Tutorial for Map, Apply, etc

Question

I have this code:

g1[x_] := 1;
g2[x_] := x;
g3[x_] := x^2;
norm[r_, s_] := Integrate[r[x] s[x] + r'[x] s'[x], {x, 0, 1}];
gram = {
        {norm[g1, g1], norm[g1, g2], norm[g1, g3]},
        {norm[g2, g1], norm[g2, g2], norm[g2, g3]},
        {norm[g3, g1], norm[g3, g2], norm[g3, g3]}
       }

Which returns:

$$ \left( \begin{array}{ccc} 1 & \frac{1}{2} & \frac{1}{3} \\ \frac{1}{2} & \frac{4}{3} & \frac{5}{4} \\ \frac{1}{3} & \frac{5}{4} & \frac{23}{15} \\ \end{array} \right) $$

I wish I could do this computation using Map with just g[x_]:= {1,x,x^2} without loops, but I don't really understand the tricky Mathematica language for such things. I don't really know if I should use Apply or Map or something else.

I have been using Mathematica for a while and I've tried to learn this kind of coding without loops but I'm still like the first day. Watching the examples I saw here is not enough for me. I just can see a bunch of # /& @ without been able to understand it. So I always ended avoiding this chapter.

Anyone knows any tutorial for this particular matter?

With respect to the title of the question, see section 5.2 of Leonid Shifrin's book or section 5.1 of Robert Wagner's book. — Michael E2, Mar 25 '15 at 23:00
On this site you can find some short animations explaining a few of Mathematica's basic commands (like Map and Apply). — Sjoerd C. de Vries, Mar 25 '15 at 23:10
You can read this answer of the Question Scan vs Map vs Apply — xyz, Mar 26 '15 at 01:34

ciao · Accepted Answer · 2015-03-25T23:03:47.797

1

Here's one way...

g[1][x_] := 1;
g[2][x_] := x;
g[3][x_] := x^2;
norm[r_, s_] := Integrate[r[x]*s[x] + r'[x]*s'[x], {x, 0, 1}];

gram=Array[norm[g[#1], g[#2]] &, {3, 3}]

or...

gram=Table[norm[a, b], {a, {g1, g2, g3}}, {b, {g1, g2, g3}}];

or...

gram=Outer[norm, {g1, g2, g3}, {g1, g2, g3}]

edited Mar 25 '15 at 23:03

answered Mar 25 '15 at 22:56

ciao

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Tutorial for Map, Apply, etc

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