![]() ![]() If the system of equations is linear, then use the \ (the backslash operator see help slash) for better speed and accuracy. Options = optimset('Display','off') % Turn off Display x0 = ones(2,2) % Make a starting guess at the solution.Find a matrix x that satisfies the equationįirst, write an M-file that computes the equations to be solved. Iteration Func-count f(x) step optimality radiusġ0 33 1.64763e-013 0.00169132 6.36e-007 2.5įirst-order optimality is less than options.TolFunĮxample 2. Options=optimset('Display','iter') % Option to display outputĪfter 33 function evaluations, a zero is found. x0 = % Make a starting guess at the solution.Thus we want to solve the following system for xįirst, write an M-file that computes F, the values of the equations at x. This example finds a zero of the system of two equations and two unknowns ![]() ![]() Minimum change in variables for finite-differencing.Ĭhoose Levenberg-Marquardt or Gauss-Newton over the trust-region dogleg algorithm.Įxample 1. Maximum change in variables for finite-differencing. These parameters are used only by the medium-scale algorithm:Ĭompare user-supplied derivatives (Jacobian) to finite-differencing derivatives. Termination tolerance on the PCG iteration. For some problems, increasing the bandwidth reduces the number of PCG iterations. By default, diagonal preconditioning is used (upper bandwidth of 0). Upper bandwidth of preconditioner for PCG. Maximum number of PCG (preconditioned conjugate gradient) iterations (see the Algorithm section below). This can be very expensive for large problems so it is usually worth the effort to determine the sparsity structure. In the worst case, if the structure is unknown, you can set JacobPattern to be a dense matrix and a full finite-difference approximation is computed in each iteration (this is the default if JacobPattern is not set). If it is not convenient to compute the Jacobian matrix J in fun, lsqnonlin can approximate J via sparse finite-differences provided the structure of J - i.e., locations of the nonzeros - is supplied as the value for JacobPattern. Sparsity pattern of the Jacobian for finite-differencing. See Nonlinear Minimization with a Dense but Structured Hessian and Equality Constraints for a similar example. Note 'Jacobian' must be set to 'on' for Jinfo to be passed from fun to jmfun. fsolve uses Jinfo to compute the preconditioner. In each case, J is not formed explicitly. The maximum number of function evaluations or iterations was exceeded. This section provides function-specific details for exitflag and output: Options provides the function-specific details for the options parameters.įunction Arguments contains general descriptions of arguments returned by fsolve. (Note that the Jacobian J is the transpose of the gradient of F.) If fun returns a vector (matrix) of m components and x has length n, where n is the length of x0, then the Jacobian J is an m-by-n matrix where J(i,j) is the partial derivative of F(i) with respect to x(j). % Jacobian of the function evaluated at x Note that by checking the value of nargout the function can avoid computing J when fun is called with only one output argument (in the case where the optimization algorithm only needs the value of F but not J). Then the function fun must return, in a second output argument, the Jacobian value J, a matrix, at x. If the Jacobian can also be computed and the Jacobian parameter is 'on', set by x = myfun is a MATLAB function such as.The function fun can be specified as a function handle. fun is a function that accepts a vector x and returns a vector F, the nonlinear equations evaluated at x. The nonlinear system of equations to solve. This section provides function-specific details for fun and options: Returns the Jacobian of fun at the solution x.įunction Arguments contains general descriptions of arguments passed in to fsolve. Returns a structure output that contains information about the optimization. Returns a value exitflag that describes the exit condition. Returns the value of the objective function fun at the solution x. Pass an empty matrix for options to use the default values for options. Passes the problem-dependent parameters P1, P2, etc., directly to the function fun. Minimizes with the optimization parameters specified in the structure options. Starts at x0 and tries to solve the equations described in fun. = fsolve(.)įsolve finds a root (zero) of a system of nonlinear equations. Fsolve (Optimization Toolbox) Optimization Toolboxįor x, where x is a vector and F(x) is a function that returns a vector value. ![]()
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