"""Compressed Sparse Row matrix format""" from __future__ import division, print_function, absolute_import __docformat__ = "restructuredtext en" __all__ = ['csr_matrix', 'isspmatrix_csr'] import numpy as np from scipy._lib.six import xrange from .base import spmatrix from ._sparsetools import csr_tocsc, csr_tobsr, csr_count_blocks, \ get_csr_submatrix, csr_sample_values from .sputils import (upcast, isintlike, IndexMixin, issequence, get_index_dtype, ismatrix) from .compressed import _cs_matrix class csr_matrix(_cs_matrix, IndexMixin): """ 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 nonzero elements 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]]) """ 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 xrange(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 tocsr.__doc__ = spmatrix.tocsr.__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[0],x[1]) def __getitem__(self, key): def asindices(x): try: x = np.asarray(x) # Check index contents, to avoid creating 64-bit arrays needlessly idx_dtype = get_index_dtype((x,), check_contents=True) if idx_dtype != x.dtype: x = x.astype(idx_dtype) except: raise IndexError('invalid index') else: return x def check_bounds(indices, N): if indices.size == 0: return (0, 0) max_indx = indices.max() if max_indx >= N: raise IndexError('index (%d) out of range' % max_indx) min_indx = indices.min() if min_indx < -N: raise IndexError('index (%d) out of range' % (N + min_indx)) return (min_indx,max_indx) def extractor(indices,N): """Return a sparse matrix P so that P*self implements slicing of the form self[[1,2,3],:] """ indices = asindices(indices) (min_indx,max_indx) = check_bounds(indices,N) if min_indx < 0: indices = indices.copy() indices[indices < 0] += N indptr = np.arange(len(indices)+1, dtype=indices.dtype) data = np.ones(len(indices), dtype=self.dtype) shape = (len(indices),N) return csr_matrix((data,indices,indptr), shape=shape) row, col = self._unpack_index(key) # First attempt to use original row optimized methods # [1, ?] if isintlike(row): # [i, j] if isintlike(col): return self._get_single_element(row, col) # [i, 1:2] elif isinstance(col, slice): return self._get_row_slice(row, col) # [i, [1, 2]] elif issequence(col): P = extractor(col,self.shape[1]).T return self[row, :] * P elif isinstance(row, slice): # [1:2,??] if ((isintlike(col) and row.step in (1, None)) or (isinstance(col, slice) and col.step in (1, None) and row.step in (1, None))): # col is int or slice with step 1, row is slice with step 1. return self._get_submatrix(row, col) elif issequence(col): # row is slice, col is sequence. P = extractor(col,self.shape[1]).T # [1:2,[1,2]] sliced = self if row != slice(None, None, None): sliced = sliced[row,:] return sliced * P elif issequence(row): # [[1,2],??] if isintlike(col) or isinstance(col,slice): P = extractor(row, self.shape[0]) # [[1,2],j] or [[1,2],1:2] extracted = P * self if col == slice(None, None, None): return extracted else: return extracted[:,col] elif ismatrix(row) and issequence(col): if len(row[0]) == 1 and isintlike(row[0][0]): # [[[1],[2]], [1,2]], outer indexing row = asindices(row) P_row = extractor(row[:,0], self.shape[0]) P_col = extractor(col, self.shape[1]).T return P_row * self * P_col if not (issequence(col) and issequence(row)): # Sample elementwise row, col = self._index_to_arrays(row, col) row = asindices(row) col = asindices(col) if row.shape != col.shape: raise IndexError('number of row and column indices differ') assert row.ndim <= 2 num_samples = np.size(row) if num_samples == 0: return csr_matrix(np.atleast_2d(row).shape, dtype=self.dtype) check_bounds(row, self.shape[0]) check_bounds(col, self.shape[1]) val = np.empty(num_samples, dtype=self.dtype) csr_sample_values(self.shape[0], self.shape[1], self.indptr, self.indices, self.data, num_samples, row.ravel(), col.ravel(), val) if row.ndim == 1: # row and col are 1d return np.asmatrix(val) return self.__class__(val.reshape(row.shape)) def getrow(self, i): """Returns a copy of row i of the matrix, as a (1 x n) CSR matrix (row vector). """ return self._get_submatrix(i, slice(None)) def getcol(self, i): """Returns a copy of column i of the matrix, as a (m x 1) CSR matrix (column vector). """ return self._get_submatrix(slice(None), i) def _get_row_slice(self, i, cslice): """Returns a copy of row self[i, cslice] """ if i < 0: i += self.shape[0] if i < 0 or i >= self.shape[0]: raise IndexError('index (%d) out of range' % i) start, stop, stride = cslice.indices(self.shape[1]) if stride == 1: # for stride == 1, _get_submatrix is ~30% faster than below row_slice = self._get_submatrix(i, cslice) else: # other strides need new code row_indices = self.indices[self.indptr[i]:self.indptr[i + 1]] row_data = self.data[self.indptr[i]:self.indptr[i + 1]] if stride > 0: ind = (row_indices >= start) & (row_indices < stop) elif stride < 0: ind = (row_indices <= start) & (row_indices > stop) if abs(stride) > 1: ind = 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))) row_slice = csr_matrix((row_data, row_indices, row_indptr), shape=shape) return row_slice def _get_submatrix(self, row_slice, col_slice): """Return a submatrix of this matrix (new matrix is created).""" M,N = self.shape def process_slice(sl, num): if isinstance(sl, slice): if sl.step not in (1, None): raise ValueError('slicing with step != 1 not supported') i0, i1 = sl.start, sl.stop if i0 is None: i0 = 0 elif i0 < 0: i0 = num + i0 if i1 is None: i1 = num elif i1 < 0: i1 = num + i1 return i0, i1 elif isintlike(sl): if sl < 0: sl += num return sl, sl + 1 else: raise TypeError('expected slice or scalar') def check_bounds(i0, i1, num): if not (0 <= i0 <= num) or not (0 <= i1 <= num) or not (i0 <= i1): raise IndexError( "index out of bounds: 0 <= %d <= %d, 0 <= %d <= %d," " %d <= %d" % (i0, num, i1, num, i0, i1)) i0, i1 = process_slice(row_slice, M) j0, j1 = process_slice(col_slice, N) check_bounds(i0, i1, M) check_bounds(j0, j1, N) indptr, indices, data = get_csr_submatrix(M, N, self.indptr, self.indices, self.data, int(i0), int(i1), int(j0), int(j1)) shape = (i1 - i0, j1 - j0) return self.__class__((data,indices,indptr), shape=shape) def isspmatrix_csr(x): return isinstance(x, csr_matrix)