In [1]:
%matplotlib inline
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 pandas as pd
import PIL as pil
import heapq
import matplotlib.pylab as pylab
pylab.rcParams['figure.figsize'] = 18, 14
import seaborn as sns
sns.set_palette("deep", desat=.6)
try:
from PIL import Image
except:
import Image
incl = 64.
sin_i2 = np.sin(incl*np.pi/180.)**2
cos_i2 = np.cos(incl*np.pi/180.)**2
In [2]:
os.chdir("C:\\science\\2FInstability\\data\\ngc2280")
plt.imshow(np.asarray(Image.open("fig.png")))
plt.plot()
Out[2]:
In [3]:
min_data = [6.198857575444754, 78.44361859536832,
7.762465159492101, 56.309142837479726,
10.218677953270706, 65.83909707167675,
11.730497918172116, 53.89525480885027,
16.054333987130516, 66.18492137228577,
23.99659337256116, 51.16823233887334]
In [4]:
maj_data = [9.027355623100306, 64.2120645312134,
9.848024316109424, 65.38169277530977,
16.00303951367781, 55.11544306757065,
16.778115501519757, 60.322656067336936,
25.851063829787233, 42.035597381342086]
In [5]:
r_mi, sig_mi = min_data[0::2], min_data[1::2]
In [6]:
r_ma, sig_ma = maj_data[0::2], maj_data[1::2]
In [7]:
sigR = lambda l: 126.*np.exp(-l/54.)
sigZ = lambda l: 31.*np.exp(-l/54.)
phi2_to_R2 = lambda l: 0.5*(1 + 0.26)
sig_min = lambda l: sqrt(sigR(l)**2 * sin_i2 + sigZ(l)**2 * cos_i2)
sig_maj = lambda l: sigR(l) * sqrt(phi2_to_R2(l)*sin_i2 + cos_i2*0.25**2)
In [8]:
fig = plt.figure(figsize=[10,6])
plt.plot(r_mi, sig_mi, 'o')
tp = np.linspace(0.1, 30., 100)
plt.plot(tp, map(sig_min, tp), '-')
plt.title('Sig_min')
plt.xlim(0, 35)
plt.ylim(0, 150)
plt.show()
Не совпадает! У них даже уравнения в работе неправильно записаны.
In [9]:
sqrt(126**2 * sin_i2 + 31**2 * cos_i2)
Out[9]:
In [10]:
fig = plt.figure(figsize=[10,6])
plt.plot(r_ma, sig_ma, 'o')
tp = np.linspace(0.1, 30., 100)
plt.plot(tp, map(sig_maj, tp), '-')
plt.title('Sig_maj')
plt.xlim(0, 35)
plt.ylim(0, 150)
plt.show()
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In [21]:
fig = plt.figure(figsize=[10,6])
for alpha in [0.3, 0.5, 0.7, 0.9]:
delta_sig = lambda l: 1 + alpha**2 * np.cos(l*np.pi/180.)**2 / np.sin(l*np.pi/180.)**2
plt.plot(np.linspace(0,90.,90), map(delta_sig,np.linspace(0,90.,90)) , label=str(alpha))
plt.legend(loc='lower left')
plt.ylim(0., 10.)
