Gradient command producing multiple functions

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Gavin Seddon
Gavin Seddon on 5 Dec 2016
Commented: Jan on 14 Feb 2017
Hello, when I use the gradient command I am given multiple functions as the answer. I assume these are the gradient at each 'root'. Is it necessary to substitute X at a specific position to generate the gradient at the position? Furthermore, will quiver generate the slope field?
G.
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Jan
Jan on 14 Feb 2017
@Gavin: Please do not attach a new question as a comment to another. Open a new thread instead.

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Accepted Answer

Jan
Jan on 5 Dec 2016
The functions you obtain from the gradient function are the derivatives with respect to the vector of the used variables. See https://www.mathworks.com/help/symbolic/gradient.html .
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Jan
Jan on 9 Dec 2016
It would be easier to answer, if you provide some details. To get the gradient at a specific point, you have to insert the coordinate values into the obtained formula.

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More Answers (1)

Guillaume
Guillaume on 5 Dec 2016
Ah, language. It's so hard to get yourself understood if you don't use the correct terms...
The gradient function does not return functions. Not one, not multiple. It returns numerical matrices / vectors.
It will return as many outputs as you have requested, so if you ask for multiple output, you'll get multiple outputs. If you ask for one, you'll only get one. Each output is the gradient of the input matrix along the corresponding dimension. I have no idea what you mean by 'root'
I also have no idea what this X you want to substitute is. You get the gradient at each point in your original matrix. If you want the gradient at points in between you either interpolate your input, or interpolate your output.
Finally, what is a slope field. quiver just plots arrow in the direction you specify. If it's the gradient of you matrix you want to plot with quiver, just pass the output of gradient to quiver (as per the example in the doc of gradient).
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Guillaume
Guillaume on 5 Dec 2016
Ah... I don't have the symbolic toolbox, so wasn't aware of this gradient overload.

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