"""Compressed Sparse Row matrix format""" __docformat__ = "restructuredtext en" __all__ = ['csr_matrix', 'isspmatrix_csr'] import numpy as np from .base import spmatrix from ._sparsetools import (csr_tocsc, csr_tobsr, csr_count_blocks, get_csr_submatrix) from .sputils import upcast, get_index_dtype from .compressed import _cs_matrix class csr_matrix(_cs_matrix): """ 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]]) """ format = 'csr' 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 .csc import csc_matrix return csc_matrix((self.data, self.indices, self.indptr), shape=(N, M), copy=copy) transpose.__doc__ = spmatrix.transpose.__doc__ def tolil(self, copy=False): from .lil import lil_matrix lil = lil_matrix(self.shape,dtype=self.dtype) self.sum_duplicates() ptr,ind,dat = self.indptr,self.indices,self.data rows, data = lil.rows, lil.data for n in range(self.shape[0]): start = ptr[n] end = ptr[n+1] rows[n] = ind[start:end].tolist() data[n] = dat[start:end].tolist() return lil tolil.__doc__ = spmatrix.tolil.__doc__ def tocsr(self, copy=False): if copy: return self.copy() else: return self tocsr.__doc__ = spmatrix.tocsr.__doc__ def tocsc(self, copy=False): idx_dtype = get_index_dtype((self.indptr, self.indices), maxval=max(self.nnz, self.shape[0])) indptr = np.empty(self.shape[1] + 1, dtype=idx_dtype) indices = np.empty(self.nnz, dtype=idx_dtype) data = np.empty(self.nnz, dtype=upcast(self.dtype)) csr_tocsc(self.shape[0], self.shape[1], self.indptr.astype(idx_dtype), self.indices.astype(idx_dtype), self.data, indptr, indices, data) from .csc import csc_matrix A = csc_matrix((data, indices, indptr), shape=self.shape) A.has_sorted_indices = True return A tocsc.__doc__ = spmatrix.tocsc.__doc__ def tobsr(self, blocksize=None, copy=True): from .bsr import bsr_matrix if blocksize is None: from .spfuncs import estimate_blocksize return self.tobsr(blocksize=estimate_blocksize(self)) elif blocksize == (1,1): arg1 = (self.data.reshape(-1,1,1),self.indices,self.indptr) return bsr_matrix(arg1, shape=self.shape, copy=copy) else: R,C = blocksize M,N = self.shape if R < 1 or C < 1 or M % R != 0 or N % C != 0: raise ValueError('invalid blocksize %s' % blocksize) blks = csr_count_blocks(M,N,R,C,self.indptr,self.indices) idx_dtype = get_index_dtype((self.indptr, self.indices), maxval=max(N//C, blks)) indptr = np.empty(M//R+1, dtype=idx_dtype) indices = np.empty(blks, dtype=idx_dtype) data = np.zeros((blks,R,C), dtype=self.dtype) csr_tobsr(M, N, R, C, self.indptr.astype(idx_dtype), self.indices.astype(idx_dtype), self.data, indptr, indices, data.ravel()) return bsr_matrix((data,indices,indptr), shape=self.shape) tobsr.__doc__ = spmatrix.tobsr.__doc__ # 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 def __iter__(self): indptr = np.zeros(2, dtype=self.indptr.dtype) shape = (1, self.shape[1]) i0 = 0 for i1 in self.indptr[1:]: indptr[1] = i1 - i0 indices = self.indices[i0:i1] data = self.data[i0:i1] yield csr_matrix((data, indices, indptr), shape=shape, copy=True) i0 = i1 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) indptr, indices, data = get_csr_submatrix( M, N, self.indptr, self.indices, self.data, i, i + 1, 0, N) return csr_matrix((data, indices, indptr), shape=(1, N), dtype=self.dtype, copy=False) def getcol(self, i): """Returns a copy of column i of the matrix, as a (m x 1) CSR 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) indptr, indices, data = get_csr_submatrix( M, N, self.indptr, self.indices, self.data, 0, M, i, i + 1) return csr_matrix((data, indices, indptr), shape=(M, 1), dtype=self.dtype, copy=False) def _get_intXarray(self, row, col): return self.getrow(row)._minor_index_fancy(col) def _get_intXslice(self, row, col): if col.step in (1, None): return self._get_submatrix(row, col, copy=True) # TODO: uncomment this once it's faster: # return self.getrow(row)._minor_slice(col) M, N = self.shape start, stop, stride = col.indices(N) ii, jj = self.indptr[row:row+2] row_indices = self.indices[ii:jj] row_data = self.data[ii:jj] if stride > 0: ind = (row_indices >= start) & (row_indices < stop) else: ind = (row_indices <= start) & (row_indices > stop) if abs(stride) > 1: ind &= (row_indices - start) % stride == 0 row_indices = (row_indices[ind] - start) // stride row_data = row_data[ind] row_indptr = np.array([0, len(row_indices)]) if stride < 0: row_data = row_data[::-1] row_indices = abs(row_indices[::-1]) shape = (1, int(np.ceil(float(stop - start) / stride))) return csr_matrix((row_data, row_indices, row_indptr), shape=shape, dtype=self.dtype, copy=False) def _get_sliceXint(self, row, col): if row.step in (1, None): return self._get_submatrix(row, col, copy=True) return self._major_slice(row)._get_submatrix(minor=col) def _get_sliceXarray(self, row, col): return self._major_slice(row)._minor_index_fancy(col) def _get_arrayXint(self, row, col): return self._major_index_fancy(row)._get_submatrix(minor=col) def _get_arrayXslice(self, row, col): if col.step not in (1, None): col = np.arange(*col.indices(self.shape[1])) return self._get_arrayXarray(row, col) return self._major_index_fancy(row)._get_submatrix(minor=col) def isspmatrix_csr(x): """Is x of csr_matrix type? Parameters ---------- x object to check for being a csr matrix Returns ------- bool True if x is a csr matrix, False otherwise Examples -------- >>> from scipy.sparse import csr_matrix, isspmatrix_csr >>> isspmatrix_csr(csr_matrix([[5]])) True >>> from scipy.sparse import csc_matrix, csr_matrix, isspmatrix_csc >>> isspmatrix_csr(csc_matrix([[5]])) False """ return isinstance(x, csr_matrix)