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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 O$_2$scl interpolation example for O$_2$sclpy
See the O$_2$sclpy documentation at
https
Step1:  Link the o2scl library
Step2:  Create a sample function to interpolate
Step3:  Create sample data from our function
Step4:  Compute the mean and standard deviation so that we can normalize the data
Step5:  Copy the data into std_vector objects
Step6:  Create the interpolators
Step7:  Create a Gaussian process from sklearn to perform the interpolation. Like the O$_2$scl class interp_krige_optim, this is a simple one-parameter version which only varies the length scale.
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Python Code:
import o2sclpy
import matplotlib.pyplot as plot
import sys
import math
import numpy
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, ConstantKernel
plots=True
if 'pytest' in sys.modules:
    plots=False
Explanation: O$_2$scl interpolation example for O$_2$sclpy
See the O$_2$sclpy documentation at
https://neutronstars.utk.edu/code/o2sclpy for more information.
End of explanation
link=o2sclpy.linker()
link.link_o2scl()
Explanation: Link the o2scl library:
End of explanation
def f(x):
    return math.sin(1.0/(0.3+x))
Explanation: Create a sample function to interpolate:
End of explanation
xa=[0 for i in range(0,20)]
ya=[0 for i in range(0,20)]
for i in range(0,20):
    if i>0:
        xa[i]=xa[i-1]+((i)/40)**2
    ya[i]=math.sin(1.0/(0.3+xa[i]))
Explanation: Create sample data from our function:
End of explanation
m=numpy.mean(ya)
s=numpy.std(ya,ddof=1)
print('mean: %7.6e, std: %7.6e' % (m,s))
ya2=[(ya[i]-m)/s for i in range(0,20)]
Explanation: Compute the mean and standard deviation so that we can normalize the data:
End of explanation
xp=o2sclpy.std_vector(link)
yp=o2sclpy.std_vector(link)
xp.resize(20)
yp.resize(20)
for i in range(0,20):
    xp[i]=xa[i]
    yp[i]=ya2[i]
Explanation: Copy the data into std_vector objects:
End of explanation
iv_lin=o2sclpy.interp_vec(link)
iv_lin.set(20,xp,yp,o2sclpy.itp_linear)
iv_csp=o2sclpy.interp_vec(link)
iv_csp.set(20,xp,yp,o2sclpy.itp_cspline)
iv_aki=o2sclpy.interp_vec(link)
iv_aki.set(20,xp,yp,o2sclpy.itp_akima)
iv_mon=o2sclpy.interp_vec(link)
iv_mon.set(20,xp,yp,o2sclpy.itp_monotonic)
iv_stef=o2sclpy.interp_vec(link)
iv_stef.set(20,xp,yp,o2sclpy.itp_steffen)
iv_ko=o2sclpy.interp_krige_optim(link)
iv_ko.set(20,xp,yp,True)
plot.plot(xa,ya,lw=0,marker='+')
plot.plot(xa,[iv_lin.eval(xa[i])*s+m for i in range(0,20)])
plot.plot(xa,[iv_csp.eval(xa[i])*s+m for i in range(0,20)])
plot.plot(xa,[iv_aki.eval(xa[i])*s+m for i in range(0,20)])
plot.plot(xa,[iv_mon.eval(xa[i])*s+m for i in range(0,20)])
plot.plot(xa,[iv_stef.eval(xa[i])*s+m for i in range(0,20)])
plot.plot(xa,[iv_ko.eval(xa[i])*s+m for i in range(0,20)])
max=xa[19]
xb=[i/2000.0*max for i in range(0,2001)]
xa2=numpy.array(xa).reshape(-1,1)
Explanation: Create the interpolators:
End of explanation
kernel=RBF(1.0,(1.0e-2,1.0e2))
gpr=GaussianProcessRegressor(kernel=kernel).fit(xa2,ya)
for hyperparameter in gpr.kernel_.hyperparameters:
    print('hp',hyperparameter)
params = gpr.kernel_.get_params()
for key in sorted(params):
    print("kp: %s : %s" % (key, params[key]))
params2=gpr.get_params()
for key in sorted(params2):
    print("gpp: %s : %s" % (key, params2[key]))
plot.rcParams['figure.figsize'] = [11, 9]
plot.semilogy(xb,[abs(f(xb[i])-(iv_lin.eval(xb[i])*s+m)) 
                  for i in range(0,2001)],color='black',lw=0.5,label='linear')
plot.semilogy(xb,[abs(f(xb[i])-(iv_csp.eval(xb[i])*s+m)) 
                  for i in range(0,2001)],color='red',lw=0.5,label='cubic spline')
plot.semilogy(xb,[abs(f(xb[i])-(iv_stef.eval(xb[i])*s+m)) 
                  for i in range(0,2001)],color='blue',lw=0.5,label='steffen')
plot.semilogy(xb,[abs(f(xb[i])-(iv_ko.eval(xb[i])*s+m)) 
                  for i in range(0,2001)],color='purple',lw=0.5,label='GP o2scl')
plot.semilogy(xb,[abs(f(xb[i])-(gpr.predict(numpy.array(xb[i]).reshape(-1,1)))) 
                  for i in range(0,2001)],color='green',lw=0.5,label='GP sklearn')
plot.legend()
Explanation: Create a Gaussian process from sklearn to perform the interpolation. Like the O$_2$scl class interp_krige_optim, this is a simple one-parameter version which only varies the length scale.
End of explanation
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