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#
# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements. See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
"""
MLlib utilities for linear algebra. For dense vectors, MLlib
uses the NumPy `array` type, so you can simply pass NumPy arrays
around. For sparse vectors, users can construct a :class:`SparseVector`
object from MLlib or pass SciPy `scipy.sparse` column vectors if
SciPy is available in their environment.
"""
import sys
import array
import struct
import numpy as np
from pyspark import since
from pyspark.ml import linalg as newlinalg
from pyspark.sql.types import UserDefinedType, StructField, StructType, ArrayType, DoubleType, \
IntegerType, ByteType, BooleanType
__all__ = ['Vector', 'DenseVector', 'SparseVector', 'Vectors',
'Matrix', 'DenseMatrix', 'SparseMatrix', 'Matrices',
'QRDecomposition']
# Check whether we have SciPy. MLlib works without it too, but if we have it, some methods,
# such as _dot and _serialize_double_vector, start to support scipy.sparse matrices.
try:
import scipy.sparse
_have_scipy = True
except:
# No SciPy in environment, but that's okay
_have_scipy = False
def _convert_to_vector(l):
if isinstance(l, Vector):
return l
elif type(l) in (array.array, np.array, np.ndarray, list, tuple, range):
return DenseVector(l)
59 ↛ 67line 59 didn't jump to line 67, because the condition on line 59 was never false elif _have_scipy and scipy.sparse.issparse(l):
assert l.shape[1] == 1, "Expected column vector"
# Make sure the converted csc_matrix has sorted indices.
csc = l.tocsc()
if not csc.has_sorted_indices:
csc.sort_indices()
return SparseVector(l.shape[0], csc.indices, csc.data)
else:
raise TypeError("Cannot convert type %s into Vector" % type(l))
def _vector_size(v):
"""
Returns the size of the vector.
Examples
--------
>>> _vector_size([1., 2., 3.])
3
>>> _vector_size((1., 2., 3.))
3
>>> _vector_size(array.array('d', [1., 2., 3.]))
3
>>> _vector_size(np.zeros(3))
3
>>> _vector_size(np.zeros((3, 1)))
3
>>> _vector_size(np.zeros((1, 3)))
Traceback (most recent call last):
...
ValueError: Cannot treat an ndarray of shape (1, 3) as a vector
"""
if isinstance(v, Vector):
return len(v)
elif type(v) in (array.array, list, tuple, range):
return len(v)
elif type(v) == np.ndarray:
if v.ndim == 1 or (v.ndim == 2 and v.shape[1] == 1):
return len(v)
else:
raise ValueError("Cannot treat an ndarray of shape %s as a vector" % str(v.shape))
100 ↛ 104line 100 didn't jump to line 104, because the condition on line 100 was never false elif _have_scipy and scipy.sparse.issparse(v):
assert v.shape[1] == 1, "Expected column vector"
return v.shape[0]
else:
raise TypeError("Cannot treat type %s as a vector" % type(v))
def _format_float(f, digits=4):
s = str(round(f, digits))
109 ↛ 111line 109 didn't jump to line 111, because the condition on line 109 was never false if '.' in s:
s = s[:s.index('.') + 1 + digits]
return s
def _format_float_list(l):
return [_format_float(x) for x in l]
def _double_to_long_bits(value):
119 ↛ 120line 119 didn't jump to line 120, because the condition on line 119 was never true if np.isnan(value):
value = float('nan')
# pack double into 64 bits, then unpack as long int
return struct.unpack('Q', struct.pack('d', value))[0]
class VectorUDT(UserDefinedType):
"""
SQL user-defined type (UDT) for Vector.
"""
@classmethod
def sqlType(cls):
return StructType([
StructField("type", ByteType(), False),
StructField("size", IntegerType(), True),
StructField("indices", ArrayType(IntegerType(), False), True),
StructField("values", ArrayType(DoubleType(), False), True)])
@classmethod
def module(cls):
return "pyspark.mllib.linalg"
@classmethod
def scalaUDT(cls):
return "org.apache.spark.mllib.linalg.VectorUDT"
def serialize(self, obj):
if isinstance(obj, SparseVector):
indices = [int(i) for i in obj.indices]
values = [float(v) for v in obj.values]
return (0, obj.size, indices, values)
151 ↛ 155line 151 didn't jump to line 155, because the condition on line 151 was never false elif isinstance(obj, DenseVector):
values = [float(v) for v in obj]
return (1, None, None, values)
else:
raise TypeError("cannot serialize %r of type %r" % (obj, type(obj)))
def deserialize(self, datum):
assert len(datum) == 4, \
"VectorUDT.deserialize given row with length %d but requires 4" % len(datum)
tpe = datum[0]
if tpe == 0:
return SparseVector(datum[1], datum[2], datum[3])
163 ↛ 166line 163 didn't jump to line 166, because the condition on line 163 was never false elif tpe == 1:
return DenseVector(datum[3])
else:
raise ValueError("do not recognize type %r" % tpe)
def simpleString(self):
return "vector"
class MatrixUDT(UserDefinedType):
"""
SQL user-defined type (UDT) for Matrix.
