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

[Ben Abbott]

On Aug 21, 2012, at 7:42 AM, vivek dogra wrote:

> On Tue, Aug 21, 2012 at 4:34 PM, Ben Abbott <address@hidden> wrote:
> 
>> On Aug 21, 2012, at 4:26 AM, vivek dogra wrote:
>> 
>> > Hello,
>> > Currently, interp1.m allows at most one identical pair of values in X.  My 
>> > concern is should it really do that? My arguments are as follows:
>> >
>> > In my opinion repeated values should not be allowed for interpolation. 
>> > Let's say i have following data points:
>> >
>> >  x  f(x)
>> > 0    4
>> > 1    6
>> > 2    8
>> > 3    10
>> >
>> > Now if i want to get f(1.5) then i will take the value midway between f(1) 
>> > and f(2) which would be 7. Now in case i have repeated values the data 
>> > points will be:
>> >
>> > x   f(x)
>> > 0    4
>> > 1    6
>> > 1    7
>> > 2    8
>> > 3   10
>> >
>> > Now in this case what f(1.5) will be? 7 or 7.5? (What will you call the 
>> > best interpolation?) There will be ambiguity in this case. Also in the 
>> > present case the sample points are nicely behaving so there is not much 
>> > difference between 7 and 7.5. Although in some cases (if let's say f(1) = 
>> > 6 and f(1) = 9) there can be lot of difference between answers when we 
>> > choose one data point over another.
>> > So Octave should not allow repeated x values.
>> 
>> Is the ambiguity due to a lack of clarity of the documentation, or does 
>> interp1() not work in a consistent manner?
>> 
>> Ben
> 
> If we go by the documentation, then interp1.m is doing fine (which in turn 
> creates confusion as to how the interp1 works).
> 
> "The discontinuous interpolant is right-continuous if @var{x} is increasing, 
> left-continuous if it is decreasing." 
> 
> I am not able to digest this statement "if @var{x} is increasing or 
> decreasing". Increasing with respect to what? 
> And what will happen in case when X is neither increasing nor decreasing.  

Increasing or descreasing with respect to X ... meaning is the original X 
increasing or decreasing.  If X is unsorted, then it will be sorted with 
increasing values.

Ben