In [1]:
import matplotlib.pyplot as plt
import numpy as np
from numpy import poly1d, polyfit, power
import scipy.optimize
from math import *
from IPython.display import HTML
from IPython.display import Image
import os
import PIL as pil
import heapq
from matplotlib.ticker import MultipleLocator, FormatStrFormatter
import matplotlib.cm as cm
import scipy.interpolate as inter
%matplotlib inline
#Размер изображений
import matplotlib.pylab as pylab
pylab.rcParams['figure.figsize'] = 12, 12
#Наклон галактики по данным Засова
incl=36.0
# Масштаб пк/секунда из NED
scale=321
#Эффективный радиус балджа
r_eb = 6.7
In [2]:
os.chdir("C:\\science\\2FInstability\\data\\ngc1167")
In [3]:
# Данные по звездной кинематике Засова 2012 вдоль большей полуоси, не исправленные за наклон
zasov_raw_data = np.loadtxt("v_stars_maZ.dat", float)
r_ma, vel_ma, e_vel_ma, sig_ma, e_sig_ma = zip(*zasov_raw_data)
# Данные по звездной кинематике Засова 2012 вдоль малой полуоси, не исправленные за наклон
zasov_raw_data = np.loadtxt("v_stars_miZ.dat", float)
r_mi, vel_mi, e_vel_mi, sig_mi, e_sig_mi = zip(*zasov_raw_data)
# Данные по кинематике газа Struve, WSRT (не исправлено за наклон)
wsrt_raw_data = np.loadtxt("v_gas_WSRT.dat", float)
r_wsrt, vel_wsrt, e_vel_wsrt = zip(*wsrt_raw_data)
# Данные по кинематике газа Noordermee 2007, WSRT (не исправлено за наклон?)
noord_raw_data = np.loadtxt("v_gas_noord.dat", float)
r_noord, vel_noord, e_vel_noord = zip(*noord_raw_data)
plt.plot(r_ma, vel_ma, '.-', label="Zasov 2008, maj")
plt.plot(r_mi, vel_mi, '.-', label="Zasov 2008, min")
plt.plot(r_wsrt, vel_wsrt, '.-', label="gas Struve")
plt.plot(r_noord, vel_noord, '.-', label="gas Noordermeer 2007")
plt.legend()
plt.plot()
Out[3]:
In [4]:
def incline_velocity(v, angle):
return v / sin(angle * pi / 180)
# Переносит центр в (r0,v0) и перегибает кривую вращения,
# а также исправляет за наклон если необходимо
def correct_rotation_curve(rdata, vdata, dvdata, r0, v0, incl):
rdata_tmp = [abs(r-r0) for r in rdata]
vdata_tmp = [incline_velocity(abs(v-v0), incl) for v in vdata]
data = zip(rdata_tmp, vdata_tmp, dvdata)
data.sort()
return zip(*data)
r_ma_b, vel_ma_b, e_vel_b = correct_rotation_curve(r_ma, vel_ma, e_vel_ma, 0.0, 4959.3, incl)
r_mi_b, vel_mi_b, e_vel_mi_b = correct_rotation_curve(r_mi, vel_mi, e_vel_mi, 0.0, 4959.3, incl)
plt.plot(r_ma_b, vel_ma_b, 'd', label = 'Zasov star maj')
plt.errorbar(r_ma_b, vel_ma_b, yerr=e_vel_b, fmt='.', marker='.', mew=0, color='blue')
plt.plot(r_mi_b, vel_mi_b, '.', label = 'Zasov star min', color='green')
plt.errorbar(r_mi_b, vel_mi_b, yerr=e_vel_mi_b, fmt='.', marker='.', mew=0, color='green')
plt.legend()
plt.plot()
Out[4]:
В дальнейшем используем только засовские данные по звездам по большой полуоси, приблизим их полиномом.
In [5]:
poly_star = poly1d(polyfit(r_ma_b, vel_ma_b, deg=3))
plt.plot(r_ma_b, vel_ma_b, 'x-', color='blue', markersize=6)
test_points = np.arange(0.0, max(r_ma_b), 0.1)
plt.plot(test_points, poly_star(test_points), '-', color='red')
plt.xlabel('$R$'); plt.ylim(0)
plt.ylabel('$V^{maj}_{\phi}(R)$')
plt.show()
Кривая вращения нам нужна для нахождения соотношения $\sigma_{\varphi}^{2}/\sigma_{R}^{2}$, которое описывается уравнением ${\displaystyle \sigma_{\varphi}^{2}/\sigma_{R}^{2}=0.5\left(1+\frac{R}{\bar{v}_{\varphi}}\frac{d\bar{v}_{\varphi}}{dR}\right)}$ (Binney & Tremaine, 1987) и приближается гладко функцией $f=0.5(1+e^{-R/R_{0}}),$ где $R_{0}$ --- характерный масштаб.
${\bf Примечание:}$ Такое приближение оправдано следующими соображениями. Для равновесного диска верно уравнение, описанное выше. Для твердотельного участка вращения в центральных областях выражение в скобках равно 2, а $\sigma_{\varphi}^{2}/\sigma_{R}^{2}=1$. На плоском участке кривой вращения на периферии диска $\sigma_{\varphi}^{2}/\sigma_{R}^{2}\thickapprox0.5$. Функция $f$ как раз аппроксимирует такое поведение отношения $\sigma_{\varphi}^{2}/\sigma_{R}^{2}$.
Изобразим получившийся профиль $\sigma_{\varphi}^{2}/\sigma_{R}^{2}$, вычисляемый через производную полинома:
In [6]:
def sigPhi_to_sigR_real(R):
return 0.5 * (1 + R*poly_star.deriv()(R) / poly_star(R))
plt.plot(test_points, [sigPhi_to_sigR_real(R) for R in test_points], 'd-', color='blue')
plt.axhline(y=0.5)
plt.axhline(y=0.0)
plt.xlabel('$R$')
plt.ylabel(r"$\sigma_{\varphi}^2/\sigma_{R}^2$")
plt.ylim(0)
plt.show()
Найдем теперь характерный масштаб $f=0.5(1+e^{-R/R_{0}})$:
In [7]:
def f(R, Ro):
return 0.5*(1 + np.exp( -R/Ro ))
xdata = test_points
ydata = sigPhi_to_sigR_real(xdata)
from scipy.optimize import curve_fit
popt, pcov = curve_fit(f, xdata, ydata, p0=[1.0])
Ro = popt[0]
plt.plot(xdata, ydata, 'x-')
plt.plot(xdata, [f(p, Ro) for p in xdata], 's')
plt.axhline(y=0.5)
plt.axhline(y=0.0)
plt.title('$R_{0} = %s $' % Ro)
plt.ylim(0, 2)
plt.show()
Теперь знаем значение отношения $\sigma_{\varphi}^{2}/\sigma_{R}^{2}$ в любой точке, заведем соответствующую функцию:
In [8]:
def sigPhi_to_sigR(R):
return sqrt(f(R, Ro))
Построим графики дисперсий скоростей на луче зрения вдоль большой и малой оси ($\sigma_{los}^{maj}$ и $\sigma_{los}^{min}$):
In [9]:
# Исправляем значения вдоль малой оси на синус угла:
def correct_min(R):
return R / cos(incl * pi / 180)
r_mi_extend = map(correct_min, r_mi)
plt.plot(r_ma, sig_ma, 's-', label='$\sigma_{los}^{maj}$')
plt.errorbar(r_ma, sig_ma, yerr=e_sig_ma, fmt='.', marker='.', mew=0, color='blue')
plt.plot(r_mi_extend, sig_mi, 's-', label='$\sigma_{los}^{min}$')
plt.errorbar(r_mi_extend, sig_mi, yerr=e_sig_mi, fmt='.', marker='.', mew=0, color='black')
plt.xlabel('$R$')
plt.ylabel('$\sigma$')
plt.legend()
plt.show()
Перегнем и приблизим полиномами:
In [10]:
bind_curve = lambda p: (abs(p[0]), abs(p[1]), p[2])
sig_maj_data = zip(r_ma, sig_ma, e_sig_ma)
sig_maj_data = map(bind_curve, sig_maj_data)
sig_maj_data.sort()
radii_maj, sig_maj_p, e_sig_maj_p = zip(*sig_maj_data)
poly_sig_maj = poly1d(polyfit(radii_maj, sig_maj_p, deg=9))
sig_min_data = zip(r_mi_extend, sig_mi, e_sig_mi)
sig_min_data = map(bind_curve, sig_min_data)
sig_min_data.sort()
radii_min, sig_min_p, e_sig_min_p = zip(*sig_min_data)
# Добавляем лишние точки чтобы протянуть дальше
num_fake_points = 10; expscale = 200.0
# fake_radii, fake_sig = zip(*[(31.0 + i, 115*exp(- i / expscale )) for i in range(1, num_fake_points+1)])
fake_radii, fake_sig = (),()
poly_sig_min = poly1d(polyfit(radii_min + fake_radii, sig_min_p + fake_sig, deg=9))
points = np.arange(0, max(radii_min), 0.1)
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='.', marker='.', mew=0, color='blue')
plt.plot(points, poly_sig_maj(points), label = '$\sigma_{los}^{maj} polyfit$', color='blue')
plt.plot(radii_min, sig_min_p, 's', label='$\sigma_{los}^{min}$', color='red')
plt.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='.', marker='.', mew=0, color='red')
plt.plot(points, poly_sig_min(points), label = '$\sigma_{los}^{min} polyfit$', color='red')
plt.plot(fake_radii, fake_sig, 'bs', color='green', label='$fake points$')
plt.legend()
plt.ylim(0,250)
plt.xlim(0,55)
plt.show()
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%%javascript
