diff --git a/notebooks/assignments/ProblemSet2_F23.ipynb b/notebooks/assignments/ProblemSet2_F23.ipynb index 6903a609..4de0748e 100644 --- a/notebooks/assignments/ProblemSet2_F23.ipynb +++ b/notebooks/assignments/ProblemSet2_F23.ipynb @@ -47,7 +47,9 @@ " !wget \"https://raw.githubusercontent.com/IDAES/idaes-pse/main/scripts/colab_helper.py\"\n", " import colab_helper\n", " colab_helper.install_idaes()\n", - " colab_helper.install_ipopt()" + " colab_helper.install_ipopt()\n", + "\n", + "import pyomo.environ as pyo" ] }, { @@ -593,36 +595,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 4. Portfolio Data Analysis\n", - "\n", - "Portfolio management is a classic example of quadratic programming (optimization). The idea is to find the optimal blend of investments that achieves a specified rate of return (or better) while minimizing the variance in rate of return. In this problem, you will use your skills in statistical analysis to analyze the stock data.\n", - "\n", - "### Historical Stock Data\n", - "\n", - "Historical daily adjusted closing prices for the last five years (obtained from Yahoo! Finance) are available for the $N=5$ stocks listed in table below. (We are actually considering index funds, but this detail does not change the analysis.) \n", - "\n", - "| Symbol | Name |\n", - "|-|-|\n", - "| GSPC | S&P 500 | \n", - "| DJI | Dow Jones Industrial Average | \n", - "| IXIC | NASDAQ Composite | \n", - "| RUT | Russell 2000 |\n", - "| VIX | CBOE Volatility Index |" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4a. Return Rate\n", - "\n", - "You are given a Stock\\_Data.csv file. Using the stock data, calculate the 1-day return rate:\n", - "\n", - "\\begin{equation}\n", - "\tr_{t,i} = \\frac{p_{t+1,i} - p_{t,i}}{p_{t,i}}\n", - "\\end{equation}\n", - "\n", - "where $p_{t+1,i}$ and $p_{t,i}$ are the *Adjusted Closing Prices* at the end of days $t+1$ and $t$, respectively, for stock $i$. These results are stored in matrix `R`. *Hint*: Use Pandas." + "## 4. Numeric Integration of Partial Differential Equations with Pyomo" ] }, { @@ -631,81 +604,117 @@ "metadata": {}, "outputs": [], "source": [ - "# This is the long path to the folder containg data files on GitHub (for the class website)\n", - "data_folder = 'https://raw.githubusercontent.com/ndcbe/data-and-computing/main/noteboohttps://raw.githubusercontent.com/ndcbe/data-and-computing/main/notebooks/data/'\n", + "%matplotlib inline\n", "\n", - "# Load the data file into Pandas\n", - "df_adj_close = pd.read_csv(data_folder + 'Stock_Data.csv')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Add your solution here" + "# Import plotting libraries\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d.axes3d import Axes3D \n", + "\n", + "# Import Pyomo\n", + "import pyomo.environ as pyo\n", + "\n", + "# Import Pyomo numeric integration features\n", + "from pyomo.dae import DerivativeVar, ContinuousSet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### 4b. Visualization\n", + "During your time at Notre Dame, you will likely want (or at least need) to solve a partial differential equation (PDE) system. In this problem, we will practice using Pyomo to numerically integrate a simple and common PDE. (Special thanks to Prof. Kantor for this problem.)\n", "\n", - "Plot the single day return rates for the 5 stocks you obtain in the previous section and check if you obtain the following profiles:\n", + "Transport of heat in a solid is described by the familiar thermal diffusion model:\n", "\n", - "![ad](https://raw.githubusercontent.com/ndcbe/data-and-computing/main/media/stock_return_plots.png)\n", + "$$\n", + "\\begin{align*}\n", + "\\rho C_p\\frac{\\partial T}{\\partial t} & = \\nabla\\cdot(k\\nabla T)\n", + "\\end{align*}\n", + "$$\n", "\n", + "We will assume the thermal conductivity $k$ is a constant, and define thermal diffusivity in the conventional way\n", "\n", - "The first plot is made for you. " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# Create figure\n", - "plt.figure(figsize=(9,15))\n", + "$$\n", + "\\begin{align*}\n", + "\\alpha & = \\frac{k}{\\rho C_p}\n", + "\\end{align*}\n", + "$$\n", "\n", - "# Create subplot for DJI\n", - "plt.subplot(5,1,1)\n", - "plt.plot(R[\"DJI\"]*100,color=\"blue\",label=\"DJI\")\n", - "plt.legend(loc='best')\n", + "We will further assume symmetry with respect to all spatial coordinates except $x$ where $x$ extends from $-X$ to $+X$. The boundary conditions are\n", "\n", - "# Add your solution here\n", + "$$\n", + "\\begin{align*}\n", + "T(t,X) & = T_{\\infty} & \\forall t > 0 \\\\\n", + "\\nabla T(t,0) & = 0 & \\forall t \\geq 0 \n", + "\\end{align*}\n", + "$$\n", "\n", - "# Show plot\n", - "plt.show()" + "where we have assumed symmetry with respect to $r$ and uniform initial conditions $T(0, x) = T_0$ for all $0 \\leq r \\leq X$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### 4c. Covariance and Correlation Matrices\n", + "### 4a. Rescaling and Dimensionless Model\n", + "\n", + "We would like a dimensionless model for two reasons: first, we only need to solve the dimensionless model once, i.e., it becomes independent of input data. Second, the dimensionless models are often scaled better for numerical solutions.\n", + "\n", + "Let's consider the following proposed scaling procedure:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "T' & = \\frac{T - T_0}{T_\\infty - T_0} \\\\\n", + "x' & = \\frac{r}{X} \\\\\n", + "t' & = t \\frac{\\alpha}{X^2}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "Show this scaling procedure gives the following dimensionless system:\n", "\n", - "Write Python code to:\n", - "1. Calculate $\\bar{r}$, the average 1-day return for each stock. Store this as the variable `R_avg`.\n", - "2. Calculate $\\Sigma_{r}$, the covariance matrix of the 1-day returns. This matrix tells us how returns for each stock vary with each other (which is important because they are correlated!). Hint: pandas has a function `cov`\n", - "3. Calculate the correlation matrix for the 1-day returns. Hint: pandas has a function `corr`.\n", + "$$\n", + "\\begin{align*}\n", + "\\frac{\\partial T'}{\\partial t'} & = \\nabla^2 T'\n", + "\\end{align*}\n", + "$$\n", "\n", - "Looking at the correlation matrix, answer the follwing questions:\n", + "with auxiliary conditions\n", "\n", - "1. Which pair of stocks have the highest **positive** correlation?\n", - "2. Which pair of stocks have the highest **negative** correlation?\n", - "3. Which pair of stocks have the lowest **absolute** correlation?\n", + "$$\n", + "\\begin{align*}\n", + "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1\\\\\n", + "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", + "\\nabla T'(t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", + "\\end{align*}\n", + "$$\n", "\n", - "Hint: Read ahead in the class website for more information on [correlation and covariance](../..//notebooks/14/Correlation-Covariance-and-Independence.ipynb)" + "Turn in your work (pencil and paper) via **Gradescope**. *Important:* Here the prime $'$ indicates the scaled variables and coordinates. It does not indicate a derivative. Thus $T'$ is scaled temperature, NOT the derivative of temperature (which begs the question of \"with respect to what?\")." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Please write one or two sentences for each question:" + "### 4b. Numeric Integration via Pyomo\n", + "\n", + "For simplicity, let's consider planar coordinates. For a slab geometry, we want to numerical integrate the following PDE:\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "\\frac{\\partial T'}{\\partial t'} & = \\frac{\\partial^2 T'}{\\partial x'^2}\n", + "\\end{align*}\n", + "$$\n", + "\n", + "with auxiliary conditions\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1 \\\\\n", + "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", + "\\frac{\\partial T'}{\\partial x'} (t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", + "\\end{align*}\n", + "$$\n", + "\n", + "Complete the following Pyomo code to integrate this PDE." ] }, { @@ -714,188 +723,129 @@ "metadata": {}, "outputs": [], "source": [ - "# Add your solution here" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "nbgrader": { - "grade": true, - "grade_id": "check-R_avg", - "locked": true, - "points": "0.5", - "solution": false - } - }, - "outputs": [], - "source": [ - "# Removed autograder test. You may delete this cell." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 4c. Markowitz Mean/Variance Portfolio Model\n", + "# Create Pyomo model\n", + "m = pyo.ConcreteModel()\n", "\n", - "The Markowitz mean/variance model, shown below, computes the optimal allocation of funds in a portfolio:\n", + "# Define sets for spatial and temporal domains\n", + "m.x = ContinuousSet(bounds=(0,1))\n", + "m.t = ContinuousSet(bounds=(0,2))\n", "\n", - "\\begin{align}\n", - "\t\t\\min_{{x} \\geq {0}} \\qquad & z:= {x}^T \\cdot {\\Sigma_r} \\cdot {x} \\\\\n", - "\t\t\\text{s.t.