{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Exercise 7.2: Working with two-dimensional arrays\n", "\n", "<hr>"]}, {"cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": ["import numpy as np"]}, {"cell_type": "markdown", "metadata": {}, "source": ["<hr>\n", "\n", "Numpy enables you do to matrix calculations on two-dimensional arrays. In exercise, you will practice doing matrix calculations on arrays. We'll start by making a matrix and a vector to practice with. You can copy and paste the code below."]}, {"cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": ["A = np.array(\n", "    [\n", "        [6.7, 1.3, 0.6, 0.7],\n", "        [0.1, 5.5, 0.4, 2.4],\n", "        [1.1, 0.8, 4.5, 1.7],\n", "        [0.0, 1.5, 3.4, 7.5],\n", "    ]\n", ")\n", "\n", "b = np.array([1.1, 2.3, 3.3, 3.9])"]}, {"cell_type": "markdown", "metadata": {}, "source": ["**a)** First, let's practice slicing.\n", "\n", "1. Print row 1 (remember, indexing starts at zero) of `A`.\n", "2. Print columns 1 and 3 of `A`.\n", "3. Print the values of every entry in `A` that is greater than 2.\n", "4. Print the diagonal of `A`. using the `np.diag()` function.\n", "\n", "**b)** The `np.linalg` module has some powerful linear algebra tools. \n", "\n", "1. First, we'll solve the linear system $\\mathsf{A}\\cdot \\mathbf{x} = \\mathbf{b}$. Try it out: use `np.linalg.solve()`. Store your answer in the Numpy array `x`.\n", "2. Now do `np.dot(A, x)` to verify that $\\mathsf{A}\\cdot \\mathbf{x} = \\mathbf{b}$.\n", "3. Use `np.transpose()` to compute the transpose of `A`.\n", "4. Use `np.linalg.inv()` to compute the inverse of `A`.\n", "\n", "**c)** Sometimes you want to convert a two-dimensional array to a one-dimensional array. This can be done with `np.ravel()`. \n", "\n", "1. See what happens when you do `B = np.ravel(A)`.\n", "2. Look of the documentation for `np.reshape()`. Then, reshape `B` to make it look like `A` again."]}, {"cell_type": "markdown", "metadata": {}, "source": ["<br />"]}], "metadata": {"anaconda-cloud": {}, "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": "3.8.10"}}, "nbformat": 4, "nbformat_minor": 4}