"""
@classmethod
def sqlType(cls):
return StructType([
StructField("type", ByteType(), False),
StructField("numRows", IntegerType(), False),
StructField("numCols", IntegerType(), False),
StructField("colPtrs", ArrayType(IntegerType(), False), True),
StructField("rowIndices", ArrayType(IntegerType(), False), True),
StructField("values", ArrayType(DoubleType(), False), True),
StructField("isTransposed", BooleanType(), False)])
@classmethod
def module(cls):
return "pyspark.mllib.linalg"
@classmethod
def scalaUDT(cls):
return "org.apache.spark.mllib.linalg.MatrixUDT"
def serialize(self, obj):
if isinstance(obj, SparseMatrix):
colPtrs = [int(i) for i in obj.colPtrs]
rowIndices = [int(i) for i in obj.rowIndices]
values = [float(v) for v in obj.values]
return (0, obj.numRows, obj.numCols, colPtrs,
rowIndices, values, bool(obj.isTransposed))
203 ↛ 208line 203 didn't jump to line 208, because the condition on line 203 was never false elif isinstance(obj, DenseMatrix):
values = [float(v) for v in obj.values]
return (1, obj.numRows, obj.numCols, None, None, values,
bool(obj.isTransposed))
else:
raise TypeError("cannot serialize type %r" % (type(obj)))
def deserialize(self, datum):
assert len(datum) == 7, \
"MatrixUDT.deserialize given row with length %d but requires 7" % len(datum)
tpe = datum[0]
if tpe == 0:
return SparseMatrix(*datum[1:])
216 ↛ 219line 216 didn't jump to line 219, because the condition on line 216 was never false elif tpe == 1:
return DenseMatrix(datum[1], datum[2], datum[5], datum[6])
else:
raise ValueError("do not recognize type %r" % tpe)
def simpleString(self):
return "matrix"
class Vector(object):
__UDT__ = VectorUDT()
"""
Abstract class for DenseVector and SparseVector
"""
def toArray(self):
"""
Convert the vector into an numpy.ndarray
Returns
-------
:py:class:`numpy.ndarray`
"""
raise NotImplementedError
def asML(self):
"""
Convert this vector to the new mllib-local representation.
This does NOT copy the data; it copies references.
Returns
-------
:py:class:`pyspark.ml.linalg.Vector`
"""
raise NotImplementedError
class DenseVector(Vector):
"""
A dense vector represented by a value array. We use numpy array for
storage and arithmetics will be delegated to the underlying numpy
array.
Examples
--------
>>> v = Vectors.dense([1.0, 2.0])
>>> u = Vectors.dense([3.0, 4.0])
>>> v + u
DenseVector([4.0, 6.0])
>>> 2 - v
DenseVector([1.0, 0.0])
>>> v / 2
DenseVector([0.5, 1.0])
>>> v * u
DenseVector([3.0, 8.0])
>>> u / v
DenseVector([3.0, 2.0])
>>> u % 2
DenseVector([1.0, 0.0])
>>> -v
DenseVector([-1.0, -2.0])
"""
def __init__(self, ar):
if isinstance(ar, bytes):
ar = np.frombuffer(ar, dtype=np.float64)
elif not isinstance(ar, np.ndarray):
ar = np.array(ar, dtype=np.float64)
if ar.dtype != np.float64:
ar = ar.astype(np.float64)
self.array = ar
@staticmethod
def parse(s):
"""
Parse string representation back into the DenseVector.
Examples
--------
>>> DenseVector.parse(' [ 0.0,1.0,2.0, 3.0]')
DenseVector([0.0, 1.0, 2.0, 3.0])
"""
start = s.find('[')
299 ↛ 300line 299 didn't jump to line 300, because the condition on line 299 was never true if start == -1:
raise ValueError("Array should start with '['.")
end = s.find(']')
302 ↛ 303line 302 didn't jump to line 303, because the condition on line 302 was never true if end == -1:
raise ValueError("Array should end with ']'.")
s = s[start + 1: end]
try:
values = [float(val) for val in s.split(',') if val]
except ValueError:
raise ValueError("Unable to parse values from %s" % s)
return DenseVector(values)
def __reduce__(self):
return DenseVector, (self.array.tostring(),)
def numNonzeros(self):
"""
Number of nonzero elements. This scans all active values and count non zeros
"""
return np.count_nonzero(self.array)
def norm(self, p):
"""
Calculates the norm of a DenseVector.
Examples
--------
>>> a = DenseVector([0, -1, 2, -3])
>>> a.norm(2)
3.7...
>>> a.norm(1)
6.0
"""
return np.linalg.norm(self.array, p)
def dot(self, other):
"""
Compute the dot product of two Vectors. We support
(Numpy array, list, SparseVector, or SciPy sparse)
and a target NumPy array that is either 1- or 2-dimensional.
Equivalent to calling numpy.dot of the two vectors.
Examples
--------
>>> dense = DenseVector(array.array('d', [1., 2.]))
>>> dense.dot(dense)
5.0
>>> dense.dot(SparseVector(2, [0, 1], [2., 1.]))
4.0
>>> dense.dot(range(1, 3))
5.0
>>> dense.dot(np.array(range(1, 3)))
5.0
>>> dense.dot([1.,])
Traceback (most recent call last):
...
AssertionError: dimension mismatch
>>> dense.dot(np.reshape([1., 2., 3., 4.], (2, 2), order='F'))
array([ 5., 11.])
>>> dense.dot(np.reshape([1., 2., 3.], (3, 1), order='F'))
Traceback (most recent call last):
...
AssertionError: dimension mismatch
"""
if type(other) == np.ndarray:
if other.ndim > 1:
assert len(self) == other.shape[0], "dimension mismatch"
return np.dot(self.array, other)
elif _have_scipy and scipy.sparse.issparse(other):
assert len(self) == other.shape[0], "dimension mismatch"
return other.transpose().dot(self.toArray())
else:
assert len(self) == _vector_size(other), "dimension mismatch"
if isinstance(other, SparseVector):
return other.dot(self)
elif isinstance(other, Vector):
return np.dot(self.toArray(), other.toArray())
else:
return np.dot(self.toArray(), other)
def squared_distance(self, other):
"""
Squared distance of two Vectors.
