Optimization and root finding (scipy.optimize)¶
Optimization¶
General-purpose¶
| minimize(fun, x0[, args, method, jac, hess, ...]) | Minimization of scalar function of one or more variables. |
| fmin(func, x0[, args, xtol, ftol, maxiter, ...]) | Minimize a function using the downhill simplex algorithm. |
| fmin_powell(func, x0[, args, xtol, ftol, ...]) | Minimize a function using modified Powell’s method. This method |
| fmin_cg(f, x0[, fprime, args, gtol, norm, ...]) | Minimize a function using a nonlinear conjugate gradient algorithm. |
| fmin_bfgs(f, x0[, fprime, args, gtol, norm, ...]) | Minimize a function using the BFGS algorithm. |
| fmin_ncg(f, x0, fprime[, fhess_p, fhess, ...]) | Unconstrained minimization of a function using the Newton-CG method. |
| leastsq(func, x0[, args, Dfun, full_output, ...]) | Minimize the sum of squares of a set of equations. |
Constrained (multivariate)¶
| fmin_l_bfgs_b(func, x0[, fprime, args, ...]) | Minimize a function func using the L-BFGS-B algorithm. |
| fmin_tnc(func, x0[, fprime, args, ...]) | Minimize a function with variables subject to bounds, using |
| fmin_cobyla(func, x0, cons[, args, ...]) | Minimize a function using the Constrained Optimization BY Linear |
| fmin_slsqp(func, x0[, eqcons, f_eqcons, ...]) | Minimize a function using Sequential Least SQuares Programming |
| nnls(A, b) | Solve argmin_x || Ax - b ||_2 for x>=0. This is a wrapper |
Global¶
| anneal(func, x0[, args, schedule, ...]) | Minimize a function using simulated annealing. |
| brute(func, ranges[, args, Ns, full_output, ...]) | Minimize a function over a given range by brute force. |
Scalar function minimizers¶
| minimize_scalar(fun[, bracket, bounds, ...]) | Minimization of scalar function of one variable. |
| fminbound(func, x1, x2[, args, xtol, ...]) | Bounded minimization for scalar functions. |
| brent(func[, args, brack, tol, full_output, ...]) | Given a function of one-variable and a possible bracketing interval, return the minimum of the function isolated to a fractional precision of tol. |
| golden(func[, args, brack, tol, full_output]) | Given a function of one-variable and a possible bracketing interval, return the minimum of the function isolated to a fractional precision of tol. |
| bracket(func[, xa, xb, args, grow_limit, ...]) | Bracket the minimum of the function. |
Rosenbrock function¶
| rosen(x) | The Rosenbrock function. |
| rosen_der(x) | The derivative (i.e. |
| rosen_hess(x) | The Hessian matrix of the Rosenbrock function. |
| rosen_hess_prod(x, p) | Product of the Hessian matrix of the Rosenbrock function with a vector. |
Fitting¶
| curve_fit(f, xdata, ydata[, p0, sigma]) | Use non-linear least squares to fit a function, f, to data. |
Root finding¶
Scalar functions¶
| brentq(f, a, b[, args, xtol, rtol, maxiter, ...]) | Find a root of a function in given interval. |
| brenth(f, a, b[, args, xtol, rtol, maxiter, ...]) | Find root of f in [a,b]. |
| ridder(f, a, b[, args, xtol, rtol, maxiter, ...]) | Find a root of a function in an interval. |
| bisect(f, a, b[, args, xtol, rtol, maxiter, ...]) | Find root of f in [a,b]. |
| newton(func, x0[, fprime, args, tol, ...]) | Find a zero using the Newton-Raphson or secant method. |
Fixed point finding:
| fixed_point(func, x0[, args, xtol, maxiter]) | Find the point where func(x) == x |
Multidimensional¶
General nonlinear solvers:
| root(fun, x0[, args, method, jac, tol, ...]) | Find a root of a vector function. |
| fsolve(func, x0[, args, fprime, ...]) | Find the roots of a function. |
| broyden1(F, xin[, iter, alpha, ...]) | Find a root of a function, using Broyden’s first Jacobian approximation. |
| broyden2(F, xin[, iter, alpha, ...]) | Find a root of a function, using Broyden’s second Jacobian approximation. |
Large-scale nonlinear solvers:
| newton_krylov(F, xin[, iter, rdiff, method, ...]) | Find a root of a function, using Krylov approximation for inverse Jacobian. |
| anderson(F, xin[, iter, alpha, w0, M, ...]) | Find a root of a function, using (extended) Anderson mixing. |
Simple iterations:
| excitingmixing(F, xin[, iter, alpha, ...]) | Find a root of a function, using a tuned diagonal Jacobian approximation. |
| linearmixing(F, xin[, iter, alpha, verbose, ...]) | Find a root of a function, using a scalar Jacobian approximation. |
| diagbroyden(F, xin[, iter, alpha, verbose, ...]) | Find a root of a function, using diagonal Broyden Jacobian approximation. |
Utility Functions¶
| line_search(f, myfprime, xk, pk[, gfk, ...]) | Find alpha that satisfies strong Wolfe conditions. |
| check_grad(func, grad, x0, *args) | Check the correctness of a gradient function by comparing it against a (forward) finite-difference approximation of the gradient. |
| show_options(solver[, method]) | Show documentation for additional options of optimization solvers. |