plt.show()
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In [3]:
pylab.rcParams['figure.figsize'] = 25, 10
#Velocity
lu = (80, 62)
lu_val = (5, 200)
rd = (432, 174)
rd_val = (30, 0)
data = [(187,110), (195,103), (267,97), (276,91), (384,82), (393,85)]
def extend_values(data, lu, lu_val, rd, rd_val):
xscale = 1.0*(rd_val[0]-lu_val[0])/(rd[0]-lu[0])
yscale = 1.0*(rd_val[1]-lu_val[1])/(lu[1]-rd[1])
extended = []
for d in data:
extended.append((xscale*(d[0]-lu[0])+lu_val[0], yscale*(rd[1] - d[1])+rd_val[1]))
return extended
e_data = extend_values(data, lu, lu_val, rd, rd_val)
plt.plot(zip(*e_data)[0],zip(*e_data)[1], 'or')
vel_fit = lambda l: 92.*np.power(l, 0.26)
plt.plot(np.linspace(5., 35., 100), map(vel_fit, np.linspace(5., 35., 100)), '--')
plt.ylim(0, 250)
plt.xlim(5, 35)
plt.show()
In [4]:
#Sig_maj
lu = (80, 174)
lu_val = (5, 150)
rd = (431, 315)
rd_val = (30, 0)
data = [(186,255), (196,254), (267,263), (277,258), (383,275)]
sig_maj_data = extend_values(data, lu, lu_val, rd, rd_val)
plt.plot(zip(*sig_maj_data)[0],zip(*sig_maj_data)[1], 'or')
sigR = lambda l: 126.*np.exp(-l/54.)
sigZ = lambda l: 31.*np.exp(-l/54.)
phi_to_R = lambda l: 0.5*(1 + 0.26)
sig_maj = lambda l: sigR(l)*sqrt((phi_to_R(l) * sin_i2 + sigZ(l)**2 * cos_i2/sigR(l)**2))
sig_min = lambda l: sqrt(sigR(l)**2 * sin_i2 + sigZ(l)**2 * cos_i2)
plt.plot(np.linspace(5., 35., 100), map(sig_maj, np.linspace(5., 35., 100)), '--')
plt.plot(np.linspace(5., 35., 100), map(sig_min, np.linspace(5., 35., 100)), '--')
plt.ylim(0, 150)
plt.xlim(5, 35)
plt.show()
In [5]:
#Sig_min
lu = (80, 314)
lu_val = (5, 150)
rd = (435, 455)
rd_val = (30, 0)
data = [(154,380), (172,402), (200,393), (218,404), (269,392), (362,406)]
sig_min_data = extend_values(data, lu, lu_val, rd, rd_val)
plt.plot(zip(*sig_min_data)[0], zip(*sig_min_data)[1], 'or')
plt.plot(np.linspace(5., 35., 100), map(sig_min, np.linspace(5., 35., 100)), '-')
plt.plot(np.linspace(5., 35., 100), map(sig_maj, np.linspace(5., 35., 100)), '-')
plt.ylim(0, 150)
plt.xlim(5, 35)
plt.show()
In [6]:
h_kin = 54.
beta = -0.26
def sig_maj_exp(R):
global alpha, sigR_0, h_kin, beta
return np.exp(-R/h_kin)*sigR_0*sqrt(0.5*(1 - beta) * sin_i2 + alpha**2 * cos_i2)
def sig_min_exp(R):
global alpha, sigR_0, h_kin
return np.exp(-R/h_kin)*sigR_0*sqrt(sin_i2 + alpha**2 * cos_i2)
alphas = np.arange(0.01, 1., 0.01)
sigmas = np.arange(10.0, 150, 0.25)
def compute_chi2_maps(alph=(), sigm=()):
'''Вычисляем все изображения, чтобы потом только настройки менять'''
image_min = np.random.uniform(size=(len(sigm), len(alph)))
image_maj = np.random.uniform(size=(len(sigm), len(alph)))
image = np.random.uniform(size=(len(sigmas), len(alphas)))
for i,si in enumerate(sigm):
for j,al in enumerate(alph):
global alpha, sigR_0
alpha = al
sigR_0 = si
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)
image_maj[i][j] = sqerr_maj
image_min[i][j] = sqerr_min
return image_maj, image_min
pics_path = "C:\\science\\2FInstability\\data\\ngc2280\\"
if not os.path.exists(pics_path):
os.makedirs(pics_path)
if os.path.isfile(pics_path + 'chi2_map_maj.npy'):
image_maj = np.load(pics_path + "chi2_map_maj.npy")
image_min = np.load(pics_path + "chi2_map_min.npy")
else:
image_maj, image_min = compute_chi2_maps(alph=alphas, sigm=sigmas)
np.save(pics_path + 'chi2_map_maj', image_maj)
np.save(pics_path + 'chi2_map_min', image_min)
In [7]:
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.):
if image is not None:
im = ax.imshow(image, cmap='jet', vmin=image.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)
ax.set_title(title, size=20.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
ax.set_xlabel(r'$\alpha$', size=20.)
ax.grid(True)
min_sigmas = np.where(image_min < image_min.min() + 10.)