Examples
--------
>>> dense1 = DenseVector(array.array('d', [1., 2.]))
>>> dense1.squared_distance(dense1)
0.0
>>> dense2 = np.array([2., 1.])
>>> dense1.squared_distance(dense2)
2.0
>>> dense3 = [2., 1.]
>>> dense1.squared_distance(dense3)
2.0
>>> sparse1 = SparseVector(2, [0, 1], [2., 1.])
>>> dense1.squared_distance(sparse1)
2.0
>>> dense1.squared_distance([1.,])
Traceback (most recent call last):
...
AssertionError: dimension mismatch
>>> dense1.squared_distance(SparseVector(1, [0,], [1.,]))
Traceback (most recent call last):
...
AssertionError: dimension mismatch
"""
assert len(self) == _vector_size(other), "dimension mismatch"
if isinstance(other, SparseVector):
return other.squared_distance(self)
elif _have_scipy and scipy.sparse.issparse(other):
return _convert_to_vector(other).squared_distance(self)
if isinstance(other, Vector):
other = other.toArray()
elif not isinstance(other, np.ndarray):
other = np.array(other)
diff = self.toArray() - other
return np.dot(diff, diff)
def toArray(self):
"""
Returns an numpy.ndarray
"""
return self.array
def asML(self):
"""
Convert this vector to the new mllib-local representation.
This does NOT copy the data; it copies references.
.. versionadded:: 2.0.0
Returns
-------
:py:class:`pyspark.ml.linalg.DenseVector`
"""
return newlinalg.DenseVector(self.array)
@property
def values(self):
"""
Returns a list of values
"""
return self.array
def __getitem__(self, item):
return self.array[item]
def __len__(self):
return len(self.array)
def __str__(self):
return "[" + ",".join([str(v) for v in self.array]) + "]"
def __repr__(self):
return "DenseVector([%s])" % (', '.join(_format_float(i) for i in self.array))
def __eq__(self, other):
if isinstance(other, DenseVector):
return np.array_equal(self.array, other.array)
461 ↛ 465line 461 didn't jump to line 465, because the condition on line 461 was never false elif isinstance(other, SparseVector):
462 ↛ 463line 462 didn't jump to line 463, because the condition on line 462 was never true if len(self) != other.size:
return False
return Vectors._equals(list(range(len(self))), self.array, other.indices, other.values)
return False
def __ne__(self, other):
return not self == other
def __hash__(self):
size = len(self)
result = 31 + size
nnz = 0
i = 0
while i < size and nnz < 128:
if self.array[i] != 0:
result = 31 * result + i
bits = _double_to_long_bits(self.array[i])
result = 31 * result + (bits ^ (bits >> 32))
nnz += 1
i += 1
return result
def __getattr__(self, item):
return getattr(self.array, item)
def __neg__(self):
return DenseVector(-self.array)
def _delegate(op):
def func(self, other):
if isinstance(other, DenseVector):
other = other.array
return DenseVector(getattr(self.array, op)(other))
return func
__add__ = _delegate("__add__")
__sub__ = _delegate("__sub__")
__mul__ = _delegate("__mul__")
__div__ = _delegate("__div__")
__truediv__ = _delegate("__truediv__")
__mod__ = _delegate("__mod__")
__radd__ = _delegate("__radd__")
__rsub__ = _delegate("__rsub__")
__rmul__ = _delegate("__rmul__")
__rdiv__ = _delegate("__rdiv__")
__rtruediv__ = _delegate("__rtruediv__")
__rmod__ = _delegate("__rmod__")
class SparseVector(Vector):
"""
A simple sparse vector class for passing data to MLlib. Users may
alternatively pass SciPy's {scipy.sparse} data types.
"""
def __init__(self, size, *args):
"""
Create a sparse vector, using either a dictionary, a list of
(index, value) pairs, or two separate arrays of indices and
values (sorted by index).
Parameters
----------
size : int
Size of the vector.
args
Active entries, as a dictionary {index: value, ...},
a list of tuples [(index, value), ...], or a list of strictly
increasing indices and a list of corresponding values [index, ...],
[value, ...]. Inactive entries are treated as zeros.
Examples
--------
>>> SparseVector(4, {1: 1.0, 3: 5.5})
SparseVector(4, {1: 1.0, 3: 5.5})
>>> SparseVector(4, [(1, 1.0), (3, 5.5)])
SparseVector(4, {1: 1.0, 3: 5.5})
>>> SparseVector(4, [1, 3], [1.0, 5.5])
SparseVector(4, {1: 1.0, 3: 5.5})
"""
self.size = int(size)
""" Size of the vector. """
assert 1 <= len(args) <= 2, "must pass either 2 or 3 arguments"
if len(args) == 1:
pairs = args[0]
if type(pairs) == dict:
pairs = pairs.items()
pairs = sorted(pairs)
self.indices = np.array([p[0] for p in pairs], dtype=np.int32)
""" A list of indices corresponding to active entries. """
self.values = np.array([p[1] for p in pairs], dtype=np.float64)
""" A list of values corresponding to active entries. """
else:
if isinstance(args[0], bytes):
assert isinstance(args[1], bytes), "values should be string too"
if args[0]:
self.indices = np.frombuffer(args[0], np.int32)
self.values = np.frombuffer(args[1], np.float64)
else:
# np.frombuffer() doesn't work well with empty string in older version
self.indices = np.array([], dtype=np.int32)
self.values = np.array([], dtype=np.float64)
else:
self.indices = np.array(args[0], dtype=np.int32)
self.values = np.array(args[1], dtype=np.float64)
assert len(self.indices) == len(self.values), "index and value arrays not same length"
for i in range(len(self.indices) - 1):
568 ↛ 569line 568 didn't jump to line 569, because the condition on line 568 was never true if self.indices[i] >= self.indices[i + 1]:
raise TypeError(
"Indices %s and %s are not strictly increasing"
% (self.indices[i], self.indices[i + 1]))
def numNonzeros(self):
"""
Number of nonzero elements. This scans all active values and count non zeros.
