How to compute the gradient at each point of an arbitrary symbolic curve defined by "n" points?

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Suhas Raghavendra Kulkarni 2022-2-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1648745-how-to-compute-the-gradient-at-each-point-of-an-arbitrary-symbolic-curve-defined-by-n-points

评论： VBBV 2022-2-13

采纳的回答： VBBV

Hello,

I have a vector of "n" points describing a spline. I would like to compute the gradient at each of the "n" points.

Each point in this vector has 3 components, each of which is a symbolic expression in multiple variables.

The reason I am computing the gradients is to compare 2 curves (one of which I know each point in a 3-D space) with this. My criterion for comparison is that the cross product of gradients at each point must be zero. I am able to compute the gradients of the known curve using the matlab function "gradient". However, when i use the same function to compute for the symbolic points, I get the error

**************************************

Error using sym/gradient (line 21)

First argument must be scalar.

***************************************

Any help on how I may proceed is apprecciated.

For ref:

known_points=[3Xn] % format double

dx_1=gradient(known_points(1,1:end));

dy_1=gradient(known_points(2,1:end));

dz_1=gradient(known_points(3,1:end));

% I am able to compute the above expressions.

unknown_points=[3Xn] %format sym

dx_2=gradient(unknown_points(1,1:end));

dy_2=gradient(unknown_points(2,1:end));

dz_2=gradient(unknown_points(3,1:end));

% I get the highlighted error when i compute the above expressions.

% alternately i have also tried dx_2=gradient(unknown_points(1,1:end), symvar(unknown_points)); to no avial.

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Answer 1

VBBV 2022-2-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1648745-how-to-compute-the-gradient-at-each-point-of-an-arbitrary-symbolic-curve-defined-by-n-points#answer_894920

编辑：VBBV 2022-2-13

在 MATLAB Online 中打开

gradient(subs(unknown_points,x,value));

If x is the symbolic variables in array unknown_points then use subs to replace the variable with your value. Then compute the gradient as above.

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Suhas Raghavendra Kulkarni 2022-2-13

Thank you for your answer. If I understand correctly, you are asking me to replce the desired values in place of the variable.

Unfortunately this is not possible as the symbolic function is actually a very long non-linear function in multiple variables. So I do not have the desired value of all the variable to replace in the expression.

Please correct me if my understanding of your answer is wrong.

VBBV 2022-2-13