"""Base class for sparse matrix formats using compressed storage.""" __all__ = [] from warnings import warn import operator import numpy as np from scipy._lib._util import _prune_array from .base import spmatrix, isspmatrix, SparseEfficiencyWarning from .data import _data_matrix, _minmax_mixin from .dia import dia_matrix from . import _sparsetools from ._sparsetools import (get_csr_submatrix, csr_sample_offsets, csr_todense, csr_sample_values, csr_row_index, csr_row_slice, csr_column_index1, csr_column_index2) from ._index import IndexMixin from .sputils import (upcast, upcast_char, to_native, isdense, isshape, getdtype, isscalarlike, isintlike, get_index_dtype, downcast_intp_index, get_sum_dtype, check_shape, matrix, asmatrix, is_pydata_spmatrix) class _cs_matrix(_data_matrix, _minmax_mixin, IndexMixin): """base matrix class for compressed row- and column-oriented matrices""" def __init__(self, arg1, shape=None, dtype=None, copy=False): _data_matrix.__init__(self) if isspmatrix(arg1): if arg1.format == self.format and copy: arg1 = arg1.copy() else: arg1 = arg1.asformat(self.format) self._set_self(arg1) elif isinstance(arg1, tuple): if isshape(arg1): # It's a tuple of matrix dimensions (M, N) # create empty matrix self._shape = check_shape(arg1) M, N = self.shape # Select index dtype large enough to pass array and # scalar parameters to sparsetools idx_dtype = get_index_dtype(maxval=max(M, N)) self.data = np.zeros(0, getdtype(dtype, default=float)) self.indices = np.zeros(0, idx_dtype) self.indptr = np.zeros(self._swap((M, N))[0] + 1, dtype=idx_dtype) else: if len(arg1) == 2: # (data, ij) format from .coo import coo_matrix other = self.__class__(coo_matrix(arg1, shape=shape)) self._set_self(other) elif len(arg1) == 3: # (data, indices, indptr) format (data, indices, indptr) = arg1 # Select index dtype large enough to pass array and # scalar parameters to sparsetools maxval = None if shape is not None: maxval = max(shape) idx_dtype = get_index_dtype((indices, indptr), maxval=maxval, check_contents=True) self.indices = np.array(indices, copy=copy, dtype=idx_dtype) self.indptr = np.array(indptr, copy=copy, dtype=idx_dtype) self.data = np.array(data, copy=copy, dtype=dtype) else: raise ValueError("unrecognized {}_matrix " "constructor usage".format(self.format)) else: # must be dense try: arg1 = np.asarray(arg1) except Exception: raise ValueError("unrecognized {}_matrix constructor usage" "".format(self.format)) from .coo import coo_matrix self._set_self(self.__class__(coo_matrix(arg1, dtype=dtype))) # Read matrix dimensions given, if any if shape is not None: self._shape = check_shape(shape) else: if self.shape is None: # shape not already set, try to infer dimensions try: major_dim = len(self.indptr) - 1 minor_dim = self.indices.max() + 1 except Exception: raise ValueError('unable to infer matrix dimensions') else: self._shape = check_shape(self._swap((major_dim, minor_dim))) if dtype is not None: self.data = self.data.astype(dtype, copy=False) self.check_format(full_check=False) def getnnz(self, axis=None): if axis is None: return int(self.indptr[-1]) else: if axis < 0: axis += 2 axis, _ = self._swap((axis, 1 - axis)) _, N = self._swap(self.shape) if axis == 0: return np.bincount(downcast_intp_index(self.indices), minlength=N) elif axis == 1: return np.diff(self.indptr) raise ValueError('axis out of bounds') getnnz.__doc__ = spmatrix.getnnz.__doc__ def _set_self(self, other, copy=False): """take the member variables of other and assign them to self""" if copy: other = other.copy() self.data = other.data self.indices = other.indices self.indptr = other.indptr self._shape = check_shape(other.shape) def check_format(self, full_check=True): """check whether the matrix format is valid Parameters ---------- full_check : bool, optional If `True`, rigorous check, O(N) operations. Otherwise basic check, O(1) operations (default True). """ # use _swap to determine proper bounds major_name, minor_name = self._swap(('row', 'column')) major_dim, minor_dim = self._swap(self.shape) # index arrays should have integer data types if self.indptr.dtype.kind != 'i': warn("indptr array has non-integer dtype ({})" "".format(self.indptr.dtype.name), stacklevel=3) if self.indices.dtype.kind != 'i': warn("indices array has non-integer dtype ({})" "".format(self.indices.dtype.name), stacklevel=3) idx_dtype = get_index_dtype((self.indptr, self.indices)) self.indptr = np.asarray(self.indptr, dtype=idx_dtype) self.indices = np.asarray(self.indices, dtype=idx_dtype) self.data = to_native(self.data) # check array shapes for x in [self.data.ndim, self.indices.ndim, self.indptr.ndim]: if x != 1: raise ValueError('data, indices, and indptr should be 1-D') # check index pointer if (len(self.indptr) != major_dim + 1): raise ValueError("index pointer size ({}) should be ({})" "".format(len(self.indptr), major_dim + 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() >= minor_dim: raise ValueError("{} index values must be < {}" "".format(minor_name, minor_dim)) if self.indices.min() < 0: raise ValueError("{} index values must be >= 0" "".format(minor_name)) 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() # assert(self.has_sorted_indices()) # TODO check for duplicates? ####################### # Boolean comparisons # ####################### def _scalar_binopt(self, other, op): """Scalar version of self._binopt, for cases in which no new nonzeros are added. Produces a new spmatrix in canonical form. """ self.sum_duplicates() res = self._with_data(op(self.data, other), copy=True) res.eliminate_zeros() return res def __eq__(self, other): # Scalar other. if isscalarlike(other): if np.isnan(other): return self.__class__(self.shape, dtype=np.bool_) if other == 0: warn("Comparing a sparse matrix with 0 using == is inefficient" ", try using != instead.", SparseEfficiencyWarning, stacklevel=3) all_true = self.__class__(np.ones(self.shape, dtype=np.bool_)) inv = self._scalar_binopt(other, operator.ne) return all_true - inv else: return self._scalar_binopt(other, operator.eq) # Dense other. elif isdense(other): return self.todense() == other # Pydata sparse other. elif is_pydata_spmatrix(other): return NotImplemented # Sparse other. elif isspmatrix(other): warn("Comparing sparse matrices using == is inefficient, try using" " != instead.", SparseEfficiencyWarning, stacklevel=3) # TODO sparse broadcasting if self.shape != other.shape: return False elif self.format != other.format: other = other.asformat(self.format) res = self._binopt(other, '_ne_') all_true = self.__class__(np.ones(self.shape, dtype=np.bool_)) return all_true - res else: return False def __ne__(self, other): # Scalar other. if isscalarlike(other): if np.isnan(other): warn("Comparing a sparse matrix with nan using != is" " inefficient", SparseEfficiencyWarning, stacklevel=3) all_true = self.__class__(np.ones(self.shape, dtype=np.bool_)) return all_true elif other != 0: warn("Comparing a sparse matrix with a nonzero scalar using !=" " is inefficient, try using == instead.", SparseEfficiencyWarning, stacklevel=3) all_true = self.__class__(np.ones(self.shape), dtype=np.bool_) inv = self._scalar_binopt(other, operator.eq) return all_true - inv else: return self._scalar_binopt(other, operator.ne) # Dense other. elif isdense(other): return self.todense() != other # Pydata sparse other. elif is_pydata_spmatrix(other): return NotImplemented # Sparse other. elif isspmatrix(other): # TODO sparse broadcasting if self.shape != other.shape: return True elif self.format != other.format: other = other.asformat(self.format) return self._binopt(other, '_ne_') else: return True def _inequality(self, other, op, op_name, bad_scalar_msg): # Scalar other. if isscalarlike(other): if 0 == other and op_name in ('_le_', '_ge_'): raise NotImplementedError(" >= and <= don't work with 0.") elif op(0, other): warn(bad_scalar_msg, SparseEfficiencyWarning) other_arr = np.empty(self.shape, dtype=np.result_type(other)) other_arr.fill(other) other_arr = self.__class__(other_arr) return self._binopt(other_arr, op_name) else: return self._scalar_binopt(other, op) # Dense other. elif isdense(other): return op(self.todense(), other) # Sparse other. elif isspmatrix(other): # TODO sparse broadcasting if self.shape != other.shape: raise ValueError("inconsistent shapes") elif self.format != other.format: other = other.asformat(self.format) if op_name not in ('_ge_', '_le_'): return self._binopt(other, op_name) warn("Comparing sparse matrices using >= and <= is inefficient, " "using <, >, or !=, instead.", SparseEfficiencyWarning) all_true = self.