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)
poly_slice_min = poly1d(polyfit(slice_alph, slice_sig, deg=3))
maj_sigmas = np.where(image_maj < image_maj.min() + 10.)
slice_alph, slice_sig = maj_sigmas[1], maj_sigmas[0]
slice_alph = map(lambda l: alphas[0] + (alphas[-1] - alphas[0])*l/len(image_maj[0]) , slice_alph)
slice_sig = map(lambda l: sigmas[0] + (sigmas[-1] - sigmas[0])*l/len(image_maj), slice_sig)
poly_slice_maj = poly1d(polyfit(slice_alph, slice_sig, deg=3))
fig, axes = plt.subplots(nrows=1, ncols=2, sharex=False, sharey=True, figsize=[15,5])
plot_chi2_map(image_maj, axes[0], log_scale=False, title='$\chi^2_{maj}$', is_contour=False, vmax=300.)
plot_chi2_map(image_min, axes[1], log_scale=False, title='$\chi^2_{min}$', is_contour=False, vmax=300.)
axes[0].plot(0.25, 126., 'o', color='m')
axes[0].errorbar(0.25, 126., xerr=0.2, yerr=29., fmt='.', marker='.', mew=0, color='m')
axes[0].plot(alphas[20:], map(poly_slice_maj, alphas[20:]), '.-', label = 'maj -> maj', color= 'red')
axes[0].plot(alphas[20:], map(poly_slice_min, alphas[20:]), '.-', label = 'min -> maj', color= 'pink')
axes[1].plot(0.25, 126., 'o', color='m')
axes[1].errorbar(0.25, 126., xerr=0.2, yerr=29., fmt='.', marker='.', mew=0, color='m')
axes[1].plot(alphas[20:], map(poly_slice_min, alphas[20:]), '.-', label = 'min -> min', color='red')
axes[1].plot(alphas[20:], map(poly_slice_maj, alphas[20:]), '.-', label = 'maj -> min', color='pink')
plt.show()
fig, axes = plt.subplots(nrows=1, ncols=2, sharex=False, sharey=False, figsize=[15,5])
plot_chi2_map((image_min + image_maj)/2, axes[0], log_scale=False, title='$\chi^2_{maj}+\chi^2_{min}$', is_contour=False, vmax=150.)
axes[0].plot(0.25, 126., 'o', color='m')
axes[0].errorbar(0.25, 126., xerr=0.2, yerr=29., fmt='.', marker='.', mew=0, color='m')
err_maj_1, err_maj_2 = [], []
err_min_1, err_min_2 = [], []
for al in alphas:
global alpha, sigR_0
alpha = al
sigR_0 = poly_slice_min(alpha)
err_maj_1.append(sum(power([sig_maj_exp(p[0]) - p[1] for p in sig_maj_data], 2))/len(sig_maj_data))
err_min_1.append(sum(power([sig_min_exp(p[0]) - p[1] for p in sig_min_data], 2))/len(sig_min_data))
sigR_0 = poly_slice_maj(alpha)
err_maj_2.append(sum(power([sig_maj_exp(p[0]) - p[1] for p in sig_maj_data], 2))/len(sig_maj_data))
err_min_2.append(sum(power([sig_min_exp(p[0]) - p[1] for p in sig_min_data], 2))/len(sig_min_data))
axes[1].plot(alphas, err_maj_1, '.-', label = 'min -> maj', color= 'red')
axes[1].plot(alphas, err_min_1, '.-', label = 'min -> min', color='orange')
axes[1].plot(alphas, err_maj_2, '.-', label = 'maj -> maj', color= 'green')
axes[1].plot(alphas, err_min_2, '.-', label = 'maj -> min', color='blue')
axes[1].legend()
plt.show()
In [8]:
alphas = np.arange(0.1, 0.8, 0.15)
sigmas = np.arange(60., 160., 15.)
