Need to interchange column and data in a 2-D Table

Hi,

I have a 2D Table (table1) where the value at a location is given by z=(x,y)

I need to obtain a 2D table (table2) such that y=(x,z)

I guess some sort of interpolation is needed to fit a function such that z =f(x,y) ,then express this as y=g(x,z) and then build table2.

Kindly help with functions to be used.

Is there some Matlab command that would do this in a single step?

To change from

     y1  y2 ... -->
x1   Z11  Z12
x2   Z21  Z22
|
V

to

     z1  z2 ... -->
x1   y11  y12
x2   y21  y22
|
V

Thanks, Francis

Answer 1

[Walter Roberson]

There is no command to do this in a single step. It is not generally possible mathematically. But see http://uk.mathworks.com/matlabcentral/answers/232829-how-can-i-look-up-and-interpolate-a-value-from-a-set-of-3d-gridded-data-i-am-given-y-and-z-dimensi

[FrancisF]

Thanks Walter for the quick reply. My question is very similar to the one in the link you provided. Looks like there is no easy solution.

[Walter Roberson]

My solution there of

[numrow, numcol] = size(Z);
xcol = interp1(X, 1:numcol, X_to_search, 'nearest', 'extrap');
ycol = interp1(Z(:,xcol), 1:numrow, Z_to_search, 'nearest', 'extrap');
Y = Y(ycol);

is pretty easy, but it has different mathematical properties than the griddedinterpolant that was posted. A difficulty is that you have not defined how to handle ambiguity, since the same z value could be associated with multiple y values even for the same x -- and if your x might not be exactly what is in your original interpolation table, you get ambiguity in multiple dimensions.