本文以csr_matrix為例來說明sparse矩陣的使用方法，其他類型的sparse矩陣可以參考https://docs.scipy.org/doc/scipy/reference/sparse.html

csr_matrix是Compressed Sparse Row matrix的縮寫組合，下面介紹其兩種初始化方法

csr_matrix((data, (row_ind, col_ind)), [shape=(M, N)])

　　where data, row_ind and col_ind satisfy the relationship a[row_ind[k], col_ind[k]] = data[k]

csr_matrix((data, indices, indptr), [shape=(M, N)])

　　is the standard CSR representation where the column indices for row i are stored in indices[indptr[i]:indptr[i+1]] and their corresponding values are stored in data[indptr[i]:indptr[i+1]]. If the shape parameter is not supplied, the matrix dimensions are inferred from the index arrays.

上述官方文檔給出了：稀疏矩陣的參數及其含義、稀疏矩陣的構造方式。闡述形式簡單明了，讀起來令人賞心悅目。

Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power

Advantages of the CSR format

• efficient arithmetic operations CSR + CSR, CSR * CSR, etc.
• efficient row slicing
• fast matrix vector products

Disadvantages of the CSR format

• slow column slicing operations (consider CSC)
• changes to the sparsity structure are expensive (consider LIL or DOK)

上述官方文檔時稀疏矩陣的一些特性以及csr_matrix的優缺點，並且在指明各種缺點的同時，提供了可以考慮的技術實現。

代碼示例1

import numpy as np
from scipy.sparse import csr_matrix

row = np.array([0, 0, 1, 2, 2, 2])
col = np.array([0, 2, 2, 0, 1, 2])
data = np.array([1, 2, 3, 4, 5, 6])
a = csr_matrix((data, (row, col)), shape=(3, 3)).toarray()

print(a)

運行結果：

array([[1, 0, 2],
       [0, 0, 3],
       [4, 5, 6]])

代碼示例2

indptr = np.array([0, 2, 3, 6])
indices = np.array([0, 2, 2, 0, 1, 2])
data = np.array([1, 2, 3, 4, 5, 6])
a = csr_matrix((data, indices, indptr), shape=(3, 3)).toarray()

print(a)

允許結果：

array([[1, 0, 2],
       [0, 0, 3],
       [4, 5, 6]])

Python scipy.sparse矩陣使用方法