points = np.arange(5., 35., 0.1)
good_pics = []
def plot_ranges_gers(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=[16,10])
plt_index = 0
# Последнее - среднее геометрическое
sqerr_majs, sqerr_mins, sqerr_mean = [],[],[]
for al in alphas_range:
for si in sigmas_range:
global alpha, sigR_0
alpha = al
sigR_0 = si
ax = axes[plt_index/ncols, plt_index % ncols]
ax.set_title(r'$\alpha = %s, \sigma_{R,0}=%s$' % (al,si))
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)
if sqerr_maj < 120. and sqerr_min < 120.:
ax.plot(30., 105., 'og', ms = 10)
ax.plot(points, [sig_maj_exp(R) for R in points], '--', color='blue')
ax.plot(points, [sig_min_exp(R) for R in points], '--', color='red')
ax.plot(zip(*sig_min_data)[0],zip(*sig_min_data)[1], 's', color='red', ms=3)
ax.plot(zip(*sig_maj_data)[0],zip(*sig_maj_data)[1], 's', color='blue', ms=3)
ax.set_ylim(0, 150)
ax.set_xlim(5, 35)
plt_index = plt_index + 1
plot_ranges_gers(sigmas, alphas, good_pics=good_pics, calc_chi=True)
plt.show()
In [9]:
from IPython.html.widgets import *
def widget_plot_maps(h_k, b, vm, contour_swap):
global alpha, sigR_0, h_kin, beta, alphas, sigmas
h_kin = h_k
beta = b
alphas = np.arange(0.1, 0.9, 0.05)
sigmas = np.arange(60.0, 160, 5.)
image_maj, image_min = compute_chi2_maps(alph=alphas, sigm=sigmas)
fig, axes = plt.subplots(nrows=1, ncols=2, sharex=False, sharey=True, figsize=[15,5])
plot_chi2_map(image_maj, axes[0], log_scale=False, title='$\chi^2_{maj}$', is_contour=False, vmax=vm)
plot_chi2_map(image_min, axes[1], log_scale=False, title='$\chi^2_{min}$', is_contour=False, vmax=vm)
if contour_swap:
norm = cm.colors.Normalize(vmax=image_min.max(), vmin=-image_min.max())
cmap = cm.PRGn
levels = np.linspace(start=image_min.min(), stop=vm, num=10)
cset=axes[0].contour(image_min, levels, hold='on', colors = 'k', origin='lower',
extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
norm = cm.colors.Normalize(vmax=image_maj.max(), vmin=-image_maj.max())
cmap = cm.PRGn
levels = np.linspace(start=image_maj.min(), stop=vm, num=10)
cset=axes[1].contour(image_maj, levels, hold='on', colors = 'k', origin='lower',
extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
axes[0].plot(0.25, 126., 'o', color='m')
axes[0].errorbar(0.25, 126., xerr=0.2, yerr=29., fmt='.', marker='.', mew=0, color='m')
axes[1].plot(0.25, 126., 'o', color='m')
axes[1].errorbar(0.25, 126., xerr=0.2, yerr=29., fmt='.', marker='.', mew=0, color='m')
plt.show()
interact(widget_plot_maps, h_k=(15., 100., 2.), b=(-0.35, -0.15, 0.01), vm = (70., 350., 10), contour_swap=False);
In [10]:
import scipy.interpolate as inter
radii_maj, sig_maj_p = zip(*sig_maj_data)
e_sig_maj_p = [8]*len(radii_maj)
spl_maj = inter.UnivariateSpline (radii_maj[::-1], sig_maj_p[::-1], k=1, s=10000)
radii_min, sig_min_p = zip(*sig_min_data)
e_sig_min_p = [8]*len(radii_min)
spl_min = inter.UnivariateSpline (radii_min[::-1], sig_min_p[::-1], k=1, s=10000)
