"""Base class for sparse matrices""" import numpy as np from ._sputils import (asmatrix, check_reshape_kwargs, check_shape, get_sum_dtype, isdense, isscalarlike, matrix, validateaxis,) from ._matrix import spmatrix __all__ = ['isspmatrix', 'issparse', 'sparray', 'SparseWarning', 'SparseEfficiencyWarning'] 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, "List of Lists"], '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"] } # These univariate ufuncs preserve zeros. _ufuncs_with_fixed_point_at_zero = frozenset([ np.sin, np.tan, np.arcsin, np.arctan, np.sinh, np.tanh, np.arcsinh, np.arctanh, np.rint, np.sign, np.expm1, np.log1p, np.deg2rad, np.rad2deg, np.floor, np.ceil, np.trunc, np.sqrt]) MAXPRINT = 50 class _spbase: """ This class provides a base class for all sparse arrays. It cannot be instantiated. Most of the work is provided by subclasses. """ __array_priority__ = 10.1 _format = 'und' # undefined @property def ndim(self) -> int: return len(self._shape) @property def _shape_as_2d(self): s = self._shape return (1, s[-1]) if len(s) == 1 else s @property def _bsr_container(self): from ._bsr import bsr_array return bsr_array @property def _coo_container(self): from ._coo import coo_array return coo_array @property def _csc_container(self): from ._csc import csc_array return csc_array @property def _csr_container(self): from ._csr import csr_array return csr_array @property def _dia_container(self): from ._dia import dia_array return dia_array @property def _dok_container(self): from ._dok import dok_array return dok_array @property def _lil_container(self): from ._lil import lil_array return lil_array def __init__(self, arg1, maxprint=MAXPRINT): self._shape = None if self.__class__.__name__ == '_spbase': raise ValueError("This class is not intended" " to be instantiated directly.") if isinstance(self, sparray) and np.isscalar(arg1): raise ValueError( "scipy sparse array classes do not support instantiation from a scalar" ) self.maxprint = maxprint @property def shape(self): return self._shape def reshape(self, *args, **kwargs): """reshape(self, shape, order='C', copy=False) Gives a new shape to a sparse array/matrix without changing its data. Parameters ---------- shape : length-2 tuple of ints The new shape should be compatible with the original shape. order : {'C', 'F'}, optional Read the elements using this index order. 'C' means to read and write the elements using C-like index order; e.g., read entire first row, then second row, etc. 'F' means to read and write the elements using Fortran-like index order; e.g., read entire first column, then second column, etc. copy : bool, optional Indicates whether or not attributes of self should be copied whenever possible. The degree to which attributes are copied varies depending on the type of sparse array being used. Returns ------- reshaped : sparse array/matrix A sparse array/matrix with the given `shape`, not necessarily of the same format as the current object. See Also -------- numpy.reshape : NumPy's implementation of 'reshape' for ndarrays """ # If the shape already matches, don't bother doing an actual reshape # Otherwise, the default is to convert to COO and use its reshape is_array = isinstance(self, sparray) shape = check_shape(args, self.shape, allow_1d=is_array) order, copy = check_reshape_kwargs(kwargs) if shape == self.shape: if copy: return self.copy() else: return self return self.tocoo(copy=copy).reshape(shape, order=order, copy=False) def resize(self, shape): """Resize the array/matrix in-place to dimensions given by ``shape`` Any elements that lie within the new shape will remain at the same indices, while non-zero elements lying outside the new shape are removed. Parameters ---------- shape : (int, int) number of rows and columns in the new array/matrix Notes ----- The semantics are not identical to `numpy.ndarray.resize` or `numpy.resize`. Here, the same data will be maintained at each index before and after reshape, if that index is within the new bounds. In numpy, resizing maintains contiguity of the array, moving elements around in the logical array but not within a flattened representation. We give no guarantees about whether the underlying data attributes (arrays, etc.) will be modified in place or replaced with new objects. """ # As an inplace operation, this requires implementation in each format. raise NotImplementedError( f'{type(self).