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
|
# -*- coding: utf-8 -*-
"""
Created on Sat Jun 21 14:07:53 2014
@author: Dan
"""
from NISE.lib.misc import *
class Inhom():
# class contains the list of weights and sampling values to use
#--------------------------Recorded attributes--------------------------
out_vars = ['inhom_sampling', 'dist_params']
#--------------------------Methods--------------------------
def __init__(self, inhom_sampling=None, **dist_params):
"""
generates the list of sampling points in the distribution and their weights
inhom dists should be normalized (int(f, dzeta) = 1.)
"""
# inherit all class attributes unless kwargs has them; then use those
# values. if kwargs is not an Omega attribute, it gets ignored
for key, value in dist_params.items():
setattr(self, key, value)
#print self.__dict__.items()
# eliminating other quadrature methods; linear works best anyways
if inhom_sampling == 'linear':
# currently the only inhomogeneity parameter that can normalize well
# in relation to the case of no inhomogeneity
if isinstance(dist_params.get('num'), int):
num = dist_params.get('num')
else:
try:
num = int(num)
except TypeError:
print 'no distribution sampling number specified; using 10 points as default'
num = 10
if 'zeta_bound' in dist_params.keys():
zeta_bound = dist_params.get('zeta_bound')
else:
zeta_bound = 3
zeta = np.linspace(-zeta_bound, zeta_bound, num=num)
# need parameter 'sigma'
sigma = dist_params.get('sigma')
# scale our sampling intervals according to sigma
zeta = zeta * sigma
self.zweight = 1 / (np.sqrt(2*np.pi)*sigma) * np.exp(- 0.5 * ((zeta / sigma)**2))
self.dzeta = np.abs(zeta[1] - zeta[0])
self.zeta = zeta
elif inhom_sampling == 'rect':
w = dist_params.get('w')
if isinstance(dist_params.get('num'), int):
num = dist_params['num']
else:
try:
num = int(num)
except TypeError:
print 'no distribution sampling number specified; using 10 points as default'
num = 10
self.zeta = np.linspace(-w,w,num=num)
self.dzeta = np.abs(self.zeta[1] - self.zeta[0])
self.zweight = np.ones(self.zeta.shape)
elif inhom_sampling == 'gh':
import NISE.hamiltonians.params.gauss_hermite as gh
# gaussian-hermite quadrature
# see http://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature
# for details
n = dist_params.get('n')
try:
gh.quad[n]
except KeyError:
print 'no table for quadrature of number {0} is available'.format(n)
print 'available quadrature numbers: {0}'.format(str(gh.quad.keys()))
sigma = dist_params.get('sigma')
self.zeta = np.array(gh.quad[n])[0]
self.zweight = np.array(gh.quad[n])[1]
self.dzeta = 1.
# substitution to inhom variables yields the following scaling:
self.zeta*= np.sqrt(2) * sigma
self.zweight*= np.pi**-0.5
else:
self.zeta = np.array([0])
self.zweight = [1.0]
self.dzeta = 1.0
self.inhom_sampling = inhom_sampling
self.dist_params = dist_params
|