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.ylim(0, 200)
plt.show()
In [11]:
from numpy import poly1d, polyfit, power
r_ma_b, vel_ma_b = zip(*e_data)
poly_star = poly1d(polyfit(r_ma_b, vel_ma_b, deg=3))
plt.plot(r_ma_b, vel_ma_b, 'o', color='blue', markersize=10)
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, 200)
plt.xlim(10, 30)
plt.ylabel('$V^{maj}_{\phi}(R)$')
plt.show()
In [12]:
def sigPhi_to_sigR_real(R):
return 0.5 * (1 + R*poly_star.deriv()(R) / poly_star(R))
test_points = np.arange(min(r_ma_b), max(r_ma_b), 0.1)
def f(R, Ro):
return 0.5*(1 + np.exp( -R/Ro ))
xdata = test_points
ydata = sigPhi_to_sigR_real(xdata)
# xdata[0] = 0
# ydata[0] = 0
from scipy.optimize import curve_fit
popt, pcov = curve_fit(f, xdata, ydata, p0=[1.0])
Ro = popt[0]
plt.plot(xdata, ydata, 's', color='r')
plt.plot(xdata, [f(p, Ro) for p in xdata], '-', linewidth=3.0, color='b')
# plt.axhline(y=0.5)
plt.axhline(y=0.0)
plt.title('$R_{0} = %s $' % Ro)
plt.ylim(0, 1)
plt.show()
def sigPhi_to_sigR(R):
return sqrt(f(R, Ro))
In [13]:
sns.reset_orig()
In [14]:
#Значение sig_los_min в cutted
sig_min_0 = spl_min(radii_min[0])
#Значение sig_R в cutted
sig_R_0 = 100.
alpha = 0.5
def sigR_exp(R):
return sig_R_0*spl_min(R)/sig_min_0
def sigZ_exp(R):
return alpha * sigR_exp(R)
def sigPhi_exp(R):
return sigPhi_to_sigR(R) * sigR_exp(R)
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):
return sig_R_0*spl_min(R)/sig_min_0 * sqrt(sigPhi_to_sigR_real(R) * sin_i**2 + alpha**2 * cos_i**2)
# return sig_R_0*spl_min(R)/sig_min_0 * sqrt(sigPhi_to_sigR(R) * 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*spl_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)
In [15]:
alphas = np.arange(0.25, 1., 0.01)
sigmas = np.arange(50.0, 200, 1.)
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
from matplotlib import cm
def plot_chi2_map(image, ax, log_scale=False, title='$\chi^2$', is_contour=False, vmax=0.):
if image is not None:
if log_scale:
image_log = np.apply_along_axis(np.log, 1, image)
vmax = image_log.max()
else:
image_log = image
if is_contour:
norm = cm.colors.Normalize(vmax=image.max(), vmin=-image.max())
cmap = cm.PRGn
levels = np.linspace(start=image_log.min(), stop=vmax, num=10)
cset=ax.contour(image_log, levels, hold='on', colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
im = ax.imshow(image_log, cmap='jet', vmin=image_log.min(), vmax=vmax, interpolation='spline16',
origin="lower", extent=[alphas[0], alphas[-1],sigmas[0],sigmas[-1]], aspect="auto")
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(im, cax=cax)
min_sigma = sigmas[int(np.where(image == image.min())[0])]
ax.set_title(title + '$,\ \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$', is_contour=True, vmax=8.)
plot_chi2_map(image_maj, axes[1], log_scale=False, title='$\chi^2_{maj}$', is_contour=True, vmax=8.)
plot_chi2_map(image_min, axes[2], log_scale=False, title='$\chi^2_{min}$', is_contour=True, vmax=8.)
