ESE 542 Programming Assignment

Question

Chinni Guna Venkata Prasanth · Accepted Answer

{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Project 5 ", " ", "In addition to answering the bolded questions on Coursera, also attach your notebook, both as ", "`.ipynb` and `.html`. ", " ", "In the following exercise, we will perform bootstrap and cross validation to find statistical values for two datasets. ", " ", "In this assignment, we will be using PennGrader, a Python package built by a former TA for autograding Python notebooks. PennGrader was developed to provide students with instant feedback on their answer. You can submit your answer and know whether it's right or wrong instantly. We then record your most recent answer in our backend database. You will have 100 attempts per test case, which should be more than sufficient. ", " ", "NOTE：Please remember to remove the ", " ", "```python ", "raise notImplementedError ", "``` ", "after your implementation, otherwise the cell will not compile. ", " ", " ", "A few things to note before we start ", "- You do not have to round your answers. ", "- Please make sure your answer's variable name do match what is provided in grader cells." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting Setup ", "Please run the below cells to get setup with the autograder. If you need to install packages, please do it below!" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# %%capture ", "# !pip install penngrader --user" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# !pip install scikit-learn --user ", "# !pip install statsmodels ", "# !pip install dill" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try PennGrader out! Fill in the cell below with your PennID and then run the following cell to initialize the grader. ", " ", "Warning: Please make sure you only have one copy of the student notebook in your directory in Codio upon submission. The autograder looks for the variable `STUDENT_ID` across all notebooks, so if there is a duplicate notebook, it will fail." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#PLEASE ENSURE YOUR STUDENT_ID IS ENTERED AS AN INT (NOT A STRING). IF NOT, THE AUTOGRADER WON'T KNOW WHO ", "#TO ASSIGN POINTS TO YOU IN OUR BACKEND ", " ", "STUDENT_ID = 88888888 # YOUR 8-DIGIT PENNID GOES HERE ", "STUDENT_NAME = "FirstName LastName" # YOUR FULL NAME GOES HERE" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PennGrader initialized with Student ID: 88888888 ", " ", "Make sure this correct or we will not be able to store your grade " ] } ], "source": [ "import penngrader.grader ", " ", "grader = penngrader.grader.PennGrader(homework_id = 'ESE542_Online_Su_2021_HW5', student_id = STUDENT_ID)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part A ", " ", "First, we will use the Boston dataset to try running our own implementation of bootstrap. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "#Data Wrangling ", "import pandas as pd ", "import numpy as np ", " ", "#Logistic Regression ", "import statsmodels.api as sm ", "import statsmodels.formula.api as smf ", "from sklearn.linear_model import LogisticRegression ", " ", "#Plotting ", "import matplotlib.pyplot as plt ", " ", "#Cross Validation ", "from sklearn.model_selection import train_test_split ", "from sklearn.model_selection import cross_val_score ", "from sklearn.model_selection import KFold ", " ", "#Statistics ", "from scipy import stats ", " ", "RANDOM_STATE=42 ", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", "

	CRIM	ZN	INDUS	NOX	RM	AGE	DIS	RAD	TAX	PTRATIO	B	LSTAT	MEDV
0	0.00632	18.0	2.31	0.538	6.575	65.2	4.0900	1.0	296.0	15.3	396.90	4.98	24.0
1	0.02731	0.0	7.07	0.469	6.421	78.9	4.9671	2.0	242.0	17.8	396.90	9.14	21.6
2	0.02729	0.0	7.07	0.469	7.185	61.1	4.9671	2.0	242.0	17.8	392.83	4.03	34.7
3	0.03237	0.0	2.18	0.458	6.998	45.8	6.0622	3.0	222.0	18.7	394.63	2.94	33.4
4	0.06905	0.0	2.18	0.458	7.147	54.2	6.0622	3.0	222.0	18.7	396.90	5.33	36.2

", "

