Linear interpolation between two values is rather simple:
def lerp(v, d):
return v[0] * (1 - d) + v[1] * d
print lerp(np.array([3, 5]), 0.75)
> 4.5
Let generalize it to arbitrary tensors of shape (2, 2, …), i.e.:
def lerp(v, d):
assert len(v.shape) >= 1 and d.shape == (len(v.shape),)
if len(v.shape) == 1:
assert v.shape[0] == 2
dd = np.array([1 - d[0], d[0]], dtype=v.dtype)
return sum(v * dd)
else:
v = [lerp(submatrix, d[1:]) for submatrix in v]
return lerp(np.array(v), d[:1])
assert lerp(np.array([3.0, 4.0]), np.array([0.75])) == 3.75
assert lerp(
np.array(xrange(8), dtype='float64').reshape((2,2,2)),
np.array([0.25, 0.5, 0.75])
) == 2.75
It works when every value is a scalar, but does not when the individual values are tensors and the shapes are not like asserted above. For instance:
assert all(lerp(
np.array([[1.0, 2.0], [3.0, 4.0]]),
np.array([0.75])
) == np.array([ 2.5, 3.5]))
How to implement that with pure numpy, without python recursion, playing with array indices etc. so that it work also with tensor values? Is there any numpy function for that?
