Compressed Sparse Row Format (CSR)

Compressed Sparse Row Format (CSR)

• • three numpy arrays: indices, indptr, data
    • indices is array of column indices
    • data is array of corresponding nonzero values
    • indptr points to row starts in indices and data
    • length is n_row + 1, last item = number of values = length of both indices and data
    • nonzero values of the i-th row are data[indptr[i]:indptr[i+1]] with column indices indices[indptr[i]:indptr[i+1]]
    • item (i, j) can be accessed as data[indptr[i]+k], where k is position of j in indices[indptr[i]:indptr[i+1]]
    • subclass of _cs_matrix (common CSR/CSC functionality)
      • subclass of _data_matrix (sparse matrix classes with .data attribute)
      • fast matrix vector products and other arithmetics (sparsetools)
      • constructor accepts:
        • deNSE matrix (array)
        • sparse matrix
        • shape tuple (create empty matrix)
        • (data, ij) tuple
        • (data, indices, indptr) tuple
        • efficient row slicing, row-oriented operations
        • slow column slicing, expensive changes to the sparsity structure
        • use:
          • actual computations (most linear solvers support this format)

            Examples¶

            • create empty CSR matrix:

              
              （图片来源网络，侵删）

              >;>> mtx = sparse.csr_matrix((3, 4), dtype=np.int8)
                     
                     >>> mtx.todense()
                     
                     matrix([[0, 0, 0, 0],
                     
                             [0, 0, 0, 0],
                     
                             [0, 0, 0, 0]], dtype=int8)
                     
                     

            • create using (data, ij) tuple:

              >>> row = np.array([0, 0, 1, 2, 2, 2])
                     
                     >>> col = np.array([0, 2, 2, 0, 1, 2])
                     
                     >>> data = np.array([1, 2, 3, 4, 5, 6])
                     
                     >>> mtx = sparse.csr_matrix((data, (row, col)), shape=(3, 3))
                     
                     >>> mtx     
                     
                     
                     
                     >>> mtx.todense()   
                     
                     matrix([[1, 0, 2],
                     
                             [0, 0, 3],
                     
                             [4, 5, 6]]...)
                     
                     >>> mtx.data        
                     
                     array([1, 2, 3, 4, 5, 6]...)
                     
                     >>> mtx.indices
                     
                     array([0, 2, 2, 0, 1, 2], dtype=int32)
                     
                     >>> mtx.indptr
                     
                     array([0, 2, 3, 6], dtype=int32)
                     
                     

            • create using (data, indices, indptr) tuple:

              
              （图片来源网络，侵删）

              >>> data = np.array([1, 2, 3, 4, 5, 6])
                     
                     >>> indices = np.array([0, 2, 2, 0, 1, 2])
                     
                     >>> indptr = np.array([0, 2, 3, 6])
                     
                     >>> mtx = sparse.csr_matrix((data, indices, indptr), shape=(3, 3))
                     
                     >>> mtx.todense()
                     
                     matrix([[1, 0, 2],
                     
                             [0, 0, 3],
                     
                             [4, 5, 6]])
                     
                     

              See https://scipy-lectures.org/advanced/scipy_sparse/csr_matrix.html

              HTTPS://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.sparse.csr_matrix.html