__name__}.resize is not implemented') def astype(self, dtype, casting='unsafe', copy=True): """Cast the array/matrix elements to a specified type. Parameters ---------- dtype : string or numpy dtype Typecode or data-type to which to cast the data. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'unsafe' for backwards compatibility. 'no' means the data types should not be cast at all. 'equiv' means only byte-order changes are allowed. 'safe' means only casts which can preserve values are allowed. 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. 'unsafe' means any data conversions may be done. copy : bool, optional If `copy` is `False`, the result might share some memory with this array/matrix. If `copy` is `True`, it is guaranteed that the result and this array/matrix do not share any memory. """ dtype = np.dtype(dtype) if self.dtype != dtype: return self.tocsr().astype( dtype, casting=casting, copy=copy).asformat(self.format) elif copy: return self.copy() else: return self @classmethod def _ascontainer(cls, X, **kwargs): if issubclass(cls, sparray): return np.asarray(X, **kwargs) else: return asmatrix(X, **kwargs) @classmethod def _container(cls, X, **kwargs): if issubclass(cls, sparray): return np.array(X, **kwargs) else: return matrix(X, **kwargs) def _asfptype(self): """Upcast array 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 range(self.shape[0]): yield self[r] def _getmaxprint(self): """Maximum number of elements to display when printed.""" return self.maxprint def count_nonzero(self): """Number of non-zero entries, equivalent to np.count_nonzero(a.toarray()) Unlike the nnz property, which return the number of stored entries (the length of the data attribute), this method counts the actual number of non-zero entries in data. """ raise NotImplementedError("count_nonzero not implemented for %s." % self.__class__.__name__) def _getnnz(self, axis=None): """Number of stored values, including explicit zeros. Parameters ---------- axis : None, 0, or 1 Select between the number of values across the whole array, in each column, or in each row. See also -------- count_nonzero : Number of non-zero entries """ raise NotImplementedError("getnnz not implemented for %s." % self.__class__.__name__) @property def nnz(self) -> int: """Number of stored values, including explicit zeros. See also -------- count_nonzero : Number of non-zero entries """ return self._getnnz() @property def size(self) -> int: """Number of stored values. See also -------- count_nonzero : Number of non-zero values. """ return self._getnnz() @property def format(self) -> str: """Format string for matrix.""" return self._format @property def T(self): """Transpose.""" return self.transpose() @property def real(self): return self._real() @property def imag(self): return self._imag() def __repr__(self): _, format_name = _formats[self.format] sparse_cls = 'array' if isinstance(self, sparray) else 'matrix' return ( f"<{format_name} sparse {sparse_cls} of dtype '{self.dtype}'\n" f"\twith {self.nnz} stored elements and shape {self.shape}>" ) def __str__(self): maxprint = self._getmaxprint() A = self.tocoo() # helper function, outputs "(i,j) v" def tostr(coords, data): pairs = zip(zip(*(c.tolist() for c in coords)), data) return '\n'.join(f' {idx}\t{val}' for idx, val in pairs) out = repr(self) if self.nnz == 0: return out out += '\n Coords\tValues\n' if self.nnz > maxprint: half = maxprint // 2 out += tostr(tuple(c[:half] for c in A.coords), A.data[:half]) out += "\n :\t:\n" half = maxprint - half out += tostr(tuple(c[-half:] for c in A.coords), A.data[-half:]) else: out += tostr(A.coords, A.data) return out def __bool__(self): # Simple -- other ideas? if self.shape == (1, 1): return self.nnz != 0 else: raise ValueError("The truth value of an array with more than one " "element is ambiguous. Use a.any() or a.all().") __nonzero__ = __bool__ # 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): raise TypeError("sparse