# scipy/scipy

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 """Compressed Block Sparse Row matrix format""" __docformat__ = "restructuredtext en" __all__ = ['bsr_matrix', 'isspmatrix_bsr'] from warnings import warn import numpy as np from data import _data_matrix from compressed import _cs_matrix from base import isspmatrix, _formats from sputils import isshape, getdtype, to_native, upcast import sparsetools from sparsetools import bsr_matvec, bsr_matvecs, csr_matmat_pass1, \ bsr_matmat_pass2, bsr_transpose, bsr_sort_indices class bsr_matrix(_cs_matrix): """Block Sparse Row matrix This can be instantiated in several ways: bsr_matrix(D, [blocksize=(R,C)]) with a dense matrix or rank-2 ndarray D bsr_matrix(S, [blocksize=(R,C)]) with another sparse matrix S (equivalent to S.tobsr()) bsr_matrix((M, N), [blocksize=(R,C), dtype]) to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype='d'. bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)]) where ``data`` and ``ij`` satisfy ``a[ij[0, k], ij[1, k]] = data[k]`` bsr_matrix((data, indices, indptr), [shape=(M, N)]) is the standard BSR representation where the block column indices for row i are stored in ``indices[indptr[i]:indices[i+1]]`` and their corresponding block 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 Data array of the matrix indices BSR format index array indptr BSR format index pointer array blocksize Block size 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. Summary of BSR format: - The Block Compressed Row (BSR) format is very similar to the Compressed Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense sub matrices like the last example below. Block matrices often arise in vector-valued finite element discretizations. In such cases, BSR is considerably more efficient than CSR and CSC for many sparse arithmetic operations. Blocksize - The blocksize (R,C) must evenly divide the shape of the matrix (M,N). That is, R and C must satisfy the relationship M % R = 0 and N % C = 0. - If no blocksize is specified, a simple heuristic is applied to determine an appropriate blocksize. Examples -------- >>> from scipy.sparse import * >>> from scipy import * >>> bsr_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]) >>> bsr_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]).repeat(4).reshape(6,2,2) >>> bsr_matrix( (data,indices,indptr), shape=(6,6) ).todense() matrix([[1, 1, 0, 0, 2, 2], [1, 1, 0, 0, 2, 2], [0, 0, 0, 0, 3, 3], [0, 0, 0, 0, 3, 3], [4, 4, 5, 5, 6, 6], [4, 4, 5, 5, 6, 6]]) """ def __init__(self, arg1, shape=None, dtype=None, copy=False, blocksize=None): _data_matrix.__init__(self) if isspmatrix(arg1): if isspmatrix_bsr(arg1) and copy: arg1 = arg1.copy() else: arg1 = arg1.tobsr(blocksize=blocksize) self._set_self( arg1 ) elif isinstance(arg1,tuple): if isshape(arg1): #it's a tuple of matrix dimensions (M,N) self.shape = arg1 M,N = self.shape #process blocksize if blocksize is None: blocksize = (1,1) else: if not isshape(blocksize): raise ValueError('invalid blocksize=%s' % blocksize) blocksize = tuple(blocksize) self.data = np.zeros( (0,) + blocksize, getdtype(dtype, default=float) ) self.indices = np.zeros( 0, dtype=np.intc ) R,C = blocksize if (M % R) != 0 or (N % C) != 0: raise ValueError('shape must be multiple of blocksize') self.indptr = np.zeros(M//R + 1, dtype=np.intc ) elif len(arg1) == 2: # (data,(row,col)) format from coo import coo_matrix self._set_self( coo_matrix(arg1, dtype=dtype).tobsr(blocksize=blocksize) ) elif len(arg1) == 3: # (data,indices,indptr) format (data, indices, indptr) = arg1 self.indices = np.array(indices, copy=copy) self.indptr = np.array(indptr, copy=copy) self.data = np.array(data, copy=copy, dtype=getdtype(dtype, data)) else: raise ValueError('unrecognized bsr_matrix constructor usage') else: #must be dense try: arg1 = np.asarray(arg1) except: raise ValueError("unrecognized form for" \ " %s_matrix constructor" % self.format) from coo import coo_matrix arg1 = coo_matrix(arg1, dtype=dtype).tobsr(blocksize=blocksize) self._set_self( arg1 ) if shape is not None: self.shape = shape # spmatrix will check for errors else: if self.shape is None: # shape not already set, try to infer dimensions try: M = len(self.indptr) - 1 N = self.indices.max() + 1 except: raise ValueError('unable to infer matrix dimensions') else: R,C = self.blocksize self.shape = (M*R,N*C) if self.shape is None: if shape is None: #TODO infer shape here raise ValueError('need to infer shape') else: self.shape = shape if dtype is not None: self.data = self.data.astype(dtype) self.check_format(full_check=False) def