I have written some code to determine an interpolation matrix over a grid of points. I originally wrote the code in matlab, where under the specified parameters it took just over 2 minutes. The equivalent code in Python however takes 40minutes!

I was expecting Python to be slower, but not be such an amount! Any feedback on the code is much appreciated.

```
import numpy as np
from numpy import linalg as LA
def g(x, y):
gx = -x * (x ** 2 + y ** 2)
gy = -y * (x ** 2 + y ** 2)
return np.array((gx, gy))
def wendland(r):
if r < 1:
return ((1-r)**4)*(4*r+1)
else:
return 0
def make_collocation_points(h, x1, x2, y1, y2):
i = 0
x = ()
y = ()
for j in range(x1,x2+1):
for k in np.arange(y1, y2, h):
if LA.norm(g(j*h, k*h) - (j*h, k*h)) > 0.00001: # Don't accept values on the chain recurrent set!
x.append(j*h)
y.append(k*h)
i += 1
return x, y, i
def get_aij(x, y, n):
a = np.zeros((n,n))
for j in range(0, n):
for k in range(0, n):
a(j, k) = (
wendland(LA.norm(g(x(j), y(j)) - g(x(k), y(k))))
- wendland(LA.norm(g(x(j), y(j)) - np.array((x(k), y(k)))))
- wendland(LA.norm((x(j), y(j)) - g(x(k), y(k))))
+ wendland(LA.norm(np.array((x(j), y(j))) - np.array((x(k), y(k)))))
)
return a
if __name__ == "__main__":
h = 0.11
x1, x2 = -15, 15
y1, y2 = -15, 15
x, y, n = make_collocation_points(h, x1, x2, y1, y2)
a = get_aij(x, y, n)
```