How can I differentiate a non linear equation in Matlab

 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?

Answer 1

[Walter Roberson]

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.

[ND]

Thanks Walter,

it returns this error

Error using sym/diff (line 67) The second argument must be a variable or a nonnegative integer specifying the number of differentiations.

[Walter Roberson]

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

[ND]

Yes that's right but please what about forth order if the power likes x^4 and I would put that diff in a FORTRAN file. It would give me an error!

Error using mupadmex Error in MuPAD command: Code generation failed due to an unexpected object of type 'RootOf'. [generate::CFany]

Also, if the equation is generated in Matlab code as generated formula and I can not imported it as above ?

syms x y

z = y == ( equation is in m.file) as generated formula

sol = solve(z, x)

diff(sol, y)

Many thanks for your help

[Walter Roberson]

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]

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.