def g(yieldCurve, zeroRates,n, verbose):
'''
generates recursively the zero curve
expressions eval('(0.06/1.05)+(1.06/(1+x)**2)-1')
solves these expressions to get the new rate
for that period
'''
if len(zeroRates) >= len(yieldCurve):
print "\n\n\t+zero curve boot strapped [%d iterations]" % (n)
return
else:
legn = ''
for i in range(0,len(zeroRates),1):
if i == 0:
legn = '%2.6f/(1+%2.6f)**%d'%(yieldCurve[n], zeroRates[i],i+1)
else:
legn = legn + ' +%2.6f/(1+%2.6f)**%d'%(yieldCurve[n], zeroRates[i],i+1)
legn = legn + '+ (1+%2.6f)/(1+x)**%d-1'%(yieldCurve[n], n+1)
# solve the expression for this iteration
if verbose:
print "-[%d] %s" % (n, legn.strip())
rate1 = solve(eval(legn), x)
# Abs here since some solutions can be complex
rate1 = min([Real(abs(r)) for r in rate1])
if verbose:
print "-[%d] solution %2.6f" % (n, float(rate1))
# stuff the new rate in the results, will be
# used by the next iteration
zeroRates.append(rate1)
g(yieldCurve, zeroRates,n+1, verbose)
def test_latex_functions():
assert latex(exp(x)) == "$e^{x}$"
assert latex(exp(1) + exp(2)) == "$e + e^{2}$"
f = Function("f")
assert latex(f(x)) == "$\\operatorname{f}\\left(x\\right)$"
beta = Function("beta")
assert latex(beta(x)) == r"$\operatorname{beta}\left(x\right)$"
assert latex(sin(x)) == r"$\operatorname{sin}\left(x\right)$"
assert latex(sin(x), fold_func_brackets=True) == r"$\operatorname{sin}x$"
assert latex(sin(2 * x ** 2), fold_func_brackets=True) == r"$\operatorname{sin}2 x^{2}$"
assert latex(sin(x ** 2), fold_func_brackets=True) == r"$\operatorname{sin}x^{2}$"
assert latex(asin(x) ** 2) == r"$\operatorname{asin}^{2}\left(x\right)$"
assert latex(asin(x) ** 2, inv_trig_style="full") == r"$\operatorname{arcsin}^{2}\left(x\right)$"
assert latex(asin(x) ** 2, inv_trig_style="power") == r"$\operatorname{sin}^{-1}\left(x\right)^{2}$"
assert latex(asin(x ** 2), inv_trig_style="power", fold_func_brackets=True) == r"$\operatorname{sin}^{-1}x^{2}$"
assert latex(factorial(k)) == r"$k!$"
assert latex(factorial(-k)) == r"$\left(- k\right)!$"
assert latex(floor(x)) == r"$\lfloor{x}\rfloor$"
assert latex(ceiling(x)) == r"$\lceil{x}\rceil$"
assert latex(abs(x)) == r"$\lvert{x}\rvert$"
assert latex(re(x)) == r"$\Re{x}$"
assert latex(im(x)) == r"$\Im{x}$"
assert latex(conjugate(x)) == r"$\overline{x}$"
assert latex(gamma(x)) == r"$\operatorname{\Gamma}\left(x\right)$"
assert latex(Order(x)) == r"$\operatorname{\mathcal{O}}\left(x\right)$"
def Theta_Equation(self, l="undef", m="undef", theta=theta):
""" l - orbital quantum number
m - magnetic quantum number """
if l == "undef":
l = self.l_val
if m == "undef":
m = self.m_val
# Prevents integer division and float l,m
l = int(l)
m = int(m)
mode = self.select_exec_mode(theta)
gL = self.Generalized_Legendre(l, m, theta).subs(theta, sympy.cos(theta))
if gL:
rat_part = sympy.sqrt(
Rational((2 * l + 1), 2) * Rational(factorial(l - sympy.abs(m)), factorial(l + sympy.abs(m)))
)
if mode == "numer":
return (rat_part * gL).evalf()
elif mode == "analit":
return (rat_part * gL).expand()
return False
def test_latex_functions():
assert latex(exp(x)) == "$e^{x}$"
assert latex(exp(1) + exp(2)) == "$e + e^{2}$"
f = Function('f')
assert latex(f(x)) == '$\\operatorname{f}\\left(x\\right)$'
beta = Function('beta')
assert latex(beta(x)) == r"$\operatorname{beta}\left(x\right)$"
assert latex(sin(x)) == r"$\operatorname{sin}\left(x\right)$"
assert latex(sin(x), fold_func_brackets=True) == r"$\operatorname{sin}x$"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"$\operatorname{sin}2 x^{2}$"
assert latex(factorial(k)) == r"$k!$"
assert latex(factorial(-k)) == r"$\left(- k\right)!$"
assert latex(floor(x)) == r"$\lfloor{x}\rfloor$"
assert latex(ceiling(x)) == r"$\lceil{x}\rceil$"
assert latex(abs(x)) == r"$\lvert{x}\rvert$"
assert latex(re(x)) == r"$\Re{x}$"
assert latex(im(x)) == r"$\Im{x}$"
assert latex(conjugate(x)) == r"$\overline{x}$"
assert latex(gamma(x)) == r"$\operatorname{\Gamma}\left(x\right)$"
assert latex(Order(x)) == r"$\operatorname{\mathcal{O}}\left(x\right)$"
def run_Lagrange_interp_abs_conv(N=[3, 6, 12, 24]):
f = sp.abs(1 - 2 * x)
f = sp.sin(2 * sp.pi * x)
fn = sp.lambdify([x], f, modules='numpy')
resolution = 50001
import numpy as np
xcoor = np.linspace(0, 1, resolution)
fcoor = fn(xcoor)
Einf = []
E2 = []
h = []
for _N in N:
psi, points = Lagrange_polynomials_01(x, _N)
u = interpolation(f, psi, points)
un = sp.lambdify([x], u, modules='numpy')
ucoor = un(xcoor)
e = fcoor - ucoor
Einf.append(e.max())
E2.append(np.sqrt(np.sum(e * e / e.size)))
h.append(1. / _N)
print Einf
print E2
print h
print N
# Assumption: error = CN**(-N)
print 'convergence rates:'
for i in range(len(E2)):
C1 = E2[i] / (N[i]**(-N[i] / 2))
C2 = Einf[i] / (N[i]**(-N[i] / 2))
print N[i], C1, C2
