 0.22775310704426716, 0.2130233869742055, 0.19945824264679135, 0.18783491234340624, 0.17889422299789343, 0.17327626715607664, 0.1714573917519723, 0.17368241155565872, 0.17989878579769375, 0.18974787478936303, 0.20266377798878593, 0.2180318255467999, 0.23531102600930212, 0.2540816325734085, 0.27403812828650714, 0.29495965518751766, 0.31667757768001903, 0.33904782802954136, 0.3619300825677492, 0.385174244522909, 0.4086141963645041, 0.432068098552457, 0.4553437053830846, 0.47824664956944946, 0.5005896283246348, 0.5222008300762091, 0.5429305497855068, 0.5626555389449914, 0.5812810976486564, 0.5987412041372286, 0.614997112454604, 0.6300348746855906, 0.6438622044880767, 0.6565050275285584, 0.6680039847136741, 0.6784110788332962, 0.6877865906130604 ], [ 0.3766804365325009, 0.3647157272866033, 0.3544046231362794, 0.3453279628568702, 0.3369462564814748, 0.3286742327287384, 0.31995703012253107, 0.3103348842580497, 0.2994899272956688, 0.28727458419131363, 0.273724155672501, 0.2590567235366158, 0.24366257135071306, 0.2280839049796064, 0.21298448544138837, 0.1991083763606253, 0.18722787635210542, 0.17808296123674075, 0.17231626748153697, 0.17040427034719696, 0.1725800690125625, 0.17876259417166399, 0.18855430877796156, 0.20135388913340904, 0.21652630917743665, 0.23352977947322223, 0.2519614704291828, 0.271544969562559, 0.2920939020444165, 0.31347311276265316, 0.3355661138744144, 0.3582513424542438, 0.3813877293321315, 0.4048092017547276, 0.4283268328414551, 0.4517364899076292, 0.4748294109123404, 0.49740330217441775, 0.5192721493168022, 0.5402736905591833, 0.5602741852392937, 0.5791706028363286, 0.5968906413360069, 0.6133910975050789, 0.6286551117186583, 0.6426887470888155, 0.6555172736079522, 0.6671814357426217, 0.6777338985468302, 0.6872359979657969 ], [ 0.3868133959919185, 0.3746340901953626, 0.3638951333478478, 0.3542107525929963, 0.3450897629255021, 0.3360013072504886, 0.3264428525914626, 0.3159992669078765, 0.30438703688673213, 0.29148246979418047, 0.2773354509142454, 0.2621709874610504, 0.24638013075702184, 0.23050077760626236, 0.21518796341106686, 0.20117307674147555, 0.18921234275910367, 0.1800268001394657, 0.17423696608505548, 0.17229237086311802, 0.17439430811794274, 0.18043158898300815, 0.18998831136707545, 0.2024602487281772, 0.2172217033601674, 0.23374891399959585, 0.2516639702287114, 0.270720323479518, 0.2907631970980945, 0.3116867896957174, 0.33339809824060873, 0.3557908131969608, 0.3787301611789176, 0.4020481768609366, 0.4255476400079072, 0.44901194409896417, 0.4722178223854624, 0.49494820460292427, 0.5170032688903534, 0.538208654095869, 0.5584205594388166, 0.5775279748449769, 0.5954525596813259, 0.6121467777707538, 0.6275908707897486, 0.6417891671183633, 0.6547661176368861, 0.6665623464786988, 0.6772309144127037, 0.6868339191849537 ], [ 0.3980674055338118, 0.385719630719681, 0.37460028778075655, 0.3643568536855769, 0.35454615743036055, 0.3446920042536257, 0.3343454118542434, 0.3231381038402721, 0.31082385794149386, 0.29730609447791, 0.28265239243523915, 0.267097291238378, 0.25103430707919877, 0.2349972539987129, 0.21963032803336502, 0.20564651270214418, 0.19377506920566231, 0.1847009134968266, 0.17899972863735972, 0.17707051892208037, 0.1790673855557447, 0.18485089295827078, 0.1940069333189834, 0.20595754600671587, 0.22011255153490886, 0.23598280574357333, 0.25322211412455026, 0.2716137932070596, 0.2910311592698374, 0.3113931289098461, 0.33262577845646674, 0.3546345059470327, 0.37728834306487535, 0.40041595960846466, 0.42381123368833234, 0.4472451328727263, 0.47048037030212614, 0.49328581877153, 0.5154486390918246, 0.5367831123006754, 0.5571359958562009, 0.5763887582330701, 0.5944573090438919, 0.6112899084462723, 0.6268638894747864, 0.6411817217734714, 0.6542668250107609, 0.6661594271320205, 0.676912666446495, 0.6865890600288924 ], [ 0.41019799591691103, 0.3977298960931927, 0.38628594692886503, 0.3755461626902245, 0.365114005352222, 0.3545667364935615, 0.3435085335213199, 0.33161862102706613, 0.318689584556336, 0.3046539544389828, 0.28959901272441363, 0.273770380255884, 0.2575646397882396, 0.24151061080310066, 0.22623850775474338, 0.21243666507018844, 0.2007972100013291, 0.1919546604552396, 0.18642303502322993, 0.18453573026894723, 0.18639252404971834, 0.19183071462306944, 0.2004536804861969, 0.2117302393758683, 0.22512436424193136, 0.24019393758392613, 0.25662981049417977, 0.27424501552065106, 0.29293770214382314, 0.3126471716375233, 0.3333145157915378, 0.3548537431340954, 0.3771357901486292, 0.3999851951617959, 0.42318708007823336, 0.4465007606430925, 0.46967605345827323, 0.49246901252950115, 0.5146549613162245, 0.5360378354001073, 0.5564557399016864, 0.5757831736129178, 0.5939306226716073, 0.6108422719044566, 0.6264925104712585, 0.6408817859874433, 0.6540322287822214, 0.6659833468391257, 0.6767879910830022, 0.6865087116545713 ], [ 0.4229814012901787, 0.41044236159554176, 0.39873548392094615, 0.3875722212541801, 0.3766005680633855, 0.3654490160258541, 0.35377327509808115, 0.34129937778744773, 0.3278588887153065, 0.3134141329387125, 0.2980728067948879, 0.2820918250815445, 0.2658700294929559, 0.24992891494763544, 0.23488041648997168, 0.2213816813055914, 0.21007906754112804, 0.20154689342005294, 0.1962286183385539, 0.19438704817195504, 0.19606886225326345, 0.20109494405969072, 0.20909590334327932, 0.21959782812158932, 0.23212856600535717, 0.24630017890281847, 0.2618439181285791, 0.27860225822407647, 0.29649549980202805, 0.31547972188910645, 0.33550769753452997, 0.35649969906915296, 0.378327466590998, 0.400811474073348, 0.42372905201485256, 0.44682938641426784, 0.4698511546330396, 0.4925393297302975, 0.514658944953909, 0.5360048531281006, 0.5564074523027513, 0.5757349078970004, 0.5938926428239021, 0.6108208951619899, 0.6264910542816093, 0.6409013500629412, 0.6540723275231183, 0.6660424117423309, 0.6768637633747903, 0.6865985440418922 ], [ 0.4362189423303748, 0.42365891856782856, 0.4117545102821114, 0.40024725531871086, 0.3888271385821407, 0.37717098462502013, 0.36498350873654195, 0.3520357776376437, 0.33819731087514304, 0.32345965054275133, 0.30795030528744805, 0.29193633461899277, 0.2758166581676966, 0.2601018810832616, 0.24538062348681672, 0.23227270703905573, 0.22137248230067494, 0.21318938712693733, 0.20809514406909638, 0.2062855110925597, 0.2077612963169954, 0.21233434971592677, 0.21966707216072756, 0.22934503785147944, 0.24096183147485334, 0.25418559702568805, 0.2687889150212546, 0.28464292128468904, 0.3016878104011224, 0.31989357624859044, 0.3392221514649222, 0.35959854963405036, 0.38089504511957484, 0.4029289377822919, 0.42547150898276165, 0.4482640276528918, 0.47103636373394775, 0.493524595123012, 0.5154853395950064, 0.5367058540395904, 0.5570099165476706, 0.5762600759841602, 0.5943570896262887, 0.611237386019762, 0.6268692895697692, 0.6412485972422994, 0.6543939483011315, 0.6663422958970912, 0.6771446819011478, 0.6868624338410135 ], [ 0.44973839800997717, 0.43720728518222246, 0.4251725489441331, 0.41340428927239053, 0.4016316917094105, 0.3895766063079787, 0.3769896035576108, 0.36368417905844463, 0.3495657860483263, 0.33465349825404966, 0.3190928683891634, 0.30315878805241886, 0.28724702345622044, 0.27185300375371824, 0.2575369787970168, 0.24487650058996, 0.23441057656140332, 0.2265838229393403, 0.2217009473733374, 0.21989962496729482, 0.2211450112224786, 0.22524684784164792, 0.2319003829638063, 0.24074757657205562, 0.25144408531115475, 0.2637117369399948, 0.27736289851859597, 0.29229568457104615, 0.30846798747587767, 0.3258613603564687, 0.34444503720627007, 0.36414795258870325, 0.3848433481011702, 0.40634691977012694, 0.42842627364433855, 0.4508175308127527, 0.47324454895347434, 0.4954370611621582, 0.5171454161713701, 0.5381509537370073, 0.5582720474417567, 0.5773664268675359, 0.5953306274533577, 0.6120974282765147, 0.6276320312692495, 0.6419275836516597, 0.6550004915506724, 0.6668858375966029, 0.6776331058672219, 0.6873023338093993 ], [ 0.4633933203684922, 0.450940326099149, 0.4388426078346347, 0.42689719207456045, 0.4148695561635322, 0.4025230441100009, 0.3896505277363001, 0.3761047221400186, 0.36182421870937537, 0.34685305552020007, 0.33135215510940536, 0.31560110906418704, 0.2999887267145122, 0.2849908846267336, 0.2711350967913123, 0.2589534469775338, 0.24892913364718183, 0.2414456455698368, 0.23674893498984884, 0.23492991423483708, 0.23592884288346694, 0.23955926639267972, 0.24554839505915269, 0.25358886366408884, 0.26339168434066434, 0.2747271086720094, 0.2874437118366498, 0.30146387874349195, 0.3167607688416293, 0.3333253589817121, 0.35113274099207314, 0.3701154188756718, 0.390148499748952, 0.4110480874626981, 0.43258089303621766, 0.4544810206477652, 0.4764694201672921, 0.4982722840249114, 0.5196360385951732, 0.5403379379378863, 0.5601922795280474, 0.5790528524933022, 0.5968124719746022, 0.6134004679168763, 0.6287788900690867, 0.6429380381589288, 0.6558917709012051, 0.6676729108795743, 0.6783289517255015, 0.6879181893691562 ], [ 0.47706110485387676, 0.46473412120477736, 0.45263948443358865, 0.4405994361618584, 0.42841280107064283, 0.4158807914476888, 0.40283479371577596, 0.3891631310707165, 0.3748341910465457, 0.35991378756792847, 0.3445749476884051, 0.3290984089691582, 0.31386214329894396, 0.2993185654492998, 0.2859592678652706, 0.2742695824602545, 0.2646788241700389, 0.2575153300724529, 0.2529759894918112, 0.2511163827110751, 0.2518616445158104, 0.255033793133919, 0.260390225559147, 0.26766778599477525, 0.27662502635155656, 0.2870739420104185, 0.29889443662072424, 0.31202962451247135, 0.3264651796334681, 0.3421993959216677, 0.3592119678693381, 0.37743883623265306, 0.3967580664929813, 0.41698834515738525, 0.437898411206032, 0.4592236159519983, 0.4806852342347426, 0.5020088451033015, 0.522939414547575, 0.5432520471147589, 0.5627583851784081, 0.5813092363556518, 0.5987942652608403, 0.6151396105605244, 0.6303041883160642, 0.6442752933198315, 0.6570639562937103, 0.6687003784575537, 0.6792296540105205, 0.688707905831721 ], [ 0.49064043065579505, 0.4784854163137817, 0.46645743519623245, 0.4544021833898604, 0.442148907309825, 0.42953305926619, 0.41642065447191823, 0.4027317868558436, 0.38846096919595297, 0.37369224424226166, 0.35860720318824985, 0.3434841268872998, 0.32868660291278756, 0.31464052040805746, 0.3017997488629365, 0.290603335980542, 0.2814303335230165, 0.274560955901739, 0.27015265771981767, 0.26823592152230924, 0.2687288241218321, 0.2714652602018043, 0.27623071682307443, 0.28280004916455004, 0.29097168012685, 0.30059238316502257, 0.31156798517498463, 0.3238583439559628, 0.3374586835837827, 0.3523724894563594, 0.36858285605162555, 0.38602905208726035, 0.4045931509835882, 0.4240984997690368, 0.4443186743032701, 0.4649934404377084, 0.4858475717608652, 0.5066089448722481, 0.527023548266821, 0.546866321302502, 0.5659477370743935, 0.5841166532706408, 0.6012602277449978, 0.6173017368851402, 0.6321970474409255, 0.6459303512967894, 0.6585096233451403, 0.669962128325146, 0.6803301921264212, 0.689667367635748 ] ] }, { "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": [ 0.5139352083206177, 0.3525698482990265, 0.8365536173805594, 0.3803107887506485, 0.004738156683743, 0.1399143049493432, 0.4254396857282235, 0.596591986169898, 0.3459359054618556, 0.3437211620125524, 0.45883448841225405, 0.3885162614844159, 0.37404203322167245, 0.3842869442259865, 0.39672685869511304, 0.40932786201132454, 0.42152493821190873, 0.4340618747966894, 0.44602174475801404, 0.40760017704824786, 0.42667930806035465, 0.3690262452363467, 0.40720578843023586, 0.41590037424570153 ], "xaxis": "x", "y": [ 0.8104050159454346, 0.4881714144721627, 0.2682372462004423, 0.38866316620260477, 0.6983593786135316, 0.8552484745159745, 0.7460297772297608, 0.8983092267471297, 0.6172875361931487, 0.8364864168041038, 0.7863775522933658, 0.781422108017134, 0.7719368778230044, 0.7801589359541169, 0.7917615983813251, 0.7991890057412705, 0.7986659573673448, 0.7884371208413415, 0.7855953054452791, 0.8134703778223665, 0.7769965244402628, 0.851652154620116, 0.8804264767498129, 0.887799867079452 ], "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": [ 0.5139352083206177, 0.3525698482990265, 0.8365536173805594, 0.3803107887506485, 0.004738156683743, 0.1399143049493432, 0.4254396857282235, 0.596591986169898, 0.3459359054618556, 0.3437211620125524, 0.45883448841225405, 0.3885162614844159, 0.37404203322167245, 0.3842869442259865, 0.39672685869511304, 0.40932786201132454, 0.42152493821190873, 0.4340618747966894, 0.44602174475801404, 0.40760017704824786, 0.42667930806035465, 0.3690262452363467, 0.40720578843023586, 0.41590037424570153 ], "xaxis": "x2", "y": [ 0.8104050159454346, 0.4881714144721627, 0.2682372462004423, 0.38866316620260477, 0.6983593786135316, 0.8552484745159745, 0.7460297772297608, 0.8983092267471297, 0.6172875361931487, 0.8364864168041038, 0.7863775522933658, 0.781422108017134, 0.7719368778230044, 0.7801589359541169, 0.7917615983813251, 0.7991890057412705, 0.7986659573673448, 0.7884371208413415, 0.7855953054452791, 0.8134703778223665, 0.7769965244402628, 0.851652154620116, 0.8804264767498129, 0.887799867079452 ], "yaxis": "y2" } ], "layout": { "annotations": [ { "font": { "size": 14 }, "showarrow": false, "text": "Mean", "x": 0.25, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" }, { "font": { "size": 14 }, "showarrow": false, "text": "Standard Error", "x": 0.8, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" } ], "autosize": false, "height": 450, "hovermode": "closest", "legend": { "orientation": "h", "x": 0, "y": -0.25 }, "margin": { "b": 100, "l": 35, "pad": 0, "r": 35, "t": 35 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "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 08-10 23:17:35] ax.service.ax_client: Retrieving contour plot with parameter 'x3' on X-axis and 'x4' on Y-axis, for metric 'l2norm'. Remaining parameters are affixed to the middle of their range.\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "linkText": "Export to plot.ly", "plotlyServerURL": "https://plot.ly", "showLink": false }, "data": [ { "autocolorscale": false, "autocontour": true, "colorbar": { "tickfont": { "size": 8 }, "ticksuffix": "", "x": 0.45, "y": 0.5 }, "colorscale": [ [ 0.0, "rgb(247,252,253)" ], [ 0.125, "rgb(229,245,249)" ], [ 0.25, "rgb(204,236,230)" ], [ 0.375, "rgb(153,216,201)" ], [ 0.5, "rgb(102,194,164)" ], [ 0.625, "rgb(65,174,118)" ], [ 0.75, "rgb(35,139,69)" ], [ 0.875, "rgb(0,109,44)" ], [ 1.0, "rgb(0,68,27)" ] ], "contours": { "coloring": "heatmap" }, "hoverinfo": "x+y+z", "ncontours": 25, "type": "contour", "x": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "xaxis": "x", "y": [ 0.0, 0.02040816326530612, 0.04081632653061224, 0.061224489795918366, 0.08163265306122448, 0.1020408163265306, 0.12244897959183673, 0.14285714285714285, 0.16326530612244897, 0.18367346938775508, 0.2040816326530612, 0.22448979591836732, 0.24489795918367346, 0.26530612244897955, 0.2857142857142857, 0.3061224489795918, 0.32653061224489793, 0.3469387755102041, 0.36734693877551017, 0.3877551020408163, 0.4081632653061224, 0.42857142857142855, 0.44897959183673464, 0.4693877551020408, 0.4897959183673469, 0.5102040816326531, 0.5306122448979591, 0.5510204081632653, 0.5714285714285714, 0.5918367346938775, 0.6122448979591836, 0.6326530612244897, 0.6530612244897959, 0.673469387755102, 0.6938775510204082, 0.7142857142857142, 0.7346938775510203, 0.7551020408163265, 0.7755102040816326, 0.7959183673469387, 0.8163265306122448, 0.836734693877551, 0.8571428571428571, 0.8775510204081632, 0.8979591836734693, 0.9183673469387754, 0.9387755102040816, 0.9591836734693877, 0.9795918367346939, 1.0 ], "yaxis": "y", "z": [ [ 0.8775995683942623, 0.880240376514142, 0.8833396723613782, 0.88689687563091, 0.8909101885501374, 0.8953766213510126, 0.9002920269254198, 0.905651143133229, 0.9114476410289651, 0.9176741771750218, 0.9243224482271918, 0.9313832461158497, 0.9388465123992074, 0.9467013907229216, 0.9549362767656349, 0.9635388655586459, 0.9724961966113701, 0.9817946978183401, 0.9914202296306256, 1.0013581314022177, 1.011593272123394, 1.0221101078746913, 1.0328927482118797, 1.0439250332450072, 1.0551906223048118, 1.066673093685858, 1.0783560529120866, 1.0902232442376119, 1.1022586567602999, 1.1144466129259176, 1.1267718240344058, 1.1392193957422758, 1.1517747679213268, 1.1644235789691986, 1.1771514553487334, 1.189943741549989, 1.2027852003153203, 1.2156597229764594, 1.2285500912626193, 1.241437824335991, 1.2543031309640935, 1.267124971161604, 1.2798812181917556, 1.2925489025182968, 