# 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.moves import xrange from .base import spmatrix, isspmatrix from .sputils import getdtype, isshape, issequence, isscalarlike from warnings import warn from .base import SparseEfficiencyWarning class lil_matrix(spmatrix): """Row-based linked list sparse matrix This is an efficient structure for constructing sparse matrices incrementally. 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``. """ 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 = 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 = (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 = 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: raise NotImplementedError def __itruediv__(self,other): if isscalarlike(other): self[:,:] = self / other return self else: raise NotImplementedError # Whenever the dimensions change, empty lists should be created for each # row def getnnz(self): return sum([len(rowvals) for rowvals in self.data]) nnz = property(fget=getnnz) 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. """ 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 _get1(self, i, j): if i < 0: i += self.shape[0] if i < 0 or i >= self.shape[0]: raise IndexError('row index out of bounds') if j < 0: j += self.shape[1] if j < 0 or j >= self.shape[1]: raise IndexError('column index out of bounds') row = self.rows[i] data = self.data[i] pos = bisect_left(row, j) if pos != len(data) and row[pos] == j: return self.dtype.type(data[pos]) else: return self.dtype.type(0) def _slicetoseq(self, j, shape): if j.start is not None and j.start < 0: start = shape + j.start elif j.start is None: start = 0 else: start = j.start if j.stop is not None and j.stop < 0: stop = shape + j.stop elif j.stop is None: stop = shape else: stop = j.stop j = list(range(start, stop, j.step or 1)) 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. """ try: i, j = index except (AssertionError, TypeError): raise IndexError('invalid index') if not np.isscalar(i) and np.isscalar(j): warn('Indexing into a lil_matrix with multiple indices is slow. ' 'Pre-converting to CSC or CSR beforehand is more efficient.', SparseEfficiencyWarning) if np.isscalar(i): if np.isscalar(j): return self._get1(i, j) if isinstance(j, slice): j = self._slicetoseq(j, self.shape[1]) if issequence(j): return self.__class__([[self._get1(i, jj) for jj in j]]) elif issequence(i) and issequence(j): return self.__class__([[self._get1(ii, jj) for (ii, jj) in zip(i, j)]]) elif issequence(i) or isinstance(i, slice): if isinstance(i, slice): i = self._slicetoseq(i, self.shape[0]) if np.isscalar(j): return self.__class__([[self._get1(ii, j)] for ii in i]) if isinstance(j, slice): j = self._slicetoseq(j, self.shape[1]) if issequence(j): return self.__class__([[self._get1(ii, jj) for jj in j] for ii in i]) else: raise IndexError def _insertat2(self, row, data, j, x): """ helper for __setitem__: insert a value in the given row/data at column j. """ if j < 0: #handle negative column indices j += self.shape[1] if j < 0 or j >= self.shape[1]: raise IndexError('column index out of bounds') if not np.isscalar(x): raise ValueError('setting an array element with a sequence') try: x = self.dtype.type(x) except: raise TypeError('Unable to convert value (%s) to dtype [%s]' % (x,self.dtype.name)) pos = bisect_left(row, j) if x != 0: if pos == len(row): row.append(j) data.append(x) elif row[pos] != j: row.insert(pos, j) data.insert(pos, x) else: data[pos] = x else: if pos < len(row) and row[pos] == j: del row[pos] del data[pos] def _setitem_setrow(self, row, data, j, xrow, xdata, xcols): if isinstance(j, slice): j = self._slicetoseq(j, self.shape[1]) if issequence(j): if xcols == len(j): for jj, xi in zip(j, xrange(xcols)): pos = bisect_left(xrow, xi) if pos != len(xdata) and xrow[pos] == xi: self._insertat2(row, data, jj, xdata[pos]) else: self._insertat2(row, data, jj, 0) elif xcols == 1: # OK, broadcast across row if len(xdata) > 0 and xrow[0] == 0: val = xdata[0] else: val = 0 for jj in j: self._insertat2(row, data, jj,val) else: raise IndexError('invalid index') elif np.isscalar(j): if not xcols == 1: raise ValueError('array dimensions are not compatible for copy') if len(xdata) > 0 and