array length is ambiguous; use getnnz()" " or shape[0]") def asformat(self, format, copy=False): """Return this array/matrix in the passed format. Parameters ---------- format : {str, None} The desired sparse format ("csr", "csc", "lil", "dok", "array", ...) or None for no conversion. copy : bool, optional If True, the result is guaranteed to not share data with self. Returns ------- A : This array/matrix in the passed format. """ if format is None or format == self.format: if copy: return self.copy() else: return self else: try: convert_method = getattr(self, 'to' + format) except AttributeError as e: raise ValueError(f'Format {format} is unknown.') from e # Forward the copy kwarg, if it's accepted. try: return convert_method(copy=copy) except TypeError: return convert_method() ################################################################### # NOTE: All arithmetic operations use csr_matrix by default. # Therefore a new sparse array 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 array/matrix.""" if isscalarlike(other): return self._mul_scalar(other) return self.tocsr().multiply(other) def maximum(self, other): """Element-wise maximum between this and another array/matrix.""" return self.tocsr().maximum(other) def minimum(self, other): """Element-wise minimum between this and another array/matrix.""" return self.tocsr().minimum(other) def dot(self, other): """Ordinary dot product Examples -------- >>> import numpy as np >>> from scipy.sparse import csr_array >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]]) >>> v = np.array([1, 0, -1]) >>> A.dot(v) array([ 1, -3, -1], dtype=int64) """ if np.isscalar(other): return self * other else: return self @ other def power(self, n, dtype=None): """Element-wise power.""" return self.tocsr().power(n, dtype=dtype) def __eq__(self, other): return self.tocsr().__eq__(other) def __ne__(self, other): return self.tocsr().__ne__(other) def __lt__(self, other): return self.tocsr().__lt__(other) def __gt__(self, other): return self.tocsr().__gt__(other) def __le__(self, other): return self.tocsr().__le__(other) def __ge__(self, other): return self.tocsr().__ge__(other) def __abs__(self): return abs(self.tocsr()) def __round__(self, ndigits=0): return round(self.tocsr(), ndigits=ndigits) def _add_sparse(self, other): return self.tocsr()._add_sparse(other) def _add_dense(self, other): return self.tocoo()._add_dense(other) def _sub_sparse(self, other): return self.tocsr()._sub_sparse(other) def _sub_dense(self, other): return self.todense() - other def _rsub_dense(self, other): # note: this can't be replaced by other + (-self) for unsigned types return other - self.todense() def __add__(self, other): # self + other if isscalarlike(other): if other == 0: return self.copy() # Now we would add this scalar to every element. raise NotImplementedError('adding a nonzero scalar to a ' 'sparse array is not supported') elif issparse(other): if other.shape != self.shape: raise ValueError("inconsistent shapes") return self._add_sparse(other) elif isdense(other): other = np.broadcast_to(other, self.shape) return self._add_dense(other) else: return NotImplemented def __radd__(self,other): # other + self return self.__add__(other) def __sub__(self, other): # self - other if isscalarlike(other): if other == 0: return self.copy() raise NotImplementedError('subtracting a nonzero scalar from a ' 'sparse array is not supported') elif issparse(other): if other.shape != self.shape: raise ValueError("inconsistent shapes") return self._sub_sparse(other) elif isdense(other): other = np.broadcast_to(other, self.shape) return self._sub_dense(other) else: return NotImplemented def __rsub__(self,other): # other - self if isscalarlike(other): if other == 0: return -self.copy() raise NotImplementedError('subtracting a sparse array from a ' 'nonzero scalar is not supported') elif isdense(other): other = np.broadcast_to(other, self.shape) return self._rsub_dense(other) else: return NotImplemented def _matmul_dispatch(self, other): """np.array-like matmul & `np.matrix`-like mul, i.e. `dot` or `NotImplemented` interpret other and call one of the following self._mul_scalar() self._matmul_vector() self._matmul_multivector() self._matmul_sparse() """ # This method has to be different from `__matmul__` because it is also # called by sparse matrix classes. # Currently matrix multiplication is only supported # for 2D arrays. Hence we unpacked and use only the # two last axes' lengths. M, N = self._shape_as_2d if other.