1.3051045144033508, 1.317524340613581, 1.3297848120859612, 1.3418628424642756, 1.3537361414012012, 1.3653834908718412 ], [ 0.8800760058286267, 0.8827309836747317, 0.8858424309853548, 0.8894097422340599, 0.8934311142704605, 0.8979035743965759, 0.9028230174760159, 0.9081842504156269, 0.9139810421395488, 0.9202061770662183, 0.9268515101123311, 0.9339080213898258, 0.9413658690309736, 0.9492144389632686, 0.9574423909433724, 0.9660377007254044, 0.9749876988529358, 0.984279107191965, 0.9938980749236742, 1.003830216247401, 1.0140606524571152, 1.0245740612941039, 1.0353547364759466, 1.0463866599685414, 1.0576535887824141, 1.0691391566778612, 1.0808269889719126, 1.0927008254967687, 1.1047446426506606, 1.116942760720992, 1.1292799181050286, 1.1417412912365463, 1.1543124400090818, 1.166979165233086, 1.179727277900591, 1.1925422979568578, 1.205409118141748, 1.2183116800478857, 1.2312327103261547, 1.2441535547768852, 1.2570541309958, 1.269913002034996, 1.2827075586674213, 1.2954142882521793, 1.3080091037301846, 1.3204677057665097, 1.3327659531837421, 1.344880220531878, 1.3567877261466508, 1.3684668188180165 ], [ 0.8829518761499742, 0.8856216404001448, 0.8887453444070701, 0.892322345863844, 0.8963508275335978, 0.9008278282382999, 0.9057492827353895, 0.9111100686879636, 0.9169040586950233, 0.9231241752228236, 0.92976244628289, 0.9368100598440136, 0.9442574152461994, 0.9520941702967547, 0.9603092832578448, 0.9688910495587615, 0.9778271337543885, 0.9871045979678765, 0.9967099287578589, 1.0066290649929637, 1.0168474298489096, 1.0273499704116573, 1.0381212085070795, 1.049145306192143, 1.0604061486992178, 1.0718874463226546, 1.0835728545027599, 1.0954461078956985, 1.1074911593279866, 1.1196923084178405, 1.132034298274782, 1.144502354112292, 1.1570821377990408, 1.1697596002191446, 1.1825207297894886, 1.1953512178905317, 1.2082360837396866, 1.221159314422699, 1.2341035752742453, 1.247050032240376, 1.2599783070154003, 1.2728665647710604, 1.2856917181893528, 1.2984297219457117, 1.3110559280214633, 1.32354547258693, 1.3358736681124581, 1.3480163786894546, 1.3599503615277049, 1.371653562735158 ], [ 0.8862278674080617, 0.8889131772206971, 0.8920493880278109, 0.8956358078408272, 0.8996705950936543, 0.9041507928615466, 0.9090723718383217, 0.9144302801414812, 0.9202184977513251, 0.9264300932445593, 0.9330572804718693, 0.9400914729650232, 0.9475233341459001, 0.9553428218439023, 0.9635392261972252, 0.9721012006964589, 0.9810167868951194, 0.990273434122904, 0.9998580163474944, 1.0097568490907405, 1.0199557099623218, 1.0304398668759376, 1.0411941182978064, 1.0522028498604816, 1.0634501112208423, 1.0749197159207833, 1.086595364866354, 1.09846079040268, 1.1104999123779837, 1.122696990004141, 1.1350367446974963, 1.14750442203842, 1.1600857597507588, 1.172766837497182, 1.1855338047858204, 1.1983725113859345, 1.2112680911722733, 1.2242045650539568, 1.2371645260350461, 1.2501289516287373, 1.2630771637223224, 1.275986932247515, 1.2888347019925603, 1.301595912734651, 1.3142453800731007, 1.3267577057006998, 1.3391076895605003, 1.3512707212317598, 1.3632231332827005, 1.3749425047767443 ], [ 0.8899036032903254, 0.8926053661905964, 0.8957544880889701, 0.8993502131118225, 0.9033906635734917, 0.9078728777459213, 0.9127928562838243, 0.9181456152378413, 0.9239252432967058, 0.9301249607271307, 0.9367371774473993, 0.9437535477936234, 0.9511650198241414, 0.9589618774585692, 0.9671337743546613, 0.9756697591695564, 0.984558292700966, 0.9937872583175569, 1.0033439680153573, 1.013215167322297, 1.0233870430602767, 1.0338452386091863, 1.0445748817463667, 1.055560630289384, 1.0667867405286608, 1.0782371625685918, 1.0898956647824383, 1.1017459859778098, 1.1137720077868019, 1.1259579307612928, 1.1382884264177981, 1.1507487271665073, 1.163324612514454, 1.176002259616115, 1.1887679515663858, 1.2016076720360254, 1.2145066470657815, 1.2274489109482671, 1.2404169674673375, 1.2533915947320329, 1.266351812056371, 1.2792750010130542, 1.2921371552991388, 1.3049132256993738, 1.317577524827695, 1.3301041587372768, 1.3424674569492874, 1.35464237783603, 1.3666048720122346, 1.3783321920776703 ], [ 0.8939776164859119, 0.8966968929887142, 0.8998594926587021, 0.9034645803137488, 0.9075102288417316, 0.9119934608374953, 0.9169102988304574, 0.9222558219001078, 0.9280242261521032, 0.9342088863221861, 0.9408024157126953, 0.947796721767695, 0.955183054870711, 0.962952048410777, 0.971093748803689, 0.9795976349602241, 0.9884526276318018, 0.9976470900911215, 1.0071688226637547, 1.0170050546506424, 1.0271424381056802, 1.0375670486988318, 1.0482643994564003, 1.0592194734764286, 1.0704167816812848, 1.0818404510848776, 1.0934743474776858, 1.1053022330686124, 1.117307953324554, 1.1294756369608634, 1.141789879010606, 1.154235862581079, 1.166799368009961, 1.179466628089717, 1.192224018860044, 1.2050576192264453, 1.217952711485692, 1.2308933119772414, 1.243861811297572, 1.256838774466638, 1.2698029168962233, 1.2827312435195837, 1.295599320988794, 1.3083816456413149, 1.3210520696526593, 1.3335842512315104, 1.3459520998312404, 1.3581301931199024, 1.3700941484011686, 1.3818209370357768 ], [ 0.8984473276975949, 0.9011853343697156, 0.9043621476220443, 0.9079768364490746, 0.9120274095710525, 0.9165108612420025, 0.9214232256333901, 0.9267596374598711, 0.9325143961508673, 0.938681030625643, 0.9452523616282502, 0.9522205586475667, 0.9595771887072206, 0.9673132547737994, 0.975419222202905, 0.9838850325101376, 0.9927001047899182, 1.0018533262605, 1.0113330346224823, 1.0211269961006149, 1.03122238411504, 1.0416057644273278, 1.0522630932829813, 1.0631797354956511, 1.0743405095436473, 1.0857297664255587, 1.0973315078313228, 1.1091295462346462, 1.1211077033100156, 1.1332500318847558, 1.145541029920267, 1.157965796205732, 1.1705100662101975, 1.1831600760498913, 1.1959022392480398, 1.2087226744289048, 1.2216066681286069, 1.234538174514163, 1.2474994389251322, 1.26047079668787, 1.2734306596972798, 1.2863556732322847, 1.2992210085380425, 1.312000750850608, 1.3246683435604778, 1.3371970535672144, 1.3495604285203828, 1.3617327226768143, 1.3736892741952367, 1.38540682264769 ], [ 0.9033090305027707, 0.9060671411479226, 0.9092590778288934, 0.9128837962889615, 0.9169392250436945, 0.9214223156419823, 0.9263291015488999, 0.9316547631940935, 0.9373936963231286, 0.943539580494235, 0.9500854444123581, 0.9570237248165162, 0.9643463158647256, 0.9720446064151145, 0.9801095032957663, 0.9885314395856875, 0.9973003680710408, 1.006405741342785, 1.0158364813881924, 1.0255809429006024, 1.0356268757857643, 1.045961393388236, 1.0565709537393961, 1.0674413616247054, 1.0785577994805, 1.0899048949837615, 1.1014668323454266, 1.1132275118436208, 1.125170756272346, 1.1372805513074848, 1.1495412877922921, 1.1619379506619545, 1.1744561830795803, 1.1870821626961992, 1.199802269390093, 1.212602587327821, 1.225468337376703, 1.2383833532816713, 1.2513296945400063, 1.2642874473362156, 1.2772347223790756, 1.2901478276740832, 1.3030015781933644, 1.3157696998785804, 1.3284252875591225, 1.3409412814416626, 1.3532909328366807, 1.3654482359752154, 1.3773883089200945, 1.3890877125762497 ], [ 0.90855788221, 0.9113376268490206, 0.9145457735151117, 0.918181146588742, 0.9222415772461021, 0.9267239584229641, 0.9316243085187477, 0.9369378412737935, 0.9426590387973292, 0.9487817243717669, 0.9552991314466599, 0.9622039652010864, 0.9694884532339244, 0.9771443823719171, 0.9851631192912351, 0.9935356136374799, 1.0022523835848807, 1.0113034852459792, 1.0206784689408204, 1.0303663269386676, 1.0403554387595972, 1.0506335213417917, 1.0611875922603424, 1.0720039547071287, 1.0830682131463403, 1.0943653284506962, 1.1058797206585447, 1.1175954254067686, 1.1294963046636488, 1.1415663006098735, 1.1537897009010578, 1.1661513564877652, 1.178636772385647, 1.1912319985416888, 1.203923295182054, 1.216696619386115, 1.2295370388189908, 1.2424281950716294, 1.2553519133670785, 1.2682880089594437, 1.281214295777965, 1.2941067720252395, 1.3069399423362167, 1.3196872326522426, 1.3323214569039277, 1.344815300123324, 1.3571417888111963, 1.369274725621877, 1.381189071573183, 1.3928612649829946 ], [ 0.914187900816032, 0.9169909621336876, 0.9202165820916848, 0.9238634351917616, 0.9279292372972052, 0.9324108055068209, 0.9373041269692559, 0.9426044339765258, 0.9483062821660169, 0.9544036282427506, 0.960889903346899, 0.9677580780816095, 0.975000715329982, 0.9826100073772612, 0.9905777945560801, 0.9988955636738335, 1.0075544258572018, 1.0165450751112313, 1.0258577307411565, 1.035482068677387, 1.0454071484991048, 1.0556213443940368, 1.0661122892917472, 1.076866841925213, 1.0878710866669226, 1.0991103757300058, 1.1105694226004905, 1.1222324536202772, 1.1340834195182588, 1.146106257039319, 1.1582851694115035, 1.1706048649652283, 1.1830506691755032, 1.1956084307550296, 1.2082641926939912, 1.2210036773407866, 1.2338116973999824, 1.246671620045664, 1.2595649820294095, 1.2724713045510305, 1.2853681112219226, 1.2982311221708807, 1.3110345830590275, 1.3237516849363469, 1.3363550341619264, 1.348817137283937, 1.36111087200183, 1.3732099215275615, 1.3850891557491072, 1.3967249485480169 ], [ 0.9201919681434182, 0.9230201750851824, 0.9262647053993185, 0.9299240651146429, 0.9339958362871692, 0.9384767419381811, 0.9433627202220866, 0.9486490050904228, 0.9543302101509912, 0.9604004119293283, 0.9668532283656, 0.9736818881755505, 0.9808792867287266, 0.9884380244159768, 0.9963504241537012, 1.004608525751842, 1.0132040563696396, 1.0221283781603603, 1.0313724163574833, 1.0409265733042887, 1.050780636045888, 1.060923686842532, 1.0713440271255437, 1.08202912591006, 1.0929656035499788, 1.1041392611019256, 1.1155351644543137, 1.1271377901770625, 1.1389312349167517, 1.150899478701894, 1.1630266711994097, 1.1752973801298991, 1.187696716120039, 1.2002102530574816, 1.2128237138397424, 1.2255224707277603, 1.2382909724618893, 1.2511122245504147, 1.2639674188428056, 1.276835759533994, 1.2896944882861985, 1.3025190818396994, 1.3152835816873611, 1.3279610126131667, 1.3405238500471046, 1.352944501689363, 1.3651957749298447, 1.3772513076557864, 1.3890859460233, 1.4006760586380025 ], [ 0.9265618392306434, 0.9294171574604374, 0.9326822025502896, 0.9363552937503465, 0.9404338606665321, 0.9449145133530217, 0.9497931220176985, 0.9550649035617719, 0.9607245115470721, 0.9667661256113185, 0.9731835358769032, 0.9799702175802594, 0.9871193910573799, 0.9946240624412683, 1.0024770410455763, 1.0106709305032504, 1.0191980923410615, 1.0280505827814157, 1.037220066065283, 1.046697710277906, 1.0564740742401384, 1.0665389961666856, 1.0768814961871143, 1.0874897052961294, 1.0983508328473115, 1.1094511834857061, 1.1207762325347066, 1.1323107659099976, 1.1440390850555207, 1.155945266083576, 1.1680134419718717, 1.180228048657754, 1.1925739528929118, 1.2050363850443333, 1.2176006486110076, 1.2302516532301235, 1.2429733773094789, 1.2557483800493967, 1.2685574544267837, 1.281379466841223, 1.294191387166086, 1.306968484870609, 1.3196846531979438, 1.33231282012666, 1.3448254073927577, 1.3571948038655013, 1.3693938253156062, 1.381396138466675, 1.3931766330542632, 1.4047117313745874 ], [ 0.9332881580541224, 0.9361726770292373, 0.9394599985247578, 0.9431482373929683, 0.9472346524172613, 0.9517157215758816, 0.9565872273963465, 0.9618443496094364, 0.9674817616231615, 0.9734937266775017, 0.979874188953338, 0.9866168544561198, 0.9937152562583819, 1.001162798769547, 1.008952776223764, 1.0170783616510026, 1.0255325643055784, 1.034308155881094, 1.0433975687438988, 1.0527927726349902, 1.062485139456918, 1.0724653084283047, 1.0827230656137417, 1.0932472523083607, 1.10402571588638, 1.1150453146565902, 1.1262919852099504, 1.1377508765401274, 1.149406548736272, 1.1612432228589222, 1.1732450502020237, 1.1853963450927458, 1.1976817069118073, 1.210085963710296, 1.2225939135133679, 1.2351899053263635, 1.2478573544588683, 1.2605783002044186, 1.2733330904668265, 1.2861002376485364, 1.2988564519714019, 1.3115768318386554, 1.3242351770240282, 1.3368043863166925, 1.349256902814507, 1.3615651743116663, 1.3737021014731277, 1.3856414520309794, 1.3973582248680967, 1.4088289534616973 ], [ 0.9403604796809326, 0.9432763961655026, 0.9465878987506905, 0.9502928813757205, 0.954388414352989, 0.958870824738328, 0.9637357873602731, 0.968978423742672, 0.9745934054084207, 0.9805750573036307, 0.9869174563724175, 0.9936145197057782, 1.0006600762758386, 1.0080479161730418, 1.0157718116394607, 1.0238255051973912, 1.0322026619433222, 1.040896785674409, 1.0499011018622728, 1.0592084143339622, 1.0688109464134783, 1.0787001806284464, 1.0888667132705718, 1.099300140619098, 1.1099889922675559, 1.120920723838675, 1.1320817767393863, 1.1434577066593712, 1.1550333747540802, 1.1667931844571378, 1.178721331261235, 1.1908020144122033, 1.2030195471755887, 1.215358310616431, 1.2278025327210629, 1.2403359285289632, 1.2529412808133302, 1.2656000541771153, 1.278292118239816, 1.290995622543016, 1.303687032487534, 1.3163413109348308, 1.3289322161019874, 1.34143268110529, 1.3538152408302153, 1.366052475076814, 1.3781174415178776, 1.389984077137821, 1.4016275521814805, 1.4130245660520828 ], [ 0.9477672989771537, 0.9507168969012321, 0.9540546099674313, 0.9577780962125985, 0.9618842210267405, 0.9663691424780343, 0.9712284079460389, 0.9764570593652055, 0.9820497435813162, 0.9880008234883394, 0.994304484776457, 1.000954832345484, 1.0079459698190136, 1.015272055276259, 1.0229273264871377, 1.0309060898075066, 1.0392026686702993, 1.0478113104241626, 1.056726054096176, 1.065940566226022, 1.0754479566993878, 1.085240590732512, 1.095309915966757, 1.1056463242783112, 1.1162390659801158, 1.1270762296313082, 1.1381447941129832, 1.1494307515504927, 1.1609192903759409, 1.1725950171642165, 1.1844421837503156, 1.1964448743715892, 1.2085871020733028, 1.2208527731760603, 1.233225507709146, 1.2456883445252191, 1.2582233943247938, 1.2708115168047445, 1.2834320874342875, 1.2960628941319203, 1.3086801762611493, 1.321258795999666, 1.3337725181489546, 1.3461943680710657, 1.3584970364238411, 1.3706533015169369, 1.382636443911739, 1.3944206325037396, 1.405981266343354, 1.4172952616080285 ], [ 0.9554960860225167, 0.9584817127001977, 0.9618477677448847, 0.9655916602359198, 0.9697100358607692, 0.9741988669533027, 0.979053554555386, 0.9842690399156964, 0.9898399219973069, 0.9957605766495432, 1.0020252721358887, 1.0086282747515747, 1.0155639374115386, 1.022826763497123, 1.030411438141993, 1.0383128197908436, 1.0465258865706053, 1.0550456349995097, 1.0638669328732107, 1.0729843335589357, 1.0823918647727473, 1.0920828102359363, 1.1020495062423743, 1.1122831760552763, 1.1227738225348536, 1.133510193451218, 1.1444798251827413, 1.1556691600309255, 1.1670637214604878, 1.1786483213820673, 1.1904072652496054, 1.2023245157569826, 1.2143837768909496, 1.2265684704774242, 1.2388615988075504, 1.2512455154626212, 1.263701652027431, 1.2762102605562304, 1.288750226650044, 1.3012989902366385, 1.3138325889168772, 1.3263258190951834, 1.3387524965056934, 1.351085790477966, 1.3632986039972903, 1.3753639726090165, 1.3872554581458094, 1.398947517268425, 1.4104158294065112, 1.4216375735286895 ], [ 0.9635333283988955, 0.9665573672448382, 0.9699539710905689, 0.9737202893124823, 0.9778527352398514, 0.9823470805773156, 0.9871985626106378, 0.9924020017659003, 0.9979519262197034, 1.0038426992730878, 1.0100686441176525, 1.0166241594790912, 1.0235038185139647, 1.0307024424227633, 1.0382151397809738, 1.0460373029232006, 1.0541645542397222, 1.0625926383159752, 1.07131726063036, 1.0803338798227473, 1.089637467647432, 1.0992222574077157, 1.1090815063948316, 1.1192072991450137, 1.1295904152310594, 1.1402202777336217, 1.1510849873836448, 1.1621714343566176, 1.1734654671130669, 1.1849520879860498, 1.1966156405002186, 1.2084399546124815, 1.2204084226701948, 1.2325039898093155, 1.2447090573569475, 1.2570053158781065, 1.269373542163991, 1.2817934052949311, 1.2942433262740303, 1.306700424398353, 1.3191405666538436, 1.331538519745658, 1.343868191578724, 1.3561029412067682, 1.3682159329127186, 1.3801805099865145, 1.391970565802147, 1.4035608931420596, 1.4149274968233962, 1.4260478591487913 ], [ 0.97186458051993, 0.9749294205456271, 0.9783588246148867, 0.982149674287288, 0.986298140411325, 0.9907997815214742, 0.9956496557973586, 1.00084244435312, 1.0063725827380274, 1.0122343964928804, 1.0184222354161419, 1.0249305998715423, 1.0317542510907216, 1.0388882961504882, 1.0463282374113476, 1.0540699761003185, 1.0621097609234504, 1.070444075623663, 1.0790694645975216, 1.0879823029508193, 1.097178525938945, 1.1066533411006803, 1.1164009525389238, 1.1264143287248873, 1.1366850415727403, 1.1472031952239814, 1.1579574492614813, 1.168935125424984, 1.180122372638501, 1.191504355851162, 1.2030654325758217, 1.2147892873491541, 1.2266590055193913, 1.2386570792631684, 1.2507653486215708, 1.2629648903049706, 1.2752358780682356, 1.2875574474721316, 1.2999076000524183, 1.3122631756471286, 1.3245999094716006, 1.3368925768788964, 1.349115217137986, 1.3612414196537115, 1.3732446519300516, 1.385098607544352, 1.3967775535842166, 1.4082566596563513, 1.4195122941453722, 1.4305222774425523 ], [ 0.9804745201427185, 0.9835825226672645, 0.9870469887267859, 0.9908645268296926, 0.9950310580933781, 0.9995419181377292, 1.004391973309287, 1.0095757492377198, 1.0150875688426197, 1.020921695842331, 1.0270724785417236, 1.033534487191434, 1.040302636565883, 1.047372283743693, 1.0547392896762184, 1.0624000324631535, 1.0703513609643727, 1.0785904801926667, 1.0871147654330835, 1.0959215103018183, 1.1050076242055984, 1.1143693050771053, 1.1240017212399314, 1.133898739113853, 1.1440527293940683, 1.1544544731764315, 1.165093173028466, 1.1759565556074612, 1.1870310364436583, 1.1983019083618627, 1.2097535157712083, 1.2213693872946774, 1.233132313927378, 1.245024372211906, 1.257026898733863, 1.269120426538107, 1.2812845998962858, 1.2934980906842979, 1.3057385432142958, 1.3179825716805955, 1.3302058261040064, 1.3423831318808, 1.3544886978976551, 1.3664963805476393, 1.3783799864303956, 1.390113594762949, 1.4016718809578075, 1.413030424814255, 1.4241659897783225, 1.4350567633073505 ], [ 0.9893470121428114, 0.9925004753106049, 0.9960022382860705, 0.9998486343276971, 1.0040353306896512, 1.0085574334824607, 1.0134096075922525, 1.018586209920063, 1.0240814333418937, 1.0298894577182125, 1.0360046029520622, 1.04242147747689, 1.0491351136606895, 1.0561410795502266, 1.0634355544170935, 1.0710153542114695, 1.078877893054035, 1.0870210692732414, 1.095443070126772, 1.104142098597736, 1.113116037802556, 1.1223620814427901, 1.1318763690519955, 1.1416536689639554, 1.1516871475157149, 1.1619682498240245, 1.1724866979803048, 1.1832305911660896, 1.194186574383486, 1.2053400332667275, 1.2166752748636858, 1.2281756672836586, 1.239823728462328, 1.25160116769256, 1.2634888890648388, 1.2754669668552296, 1.2875146048568122, 1.2996100961118509, 1.311730803235306, 1.323853179040643, 1.3359528418765236, 1.3480047118691811, 1.359983205706776, 1.3718624805744966, 1.3836167131919996, 1.3952203976650268, 1.4066486456791967, 1.4178774739430748, 1.4288840662473565, 1.439647000611508 ], [ 0.9984651795353856, 1.0016663013857374, 1.0052075300345922, 1.009084924377526, 1.0132938969240564, 1.0178293210666274, 1.0226856540659757, 1.0278570742898148, 1.0333376304211246, 1.039121399300149, 1.0452026477142493, 1.0515759917367054, 1.0582365451076474, 1.0651800457022746, 1.0724029465718017, 1.0799024558852428, 1.0876765092348264, 1.0957236594364415, 1.1040428744747701, 1.1126332443980047, 1.1214936122080004, 1.1306221596447381, 1.1400159920215995, 1.1496707722264627, 1.1595804493795954, 1.1697371122226519, 1.1801309744061235, 1.1907504742485817, 1.2015824517635463, 1.2126123562547562, 1.2238244413538348, 1.2352019192827952, 1.2467270654178986, 1.25838127894485, 1.2701451109431414, 1.2819982705774682, 1.2939196193997458, 1.3058871659053886, 1.3178780754705572, 1.3298687113524037, 1.3418347192097397, 1.3537511615344993, 1.3655927013984575, 1.3773338287031884, 1.3889491176318653, 1.4004135015142114, 1.4117025506773895, 1.4227927397132225, 1.4336616925392014, 1.4442883962664606 ], [ 1.0078114815859383, 1.0110623225562405, 1.0146450789594572, 1.018555539237685, 1.0227888635303546, 1.02733969278646, 1.0322022741561496, 1.0373706014767095, 1.0428385689020978, 1.0486001347174507, 1.0546494910440454, 1.060981233379329, 1.0675905216469532, 1.0744732216397672, 1.0816260125819581, 1.0890464434967932, 1.0967329191154063, 1.1046845967211143, 1.1129011804133393, 1.1213826101698223, 1.1301286595740445, 1.1391384753840275, 1.148410108985359, 1.1579400980413188, 1.167723151943478, 1.1777519766974456, 1.1880172480415958, 1.1985077133445783, 1.2092103809299493, 1.220110745670536, 1.2311930041861925, 1.2424402292675634, 1.2538344938824717, 1.265356951208342, 1.2769878836042639, 1.2887067325535269, 1.3004921193652403, 1.3123218665054395, 1.3241730311358304, 1.3360219631374906, 1.3478443979480714, 1.3596155901484677, 1.3713104881920035, 1.3829039453663061, 1.3943709579583174, 1.405686919063796, 1.4168278755504962, 1.4277707761258673, 1.4384936999529856, 1.4489760574536985 ], [ 1.0173677986744663, 1.0206702445270952, 1.0242964435054525, 1.0282419203539475, 1.0325015883454158, 1.0370698596892145, 1.0419407726682703, 1.047108134588354, 1.0525656789222035, 1.0583072340873094, 1.0643269000075002, 1.0706192268484716, 1.0771793879495397, 1.0840033359053425, 1.0910879270385019, 1.0984309955496285, 1.1060313554327208, 1.1138887075869999, 1.122003433840196, 1.1303762709768186, 1.1390078766769716, 1.1478983225171608, 1.1570465703559685, 1.1664499995627309, 1.1761040478616445, 1.1860020076720148, 1.1961349884661214, 1.206492023311252, 1.2170602736460487, 1.227825276351497, 1.2387711826387502, 1.2498809557367823, 1.2611365161938137, 1.272518840943511, 1.284008030054925, 1.29558335479039, 1.307223297627907, 1.3189055933448464, 1.3306072805118874, 1.342304773001778, 1.3539739597897325, 1.3655903381314893, 1.3771291808953379, 1.3885657344381666, 1.3998754397900306, 1.4110341675017735, 1.4220184554301176, 1.432805738870027, 1.443374563555649, 1.4537047738483504 ], [ 1.0271155233641571, 1.0304712495953114, 1.0341426192562442, 1.038124902717, 1.042412774763384, 1.047000425792308, 1.051881690061953, 1.0570501903272522, 1.062499497561057, 1.068223303594648, 1.074215603296507, 1.0804708811941022, 1.0869842950460185, 1.0937518456120134, 1.100770517682995, 1.1080383725909442, 1.1155545678762648, 1.1233192775419838, 1.1313334893970748, 1.139598667507681, 1.148116288884189, 1.1568872911150634, 1.165911493780396, 1.1751870709881775, 1.1847101477887834, 1.1944745690303773, 1.2044718527747582, 1.2146913035619187, 1.2251202344835572, 1.2357442371322083, 1.2465474451784777, 1.2575127559608692, 1.268621997153157, 1.279856043887136, 1.2911949007548806, 1.30261776377547, 1.314103074319998, 1.325628574269034, 1.3371713705607187, 1.3487080167978258, 1.3602146183979191, 1.371666965358501, 1.3830406933802115, 1.394311470548633, 1.4054552036945958, 1.416448256371216, 1.4272676692776325, 1.4378913738908603, 1.448298390874752, 1.4584690062874035 ], [ 1.0370356568894519, 1.0404460956948474, 1.0441641403570612, 1.048184818400811, 1.0525025770202325, 1.0571113946081128, 1.0620049095399842, 1.0671765657616863, 1.0726197741689358, 1.0783280879836745, 1.0842953892082754, 1.090516081606284, 1.096985283293859, 1.103699008669744, 1.110654324866702, 1.1178494622712727, 1.1252838527638809, 1.132958065298603, 1.1408736099208965, 1.1490325925698772, 1.1574372262638706, 1.1660892364356499, 1.174989229739282, 1.1841361139024411, 1.1935266517265304, 1.203155204545197, 1.2130136785558974, 1.223091645965552, 1.233376584511116, 1.243854169479984, 1.2545085605783017, 1.2653226458678608, 1.2762782283078788, 1.287356159361371, 1.2985364341751975, 1.3097982645030632, 1.3211201427021357, 1.3324799067211215, 1.3438548137699389, 1.3552216290570618, 1.3665567346442413, 1.3778362614932977, 1.3890362451771354, 1.4001328029055005, 1.4111023269697567, 1.4219216878171612, 1.4325684389151516, 1.4430210153816838, 1.453258918935434, 1.4632628828842902 ], [ 1.0471089100344548, 1.0505752208639487, 1.0543411875772348, 1.0584016081712266, 1.0627507152216114, 1.0673822873577594, 1.0722897780724834, 1.0774664615990421, 1.0829055950930202, 1.0886005956542733, 1.094545229697479, 1.100733810651825, 1.107161398686825, 1.1138239927959883, 1.1207187007948416, 1.127843866507313, 1.1351991262623804, 1.1427853609424052, 1.1506045094249557, 1.1586592198308818, 1.1669523401020188, 1.175486286190496, 1.1842623633114768, 1.193280137810601, 1.2025369527844734, 1.2120276491016637, 1.2217445061298962, 1.2316773705446924, 1.2418139114854456, 1.2521399316848227, 1.262639674171842, 1.2732960852653141, 1.2840910183006327, 1.295005381671644, 1.3060192454329493, 1.3171119232155732, 1.3282620438167185, 1.3394476231155195, 1.3506461439607371, 1.361834649651097, 1.3729898550046586, 1.3840882772319492, 1.3951063867241766, 1.4060207756220742, 1.4168083399656752, 1.4274464696345421, 1.4379132393509135, 1.4481875937851316, 1.4582495202168226, 1.4680802031375575 ], [ 1.0573158071397513, 1.060838851767376, 1.0646537015375763, 1.068754939585779, 1.0731365984423364, 1.0777922711332746, 1.0827152395872435, 1.087898620229046, 1.093335526202116, 1.0990192450336551, 1.1049434296228056, 1.1111022990144146, 1.1174908432474882, 1.1241050232594796, 1.1309419519447814, 1.1380000357157403, 1.1452790476985228, 1.1527800960712975, 1.1605054486713493, 1.1684581845684403, 1.1766416698736921, 1.1850588960787056, 1.1937117617333282, 1.2026004039494957, 1.2117226817375741, 1.2210738782086252, 1.2306466364362916, 1.2404310940206738, 1.2504151500287803, 1.260584790342576, 1.270924409149308, 1.2814170865091683, 1.292044805807294, 1.3027886138836065, 1.3136287375208655, 1.324544673095818, 1.3355152643197135, 1.3465187792952849, 1.357532994670036, 1.36853529210335, 1.3795027703365754, 1.3904123744189067, 1.4012410418556267, 1.4119658636318955, 1.4225642564030345, 1.4330141408373742, 1.4432941202980922, 1.4533836538160778, 1.4632632176092013, 1.4729144501546376 ], [ 1.0676367917742413, 1.0712171146442877, 1.0750814992897115, 1.0792243295713544, 1.0836394536697855, 1.088320294557916, 1.0932599776569163, 1.0984514756694468, 1.1038877701922618, 1.1095620291433101, 1.115467798186257, 1.1215992030201525, 1.1279511573440573, 1.134519568093739, 1.1413015246529696, 1.1482954517052755, 1.1555011963771231, 1.1629200112356544, 1.1705543904900755, 1.1784077251794174, 1.186483770693767, 1.1947859645422911, 1.2033166792935126, 1.2120765241718523, 1.221063804091479, 1.2302742070806927, 1.2397007350755778, 1.249333840594452, 1.2591616997486887, 1.2691705453837492, 1.2793449972451059, 1.289668348979852, 1.3001227954903765, 1.3106896026852601, 1.3213492324650205, 1.332081439298504, 1.3428653533759582, 1.3536795618505235, 1.3645021960852626, 1.3753110299375912, 1.3860835919417784, 1.3967972924888834, 1.4074295655055191, 1.417958022625656, 1.4283606165051084, 1.4386158088713803, 1.4487027382416855, 1.4586013820334693, 1.4682927080249615, 1.4777588107358195 ], [ 1.078052332459089, 1.0816901468520774, 1.0856043921678276, 1.089789269113151, 1.0942384578976787, 1.0989452278825849, 1.1039025642113227, 1.1091033114980309, 1.114540334292645, 1.1202066935220532, 1.1260958373177867, 1.1322018034092731, 1.138519428305349, 1.145044555376041, 1.1517742290984305, 1.1587068555639841, 1.1658422998316076, 1.1731818805947294, 1.1807282170081566, 1.1884848899363525, 1.1964559079524717, 1.2046450153734016, 1.2130549296687099, 1.2216866259209733, 1.2305387809851345, 1.2396074503699142, 1.248885992868289, 1.2583652042611315, 1.2680335892872574, 1.2778776951524, 1.2878824437217755, 1.2980314226090581, 1.3083071185618043, 1.3186910943832897, 1.3291641211183824, 1.3397062809731621, 1.3502970555456588, 1.360915410832852, 1.3715398869669333, 1.3821486976283701, 1.3927198417663824, 1.4032312284591646, 1.4136608142544507, 1.4239867510320374, 1.4341875413217622, 1.4442421971546915, 1.4541303979918858, 1.4638326431044046, 1.4733303939691424, 1.4826062027526459 ], [ 1.088543026750098, 1.0922382070600454, 1.0962023026691223, 1.1004293474609215, 1.1049128703633417, 1.1096460040262952, 1.1146216102160005, 1.119832422054803, 1.125271202903447, 1.130930921194709, 1.1368049397816822, 1.142887217189638, 1.149172516277875, 1.1556566127903982, 1.1623364914950054, 1.1692105104348276, 1.1762785041097172, 1.1835417857983896, 1.1910030028587104, 1.1986658056122865, 1.2065343185180175, 1.2146124501760291, 1.2229031298337325, 1.2314075888282894, 1.2401248000620262, 1.2490511485861113, 1.258180348400605, 1.267503567306797, 1.2770096900462216, 1.2866856443847507, 1.296516728626232, 1.3064869015666822, 1.3165790181910584, 1.3267750114013948, 1.3370560301361711, 1.3474025481074605, 1.3577944569333418, 1.3682111547724556, 1.3786316383001944, 1.3890346029076932, 1.3993985536471765, 1.4097019276338263, 1.419923227187136, 1.4300411618332283, 1.4400347963506106, 1.4498837013401116, 1.4595681023709226, 1.4690690236232076, 1.478368422113026, 1.4874493090136578 ], [ 1.0990897019844719, 1.102841782131189, 1.106855378082024, 1.1111243731893472, 1.115642161807461, 1.1204017568900475, 1.1253959139861902, 1.130617271792405, 1.1360585090996331, 1.1417125175031806, 1.1475725885190975, 1.153632612604428, 1.159887285733678, 1.1663323162070764, 1.1729646196534724, 1.179782483100053, 1.1867856693709957, 1.193975422559069, 1.201354328967785, 1.208925994561185, 1.2166945276366268, 1.224663862461012, 1.2328370096261039, 1.2412153486606157, 1.2497980729542688, 1.2585818581758637, 1.2675607695117013, 1.2767263718336757, 1.2860679763922918, 1.2955729519720556, 1.305227041374296, 1.3150146453518101, 1.3249190571333689, 1.3349226466839499, 1.3450070034607913, 1.3551530503722133, 1.3653411416162724, 1.375551154885784, 1.3857625855072242, 1.3959546472943147, 1.406106382592709, 1.416196782202167, 1.4262049144859414, 1.4361100619084246, 1.44589186242082, 1.4555304525251542, 1.4650066084987574, 1.4743018821636718, 1.4833987277336114, 1.4922806166389273 ], [ 1.1096735110816933, 1.1134816888212593, 1.117544098678974, 1.1218544895538556, 1.1264061377443155, 1.1311919533830048, 1.1362046029081831, 1.1414366477345483, 1.1468806989718596, 1.1525295875705206, 1.1583765485492157, 1.1644154168121978, 1.1706408302200182, 1.1770484326163753, 1.1836350648618996, 1.1903989250038989, 1.1973396694743434, 1.2044584173332844, 1.2117576140056958, 1.2192407179617106, 1.2269117006006864, 1.234774394185692, 1.2428317695282167, 1.251085252702589, 1.2595341846933608, 1.2681754915886694, 1.2770035809989824, 1.2860104325997719, 1.2951858217636143, 1.3045176091731914, 1.3139920406104433, 1.3235940204573668, 1.3333073418209564, 1.3431148711135934, 1.3529986940641194, 1.3629402341498096, 1.3729203548109068, 1.3829194551108215, 1.3929175659927704, 1.4028944517510948, 1.4128297191601584, 1.4227029349780924, 1.43249375122001, 1.4421820365956504, 1.4517480117666692, 1.4611723855689631, 1.470436489055456, 1.4795224041422106, 1.4884130837754888, 1.4970924608570204 ], [ 1.1202760219517909, 1.1241391686162339, 1.128249378517932, 1.1326002818541292, 1.1371850530552239, 1.1419965159911587, 1.1470272648128463, 1.1522698005752618, 1.157716683468486, 1.1633607000016128, 1.1691950437406962, 1.1752135070270884, 1.1814106792292016, 1.1877821441106247, 1.194324664315272, 1.201036334313464, 1.2079166745498753, 1.2149666307769864, 1.2221884383428698, 1.2295853188738908, 1.2371610022801838, 1.244919107841015, 1.2528624602607277, 1.2609924410880728, 1.2693084708712632, 1.2778076848063957, 1.2864848179466164, 1.2953322727037906, 1.3043403144373338, 1.313497334272476, 1.3227901274851221, 1.3322041527214108, 1.3417237547576695, 1.351332347224213, 1.3610125603719478, 1.3707463630344412, 1.380515168691649, 1.3902999343288756, 1.4000812587028948, 1.409839484399065, 1.4195548060704293, 1.4292073856260523, 1.4387774738797234, 1.4482455372292142, 1.4575923872567647, 1.4667993106866128, 1.47584819688608, 1.484721660039816, 1.4934031532490828, 1.5018770720873145 ], [ 1.1308792992946506, 1.1347959743062046, 1.1389526572318367, 1.1433428749261356, 1.1479597157203147, 1.1527959333406563, 1.1578440660218954, 1.163096570924567, 1.1685459736292216, 1.1741850319744154, 1.1800069127248256, 1.1860053783331312, 1.1921749791381588, 1.1985112433578584, 1.2050108527584924, 1.2116717856056987, 1.218493400769302, 1.2254764295553566, 1.2326228392964482, 1.2399355411174582, 1.2474179380224164, 1.2550733456658478, 1.2629043546987104, 1.2709122245476316, 1.2790963939939577, 1.287454165605157, 1.2959805803621833, 1.3046684605271286, 1.3135085741769315, 1.3224898676224055, 1.3315997188168407, 1.340824179103225, 1.3501481859323399, 1.3595557415919641, 1.3690300611116106, 1.3785536966132246, 1.3881086464837817, 1.3976764569976337, 1.4072383223657696, 1.416775187290288, 1.4262678543261886, 1.4356970968605867, 1.445043777344865, 1.454288969532423, 1.4634140828436368, 1.4724009865644994, 1.4812321313629522, 1.489890665558573, 1.498360543689864, 1.5066266251683451 ], [ 1.1414659778527045, 1.1454344472298696, 1.1496359815939559, 