Compressed Sparse Row matrix
This can be instantiated in several ways: csr_matrix(D) with a dense matrix or rank-2 ndarray D
csr_matrix(S) with another sparse matrix S (equivalent to S.tocsr())
csr_matrix((M, N), dtype) to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype='d'.
csr_matrix((data, (row_ind, col_ind)), shape=(M, N)) where ``data``, ``row_ind`` and ``col_ind`` satisfy the relationship ``arow_ind[k], col_ind[k] = datak``.
csr_matrix((data, indices, indptr), shape=(M, N)) is the standard CSR representation where the column indices for row i are stored in ``indicesindptr[i]:indptr[i+1]`` and their corresponding values are stored in ``dataindptr[i]:indptr[i+1]``. If the shape parameter is not supplied, the matrix dimensions are inferred from the index arrays.
Attributes ---------- 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 CSR format data array of the matrix indices CSR format index array of the matrix indptr CSR format index pointer array of the matrix has_sorted_indices Whether indices are sorted
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)
Examples --------
>>> import numpy as np >>> from scipy.sparse import csr_matrix >>> csr_matrix((3, 4), dtype=np.int8).toarray() array([0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0], dtype=int8)
>>> 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) >>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray() array([1, 0, 2],
[0, 0, 3],
[4, 5, 6])
>>> 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])
As an example of how to construct a CSR matrix incrementally, the following snippet builds a term-document matrix from texts:
>>> docs = ['hello', 'world', 'hello'], ['goodbye', 'cruel', 'world'] >>> indptr = 0 >>> indices = >>> data = >>> vocabulary = {
}
>>> for d in docs: ... for term in d: ... index = vocabulary.setdefault(term, len(vocabulary)) ... indices.append(index) ... data.append(1) ... indptr.append(len(indices)) ... >>> csr_matrix((data, indices, indptr), dtype=int).toarray() array([2, 1, 0, 0],
[0, 1, 1, 1])