From 2d2b7b9f5731dc5c7bda29c917a6cc5f17b5160e Mon Sep 17 00:00:00 2001 From: Christian Kolset Date: Thu, 24 Apr 2025 17:39:37 -0600 Subject: Updated markdown formatting for latex conversion. --- tutorials/module_1/array.md | 34 ++++++++++++++++------------------ 1 file changed, 16 insertions(+), 18 deletions(-) (limited to 'tutorials/module_1/array.md') diff --git a/tutorials/module_1/array.md b/tutorials/module_1/array.md index c8f2452..3385231 100644 --- a/tutorials/module_1/array.md +++ b/tutorials/module_1/array.md @@ -19,14 +19,13 @@ A three-dimensional array would be like a set of tables, perhaps stacked as thou If the load on this block changes over time, then we may want to add a 4th dimension i.e. additional sets of 3-D arrays for each time increment. As you can see - the more dimensions we add, the more complicated of a problem we have to solve. It is possible to increase the number of dimensions to the n-th order. This course we will not be going beyond dimensional analysis. ---- -# Numpy - the python's array library +## Numpy - the python's array library In this tutorial we will be introducing arrays and we will be using the numpy library. Arrays, lists, vectors, matrices, sets - You might've heard of them before, they all store data. In programming, an array is a variable that can hold more than one value at a time. We will be using the Numpy python library to create arrays. Since we already have installed Numpy previously, we can start using the package. Before importing our first package, let's as ourselves *what is a package?* A package can be thought of as pre-written python code that we can re-use. This means the for every script that we write in python we need to tell it to use a certain package. We call this importing a package. -## Importing Numpy +### Importing Numpy When using packages in python, we need to let it know what package we will be using. This is called importing. To import numpy we need to declare it a the start of a script as follows: ```python import numpy as np @@ -34,8 +33,7 @@ import numpy as np - `import` - calls for a library to use, in our case it is Numpy. - `as` - gives the library an alias in your script. It's common convention in Python programming to make the code shorter and more readable. We will be using *np* as it's a standard using in many projects. ---- -# Creating arrays +## Creating arrays Now that we have imported the library we can create a one dimensional array or *vector* with three elements. ```python x = np.array([1,2,3]) @@ -52,9 +50,9 @@ matrix = np.array([[1,2,3], *Note: for every array we nest, we get a new dimension in our data structure.* -## Numpy array creation functions +### Numpy array creation functions Numpy comes with some built-in function that we can use to create arrays quickly. Here are a couple of functions that are commonly used in python. -### np.arange +#### np.arange The `np.arange()` function returns an array with evenly spaced values within a specified range. It is similar to the built-in `range()` function in Python but returns a Numpy array instead of a list. The parameters for this function are the start value (inclusive), the stop value (exclusive), and the step size. If the step size is not provided, it defaults to 1. ```python @@ -64,7 +62,7 @@ array([0. , 1., 2., 3. ]) In this example, `np.arange(4)` generates an array starting from 0 and ending before 4, with a step size of 1. -### np.linspace +#### np.linspace The `np.linspace()` function returns an array of evenly spaced values over a specified range. Unlike `np.arange()`, which uses a step size to define the spacing between elements, `np.linspace()` uses the number of values you want to generate and calculates the spacing automatically. It accepts three parameters: the start value, the stop value, and the number of samples. ```python @@ -81,14 +79,14 @@ x = np.linspace(0,100,101) y = np.sin(x) ``` -### Other useful functions +#### Other useful functions - `np.zeros()` - `np.ones()` - `np.eye()` -## Working with Arrays +### Working with Arrays Now that we have been introduced to some ways to create arrays using the Numpy functions let's start using them. -### Indexing +#### Indexing Indexing in Python allows you to access specific elements within an array based on their position. This means you can directly retrieve and manipulate individual items as needed. Python uses **zero-based indexing**, meaning the first element is at position **0** rather than **1**. This approach is common in many programming languages. For example, in a list with five elements, the first element is at index `0`, followed by elements at indices `1`, `2`, `3`, and `4`. @@ -102,22 +100,22 @@ thrust_lbf = np.array(0.603355, 2.019083, 2.808092, 4.054973, 1.136618, 0.943668 ``` Due to the nature of zero-based indexing. If we want to call the value `4.054973` that will be the 3rd index. -### Operations on arrays +#### Operations on arrays - Arithmetic operations (`+`, `-`, `*`, `/`, `**`) - `np.add()`, `np.subtract()`, `np.multiply()`, `np.divide()` - `np.dot()` for dot product - `np.matmul()` for matrix multiplication - `np.linalg.inv()`, `np.linalg.det()` for linear algebra -#### Statistics +##### Statistics - `np.mean()`, `np.median()`, `np.std()`, `np.var()` - `np.min()`, `np.max()`, `np.argmin()`, `np.argmax()` - Summation along axes: `np.sum(arr, axis=0)` -#### Combining arrays +##### Combining arrays - Concatenation: `np.concatenate((arr1, arr2), axis=0)` - Stacking: `np.vstack()`, `np.hstack()` - Splitting: `np.split()` -# Exercise +## Exercise Let's solve a statics problem given the following problem A simply supported bridge of length L=20L = 20L=20 m is subjected to three point loads: @@ -128,7 +126,7 @@ A simply supported bridge of length L=20L = 20L=20 m is subjected to three point The bridge is supported by two reaction forces at points AAA (left support) and BBB (right support). We assume the bridge is in static equilibrium, meaning the sum of forces and sum of moments about any point must be zero. -#### Equilibrium Equations: +##### Equilibrium Equations: 1. **Sum of Forces in the Vertical Direction**: $RA+RB−P1−P2−P3=0R_A + R_B - P_1 - P_2 - P_3 = 0RA​+RB​−P1​−P2​−P3​=0$ @@ -137,12 +135,12 @@ The bridge is supported by two reaction forces at points AAA (left support) and 3. **Sum of Moments About Point B**: $20RA−15P3−10P2−5P1=020 R_A - 15 P_3 - 10 P_2 - 5 P_1 = 020RA​−15P3​−10P2​−5P1​=0$ -#### System of Equations: +##### System of Equations: {RA+RB−10−15−20=05(10)+10(15)+15(20)−20RB=020RA−5(10)−10(15)−15(20)=0\begin{cases} R_A + R_B - 10 - 15 - 20 = 0 \\ 5(10) + 10(15) + 15(20) - 20 R_B = 0 \\ 20 R_A - 5(10) - 10(15) - 15(20) = 0 \end{cases}⎩ -## Solution +### Solution ```python import numpy as np -- cgit v1.2.3