1.1540640193841847, 1.1587115781213315, 1.1635713569752377, 1.1686358540466986, 1.1738974984129733, 1.179348796625993, 1.1849824928103982, 1.1907917406787563, 1.1967702844996755, 1.202912644082696, 1.2092142958665493, 1.2156718378890934, 1.2222831206510114, 1.2290473192061724, 1.2359649161491342, 1.2430375643421636, 1.250267807136881, 1.2576586554527212, 1.2652130523194645, 1.2729332861823617, 1.2808204316384104, 1.2888738923829062, 1.2970910972903829, 1.3054673660071052, 1.3139959273657564, 1.3226680518465428, 1.3314732517210546, 1.3403995071487826, 1.3494334879994263, 1.358560754200629, 1.3677659284170196, 1.3770328423949898, 1.3863446623923474, 1.395684000522745, 1.4050330185240398, 1.414373529224141, 1.4236870994128077, 1.4329551562873053, 1.4421590983005521, 1.4512804101610537, 1.4603007809138675, 1.4692022234441293, 1.4779671933611107, 1.4865787050160932, 1.4950204423620064, 1.5032768624572488, 1.5113332896301683 ], [ 1.1520193264831695, 1.1560375844894717, 1.1602820760897123, 1.1647461657733225, 1.169422815007499, 1.1743046833785047, 1.1793842439222382, 1.1846539126113977, 1.1901061915750757, 1.1957338250410028, 1.201529966105454, 1.207488351095459, 1.213603476280741, 1.2198707687656734, 1.2262867393356196, 1.2328490998948443, 1.2395568226204694, 1.246410113938819, 1.2534102771346487, 1.2605594465184802, 1.267860195325714, 1.2753150458510165, 1.2829259354611608, 1.2906937061305566, 1.2986176818536406, 1.3066953786807072, 1.3149223634742973, 1.3232922495171209, 1.331796797643462, 1.3404260838511317, 1.3491686969840961, 1.3580119389742624, 1.3669420109158226, 1.375944177798215, 1.3850029115807236, 1.39410201628114, 1.403224740400303, 1.4123538820599852, 1.4214718913810491, 1.4305609733879188, 1.4396031934268096, 1.4485805859105212, 1.4574752662304415, 1.4662695449243328, 1.4749460426445364, 1.483487804115064, 1.4918784090745885, 1.5001020781566683, 1.5081437717387125, 1.515989279977486 ], [ 1.1625233027222672, 1.166589095800925, 1.1708744021619588, 1.1753725263162003, 1.1800763878473421, 1.1849786210323947, 1.1900716880772504, 1.1953480058314498, 1.2008000854186054, 1.206420683586275, 1.21220296363989, 1.2181406624387499, 1.2242282579206054, 1.2304611288035983, 1.2368356943972365, 1.2433495180350074, 1.2500013533183565, 1.2567911098555427, 1.2637197170962282, 1.2707888738246345, 1.278000687674155, 1.285357230795838, 1.292860057997392, 1.3005097447113931, 1.3083054994112953, 1.3162448892893683, 1.3243236946984553, 1.3325358846228572, 1.3408736885895627, 1.349327732858716, 1.3578872097259784, 1.3665400553373754, 1.3752731200839345, 1.3840723237410923, 1.3929227936381638, 1.401808987951262, 1.4107148080207113, 1.4196237039629835, 1.4285187773398276, 1.437382883710478, 1.446198736831573, 1.4549490152645717, 1.463616471292781, 1.4721840413713192, 1.4806349568358645, 1.488952853266022, 1.4971218767195225, 1.5051267850061234, 1.5129530422365371, 1.5205869050428253 ], [ 1.1729625978015819, 1.1770734499813311, 1.1813972061929574, 1.1859271244038456, 1.1906560958348085, 1.1955767429414794, 1.2006815303841847, 1.2059628887283995, 1.2114133501523288, 1.2170256947603808, 1.2227931051178167, 1.2287093252114676, 1.2347688180683738, 1.2409669136187849, 1.2472999350852734, 1.2537652885201462, 1.2603614969217758, 1.2670881591387007, 1.2739458165338091, 1.2809357188835968, 1.2880594953887299, 1.2953187544029503, 1.3027146514524701, 1.3102474736826044, 1.317916286611808, 1.3257186765222526, 1.3336506031305775, 1.3417063581582542, 1.3498786110489105, 1.3581585158835492, 1.3665358532958214, 1.3749991857798638, 1.3835360115357906, 1.3921329086961352, 1.4007756671186504, 1.4094494084753846, 1.4181386972478718, 1.4268276458487863, 1.4355000168763723, 1.444139324845798, 1.452728938905254, 1.4612521872079705, 1.4696924628709276, 1.4780333308503086, 1.4862586346147877, 1.49435260119548, 1.5022999430237274, 1.5100859549189918, 1.5176966046433618, 1.5251186155781324 ], [ 1.1833226723292951, 1.1874759113660178, 1.1918355566181258, 1.1963948323575664, 1.2011466142450553, 1.2060835255297346, 1.2111980455574665, 1.2164826301936373, 1.2219298432641732, 1.2275324974035904, 1.2332838016868959, 1.2391775120185073, 1.2452080783619395, 1.2513707804784575, 1.2576618409968634, 1.2640785017289982, 1.270619046962448, 1.2772827572541499, 1.2840697805102697, 1.2909809149618863, 1.2980173108047217, 1.3051801115492927, 1.3124700686221145, 1.3198871693248622, 1.327430316416718, 1.3350970877262414, 1.3428835893935314, 1.3507844009526455, 1.3587925983733509, 1.366899834534351, 1.3750964554828882, 1.3833716338269404, 1.3917135056979533, 1.4001093031250356, 1.4085454782167541, 1.4170078187608586, 1.4254815567212844, 1.433951471890366, 1.4424019929774092, 1.450817297991915, 1.4591814151493225, 1.467478324850898, 1.4756920626660455, 1.4838068227240893, 1.491807060524766, 1.4996775939040548, 1.5074037007372236, 1.514971211912307, 1.5223665981508245, 1.5295770493724377 ], [ 1.1935897830565445, 1.1977825666782451, 1.2021753708213256, 1.2067613982666534, 1.211533521131879, 1.2164843751251182, 1.2216064653773624, 1.226892283314237, 1.2323344334955926, 1.2379257686099006, 1.2436595297922037, 1.249529488069111, 1.255530080971423, 1.2616565362108634, 1.267904971945958, 1.2742724609557026, 1.2807570447042915, 1.287357683816855, 1.2940741349543088, 1.3009067510972354, 1.307856212387495, 1.314923206080656, 1.3221080838729031, 1.3294105298643708, 1.336829270931239, 1.344361853594801, 1.3520044998432952, 1.3597520420250941, 1.3675979268766145, 1.3755342727538042, 1.3835519624728876, 1.3916407559191464, 1.3997894102865633, 1.4079858000579182, 1.4162170326277321, 1.4244695583101252, 1.4327292752605323, 1.440981630715645, 1.4492117201600387, 1.4574043858044978, 1.465544315312612, 1.473616141184763, 1.481604540697189, 1.4894943358521813, 1.4972705924499932, 1.504918717151624, 1.512424551261696, 1.5197744599140988, 1.526955415378254, 1.5339550733075424 ], [ 1.2037510013063377, 1.2079803430424454, 1.2124034326370658, 1.2170134628848084, 1.221803313532049, 1.2267656434050322, 1.2318929933433194, 1.2371778992526632, 1.2426130140369374, 1.2481912364164514, 1.253905843637648, 1.2597506237834366, 1.2657200017904922, 1.2718091514297543, 1.278014083596784, 1.2843316996717984, 1.2907597980498335, 1.2972970229798706, 1.303942748308239, 1.3106968948964342, 1.3175596888577867, 1.32453137681616, 1.3316119219091853, 1.338800708051408, 1.346096278779399, 1.3534961310442457, 1.3609965752310158, 1.3685926628633998, 1.3762781751667654, 1.3840456603634017, 1.3918865056191856, 1.3997910303959684, 1.4077485905472908, 1.4157476857433289, 1.423776065894529, 1.4318208346883055, 1.4398685500031216, 1.4479053218740834, 1.455916909014319, 1.4638888148317308, 1.4718063835874178, 1.47965489694749, 1.4874196707734129, 1.495086151630745, 1.5026400122031072, 1.5100672445892176, 1.5173542503371875, 1.5244879260279338, 1.531455743248672, 1.5382458218878605 ], [ 1.2137942237501227, 1.2180570179393184, 1.222507401387317, 1.2271385676591406, 1.2319434144125667, 1.236914633213851, 1.2420448093526528, 1.247326530828922, 1.2527525051186943, 1.2583156815782444, 1.2640093763821367, 1.2698273956893895, 1.2757641513111717, 1.2818147616008693, 1.2879751288042938, 1.2942419830430802, 1.3006128829564512, 1.3070861643668923, 1.3136608316306222, 1.3203363916780377, 1.327112637617178, 1.3339893959461822, 1.3409662572369863, 1.3480423130325274, 1.3552159207537235, 1.3624845138121193, 1.3698444670546601, 1.3772910198861403, 1.384818252638336, 1.3924191071449825, 1.400085440423747, 1.4078081005508163, 1.41557701551963, 1.423381288287818, 1.4312092936627032, 1.4390487747289442, 1.4468869379977352, 1.4547105473503255, 1.4625060172556754, 1.4702595057965413, 1.4779570078720154, 1.4855844486652985, 1.4931277771531106, 1.500573059140031, 1.5079065690586757, 1.5151148796000475, 1.5221849481327772, 1.529104198833312, 1.5358605994745902, 1.5424427319005904 ], [ 1.2237081762796036, 1.228001221955376, 1.2324758134216145, 1.2371251549863658, 1.2419421715888324, 1.246919596118299, 1.2520500659063172, 1.2573262274356174, 1.2627408477429447, 1.268286930266639, 1.273957831982248, 1.2797473775814487, 1.2856499652198876, 1.291660657092653, 1.297775246988932, 1.30399029633494, 1.3103031304518717, 1.3167117882446049, 1.3232149215803364, 1.3298116451858177, 1.336501343495913, 1.3432834465601566, 1.3501571916176673, 1.3571213891462381, 1.3641742114505044, 1.371313018310176, 1.378534228720895, 1.3858332416157877, 1.393204402943173, 1.400641012517723, 1.4081353620300707, 1.4156787953464554, 1.423261783269425, 1.430874006662691, 1.438504443735182, 1.4461414589613593, 1.4537728923973519, 1.4613861489911109, 1.4689682879267485, 1.4765061121813985, 1.4839862584056602, 1.4913952870558185, 1.4987197724765777, 1.5059463924051588, 1.5130620161731565, 1.5200537907378342, 1.5269092235873603, 1.5336162615350133, 1.540163364441526, 1.5465395729759113 ], [ 1.2334824117453964, 1.2378024351906303, 1.2422980771223249, 1.246962561760267, 1.251788849781439, 1.2567697229691905, 1.2618978772046432, 1.2671660227312371, 1.272566990068424, 1.2780938392581522, 1.2837399692916331, 1.2894992235989682, 1.2953659864445244, 1.3013352640660178, 1.3074027436068794, 1.3135648225765608, 1.31981860203626, 1.3261618382337137, 1.3325928501572764, 1.3391103843502965, 1.345713442886399, 1.3524010848963715, 1.3591722155356911, 1.3660253779662601, 1.3729585633540482, 1.3799690511584988, 1.3870532877335702, 1.39420680641653, 1.4014241878140679, 1.4086990556310697, 1.4160241014630945, 1.4233911314444612, 1.430791128191909, 1.4382143226760904, 1.4456502720762068, 1.4530879410173543, 1.4605157846742016, 1.4679218329827566, 1.4752937756466982, 1.4826190478141865, 1.4898849163079644, 1.497078566185935, 1.5041871872502286, 1.5111980599527017, 1.5180986399939815, 1.5248766407989582, 1.531520112982662, 1.538017519899224, 1.5443578083910747, 1.5505304739202352 ], [ 1.243107302327913, 1.2474509781667324, 1.2519644622962316, 1.2566410072105463, 1.261473616887735, 1.2664551286160706, 1.2715783023407436, 1.2768359163702678, 1.2822208677478026, 1.2877262749455485, 1.2933455797843358, 1.2990726446421936, 1.30490184015592, 1.3108281178458128, 1.3168470615667331, 1.3229549116176265, 1.3291485559546437, 1.3354254844410942, 1.3417837045038499, 1.3482216198230685, 1.3547378773864756, 1.361331191800128, 1.3680001584772006, 1.3747430686305675, 1.3815577385610576, 1.3884413636390545, 1.3953904040778544, 1.4024005057812357, 1.4094664559388648, 1.416582170205625, 1.4237407065319219, 1.43093430002579, 1.4381544134250253, 1.445391798531734, 1.4526365649985082, 1.4598782539018722, 1.4671059144310643, 1.4743081826830966, 1.4814733619781844, 1.48858950432479, 1.4956444927216241, 1.5026261239380754, 1.509522191312654, 1.5163205669887558, 1.5230092828949429, 1.5295766096907892, 1.536011132847765, 1.5423018250225755, 1.5484381139056902, 1.5544099447883182 ], [ 1.252574027276892, 1.2569379980334296, 1.2614660848112862, 1.2661515759499091, 1.2709875254383896, 1.2759668317914772, 1.281082323647274, 1.2863268508566645, 1.2916933793297687, 1.2971750873102748, 1.302765460077373, 1.308458379359865, 1.3142482030517537, 1.3201298302420532, 1.326098746252032, 1.332151042475659, 1.3382834065111322, 1.3444930794740932, 1.350777779517042, 1.3571355933078075, 1.3635648402299196, 1.3700639168999518, 1.3766311317391833, 1.3832645403582882, 1.3899617921904825, 1.3967199972022835, 1.4035356189516248, 1.410404397257438, 1.4173213008329404, 1.4242805078563177, 1.4312754108599652, 1.4382986415602692, 1.4453421112059477, 1.4523970624811795, 1.4594541297254453, 1.4665034050235866, 1.4735345084346558, 1.480536661190301, 1.4874987610784527, 1.4944094594491941, 1.5012572393696653, 1.5080304944524656, 1.5147176078258426, 1.5213070306344918, 1.5277873593814717, 1.5341474113602345, 1.540376297391, 1.5464634910719348, 1.5523988937833533, 1.558172894740479 ], [ 1.261874556712123, 1.2662554508132668, 1.270794887263151, 1.275486197055264, 1.280322490100674, 1.2852967310565429, 1.2904018211122001, 1.2956306844566388, 1.3009763576817097, 1.306432079838068, 1.311991380274697, 1.317648160793733, 1.3233967681021768, 1.329232052129652, 1.3351494056210393, 1.3411447806331334, 1.3472146782837473, 1.35335610939339, 1.359566525510795, 1.365843722092898, 1.3721857180582246, 1.3785906181948122, 1.3850564665969314, 1.3915811001140217, 1.3981620105613823, 1.4047962232109177, 1.411480197093749, 1.4182097502773612, 1.4249800109322974, 1.4317853930183055, 1.438619594008431, 1.4454756112946463, 1.4523457737159426, 1.4592217848750086, 1.4660947753905973, 1.4729553618110294, 1.4797937104714745, 1.4865996050400572, 1.49336251683537, 1.5000716772103009, 1.5067161514032537, 1.513284913285613, 1.519766920412149, 1.5261511887347008, 1.5324268662891323, 1.538583305125612, 1.5446101307323388, 1.5504973082071427, 1.5562352044618395, 1.5618146457992679 ], [ 1.2710016321243955, 1.275396080358606, 1.2799436163777527, 1.284637619916896, 1.289471261985667, 1.2944375775840031, 1.2995295436554535, 1.3047401609775273, 1.3100625382583393, 1.3154899762303196, 1.3210160490272775, 1.3266346796376713, 1.3323402058019258, 1.3381274324417383, 1.3439916666678606, 1.3499287317068243, 1.3559349567988048, 1.3620071412875892, 1.3681424927190131, 1.3743385406656716, 1.3805930299915494, 1.3869037990861166, 1.393268649945378, 1.3996852176275163, 1.4061508464469517, 1.4126624793288542, 1.4192165652025848, 1.4258089874432383, 1.4324350144777587, 1.439089272020626, 1.445765735167767, 1.4524577378235424, 1.459157996635682, 1.4658586466708008, 1.4725512863556085, 1.4792270296135526, 1.4858765635463866, 1.492490210379537, 1.4990579926754535, 1.5055697010129387, 1.512014963441076, 1.51838331606255, 1.5246642741035852, 1.5308474028066588, 1.5369223874545896, 1.5428791018125994, 1.5487076742677899, 1.5543985509573297, 1.5599425552095458, 1.5653309426757567 ], [ 1.2799487441581678, 1.284353394627422, 1.2889057977779124, 1.293599387502089, 1.2984274004205008, 1.3033829454517565, 1.3084590779506102, 1.3136488771097614, 1.318945524931401, 1.324342384654308, 1.3298330760939954, 1.335411544953945, 1.3410721228458826, 1.346809574582072, 1.3526191293463712, 1.3584964926860768, 1.364437836947554, 1.3704397688232866, 1.3764992740464417, 1.3826136408548082, 1.3887803654782556, 1.3949970443688704, 1.4012612589753806, 1.4075704593925251, 1.4139218531075919, 1.420312304347058, 1.4267382483261557, 1.4331956232267873, 1.4396798212031616, 1.4461856583431238, 1.452707362439837, 1.45923857671831, 1.4657723773075566, 1.4723013021911173, 1.478817389518766, 1.485312223428153, 1.4917769858290053, 1.498202512887421, 1.5045793551810356, 1.5108978406649098, 1.5171481396946347, 1.5233203314084887, 1.5294044707893462, 1.5353906557245687, 1.541269093372084, 1.5470301651335445, 1.552664489538841, 1.5581629823645247, 1.563516913343963, 1.568717958879614 ], [ 1.2887101081985357, 1.2931216398175949, 1.297675708668094, 1.3023658075984446, 1.3071852427601565, 1.3121272000294648, 1.3171848153827785, 1.3223512479350084, 1.3276197540016106, 1.3329837601802417, 1.3384369330893122, 1.3439732430823867, 1.3495870190240544, 1.355272991118636, 1.3610263188857314, 1.3668426017291277, 1.3727178701826326, 1.3786485568412765, 1.3846314471565493, 1.3906636115983184, 1.3967423220252595, 1.4028649562949258, 1.4090288960211774, 1.4152314228227705, 1.421469618341641, 1.427740272761453, 1.434039805622996, 1.4403642015639924, 1.446708962378921, 1.4530690756576021, 1.4594389993354318, 1.4658126608338156, 1.4721834690929314, 1.4785443376637024, 1.4848877170713022, 1.4912056348200362, 1.4974897416174795, 1.5037313626068172, 1.509921552579955, 1.5160511542855706, 1.5221108590429937, 1.528091268930548, 1.5339829598454524, 1.5397765447428737, 1.5454627363645215, 1.5510324087712704, 1.55647665700622, 1.5617868542378377, 1.5669547057704332, 1.5719722993602767 ] ], "zauto": true, "zmax": 1.5719722993602767, "zmin": -1.5719722993602767 }, { "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": [ [ 0.08718683628751886, 0.08467878648372147, 0.08220954996020192, 0.0797763985141304, 0.07737597544777967, 0.07500438119402879, 0.07265728074082455, 0.07033003092901491, 0.06801782495521347, 0.06571585082973497, 0.06341946015849524, 0.0611243434595527, 0.05882670829567512, 0.05652345679637714, 0.0542123596417198, 0.05189222427013283, 0.04956305594593218, 0.04722621138644983, 0.04488454593343668, 0.042542556815320806, 0.040206526964479024, 0.0378846762041586, 0.03558732940691015, 0.033327114207625706, 0.03111920316592028, 