Which visualization tool should I use?

Question

We consider the below function :

$f(x,y,z,a) = x*y*z*a$, where $x,y \in \mathbb{Q}\cap[0,1000],$ $ a\in\{2,3\} $

and $z=z(x)$, taking values from the below table based on the level-range that $x$ belongs to. For instance, if $x=150$, then $z=5.$

I am looking for the proper visualization tool that can produce all possible 2-dim and 3-dim graphs of the above function.\

For instance,

• if I fix $x=150$ and $a=2$, I want the 2-dim graph $(y,f(150,y,5,2))$
• if I fix $a=2$, I want the 3-dim graph $(x,y, f(x,y,z(x),2) )$
• and if I fix $y=10.5$, I want the two 2-dim graphs $(x,f(x,10.5,z(x),2))$ and $(x,f(x,10.5,z(x),3))$

I would like your suggestions on the above. Would Tableau do the job here ? I am not familiar with any tool and I am trying to chose the most situable to start with. Should I consider some other tool maybe? (Power BI or ??)

In addition, please advise on the functionality and the advanced options provided by the above tools.

Answer 1

Based on your explanation, $z$ is not a parameter so your function can be simplified like this:

$$f(x,y,a) = x*y*z(x)*a\text{, where } x,y \in \mathbb{Q}\cap[0,1000], a\in\{2,3\} $$

Note that $z(x)$ is a piecewise function. Also $a$ can have only two values so $f$ can be divided into $f_2$ and $f_3$, each of these having only two arguments so it simplifies things.

I don't know Tableau or Powerbi so I can't advise about that. I use R and I played a bit with your function. For a global visualization I came up with a kind of heat map like this:

In case you're interested, I did it like this with R:

library(ggplot2)

myrandomdata <- function(n) {
  a2 <- data.frame(x=runif(n,0,1000),y=runif(n,0,1000),z=20,a=rep(2,n))
  a3 <- data.frame(x=runif(n,0,1000),y=runif(n,0,1000),z=20,a=rep(3,n))
  df <- rbind(a2,a3)
  df$z[df$z<=500] <- 10
  df$z[df$z<=200] <- 5
  df$z[df$z<=100] <- 2
  df$f <- df$x *df$y * df$z * df$a
  df
}

df <- myrandomdata(50000)
ggplot(df,aes(x,y,colour=f))+geom_point()+facet_grid(a~.)+scale_color_gradient(low="blue", high="red")

(using random sampling is probably not the standard way but it was the easy way)