{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "## How to start coding using Python language:\n", "\n", "1. Using Anaconda distribution: Download and install Anaconda from [here](https://www.anaconda.com/products/distribution). Install and lunch jupyter-notebook or jupyterlab from there.\n", "\n", "2. Using jupyterhub with you Aalto email address from [here](https://scicomp.aalto.fi/aalto/jupyterhub/).\n", "\n", "3. Google colab\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Exercise 1. Array creation and accessing elements in an array\n", "Create a 2d array (a matrix) $\\mathbf{M}$ of shape (3, 2), containing 6 values.\n", "\n", "Access element in the second row and first column.\n", "\n", "Access the second row of the matrix and name it $\\mathbf{v}$. What is the shape of this vector?\n", "\n", "Compute the Matrix-Vector multiplication of $\\mathbf{v}$ and $\\mathbf{M}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1, 2],\n", " [4, 5],\n", " [6, 9]])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = np.array([[1, 2], [4, 5], [6, 9]])\n", "M" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M[1, 0]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4, 5])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = M[1]\n", "v" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2,)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.shape" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([14, 41, 69])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M @ v" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Exercise 2.\n", "Find the Euclidean norm of a vector (1d array) using NumPy\n", "\n", "$\\|{\\mathbf{x}}_2\\| = \\sqrt{\\sum_{i=1}^n x_i^2} $" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.729746940310715" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def euclidean_norm_numpy(x):\n", " res = np.sqrt(np.sum(x**2))\n", " return res\n", "\n", "my_vector = np.array([0.5, -1.2, 3.3, 4.5])\n", "euclidean_norm_numpy(my_vector)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.729746940310715" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.norm(my_vector)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3.\n", "Write a function that computes the Euclidean norms of a matrix (2d array) in a row-wise fashion. Hint: use the axis argument of `np.sum`.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def euclidean_norm_2d(X):\n", " norm_X = np.sqrt(np.sum(X**2 , axis =1))\n", " return norm_X\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4.68401537, 4.59782557])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "my_matrix = np.array([[0.5, -1.2, 4.5],\n", " [-3.2, 1.9, 2.7]])\n", "# Should return an array of size 2.\n", "euclidean_norm_2d(my_matrix)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([4.68401537, 4.59782557])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# another way\n", "np.linalg.norm(my_matrix, axis =1)" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Exercise 4. Solving linear equations\n", "Consider the problem of solving $\\mathbf{A} \\mathbf{x} = \\mathbf{b}$.\n", "\\begin{align*}\n", " 2 x_1 + 3 x_2 + 4 x_3 &= 19\\\\\n", " 4 x_1 + 11 x_2 + 14 x_3 &= 55\\\\\n", " 2 x_1 + 8 x_2 + 17 x_3 &= 50\n", "\\end{align*}\n", "In the lecture slides, we found $\\mathbf{x}$ using Gaussian elimination method. The solution was $\\mathbf{x} = \\begin{bmatrix} 4 \\\\ 1\\\\ 2 \\end{bmatrix}$.\n", "\n", "Write a numpy code for solving $\\mathbf{x}$\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "array([[19],\n", " [55],\n", " [50]])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.array([[2, 3, 4], [4, 11, 14], [2, 8, 17]])\n", "b = np.array([[19, 55, 50]]).T\n", "b" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "array([[4.],\n", " [1.],\n", " [2.]])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.inv(A) @ b" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "array([[4.],\n", " [1.],\n", " [2.]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.solve(A, b) # numerically more stable" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Exercise 5. Compute Jacobian\n", "\n", "For the $ \\mathbf{f}: \\mathbb{R}^2 \\rightarrow \\mathbb{R}^2$ and the vector $\\mathbf{x} =\\begin{bmatrix} x_1 \\\\ x_2 \\end{bmatrix} $\n", " we have the vector-value function as $f = \\begin{bmatrix} x_1^2 x_2 \\\\ 5 x_1 + \\sin{x_2} \\end{bmatrix}$. We want to find the jacobian of $\\mathbf{f}$.\n", " \n", "We have $f_1(\\mathbf{x}) = x_1^2 x_2$ and $f_2(\\mathbf{x}) = 5 x_1 + \\sin{x_2}$\n", "\n", "Jacobian is: \n", "\\begin{equation*}\n", " \\mathbf{F}_{\\mathbf{x}}(\\mathbf{x}) = \\begin{bmatrix} \\frac{\\partial \\mathbf{f(\\mathbf{x})}}{\\partial{x_1}} & \\frac{\\partial \\mathbf{f(\\mathbf{x})}}{\\partial {x_2}} \\end{bmatrix} = \\begin{bmatrix} \\frac{\\partial {f_1(\\mathbf{x})}}{\\partial{x_1}} & \\frac{\\partial {f_1(\\mathbf{x})}}{\\partial{x_2}} \\\\ \\frac{\\partial {f_2(\\mathbf{x})}}{\\partial{x_1}} & \\frac{\\partial {f_2(\\mathbf{x})}}{\\partial{x_2}} \\end{bmatrix} = \n", "\\begin{bmatrix} 2x_1 x_2 & x_1^2 \\\\ 5 & \\cos(x_2)\\end{bmatrix}\n", "\\end{equation*}\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "x = np.array([1. , 0])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "def f_function(x):\n", " x_1 = x[0]\n", " x_2 = x[1]\n", " f = np.array([[x_1**2 * x_2],\n", " [5*x_1 + np.sin(x_2)]])\n", " return f\n", "\n", "def F_function(x):\n", " x_1 = x[0]\n", " x_2 = x[1]\n", " F = np.array([[2*x_1*x_2, x_1**2], \n", " [5, np.cos(x_2)]])\n", " return F\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "array([[0., 1.],\n", " [5., 1.]])