} \\qquad & {\\bar{r}}^T \\cdot {x} \\geq \\rho \\\\\n", - "\t\t & \\sum_{i =1}^N x_i = 1 \n", - "\\end{align} \n", + "# Define scaled temperature indexed by time and space\n", + "m.T = pyo.Var(m.t, m.x)\n", "\n", + "# Define variables for the derivates\n", + "m.dTdt = DerivativeVar(m.T, wrt=m.t)\n", + "m.dTdx = DerivativeVar(m.T, wrt=m.x)\n", + "m.d2Tdx2 = DerivativeVar(m.T, wrt=(m.x, m.x))\n", "\n", - "where $x_i$ is the fraction of funds invested in stock $i$ and $x = [x_1, x_2, ..., x_N]^T$. The objective is to minimize the variance of the return rate. (As practice for the next exam, try deriving this from the error propagation formulas.) This requires the expected return rate to be at least $\\rho$. Finally, the allocation of funds must sum to 100%.\n", + "# Define PDE equation\n", + "def pde(m, t, x):\n", + " if t == 0:\n", + " return pyo.Constraint.Skip\n", + " elif x == 0 or x == 1:\n", + " return pyo.Constraint.Skip\n", + " # Add your solution here\n", "\n", - "Write Python code to solve for $\\rho = 0.08\\%.$ Report both the optimal allocation of funds and the standard deviation of the return rate. \n", - "*Hint*:\n", - "1. Be mindful of units.\n", - "2. You can solve with problem using the Pyomo function given below\n", - "3. $:=$ means ''defined as''\n", + "m.pde = pyo.Constraint(m.t, m.x, rule=pde)\n", "\n", - "Store your answer in `std_dev`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "R_avg_tolist = R_avg.values.tolist()\n", - "Cov_list = Cov.values.tolist()\n", + "# Define first auxilary condition\n", + "def initial_condition(m, x):\n", + " if x == 0 or x == 1:\n", + " return pyo.Constraint.Skip\n", + " # Add your solution here\n", "\n", - "# Optimization Problem\n", - "def create_model(rho,R_avg,Cov):\n", - " \n", - " '''\n", - " This function solves for the optimal allocation of funds in a portfolio \n", - " by minimizing the variance of the return rate\n", - " \n", - " Arguments:\n", - " rho: required portfolio expected return\n", - " Ravg: average return rates (list)\n", - " Cov: covariance matrix\n", - " \n", - " Returns:\n", - " m: Pyomo concrete model\n", - " \n", - " '''\n", - " \n", - " m = pyo.ConcreteModel()\n", - " init_x = {}\n", - " m.idx = pyo.Set(initialize=[0,1,2,3,4])\n", - " for i in m.idx:\n", - " init_x[i] = 0\n", - " m.x = pyo.Var(m.idx,initialize=init_x,bounds=(0,None))\n", - " \n", - " def Obj_func(m):\n", - " b = []\n", - " mult_result = 0\n", - " for i in m.idx:\n", - " a = 0\n", - " for j in m.idx:\n", - " a+= m.x[j]*Cov[j][i]\n", - " b.append(a)\n", - " for i in m.idx:\n", - " mult_result += b[i]*m.x[i]\n", - " \n", - " return mult_result\n", - " m.OBJ = pyo.Objective(rule=Obj_func)\n", - " \n", - " def constraint1(m):\n", - " # Add your solution here\n", + "m.ic = pyo.Constraint(m.x, rule = initial_condition)\n", "\n", - " m.C1 = pyo.Constraint(rule=constraint1)\n", - " \n", - " def constraint2(m):\n", - " # Add your solution here\n", + "# Define second auxilary condition\n", + "def boundary_condition1(m, t):\n", + " # Add your solution here\n", "\n", - " m.C2 = pyo.Constraint(rule=constraint2)\n", - " \n", - " return m\n" + "m.bc1 = pyo.Constraint(m.t, rule = boundary_condition1)\n", + "\n", + "# Define third auxilary condition\n", + "@m.Constraint(m.t)\n", + "def boundary_condition2(m, t):\n", + " # Add your solution here \n", + "\n", + "m.bc2 = pyo.Constraint(m.t, rule=boundary_condition2)\n", + "\n", + "# Define dummy objective\n", + "m.obj = pyo.Objective(expr=1)\n", + "\n", + "# Discretize spatial coordinate with forward finite difference and 50 elements\n", + "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.x)\n", + "\n", + "# Discretize time coordinate with forward finite difference and 50 elements\n", + "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.t)\n", + "pyo.SolverFactory('ipopt').solve(m, tee=True).write()" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "rho = 0.0008\n", - "model1 = create_model(rho,R_avg_tolist,Cov_list)\n", - "\n", - "#Solve Pyomo in the method learned in Class 11\n", - "\n", - "# Add your solution here" + "### 4c. Visualize Solution " ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "nbgrader": { - "grade": true, - "grade_id": "standard-deviation", - "locked": true, - "points": "0.5", - "solution": false - } - }, - "outputs": [], - "source": [ - "# Removed autograder test. You may delete this cell." - ] - }, - { - "cell_type": "markdown", "metadata": {}, + "outputs": [], "source": [ - "### 4e. Volatility and Expected Return Tradeoff\n", + "# Extract indices\n", + "x = sorted(m.x)\n", + "t = sorted(m.t)\n", "\n", - "We will now perform sensitivity analysis of the optimization problem in 3d to characterize the tradeoff between return and risk.\n", + "# Create numpy arrays to hold the solution\n", + "xgrid = np.zeros((len(t), len(x)))\n", + "# Hint: define tgrid and Tgrid the same way\n", + "# Add your solution here\n", + "\n", + "# Loop over time\n", + "for i in range(0, len(t)):\n", + " # Loop over space\n", + " for j in range(0, len(x)):\n", + " # Copy values\n", + " xgrid[i,j] = x[j]\n", + " tgrid[i,j] = t[i]\n", + " # Hint: how to access values from Pyomo variable m.T?\n", + " # Add your solution here\n", "\n", - "Write Python code to:\n", - "1. Solve the optimization problem for many values of $\\rho$ between min($\\bar{r}$) and max($\\bar{r}$) and save the results. Use the Pyomo function created in 3d.\n", - "2. Plot $\\rho$ versus $\\sqrt{z}$ (using the saved results).\n", - "3. Write at least one sentence to interpret and discuss your plot.\n", + "# Create a 3D wireframe plot of the solution\n", + "# Hint: consult the matplotlib documentation\n", + "# https://matplotlib.org/stable/gallery/mplot3d/wire3d.html\n", "\n", - "Submit your plot and discussion via **Gradescope**." + "# Add your solution here" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "rho_vals = np.arange(0.0005,0.0038,0.0001)\n", - "std_dev = []\n", + "Write a few sentences to describe the PDE solution. Is it what you expect based on your prior knowledge of this system? Each person brings different prior knwoledge to this class, you everyone should have a distinct answer. In other words, there is no \"right answer\". Instead, this is helping you practice interpreting results based on your knowledge which is a critical skill in graduate school.\n", "\n", - "# Add your solution here" + "**Discussion:**" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "#Plot\n", + "## Submission Instructions and Tips\n", "\n", - "# Add your solution here" + "1. Answer discussion questions in this notebook.\n", + "2. When asked to store a solution in a specific variable, please also print that variable.\n", + "3. Turn in this notebook via Gradescope.\n", + "4. Also turn in written (pencil and paper) work via Gradescope.\n", + "5. Even if you are not required to turn in pseudocode, you should always write pseudocode. It takes only a few minutes and can save you *hours* of time.\n", + "6. We are not using the autograder for CBE 60258, so please skip those instructions." ] }, { "cell_type": "markdown", "metadata": {}, - "source": [ - "**Discussion**:" - ] + "source": [] } ], "metadata": { diff --git a/notebooks/assignments/ProblemSet3_F23.ipynb b/notebooks/assignments/ProblemSet3_F23.ipynb index 22c5545e..c5f3bcd0 100644 --- a/notebooks/assignments/ProblemSet3_F23.ipynb +++ b/notebooks/assignments/ProblemSet3_F23.ipynb @@ -45,7 +45,16 @@ "import math\n", "import numpy as np\n", "import scipy.stats as stats\n", - "from scipy import optimize" + "from scipy import optimize\n", + "\n", + "import sys\n", + "if \"google.colab\" in sys.modules:\n", + " !wget \"https://raw.githubusercontent.com/IDAES/idaes-pse/main/scripts/colab_helper.py\"\n", + " import colab_helper\n", + " colab_helper.install_idaes()\n", + " colab_helper.install_ipopt()\n", + "\n", + "import pyomo.environ as pyo" ] }, { @@ -1088,310 +1097,363 @@ "# Removed autograder test. You may delete this cell." ] }, - { - "cell_type": "markdown", - "metadata": { - "id": "1y6sHpO5d-fR" - }, - "source": [ - "## 3. Numeric Integration of Partial Differential Equations with Pyomo" - ] - }, { "cell_type": "code", "execution_count": null, "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 357 + }, "executionInfo": { - "elapsed": 404, + "elapsed": 1668, "status": "ok", - "timestamp": 1664677364866, + "timestamp": 1664677559084, "user": { "displayName": "Alexander Dowling", "userId": "00988067626794866502" }, "user_tz": 240 }, - "id": "OyvMIfLdd-fR" + "id": "qLQGM8Urd-fT", + "outputId": "751136c4-d2eb-4edc-c183-e30b80d82128" }, "outputs": [], "source": [ - "%matplotlib inline\n", + "# Extract indices\n", + "x = sorted(m.x)\n", + "t = sorted(m.t)\n", "\n", - "# Import plotting libraries\n", - "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.mplot3d.axes3d import Axes3D \n", + "# Create numpy arrays to hold the solution\n", + "xgrid = np.zeros((len(t), len(x)))\n", + "# Hint: define tgrid and Tgrid the same way\n", + "# Add your solution here\n", "\n", - "import sys\n", - "if \"google.colab\" in sys.modules:\n", - " !wget \"https://raw.githubusercontent.com/IDAES/idaes-pse/main/scripts/colab_helper.py\"\n", - " import colab_helper\n", - " colab_helper.install_idaes()\n", - " colab_helper.install_ipopt()\n", + "# Loop over time\n", + "for i in range(0, len(t)):\n", + " # Loop over space\n", + " for j in range(0, len(x)):\n", + " # Copy values\n", + " xgrid[i,j] = x[j]\n", + " tgrid[i,j] = t[i]\n", + " # Hint: how to access values from Pyomo variable m.T?