"""Compressed Sparse Column matrix format""" __docformat__ = "restructuredtext en" __all__ = ['csc_array', 'csc_matrix', 'isspmatrix_csc'] import numpy as np from ._matrix import spmatrix from ._base import _spbase, sparray from ._sparsetools import csc_tocsr, expandptr from ._sputils import upcast from ._compressed import _cs_matrix class _csc_base(_cs_matrix): _format = 'csc' def transpose(self, axes=None, copy=False): if axes is not None and axes != (1, 0): raise ValueError("Sparse arrays/matrices do not support " "an 'axes' parameter because swapping " "dimensions is the only logical permutation.") M, N = self.shape return self._csr_container((self.data, self.indices, self.indptr), (N, M), copy=copy) transpose.__doc__ = _spbase.transpose.__doc__ def __iter__(self): yield from self.tocsr() def tocsc(self, copy=False): if copy: return self.copy() else: return self tocsc.__doc__ = _spbase.tocsc.__doc__ def tocsr(self, copy=False): M,N = self.shape idx_dtype = self._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) A = self._csr_container( (data, indices, indptr), shape=self.shape, copy=False ) A.has_sorted_indices = True return A tocsr.__doc__ = _spbase.tocsr.__doc__ 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) 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). """ M, N = self.shape i = int(i) if i < 0: i += M if i < 0 or i >= M: raise IndexError('index (%d) out of range' % i) return self._get_submatrix(minor=i).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) return self._get_submatrix(major=i, copy=True) def _get_intXarray(self, row, col): return self._major_index_fancy(col)._get_submatrix(minor=row) def _get_intXslice(self, row, col): if col.step in (1, None): return self._get_submatrix(major=col, minor=row, copy=True) return self._major_slice(col)._get_submatrix(minor=row) def _get_sliceXint(self, row, col): if row.step in (1, None): return self._get_submatrix(major=col, minor=row, copy=True) return self._get_submatrix(major=col)._minor_slice(row) def _get_sliceXarray(self, row, col): return self._major_index_fancy(col)._minor_slice(row) def _get_arrayXint(self, row, col): return self._get_submatrix(major=col)._minor_index_fancy(row) def _get_arrayXslice(self, row, col): return self._major_slice(col)._minor_index_fancy(row) # these functions are used by the parent class (_cs_matrix) # to remove redundancy between csc_array and csr_matrix @staticmethod def _swap(x): """swap the members of x if this is a column-oriented matrix """ return x[1], x[0] def isspmatrix_csc(x): """Is `x` of csc_matrix type? Parameters ---------- x object to check for being a csc matrix Returns ------- bool True if `x` is a csc matrix, False otherwise Examples -------- >>> from scipy.sparse import csc_array, csc_matrix, coo_matrix, isspmatrix_csc >>> isspmatrix_csc(csc_matrix([[5]])) True >>> isspmatrix_csc(csc_array([[5]])) False >>> isspmatrix_csc(coo_matrix([[5]])) False """ return isinstance(x, csc_matrix) # This namespace class separates array from matrix with isinstance class csc_array(_csc_base, sparray): """ Compressed Sparse Column array. This can be instantiated in several ways: csc_array(D) where D is a 2-D ndarray csc_array(S) with another sparse array or matrix S (equivalent to S.tocsc()) csc_array((M, N), [dtype]) to construct an empty array with shape (M, N) dtype is optional, defaulting to dtype='d'. csc_array((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_array((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 array dimensions are inferred from the index arrays. Attributes ---------- dtype : dtype Data type of the array shape : 2-tuple Shape of the array ndim : int Number of dimensions (this is always 2) nnz size data CSC format data array of the array indices CSC format index array of the array indptr CSC format index pointer array of the array has_sorted_indices has_canonical_format T Notes ----- Sparse arrays 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) Canonical format - Within each column, indices are sorted by row. - There are no duplicate entries. Examples -------- >>> import numpy as np >>> from scipy.sparse import csc_array >>> csc_array((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_array((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_array((data, indices, indptr), shape=(3, 3)).toarray() array([[1, 0, 4], [0, 0, 5], [2, 3, 6]]) """ class csc_matrix(spmatrix, _csc_base): """ Compressed Sparse Column matrix. This can be instantiated in several ways: csc_matrix(D) where D is a 2-D ndarray csc_matrix(S) with another sparse array or 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 size data CSC format data array of the matrix indices CSC format index array of the matrix indptr CSC format index pointer array of the matrix has_sorted_indices has_canonical_format T 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) Canonical format - Within each column, indices are sorted by row. - There are no duplicate entries. 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]]) """