NumPy

NumPy is the fundamental package for scientific computing with Python.

Basics

One of the most commonly used functions of NumPy are NumPy arrays: The essential difference between lists and NumPy arrays is functionality and speed. lists give you basic operation, but NumPy adds basic statistics, linear algebra, histograms, etc.

The most important difference for data science is the ability to do element-wise calculations with NumPy arrays.

axis 0 always refers to row

axis 1 always refers to column

Operator	Description	Documentation
np.array([1,2,3])	1d array	link
np.array([(1,2,3),(4,5,6)])	2d array	see above
np.arange(start,stop,step)	range array	link

Operators	Description	Documentation
np.linspace(0,2,9)	Add evenly spaced values btw interval to array of length	link
np.zeros((1,2))	Create and array filled with zeros	link
np.ones((1,2))	Creates an array filled with ones	link
np.random.randint(0, 5, (5,5))	Creates random array	link
np.empty((2,2))	Creates an empty array	link

Examples

import numpy as np

# 1 dimensional
x = np.array([1,2,3])
# 2 dimensional
y = np.array([(1,2,3),(4,5,6)])

x = np.arange(3)
>>> array([0, 1, 2])

y = np.arange(3.0)
>>> array([ 0.,  1.,  2.])

x = np.arange(3,7)
>>> array([3, 4, 5, 6])

y = np.arange(3,7,2)
>>> array([3, 5])

Array

Array Properties

Syntax	Description	Documentation
array.shape	Dimensions (Rows,Columns)	link
len(array)	Length of Array	link
array.ndim	Number of Array Dimensions	link
array.size	Number of Array Elements	link
array.dtype	Data Type	link
array.astype(type)	Converts to Data Type	link
type(array)	Type of Array	link

Copying

Operators	Descriptions	Documentation
np.copy(array)	Creates copy of array	link
other = array.copy()	Creates deep copy of array	see above

Array Manipulation Routines

Slicing and Subsetting

Operator	Description	Documentation
array[i]	1d array at index i	link
array[i,j]	2d array at index[i][j]	see above
array[i<4]	Boolean Indexing	see above
array[0:3]	Select items of index 0, 1 and 2	see above
array[0:2,1]	Select items of rows 0 and 1 at column 1	see above
array[:1]	Select items of row 0 (equals array[0:1, :])	see above
array[1:2, :]	Select items of row 1	see above
[comment]: <> (	array[1,...]	equals array[1,:,:]
array[ : :-1]	Reverses array	see above

Examples

b = np.array([(1, 2, 3), (4, 5, 6)])

# The index *before* the comma refers to *rows*,
# the index *after* the comma refers to *columns*
print(b[0:1, 2])
>>> [3]

print(b[:len(b), 2])
>>> [3 6]

print(b[0, :])
>>> [1 2 3]

print(b[0, 2:])
>>> [3]

print(b[:, 0])
>>> [1 4]

c = np.array([(1, 2, 3), (4, 5, 6)])
d = c[1:2, 0:2]
print(d)
>>> [[4 5]]

Combining Arrays

Operator	Description	Documentation
np.concatenate((a,b),axis=0)	Concatenates 2 arrays, adds to end	link
np.vstack((a,b))	Stack array row-wise	link
np.hstack((a,b))	Stack array column wise	link

Example

import numpy as np
a = np.array([1, 3, 5])
b = np.array([2, 4, 6])

# Stack two arrays row-wise
print(np.vstack((a,b)))
>>> [[1 3 5]
     [2 4 6]]

# Stack two arrays column-wise
print(np.hstack((a,b)))
>>> [1 3 5 2 4 6]

Shaping Arrays

Operator	Description	Documentation
other = ndarray.flatten()	Flattens a 2d array to 1d	link
ravel	Return a contiguous flattened array	link
reshape	reshape an array	link
resize	Return a new array with the specified shape	link
array = np.transpose(other) array.T	Transpose array	link

Mathematics

Operations

Operator	Description	Documentation
np.add(x,y) x + y	Addition	link
np.substract(x,y) x - y	Subtraction	link
np.divide(x,y) x / y	Division	link
np.multiply(x,y) x * y	Multiplication	link
np.sqrt(x)	Square Root	link
np.sin(x)	Element-wise sine	link
np.cos(x)	Element-wise cosine	link
np.log(x)	Element-wise natural log	link
np.dot(x,y)	Dot product, x @ y	link

Remember: NumPy array operations work element-wise.

Example

# If a 1d array is added to a 2d array (or the other way), NumPy
# chooses the array with smaller dimension and adds it to the one
# with bigger dimension
a = np.array([1, 2, 3])
b = np.array([(1, 2, 3), (4, 5, 6)])
print(np.add(a, b))
>>> [[2 4 6]
     [5 7 9]]

Comparison

Operator	Description	Documentation
np.array_equal(x,y)	Array-wise comparison	link

Example

# Using comparison operators will create boolean NumPy arrays
z = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
c = z < 6
print(c)
>>> [ True  True  True  True  True False False False False False]

More (Reduction)

Operator	Description	Documentation
array.sum()	Array-wise sum	link
array.min()	Array-wise minimum value	link
array.max(axis=0)	Maximum value of specified axis

Rules for broadcasting

In NumPy, broadcasting adheres to a strict set of regulations that govern how two arrays interact with one another. These rules are as follows:

1. When the number of dimensions between two arrays differs, the array with fewer dimensions is padded with ones on its leading (left) side to match the number of dimensions of the other array.
2. If the shape of the two arrays doesn't match in any dimension, the array with a shape of 1 in that dimension is expanded to match the shape of the other array.
3. If the sizes of the arrays conflict in any dimension and neither is equal to 1, an error is raised.

Keywords

• Array-Oriented Programming (陣列導向程式設計)： Working with whole matrices or arrays of data at once, so you don’t have to write a loop for every item.
• Functional-Style Programming (函式風格程式設計)：A paradigm that builds programs by composing pure functions—functions that don’t change external state or data.
• Internal iteration (內部迭代)：Letting a built-in method or function do the looping for you instead of writing the for loop yourself.
• Chain Method (串接呼叫)：Linking several operations together in one line because each step returns the same item, for example: text.strip().lower().split().
• Fancy Indexing (進階索引)：Picking out multiple items from a list or array using a list of positions or a mask of True/False values instead of one index at a time.
• Copies (複本)：Making a totally new version of a data structure so you can change it without affecting the original.
• Views (檢視)： Making a "window" into the original data so that if you change the view, you also change the original.
• Reduction (歸約)：Turning a list of values into one single result, like adding everything up or finding the highest value.
• Vectorization (向量化)：Performing operations on entire arrays instead of individual elements to greatly speed up computations, commonly used in NumPy.
• Broadcasting (廣播機制)：Allowing operations between arrays of different shapes by “stretching” the smaller one to match the larger’s dimensions.
• Universal functions (通用函式)：NumPy’s element-wise functions implemented in C for fast array operations, avoiding Python-level loops.
• Statically typed (靜態型別)：A language characteristic where variable types are checked at compile time and cannot change, requiring explicit type declarations (e.g., C, Java).
• Compiled routines (編譯後函式)：Functions translated into machine code before execution for faster performance compared to interpreting code line by line.