def run_Lagrange_interp_abs_conv(N=[3, 6, 12, 24]):
f = sm.abs(1-2*x)
f = sm.sin(2*sm.pi*x)
fn = sm.lambdify([x], f, modules='numpy')
resolution = 50001
import numpy as np
xcoor = np.linspace(0, 1, resolution)
fcoor = fn(xcoor)
Einf = []
E2 = []
h = []
for _N in N:
psi, points = Lagrange_polynomials_01(x, _N)
u = interpolation(f, psi, points)
un = sm.lambdify([x], u, modules='numpy')
ucoor = un(xcoor)
e = fcoor - ucoor
Einf.append(e.max())
E2.append(np.sqrt(np.sum(e*e/e.size)))
h.append(1./_N)
print Einf
print E2
print h
print N
# Assumption: error = CN**(-N)
print 'convergence rates:'
for i in range(len(E2)):
C1 = E2[i]/(N[i]**(-N[i]/2))
C2 = Einf[i]/(N[i]**(-N[i]/2))
print N[i], C1, C2
def sp_derive():
import sympy as sp
vars = 'G_s, s_n, s_p_n, w_n, dw_n, ds_n, G_s, G_w, c, phi'
syms = sp.symbols(vars)
for var, sym in zip(vars.split(','), syms):
globals()[var.strip()] = sym
s_n1 = s_n + ds_n
w_n1 = w_n + dw_n
tau_trial = G_s * (s_n1 - s_p_n)
print('diff', sp.diff(tau_trial, ds_n))
print(tau_trial)
sig_n1 = G_w * w_n1
print(sig_n1)
tau_fr = (c + sig_n1 * sp.tan(phi)) * \
sp.Heaviside(sig_n1 - c / sp.tan(phi))
print(tau_fr)
d_tau_fr = sp.diff(tau_fr, dw_n)
print(d_tau_fr)
f_trial = sp.abs(tau_trial) - tau_fr
print(f_trial)
d_gamma = f_trial / G_s
print('d_gamma')
sp.pretty_print(d_gamma)
print('d_gamma_s')
sp.pretty_print(sp.diff(d_gamma, ds_n))
print('tau_n1')
tau_n1 = sp.simplify(tau_trial - d_gamma * G_s * sp.sign(tau_trial))
sp.pretty_print(tau_n1)
print('dtau_n1_w')
dtau_n1_w = sp.diff(tau_n1, dw_n)
sp.pretty_print(dtau_n1_w)
print('dtau_n1_s')
dtau_n1_s = sp.diff(d_gamma * sp.sign(tau_trial), ds_n)
print(dtau_n1_s)
s_p_n1 = s_p_n + d_gamma * sp.sign(tau_trial)
print(s_p_n1)
def test_latex_functions():
assert latex(exp(x)) == "$e^{x}$"
assert latex(exp(1)+exp(2)) == "$e + e^{2}$"
f = Function('f')
assert latex(f(x)) == '$\\operatorname{f}\\left(x\\right)$'
beta = Function('beta')
assert latex(beta(x)) == r"$\operatorname{beta}\left(x\right)$"
assert latex(sin(x)) == r"$\operatorname{sin}\left(x\right)$"
assert latex(sin(x), fold_func_brackets=True) == r"$\operatorname{sin}x$"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"$\operatorname{sin}2 x^{2}$"
assert latex(factorial(k)) == r"$k!$"
assert latex(factorial(-k)) == r"$\left(- k\right)!$"
assert latex(floor(x)) == r"$\lfloor{x}\rfloor$"
assert latex(ceiling(x)) == r"$\lceil{x}\rceil$"
assert latex(abs(x)) == r"$\lvert{x}\rvert$"
assert latex(re(x)) == r"$\Re{x}$"
assert latex(im(x)) == r"$\Im{x}$"
assert latex(conjugate(x)) == r"$\overline{x}$"
assert latex(gamma(x)) == r"$\operatorname{\Gamma}\left(x\right)$"
assert latex(Order(x)) == r"$\operatorname{\mathcal{O}}\left(x\right)$"
def sp_derive():
import sympy as sp
vars = 'G_s, s_n, s_p_n, w_n, dw_n, ds_n, G_s, G_w, c, phi'
syms = sp.symbols(vars)
for var, sym in zip(vars.split(','), syms):
globals()[var.strip()] = sym
s_n1 = s_n + ds_n
w_n1 = w_n + dw_n
tau_trial = G_s * (s_n1 - s_p_n)
print 'diff', sp.diff(tau_trial, ds_n)
print tau_trial
sig_n1 = G_w * w_n1
print sig_n1
tau_fr = (c + sig_n1 * sp.tan(phi)) * sp.Heaviside(sig_n1 - c / sp.tan(phi))
print tau_fr
d_tau_fr = sp.diff(tau_fr, dw_n)
print d_tau_fr
f_trial = sp.abs(tau_trial) - tau_fr
print f_trial
d_gamma = f_trial / G_s
print 'd_gamma'
sp.pretty_print(d_gamma)
print 'd_gamma_s'
sp.pretty_print(sp.diff(d_gamma, ds_n))
print 'tau_n1'
tau_n1 = sp.simplify(tau_trial - d_gamma * G_s * sp.sign(tau_trial))
sp.pretty_print(tau_n1)
print 'dtau_n1_w'
dtau_n1_w = sp.diff(tau_n1, dw_n)
sp.pretty_print(dtau_n1_w)
print 'dtau_n1_s'
dtau_n1_s = sp.diff(d_gamma * sp.sign(tau_trial), ds_n)
print dtau_n1_s
s_p_n1 = s_p_n + d_gamma * sp.sign(tau_trial)
print s_p_n1
def chop(expr, tol = 1e-10):
"""suppress small numerical values"""
expr = sp.expand(sp.sympify(expr))
if expr.is_Symbol: return expr
assert expr.is_Add
return sp.Add(*[term for term in expr.as_Add() if sp.abs(term.as_coeff_terms()[0]) >= tol])
def abs(*args, **kw):
arg0 = args[0]
if isinstance(arg0, (int, float, long)):
return _math.abs(*args,**kw)
elif isinstance(arg0, complex):
return _cmath.abs(*args,**kw)
elif isinstance(arg0, _sympy.Basic):
return _sympy.abs(*args,**kw)
else:
return _numpy.abs(*args,**kw)
def run_Lagrange_leastsq_abs(N):
"""Least-squares with of Lagrange polynomials for |1-2x|."""
f = sm.abs(1-2*x)
# This f will lead to failure of sympy integrate, fallback on numerical int.
psi, points = Lagrange_polynomials_01(x, N)
Omega=[0, 1]
u = least_squares(f, psi, Omega)
comparison_plot(f, u, Omega, filename='Lagrange_ls_abs_%d.pdf' % (N+1),
plot_title='Least squares approximation by '\
'Lagrange polynomials of degree %d' % N)
def run_Lagrange_leastsq_abs(N):
"""Least-squares with of Lagrange polynomials for |1-2x|."""
