I have a function
f[x_,y_,z_]:= a^x b^y c^z
and I want to evaluate it for various values of x,y,z always coming in triples. This means I have a database with columns x,y,z and rows vectors say A,B,C. (Sorry I could not write a Latex table here for some reason!)
How does one create such a table on Mathematica and then asks the function to directly compute 1) f[vector A] instead f[x,y,z] and 2) say the sum or product of vectors A,B, and C?
I recommend looking into Dataset.
Here is a test dataset:
data = Dataset@
Table[<|"x" -> RandomReal[], "y" -> RandomReal[],
"z" -> RandomReal[]|>, {i, 9}]
Then you can apply your function like this:
f[data[1, "x"], data[1, "y"], data[1, "z"]]
or shorter:
f @@ data[1]
Which applies your function to the first row (or row vector A in your question).
With a dataset you can use Total like this to get a sum per row:
data[1, Total]
f @@ {X, Y, Z}- seeApply$\endgroup$Dataset, which has a convenient (and I think optimized)Querysyntax, or withAssociation, from which you canLookup. That said, there are probably a dozen different ways to get this done. $\endgroup$\begin{bmatrix} ... \end{bmatrix}if you want to draw a table with mathjax. $\endgroup$Dataset, but the question seems to be only about how to apply a function to a list of vectors. For this all you need isf @@@ {A,B,C}. Don't make aDatasetif you don't plan to use the querying functionality. $\endgroup$