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{{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
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) noexcept 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 double val
cdef double innerprod = 0.0
cdef double 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) noexcept 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 double val
cdef double mu = 1.0 / num_iter
cdef double average_a = self.average_a
cdef double 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) noexcept 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 double 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) noexcept 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) noexcept 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) noexcept nogil:
"""The L2 norm of the weight vector. """
return sqrt(self.sq_norm)
{{endfor}}
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