$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')
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In [12]:
spl_maj = poly_sig_maj
spl_min = poly_sig_min
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='.', marker='.', mew=0, color='blue')
plt.plot(points, spl_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
plt.plot(radii_min, sig_min_p, 's', label='$\sigma_{los}^{min}$', color='red')
plt.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='.', marker='.', mew=0, color='red')
plt.plot(points, spl_min(points), label = '$\sigma_{los}^{min}\, splinefit$', color='red')
plt.legend()
plt.ylim(0,250)
plt.xlim(0,55)
plt.show()
poly_sig_maj = spl_maj
poly_sig_min = spl_min
In [13]:
#Значение sig_los_min в 0
sig_min_0 = poly_sig_min(0)
print sig_min_0
И восстановим профили $\sigma_{los}^{maj}$ и $\sigma_{los}^{min}$. Связь профилей описывается следующими уравнениями: $$\sigma_{los,maj}^2=\sigma_{\varphi}^2\sin^2i+\sigma_Z^2\cos^2i$$ $$\sigma_{los,min}^2=\sigma_R^2\sin^2i+\sigma_Z^2\cos^2i$$
In [14]:
# def sig_maj_exp(R):
# return sqrt(sigPhi_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
# def sig_min_exp(R):
# return sqrt(sigR_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
cos_i, sin_i = cos(incl * pi / 180), sin(incl * pi / 180)
def sig_maj_exp(R):
tmp = sigPhi_to_sigR_real(R) * sin_i**2 + alpha**2 * cos_i**2
if tmp > 0:
return sig_R_0*poly_sig_min(R)/sig_min_0 * sqrt(sigPhi_to_sigR_real(R) * sin_i**2 + alpha**2 * cos_i**2)
else:
return -1000000
# return sig_R_0*spl_min(R)/sig_min_0 * sqrt(sigPhi_to_sigR(R)**2 * sin_i**2 + alpha**2 * cos_i**2)
# return sqrt(sigPhi_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
def sig_min_exp(R):
return sig_R_0*poly_sig_min(R)/sig_min_0 * sqrt(sin_i**2 + alpha**2 * cos_i**2)
# return sqrt(sigR_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
Теперь то, с чего надо было начинать - построим картинки для разных значений $\alpha$ и $\sigma_{R,0}$. Для того, чтобы найти где минимум, попробуем построить просто двумерные карты $\chi^2$ для разных $\sigma_{R,0}$ $\alpha$: (это очень долго, так что пересчитывать в крайнем случае)
In [15]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
def calc_chi2_normal(obs, obserr, predicted):
return sum([(o-p)**2/err**2 for (o,p,err) in zip(obs, predicted, obserr)])/len(obs)
def compute_chi2_maps(alphas=(), sigmas=()):
'''Вычисляем все изображения, чтобы потом только настройки менять'''
image_min = np.random.uniform(size=(len(sigmas), len(alphas)))
image_maj = np.random.uniform(size=(len(sigmas), len(alphas)))
image = np.random.uniform(size=(len(sigmas), len(alphas)))
for i,si in enumerate(sigmas):
for j,al in enumerate(alphas):
global alpha, sig_R_0
alpha = al
sig_R_0 = si
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
sqerr_min = calc_chi2_normal(sig_min_p, e_sig_min_p, [sig_min_exp(r) for r in radii_min])
sqerr_sum = 0.5*sqerr_maj+0.5*sqerr_min
image[i][j] = sqerr_sum
image_maj[i][j] = sqerr_maj
image_min[i][j] = sqerr_min
return image, image_maj, image_min
image, image_maj, image_min = compute_chi2_maps(alphas=alphas, sigmas=sigmas)
In [16]:
from mpl_toolkits.axes_grid1 import make_axes_locatable
def plot_chi2_map(image, ax, log_scale=False, title='$\chi^2$', is_contour=False, vmax=0.):
'''Рисуем получившиеся карты.
Colormaps: http://wiki.scipy.org/Cookbook/Matplotlib/Show_colormaps'''
if image is not None:
if log_scale:
image_log = np.apply_along_axis(np.log, 1, image)
vmax = image_log.max()
else:
image_log = image
if is_contour:
norm = plt.cm.colors.Normalize(vmax=image.max(), vmin=-image.max())
cmap = plt.cm.PRGn
levels = np.concatenate([np.array([image_log.min()*1.1,]), np.linspace(start=image_log.min(), stop=vmax, num=10)])
levels = sorted(levels)
cset=ax.contour(image_log, levels, hold='on', colors = 'k', origin='lower',
extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
ax.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
im = ax.imshow(image_log, cmap='jet', vmin=image_log.min(), vmax=vmax, interpolation='spline16',
origin="lower", extent=[alphas[0], alphas[-1],sigmas[0],sigmas[-1]], aspect="auto")
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(im, cax=cax)
min_sigma = sigmas[int(np.where(image == image.min())[0])]
ax.set_title(title + '$,\ \sigma(min)=%s$' % min_sigma, size=20.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
ax.grid(True)
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=True, figsize=[16,16])
plot_chi2_map(image, axes[0], log_scale=False, title='$\chi^2 = (\chi^2_{maj} + \chi^2_{min})/2$', is_contour=False, vmax=30.)
plot_chi2_map(image_maj, axes[1], log_scale=False, title='$\chi^2_{maj}$', is_contour=False, vmax=30.)
plot_chi2_map(image_min, axes[2], log_scale=False, title='$\chi^2_{min}$', is_contour=False, vmax=20.)
plt.show()
In [17]:
# Перебор alpha
alphas = np.arange(0.1, 0.7, 0.11)
# Перебор sig_R_0
sigmas = np.arange(270., 350., 16.)
# Те картинки, на которые стоит обратить особое внимание
good_pics = []
def plot_ranges(sigmas_range, alphas_range, good_pics=[], calc_chi=False, best_err=3):
nrows = alphas.size
ncols = sigmas.size
fig, axes = plt.subplots(nrows=nrows, ncols=ncols, sharex=True, sharey=True, figsize=[16,18])
plt_index = 0
sqerr_majs, sqerr_mins, sqerr_mean = [],[],[]
for al in alphas_range:
for si in sigmas_range:
global alpha, sig_R_0
alpha = al
sig_R_0 = si
ax = axes[plt_index/ncols, plt_index % ncols]
ax.set_title(r'$\alpha = %s, \sigma_{R,0}=%s$' % (al,si))
# ax.plot(points, poly_sig_maj(points), '-', color='blue')
ax.plot(points, [sig_maj_exp(Rr) for Rr in points], '--', color='blue')
# ax.plot(points, poly_sig_min(points), '-', color='red')
ax.plot(points, [sig_min_exp(R) for R in points], '--', color='red')
if calc_chi:
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(p[0]) for p in sig_maj_data])
sqerr_min = calc_chi2_normal(sig_min_p, e_sig_min_p, [sig_min_exp(p[0]) for p in sig_min_data])
# sqerr_maj = sum(power([sig_maj_exp(p[0]) - p[1] for p in sig_maj_data], 2))/len(sig_maj_data)
# sqerr_min = sum(power([sig_min_exp(p[0]) - p[1] for p in sig_min_data], 2))/len(sig_min_data)
ax.text(1, 220, "$maj=%5.2f\, min=%5.2f$" % (sqerr_maj, sqerr_min), fontsize=12)
sqerr_majs.append(sqerr_maj);sqerr_mins.append(sqerr_min)
sqerr_mean.append(0.5*sqerr_maj+0.5*sqerr_min)
ax.set_ylim(0, 250)
ax.set_xlim(0, 60)
ax.plot(radii_min, sig_min_p, 's', color='red', ms=1.7)
ax.plot(radii_maj, sig_maj_p, 's', color='blue', ms=1.7)
chima = [300*(p[1]-sig_maj_exp(p[0]))**2/p[2]**2/len(sig_maj_data) for p in sig_maj_data]
# ax.plot(radii_maj, chima, '.-', color='m')
ax.fill_between(radii_maj, chima, [0]*len(chima), color='m', alpha=0.5)
# print zip(chima, [(p[1]-sig_maj_exp(p[0]))**2 for p in sig_maj_data], sig_maj_p,
# [sig_maj_exp(p[0]) for p in sig_maj_data], e_sig_maj_p)
chimi = [300*(p[1]-sig_min_exp(p[0]))**2/p[2]**2/len(sig_min_data) for p in sig_min_data]
# ax.plot(radii_maj, chima, '.-', color='m')
ax.fill_between(radii_min, chimi, [0]*len(chimi), color='y', alpha=0.7)
if (plt_index/ncols, plt_index % ncols) in good_pics:
ax.plot([40], [200], 'o', markersize=12., color=(0.2,1.0,0.))
