Mathematica Looping through vectorized functions for a piecewise solution

[member 428835]

Hi PF!

Can someone explain the second line of the proposed solution on this thread to me

https://mathematica.stackexchange.com/questions/138919/how-to-implement-a-loop-inside-piecewise

Specifically, I have a function un(x) that looks like

I am trying to make this function piecewise such that un[x][[1]] is plotted over a domain $x\in(0,2h)$ and then un[x][[2]] $x\in(2h,4h)$. I'm unsure how to loop through this procedure. Ultimately un[x] will have many more components, so automating this would be helpful.

Thanks!

 

[Dale]

Can someone explain the second line of the proposed solution on this thread to me

It is just a list of powers of x.

 

[member 428835]

It is just a list of powers of x.

Oh shoot, I said second but I meant first. Sorry, it's been a busy day.

 

[Dale]

The hashtags and the ampersand denote a “pure function” that is not given a name. It is a very useful construction, I highly recommend learning to use them.

http://reference.wolfram.com/language/tutorial/PureFunctions.html

Once that function is defined it is applied to {0,1,2}

 

[member 428835]

The hashtags and the ampersand denote a “pure function” that is not given a name. It is a very useful construction, I highly recommend learning to use them.

http://reference.wolfram.com/language/tutorial/PureFunctions.html

Once that function is defined it is applied to {0,1,2}

Got it! Looked it up and it makes sense. However, the following code seems to only fork when I put $x$ in the table (I get results if I put $x+1-1$ and also if I put a constant) but if I put $2x$ or $x+1$ I do not get an output. Any ideas?

h = 0.25;
cond = 2 (# - 1) h < x < 2 # h & /@ Range[1, 1/(2 h)];
f = Table[x+1, {i, 1, 1/(2 h)}];
g = Piecewise[Transpose[{f, cond}]];
Plot[g, {x, 0, 1}, PlotRange -> {{0, 1}, {0, 3}}]
[code/]

 

[DrClaude]

f = Table[x+1, {i, 1, 1/(2 h)}];

This only create a certain number of copies of the same function (here $x+1$).

 

[member 428835]

This only create a certain number of copies of the same function (here $x+1$).

Yea, I think I had to clear my Kernal. For some reason it was only allowing $x$ and not something like $x+1$. I have it working now and finally understand (to some level) pure functions! Thanks all!