__class__ is np.ndarray: # Fast path for the most common case if other.shape == (N,): return self._matmul_vector(other) elif other.shape == (N, 1): result = self._matmul_vector(other.ravel()) if self.ndim == 1: return result return result.reshape(M, 1) elif other.ndim == 2 and other.shape[0] == N: return self._matmul_multivector(other) 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._matmul_sparse(other) # If it's a list or whatever, treat it like an array other_a = np.asanyarray(other) if other_a.ndim == 0 and other_a.dtype == np.object_: # Not interpretable as an array; return NotImplemented so that # other's __rmatmul__ can kick in if that's implemented. return NotImplemented try: other.shape except AttributeError: other = other_a 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._matmul_vector(np.ravel(other)) if isinstance(other, np.matrix): result = self._ascontainer(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] != N: raise ValueError('dimension mismatch') result = self._matmul_multivector(np.asarray(other)) if isinstance(other, np.matrix): result = self._ascontainer(result) return result else: raise ValueError('could not interpret dimensions') def __mul__(self, other): return self.multiply(other) def __rmul__(self, other): # other * self return self.multiply(other) # by default, use CSR for __mul__ handlers def _mul_scalar(self, other): return self.tocsr()._mul_scalar(other) def _matmul_vector(self, other): return self.tocsr()._matmul_vector(other) def _matmul_multivector(self, other): return self.tocsr()._matmul_multivector(other) def _matmul_sparse(self, other): return self.tocsr()._matmul_sparse(other) def _rmatmul_dispatch(self, other): if isscalarlike(other): return self._mul_scalar(other) else: # Don't use asarray unless we have to try: tr = other.transpose() except AttributeError: tr = np.asarray(other).transpose() ret = self.transpose()._matmul_dispatch(tr) if ret is NotImplemented: return NotImplemented return ret.transpose() ####################### # matmul (@) operator # ####################### def __matmul__(self, other): if isscalarlike(other): raise ValueError("Scalar operands are not allowed, " "use '*' instead") return self._matmul_dispatch(other) def __rmatmul__(self, other): if isscalarlike(other): raise ValueError("Scalar operands are not allowed, " "use '*' instead") return self._rmatmul_dispatch(other) #################### # Other Arithmetic # #################### def _divide(self, other, true_divide=False, rdivide=False): if isscalarlike(other): if rdivide: if true_divide: return np.true_divide(other, self.todense()) else: return np.divide(other, self.todense()) if true_divide and np.can_cast(self.dtype, np.float64): return self.astype(np.float64)._mul_scalar(1./other) else: r = self._mul_scalar(1./other) scalar_dtype = np.asarray(other).dtype if (np.issubdtype(self.dtype, np.integer) and np.issubdtype(scalar_dtype, np.integer)): return r.astype(self.dtype) else: return r elif isdense(other): if not rdivide: if true_divide: recip = np.true_divide(1., other) else: recip = np.divide(1., other) return self.multiply(recip) else: if true_divide: return np.true_divide(other, self.todense()) else: return np.divide(other, self.todense()) elif issparse(other): if rdivide: return other._divide(self, true_divide, rdivide=False) self_csr = self.tocsr() if true_divide and np.can_cast(self.dtype, np.float64): return self_csr.astype(np.float64)._divide_sparse(other) else: return self_csr._divide_sparse(other) else: return NotImplemented def __truediv__(self, other): return self._divide(other, true_divide=True) def __div__(self, other): # Always do true division return self._divide(other, true_divide=True) def __rtruediv__(self, other): # Implementing this as the inverse would be too magical -- bail out return NotImplemented def __rdiv__(self, other): # Implementing this as the inverse would be too magical -- bail out return NotImplemented def __neg__(self): return -self.tocsr() def __iadd__(self, other): return NotImplemented def __isub__(self, other): return NotImplemented def __imul__(self, other): return NotImplemented def __idiv__(self, other): return self.