\n", + " # Add your solution here\n", "\n", - "# Import Pyomo\n", - "import pyomo.environ as pyo\n", + "# Create a 3D wireframe plot of the solution\n", + "# Hint: consult the matplotlib documentation\n", + "# https://matplotlib.org/stable/gallery/mplot3d/wire3d.html\n", "\n", - "# Import Pyomo numeric integration features\n", - "from pyomo.dae import DerivativeVar, ContinuousSet" + "# Add your solution here" ] }, { "cell_type": "markdown", - "metadata": { - "id": "_GdDQNuud-fR" - }, + "metadata": {}, "source": [ - "During your time at Notre Dame, you will likely want (or at least need) to solve a partial differential equation (PDE) system. In this problem, we will practice using Pyomo to numerically integrate a simple and common PDE. (Special thanks to Prof. Kantor for this problem.)\n", + "## 3. Portfolio Data Analysis\n", "\n", - "Transport of heat in a solid is described by the familiar thermal diffusion model:\n", + "Portfolio management is a classic example of quadratic programming (optimization). The idea is to find the optimal blend of investments that achieves a specified rate of return (or better) while minimizing the variance in rate of return. In this problem, you will use your skills in statistical analysis to analyze the stock data.\n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\rho C_p\\frac{\\partial T}{\\partial t} & = \\nabla\\cdot(k\\nabla T)\n", - "\\end{align*}\n", - "$$\n", + "### Historical Stock Data\n", "\n", - "We will assume the thermal conductivity $k$ is a constant, and define thermal diffusivity in the conventional way\n", + "Historical daily adjusted closing prices for the last five years (obtained from Yahoo! Finance) are available for the $N=5$ stocks listed in table below. (We are actually considering index funds, but this detail does not change the analysis.) \n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\alpha & = \\frac{k}{\\rho C_p}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "We will further assume symmetry with respect to all spatial coordinates except $x$ where $x$ extends from $-X$ to $+X$. The boundary conditions are\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "T(t,X) & = T_{\\infty} & \\forall t > 0 \\\\\n", - "\\nabla T(t,0) & = 0 & \\forall t \\geq 0 \n", - "\\end{align*}\n", - "$$\n", - "\n", - "where we have assumed symmetry with respect to $r$ and uniform initial conditions $T(0, x) = T_0$ for all $0 \\leq r \\leq X$. " + "| Symbol | Name |\n", + "|-|-|\n", + "| GSPC | S&P 500 | \n", + "| DJI | Dow Jones Industrial Average | \n", + "| IXIC | NASDAQ Composite | \n", + "| RUT | Russell 2000 |\n", + "| VIX | CBOE Volatility Index |" ] }, { "cell_type": "markdown", - "metadata": { - "id": "S9E0AZB2d-fR" - }, + "metadata": {}, "source": [ - "### 3a. Rescaling and Dimensionless Model\n", + "### 3a. Return Rate\n", "\n", - "We would like a dimensionless model for two reasons: first, we only need to solve the dimensionless model once, i.e., it becomes independent of input data. Second, the dimensionless models are often scaled better for numerical solutions.\n", + "You are given a Stock\\_Data.csv file. Using the stock data, calculate the 1-day return rate:\n", "\n", - "Let's consider the following proposed scaling procedure:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "T' & = \\frac{T - T_0}{T_\\infty - T_0} \\\\\n", - "x' & = \\frac{r}{X} \\\\\n", - "t' & = t \\frac{\\alpha}{X^2}\n", - "\\end{align*}\n", - "$$\n", - "\n", - "Show this scaling procedure gives the following dimensionless system:\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "\\frac{\\partial T'}{\\partial t'} & = \\nabla^2 T'\n", - "\\end{align*}\n", - "$$\n", - "\n", - "with auxiliary conditions\n", + "\\begin{equation}\n", + "\tr_{t,i} = \\frac{p_{t+1,i} - p_{t,i}}{p_{t,i}}\n", + "\\end{equation}\n", "\n", - "$$\n", - "\\begin{align*}\n", - "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1\\\\\n", - "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", - "\\nabla T'(t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", - "\\end{align*}\n", - "$$\n", + "where $p_{t+1,i}$ and $p_{t,i}$ are the *Adjusted Closing Prices* at the end of days $t+1$ and $t$, respectively, for stock $i$. These results are stored in matrix `R`. *Hint*: Use Pandas." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# This is the long path to the folder containg data files on GitHub (for the class website)\n", + "data_folder = 'https://raw.githubusercontent.com/ndcbe/data-and-computing/main/noteboohttps://raw.githubusercontent.com/ndcbe/data-and-computing/main/notebooks/data/'\n", "\n", - "Turn in your work (pencil and paper) via **Gradescope**. *Important:* Here the prime $'$ indicates the scaled variables and coordinates. It does not indicate a derivative. Thus $T'$ is scaled temperature, NOT the derivative of temperature (which begs the question of \"with respect to what?\")." + "# Load the data file into Pandas\n", + "df_adj_close = pd.read_csv(data_folder + 'Stock_Data.csv')" ] }, { - "cell_type": "markdown", - "metadata": { - "id": "vY4nyAGid-fS" - }, + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ - "### 3b. Numeric Integration via Pyomo" + "# Add your solution here" ] }, { "cell_type": "markdown", - "metadata": { - "id": "y3qGQ6Had-fS" - }, + "metadata": {}, "source": [ - "For simplicity, let's consider planar coordinates. For a slab geometry, we want to numerical integrate the following PDE:\n", + "### 3b. Visualization\n", "\n", - "$$\n", - "\\begin{align*}\n", - "\\frac{\\partial T'}{\\partial t'} & = \\frac{\\partial^2 T'}{\\partial x'^2}\n", - "\\end{align*}\n", - "$$\n", + "Plot the single day return rates for the 5 stocks you obtain in the previous section and check if you obtain the following profiles:\n", "\n", - "with auxiliary conditions\n", + "![ad](https://raw.githubusercontent.com/ndcbe/data-and-computing/main/media/stock_return_plots.png)\n", "\n", - "$$\n", - "\\begin{align*}\n", - "T'(0, x') & = 0 & \\forall 0 \\leq x' \\leq 1 \\\\\n", - "T'(t', 1) & = 1 & \\forall t' > 0\\\\\n", - "\\frac{\\partial T'}{\\partial x'} (t', 0) & = 0 & \\forall t' \\geq 0 \\\\\n", - "\\end{align*}\n", - "$$\n", "\n", - "Complete the following Pyomo code to integrate this PDE." + "The first plot is made for you. " ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "executionInfo": { - "elapsed": 2497, - "status": "ok", - "timestamp": 1664677371426, - "user": { - "displayName": "Alexander Dowling", - "userId": "00988067626794866502" - }, - "user_tz": 240 - }, - "id": "yM3uKVfGd-fS", - "outputId": "4150d75e-328b-4ce3-a77e-7951f7c2a89d" - }, + "metadata": {}, "outputs": [], "source": [ - "# Create Pyomo model\n", - "m = pyo.ConcreteModel()\n", + "# Create figure\n", + "plt.figure(figsize=(9,15))\n", "\n", - "# Define sets for spatial and temporal domains\n", - "m.x = ContinuousSet(bounds=(0,1))\n", - "m.t = ContinuousSet(bounds=(0,2))\n", + "# Create subplot for DJI\n", + "plt.subplot(5,1,1)\n", + "plt.plot(R[\"DJI\"]*100,color=\"blue\",label=\"DJI\")\n", + "plt.legend(loc='best')\n", "\n", - "# Define scaled temperature indexed by time and space\n", - "m.T = pyo.Var(m.t, m.x)\n", + "# Add your solution here\n", "\n", - "# Define variables for the derivates\n", - "m.dTdt = DerivativeVar(m.T, wrt=m.t)\n", - "m.dTdx = DerivativeVar(m.T, wrt=m.x)\n", - "m.d2Tdx2 = DerivativeVar(m.T, wrt=(m.x, m.x))\n", + "# Show plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3c. Covariance and Correlation Matrices\n", "\n", - "# Define PDE equation\n", - "def pde(m, t, x):\n", - " if t == 0:\n", - " return pyo.Constraint.Skip\n", - " elif x == 0 or x == 1:\n", - " return pyo.Constraint.Skip\n", - " # Add your solution here\n", + "Write Python code to:\n", + "1. Calculate $\\bar{r}$, the average 1-day return for each stock. Store this as the variable `R_avg`.\n", + "2. Calculate $\\Sigma_{r}$, the covariance matrix of the 1-day returns. This matrix tells us how returns for each stock vary with each other (which is important because they are correlated!). Hint: pandas has a function `cov`\n", + "3. Calculate the correlation matrix for the 1-day returns. Hint: pandas has a function `corr`.