Span (#24)

* Changing chebyshev implementation to remove numpy dependencies
* Update span.py

pina/chebyshev.py

@@ -1,7 +1,9 @@
-import numpy as np
+import torch
+
+
 def chebyshev_roots(n):
     """ Return the roots of *n* Chebyshev polynomials (between [-1, 1]) """
-    coefficents = np.zeros(n+1)
-    coefficents[-1] = 1
-    return np.polynomial.chebyshev.chebroots(coefficents)
-
+    pi = torch.acos(torch.zeros(1)).item() * 2
+    k = torch.arange(n)
+    nodes = torch.sort(torch.cos(pi * (k + 0.5) / n))[0]
+    return nodes

pina/span.py

@@ -1,4 +1,3 @@
-import numpy as np
 from .chebyshev import chebyshev_roots
 import torch
 
@@ -32,20 +31,20 @@ class Span(Location):
         """
         """
         if mode == 'random':
-            pts = np.random.uniform(size=(n, 1))
+            pts = torch.rand(size=(n, 1))
         elif mode == 'chebyshev':
-            pts = np.array([chebyshev_roots(n) * .5 + .5]).reshape(-1, 1)
+            pts = chebyshev_roots(n).mul(.5).add(.5).reshape(-1, 1)
         elif mode == 'grid':
-            pts = np.linspace(0, 1, n).reshape(-1, 1)
+            pts = torch.linspace(0, 1, n).reshape(-1, 1)
         elif mode == 'lh' or mode == 'latin':
             from scipy.stats import qmc
             sampler = qmc.LatinHypercube(d=1)
             pts = sampler.random(n)
+            pts = torch.from_numpy(pts)
 
         pts *= bounds[1] - bounds[0]
         pts += bounds[0]
 
-        pts = pts.astype(np.float32)
         return pts
 
     def sample(self, n, mode='random', variables='all'):
@@ -56,10 +55,9 @@ class Span(Location):
         result = None
         for variable in variables:
             if variable in self.range_.keys():
-                bound = np.asarray(self.range_[variable])
+                bound = torch.tensor(self.range_[variable])
                 pts_variable = self._sample_range(n, mode, bound)
-                pts_variable = LabelTensor(
-                    torch.from_numpy(pts_variable), [variable])
+                pts_variable = LabelTensor(pts_variable, [variable])
 
             elif variable in self.fixed_.keys():
                 value = self.fixed_[variable]