f = sp.abs(1 - 2 * x)
# This f will lead to failure of sympy integrate, fallback on numerical int.
psi, points = Lagrange_polynomials_01(x, N)
Omega = [0, 1]
u = least_squares(f, psi, Omega)
comparison_plot(f, u, Omega, filename='Lagrange_ls_abs_%d' % (N+1),
plot_title='Least squares approximation by '\
'Lagrange polynomials of degree %d' % N)
def abs(*args, **kw):
arg0 = args[0]
if isinstance(arg0, (int, float, long)):
return _math.abs(*args,**kw)
elif isinstance(arg0, complex):
return _cmath.abs(*args,**kw)
elif isinstance(arg0, _sympy.Basic):
return _sympy.abs(*args,**kw)
else:
return _numpy.abs(*args,**kw)
def Generalized_Legendre(self, n=0, m=0, x=x):
mode = self.select_exec_mode(x)
if mode != "undef":
legendre_polinomial = self.Legendre(n=n, x=x)
rat_part = (1 - (x ** 2)) ** (sympy.abs(m) / 2.0)
diff_part = sympy.diff(legendre_polinomial, x, abs(m))
return (rat_part * diff_part).expand()
else:
return False
def Phi_Equation(self, m="undef", phi=phi):
if m == "undef":
m = self.m_val
m = int(m)
mode = self.select_exec_mode(phi)
if mode == "numer":
phi_val = self.phi
self.phi = Symbol("phi")
elif mode == "custom_var":
self.phi = Symbol(phi)
elif mode == "undef":
return False
left_part = 1 / sympy.sqrt(2 * sympy.pi)
right_part = sympy.cos(sympy.abs(m) * self.phi) if m >= 0 else sympy.sin(sympy.abs(m) * self.phi)
if mode == "numer":
return (left_part * right_part).evalf()
elif mode == "analit" or mode == "custom_var":
return (left_part * right_part).expand()
def R_par(m, theta_i):
"""
Fraction of parallel-polarized light that is reflected (R_p).
Calculate reflected fraction of incident power (or flux) assuming that
the E-field of the incident light is parallel to the plane of incidence
Args:
m : complex index of refraction [-]
theta_i : incidence angle from normal [radians]
Returns:
reflected power [-]
"""
return sympy.abs(r_par_amplitude(m, theta_i))**2
def R_per(m, theta_i):
"""
Fraction of perpendicular-polarized light that is reflected (R_s).
Calculates reflected fraction of incident power (or flux) assuming that
the E-field of the incident light is perpendicular to the plane of incidence
Args:
m : complex index of refraction [-]
theta_i : incidence angle from normal [radians]
Returns:
reflected irradiance [-]
"""
return sympy.abs(r_per(m, theta_i))**2
def l2_norm(f, lim):
"""
Calculates L2 norm of the function "f", over the domain lim=(x, a, b).
x ...... the independent variable in f over which to integrate
a, b ... the limits of the interval
Example:
>>> l2_norm(1, (x, -1, 1))
2**(1/2)
>>> l2_norm(x, (x, -1, 1))
1/3*6**(1/2)
"""
return sqrt(integrate(abs(f)**2, lim))
def test_maxima_functions():
assert parse_maxima('expand( (x+1)^2)') == x**2 + 2*x + 1
assert parse_maxima('factor( x**2 + 2*x + 1)') == (x+1)**2
assert parse_maxima('trigsimp(2*cos(x)^2 + sin(x)^2)') == 2 - sin(x)**2
assert parse_maxima('trigexpand(sin(2*x)+cos(2*x))') == (-1) + 2*cos(x)**2 + 2*cos(x)*sin(x)
assert parse_maxima('solve(x^2-4,x)') == [2, -2]
assert parse_maxima('limit((1+1/x)^x,x,inf)') == E
assert parse_maxima('limit(sqrt(-x)/x,x,0,minus)') == -oo
assert parse_maxima('diff(x^x, x)') == x**x*(1 + log(x))
assert parse_maxima('sum(k, k, 1, n)') == (n**2 +n)/2
assert parse_maxima('product(k, k, 1, n)',
name_dict=dict(
n=Symbol('n',integer=True),
k=Symbol('k',integer=True)
)
) == factorial(n)
assert parse_maxima('ratsimp((x^2-1)/(x+1))') == x-1
assert abs( parse_maxima('float(sec(%pi/3) + csc(%pi/3))') - 3.154700538379252) < 10**(-5)
def T_per(m, theta_i):
"""
Fraction of perpendicular-polarized light that is transmitted (T_s).
Calculate transmitted fraction of incident power (or flux) assuming that
the E-field of the incident light is perpendicular to the plane of incidence
Args:
m : complex index of refraction [-]
theta_i : incidence angle from normal [radians]
Returns:
transmitted field amplitude [-]
"""
c = sympy.cos(theta_i)
s = sympy.sin(theta_i)
d = sympy.sqrt(m * m - s * s) # m*cos(theta_t)
ts = 2 * c / (c + d)
return d / c * sympy.abs(ts)**2
def T_par(m, theta_i):
"""
Fraction of parallel-polarized light that is transmitted (T_p).
Calculate transmitted fraction of incident power (or flux) assuming that
the E-field of the incident light is parallel to the plane of incidence
Args:
m : complex index of refraction [-]
theta_i : incidence angle from normal [radians]
Returns:
transmitted irradiance [-]
"""
c = sympy.cos(theta_i)
s = sympy.sin(theta_i)
d = sympy.sqrt(m * m - s * s) # m*cos(theta_t)
tp = 2 * c * m / (m * m * c + d)
return d / c * sympy.abs(tp)**2
def test_maxima_functions():
assert parse_maxima('expand( (x+1)^2)') == x**2 + 2 * x + 1
assert parse_maxima('factor( x**2 + 2*x + 1)') == (x + 1)**2
assert parse_maxima('trigsimp(2*cos(x)^2 + sin(x)^2)') == 2 - sin(x)**2
assert parse_maxima('trigexpand(sin(2*x)+cos(2*x))') == (
-1) + 2 * cos(x)**2 + 2 * cos(x) * sin(x)
assert parse_maxima('solve(x^2-4,x)') == [2, -2]
assert parse_maxima('limit((1+1/x)^x,x,inf)') == E
assert parse_maxima('limit(sqrt(-x)/x,x,0,minus)') == -oo
assert parse_maxima('diff(x^x, x)') == x**x * (1 + log(x))
assert parse_maxima('sum(k, k, 1, n)') == (n**2 + n) / 2
assert parse_maxima('product(k, k, 1, n)',
name_dict=dict(n=Symbol('n', integer=True),
k=Symbol('k',
integer=True))) == factorial(n)
assert parse_maxima('ratsimp((x^2-1)/(x+1))') == x - 1
assert abs(
parse_maxima('float(sec(%pi/3) + csc(%pi/3))') -
3.154700538379252) < 10**(-5)
def test_latex_functions():
assert latex(exp(x)) == "e^{x}"
assert latex(exp(1)+exp(2)) == "e + e^{2}"
f = Function('f')
assert latex(f(x)) == '\\operatorname{f}\\left(x\\right)'
beta = Function('beta')
assert latex(beta(x)) == r"\operatorname{beta}\left(x\right)"
assert latex(sin(x)) == r"\operatorname{sin}\left(x\right)"
assert latex(sin(x), fold_func_brackets=True) == r"\operatorname{sin}x"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"\operatorname{sin}2 x^{2}"
assert latex(sin(x**2), fold_func_brackets=True) == \
r"\operatorname{sin}x^{2}"
assert latex(asin(x)**2) == r"\operatorname{asin}^{2}\left(x\right)"
assert latex(asin(x)**2,inv_trig_style="full") == \
r"\operatorname{arcsin}^{2}\left(x\right)"
assert latex(asin(x)**2,inv_trig_style="power") == \
r"\operatorname{sin}^{-1}\left(x\right)^{2}"
assert latex(asin(x**2),inv_trig_style="power",fold_func_brackets=True) == \
r"\operatorname{sin}^{-1}x^{2}"
assert latex(factorial(k)) == r"k!"