__itruediv__(other) def __itruediv__(self, other): return NotImplemented def __pow__(self, *args, **kwargs): return self.power(*args, **kwargs) def transpose(self, axes=None, copy=False): """ Reverses the dimensions of the sparse array/matrix. Parameters ---------- axes : None, optional This argument is in the signature *solely* for NumPy compatibility reasons. Do not pass in anything except for the default value. copy : bool, optional Indicates whether or not attributes of `self` should be copied whenever possible. The degree to which attributes are copied varies depending on the type of sparse array/matrix being used. Returns ------- p : `self` with the dimensions reversed. Notes ----- If `self` is a `csr_array` or a `csc_array`, then this will return a `csc_array` or a `csr_array`, respectively. See Also -------- numpy.transpose : NumPy's implementation of 'transpose' for ndarrays """ return self.tocsr(copy=copy).transpose(axes=axes, copy=False) def conjugate(self, copy=True): """Element-wise complex conjugation. If the array/matrix is of non-complex data type and `copy` is False, this method does nothing and the data is not copied. Parameters ---------- copy : bool, optional If True, the result is guaranteed to not share data with self. Returns ------- A : The element-wise complex conjugate. """ if np.issubdtype(self.dtype, np.complexfloating): return self.tocsr(copy=copy).conjugate(copy=False) elif copy: return self.copy() else: return self def conj(self, copy=True): return self.conjugate(copy=copy) conj.__doc__ = conjugate.__doc__ def _real(self): return self.tocsr()._real() def _imag(self): return self.tocsr()._imag() def nonzero(self): """Nonzero indices of the array/matrix. Returns a tuple of arrays (row,col) containing the indices of the non-zero elements of the array. Examples -------- >>> from scipy.sparse import csr_array >>> A = csr_array([[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 array, as an (m x 1) sparse array (column vector). """ if self.ndim == 1: raise ValueError("getcol not provided for 1d arrays. Use indexing A[j]") # 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 N = self.shape[-1] if j < 0: j += N if j < 0 or j >= N: raise IndexError("index out of bounds") col_selector = self._csc_container(([1], [[j], [0]]), shape=(N, 1), dtype=self.dtype) result = self @ col_selector return result def _getrow(self, i): """Returns a copy of row i of the array, as a (1 x n) sparse array (row vector). """ if self.ndim == 1: raise ValueError("getrow not meaningful for a 1d array") # 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 M = self.shape[0] if i < 0: i += M if i < 0 or i >= M: raise IndexError("index out of bounds") row_selector = self._csr_container(([1], [[0], [i]]), shape=(1, M), dtype=self.dtype) return row_selector @ self # The following dunder methods cannot be implemented. # # def __array__(self): # # Sparse matrices rely on NumPy wrapping them in object arrays under # # the hood to make unary ufuncs work on them. So we cannot raise # # TypeError here - which would be handy to not give users object # # arrays they probably don't want (they're looking for `.toarray()`). # # # # Conversion with `toarray()` would also break things because of the # # behavior discussed above, plus we want to avoid densification by # # accident because that can too easily blow up memory. # # def __array_ufunc__(self): # # We cannot implement __array_ufunc__ due to mismatching semantics. # # See gh-7707 and gh-7349 for details. # # def __array_function__(self): # # We cannot implement __array_function__ due to mismatching semantics. # # See gh-10362 for details. def todense(self, order=None, out=None): """ Return a dense representation of this sparse array/matrix. Parameters ---------- order : {'C', 'F'}, optional Whether to store multi-dimensional data in C (row-major) or Fortran (column-major) order in memory. The default is 'None', which provides no ordering guarantees. Cannot be specified in conjunction with the `out` argument. out : ndarray, 2-D, optional If specified, uses this array (or `numpy.matrix`) as the output buffer instead of allocating a new array to return. The provided array must have the same shape and dtype as the sparse array/matrix on which you are calling the method. Returns ------- arr : numpy.matrix, 2-D A NumPy matrix object with the same shape and containing the same data represented by the sparse array/matrix, with the requested memory order. If `out` was passed and was an array (rather than a `numpy.matrix`), it will be filled with the appropriate values and returned wrapped in a `numpy.matrix` object that shares the same memory. """ return self._ascontainer(self.toarray(order=order, out=out)) def toarray(self, order=None, out=None): """ Return a dense ndarray representation of this sparse array/matrix. Parameters ---------- order : {'C', 'F'}, optional Whether to store multidimensional data in C (row-major) or Fortran (column-major) order in memory. The default is 'None', which provides no ordering guarantees. Cannot be specified in conjunction with the `out` argument. out : ndarray, 2-D, optional If specified, uses this array as the output buffer instead of allocating a new array to return. The provided array must have the same shape and dtype as the sparse array/matrix on which you are calling the method. For most sparse types, `out` is required to be memory contiguous (either C or Fortran ordered). Returns ------- arr : ndarray, 2-D An array with the same shape and containing the same data represented by the sparse array/matrix, with the requested memory order. If `out` was passed, the same object is returned after being modified in-place to contain the appropriate values. """ return self.tocoo(copy=False).toarray(order=order, out=out) # Any sparse array format deriving from _spbase must define one of # tocsr or tocoo. The other conversion methods may be implemented for # efficiency, but are not required. def tocsr(self, copy=False): """Convert this array/matrix to Compressed Sparse Row format. With copy=False, the data/indices may be shared between this array/matrix and the resultant csr_array/matrix. """ return self.tocoo(copy=copy).tocsr(copy=False) def todok(self, copy=False): """Convert this array/matrix to Dictionary Of Keys format. With copy=False, the data/indices may be shared between this array/matrix and the resultant dok_array/matrix. """ return self.tocoo(copy=copy).todok(copy=False) def tocoo(self, copy=False): """Convert this array/matrix to COOrdinate format. With copy=False, the data/indices may be shared between this array/matrix and the resultant coo_array/matrix. """ return self.tocsr(copy=False).tocoo(copy=copy) def tolil(self, copy=False): """Convert this array/matrix to List of Lists format. With copy=False, the data/indices may be shared between this array/matrix and the resultant lil_array/matrix. """ return self.tocsr(copy=False).tolil(copy=copy) def todia(self, copy=False): """Convert this array/matrix to sparse DIAgonal format. With copy=False, the data/indices may be shared between this array/matrix and the resultant dia_array/matrix. """ return self.tocoo(copy=copy).todia(copy=False) def tobsr(self, blocksize=None, copy=False): """Convert this array/matrix to Block Sparse Row format. With copy=False, the data/indices may be shared between this array/matrix and the resultant bsr_array/matrix. When blocksize=(R, C) is provided, it will be used for construction of the bsr_array/matrix. """ return self.tocsr(copy=False).tobsr(blocksize=blocksize, copy=copy) def tocsc(self, copy=False): """Convert this array/matrix to Compressed Sparse Column format. With copy=False, the data/indices may be shared between this array/matrix and the resultant csc_array/matrix. """ return self.tocsr(copy=copy).tocsc(copy=False) def copy(self): """Returns a copy of this array/matrix. No data/indices will be shared between the returned value and current array/matrix. """ return self.