def dlfParamsdz(z, pPhiStar, pMStar, pAlpha, pBeta):
dlog10phiStardz = T.deriv(T(pPhiStar))(1 + z)
dmStardz = T.deriv(T(pMStar))(1 + z)
dalphadz = T.deriv(T(pAlpha))(1 + z)
h, f0, z0, a, b = pBeta
zeta = np.log10((1.0 + z) / (1.0 + z0))
dbetadz = (-f0 * (a * 10.0**((a - 1) * zeta) /
(1.0 + z0) + b * 10.0**((b - 1) * zeta) / (1.0 + z0)) /
(10.0**(a * zeta) + 10.0**(b * zeta))**2)
return dlog10phiStardz, dmStardz, dalphadz, dbetadz
def lfParams(z, pPhiStar, pMStar, pAlpha, pBeta):
log10phiStar = T(pPhiStar)(1 + z)
# mStar = T(pMStar)(1+z)
# mStar = np.polyval(pMStar, np.log10(1.0+z))
mStar = np.polyval(pMStar, 1.0 + z)
alpha = T(pAlpha)(1 + z)
h, f0, z0, a, b = pBeta
zeta = np.log10((1.0 + z) / (1.0 + z0))
beta = h + f0 / (10.0**(a * zeta) + 10.0**(b * zeta))
return log10phiStar, mStar, alpha, beta
def calc_opac(self):
""" calculates the opacities from the Chebyshev coefficients for the whole T, P range"""
for t in range(0, len(self.temp_list)):
for p in range(0, len(self.press_list)):
for n in range(0, self.nbins_counted):
#pick block in descending bin order, but ascending P and T order
pick_block = t * len(
self.press_list) * self.nbins_counted + (
p + 1) * self.nbins_counted - 1 - n
#chebyshev series with the correct coefficients
series = T(
self.coeffs[self.ncoeffs * pick_block:self.ncoeffs *
(pick_block + 1)])
for y in range(0, self.ny):
yp = self.ypoints[y]
if yp >= self.ystart[pick_block]:
self.ky.append(
np.exp(
series((2.0 * yp - 1.0 -
self.ystart[pick_block]) /
(1.0 - self.ystart[pick_block]))))
else:
self.ky.append(self.kmin)
def calc_opac(self):
""" calculates the opacities from the Chebyshev coefficients """
for b in range(self.nbins_perfile):
# chebyshev series with the correct coefficients
series = T(self.coeffs[self.ncoeffs*b:self.ncoeffs*(b+1)])
for y in range(self.ny):
yp = self.ypoints[y]
if yp >= self.ystart[b]:
arg = (2.0*yp-1.0-self.ystart[b])/(1.0-self.ystart[b])
self.ky.append(np.exp(series(arg)))
else:
self.ky.append(self.kmin)
def func(z, p0, p1, p2, p3):
return T([p0, p1, p2, p3])(z)
def func(z, p0, p1, p2):
return T([p0, p1, p2])(z)
def func(z, p0, p1, p2):
zeta = np.log10((1.0 + z) / (1.0 + 3.5))
return T([p0, p1, p2])(1 + z)
def func(z, p0, p1):
return T([p0, p1])(z)
def func(z, p0, p1):
return T([p0, p1], domain=[3.7, 7.])(z)
downerr = c - l
ax.scatter(zmean, c, color='k', edgecolor='None', zorder=2)
ax.errorbar(zmean,
c,
ecolor='k',
capsize=0,
xerr=np.vstack((left, right)),
yerr=np.vstack((uperr, downerr)),
fmt='None',
zorder=2)
z = np.linspace(0, 7, 500)
coeffs = chebfit(zmean[:-1] + 1.0, c[:-1], 1)
print(coeffs)
plt.plot(z, T(coeffs)(z + 1), lw=2, c='forestgreen')
plt.savefig('cfit_alpha.pdf', bbox_inches='tight')
