Scipy (Python 的科学计算包)

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[TOC]

sparse

kron

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>>> from scipy import sparse
>>> A = sparse.csr_matrix(np.array([[0, 2], [5, 0]]))
>>> B = sparse.csr_matrix(np.array([[1, 2], [3, 4]]))
>>> sparse.kron(A, B).toarray()
array([[ 0,  0,  2,  4],
       [ 0,  0,  6,  8],
       [ 5, 10,  0,  0],
       [15, 20,  0,  0]])

>>> sparse.kron(A, [[1, 2], [3, 4]]).toarray()
array([[ 0,  0,  2,  4],
       [ 0,  0,  6,  8],
       [ 5, 10,  0,  0],
       [15, 20,  0,  0]])

$A \times B$ 如果A是一个m×n的矩阵，而B是一个p×q的矩阵，克罗内克积则是一个mp×nq的分块矩阵

image-20200828144756226 image-20200828144810260

csr_matrix

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from scipy.sparse import *

row =  [0,0,0,1,1,1,2,2,2]#行指标
col =  [0,1,2,0,1,2,0,1,2]#列指标
data = [1,0,1,0,1,1,1,1,0]#在行指标列指标下的数字
team = csr_matrix((data,(row,col)),shape=(3,3))
print(team)
print(team.todense())

输出结果：
 (0, 0)    1
  (0, 1)    0
  (0, 2)    1
  (1, 0)    0
  (1, 1)    1
  (1, 2)    1
  (2, 0)    1
  (2, 1)    1
  (2, 2)    0
[[1 0 1]
 [0 1 1]
 [1 1 0]]

lil_matrix

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>>> a = np.arange(100).reshape(10, 10)
>>> a
array([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
       [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
       [40, 41, 42, 43, 44, 45, 46, 47, 48, 49],
       [50, 51, 52, 53, 54, 55, 56, 57, 58, 59],
       [60, 61, 62, 63, 64, 65, 66, 67, 68, 69],
       [70, 71, 72, 73, 74, 75, 76, 77, 78, 79],
       [80, 81, 82, 83, 84, 85, 86, 87, 88, 89],
       [90, 91, 92, 93, 94, 95, 96, 97, 98, 99]])

>>> lilm = scipy.sparse.lil_matrix(a)

>>> lilm[[1, 2, 3], :].toarray() # extract the rows first...
array([[10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
       [30, 31, 32, 33, 34, 35, 36, 37, 38, 39]])

>>> lilm[[1, 2, 3], :][:, [4, 5, 6]].toarray() # ...then the columns
array([[14, 15, 16],
       [24, 25, 26],
       [34, 35, 36]])

安装

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sudo apt-get install python-scipy libsuitesparse-dev
pip install --user scikit-sparse

cholesky