Lab2 Vector Calculation

Basic usage of NumPy

Idea

Vectorization and broadcasting are two important concepts in NumPy. They are the key to make NumPy faster than pure Python.

• Vectorization describes the absence of any explicit looping, indexing, etc., in the code.
• Broadcasting is the term used to describe the implicit element-by-element behavior of operations.

Learn NumPy

I recommend you to learn following tutorials:

• A Visual Intro to NumPy and Data Representation – Jay Alammar – Visualizing machine learning one concept at a time.
  • Creating Arrays:np.array([1, 2, 3]), np.ones(), np.zeros(), np.random.random()
  • Array Arithmetic: +, -, *, / all position-wise
  • Indexing: data[0:2], data[1:]
  • Aggregation: min(), max(), sum()
  • Creating Matrices
  • Matrix Arithmetic
    • position-wise
    • broadcast
  • Dot Product data.dot(otherMatrix)
  • Matrix Indexing
    • data[0:2, 0]
    • data[1:3]
  • Transposing and Reshaping: data.T, data.reshape()
  • More dimension: the last axis is looped over the fastest, while the first is the slowest.
  • Practical usage:
    • error = (1/n) * np.sum(np.square(y - y_predicted))
• NumPy Illustrated: The Visual Guide to NumPy | by Lev Maximov | Better Programming
  • NumPy Array vs. Python List
  • 1D Arrays
    • dtype, shape
    • np.zeros_like(a), np.zeros(n, int)

Check it

You should learn:

• Array creation
• Indexing on ndarrays
• I/O with NumPy
• Data types
• Broadcasting
• Copies and views
• Structured arrays
• Universal functions (ufuncs) basics

You can make use of this cheetsheet for review: Python_Cheat_Sheets.pdf (itu.edu.tr)

Array

Some terminology in NumPy:

• vector: 1d array
• matrix: 2d array
• tensor: 3d or higher dimensional array
• axes: dimensions

Attributes of array:

• dtype: data type
• ndim: number of dimensions
• shape: a tuple of integers, indicating the size of the array in each dimension

Create an array:

• np.array(list): create an array from a list
• np.zeros(n): create an n-dimensional array full of zeros
• np.ones(n): create an n-dimensional array full of ones
• np.empty(n): create an n-dimensional array full of random numbers
• np.arange(start, end, step): create an array from start to end with step
• np.linspace(start, end, num=): create an array from start to end with num elements

Use dtype keyword argument to specify the data type of the array. For example, np.array([1, 2, 3], dtype=np.float32).

Manipulate

Operating on arrays with different types will upcast to the more precise one.

Arithmetic operations: usually element-wise.

• +, -, *, /, **, %, //
• inplace operations: +=, -=, *=, /=, **=, %=, //=

Matrix product:

• @ operator: a @ b
• dot function: A.dot(B)

Sorting:

• np.sort(arr): sort an array, return a sorted copy
• np.argsort()
• np.lexsort()
• np.searchsorted(): find elements in a sorted array
• np.partition(): partial sort

Concatenate:

• Vectors: np.concatenate((a1, a2, ...)): concatenate arrays
• Multidimensional arrays: np.concatenate((a1, a2, ...), axis=): concatenate arrays along a specific axis.
  • Note: You can only concatenate arrays on existing axes.

Info:

• ndarray.ndim: number of dimensions
• ndarray.size: total number of elements
• ndarray.shape: mentioned above

Reshape: - arr.reshape(shape) - np.reshape(arr, newshape=(,), order='C') - newshape: a tuple of integers - order: - C: row-major, C-like index order - F: column-major, Fortran-like index order - A: if a is Fortran contiguous then Fortran-like, otherwise row-major