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R Commands in Euler

This is a collection of some basic R commands. R is a completely
different system than Euler with advanced object data types, which
Euler does not provide. For Euler's way to do things in statistcs see
the following notebook.

../12 - Introduction to Statistics

However, it might be nice to translate some functionality to Euler.

r.e

This is a work in progress!! Currently, only a few basic commands are
in r.e.
>load r
R Commands in Euler.
We cannot define the <- operator for assignments. It might be
interesting to add this to the kernel of Euler, however. So we keep
using := or =.
>x := c(4,5,6,8,9,4,5,2)
[ 4  5  6  8  9  4  5  2 ]
The summary function computes some quantiles.
>summary(x)
Min: 2
1st: 4
Med: 5
Mea: 5.375
3rd: 6.5
Max: 9
The following is a nice function, which is implemented in Euler in a
vary simple way.

function rep(v,n) := redim(dup(v,n),n*cols(v));
>rep(1:3,5)
[ 1  2  3  1  2  3  1  2  3  1  2  3  1  2  3 ]
It can also work like multdup in Euler.
>rep(c(1,4,5),c(2,3,2))
[ 1  1  4  4  4  5  5 ]
The seq function works much like the : operator.
>seq(1,10)
[ 1  2  3  4  5  6  7  8  9  10 ]
>seq(1,10,2)
[ 1  3  5  7  9 ]
But it can also work like linspace.
>seq(1,10,length=5)
[ 1  3.25  5.5  7.75  10 ]
The matrix function exists in Euler in a different meaning. We do not
want to overload it, so we call it matr.
>shortformat; matr(1:10,2)
          1           6 
          2           7 
          3           8 
          4           9 
          5          10 
>matr(1:10,ncol=5)
          1           3           5           7           9 
          2           4           6           8          10 
>matr(1:10,ncol=5,>byrow)
          1           2           3           4           5 
          6           7           8           9          10 
The | and _ operators are functions in R.
>cbind(1:3,4)
          1           4 
          2           4 
          3           4 
>rbind(1:3,4)
          1           2           3 
          4           4           4 
We can mimic the apply function.
>apply(cbind(1:6,2:7),2,"mean")
[ 3.5  4.5 ]

Distributions

R knows lots of distributions. For the plotting command, see below.
>x=seq(-5,10,0.5); rplot(x,dnorm(x,3,2),"b"); insimg;

R Commands in Euler

The distribution of Gauß is called pnorm, and the quantile (inverse
distribution) is called qnorm.
>qnorm(pnorm(1,0,2),0,2)
1
The default is the N(0,1) distribution.
>qnorm(0.99)
2.3263
>v:=rnorm(100000); mean(v), dev(v)
0.00059283
0.99791

Plots

R uses a plot command with some parameters. Since we cannot overwrite
Eulers plot, we call the plot function rplot(). 

The parameters allow the default point plots "p", line plots "l", both
"b", histogram plots "h", and surface plots "s".
>x:=seq(-1,1,0.05); rplot(x,x^3-x,"l"); insimg;

R Commands in Euler

>x1=rnorm(100); x2=rnorm(1000);
>par(mfrow=c(2,2));
>rhist(x1); rboxplot(x1);
>rhist(x2); rboxplot(x2);
>insimg;

R Commands in Euler

>par(mfcol=c(1,1));
>x:=seq(-10,10);
>y:=x+rnorm(length(x),0,4);
>rplot(x,y); p=polyfit(x,y,1); abline(p); insimg;

R Commands in Euler

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