CS_ALearn/Book4_Power-of-Matrix
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Iris Series: Visualize Math -- From Arithmetic Basics to Machine Learning
2025-02-01 17:00:33 +08:00
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Book4_Ch05_Python_Codes/Bk4_Ch5_01.py
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###############
# Authored by Weisheng Jiang
# Book 4 | From Basic Arithmetic to Machine Learning
# Published and copyrighted by Tsinghua University Press
# Beijing, China, 2022
###############
# Bk4_Ch5_01.py
import numpy as np
a = np.array([[1],
[2],
[3]])
a_1D = np.array([1,2,3])
b = np.array([[-4],
[-5],
[-6]])
b_1D = np.array([-4,-5,-6])
#%% sum of the elements in a
print(np.einsum('ij->',a))
print(np.einsum('i->',a_1D))
#%% element-wise multiplication of a and b
print(np.einsum('ij,ij->ij',a,b))
print(np.einsum('i,i->i',a_1D,b_1D))
#%% inner product of a and b
print(np.einsum('ij,ij->',a,b))
print(np.einsum('i,i->',a_1D,b_1D))
#%% outer product of a and itself
print(np.einsum('ij,ji->ij',a,a))
print(np.einsum('i,j->ij',a_1D,a_1D))
#%% outer product of a and b
print(np.einsum('ij,ji->ij',a,b))
print(np.einsum('i,j->ij',a_1D,b_1D))
#%%
# A is a square matrix
A = np.array([[1,2,3],
[4,5,6],
[7,8,9]])
B = np.array([[-1,-4,-7],
[-2,-5,-8],
[-3,-6,-9]])
#%% transpose of A
print(np.einsum('ji',A))
#%% sum of all values in A
print(np.einsum('ij->',A))
#%% sum across rows
print(np.einsum('ij->j',A))
#%% sum across columns
print(np.einsum('ij->i',A))
#%% extract main diagonal of A
print(np.einsum('ii->i',A))
#%% calculate the trace of A
print(np.einsum('ii->',A))
#%% matrix multiplication of A and B
print(np.einsum('ij,jk->ik', A, B))
#%% sum of all elements in the matrix multiplication of A and B
print(np.einsum('ij,jk->', A, B))
#%% first matrix multiplication, then transpose
print(np.einsum('ij,jk->ki', A, B))
#%% element-wise multiplication of A and B
print(np.einsum('ij,ij->ij', A, B))