check_format(self, full_check=True): """check whether the matrix format is valid *Parameters*: full_check: True - rigorous check, O(N) operations : default False - basic check, O(1) operations """ M,N = self.shape R,C = self.blocksize # index arrays should have integer data types if self.indptr.dtype.kind != 'i': warn("indptr array has non-integer dtype (%s)" \ % self.indptr.dtype.name ) if self.indices.dtype.kind != 'i': warn("indices array has non-integer dtype (%s)" \ % self.indices.dtype.name ) # only support 32-bit ints for now self.indptr = np.asarray(self.indptr, np.intc) self.indices = np.asarray(self.indices, np.intc) self.data = to_native(self.data) # check array shapes if np.rank(self.indices) != 1 or np.rank(self.indptr) != 1: raise ValueError("indices, and indptr should be rank 1") if np.rank(self.data) != 3: raise ValueError("data should be rank 3") # check index pointer if (len(self.indptr) != M//R + 1 ): raise ValueError("index pointer size (%d) should be (%d)" % (len(self.indptr), M//R + 1)) if (self.indptr[0] != 0): raise ValueError("index pointer should start with 0") # check index and data arrays if (len(self.indices) != len(self.data)): raise ValueError("indices and data should have the same size") if (self.indptr[-1] > len(self.indices)): raise ValueError("Last value of index pointer should be less than " "the size of index and data arrays") self.prune() if full_check: #check format validity (more expensive) if self.nnz > 0: if self.indices.max() >= N//C: print "max index",self.indices.max() raise ValueError("column index values must be < %d" % (N//C)) if self.indices.min() < 0: raise ValueError("column index values must be >= 0") if np.diff(self.indptr).min() < 0: raise ValueError("index pointer values must form a " "non-decreasing sequence") #if not self.has_sorted_indices(): # warn('Indices were not in sorted order. Sorting indices.') # self.sort_indices(check_first=False) def _get_blocksize(self): return self.data.shape[1:] blocksize = property(fget=_get_blocksize) def getnnz(self): R,C = self.blocksize return self.indptr[-1] * R * C nnz = property(fget=getnnz) def __repr__(self): nnz = self.getnnz() format = self.getformat() return "<%dx%d sparse matrix of type '%s'\n" \ "\twith %d stored elements (blocksize = %dx%d) in %s format>" % \ ( self.shape + (self.dtype.type, nnz) + self.blocksize + \ (_formats[format][1],) ) def diagonal(self): """Returns the main diagonal of the matrix """ M,N = self.shape R,C = self.blocksize y = np.empty(min(M,N), dtype=upcast(self.dtype)) sparsetools.bsr_diagonal(M//R, N//C, R, C, \ self.indptr, self.indices, np.ravel(self.data), y) return y ########################## # NotImplemented methods # ########################## def getdata(self,ind): raise NotImplementedError def __getitem__(self,key): raise NotImplementedError def __setitem__(self,key,val): raise NotImplementedError ###################### # Arithmetic methods # ###################### def matvec(self, other): return self * other def matmat(self, other): return self * other def _mul_vector(self, other): M,N = self.shape R,C = self.blocksize result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype)) bsr_matvec(M//R, N//C, R, C, \ self.indptr, self.indices, self.data.ravel(), other, result) return result def _mul_multivector(self,other): R,C = self.blocksize M,N = self.shape n_vecs = other.shape[1] #number of column vectors result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype)) bsr_matvecs(M//R, N//C, n_vecs, R, C, \ self.indptr, self.indices, self.data.ravel(), \ other.ravel(), result.ravel()) return result def _mul_sparse_matrix(self, other): M, K1 = self.shape K2, N = other.shape indptr = np.empty_like( self.indptr ) R,n = self.blocksize #convert to this format if isspmatrix_bsr(other): C = other.blocksize[1] else: C = 1 from csr import isspmatrix_csr if isspmatrix_csr(other) and n == 1: other = other.tobsr(blocksize=(n,C), copy=False) #lightweight conversion else: other = other.tobsr(blocksize=(n,C)) csr_matmat_pass1( M//R, N//C, \ self.indptr, self.indices, \ other.indptr, other.indices, \ indptr) bnnz = indptr[-1] indices = np.empty(bnnz, dtype=np.intc) data = np.empty(R*C*bnnz, dtype=upcast(self.dtype,other.dtype)) bsr_matmat_pass2( M//R, N//C, R, C, n, \ self.indptr, self.indices, np.ravel(self.data), \ other.indptr, other.indices, np.ravel(other.data), \ indptr, indices, data) data = data.reshape(-1,R,C) #TODO eliminate zeros return bsr_matrix((data,indices,indptr),shape=(M,N),blocksize=(R,C)) ###################### # Conversion methods # ###################### def tobsr(self,blocksize=None,copy=False): if