plt_index = plt_index + 1
if calc_chi:
best_maj_err = heapq.nsmallest(best_err, sqerr_majs)
for b_maj in best_maj_err:
b_maj_ind = sqerr_majs.index(b_maj)
ax = axes[b_maj_ind/ncols, b_maj_ind % ncols]
#ax.plot([35], [200], 'o', markersize=12., color='b')
ax.text(35, 200, "%s" % (best_maj_err.index(b_maj)+1), fontsize=12, color='b',
bbox=dict(facecolor='none', edgecolor='b', boxstyle='round'))
best_min_err = heapq.nsmallest(best_err, sqerr_mins)
for b_min in best_min_err:
b_min_ind = sqerr_mins.index(b_min)
ax = axes[b_min_ind/ncols, b_min_ind % ncols]
#ax.plot([30], [200], 'o', markersize=12., color='r')
ax.text(30, 200, "%s" % (best_min_err.index(b_min)+1), fontsize=12, color='r',
bbox=dict(facecolor='none', edgecolor='r', boxstyle='round'))
best_mean_err = heapq.nsmallest(best_err, sqerr_mean)
for b_mean in best_mean_err:
b_mean_ind = sqerr_mean.index(b_mean)
ax = axes[b_mean_ind/ncols, b_mean_ind % ncols]
ax.text(25, 200, "%s" % (best_mean_err.index(b_mean)+1), fontsize=12, color='g',
bbox=dict(facecolor='none', edgecolor='g', boxstyle='round'))
plot_ranges(sigmas, alphas, good_pics=good_pics, calc_chi=True)
plt.show()
In [18]:
main_slice = lambda l: sig_min_0/sqrt(sin_i**2 + cos_i**2 * l**2)
def calc_chi2_normal(obs, obserr, predicted):
return sum([(o-p)**2/err**2 for (o,p,err) in zip(obs, predicted, obserr)])/len(obs)
# os.chdir("C:\\Users\\root\\Dropbox\\RotationCurves\\PhD\\paper1\\text\\imgs")
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
import matplotlib.mlab as mlab
import matplotlib
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=True, sharey=False, figsize=[8,16])
ax = axes[0]
# levels = np.linspace(start=image_min.min(), stop=20., num=5)
# levels = [100., 125., 150., 175., 200.]
# levels = [image_min.min()+0.02, image_min.min()+0.4, image_min.min()+1.1, image_min.min()+2.,
# image_min.min()+3.1, image_min.min()+4.1]
# levels = np.linspace(start=image_min.min()+0.1, stop=image_min.min()+4.1, num=5)
levels = np.linspace(start=image_min.min()*1.1, stop=image_min.min()*1.1+4, num=5)
# im = ax.imshow(image_min, cmap='jet', vmin=image_min.min(), vmax=20., interpolation='spline16',
# origin="lower", aspect="auto")
# plt.show()
cset=ax.contour(image_min, levels, colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
min_map_gutter = cset.collections[0].get_paths()
v1,v2 = min_map_gutter[1].vertices, min_map_gutter[0].vertices
x1,x2 = v1[:,0], v2[:,0]
y1,y2 = v1[:,1], v2[:,1]
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
ax.text(0.87, 280, '$\chi^2_{min}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
# ax.set_ylim(180, 300)
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
min_sigmas = np.where(image_min < image_min.min() + 0.03)
slice_alph, slice_sig = min_sigmas[1], min_sigmas[0]
slice_alph = map(lambda l: alphas[0] + (alphas[-1] - alphas[0])*l/len(image_min[0]) , slice_alph)
slice_sig = map(lambda l: sigmas[0] + (sigmas[-1] - sigmas[0])*l/len(image_min), slice_sig)
# ax.plot(slice_alph, slice_sig, '.', color='pink')
poly_slice = poly1d(polyfit(slice_alph, slice_sig, deg=3))
# ax.plot(xx, poly_slice(xx), '.-', color='black')
ax = axes[1]
# levels = np.linspace(start=image_maj.min()-4.3, stop=10., num=10)
# levels = [7., 10., 50., 100.]
# levels = [image_maj.min()+0.2, image_maj.min()+0.7, image_maj.min()+1.1, image_maj.min()+2.1, image_maj.min()+3.1,
# image_maj.min()+4.1]
levels = np.linspace(start=image_maj.min()+0.3, stop=image_maj.min()+4.1, num=5)
cset=ax.contour(image_maj, levels, hold='on', colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
ax.text(0.87, 280, '$\chi^2_{maj}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
# ax.set_ylim(150, 320)
ax = axes[2]
err_maj = []
for al in alphas:
global alpha, sig_R_0
alpha = al
sig_R_0 = main_slice(al)
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj.append(sqerr_maj)
ax.plot(alphas, err_maj, '--', color='black')
err_maj1 = []
for pa in zip(x2,y2):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj1.append(sqerr_maj)
# ax.plot(x2, err_maj1, '-', color='black')
err_maj2 = []
for pa in zip(x1,y1):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj2.append(sqerr_maj)
# ax.plot(x1, err_maj2, '-', color='black')
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
import scipy.interpolate as sp
try:
f1 = sp.interp1d(x2, err_maj1, kind='linear')
ax.fill_between(x1, map(f1, x1), err_maj2, color='grey', alpha=0.3)
except Exception:
f2 = sp.interp1d(x1, err_maj2, kind='linear')
ax.fill_between(x2, map(f2, x2), err_maj1, color='grey', alpha=0.3)
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
# ax.set_ylim(3.1, 3.5)
fig.subplots_adjust(hspace=0.)
axes[0].yaxis.get_major_ticks()[0].set_visible(False)
axes[1].yaxis.get_major_ticks()[0].set_visible(False)
ax.set_xlim(0.25, 0.99)
# plt.savefig('ngc1167_maps.eps', format='eps')
# plt.savefig('ngc1167_maps.png', format='png')
# plt.savefig('ngc1167_maps.pdf', format='pdf', dpi=150)
plt.show()
In [19]:
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=True, figsize=[12,24])
plot_chi2_map(image_maj, axes[0], log_scale=False, title='$\chi^2_{maj}$', is_contour=False, vmax=10.)
plot_chi2_map(image_min, axes[1], log_scale=False, title='$\chi^2_{min}$', is_contour=False, vmax=10.)
corr_image = (image_min*len(sig_min_p) + image_maj*len(sig_maj_p)) / (len(sig_min_p) + len(sig_maj_p))
print 'N1_maj={},\t N2_min={},\t chi^2_corr[0][0]={} (was {} and {})'.format(len(sig_maj_p), len(sig_min_p), corr_image[0][0],
image_min[0][0], image_maj[0][0])
plot_chi2_map(corr_image, axes[2], log_scale=False, title='$\chi^2$', is_contour=True, vmax=5.)