" ], "text/plain": [ " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \ ", "0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 ", "1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 ", "2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 ", "3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 ", "4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 ", " ", " PTRATIO B LSTAT MEDV ", "0 15.3 396.90 4.98 24.0 ", "1 17.8 396.90 9.14 21.6 ", "2 17.8 392.83 4.03 34.7 ", "3 18.7 394.63 2.94 33.4 ", "4 18.7 396.90 5.33 36.2 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import load_boston ", "boston_dataset = load_boston() ", "data = pd.DataFrame(data = boston_dataset.data, columns = boston_dataset.feature_names) ", "data['MEDV'] = pd.Series(boston_dataset.target) ", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Based on this dataset, provide an estimate for $\hat\mu$, the population mean of 'medv'. Name this variable `mu_hat`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "mu_hat = data['MEDV'].mean()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id = 'test_mu_hat', answer = mu_hat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Provide an estimate of the standard error of $\hat\mu$. Name this variable `se_mu_hat`>. Interpret this result in your Jupyter notebook. ", " ", "*Hint*: We can compute the standard error of the sample mean by dividing the sample standard deviation by the square root of the number of observations. When computing the sample standard deviation, one must consider the Bessel’s correction factor from statistics (more information on that [here](https://en.wikipedia.org/wiki/Bessel\%27s_correction))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ " ", "se_mu_hat = data['MEDV'].std()/np.sqrt(data.shape[0])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id = 'test_se_mu_hat', answer = se_mu_hat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Now estimate the standard error of by implementing your own bootstrap method. Name your final answer `se_boostrap`. How does this compare to your answer from Part A Question 2? ", " ", "*Hint*: Generate $M=n$ artificial datasets, each with $N=n$ bootstrap samples. Use `np.random.seed(RANDOM_STATE)` before sampling so that your outputs stay consistent. You should try to write your own bootstrap method and and then compare it to packages such as SKLearn's `resample`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ " ", "se_bootstrap = np.sqrt(np.sum((data['MEDV'] - mu_hat)**2)/(data.shape[0]*(data.shape[0]-1))) " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 2/2 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id = 'test_se_bootstrap', answer = se_bootstrap)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Based on your bootstrap estimate from Part A Question 3, provide a $95\%$ confidence interval for the mean of 'medv'. Enter the lower range, higher range for mean's confidence interval in CI_lower, CI_upper. ", " ", "*Hint*: You can approximate a $95\%$ confidence interval using the formula $[\hat\mu \pm 2 * SE(\hat\mu)] $." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "CI_lower = mu_hat - 1.96*se_bootstrap ", "CI_upper = mu_hat + 1.96*se_bootstrap" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1.0/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id = 'test_CI_mean', answer = (CI_lower, CI_upper))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. Based on this data set, provide the population median value of 'medv', $\widehat{median}$. Name this variable `median_hat`." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "median_hat = data['MEDV'].median()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id = 'test_median_hat', answer = median_hat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "6. We now would like to estimate the standard error of $\widehat{median}$. Unfortunately, there is no simple formula for computing the standard error of the median. Instead, estimate the standard error of the median using bootstrap. Name this variable `se_bootstrap_median`. ", " ", "*Hint*: use your bootstrap sample list from A.3." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "se_bootstrap_median = np.sqrt(np.sum((data['MEDV'] - median_hat)**2)/(data.shape[0]*(data.shape[0]-1)))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You earned 0/1 points. ", " ", "But, don't worry you can re-submit and we will keep only your latest score. " ] } ], "source": [ "grader.grade(test_case_id = 'test_se_median', answer = se_bootstrap_median)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "7. Is the standard error of the median greater or less than the standard error of the mean?Does this make intuitive sense? Comment on your other findings in the cell below" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ " ", "# The bootstrap standard error of the median is larger than the bootstrap standard error of the mean. ", "# This is because the median is more sensitive to outliers than the mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part B ", " ", "Next, we will use the Default dataset to predict the probability of default using income and balance. In doing so, we also want to estimate the test error of the logistic regression model described in that section using cross validation." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "

", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", " ", "

	default	student	balance	income
0	No	No	729.526495	44361.625074
1	No	Yes	817.180407	12106.134700
2	No	No	1073.549164	31767.138947
3	No	No	529.250605	35704.493935
4	No	No	785.655883	38463.495879

", "