#plt.close('all')
elif case == 1:
fig = plt.figure(figsize=(7, 7), dpi=100)
ax = fig.add_subplot(1, 1, 1)
ax.tick_params('both', which='major', length=7, width=1)
ax.tick_params('both', which='minor', length=5, width=1)
ax.set_ylabel(r'$\beta$')
ax.set_xlabel('$z$')
ax.set_xlim(0., 7)
print("Elevation")
x=np.arange(5)
print(poly(x))
y=np.arange(6).reshape(3,2)
print(y)
print(poly(y))
print(p(poly))
print(poly.roots())
from numpy.polynomial import Chebyshev as T
#print(p + poly([1],domain=[0,1]))# you gor error because Traceback(most recent call last) and different dommine name
print("\n ")
print("Chebyshev ")
print(poly(T([0, 1])))
print("calculus")
print("\n")
newdata =p([4,6])
print(newdata)
print(newdata.integ())
print(newdata.integ(1))
print(newdata.integ(lbnd=-1))
print(newdata.integ(lbnd=-1, k=1))
print("\n")
exa=p([1,2,3])
print(exa.deriv(1))
import matplotlib.pyplot as plt
from numpy.polynomial import Chebyshev as T
x = np.linspace(-1, 1, 100)
def atz(self, z, p):
"""Redshift evolution of QLF parameters."""
return T(p)(1+z)
def plot_m_star(fig, composite, sample=False):
mpl.rcParams['font.size'] = '14'
ax = fig.add_subplot(nplots_x, nplots_y, plot_number + 2)
ax.yaxis.tick_right()
ax.yaxis.set_ticks_position('both')
ax.yaxis.set_label_position('right')
ax.set_xlim(zmin, zmax)
ax.set_ylim(-32, -23)
if composite is not None:
bf = composite.bf.x
if sample:
for theta in composite.samples[np.random.randint(len(
composite.samples),
size=900)]:
params = composite.getparams(theta)
M = composite.atz(z, params[1])
ax.plot(z, M, color='k', alpha=0.02, zorder=3)
M = composite.atz(z, composite.getparams(bf)[1])
ax.plot(z, M, color='k', zorder=4)
zmean, zl, zu, u, l, c = np.loadtxt('M_star.dat', unpack=True)
select = zmean > 3.6
zl = zl[select]
zu = zu[select]
u = u[select]
l = l[select]
c = c[select]
zmean = zmean[select]
left = zmean - zl
right = zu - zmean
uperr = u - c
downerr = c - l
ax.scatter(zmean, c, color='k', edgecolor='None', zorder=2)
ax.errorbar(zmean,
c,
ecolor='k',
capsize=0,
xerr=np.vstack((left, right)),
yerr=np.vstack((uperr, downerr)),
fmt='None',
zorder=2)
# zm, cm, uperr, downerr = np.loadtxt('Data/manti.txt', usecols=(0,4,5,6), unpack=True)
# ax.scatter(zm, cm, color='k', edgecolor='None', zorder=2)
# ax.errorbar(zm, cm, ecolor='k', capsize=0,
# yerr=np.vstack((uperr, downerr)),
# fmt='None', zorder=2)
zc = np.linspace(0, 7, 500)
coeffs = chebfit(zmean + 1, c, 1)
print coeffs
plt.plot(zc, T(coeffs)(zc + 1), lw=2, c='goldenrod')
def func(z, p0, p1):
return T([p0, p1])(z)
sigma = np.abs(uperr + downerr)
popt, pcov = curve_fit(func, zmean + 1, c, sigma=sigma, p0=[coeffs])
print popt
plt.plot(zc, func(zc + 1, *popt), lw=2, c='r', dashes=[8, 3])