__class__(np.ones(self.shape, dtype=np.bool_)) res = self._binopt(other, '_gt_' if op_name == '_le_' else '_lt_') return all_true - res else: raise ValueError("Operands could not be compared.") def __lt__(self, other): return self._inequality(other, operator.lt, '_lt_', "Comparing a sparse matrix with a scalar " "greater than zero using < is inefficient, " "try using >= instead.") def __gt__(self, other): return self._inequality(other, operator.gt, '_gt_', "Comparing a sparse matrix with a scalar " "less than zero using > is inefficient, " "try using <= instead.") def __le__(self, other): return self._inequality(other, operator.le, '_le_', "Comparing a sparse matrix with a scalar " "greater than zero using <= is inefficient, " "try using > instead.") def __ge__(self, other): return self._inequality(other, operator.ge, '_ge_', "Comparing a sparse matrix with a scalar " "less than zero using >= is inefficient, " "try using < instead.") ################################# # Arithmetic operator overrides # ################################# def _add_dense(self, other): if other.shape != self.shape: raise ValueError('Incompatible shapes.') dtype = upcast_char(self.dtype.char, other.dtype.char) order = self._swap('CF')[0] result = np.array(other, dtype=dtype, order=order, copy=True) M, N = self._swap(self.shape) y = result if result.flags.c_contiguous else result.T csr_todense(M, N, self.indptr, self.indices, self.data, y) return matrix(result, copy=False) def _add_sparse(self, other): return self._binopt(other, '_plus_') def _sub_sparse(self, other): return self._binopt(other, '_minus_') def multiply(self, other): """Point-wise multiplication by another matrix, vector, or scalar. """ # Scalar multiplication. if isscalarlike(other): return self._mul_scalar(other) # Sparse matrix or vector. if isspmatrix(other): if self.shape == other.shape: other = self.__class__(other) return self._binopt(other, '_elmul_') # Single element. elif other.shape == (1, 1): return self._mul_scalar(other.toarray()[0, 0]) elif self.shape == (1, 1): return other._mul_scalar(self.toarray()[0, 0]) # A row times a column. elif self.shape[1] == 1 and other.shape[0] == 1: return self._mul_sparse_matrix(other.tocsc()) elif self.shape[0] == 1 and other.shape[1] == 1: return other._mul_sparse_matrix(self.tocsc()) # Row vector times matrix. other is a row. elif other.shape[0] == 1 and self.shape[1] == other.shape[1]: other = dia_matrix((other.toarray().ravel(), [0]), shape=(other.shape[1], other.shape[1])) return self._mul_sparse_matrix(other) # self is a row. elif self.shape[0] == 1 and self.shape[1] == other.shape[1]: copy = dia_matrix((self.toarray().ravel(), [0]), shape=(self.shape[1], self.shape[1])) return other._mul_sparse_matrix(copy) # Column vector times matrix. other is a column. elif other.shape[1] == 1 and self.shape[0] == other.shape[0]: other = dia_matrix((other.toarray().ravel(), [0]), shape=(other.shape[0], other.shape[0])) return other._mul_sparse_matrix(self) # self is a column. elif self.shape[1] == 1 and self.shape[0] == other.shape[0]: copy = dia_matrix((self.toarray().ravel(), [0]), shape=(self.shape[0], self.shape[0])) return copy._mul_sparse_matrix(other) else: raise ValueError("inconsistent shapes") # Assume other is a dense matrix/array, which produces a single-item # object array if other isn't convertible to ndarray. other = np.atleast_2d(other) if other.ndim != 2: return np.multiply(self.toarray(), other) # Single element / wrapped object. if other.size == 1: return self._mul_scalar(other.flat[0]) # Fast case for trivial sparse matrix. elif self.shape == (1, 1): return np.multiply(self.toarray()[0, 0], other) from .coo import coo_matrix ret = self.tocoo() # Matching shapes. if self.shape == other.shape: data = np.multiply(ret.data, other[ret.row, ret.col]) # Sparse row vector times... elif self.shape[0] == 1: if other.shape[1] == 1: # Dense column vector. data = np.multiply(ret.data, other) elif other.shape[1] == self.shape[1]: # Dense matrix. data = np.multiply(ret.data, other[:, ret.col]) else: raise ValueError("inconsistent shapes") row = np.repeat(np.arange(other.shape[0]), len(ret.row)) col = np.tile(ret.col, other.shape[0]) return coo_matrix((data.view(np.ndarray).ravel(), (row, col)), shape=(other.shape[0], self.shape[1]), copy=False) # Sparse column vector times... elif self.shape[1] == 1: if other.shape[0] == 1: # Dense row vector. data = np.multiply(ret.data[:, None], other) elif other.shape[0] == self.shape[0]: # Dense matrix. data = np.multiply(ret.data[:, None], other[ret.row]) else: raise ValueError("inconsistent shapes") row = np.repeat(ret.row, other.shape[1]) col = np.tile(np.arange(other.shape[1]), len(ret.col)) return coo_matrix((data.view(np.ndarray).ravel(), (row, col)), shape=(self.shape[0], other.shape[1]), copy=False) # Sparse matrix times dense row vector. elif other.shape[0] == 1 and self.shape[1] == other.shape[1]: data = np.multiply(ret.data, other[:, ret.col].ravel()) # Sparse matrix times dense column vector. elif other.shape[1] == 1 and self.shape[0] == other.shape[0]: data = np.multiply(ret.data, other[ret.row].ravel()) else: raise ValueError("inconsistent