# [Numpy-discussion] Vectorization of variant of piecewise or interpolation function

Juan Nunez-Iglesias jni.soma at gmail.com
Sun Oct 15 22:29:46 EDT 2017

```Hi Seth,

The function you’re looking for is `np.digitize`:

In [1]: t = np.array([0.5,1,1.5,2.5,3,10])
...: table = np.array([[0,3],[1,0],[2,5],[3,-1]])
...:
In [2]: lookup, values = table[:, 0], table[:, 1:]
In [3]: values = np.concatenate((values[0:1], values), axis=0)
In [4]: indices = np.digitize(t, lookup)
In [5]: values[indices]
Out[5]:
array([[ 3],
[ 0],
[ 0],
[ 5],
[-1],
[-1]])

Note the call to concatenate. Depending on how exactly you want your bins to align, you might need to concatenate at the end or at the start of the `values` array.

Hope this helps!

Juan.

On 16 Oct 2017, 1:17 PM +1100, Seth Ghandi <seth.ghandi.2017 at gmail.com>, wrote:
> Hi everybody,
>
> I am new to newpy and am trying to define a variant of piecewise or zero holder interpolation function, say ZeroOrderInterpolation(t,a), where t is an 1D array of size, say p, consisting of real numbers, and a is a 2D array of size, say nxm, with first column consisting of increasing real numbers. This function should return an array, say y, of size px(m-1) such that y[i,:] is equal to
> a[n,1:] if a[n,0] <= t[i], and
> a[k,1:] if k < n and a[k,0] <= t[i] < a[k+1,0].
> Note that t[0] is assumed to be at least equal to a[0,0].
>
> I have the following script made of "for loops" and I am trying to vectorize it so as to make it faster for large arrays.
>
> def ZeroOrderInterpolation(t,a):
> import numpy as np
> p = t.shape[0]
> n, m = a.shape
> if n == 1:
> return a[0,1:]
> y = np.zeros((p,m-1))
> for i in range(p):
> if a[n-1,0] <= t[i]:
> y[i] = a[n-1,1:]
> else:
> for j in range(n-1):
> if (a[j,0] <= t[i]) and (t[i] <= a[j+1,0]):
> y[i] = a[j,1:]
> return y
>
> import numpy as np
> t = np.array([0.5,1,1.5,2.5,3,10])
> table = np.array([[0,3],[1,0],[2,5],[3,-1]])
> ZeroOrderInterpolation(t,table)
>
> [Out]: array([[ 3.],
> [ 0.],
> [ 0.],
> [ 5.],
> [-1.],
> [-1.]])
>
>
> Any help for a vectorization "à la numpy" of this fucntion will be apprecaited.
>
> Best regards,
> _______________________________________________
> NumPy-Discussion mailing list
> NumPy-Discussion at python.org
> https://mail.python.org/mailman/listinfo/numpy-discussion
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