how to get the gradient of fucntion from vectors to scalars by matlab?

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DARAN XU 2018-9-23

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https://ww2.mathworks.cn/matlabcentral/answers/420315-how-to-get-the-gradient-of-fucntion-from-vectors-to-scalars-by-matlab

回答： Arun Mathamkode 2018-9-26

here is the question: f:R^600 -> R f(x)=(Ax-b)^2 where A is a 400*600 matrix and b is 400*1 and both of them are given. how can I get the gradieint(f) at some given x0 by matlab ?

    m=400
    n=600
    A=randn(m,n)
    b=randn(m,1)
    syms x
    f= 0.5*norm(A*x-b)^2
    gradient(f,x)

however it does not work because it seems it regard x as scalar, not a vector.

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Answer 1

Arun Mathamkode 2018-9-26

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I assume you are referring to the gradient of L2 norm squared. You can directly apply the closed form expression of the gradient. The gradient of f at some given x0 will be A'*A*x0-A'*b.