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"""Base class for sparse matrix formats using compressed storage."""
from __future__ import division, print_function, absolute_import
__all__ = []
from warnings import warn
import operator
import numpy as np
from scipy._lib.six import zip as izip
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 .sputils import (upcast, upcast_char, to_native, isdense, isshape,
getdtype, isscalarlike, IndexMixin, get_index_dtype,
downcast_intp_index, get_sum_dtype, check_shape)
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 %s_matrix constructor usage" %
self.format)
else:
# must be dense
try:
arg1 = np.asarray(arg1)
except:
raise ValueError("unrecognized %s_matrix constructor usage" %
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:
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 = np.asarray(self.data, dtype=dtype)
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 (%s)"
% self.indptr.dtype.name)
if self.indices.dtype.kind != 'i':
warn("indices array has non-integer dtype (%s)"
% self.indices.dtype.name)
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
if self.data.ndim != 1 or self.indices.ndim != 1 or self.indptr.ndim != 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 (%d) should be (%d)" %
(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("%s index values must be < %d" %
(minor_name,minor_dim))
if self.indices.min() < 0:
raise ValueError("%s index values must be >= 0" %
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)
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
# Sparse other.
elif isspmatrix(other):
warn("Comparing sparse matrices using == is inefficient, try using"
" != instead.", SparseEfficiencyWarning)
#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)
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)
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
# 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))
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.")
#################################
# Arithmatic 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
_sparsetools.csr_todense(M, N, self.indptr, self.indices, self.data, y)
return np.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),
maxval=M*N)
indptr = np.empty(major_axis + 1, dtype=idx_dtype)
fn = getattr(_sparsetools, self.format + '_matmat_pass1')
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),
indptr)
nnz = indptr[-1]
idx_dtype = get_index_dtype((self.indptr, self.indices,
other.indptr, other.indices),
maxval=nnz)
indptr = np.asarray(indptr, 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_pass2')
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:
raise ValueError("k exceeds matrix dimensions")
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)
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 = np.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):
"""Reduce nonzeros with a ufunc over the minor axis when non-empty
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
"""
major_index = np.flatnonzero(np.diff(self.indptr))
value = ufunc.reduceat(self.data,
downcast_intp_index(self.indptr[major_index]))
return major_index, value
#######################
# Getting and Setting #
#######################
def __setitem__(self, index, x):
# Process arrays from IndexMixin
i, j = self._unpack_index(index)
i, j = self._index_to_arrays(i, j)
if isspmatrix(x):
broadcast_row = x.shape[0] == 1 and i.shape[0] != 1
broadcast_col = x.shape[1] == 1 and i.shape[1] != 1
if not ((broadcast_row or x.shape[0] == i.shape[0]) and
(broadcast_col or x.shape[1] == i.shape[1])):
raise ValueError("shape mismatch in assignment")
# clear entries that will be overwritten
ci, cj = self._swap((i.ravel(), j.ravel()))
self._zero_many(ci, cj)
x = x.tocoo(copy=True)
x.sum_duplicates()
r, c = x.row, x.col
x = np.asarray(x.data, dtype=self.dtype)
if broadcast_row:
r = np.repeat(np.arange(i.shape[0]), len(r))
c = np.tile(c, i.shape[0])
x = np.tile(x, i.shape[0])
if broadcast_col:
r = np.repeat(r, i.shape[1])
c = np.tile(np.arange(i.shape[1]), len(c))
x = np.repeat(x, i.shape[1])
# only assign entries in the new sparsity structure
i = i[r, c]
j = j[r, c]
else:
# Make x and i into the same shape
x = np.asarray(x, dtype=self.dtype)
x, _ = np.broadcast_arrays(x, i)
if x.shape != i.shape:
raise ValueError("shape mismatch in assignment")
if np.size(x) == 0:
return
i, j = self._swap((i.ravel(), j.ravel()))
self._set_many(i, j, x.ravel())
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))
check_bounds(i, M)
check_bounds(j, N)
i = np.asarray(i, dtype=self.indices.dtype)
j = np.asarray(j, dtype=self.indices.dtype)
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)
n_samples = len(x)
offsets = np.empty(n_samples, dtype=self.indices.dtype)
ret = _sparsetools.csr_sample_offsets(M, N, self.indptr, self.indices,
n_samples, i, j, offsets)
if ret == 1:
# rinse and repeat
self.sum_duplicates()
_sparsetools.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 %s_matrix is expensive. "
"lil_matrix is more efficient." % self.format,
SparseEfficiencyWarning)
# 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 = _sparsetools.csr_sample_offsets(M, N, self.indptr, self.indices,
n_samples, i, j, offsets)
if ret == 1:
# rinse and repeat
self.sum_duplicates()
_sparsetools.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(izip(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.asarray(np.ediff1d(self.indptr, to_begin=0), dtype=idx_dtype)
nnzs[1:][ui] += new_nnzs
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)
def _get_single_element(self, row, col):
M, N = self.shape
if (row < 0):
row += M
if (col < 0):
col += N
if not (0 <= row < M) or not (0 <= col < N):
raise IndexError("index out of bounds: 0<=%d<%d, 0<=%d<%d" %
(row, M, col, N))
major_index, minor_index = self._swap((row, col))
start = self.indptr[major_index]
end = self.indptr[major_index + 1]
if self.has_sorted_indices:
# Copies may be made, if dtypes of indices are not identical
minor_index = self.indices.dtype.type(minor_index)
minor_indices = self.indices[start:end]
insert_pos_left = np.searchsorted(
minor_indices, minor_index, side='left')
insert_pos_right = insert_pos_left + np.searchsorted(
minor_indices[insert_pos_left:], minor_index, side='right')
return self.data[start + insert_pos_left:
start + insert_pos_right].sum(dtype=self.dtype)
else:
return np.compress(minor_index == self.indices[start:end],
self.data[start:end]).sum(dtype=self.dtype)
def _get_submatrix(self, slice0, slice1):
"""Return a submatrix of this matrix (new matrix is created)."""
slice0, slice1 = self._swap((slice0,slice1))
shape0, shape1 = self._swap(self.shape)
def _process_slice(sl, num):
if isinstance(sl, slice):
i0, i1 = sl.start, sl.stop
if i0 is None:
i0 = 0
elif i0 < 0:
i0 = num + i0
if i1 is None:
i1 = num
elif i1 < 0:
i1 = num + i1
return i0, i1
elif np.isscalar(sl):
if sl < 0:
sl += num
return sl, sl + 1
else:
return sl[0], sl[1]
def _in_bounds(i0, i1, num):
if not (0 <= i0 < num) or not (0 < i1 <= num) or not (i0 < i1):
raise IndexError("index out of bounds: 0<=%d<%d, 0<=%d<%d, %d<%d" %
(i0, num, i1, num, i0, i1))
i0, i1 = _process_slice(slice0, shape0)
j0, j1 = _process_slice(slice1, shape1)
_in_bounds(i0, i1, shape0)
_in_bounds(j0, j1, shape1)
aux = _sparsetools.get_csr_submatrix(shape0, shape1,
self.indptr, self.indices,
self.data,
i0, i1, j0, j1)
data, indices, indptr = aux[2], aux[1], aux[0]
shape = self._swap((i1 - i0, j1 - j0))
return self.__class__((data, indices, indptr), shape=shape)
######################
# 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)
_sparsetools.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])
###################
# 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 = np.matrix(out)
else:
# integers types go with nan <-> 0
out = r
return out