code: def _minimize_slsqp(
      func,
      x0,
      args=(),
      jac=None,
      bounds=None,
      constraints=(),
      maxiter=100,
      ftol=1.0e-6,
      iprint=1,
      disp=False,
      eps=_epsilon,
      callback=None,
      **unknown_options,
  ):
      """
      Minimize a scalar function of one or more variables using Sequential
      Least SQuares Programming (SLSQP).
  
      Options
      -------
      ftol : float
          Precision goal for the value of f in the stopping criterion.
      eps : float
          Step size used for numerical approximation of the Jacobian.
      disp : bool
          Set to True to print convergence messages. If False,
          `verbosity` is ignored and set to 0.
      maxiter : int
          Maximum number of iterations.
  
      """
      _check_unknown_options(unknown_options)
      fprime = jac
      iter = maxiter
      acc = ftol
      epsilon = eps
  
      if not disp:
          iprint = 0
  
      # Constraints are triaged per type into a dictionary of tuples
      if isinstance(constraints, dict):
          constraints = (constraints,)
  
      cons = {"eq": (), "ineq": ()}
      for ic, con in enumerate(constraints):
          # check type
          try:
              ctype = con["type"].lower()
          except KeyError:
              raise KeyError("Constraint %d has no type defined." % ic)
          except TypeError:
              raise TypeError(
                  "Constraints must be defined using a " "dictionary."
              )
          except AttributeError:
              raise TypeError("Constraint's type must be a string.")
          else:
              if ctype not in ["eq", "ineq"]:
                  raise ValueError(
                      "Unknown constraint type '%s'." % con["type"]
                  )
  
          # check function
          if "fun" not in con:
              raise ValueError(
                  "Constraint %d has no function defined." % ic
              )
  
          # check Jacobian
          cjac = con.get("jac")
          if cjac is None:
              # approximate Jacobian function.  The factory function is needed
              # to keep a reference to `fun`, see gh-4240.
              def cjac_factory(fun):
                  def cjac(x, *args):
                      return approx_jacobian(x, fun, epsilon, *args)
  
                  return cjac
  
              cjac = cjac_factory(con["fun"])
  
          # update constraints' dictionary
          cons[ctype] += (
              {
                  "fun": con["fun"],
                  "jac": cjac,
                  "args": con.get("args", ()),
              },
          )
  
      exit_modes = {
          -1: "Gradient evaluation required (g & a)",
          0: "Optimization terminated successfully.",
          1: "Function evaluation required (f & c)",
          2: "More equality constraints than independent variables",
          3: "More than 3*n iterations in LSQ subproblem",
          4: "Inequality constraints incompatible",
          5: "Singular matrix E in LSQ subproblem",
          6: "Singular matrix C in LSQ subproblem",
          7: "Rank-deficient equality constraint subproblem HFTI",
          8: "Positive directional derivative for linesearch",
          9: "Iteration limit exceeded",
      }
  
      # Wrap func
      feval, func = wrap_function(func, args)
  
      # Wrap fprime, if provided, or approx_jacobian if not
      if fprime:
          geval, fprime = wrap_function(fprime, args)
      else:
          geval, fprime = wrap_function(
              approx_jacobian, (func, epsilon)
          )
  
      # Transform x0 into an array.
      x = asfarray(x0).flatten()
  
      # Set the parameters that SLSQP will need
      # meq, mieq: number of equality and inequality constraints
      meq = sum(
          map(
              len,
              [atleast_1d(c["fun"](x, *c["args"])) for c in cons["eq"]],
          )
      )
      mieq = sum(
          map(
              len,
              [
                  atleast_1d(c["fun"](x, *c["args"]))
                  for c in cons["ineq"]
              ],
          )
      )
      # m = The total number of constraints
      m = meq + mieq
      # la = The number of constraints, or 1 if there are no constraints
      la = array([1, m]).max()
      # n = The number of independent variables
      n = len(x)
  
      # Define the workspaces for SLSQP
      n1 = n + 1
      mineq = m - meq + n1 + n1
      len_w = (
          (3 * n1 + m) * (n1 + 1)
          + (n1 - meq + 1) * (mineq + 2)
          + 2 * mineq
          + (n1 + mineq) * (n1 - meq)
          + 2 * meq
          + n1
          + ((n + 1) * n) // 2
          + 2 * m
          + 3 * n
          + 3 * n1
          + 1
      )
      len_jw = mineq
      w = zeros(len_w)
      jw = zeros(len_jw)
  
      # Decompose bounds into xl and xu
      if bounds is None or len(bounds) == 0:
          xl = np.empty(n, dtype=float)
          xu = np.empty(n, dtype=float)
          xl.fill(np.nan)
          xu.fill(np.nan)
      else:
          bnds = array(bounds, float)
          if bnds.shape[0] != n:
              raise IndexError(
                  "SLSQP Error: the length of bounds is not "
                  "compatible with that of x0."
              )
  
          with np.errstate(invalid="ignore"):
              bnderr = bnds[:, 0] > bnds[:, 1]
  
          if bnderr.any():
              raise ValueError(
                  "SLSQP Error: lb > ub in bounds %s."
                  % ", ".join(str(b) for b in bnderr)
              )
          xl, xu = bnds[:, 0], bnds[:, 1]
  
          # Mark infinite bounds with nans; the Fortran code understands this
          infbnd = ~isfinite(bnds)
          xl[infbnd[:, 0]] = np.nan
          xu[infbnd[:, 1]] = np.nan
  