plt.show()
In [17]:
tex_imgs_dir = "C:\\Users\\root\\Dropbox\\RotationCurves\\PhD\\paper1\\text\\imgs"
try:
os.chdir(tex_imgs_dir)
except:
tex_imgs_dir = "C:\\Users\\Alex March\\Dropbox\\RotationCurves\\PhD\\paper1\\text\\imgs"
os.chdir(tex_imgs_dir)
In [19]:
cos_i, sin_i = cos(incl * pi / 180), sin(incl * pi / 180)
main_slice = lambda l: sig_min_0/sqrt(sin_i**2 + cos_i**2 * l**2)
import matplotlib.mlab as mlab
import matplotlib
fig, axes = plt.subplots(nrows=3, ncols=1, sharex=True, sharey=False, figsize=[8,16])
ax = axes[0]
levels = np.linspace(start=image_min.min()*1.1, stop=image_min.min()*1.1+4, num=5)
cset=ax.contour(image_min, levels, colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
min_map_gutter = cset.collections[0].get_paths()
v1,v2 = min_map_gutter[1].vertices, min_map_gutter[0].vertices
x1,x2 = v1[:,0], v2[:,0]
y1,y2 = v1[:,1], v2[:,1]
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
ax.text(0.87, 90, '$\chi^2_{min}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.set_ylim(40, 100)
min_sigmas = np.where(image_min < image_min.min() + 0.03)
slice_alph, slice_sig = min_sigmas[1], min_sigmas[0]
slice_alph = map(lambda l: alphas[0] + (alphas[-1] - alphas[0])*l/len(image_min[0]) , slice_alph)
slice_sig = map(lambda l: sigmas[0] + (sigmas[-1] - sigmas[0])*l/len(image_min), slice_sig)
# ax.plot(slice_alph, slice_sig, '.', color='pink')
poly_slice = poly1d(polyfit(slice_alph, slice_sig, deg=3))
# ax.plot(xx, poly_slice(xx), '.-', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
ax = axes[1]
levels = np.append(np.linspace(start=image_maj.min()+0.1, stop=image_maj.min()+4.1, num=6), np.array([image_maj.min()+0.25]))
levels = np.linspace(start=image_maj.min()*1.1, stop=image_maj.min()*1.1+5, num=6)
cset=ax.contour(image_maj, levels, hold='on', colors = 'k', origin='lower', extent=[alphas[0],alphas[-1],sigmas[0],sigmas[-1]])
plt.clabel(cset, inline=1, fontsize=10, fmt='%1.1f',)
ax.text(0.87, 110, '$\chi^2_{maj}$', size = 24.)
ax.set_ylabel('$\sigma_{R,0}$', size=20.)
xx = np.arange(0.25, 1.0, 0.01)
ax.plot(xx, map(main_slice, xx), '--', color='black')
ax.fill_between(x1, y1, 0, color='gray', alpha=0.3)
ax.fill_between(x2, y2, 0, color='white')
ax.set_ylim(40, 120)
ax = axes[2]
err_maj = []
for al in alphas:
global alpha, sig_R_0
alpha = al
sig_R_0 = main_slice(al)
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj.append(sqerr_maj)
ax.plot(alphas, err_maj, '--', color='black')
err_maj1 = []
for pa in zip(x2,y2):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj1.append(sqerr_maj)
# ax.plot(x2, err_maj1, '-', color='black')
err_maj2 = []
for pa in zip(x1,y1):
global alpha, sig_R_0
alpha = pa[0]
sig_R_0 = pa[1]
sqerr_maj = calc_chi2_normal(sig_maj_p, e_sig_maj_p, [sig_maj_exp(r) for r in radii_maj])
err_maj2.append(sqerr_maj)
# ax.plot(x1, err_maj2, '-', color='black')
ax.set_ylabel(r'$\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(3., 3.8)
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('ngc2280_maps.eps', format='eps')
plt.savefig('ngc2280_maps.png', format='png')
plt.savefig('ngc2280_maps.pdf', format='pdf', dpi=150)
plt.show()