__class__(self, copy=True) def sum(self, axis=None, dtype=None, out=None): """ Sum the array/matrix elements over a given axis. Parameters ---------- axis : {-2, -1, 0, 1, None} optional Axis along which the sum is computed. The default is to compute the sum of all the array/matrix elements, returning a scalar (i.e., `axis` = `None`). dtype : dtype, optional The type of the returned array/matrix and of the accumulator in which the elements are summed. The dtype of `a` is used by default unless `a` has an integer dtype of less precision than the default platform integer. In that case, if `a` is signed then the platform integer is used while if `a` is unsigned then an unsigned integer of the same precision as the platform integer is used. .. versionadded:: 0.18.0 out : np.matrix, optional Alternative output matrix in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. .. versionadded:: 0.18.0 Returns ------- sum_along_axis : np.matrix A matrix with the same shape as `self`, with the specified axis removed. See Also -------- numpy.matrix.sum : NumPy's implementation of 'sum' for matrices """ validateaxis(axis) # Mimic numpy's casting. res_dtype = get_sum_dtype(self.dtype) if self.ndim == 1: if axis not in (None, -1, 0): raise ValueError("axis must be None, -1 or 0") ret = (self @ np.ones(self.shape, dtype=res_dtype)).astype(dtype) if out is not None: if any(dim != 1 for dim in out.shape): raise ValueError("dimensions do not match") out[...] = ret return ret # We use multiplication by a matrix of ones to achieve this. # For some sparse array formats more efficient methods are # possible -- these should override this function. M, N = self.shape if axis is None: # sum over rows and columns return ( self @ self._ascontainer(np.ones((N, 1), dtype=res_dtype)) ).sum(dtype=dtype, out=out) if axis < 0: axis += 2 # axis = 0 or 1 now if axis == 0: # sum over columns ret = self._ascontainer( np.ones((1, M), dtype=res_dtype) ) @ self else: # sum over rows ret = self @ self._ascontainer( np.ones((N, 1), dtype=res_dtype) ) if out is not None and out.shape != ret.shape: raise ValueError("dimensions do not match") return ret.sum(axis=axis, dtype=dtype, out=out) def mean(self, axis=None, dtype=None, out=None): """ Compute the arithmetic mean along the specified axis. Returns the average of the array/matrix elements. The average is taken over all elements in the array/matrix by default, otherwise over the specified axis. `float64` intermediate and return values are used for integer inputs. Parameters ---------- axis : {-2, -1, 0, 1, None} optional Axis along which the mean is computed. The default is to compute the mean of all elements in the array/matrix (i.e., `axis` = `None`). dtype : data-type, optional Type to use in computing the mean. For integer inputs, the default is `float64`; for floating point inputs, it is the same as the input dtype. .. versionadded:: 0.18.0 out : np.matrix, optional Alternative output matrix in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. .. versionadded:: 0.18.0 Returns ------- m : np.matrix See Also -------- numpy.matrix.mean : NumPy's implementation of 'mean' for matrices """ validateaxis(axis) res_dtype = self.dtype.type integral = (np.issubdtype(self.dtype, np.integer) or np.issubdtype(self.dtype, np.bool_)) # output dtype if dtype is None: if integral: res_dtype = np.float64 else: res_dtype = np.dtype(dtype).type # intermediate dtype for summation inter_dtype = np.float64 if integral else res_dtype inter_self = self.astype(inter_dtype) if self.ndim == 1: if axis not in (None, -1, 0): raise ValueError("axis must be None, -1 or 0") res = inter_self / self.shape[-1] return res.sum(dtype=res_dtype, out=out) if axis is None: return (inter_self / (self.shape[0] * self.shape[1]))\ .sum(dtype=res_dtype, out=out) if axis < 0: axis += 2 # axis = 0 or 1 now if axis == 0: return (inter_self * (1.0 / self.shape[0])).sum( axis=0, dtype=res_dtype, out=out) else: return (inter_self * (1.0 / self.shape[1])).sum( axis=1, dtype=res_dtype, out=out) def diagonal(self, k=0): """Returns the kth diagonal of the array/matrix. Parameters ---------- k : int, optional Which diagonal to get, corresponding to elements a[i, i+k]. Default: 0 (the main diagonal). .. versionadded:: 