"""
return np.count_nonzero(self.values)
def norm(self, p):
"""
Calculates the norm of a SparseVector.
Examples
--------
>>> a = SparseVector(4, [0, 1], [3., -4.])
>>> a.norm(1)
7.0
>>> a.norm(2)
5.0
"""
return np.linalg.norm(self.values, p)
def __reduce__(self):
return (
SparseVector,
(self.size, self.indices.tostring(), self.values.tostring()))
@staticmethod
def parse(s):
"""
Parse string representation back into the SparseVector.
Examples
--------
>>> SparseVector.parse(' (4, [0,1 ],[ 4.0,5.0] )')
SparseVector(4, {0: 4.0, 1: 5.0})
"""
start = s.find('(')
609 ↛ 610line 609 didn't jump to line 610, because the condition on line 609 was never true if start == -1:
raise ValueError("Tuple should start with '('")
end = s.find(')')
612 ↛ 613line 612 didn't jump to line 613, because the condition on line 612 was never true if end == -1:
raise ValueError("Tuple should end with ')'")
s = s[start + 1: end].strip()
size = s[: s.find(',')]
try:
size = int(size)
except ValueError:
raise ValueError("Cannot parse size %s." % size)
ind_start = s.find('[')
623 ↛ 624line 623 didn't jump to line 624, because the condition on line 623 was never true if ind_start == -1:
raise ValueError("Indices array should start with '['.")
ind_end = s.find(']')
626 ↛ 627line 626 didn't jump to line 627, because the condition on line 626 was never true if ind_end == -1:
raise ValueError("Indices array should end with ']'")
new_s = s[ind_start + 1: ind_end]
ind_list = new_s.split(',')
try:
indices = [int(ind) for ind in ind_list if ind]
except ValueError:
raise ValueError("Unable to parse indices from %s." % new_s)
s = s[ind_end + 1:].strip()
val_start = s.find('[')
637 ↛ 638line 637 didn't jump to line 638, because the condition on line 637 was never true if val_start == -1:
raise ValueError("Values array should start with '['.")
val_end = s.find(']')
640 ↛ 641line 640 didn't jump to line 641, because the condition on line 640 was never true if val_end == -1:
raise ValueError("Values array should end with ']'.")
val_list = s[val_start + 1: val_end].split(',')
try:
values = [float(val) for val in val_list if val]
except ValueError:
raise ValueError("Unable to parse values from %s." % s)
return SparseVector(size, indices, values)
def dot(self, other):
"""
Dot product with a SparseVector or 1- or 2-dimensional Numpy array.
Examples
--------
>>> a = SparseVector(4, [1, 3], [3.0, 4.0])
>>> a.dot(a)
25.0
>>> a.dot(array.array('d', [1., 2., 3., 4.]))
22.0
>>> b = SparseVector(4, [2], [1.0])
>>> a.dot(b)
0.0
>>> a.dot(np.array([[1, 1], [2, 2], [3, 3], [4, 4]]))
array([ 22., 22.])
>>> a.dot([1., 2., 3.])
Traceback (most recent call last):
...
AssertionError: dimension mismatch
>>> a.dot(np.array([1., 2.]))
Traceback (most recent call last):
...
AssertionError: dimension mismatch
>>> a.dot(DenseVector([1., 2.]))
Traceback (most recent call last):
...
AssertionError: dimension mismatch
>>> a.dot(np.zeros((3, 2)))
Traceback (most recent call last):
...
AssertionError: dimension mismatch
"""
if isinstance(other, np.ndarray):
684 ↛ 685line 684 didn't jump to line 685, because the condition on line 684 was never true if other.ndim not in [2, 1]:
raise ValueError("Cannot call dot with %d-dimensional array" % other.ndim)
assert len(self) == other.shape[0], "dimension mismatch"
return np.dot(self.values, other[self.indices])
assert len(self) == _vector_size(other), "dimension mismatch"
if isinstance(other, DenseVector):
return np.dot(other.array[self.indices], self.values)
elif isinstance(other, SparseVector):
# Find out common indices.
self_cmind = np.in1d(self.indices, other.indices, assume_unique=True)
self_values = self.values[self_cmind]
if self_values.size == 0:
return 0.0
else:
other_cmind = np.in1d(other.indices, self.indices, assume_unique=True)
return np.dot(self_values, other.values[other_cmind])
else:
return self.dot(_convert_to_vector(other))
def squared_distance(self, other):
"""
Squared distance from a SparseVector or 1-dimensional NumPy array.
Examples
--------
>>> a = SparseVector(4, [1, 3], [3.0, 4.0])
>>> a.squared_distance(a)
0.0
>>> a.squared_distance(array.array('d', [1., 2., 3., 4.]))
11.0
>>> a.squared_distance(np.array([1., 2., 3., 4.]))
