Why does gradient function calculates wrong dimensions?

Question

Michael Mauersberger 2020-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/521911-why-does-gradient-function-calculates-wrong-dimensions

评论： Michael Mauersberger 2020-4-30

采纳的回答： Ameer Hamza

在 MATLAB Online 中打开

Hi there,

Why does the gradient function calculates the first two dimensions wrong?

Example:

[mshx,mshy,mshz] = ndgrid(0:.1:10,0:.1:10,0:.1:10);
[gxx,gyx,gzx] = gradient(mshx);
[gxy,gyy,gzy] = gradient(mshy);
[gxz,gyz,gzz] = gradient(mshz);

Here all gij are zero except for gyx, gxy, gzz. But how can I calculate the gradient more consistently so that all gij are zero except for gxx, gyy, gzz?

Thank you for your help.

Best regards

Michael

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Answer 1

Ameer Hamza 2020-4-30

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https://ww2.mathworks.cn/matlabcentral/answers/521911-why-does-gradient-function-calculates-wrong-dimensions#answer_429347

编辑：Ameer Hamza 2020-4-30

在 MATLAB Online 中打开

Use meshgrid instead of ndgrid

[mshx,mshy,mshz] = meshgrid(0:.1:10,0:.1:10,0:.1:10);
[gxx,gyx,gzx] = gradient(mshx);
[gxy,gyy,gzy] = gradient(mshy);
[gxz,gyz,gzz] = gradient(mshz);

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Stephen23 2020-4-30

编辑：Stephen23 2020-4-30

在 MATLAB Online 中打开

Note that using meshgrid is not a general solution, it fails for N==1, i.e. when the input is a vector:

>> mshx = meshgrid(0:10);
>> gradient(mshx) % oops!
ans =
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1
   1     1     1     1     1     1     1     1     1     1

It could be made to work by providing the first input argument as a scalar and the second as the vector, but that requires special-case handling. This is not just a theoretical problem: it will be relevant if you write a general solution for any N, e.g. with comma-separated lists as to provide the inputs/outputs of the gridding function and calling gradient in a loop on the outputs.

The solution I gave in my answer to your other (identical) question works for all N, no special cases.

Michael Mauersberger 2020-4-30