How can I look up and interpolate a value from a set of 3D gridded data? I am given Y and Z dimensions, and need to find X.

I am trying to look up and interpolate to the nearest X value from a set of gridded data. This data is a formatted so that X is an 12x1 column vector, Y is a 17x1 column vector, and Z is a 12x17 matrix.

Here is an example data set:

X  =[11;10;9;8;7;6;5;4;3;2;1;0]

Y=[0;1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16]

Z=[ 3.50   3.32  3.12  2.89  2.63  2.30  1.91  1.51  1.18  0.88  0.59  0.29;
    3.29   3.08  2.85  2.59  2.29  1.95  1.58  1.22  0.92  0.68  0.45  0.22;
    3.35   3.12  2.87  2.58  2.26  1.92  1.57  1.21  0.90  0.65  0.43  0.22;
    3.41   3.17  2.90  2.60  2.29  1.95  1.62  1.28  0.95  0.68  0.45  0.23;
    3.45   3.20  2.93  2.64  2.34  2.02  1.70  1.37  1.03  0.74  0.49  0.24;
    3.47   3.22  2.96  2.69  2.40  2.10  1.78  1.46  1.12  0.80  0.53  0.26;
    3.48   3.25  3.00  2.74  2.46  2.17  1.87  1.54  1.21  0.87  0.57  0.28;
    3.50   3.27  3.03  2.78  2.52  2.24  1.95  1.63  1.29  0.94  0.61  0.31;
    3.50   3.29  3.06  2.83  2.57  2.31  2.02  1.70  1.37  1.01  0.66  0.33;
    3.50   3.30  3.08  2.86  2.62  2.36  2.08  1.78  1.44  1.08  0.71  0.35;
    3.49   3.29  3.09  2.87  2.64  2.40  2.13  1.84  1.51  1.15  0.76  0.38;
    3.45   3.27  3.07  2.87  2.65  2.42  2.17  1.89  1.57  1.21  0.81  0.41;
    3.37   3.20  3.02  2.83  2.63  2.41  2.17  1.91  1.62  1.27  0.87  0.43;
    3.09   2.93  2.77  2.59  2.40  2.20  1.98  1.74  1.47  1.15  0.77  0.39;
    2.47   2.33  2.17  2.01  1.85  1.67  1.47  1.26  1.03  0.78  0.52  0.26;
    1.90   1.78  1.65  1.51  1.38  1.23  1.07  0.91  0.73  0.55  0.37  0.18;
    1.47   1.37  1.27  1.16  1.05  0.93  0.81  0.68  0.54  0.41  0.27  0.14]

I would like to be able to take a Y and Z value, and look up an X value.

I've tried griddedInterpolant, but was not able figure out the function.

Any help appreciated

Answer 1

[Andrei Bobrov]

F = griddedInterpolant({Y,flip(X)},flip(Z,2));

z = [3;2;1];
y = [0;8;3];
your_x = arrayfun(@(y,z)fzero(@(x)z - F(y,x),0),y,z);

[John Bulzacchelli]

Thank you Andrei - this worked perfectly.

Answer 2

[Walter Roberson]

http://uk.mathworks.com/matlabcentral/answers/231640-convert-3d-lookup-table

[John Bulzacchelli]

Thanks, Walter. I'm struggling to even get your example function to work - it returns the error for line 10 that my input arguments must be double.

I tried entering in my arguments as: X=double(52) Z=double(10) Then calling the function as: Y=lookup(X,Z)

Also as:

XYZ = [0 40    50  60
       0.70 22.70 9.24 6.78
       0.65 20.45 8.85 6.42
       0.60 19.23 8.48 6.69
       0.55 18.04 8.03 6.28
       0.50 16.89 7.63 6.49];

[numrow, numcol] = size(XYZ);
xcol = interp(XYZ(1,:), 1:numcol, double(52), 'nearest');
yrow = interp1(XYZ(:, xcol), 1:numrow, double(10), 'nearest');
Y = XYZ(yrow, 1);

[Walter Roberson]

I corrected some errors in that routine just now.

In terms of your existing variables:

[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);