scipy csr_matrix和csc_matrix函数详解

在用Python进行科学运算时，常常需要把一个稀疏的np.array压缩，这时候就用到scipy库中的sparse.csr_matrix(csr:Compressed
Sparse Row marix) 和sparse.csc_matric(csc:Compressed Sparse Column marix)

scipy.sparse.csr_matrix

官方API介绍(省略前几种容易理解的了) 

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.

#  示例解读
>>> 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]])
# 按row行来压缩
# 对于第i行，列是indices[indptr[i]:indptr[i+1]] 数据是data[indptr[i]:indptr[i+1]]
# 在本例中
# 第0行，有非0的数据列是indptr[indices[0]:indices[1]] = indptr[0,2] = [0,2]
# 数据是data[indptr[0]:indptr[1]] = data[0,2] = [1,2],所以在第0行第0列是1，第2列是2
# 第1行，有非0的数据列是indptr[indices[1]:indices[2]] = indptr[2,3] = [2]
# 数据是data[indptr[1]:indptr[2] = data[2,3] = [3],所以在第1行第2列是3
# 第2行，有非0的数据列是indptr[indices[2]:indices[3]] = indptr[3,6] = [0,1,2]
# 数据是data[indptr[2]:indptr[3]] = data[3,6] = [4,5,6],所以在第2行第0列是4，第1列是5,第2列是6

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scipy.sparse.csc_matrix

官方API介绍(省略前几种容易理解的了) 

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

is the standard CSC representation where the row indices for column 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.

#  示例解读
>>> 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])
>>> csc_matrix((data, indices, indptr), shape=(3, 3)).toarray()
array([[1, 0, 4],
[0, 0, 5],
[2, 3, 6]])
# 按col列来压缩
# 对于第i列，行是indices[indptr[i]:indptr[i+1]] 数据是data[indptr[i]:indptr[i+1]]
# 在本例中
# 第0列，有非0的数据行是indptr[indices[0]:indices[1]] = indptr[0,2] = [0,2]
# 数据是data[indptr[0]:indptr[1]] = data[0,2] = [1,2],所以在第0列第0行是1，第2行是2
# 第1行，有非0的数据行是indptr[indices[1]:indices[2]] = indptr[2,3] = [2]
# 数据是data[indptr[1]:indptr[2] = data[2,3] = [3],所以在第1列第2行是3
# 第2行，有非0的数据行是indptr[indices[2]:indices[3]] = indptr[3,6] = [0,1,2]
# 数据是data[indptr[2]:indptr[3]] = data[3,6] = [4,5,6],所以在第2列第0行是4，第1行是5,第2行是6

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