shapes") ret.data = data.view(np.ndarray).ravel() return ret ########################### # Multiplication handlers # ########################### def _mul_vector(self, other): M, N = self.shape # output array result = np.zeros(M, dtype=upcast_char(self.dtype.char, other.dtype.char)) # csr_matvec or csc_matvec fn = getattr(_sparsetools, self.format + '_matvec') fn(M, N, self.indptr, self.indices, self.data, other, result) return result def _mul_multivector(self, other): M, N = self.shape n_vecs = other.shape[1] # number of column vectors result = np.zeros((M, n_vecs), dtype=upcast_char(self.dtype.char, other.dtype.char)) # csr_matvecs or csc_matvecs fn = getattr(_sparsetools, self.format + '_matvecs') fn(M, N, n_vecs, self.indptr, self.indices, self.data, other.ravel(), result.ravel()) return result def _mul_sparse_matrix(self, other): M, K1 = self.shape K2, N = other.shape major_axis = self._swap((M, N))[0] other = self.__class__(other) # convert to this format idx_dtype = get_index_dtype((self.indptr, self.indices, other.indptr, other.indices)) fn = getattr(_sparsetools, self.format + '_matmat_maxnnz') nnz = fn(M, N, np.asarray(self.indptr, dtype=idx_dtype), np.asarray(self.indices, dtype=idx_dtype), np.asarray(other.indptr, dtype=idx_dtype), np.asarray(other.indices, dtype=idx_dtype)) idx_dtype = get_index_dtype((self.indptr, self.indices, other.indptr, other.indices), maxval=nnz) indptr = np.empty(major_axis + 1, dtype=idx_dtype) indices = np.empty(nnz, dtype=idx_dtype) data = np.empty(nnz, dtype=upcast(self.dtype, other.dtype)) fn = getattr(_sparsetools, self.format + '_matmat') fn(M, N, np.asarray(self.indptr, dtype=idx_dtype), np.asarray(self.indices, dtype=idx_dtype), self.data, np.asarray(other.indptr, dtype=idx_dtype), np.asarray(other.indices, dtype=idx_dtype), other.data, indptr, indices, data) return self.__class__((data, indices, indptr), shape=(M, N)) def diagonal(self, k=0): rows, cols = self.shape if k <= -rows or k >= cols: return np.empty(0, dtype=self.data.dtype) fn = getattr(_sparsetools, self.format + "_diagonal") y = np.empty(min(rows + min(k, 0), cols - max(k, 0)), dtype=upcast(self.dtype)) fn(k, self.shape[0], self.shape[1], self.indptr, self.indices, self.data, y) return y diagonal.__doc__ = spmatrix.diagonal.__doc__ ##################### # Other binary ops # ##################### def _maximum_minimum(self, other, npop, op_name, dense_check): if isscalarlike(other): if dense_check(other): warn("Taking maximum (minimum) with > 0 (< 0) number results" " to a dense matrix.", SparseEfficiencyWarning, stacklevel=3) other_arr = np.empty(self.shape, dtype=np.asarray(other).dtype) other_arr.fill(other) other_arr = self.__class__(other_arr) return self._binopt(other_arr, op_name) else: self.sum_duplicates() new_data = npop(self.data, np.asarray(other)) mat = self.__class__((new_data, self.indices, self.indptr), dtype=new_data.dtype, shape=self.shape) return mat elif isdense(other): return npop(self.todense(), other) elif isspmatrix(other): return self._binopt(other, op_name) else: raise ValueError("Operands not compatible.") def maximum(self, other): return self._maximum_minimum(other, np.maximum, '_maximum_', lambda x: np.asarray(x) > 0) maximum.__doc__ = spmatrix.maximum.__doc__ def minimum(self, other): return self._maximum_minimum(other, np.minimum, '_minimum_', lambda x: np.asarray(x) < 0) minimum.__doc__ = spmatrix.minimum.__doc__ ##################### # Reduce operations # ##################### def sum(self, axis=None, dtype=None, out=None): """Sum the matrix over the given axis. If the axis is None, sum over both rows and columns, returning a scalar. """ # The spmatrix base class already does axis=0 and axis=1 efficiently # so we only do the case axis=None here if (not hasattr(self, 'blocksize') and axis in self._swap(((1, -1), (0, 2)))[0]): # faster than multiplication for large minor axis in CSC/CSR res_dtype = get_sum_dtype(self.dtype) ret = np.zeros(len(self.indptr) - 1, dtype=res_dtype) major_index, value = self._minor_reduce(np.add) ret[major_index] = value ret = asmatrix(ret) if axis % 2 == 1: ret = ret.T if out is not None and out.shape != ret.shape: raise ValueError('dimensions do not match') return ret.sum(axis=(), dtype=dtype, out=out) # spmatrix will handle the remaining situations when axis # is in {None, -1, 0, 1} else: return spmatrix.sum(self, axis=axis, dtype=dtype, out=out) sum.__doc__ = spmatrix.sum.