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# scipy/scipy

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 """Base class for sparse matrices""" __all__ = ['spmatrix', 'isspmatrix', 'issparse', 'SparseWarning','SparseEfficiencyWarning'] from warnings import warn import numpy as np from sputils import isdense, isscalarlike, isintlike class SparseWarning(Warning): pass class SparseFormatWarning(SparseWarning): pass class SparseEfficiencyWarning(SparseWarning): pass # The formats that we might potentially understand. _formats = {'csc':[0, "Compressed Sparse Column"], 'csr':[1, "Compressed Sparse Row"], 'dok':[2, "Dictionary Of Keys"], 'lil':[3, "LInked List"], 'dod':[4, "Dictionary of Dictionaries"], 'sss':[5, "Symmetric Sparse Skyline"], 'coo':[6, "COOrdinate"], 'lba':[7, "Linpack BAnded"], 'egd':[8, "Ellpack-itpack Generalized Diagonal"], 'dia':[9, "DIAgonal"], 'bsr':[10, "Block Sparse Row"], 'msr':[11, "Modified compressed Sparse Row"], 'bsc':[12, "Block Sparse Column"], 'msc':[13, "Modified compressed Sparse Column"], 'ssk':[14, "Symmetric SKyline"], 'nsk':[15, "Nonsymmetric SKyline"], 'jad':[16, "JAgged Diagonal"], 'uss':[17, "Unsymmetric Sparse Skyline"], 'vbr':[18, "Variable Block Row"], 'und':[19, "Undefined"] } MAXPRINT = 50 class spmatrix(object): """ This class provides a base class for all sparse matrices. It cannot be instantiated. Most of the work is provided by subclasses. """ __array_priority__ = 10.1 ndim = 2 def __init__(self, maxprint=MAXPRINT): self.format = self.__class__.__name__[:3] self._shape = None if self.format == 'spm': raise ValueError, "This class is not intended" \ " to be instantiated directly." self.maxprint = maxprint def set_shape(self,shape): shape = tuple(shape) if len(shape) != 2: raise ValueError("Only two-dimensional sparse arrays " "are supported.") try: shape = int(shape[0]),int(shape[1]) #floats, other weirdness except: raise TypeError('invalid shape') if not (shape[0] >= 1 and shape[1] >= 1): raise ValueError('invalid shape') if (self._shape != shape) and (self._shape is not None): try: self = self.reshape(shape) except NotImplementedError: raise NotImplementedError("Reshaping not implemented for %s." % self.__class__.__name__) self._shape = shape def get_shape(self): return self._shape shape = property(fget=get_shape, fset=set_shape) def reshape(self,shape): raise NotImplementedError def astype(self, t): return self.tocsr().astype(t).asformat(self.format) def asfptype(self): """Upcast matrix to a floating point format (if necessary)""" fp_types = ['f','d','F','D'] if self.dtype.char in fp_types: return self else: for fp_type in fp_types: if self.dtype <= np.dtype(fp_type): return self.astype(fp_type) raise TypeError,'cannot upcast [%s] to a floating \ point format' % self.dtype.name def __iter__(self): for r in xrange(self.shape[0]): yield self[r,:] def getmaxprint(self): try: maxprint = self.maxprint except AttributeError: maxprint = MAXPRINT return maxprint #def typecode(self): # try: # typ = self.dtype.char # except AttributeError: # typ = None # return typ def getnnz(self): try: return self.nnz except AttributeError: raise AttributeError, "nnz not defined" def getformat(self): try: format = self.format except AttributeError: format = 'und' return format @np.deprecate def rowcol(self, num): return (None, None) @np.deprecate def getdata(self, num): return None @np.deprecate def listprint(self, start, stop): """Provides a way to print over a single index. """ return '\n'.join([' %s\t%s' % (self.rowcol(ind), self.getdata(ind)) for ind in xrange(start,stop)]) + '\n' def __repr__(self): nnz = self.getnnz() format = self.getformat() return "<%dx%d sparse matrix of type '%s'\n" \ "\twith %d stored elements in %s format>" % \ (self.shape + (self.dtype.type, nnz, _formats[format][1])) def __str__(self): maxprint = self.getmaxprint() A = self.tocoo() nnz = self.getnnz() # helper function, outputs "(i,j) v" def tostr(row,col,data): triples = zip(zip(row,col),data) return '\n'.join( [ (' %s\t%s' % t) for t in triples] ) if nnz > maxprint: half = maxprint // 2 out = tostr(A.row[:half], A.col[:half], A.data[:half]) out += "\n :\t:\n" half = maxprint - maxprint//2 out += tostr(A.row[-half:], A.col[-half:], A.data[-half:]) else: out = tostr(A.row, A.col, A.data) return out def __nonzero__(self): # Simple -- other ideas? return self.getnnz() > 0 # What should len(sparse) return? For consistency with dense matrices, # perhaps it should be the number of rows? But for some uses the number of # non-zeros is more important. For now, raise an exception! def __len__(self): # return self.getnnz() raise TypeError, "sparse matrix length is ambiguous; use getnnz()" \ " or shape[0]" def asformat(self, format): """Return this matrix in a given sparse format Parameters ---------- format : {string, None} desired sparse matrix format - None