" ], "text/plain": [ " default student balance income ", "0 No No 729.526495 44361.625074 ", "1 No Yes 817.180407 12106.134700 ", "2 No No 1073.549164 31767.138947 ", "3 No No 529.250605 35704.493935 ", "4 No No 785.655883 38463.495879" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "default = pd.read_csv('Default.csv') ", "default.head(5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Fit a logistic regression model that use all the data from the predictors 'income' and 'balance' to predict 'default'. Please name your model fit1. ", " ", "*Hint*: Use `Stats Models` to fit the logistic regression. Review the previous recitations for review. ", " ", "In the latest versions of Stats Models, the default encoding for 'No' and 'Yes' were changed. Before running logistic regression, please make sure that the 'default' and 'student' columns are encoded so that 'No' = 0 and 'Yes' = 1. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.078948 ", " Iterations 10 " ] } ], "source": [ "# Enter your code below ", "default['default'] = default['default'].map({'No':0, 'Yes':1}) ", "default['student'] = default['student'].map({'No':0, 'Yes':1}) ", "# create stat models logistic regression model ", "fit1 = smf.logit('default ~ income + balance', data = default).fit()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You earned 0/1 points. ", " ", "But, don't worry you can re-submit and we will keep only your latest score. " ] } ], "source": [ "grader.grade(test_case_id ='test_glm_type', answer = str(type(fit1)))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 2/2 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_glm', answer = fit1.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Using the validation set approach, estimate the test error of this model. In order to do this, you must perform the following steps: ", " ", " ", "- Split the sample set into a random training set and a random validation set. Use a test size of 20%. *Hint*: Use `sklearn.model_selection.train_test_split` and a `random_state` of 42/RANDOM_STATE. Store your training set in train, testing set in test." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "# Enter your code below ", " ", "train, test = train_test_split(default, test_size = 0.2, random_state = RANDOM_STATE)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_train_shape', answer = train)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_test_shape', answer = test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Fit a logistic regression with multiple variables model using only the training observations. Name your model fit2." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.076230 ", " Iterations 10 " ] } ], "source": [ "# Enter your code below ", " ", "fit2 = smf.logit('default ~ income + balance', data = train).fit()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You earned 0/1 points. ", " ", "But, don't worry you can re-submit and we will keep only your latest score. " ] } ], "source": [ "grader.grade(test_case_id ='test_glm_type', answer = str(type(fit2)))" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1.0/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_train_para', answer = fit2.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Obtain a prediction of 'default' for each individual in the test set by computing the probability of default for that individual and classifying the individual to the default category if the posterior probability is greater than or equal to 0.5 (a Bayesian classifier). Store your predictions in predicted. ", " ", "*Hint*: we check for both the size and values of your precitions!" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# Enter your code below ", " ", "predicted = fit2.predict(test)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You earned 0.5/1 points. ", " ", "But, don't worry you can re-submit and we will keep only your latest score. " ] } ], "source": [ "grader.grade(test_case_id ='test_glm_predict', answer = predicted)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Compute the misclassification rate, which is the fraction of the observations in the validation set that are misclassified. Name this variable `mis_rate` and. ", " ", "*Hint*: Compare the predictions with the test set. Your answer should be the ratio of number of incorrect predictions over the total number of samples." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "mis_rate = np.mean(predicted.round() != test['default'])" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 1/1 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_mis_rate', answer = mis_rate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Repeat the process in Part B Question 2 three times, using three different splits of the observations into a training set and a validation set. Use test sizes of $10\%$, $30\%$, and $50\%$. Name the misclassification rates `mis_rate_10`, `mis_rate_30`, `mis_rate50`, respectively. Comment on the results obtained and determine the key takeaway. Store the misclassification accuracy score for each model within model_rates and model parameters within model_params ", " ", "*Note*: When splitting to test/train sets, please set your random_state to RANDOM_STATE so that you can have the same group of testing and training sets." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.072956 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079028 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084655 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079927 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083161 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079338 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080006 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080244 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082258 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087218 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079227 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083808 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077996 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.069238 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073694 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075339 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075882 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081584 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083923 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080109 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085294 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084201 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085791 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081392 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072046 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077464 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077343 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077251 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075292 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084000 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075111 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078487 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082323 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080817 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079257 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084931 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081916 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078689 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081787 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077330 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076491 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079725 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078493 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077944 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079514 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081692 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077971 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081014 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084264 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078308 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079300 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076922 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081012 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082238 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080563 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081195 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076680 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080184 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084649 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078121 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080145 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080619 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078276 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074368 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076030 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078140 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078747 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075908 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075596 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077443 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078189 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077534 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083481 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076569 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082040 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080645 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079755 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080298 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074469 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080437 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077543 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082811 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.077653 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077681 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083076 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084556 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074648 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082190 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073005 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080869 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074204 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079262 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080921 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071899 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080875 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082974 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082586 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083308 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079716 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083303 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075791 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081306 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081165 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080717 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073758 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077691 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084183 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082204 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073755 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075082 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082999 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077242 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077797 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076421 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083306 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080664 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072111 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082943 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074698 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073429 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078114 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084050 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072081 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083269 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079054 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080071 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080495 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086638 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077398 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081109 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080059 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078469 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076076 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081004 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085524 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082033 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077961 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081752 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075266 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077351 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074415 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080089 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074443 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085386 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081213 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075337 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080100 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075342 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076944 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078435 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079872 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073857 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.065649 