Re: normalize a table

• To: mathgroup at smc.vnet.net
• Subject: [mg72806] Re: normalize a table
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Sat, 20 Jan 2007 03:40:47 -0500 (EST)
• References: <eopmgk\$rr4\$1@smc.vnet.net>

```Ruth wrote:
> Hi,
>
> I want to do something really simple, which is take a table made of
> pairs and normalize the first number in each pair by dividing by the
> largest.
>
> For instance, I want to transform this list
>
> {{1,0.2},{2,0.3},{3,0.4},{4,0.5}}
>
> into this one
>
> {{1/4, 0.2}, {1/2, 0.3}, {3/4, 0.4}, {1, 0.5}}
>
> The way i did it is through the chain of commands
>
> firsttable={{1,0.2},{2,0.3},{3,0.4},{4,0.5}};
>
>
> top=Max[Table[firsttable[[i,1]],{i,1,Length[firsttable]}]];
>
>
> mytable=Do[newtable=ReplacePart[newtable,newtable[[i,1]]/top,{i,
> 1}],{i,1,Length[firsttable]}]
>
> There must be a more elegant way to do it, but @&# and commands like
> those are still hard to handle for me, and I could not work it out
>
>
> Ruth

There are many ways to do it. Here are four.

In[1]:=
firsttable = {{1,0.2},{2,0.3},{3,0.4},{4,0.5}};
Transpose@MapAt[#/Max@#&, Transpose@firsttable, 1]
Transpose@{#[[1]]/Max@#[[1]],#[[2]]}&@Transpose@firsttable
Transpose@ReplacePart[#,#[[1]]/Max@#[[1]],1]&@Transpose@firsttable
Transpose@{firsttable[[All,1]]/Max@firsttable[[All,1]],
firsttable[[All,2]]}

Out[2]= {{1/4, 0.2}, {1/2, 0.3}, {3/4, 0.4}, {1, 0.5}}
Out[3]= {{1/4, 0.2}, {1/2, 0.3}, {3/4, 0.4}, {1, 0.5}}
Out[4]= {{1/4, 0.2}, {1/2, 0.3}, {3/4, 0.4}, {1, 0.5}}
Out[5]= {{1/4, 0.2}, {1/2, 0.3}, {3/4, 0.4}, {1, 0.5}}

```

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