Add measured locations as parameters for approx1 and approx2

[shyams2]

I've implemented an interp1d and interp2d function similar to the one found in scipy. Rather than having the user manually transform the input points from [0, N-1] when using approx1 and approx2, this function takes care of the transformation by taking the input data points in addition to the interpolation points.

However, there is one issue: I'm using sum to get a scalar value:

dx   = sum(x_input[1, 0, 0, 0] - x_input[0, 0, 0, 0])
pos0 = (x_interpolated - sum(x_input[0, 0, 0, 0]))/dx

Do you recommend using something else?

[pavanky]

@ShyamSS-95 May be we can expand approx1 / approx2 by adding additional variables instead of introducing new functions ?

You could also convert the scaling into a function

@af.broadcast
def _scale_pos(x_orig, x_curr):
    x0 = x_orig[0, 0, 0, 0]
    dx   = af.abs(x_orig[1, 0, 0, 0] - x0)
    return (x_curr - x0) / dx

Since you are using broadcasting, you dont need to get the scalar outside.

[shyams2]

@pavanky I've made the changes to approx1/2 itself. Take a look and let me know if its fine :)

[pavanky]

@ShyamSS-95

1. I am a bit hesitant to change the variable names, but the original names were terrible so let me see if I can find out what other libs are calling them.

2. This breaks the behavior of old approx. I was thinking the new parameter will be optional.

[shyams2]

@pavanky

Ah OK. But I'm still not clear on how that would work. To clarify, would it be something like this?:

approx1(signal, pos0 = None, method=INTERP.LINEAR, off_grid=0.0,
        x_interpolated = None, x_input = None
       ):
   output = Array() 
   if(x_interpolated is not None and x_input is not None):
        pos0   = _scale_pos_axis0(x_interpolated, x_input)

    safe_call(backend.get().af_approx1(c_pointer(output.arr), signal.arr, pos0.arr,
                                       method.value, c_float_t(off_grid)))
   return output

Then for the old behaviour, this can be used:
approx1(signal, pos0)
For the interp1d like behaviour:
approx1(signal, x_interpolated = whatever, x_input = whatever)

[pavanky]

@ShyamSS-95 x_interpolated and pos0 should be the same thing?

[shyams2]

@pavanky

Oh. So, if x_interpolated alone is provided, then it is assumed to have pos0 form(when x_input is None)?

[pavanky]

@ShyamSS-95 yes

[shyams2]

@pavanky
I've made changes to retain the earlier approx behaviour as well. Let me know if it's alright, and what the variable names need to be changed to.

[pavanky]

One last thing, can you shorten the input names ? May be something like numpy? https://docs.scipy.org/doc/numpy/reference/generated/numpy.interp.html