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## RE: Convert array to function

 From: Allen.Windhorn Subject: RE: Convert array to function Date: Fri, 19 Dec 2014 14:56:38 +0000

```Marco,

> -----Original Message-----
> From: address@hidden
>
> I have a curve that is described as a vector v with n-elements,
> each containing a pair:
>
>   v=[0,0; 2,2; 4,2; 6,6; 10,6]
>
> ASCII-art visualised:
>
>    ^
>    |
>  10|
>    |
>   8|
>    |
>   6|           xxxxxxxxx
>    |          x
>   4|         x
>    |        x
>   2|   xxxxx
>    |  x
>    +---------------------->
>    0   2   4   6   8   10
>
> I am only interested in the x-range [0:10] meaning the values below
> 0 and above 10 can be ignored.
>
> Vector v is given and I have to define a function that evaluates to
> the points described by the vector. The points are always connected
> by straight lines. So the function should (with the example values
> for v as stated above) at point 1 evaluate to 1, at point 2
> evaluate to 2, at point 8 evaluate to 6, etc.
>
> The pairs are not necessarily equally spaced and the number of
> elements in v is not constant. (This will be automated and the v is
> the input I receive.)
>
> The question: Is there an octave function which I can feed the
> vector with pairs (v) and obtain a function which I can evaluate at
> any point within the range?

Linear interpolation using interp1 works.

octave:3>  v=[0,0; 2,2; 4,2; 6,6; 10,6]
v =

0    0
2    2
4    2
6    6
10    6

% Split the vector into x and y parts:
octave:4> x = v(:,1)
xx =

0
2
4
6
10

octave:5> y = v(:,2)
yy =

0
2
2
6
6

% Make a function from the table:
octave:11> f = @(x) interp1(xx, yy, x);

% See if it works:
octave:11> x = 0:0.5:10
octave:12> y = f(x);
octave:13> plot(x,y)

% Success!

Regards,
Allen
```

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