plt.show()
In [ ]:
In [20]:
import scipy.optimize as opt
def chisqfunc((x_sig, x_alpha)):
global sig_R_0, alpha
sig_R_0 = x_sig
alpha = x_alpha
sqerr_ma = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
sqerr_mi = calc_chi2_normal(sig_min_p, e_sig_min_p, [sig_min_exp(r) for r in radii_min])
chisq = (sqerr_mi*len(sig_min_p) + sqerr_ma*len(sig_maj_p)) / (len(sig_min_p) + len(sig_maj_p))
return chisq
x0 = np.array([100., 0.5])
res = opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B')
print res
In [21]:
def gen_next_normal(radii, sig, esig):
randomDelta = np.array([np.random.normal(0., derr/2, 1)[0] for derr in esig] )
randomdataY = sig + randomDelta
return zip(radii, randomdataY)
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='o', marker='.', color='blue')
plt.plot(points, poly_sig_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
for i in range(3):
r, s = zip(*gen_next_normal(radii_maj, sig_maj_p, e_sig_maj_p))
plt.plot(r, s, 's', color='red')
plt.ylim(0., 400.)
plt.legend()
plt.show()
In [22]:
import time
N = 300
result = []
start_time = time.time()
for i in log_progress(range(N)):
global poly_sig_maj, poly_sig_min
r, s = zip(*gen_next_normal(radii_maj, sig_maj_p, e_sig_maj_p))
# poly_sig_maj = inter.UnivariateSpline(r, s, k=3, s=10000., w=w(e_sig_maj_p))
poly_sig_maj = poly1d(polyfit(r, s, deg=9))
r, s = zip(*gen_next_normal(radii_min, sig_min_p, e_sig_min_p))
# poly_sig_min = inter.UnivariateSpline(r, s, k=3, s=10000., w=w(e_sig_min_p))
poly_sig_min = poly1d(polyfit(r, s, deg=9))
# result.append((opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B').x,
# poly_sig_maj.get_coeffs(), poly_sig_min.get_coeffs()))
result.append((opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B').x,
poly_sig_maj.coeffs, poly_sig_min.coeffs))
print("--- %s seconds ---" % (time.time() - start_time))
In [23]:
len(result)
Out[23]:
In [24]:
s, _, _ = zip(*result)
s,a = zip(*s)
plt.plot(a, s, '.')
plt.plot(alphas, map(main_slice, alphas), '--')
# plt.xlim(0.0, 0.99)
plt.ylim(0, 420)
plt.show()
In [ ]:
In [25]:
sig_maj_data = zip(r_ma[:-1], sig_ma[:-1], e_sig_ma[:-1])
sig_maj_data = map(bind_curve, sig_maj_data)
sig_maj_data.sort()
radii_maj1, sig_maj_p1, e_sig_maj_p1 = zip(*sig_maj_data)
sig_min_data = zip(r_mi_extend, sig_mi, e_sig_mi)
sig_min_data = map(bind_curve, sig_min_data)
sig_min_data.sort()
radii_min1, sig_min_p1, e_sig_min_p1 = zip(*sig_min_data)
points = np.arange(0, max(radii_min), 0.1)
In [26]:
# Граница. по которой обрезаем
cutted = r_eb
sig_maj_data = zip(radii_maj1, sig_maj_p1, e_sig_maj_p1)
sig_maj_data = filter(lambda l: l[0] > cutted, sig_maj_data)
radii_maj, sig_maj_p, e_sig_maj_p = zip(*sig_maj_data)
sig_min_data = zip(radii_min1, sig_min_p1, e_sig_min_p1)
sig_min_data = filter(lambda l: l[0] > cutted, sig_min_data)
radii_min, sig_min_p, e_sig_min_p = zip(*sig_min_data)
def w(arr):
return map(lambda l: 1/(1. + l**2), arr)
spl_maj = inter.UnivariateSpline(radii_maj[::-1], sig_maj_p[::-1], k=3, s=10000., w=w(e_sig_maj_p))
spl_min = inter.UnivariateSpline(radii_min[::-1], sig_min_p[::-1], k=3, s=10000., w=w(e_sig_min_p))
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='.', marker='.', mew=0, color='blue')
plt.plot(points, spl_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
plt.plot(radii_min, sig_min_p, 's', label='$\sigma_{los}^{min}$', color='red')
plt.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='.', marker='.', mew=0, color='red')
plt.plot(points, spl_min(points), label = '$\sigma_{los}^{min}\, splinefit$', color='red')
plt.axvline(x=cutted, color='black')
plt.legend()
plt.ylim(0,250)
plt.xlim(0,55)
plt.show()
poly_sig_maj = spl_maj
poly_sig_min = spl_min
In [27]:
#Значение sig_los_min в 0
sig_min_0 = poly_sig_min(0)
print sig_min_0
И восстановим профили $\sigma_{los}^{maj}$ и $\sigma_{los}^{min}$. Связь профилей описывается следующими уравнениями: $$\sigma_{los,maj}^2=\sigma_{\varphi}^2\sin^2i+\sigma_Z^2\cos^2i$$ $$\sigma_{los,min}^2=\sigma_R^2\sin^2i+\sigma_Z^2\cos^2i$$
In [28]:
# def sig_maj_exp(R):
# return sqrt(sigPhi_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
# def sig_min_exp(R):
# return sqrt(sigR_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
cos_i, sin_i = cos(incl * pi / 180), sin(incl * pi / 180)
def sig_maj_exp(R):
tmp = sigPhi_to_sigR_real(R) * sin_i**2 + alpha**2 * cos_i**2
if tmp > 0:
return sig_R_0*poly_sig_min(R)/sig_min_0 * sqrt(sigPhi_to_sigR_real(R) * sin_i**2 + alpha**2 * cos_i**2)
else:
return -1000000
# return sig_R_0*spl_min(R)/sig_min_0 * sqrt(sigPhi_to_sigR(R)**2 * sin_i**2 + alpha**2 * cos_i**2)
# return sqrt(sigPhi_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
def sig_min_exp(R):
return sig_R_0*poly_sig_min(R)/sig_min_0 * sqrt(sin_i**2 + alpha**2 * cos_i**2)
# return sqrt(sigR_exp(R)**2 * sin(incl*pi/180)**2 + sigZ_exp(R)**2 * cos(incl*pi/180)**2)
Теперь то, с чего надо было начинать - построим картинки для разных значений $\alpha$ и $\sigma_{R,0}$. Для того, чтобы найти где минимум, попробуем построить просто двумерные карты $\chi^2$ для разных $\sigma_{R,0}$ $\alpha$: (это очень долго, так что пересчитывать в крайнем случае)
In [29]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
def calc_chi2_normal(obs, obserr, predicted):
return sum([(o-p)**2/err**2 for (o,p,err) in zip(obs, predicted, obserr)])/len(obs)
def compute_chi2_maps(alphas=(), sigmas=()):
'''Вычисляем все изображения, чтобы потом только настройки менять'''
image_min = np.random.uniform(size=(len(sigmas), len(alphas)))
image_maj = np.random.uniform(size=(len(sigmas), len(alphas)))
image = np.random.uniform(size=(len(sigmas), len(alphas)))
for i,si in enumerate(sigmas):
for j,al in enumerate(alphas):
global alpha, sig_R_0
alpha = al
sig_R_0 = si
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
sqerr_min = calc_chi2_normal(sig_min_p, e_sig_min_p, [sig_min_exp(r) for r in radii_min])
sqerr_sum = 0.5*sqerr_maj+0.5*sqerr_min
image[i][j] = sqerr_sum
image_maj[i][j] = sqerr_maj
image_min[i][j] = sqerr_min
return image, image_maj, image_min
image, image_maj, image_min = compute_chi2_maps(alphas=alphas, sigmas=sigmas)
In [30]:
from mpl_toolkits.axes_grid1 import make_axes_locatable
def plot_chi2_map(image, ax, log_scale=False, title='$\chi^2$', is_contour=False, vmax=0.):
'''Рисуем получившиеся карты.
