Finding the gradient of the function

Question

Amy Topaz 2022-4-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1696530-finding-the-gradient-of-the-function

评论： DGM 2022-4-17

I need to find the gradient (differentiation) of the below function k1 wrt a11 for the values of z1 and plot with respect a11.

z1 = [0.00008 0.009]';
a11 = -2:0.002:2;
k1 = atan(((0.02 + a11)./z1)) + atan((0.03 - a11)./z1);

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DGM 2022-4-17

Edited to restore deleted question.

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Answer 1

Star Strider 2022-4-14

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1696530-finding-the-gradient-of-the-function#answer_942795

在 MATLAB Online 中打开

Symbolically —

syms a11 z1

sympref('AbbreviateOutput',false);

k1 = atan(((0.02 + a11)./z1)) + atan((0.03 - a11)./z1)

k1 =

grad_k1 = gradient(k1)

grad_k1 =

grad_k1_fcn = matlabFunction(grad_k1)

grad_k1_fcn = function_handle with value:

@(a11,z1)[1.0./(z1.*(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0))-1.0./(z1.*(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0));-(1.0./z1.^2.*(a11+1.0./5.0e+1))./(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0)+(1.0./z1.^2.*(a11-3.0./1.0e+2))./(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0)]

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Amy Topaz 2022-4-14

Could you plot and show me the plot please

Star Strider 2022-4-14

编辑：Star Strider 2022-4-14

在 MATLAB Online 中打开

Sure!

syms a11 z1

sympref('AbbreviateOutput',false);

k1 = atan(((0.02 + a11)./z1)) + atan((0.03 - a11)./z1)

k1 =

grad_k1 = gradient(k1)

grad_k1 =

grad_k1_fcn = matlabFunction(grad_k1)

grad_k1_fcn = function_handle with value:

@(a11,z1)[1.0./(z1.*(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0))-1.0./(z1.*(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0));-(1.0./z1.^2.*(a11+1.0./5.0e+1))./(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0)+(1.0./z1.^2.*(a11-3.0./1.0e+2))./(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0)]

figure

hfs = fsurf(grad_k1, [-1 1 -1 1]*4, 'MeshDensity',75);

hfs(1).EdgeColor = 'interp'; % Optional

hfs(2).EdgeColor = 'interp'; % Optional

EDIT — (14 Apr 2022 at 13:22)

Changed (increased) 'MeshDensity'.

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