import numpy
import pylab
from numpy import zeros, ones, linspace, kron, linalg, exp, sqrt, diag, \
arctan, pi
from arbinterp import interp_1d
from compinterp import lagrange_1d, linear_1d, spline_1d
CASE = 'runge'
def func(x):
f = 1.0 / (1.0 + x**2)
return f
pylab.matplotlib.interactive(False)
n = 10
x = linspace(-5, 5, n)
y = func(x)
y = interp_1d(y, x, fx)
# 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
dxall = exp(numpy.random.normal(size=xall.size) * 0.5) * 0.02
exall = dxall * numpy.random.normal(size=xall.size)
for n in n_list:
x = xall[:n]
dx = dxall[:n]
fx = func(x) + exall[:n]
fy, sig = interp_1d(y, x, fx, dx, 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.bar(x, x*0, bottom=fx, yerr=dx, width=0, ecolor='k')
pylab.plot(numpy.array([x,x]), numpy.array([fx+dx, fx-dx]), color='k', \
linewidth=3)
# pylab.plot(x, fx+dx, 'v', color='k')
# pylab.plot(x, fx-dx, '^', color='k')
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())])
y = linspace(-5, 5, 250)
fye, fype = func(y)
pylab.figure(figsize=(5,3))
pylab.plot(y, fye, '-k')
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 = [], []
linf_g, l2_g = [], []
for n in n_list:
x = linspace(-5, 5, n)
fx, fpx = func(x)
fy_g, sig_g = interp_1d(y, x, fx, None, x, fpx, compute_dfz=True)
fy, sig = interp_1d(y, x, fx, compute_dfz=True)
pylab.figure(figsize=(5,3))
pylab.plot(y, fye, '--k')
pylab.plot(y, fy_g, '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
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='center', fontsize=16)
pylab.savefig('output/%s/uniform_%s_grad_1d_%03d.png' % (CASE, CASE, n))
linf.append(abs(fy-fye).max())
from compinterp import lagrange_1d pylab.matplotlib.interactive(False) gamma = 16.0 y = linspace(0, 1, 250) fye = exp(-((y-0.5)*16)**2) n_list = range(4, 50, 4) linf, l2 = [], [] xall = (cos(random.random(size=n_list[-1]) * pi) + 1) / 2.0 for n in n_list: x = xall[:n] fx = exp(-((x-0.5)*16)**2) fy, sig = interp_1d(y, x, fx, gamma, compute_sigma=True) fy_l = lagrange_1d(y, x, fx) if abs(fy_l).max() > 1.0E3: fy_l[:] = 0.0 sig[sig>1000] = 1000; sig[sig<-1000] = -1000 pylab.figure() pylab.plot(y, fy, 'b') pylab.plot(y, fy + sig, ':b') pylab.plot(y, fy - sig, ':b') pylab.plot(y, fy_l, '-.g') pylab.plot(y, fye, '--r') pylab.plot(x, fx, '+') pylab.ylim([-0.2, 1.2]) linf.append(abs(fy-fye).max()) l2.append(sqrt(((fy-fye)**2).sum())) print n, linf[-1], l2[-1]