Colormaps: http://wiki.scipy.org/Cookbook/Matplotlib/Show_colormaps'''
if image is not None:
if log_scale:
image_log = np.apply_along_axis(np.log, 1, image)
vmax = image_log.max()
else:
image_log = image
if is_contour:
norm = plt.cm.colors.Normalize(vmax=image.max(), vmin=-image.max())
cmap = plt.cm.PRGn
levels = np.concatenate([np.array([image_log.min()*1.1,]), np.linspace(start=image_log.min(), stop=vmax, num=10)])
levels = sorted(levels)
cset=ax.contour(image_log, levels, hold='on', colors = 'k', origin='lower',
extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
ax.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
im = ax.imshow(image_log, cmap='jet', vmin=image_log.min(), vmax=vmax, interpolation='spline16',
origin="lower", extent=[alphas[0], alphas[-1],sigmas[0],sigmas[-1]], aspect="auto")
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(im, cax=cax)
min_sigma = sigmas[int(np.where(image == image.min())[0])]
ax.set_title(title + '$,\ \sigma(min)=%s$' % min_sigma, size=20.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
ax.grid(True)
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=True, figsize=[16,16])
plot_chi2_map(image, axes[0], log_scale=False, title='$\chi^2 = (\chi^2_{maj} + \chi^2_{min})/2$', is_contour=False, vmax=30.)
plot_chi2_map(image_maj, axes[1], log_scale=False, title='$\chi^2_{maj}$', is_contour=False, vmax=30.)
plot_chi2_map(image_min, axes[2], log_scale=False, title='$\chi^2_{min}$', is_contour=False, vmax=20.)
plt.show()
In [31]:
# Перебор alpha
alphas = np.arange(0.1, 0.7, 0.11)
# Перебор sig_R_0
sigmas = np.arange(270., 350., 16.)
# Те картинки, на которые стоит обратить особое внимание
good_pics = []
plot_ranges(sigmas, alphas, good_pics=good_pics, calc_chi=True)
plt.show()
In [32]:
main_slice = lambda l: sig_min_0/sqrt(sin_i**2 + cos_i**2 * l**2)
def calc_chi2_normal(obs, obserr, predicted):
return sum([(o-p)**2/err**2 for (o,p,err) in zip(obs, predicted, obserr)])/len(obs)
# os.chdir("C:\\Users\\root\\Dropbox\\RotationCurves\\PhD\\paper1\\text\\imgs")
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
import matplotlib.mlab as mlab
import matplotlib
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=True, sharey=False, figsize=[8,16])
ax = axes[0]
# levels = np.linspace(start=image_min.min(), stop=20., num=5)
# levels = [100., 125., 150., 175., 200.]
# levels = [image_min.min()+0.02, image_min.min()+0.4, image_min.min()+1.1, image_min.min()+2.,
# image_min.min()+3.1, image_min.min()+4.1]
# levels = np.linspace(start=image_min.min()+0.1, stop=image_min.min()+4.1, num=5)
levels = np.linspace(start=image_min.min()*1.1, stop=image_min.min()*1.1+4, num=5)
# im = ax.imshow(image_min, cmap='jet', vmin=image_min.min(), vmax=20., interpolation='spline16',
# origin="lower", aspect="auto")
# plt.show()
cset=ax.contour(image_min, levels, colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
min_map_gutter = cset.collections[0].get_paths()
v1,v2 = min_map_gutter[1].vertices, min_map_gutter[0].vertices
x1,x2 = v1[:,0], v2[:,0]
y1,y2 = v1[:,1], v2[:,1]
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
ax.text(0.87, 280, '$\chi^2_{min}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
# ax.set_ylim(180, 300)
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
min_sigmas = np.where(image_min < image_min.min() + 0.03)
slice_alph, slice_sig = min_sigmas[1], min_sigmas[0]
slice_alph = map(lambda l: alphas[0] + (alphas[-1] - alphas[0])*l/len(image_min[0]) , slice_alph)
slice_sig = map(lambda l: sigmas[0] + (sigmas[-1] - sigmas[0])*l/len(image_min), slice_sig)
# ax.plot(slice_alph, slice_sig, '.', color='pink')
poly_slice = poly1d(polyfit(slice_alph, slice_sig, deg=3))
# ax.plot(xx, poly_slice(xx), '.-', color='black')
ax = axes[1]
# levels = np.linspace(start=image_maj.min()-4.3, stop=10., num=10)
# levels = [7., 10., 50., 100.]
# levels = [image_maj.min()+0.2, image_maj.min()+0.7, image_maj.min()+1.1, image_maj.min()+2.1, image_maj.min()+3.1,
# image_maj.min()+4.1]
levels = np.linspace(start=image_maj.min()+0.3, stop=image_maj.min()+4.1, num=5)
cset=ax.contour(image_maj, levels, hold='on', colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
ax.text(0.87, 280, '$\chi^2_{maj}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
# ax.set_ylim(150, 320)
ax = axes[2]
err_maj = []
for al in alphas:
global alpha, sig_R_0
alpha = al
sig_R_0 = main_slice(al)
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj.append(sqerr_maj)
ax.plot(alphas, err_maj, '--', color='black')
err_maj1 = []
for pa in zip(x2,y2):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj1.append(sqerr_maj)
# ax.plot(x2, err_maj1, '-', color='black')
err_maj2 = []
for pa in zip(x1,y1):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj2.append(sqerr_maj)
# ax.plot(x1, err_maj2, '-', color='black')
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
import scipy.interpolate as sp
try:
f1 = sp.interp1d(x2, err_maj1, kind='linear')
ax.fill_between(x1, map(f1, x1), err_maj2, color='grey', alpha=0.3)
except Exception:
f2 = sp.interp1d(x1, err_maj2, kind='linear')
ax.fill_between(x2, map(f2, x2), err_maj1, color='grey', alpha=0.3)
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
# ax.set_ylim(3.1, 3.5)
fig.subplots_adjust(hspace=0.)
axes[0].yaxis.get_major_ticks()[0].set_visible(False)
axes[1].yaxis.get_major_ticks()[0].set_visible(False)
ax.set_xlim(0.25, 0.99)
plt.show()
In [33]:
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=True, figsize=[12,24])
plot_chi2_map(image_maj, axes[0], log_scale=False, title='$\chi^2_{maj}$', is_contour=False, vmax=10.)
plot_chi2_map(image_min, axes[1], log_scale=False, title='$\chi^2_{min}$', is_contour=False, vmax=10.)
corr_image = (image_min*len(sig_min_p) + image_maj*len(sig_maj_p)) / (len(sig_min_p) + len(sig_maj_p))
print 'N1_maj={},\t N2_min={},\t chi^2_corr[0][0]={} (was {} and {})'.format(len(sig_maj_p), len(sig_min_p), corr_image[0][0],
image_min[0][0], image_maj[0][0])
plot_chi2_map(corr_image, axes[2], log_scale=False, title='$\chi^2$', is_contour=True, vmax=5.)
plt.show()
In [ ]:
In [34]:
import scipy.optimize as opt
def chisqfunc((x_sig, x_alpha)):
global sig_R_0, alpha
sig_R_0 = x_sig
alpha = x_alpha
sqerr_ma = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
sqerr_mi = calc_chi2_normal(sig_min_p, e_sig_min_p, [sig_min_exp(r) for r in radii_min])
chisq = (sqerr_mi*len(sig_min_p) + sqerr_ma*len(sig_maj_p)) / (len(sig_min_p) + len(sig_maj_p))
# print sig_R_0, alpha, chisq
return chisq
x0 = np.array([100., 0.5])
res = opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B')
print res
In [35]:
def gen_next_normal(radii, sig, esig):
randomDelta = np.array([np.random.normal(0., derr/2, 1)[0] for derr in esig] )
randomdataY = sig + randomDelta
return zip(radii, randomdataY)
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='o', marker='.', color='blue')
plt.plot(points, poly_sig_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
for i in range(3):
r, s = zip(*gen_next_normal(radii_maj, sig_maj_p, e_sig_maj_p))
plt.plot(r, s, 's', color='red')
# plt.ylim(0., 80.)
plt.legend()
plt.show()
In [36]:
os.chdir("C:\\science\\2FInstability\\data\\ngc1167")
pics_path = '.cutted\\pics\\'
import time
sig_min_0 = 200.