assert latex(factorial(-k)) == r"\left(- k\right)!"
assert latex(floor(x)) == r"\lfloor{x}\rfloor"
assert latex(ceiling(x)) == r"\lceil{x}\rceil"
assert latex(abs(x)) == r"\lvert{x}\rvert"
assert latex(re(x)) == r"\Re{x}"
assert latex(im(x)) == r"\Im{x}"
assert latex(conjugate(x)) == r"\overline{x}"
assert latex(gamma(x)) == r"\operatorname{\Gamma}\left(x\right)"
assert latex(Order(x)) == r"\operatorname{\mathcal{O}}\left(x\right)"
def test_latex_functions():
assert latex(exp(x)) == "e^{x}"
assert latex(exp(1)+exp(2)) == "e + e^{2}"
f = Function('f')
assert latex(f(x)) == '\\operatorname{f}\\left(x\\right)'
beta = Function('beta')
assert latex(beta(x)) == r"\operatorname{beta}\left(x\right)"
assert latex(sin(x)) == r"\operatorname{sin}\left(x\right)"
assert latex(sin(x), fold_func_brackets=True) == r"\operatorname{sin}x"
assert latex(sin(2*x**2), fold_func_brackets=True) == \
r"\operatorname{sin}2 x^{2}"
assert latex(sin(x**2), fold_func_brackets=True) == \
r"\operatorname{sin}x^{2}"
assert latex(asin(x)**2) == r"\operatorname{asin}^{2}\left(x\right)"
assert latex(asin(x)**2,inv_trig_style="full") == \
r"\operatorname{arcsin}^{2}\left(x\right)"
assert latex(asin(x)**2,inv_trig_style="power") == \
r"\operatorname{sin}^{-1}\left(x\right)^{2}"
assert latex(asin(x**2),inv_trig_style="power",fold_func_brackets=True) == \
r"\operatorname{sin}^{-1}x^{2}"
assert latex(factorial(k)) == r"k!"
assert latex(factorial(-k)) == r"\left(- k\right)!"
assert latex(floor(x)) == r"\lfloor{x}\rfloor"
assert latex(ceiling(x)) == r"\lceil{x}\rceil"
assert latex(abs(x)) == r"\lvert{x}\rvert"
assert latex(re(x)) == r"\Re{x}"
assert latex(im(x)) == r"\Im{x}"
assert latex(conjugate(x)) == r"\overline{x}"
assert latex(gamma(x)) == r"\operatorname{\Gamma}\left(x\right)"
assert latex(Order(x)) == r"\operatorname{\mathcal{O}}\left(x\right)"
def SGN_S(x):
return x/abs(x)
def test_ccode_exceptions():
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(abs(x)) == "fabs(x)"
def eval_cross_section(N_atoms_uc, csection, kaprange, tau_list, eig_list, kapvect, wtlist,
fflist, temperature, eief = True, efixed = 14.7):
"""
N_atoms_uc - number of atoms in unit cell
csection - analytic cross-section expression
kaprange - kappa modulus
kapvect - list of kappa vectors
tau_list - list of taus
eig_list - list of eigenvalues
wtlist - list of omegas
fflist - magnetic form factor list
temperature - temperature
eief - True => E_initial = efixed, False => E_final = efixed
efixed - fixed energy; either E_final or E_initial, subject to eief
"""
print "begin part 2"
# Kappa vector
kap = sp.Symbol('kappa', real = True)
t = sp.Symbol('t', real = True)
w = sp.Symbol('w', real = True)
tau = sp.Symbol('tau', real = True)
Q = sp.Symbol('q', real = True)
L = sp.Symbol('L', real = True)
wq = sp.Symbol('wq', real = True)
kapxhat = sp.Symbol('kapxhat',real=True)
kapyhat = sp.Symbol('kapyhat',real=True)
kapzhat = sp.Symbol('kapzhat',real=True)
kapunit = kapvect.copy()
kapunit[:,0]=kapvect[:,0]/kaprange
kapunit[:,1]=kapvect[:,1]/kaprange
kapunit[:,2]=kapvect[:,2]/kaprange
# Front constants and stuff for the cross-section
boltz = 8.617343e-2
gamr0 = 1.913*2.818
hbar = 1#6.582*10**-13
g = 2.0
temperature = temperature
debye_waller = 1.0 #exp(-2*W)
front_constant = ((gamr0**2)*debye_waller/(2*pi*hbar)).evalf() #(gamr0)**2#/(2*pi*hbar)
print front_constant
# kappa, omegas, tau, eigs
temp1 = []
for kapi in range(len(kapvect)):
temp2 =[]
for wi in range(len(wtlist)):
temp3=[]
for taui in range(len(tau_list)):
print 'k,w,t',kapi,wi,taui
ws=[]
csectempp = deepcopy(csection)
csectempm = deepcopy(csection)
#qvalp = kapvect[kapi] - tau_list[taui] + qmins
#qvalm = kapvect[kapi] - tau_list[taui] - qplus
csectempp = csectempp.subs(sp.DiracDelta(kap - Q - tau),sp.S(1))
csectempp = csectempp.subs(sp.DiracDelta(kap + Q - tau),sp.S(0))
csectempm = csectempm.subs(sp.DiracDelta(kap - Q - tau),sp.S(0))
csectempm = csectempm.subs(sp.DiracDelta(kap + Q - tau),sp.S(1))
csectempp = csectempp.subs(kapxhat,kapunit[kapi,0])
csectempp = csectempp.subs(kapyhat,kapunit[kapi,1])
csectempp = csectempp.subs(kapzhat,kapunit[kapi,2])
csectempm = csectempm.subs(kapxhat,kapunit[kapi,0])
csectempm = csectempm.subs(kapyhat,kapunit[kapi,1])
csectempm = csectempm.subs(kapzhat,kapunit[kapi,2])
for eigi in range(len(eig_list[taui])):
eigcsecp=deepcopy(csectempp)
eigcsecm=deepcopy(csectempm)
eigtemp = deepcopy(eig_list[0][eigi])
