In [1]:

    

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns


    

In [2]:

    

x=np.linspace(0,4*np.pi,10)
x


    

    
Out[2]:





array([  0.        ,   1.3962634 ,   2.7925268 ,   4.1887902 ,
         5.58505361,   6.98131701,   8.37758041,   9.77384381,
        11.17010721,  12.56637061])

In [4]:

    

f=np.sin(x)
f


    

    
Out[4]:





array([  0.00000000e+00,   9.84807753e-01,   3.42020143e-01,
        -8.66025404e-01,  -6.42787610e-01,   6.42787610e-01,
         8.66025404e-01,  -3.42020143e-01,  -9.84807753e-01,
        -4.89858720e-16])

In [5]:

    

plt.plot(x,f,marker='o')
plt.xlabel('x')
plt.ylabel('f(x)');


    

In [20]:

    

from scipy.interpolate import interp1d


    

In [12]:

    

x=np.linspace(0,4*np.pi,10)
f=np.sin(x)


    

In [22]:

    

sin_approx = interp1d(x, f, kind='cubic')


    

In [26]:

    

newx = np.linspace(0,4*np.pi,100)
newf = sin_approx(newx)


    

In [28]:

    

plt.plot(x, f, marker='o', linestyle='', label='original data')
plt.plot(newx, newf, marker='.', label='interpolated');
plt.legend();
plt.xlabel('x')
plt.ylabel('f(x)');


    

In [29]:

    

plt.plot(newx, np.abs(np.sin(newx)-sin_approx(newx)))
plt.xlabel('x')
plt.ylabel('Absolute error');


    

In [38]:

    

x = 4*np.pi*np.random.rand(15)
f = np.sin(x)


    

In [39]:

    

sin_approx = interp1d(x, f, kind='cubic')


    

In [40]:

    

newx = np.linspace(np.min(x), np.max(x),100)
newf = sin_approx(newx)


    

In [41]:

    

plt.plot(x,f,marker='o',linestyle='',label='original data')
plt.plot(newx, newf, marker='.', label='interpolated');
plt.legend();
plt.xlabel('x')
plt.ylabel('f(x)');


    

In [42]:

    

plt.plot(newx, np.abs(np.sin(newx)-sin_approx(newx)))
plt.xlabel('x')
plt.ylabel('Absolute error');


    

In [44]:

    

from scipy.interpolate import interp2d


    

In [47]:

    

def wave2d(x, y):
    return np.sin(2*np.pi*x)*np.sin(3*np.pi*y)


    

In [49]:

    

x = np.linspace(0.0,1.0,10)
y = np.linspace(0.0,1.0,10)


    

In [50]:

    

X, Y = np.meshgrid(x,y)
Z = wave2d(X,Y)


    

In [51]:

    

plt.pcolor(X, Y, Z)
plt.colorbar();
plt.scatter(X, Y);
plt.xlim(0,1)
plt.ylim(0,1)
plt.xlabel('x')
plt.ylabel('y');


    

In [ ]: