How to get a y-z; x table from a x-y; z Table Data?

Hello. I am trying to edit the table data. Think that we have the z values according to each x and y values. Iwould like get the x values according to each y and z values.

As an example;

X=[1 2 3 4 5];
Y=[30;40;50;60];
Z=[1 2 3 4 5; 3 4 5 6 7; 5 6 7 8 10; 7 8 10 11 13];

So the table is;

     Y
     ^   1  2  3  4  5 -> X
     |  ---------------
    30 ! 1  2  3  4  5
    40 ! 3  4  5  6  7
    50 ! 5  6  7  8 10
    60 ! 7  8 10 11 13

I would like rearrange the table which looks like this:

   Y
   ^   1  4  7  10  13 -> Z
   |  ---------------
  30 ! 1  4
  40 !    2  5
  50 !       3  5
  60 !       1     5

To be able to make an accurate interpolation (and no need to extrapolation); the given data table is extendable. I men it could be provided some more extra values. So the given data table could be like this :

     Y
     ^   1  2  3  4  5  6  7 ...-> X
     |  --------------------
    30 ! 1  2  3  4  5  6  7
    40 ! 3  4  5  6  7  8  9
    50 ! 5  6  7  8 10 11 12
    60 ! 7  8 10 11 13 15 16
    70 ! 9 10 12 13 15 17 18
    80 !10 11 13 14 16 18 20
    ...

And I need the z data table 1-13 only.

[Stephen23]

See earlier question:

https://www.mathworks.com/matlabcentral/answers/325157-how-to-back-interpolation-to-find-x-from-z-and-y

Answer 1

[Stephen23]

One solution using TriScatteredInterp:

>> X = [1,2,3,4,5,6,7];
>> Y = [30,40,50,60,70,80];
>> Z = [1,2,3,4,5,6,7;3,4,5,6,7,8,9;5,6,7,8,10,11,12;7,8,10,11,13,15,16;9,10,12,13,15,17,18;10,11,13,14,16,18,20];
>> [Xm,Ym] = meshgrid(X,Y);
>> F = TriScatteredInterp(Z(:),Ym(:),Xm(:));
>> Zv = 1:13; % new columns
>> Yv = 30:10:80; % new rows
>> [Zn,Yn] = meshgrid(Zv,Yv);
>> Xn = F(Zn,Yn)
Xn =
Columns 1 through 7
          1            2            3            4            5            6            7
        NaN          NaN            1            2            3            4            5
        NaN          NaN          NaN          NaN            1            2            3
        NaN          NaN          NaN          NaN          NaN          NaN            1
        NaN          NaN          NaN          NaN          NaN          NaN          NaN
        NaN          NaN          NaN          NaN          NaN          NaN          NaN
Columns 8 through 13
        NaN          NaN          NaN          NaN          NaN          NaN
          6            7            7          NaN          NaN          NaN
          4          4.5            5            6            7            7
          2          2.5            3            4          4.5            5
        NaN            1            2          2.5            3            4
        NaN          NaN            1            2          2.5            3

X values outside those defined in the original matrices are indicated with NaN. If you have a newer MATLAB version then use scatteredInterpolant (which can also extrapolate).

[ercan duzgun]

Dear Stephen Cobeldick;

Thanks a lot. This works very well. This was what I needed.. Regards, Ercan