0.02898161468264824, 0.02693557856282742, 0.025005946325883436, 0.0232215673310616, 0.021615439744210665, 0.020224273083534, 0.019086917709566366, 0.018241107326761763, 0.017718436920401582, 0.017538622119109528, 0.01770529494384717, 0.018205586566604003, 0.01901391931119703, 0.020098148323879232, 0.021425429347682462, 0.02296616800501412, 0.024695817654539296, 0.026595107489584775, 0.02864942006478797, 0.030847848711102306, 0.03318223316924863, 0.03564630571044884, 0.03823498781857224, 0.04094383563425354, 0.04376861761589628 ], [ 0.08542258720063256, 0.08288149323456466, 0.08038174646956148, 0.07792073975572625, 0.0754951938606896, 0.07310123890363729, 0.07073451896593, 0.06839031813420221, 0.06606370539835374, 0.06374969514368561, 0.06144341949157046, 0.05914030848722308, 0.05683627411948839, 0.05452789438443647, 0.052212594060695124, 0.04988881953667426, 0.047556205912346376, 0.045215735702268785, 0.042869889833160216, 0.04052279333973991, 0.03818036035031876, 0.03585044580026727, 0.033543015010815184, 0.03127034689415173, 0.02904729169139542, 0.026891608114703484, 0.02482440280573662, 0.02287067613175897, 0.021059920551550846, 0.019426585408948597, 0.01800997888692783, 0.016852850399744324, 0.01599771815542997, 0.015480529473466308, 0.015322951618726627, 0.015526714211493705, 0.016073529895042828, 0.016930958861322006, 0.01806091056564523, 0.019426842277992164, 0.020997809624628112, 0.022749670878712425, 0.024664580645068476, 0.026729775582165716, 0.028936246208448972, 0.031277558209620276, 0.03374889956407168, 0.036346347029076305, 0.03906631894410648, 0.04190517906394351 ], [ 0.08371567037512365, 0.0811420076991858, 0.07861240947624996, 0.07612443430717458, 0.07367492580437456, 0.07126008882704347, 0.06887559032669827, 0.06651668332362817, 0.06417835160812238, 0.06185547196649371, 0.059542990128024456, 0.057236106256271686, 0.054930465689275544, 0.052622350774330605, 0.050308870038426864, 0.04798814157472031, 0.04565946840353636, 0.043323504694168125, 0.04098241315423788, 0.03864001569853905, 0.03630194186261642, 0.03397578258175429, 0.03167126125528712, 0.029400439807680704, 0.027177984802889663, 0.025021526518172462, 0.022952148080484704, 0.020995030734109143, 0.019180228213551864, 0.01754339654422528, 0.016125994836904693, 0.014973984218698947, 0.01413366428284158, 0.013643858592648009, 0.013526143591321314, 0.013778090078970998, 0.014374411203442402, 0.015275676547071683, 0.016439158818101745, 0.017826690111294098, 0.019408083874823463, 0.021161321509703266, 0.023071194657372094, 0.02512755254873092, 0.027323697266669528, 0.029655096988213312, 0.03211841807105485, 0.0347108216281725, 0.037429464883380684, 0.040271158547280875 ], [ 0.0820664941086561, 0.07946065182735207, 0.07690177662739643, 0.07438764157320357, 0.07191526299543706, 0.06948097041022437, 0.06708050252578397, 0.06470912822291428, 0.0623617903779418, 0.06003326948550623, 0.05771836330220612, 0.05541207822375934, 0.05310982786353275, 0.050807634336806934, 0.048502328076084796, 0.04619174260377528, 0.043874901565820114, 0.041552196492880195, 0.03922555524232769, 0.0368986029721701, 0.03457681997275298, 0.032267704008426525, 0.02998094940235212, 0.02772866141531077, 0.025525632821378545, 0.023389719242811535, 0.021342356782701747, 0.019409257288113154, 0.01762126173884655, 0.016015165660502824, 0.014633954584413831, 0.013525269095310221, 0.012736424534155062, 0.012305140221418528, 0.01224853329913229, 0.01255691136632274, 0.013197582766161793, 0.014126404582778846, 0.015299654574894576, 0.01668111875383004, 0.018244124393369122, 0.019970580748721045, 0.021848945945818744, 0.023872173477334648, 0.026036028960668846, 0.028337834475571175, 0.03077557590307596, 0.03334728593101705, 0.036050628427836386, 0.03888263012933932 ], [ 0.08047525153545937, 0.07783751717135054, 0.07524983756790908, 0.07271025290613096, 0.07021600657374817, 0.06776360752307703, 0.06534892021210342, 0.06296728150138037, 0.060613642777577026, 0.05828273454396595, 0.05596924983769329, 0.05366804217150441, 0.051374333305884916, 0.049083926070602156, 0.046793417690342586, 0.044500409634164934, 0.04220371090538371, 0.03990353292661433, 0.03760167578377087, 0.03530170764315626, 0.03300914178348602, 0.030731619118757263, 0.028479108658518566, 0.026264144410110726, 0.024102124799606148, 0.022011708424639027, 0.020015342395111668, 0.018139940870857196, 0.016417653771716605, 0.014886455339027481, 0.013589846005972068, 0.012574336369246805, 0.011883150949157392, 0.011546155010551925, 0.011570018466084037, 0.011935488064116264, 0.012604761054566585, 0.013534062303369957, 0.014684000017378684, 0.016024408902643585, 0.017534728407384848, 0.01920221177721225, 0.021019624426413922, 0.0229832049739445, 0.025091107759388047, 0.027342300672380474, 0.029735819035615053, 0.03227027645073977, 0.034943556353259485, 0.03775263200380932 ], [ 0.07894196093617271, 0.07627250627197141, 0.07365637597703173, 0.0710919338033572, 0.06857670891555674, 0.06610744929380549, 0.06368020419428082, 0.061290435664262136, 0.05893315793867906, 0.056603102398046834, 0.05429490473474261, 0.05200331014033282, 0.04972339176470433, 0.04745077746468571, 0.04518187999654794, 0.042914126338170086, 0.040646182768796627, 0.038378173700303324, 0.03611189406226845, 0.03385101733018384, 0.03160130411244108, 0.029370819657760724, 0.0271701727477977, 0.025012792972642722, 0.022915267222279948, 0.02089775575330904, 0.018984493786782162, 0.017204333979705097, 0.015591154777254508, 0.014183688340037264, 0.013023896963603647, 0.012152705116492378, 0.011602493395971723, 0.011388200863583393, 0.011501991643916335, 0.011915986852686803, 0.012591971773955558, 0.013492134091855129, 0.014585910529993692, 0.015852096071157607, 0.01727788009057969, 0.01885667775001239, 0.020585901294593718, 0.022465143473362575, 0.02449486295793125, 0.026675502103676356, 0.029006927549701352, 0.03148809524475264, 0.03411686739136591, 0.03688993336259446 ], [ 0.07746651525597895, 0.07476538391047419, 0.07212102211848098, 0.06953217724763268, 0.06699672719560543, 0.06451172327731257, 0.062073463560936654, 0.05967759743023705, 0.057319260935502096, 0.054993241242810284, 0.052694167300714974, 0.0504167228180653, 0.04815587688507202, 0.04590712715842231, 0.04366675054122764, 0.04143205677312055, 0.039201641340627015, 0.036975635641267435, 0.03475595438349961, 0.03254654274388552, 0.030353628731755948, 0.02818598927580559, 0.02605524111863167, 0.02397616816199248, 0.021967091892352457, 0.02005027309668374, 0.018252285478220002, 0.016604197952306658, 0.015141210523879114, 0.013901116653030272, 0.01292078514681586, 0.012230255907968007, 0.011845598865445004, 0.011763879334262841, 0.01196392522769275, 0.012413298443937869, 0.013077684817448549, 0.01392819077074547, 0.014944627724029954, 0.01611545751999024, 0.017435970069606486, 0.018905978184710813, 0.02052773774501171, 0.02230435693757813, 0.02423871017487713, 0.026332766594848223, 0.028587218844734117, 0.031001312211357254, 0.03357280106150658, 0.03629798522005354 ], [ 0.07604874025607126, 0.07331583772244264, 0.07064331548129488, 0.06803036785551717, 0.06547528845654459, 0.06297550081130851, 0.06052762066024619, 0.05812755165282437, 0.0557706149429907, 0.05345171184823717, 0.05116551738734876, 0.04890670127438294, 0.04667017194610401, 0.044451338559172, 0.042246385721779446, 0.040052556110388327, 0.037868437125364425, 0.03569424937531394, 0.033532136994246946, 0.031386462409046266, 0.02926411077003731, 0.027174810946028836, 0.02513147893174964, 0.023150582020759636, 0.0212525010197917, 0.019461820461123564, 0.017807384474593603, 0.016321802443671513, 0.015039895706962625, 0.013995486650058911, 0.013216286070847523, 0.012717794994569936, 0.012498754129649878, 0.01254112117029301, 0.012815414579464746, 0.013288952679147622, 0.013933211889921075, 0.01472799932040152, 0.015662336497359403, 0.016733154921199197, 0.017943023540687785, 0.01929776946976543, 0.020804453893341495, 0.022469874093009552, 0.024299587500959886, 0.02629736693699815, 0.028464969367300072, 0.03080210956109751, 0.03330655532642871, 0.03597428866244709 ], [ 0.07468846037066894, 0.07192354730863691, 0.06922277672195631, 0.06658585612876793, 0.06401156556784085, 0.061497774028570734, 0.05904148848914512, 0.05663893841433588, 0.05428569738180485, 0.05197684211279386, 0.04970714768312759, 0.04747131621749955, 0.04526423507778085, 0.04308125960689581, 0.04091851503717447, 0.03877321234552291, 0.03664397371696182, 0.03453116485700191, 0.03243723351187875, 0.03036705577603828, 0.028328293140587817, 0.026331761878047612, 0.02439180869711041, 0.02252666623675648, 0.020758718459569822, 0.019114525414619613, 0.017624329810094107, 0.0163206171861093, 0.015235239504053005, 0.014394890065322416, 0.013815604000102687, 0.01349825362313136, 0.013427597460365528, 0.013576110249101662, 0.013911158544732957, 0.01440242087899636, 0.0150270373015894, 0.015771721101344123, 0.016632398821620847, 0.017612382841552556, 0.018719959353921324, 0.019965991308887897, 0.021361878962651282, 0.02291802999315401, 0.024642858498825256, 0.026542247623492058, 0.028619368436332095, 0.03087474065961768, 0.03330643708737489, 0.035910359803294635 ], [ 0.07338557099106198, 0.07058826061775865, 0.06785898775291092, 0.06519804173474862, 0.06260476308491285, 0.060077543616107044, 0.05761385965064007, 0.05521034250118868, 0.05286288929184521, 0.050566815799016965, 0.04831705135774381, 0.04610837414678813, 0.04393568351307717, 0.04179430462368087, 0.03968031984324905, 0.03759092099767146, 0.03552477719385164, 0.03348241406306231, 0.03146660184892691, 0.029482750846144337, 0.027539311629943126, 0.02564817116194685, 0.02382501879294748, 0.022089619952400972, 0.020465869193030686, 0.018981391538326262, 0.01766633875933587, 0.01655096543766159, 0.015661748528281297, 0.015016447507461493, 0.014619532610233325, 0.014460134848908205, 0.014514071072521331, 0.014749523866471588, 0.015134111539946002, 0.01564083623794423, 0.016251552822711596, 0.016957924848975316, 0.017760543215098443, 0.0186669976253317, 0.019689532438957203, 0.02084271891096624, 0.02214141613118973, 0.023599173382495005, 0.025227130600093375, 0.02703339513925405, 0.029022817184892153, 0.03119705859828906, 0.03355484941029295, 0.03609234387948397 ], [ 0.07214011555764373, 0.0693098760246797, 0.06655167846554648, 0.06386646438422112, 0.06125421166327048, 0.05871391605636714, 0.05624360567568816, 0.05384039408690347, 0.051500576750331276, 0.049219774214350656, 0.04699312373356834, 0.04481551897448761, 0.0426818953746219, 0.04058755677244989, 0.0385285373750722, 0.036501992190935514, 0.03450660882722448, 0.03254303390193086, 0.030614307691988137, 0.028726299739390223, 0.02688813347859683, 0.025112575231833214, 0.02341633553907354, 0.021820180421246095, 0.02034867106219964, 0.019029252311408156, 0.01789034480372539, 0.01695818386164809, 0.0162525568339939, 0.015782356702241457, 0.01554262005716152, 0.01551469078518316, 0.015669937951375255, 0.0159757661695042, 0.01640177768867574, 0.0169243617302951, 0.017529056273328528, 0.018210909067334347, 0.018973439902658467, 0.019826807349183875, 0.020785641722304387, 0.021866863772540282, 0.02308770694174593, 0.024464089287287875, 0.026009418466680482, 0.027733850017980493, 0.02964396072598278, 0.031742756602614226, 0.03402991638924355, 0.03650217520229943 ], [ 0.07095236551513176, 0.06808852818774473, 0.06530081822930275, 0.0625909005295708, 0.05995946934433264, 0.05740620875762692, 0.054929785184932314, 0.05252787912374336, 0.05019726279922563, 0.04793392918851217, 0.0457332761365692, 0.04359034698601394, 0.041500126513386346, 0.03945788825212881, 0.03745958678474866, 0.03550228656350784, 0.033584617386055275, 0.03170724560559626, 0.029873348717031737, 0.02808907740967028, 0.026363980388567246, 0.024711348330962127, 0.02314839789716668, 0.02169615955340661, 0.02037885798300402, 0.01922251050473972, 0.018252493102497293, 0.017490055108750194, 0.016948280766331245, 0.016628649992546363, 0.016519662052946874, 0.016598459723131755, 0.016835146028864195, 0.017198354619047344, 0.017660372471055483, 0.018200687957271137, 0.018807661864333327, 0.019478600542911145, 0.020218726740447848, 0.021039514852514117, 0.021956741345715906, 0.02298849387732579, 0.024153312471323095, 0.025468592658050022, 0.02694934305900032, 0.028607345404966032, 0.030450714148829668, 0.032483806260887045, 0.03470740088763113, 0.037119058321782875 ], [ 0.06982290087597329, 0.06692467543826637, 0.06410670996732945, 0.0613714637656605, 0.05872042770039289, 0.05615406117188889, 0.05367175908121345, 0.051271857679462844, 0.048951688086195606, 0.04670768541190423, 0.044535559717095094, 0.04243053249923725, 0.04038763915616577, 0.038402094191276694, 0.03646971214017147, 0.03458737363819432, 0.03275352287788615, 0.03096867971078226, 0.029235945929266857, 0.027561478867746826, 0.02595489304655469, 0.024429527504318805, 0.02300247820621759, 0.02169424161373911, 0.020527761748728116, 0.019526662185706176, 0.018712554737398454, 0.018101627817531146, 0.01770120649342132, 0.01750739934713891, 0.017504905589996587, 0.017669359946936074, 0.01797158693637603, 0.018382469084673295, 0.018877155448664196, 0.01943786016272765, 0.020055106425201412, 0.020727672957447325, 0.02146164288839643, 0.02226892523135455, 0.023165526398476164, 0.024169764293838207, 0.02530056401298699, 0.0265759453146551, 0.02801179029392255, 0.029620951049586283, 0.031412718192019594, 0.033392628537681095, 0.03556255519740815, 0.037921003570122756 ], [ 0.06875268883948432, 0.06581918612708125, 0.06297008426115297, 0.060208706462588225, 0.057537420485158454, 0.05495754968633008, 0.05246931069350886, 0.05007178823395872, 0.04776295824629528, 0.04553977004792956, 0.043398296867417065, 0.04133396134572076, 0.039341838712845356, 0.03741703548465757, 0.03555513607904018, 0.03375270414704209, 0.03200781994876933, 0.030320629679059827, 0.028693876451240007, 0.027133373825694397, 0.025648368320593844, 0.024251713734025897, 0.02295974564993645, 0.021791704843000543, 0.020768535416424705, 0.01991092352909212, 0.01923660687598006, 0.018757301872930624, 0.018475975839655868, 0.018385394143357988, 0.018468643261170606, 0.01870167417451044, 0.01905718076559907, 0.019508749825143473, 0.02003433270613973, 0.020618509773415283, 0.021253467234061532, 0.021938901396730534, 0.022681172854717303, 0.023492010689225892, 0.024386993709956603, 0.025383966773370573, 0.026501506148408505, 0.027757525639038858, 0.029168101419425344, 0.030746575630522573, 0.03250297116170823, 0.034443715614291506, 0.036571639408062594, 0.038886189512873856 ], [ 0.06774315762672435, 0.06477342101843357, 0.06189219056599192, 0.059103719769705285, 0.05641133204998891, 0.05381730371744992, 0.05132276849159574, 0.048927655726737414, 0.046630675918046365, 0.04442936748967294, 0.04232021789432631, 0.04029886936456385, 0.03836041513214525, 0.03649978571878677, 0.03471221740961887, 0.03299378683041952, 0.031341987212379185, 0.029756313672181223, 0.02823881623004507, 0.026794568983432212, 0.025431989677954375, 0.024162923894587036, 0.023002383216683683, 0.021967806271741584, 0.021077719202504577, 0.020349747047375428, 0.019798106532636937, 0.019430982911447486, 0.019248450190491043, 0.019241647027213198, 0.019393637382638128, 0.01968184754299581, 0.020081459397766704, 0.020568915740821137, 0.021124812300851024, 0.021735776404082044, 0.02239527393053528, 0.023103516691199942, 0.023866731007554084, 0.024696034629841056, 0.025606112399327807, 0.026613824594238597, 0.027736844012183633, 0.028992398212445925, 0.030396182727269072, 0.0319614992608055, 0.033698653973059406, 0.03561462513253247, 0.037712981834178996, 0.03999401270033158 ], [ 0.06679626241342354, 0.06378930847342704, 0.06087488220875818, 0.058058228676544206, 0.05534370231454339, 0.052734619982729485, 0.05023312859313389, 0.04784010084556618, 0.0455550751206686, 0.043376257124887144, 0.04130060077414722, 0.03932398344128795, 0.0374414856879093, 0.03564777793134168, 0.03393760657583423, 0.032306360765605724, 0.030750689075418763, 0.029269123970319836, 0.027862661043122548, 0.026535229407383596, 0.025293978127695398, 0.02414929066903834, 0.023114427630991388, 0.022204697299587548, 0.021436084183748035, 0.020823355175294107, 0.020377827032617295, 0.020105187874030914, 0.02000392210969258, 0.020064863942772494, 0.020272140015505414, 0.020605348352780332, 0.021042457024398272, 0.021562756334842725, 0.022149293153319004, 0.02279046436718283, 0.023480714710839817, 0.0242204722568265, 0.025015532652290555, 