# scipy/scipy

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 """LInked List sparse matrix class """ from __future__ import division, print_function, absolute_import __docformat__ = "restructuredtext en" __all__ = ['lil_matrix','isspmatrix_lil'] from bisect import bisect_left import numpy as np from scipy._lib.six import xrange, zip from .base import spmatrix, isspmatrix from .sputils import (getdtype, isshape, isscalarlike, IndexMixin, upcast_scalar, get_index_dtype, isintlike, check_shape, check_reshape_kwargs) from . import _csparsetools class lil_matrix(spmatrix, IndexMixin): """Row-based linked list sparse matrix This is a structure for constructing sparse matrices incrementally. Note that inserting a single item can take linear time in the worst case; to construct a matrix efficiently, make sure the items are pre-sorted by index, per row. This can be instantiated in several ways: lil_matrix(D) with a dense matrix or rank-2 ndarray D lil_matrix(S) with another sparse matrix S (equivalent to S.tolil()) lil_matrix((M, N), [dtype]) to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype='d'. 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 LIL format data array of the matrix rows LIL format row index array of the matrix Notes ----- Sparse matrices can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power. Advantages of the LIL format - supports flexible slicing - changes to the matrix sparsity structure are efficient Disadvantages of the LIL format - arithmetic operations LIL + LIL are slow (consider CSR or CSC) - slow column slicing (consider CSC) - slow matrix vector products (consider CSR or CSC) Intended Usage - LIL is a convenient format for constructing sparse matrices - once a matrix has been constructed, convert to CSR or CSC format for fast arithmetic and matrix vector operations - consider using the COO format when constructing large matrices Data Structure - An array (``self.rows``) of rows, each of which is a sorted list of column indices of non-zero elements. - The corresponding nonzero values are stored in similar fashion in ``self.data``. """ format = 'lil' def __init__(self, arg1, shape=None, dtype=None, copy=False): spmatrix.__init__(self) self.dtype = getdtype(dtype, arg1, default=float) # First get the shape if isspmatrix(arg1): if isspmatrix_lil(arg1) and copy: A = arg1.copy() else: A = arg1.tolil() if dtype is not None: A = A.astype(dtype) self._shape = check_shape(A.shape) self.dtype = A.dtype self.rows = A.rows self.data = A.data elif isinstance(arg1,tuple): if isshape(arg1): if shape is not None: raise ValueError('invalid use of shape parameter') M, N = arg1 self._shape = check_shape((M, N)) self.rows = np.empty((M,), dtype=object) self.data = np.empty((M,), dtype=object) for i in range(M): self.rows[i] = [] self.data[i] = [] else: raise TypeError('unrecognized lil_matrix constructor usage') else: # assume A is dense try: A = np.asmatrix(arg1) except TypeError: raise TypeError('unsupported matrix type') else: from .csr import csr_matrix A = csr_matrix(A, dtype=dtype).tolil() self._shape = check_shape(A.shape) self.dtype = A.dtype self.rows = A.rows self.data = A.data def __iadd__(self,other): self[:,:] = self + other return self def __isub__(self,other): self[:,:] = self - other return self def __imul__(self,other): if isscalarlike(other): self[:,:] = self * other return self else: return NotImplemented def __itruediv__(self,other): if isscalarlike(other): self[:,:] = self / other return self else: return NotImplemented # Whenever the dimensions change, empty lists should be created for each # row def getnnz(self, axis=None): if axis is None: return sum([len(rowvals) for rowvals in self.data]) if axis < 0: axis += 2 if axis == 0: out = np.zeros(self.shape[1], dtype=np.intp) for row in self.rows: out[row] += 1 return out elif axis == 1: return np.array([len(rowvals) for rowvals in self.data], dtype=np.intp) else: raise ValueError('axis out of bounds') def count_nonzero(self): return sum(np.count_nonzero(rowvals) for rowvals in self.data) getnnz.__doc__ = spmatrix.getnnz.