# def func(x):
# f = exp(-x**2)
# f[x<0] *= -1
# return f
n = 9 # number of data points
# ========================= Tune this =========================
y = linspace(-5, 5, 250)
fye = func(y)
x = linspace(-5, 5, n)
fx = func(x)
# --------- use of interp1d class ----------
interp = interp_1d(x, fx, l=1, verbose=0)
fy, sig = interp.interp(y, compute_df=True)
# ------------------------------------------
pylab.figure(figsize=(10,6))
pylab.plot(y, fye, '--r')
pylab.plot(y, fy, 'k')
pylab.plot(y, fy + 3*sig, ':b')
pylab.plot(y, fy - 3*sig, ':b')
pylab.plot(x, fx, 'ok')
pylab.ylim([fye.min()-0.2*(fye.max()-fye.min()), \
fye.max()+0.2*(fye.max()-fye.min())])
pylab.xlabel('$x$', verticalalignment='center', fontsize=16);
pylab.ylabel('$f(x)$', horizontalalignment='right', fontsize=16)
linf = abs(fy-fye).max()
pylab.ylim([fye.min()-0.2*(fye.max()-fye.min()), \
fye.max()+0.2*(fye.max()-fye.min())])
pylab.savefig('output/%s/%s_exact.png' % (CASE, CASE))
# my interpolation
linf, l2 = [], []
xall = []
for line in file('quasi-random/niederreiter_1d.txt').readlines():
xall.append(float(line))
xall = numpy.array(xall) * 10 - 5
for n in n_list:
x = xall[:n]
fx = func(x)
fy, sig = interp_1d(y, x, fx, compute_dfz=True)
pylab.figure(figsize=(5,3))
pylab.plot(y, fye, '--k')
pylab.plot(y, fy, 'k')
# pylab.plot(y, fy + sig, ':b')
# pylab.plot(y, fy - sig, ':b')
# pylab.plot(y, fy_l, '-.g')
pylab.plot(x, fx, 'ok')
margin = 0.2
if CASE == 'step': margin = 0.5
pylab.ylim([fye.min()-margin*(fye.max()-fye.min()), \
fye.max()+margin*(fye.max()-fye.min())])
pylab.xlabel('$x$', verticalalignment='center', fontsize=16);
pylab.ylabel('$f(x)$', horizontalalignment='right', fontsize=16)
pylab.savefig('output/%s/random_%s_1d_%03d.png' % (CASE, CASE, n))
linf.append(abs(fy-fye).max())