N = 100000
result = []
start_time = time.time()
# fig, (ax1, ax2) = plt.subplots(nrows=2, ncols=1, figsize=(16, 16))
if not os.path.exists(pics_path):
os.makedirs(pics_path)
if os.path.isfile(pics_path + 'monte_carlo.npy'):
result = np.load(pics_path + "monte_carlo.npy")
else:
for i in log_progress(range(N)):
global poly_sig_maj, poly_sig_min
r, s = zip(*gen_next_normal(radii_maj, sig_maj_p, e_sig_maj_p))
poly_sig_maj = inter.UnivariateSpline(r, s, k=3, s=10000., w=w(e_sig_maj_p))
# poly_sig_maj = inter.UnivariateSpline(r, s, k=3, s=10000.)
# ax1.plot(points, poly_sig_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
r, s = zip(*gen_next_normal(radii_min, sig_min_p, e_sig_min_p))
poly_sig_min = inter.UnivariateSpline(r, s, k=3, s=10000., w=w(e_sig_min_p))
# poly_sig_min = inter.UnivariateSpline(r, s, k=3, s=10000.)
# ax2.plot(points, poly_sig_min(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='red')
result.append((opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B').x,
poly_sig_maj.get_coeffs(), poly_sig_min.get_coeffs()))
np.save(pics_path + 'monte_carlo', np.array(result))
print("--- %s seconds ---" % (time.time() - start_time))
# ax1.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='o', marker='.', color='red')
# ax2.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='o', marker='.', color='blue')
# ax1.set_ylim(0., 250.)
# ax2.set_ylim(0., 250.)
# plt.show()
In [37]:
len(result)
Out[37]:
In [38]:
s, _, _ = zip(*result)
s,a = zip(*s)
plt.plot(a, s, '.')
plt.plot(alphas, map(main_slice, alphas), '--')
# plt.xlim(0.0, 0.99)
plt.ylim(0, 420)
plt.show()
In [39]:
from scipy.stats import norm
fig = plt.figure(figsize=(12,6))
ax = fig.add_subplot(111)
n, bins, patches = ax.hist(s, 20, normed=1, facecolor='green', alpha=0.75)
mu, std = norm.fit(s)
xmin, xmax = plt.xlim()
x = np.linspace(xmin, xmax, 100)
p = norm.pdf(x, mu, std)
plt.plot(x, p, 'k', linewidth=2)
ax.set_title('$\mu=%s,\ \sigma=%s$' % (mu, std), fontsize=18)
ax.grid(True)
plt.show()
In [40]:
min_n = len(radii_min)
def func(x, alph, sig):
global alpha, sig_R_0
alpha = alph
sig_R_0 = sig
return [sig_min_exp(x[l]) if l > min_n else sig_maj_exp(x[l]) for l in range(len(x))]
In [41]:
rr = radii_maj + radii_min
print len(rr), min_n
sgs = sig_maj_p + sig_min_p
esgs = e_sig_maj_p + e_sig_min_p
esgs = [l/2 for l in esgs]
In [42]:
popt, pcov = opt.curve_fit(func, rr, sgs, sigma=esgs, absolute_sigma=True)
print popt, pcov
s_sq = np.array([((np.array(func(rr, popt[0], popt[1]))-np.array(sgs))**2)[l]/esgs[l] for l in range(len(rr))]).sum()/(len(rr)-2)
pcov = pcov * s_sq
for i in range(len(pcov)):
print sqrt(pcov[i][i])
In [43]:
def err_pcov(popt, pcov):
s_sq = np.array([((np.array(func(rr, popt[0], popt[1]))-np.array(sgs))**2)[l]
/esgs[l]**2 for l in range(len(rr))]).sum()/(len(rr)-2)
pcov = pcov * s_sq
return (sqrt(pcov[0][0]), sqrt(pcov[1][1]))
In [44]:
import time
N = 100
result1 = []
start_time = time.time()
for i in log_progress(range(N)):
global spl_maj, spl_min
r, s = zip(*gen_next_normal(radii_maj, sig_maj_p, e_sig_maj_p))
r1, s1 = zip(*gen_next_normal(radii_min, sig_min_p, e_sig_min_p))
rr = r + r1
sgs = s + s1
popt, pcov = opt.curve_fit(func, rr, sgs, sigma=esgs, absolute_sigma=True)
err = err_pcov(popt, pcov)
result1.append((popt[0], popt[1], err[0], err[1]))
print("--- %s seconds ---" % (time.time() - start_time))
In [45]:
a,s,erra,errs = zip(*result1)
# plt.plot(a, s, '.')
plt.errorbar(a, s, yerr=errs, xerr=erra, fmt='o', marker='.', color='red')
plt.plot(alphas, map(main_slice, alphas), '--')
plt.xlim(0.0, 0.99)
plt.ylim(0, 400)
plt.show()
In [46]:
plt.errorbar(a, s, yerr=errs, fmt='o', marker='.', color='red')
plt.plot(alphas, map(main_slice, alphas), '--')
plt.xlim(0.0, 0.99)
plt.ylim(0, 400)
plt.show()
In [47]:
cutted = 15.0
bind_curve = lambda p: (abs(p[0]), abs(p[1]), p[2])
sig_maj_data = zip(r_ma, sig_ma, e_sig_ma)
sig_maj_data = map(bind_curve, sig_maj_data)
sig_maj_data.sort()
sig_maj_data = filter(lambda l: l[0] > cutted, sig_maj_data)
radii_maj, sig_maj_p, e_sig_maj_p = zip(*sig_maj_data)
sig_min_data = zip(r_mi_extend, sig_mi, e_sig_mi)
sig_min_data = map(bind_curve, sig_min_data)
sig_min_data.sort()
sig_min_data = filter(lambda l: l[0] > cutted, sig_min_data)
radii_min, sig_min_p, e_sig_min_p = zip(*sig_min_data)
def fuu(x, A, B):
return A*x + B
# ind = [True if radii_min[l] > 15. and radii_min[l] < 30. else False for l in range(len(radii_min))]
#from 15'' to 30''
A,B = curve_fit(fuu, radii_min[:14], map(np.log, sig_min_p[:14]))[0]
print A, B
In [48]:
def fuu1(x, A, B):
return np.exp(A*x+B)
In [49]:
h_kin = float("{0:.2f}".format(-1./A))
print h_kin
plt.plot(points, fuu1(points, A, B), 'x', color='red')
plt.plot(points, map(lambda l: np.exp(B)*np.exp(-l/h_kin), points), '+')
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='.', marker='.', mew=0, color='blue')
plt.plot(points, spl_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
plt.plot(radii_min, sig_min_p, 's', label='$\sigma_{los}^{min}$', color='red')
plt.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='.', marker='.', mew=0, color='red')
plt.plot(points, spl_min(points), label = '$\sigma_{los}^{min}\, splinefit$', color='red')
plt.axvline(x=radii_min[14], color='black')
plt.legend()
plt.ylim(0, 250)
plt.show()
In [50]:
sig_min_0 = fuu1(radii_min[0], A, B)
def sigR_ger_exp(R):
return sig_R_0*exp(-R/h_kin)/exp(-radii_min[0]/h_kin)
def sigZ_ger_exp(R):
return sigR_ger_exp(R)*alpha
def sig_maj_exp(R):
return sqrt(sigPhi_to_sigR_real(R) * sigR_ger_exp(R)**2 * sin_i**2 + sigZ_ger_exp(R)**2 * cos_i**2)
def sig_min_exp(R):
return sqrt(sigR_ger_exp(R)**2 * sin_i**2 + sigZ_ger_exp(R)**2 * cos_i**2)
In [51]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
radii_maj1, sig_maj_p1, e_sig_maj_p1 = radii_maj, sig_maj_p, e_sig_maj_p
radii_min1, sig_min_p1, e_sig_min_p1 = radii_min, sig_min_p, e_sig_min_p
sig_maj_data = zip(radii_maj, sig_maj_p, e_sig_maj_p)
sig_maj_data = filter(lambda l: l[0] < radii_min[14], sig_maj_data)
radii_maj, sig_maj_p, e_sig_maj_p = zip(*sig_maj_data)
radii_min, sig_min_p, e_sig_min_p = radii_min[:14], sig_min_p[:14], e_sig_min_p[:14]
image, image_maj, image_min = compute_chi2_maps(alphas=alphas, sigmas=sigmas)
radii_maj, sig_maj_p, e_sig_maj_p = radii_maj1, sig_maj_p1, e_sig_maj_p1
radii_min, sig_min_p, e_sig_min_p = radii_min1, sig_min_p1, e_sig_min_p1
sig_maj_data = zip(radii_maj, sig_maj_p, e_sig_maj_p)
sig_min_data = zip(radii_min, sig_min_p, e_sig_min_p)
In [52]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=True, figsize=[12,24])
plot_chi2_map(image_maj, axes[0], log_scale=False, title='$\chi^2_{maj}$', is_contour=True, vmax=10.)
plot_chi2_map(image_min, axes[1], log_scale=False, title='$\chi^2_{min}$', is_contour=True, vmax=10.)
corr_image = (image_min*len(sig_min_p) + image_maj*len(sig_maj_p)) / (len(sig_min_p) + len(sig_maj_p))
print 'N1_maj={},\t N2_min={},\t chi^2_corr[0][0]={} (was {} and {})'.format(len(sig_maj_p), len(sig_min_p), corr_image[0][0],
image_min[0][0], image_maj[0][0])
plot_chi2_map(corr_image, axes[2], log_scale=False, title='$\chi^2$', is_contour=True, vmax=10.)