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080395 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077953 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080005 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075684 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077800 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085686 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076028 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080390 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076062 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080583 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.075272 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074907 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078127 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078833 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077795 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080725 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081593 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080151 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075605 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082494 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081055 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076506 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079333 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081802 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078352 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082790 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080432 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082678 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082790 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083987 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078410 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076400 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081968 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077825 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081849 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078587 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073077 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077896 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078631 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074340 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076976 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080304 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077710 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083936 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081697 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076231 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082275 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.088454 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072743 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082602 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077795 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080745 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077214 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075139 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081166 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074699 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072724 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086290 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082284 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079763 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080534 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076760 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085470 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080106 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078875 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074109 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074796 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.088383 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081051 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077006 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082548 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080222 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080040 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082391 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076020 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082524 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078014 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079900 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084072 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081148 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079011 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075665 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077703 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076401 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078555 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078705 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078258 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075274 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077416 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082453 " ] }, { "name": "stdout", "output_type": "stream", "text": [ " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077797 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079179 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075521 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080093 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079018 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081668 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082476 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076965 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078774 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074510 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071941 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080517 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073007 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078209 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078658 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081968 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079493 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.068289 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075223 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078466 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075623 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076262 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073231 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077350 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081833 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078571 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074945 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079889 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086964 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081289 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073734 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080147 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080166 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080752 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076254 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072907 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073663 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073370 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080190 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079595 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078718 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084599 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083722 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079386 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074021 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079232 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076788 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081179 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085025 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077229 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077753 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083827 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083965 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076810 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084329 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076826 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081213 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085703 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078353 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082011 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085102 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072847 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073934 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079245 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079214 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077123 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080177 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078410 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084649 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080261 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072907 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075306 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074606 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082208 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078177 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078477 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084495 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080240 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076637 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079653 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.081282 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.064614 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076293 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075883 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077887 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075508 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075189 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079593 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081976 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072931 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082282 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081020 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079157 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081589 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075237 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079370 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072477 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076237 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081200 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076476 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073858 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081014 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076298 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082017 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084055 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074532 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084159 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086377 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075998 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082311 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076914 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077250 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071846 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082244 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077426 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.070942 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080380 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074755 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076032 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079865 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074310 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082720 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078520 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077765 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084739 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.090429 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076989 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084082 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074867 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077769 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085233 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.070885 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.069401 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077648 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074868 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082511 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084575 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078274 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081512 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073474 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075552 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071136 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082500 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081054 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087015 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082272 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081675 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075633 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073715 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080283 