# scipy/scipy

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 """Compressed Sparse Row matrix format""" __docformat__ = "restructuredtext en" __all__ = ['csr_matrix', 'isspmatrix_csr'] from warnings import warn import numpy as np from sparsetools import csr_tocsc, csr_tobsr, csr_count_blocks, \ get_csr_submatrix, csr_sample_values from sputils import upcast, isintlike 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, ij), [shape=(M, N)]) where ``data`` and ``ij`` satisfy the relationship ``a[ij[0, k], ij[1, 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 -------- >>> from scipy.sparse import * >>> from scipy import * >>> csr_matrix( (3,4), dtype=int8 ).todense() matrix([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]], dtype=int8) >>> row = array([0,0,1,2,2,2]) >>> col = array([0,2,2,0,1,2]) >>> data = array([1,2,3,4,5,6]) >>> csr_matrix( (data,(row,col)), shape=(3,3) ).todense() matrix([[1, 0, 2], [0, 0, 3], [4, 5, 6]]) >>> indptr = array([0,2,3,6]) >>> indices = array([0,2,2,0,1,2]) >>> data = array([1,2,3,4,5,6]) >>> csr_matrix( (data,indices,indptr), shape=(3,3) ).todense() matrix([[1, 0, 2], [0, 0, 3], [4, 5, 6]]) """ def transpose(self, copy=False): from csc import csc_matrix M,N = self.shape return csc_matrix((self.data,self.indices,self.indptr), shape=(N,M), copy=copy) def tolil(self): from lil import lil_matrix lil = lil_matrix(self.shape,dtype=self.dtype) self.sort_indices() #lil_matrix needs sorted column indices 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 def tocsr(self, copy=False): if copy: return self.copy() else: return self def tocsc(self): indptr = np.empty(self.shape[1] + 1, dtype=np.intc) indices = np.empty(self.nnz, dtype=np.intc) data = np.empty(self.nnz, dtype=upcast(self.dtype)) csr_tocsc(self.shape[0], self.shape[1], \ self.indptr, self.indices, 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 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) indptr = np.empty(M//R + 1, dtype=np.intc) indices = np.empty(blks, dtype=np.intc) data = np.zeros((blks,R,C), dtype=self.dtype) csr_tobsr(M, N, R, C, self.indptr, self.indices, self.data, \ indptr, indices, data.ravel() ) return bsr_matrix((data,indices,indptr), shape=self.shape) # 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, dtype=np.intc) except: raise IndexError('invalid index') else: return x def check_bounds(indices,N): 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=np.intc) data = np.ones(len(indices), dtype=self.dtype) shape = (len(indices),N) return csr_matrix((data,indices,indptr), shape=shape) if isinstance(key, tuple): row = key[0] col = key[1] if isintlike(row): #[1,??] if isintlike(col): return self._get_single_element(row, col) #[i,j] elif isinstance(col, slice): return self._get_row_slice(row, col) #[i,1:2] else: P = extractor(col,self.shape[1]).T #[i,[1,2]] return self[row,:]*P elif isinstance(row, slice): #[1:2,??] if isintlike(col) or isinstance(col, slice): return self._get_submatrix(row, col) #[1:2,j] else: P = extractor(col,self.shape[1]).T #[1:2,[1,2]] return self[row,:]*P else: #[[1,2],??] or [[[1],[2]],??] if isintlike(col) or isinstance(col,slice): P = extractor(row, self.shape[0]) #[[1,2],j] or [[1,2],1:2] return (P*self)[:,col] else: row = asindices(row) col = asindices(col) if len(row.shape) == 1: if len(row) != len(col): #[[1,2],[1,2]] raise IndexError('number of row and column indices differ') check_bounds(row, self.shape[0]) check_bounds(col, self.shape[1]) num_samples = len(row) 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, col, val) #val = [] #for i,j in zip(row,col): # val.append(self._get_single_element(i,j)) return np.asmatrix(val) elif len(row.shape) == 2: row = np.ravel(row) #[[[1],[2]],[1,2]] P = extractor(row, self.shape[0]) return (P*self)[:,col] else: raise NotImplementedError('unsupported indexing') elif isintlike(key) or isinstance(key,slice): return self[key,:] #[i] or [1:2] else: return self[asindices(key),:] #[[1,2]] def _get_single_element(self,row,col): """Returns the single element self[row, col] """ M, N = self.shape if (row < 0): row += M if (col < 0): col += N if not (0<=row= self.shape[0]: raise IndexError('index (%d) out of range' % i ) start, stop, stride = cslice.indices(self.shape[1]) if stride != 1: raise ValueError("slicing with step != 1 not supported") if stop <= start: raise ValueError("slice width must be >= 1") #TODO make [i,:] faster #TODO implement [i,x:y:z] indices = [] for ind in xrange(self.indptr[i], self.indptr[i+1]): if self.indices[ind] >= start and self.indices[ind] < stop: indices.append(ind) index = self.indices[indices] - start data = self.data[indices] indptr = np.array([0, len(indices)]) return csr_matrix( (data, index, indptr), shape=(1, stop-start) ) 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
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