0.025876097731097697, 0.02681563089083745, 0.02784964538402046, 0.02899450844567822, 0.03026632554048354, 0.031679959085822135, 0.03324822723412351, 0.03498131533442031, 0.03688641429850325, 0.03896757886896906, 0.04122577924986608 ], [ 0.06591453998216326, 0.062869408805243, 0.059920691383556386, 0.05707467827544014, 0.05433682448336919, 0.05171157131184755, 0.04920217370919496, 0.046810547568973335, 0.044537155402602495, 0.042380951878735466, 0.04033941199771972, 0.03840866312458638, 0.036583736933587845, 0.034858948188945825, 0.03322839455664393, 0.03168655639682654, 0.030228959349882373, 0.028852847264785996, 0.02755780004648253, 0.02634622104362612, 0.025223611751679077, 0.024198548201920297, 0.023282276006733327, 0.022487857206463315, 0.021828845834057916, 0.021317556480487682, 0.02096312413847985, 0.02076970274374864, 0.020735240506743222, 0.020851219211280442, 0.021103526225124736, 0.02147431555512659, 0.021944444474277205, 0.022495956861184992, 0.023114150027746878, 0.023788951170752713, 0.024515544605114552, 0.025294349040841862, 0.026130515223675686, 0.027033116020838948, 0.028014168813014776, 0.029087592205853222, 0.030268169696987115, 0.0315705748454304, 0.03300850237151787, 0.03459394219517019, 0.03633662432884399, 0.038243649893324495, 0.040319308165727805, 0.04256506417101903 ], [ 0.0651011484919023, 0.06201696383270463, 0.05903288986286191, 0.05615630673690245, 0.053393830950082946, 0.050751105534815384, 0.04823258433651457, 0.045841325203736516, 0.043578812558063375, 0.041444834946105076, 0.03943744651063219, 0.03755304130353577, 0.03578656456250537, 0.0341318746240749, 0.03258225321623285, 0.031131041883031126, 0.029772360768146666, 0.028501846033881624, 0.027317326779434162, 0.026219353621190083, 0.02521149022226771, 0.02430028645726687, 0.02349486859096099, 0.022806111232696054, 0.02224540461415778, 0.02182310606970178, 0.021546864694853056, 0.021420109345221417, 0.021441043065169307, 0.021602437659221638, 0.02189235381002523, 0.022295674238506834, 0.022796125551067026, 0.023378364128169356, 0.024029741631789257, 0.02474151050664744, 0.025509404457360652, 0.026333664051341323, 0.027218643759029524, 0.028172144490759565, 0.0292045923814099, 0.030328153637310142, 0.031555849284431205, 0.03290071626096627, 0.03437505098565743, 0.03598976480117422, 0.03775387413229434, 0.039674139760300146, 0.04175485906004467, 0.04399780364725601 ], [ 0.06435988861512626, 0.06123592734755573, 0.05821553064185109, 0.05530719980551725, 0.052518761931637244, 0.049857128921386475, 0.04732803683977516, 0.044935779982792114, 0.04268296163866931, 0.040570291297047624, 0.038596464313357066, 0.03675816252750221, 0.03505021071026242, 0.03346591224462287, 0.03199756788566104, 0.03063715555024026, 0.029377120618138464, 0.028211200161356552, 0.027135185882627172, 0.026147523216869896, 0.025249649973824433, 0.024445996911282627, 0.023743603036340388, 0.023151338385383798, 0.022678776116421384, 0.02233481501566777, 0.02212622155455519, 0.022056325472631432, 0.022124136147304636, 0.022324111897293095, 0.022646691747806747, 0.023079515048735032, 0.023609077984713674, 0.02422248129367843, 0.02490894371634327, 0.025660867551905893, 0.026474386134241742, 0.027349439395573976, 0.02828948519472734, 0.02930096622661718, 0.03039263611119626, 0.03157482311981353, 0.03285868724464675, 0.03425551003030701, 0.03577604649274222, 0.03742996230866705, 0.03922537465543011, 0.04116850963858289, 0.04326348233342789, 0.0455121974292764 ], [ 0.06369520228115119, 0.060530972013143954, 0.05747346530352573, 0.05453232092398337, 0.05171661038452288, 0.049034567374723954, 0.046493281562100405, 0.04409836964032433, 0.04185364632668161, 0.03976082903257234, 0.03781932012371178, 0.036026116936752256, 0.03437589838146903, 0.0328613249616291, 0.03147356533730233, 0.030203029221324215, 0.02904024885302409, 0.027976817099358366, 0.027006267150357786, 0.026124772678053125, 0.025331560768435343, 0.024628961485989344, 0.024022062364997845, 0.02351798581844174, 0.023124855310355463, 0.022850558976415587, 0.022701458647856373, 0.02268122846788953, 0.022790029852510503, 0.02302421247308968, 0.023376648255746764, 0.02383766184933705, 0.02439636722760733, 0.02504212567752181, 0.025765844686830217, 0.02656092493945462, 0.027423782192649807, 0.028353971268608, 0.029353995714625544, 0.030428901385162882, 0.03158574144217968, 0.0328329801129839, 0.03417988302907125, 0.03563592730466735, 0.0372102551773286, 0.03891118962979311, 0.04074582693630017, 0.04271971773054554, 0.04483664389108874, 0.047098493080578875 ], [ 0.06311214546899219, 0.05990746823124713, 0.05681233165495223, 0.053837510529429235, 0.050993335808461486, 0.04828939722268935, 0.045734192342125723, 0.043334732287546134, 0.04109612643509228, 0.03902118333915046, 0.037110080368987976, 0.035360166075227406, 0.033765961677336406, 0.03231941621853099, 0.031010441464320016, 0.029827709887020864, 0.028759649714392727, 0.027795526186439438, 0.02692646919449382, 0.026146302529932948, 0.025452051887142137, 0.024844054217253005, 0.02432565066384996, 0.023902505478808934, 0.023581640537302082, 0.023370302807131992, 0.02327479544302998, 0.023299414563397274, 0.023445648089298023, 0.023711792811861747, 0.024093098003863896, 0.024582434057287883, 0.02517134759380896, 0.02585126794094316, 0.026614620279153352, 0.027455669773251156, 0.02837102209598982, 0.029359792827463545, 0.03042350892926904, 0.03156582110359847, 0.032792099141501566, 0.034108966556994656, 0.035523814604880806, 0.037044323212092785, 0.03867800826674239, 0.04043181024453172, 0.042311736752816055, 0.04432256967327943, 0.04646764505689396, 0.04874871030675795 ], [ 0.06261633201081185, 0.05937143088016761, 0.056238506309761, 0.053229447847007186, 0.05035583887641033, 0.04762863625063683, 0.045057777036562115, 0.042651718567047324, 0.040416932476823514, 0.03835739265339182, 0.03647411855165299, 0.03476485381141498, 0.03322396790540286, 0.0318426577195898, 0.030609492041573566, 0.029511287442319307, 0.028534239649669016, 0.02766517626934765, 0.026892760534061325, 0.02620847225817871, 0.025607223914808918, 0.025087530807055926, 0.024651230793041788, 0.024302821208792288, 0.024048528831677678, 0.02389524323766795, 0.02384943325553412, 0.023916153871638167, 0.02409825578605143, 0.02439592252478179, 0.024806642261425187, 0.025325642480208372, 0.025946694760442604, 0.02666309861949761, 0.02746863077513484, 0.028358298697393935, 0.029328823018069283, 0.030378849169124526, 0.0315089339337381, 0.03272136812439047, 0.03401989289676866, 0.035409355231329376, 0.03689533525393915, 0.038483767919271564, 0.04018057508847768, 0.04199132064600953, 0.04392089980379782, 0.04597327281851156, 0.048151251963343716, 0.05045634821089729 ], [ 0.062213846295042494, 0.058929430687780296, 0.055759017584916144, 0.05271556890232922, 0.04981188878196701, 0.04706028497588025, 0.04447213728007599, 0.04205737389864094, 0.03982387328826696, 0.037776833001100935, 0.03591817588292319, 0.03424609118976132, 0.032754823262052556, 0.031434811621723624, 0.030273246267212547, 0.029255033139963988, 0.02836408193163371, 0.027584754094493933, 0.026903264669523478, 0.026308830287328732, 0.025794398836247828, 0.025356874558118244, 0.024996847179327528, 0.02471791951115646, 0.024525779007971035, 0.02442716204611113, 0.02442882661789212, 0.02453661304212914, 0.024754664889269248, 0.025084902655213993, 0.025526850078432178, 0.026077863497767063, 0.026733712504118774, 0.02748936293269757, 0.028339778574886842, 0.02928059395821559, 0.030308581625352975, 0.03142190321840413, 0.03262017431683018, 0.03390438825325257, 0.03527674288398776, 0.036740405749298405, 0.03829924344446247, 0.039957533402623466, 0.041719671532926134, 0.04358988687944198, 0.04557197371788322, 0.047669051222451346, 0.049883360139932886, 0.05221610430013592 ], [ 0.061911124171079045, 0.0585884684887135, 0.05538141554832731, 0.0523039357921939, 0.04936999618416025, 0.04659320861301704, 0.043986365402819666, 0.04156085636536473, 0.03932598035112221, 0.03728819303114127, 0.035450369617113814, 0.03381119872858567, 0.032364847845549265, 0.031101035206542088, 0.030005596185245415, 0.02906154664281903, 0.028250541401175982, 0.02755453347444747, 0.026957387164899423, 0.026446200322132195, 0.02601214702423244, 0.02565074838088668, 0.02536159314589486, 0.025147630473521455, 0.02501421282847785, 0.024968061134723506, 0.02501627037036203, 0.0251654140264269, 0.02542078343995623, 0.025785820512139634, 0.026261829356729643, 0.02684803091802338, 0.02754194440671966, 0.028339987805350287, 0.029238144855025464, 0.030232564782959725, 0.03132001682710762, 0.032498177946067575, 0.03376576886136986, 0.03512256900452556, 0.03656934209056882, 0.03810769870035861, 0.03973991569518846, 0.0414687270970986, 0.04329709798796153, 0.04522799172862047, 0.04726414064091318, 0.04940783040275233, 0.05166070809123995, 0.054023622658826244 ], [ 0.06171480327764799, 0.05835581280097745, 0.055113598454833226, 0.05200305476360771, 0.04903922707799523, 0.046236952323910174, 0.04361036797003519, 0.04117227641132793, 0.038933371863846704, 0.03690137023855126, 0.03508012795430748, 0.03346888458945018, 0.03206179924430241, 0.030847949264732343, 0.029811906174826614, 0.028934899588908523, 0.028196451660585715, 0.027576252669617184, 0.02705598798401471, 0.026620833574450234, 0.0262604068259181, 0.025969073875281346, 0.025745647524976743, 0.02559262570558719, 0.025515182247349208, 0.025520108748094544, 0.025614833706080926, 0.025806562442372488, 0.02610154216704232, 0.026504476455608685, 0.027018154440727915, 0.027643363699665455, 0.028379099562197394, 0.029223002121862914, 0.03017190039656483, 0.031222345208406065, 0.03237105204038975, 0.03361522160083679, 0.03495273910513433, 0.03638226936128672, 0.03790326848617903, 0.03951593083667094, 0.041221086000191164, 0.043020057686756936, 0.04491449475890874, 0.04690618424080326, 0.048996856417307624, 0.05118799245497827, 0.053480644842132406, 0.055875280048421544 ], [ 0.061631546379901654, 0.05823880401015672, 0.05496359817113328, 0.05182164449079694, 0.04882895712372977, 0.04600148670411627, 0.04335460959828417, 0.04090244812935951, 0.038657022166432485, 0.03662726991106754, 0.03481802952662119, 0.03322913404661272, 0.031854818701151234, 0.03068364395952567, 0.029699077123787523, 0.028880752046495026, 0.028206273572028904, 0.027653301791211227, 0.027201583916654802, 0.02683461419937769, 0.026540685243757415, 0.026313225168470743, 0.026150465219784192, 0.026054613255763814, 0.026030777536027176, 0.026085867555986946, 0.0262276101068708, 0.02646371528744332, 0.0268011709444607, 0.027245657778688682, 0.02780112682232955, 0.028469605514589005, 0.029251265963227642, 0.03014472104006205, 0.031147459119865537, 0.03225631577051126, 0.033467904435011485, 0.03477896434127531, 0.03618661357271868, 0.037688512144078735, 0.03928294638309546, 0.040968846681886606, 0.042745749504476425, 0.04461371341329251, 0.04657319847322788, 0.04862491864349388, 0.05076967730969541, 0.05300819651741616, 0.055340950394308856, 0.057768012483021394 ], [ 0.061667843928572226, 0.058244631781677714, 0.05493933133972448, 0.05176836098722645, 0.04874857192409755, 0.04589688722166829, 0.04322977802262861, 0.04076254936647403, 0.03850842911829592, 0.03647749418635025, 0.03467552949257531, 0.03310298724432118, 0.03175427253786411, 0.030617591552347306, 0.02967553248770472, 0.028906407982564632, 0.02828621104066972, 0.027790886597779525, 0.02739854770271559, 0.027091283678481563, 0.02685630247530418, 0.026686294474147065, 0.026579069923188658, 0.02653666661728413, 0.026564201295391027, 0.026668718309166815, 0.026858188315763715, 0.02714068887879639, 0.027523726690986208, 0.02801366638657383, 0.028615283543528817, 0.029331499302931153, 0.030163342371660923, 0.03111013129360894, 0.032169816105882654, 0.033339395011211075, 0.03461533111617929, 0.035993920274333194, 0.037471586787565424, 0.03904510116324655, 0.040711723105848904, 0.04246927646929002, 0.044316163985892144, 0.04625133002405433, 0.04827418014426684, 0.05038446691793683, 0.05258215215736327, 0.05486725611786205, 0.057239704154885884, 0.05969918062353407 ], [ 0.06182980465270547, 0.058380095765267724, 0.055048327533746354, 0.051851491363869504, 0.048807125964761354, 0.045932960091300004, 0.043246381627103044, 0.04076369928801113, 0.038499184054261816, 0.03646392043463483, 0.03466456492307583, 0.033102190736987384, 0.031771467055951116, 0.030660437401585805, 0.029751091789064307, 0.02902077069351593, 0.028444241701551156, 0.02799612388429314, 0.027653256740852825, 0.027396633714964435, 0.02721262439767352, 0.0270933649944377, 0.027036372931324278, 0.027043597350892068, 0.027120201940695112, 0.027273356980533184, 0.0275112090436058, 0.027842063173862973, 0.02827372664359779, 0.02881295874277687, 0.029465021990108736, 0.030233379149522222, 0.03111958548078219, 0.03212338766908918, 0.033242991680368865, 0.03447543179302856, 0.03581697112575954, 0.03726348064226397, 0.03881076497680006, 0.040454820720032515, 0.042192023731569384, 0.04401924793314683, 0.04593392102422123, 0.04793402424444153, 0.050018044501115945, 0.05218488815180461, 0.054433766462477495, 0.05676406313164032, 0.05917519416218784, 0.06166646971141279 ], [ 0.062122945174123305, 0.05865136268754734, 0.05529744982275255, 0.05207863427818165, 0.04901298038091893, 0.046118836645081915, 0.043414302558971274, 0.040916476258187354, 0.038640465127751954, 0.036598185617621425, 0.03479704980199424, 0.03323872491745512, 0.03191822951701405, 0.03082365187858033, 0.0299367046615403, 0.029234162907976254, 0.028690020341983858, 0.0282780208081798, 0.0279741389835555, 0.027758610221456686, 0.0276172191725867, 0.027541718697875903, 0.02752943436042627, 0.027582274110973744, 0.027705454546527213, 0.027906238463399097, 0.02819286758192016, 0.028573733575146705, 0.02905673445733149, 0.029648748093641132, 0.030355199499245075, 0.03117975068259797, 0.03212415855375035, 0.03318832192187899, 0.03437049654203571, 0.03566762514301917, 0.037075719792053104, 0.03859024292350599, 0.04020645029514725, 0.041919675466254996, 0.043725547398544375, 0.04562014034509959, 0.04760005961840437, 0.04966246944467788, 0.05180507077872988, 0.05402603808358597, 0.056323924801094945, 0.058697547550308656, 0.06114585895089874, 0.06366781835796317 ], [ 0.06255199096704828, 0.059063734947499905, 0.05569262616237156, 0.05245638925969897, 0.04937344585529652, 0.04646256670324642, 0.04374233976580765, 0.04123041322793682, 0.03894249235848611, 0.0368911136139395, 0.03508429233706786, 0.03352423267014046, 0.032206370551555605, 0.03111904684724608, 0.03024403683720506, 0.02955799127780548, 0.02903462443381784, 0.028647298800428087, 0.028371569317546114, 0.028187275112384023, 0.02807987808497741, 0.028040911791937052, 0.028067591210736598, 0.028161803110016734, 0.028328794142537413, 0.02857586228594555, 0.028911249473427648, 0.02934329136927675, 0.02987977740324566, 0.03052744802600949, 0.03129159140543891, 0.03217575154240869, 0.0331815833720138, 0.03430887730694329, 0.03555574228397507, 0.03691890615353512, 0.038394078799896675, 0.039976326757699666, 0.04166042091214008, 0.043441133522195405, 0.04531347293689459, 0.04727285282344471, 0.04931519805734874, 0.05143699265723496, 0.053635277115592545, 0.055907603686416854, 0.058251958881685384, 0.06066666268630458, 0.06315025384463614, 0.06570137001058415 ], [ 0.06312070112132492, 0.059621446295304054, 0.05623861103389577, 0.05299007897175221, 0.04989446011589115, 0.04697074644827392, 0.04423778376678195, 0.04171351841550478, 0.03941399694948436, 0.03735214064722724, 0.03553638913538466, 0.03396939948458236, 0.03264707020258488, 0.03155818786937225, 0.030684926351387986, 0.03000426009419573, 0.029490133706267446, 0.029116042322572443, 0.028857586595151797, 0.028694587590294293, 0.02861245528937273, 0.02860266672960757, 0.028662396169257975, 0.028793509662385534, 0.02900123751274524, 0.02929283353138655, 0.029676430319310994, 0.03016016245825017, 0.03075152351721642, 0.031456886100418247, 0.03228113714014905, 0.03322742373719107, 0.0342970309835631, 0.03548940913858547, 0.036802343389270416, 0.03823223385499112, 0.0397744394545757, 0.04142363921901417, 0.04317417397229295, 0.045020343820766355, 0.046956648290129466, 0.04897796449203492, 0.051079664390356765, 0.053257675768134685, 0.05550849361342403, 0.057829149877130386, 0.060217150213189824, 0.06267038653443392, 0.06518703406537445, 0.06776544107472685 ], [ 0.06383172810902123, 0.06032749876363198, 0.05693879526449479, 0.05368352703317084, 0.05058032838048721, 