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speed ups for normal cdf

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This commit is contained in:
James Hensman 2015-04-09 15:42:02 +01:00
parent 337bf67559
commit 1e30ffd730
7 changed files with 38 additions and 96 deletions
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4
GPy/util/misc.py
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@ -23,7 +23,7 @@ def chain_1(df_dg, dg_dx):
"""
if np.all(dg_dx==1.):
return df_dg
if len(df_dg) > 1 and df_dg.shape[-1] > 1:
if len(df_dg) > 1 and len(df_dg.shape)>1 and df_dg.shape[-1] > 1:
import ipdb; ipdb.set_trace() # XXX BREAKPOINT
raise NotImplementedError('Not implemented for matricies yet')
return df_dg * dg_dx
@ -37,7 +37,7 @@ def chain_2(d2f_dg2, dg_dx, df_dg, d2g_dx2):
"""
if np.all(dg_dx==1.) and np.all(d2g_dx2 == 0):
return d2f_dg2
if len(d2f_dg2) > 1 and d2f_dg2.shape[-1] > 1:
if len(d2f_dg2) > 1 and len(d2f_dg2.shape)>1 and d2f_dg2.shape[-1] > 1:
raise NotImplementedError('Not implemented for matricies yet')
#dg_dx_2 = np.clip(dg_dx, 1e-12, _lim_val_square)**2
dg_dx_2 = dg_dx**2

72
GPy/util/univariate_Gaussian.py
View file

@ -1,77 +1,15 @@
# Copyright (c) 2012, 2013 Ricardo Andrade
# Copyright (c) 2015 James Hensman
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from scipy import weave
from scipy.special import ndtr as std_norm_cdf
#define a standard normal pdf
_sqrt_2pi = np.sqrt(2*np.pi)
def std_norm_pdf(x):
"""Standard Gaussian density function"""
return 1./np.sqrt(2.*np.pi)*np.exp(-.5*x**2)
def std_norm_cdf(x):
"""
Cumulative standard Gaussian distribution
Based on Abramowitz, M. and Stegun, I. (1970)
"""
x_shape = np.asarray(x).shape
if len(x_shape) == 0 or x_shape[0] == 1:
sign = np.sign(x)
x *= sign
x /= np.sqrt(2.)
t = 1.0/(1.0 + 0.3275911*x)
erf = 1. - np.exp(-x**2)*t*(0.254829592 + t*(-0.284496736 + t*(1.421413741 + t*(-1.453152027 + t*(1.061405429)))))
cdf_x = 0.5*(1.0 + sign*erf)
return cdf_x
else:
x = np.atleast_1d(x).copy()
cdf_x = np.zeros_like(x)
sign = np.ones_like(x)
neg_x_ind = x<0
sign[neg_x_ind] = -1.0
x[neg_x_ind] = -x[neg_x_ind]
x /= np.sqrt(2.)
t = 1.0/(1.0 + 0.3275911*x)
erf = 1. - np.exp(-x**2)*t*(0.254829592 + t*(-0.284496736 + t*(1.421413741 + t*(-1.453152027 + t*(1.061405429)))))
cdf_x = 0.5*(1.0 + sign*erf)
cdf_x = cdf_x.reshape(x_shape)
return cdf_x
def std_norm_cdf_weave(x):
"""
Cumulative standard Gaussian distribution
Based on Abramowitz, M. and Stegun, I. (1970)
A weave implementation of std_norm_cdf, which is faster. this is unused,
because of the difficulties of a weave dependency. (see github issue #94)
"""
#Generalize for many x
x = np.asarray(x).copy()
cdf_x = np.zeros_like(x)
N = x.size
support_code = "#include <math.h>"
code = """
double sign, t, erf;
for (int i=0; i<N; i++){
sign = 1.0;
if (x[i] < 0.0){
sign = -1.0;
x[i] = -x[i];
}
x[i] = x[i]/sqrt(2.0);
t = 1.0/(1.0 + 0.3275911*x[i]);
erf = 1. - exp(-x[i]*x[i])*t*(0.254829592 + t*(-0.284496736 + t*(1.421413741 + t*(-1.453152027 + t*(1.061405429)))));
//return_val = 0.5*(1.0 + sign*erf);
cdf_x[i] = 0.5*(1.0 + sign*erf);
}
"""
weave.inline(code, arg_names=['x', 'cdf_x', 'N'], support_code=support_code)
return cdf_x
return np.exp(-np.square(x)/2)/_sqrt_2pi
def inv_std_norm_cdf(x):
"""