for no format conversion - "csr" for csr_matrix format - "csc" for csc_matrix format - "lil" for lil_matrix format - "dok" for dok_matrix format and so on """ if format is None or format == self.format: return self else: return getattr(self,'to' + format)() ################################################################### # NOTE: All arithmetic operations use csr_matrix by default. # Therefore a new sparse matrix format just needs to define a # .tocsr() method to provide arithmetic support. Any of these # methods can be overridden for efficiency. #################################################################### def multiply(self, other): """Point-wise multiplication by another matrix """ return self.tocsr().multiply(other) def __abs__(self): return abs(self.tocsr()) def __add__(self, other): # self + other return self.tocsr().__add__(other) def __radd__(self, other): # other + self return self.tocsr().__radd__(other) def __sub__(self, other): # self - other #note: this can't be replaced by self + (-other) for unsigned types return self.tocsr().__sub__(other) def __rsub__(self, other): # other - self return self.tocsr().__rsub__(other) # old __mul__ interfaces @np.deprecate def matvec(self,other): return self * other @np.deprecate def matmat(self,other): return self * other @np.deprecate def dot(self, other): return self * other @np.deprecate def rmatvec(self, other, conjugate=True): """Multiplies the vector 'other' by the sparse matrix, returning a dense vector as a result. If 'conjugate' is True: - returns A.transpose().conj() * other Otherwise: - returns A.transpose() * other. """ if conjugate: return self.conj().transpose() * other else: return self.transpose() * other def __mul__(self, other): """interpret other and call one of the following self._mul_scalar() self._mul_vector() self._mul_multivector() self._mul_sparse_matrix() """ M,N = self.shape if isscalarlike(other): # scalar value return self._mul_scalar(other) if issparse(other): if self.shape[1] != other.shape[0]: raise ValueError('dimension mismatch') return self._mul_sparse_matrix(other) try: other.shape except AttributeError: # If it's a list or whatever, treat it like a matrix other = np.asanyarray(other) other = np.asanyarray(other) if other.ndim == 1 or other.ndim == 2 and other.shape[1] == 1: # dense row or column vector if other.shape != (N,) and other.shape != (N,1): raise ValueError('dimension mismatch') result = self._mul_vector(np.ravel(other)) if isinstance(other, np.matrix): result = np.asmatrix(result) if other.ndim == 2 and other.shape[1] == 1: # If 'other' was an (nx1) column vector, reshape the result result = result.reshape(-1,1) return result elif other.ndim == 2: ## # dense 2D array or matrix ("multivector") if other.shape[0] != self.shape[1]: raise ValueError('dimension mismatch') result = self._mul_multivector(np.asarray(other)) if isinstance(other, np.matrix): result = np.asmatrix(result) return result else: raise ValueError('could not interpret dimensions') # by default, use CSR for __mul__ handlers def _mul_scalar(self, other): return self.tocsr()._mul_scalar(other) def _mul_vector(self, other): return self.tocsr()._mul_vector(other) def _mul_multivector(self, other): return self.tocsr()._mul_multivector(other) def _mul_sparse_matrix(self, other): return self.tocsr()._mul_sparse_matrix(other) def __rmul__(self, other): # other * self if isscalarlike(other): return self.__mul__(other) else: # Don't use asarray unless we have to try: tr = other.transpose() except AttributeError: tr = np.asarray(other).transpose() return (self.transpose() * tr).transpose() #################### # Other Arithmetic # #################### def __truediv__(self, other): if isscalarlike(other): return self * (1./other) else: return self.tocsr().__truediv__(other) def __div__(self, other): # Always do true division return self.__truediv__(other) def __neg__(self): return -self.tocsr() def __iadd__(self, other): raise NotImplementedError def __isub__(self, other): raise NotImplementedError def __imul__(self, other): raise NotImplementedError def __idiv__(self, other): return self.__itruediv__(other) def __itruediv__(self, other): raise NotImplementedError def __pow__(self, other): if self.shape[0] != self.shape[1]: raise TypeError('matrix is not square') if isintlike(other): other = int(other) if other < 0: raise ValueError('exponent must be >= 0') if other == 0: from construct import identity return identity( self.shape[0], dtype=self.dtype ) elif other == 1: return self.copy() else: result = self for i in range(1,other): result = result*self return result elif isscalarlike(other): raise ValueError('exponent must be an integer') elif isspmatrix(other): warn('Using ** for elementwise multiplication is deprecated.'