0.04764821590455875, 0.044906065875143314, 0.04237187204039551, 0.040061763361836616, 0.037988803687370884, 0.036161664989696356, 0.03458335414340817, 0.03325025305309657, 0.032151760035281654, 0.03127075719822228, 0.030584968792065136, 0.03006906481113071, 0.029697180210528303, 0.02944542685003588, 0.029293990133618917, 0.02922850380425445, 0.0292405529608548, 0.029327336914018516, 0.029490690468941462, 0.029735764870787027, 0.0300696731599592, 0.03050031702189606, 0.031035484187542903, 0.0316821997153692, 0.03244626821534293, 0.033331953375376124, 0.03434177460324472, 0.03547642590137228, 0.03673482477371519, 0.03811428387667525, 0.03961077894490953, 0.04121927437954855, 0.04293406638570355, 0.044749110215306906, 0.046658308302690084, 0.04865574612019773, 0.050735870552012625, 0.05289361112614651, 0.05512444797631176, 0.057424432528605344, 0.059790168122533884, 0.06221875840177651, 0.06470773151896181, 0.06725494807187027, 0.06985850026462885 ], [ 0.06468652114889442, 0.061183551753900584, 0.057795077914416355, 0.05453890911079417, 0.05143354928988502, 0.048497854533470906, 0.04575051752286356, 0.043209342935292015, 0.0408902967741074, 0.038806353158560354, 0.03696622721129012, 0.03537316427899573, 0.03402402885019123, 0.032908962130847, 0.03201181961812402, 0.03131145360677914, 0.030783710264503463, 0.03040383640397006, 0.030148897195487866, 0.02999981278006622, 0.029942713003473086, 0.02996945668376923, 0.030077334805183282, 0.03026813748957696, 0.030546866746149922, 0.030920388893330656, 0.0313962474120607, 0.03198174167078046, 0.03268327441546407, 0.03350591663957561, 0.034453134000375085, 0.0355266411978997, 0.0367263728247254, 0.038050566516766485, 0.03949594738350232, 0.04105799061132355, 0.04273123047809177, 0.04450958257206773, 0.04638665085657538, 0.04835599927608781, 0.050411375940682866, 0.05254688485077285, 0.054757105123704464, 0.0570371609589259, 0.0593827475783943, 0.06179011952697258, 0.06425604830985768, 0.06677775655329307, 0.06935283578749274, 0.07197915460965794 ], [ 0.06568527812016302, 0.062189869468925935, 0.05880780805845821, 0.0555566872757564, 0.05245473918583543, 0.049520491558201325, 0.04677226116033213, 0.04422745263579052, 0.04190165097248187, 0.03980753359426397, 0.037953687391770775, 0.036343488706089576, 0.03497426819401058, 0.03383700382359992, 0.03291673337705704, 0.032193747653841136, 0.03164545042724312, 0.031248610825723173, 0.030981641988662035, 0.030826538378042268, 0.030770183004199488, 0.030804870434488946, 0.030928052530587724, 0.031141464927128173, 0.0314498920592536, 0.03185984835245636, 0.03237839547202074, 0.033012214812269305, 0.033766957379863, 0.03464683304851627, 0.0356543841323453, 0.03679039905120437, 0.038053939306575385, 0.03944246311002133, 0.040952029136359785, 0.04257755873302317, 0.044313130499397335, 0.0461522807937495, 0.048088287521502765, 0.05011442073919343, 0.052224150173422565, 0.054411305382553524, 0.05667018848183827, 0.05899564217847109, 0.061383077628654074, 0.06382846766236917, 0.06632831146878111, 0.06887957704822119, 0.07147962769459822, 0.07412613851429989 ], [ 0.06682694681435904, 0.0633453274544977, 0.05997579722805632, 0.05673562848676603, 0.05364265590406293, 0.0507149328995422, 0.04797023602350889, 0.0454253927532685, 0.04309542656150515, 0.04099254821230894, 0.03912507484621202, 0.03749642100166412, 0.03610435907641344, 0.034940762705897424, 0.03399200014915565, 0.03324003184201113, 0.032664113753889064, 0.03224286524783898, 0.03195637333342511, 0.031787996863274146, 0.03172559992068525, 0.031762063388221615, 0.03189507022982966, 0.032126299494435774, 0.03246025984898466, 0.03290301999391619, 0.03346105047992258, 0.0341403058262237, 0.034945586038866584, 0.03588015297742743, 0.036945549530155386, 0.03814156984308085, 0.03946634103581422, 0.040916488227273985, 0.042487360295000165, 0.04417329481258424, 0.045967900495852566, 0.04786433679250971, 0.0498555736223266, 0.05193461898649294, 0.05409470708770354, 0.05632944388042727, 0.058632910232947706, 0.0609997251381059, 0.06342507285787356, 0.06590469875955467, 0.06843487908340011, 0.07101237009044675, 0.07363434203810676, 0.07629830325019901 ], [ 0.06810927224689366, 0.06464747374000607, 0.06129639645335724, 0.05807289925797456, 0.054994311972348324, 0.05207809230957044, 0.0493413442220261, 0.046800179632795584, 0.044468923452617146, 0.04235919359322745, 0.040478933220963964, 0.03883152463462891, 0.03741515669554092, 0.03622262805176393, 0.035241727002523766, 0.03445623274332409, 0.033847453175642056, 0.033396090665275144, 0.033084147952293655, 0.03289657336806366, 0.03282239752805205, 0.032855217429468744, 0.03299301420717285, 0.03323741717782349, 0.03359261715490842, 0.03406416360184889, 0.03465785062535254, 0.03537882568472171, 0.03623097339314345, 0.037216562135043055, 0.03833610597400553, 0.03958838572094366, 0.04097058000384098, 0.04247846862168599, 0.04410667994247251, 0.04584896011571656, 0.04769844563714646, 0.04964792395974162, 0.05169007025381263, 0.05381765209625682, 0.05602369741647141, 0.05830162405640179, 0.06064533162789857, 0.06304925798874657, 0.06550840373819194, 0.06801832880644866, 0.07057512560419002, 0.07317537338667063, 0.0758160785138497, 0.07849460517069945 ], [ 0.06952888334994729, 0.06609263575427797, 0.06276562637812307, 0.0595642216599118, 0.05650515841028091, 0.053605203417600604, 0.050880689117598965, 0.04834691375597716, 0.046017411585839066, 0.04390312692437365, 0.042011564352224424, 0.04034602940972405, 0.038905106487698404, 0.03768252559280779, 0.03666753272671295, 0.03584579796507118, 0.03520078748939209, 0.034715421309743706, 0.0343737686959356, 0.03416251797086506, 0.034071999123226414, 0.03409662559187672, 0.03423473506566671, 0.034487921601565, 0.03486003501849254, 0.03535605815993265, 0.03598105405984873, 0.036739317062530995, 0.037633789263364484, 0.03866574025352289, 0.03983466799979499, 0.04113836325634252, 0.04257308215892482, 0.04413378224945329, 0.04581438901282054, 0.047608069671106444, 0.049507497912567394, 0.05150509815404868, 0.053593261678583436, 0.055764530035082194, 0.05801174359202931, 0.0603281551189042, 0.06270750974518403, 0.06514409368364958, 0.06763275479893774, 0.070168898551408, 0.07274846312326635, 0.07536787768131727, 0.07802400776675278, 0.08071409173112812 ], [ 0.0710814100425803, 0.0676760613867853, 0.06437834555260764, 0.06120407178176772, 0.05816931554641491, 0.05529008372218492, 0.05258187118158131, 0.05005910316992513, 0.04773447382674509, 0.045618215846434586, 0.04371736797272321, 0.042035139901098306, 0.040570497485076615, 0.03931809155583406, 0.038268620713091915, 0.0374096514062769, 0.036726830293462645, 0.03620533756510376, 0.03583137051883442, 0.035593431105418544, 0.03548322376479932, 0.03549604303750141, 0.03563062749274942, 0.03588855489853514, 0.036273329540901705, 0.036789348267954824, 0.037440921781920086, 0.038231481105633285, 0.03916303533115105, 0.04023588651462421, 0.041448565207117885, 0.04279792998704654, 0.044279372662978315, 0.045887079977055635, 0.047614315505571804, 0.04945369744898268, 0.05139745725756403, 0.053437670459953, 0.05556645529069443, 0.05777613746339775, 0.06005938123579429, 0.06240928809480257, 0.06481946516180931, 0.06728406591721238, 0.06979780616769757, 0.07235595839503434, 0.07495432776894287, 0.07758921319183261, 0.08025735676808887, 0.08295588504461736 ], [ 0.07276162059562664, 0.06939208146493638, 0.0661284409587274, 0.06298590087628926, 0.05997982661625765, 0.05712542126587669, 0.05443730661706271, 0.05192901061036791, 0.04961237531688146, 0.04749692055820325, 0.04558922375800571, 0.043892401473518645, 0.04240579381998962, 0.04112494982461508, 0.040041982415749224, 0.03914630638547759, 0.03842570117792776, 0.03786757041146075, 0.037460220922262526, 0.03719396989870203, 0.03706191417073381, 0.03706025594201381, 0.03718816105588759, 0.03744721063327152, 0.03784057461112222, 0.03837207061250467, 0.03904526761536141, 0.039862756805888855, 0.040825656728219716, 0.04193336411382228, 0.04318351943624687, 0.044572133393840634, 0.04609381575214968, 0.047742055381354384, 0.049509513164982685, 0.051388302608966374, 0.0533702437153728, 0.055447083242845314, 0.057610679227882294, 0.05985315034787797, 0.062166992103896083, 0.06454516243906555, 0.06698113964728057, 0.06946895548467291, 0.07200320639083085, 0.07457904571618736, 0.07719215985308035, 0.07983873117453871, 0.0825153906784202, 0.08521916319407645 ], [ 0.07456356931865801, 0.07123428138593502, 0.06800902582122964, 0.06490236115393182, 0.06192891264014035, 0.05910305869641446, 0.0564385394110189, 0.05394799081558814, 0.051642421611212436, 0.04953066653368827, 0.0476188705253095, 0.0459100759945064, 0.0444039951715159, 0.043097043816718014, 0.04198268654207417, 0.04105209847405631, 0.04029509065327472, 0.03970119074862226, 0.03926073110980282, 0.03896578423691885, 0.03881080601699807, 0.03879289639812804, 0.03891165538788937, 0.03916868428081356, 0.03956684120793327, 0.0401093928252284, 0.04079920397892238, 0.04163807782699017, 0.042626311585391166, 0.04376248270957237, 0.04504343973892844, 0.04646444812200969, 0.04801943435934761, 0.04970127734772159, 0.05150210785635402, 0.0534135904208405, 0.05542717339754014, 0.057534301226615625, 0.05972658817503991, 0.06199595565953991, 0.06433473648907245, 0.06673574969217567, 0.06919234947652146, 0.07169845159494664, 0.074248540116154, 0.07683765738428495, 0.07946137981122801, 0.08211578206292765, 0.0847973921476626, 0.08750313986087908 ], [ 0.07648074565421106, 0.07319567129641484, 0.07001263222102606, 0.0669455217118545, 0.06400821192618628, 0.06121425585442604, 0.0585765257141001, 0.05610679463404763, 0.0538152797881572, 0.051710179376680945, 0.04979725109462098, 0.04807949236615493, 0.04655698773670403, 0.045226981415703235, 0.044084210063684674, 0.043121493592979385, 0.042330536079666095, 0.041702844908394064, 0.0412306451746988, 0.040907657075023994, 0.040729620565209644, 0.04069449196971876, 0.04080229370864524, 0.041054658816777855, 0.04145416279721071, 0.042003564948242346, 0.042705083635763544, 0.04355980675487858, 0.04456729853320416, 0.0457254192212697, 0.04703033655344003, 0.04847668415320432, 0.05005781364356653, 0.05176609097924718, 0.0535931982781429, 0.0555304152715817, 0.05756886604523054, 0.059699725418659345, 0.06191438489983139, 0.0642045811855213, 0.0665624914409126, 0.06898079979767324, 0.07145273919585278, 0.0739721122050499, 0.07653329398182981, 0.07913122013774683, 0.08176136202187366, 0.08441969174736363, 0.08710263918100766, 0.08980704303392255 ], [ 0.07850621743877748, 0.07526884656727446, 0.07213138925235246, 0.06910706439233237, 0.06620899315278486, 0.06344991913496646, 0.060841878195114746, 0.058395826974543416, 0.05612124877918181, 0.05402576676134516, 0.05211480563152377, 0.050391351460356226, 0.04885586086945117, 0.04750636264090109, 0.04633877475380567, 0.04534742934522197, 0.044525761905212013, 0.043867086745100065, 0.04336535686551522, 0.0430157996884859, 0.04281533404380609, 0.042762707024851354, 0.04285833590647291, 0.04310389068511431, 0.043501695851212684, 0.044054055975672274, 0.044762613117713554, 0.04562782562701105, 0.04664862421940079, 0.04782226234649106, 0.04914434380915597, 0.0506089879463406, 0.052209083534829025, 0.05393658467865606, 0.055782811182023606, 0.05773872774546902, 0.059795187489114214, 0.06194313402349448, 0.0641737621015983, 0.06647864014906307, 0.06884979936765728, 0.07127979434016757, 0.07376173969108123, 0.07628932675563921, 0.07885682360134626, 0.0814590612361597, 0.08409140845723959, 0.08674973753296819, 0.08943038273884135, 0.09213009364985118 ], [ 0.08063276303672559, 0.07744613289184982, 0.07435718081726242, 0.0713784536249679, 0.06852233627826565, 0.06580079229297851, 0.06322506562552961, 0.06080535444426546, 0.05855047509991868, 0.05646754337111174, 0.05456170810622164, 0.05283597742691875, 0.05129117704806231, 0.04992607173347387, 0.048737663544335404, 0.047721655668198734, 0.0468730420745576, 0.04618675679581967, 0.04565829863770608, 0.045284242828270156, 0.04506256315792801, 0.044992715642096025, 0.045075473068467424, 0.04531254140896152, 0.04570602503013389, 0.046257829860887334, 0.04696909738292382, 0.04783974759484949, 0.04886818097205438, 0.05005115605439764, 0.05138382908920765, 0.05285992119014281, 0.05447196900749454, 0.05621161567291978, 0.058069906375770815, 0.060037563491075654, 0.06210522661433634, 0.06426365134088698, 0.06650386651836501, 0.06881729316440882, 0.07119582983454735, 0.07363190958464193, 0.07611853334354389, 0.07864928389000495, 0.08121832395691313, 0.08382038139452626, 0.08645072385993462, 0.08910512516370295, 0.09177982517276402, 0.09447148500867339 ], [ 0.08285298898330995, 0.07971971277171802, 0.07668178016373654, 0.07375107795401917, 0.0709392798400285, 0.06825760835251464, 0.06571656859353894, 0.0633256647857274, 0.06109311702209871, 0.05902560219704972, 0.057128048580986496, 0.055403516111183417, 0.05385319232216904, 0.05247652547579692, 0.05127150152124102, 0.05023505131120393, 0.04936355208776616, 0.04865336703242857, 0.0481013534342744, 0.047705267720269805, 0.04746400621896976, 0.04737764339327686, 0.047447260796387954, 0.04767459419433558, 0.048061555993561364, 0.0486097087417143, 0.04931976897256496, 0.05019120883716567, 0.051221999601141786, 0.0524085127153072, 0.053745567812114904, 0.05522659796459635, 0.056843893192875264, 0.058588882855549765, 0.060452423590294256, 0.06242506861841728, 0.06449730371732225, 0.06665974320326044, 0.06890328509150369, 0.07121922820707616, 0.0735993558194519, 0.0760359909168859, 0.07852202802771137, 0.08105094592650657, 0.0836168048907145, 0.08621423154461416, 0.08883839380853724, 0.09148496807638307, 0.09415010045951233, 0.09683036373339601 ], [ 0.08515943148089986, 0.08208173220618369, 0.07909696068297992, 0.07621636371076261, 0.07345093628278851, 0.07081120562289307, 0.06830699579687387, 0.06594718393102737, 0.0637394640871978, 0.06169013964063893, 0.05980396850470235, 0.0580840864157085, 0.0565320304202005, 0.05514787681005706, 0.053930495022884384, 0.05287790267116111, 0.05198768934599025, 0.05125746153268884, 0.05068525147590853, 0.05026983209207629, 0.050010889517886445, 0.04990902400698342, 0.04996557579820338, 0.050182300538528034, 0.05056094314576371, 0.0511027743522395, 0.05180815722274722, 0.052676201360809666, 0.05370454319032221, 0.054889266802661235, 0.05622495714999224, 0.057704860407496644, 0.05932111735607261, 0.06106503443364426, 0.06292736169627985, 0.06489855465740722, 0.06696900540138888, 0.06912923581318596, 0.0713700513976367, 0.07368265783536244, 0.07605874440960675, 0.07849053918534768, 0.08097084077914102, 0.08349303109458053, 0.08605107277395282, 0.088639494491908, 0.09125336667319718, 0.09388826978261265, 0.09654025700819968, 0.09920581291920577 ], [ 0.08754464146591343, 0.08452438796170532, 0.08159458420095289, 0.07876586312290647, 0.07604857883419609, 0.0734526126754666, 0.07098716711623661, 0.06866055810846912, 0.06648002036170005, 0.06445154335086566, 0.06257975787010962, 0.06086789261968837, 0.05931781677249434, 0.057930177216753996, 0.05670462841010153, 0.05564013960017942, 0.054735350545443436, 0.053988935402203765, 0.05339992783532402, 0.05296796084506331, 0.05269338332160365, 0.052577231392568, 0.05262105392955663, 0.05282661436361251, 0.05319551070148613, 0.053728768122371845, 0.054426461048063715, 0.0552874137680681, 0.05630901275984402, 0.057487143855579376, 0.058816248028590604, 0.06028947464669435, 0.06189890262494262, 0.06363579808664956, 0.0654908804812455, 0.06745457547879609, 0.06951724029347231, 0.07166935384660551, 0.07390166951508935, 0.07620533187172597, 0.07857196095697142, 0.08099370856737796, 0.08346329118931695, 0.08597400388259906, 0.0885197188803743, 0.09109487208557437, 0.09369444010363233, 0.0963139099991485, 0.09894924360821068, 0.10159683796780926 ], [ 0.09000125396732805, 0.08703999685783174, 0.08416666906911263, 0.08139132016888391, 0.07872370433507288, 0.07617310782372305, 0.07374817010443203, 0.0714567085937786, 0.06930555975252067, 0.06730045151920384, 0.06544592295936714, 0.06374530590586697, 0.06220077967547885, 0.06081350343553547, 0.05958382176988262, 0.0585115284224144, 0.05759616266790163, 0.05683730427401423, 0.05623482860682605, 0.055789084695549856, 0.05550096671782295, 0.05537186287377181, 0.055403483125038615, 0.05559758578927048, 0.05595563892474034, 0.05647846248568789, 0.057165899210336206, 0.05801655579477301, 0.05902764278615827, 0.06019492499549591, 0.061512777820455895, 0.06297433186518234, 