How to make a list plot from a "vector array"?

Question

I have an (excel) table where my first column have decimals from -3 to 3, and the other columns have associated values, in such a way that i have a "vector array" similar to this:

x1 -> {y1, y2, y3}
x2 -> {y2, y4, y5, y6}
x3 -> {y1, y5, y7}
x4 -> {y2, y8}
x3 -> {y2, y6, y7, y8, y9}

I have more than 600 "rows" or vectors. Some "x" values could be duplicated, but most of the "y" values wont, but it's possible.

How could i plot the vectors in a scatterplot? I would like to have something like this:

Could it be done with ListPlot?

Answer 1

data = {x1 -> {y1, y2, y3}, 
x2 -> {y2, y4, y5, y6}, 
x3 -> {y1, y5, y7}, 
x4 -> {y2, y8}, 
x3 -> {y2, y6, y7, y8, y9}};

We can change the head of each element of data to a List, then Thread each one together

Thread /@ (List @@@ data)

(*

{{{x1, y1}, {x1, y2}, {x1, y3}}, {{x2, y2}, {x2, y4}, {x2, y5}, {x2, 
   y6}}, {{x3, y1}, {x3, y5}, {x3, y7}}, {{x4, y2}, {x4, y8}}, {{x3, 
   y2}, {x3, y6}, {x3, y7}, {x3, y8}, {x3, y9}}}

*)

An example with numerical data:

SeedRandom[1001];
n = 20;
xArr = Round[RandomReal[{-3, 3}, n], 0.1];
data = # -> RandomInteger[{0, 2500}, RandomInteger[{1, 10}]] & /@ xArr;

formattedData = Thread /@ (List @@@ data);

ListPlot[formattedData, PlotRange -> All, Frame -> True, 
 GridLines -> {Range[-3, 3, 0.5], Range[0, 2500, 500]}, 
 PlotMarkers -> Graphics[{PointSize[0.03], Point[{0, 0}]}]]

Answer 2

If your data is in the form of

data = {x1 -> {y1, y2, y3},
  x2 -> {y2, y4, y5, y6},
  x3 -> {y1, y5, y7},
  x4 -> {y2, y8},
  x3 -> {y2, y6, y7, y8, y9}};

you can use the following code to convert it into normal points, and then use ListPlot.

Flatten[Table[
  Table[{data[[i, 1]], data[[i, 2, j]]}, {j, 1, 
    Length[data[[i, 2]]]}], {i, 1, Length[data]}], 1]

(*{{x1,y1},{x1,y2},{x1,y3},{x2,y2},{x2,y4},{x2,y5},{x2,y6},{x3,y1},{\
x3,y5},{x3,y7},{x4,y2},{x4,y8},{x3,y2},{x3,y6},{x3,y7},{x3,y8},{x3,y9}\
}*)

If you importe the Excel table directly, the data is more likely to look like this.

data = {{x1, y1, y2, y3},
   {x2, y2, y4, y5, y6},
   {x3, y1, y5, y7},
   {x4, y2, y8},
   {x3, y2, y6, y7, y8, y9}};

Then you can use

Flatten[Table[
  Table[{data[[i, 1]], data[[i, j]]}, {j, 2, Length[data[[i]]]}], {i, 
   1, Length[data]}], 1]

Answer 3

As @houzw points out, when importing the table directly from Excel, the data structure looks like this:

data = {
        {x1, y1, y2, y3},
        {x2, y2, y4, y5, y6},
        {x3, y1, y5, y7},
        {x4, y2, y8},
        {x3, y2, y6, y7, y8, y9}
       };

To get the point structure you need from the above ragged array, the following form is shorter:

Thread[{#1, {##2}}] & @@@ data// SortBy[Length] // Column[#, Spacings -> 1.5] &

Grabbing the @ydd's example:

SeedRandom[1001];
n = 20;
xArr = Round[RandomReal[{-3, 3}, n], 0.1];
data = {#, Splice@RandomInteger[{0, 2500}, RandomInteger[{1, 10}]]} & /@ xArr;

formattedData = Thread[{#1, {##2}}] & @@@ data;

ListPlot[formattedData, PlotRange -> All, Frame -> True, 
GridLines -> {Range[-3, 3, 0.5], Range[0, 2500, 500]}, 
PlotMarkers -> Graphics[{PointSize[0.03], Point[{0, 0}]}]]