![]() ![]() You probably want to convert these back into real numbers and so you can use double to cast them back. I should probably tell you that when you're doing computation using the Symbolic Math Toolbox, the data type of the numbers as you're calculating them are a sym object. % Transpose and convert back to number representation % Must transpose into a row vector as this is required by subs % disp('n = ') disp(n) disp('x = ') disp(xout) disp('tol = ') disp(tol) įunction = Jacobian2D(f, J, x0, tol)Įp = 1 % Note: eps is a reserved keyword in MATLAB Now, make your script into a function: % To run in MATLAB, do: Your function requires the initial guess x0, the function f(x) as a column vector, the Jacobian matrix as a 2 x 2 matrix and the tolerance tol.īefore you run your script, you will need to generate your parameters: syms x y % Make x,y symbolicį1 = x^2 + y^3 - 1 % Make your two equations (from your example) Now that we have that established, let's tackle your code one piece at a time to truly make this dynamic. I will defer to the code and you can see it then. We can do the same thing for matrices, but for brevity I won't show you how to do that. ![]() Out = subs(z,, ) % Produces a 2 x 1 vector with The way you call the subs command will be slightly different: syms x, y % Two variables nowĭzx = diff(z, 'x') % Differentiate with respect to x - Should give 2*y^2 + 1ĭzy = diff(z, 'y') % Differentiate with respect to y - Should give 4*x*y + 6 % This should give 2*(3^2) + 6*3 + 3 = 39īecause this is 2D, we're going to need 2D functions. Out = subs(y, 3) % The subs command will substitute all x's in y with the value 3 Let's start with some basics: syms x ĭy = diff(y) % Derivative with respect to x. This tells MATLAB that you are now going to treat this variable as "symbolic" (i.e. You first need to use the syms command, followed by any variable you want. This way, you can use MATLAB to tackle derivatives of functions for you. If you want to make your script truly dynamic, then I would recommend that you use the Symbolic Math Toolbox. If you don't mind, I'd like to restructure your code so that it is more dynamic and more user friendly to read. So with this script, I had implemented the function and the Jacobian matrix into the actual script and I am struggling to work out how I can actually create a script with the input parameters required. m files.Īs an example of a script I wrote that implements Newton's method, I have: n=0 %initialize iteration counter The relative error is 0 because we have found the exact root and a function.I am trying to write a function that implements Newton's method in two dimensions and whilst I have done this, I have to now adjust my script so that the input parameters of my function must be f(x) in a column vector, the Jacobian matrix of f(x), the initial guess x0 and the tolerance where the function f(x) and its Jacobian matrix are in separate. The following formula gives the next value of x (hopefully closer to the root) We can reach the original root if we repeat the same step for the new value of x. Using equation of line y = mx 0 + c we can calculate the point where it meets x axis, in a hope that the original function will meet x-axis somewhere near. Newton Raphson Method uses to the slope of the function at some point to get closer to the root. Newton Raphson Method is an open method of root finding which means that it needs a single initial guess to reach the solution instead of narrowing down two initial guesses. Newton Raphson Method is yet another numerical method to approximate the root of a polynomial. ![]()
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