![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/174299/image.png)
Best fit of a surface
80 次查看(过去 30 天)
显示 更早的评论
Dear all, i have a matrix A(188x215) but is has many pics as you can see in the image
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/155853/image.jpeg)
i would like to visualize a plane that best fits this matrix.
So far i made it with some for cycles but i do think that there can be a better way to solve that.
Any help would be appreciated
0 个评论
采纳的回答
arich82
2014-1-31
If you're just looking for a best fit plane (for some definition of 'best'), you can use the backslash operator, just like finding the the least-squares fit for a line.
For a line, you have data x and y, but unknown coeffcients m abnd b:
y1 = m*x1 + b;
y2 = m*x2 + b;
y3 = m*x3 + b;
...
This represents an overdetermined system X*M = Y, where we can solve M = [b; m]
X = [ ...
1, x1; ...
1, x2; ...
1, x3; ...
];
Y = [y1; y2; y3;];
M = X\Y;
For a plane, we have the general equation
0 = a*(x - x0) + b*(y - y0) + c*(z - z0)
z = (1/c)*(a*x0 + b*y0 + c*z0) - ((a/c)*x + *b/c)*y);
Let C = (1/c)*(a*x0 + b*y0 + c*z0), A = -a/c, B = -b/c, then for M = [C, A, B], you again have the overdetermined equation Z = X*M, which can be solved via backslash:
X = [ ...
1, x1, y1; ...
1, x2, y2; ...
1, x3, y3; ...
];
Z = [z1; z2; z3;];
M = X\Z;
In general, if you have vectors of data x(:), y(:), z(:) of length n, then you can create the data variables as X = [ones(n, 1), x(:), y(:)]. Below is a full example:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/174299/image.png)
m = 188;
n = 215;
[y, x] = meshgrid(1:n, 1:m);
z = sind(10*x + 5*y) + log(x.*y); % filler data; this would be your A matrix
X = [ones(m*n, 1), x(:), y(:)];
M = X\z(:);
figure;
surf(x, y, z, 'EdgeColor', 'none'); % original wavy data
hold all;
surf(x, y, reshape(X*M, m, n), 'EdgeColor', 'none', 'FaceColor', 'b'); % blue fitted-plane
Alternatively, if you just want to get rid of the peaks, you might consider filtering your data (e.g. filter2).
Hope this helps.
--Andy
4 个评论
arich82
2014-2-1
Matt J--
Do you have a reference thread for the QR stability comment? Or a pathological case where mldivide would fail in fitting a simple plane? I'm genuinely interested.
Once upon a time, the Matlab help documentation described mldivide as using QR for non-square matrices, though perhaps there was some option for a more stable decomp that wasn't used by default. (It now appears there's just a brief comment under "Systems of Linear Equations" about mldivide and qr; it would be nice MW didn't gut their help docs...) The mldivide doc no longer offers any real info, and the new example in qr shows a "Q-less" solution to a system of linear equations, but doesn't offer any insights on what might be different with the backslash operator.
Matt J
2014-2-1
Once upon a time, the Matlab help documentation described mldivide as using QR for non-square matrices,
It still does,
so I guess it doesn't matter if all you want is the fit. If you wanted an error analysis of the fit, like polyfit provides for example, it helps to do the QR decomp explicitly and reuse it for the error analysis...
更多回答(1 个)
另请参阅
类别
在 Help Center 和 File Exchange 中查找有关 Polynomials 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!