Re: Should interp1.m function allow jumps in X-values?

[Ben Abbott]

On Aug 21, 2012, at 10:35 AM, Juan Pablo Carbajal wrote:

> On Tue, Aug 21, 2012 at 3:26 PM, vivek dogra <address@hidden> wrote:
>> On Tue, Aug 21, 2012 at 6:30 PM, Michael D Godfrey
>> <address@hidden> wrote:
>>> 
>>> On 08/21/2012 08:57 AM, vivek dogra wrote:
>>> 
>>> Although if it has identical values then it is always favoring increasing
>>> order
>>> 
>>> I think you need to read the code again taking into account:
>>> 
>>> octave:1> X = [ 1 2 2 3];
>>> octave:2> issorted(X)
>>> ans =  1
>>> 
>> 
>> Sorry i am not able to make myself clear. My understanding of the code is as
>> follows:
>> 
>> ## check whether x is sorted; sort if not.
>>  if (! issorted (x, "either"))
>> ## Check if X is sorted either in ascending or descending order.
>>    [x, p] = sort (x);
>> ##  If it is not sorted, sort it  ("X is sorted in ascending order by
>> default")
>>    y = y(p,:);
>>  endif
>> 
>> My point:
>> 1st case: X having distinct values, everything is alright!
>> 
>> 2nd case: X is increasing or decreasing (sorted) and X has at most one
>> identical pair. interp1 gives answer as mentioned in the documentation.
>> 
>> 3rd case: X is neither increasing nor decreasing (unsorted) and have
>> identical values ==> Octave will always sort it in ascending order.
>> 
>> In the following example which is 3rd case (X is unsorted and and have
>> identical values):
>> 
>> 
>> X = [ 2 1 3 2];
>> Y = [ 2 1 3 10];                               # i get 10 because of some
>> error in an experiment
>> 
>> Now because Octave will always sort it in ascending order, i.e. After
>> sorting:
>> 
>> X = [ 1 2 2 3];
>> Y = [ 1 2 10 3];
>> 
>> Now as X is increasing now it is right continuous therefore to interpolate
>> Octave will use value of 2 as 10, which is incorrect. (Octave has decided
>> for the user)
>> 
>> Please reply to this situation. I would like to have a discussion on what
>> will happen in some practical situation like this?
> 
> I repeat.
> If X there are repeated values of X with different values of Y. You
> can't do interpolation. It is not defined, no continuous function can
> go through your values. You may want to fix you data or do a
> regression.
> 
> interp1 calculates an interpolant, so it should either ignore the
> repeated values or give an error. If it does some other calculation,
> and therefore not returning an interpolant, it should give a warning.


I agree that linear piece-wise continuous interpolation is not possible for 
repeated values of X.  However, discontinuous interpolation is not only 
possible but has is already implemented by interp1.m, and is documented in its 
doc-string.

If I understand Vivek's concern, the issue is how to tell interp1() that the 
interpolant is to produce a left-continuous or right-continuous output.  
Perhaps, we should support an option? What about "-right" and "-left", with 
"-right" being the default when X is unsorted?

        X = [ 2 1 3 2];
        Y = [ 2 1 3 10]; 
        x = 1:0.5:3
        y_right = interp1 (X, Y, x, "-right")
        y_left = interp1 (X, Y, x, "-left")

Ben