\n", "\n", - "m.pde = pyo.Constraint(m.t, m.x, rule=pde)\n", + "Looking at the correlation matrix, answer the follwing questions:\n", "\n", - "# Define first auxilary condition\n", - "def initial_condition(m, x):\n", - " if x == 0 or x == 1:\n", - " return pyo.Constraint.Skip\n", - " # Add your solution here\n", + "1. Which pair of stocks have the highest **positive** correlation?\n", + "2. Which pair of stocks have the highest **negative** correlation?\n", + "3. Which pair of stocks have the lowest **absolute** correlation?\n", "\n", - "m.ic = pyo.Constraint(m.x, rule = initial_condition)\n", + "Hint: Read ahead in the class website for more information on [correlation and covariance](../..//notebooks/14/Correlation-Covariance-and-Independence.ipynb)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Please write one or two sentences for each of the above questions:\n", + "1. Fill in here\n", + "2. Fill in here\n", + "3. Fill in here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3d. Markowitz Mean/Variance Portfolio Model\n", "\n", - "# Define second auxilary condition\n", - "def boundary_condition1(m, t):\n", - " # Add your solution here\n", + "The Markowitz mean/variance model, shown below, computes the optimal allocation of funds in a portfolio:\n", "\n", - "m.bc1 = pyo.Constraint(m.t, rule = boundary_condition1)\n", + "\\begin{align}\n", + "\t\t\\min_{{x} \\geq {0}} \\qquad & z:= {x}^T \\cdot {\\Sigma_r} \\cdot {x} \\\\\n", + "\t\t\\text{s.t.} \\qquad & {\\bar{r}}^T \\cdot {x} \\geq \\rho \\\\\n", + "\t\t & \\sum_{i =1}^N x_i = 1 \n", + "\\end{align} \n", "\n", - "# Define third auxilary condition\n", - "@m.Constraint(m.t)\n", - "def boundary_condition2(m, t):\n", - " # Add your solution here \n", "\n", - "m.bc2 = pyo.Constraint(m.t, rule=boundary_condition2)\n", + "where $x_i$ is the fraction of funds invested in stock $i$ and $x = [x_1, x_2, ..., x_N]^T$. The objective is to minimize the variance of the return rate. (As practice for the next exam, try deriving this from the error propagation formulas.) This requires the expected return rate to be at least $\\rho$. Finally, the allocation of funds must sum to 100%.\n", "\n", - "# Define dummy objective\n", - "m.obj = pyo.Objective(expr=1)\n", + "Write Python code to solve for $\\rho = 0.08\\%.$ Report both the optimal allocation of funds and the standard deviation of the return rate. \n", + "*Hint*:\n", + "1. Be mindful of units.\n", + "2. You can solve with problem using the Pyomo function given below\n", + "3. $:=$ means ''defined as''\n", "\n", - "# Discretize spatial coordinate with forward finite difference and 50 elements\n", - "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.x)\n", + "Store your answer in `std_dev`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "R_avg_tolist = R_avg.values.tolist()\n", + "Cov_list = Cov.values.tolist()\n", "\n", - "# Discretize time coordinate with forward finite difference and 50 elements\n", - "pyo.TransformationFactory('dae.finite_difference').apply_to(m, nfe=50, scheme='FORWARD', wrt=m.t)\n", - "pyo.SolverFactory('ipopt').solve(m, tee=True).write()" + "# Optimization Problem\n", + "def create_model(rho,R_avg,Cov):\n", + " \n", + " '''\n", + " This function solves for the optimal allocation of funds in a portfolio \n", + " by minimizing the variance of the return rate\n", + " \n", + " Arguments:\n", + " rho: required portfolio expected return\n", + " Ravg: average return rates (list)\n", + " Cov: covariance matrix\n", + " \n", + " Returns:\n", + " m: Pyomo concrete model\n", + " \n", + " '''\n", + " \n", + " m = pyo.ConcreteModel()\n", + " init_x = {}\n", + " m.idx = pyo.Set(initialize=[0,1,2,3,4])\n", + " for i in m.idx:\n", + " init_x[i] = 0\n", + " m.x = pyo.Var(m.idx,initialize=init_x,bounds=(0,None))\n", + " \n", + " def Obj_func(m):\n", + " b = []\n", + " mult_result = 0\n", + " for i in m.idx:\n", + " a = 0\n", + " for j in m.idx:\n", + " a+= m.x[j]*Cov[j][i]\n", + " b.append(a)\n", + " for i in m.idx:\n", + " mult_result += b[i]*m.x[i]\n", + " \n", + " return mult_result\n", + " m.OBJ = pyo.Objective(rule=Obj_func)\n", + " \n", + " def constraint1(m):\n", + " # Add your solution here\n", + "\n", + " m.C1 = pyo.Constraint(rule=constraint1)\n", + " \n", + " def constraint2(m):\n", + " # Add your solution here\n", + "\n", + " m.C2 = pyo.Constraint(rule=constraint2)\n", + " \n", + " return m" ] }, { - "cell_type": "markdown", - "metadata": { - "id": "ZuOBPYd5d-fT" - }, + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], "source": [ - "### 3c. Visualize Solution " + "rho = 0.0008\n", + "model1 = create_model(rho,R_avg_tolist,Cov_list)\n", + "\n", + "#Solve Pyomo in the method learned in Class 11\n", + "\n", + "# Add your solution here" ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 357 - }, - "executionInfo": { - "elapsed": 1668, - "status": "ok", - "timestamp": 1664677559084, - "user": { - "displayName": "Alexander Dowling", - "userId": "00988067626794866502" - }, - "user_tz": 240 - }, - "id": "qLQGM8Urd-fT", - "outputId": "751136c4-d2eb-4edc-c183-e30b80d82128" - }, + "metadata": {}, "outputs": [], "source": [ - "# Extract indices\n", - "x = sorted(m.x)\n", - "t = sorted(m.t)\n", + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3e. Volatility and Expected Return Tradeoff\n", "\n", - "# Create numpy arrays to hold the solution\n", - "xgrid = np.zeros((len(t), len(x)))\n", - "# Hint: define tgrid and Tgrid the same way\n", - "# Add your solution here\n", + "We will now perform sensitivity analysis of the optimization problem in 3d to characterize the tradeoff between return and risk.\n", "\n", - "# Loop over time\n", - "for i in range(0, len(t)):\n", - " # Loop over space\n", - " for j in range(0, len(x)):\n", - " # Copy values\n", - " xgrid[i,j] = x[j]\n", - " tgrid[i,j] = t[i]\n", - " # Hint: how to access values from Pyomo variable m.T?\n", - " # Add your solution here\n", + "Write Python code to:\n", + "1. Solve the optimization problem for many values of $\\rho$ between min($\\bar{r}$) and max($\\bar{r}$) and save the results. Use the Pyomo function created in 3d.\n", + "2. Plot $\\rho$ versus $\\sqrt{z}$ (using the saved results).\n", + "3. Write at least one sentence to interpret and discuss your plot." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "rho_vals = np.arange(0.0005,0.0038,0.0001)\n", + "std_dev = []\n", "\n", - "# Create a 3D wireframe plot of the solution\n", - "# Hint: consult the matplotlib documentation\n", - "# https://matplotlib.org/stable/gallery/mplot3d/wire3d.html\n", + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Plot\n", "\n", "# Add your solution here" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Discussion**:" + ] + }, { "cell_type": "markdown", "metadata": { "id": "X1GR0jYZd-e9" }, "source": [ - "**Submission Instructions and Tips:**\n", + "## Submission Instructions and Tips\n", + "\n", "1. Answer discussion questions in this notebook.\n", "2. When asked to store a solution in a specific variable, please also print that variable.\n", "3. Turn in this notebook via Gradescope.\n", @@ -1399,6 +1461,11 @@ "5. Even if you are not required to turn in pseudocode, you should always write pseudocode. It takes only a few minutes and can save you *hours* of time.\n", "6. For this assignment especially, read the problem statements twice. They contain important information and tips that are easy to miss on the first read." ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] } ], "metadata": { diff --git a/notebooks/assignments/ProblemSet4_F23.ipynb b/notebooks/assignments/ProblemSet4_F23.ipynb new file mode 100644 index 00000000..f2330c0c --- /dev/null +++ b/notebooks/assignments/ProblemSet4_F23.ipynb @@ -0,0 +1,321 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem Set 4\n", + "\n", + "CBE 60258, University of Notre Dame. © Prof. Alexander Dowling, 2023\n", + "\n", + "You may not distribution the solutions without written permissions from Prof. Alexander Dowling.\n", + "\n", + "**Your Name and Email:**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import Libraries" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Measuring Acceleration Two Ways\n", + "\n", + "You and a classmate want to measure the acceleration of a cart rolling down an incline plane, but disagree on the best approach. The cart starts at rest and travels distance $l = 1.0$ m. The location of the finish line is measured with negligible uncertainty. You (student 1) measure the instantaneous velocity $v = 3.2 \\pm 0.1 $ m/s at the finish line. Your classmate (student 2) instead measures the elapsed time $t = 0.63 \\pm 0.01$s." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1a. Approach 1\n", + "\n", + "Calculate the acceleration for approach 1,\n", + "\\begin{equation}\n", + "\ta_1 = \\frac{v^2}{2l} ~,\n", + "\\end{equation}\n", + "\n", + "and estimate the associated uncertainty. Round your answer to the correct number of significant digits and store your answers in variables `A1` for acceleration and `U_A1` for the uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "nbgrader": { + "grade": true, + "grade_id": "acceleration-a", + "locked": true, + "points": "0.4", + "solution": false + } + }, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1b. Approach 2\n", + "\n", + "Calculate the acceleration for approach 2,\n", + "\\begin{equation}\n", + "\ta_2 = \\frac{2 l}{t^2}~,\n", + "\\end{equation}\n", + "\n", + "and estimate the associated uncertainty. Round your answer to the correct number of significant digits and store your answers in variables `A2` for acceleration and `U_A2` for the uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "nbgrader": { + "grade": true, + "grade_id": "acceleration-b", + "locked": true, + "points": "0.4", + "solution": false + } + }, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1c. Weighted Average\n", + "\n", + "A third classmate suggests to use a weighted average of your two calculations:\n", + "\n", + "$$\n", + "\ta_{3} = w a_1 + (1-w) a_2\n", + "$$\n", + "\n", + "where $0 \\leq w \\leq 1$ is the weight you place on the approach 1 calculation calculations. Determine the value of $w$ that minimizes the uncertainty in $a_3$. Do the following steps: \n", + "1. Make a plot to graphically determine this value of $w$ and from the plot, read the minimum value for $w$ and save it as the variable `weight`. Submit your plot via **Gradescope**.\n", + "2. Then calculate the acceleration and uncertainty from the above equation. Round your answer for acceleration and corresponding uncertainty to the correct number of significant digits and store your answers in variables `A3` for acceleration and `U_A3` for the uncertainty. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here\n", + "\n", + "print(\"weight =\",weight)\n", + "print(\"A3 =\",A3)\n", + "print(\"U_A3 =\",U_A3)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "nbgrader": { + "grade": true, + "grade_id": "acceleration-c", + "locked": true, + "points": "0.3", + "solution": false + } + }, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 1d. Analysis\n", + "\n", + "Write one or two sentences (each) to answer the following questions:\n", + "\n", + "1. If restricted to use only $a_1$ or $a_2$, which would you choose? Why?\n", + "2. How can a weighted average reduce the uncertainty? Why does this make sense?\n", + "3. Why does the uncertainty in $a_3$ depend on $w$?\n", + "\n", + "Record your answers below." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Q1:\n", + " \n", + "Q2:\n", + " \n", + "Q3:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Calorimetry for Food Analysis\n", + "\n", + "As an intern at Tasty Foods, Inc., you are asked to estimate the caloric content (kilo-calories per gram) of mayo: You burn a $0.40 \\pm 0.01$ gram sample of mayo in a calorimeter and measure a 2.75 $\\pm$ 0.02 $^\\circ{}$C temperature increase. You then calculate caloric content $C$:\n", + "\n", + "\\begin{equation}\n", + "\tC = \\frac{c ~ H ~ \\Delta T}{m} \n", + "\\end{equation}\n", + "\n", + "where $c = 0.2390$ kcal/kJ is a conversion factor. Assume the calorimeter heat capacity $H = 4.0$ kJ/$^\\circ{}$ C is known with negligible uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2b. Relative Uncertainty\n", + "\n", + "Find the relative uncertainty in $C$ by doing the following:\n", + "\n", + "1. Set $\\sigma_m = 0.01 m$ and $\\sigma_{\\Delta T} = 0$ and recalculate $\\sigma_C$. This tells us the impact of 1% uncertainty in $m$. Store your answer as variable `U_C_mass`.\n", + "2. Set $\\sigma_m = 0$ and $\\sigma_{\\Delta T} = 0.01 \\Delta T$ and recalculate $\\sigma_C$. This tells us the impact of 1% uncertainty in $\\Delta T$. Store your answer as variable `U_C_temperature`.\n", + "\n", + "*Hint*: Use the $m$ and $\\Delta T$ data reported above.\n", + "\n", + "Remember to store your answer using the correct number of significant digits." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 2c. Which is better?\n", + "\n", + "Which would provide a greater reduction in $\\sigma_C$: i) reducing the uncertainty in $m$ to 0.005 g OR ii) reducing the uncertainty in $\\Delta T$ to 0.001 $^\\circ{}$C? Do the following steps:\n", + "1. Calculate the uncertainty for each scenario, storing your variables as i) `Reduce_mass` and ii) `Reduce_temperature`. \n", + "2. After determining which method would provide a greater reduction in $\\sigma_C$, set the variable `method` equal to either 1, for reducing the uncertainty in mass, or 2, for reducing the uncertainty in temperature, to save which method you found would more significantly reduce $\\sigma_C$.\n", + "\n", + "Remember to use the correct number of significant digits." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Add your solution here" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Removed autograder test. You may delete this cell." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/contrib-dev/Alcohol_Pharmacokinetics.ipynb b/notebooks/contrib-dev/Alcohol_Pharmacokinetics.ipynb new file mode 100644 index 00000000..3a7a7715 --- /dev/null +++ b/notebooks/contrib-dev/Alcohol_Pharmacokinetics.ipynb @@ -0,0 +1,1075 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "Z86_V7zJ-JWe" + }, + "source": [ + "# Alcohol Pharmacokinetics and Blood Alcohol Content % Modeling\n", + "\n", + "Prepared by: Phuong Cao - tcao2@nd.edu and Cleveland Keal - ckeal@nd.edu\n", + "\n", + "Edited by: Feng Gao - fgao2@nd.edu\n", + "\n", + "Based on Problem 6-7b of Fogler, H. S. (2006). 6. In Elements of chemical reaction engineering (3rd ed., pp. 323–324). essay, Prentice-Hall of India. ISBN 978-0135317082\n", + "\n", + "\n", + "## Problem Description\n", + "This problem is meant to provide practice for undergraduate students in using coding to model and understand chemical engineering reaction kinetics and have a better understanding of the kinetics of alcohol in the body.\n", + "\n", + "Aditionaly, doing this project is a chance to learn and practice solving ODE equation.\n", + "\n", + "After working on this project, the students also be more familier using Numpy library which help in constructing array, matrix, and multiple mathematics functions, Scipi library which help in solving integral function more efficiently in this project, and Matplotlib which provides visualization when they graph." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dqQfTbSOYWuK" + }, + "source": [ + "**Useful links to review library**\n", + "1. Numpy\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/NumPy.html?highlight=numpy#getting-started-with-numpy-arrays\n", + "\n", + "2. Scipy\n", + "\n", + " https://docs.scipy.org/doc/numpy-1.15.0/user/quickstart.html\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/04/Linear-Algebra-in-Numpy.html?highlight=scipy#scipy\n", + " \n", + "3. Matplotlib\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html#matplotlib-basics\n", + "\n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html#customizing-plots\n", + " \n", + " https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html#plotting-multiple-lines" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "0HeZgROq6gnm" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import integrate" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QblP7is2GEYt" + }, + "source": [ + "## Background: Modeling Blood Alcohol Content %\n", + "\n", + "Pharmacokinetics concerns the ingestion, distribution, reaction, and elimination reaction of drugs in the body. Consider the application of pharmacokinetics to a common American passtime, drinking.\n", + "\n", + "One of the most commonly ordered drinks is a martini, therefore we shall model changes in Blood alcohol % after having a given amount of tall martinis.\n", + "\n", + "Blood Alcohol Content % (BAC) is a percent value of grams of alcohol per 100 mililiters of blood, and can be modelded by determining:\n", + "* The amount of alcohol ingested\n", + "* the rate you drink the alcohol\n", + "* How long it takes for the alcohol to leave the intestine and enter the bloodstream.\n", + "* how long it takes for your body to break down the alcohol\n", + "\n", + "We will be using Ordinary Differential Equations (ODEs) to find the kinetics\n", + "\n", + "Some important info to solve these problems are:\n", + "\n", + "\n", + "* Blood Volume(L) is about 8% of the body's weight (kg)\n", + "* A tall martini is 150mL and is 30% ABV (Alcohol by Volume)\n", + "* The density of alcohol is 0.789 g/mL\n", + "* The legal limit in the U.S. is 0.08% or 0.08 g alcohol per 100 mililiter of blood\n", + "* The human body typically metabolizes alcohol at a constant rate, with the average rate being ~10 mL of pure ethanol per hour.