# scipy/scipy

232 lines (182 sloc) 7.14 KB
 """Compressed Sparse Column matrix format""" from __future__ import division, print_function, absolute_import __docformat__ = "restructuredtext en" __all__ = ['csc_matrix', 'isspmatrix_csc'] import numpy as np from .base import spmatrix from ._sparsetools import csc_tocsr from . import _sparsetools from .sputils import upcast, isintlike, IndexMixin, get_index_dtype from .compressed import _cs_matrix class csc_matrix(_cs_matrix, IndexMixin): """ Compressed Sparse Column matrix This can be instantiated in several ways: csc_matrix(D) with a dense matrix or rank-2 ndarray D csc_matrix(S) with another sparse matrix S (equivalent to S.tocsc()) csc_matrix((M, N), [dtype]) to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype='d'. csc_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]``. 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. 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 nonzero elements data Data array of the matrix indices CSC format index array indptr CSC format index pointer array 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 CSC format - efficient arithmetic operations CSC + CSC, CSC * CSC, etc. - efficient column slicing - fast matrix vector products (CSR, BSR may be faster) Disadvantages of the CSC format - slow row slicing operations (consider CSR) - changes to the sparsity structure are expensive (consider LIL or DOK) Examples -------- >>> import numpy as np >>> from scipy.sparse import csc_matrix >>> csc_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, 2, 2, 0, 1, 2]) >>> col = np.array([0, 0, 1, 2, 2, 2]) >>> data = np.array([1, 2, 3, 4, 5, 6]) >>> csc_matrix((data, (row, col)), shape=(3, 3)).toarray() array([[1, 0, 4], [0, 0, 5], [2, 3, 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]) >>> csc_matrix((data, indices, indptr), shape=(3, 3)).toarray() array([[1, 0, 4], [0, 0, 5], [2, 3, 6]]) """ format = 'csc' def transpose(self, axes=None, copy=False): if axes is not None: raise ValueError(("Sparse matrices do not support " "an 'axes' parameter because swapping " "dimensions is the only logical permutation.")) M, N = self.shape from .csr import csr_matrix return csr_matrix((self.data, self.indices, self.indptr), (N, M), copy=copy) transpose.__doc__ = spmatrix.transpose.__doc__ def __iter__(self): for r in self.tocsr(): yield r def tocsc(self, copy=False): if copy: return self.copy() else: return self tocsc.__doc__ = spmatrix.tocsc.__doc__ def tocsr(self, copy=False): M,N = self.shape idx_dtype = get_index_dtype((self.indptr, self.indices), maxval=max(self.nnz, N)) indptr = np.empty(M + 1, dtype=idx_dtype) indices = np.empty(self.nnz, dtype=idx_dtype) data = np.empty(self.nnz, dtype=upcast(self.dtype)) csc_tocsr(M, N, self.indptr.astype(idx_dtype), self.indices.astype(idx_dtype), self.data, indptr, indices, data) from .csr import csr_matrix A = csr_matrix((data, indices, indptr), shape=self.shape, copy=False) A.has_sorted_indices = True return A tocsr.__doc__ = spmatrix.tocsr.__doc__ def __getitem__(self, key): # Use CSR to implement fancy indexing. row, col = self._unpack_index(key) # Things that return submatrices. row or col is a int or slice. if (isinstance(row, slice) or isinstance(col, slice) or isintlike(row) or isintlike(col)): return self.T[col, row].T # Things that return a sequence of values. else: return self.T[col, row] def nonzero(self): # CSC can't use _cs_matrix's .nonzero method because it # returns the indices sorted for self transposed. # Get row and col indices, from _cs_matrix.tocoo major_dim, minor_dim = self._swap(self.shape) minor_indices = self.indices major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype) _sparsetools.expandptr(major_dim, self.indptr, major_indices) row, col = self._swap((major_indices, minor_indices)) # Remove explicit zeros nz_mask = self.data != 0 row = row[nz_mask] col = col[nz_mask] # Sort them to be in C-style order ind = np.argsort(row, kind='mergesort') row = row[ind] col = col[ind] return row, col nonzero.__doc__ = _cs_matrix.nonzero.__doc__ def getrow(self, i): """Returns a copy of row i of the matrix, as a (1 x n) CSR matrix (row vector). """ # we convert to CSR to maintain compatibility with old impl. # in spmatrix.getrow() return self._get_submatrix(i, slice(None)).tocsr() def getcol(self, i): """Returns a copy of column i of the matrix, as a (m x 1) CSC matrix (column vector). """ M, N = self.shape i = int(i) if i < 0: i += N if i < 0 or i >= N: raise IndexError('index (%d) out of range' % i) idx = slice(*self.indptr[i:i+2]) data = self.data[idx].copy() indices = self.indices[idx].copy() indptr = np.array([0, len(indices)], dtype=self.indptr.dtype) return csc_matrix((data, indices, indptr), shape=(M, 1), dtype=self.dtype, copy=False) # these functions are used by the parent class (_cs_matrix) # to remove redudancy between csc_matrix and csr_matrix def _swap(self, x): """swap the members of x if this is a column-oriented matrix """ return x[1], x[0] def isspmatrix_csc(x): return isinstance(x, csc_matrix)