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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 ``a[row_ind[k], col_ind[k]] = data[k]``.
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.
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]])
Duplicate entries are summed together:
>>> row = np.array([0, 1, 2, 0])
>>> col = np.array([0, 1, 1, 0])
>>> data = np.array([1, 2, 4, 8])
>>> csr_matrix((data, (row, col)), shape=(3, 3)).toarray()
array([[9, 0, 0],
[0, 2, 0],
[0, 4, 0]])
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]])
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