__doc__ def _minor_reduce(self, ufunc, data=None): """Reduce nonzeros with a ufunc over the minor axis when non-empty Can be applied to a function of self.data by supplying data parameter. Warning: this does not call sum_duplicates() Returns ------- major_index : array of ints Major indices where nonzero value : array of self.dtype Reduce result for nonzeros in each major_index """ if data is None: data = self.data major_index = np.flatnonzero(np.diff(self.indptr)) value = ufunc.reduceat(data, downcast_intp_index(self.indptr[major_index])) return major_index, value ####################### # Getting and Setting # ####################### def _get_intXint(self, row, col): M, N = self._swap(self.shape) major, minor = self._swap((row, col)) indptr, indices, data = get_csr_submatrix( M, N, self.indptr, self.indices, self.data, major, major + 1, minor, minor + 1) return data.sum(dtype=self.dtype) def _get_sliceXslice(self, row, col): major, minor = self._swap((row, col)) if major.step in (1, None) and minor.step in (1, None): return self._get_submatrix(major, minor, copy=True) return self._major_slice(major)._minor_slice(minor) def _get_arrayXarray(self, row, col): # inner indexing idx_dtype = self.indices.dtype M, N = self._swap(self.shape) major, minor = self._swap((row, col)) major = np.asarray(major, dtype=idx_dtype) minor = np.asarray(minor, dtype=idx_dtype) val = np.empty(major.size, dtype=self.dtype) csr_sample_values(M, N, self.indptr, self.indices, self.data, major.size, major.ravel(), minor.ravel(), val) if major.ndim == 1: return asmatrix(val) return self.__class__(val.reshape(major.shape)) def _get_columnXarray(self, row, col): # outer indexing major, minor = self._swap((row, col)) return self._major_index_fancy(major)._minor_index_fancy(minor) def _major_index_fancy(self, idx): """Index along the major axis where idx is an array of ints. """ idx_dtype = self.indices.dtype indices = np.asarray(idx, dtype=idx_dtype).ravel() _, N = self._swap(self.shape) M = len(indices) new_shape = self._swap((M, N)) if M == 0: return self.__class__(new_shape) row_nnz = np.diff(self.indptr) idx_dtype = self.indices.dtype res_indptr = np.zeros(M+1, dtype=idx_dtype) np.cumsum(row_nnz[idx], out=res_indptr[1:]) nnz = res_indptr[-1] res_indices = np.empty(nnz, dtype=idx_dtype) res_data = np.empty(nnz, dtype=self.dtype) csr_row_index(M, indices, self.indptr, self.indices, self.data, res_indices, res_data) return self.__class__((res_data, res_indices, res_indptr), shape=new_shape, copy=False) def _major_slice(self, idx, copy=False): """Index along the major axis where idx is a slice object. """ if idx == slice(None): return self.copy() if copy else self M, N = self._swap(self.shape) start, stop, step = idx.indices(M) M = len(range(start, stop, step)) new_shape = self._swap((M, N)) if M == 0: return self.__class__(new_shape) row_nnz = np.diff(self.indptr) idx_dtype = self.indices.dtype res_indptr = np.zeros(M+1, dtype=idx_dtype) np.cumsum(row_nnz[idx], out=res_indptr[1:]) if step == 1: all_idx = slice(self.indptr[start], self.indptr[stop]) res_indices = np.array(self.indices[all_idx], copy=copy) res_data = np.array(self.data[all_idx], copy=copy) else: nnz = res_indptr[-1] res_indices = np.empty(nnz, dtype=idx_dtype) res_data = np.empty(nnz, dtype=self.dtype) csr_row_slice(start, stop, step, self.indptr, self.indices, self.data, res_indices, res_data) return self.__class__((res_data, res_indices, res_indptr), shape=new_shape, copy=False) def _minor_index_fancy(self, idx): """Index along the minor axis where idx is an array of ints. """ idx_dtype = self.indices.dtype idx = np.asarray(idx, dtype=idx_dtype).ravel() M, N = self._swap(self.shape) k = len(idx) new_shape = self._swap((M, k)) if k == 0: return self.__class__(new_shape) # pass 1: count idx entries and compute new indptr col_offsets = np.zeros(N, dtype=idx_dtype) res_indptr = np.empty_like(self.indptr) csr_column_index1(k, idx, M, N, self.indptr, self.indices, col_offsets, res_indptr) # pass 2: copy indices/data for selected idxs col_order = np.argsort(idx).astype(idx_dtype, copy=False) nnz = res_indptr[-1] res_indices = np.empty(nnz, dtype=idx_dtype) res_data = np.empty(nnz, dtype=self.dtype) csr_column_index2(col_order, col_offsets, len(self.indices), self.indices, self.data, res_indices, res_data) return self.__class__((res_data, res_indices, res_indptr), shape=new_shape, copy=False) def _minor_slice(self, idx, copy=False): """Index along the minor axis where idx is a slice object. """ if idx == slice(None): return self.copy() if copy else self M, N = self._swap(self.shape) start, stop, step = idx.indices(N) N = len(range(start, stop, step)) if N == 0: return self.