11.0
>>> b = SparseVector(4, [2], [1.0])
>>> a.squared_distance(b)
26.0
>>> b.squared_distance(a)
26.0
>>> b.squared_distance([1., 2.])
Traceback (most recent call last):
...
AssertionError: dimension mismatch
>>> b.squared_distance(SparseVector(3, [1,], [1.0,]))
Traceback (most recent call last):
...
AssertionError: dimension mismatch
"""
assert len(self) == _vector_size(other), "dimension mismatch"
if isinstance(other, np.ndarray) or isinstance(other, DenseVector):
737 ↛ 738line 737 didn't jump to line 738, because the condition on line 737 was never true if isinstance(other, np.ndarray) and other.ndim != 1:
raise ValueError("Cannot call squared_distance with %d-dimensional array" %
other.ndim)
if isinstance(other, DenseVector):
other = other.array
sparse_ind = np.zeros(other.size, dtype=bool)
sparse_ind[self.indices] = True
dist = other[sparse_ind] - self.values
result = np.dot(dist, dist)
other_ind = other[~sparse_ind]
result += np.dot(other_ind, other_ind)
return result
elif isinstance(other, SparseVector):
result = 0.0
i, j = 0, 0
while i < len(self.indices) and j < len(other.indices):
if self.indices[i] == other.indices[j]:
diff = self.values[i] - other.values[j]
result += diff * diff
i += 1
j += 1
elif self.indices[i] < other.indices[j]:
result += self.values[i] * self.values[i]
i += 1
else:
result += other.values[j] * other.values[j]
j += 1
while i < len(self.indices):
result += self.values[i] * self.values[i]
i += 1
while j < len(other.indices):
result += other.values[j] * other.values[j]
j += 1
return result
else:
return self.squared_distance(_convert_to_vector(other))
def toArray(self):
"""
Returns a copy of this SparseVector as a 1-dimensional NumPy array.
"""
arr = np.zeros((self.size,), dtype=np.float64)
arr[self.indices] = self.values
return arr
def asML(self):
"""
Convert this vector to the new mllib-local representation.
This does NOT copy the data; it copies references.
.. versionadded:: 2.0.0
Returns
-------
:py:class:`pyspark.ml.linalg.SparseVector`
"""
return newlinalg.SparseVector(self.size, self.indices, self.values)
def __len__(self):
return self.size
def __str__(self):
inds = "[" + ",".join([str(i) for i in self.indices]) + "]"
vals = "[" + ",".join([str(v) for v in self.values]) + "]"
return "(" + ",".join((str(self.size), inds, vals)) + ")"
def __repr__(self):
inds = self.indices
vals = self.values
entries = ", ".join(["{0}: {1}".format(inds[i], _format_float(vals[i]))
for i in range(len(inds))])
return "SparseVector({0}, {{{1}}})".format(self.size, entries)
def __eq__(self, other):
813 ↛ 816line 813 didn't jump to line 816, because the condition on line 813 was never false if isinstance(other, SparseVector):
return other.size == self.size and np.array_equal(other.indices, self.indices) \
and np.array_equal(other.values, self.values)
elif isinstance(other, DenseVector):
if self.size != len(other):
return False
return Vectors._equals(self.indices, self.values, list(range(len(other))), other.array)
return False
def __getitem__(self, index):
inds = self.indices
vals = self.values
if not isinstance(index, int):
raise TypeError(
"Indices must be of type integer, got type %s" % type(index))
if index >= self.size or index < -self.size:
raise IndexError("Index %d out of bounds." % index)
if index < 0:
index += self.size
if (inds.size == 0) or (index > inds.item(-1)):
return 0.
insert_index = np.searchsorted(inds, index)
row_ind = inds[insert_index]
if row_ind == index:
return vals[insert_index]
return 0.
def __ne__(self, other):
return not self.__eq__(other)
def __hash__(self):
result = 31 + self.size
nnz = 0
i = 0
while i < len(self.values) and nnz < 128:
851 ↛ 856line 851 didn't jump to line 856, because the condition on line 851 was never false if self.values[i] != 0:
result = 31 * result + int(self.indices[i])
bits = _double_to_long_bits(self.values[i])
result = 31 * result + (bits ^ (bits >> 32))
nnz += 1
i += 1
return result
class Vectors(object):
"""
Factory methods for working with vectors.
Notes
-----
Dense vectors are simply represented as NumPy array objects,
so there is no need to covert them for use in MLlib. For sparse vectors,
the factory methods in this class create an MLlib-compatible type, or users
can pass in SciPy's `scipy.sparse` column vectors.
"""
@staticmethod
def sparse(size, *args):
"""
Create a sparse vector, using either a dictionary, a list of
(index, value) pairs, or two separate arrays of indices and
values (sorted by index).
Parameters
----------
size : int
Size of the vector.
args
Non-zero entries, as a dictionary, list of tuples,
or two sorted lists containing indices and values.
Examples
--------
>>> Vectors.sparse(4, {1: 1.0, 3: 5.5})
SparseVector(4, {1: 1.0, 3: 5.5})
>>> Vectors.sparse(4, [(1, 1.0), (3, 5.5)])
SparseVector(4, {1: 1.0, 3: 5.5})
>>> Vectors.sparse(4, [1, 3], [1.0, 5.5])
SparseVector(4, {1: 1.0, 3: 5.5})
"""
return SparseVector(size, *args)
@staticmethod
def dense(*elements):
"""
Create a dense vector of 64-bit floats from a Python list or numbers.
