code: def fmin_l_bfgs_b(
      func,
      x0,
      fprime=None,
      args=(),
      approx_grad=0,
      bounds=None,
      m=10,
      factr=1e7,
      pgtol=1e-5,
      epsilon=1e-8,
      iprint=-1,
      maxfun=15000,
      maxiter=15000,
      disp=None,
      callback=None,
      maxls=20,
  ):
      """
      Minimize a function func using the L-BFGS-B algorithm.
  
      Parameters
      ----------
      func : callable f(x,*args)
          Function to minimise.
      x0 : ndarray
          Initial guess.
      fprime : callable fprime(x,*args), optional
          The gradient of `func`.  If None, then `func` returns the function
          value and the gradient (``f, g = func(x, *args)``), unless
          `approx_grad` is True in which case `func` returns only ``f``.
      args : sequence, optional
          Arguments to pass to `func` and `fprime`.
      approx_grad : bool, optional
          Whether to approximate the gradient numerically (in which case
          `func` returns only the function value).
      bounds : list, optional
          ``(min, max)`` pairs for each element in ``x``, defining
          the bounds on that parameter. Use None or +-inf for one of ``min`` or
          ``max`` when there is no bound in that direction.
      m : int, optional
          The maximum number of variable metric corrections
          used to define the limited memory matrix. (The limited memory BFGS
          method does not store the full hessian but uses this many terms in an
          approximation to it.)
      factr : float, optional
          The iteration stops when
          ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``,
          where ``eps`` is the machine precision, which is automatically
          generated by the code. Typical values for `factr` are: 1e12 for
          low accuracy; 1e7 for moderate accuracy; 10.0 for extremely
          high accuracy. See Notes for relationship to `ftol`, which is exposed
          (instead of `factr`) by the `scipy.optimize.minimize` interface to
          L-BFGS-B.
      pgtol : float, optional
          The iteration will stop when
          ``max{|proj g_i | i = 1, ..., n} <= pgtol``
          where ``pg_i`` is the i-th component of the projected gradient.
      epsilon : float, optional
          Step size used when `approx_grad` is True, for numerically
          calculating the gradient
      iprint : int, optional
          Controls the frequency of output. ``iprint < 0`` means no output;
          ``iprint = 0``    print only one line at the last iteration;
          ``0 < iprint < 99`` print also f and ``|proj g|`` every iprint iterations;
          ``iprint = 99``   print details of every iteration except n-vectors;
          ``iprint = 100``  print also the changes of active set and final x;
          ``iprint > 100``  print details of every iteration including x and g.
      disp : int, optional
          If zero, then no output.  If a positive number, then this over-rides
          `iprint` (i.e., `iprint` gets the value of `disp`).
      maxfun : int, optional
          Maximum number of function evaluations.
      maxiter : int, optional
          Maximum number of iterations.
      callback : callable, optional
          Called after each iteration, as ``callback(xk)``, where ``xk`` is the
          current parameter vector.
      maxls : int, optional
          Maximum number of line search steps (per iteration). Default is 20.
  
      Returns
      -------
      x : array_like
          Estimated position of the minimum.
      f : float
          Value of `func` at the minimum.
      d : dict
          Information dictionary.
  
          * d['warnflag'] is
  
            - 0 if converged,
            - 1 if too many function evaluations or too many iterations,
            - 2 if stopped for another reason, given in d['task']
  
          * d['grad'] is the gradient at the minimum (should be 0 ish)
          * d['funcalls'] is the number of function calls made.
          * d['nit'] is the number of iterations.
  
      See also
      --------
      minimize: Interface to minimization algorithms for multivariate
          functions. See the 'L-BFGS-B' `method` in particular. Note that the
          `ftol` option is made available via that interface, while `factr` is
          provided via this interface, where `factr` is the factor multiplying
          the default machine floating-point precision to arrive at `ftol`:
          ``ftol = factr * numpy.finfo(float).eps``.
  
      Notes
      -----
      License of L-BFGS-B (FORTRAN code):
  
      The version included here (in fortran code) is 3.0
      (released April 25, 2011).  It was written by Ciyou Zhu, Richard Byrd,
      and Jorge Nocedal <nocedal@ece.nwu.edu>. It carries the following
      condition for use:
  
      This software is freely available, but we expect that all publications
      describing work using this software, or all commercial products using it,
      quote at least one of the references given below. This software is released
      under the BSD License.
  
      References
      ----------
      * R. H. Byrd, P. Lu and J. Nocedal. A Limited Memory Algorithm for Bound
        Constrained Optimization, (1995), SIAM Journal on Scientific and
        Statistical Computing, 16, 5, pp. 1190-1208.
      * C. Zhu, R. H. Byrd and J. Nocedal. L-BFGS-B: Algorithm 778: L-BFGS-B,
        FORTRAN routines for large scale bound constrained optimization (1997),
        ACM Transactions on Mathematical Software, 23, 4, pp. 550 - 560.
      * J.L. Morales and J. Nocedal. L-BFGS-B: Remark on Algorithm 778: L-BFGS-B,
        FORTRAN routines for large scale bound constrained optimization (2011),
        ACM Transactions on Mathematical Software, 38, 1.
  
      """
      # handle fprime/approx_grad
      if approx_grad:
          fun = func
          jac = None
      elif fprime is None:
          fun = MemoizeJac(func)
          jac = fun.derivative
      else:
          fun = func
          jac = fprime
  
      # build options
      if disp is None:
          disp = iprint
      opts = {
          "disp": disp,
          "iprint": iprint,
          "maxcor": m,
          "ftol": factr * np.finfo(float).eps,
          "gtol": pgtol,
          "eps": epsilon,
          "maxfun": maxfun,
          "maxiter": maxiter,
          "callback": callback,
          "maxls": maxls,
      }
  
      res = _minimize_lbfgsb(
          fun, x0, args=args, jac=jac, bounds=bounds, **opts
      )
      d = {
          "grad": res["jac"],
          "task": res["message"],
          "funcalls": res["nfev"],
          "nit": res["nit"],
          "warnflag": res["status"],
      }
      f = res["fun"]
      x = res["x"]
  
      return x, f, d
  
file_path: catboost/contrib/python/scipy/py2/scipy/optimize/lbfgsb.py
imports: from __future__ import division, print_function, absolute_import
  import numpy
  from numpy import array, asarray, float64, int32, zeros
  from .None import _lbfgsb
  from .optimize import MemoizeJac, OptimizeResult, _check_unknown_options, wrap_function, _approx_fprime_helper
  from scipy.sparse.linalg import LinearOperator
label_desc: Use image node_id 1 for calling a global function with example usage: fmin_l_bfgs_b(func, x0, fprime, args, approx_grad, bounds, m, factr, pgtol, epsilon, iprint, maxfun, maxiter, disp, callback, maxls) and returns: x,  f,  d