稀疏矩阵
作者:互联网
目录
稀疏矩阵
插播一期稀疏矩阵。
为什么稀疏矩阵
在实际应用中,矩阵大多时候都是稀疏的(例如大图的邻接矩阵),稀疏矩阵能减少存储空间,加快计算速度。
常用稀疏矩阵
1. coo:Coordinate matrix
采用三个数组,row,col,data,分别表示 行坐标,列坐标,和该坐标系下对应的值。下面的例子是用scipy.sparse创建coo稀疏矩阵。
>>> from scipy.sparse import coo_matrix
>>> row = np.array([0, 3, 1, 0])
>>> col = np.array([0, 3, 1, 2])
>>> data = np.array([4, 5, 7, 9])
>>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
array([[4, 0, 9, 0],
[0, 7, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 5]])
优点:
-
方便稀疏格式之间的快速转换;
-
允许重复条目(参见示例);
-
与 CSR/CSC 格式之间的快速转换;
缺点 :
- 不支持数学运算;
- 不支持切片(slice)。
2. csr和csc:Compressed Sparse Row/Column matrix
分别代表按行和按列的压缩方式。下面只介绍csr,csc和csr类似。
采用三个数组,data,indices,indptr,分别表示 数值,列号,和偏移量。对应的稠密矩阵的第\(i\) 行的数据表示为(python):
for i in range(len(indptr)-1):
for j in range(indptr[i],indptr[i+1]):
matrix[i][indices[j]] = data[j]
下面用scipy.sparse创建csr稀疏矩阵的例子:
>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> 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])
>>> csr_matrix((data, indices, indptr), shape=(3, 3)).toarray()
array([[1, 0, 2],
[0, 0, 3],
[4, 5, 6]])
优点:
-
高效算术运算 CSR + CSR、CSR * CSR 等;
-
高效的行切片(row slice);
-
快速矩阵向量乘积 ;
缺点:
- 缓慢的列切片(column slice)操作(考虑使用CSC);
- 稀疏结构的改变代价高昂(考虑 LIL 或 DOK)。
All conversions among the CSR, CSC, and COO formats are efficient, linear-time operations.
python中的scipy.sparse
支持的稀疏格式
矩阵格式 | 描述 |
---|---|
bsr_matrix (arg1[, shape, dtype, copy, blocksize]) |
Block Sparse Row matrix |
coo_matrix (arg1[, shape, dtype, copy]) |
A sparse matrix in COOrdinate format. |
csc_matrix (arg1[, shape, dtype, copy]) |
Compressed Sparse Column matrix |
csr_matrix (arg1[, shape, dtype, copy]) |
Compressed Sparse Row matrix |
dia_matrix (arg1[, shape, dtype, copy]) |
Sparse matrix with DIAgonal storage |
dok_matrix (arg1[, shape, dtype, copy]) |
Dictionary Of Keys based sparse matrix. |
lil_matrix (arg1[, shape, dtype, copy]) |
Row-based list of lists sparse matrix |
spmatrix ([maxprint]) |
This class provides a base class for all sparse matrices. |
常用api
API | 描述 |
---|---|
eye (m[, n, k, dtype, format]) |
Sparse matrix with ones on diagonal |
identity (n[, dtype, format]) |
Identity matrix in sparse format |
hstack (blocks[, format, dtype]) |
Stack sparse matrices horizontally (column wise) |
vstack (blocks[, format, dtype]) |
Stack sparse matrices vertically (row wise) |
random (m, n[, density, format, dtype, …]) |
Generate a sparse matrix of the given shape and density with randomly distributed values. |
save_npz (file, matrix[, compressed]) |
Save a sparse matrix to a file using .npz format. |
load_npz (file) |
Load a sparse matrix from a file using .npz format. |
multiply (other) |
Point-wise multiplication by another matrix |
power (n[, dtype]) |
This function performs element-wise power. |
dot (other) |
Ordinary dot product |
标签:matrix,dtype,矩阵,稀疏,shape,sparse 来源: https://www.cnblogs.com/clearhanhui/p/15347044.html