__class__(self._swap((M, N))) if step == 1: return self._get_submatrix(minor=idx, copy=copy) # TODO: don't fall back to fancy indexing here return self._minor_index_fancy(np.arange(start, stop, step)) def _get_submatrix(self, major=None, minor=None, copy=False): """Return a submatrix of this matrix. major, minor: None, int, or slice with step 1 """ M, N = self._swap(self.shape) i0, i1 = _process_slice(major, M) j0, j1 = _process_slice(minor, N) if i0 == 0 and j0 == 0 and i1 == M and j1 == N: return self.copy() if copy else self indptr, indices, data = get_csr_submatrix( M, N, self.indptr, self.indices, self.data, i0, i1, j0, j1) shape = self._swap((i1 - i0, j1 - j0)) return self.__class__((data, indices, indptr), shape=shape, dtype=self.dtype, copy=False) def _set_intXint(self, row, col, x): i, j = self._swap((row, col)) self._set_many(i, j, x) def _set_arrayXarray(self, row, col, x): i, j = self._swap((row, col)) self._set_many(i, j, x) def _set_arrayXarray_sparse(self, row, col, x): # clear entries that will be overwritten self._zero_many(*self._swap((row, col))) M, N = row.shape # matches col.shape broadcast_row = M != 1 and x.shape[0] == 1 broadcast_col = N != 1 and x.shape[1] == 1 r, c = x.row, x.col x = np.asarray(x.data, dtype=self.dtype) if x.size == 0: return if broadcast_row: r = np.repeat(np.arange(M), len(r)) c = np.tile(c, M) x = np.tile(x, M) if broadcast_col: r = np.repeat(r, N) c = np.tile(np.arange(N), len(c)) x = np.repeat(x, N) # only assign entries in the new sparsity structure i, j = self._swap((row[r, c], col[r, c])) self._set_many(i, j, x) def _setdiag(self, values, k): if 0 in self.shape: return M, N = self.shape broadcast = (values.ndim == 0) if k < 0: if broadcast: max_index = min(M + k, N) else: max_index = min(M + k, N, len(values)) i = np.arange(max_index, dtype=self.indices.dtype) j = np.arange(max_index, dtype=self.indices.dtype) i -= k else: if broadcast: max_index = min(M, N - k) else: max_index = min(M, N - k, len(values)) i = np.arange(max_index, dtype=self.indices.dtype) j = np.arange(max_index, dtype=self.indices.dtype) j += k if not broadcast: values = values[:len(i)] self[i, j] = values def _prepare_indices(self, i, j): M, N = self._swap(self.shape) def check_bounds(indices, bound): idx = indices.max() if idx >= bound: raise IndexError('index (%d) out of range (>= %d)' % (idx, bound)) idx = indices.min() if idx < -bound: raise IndexError('index (%d) out of range (< -%d)' % (idx, bound)) i = np.array(i, dtype=self.indices.dtype, copy=False, ndmin=1).ravel() j = np.array(j, dtype=self.indices.dtype, copy=False, ndmin=1).ravel() check_bounds(i, M) check_bounds(j, N) return i, j, M, N def _set_many(self, i, j, x): """Sets value at each (i, j) to x Here (i,j) index major and minor respectively, and must not contain duplicate entries. """ i, j, M, N = self._prepare_indices(i, j) x = np.array(x, dtype=self.dtype, copy=False, ndmin=1).ravel() n_samples = x.size offsets = np.empty(n_samples, dtype=self.indices.dtype) ret = csr_sample_offsets(M, N, self.indptr, self.indices, n_samples, i, j, offsets) if ret == 1: # rinse and repeat self.sum_duplicates() csr_sample_offsets(M, N, self.indptr, self.indices, n_samples, i, j, offsets) if -1 not in offsets: # only affects existing non-zero cells self.data[offsets] = x return else: warn("Changing the sparsity structure of a {}_matrix is expensive." " lil_matrix is more efficient.".format(self.format), SparseEfficiencyWarning, stacklevel=3) # replace where possible mask = offsets > -1 self.data[offsets[mask]] = x[mask] # only insertions remain mask = ~mask i = i[mask] i[i < 0] += M j = j[mask] j[j < 0] += N self._insert_many(i, j, x[mask]) def _zero_many(self, i, j): """Sets value at each (i, j) to zero, preserving sparsity structure. Here (i,j) index major and minor respectively. """ i, j, M, N = self._prepare_indices(i, j) n_samples = len(i) offsets = np.empty(n_samples, dtype=self.indices.dtype) ret = csr_sample_offsets(M, N, self.indptr, self.indices, n_samples, i, j, offsets) if ret == 1: # rinse and repeat self.sum_duplicates() csr_sample_offsets(M, N, self.indptr, self.indices, n_samples, i, j, offsets) # only assign zeros to the existing sparsity structure self.data[offsets[offsets > -1]] = 0 def _insert_many(self, i, j, x): """Inserts new nonzero at each (i, j) with value x Here (i,j) index major and minor respectively. i, j and x must be non-empty, 1d arrays. Inserts each major group (e.g. all entries per row) at a time. Maintains has_sorted_indices property. Modifies i, j, x in place. """ order = np.argsort(i, kind='mergesort') # stable for duplicates i = i.take(order, mode='clip') j = j.take(order, mode='clip') x = x.take(order, mode='clip') do_sort = self.has_sorted_indices # Update index data type idx_dtype = get_index_dtype((self.indices, self.indptr), maxval=(self.indptr[-1] + x.size)) self.indptr = np.asarray(self.indptr, dtype=idx_dtype) self.indices = np.asarray(self.indices, dtype=idx_dtype) i = np.asarray(i, dtype=idx_dtype) j = np.asarray(j, dtype=idx_dtype) # Collate old and new in chunks by major index indices_parts = [] data_parts = [] ui, ui_indptr = np.unique(i, return_index=True) ui_indptr = np.append(ui_indptr, len(j)) new_nnzs = np.diff(ui_indptr) prev = 0 for c, (ii, js, je) in enumerate(zip(ui, ui_indptr, ui_indptr[1:])): # old entries start = self.indptr[prev] stop = self.indptr[ii] indices_parts.append(self.indices[start:stop]) data_parts.append(self.data[start:stop]) # handle duplicate j: keep last setting uj, uj_indptr = np.unique(j[js:je][::-1], return_index=True) if len(uj) == je - js: indices_parts.append(j[js:je]) data_parts.append(x[js:je]) else: indices_parts.append(j[js:je][::-1][uj_indptr]) data_parts.append(x[js:je][::-1][uj_indptr]) new_nnzs[c] = len(uj) prev = ii # remaining old entries start = self.indptr[ii] indices_parts.append(self.indices[start:]) data_parts.append(self.data[start:]) # update attributes self.indices = np.concatenate(indices_parts) self.data = np.concatenate(data_parts) nnzs = np.empty(self.indptr.shape, dtype=idx_dtype) nnzs[0] = idx_dtype(0) indptr_diff = np.diff(self.indptr) indptr_diff[ui] += new_nnzs nnzs[1:] = indptr_diff self.indptr = np.cumsum(nnzs, out=nnzs) if do_sort: # TODO: only sort where necessary self.has_sorted_indices = False self.sort_indices() self.check_format(full_check=False) ###################### # Conversion methods # ###################### def tocoo(self, copy=True): major_dim, minor_dim = self._swap(self.shape) minor_indices = self.indices major_indices = np.empty(len(minor_indices), dtype=self.indices.dtype) _sparsetools.expandptr(major_dim, self.indptr, major_indices) row, col = self._swap((major_indices, minor_indices)) from .coo import coo_matrix return coo_matrix((self.data, (row, col)), self.shape, copy=copy, dtype=self.dtype) tocoo.__doc__ = spmatrix.tocoo.__doc__ def toarray(self, order=None, out=None): if out is None and order is None: order = self._swap('cf')[0] out = self._process_toarray_args(order, out) if not (out.flags.c_contiguous or out.flags.f_contiguous): raise ValueError('Output array must be C or F contiguous') # align ideal order with output array order if out.flags.c_contiguous: x = self.tocsr() y = out else: x = self.tocsc() y = out.T M, N = x._swap(x.shape) csr_todense(M, N, x.indptr, x.indices, x.data, y) return out toarray.__doc__ = spmatrix.toarray.__doc__ ############################################################## # methods that examine or modify the internal data structure # ############################################################## def eliminate_zeros(self): """Remove zero entries from the matrix This is an *in place* operation """ M, N = self._swap(self.shape) _sparsetools.csr_eliminate_zeros(M, N, self.indptr, self.indices, self.data) self.prune() # nnz may have changed def __get_has_canonical_format(self): """Determine whether the matrix has sorted indices and no duplicates Returns - True: if the above applies - False: otherwise has_canonical_format implies has_sorted_indices, so if the latter flag is False, so will the former be; if the former is found True, the latter flag is also set. """ # first check to see if result was cached if not getattr(self, '_has_sorted_indices', True): # not sorted => not canonical self._has_canonical_format = False elif not hasattr(self, '_has_canonical_format'): self.has_canonical_format = _sparsetools.csr_has_canonical_format( len(self.indptr) - 1, self.indptr, self.indices) return self._has_canonical_format def __set_has_canonical_format(self, val): self._has_canonical_format = bool(val) if val: self.has_sorted_indices = True has_canonical_format = property(fget=__get_has_canonical_format, fset=__set_has_canonical_format) def sum_duplicates(self): """Eliminate duplicate matrix entries by adding them together The is an *in place* operation """ if self.has_canonical_format: return self.sort_indices() M, N = self._swap(self.shape) _sparsetools.csr_sum_duplicates(M, N, self.indptr, self.indices, self.data) self.prune() # nnz may have changed self.has_canonical_format = True def __get_sorted(self): """Determine whether the matrix has sorted indices Returns - True: if the indices of the matrix are in