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Numpy is a powerful Python calculation library. It provides a wide range of mathematical functions that can perform various operations on arrays and matrices. This article will sort out some basic and commonly used mathematical operations.
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Basic mathematical operations: Numpy provides many basic mathematical functions for performing operations such as addition, subtraction, multiplication, and division on arrays. These functions include
numpy.add(), numpy.subtract(), numpy.multiply(), and numpy.divide(). -
Linear algebra functions: Numpy also provides a number of linear algebra functions for performing operations such as matrix multiplication, determinants, and inversions. These functions include
numpy.dot(), numpy.linalg.det(), and numpy.linalg.inv(). -
Statistical and probability functions: Numpy provides a number of statistical and probability functions for performing operations such as mean, median, standard deviation, and correlation. These functions include
numpy.mean(), numpy.median(), numpy.std(), and numpy.corrcoef(). -
Trigonometric and logarithmic functions: Numpy also provides a number of trigonometric and logarithmic functions for performing operations such as sine, cosine, tangent and logarithm. These functions include
numpy.sin(), numpy.cos(), numpy.tan(), and numpy.log().
Basic mathematical operations
We’ll cover basic math operations:
Addition
Use numpy.add() to add two array elements one at a time. For example, to add two arrays a and b, you can use the following code:
import numpy as np a = np.array([1, 2, 3]) b = np.array([4, 5, 6]) c = np.add(a, b) print(c) # Output: [5, 7, 9]
You can also use the + operator:
c = a + b print(c) # Output: [5, 7, 9]
Subtraction
numpy.subtract() can be used to subtract an array from another element. For example, to subtract array b from array a, you would use the following code:
import numpy as np a = np.array([1, 2, 3]) b = np.array([4, 5, 6]) c = np.subtract(a, b) print(c) # Output: [-3, -3, -3]
You can also use the – operator:
c = a - b print(c) # Output: [-3, -3, -3]
Multiplication
The numpy.multiply() function can be used to multiply two arrays element-wise. For example, to multiply two arrays a and b, you can use the following code:
import numpy as np a = np.array([1, 2, 3]) b = np.array([4, 5, 6]) c = np.multiply(a, b) print(c) # Output: [4, 10, 18]
You can also use the * operator:
c = a * b print(c) # Output: [4, 10, 18]
One thing to note is that this is element-wise multiplication, and dot product multiplication uses dot, which will be introduced later. Therefore, this operation requires that the dimensions of the two variables are the same. If they are different, the broadcast operation will be performed first.
Division
The numpy.divide() function can be used to divide an array by another element. For example, to divide array a by array b, you would use the following code:
import numpy as np a = np.array([1, 2, 3]) b = np.array([4, 5, 6]) c = np.divide(a, b) print(c) # Output: [0.25, 0.4, 0.5]
You can also use the / operator:
c = a / b print(c) # Output: [0.25, 0.4, 0.5]
Again: all of the above functions are applied element wise on the input array, so they return an array with the same shape as the input.
Linear algebra function
The most common linear algebra function has
Dot product
The numpy.dot() function can be used to calculate the dot product of two arrays. For example, to calculate the dot product of two 1-D arrays a and b, you can use the following code:
import numpy as np a = np.array([1, 2, 3]) b = np.array([4, 5, 6]) c = np.dot(a, b) print(c) #Output: 32
Or use the @ operator directly
c = a @ b print(c) #Output: 32
Matrix multiplication
The numpy.matmul() function can be used to perform matrix multiplication of two arrays. For example, to perform matrix multiplication of two 2-D arrays a and b, you can use the following code:
import numpy as np a = np.array([[1, 2], [3, 4]]) b = np.array([[5, 6], [7, 8]]) c = np.matmul(a, b) print(c) #Output: # [[19 22] # [43 50]]
Matrix multiplication can be performed using the @ operator:
c = a @ b print(c) #Output: # [[19 22] # [43 50]]
Transpose
The numpy.transpose() function can be used to transpose an array. For example, to transpose a 2-D array a, you would use the following code:
import numpy as np a = np.array([[1, 2], [3, 4]]) b = np.transpose(a) print(b) #Output: # [[1 3] # [2 4]]
You can also use the .T attribute directly to transpose the array:
b = a.T print(b) #Output: # [[1 3] # [2 4]]
Determinant
The numpy.linalg.det() function can be used to calculate the determinant of a square array. For example, to calculate the determinant of a two-dimensional array a, you can use the following code:
import numpy as np a = np.array([[1, 2], [3, 4]]) d = np.linalg.det(a) print(d) # Output: -2.000000000000000
Note that the input array must be a square array, i.e. it must have the same number of rows and columns.
Inverse
The numpy.linalg.inv() function can be used to calculate the inverse inverse of a square array. For example, to calculate the inverse of a 2-D array a, you can use the following code:
import numpy as np a = np.array([[1, 2], [3, 4]]) b = np.linalg.inv(a) print(b) #Output: # [[-twenty one. ] # [ 1.5 -0.5]]
It should be noted that the input array must be a square matrix and the determinant must be non-zero. Otherwise, numpy will raise LinAlgError.
The above are our commonly used linear algebra functions. There are more functions to calculate linear algebra operations on matrices and arrays. You can view the Numpy documentation.
Trigonometric and logarithmic functions
Numpy contains some of the most commonly used trigonometric functions including Numpy .sin(), Numpy .cos(), Numpy .tan(), Numpy .arcsin(), Numpy .arccos(), Numpy .arctan() or Numpy .log(). Example of numpy.sin():
import numpy as np a = np.array([0, 30, 45, 60, 90]) b = np.sin(a) print(b) # Output: [ 0. 0.5 0.70710678 0.8660254 1. ]
numpy.logComputes the natural logarithm as the reciprocal of an exponential function, so log(exp(x)) = x. The natural logarithm is the logarithm with base e.
import numpy as np np.log([1, np.e, np.e**2, 0]) #array([ 0., 1., 2., -Inf])
The above is a summary of commonly used mathematical functions in Numpy. I hope it will be helpful to you. In addition, Numpy’s documentation is very detailed. If you want to find any functions, you can directly query: https://numpy.org/doc/
Author: Mario Rodriguez
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