spinmag = sp.Symbol('S', real = True)
kx = sp.Symbol('kx', real = True)
ky = sp.Symbol('ky', real = True)
kz = sp.Symbol('kz', real = True)
eigtemp = eigtemp.subs(spinmag, sp.S(1.0))
eigtemp = eigtemp.subs(kx, kapvect[kapi][0])
eigtemp = eigtemp.subs(ky, kapvect[kapi][1])
eigtemp = eigtemp.subs(kz, kapvect[kapi][2])
eigtemp = sp.abs(eigtemp.evalf(chop=True))
# sp.Pow( sp.exp(-np.abs(eig_list[0][eigi])/boltz) - 1 ,-1) #\temperature term taken out
nval = sp.Pow(sp.exp(sp.abs(eigtemp)/(boltz*temperature))-1,-1).evalf()
for i in range(N_atoms_uc):
nq = sp.Symbol('n%i'%(i,), real = True)
eigcsecp = eigcsecp.subs(nq,nval)
eigcsecm = eigcsecm.subs(nq,nval)
wvalp = eigtemp - wtlist[wi]
wvalm = eigtemp + wtlist[wi]
eigcsecp = eigcsecp.subs((w-wq),wvalp)
eigcsecp = eigcsecp.subs((w+wq),wvalm)
eigcsecp = sp.re(eigcsecp.evalf(chop = True))
eigcsecm = eigcsecm.subs((w-wq),wvalp)
eigcsecm = eigcsecm.subs((w+wq),wvalm)
eigcsecm = sp.re(eigcsecm.evalf(chop = True))
# if np.abs(wvalp) < 0.1:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w - wq), sp.S(1))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(w - wq), sp.S(0))
# else:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w - wq), sp.S(0))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(w - wq), sp.S(0))
# if np.abs(wvalm) < 0.1:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w + wq), sp.S(0))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(w + wq), sp.S(1))
# else:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w + wq), sp.S(0))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(wq + w), sp.S(0))
# eief == True => ei=efixed
# eief == False => ef=efixed
kpk = 0.
if eief == True:
ei = efixed
ef = ei - eigtemp
kpk = ef/ei
else:
ef = efixed
ei = ef + eigtemp
kpk = ef/ei
ws.append(kpk*(eigcsecp+eigcsecm))
temp3.append(sum(ws))
temp2.append(np.sum(np.array(temp3)))
temp1.append(temp2)
temp1 = np.array(temp1)
csdata = np.array(sp.re(temp1.T))
print csdata.shape
#Multiply data by front constants
csdata = front_constant*csdata
#Multiply by Form Factor
print fflist.shape
csdata = fflist*csdata
return kapvect, wtlist, csdata
def test_parser():
assert abs(parse_maxima('float(1/3)') - 0.333333333) < 10**(-5)
assert parse_maxima('13^26') == 91733330193268616658399616009
assert parse_maxima('sin(%pi/2) + cos(%pi/3)') == Rational(3, 2)
assert parse_maxima('log(%e)') == 1
def test_ccode_exceptions():
assert ccode(ceiling(x)) == "ceil(x)"
assert ccode(abs(x)) == "fabs(x)"
def test_parser():
assert abs(parse_maxima('float(1/3)') - 0.333333333) < 10**(-5)
assert parse_maxima('13^26') == 91733330193268616658399616009
assert parse_maxima('sin(%pi/2) + cos(%pi/3)') == Rational(3,2)
assert parse_maxima('log(%e)') == 1
def eval_cross_section(N_atoms_uc, csection, kaprange, tau_list, eig_list, kapvect, wtlist,
fflist, temperature, eief = True, efixed = 14.7):
"""
N_atoms_uc - number of atoms in unit cell
csection - analytic cross-section expression
kaprange - kappa modulus
kapvect - list of kappa vectors
tau_list - list of taus
eig_list - list of eigenvalues
wtlist - list of omegas
fflist - magnetic form factor list
temperature - temperature
eief - True => E_initial = efixed, False => E_final = efixed
efixed - fixed energy; either E_final or E_initial, subject to eief
"""
print "Begin Numerical Evaluation of Cross-Section"
kapunit = kapvect.copy()
kapunit[:,0]=kapvect[:,0]/kaprange
kapunit[:,1]=kapvect[:,1]/kaprange
kapunit[:,2]=kapvect[:,2]/kaprange
temperature = temperature
front_constant = ((GAMMA_R0_VALUE**2)*DEBYE_WALLER_VALUE/(2*pi*HBAR_VALUE)).evalf() #(gamr0)**2#/(2*pi*hbar)
print front_constant
# kappa, omegas, tau, eigs
temp1 = []
for kapi in range(len(kapvect)):
temp2 =[]
for wi in range(len(wtlist)):
temp3=[]
for taui in range(len(tau_list)):
# print 'k,w,t',kapi,wi,taui
ws=[]
#qplus = kapvect[kapi] + tau_list[taui]
#qmins = tau_list[taui] - kapvect[kapi]
csectempp = copy(csection)
csectempm = copy(csection)
#qvalp = kapvect[kapi] - tau_list[taui] + qmins
#qvalm = kapvect[kapi] - tau_list[taui] - qplus
csectempp = csectempp.subs(DD_KTMQ_SYM,sp.S(1))
csectempp = csectempp.subs(DD_KTPQ_SYM,sp.S(0))
csectempm = csectempm.subs(DD_KTMQ_SYM,sp.S(0))
csectempm = csectempm.subs(DD_KTPQ_SYM,sp.S(1))