Examples
--------
>>> Vectors.dense([1, 2, 3])
DenseVector([1.0, 2.0, 3.0])
>>> Vectors.dense(1.0, 2.0)
DenseVector([1.0, 2.0])
"""
if len(elements) == 1 and not isinstance(elements[0], (float, int)):
# it's list, numpy.array or other iterable object.
elements = elements[0]
return DenseVector(elements)
@staticmethod
def fromML(vec):
"""
Convert a vector from the new mllib-local representation.
This does NOT copy the data; it copies references.
.. versionadded:: 2.0.0
Parameters
----------
vec : :py:class:`pyspark.ml.linalg.Vector`
Returns
-------
:py:class:`pyspark.mllib.linalg.Vector`
"""
if isinstance(vec, newlinalg.DenseVector):
return DenseVector(vec.array)
934 ↛ 937line 934 didn't jump to line 937, because the condition on line 934 was never false elif isinstance(vec, newlinalg.SparseVector):
return SparseVector(vec.size, vec.indices, vec.values)
else:
raise TypeError("Unsupported vector type %s" % type(vec))
@staticmethod
def stringify(vector):
"""
Converts a vector into a string, which can be recognized by
Vectors.parse().
Examples
--------
>>> Vectors.stringify(Vectors.sparse(2, [1], [1.0]))
'(2,[1],[1.0])'
>>> Vectors.stringify(Vectors.dense([0.0, 1.0]))
'[0.0,1.0]'
"""
return str(vector)
@staticmethod
def squared_distance(v1, v2):
"""
Squared distance between two vectors.
a and b can be of type SparseVector, DenseVector, np.ndarray
or array.array.
Examples
--------
>>> a = Vectors.sparse(4, [(0, 1), (3, 4)])
>>> b = Vectors.dense([2, 5, 4, 1])
>>> a.squared_distance(b)
51.0
"""
v1, v2 = _convert_to_vector(v1), _convert_to_vector(v2)
return v1.squared_distance(v2)
@staticmethod
def norm(vector, p):
"""
Find norm of the given vector.
"""
return _convert_to_vector(vector).norm(p)
@staticmethod
def parse(s):
"""Parse a string representation back into the Vector.
Examples
--------
>>> Vectors.parse('[2,1,2 ]')
DenseVector([2.0, 1.0, 2.0])
>>> Vectors.parse(' ( 100, [0], [2])')
SparseVector(100, {0: 2.0})
"""
if s.find('(') == -1 and s.find('[') != -1:
return DenseVector.parse(s)
991 ↛ 994line 991 didn't jump to line 994, because the condition on line 991 was never false elif s.find('(') != -1:
return SparseVector.parse(s)
else:
raise ValueError(
"Cannot find tokens '[' or '(' from the input string.")
@staticmethod
def zeros(size):
return DenseVector(np.zeros(size))
@staticmethod
def _equals(v1_indices, v1_values, v2_indices, v2_values):
"""
Check equality between sparse/dense vectors,
v1_indices and v2_indices assume to be strictly increasing.
"""
v1_size = len(v1_values)
v2_size = len(v2_values)
k1 = 0
k2 = 0
all_equal = True
while all_equal:
while k1 < v1_size and v1_values[k1] == 0:
k1 += 1
while k2 < v2_size and v2_values[k2] == 0:
k2 += 1
if k1 >= v1_size or k2 >= v2_size:
return k1 >= v1_size and k2 >= v2_size
all_equal = v1_indices[k1] == v2_indices[k2] and v1_values[k1] == v2_values[k2]
k1 += 1
k2 += 1
return all_equal
class Matrix(object):
__UDT__ = MatrixUDT()
"""
Represents a local matrix.
"""
def __init__(self, numRows, numCols, isTransposed=False):
self.numRows = numRows
self.numCols = numCols
self.isTransposed = isTransposed
def toArray(self):
"""
Returns its elements in a NumPy ndarray.
"""
raise NotImplementedError
def asML(self):
"""
Convert this matrix to the new mllib-local representation.
This does NOT copy the data; it copies references.
"""
raise NotImplementedError
@staticmethod
def _convert_to_array(array_like, dtype):
"""
Convert Matrix attributes which are array-like or buffer to array.
"""
if isinstance(array_like, bytes):
return np.frombuffer(array_like, dtype=dtype)
return np.asarray(array_like, dtype=dtype)
class DenseMatrix(Matrix):
"""
Column-major dense matrix.
"""
def __init__(self, numRows, numCols, values, isTransposed=False):
Matrix.__init__(self, numRows, numCols, isTransposed)
values = self._convert_to_array(values, np.float64)
assert len(values) == numRows * numCols
self.values = values
def __reduce__(self):
return DenseMatrix, (
self.numRows, self.numCols, self.values.tostring(),
int(self.isTransposed))
def __str__(self):
"""
Pretty printing of a DenseMatrix
Examples
--------
>>> dm = DenseMatrix(2, 2, range(4))
>>> print(dm)
DenseMatrix([[ 0., 2.],
[ 1., 3.]])
>>> dm = DenseMatrix(2, 2, range(4), isTransposed=True)
>>> print(dm)
DenseMatrix([[ 0., 1.],
[ 2., 3.]])
"""
# Inspired by __repr__ in scipy matrices.
array_lines = repr(self.toArray()).splitlines()
# We need to adjust six spaces which is the difference in number
# of letters between "DenseMatrix" and "array"
x = '\n'.join([(" " * 6 + line) for line in array_lines[1:]])
return array_lines[0].replace("array", "DenseMatrix") + "\n" + x
def __repr__(self):
"""
Representation of a DenseMatrix
Examples
--------
>>> dm = DenseMatrix(2, 2, range(4))
>>> dm
DenseMatrix(2, 2, [0.0, 1.0, 2.0, 3.0], False)
"""
# If the number of values are less than seventeen then return as it is.
# Else return first eight values and last eight values.
if len(self.values) < 17:
entries = _format_float_list(self.values)
else:
entries = (
_format_float_list(self.values[:8]) +
["..."] +
_format_float_list(self.values[-8:])
)
entries = ", ".join(entries)
return "DenseMatrix({0}, {1}, [{2}], {3})".format(
self.numRows, self.numCols, entries, self.isTransposed)
def toArray(self):
"""
Return an numpy.ndarray
Examples
--------
>>> m = DenseMatrix(2, 2, range(4))
>>> m.toArray()
array([[ 0., 2.],
[ 1., 3.]])
"""
if self.isTransposed:
return np.asfortranarray(
self.values.reshape((self.numRows, self.numCols)))
else:
return self.values.reshape((self.numRows, self.numCols), order='F')
def toSparse(self):
"""Convert to SparseMatrix"""
if self.isTransposed:
values = np.ravel(self.toArray(), order='F')
else:
values = self.values
indices = np.nonzero(values)[0]
colCounts = np.bincount(indices // self.numRows)
colPtrs = np.cumsum(np.hstack(
(0, colCounts, np.zeros(self.numCols - colCounts.size))))
values = values[indices]
rowIndices = indices % self.numRows
return SparseMatrix(self.numRows, self.numCols, colPtrs, rowIndices, values)
def asML(self):
"""
Convert this matrix to the new mllib-local representation.
This does NOT copy the data; it copies references.
.. versionadded:: 2.0.0
Returns
-------
:py:class:`pyspark.ml.linalg.DenseMatrix`
"""
return newlinalg.DenseMatrix(self.numRows, self.numCols, self.values, self.isTransposed)
def __getitem__(self, indices):
i, j = indices
if i < 0 or i >= self.numRows:
raise IndexError("Row index %d is out of range [0, %d)"
% (i, self.numRows))
1175 ↛ 1176line 1175 didn't jump to line 1176, because the condition on line 1175 was never true if j >= self.numCols or j < 0:
raise IndexError("Column index %d is out of range [0, %d)"
% (j, self.numCols))
if self.isTransposed:
return self.values[i * self.numCols + j]
else:
return self.values[i + j * self.numRows]
def __eq__(self, other):
1185 ↛ 1186line 1185 didn't jump to line 1186, because the condition on line 1185 was never true if (self.numRows != other.numRows or self.numCols != other.numCols):
return False
if isinstance(other, SparseMatrix):
return np.all(self.toArray() == other.toArray())
self_values = np.ravel(self.toArray(), order='F')
other_values = np.ravel(other.toArray(), order='F')
return np.all(self_values == other_values)
class SparseMatrix(Matrix):
"""Sparse Matrix stored in CSC format."""
def __init__(self, numRows, numCols, colPtrs, rowIndices, values,
isTransposed=False):
Matrix.__init__(self, numRows, numCols, isTransposed)
self.colPtrs = self._convert_to_array(colPtrs, np.int32)
self.rowIndices = self._convert_to_array(rowIndices, np.int32)
self.values = self._convert_to_array(values, np.float64)
if self.isTransposed:
1205 ↛ 1206line 1205 didn't jump to line 1206, because the condition on line 1205 was never true if self.colPtrs.size != numRows + 1:
raise ValueError("Expected colPtrs of size %d, got %d."
% (numRows + 1, self.colPtrs.size))
else:
1209 ↛ 1210line 1209 didn't jump to line 1210, because the condition on line 1209 was never true if self.colPtrs.size != numCols + 1:
raise ValueError("Expected colPtrs of size %d, got %d."
% (numCols + 1, self.colPtrs.size))
1212 ↛ 1213line 1212 didn't jump to line 1213, because the condition on line 1212 was never true if self.rowIndices.size != self.values.size:
raise ValueError("Expected rowIndices of length %d, got %d."
% (self.rowIndices.size, self.values.size))
def __str__(self):
"""
Pretty printing of a SparseMatrix
Examples
--------
>>> sm1 = SparseMatrix(2, 2, [0, 2, 3], [0, 1, 1], [2, 3, 4])
>>> print(sm1)
2 X 2 CSCMatrix
(0,0) 2.0
(1,0) 3.0
(1,1) 4.0
>>> sm1 = SparseMatrix(2, 2, [0, 2, 3], [0, 1, 1], [2, 3, 4], True)
>>> print(sm1)
2 X 2 CSRMatrix
(0,0) 2.0
(0,1) 3.0
(1,1) 4.0
"""
spstr = "{0} X {1} ".format(self.numRows, self.numCols)
if self.isTransposed:
spstr += "CSRMatrix\n"
else:
spstr += "CSCMatrix\n"
cur_col = 0
smlist = []
