def test_exponential(self):
degree = 5
p = approximate_taylor_polynomial(np.exp, 0, degree, 1, 15)
for i in xrange(degree+1):
assert_almost_equal(p(0),1)
p = p.deriv()
assert_almost_equal(p(0),0)
def test_exponential(self):
degree = 5
p = approximate_taylor_polynomial(np.exp, 0, degree, 1, 15)
for i in xrange(degree+1):
assert_almost_equal(p(0),1)
p = p.deriv()
assert_almost_equal(p(0),0)
def taylor(self, gr, x, degree):
def f(grs):
res = []
for i in grs:
res += [self.npv(gr=i)]
return res
#approx = approximate_taylor_polynomial(f, x=x, degree=degree, scale=gr)
return approximate_taylor_polynomial(f, x=x, degree=degree, scale=gr)
def _get_polynomial(self, order, scale):
# this is the function for K, given a normalized (0,1) bandwidth
def f(x):
return (np.tan(x / 2) - 1) / (np.tan(x / 2) + 1)
# calculate taylor series coefficients
p = approximate_taylor_polynomial(f,
x=self.x0,
degree=order,
scale=scale)
return p.coeffs.astype('float32')
def _get_polynomial(self, order, scale):
# this is the function for the gain, given a normalized bandwidth
def f(x):
return 1 / (1 + np.tan(x * np.pi / 2))
# calculate taylor series coefficients
p = approximate_taylor_polynomial(f,
x=self.x0,
degree=order,
scale=scale)
return p.coeffs.astype('float32')
def pade_propagator_coefs_m(*, pade_order, diff2, k0, dx, spe=False, alpha=0):
if spe:
def sqrt_1plus(x):
return 1 + x / 2
elif alpha == 0:
def sqrt_1plus(x):
return np.sqrt(1 + x)
else:
raise Exception('alpha not supported')
def propagator_func(s):
return np.exp(1j * k0 * dx * (sqrt_1plus(diff2(s)) - 1))
taylor_coefs = approximate_taylor_polynomial(
propagator_func, 0, pade_order[0] + pade_order[1] + 5, 0.01)
p, q = pade(taylor_coefs, pade_order[0], pade_order[1])
pade_coefs = list(
zip_longest([-1 / complex(v) for v in np.roots(p)],
[-1 / complex(v) for v in np.roots(q)],
fillvalue=0.0j))
return pade_coefs
from scipy import sin
xvals = np.linspace(-10, 10)
def fitfunc(x):
"""Function to fit with Taylor series."""
return sin(x)
yf = fitfunc(xvals)
x0 = 0
n = 2
scale = 0.5
tfit = approximate_taylor_polynomial(fitfunc, x0, n, scale)
yt = tfit(xvals)
# create bokeh data sources for the two graphs
fsource = ColumnDataSource(data=dict(x=xvals, y=yf))
tsource = ColumnDataSource(data=dict(x=xvals, y=yt))
# Set up plot
plot = figure(plot_height=400,
plot_width=600,
title="Series Approximation",
tools="crosshair,pan,reset,save,wheel_zoom",
y_range=[-2, 2],
x_range=[-6, 6])
# colors are dark for use in the dark optics labs