How can I make a list plot from three arrays, plotting values of the 2nd and 3rd arrays against the 1st?

Question

Very new to Mathematica, so pardon my ignorance.

I am trying to plot x vs y1 and x vs y2 on the same ListPlot.

Here is what the data look like:

x = {1,2,3,4}

y1 = {3,4,5,6]

y2 results from FindIteration and gives me a result like this:

y2 = {{5},{6},{8},{9}}

How can I convert y2 such so it has the same shape as x and y1?

My iteration code is

Do[y2new = 
  ynew /. FindInstance[
    function1[x[[i]], ynew] == function2[x[[i]], ynew], ynew, Reals];
 y2[[i]] = ynew, {i, Length[x]}]

Is there a way to change the assignment of y2 values so the resulting array y2 has the same shape as x and y1?

Answer 1

x = {1, 2, 3, 4};
y1 = {3, 4, 5, 6};
y2 = {{5}, {6}, {8}, {9}};

To correct y2 when has been already generated, you just need to apply Flatten to y2 and then plot the transpose of x and the flattened y2.

ListPlot[
  {Transpose[{x, y1}], Transpose[{x, Flatten[y2]}]}, 
  PlotLegends -> SwatchLegend[{"y1", "y2"}]]

Now let's look into generating the flat form of y2 directly. You did provide definitions for the two functions for which you are giving FindInstance, so I will use these two

f1[x_, y_] := Sin[x + 2 π y]
f2[x_, y_] := Cos[x + 2 π y]

I will use Map in its operator form, /@, to generate the list y2. Doing so will make the code much simpler than your Do-loop.

N[FindInstance[f1[#, y] == f2[#, y] && 0 <= y <= 1, y]][[1, 1, 2]] & /@

x

{0.465845, 0.30669, 0.147535, 0.98838}

Note tha t I use the part specification [[1, 1, 2]] to extract the numerical values for the list of instance found by FindInstance. Were I to use the usual extraction method

y /. N[FindInstance[f1[#, y] == f2[#, y] && 0 <= y <= 1, y]] & /@ x

I would get

{{0.465845}, {0.30669}, {0.147535}, {0.98838}}

a list of the same shape as the one that you generate.

Answer 2

x = {1, 2, 3, 4}
y1 = {3, 4, 5, 6}
y2 = {{5}, {6}, {8}, {9}}
data = MapThread[{{#1, #2}, {#1, #3}} &, {x, y1, Catenate@y2}]
ListPlot[Transpose@data]