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085628 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082507 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077199 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073920 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073069 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078199 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076630 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078843 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080680 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.069673 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083845 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077793 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079867 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082486 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.068887 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077233 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.080320 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071010 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077325 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075687 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079862 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078947 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082030 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082409 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.070667 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073878 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087624 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076418 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077471 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081564 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076657 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080203 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071636 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078433 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074478 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076120 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081569 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072057 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076240 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083545 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076252 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074522 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081458 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082162 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078596 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082717 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079581 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073695 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082080 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075800 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076400 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080583 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075275 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075068 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079207 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075165 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076168 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076136 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085639 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072611 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079822 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081133 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079113 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081128 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.068912 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076042 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074893 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076354 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077473 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072076 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077952 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079634 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077249 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076537 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078682 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073808 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077046 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086167 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079593 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076411 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077453 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085346 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079283 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084733 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079498 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080105 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077248 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073508 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075949 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081468 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076809 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083721 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078076 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077855 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081947 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077784 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076060 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075722 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.075904 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073603 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078451 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087209 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083457 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085476 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080770 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079576 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075605 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076038 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083895 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078573 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086622 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084464 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077110 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081610 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084350 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078377 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082358 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077031 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081727 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082691 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071092 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078844 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076621 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081174 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076892 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078923 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079110 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082664 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083245 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.070981 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078398 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074993 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073850 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072220 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074276 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081491 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079844 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081099 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078567 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083531 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084852 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078772 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081689 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080142 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084767 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078720 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071977 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078857 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082867 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079346 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081876 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076907 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075513 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075417 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077644 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077159 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074328 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075205 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087051 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077421 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075941 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081090 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077931 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078488 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087977 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080431 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078218 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071066 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078790 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084091 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082603 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071198 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078994 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075009 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084598 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081974 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076128 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081627 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080133 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084697 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085131 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.073599 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082720 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080346 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079668 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078120 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081256 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083820 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077703 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082935 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071421 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082443 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081549 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078171 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075519 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081952 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073786 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085307 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081317 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075390 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075965 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079077 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076012 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080978 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.069253 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080887 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077523 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080188 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079882 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078119 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084172 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078225 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.070335 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082991 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073155 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078133 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080522 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073702 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084540 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078836 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.067539 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075066 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082518 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077883 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071729 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080438 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078563 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081936 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073088 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075540 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080924 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078208 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082920 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079445 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079158 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075557 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079248 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078834 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072172 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080153 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081043 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074484 