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scipy.optimize.

# fminbound

scipy.optimize.fminbound(func, x1, x2, args=(), xtol=1e-05, maxfun=500, full_output=0, disp=1)

  Bounded minimization for scalar functions.

  Parameters:
    func callable f(x,*args)

      Objective function to be minimized (must accept and return scalars).

    x1, x2 float or array scalar

      Finite optimization bounds.

    args tuple, optional

      Extra arguments passed to function.

    xtol float, optional

      The convergence tolerance.

    maxfun int, optional

      Maximum number of function evaluations allowed.

    full_output bool, optional

      If True, return optional outputs.

    disp: int, optional

      If non-zero, print messages.

      `0` : no message printing.

      `1` : non-convergence notification messages only.

      `2` : print a message on convergence too.

      `3` : print iteration results.

  Returns:
    xopt ndarray

      Parameters (over given interval) which minimize the objective function.

    fval number

      (Optional output) The function value evaluated at the minimizer.

    ierr int

      (Optional output) An error flag (0 if converged, 1 if maximum number of function calls reached).

    numfunc int

      (Optional output) The number of function calls made.

  See also

  `minimize_scalar`

    Interface to minimization algorithms for scalar univariate functions. See the ‘Bounded’ method in particular.

  Notes

  Finds a local minimizer of the scalar function func in the interval x1 < xopt < x2 using Brent’s method. (See `brent` for auto-bracketing.)

  References

  [1]

  Forsythe, G.E., M. A. Malcolm, and C. B. Moler. “Computer Methods for Mathematical Computations.” Prentice-Hall Series in Automatic Computation 259 (1977).

  [2]

  Brent, Richard P. Algorithms for Minimization Without Derivatives. Courier Corporation, 2013.

  Examples

  `fminbound` finds the minimizer of the function in the given range. The following examples illustrate this.

      >>> from scipy import optimize
      >>> def f(x):
      ...     return (x-1)**2
      >>> minimizer = optimize.fminbound(f, -4, 4)
      >>> minimizer
      1.0
      >>> minimum = f(minimizer)
      >>> minimum
      0.0
      >>> res = optimize.fminbound(f, 3, 4, full_output=True)
      >>> minimizer, fval, ierr, numfunc = res
      >>> minimizer
      3.000005960860986
      >>> minimum = f(minimizer)
      >>> minimum, fval
      (4.000023843479476, 4.000023843479476)