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Evaluate two variable functions at given points?

Okkes Dulgerci
Posted 9 years ago
POSTED BY: Okkes Dulgerci
6 Replies
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Okkes Dulgerci
Okkes Dulgerci
Posted 9 years ago

It helped a lot, thank you all..
POSTED BY: Okkes Dulgerci

There is nothing wrong in generating lists of expressions and then use proper programming to calculate the results. The WL does not "insist" on a specific programming style and there are several ways of doing the required task. The best of all is to mix procedural, functional and rewrite rules programming styles so the program will be elegant, short and efficient. IMHO, the original poster used expressions such as

f[1,1][x_,y_]:=4x

just to clarify what he meant in his original post

best

yehuda
POSTED BY: Yehuda Ben-Shimol

A similar method to the one Gianluca proposed could be:

f = Map[Function[{pt}, # /. {x :> pt[[1]], y :> pt[[2]]}] &, f, {2}];

a function call would then look like this (I admit this is not exactly what you want ...):

f[[1, 3]][pts[[1, 3]]]

or likewise

dims = Dimensions[f];
Table[f[[n, m]][pts[[n, m]]], {n, 1, dims[[1]]}, {m, 1, dims[[2]]}]

Regards -- Henrik
POSTED BY: Henrik Schachner

The way you have defined f, it is a little awkward to make it behave like a function. This is a solution, that uses two new symbols myF and myPts, which behave the way you want:

Clear[myF, x, y];
Do[myF[n, m][{x_, y_}] = f[[n, m]], {n, Length[f]},
 {m, Length[f[[1]]]}]
myPts[n_, m_] := pts[[n, m]];
myF[1, 1][myPts[1, 1]]
POSTED BY: Gianluca Gorni
Okkes Dulgerci
Okkes Dulgerci
Posted 9 years ago

Thanks for your reply. Sorry my unclear explanation. This is what I want

f[1,1][x_,y_]:=4x,  then f[1,1][pts[1,1]]=f[1,1][1/12, 1/6]=4*1/12=1/3
 f[1,2][x_,y_]:=4y, then f[1,2][pts[1,2]]=f[1,2][1/6, 1/12]=4*1/12=1/3
 f[1,3][x_,y_]:= 1 - 4 x + 4 y,  then f[1,3][pts[1,3]]=f[1,3][1/3, 1/6]=1-4*1/3+4*1/6=1/3
POSTED BY: Okkes Dulgerci
POSTED BY: Yehuda Ben-Shimol
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