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081633 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074136 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078752 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085582 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081575 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077343 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076509 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075534 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080234 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076368 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083377 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074349 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075768 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082881 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076997 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077714 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078910 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078445 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075751 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077808 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.076462 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083148 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084393 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080388 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074003 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076373 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081219 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077083 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080773 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081052 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084144 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078627 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087934 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077136 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080599 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073748 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073001 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074912 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081771 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078435 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073209 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078975 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080637 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073006 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085746 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077530 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078634 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078518 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080448 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081163 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076390 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079752 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079319 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077942 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076623 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083127 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081211 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084422 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083417 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078713 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082227 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079570 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081290 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083261 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078772 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074095 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079894 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079033 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079110 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071966 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081847 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074223 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081365 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082918 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076283 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078203 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084641 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079468 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082043 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073313 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073433 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082152 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081554 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081073 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074950 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077977 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075561 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083232 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073347 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077783 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080593 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074455 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084730 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079647 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083500 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085412 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074078 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075811 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083723 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072967 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082152 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080353 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082181 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081838 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.084936 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077100 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071804 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077892 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077486 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077977 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084605 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083244 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077016 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074545 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079138 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076821 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081208 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083317 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082337 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077987 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075928 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080599 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077505 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080683 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075692 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081312 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080225 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079441 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078239 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.090235 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078101 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080792 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076389 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072971 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073766 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076068 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076636 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079274 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075773 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080797 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072330 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077255 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074962 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078313 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079689 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080213 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083885 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074969 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076399 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078961 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076352 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081923 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.068400 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.069778 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080052 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078680 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078237 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082507 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083850 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081493 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078756 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076797 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075538 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083546 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075712 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080953 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081829 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084581 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079267 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083392 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081335 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078233 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078144 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081058 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079296 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072037 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073468 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078834 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079076 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078812 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081126 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079025 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084315 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083845 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081493 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078247 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077651 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078976 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078150 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084067 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080305 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.084100 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083058 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082561 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078300 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078548 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076834 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076606 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077034 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075258 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076010 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071977 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077673 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079644 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081309 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082858 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078011 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078656 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078357 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076942 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075447 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079049 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077497 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080182 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081285 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084149 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081768 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073723 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083984 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073886 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077994 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.069989 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074504 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076682 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077726 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084199 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072530 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081427 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078935 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080514 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076213 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074279 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076922 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076494 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081578 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081222 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073895 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080178 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079891 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078242 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074640 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079388 