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Learning Goals of The Project\n", + "* Understanding Pharmacokinetics: Modoling the kinetics of alcohol absorption and elimination in the body as a fundamental aspect of pharmacokinetics.\n", + "* Mathematical Modeling: Using ordinary differential equation (ODE) to model the kinetics of alcohol in the body to predict its behavior in biological systems.\n", + "* Simulation: By writing and revising Python code, the translation of theoretical models into practical simulations is strengthened.\n", + "* Visualization: Creating plots to visualize the changes in alcohol concentration over time, which is essential for interpreting and communicating complex data in a clear and accessible way." + ], + "metadata": { + "id": "nKKJx9juPhZF" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "CNv59kkv2poo" + }, + "source": [ + "## Analysis" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zEE6J3UhC1vu" + }, + "source": [ + "### 1A Calculating Alcohol Ingestion\n", + "\n", + "\n", + " Make a function that determines the total amount of alcohol one will drink in a given \"session\" based on martinis drink and body weight.\n", + "\n", + "**Watch your units!**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JIpTfjhd2pop" + }, + "source": [ + "This function helps to etermine the initial alcohol concentration in the intestine based on number of tall martinis drink and body weight(kg)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "JxI2t20j93Ap" + }, + "outputs": [], + "source": [ + "def drinks(m, n):\n", + " \"\"\"Determines the initial alcohol concentration in the intestine based on\n", + " of tall martinis drink and body weight(kg)\n", + " Args:\n", + " n: number of martinis drink\n", + " m: Body weight (kg)\n", + " Returns:\n", + " CT: The total amount concentration of alcohol ingested,\n", + " Ca0 for the differential equation\n", + " \"\"\"\n", + "\n", + " # add your solution here\n", + " ### BEGIN SOLUTION\n", + " # Alcohol by Volume\n", + " ABV = 0.3 # unit %\n", + "\n", + " # Alcohol density\n", + " den = 0.789 # unit g/mL\n", + "\n", + " # Blood volume\n", + " L_blood = m * 0.08 # unit L\n", + "\n", + " # Volume of martini\n", + " V = 150 * n # unit mL\n", + "\n", + " # Volume of alcohol\n", + " Va = V * ABV # unit mL\n", + "\n", + " # Mass of alcohol\n", + " g_alcohol = den * Va # unit g\n", + " ### END SOLUTION\n", + "\n", + " CT = g_alcohol / (L_blood)\n", + " return CT\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vCz0zsqbKBgf" + }, + "source": [ + "### 1B. ODE Equations\n", + "\n", + "\n", + "The Pharmacokinetics of alcohol involves 3 reactions occuring:\n", + "\n", + "__1. Rate of alcohol injestion (how fast one drinks or how fast the alcohol enters ones stomach)__\n", + "\n", + "\\begin{equation}\n", + "r_0 = \\frac{d[C_0]}{dt} = -k_0 \\cdot [C_0]\n", + "\\end{equation}\n", + "rate of injestion into the gastrointestinal tract is a first-order reaction with a specific reaction rate constant of about 10 $h^{-1}$ ($h^{-1}$ is per hour since it's a first-order reaction)\n", + "\n", + "__2. Rate of alcohol distribution (how fast the alcohol leaves ones stomach and enters the bloodstream)__\n", + "\\begin{equation}\n", + "r_1 = \\frac{d[C_A]}{dt} = k_0 \\cdot [C_0] - k_1 \\cdot [C_A]\n", + "\\end{equation}\n", + "rate of absorption from the gastrointestinal tract into the bloodstream and body is a first-order reaction with a specific reaction rate constant of 10 $h^{-1}$ ($h^{-1}$ is per hour since it's a first-order reaction)\n", + "\n", + "__3. Rate of alcohol elimination (how fast the body breaks down alcohol after entering the bloodstream)__\n", + "\\begin{equation}\n", + "r_2 = -r_1 - k_2\n", + "\\end{equation}\n", + "The rate at which ethanol is broken down in the bloodstream is limited by regeneration of a coenzyme. Consequently, the process may be modeled as a zero-order reaction with a specific reaction rate constant k_2 of 1.92 g/h-L of blood (zero-order reation).\n", + "\n", + "\n", + "Make a function that sets up the ODE solver for alcohol entering the stomach(dC0/dt) leaving the intestine (dCa/dt), entering the blood and being broken down (dCb/dt), Then turn it into Blood alcohol % (dBAC/dt)\n", + "\n", + "Derive a formula to find Ca, Cb, and BAC using the rate laws, turn in the written work into **Gradescope**\n", + "\n", + "Hint: You dont need to use r0 when deriving dCb/dt\n", + "\n", + "* [Scipy reaction rate help](https://ndcbe.github.io/data-and-computing/notebooks/07/Example-Reaction-Rates.html)\n", + "* [Scipy.integrate help](https://docs.scipy.org/doc/scipy/reference/integrate.html#)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "fu_R4FsO6ej4" + }, + "outputs": [], + "source": [ + "def f(t, y):\n", + " \"\"\"RHS of differential equation for reaction kinetics\n", + " Args:\n", + " t: time\n", + " y: values for differential questions, [CA, CB, BAC]\n", + " Returns:\n", + " dydt: first derivation of y w.r.t. t\n", + " \"\"\"\n", + "\n", + " # Unpack current values of y\n", + " C0, CA, CB, BAC = y\n", + "\n", + " # dC0 rate constant.\n", + " # if statement added so models don't go below 0\n", + " if C0 < 0:\n", + " k0 = 0\n", + " else:\n", + " k0 = 10 # 1/h\n", + "\n", + " # dCa rate constant\n", + " k1 = 10 # 1/h\n", + "\n", + " # dCb and dBAC rate constant\n", + " # if statement added so models don't go below 0\n", + " if CB < 0:\n", + " k2 = 0\n", + " else:\n", + " k2 = 1.92 # g/hL\n", + "\n", + " # Store equations as a list in the variable dydt\n", + "\n", + " # Add your solution here\n", + " ### BEGIN SOLUTION\n", + " dC0 = -k0 * C0\n", + " dCA = (k0 * C0) - k1 * CA\n", + " dCB = k1 * CA - k2\n", + " # BAC is in g/dL, CB is in g/L, so divided by 10\n", + " dBAC = dCB / 10 # g/100mL\n", + " ### END SOLUTION\n", + " dydt = [dC0, dCA, dCB, dBAC]\n", + "\n", + " return dydt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zUVAuNrrEdgP" + }, + "source": [ + "\n", + "Discuss in 3-5 sentences what theses ODEs say about the Pharmacokinetics of alcohol.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "rFj5qSrOM1H9" + }, + "source": [ + "**Discussion:**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-XjcPqq0K6K0" + }, + "source": [ + "### 1C. BAC Modeling: Sobering up\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "tTT4vyOBN-AE" + }, + "source": [ + "This function solves the ODE for dCa/dt, dCb/dt, and dBAC/dt that you made in part 1B.\n", + "\n", + "**Its important to note that this ODE assumes that a person of \"m\" weight drinks \"n\" number of drinks on a moderatley full stomach at a given rate then stops.**" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "HjigLETp9QIi" + }, + "outputs": [], + "source": [ + "def SolveODE(CT, tmax, f):\n", + " \"\"\"Solves differential equation for reaction kinetics\n", + " Args:\n", + " CT: initial concentration of C0\n", + " tmax: the amount of time passed/ the x value of the model\n", + " f: the Setup function for the solver\n", + " Returns:\n", + " C0: Concentration profile of alcohol in the stomach\n", + " CA: Concentration profile of alcohol in the intestine\n", + " CB: Concentration profile of alcohol in the blood\n", + " BAC: % value of CB\n", + " t: Time array for the simulation\n", + " \"\"\"\n", + "\n", + " # Initial values\n", + " C00 = CT\n", + " CA0 = 0.0\n", + " CB0 = 0.0\n", + " BAC0 = 0.0\n", + "\n", + " # Bundle initial conditions for ODE solver\n", + " y0 = [C00, CA0, CB0, BAC0]\n", + " t = np.arange(0, tmax, 0.1)\n", + " tspan = [np.min(t), np.max(t)]\n", + "\n", + " # Call the ODE solver\n", + " soln = integrate.solve_ivp(f, tspan, y0, t_eval=t, method=\"RK23\")\n", + "\n", + " # print(soln)\n", + " C0 = soln.y[0]\n", + " CA = soln.y[1]\n", + " CB = soln.y[2]\n", + " BAC = soln.y[3]\n", + "\n", + " return C0, CA, CB, BAC, t" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "euVwk3g2tcXP" + }, + "source": [ + "This function puts it all together and places the model info into an array." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "SndkzVLDtfqX" + }, + "outputs": [], + "source": [ + "def Model_info(n, m, tmax):\n", + " \"\"\"Puts the previous functions together,\n", + " and puts the information into a single variable array\n", + " Args:\n", + " n: number of martinis drink\n", + " m: body weight (kg)\n", + " tmax: the amount of time passed/ the x value of the model\n", + "\n", + " Returns:\n", + " S: The tuple contains all concentrations and time array\n", + " \"\"\"\n", + " # Calculate initial alcohol concentration in the stomach\n", + " CT = drinks(m, n)\n", + "\n", + " # Solve the ODEs to get the concentration profiles and BAC over time\n", + " C0, CA, CB, BAC, t = SolveODE(CT, tmax, f)\n", + "\n", + " # Bundle the results into a single tuple\n", + " S = (C0, CA, CB, BAC, t)\n", + "\n", + " return S" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aPFWWK3CE3l2" + }, + "source": [ + "A 75kg person drinks 2 tall martinis over the course of an hour (as determined by k0). How long must they wait to drive after the hour of drinking? You can do this just by modeling **Ca and BAC or C0 and BAC**. Remember, In most states the legal intoxication limit is 0.08 % Blood Alcohol Content (BAC) or 0.08 g ethanol for every 100 mililiter of blood. **Plot the model using a twin axis.