How can I differentiate a non linear equation in Matlab

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ND 2015-9-23

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https://ww2.mathworks.cn/matlabcentral/answers/244729-how-can-i-differentiate-a-non-linear-equation-in-matlab

评论： Walter Roberson 2015-9-25

采纳的回答： Walter Roberson

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y = 5.0*10^-10*x +7.0*10^-25*x^3

I need to solve equation above for (x) , then differentiate (getting jacobian) for (y)

like:

sol ={solve(y,x)}

diff1= diff(sol,y)

Is that possible?

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Answer 1

Walter Roberson 2015-9-23

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Yes, just use

syms x
y = 5.0*10^-10*x +7.0*10^-25*x^3
sol = solve(y, x)
diff(sol, y)

But remember that there are multiple solutions for x because there are three roots to the cubic.

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Walter Roberson 2015-9-25

在 MATLAB Online 中打开

For those particular parameters, the Fortran code for the real root

       Root1 = 0.52920000000000D14 * ((dble(52920 * y) + 0.42D2 * sqrt(dble
     #(1587600 * y ** 2 + 42))) ** (0.2D1 / 0.3D1) + 0.42D2) * (dble(y) 
     #+ sqrt(dble(1587600 * y ** 2 + 42)) / 0.1260D4) * (dble(52920 * y)
     # + 0.42D2 * sqrt(dble(1587600 * y ** 2 + 42))) ** (-0.4D1 / 0.3D1)
     # * dble((1587600 * y ** 2 + 42) ** (-0.1D1 / 0.2D1))

Part of the difficulty is that you have not restricted yourself to real roots. The code generation tools I use for Fortran have trouble with long expressions that involve complex numbers :(

I did some tests with

y == 5*10^(-10)*x +7*10^(-25)*x^3 + A * x^4

and it appears to me that Fortran does not have the precision needed to evaluate the roots.

Is it a particular 4-degree polynomial that you will be working with, or do you need to run through a bunch of them?

Walter Roberson 2015-9-25

在 MATLAB Online 中打开

You mean like

fortran(S,'file',fileName)

You can construct the general pattern for order 3 equations

syms x y A B C D
z = y == A * x.^3 + B * x.^2 + C * x + D;
sol = solve(z,y);
dsol = simplify(diff(sol(1),y));
fortran(dsol, 'filename', 'dinvcubic.f')

Once generated you would only need to invoke it after assigning appropriate values to A, B, C, D

The same technique can be used for order 4, but the expressions get very long, and the code might not have enough precision for accurate answers for some ranges.

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