blocksize not in [None, self.blocksize]: return self.tocsr().tobsr(blocksize=blocksize) if copy: return self.copy() else: return self def tocsr(self): return self.tocoo(copy=False).tocsr() #TODO make this more efficient def tocsc(self): return self.tocoo(copy=False).tocsc() def tocoo(self,copy=True): """Convert this matrix to COOrdinate format. When copy=False the data array will be shared between this matrix and the resultant coo_matrix. """ M,N = self.shape R,C = self.blocksize row = (R * np.arange(M//R)).repeat(np.diff(self.indptr)) row = row.repeat(R*C).reshape(-1,R,C) row += np.tile(np.arange(R).reshape(-1,1), (1,C)) row = row.reshape(-1) col = (C * self.indices).repeat(R*C).reshape(-1,R,C) col += np.tile(np.arange(C), (R,1)) col = col.reshape(-1) data = self.data.reshape(-1) if copy: data = data.copy() from coo import coo_matrix return coo_matrix((data,(row,col)), shape=self.shape) def transpose(self): R,C = self.blocksize M,N = self.shape NBLK = self.nnz//(R*C) if self.nnz == 0: return bsr_matrix((N,M), blocksize=(C,R)) indptr = np.empty( N//C + 1, dtype=self.indptr.dtype) indices = np.empty( NBLK, dtype=self.indices.dtype) data = np.empty( (NBLK,C,R), dtype=self.data.dtype) bsr_transpose(M//R, N//C, R, C, \ self.indptr, self.indices, self.data.ravel(), \ indptr, indices, data.ravel()) return bsr_matrix((data,indices,indptr), shape=(N,M)) ############################################################## # methods that examine or modify the internal data structure # ############################################################## def eliminate_zeros(self): R,C = self.blocksize M,N = self.shape mask = (self.data != 0).reshape(-1,R*C).sum(axis=1) #nonzero blocks nonzero_blocks = mask.nonzero()[0] if len(nonzero_blocks) == 0: return #nothing to do self.data[:len(nonzero_blocks)] = self.data[nonzero_blocks] from csr import csr_matrix # modifies self.indptr and self.indices *in place* proxy = csr_matrix((mask,self.indices,self.indptr),shape=(M//R,N//C)) proxy.eliminate_zeros() self.prune() def sum_duplicates(self): raise NotImplementedError def sort_indices(self): """Sort the indices of this matrix *in place* """ if self.has_sorted_indices: return R,C = self.blocksize M,N = self.shape bsr_sort_indices(M//R, N//C, R, C, self.indptr, self.indices, self.data.ravel()) self.has_sorted_indices = True def prune(self): """ Remove empty space after all non-zero elements. """ R,C = self.blocksize M,N = self.shape if len(self.indptr) != M//R + 1: raise ValueError("index pointer has invalid length") bnnz = self.indptr[-1] if len(self.indices) < bnnz: raise ValueError("indices array has too few elements") if len(self.data) < bnnz: raise ValueError("data array has too few elements") self.data = self.data[:bnnz] self.indices = self.indices[:bnnz] # utility functions def _binopt(self, other, op, in_shape=None, out_shape=None): """apply the binary operation fn to two sparse matrices""" # ideally we'd take the GCDs of the blocksize dimensions # and explode self and other to match other = self.__class__(other, blocksize=self.blocksize) # e.g. bsr_plus_bsr, etc. fn = getattr(sparsetools, self.format + op + self.format) R,C = self.blocksize max_bnnz = len(self.data) + len(other.data) indptr = np.empty_like(self.indptr) indices = np.empty(max_bnnz, dtype=np.intc) data = np.empty(R*C*max_bnnz, dtype=upcast(self.dtype,other.dtype)) fn(self.shape[0]//R, self.shape[1]//C, R, C, self.indptr, self.indices, np.ravel(self.data), other.indptr, other.indices, np.ravel(other.data), indptr, indices, data) actual_bnnz = indptr[-1] indices = indices[:actual_bnnz] data = data[:R*C*actual_bnnz] if actual_bnnz < max_bnnz/2: indices = indices.copy() data = data.copy() data = data.reshape(-1,R,C) return self.__class__((data, indices, indptr), shape=self.shape) # needed by _data_matrix def _with_data(self,data,copy=True): """Returns a matrix with the same sparsity structure as self, but with different data. By default the structure arrays (i.e. .indptr and .indices) are copied. """ if copy: return self.__class__((data,self.indices.copy(),self.indptr.copy()), \ shape=self.shape,dtype=data.dtype) else: return self.__class__((data,self.indices,self.indptr), \ shape=self.shape,dtype=data.dtype) # # these functions are used by the parent class # # to remove redudancy between bsc_matrix and bsr_matrix # def _swap(self,x): # """swap the members of x if this is a column-oriented matrix # """ # return (x[0],x[1]) from sputils import _isinstance def isspmatrix_bsr(x): return _isinstance(x, bsr_matrix)
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