0.06457168048808076, 0.06629612267144976, 0.06813841588881554, 0.07008901878049024, 0.07213830970827509, 0.07427677328511083, 0.07649515193569681, 0.07878456311666324, 0.08113658504940435, 0.0835433149393611, 0.08599740398418736, 0.08849207330653715, 0.09102111452031121, 0.09357887811873165, 0.0961602523604669, 0.09876063487961503, 0.10137589887485643, 0.10400235544179434 ], [ 0.09252204313133457, 0.08962104912561929, 0.086805440890421, 0.0840847178664321, 0.08146807659969316, 0.07896425854870939, 0.07658139612179005, 0.07432686598997656, 0.07220716073765417, 0.07022779124288211, 0.06839323230932447, 0.06670692250290894, 0.06517132552193458, 0.06378805468518925, 0.0625580546142387, 0.06148182575335541, 0.0605596692894332, 0.05979192384645643, 0.05917916255869484, 0.05872232093219087, 0.058422732742210416, 0.05828206258825975, 0.058302138114921354, 0.058484699918070315, 0.05883109997482832, 0.059341987448725556, 0.06001702222556468, 0.060854651252300725, 0.06185197196862521, 0.06300469333487085, 0.06430719114346005, 0.06575264306452058, 0.06733322182693595, 0.06904032245655202, 0.0708648009127849, 0.07279720550771486, 0.07482798774449305, 0.07694768449539796, 0.0791470679730081, 0.08141726336589819, 0.0837498362703323, 0.08613685330748418, 0.08857091981566728, 0.0910451984993918, 0.09355341261573022, 0.09608983684307632, 0.09864927851353673, 0.10122705145916115, 0.10381894435211074, 0.10642118511630261 ], [ 0.0950999646445402, 0.09226024816231755, 0.08950336884700799, 0.08683831062650915, 0.0842737545878858, 0.08181794574845051, 0.07947856150204977, 0.07726258980614259, 0.0751762265363957, 0.0732248021085371, 0.07141274707039279, 0.06974360455877503, 0.0682200940959029, 0.06684422620744604, 0.06561746114562109, 0.06454089831359368, 0.06361547683577118, 0.06284216328905133, 0.06222210104195092, 0.061756697770569635, 0.0614476338037087, 0.06129678352626802, 0.06130605388610254, 0.06147715620045592, 0.06181133772822606, 0.06230910582348597, 0.06296997858706146, 0.0637922915613327, 0.06477308115840885, 0.0659080541176768, 0.06719164070693652, 0.0686171197331124, 0.07017679709532867, 0.07186221702664435, 0.07366438591001204, 0.07557399165824338, 0.07758160598394408, 0.07967786144815474, 0.08185359925434853, 0.08409998696575834, 0.08640860756480169, 0.08877152262690016, 0.09118131302687105, 0.09363110073889633, 0.09611455511927004, 0.09862588672186849, 0.10115983129577857, 0.10371162621792183, 0.10627698125677884, 0.10885204526002654 ], [ 0.0977281874163705, 0.09495053901985925, 0.09225319045668152, 0.0896446449763603, 0.08713310912720029, 0.08472637691464673, 0.08243171812798482, 0.08025577789531414, 0.07820449537538736, 0.07628304969094608, 0.0744958404741008, 0.07284650850662817, 0.07133799880207009, 0.06997266419268332, 0.06875240240511692, 0.06767881434112433, 0.06675336664134136, 0.06597753851515462, 0.06535293211351664, 0.0648813279888155, 0.06456467256539197, 0.06440499260098483, 0.06440424131908089, 0.06456409071532, 0.06488569274786224, 0.0653694371268335, 0.06601473419353314, 0.06681984775184764, 0.06778179544483191, 0.06889632486920379, 0.0701579639434403, 0.07156013580305942, 0.07309532285970373, 0.0747552620728817, 0.07653115370153066, 0.07841386812148309, 0.08039413881612376, 0.08246273353372947, 0.08461059921959986, 0.08682897929808597, 0.08910950405379348, 0.09144425626703383, 0.09382581501935372, 0.09624728086229847, 0.09870228549490757, 0.10118498885765842, 0.10369006622201131, 0.1062126875045534, 0.10874849070226976, 0.11129355105155006 ] ] }, { "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": [ 0.953548789024353, 0.013713794760406017, 0.8562620198354125, 0.9712210400030017, 0.31559087336063385, 0.778985702432692, 0.635171796709968, 0.5917691818905915, 0.7968686587048557, 0.7198924979852501, 0.6810220369012258, 0.6694215154581032, 0.6366952505637699, 0.6392396405368526, 0.6406615816551005, 0.6250724260033991, 0.5845968663452821, 0.5317419224781321, 0.5273435516652855, 0.4561589103419764, 0.3629805870726495, 0.4542638332494568, 0.39488582944328565, 0.3979049095431627 ], "xaxis": "x", "y": [ 0.19757267832756042, 0.0578758055344224, 0.7557264706119895, 0.6636570580303669, 0.3147067427635193, 0.23079447634518147, 0.1557980746801847, 0.1688913936057323, 0.134418268179362, 0.15719856669715504, 0.14514611709360925, 0.04761225355889841, 0.21223349741238978, 0.24750174406451164, 0.2942740522878425, 0.35094432150725985, 0.4297018125503037, 0.5299127350624394, 0.5849080287645086, 0.5729713424344424, 0.602167669119024, 0.5862441767630591, 0.5594486009641354, 0.5637597978063251 ], "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": [ 0.953548789024353, 0.013713794760406017, 0.8562620198354125, 0.9712210400030017, 0.31559087336063385, 0.778985702432692, 0.635171796709968, 0.5917691818905915, 0.7968686587048557, 0.7198924979852501, 0.6810220369012258, 0.6694215154581032, 0.6366952505637699, 0.6392396405368526, 0.6406615816551005, 0.6250724260033991, 0.5845968663452821, 0.5317419224781321, 0.5273435516652855, 0.4561589103419764, 0.3629805870726495, 0.4542638332494568, 0.39488582944328565, 0.3979049095431627 ], "xaxis": "x2", "y": [ 0.19757267832756042, 0.0578758055344224, 0.7557264706119895, 0.6636570580303669, 0.3147067427635193, 0.23079447634518147, 0.1557980746801847, 0.1688913936057323, 0.134418268179362, 0.15719856669715504, 0.14514611709360925, 0.04761225355889841, 0.21223349741238978, 0.24750174406451164, 0.2942740522878425, 0.35094432150725985, 0.4297018125503037, 0.5299127350624394, 0.5849080287645086, 0.5729713424344424, 0.602167669119024, 0.5862441767630591, 0.5594486009641354, 0.5637597978063251 ], "yaxis": "y2" } ], "layout": { "annotations": [ { "font": { "size": 14 }, "showarrow": false, "text": "Mean", "x": 0.25, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" }, { "font": { "size": 14 }, "showarrow": false, "text": "Standard Error", "x": 0.8, "xanchor": "center", "xref": "paper", "y": 1, "yanchor": "bottom", "yref": "paper" } ], "autosize": false, "height": 450, "hovermode": "closest", "legend": { "orientation": "h", "x": 0, "y": -0.25 }, "margin": { "b": 100, "l": 35, "pad": 0, "r": 35, "t": 35 }, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "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": [ -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.7738002951705187, -0.9944653056346245, -1.3315088715583177, -1.7907915444598044, -2.3942467734097646, -2.803659512356476, -2.8050099609556045, -2.9778433102518798, -2.9778433102518798, -3.004563468220752, -3.0853479591224566, -3.0853479591224566, -3.0853479591224566 ] }, { "fill": "tonexty", "fillcolor": "rgba(128,177,211,0.3)", "legendgroup": "objective value", "line": { "color": "rgba(128,177,211,1)" }, "mode": "lines", "name": "objective value", "text": [ "
Parameterization:
x1: 0.5139352083206177
x2: 0.8104050159454346
x3: 0.953548789024353
x4: 0.19757267832756042
x5: 0.6414160132408142
x6: 0.031124398112297058", "
Parameterization:
x1: 0.3525698482990265
x2: 0.4881714144721627
x3: 0.013713794760406017
x4: 0.0578758055344224
x5: 0.13016737531870604
x6: 0.19689504988491535", "
Parameterization:
x1: 0.8365536173805594
x2: 0.2682372462004423
x3: 0.8562620198354125
x4: 0.7557264706119895
x5: 0.9527171514928341
x6: 0.6698648389428854", "
Parameterization:
x1: 0.3803107887506485
x2: 0.38866316620260477
x3: 0.9712210400030017
x4: 0.6636570580303669
x5: 0.16074097342789173
x6: 0.7688065730035305", "
Parameterization:
x1: 0.004738156683743
x2: 0.6983593786135316
x3: 0.31559087336063385
x4: 0.3147067427635193
x5: 0.45515180844813585
x6: 0.21305783838033676", "
Parameterization:
x1: 0.1399143049493432
x2: 0.8552484745159745
x3: 0.778985702432692
x4: 0.23079447634518147
x5: 0.05297510325908661
x6: 0.3384505659341812", "
Parameterization:
x1: 0.4254396857282235
x2: 0.7460297772297608
x3: 0.635171796709968
x4: 0.1557980746801847
x5: 0.587565364206661
x6: 0.03604335363487496", "
Parameterization:
x1: 0.596591986169898
x2: 0.8983092267471297
x3: 0.5917691818905915
x4: 0.1688913936057323
x5: 0.6990798297810389
x6: 2.327999866689918e-18", "
Parameterization:
x1: 0.3459359054618556
x2: 0.6172875361931487
x3: 0.7968686587048557
x4: 0.134418268179362
x5: 0.5449577079613026
x6: 0.04645357671399583", "
Parameterization:
x1: 0.3437211620125524
x2: 0.8364864168041038
x3: 0.7198924979852501
x4: 0.15719856669715504
x5: 0.5433459601918766
x6: 0.09523426211179316", "
Parameterization:
x1: 0.45883448841225405
x2: 0.7863775522933658
x3: 0.6810220369012258
x4: 0.14514611709360925
x5: 0.4650459365173431
x6: 0.03630806473368671", "
Parameterization:
x1: 0.3885162614844159
x2: 0.781422108017134
x3: 0.6694215154581032
x4: 0.04761225355889841
x5: 0.6032618555913896
x6: 0.15475703149070968", "
Parameterization:
x1: 0.37404203322167245
x2: 0.7719368778230044
x3: 0.6366952505637699
x4: 0.21223349741238978
x5: 0.5288161783122434
x6: 0.03091861246788227", "
Parameterization:
x1: 0.3842869442259865
x2: 0.7801589359541169
x3: 0.6392396405368526
x4: 0.24750174406451164
x5: 0.5051049253072115
x6: 0.013338035752169122", "
Parameterization:
x1: 0.39672685869511304
x2: 0.7917615983813251
x3: 0.6406615816551005
x4: 0.2942740522878425
x5: 0.4780043837531798
x6: 4.222403554779128e-12", "
Parameterization:
x1: 0.40932786201132454
x2: 0.7991890057412705
x3: 0.6250724260033991
x4: 0.35094432150725985
x5: 0.4348696686560271
x6: 5.636103385790143e-12", "
Parameterization:
x1: 0.42152493821190873
x2: 0.7986659573673448
x3: 0.5845968663452821
x4: 0.4297018125503037
x5: 0.38030305044948876
x6: 0.005658883575740052", "
Parameterization:
x1: 0.4340618747966894
x2: 0.7884371208413415
x3: 0.5317419224781321
x4: 0.5299127350624394
x5: 0.32814944952468106
x6: 0.00018060137525283663", "
Parameterization:
x1: 0.44602174475801404
x2: 0.7855953054452791
x3: 0.5273435516652855
x4: 0.5849080287645086
x5: 0.29492185732968074
x6: 0.000637143190351287", "
Parameterization:
x1: 0.40760017704824786
x2: 0.8134703778223665
x3: 0.4561589103419764
x4: 0.5729713424344424
x5: 0.37606786996361247
x6: 1.0141029176280772e-16", "
Parameterization:
x1: 0.42667930806035465
x2: 0.7769965244402628
x3: 0.3629805870726495
x4: 0.602167669119024
x5: 0.44434059140581167
x6: 0.0", "
Parameterization:
x1: 0.3690262452363467
x2: 0.851652154620116
x3: 0.4542638332494568
x4: 0.5862441767630591
x5: 0.3437971667711557
x6: 4.237679527972321e-17", "
Parameterization:
x1: 0.40720578843023586
x2: 0.8804264767498129
x3: 0.39488582944328565
x4: 0.5594486009641354
x5: 0.32181171640762957
x6: 0.0", "
Parameterization:
x1: 0.41590037424570153
x2: 0.887799867079452
x3: 0.3979049095431627
x4: 0.5637597978063251
x5: 0.3345045544460163
x6: 0.0", "
Parameterization:
x1: 0.40421794804692074
x2: 0.8821217195305128
x3: 0.3837841932845857
x4: 0.5663747092663836
x5: 0.29867009626339924
x6: 0.08098497954114325" ], "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": [ -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.7738002951705187, -0.9944653056346245, -1.3315088715583177, -1.7907915444598044, -2.3942467734097646, -2.803659512356476, -2.8050099609556045, -2.9778433102518798, -2.9778433102518798, -3.004563468220752, -3.0853479591224566, -3.0853479591224566, -3.0853479591224566 ] }, { "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": [ -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.5902783985001354, -0.7738002951705187, -0.9944653056346245, -1.3315088715583177, -1.7907915444598044, -2.3942467734097646, -2.803659512356476, -2.8050099609556045, -2.9778433102518798, -2.9778433102518798, -3.004563468220752, -3.0853479591224566, -3.0853479591224566, -3.0853479591224566 ] }, { "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, -0.5902783985001354 ] } ], "layout": { "showlegend": true, "template": { "data": { "bar": [ { "error_x": { "color": "#2a3f5f" }, "error_y": { "color": "#2a3f5f" }, "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "bar" } ], "barpolar": [ { "marker": { "line": { "color": "#E5ECF6", "width": 0.5 }, "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "barpolar" } ], "carpet": [ { "aaxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "baxis": { "endlinecolor": "#2a3f5f", "gridcolor": "white", "linecolor": "white", "minorgridcolor": "white", "startlinecolor": "#2a3f5f" }, "type": "carpet" } ], "choropleth": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "choropleth" } ], "contour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "contour" } ], "contourcarpet": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "contourcarpet" } ], "heatmap": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmap" } ], "heatmapgl": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "heatmapgl" } ], "histogram": [ { "marker": { "pattern": { "fillmode": "overlay", "size": 10, "solidity": 0.2 } }, "type": "histogram" } ], "histogram2d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2d" } ], "histogram2dcontour": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "colorscale": [ [ 0.0, "#0d0887" ], [ 0.1111111111111111, "#46039f" ], [ 0.2222222222222222, "#7201a8" ], [ 0.3333333333333333, "#9c179e" ], [ 0.4444444444444444, "#bd3786" ], [ 0.5555555555555556, "#d8576b" ], [ 0.6666666666666666, "#ed7953" ], [ 0.7777777777777778, "#fb9f3a" ], [ 0.8888888888888888, "#fdca26" ], [ 1.0, "#f0f921" ] ], "type": "histogram2dcontour" } ], "mesh3d": [ { "colorbar": { "outlinewidth": 0, "ticks": "" }, "type": "mesh3d" } ], "parcoords": [ { "line": { "colorbar": { "outlinewidth": 0, "ticks": "" } }, "type": "parcoords" } ], "pie": [ { "automargin": true, "type": "pie" } ], "scatter": [ { "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 08-10 23:17:36] 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 08-10 23:17:36] 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": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:36] 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": [ "from ax.storage.sqa_store.structs import DBSettings\n", "\n", "# URL is of the form \"dialect+driver://username:password@host:port/database\".\n", "db_settings = DBSettings(url=\"sqlite:///foo.db\")\n", "# Instead of URL, can provide a `creator function`; can specify custom encoders/decoders if necessary.\n", "new_ax = AxClient(db_settings=db_settings)" ] }, { "cell_type": "markdown", "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": 17, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] ax.service.ax_client: Generated new trial 25 with parameters {'x1': 0.4, 'x2': 0.89, 'x3': 0.41, 'x4': 0.57, 'x5': 0.3, 'x6': 0.04}.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] ax.service.ax_client: Registered failure of trial 25.\n" ] } ], "source": [ "_, trial_index = ax_client.get_next_trial()\n", "ax_client.log_trial_failure(trial_index=trial_index)" ] }, { "cell_type": "markdown", "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": 18, "metadata": { "collapsed": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] ax.service.ax_client: Attached custom parameterization {'x1': 0.9, 'x2': 0.9, 'x3': 0.9, 'x4': 0.9, 'x5': 0.9, 'x6': 0.9} as trial 26.\n" ] }, { "data": { "text/plain": [ "({'x1': 0.9, 'x2': 0.9, 'x3': 0.9, 'x4': 0.9, 'x5': 0.9, 'x6': 0.9}, 26)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.attach_trial(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": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] 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" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter x. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] ax.service.utils.instantiation: Inferred value type of ParameterType.FLOAT for parameter y. If that is not the expected value type, you can explicity specify 'value_type' ('int', 'float', 'bool' or 'str') in parameter dict.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] ax.modelbridge.dispatch_utils: Using GPEI (Bayesian optimization) since there are more continuous parameters than there are categories for the unordered categorical parameters.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "[INFO 08-10 23:17:41] 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": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(5, 10), (-1, 10)]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ax_client.get_max_parallelism() # Max parallelism is now 10 for all stages of the optimization." ] } ], "metadata": { "kernelspec": { "display_name": "python3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.11" } }, "nbformat": 4, "nbformat_minor": 2 }