sorted order - False: otherwise """ # first check to see if result was cached if not hasattr(self, '_has_sorted_indices'): self._has_sorted_indices = _sparsetools.csr_has_sorted_indices( len(self.indptr) - 1, self.indptr, self.indices) return self._has_sorted_indices def __set_sorted(self, val): self._has_sorted_indices = bool(val) has_sorted_indices = property(fget=__get_sorted, fset=__set_sorted) def sorted_indices(self): """Return a copy of this matrix with sorted indices """ A = self.copy() A.sort_indices() return A # an alternative that has linear complexity is the following # although the previous option is typically faster # return self.toother().toother() def sort_indices(self): """Sort the indices of this matrix *in place* """ if not self.has_sorted_indices: _sparsetools.csr_sort_indices(len(self.indptr) - 1, self.indptr, self.indices, self.data) self.has_sorted_indices = True def prune(self): """Remove empty space after all non-zero elements. """ major_dim = self._swap(self.shape)[0] if len(self.indptr) != major_dim + 1: raise ValueError('index pointer has invalid length') if len(self.indices) < self.nnz: raise ValueError('indices array has fewer than nnz elements') if len(self.data) < self.nnz: raise ValueError('data array has fewer than nnz elements') self.indices = _prune_array(self.indices[:self.nnz]) self.data = _prune_array(self.data[:self.nnz]) def resize(self, *shape): shape = check_shape(shape) if hasattr(self, 'blocksize'): bm, bn = self.blocksize new_M, rm = divmod(shape[0], bm) new_N, rn = divmod(shape[1], bn) if rm or rn: raise ValueError("shape must be divisible into %s blocks. " "Got %s" % (self.blocksize, shape)) M, N = self.shape[0] // bm, self.shape[1] // bn else: new_M, new_N = self._swap(shape) M, N = self._swap(self.shape) if new_M < M: self.indices = self.indices[:self.indptr[new_M]] self.data = self.data[:self.indptr[new_M]] self.indptr = self.indptr[:new_M + 1] elif new_M > M: self.indptr = np.resize(self.indptr, new_M + 1) self.indptr[M + 1:].fill(self.indptr[M]) if new_N < N: mask = self.indices < new_N if not np.all(mask): self.indices = self.indices[mask] self.data = self.data[mask] major_index, val = self._minor_reduce(np.add, mask) self.indptr.fill(0) self.indptr[1:][major_index] = val np.cumsum(self.indptr, out=self.indptr) self._shape = shape resize.__doc__ = spmatrix.resize.__doc__ ################### # utility methods # ################### # 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) def _binopt(self, other, op): """apply the binary operation fn to two sparse matrices.""" other = self.__class__(other) # e.g. csr_plus_csr, csr_minus_csr, etc. fn = getattr(_sparsetools, self.format + op + self.format) maxnnz = self.nnz + other.nnz idx_dtype = get_index_dtype((self.indptr, self.indices, other.indptr, other.indices), maxval=maxnnz) indptr = np.empty(self.indptr.shape, dtype=idx_dtype) indices = np.empty(maxnnz, dtype=idx_dtype) bool_ops = ['_ne_', '_lt_', '_gt_', '_le_', '_ge_'] if op in bool_ops: data = np.empty(maxnnz, dtype=np.bool_) else: data = np.empty(maxnnz, dtype=upcast(self.dtype, other.dtype)) fn(self.shape[0], self.shape[1], np.asarray(self.indptr, dtype=idx_dtype), np.asarray(self.indices, dtype=idx_dtype), self.data, np.asarray(other.indptr, dtype=idx_dtype), np.asarray(other.indices, dtype=idx_dtype), other.data, indptr, indices, data) A = self.__class__((data, indices, indptr), shape=self.shape) A.prune() return A def _divide_sparse(self, other): """ Divide this matrix by a second sparse matrix. """ if other.shape != self.shape: raise ValueError('inconsistent shapes') r = self._binopt(other, '_eldiv_') if np.issubdtype(r.dtype, np.inexact): # Eldiv leaves entries outside the combined sparsity # pattern empty, so they must be filled manually. # Everything outside of other's sparsity is NaN, and everything # inside it is either zero or defined by eldiv. out = np.empty(self.shape, dtype=self.dtype) out.fill(np.nan) row, col = other.nonzero() out[row, col] = 0 r = r.tocoo() out[r.row, r.col] = r.data out = matrix(out) else: # integers types go with nan <-> 0 out = r return out def _process_slice(sl, num): if sl is None: i0, i1 = 0, num elif isinstance(sl, slice): i0, i1, stride = sl.indices(num) if stride != 1: raise ValueError('slicing with step != 1 not supported') i0 = min(i0, i1) # give an empty slice when i0 > i1 elif isintlike(sl): if sl < 0: sl += num i0, i1 = sl, sl + 1 if i0 < 0 or i1 > num: raise IndexError('index out of bounds: 0 <= %d < %d <= %d' % (i0, i1, num)) else: raise TypeError('expected slice or scalar') return i0, i1