sp.coo_matrix(), sp.eye()

sp.coo_matrix()

坐标格式的稀疏矩阵。

也被称为“ijv”或“三重”格式。

这可以通过几种方式实例化:

        coo_matrix(D)

                密集矩阵D;

        coo_matrix(S)

                与另一个稀疏矩阵S(等价于S.tocoo())

        coo_matrix((M, N), [dtype])

                构造一个形状为(M, N)的空矩阵

        coo_matrix((data, (i, j)), [shape=(M, N)])

                从三个数组构造:

                        1. data[:] the entries of the matrix, in any order       矩阵的元素，以任何顺序  

                        2. i[:]  the row indices of the matrix entries  矩阵项的行下标

                        3. j[:]  the column indices of the matrix entries 矩阵项的列下标

参数：

 dtype : dtype
        Data type of the matrix
    shape : 2-tuple
        Shape of the matrix
    ndim : int
        Number of dimensions (this is always 2)
    nnz
        Number of stored values, including explicit zeros
    data
        COO format data array of the matrix
    row
        COO format row index array of the matrix
    col
        COO format column index array of the matrix

稀疏矩阵可以用于算术运算:它们支持加，减，乘，除，矩阵幂。

        COO格式优势

                方便稀疏格式之间的快速转换；

                允许重复条目(见示例)

                非常快速的转换CSR/CSC格式
 

>>> from scipy.sparse import coo_matrix
>>> import numpy as np
>>> coo_matrix((3, 4), dtype=np.int8).toarray()
array([[0, 0, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 0]], dtype=int8)
>>> # Constructing a matrix using ijv format
>>> 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]])
>>> # Constructing a matrix with duplicate indices
>>> row  = np.array([0, 0, 1, 3, 1, 0, 0])
>>> col  = np.array([0, 2, 1, 3, 1, 0, 0])
>>> data = np.array([1, 1, 1, 1, 1, 1, 1])
>>> coo = coo_matrix((data, (row, col)), shape=(4, 4))
>>> coo = coo_matrix((data, (row, col)), shape=(4, 4))
>>> coo.toarray()
array([[3, 0, 1, 0],
       [0, 2, 0, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 1]])
>>> #保持重复索引，直到隐式或显式求和

sp.eye()

eye(N, M=None, k=0, dtype=float) 是scipy包中的一个创建特殊矩阵(单位矩阵E)的方法

>>> from scipy import *
 
>>> eye(3)
[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]
>>> eye(3,3)
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])
>>> eye(3,4)
array([[1., 0., 0., 0.],
       [0., 1., 0., 0.],
       [0., 0., 1., 0.]])
>>> eye(3,4,1)
array([[0., 1., 0., 0.],
       [0., 0., 1., 0.],
       [0., 0., 0., 1.]])
>>> eye(3,4,2)
array([[0., 0., 1., 0.],
       [0., 0., 0., 1.],
       [0., 0., 0., 0.]])