python实现稀疏矩阵示例代码

>>> from scipy import sparse

>>> help(sparse)

  Usage information
  =================

  There are seven available sparse matrix types:

    1. csc_matrix: Compressed Sparse Column format
    2. csr_matrix: Compressed Sparse Row format
    3. bsr_matrix: Block Sparse Row format
    4. lil_matrix: List of Lists format
    5. dok_matrix: Dictionary of Keys format
    6. coo_matrix: COOrdinate format (aka IJV, triplet format)
    7. dia_matrix: DIAgonal format

  To construct a matrix efficiently, use either dok_matrix or lil_matrix.
  The lil_matrix class supports basic slicing and fancy
  indexing with a similar syntax to NumPy arrays. As illustrated below,
  the COO format may also be used to efficiently construct matrices.

  To perform manipulations such as multiplication or inversion, first
  convert the matrix to either CSC or CSR format. The lil_matrix format is
  row-based, so conversion to CSR is efficient, whereas conversion to CSC
  is less so.

  All conversions among the CSR, CSC, and COO formats are efficient,
  linear-time operations.

>>> row = [2,2,3,2]
>>> col = [3,4,2,3]
>>> c = sparse.coo_matrix((data,(row,col)),shape=(5,6))
>>> print c.toarray()
[[0 0 0 0 0 0]
 [0 0 0 0 0 0]
 [0 0 0 5 2 0]
 [0 0 3 0 0 0]
 [0 0 0 0 0 0]]

>>> import numpy as np
>>> from scipy.sparse import dok_matrix
>>> S = dok_matrix((5, 5), dtype=np.float32)
>>> for i in range(5):
...   for j in range(5):
...       S[i, j] = i + j
...
>>> print S.toarray()
[[ 0. 1. 2. 3. 4.]
 [ 1. 2. 3. 4. 5.]
 [ 2. 3. 4. 5. 6.]
 [ 3. 4. 5. 6. 7.]
 [ 4. 5. 6. 7. 8.]]

>>> from scipy.sparse import lil_matrix
>>> l = lil_matrix((6,5))
>>> l[2,3] = 1
>>> l[3,4] = 2
>>> l[3,2] = 3
>>> print l.toarray()
[[ 0. 0. 0. 0. 0.]
 [ 0. 0. 0. 0. 0.]
 [ 0. 0. 0. 1. 0.]
 [ 0. 0. 3. 0. 2.]
 [ 0. 0. 0. 0. 0.]
 [ 0. 0. 0. 0. 0.]]
>>> print l.data
[[] [] [1.0] [3.0, 2.0] [] []]
>>> print l.rows
[[] [] [3] [2, 4] [] []]

>>> 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]])

 Notes
 | -----
 |
 | 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)