ax.set_xticks((0, 1, 2, 3, 4, 5, 6, 7))
ax.set_ylabel(r'$M_*$')
ax.set_xticklabels('')
return
def plot_phi_star(fig, composite, sample=False):
mpl.rcParams['font.size'] = '14'
ax = fig.add_subplot(nplots_x, nplots_y, plot_number + 1)
ax.set_xlim(zmin, zmax)
ax.set_ylim(-13, -5)
if composite is not None:
bf = composite.bf.x
if sample:
for theta in composite.samples[np.random.randint(len(
composite.samples),
size=900)]:
params = composite.getparams(theta)
phi = composite.atz(z, params[0])
ax.plot(z, phi, color='k', alpha=0.02, zorder=1)
phi = composite.atz(z, composite.getparams(bf)[0])
ax.plot(z, phi, color='k', zorder=2)
zmean, zl, zu, u, l, c = np.loadtxt('phi_star.dat', unpack=True)
select = zmean > 3.6
zl = zl[select]
zu = zu[select]
u = u[select]
l = l[select]
c = c[select]
zmean = zmean[select]
left = zmean - zl
right = zu - zmean
uperr = u - c
downerr = c - l
ax.scatter(zmean, c, color='k', edgecolor='None', zorder=2)
ax.errorbar(zmean,
c,
ecolor='k',
capsize=0,
xerr=np.vstack((left, right)),
yerr=np.vstack((uperr, downerr)),
fmt='None',
zorder=2)
zc = np.linspace(0, 7, 500)
coeffs = chebfit(zmean + 1, c, 2)
print coeffs
plt.plot(zc, T(coeffs)(zc + 1), lw=2, c='goldenrod')
def func(z, p0, p1, p2):
return T([p0, p1, p2])(z)
sigma = uperr + downerr
popt, pcov = curve_fit(func, zmean + 1, c, sigma=sigma, p0=[coeffs])
print popt
plt.plot(zc, func(zc + 1, *popt), lw=2, c='r', dashes=[8, 3])
# zm, cm, uperr, downerr = np.loadtxt('Data/manti.txt', usecols=(0,1,2,3), unpack=True)
# ax.scatter(zm, cm, color='k', edgecolor='None', zorder=2)
# ax.errorbar(zm, cm, ecolor='k', capsize=0,
# yerr=np.vstack((uperr, downerr)),
# fmt='None', zorder=2)
ax.set_xticks((0, 1, 2, 3, 4, 5, 6, 7))
ax.set_ylabel(
r'$\log_{10}\left(\phi_*/\mathrm{mag}^{-1}\mathrm{cMpc}^{-3}\right)$')
ax.set_xticklabels('')
return
def plot_alpha(fig, composite, sample=False):
mpl.rcParams['font.size'] = '14'
ax = fig.add_subplot(nplots_x, nplots_y, plot_number + 3)
ax.set_xlim(zmin, zmax)
ax.set_ylim(-6.5, -3)
if composite is not None:
bf = composite.bf.x
if sample:
for theta in composite.samples[np.random.randint(len(
composite.samples),
size=900)]:
params = composite.getparams(theta)
alpha = composite.atz(z, params[2])
ax.plot(z, alpha, color='k', alpha=0.02, zorder=3)
alpha = composite.atz(z, composite.getparams(bf)[2])
ax.plot(z, alpha, color='k', zorder=4)
zmean, zl, zu, u, l, c = np.loadtxt('alpha.dat', unpack=True)
select = zmean > 3.6
zl = zl[select]
zu = zu[select]
u = u[select]
l = l[select]
c = c[select]
zmean = zmean[select]
left = zmean - zl
right = zu - zmean
uperr = u - c
downerr = c - l
ax.scatter(zmean, c, color='k', edgecolor='None', zorder=2)
ax.errorbar(zmean,
c,
