1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
|
{{py:
"""
Efficient (dense) parameter vector implementation for linear models.
Template file for easily generate fused types consistent code using Tempita
(https://github.com/cython/cython/blob/master/Cython/Tempita/_tempita.py).
Generated file: weight_vector.pxd
Each class is duplicated for all dtypes (float and double). The keywords
between double braces are substituted in setup.py.
"""
# name_suffix, c_type, reset_wscale_threshold
dtypes = [('64', 'double', 1e-9),
('32', 'float', 1e-6)]
}}
# cython: binding=False
#
# Author: Peter Prettenhofer <peter.prettenhofer@gmail.com>
# Lars Buitinck
# Danny Sullivan <dsullivan7@hotmail.com>
#
# License: BSD 3 clause
# WARNING: Do not edit this .pyx file directly, it is generated from its .pyx.tp
cimport cython
from libc.limits cimport INT_MAX
from libc.math cimport sqrt
from ._cython_blas cimport _dot, _scal, _axpy
{{for name_suffix, c_type, reset_wscale_threshold in dtypes}}
cdef class WeightVector{{name_suffix}}(object):
"""Dense vector represented by a scalar and a numpy array.
The class provides methods to ``add`` a sparse vector
and scale the vector.
Representing a vector explicitly as a scalar times a
vector allows for efficient scaling operations.
Attributes
----------
w : ndarray, dtype={{c_type}}, order='C'
The numpy array which backs the weight vector.
aw : ndarray, dtype={{c_type}}, order='C'
The numpy array which backs the average_weight vector.
w_data_ptr : {{c_type}}*
A pointer to the data of the numpy array.
wscale : {{c_type}}
The scale of the vector.
n_features : int
The number of features (= dimensionality of ``w``).
sq_norm : {{c_type}}
The squared norm of ``w``.
"""
def __cinit__(self,
{{c_type}}[::1] w,
{{c_type}}[::1] aw):
if w.shape[0] > INT_MAX:
raise ValueError("More than %d features not supported; got %d."
% (INT_MAX, w.shape[0]))
self.w = w
self.w_data_ptr = &w[0]
self.wscale = 1.0
self.n_features = w.shape[0]
self.sq_norm = _dot(self.n_features, self.w_data_ptr, 1, self.w_data_ptr, 1)
self.aw = aw
if self.aw is not None:
self.aw_data_ptr = &aw[0]
self.average_a = 0.0
self.average_b = 1.0
cdef void add(self, {{c_type}} *x_data_ptr, int *x_ind_ptr, int xnnz,
{{c_type}} c) nogil:
"""Scales sample x by constant c and adds it to the weight vector.
This operation updates ``sq_norm``.
Parameters
----------
x_data_ptr : {{c_type}}*
The array which holds the feature values of ``x``.
x_ind_ptr : np.intc*
The array which holds the feature indices of ``x``.
xnnz : int
The number of non-zero features of ``x``.
c : {{c_type}}
The scaling constant for the example.
"""
cdef int j
cdef int idx
cdef {{c_type}} val
cdef {{c_type}} innerprod = 0.0
cdef {{c_type}} xsqnorm = 0.0
# the next two lines save a factor of 2!
cdef {{c_type}} wscale = self.wscale
cdef {{c_type}}* w_data_ptr = self.w_data_ptr
for j in range(xnnz):
idx = x_ind_ptr[j]
val = x_data_ptr[j]
innerprod += (w_data_ptr[idx] * val)
xsqnorm += (val * val)
w_data_ptr[idx] += val * (c / wscale)
self.sq_norm += (xsqnorm * c * c) + (2.0 * innerprod * wscale * c)
# Update the average weights according to the sparse trick defined
# here: https://research.microsoft.com/pubs/192769/tricks-2012.pdf
# by Leon Bottou
cdef void add_average(self, {{c_type}} *x_data_ptr, int *x_ind_ptr, int xnnz,
{{c_type}} c, {{c_type}} num_iter) nogil:
"""Updates the average weight vector.
Parameters
----------
x_data_ptr : {{c_type}}*
The array which holds the feature values of ``x``.
x_ind_ptr : np.intc*
The array which holds the feature indices of ``x``.
xnnz : int
The number of non-zero features of ``x``.
c : {{c_type}}
The scaling constant for the example.
num_iter : {{c_type}}
The total number of iterations.
"""
cdef int j
cdef int idx
cdef {{c_type}} val
cdef {{c_type}} mu = 1.0 / num_iter
cdef {{c_type}} average_a = self.average_a
cdef {{c_type}} wscale = self.wscale
cdef {{c_type}}* aw_data_ptr = self.aw_data_ptr
for j in range(xnnz):
idx = x_ind_ptr[j]
val = x_data_ptr[j]
aw_data_ptr[idx] += (self.average_a * val * (-c / wscale))
# Once the sample has been processed
# update the average_a and average_b
if num_iter > 1:
self.average_b /= (1.0 - mu)
self.average_a += mu * self.average_b * wscale
cdef {{c_type}} dot(self, {{c_type}} *x_data_ptr, int *x_ind_ptr,
int xnnz) nogil:
"""Computes the dot product of a sample x and the weight vector.
Parameters
----------
x_data_ptr : {{c_type}}*
The array which holds the feature values of ``x``.
x_ind_ptr : np.intc*
The array which holds the feature indices of ``x``.
xnnz : int
The number of non-zero features of ``x`` (length of x_ind_ptr).
Returns
-------
innerprod : {{c_type}}
The inner product of ``x`` and ``w``.
"""
cdef int j
cdef int idx
cdef {{c_type}} innerprod = 0.0
cdef {{c_type}}* w_data_ptr = self.w_data_ptr
for j in range(xnnz):
idx = x_ind_ptr[j]
innerprod += w_data_ptr[idx] * x_data_ptr[j]
innerprod *= self.wscale
return innerprod
cdef void scale(self, {{c_type}} c) nogil:
"""Scales the weight vector by a constant ``c``.
It updates ``wscale`` and ``sq_norm``. If ``wscale`` gets too
small we call ``reset_swcale``."""
self.wscale *= c
self.sq_norm *= (c * c)
if self.wscale < {{reset_wscale_threshold}}:
self.reset_wscale()
cdef void reset_wscale(self) nogil:
"""Scales each coef of ``w`` by ``wscale`` and resets it to 1. """
if self.aw_data_ptr != NULL:
_axpy(self.n_features, self.average_a,
self.w_data_ptr, 1, self.aw_data_ptr, 1)
_scal(self.n_features, 1.0 / self.average_b, self.aw_data_ptr, 1)
self.average_a = 0.0
self.average_b = 1.0
_scal(self.n_features, self.wscale, self.w_data_ptr, 1)
self.wscale = 1.0
cdef {{c_type}} norm(self) nogil:
"""The L2 norm of the weight vector. """
return sqrt(self.sq_norm)
{{endfor}}
|