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F_function(x)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "import autograd.numpy as np # Thinly-wrapped version of Numpy # install it: pip install autograd\n", "from autograd import jacobian" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "text/plain": [ "array([[[0., 1.]],\n", "\n", " [[5., 1.]]])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "jacobian(f_function)(x)" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "## Matplotlib" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Matplotlib is a plotting library for Python" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_values = np.linspace(-3, 3, 100)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.plot(x_values, np.sin(x_values), label=\"Sinusoid\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"sin(x)\")\n", "plt.title(\"Matplotlib example\")\n", "plt.legend(loc=\"upper left\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Exercise 6:\n", "Plot Gaussian distribution with mean $1$ and variance $0.7$\n", "\\begin{equation}\n", "p(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}} e^{(-\\frac{1}{2}(\\frac{x - \\mu}{\\sigma})^2)}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "mu = 1\n", "sigma = np.sqrt(0.7)\n", "def Gaussian_distribution(x):\n", " return 1/sigma*np.sqrt(2*np.pi) * np.exp(-0.5*(x-mu)**2/sigma**2)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(-5,5,100)\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.plot(x, Gaussian_distribution(x), \"b\", label=\"Gaussian distribution\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"p(x)\")\n", "plt.title(\"Gaussian distribution with $\\mu =$ {}, and $\\sigma = $ {}\".format(mu, sigma))\n", "plt.legend(loc=\"upper left\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy.stats as stats\n", "\n", "plt.figure(figsize=(10,5))\n", "x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)\n", "plt.plot(x, stats.norm.pdf(x, mu, sigma))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 7: Optimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Consider a function $f(\\mathbf{x}) = \\mathbf{x}^T \\mathbf{A} \\mathbf{x} + \\mathbf{v}^T \\mathbf{x}$, where $\\mathbf{x}, \\mathbf{v} \\in \\mathbb{R}^{d_n}$ and $\\mathbf{A}$ is a\n", "positive definite matrix.Minimize the function numerically.\n", "\n", "Plot the function and check that the minimum is where it is supposed to\n", "be" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.04742854, 0.49891988])" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.optimize\n", "d_n = 2;\n", "# A = np.random.randn((d_n, d_n));\n", "# A = A @ A.T + np.eye(d_n);\n", "\n", "A = np.diag([1., 2.])\n", "v = np.random.randn(d_n, 1);\n", "f = lambda x: x.T @ A @ x + v.T @ x\n", "x0 = np.array([[0.0], [0.0]])\n", "res = scipy.optimize.minimize(f, x0=x0)\n", "res.x" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x0s = np.linspace(-3,3,100) # creating linearly spaced values in the interval (-3, 3). \n", "x1s = np.linspace(-3,3,100)\n", "gridx0, gridx1 = np.meshgrid(x0s,x1s) # create a rectangular grid \n", "z = np.zeros(gridx0.shape)\n", "for i in range(gridx0.shape[0]): # Access each index of the grid\n", " for j in range(gridx0.shape[1]):\n", " cx = np.array([gridx0[i,j],gridx1[i,j]]) # get the corresponding index in the rectangle\n", " z[i,j] = f(cx) # evaluate f\n", "\n", "plt.figure(figsize=(10,5))\n", "plt.contourf(x0s, x1s, z) # display three-dimensional data in two dimensions using contours or color-coded regions\n", "plt.colorbar()\n", "plt.plot(res.x[0], res.x[1], 'r*');" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(10,10))\n", "ax = plt.axes(projection='3d')\n", "ax.contour3D(x0s,x1s,z, 50, cmap='binary')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "ax.set_zlabel('z');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Condition" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "positive\n" ] } ], "source": [ "my_variable = 5\n", "if my_variable < 0:\n", " print(\"negative\")\n", "elif my_variable == 0:\n", " print(\"null\")\n", "else: # my_variable > 0\n", " print(\"positive\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# `For` loop\n", "\n", "If the goal is simply to iterate over a range of numbers, we can do so directly as follows" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "1\n", "2\n", "3\n", "4\n", "5\n", "6\n", "7\n", "8\n", "9\n" ] } ], "source": [ "for element in range(10):\n", " print(element)" ] }, { "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": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 1 }