\n", + "* [Twin axis plot help](https://matplotlib.org/stable/gallery/subplots_axes_and_figures/two_scales.html#sphx-glr-gallery-subplots-axes-and-figures-two-scales-py)\n", + "* [Matplotlib help](https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html?highlight=matplotlib)\n", + "\n", + "*Hint: variable \"C\" is a list containing all of the information you need.*\n", + "\n", + "Extra credit: Make 2 twin axis plots. One for Ca and BAC and one for C0 and BAC*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "mptOLBnM2pos" + }, + "source": [ + "**Answer (after plotting):**" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "id": "7u4B7OoaL7fq", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 834 + }, + "outputId": "cc950505-b381-45d2-892e-bf2bee5832e8" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Time to sober up to below the legal limit: 2.10 hours\n" + ] + } + ], + "source": [ + "# You can change tmax(3) here. Increase tmax to 10 h\n", + "C = Model_info(2, 75, 10)\n", + "\n", + "# Add your solution here\n", + "### BEGIN SOLUTION\n", + "# Plot CA and BAC\n", + "fig, ax1 = plt.subplots(figsize=(6.4, 4), dpi=100)\n", + "ax1.set_xlabel(\"time (hr)\", fontsize=14)\n", + "ax1.set_ylabel(\"CA (g/L)\", color=\"green\", fontsize=14)\n", + "ax1.plot(C[4], C[1], color=\"green\")\n", + "ax1.tick_params(axis=\"y\", labelcolor=\"green\")\n", + "\n", + "ax2 = ax1.twinx()\n", + "ax2.set_ylabel(\"BAC (%)\", color=\"red\", fontsize=14)\n", + "ax2.plot(C[4], C[3], color=\"red\")\n", + "ax2.tick_params(axis=\"y\", labelcolor=\"red\")\n", + "\n", + "plt.title(\"Alcohol Absorption Kinetics\", fontsize=16, fontweight=\"bold\")\n", + "plt.show()\n", + "\n", + "# Plot C0 and BAC\n", + "fig, ax1 = plt.subplots(figsize=(6.4, 4), dpi=100)\n", + "ax1.set_xlabel(\"time (hr)\", fontsize=14)\n", + "ax1.set_ylabel(\"C0 (g/L)\", color=\"blue\", fontsize=14)\n", + "ax1.plot(C[4], C[0], color=\"blue\")\n", + "ax1.tick_params(axis=\"y\", labelcolor=\"blue\")\n", + "\n", + "ax2 = ax1.twinx()\n", + "ax2.set_ylabel(\"BAC (%)\", color=\"red\", fontsize=14)\n", + "ax2.plot(C[4], C[3], color=\"red\")\n", + "ax2.tick_params(axis=\"y\", labelcolor=\"red\")\n", + "\n", + "plt.title(\"Alcohol Consumption and Elimination Kinetics\", fontsize=16, fontweight=\"bold\")\n", + "plt.show()\n", + "\n", + "# Find the time when BAC falls below the legal limit\n", + "legal_limit = 0.08 # 0.08%\n", + "\n", + "# Find the index where BAC first exceeds the legal limit\n", + "above_limit_indices = np.where(C[3] > legal_limit)[0]\n", + "\n", + "# If there's at least one point where BAC is above the limit, proceed\n", + "if above_limit_indices.size > 0:\n", + " # Find the first index where BAC is above the limit\n", + " first_above_index = above_limit_indices[0]\n", + "\n", + " # Search from the first_above_index to avoid catching the initial rise\n", + " below_limit_indices = np.where(C[3][first_above_index:] < legal_limit)[0]\n", + "\n", + " # Avoid the first time\n", + " if below_limit_indices.size > 0:\n", + " # Add first_above_index to it to get the index in the original array\n", + " first_below_index = below_limit_indices[0] + first_above_index\n", + "\n", + " # Find the time\n", + " time_falls_below = C[4][first_below_index]\n", + " print(f\"Time to sober up to below the legal limit: {time_falls_below:.2f} hours\")\n", + " else:\n", + " print(\"BAC does not fall below the legal limit within the time frame.\")\n", + "else:\n", + " print(\"BAC never exceeds the legal limit within the time frame.\")\n", + "\n", + "\n", + "### END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "C3HXfCDa2-M0" + }, + "source": [ + "Using the plotted kinetics **Discuss in 3-6 sentences** how long it takes for alcohol to enter the blood stream vs how long it takes for the alcohol to break down. How would BAC change over time if the person weighed more/less? If they drink more/less?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VK-3NOub6R64" + }, + "source": [ + "**Discussion:**" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## 1D. Example of Forward Euler Method for ODEs\n", + "\n", + "The Forward Euler method is a straightforward numerical approach for solving ODEs.\n", + "\n", + "Given the Pharmacokineticsm, simplify it and and consider a first-order linear ODE of the form:\n", + "\n", + "$$\n", + "\\frac{dC}{dt} = -kC\n", + "$$\n", + "\n", + "where ( C ) represents the concentration of a substance (e.g., alcohol in the blood), and ( k ) is the rate constant for elimination.\n", + "\n", + "The Forward Euler method approximates the derivative at a point by considering the slope of the line connecting the current point and the next point, which can be expressed as:\n", + "\n", + "$$\n", + "\\frac{dC}{dt} \\approx \\frac{C(t+\\Delta t) - C(t)}{\\Delta t}\n", + "$$\n", + "\n", + "Using this approximation, we can update the concentration ( C ) at each time step ( ${\\Delta t}$ ) as follows:\n", + "\n", + "$$\n", + "C(t+\\Delta t) = C(t) - kC(t)\\Delta t\n", + "$$\n", + "\n", + "This method iteratively updates the value of ( C ) over time, allowing us to model the change in concentration due to the process described by the ODE." + ], + "metadata": { + "id": "bW6nx9fvchxy" + } + }, + { + "cell_type": "code", + "source": [ + "def forward_euler(k, C0, tmax, dt):\n", + " \"\"\"\n", + " Solves the ODE using the forward Euler method.\n", + "\n", + " Args:\n", + " k: Rate constant for elimination\n", + " C0: Initial concentration of alcohol\n", + " tmax: Maximum time to run the simulation\n", + " dt: Time step size\n", + "\n", + " Returns:\n", + " t_values: Array of time values\n", + " C_values: Array of concentration values\n", + " \"\"\"\n", + " t_values = np.arange(0, tmax, dt)\n", + " C_values = np.zeros_like(t_values)\n", + "\n", + " # Initial condition\n", + " C_values[0] = C0\n", + "\n", + " # Time-stepping loop\n", + " for i in range(1, len(t_values)):\n", + " C_values[i] = C_values[i-1] - k * C_values[i-1] * dt\n", + "\n", + " return t_values, C_values\n", + "\n", + "# Parameters\n", + "k = 0.2 # Example elimination rate constant\n", + "C0 = 1.0 # Initial concentration\n", + "tmax = 10 # Total time\n", + "dt = 0.1 # Time step size\n", + "\n", + "# Run the simulation\n", + "t_values, C_values = forward_euler(k, C0, tmax, dt)\n", + "\n", + "# Plot the results\n", + "plt.plot(t_values, C_values, label='Forward Euler')\n", + "plt.xlabel('Time (hr)', fontsize=14)\n", + "plt.ylabel('Concentration (g/L)', fontsize=14)\n", + "plt.title('Alcohol Metabolism Over Time', fontsize=16, fontweight=\"bold\")\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 479 + }, + "id": "JdDCUs4QdgrK", + "outputId": "2b0ac5ed-b378-418b-e48a-b477614fd42e" + }, + "execution_count": 23, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KqQHne6ZWe_N" + }, + "source": [ + "### 2A. Alcohol Poisoning\n", + "\n", + "[According to the Cleveland Clinic](https://my.clevelandclinic.org/health/diagnostics/22689-blood-alcohol-content-bac#:~:text=BAC%200.30%25%20to%200.40%25%3A,arrest%20(absence%20of%20breathing).), Alcohol Poisoning occurs when you have a Blood Alcohol Content above 0.3%, at that point you start Blacking out and have a potentially lethal amount of alcohol in your blood. Another commonly ordered drink is a shot, which is about 45 mL and 40% ABV.\n", + "Therefore, we're going to model how many shots one can drink before poisoning themself.