__doc__ count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__ def __str__(self): val = '' for i, row in enumerate(self.rows): for pos, j in enumerate(row): val += " %s\t%s\n" % (str((i, j)), str(self.data[i][pos])) return val[:-1] def getrowview(self, i): """Returns a view of the 'i'th row (without copying). """ new = lil_matrix((1, self.shape[1]), dtype=self.dtype) new.rows[0] = self.rows[i] new.data[0] = self.data[i] return new def getrow(self, i): """Returns a copy of the 'i'th row. """ i = self._check_row_bounds(i) new = lil_matrix((1, self.shape[1]), dtype=self.dtype) new.rows[0] = self.rows[i][:] new.data[0] = self.data[i][:] return new def _check_row_bounds(self, i): if i < 0: i += self.shape[0] if i < 0 or i >= self.shape[0]: raise IndexError('row index out of bounds') return i def _check_col_bounds(self, j): if j < 0: j += self.shape[1] if j < 0 or j >= self.shape[1]: raise IndexError('column index out of bounds') return j def __getitem__(self, index): """Return the element(s) index=(i, j), where j may be a slice. This always returns a copy for consistency, since slices into Python lists return copies. """ # Scalar fast path first if isinstance(index, tuple) and len(index) == 2: i, j = index # Use isinstance checks for common index types; this is # ~25-50% faster than isscalarlike. Other types are # handled below. if ((isinstance(i, int) or isinstance(i, np.integer)) and (isinstance(j, int) or isinstance(j, np.integer))): v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows, self.data, i, j) return self.dtype.type(v) # Utilities found in IndexMixin i, j = self._unpack_index(index) # Proper check for other scalar index types i_intlike = isintlike(i) j_intlike = isintlike(j) if i_intlike and j_intlike: v = _csparsetools.lil_get1(self.shape[0], self.shape[1], self.rows, self.data, i, j) return self.dtype.type(v) elif j_intlike or isinstance(j, slice): # column slicing fast path if j_intlike: j = self._check_col_bounds(j) j = slice(j, j+1) if i_intlike: i = self._check_row_bounds(i) i = xrange(i, i+1) i_shape = None elif isinstance(i, slice): i = xrange(*i.indices(self.shape[0])) i_shape = None else: i = np.atleast_1d(i) i_shape = i.shape if i_shape is None or len(i_shape) == 1: return self._get_row_ranges(i, j) i, j = self._index_to_arrays(i, j) if i.size == 0: return lil_matrix(i.shape, dtype=self.dtype) new = lil_matrix(i.shape, dtype=self.dtype) i, j = _prepare_index_for_memoryview(i, j) _csparsetools.lil_fancy_get(self.shape[0], self.shape[1], self.rows, self.data, new.rows, new.data, i, j) return new def _get_row_ranges(self, rows, col_slice): """ Fast path for indexing in the case where column index is slice. This gains performance improvement over brute force by more efficient skipping of zeros, by accessing the elements column-wise in order. Parameters ---------- rows : sequence or xrange Rows indexed. If xrange, must be within valid bounds. col_slice : slice Columns indexed """ j_start, j_stop, j_stride = col_slice.indices(self.shape[1]) col_range = xrange(j_start, j_stop, j_stride) nj = len(col_range) new = lil_matrix((len(rows), nj), dtype=self.dtype) _csparsetools.lil_get_row_ranges(self.shape[0], self.shape[1], self.rows, self.data, new.rows, new.data, rows, j_start, j_stop, j_stride, nj) return new def __setitem__(self, index, x): # Scalar fast path first if isinstance(index, tuple) and len(index) == 2: i, j = index # Use isinstance checks for common index types; this is # ~25-50% faster than isscalarlike. Scalar index # assignment for other types is handled below together # with fancy indexing. if ((isinstance(i, int) or isinstance(i, np.integer)) and (isinstance(j, int) or isinstance(j, np.integer))): x = self.dtype.type(x) if x.size > 1: # Triggered if input was an ndarray raise ValueError("Trying to assign a sequence to an item") _csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows, self.data, i, j, x) return # General indexing i, j = self._unpack_index(index) # shortcut for common case of full matrix assign: if (isspmatrix(x) and isinstance(i, slice) and i == slice(None) and isinstance(j, slice) and j == slice(None) and x.shape == self.shape): x = lil_matrix(x, dtype=self.dtype) self.rows = x.rows self.data = x.data return i, j = self._index_to_arrays(i, j) if isspmatrix(x): x = x.toarray() # Make x and i into the same shape x = np.asarray(x, dtype=self.dtype) x, _ = np.broadcast_arrays(x, i) if x.shape != i.shape: raise ValueError("shape mismatch in assignment") # Set values i, j, x = _prepare_index_for_memoryview(i, j, x) _csparsetools.lil_fancy_set(self.shape[0], self.shape[1], self.rows, self.data, i, j, x) def _mul_scalar(self, other): if other == 0: # Multiply by zero: return the zero matrix new = lil_matrix(self.shape, dtype=self.dtype) else: res_dtype = upcast_scalar(self.dtype, other) new = self.copy() new = new.astype(res_dtype) # Multiply this scalar by every element. for j, rowvals in enumerate(new.data): new.data[j] = [val*other for val in rowvals] return new def __truediv__(self, other): # self / other if isscalarlike(other): new = self.copy() # Divide every element by this scalar for j, rowvals in enumerate(new.data): new.data[j] = [val/other for val in rowvals] return new else: return self.tocsr() / other def copy(self): from copy import deepcopy new = lil_matrix(self.shape, dtype=self.dtype) new.data = deepcopy(self.data) new.rows = deepcopy(self.rows) return new copy.__doc__ = spmatrix.copy.__doc__ def reshape(self, *args, **kwargs): shape = check_shape(args, self.shape) order, copy = check_reshape_kwargs(kwargs) # Return early if reshape is not required if shape == self.shape: if copy: return self.copy() else: return self new = lil_matrix(shape, dtype=self.dtype) if order == 'C': ncols = self.shape[1] for i, row in enumerate(self.rows): for col, j in enumerate(row): new_r, new_c = np.unravel_index(i * ncols + j, shape) new[new_r, new_c] = self[i, j] elif order == 'F': nrows = self.shape[0] for i, row in enumerate(self.rows): for col, j in enumerate(row): new_r, new_c = np.unravel_index(i + j * nrows, shape, order) new[new_r, new_c] = self[i, j] else: raise ValueError("'order' must be 'C' or 'F'") return new reshape.__doc__ = spmatrix.reshape.__doc__ def resize(self, *shape): shape = check_shape(shape) new_M, new_N = shape M, N = self.shape if new_M < M: self.rows = self.rows[:new_M] self.data = self.data[:new_M] elif new_M > M: self.rows = np.resize(self.rows, new_M) self.data = np.resize(self.data, new_M) for i in range(M, new_M): self.rows[i] = [] self.data[i] = [] if new_N < N: for row, data in zip(self.rows, self.data): trunc = bisect_left(row, new_N) del row[trunc:] del data[trunc:] self._shape = shape resize.__doc__ = spmatrix.resize.__doc__ def toarray(self, order=None, out=None): d = self._process_toarray_args(order, out) for i, row in enumerate(self.rows): for pos, j in enumerate(row): d[i, j] = self.data[i][pos] return d toarray.__doc__ = spmatrix.toarray.__doc__ def transpose(self, axes=None, copy=False): return self.tocsr(copy=copy).transpose(axes=axes, copy=False).tolil(copy=False) transpose.__doc__ = spmatrix.transpose.__doc__ def tolil(self, copy=False): if copy: return self.copy() else: return self tolil.__doc__ = spmatrix.tolil.__doc__ def tocsr(self, copy=False): lst = [len(x) for x in self.rows] idx_dtype = get_index_dtype(maxval=max(self.shape[1], sum(lst))) indptr = np.cumsum([0] + lst, dtype=idx_dtype) indices = np.array([x for y in self.rows for x in y], dtype=idx_dtype) data = np.array([x for y in self.data for x in y], dtype=self.dtype) from .csr import csr_matrix return csr_matrix((data, indices, indptr), shape=self.shape) tocsr.__doc__ = spmatrix.tocsr.__doc__ def _prepare_index_for_memoryview(i, j, x=None): """ Convert index and data arrays to form suitable for passing to the Cython fancy getset routines. The conversions are necessary since to (i) ensure the integer index arrays are in one of the accepted types, and (ii) to ensure the arrays are writable so that Cython memoryview support doesn't choke on them. Parameters ---------- i, j Index arrays x : optional Data arrays Returns ------- i, j, x Re-formatted arrays (x is omitted, if input was None) """ if i.dtype > j.dtype: j = j.astype(i.dtype) elif i.dtype < j.dtype: i = i.astype(j.dtype) if not i.flags.writeable or i.dtype not in (np.int32, np.int64): i = i.astype(np.intp) if not j.flags.writeable or j.dtype not in (np.int32, np.int64): j = j.astype(np.intp) if x is not None: if not x.flags.writeable: x = x.copy() return i, j, x else: return i, j def isspmatrix_lil(x): """Is x of lil_matrix type? Parameters ---------- x object to check for being a lil matrix Returns ------- bool True if x is a lil matrix, False otherwise Examples -------- >>> from scipy.sparse import lil_matrix, isspmatrix_lil >>> isspmatrix_lil(lil_matrix([[5]])) True >>> from scipy.sparse import lil_matrix, csr_matrix, isspmatrix_lil >>> isspmatrix_lil(csr_matrix([[5]])) False """ return isinstance(x, lil_matrix)