# csectempp = csectempp.subs(sp.DiracDelta(KAP_SYM - Q_SYM - TAU_SYM),sp.S(1))
# csectempp = csectempp.subs(sp.DiracDelta(KAP_SYM + Q_SYM - TAU_SYM),sp.S(0))
# csectempm = csectempm.subs(sp.DiracDelta(KAP_SYM - Q_SYM - TAU_SYM),sp.S(0))
# csectempm = csectempm.subs(sp.DiracDelta(KAP_SYM + Q_SYM - TAU_SYM),sp.S(1))
# print 'm'
# print csectempm
# print 'p'
# print csectempp
csectempp = csectempp.subs(KAPXHAT_SYM,kapunit[kapi,0])
csectempp = csectempp.subs(KAPYHAT_SYM,kapunit[kapi,1])
csectempp = csectempp.subs(KAPZHAT_SYM,kapunit[kapi,2])
csectempm = csectempm.subs(KAPXHAT_SYM,kapunit[kapi,0])
csectempm = csectempm.subs(KAPYHAT_SYM,kapunit[kapi,1])
csectempm = csectempm.subs(KAPZHAT_SYM,kapunit[kapi,2])
for eigi in range(len(eig_list[taui])):
eigcsecp=copy(csectempp)
eigcsecm=copy(csectempm)
# print 'a'
# print eigcsecp
# print eigcsecm
eigtemp = copy(eig_list[0][eigi])
# print 'eig', eigtemp
# print 'kappa'
# print kapvect[kapi][0]
# print kapvect[kapi][1]
# print kapvect[kapi][2]
eigtemp = eigtemp.subs(S_SYM, sp.S(1.0))
eigtemp = eigtemp.subs(KX_SYM, kapvect[kapi][0])
eigtemp = eigtemp.subs(KY_SYM, kapvect[kapi][1])
eigtemp = eigtemp.subs(KZ_SYM, kapvect[kapi][2])
eigtemp = sp.abs(eigtemp.evalf(chop=True))
# sp.Pow( sp.exp(-np.abs(eig_list[0][eigi])/boltz) - 1 ,-1) #\temperature term taken out
# print 'eig'
# print eigtemp.evalf()
# print 'a'
# print eigcsecp
# print eigcsecm
nval = sp.Pow(sp.exp(sp.abs(eigtemp)/(BOLTZ_VALUE*temperature))-1,-1).evalf()
for i in range(N_atoms_uc):
nq = sp.Symbol('n%i'%(i,), real = True)
eigcsecp = eigcsecp.subs(nq,nval)
eigcsecm = eigcsecm.subs(nq,nval)
# print 'b'
# print eigcsecp
# print eigcsecm
wvalp = eigtemp - wtlist[wi]
wvalm = eigtemp + wtlist[wi]
# print 'w vals'
# print wvalp
# print wvalm
eigcsecp = eigcsecp.subs((W_SYM - WQ_SYM),wvalp)
eigcsecp = eigcsecp.subs((W_SYM + WQ_SYM),wvalm)
eigcsecp = sp.re(eigcsecp.evalf(chop = True))
eigcsecm = eigcsecm.subs((W_SYM - WQ_SYM),wvalp)
eigcsecm = eigcsecm.subs((W_SYM + WQ_SYM),wvalm)
eigcsecm = sp.re(eigcsecm.evalf(chop = True))
# if np.abs(wvalp) < 0.1:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w - wq), sp.S(1))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(w - wq), sp.S(0))
# else:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w - wq), sp.S(0))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(w - wq), sp.S(0))
# if np.abs(wvalm) < 0.1:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w + wq), sp.S(0))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(w + wq), sp.S(1))
# else:
# eigcsecp = eigcsecp.subs(sp.DiracDelta(w + wq), sp.S(0))
# eigcsecm = eigcsecm.subs(sp.DiracDelta(wq + w), sp.S(0))
#
# print 'p'
# print eigcsecp
# print 'm'
# print eigcsecm
# eief == True => ei=efixed
# eief == False => ef=efixed
kpk = 0.
if eief == True:
ei = efixed
ef = ei - eigtemp
kpk = ef/ei
else:
ef = efixed
ei = ef + eigtemp
kpk = ef/ei
ws.append(kpk*(eigcsecp+eigcsecm))
temp3.append(sum(ws))
temp2.append(np.sum(np.array(temp3)))
temp1.append(temp2)
temp1 = np.array(temp1)
csdata = np.array(sp.re(temp1.T))
print csdata.shape
#Multiply data by front constants
#csdata = front_constant*csdata
#Multiply by Form Factor
print fflist.shape
csdata = (0.5*G_VALUE*fflist)**2*csdata
return kapvect, wtlist, csdata
def Square_Wave_Function_Ion_Negative(self, R="undef"):
if R == "undef":
R = self.R
return sympy.abs(self.Wave_Function_Ion_Negative(R)) ** 2
def single_cross_section_calc(theta, phi, rad, N_atoms_uc, atom_list, csection, tau, eig_list, wt,
temperature, eief = True, efixed = 14.7):
temperature = temperature
front_constant = ((GAMMA_R0_VALUE**2)*DEBYE_WALLER_VALUE/(2*pi*HBAR_VALUE)).evalf()
kx = rad*np.sin(theta)*np.cos(phi)
ky = rad*np.sin(theta)*np.sin(phi)
kz = rad*np.cos(theta)
kap = np.array([kx,ky,kz])
kapunit = kap.copy()
kapunit[0]=kap[0]/rad
kapunit[1]=kap[1]/rad
kapunit[2]=kap[2]/rad
ws=[]
#csectempp = deepcopy(csection) #good
#csectempm = deepcopy(csection) #good
csectempp = copy(csection) #good
csectempm = copy(csection) #good
cs_expr = sp.lambdify((KAP_SYM,Q_SYM,TAU_SYM,W_SYM,WQ_SYM,KAPXHAT_SYM,KAPYHAT_SYM,KAPZHAT_SYM), expr2, modules = "numpy")
#res_np = expr_np(Svals[:,newaxis,newaxis,newaxis],xvals[newaxis,:,newaxis,newaxis],yvals[newaxis,newaxis,:,newaxis],zvals[newaxis,newaxis,newaxis,:])
res_np2 = expr_np2(xvals[:,newaxis,newaxis],yvals[newaxis,:,newaxis],zvals[newaxis,newaxis,:])
csectempp = csectempp.subs(sp.DiracDelta(KAP_SYM - Q_SYM - TAU_SYM),sp.S(1))
csectempp = csectempp.subs(sp.DiracDelta(KAP_SYM + Q_SYM - TAU_SYM),sp.S(0))