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xINBmJfub4Ll" + }, + "source": [ + "Rework, the drinks function to calculate Cai for shots" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "sl6ESBLkcJCl" + }, + "outputs": [], + "source": [ + "def drinks(m, n):\n", + " \"\"\"Determines the initial alcohol concentration in the intestine based on\n", + " # of tall martinis drink and body weight(kg)\n", + " Args:\n", + " n: number of martinis drink\n", + " m: Body weight (kg)\n", + " Returns:\n", + " CT: The total amount concentration of alcohol ingested,\n", + " Ca0 for the differential equation\n", + " \"\"\"\n", + " # add your solution here\n", + " ### BEGIN SOLUTION\n", + " ABV = 0.4\n", + " blood = m * 0.08\n", + " den = 0.789 # g/mL\n", + " V = 45 * n\n", + " Va = V * ABV\n", + " mass_alcohol = den * Va\n", + " CT = mass_alcohol / blood\n", + " ### END SOLUTION\n", + "\n", + " return CT" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qPoxjY2mcZk2" + }, + "source": [ + "### 2B. Alcohol Poisoning Modeling\n", + "\n", + "Use the ODE models and kinetics plots to determine how many shots a 60 kg person can drink before getting alcohol poisoning *assuming they drink all of the shot within an hour*\n", + "\n", + "*Hint: plots and code can be reused*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "V1IAmZZg2pou" + }, + "source": [ + "**Answer (after graphing):**" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "id": "VXm7s7KZcyS4", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 862 + }, + "outputId": "e618dd86-7572-4a72-c5be-dc8f70232622" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The number of shots leading to alcohol poisoning is: 2\n" + ] + } + ], + "source": [ + "# Change n,m and tmax here\n", + "C = Model_info(11, 60, 3)\n", + "\n", + "# Add your solution here\n", + "### BEGIN SOLUTION\n", + "# Display the plots\n", + "# Fig 1\n", + "fig, ax1 = plt.subplots(figsize=(6.4, 4), dpi=100)\n", + "ax1.set_xlabel(\"time (hr)\", fontsize=14)\n", + "ax1.set_ylabel(\"CA (g/L)\", color=\"green\", fontsize=14)\n", + "ax1.plot(C[4], C[1], color=\"green\")\n", + "ax1.tick_params(axis=\"y\", labelcolor=\"green\")\n", + "\n", + "ax2 = ax1.twinx()\n", + "ax2.set_ylabel(\"BAC (%)\", color=\"red\", fontsize=14)\n", + "ax2.plot(C[4], C[3], color=\"red\")\n", + "ax2.tick_params(axis=\"y\", labelcolor=\"red\")\n", + "\n", + "fig.tight_layout()\n", + "plt.title(\"Alcohol Absorption Kinetics\", fontsize=16, fontweight=\"bold\")\n", + "max_BAC = max(C[3])\n", + "\n", + "# Fig 2\n", + "fig, ax1 = plt.subplots(figsize=(6.4, 4), dpi=100)\n", + "ax1.set_xlabel(\"time (hr)\", fontsize=14)\n", + "ax1.set_ylabel(\"C0 (g/L)\", color=\"blue\", fontsize=14)\n", + "ax1.plot(C[4], C[0], color=\"blue\")\n", + "ax1.tick_params(axis=\"y\", labelcolor=\"blue\")\n", + "\n", + "ax2 = ax1.twinx()\n", + "ax2.set_ylabel(\"BAC (%)\", color=\"red\", fontsize=14)\n", + "ax2.plot(C[4], C[3], color=\"red\")\n", + "ax2.tick_params(axis=\"y\", labelcolor=\"red\")\n", + "\n", + "fig.tight_layout()\n", + "plt.title(\"Alcohol Consumption and Elimination Kinetics\", fontsize=16, fontweight=\"bold\")\n", + "plt.show()\n", + "\n", + "# Determine the number of shots\n", + "# Initial parameters\n", + "m = 60 # kg\n", + "tmax = 1 # hour\n", + "n = 1 # start with one shot\n", + "poisoning_threshold = 0.3\n", + "\n", + "# Loop to find the number of shots leading to alcohol poisoning\n", + "while True:\n", + " # Run the model with the current number of shots\n", + " C = Model_info(n, m, tmax)\n", + " max_BAC = max(C[3])\n", + "\n", + " # Check if the maximum BAC exceeds the poisoning threshold\n", + " if max_BAC >= poisoning_threshold:\n", + " break\n", + " else:\n", + " n += 1\n", + "\n", + "# Print the result\n", + "print(f\"The number of shots leading to alcohol poisoning is: {n}\")\n", + "\n", + "### END SOLUTION" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BBnIfGlbiECT" + }, + "source": [ + "Some people can develop a tolerance to alcohol. So they may not feel the same effects of alcohol even after drinking the same amount they used to drink. This doesn’t mean their BAC is lower. It just means they experience the effects of alcohol differently.\n", + "\n", + "Discuss, in 3-5 sentences, why that might be the case, and why weight does affect ones BAC." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "jILMmNSskVhk" + }, + "source": [ + "**Discussion:**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FB5Vk9Sild8M" + }, + "source": [ + "### 3A. Pharmacokinetics Factors\n", + "\n", + "Given what you now know about how BAC changes over time and how weight and number of drinks affect those kinetics, we will now explore other factors that affect those kinetics\n", + "\n", + "1. The rate at which one drinks (k0)\n", + "2. How much one eats before drinking (k1)\n", + "\n", + " \"Thus, alcohol consumed after a heavy meal is released to the duodenum\n", + "slowly, reducing the rate of absorption and thereby attenuating the subsequent blood alcohol curve.\"\n", + "\n", + " *Source:(Gentry, R.T. (2000), Effect of Food on the Pharmacokinetics of Alcohol Absorption. Alcoholism: Clinical and Experimental Research, 24: 403-404. https://doi.org/10.1111/j.1530-0277.2000.tb01996.x)*\n", + "\n", + "\n", + "Change the \"f\" function to account for someone drinking faster/slower and having more/less food in ones stomach before drinking and model how that affects the BAC over time *under the same n and m values*.\n", + "\n", + "**Discuss those effects in 3-5 sentences.**" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "id": "mm5n_n1mDmBJ" + }, + "outputs": [], + "source": [ + "def f(t, y):\n", + " \"\"\"RHS of differential equation for reaction kinetics\n", + " Args:\n", + " t: time\n", + " y: values for differential questions, [CA, CB, BAC]\n", + " Returns:\n", + " dydt: first derivation of y w.r.t. t\n", + "\n", + " \"\"\"\n", + " # unpack current values of y\n", + " C0, CA, CB, BAC = y\n", + "\n", + " # dC0 rate constant.\n", + " # How fast is one drinking? Define parameters here\n", + " if C0 < 0:\n", + " k0 = 0 # 1/h\n", + " else:\n", + " k0 = 10 # 1/h\n", + "\n", + " # dCa rate constant.\n", + " # How much did one eat? Define parameters here\n", + " k1 = 10 # 1/h\n", + " # dCb and dBAC rate constant\n", + " # if statment added so they dont go below 0\n", + " if BAC < 0:\n", + " k2 = 0 # g/hL\n", + " else:\n", + " k2 = 1.92 # g/hL\n", + "\n", + " # Store equations as a list in the variable dydt\n", + "\n", + " # Add your solution here\n", + " ### BEGIN SOLUTION\n", + " dC0 = -k0 * C0\n", + " dCA = (k0 * C0) - k1 * CA\n", + " dCB = k1 * CA - k2\n", + " dBAC = dCB / 10 # %\n", + " dydt = dC0, dCA, dCB, dBAC\n", + " ### END SOLUTION\n", + "\n", + " return dydt" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "id": "hYEyhOgwLIqD", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 868 + }, + "outputId": "54b4a379-7652-4e08-c5fe-1671cbdb45cd" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Maximum BAC reached: 1.63%\n", + "\n", + "\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" + }, + "metadata": {} + } + ], + "source": [ + "# add input values into the function\n", + "C = Model_info(10, 100, 6)\n", + "\n", + "# Add your solution here\n", + "### BEGIN SOLUTION\n", + "# Plot CA and BAC\n", + "fig, ax1 = plt.subplots(figsize=(6.4, 4), dpi=100)\n", + "ax1.set_xlabel(\"time (hr)\", fontsize=14)\n", + "ax1.set_ylabel(\"CA (g/L)\", fontsize=14, color=\"green\")\n", + "ax1.plot(C[4], C[1], color=\"green\")\n", + "ax1.tick_params(axis=\"y\", labelcolor=\"green\")\n", + "\n", + "ax2 = ax1.twinx()\n", + "ax2.set_ylabel(\"BAC (%)\", fontsize=14, color=\"red\")\n", + "ax2.plot(C[4], C[3], color=\"red\")\n", + "ax2.tick_params(axis=\"y\", labelcolor=\"red\")\n", + "\n", + "plt.title(\"Alcohol Absorption Kinetics\", fontsize=16, fontweight=\"bold\")\n", + "\n", + "# Plot C0 and BAC\n", + "fig, ax1 = plt.subplots(figsize=(6.4, 4), dpi=100)\n", + "ax1.set_xlabel(\"time (hr)\", fontsize=14)\n", + "ax1.set_ylabel(\"C0 (g/L)\", fontsize=14, color=\"blue\")\n", + "ax1.plot(C[4], C[0], color=\"blue\")\n", + "ax1.tick_params(axis=\"y\", labelcolor=\"blue\")\n", + "\n", + "ax2 = ax1.twinx()\n", + "ax2.set_ylabel(\"BAC (%)\", fontsize=14, color=\"red\")\n", + "ax2.plot(C[4], C[3], color=\"red\")\n", + "ax2.tick_params(axis=\"y\", labelcolor=\"red\")\n", + "\n", + "plt.title(\"Alcohol Consumption and Elimination Kinetics\", fontsize=16, fontweight=\"bold\")\n", + "\n", + "# Determine the maximum BAC reached\n", + "max_BAC = max(C[3])\n", + "print(f\"Maximum BAC reached: {max_BAC:.2f}%\")\n", + "print(\"\\n\")\n", + "\n", + "plt.show()\n", + "### END SOLUTION\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QYczsCo2_iqV" + }, + "source": [ + "### 3B. Final Discussion\n", + "Given what you now know about how BAC changes over time and what affects those changes. Discuss in 1-3 sentences how your BAC will/won't change over the various scenarios:\n", + "\n", + "\n", + "1. Drink on an empty stomach\n", + "2. One drink everything over the course of 5 hours instead of all at once\n", + "3. You drink water in between drinks **But drinks at the same rate** (*Trick Question: Water doesnt nessecarily change your BAC, it just stops you from drinking too much too fast*)\n", + "\n", + "\n", + "Even if the amount one drinks doesn't change.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-VK2faIvpSvj" + }, + "source": [ + "**Discussion:**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1AQYs1r4jA0N" + }, + "source": [ + "Reminder: Drink Responsibly!" + ] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "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": "3.9.16" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file