ecolor='k',
capsize=0,
xerr=np.vstack((left, right)),
yerr=np.vstack((uperr, downerr)),
fmt='None',
zorder=2)
# zm, cm, uperr, downerr = np.loadtxt('Data/manti.txt', usecols=(0,10,11,12), unpack=True)
# ax.scatter(zm, cm, color='k', edgecolor='None', zorder=2, label='Manti et al.\ 2017')
# ax.errorbar(zm, cm, ecolor='k', capsize=0,
# yerr=np.vstack((uperr, downerr)),
# fmt='None', zorder=2)
zc = np.linspace(0, 7, 500)
coeffs = chebfit(zmean + 1.0, c, 1)
print coeffs
plt.plot(zc, T(coeffs)(zc + 1), lw=2, c='goldenrod')
def func(z, p0, p1):
return T([p0, p1])(z)
sigma = uperr + downerr
popt, pcov = curve_fit(func, zmean + 1, c, sigma=sigma, p0=[coeffs])
print popt
plt.plot(zc, func(zc + 1, *popt), lw=2, c='r', dashes=[8, 3])
# plt.legend(loc='upper left', fontsize=10, handlelength=1,
# frameon=False, framealpha=0.0, labelspacing=.1,
# handletextpad=0.1, borderpad=0.01, scatterpoints=1)
ax.set_xticks((0, 1, 2, 3, 4, 5, 6, 7))
ax.set_ylabel(r'$\alpha$ (bright-end slope)')
ax.set_xlabel('$z$')
return
def plotParams(zmin, zmax):
mpl.rcParams['font.size'] = '14'
fig = plt.figure(figsize=(6, 6), dpi=100)
K = 4
nplots_x = 2
nplots_y = 2
nplots = 4
factor = 2.0 # size of one side of one panel
lbdim = 0.5 * factor # size of left/bottom margin
trdim = 0.2 * factor # size of top/right margin
whspace = 0.1 # w/hspace size
plotdim = factor * K + factor * (K - 1.) * whspace
dim = lbdim + plotdim + trdim
lb = lbdim / dim
tr = (lbdim + plotdim) / dim
fig.subplots_adjust(left=lb,
bottom=lb,
right=tr,
top=tr,
wspace=whspace,
hspace=whspace)
zmin = 0
zmax = 15
zc = np.linspace(zmin, zmax, num=500)
ax = fig.add_subplot(nplots_x, nplots_y, 1)
ax.set_xlim(zmin, zmax)
ax.set_ylim(-50, 0)
ax.plot(zc, T(p_log10phiStar)(1 + zc), c='k', lw=2)
ax.set_ylabel(r'$\log_{10}\phi_*$')
ax.set_xticklabels('')
ax = fig.add_subplot(nplots_x, nplots_y, 2)
ax.yaxis.tick_right()
ax.yaxis.set_ticks_position('both')
ax.yaxis.set_label_position('right')
ax.set_xlim(zmin, zmax)
ax.set_ylim(-150, -20)
ax.plot(zc, T(p_MStar)(1 + zc), c='k', lw=2)
ax.set_ylabel(r'$M_*$')
ax.set_xticklabels('')
ax = fig.add_subplot(nplots_x, nplots_y, 3)
ax.set_xlim(zmin, zmax)
ax.set_ylim(-8, -3)
ax.plot(zc, T(p_alpha)(1 + zc), c='k', lw=2)
ax.set_ylabel(r'$\alpha$')
ax = fig.add_subplot(nplots_x, nplots_y, 4)
ax.yaxis.tick_right()
ax.yaxis.set_ticks_position('both')
ax.yaxis.set_label_position('right')
ax.set_xlim(zmin, zmax)
ax.set_ylim(-2.6, -1.5)
h, f0, z0, a, b = p_beta
zeta = np.log10((1.0 + zc) / (1.0 + z0))
beta = h + f0 / (10.0**(a * zeta) + 10.0**(b * zeta))
ax.plot(zc, beta, c='k', lw=2)
ax.set_ylabel(r'$\beta$')
plt.savefig('evolutionFC.pdf', bbox_inches='tight')
mpl.rcParams['font.size'] = '22'
return