      # Clip initial guess to bounds (SLSQP may fail with bounds-infeasible
      # initial point)
      have_bound = np.isfinite(xl)
      x[have_bound] = np.clip(x[have_bound], xl[have_bound], np.inf)
      have_bound = np.isfinite(xu)
      x[have_bound] = np.clip(x[have_bound], -np.inf, xu[have_bound])
  
      # Initialize the iteration counter and the mode value
      mode = array(0, int)
      acc = array(acc, float)
      majiter = array(iter, int)
      majiter_prev = 0
  
      # Initialize internal SLSQP state variables
      alpha = array(0, float)
      f0 = array(0, float)
      gs = array(0, float)
      h1 = array(0, float)
      h2 = array(0, float)
      h3 = array(0, float)
      h4 = array(0, float)
      t = array(0, float)
      t0 = array(0, float)
      tol = array(0, float)
      iexact = array(0, int)
      incons = array(0, int)
      ireset = array(0, int)
      itermx = array(0, int)
      line = array(0, int)
      n1 = array(0, int)
      n2 = array(0, int)
      n3 = array(0, int)
  
      # Print the header if iprint >= 2
      if iprint >= 2:
          print("%5s %5s %16s %16s" % ("NIT", "FC", "OBJFUN", "GNORM"))
  
      while 1:
          if (
              mode == 0 or mode == 1
          ):  # objective and constraint evaluation required
              # Compute objective function
              fx = func(x)
              try:
                  fx = float(np.asarray(fx))
              except (TypeError, ValueError):
                  raise ValueError(
                      "Objective function must return a scalar"
                  )
              # Compute the constraints
              if cons["eq"]:
                  c_eq = concatenate(
                      [
                          atleast_1d(con["fun"](x, *con["args"]))
                          for con in cons["eq"]
                      ]
                  )
              else:
                  c_eq = zeros(0)
              if cons["ineq"]:
                  c_ieq = concatenate(
                      [
                          atleast_1d(con["fun"](x, *con["args"]))
                          for con in cons["ineq"]
                      ]
                  )
              else:
                  c_ieq = zeros(0)
  
              # Now combine c_eq and c_ieq into a single matrix
              c = concatenate((c_eq, c_ieq))
  
          if mode == 0 or mode == -1:  # gradient evaluation required
              # Compute the derivatives of the objective function
              # For some reason SLSQP wants g dimensioned to n+1
              g = append(fprime(x), 0.0)
  
              # Compute the normals of the constraints
              if cons["eq"]:
                  a_eq = vstack(
                      [
                          con["jac"](x, *con["args"])
                          for con in cons["eq"]
                      ]
                  )
              else:  # no equality constraint
                  a_eq = zeros((meq, n))
  
              if cons["ineq"]:
                  a_ieq = vstack(
                      [
                          con["jac"](x, *con["args"])
                          for con in cons["ineq"]
                      ]
                  )
              else:  # no inequality constraint
                  a_ieq = zeros((mieq, n))
  
              # Now combine a_eq and a_ieq into a single a matrix
              if m == 0:  # no constraints
                  a = zeros((la, n))
              else:
                  a = vstack((a_eq, a_ieq))
              a = concatenate((a, zeros([la, 1])), 1)
  
          # Call SLSQP
          slsqp(
              m,
              meq,
              x,
              xl,
              xu,
              fx,
              c,
              g,
              a,
              acc,
              majiter,
              mode,
              w,
              jw,
              alpha,
              f0,
              gs,
              h1,
              h2,
              h3,
              h4,
              t,
              t0,
              tol,
              iexact,
              incons,
              ireset,
              itermx,
              line,
              n1,
              n2,
              n3,
          )
  
          # call callback if major iteration has incremented
          if callback is not None and majiter > majiter_prev:
              callback(np.copy(x))
  
          # Print the status of the current iterate if iprint > 2 and the
          # major iteration has incremented
          if iprint >= 2 and majiter > majiter_prev:
              print(
                  "%5i %5i % 16.6E % 16.6E"
                  % (majiter, feval[0], fx, linalg.norm(g))
              )
  
          # If exit mode is not -1 or 1, slsqp has completed
          if abs(mode) != 1:
              break
  
          majiter_prev = int(majiter)
  
      # Optimization loop complete.  Print status if requested
      if iprint >= 1:
          print(
              exit_modes[int(mode)]
              + "    (Exit mode "
              + str(mode)
              + ")"
          )
          print("            Current function value:", fx)
          print("            Iterations:", majiter)
          print("            Function evaluations:", feval[0])
          print("            Gradient evaluations:", geval[0])
  
      return OptimizeResult(
          x=x,
          fun=fx,
          jac=g[:-1],
          nit=int(majiter),
          nfev=feval[0],
          njev=geval[0],
          status=int(mode),
          message=exit_modes[int(mode)],
          success=(mode == 0),
      )
  
file_path: catboost/contrib/python/scipy/py2/scipy/optimize/slsqp.py
imports: from __future__ import division, print_function, absolute_import
  import numpy
  from scipy.optimize._slsqp import slsqp
  from numpy import zeros, array, linalg, append, asfarray, concatenate, finfo, sqrt, vstack, exp, inf, isfinite, atleast_1d
  from .optimize import wrap_function, OptimizeResult, _check_unknown_options
label_desc: Use image node_id 3 for calling a global function with example usage: _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback) and returns: OptimizeResult, cjac, approx_jacobian