csectempm = csectempm.subs(sp.DiracDelta(KAP_SYM - Q_SYM - TAU_SYM),sp.S(0))
csectempm = csectempm.subs(sp.DiracDelta(KAP_SYM + Q_SYM - TAU_SYM),sp.S(1))
csectempp = csectempp.subs(KAPXHAT_SYM,kapunit[0])
csectempp = csectempp.subs(KAPYHAT_SYM,kapunit[1])
csectempp = csectempp.subs(KAPZHAT_SYM,kapunit[2])
csectempm = csectempm.subs(KAPXHAT_SYM,kapunit[0])
csectempm = csectempm.subs(KAPYHAT_SYM,kapunit[1])
csectempm = csectempm.subs(KAPZHAT_SYM,kapunit[2])
for eigi in range(len(eig_list)):
#eigcsecp=deepcopy(csectempp) #good
#eigcsecm=deepcopy(csectempm)
#eigtemp = deepcopy(eig_list[0][eigi])
eigcsecp=copy(csectempp) #good
eigcsecm=copy(csectempm)
eigtemp = copy(eig_list[0][eigi])
eig_expr = sp.lambdify((S_SYM,KX_SYM,KY_SYM,KZ_SYM), sp.abs(eigtemp))#, modules = "numpy")
eigval = eig_expr(S(1.0),kap[0],kap[1],kap[2]).evalf(chop=True)
eigtemp = eigtemp.subs(S_SYM, sp.S(1.0))
eigtemp = eigtemp.subs(KX_SYM, kap[0])
eigtemp = eigtemp.subs(KY_SYM, kap[1])
eigtemp = eigtemp.subs(KZ_SYM, kap[2])
eigtemp = sp.abs(eigtemp.evalf(chop=True)) #works
#eigtemp = chop(np.abs(eigtemp))
nval = sp.Pow(sp.exp(eigtemp/(BOLTZ_VALUE*temperature))-1,-1).evalf() #works
#nval = np.power(np.exp(np.abs(eigtemp)/(BOLTZ*temperature))-1,-1)
for i in range(N_atoms_uc):
nq = sp.Symbol('n%i'%(i,), real = True)
eigcsecp = eigcsecp.subs(nq,nval)
eigcsecm = eigcsecm.subs(nq,nval)
wvalp = eigtemp - wt
wvalm = eigtemp + wt
eigcsecp = eigcsecp.subs((W_SYM - WQ_SYM),wvalp)
eigcsecp = eigcsecp.subs((W_SYM + WQ_SYM),wvalm)
eigcsecp = sp.re(eigcsecp.evalf(chop = True)) # works
#eigcsecp = chop(eigcsecp)
eigcsecm = eigcsecm.subs((W_SYM - WQ_SYM),wvalp)
eigcsecm = eigcsecm.subs((W_SYM + WQ_SYM),wvalm)
eigcsecm = sp.re(eigcsecm.evalf(chop = True)) #works
#eigcsecm = chop(eigcsecm)
# eief == True => ei=efixed
# eief == False => ef=efixed
kpk = 0.
if eief == True:
ei = efixed
ef = ei - eigtemp
kpk = ef/ei
else:
ef = efixed
ei = ef + eigtemp
kpk = ef/ei
ws.append(kpk*(eigcsecp+eigcsecm))
csdata = sp.re(sum(ws))
#Multiply data by front constants
csdata = front_constant*csdata
#Multiply by Form Factor
csdata = G_VALUE*csdata
#print kx,'\t\t',ky,'\t\t',kz,'\t\t',csdata
return csdata#*np.sin(theta)*rad**2
lf = lambdify_t(f)
tt = np.arange(dt,t+dt,dt)
return lf(tt).sum() * dt
_gexpr = gamma_expr(5.4, 5.2) - 0.35 * gamma_expr(10.8, 7.35)
_gexpr = _gexpr / _getint(_gexpr)
_glover = lambdify_t(_gexpr)
glover = implemented_function('glover', _glover)
glovert = lambdify_t(glover(T))
# Derivative of Glover HRF
_dgexpr = _gexpr.diff(T)
dpos = sympy.Derivative((T >= 0), T)
_dgexpr = _dgexpr.subs(dpos, 0)
_dgexpr = _dgexpr / _getint(sympy.abs(_dgexpr))
_dglover = lambdify_t(_dgexpr)
dglover = implemented_function('dglover', _dglover)
dglovert = lambdify_t(dglover(T))
del(_glover); del(_gexpr); del(dpos); del(_dgexpr); del(_dglover)
# AFNI's HRF
_aexpr = ((T >= 0) * T)**8.6 * sympy.exp(-T/0.547)
_aexpr = _aexpr / _getint(_aexpr)
_afni = lambdify_t(_aexpr)
afni = implemented_function('afni', _afni)
afnit = lambdify_t(afni(T))
return lf(tt).sum() * dt
deft = DeferredVector('t')
_gexpr = gamma_params(5.4, 5.2) - 0.35 * gamma_params(10.8,7.35)
_gexpr = _gexpr / _getint(_gexpr)
_glover = vectorize(_gexpr)
glover = aliased_function('glover', _glover)
n = {}
glovert = vectorize(glover(deft))
# Derivative of Glover HRF
_dgexpr = _gexpr.diff(t)
dpos = Derivative((t >= 0), t)
_dgexpr = _dgexpr.subs(dpos, 0)
_dgexpr = _dgexpr / _getint(abs(_dgexpr))
_dglover = vectorize(_dgexpr)
dglover = aliased_function('dglover', _dglover)
dglovert = vectorize(dglover(deft))
del(_glover); del(_gexpr); del(dpos); del(_dgexpr); del(_dglover)
# AFNI's HRF
_aexpr = ((t >= 0) * t)**8.6 * exp(-t/0.547)
_aexpr = _aexpr / _getint(_aexpr)
_afni = vectorize(_aexpr)
afni = aliased_function('afni', _afni)
afnit = vectorize(afni(deft))
# Primitive of the HRF -- temoprary fix to handle blocks
def gen_mag(self, ident, val):
return sym.abs(val.exp)
def test_abs():
assert str(abs(x)) == "abs(x)"
assert str(abs(Rational(1,6))) == "1/6"
assert str(abs(Rational(-1,6))) == "1/6"
def test_abs():
assert str(abs(x)) == "abs(x)"
assert str(abs(Rational(1, 6))) == "1/6"
assert str(abs(Rational(-1, 6))) == "1/6"
def single_cross_section_calc(theta, phi, rad, N_atoms_uc, atom_list, csection, tau, eig_list, wt,
temperature, eief = True, efixed = 14.7):
temperature = temperature
front_constant = ((GAMMA_R0_VALUE**2)*DEBYE_WALLER_VALUE/(2*pi*HBAR_VALUE)).evalf()