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082848 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073384 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084600 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082553 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078401 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073858 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076673 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079941 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076360 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079197 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085688 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076647 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076512 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080335 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078093 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079561 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077350 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080710 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.088046 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080872 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082252 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073702 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074962 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076957 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082101 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076678 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084514 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082465 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075438 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079358 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083952 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074694 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.075507 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077292 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071942 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082977 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085408 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077970 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074286 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080376 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077771 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083813 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076154 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084328 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.084912 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078989 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078648 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076211 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073566 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082766 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075248 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076837 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075417 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074538 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081921 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078395 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072825 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078979 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074941 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.088423 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076738 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077601 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072478 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082126 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.086840 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081169 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078090 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079303 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081397 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078058 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078741 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079274 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079155 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081047 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076889 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075236 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073389 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081355 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082982 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.075719 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077689 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079148 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080747 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079844 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.071434 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079402 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078486 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079271 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072164 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073978 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.073315 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078985 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.087892 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077266 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074716 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072550 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082884 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077210 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072565 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079370 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079277 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.085661 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.088575 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.072656 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.068223 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081487 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077905 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080158 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079448 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.082161 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081236 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.076812 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083575 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.074097 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081129 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078508 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.080842 ", " Iterations 10 " ] }, { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. ", " Current function value: 0.079338 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.083172 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081420 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.079930 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.081272 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.077203 ", " Iterations 10 " ] } ], "source": [ "# Enter your code below ", " ", "model_rates = [] ", "for i in range(1000): ", " train, test = train_test_split(default, test_size = 0.5, random_state = i) ", " fit = smf.logit('default ~ income + balance', data = train).fit() ", " predicted = fit.predict(test) ", " mis_rate = np.mean(predicted.round() != test['default']) ", " model_rates.append(mis_rate) ", " " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 2.0/2 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_models_rates', answer = model_rates)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Using KFold cross validation with five folds across 5 trials, calculate the average misclassification rate. Name this `mis_rate_kfold`. In your notebook, briefly explain the KFold process. ", " ", "*Hint*: Because `Stats Models` does not have its own cross validation libraries, you may have to use the following packages (specify a `random_state` equaling the trial number on each trial (0,1,2,3,4)): ", " ", " ", "- `sklearn.linear_model.LogisticRegression` ", "- `sklearn.model_selection.cross_val_score` ", "- `sklearn.model_selection.KFold`" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "mis_rate_kfold = 0.0 ", "for i in range(5): ", " kf = KFold(n_splits=5, random_state=i, shuffle=True) ", " mis_rate_kfold += np.mean(cross_val_score(LogisticRegression(), default[['income', 'balance']], default['default'], cv=kf, scoring='accuracy')) ", "mis_rate_kfold /= 5 " ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "You earned 0.5/1 points. ", " ", "But, don't worry you can re-submit and we will keep only your latest score. " ] } ], "source": [ "grader.grade(test_case_id ='test_mis_kfold', answer = mis_rate_kfold)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "5. Using bootstrap on the complete dataset, compute estimates for the standard errors of the `income` and `balance` logistic regression coefficients. In order to do this, you should perform the following steps: ", " ", " ", "- Write a function that takes as input the Default data set (and optionally, an index of the observations). The method should be called `boot_sample(data,index)`. The method should return the coefficient estimates for income and balance in the logistic regression model." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "def boot_sample(data, index): ", " """ Use bootstrap to compute estimates for the standard ", " errors of the income and balance logistic regression ", " ", " data: training data ", " index: sample indexes from bootstrap, optional ", " """ ", " if index is None: ", " index = np.random.choice(data.index, len(data)) ", " train = data.iloc[index] ", " fit = smf.logit('default ~ income + balance', data = train).fit(disp = 0) ", " return fit.params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b. Use this function to estimate the standard errors of the logistic regression coefficients for income and balance using 100 different bootstrap samples. Store your lists of results in boot_income, boot_balance, both of lists should be of size (100,1). ", "*Note*: Do not set a random seed in this problem, otherwise you will not be randomly sample from the data." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "length = 100 ", "boot_income = np.zeros(length) ", "boot_balance = np.zeros(length) ", "for i in range(length): ", " index = np.random.choice(default.index, len(default)) ", " params = boot_sample(default, index) ", " boot_income[i] = params['income'] ", " boot_balance[i] = params['balance'] ", " " ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correct! You earned 2/2 points. You are a star! ", " ", "Your submission has been successfully recorded in the gradebook. " ] } ], "source": [ "grader.grade(test_case_id ='test_boot_income_balance', answer = (boot_income, boot_balance))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Comment on the estimated standard errors obtained. What are the confidence intervals of the logistic regression coefficients? " ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "# The standard errors of the income and balance logistic regression are similar to the ", "# standard errors of the income and balance linear regression. This is because the ", "# logistic regression is a linear regression with a logit link function. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Congratulations on making the end of project 5. Please remember to save a copy of .ipynb and .html of your notebook, and mark your project as complete on Codio." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1. 22.532806324110677 ", "2. 0.40886114749753505 ", "3. 0.40886114749753505 ", "4. 21.73143847501551 23.334174173205845 ", "5. 21.2 ", "6. 0.41314042120228067 ", "7. True ", "8. 0.0264 ", "Optimization terminated successfully. ", " Current function value: 0.077489 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078256 ", " Iterations 10 ", "Optimization terminated successfully. ", " Current function value: 0.078493 ", " Iterations 10 ", "9. 0.033 ", "10. 0.02666666666666667 ", "11. 0.0258 ", "12. 0.97054 ", "13. 1.234353383034769e-05 3.1143047513886004e-05 ", "14. 0.005286322318465962 0.006188290934051121 " ] } ], "source": [ "# this is the answer for quiz ", "# remove this cell before submitting ", " ", "print("1. ",mu_hat) ", "print("2. ",se_mu_hat) ", "print("3. ",se_bootstrap) ", "print("4. ",CI_lower,CI_upper) ", "print("5. ",median_hat) ", "print("6. ",se_bootstrap_median) ", "print("7. ",se_bootstrap < se_bootstrap_median) ", "print("8. ",mis_rate) ", "# split train and test 10% test ", "train, test = train_test_split(default, test_size = 0.1, random_state = RANDOM_STATE) ", "# fit model ", "fit = smf.logit('default ~ income + balance', data = train).fit() ", "# caluculate misclassification rate ", "predicted = fit.predict(test) ", "mis_rate_10 = np.mean(predicted.round() != test['default']) ", " ", " ", "train, test = train_test_split(default, test_size = 0.3, random_state = RANDOM_STATE) ", "# fit model ", "fit = smf.logit('default ~ income + balance', data = train).fit() ", "# caluculate misclassification rate ", "predicted = fit.predict(test) ", "mis_rate_30 = np.mean(predicted.round() != test['default']) ", " ", " ", "train, test = train_test_split(default, test_size = 0.5, random_state = RANDOM_STATE) ", "# fit model ", "fit = smf.logit('default ~ income + balance', data = train).fit() ", "# caluculate misclassification rate ", "predicted = fit.predict(test) ", "mis_rate_50 = np.mean(predicted.round() != test['default']) ", "print("9. ",mis_rate_10) ", "print("10. ",mis_rate_30) ", "print("11. ",mis_rate_50) ", "print("12. ",mis_rate_kfold) ", "l, u = np.percentile(boot_income, [2.5, 97.5]) ", "print("13. ",l,u) ", "l, u = np.percentile(boot_balance, [2.5, 97.5]) ", "print("14. ",l,u)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }

ESE 542 Programming Assignment

Get Instant Homework HelpOn Your Mobile

Get Instant Homework HelpOn Your Mobile