plt.show()
In [53]:
alphas = np.arange(0.3, 0.9, 0.11)
sigmas = np.arange(286., 366., 16.)
plot_ranges(sigmas, alphas, good_pics=good_pics, calc_chi=True)
plt.show()
In [54]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
import matplotlib.mlab as mlab
import matplotlib
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=True, sharey=False, figsize=[8,16])
ax = axes[0]
levels = np.linspace(start=image_min.min()*1.1, stop=image_min.min()*1.1+4, num=5)
levels = np.linspace(start=image_min.min()*1.2, stop=image_min.min()*1.1+14, num=5)
cset=ax.contour(image_min, levels, colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
min_map_gutter = cset.collections[0].get_paths()
v1,v2 = min_map_gutter[1].vertices, min_map_gutter[0].vertices
x1,x2 = v1[:,0], v2[:,0]
y1,y2 = v1[:,1], v2[:,1]
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
# ax.text(0.87, 172, '$\chi^2_{min}$', size = 24.)
ax.text(0.87, 130, '$\chi^2_{min}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.set_ylim(100, 400)
# ax.set_ylim(40, 200)
min_sigmas = np.where(image_min < image_min.min() + 0.03)
slice_alph, slice_sig = min_sigmas[1], min_sigmas[0]
slice_alph = map(lambda l: alphas[0] + (alphas[-1] - alphas[0])*l/len(image_min[0]) , slice_alph)
slice_sig = map(lambda l: sigmas[0] + (sigmas[-1] - sigmas[0])*l/len(image_min), slice_sig)
# ax.plot(slice_alph, slice_sig, '.', color='pink')
poly_slice = poly1d(polyfit(slice_alph, slice_sig, deg=3))
# ax.plot(xx, poly_slice(xx), '.-', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
ax = axes[1]
# levels = np.append(np.linspace(start=image_maj.min()+0.1, stop=image_maj.min()+4.1, num=6), np.array([image_maj.min()+0.25]))
levels = np.linspace(start=image_maj.min()*1.1, stop=image_maj.min()*1.1+5, num=6)
# levels = [image_maj.min()+0.1, image_maj.min()+0.25, image_maj.min()+1.1, image_maj.min()+2.1, image_maj.min()+3.1,
# image_maj.min()+4.1]
levels = sorted(levels)
cset=ax.contour(image_maj, levels, hold='on', colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
# ax.text(0.87, 172, '$\chi^2_{maj}$', size = 24.)
ax.text(0.87, 110, '$\chi^2_{maj}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
ax.set_ylim(100, 400)
# ax.set_ylim(50, 120)
ax = axes[2]
err_maj = []
for al in alphas:
global alpha, sig_R_0
alpha = al
sig_R_0 = main_slice(al)
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj.append(sqerr_maj)
ax.plot(alphas, err_maj, '--', color='black')
err_maj1 = []
for pa in zip(x2,y2):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj1.append(sqerr_maj)
# ax.plot(x2, err_maj1, '-', color='black')
err_maj2 = []
for pa in zip(x1,y1):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj2.append(sqerr_maj)
# ax.plot(x1, err_maj2, '-', color='black')
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
import scipy.interpolate as sp
try:
f1 = sp.interp1d(x2, err_maj1, kind='linear')
ax.fill_between(x1, map(f1, x1), err_maj2, color='grey', alpha=0.3)
except Exception:
f2 = sp.interp1d(x1, err_maj2, kind='linear')
ax.fill_between(x2, map(f2, x2), err_maj1, color='grey', alpha=0.3)
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
ax.set_ylim(0.5, 3.)
fig.subplots_adjust(hspace=0.)
axes[0].yaxis.get_major_ticks()[0].set_visible(False)
axes[1].yaxis.get_major_ticks()[0].set_visible(False)
ax.set_xlim(0.25, 0.99)
plt.show()
In [55]:
import time
N = 100
result = []
start_time = time.time()
fig, (ax1, ax2) = plt.subplots(nrows=2, ncols=1, figsize=(16, 16))
sig_maj_data = zip(radii_maj, sig_maj_p, e_sig_maj_p)
sig_maj_data = filter(lambda l: l[0] < radii_min[14], sig_maj_data)
radii_maj, sig_maj_p, e_sig_maj_p = zip(*sig_maj_data)
radii_min, sig_min_p, e_sig_min_p = radii_min[:14], sig_min_p[:14], e_sig_min_p[:14]
radii_maj2, sig_maj_p2, e_sig_maj_p2 = radii_maj, sig_maj_p, e_sig_maj_p
radii_min2, sig_min_p2, e_sig_min_p2 = radii_min, sig_min_p, e_sig_min_p
for i in log_progress(range(N)):
global radii_min, radii_maj, sig_min_p, sig_maj_p
global A,B,h_kin
r, s = zip(*gen_next_normal(radii_maj2, sig_maj_p2, e_sig_maj_p2))
radii_maj, sig_maj_p = r, s
ax1.plot(points, spl_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
r, s = zip(*gen_next_normal(radii_min2, sig_min_p2, e_sig_min_p2))
A, B = curve_fit(fuu, r, map(np.log, s))[0]
# print A,B
h_kin = float("{0:.2f}".format(-1./A))
# print h_kin
radii_min, sig_min_p = r, s
ax2.plot(points, map(lambda l: np.exp(B)*np.exp(-l/h_kin), points), '-', color='red')
ax2.plot(points, fuu1(points, A, B), 'x', color='red')
res = opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B')
result.append(res.x)
print("--- %s seconds ---" % (time.time() - start_time))
ax1.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='o', marker='.', color='red')
ax2.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='o', marker='.', color='blue')
ax1.set_ylim(0., 210.)
ax2.set_ylim(0., 250.)
plt.show()
radii_maj, sig_maj_p, e_sig_maj_p = radii_maj1, sig_maj_p1, e_sig_maj_p1
radii_min, sig_min_p, e_sig_min_p = radii_min1, sig_min_p1, e_sig_min_p1
In [56]:
s,a = zip(*result)
plt.plot(a, s, '.')
plt.plot(alphas, map(main_slice, alphas), '--')
# plt.xlim(0.0, 0.99)
plt.ylim(0, 400)
plt.show()
In [ ]:
In [ ]:
In [57]:
bind_curve = lambda p: (abs(p[0]), abs(p[1]), p[2])
sig_maj_data = zip(r_ma, sig_ma, e_sig_ma)
sig_maj_data = map(bind_curve, sig_maj_data)
sig_maj_data.sort()
sig_maj_data = filter(lambda l: l[0] > 30. and l[0] < 62., sig_maj_data)
radii_maj, sig_maj_p, e_sig_maj_p = zip(*sig_maj_data)
sig_min_data = zip(r_mi_extend, sig_mi, e_sig_mi)
sig_min_data = map(bind_curve, sig_min_data)
sig_min_data.sort()
sig_min_data = filter(lambda l: l[0] > 30. and l[0] < 62. and l[1] > 100., sig_min_data)
radii_min, sig_min_p, e_sig_min_p = zip(*sig_min_data)
def fuu(x, A, B):
return A*x + B
#from 30'' to 60''
A,B = curve_fit(fuu, radii_min, map(np.log, sig_min_p))[0]
print A, B
In [58]:
def fuu1(x, A, B):
return np.exp(A*x+B)
In [59]:
h_kin = float("{0:.2f}".format(-1./A))
print h_kin
plt.plot(points, fuu1(points, A, B), 'x', color='red')
plt.plot(points, map(lambda l: np.exp(B)*np.exp(-l/h_kin), points), '+')
plt.plot(radii_maj, sig_maj_p, 's', label='$\sigma_{los}^{maj}$', color='blue')
plt.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='.', marker='.', mew=0, color='blue')
plt.plot(points, spl_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
plt.plot(radii_min, sig_min_p, 's', label='$\sigma_{los}^{min}$', color='red')
plt.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='.', marker='.', mew=0, color='red')
plt.plot(points, spl_min(points), label = '$\sigma_{los}^{min}\, splinefit$', color='red')
# plt.axvline(x=radii_min[14], color='black')
plt.legend()
plt.ylim(0, 250)
plt.show()
In [60]:
sig_min_0 = fuu1(radii_min[0], A, B)
def sigR_ger_exp(R):
return sig_R_0*exp(-R/h_kin)/exp(-radii_min[0]/h_kin)
def sigZ_ger_exp(R):
return sigR_ger_exp(R)*alpha
def sig_maj_exp(R):
return sqrt(sigPhi_to_sigR_real(R) * sigR_ger_exp(R)**2 * sin_i**2 + sigZ_ger_exp(R)**2 * cos_i**2)
def sig_min_exp(R):
return sqrt(sigR_ger_exp(R)**2 * sin_i**2 + sigZ_ger_exp(R)**2 * cos_i**2)
In [61]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
radii_maj1, sig_maj_p1, e_sig_maj_p1 = radii_maj, sig_maj_p, e_sig_maj_p
radii_min1, sig_min_p1, e_sig_min_p1 = radii_min, sig_min_p, e_sig_min_p
image, image_maj, image_min = compute_chi2_maps(alphas=alphas, sigmas=sigmas)
radii_maj, sig_maj_p, e_sig_maj_p = radii_maj1, sig_maj_p1, e_sig_maj_p1
radii_min, sig_min_p, e_sig_min_p = radii_min1, sig_min_p1, e_sig_min_p1
sig_maj_data = zip(radii_maj, sig_maj_p, e_sig_maj_p)
sig_min_data = zip(radii_min, sig_min_p, e_sig_min_p)
In [62]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=False, sharey=True, figsize=[12,24])
plot_chi2_map(image_maj, axes[0], log_scale=False, title='$\chi^2_{maj}$', is_contour=True, vmax=10.)