# Display first 16 values.
if len(self.values) <= 16:
zipindval = zip(self.rowIndices, self.values)
else:
zipindval = zip(self.rowIndices[:16], self.values[:16])
for i, (rowInd, value) in enumerate(zipindval):
if self.colPtrs[cur_col + 1] <= i:
cur_col += 1
if self.isTransposed:
smlist.append('({0},{1}) {2}'.format(
cur_col, rowInd, _format_float(value)))
else:
smlist.append('({0},{1}) {2}'.format(
rowInd, cur_col, _format_float(value)))
spstr += "\n".join(smlist)
if len(self.values) > 16:
spstr += "\n.." * 2
return spstr
def __repr__(self):
"""
Representation of a SparseMatrix
Examples
--------
>>> sm1 = SparseMatrix(2, 2, [0, 2, 3], [0, 1, 1], [2, 3, 4])
>>> sm1
SparseMatrix(2, 2, [0, 2, 3], [0, 1, 1], [2.0, 3.0, 4.0], False)
"""
rowIndices = list(self.rowIndices)
colPtrs = list(self.colPtrs)
if len(self.values) <= 16:
values = _format_float_list(self.values)
else:
values = (
_format_float_list(self.values[:8]) +
["..."] +
_format_float_list(self.values[-8:])
)
rowIndices = rowIndices[:8] + ["..."] + rowIndices[-8:]
if len(self.colPtrs) > 16:
colPtrs = colPtrs[:8] + ["..."] + colPtrs[-8:]
values = ", ".join(values)
rowIndices = ", ".join([str(ind) for ind in rowIndices])
colPtrs = ", ".join([str(ptr) for ptr in colPtrs])
return "SparseMatrix({0}, {1}, [{2}], [{3}], [{4}], {5})".format(
self.numRows, self.numCols, colPtrs, rowIndices,
values, self.isTransposed)
def __reduce__(self):
return SparseMatrix, (
self.numRows, self.numCols, self.colPtrs.tostring(),
self.rowIndices.tostring(), self.values.tostring(),
int(self.isTransposed))
def __getitem__(self, indices):
i, j = indices
if i < 0 or i >= self.numRows:
raise IndexError("Row index %d is out of range [0, %d)"
% (i, self.numRows))
1309 ↛ 1310line 1309 didn't jump to line 1310, because the condition on line 1309 was never true if j < 0 or j >= self.numCols:
raise IndexError("Column index %d is out of range [0, %d)"
% (j, self.numCols))
# If a CSR matrix is given, then the row index should be searched
# for in ColPtrs, and the column index should be searched for in the
# corresponding slice obtained from rowIndices.
if self.isTransposed:
j, i = i, j
colStart = self.colPtrs[j]
colEnd = self.colPtrs[j + 1]
nz = self.rowIndices[colStart: colEnd]
ind = np.searchsorted(nz, i) + colStart
if ind < colEnd and self.rowIndices[ind] == i:
return self.values[ind]
else:
return 0.0
def toArray(self):
"""
Return an numpy.ndarray
"""
A = np.zeros((self.numRows, self.numCols), dtype=np.float64, order='F')
for k in range(self.colPtrs.size - 1):
startptr = self.colPtrs[k]
endptr = self.colPtrs[k + 1]
if self.isTransposed:
A[k, self.rowIndices[startptr:endptr]] = self.values[startptr:endptr]
else:
A[self.rowIndices[startptr:endptr], k] = self.values[startptr:endptr]
return A
def toDense(self):
densevals = np.ravel(self.toArray(), order='F')
return DenseMatrix(self.numRows, self.numCols, densevals)
def asML(self):
"""
Convert this matrix to the new mllib-local representation.
This does NOT copy the data; it copies references.
.. versionadded:: 2.0.0
Returns
-------
:py:class:`pyspark.ml.linalg.SparseMatrix`
"""
return newlinalg.SparseMatrix(self.numRows, self.numCols, self.colPtrs, self.rowIndices,
self.values, self.isTransposed)
# TODO: More efficient implementation:
def __eq__(self, other):
return np.all(self.toArray() == other.toArray())
class Matrices(object):
@staticmethod
def dense(numRows, numCols, values):
"""
Create a DenseMatrix
"""
return DenseMatrix(numRows, numCols, values)
@staticmethod
def sparse(numRows, numCols, colPtrs, rowIndices, values):
"""
Create a SparseMatrix
"""
return SparseMatrix(numRows, numCols, colPtrs, rowIndices, values)
@staticmethod
def fromML(mat):
"""
Convert a matrix from the new mllib-local representation.
This does NOT copy the data; it copies references.
.. versionadded:: 2.0.0
Parameters
----------
mat : :py:class:`pyspark.ml.linalg.Matrix`
Returns
-------
:py:class:`pyspark.mllib.linalg.Matrix`
"""
if isinstance(mat, newlinalg.DenseMatrix):
return DenseMatrix(mat.numRows, mat.numCols, mat.values, mat.isTransposed)
1398 ↛ 1402line 1398 didn't jump to line 1402, because the condition on line 1398 was never false elif isinstance(mat, newlinalg.SparseMatrix):
return SparseMatrix(mat.numRows, mat.numCols, mat.colPtrs, mat.rowIndices,
mat.values, mat.isTransposed)
else:
raise TypeError("Unsupported matrix type %s" % type(mat))
class QRDecomposition(object):
"""
Represents QR factors.
"""
def __init__(self, Q, R):
self._Q = Q
self._R = R
@property
@since('2.0.0')
def Q(self):
"""
An orthogonal matrix Q in a QR decomposition.
May be null if not computed.
"""
return self._Q
@property
@since('2.0.0')
def R(self):
"""
An upper triangular matrix R in a QR decomposition.
"""
return self._R
def _test():
import doctest
import numpy
try:
# Numpy 1.14+ changed it's string format.
numpy.set_printoptions(legacy='1.13')
except TypeError:
pass
(failure_count, test_count) = doctest.testmod(optionflags=doctest.ELLIPSIS)
1440 ↛ 1441line 1440 didn't jump to line 1441, because the condition on line 1440 was never true if failure_count:
sys.exit(-1)
if __name__ == "__main__":
_test()
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