xrow[0] == 0: self._insertat2(row, data, j, xdata[0]) else: self._insertat2(row, data, j, 0) else: raise ValueError('invalid column value: %s' % str(j)) def __setitem__(self, index, x): try: i, j = index except (ValueError, TypeError): raise IndexError('invalid index') # shortcut for common case of single entry assign: if np.isscalar(x) and np.isscalar(i) and np.isscalar(j): self._insertat2(self.rows[i], self.data[i], j, x) return # shortcut for common case of full matrix assign: if isspmatrix(x): if isinstance(i, slice) and i == slice(None) and \ isinstance(j, slice) and j == slice(None): x = lil_matrix(x, dtype=self.dtype) self.rows = x.rows self.data = x.data return if isinstance(i, tuple): # can't index lists with tuple i = list(i) if np.isscalar(i): rows = [self.rows[i]] datas = [self.data[i]] else: rows = self.rows[i] datas = self.data[i] x = lil_matrix(x, copy=False) xrows, xcols = x.shape if xrows == len(rows): # normal rectangular copy for row, data, xrow, xdata in zip(rows, datas, x.rows, x.data): self._setitem_setrow(row, data, j, xrow, xdata, xcols) elif xrows == 1: # OK, broadcast down column for row, data in zip(rows, datas): self._setitem_setrow(row, data, j, x.rows[0], x.data[0], xcols) # needed to pass 'test_lil_sequence_assignement' unit test: # -- set row from column of entries -- elif xcols == len(rows): x = x.T for row, data, xrow, xdata in zip(rows, datas, x.rows, x.data): self._setitem_setrow(row, data, j, xrow, xdata, xrows) else: raise IndexError('invalid index') def _mul_scalar(self, other): if other == 0: # Multiply by zero: return the zero matrix new = lil_matrix(self.shape, dtype=self.dtype) else: new = self.copy() # Multiply this scalar by every element. new.data[:] = [[val*other for val in rowvals] for rowvals in new.data] return new def __truediv__(self, other): # self / other if isscalarlike(other): new = self.copy() # Divide every element by this scalar new.data = [[val/other for val in rowvals] for rowvals in new.data] return new else: return self.tocsr() / other ## This code doesn't work with complex matrices # def multiply(self, other): # """Point-wise multiplication by another lil_matrix. # # """ # if np.isscalar(other): # return self.__mul__(other) # # if isspmatrix_lil(other): # reference,target = self,other # # if reference.shape != target.shape: # raise ValueError("Dimensions do not match.") # # if len(reference.data) > len(target.data): # reference,target = target,reference # # new = lil_matrix(reference.shape) # for r,row in enumerate(reference.rows): # tr = target.rows[r] # td = target.data[r] # rd = reference.data[r] # L = len(tr) # for c,column in enumerate(row): # ix = bisect_left(tr,column) # if ix < L and tr[ix] == column: # new.rows[r].append(column) # new.data[r].append(rd[c] * td[ix]) # return new # else: # raise ValueError("Point-wise multiplication only allowed " # "with another lil_matrix.") 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 def reshape(self,shape): new = lil_matrix(shape, dtype=self.dtype) j_max = self.shape[1] for i,row in enumerate(self.rows): for col,j in enumerate(row): new_r,new_c = np.unravel_index(i*j_max + j,shape) new[new_r,new_c] = self[i,j] return new def toarray(self, order=None, out=None): """See the docstring for `spmatrix.toarray`.""" 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 def transpose(self): return self.tocsr().transpose().tolil() def tolil(self, copy=False): if copy: return self.copy() else: return self def tocsr(self): """ Return Compressed Sparse Row format arrays for this matrix. """ indptr = np.asarray([len(x) for x in self.rows], dtype=np.intc) indptr = np.concatenate( (np.array([0], dtype=np.intc), np.cumsum(indptr)) ) nnz = indptr[-1] indices = [] for x in self.rows: indices.extend(x) indices = np.asarray(indices, dtype=np.intc) data = [] for x in self.data: data.extend(x) data = np.asarray(data, dtype=self.dtype) from .csr import csr_matrix return csr_matrix((data, indices, indptr), shape=self.shape) def tocsc(self): """ Return Compressed Sparse Column format arrays for this matrix. """ return self.tocsr().tocsc() def isspmatrix_lil( x ): return isinstance(x, lil_matrix)
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