kx = rad*np.sin(theta)*np.cos(phi)
ky = rad*np.sin(theta)*np.sin(phi)
kz = rad*np.cos(theta)
kap = np.array([kx,ky,kz])
# kapunit = kap.copy()
# kapunit[0]=kap[0]/rad
# kapunit[1]=kap[1]/rad
# kapunit[2]=kap[2]/rad
ws=[]
#csectempp = deepcopy(csection) #good
#csectempm = deepcopy(csection) #good
csectempp = copy(csection) #good
csectempm = copy(csection) #good
csectempp = csectempp.subs(DD_KTMQ_SYM,sp.S(1))
csectempp = csectempp.subs(DD_KTPQ_SYM,sp.S(0))
csectempm = csectempm.subs(DD_KTMQ_SYM,sp.S(0))
csectempm = csectempm.subs(DD_KTPQ_SYM,sp.S(1))
# csectempp = csectempp.subs(sp.DiracDelta(KAP_SYM - Q_SYM - TAU_SYM),sp.S(1))
# csectempp = csectempp.subs(sp.DiracDelta(KAP_SYM + Q_SYM - TAU_SYM),sp.S(0))
# csectempm = csectempm.subs(sp.DiracDelta(KAP_SYM - Q_SYM - TAU_SYM),sp.S(0))
# csectempm = csectempm.subs(sp.DiracDelta(KAP_SYM + Q_SYM - TAU_SYM),sp.S(1))
csectempp = csectempp.subs(KAPXHAT_SYM,kap[0]/rad)
csectempp = csectempp.subs(KAPYHAT_SYM,kap[1]/rad)
csectempp = csectempp.subs(KAPZHAT_SYM,kap[2]/rad)
csectempm = csectempm.subs(KAPXHAT_SYM,kap[0]/rad)
csectempm = csectempm.subs(KAPYHAT_SYM,kap[1]/rad)
csectempm = csectempm.subs(KAPZHAT_SYM,kap[2]/rad)
# eig_list = eig_list[0].tolist()
# eig_func = sp.lambdify((S_SYM,KX_SYM,KY_SYM,KZ_SYM),eig_list,modules="numpy")
# eigens = np.abs(np.array(eig_func(sp.S(1,0),kx,ky,kz)))
# cs_func = sp.lambdify((DD_KTPQ_SYM,DD_KTMQ_SYM,KAPXHAT_SYM,KAPYHAT_SYM,KAPZHAT_SYM,W_SYM,WQ_SYM)
# ,[csection,csection],modules="numpy")
# csvals = cs_func([1,0],[0,1],kap[0]/rad,kap[1]/rad,kap[2]/rad,)
for eigi in range(len(eig_list)):
# for eigi in eigens:
#eigcsecp=deepcopy(csectempp) #good
#eigcsecm=deepcopy(csectempm)
#eigtemp = deepcopy(eig_list[0][eigi])
eigcsecp=copy(csectempp) #good
eigcsecm=copy(csectempm)
eigtemp = copy(eig_list[0][eigi]) #good
eigtemp = eigtemp.subs(S_SYM, sp.S(1.0))
eigtemp = eigtemp.subs(KX_SYM, kap[0])
eigtemp = eigtemp.subs(KY_SYM, kap[1])
eigtemp = eigtemp.subs(KZ_SYM, kap[2])
eigtemp = sp.abs(eigtemp.evalf(chop=True)) #works
#eigtemp = chop(np.abs(eigtemp))
# nval = sp.Pow(sp.exp(eigi/(BOLTZ_VALUE*temperature))-1,-1).evalf()
#nval = sp.Pow(sp.exp(eigtemp/(BOLTZ_VALUE*temperature))-1,-1).evalf() #works
#nval = np.power(np.exp(np.abs(eigtemp)/(BOLTZ*temperature))-1,-1)
nval = sp.S(0)
for i in range(N_atoms_uc):
nq = sp.Symbol('n%i'%(i,), real = True)
eigcsecp = eigcsecp.subs(nq,nval)
eigcsecm = eigcsecm.subs(nq,nval)
wvalp = eigtemp - wt
wvalm = eigtemp + wt
# wvalp = eigi - wt
# wvalm = eigi + wt
eigcsecp = eigcsecp.subs((W_SYM - WQ_SYM),wvalp)
eigcsecp = eigcsecp.subs((W_SYM + WQ_SYM),wvalm)
eigcsecp = sp.re(eigcsecp.evalf(chop = True)) # works
#eigcsecp = chop(eigcsecp)
eigcsecm = eigcsecm.subs((W_SYM - WQ_SYM),wvalp)
eigcsecm = eigcsecm.subs((W_SYM + WQ_SYM),wvalm)
eigcsecm = sp.re(eigcsecm.evalf(chop = True)) #works
#eigcsecm = chop(eigcsecm)
# eief == True => ei=efixed
# eief == False => ef=efixed
kpk = 0.
if eief == True:
ei = efixed
# ef = ei - eigi
ef = ei - eigtemp
kpk = ef/ei
else:
ef = efixed
# ef = ei + eigi
ei = ef + eigtemp
kpk = ef/ei
ws.append(kpk*(eigcsecp+eigcsecm))
csdata = sp.re(sum(ws))
#Multiply data by front constants
csdata = front_constant*csdata
# CHECK THIS! THIS IS IMPORTANT AND MAY SCREW THINGS UP
#Multiply by Form Factor
ff = 0
for i in range(N_atoms_uc):
el = elements[atom_list[i].atomicNum]
val = atom_list[i].valence
if val != None:
Mq = el.magnetic_ff[val].M_Q(rad)
else:
Mq = el.magnetic_ff[0].M_Q(rad)
ff = Mq
csdata = (0.5*G_VALUE*ff)**2*csdata
#print kx,'\t\t',ky,'\t\t',kz,'\t\t',csdata
return csdata#*np.sin(theta)*rad**2
plotlist = np.array([[(k+1)/256., vtrans[k%256]] for k in range(768)])
plt.plot(plotlist[:,0], plotlist[:,1])
# what does the following line do?
plt.axhline(0)
# add labels
plt.show()
plot3(1, 2700.0)
plot3(1/3., 200.0)
plot3(3.0, 5.0)
eq2 = (ir * (r + 1/(1j*omega*c) + 1j*omega*l) + vo - 1,
ir - (1j*omega*c + 1/(1j*omega*l)) * vo)
sol2 = # complete this line
vos2 = simplify(sol2[vo])
irs = simplify(sol2[ir])
# why should irs be passed to sympy.abs() before squaring?
power = (r**2) *( sympy.abs(irs)**2)
flist3 = [sympy.abs(vos2.subs(numvalue).subs({r: 10.0*3**s}))
for s in range(0, 3)]
omega_axis = np.linspace(10000, 70000, 1000)
lines = # ...
# what does plt.setp() do?
plt.setp(lines[0], lw=2)
plt.setp(lines[1], ls='--'
# add labels and ticks
plt.minorticks_on()
plt.show()
# replicate fig. 2.10