1.0 See also -------- numpy.diagonal : Equivalent numpy function. Examples -------- >>> from scipy.sparse import csr_array >>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]]) >>> A.diagonal() array([1, 0, 5]) >>> A.diagonal(k=1) array([2, 3]) """ return self.tocsr().diagonal(k=k) def trace(self, offset=0): """Returns the sum along diagonals of the sparse array/matrix. Parameters ---------- offset : int, optional Which diagonal to get, corresponding to elements a[i, i+offset]. Default: 0 (the main diagonal). """ return self.diagonal(k=offset).sum() def setdiag(self, values, k=0): """ Set diagonal or off-diagonal elements of the array/matrix. Parameters ---------- values : array_like New values of the diagonal elements. Values may have any length. If the diagonal is longer than values, then the remaining diagonal entries will not be set. If values are longer than the diagonal, then the remaining values are ignored. If a scalar value is given, all of the diagonal is set to it. k : int, optional Which off-diagonal to set, corresponding to elements a[i,i+k]. Default: 0 (the main diagonal). """ M, N = self.shape if (k > 0 and k >= N) or (k < 0 and -k >= M): raise ValueError("k exceeds array dimensions") self._setdiag(np.asarray(values), k) def _setdiag(self, values, k): """This part of the implementation gets overridden by the different formats. """ M, N = self.shape if k < 0: if values.ndim == 0: # broadcast max_index = min(M+k, N) for i in range(max_index): self[i - k, i] = values else: max_index = min(M+k, N, len(values)) if max_index <= 0: return for i, v in enumerate(values[:max_index]): self[i - k, i] = v else: if values.ndim == 0: # broadcast max_index = min(M, N-k) for i in range(max_index): self[i, i + k] = values else: max_index = min(M, N-k, len(values)) if max_index <= 0: return for i, v in enumerate(values[:max_index]): self[i, i + k] = v def _process_toarray_args(self, order, out): if out is not None: if order is not None: raise ValueError('order cannot be specified if out ' 'is not None') if out.shape != self.shape or out.dtype != self.dtype: raise ValueError('out array must be same dtype and shape as ' 'sparse array') out[...] = 0. return out else: return np.zeros(self.shape, dtype=self.dtype, order=order) def _get_index_dtype(self, arrays=(), maxval=None, check_contents=False): """ Determine index dtype for array. This wraps _sputils.get_index_dtype, providing compatibility for both array and matrix API sparse matrices. Matrix API sparse matrices would attempt to downcast the indices - which can be computationally expensive and undesirable for users. The array API changes this behaviour. See discussion: https://github.com/scipy/scipy/issues/16774 The get_index_dtype import is due to implementation details of the test suite. It allows the decorator ``with_64bit_maxval_limit`` to mock a lower int32 max value for checks on the matrix API's downcasting behaviour. """ from ._sputils import get_index_dtype # Don't check contents for array API return get_index_dtype(arrays, maxval, (check_contents and not isinstance(self, sparray))) class sparray: """A namespace class to separate sparray from spmatrix""" sparray.__doc__ = _spbase.__doc__ def issparse(x): """Is `x` of a sparse array or sparse matrix type? Parameters ---------- x object to check for being a sparse array or sparse matrix Returns ------- bool True if `x` is a sparse array or a sparse matrix, False otherwise Examples -------- >>> import numpy as np >>> from scipy.sparse import csr_array, csr_matrix, issparse >>> issparse(csr_matrix([[5]])) True >>> issparse(csr_array([[5]])) True >>> issparse(np.array([[5]])) False >>> issparse(5) False """ return isinstance(x, _spbase) def isspmatrix(x): """Is `x` of a sparse matrix type? Parameters ---------- x object to check for being a sparse matrix Returns ------- bool True if `x` is a sparse matrix, False otherwise Examples -------- >>> import numpy as np >>> from scipy.sparse import csr_array, csr_matrix, isspmatrix >>> isspmatrix(csr_matrix([[5]])) True >>> isspmatrix(csr_array([[5]])) False >>> isspmatrix(np.array([[5]])) False >>> isspmatrix(5) False """ return isinstance(x, spmatrix)