\ 'Use .multiply() instead', DeprecationWarning) return self.multiply(other) else: raise NotImplementedError def __getattr__(self, attr): if attr == 'A': return self.toarray() elif attr == 'T': return self.transpose() elif attr == 'H': return self.getH() elif attr == 'real': return self._real() elif attr == 'imag': return self._imag() elif attr == 'size': return self.getnnz() else: raise AttributeError, attr + " not found" def transpose(self): return self.tocsr().transpose() def conj(self): return self.tocsr().conj() def conjugate(self): return self.conj() # Renamed conjtranspose() -> getH() for compatibility with dense matrices def getH(self): return self.transpose().conj() def _real(self): return self.tocsr()._real() def _imag(self): return self.tocsr()._imag() def nonzero(self): """nonzero indices Returns a tuple of arrays (row,col) containing the indices of the non-zero elements of the matrix. Example ------- >>> from scipy.sparse import csr_matrix >>> A = csr_matrix([[1,2,0],[0,0,3],[4,0,5]]) >>> A.nonzero() (array([0, 0, 1, 2, 2]), array([0, 1, 2, 0, 2])) """ # convert to COOrdinate format A = self.tocoo() nz_mask = A.data != 0 return (A.row[nz_mask],A.col[nz_mask]) def getcol(self, j): """Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector). """ # Spmatrix subclasses should override this method for efficiency. # Post-multiply by a (n x 1) column vector 'a' containing all zeros # except for a_j = 1 from csc import csc_matrix n = self.shape[1] a = csc_matrix((n, 1), dtype=self.dtype) a[j, 0] = 1 return self * a def getrow(self, i): """Returns a copy of row i of the matrix, as a (1 x n) sparse matrix (row vector). """ # Spmatrix subclasses should override this method for efficiency. # Pre-multiply by a (1 x m) row vector 'a' containing all zeros # except for a_i = 1 from csr import csr_matrix m = self.shape[0] a = csr_matrix((1, m), dtype=self.dtype) a[0, i] = 1 return a * self #def __array__(self): # return self.toarray() def todense(self): return np.asmatrix(self.toarray()) def toarray(self): return self.tocoo().toarray() def todok(self): return self.tocoo().todok() def tocoo(self): return self.tocsr().tocoo() def tolil(self): return self.tocsr().tolil() def todia(self): return self.tocoo().todia() def tobsr(self, blocksize=None): return self.tocsr().tobsr(blocksize=blocksize) def copy(self): return self.__class__(self,copy=True) def sum(self, axis=None): """Sum the matrix over the given axis. If the axis is None, sum over both rows and columns, returning a scalar. """ # We use multiplication by an array of ones to achieve this. # For some sparse matrix formats more efficient methods are # possible -- these should override this function. m, n = self.shape if axis == 0: # sum over columns return np.asmatrix(np.ones((1, m), dtype=self.dtype)) * self elif axis == 1: # sum over rows return self * np.asmatrix(np.ones((n, 1), dtype=self.dtype)) elif axis is None: # sum over rows and columns return ( self * np.asmatrix(np.ones((n, 1), dtype=self.dtype)) ).sum() else: raise ValueError, "axis out of bounds" def mean(self, axis=None): """Average the matrix over the given axis. If the axis is None, average over both rows and columns, returning a scalar. """ if axis == 0: mean = self.sum(0) mean *= 1.0 / self.shape[0] return mean elif axis == 1: mean = self.sum(1) mean *= 1.0 / self.shape[1] return mean elif axis is None: return self.sum(None) * 1.0 / (self.shape[0]*self.shape[1]) else: raise ValueError, "axis out of bounds" def diagonal(self): """Returns the main diagonal of the matrix """ #TODO support k != 0 return self.tocsr().diagonal() def setdiag(self, values, k=0): """Fills the diagonal elements {a_ii} with the values from the given sequence. If k != 0, fills the off-diagonal elements {a_{i,i+k}} instead. values may have any length. If the diagonal is longer than values, then the remaining diagonal entries will not be set. If values if longer than the diagonal, then the remaining values are ignored. """ M, N = self.shape if (k > 0 and k >= N) or (k < 0 and -k >= M): raise ValueError, "k exceedes matrix dimensions" if k < 0: max_index = min(M+k, N, len(values)) for i,v in enumerate(values[:max_index]): self[i - k, i] = v else: max_index = min(M, N-k, len(values)) for i,v in enumerate(values[:max_index]): self[i, i + k] = v def save(self, file_name, format = '%d %d %f\n'): #deprecated on Dec 14 2007 #remove after 0.7 release warn('save() is deprecated, consider using mmwrite() or savemat()' \ ' provided by scipy.io instead', DeprecationWarning) try: fd = open(file_name, 'w') except Exception, e: raise e, file_name fd.write('%d %d\n' % self.shape) fd.write('%d\n' % self.size) for ii in xrange(self.size): ir, ic = self.rowcol(ii) data = self.getdata(ii) fd.write(format % (ir, ic, data)) fd.close() from sputils import _isinstance def isspmatrix(x): return _isinstance(x, spmatrix) issparse = isspmatrix
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