How to do 2D interpolation

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Mekala balaji
Mekala balaji 2017-8-29
评论： Josh Meyer 2017-9-5
Hi,
I have below data, I only knew 1D interpolation(using interp1), but I want to use 2D interpolation, please some one help me,
X y1 y2
1.2 2.03 1.23
2.5 4.20 3.21
3.5 5.60 4.65
4.0 6.12 4.85
5.7 6.78 5.05
6.2 7.27 6.05
I want to predict y1 & y2 for new X= 0.8,8.3
Many thanks in advance,

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回答（2 个）

Akira Agata
Akira Agata 2017-8-30
Looking at your data, curve fitting could be suitable to evaluate y1 and y2 at x = 0.8, 8.3. Here is the sample code to fit the data by 3rd order polynomial, and evaluate the target values.
A = [1.2 2.03 1.23
2.5 4.20 3.21
3.5 5.60 4.65
4.0 6.12 4.85
5.7 6.78 5.05
6.2 7.27 6.05];
f1 = polyfit(A(:,1),A(:,2),3);
f2 = polyfit(A(:,1),A(:,3),3);
xq = [0.8; 8.3];
T = table(xq, polyval(f1,xq), polyval(f2,xq),...
'VariableNames',{'QueryPoint','y1','y2'});
The output is as follows:
T =
2×3 table
QueryPoint y1 y2
__________ ______ ________
0.8 1.0776 0.041437
8.3 7.6596 9.307
Josh Meyer
Josh Meyer 2017-8-29
Assuming that y1 and y2 are separate functions evaluated at the points in X, you are still just doing 1-D interpolation. Moreover, since you want to know the values of these functions at X = [0.8 8.3], and these query points lie outside the sample points, you really want to do extrapolation.
So you can still use interp1, but you need to specify a method and 'extrap' to evaluate these query points, for example:
A = [1.2 2.03 1.23
2.5 4.20 3.21
3.5 5.60 4.65
4.0 6.12 4.85
5.7 6.78 5.05
6.2 7.27 6.05];
xq = [0.8 8.3];
F = interp1(A(:,1),A(:,2:3),xq,'linear','extrap');
T = table(xq,F(:,1),F(:,2),'VariableNames',{'QueryPoint','y1','y2'})
T =
2×3 table
QueryPoint y1 y2
__________ ______ _______
0.8 1.3623 0.62077
8.3 9.328 10.25
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Mekala balaji
Mekala balaji 2017-8-31
Sir,
When we use "extrap", will it predict outside range (extrapolation) as with in range prediction?
how to replace "table"
Josh Meyer
Josh Meyer 2017-9-5
  • You can't replace table, but since it was just meant to show the data in a tidy format you don't even need that command. Just delete the whole T = table(...) line and examine the output F instead.
  • 'extrap' just means that interior points are interpolated and exterior points are extrapolated.

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