plot_chi2_map(image_min, axes[1], log_scale=False, title='$\chi^2_{min}$', is_contour=True, vmax=10.)
corr_image = (image_min*len(sig_min_p) + image_maj*len(sig_maj_p)) / (len(sig_min_p) + len(sig_maj_p))
print 'N1_maj={},\t N2_min={},\t chi^2_corr[0][0]={} (was {} and {})'.format(len(sig_maj_p), len(sig_min_p), corr_image[0][0],
image_min[0][0], image_maj[0][0])
plot_chi2_map(corr_image, axes[2], log_scale=False, title='$\chi^2$', is_contour=True, vmax=10.)
plt.show()
In [63]:
alphas = np.arange(0.3, 0.9, 0.11)
sigmas = np.arange(156., 236., 16.)
plot_ranges(sigmas, alphas, good_pics=good_pics, calc_chi=True)
plt.show()
In [64]:
alphas = np.arange(0.1, 1.2, 0.03)
sigmas = np.arange(100.0, 400, 3.)
import matplotlib.mlab as mlab
import matplotlib
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=True, sharey=False, figsize=[8,16])
ax = axes[0]
levels = np.linspace(start=image_min.min()*1.1, stop=image_min.min()*1.1+4, num=5)
levels = np.linspace(start=image_min.min()*1.2, stop=image_min.min()*1.1+14, num=5)
cset=ax.contour(image_min, levels, colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
min_map_gutter = cset.collections[0].get_paths()
v1,v2 = min_map_gutter[1].vertices, min_map_gutter[0].vertices
x1,x2 = v1[:,0], v2[:,0]
y1,y2 = v1[:,1], v2[:,1]
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
# ax.text(0.87, 172, '$\chi^2_{min}$', size = 24.)
ax.text(0.87, 130, '$\chi^2_{min}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.set_ylim(100, 400)
# ax.set_ylim(40, 200)
min_sigmas = np.where(image_min < image_min.min() + 0.03)
slice_alph, slice_sig = min_sigmas[1], min_sigmas[0]
slice_alph = map(lambda l: alphas[0] + (alphas[-1] - alphas[0])*l/len(image_min[0]) , slice_alph)
slice_sig = map(lambda l: sigmas[0] + (sigmas[-1] - sigmas[0])*l/len(image_min), slice_sig)
# ax.plot(slice_alph, slice_sig, '.', color='pink')
poly_slice = poly1d(polyfit(slice_alph, slice_sig, deg=3))
# ax.plot(xx, poly_slice(xx), '.-', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
ax = axes[1]
# levels = np.append(np.linspace(start=image_maj.min()+0.1, stop=image_maj.min()+4.1, num=6), np.array([image_maj.min()+0.25]))
levels = np.linspace(start=image_maj.min()*1.1, stop=image_maj.min()*1.1+5, num=6)
# levels = [image_maj.min()+0.1, image_maj.min()+0.25, image_maj.min()+1.1, image_maj.min()+2.1, image_maj.min()+3.1,
# image_maj.min()+4.1]
levels = sorted(levels)
cset=ax.contour(image_maj, levels, hold='on', colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
# ax.text(0.87, 172, '$\chi^2_{maj}$', size = 24.)
ax.text(0.87, 110, '$\chi^2_{maj}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
ax.set_ylim(100, 400)
# ax.set_ylim(50, 120)
ax = axes[2]
err_maj = []
for al in alphas:
global alpha, sig_R_0
alpha = al
sig_R_0 = main_slice(al)
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj.append(sqerr_maj)
ax.plot(alphas, err_maj, '--', color='black')
err_maj1 = []
for pa in zip(x2,y2):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj1.append(sqerr_maj)
# ax.plot(x2, err_maj1, '-', color='black')
err_maj2 = []
for pa in zip(x1,y1):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj2.append(sqerr_maj)
# ax.plot(x1, err_maj2, '-', color='black')
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
import scipy.interpolate as sp
try:
f1 = sp.interp1d(x2, err_maj1, kind='linear')
ax.fill_between(x1, map(f1, x1), err_maj2, color='grey', alpha=0.3)
except Exception:
f2 = sp.interp1d(x1, err_maj2, kind='linear')
ax.fill_between(x2, map(f2, x2), err_maj1, color='grey', alpha=0.3)
ax.set_ylabel(r'$\chi^2$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
ax.set_ylim(0.5, 3.)
fig.subplots_adjust(hspace=0.)
axes[0].yaxis.get_major_ticks()[0].set_visible(False)
axes[1].yaxis.get_major_ticks()[0].set_visible(False)
ax.set_xlim(0.25, 0.99)
plt.show()
In [65]:
import time
N = 100
result = []
start_time = time.time()
fig, (ax1, ax2) = plt.subplots(nrows=2, ncols=1, figsize=(16, 16))
radii_maj2, sig_maj_p2, e_sig_maj_p2 = radii_maj, sig_maj_p, e_sig_maj_p
radii_min2, sig_min_p2, e_sig_min_p2 = radii_min, sig_min_p, e_sig_min_p
for i in log_progress(range(N)):
global radii_min, radii_maj, sig_min_p, sig_maj_p
global A,B,h_kin
r, s = zip(*gen_next_normal(radii_maj2, sig_maj_p2, e_sig_maj_p2))
radii_maj, sig_maj_p = r, s
ax1.plot(points, spl_maj(points), label = '$\sigma_{los}^{maj}\, splinefit$', color='blue')
r, s = zip(*gen_next_normal(radii_min2, sig_min_p2, e_sig_min_p2))
A, B = curve_fit(fuu, r, map(np.log, s))[0]
# print A,B
h_kin = float("{0:.2f}".format(-1./A))
# print h_kin
radii_min, sig_min_p = r, s
ax2.plot(points, map(lambda l: np.exp(B)*np.exp(-l/h_kin), points), '-', color='red')
ax2.plot(points, fuu1(points, A, B), 'x', color='red')
res = opt.minimize(chisqfunc, x0, bounds=[(sigmas[0], sigmas[-1]), (alphas[0], alphas[-1])], method='L-BFGS-B')
result.append(res.x)
print("--- %s seconds ---" % (time.time() - start_time))
ax1.errorbar(radii_maj, sig_maj_p, yerr=e_sig_maj_p, fmt='o', marker='.', color='red')
ax2.errorbar(radii_min, sig_min_p, yerr=e_sig_min_p, fmt='o', marker='.', color='blue')
ax1.set_ylim(0., 210.)
ax2.set_ylim(0., 250.)
plt.show()
radii_maj, sig_maj_p, e_sig_maj_p = radii_maj1, sig_maj_p1, e_sig_maj_p1
radii_min, sig_min_p, e_sig_min_p = radii_min1, sig_min_p1, e_sig_min_p1
In [66]:
s,a = zip(*result)
plt.plot(a, s, '.')
plt.plot(alphas, map(main_slice, alphas), '--')
# plt.xlim(0.0, 0.99)
plt.ylim(0, 400)
plt.show()
In [ ]: