"""
A top-level linear programming interface. Currently this interface solves
linear programming problems via the Simplex and Interior-Point methods.

.. versionadded:: 0.15.0

Functions
---------
.. autosummary::
   :toctree: generated/

    linprog
    linprog_verbose_callback
    linprog_terse_callback

"""

from __future__ import division, print_function, absolute_import

import numpy as np

from .optimize import OptimizeResult, OptimizeWarning
from warnings import warn
from ._linprog_ip import _linprog_ip
from ._linprog_simplex import _linprog_simplex
from ._linprog_rs import _linprog_rs
from ._linprog_util import (
    _parse_linprog, _presolve, _get_Abc, _postprocess
    )

__all__ = ['linprog', 'linprog_verbose_callback', 'linprog_terse_callback']

__docformat__ = "restructuredtext en"


def linprog_verbose_callback(res):
    """
    A sample callback function demonstrating the linprog callback interface.
    This callback produces detailed output to sys.stdout before each iteration
    and after the final iteration of the simplex algorithm.

    Parameters
    ----------
    res : A `scipy.optimize.OptimizeResult` consisting of the following fields:

        x : 1D array
            The independent variable vector which optimizes the linear
            programming problem.
        fun : float
            Value of the objective function.
        success : bool
            True if the algorithm succeeded in finding an optimal solution.
        slack : 1D array
            The values of the slack variables. Each slack variable corresponds
            to an inequality constraint. If the slack is zero, then the
            corresponding constraint is active.
        con : 1D array
            The (nominally zero) residuals of the equality constraints, that is,
            ``b - A_eq @ x``
        phase : int
            The phase of the optimization being executed. In phase 1 a basic
            feasible solution is sought and the T has an additional row
            representing an alternate objective function.
        status : int
            An integer representing the exit status of the optimization::

                 0 : Optimization terminated successfully
                 1 : Iteration limit reached
                 2 : Problem appears to be infeasible
                 3 : Problem appears to be unbounded
                 4 : Serious numerical difficulties encountered

        nit : int
            The number of iterations performed.
        message : str
            A string descriptor of the exit status of the optimization.
    """
    x = res['x']
    fun = res['fun']
    phase = res['phase']
    status = res['status']
    nit = res['nit']
    message = res['message']
    complete = res['complete']

    saved_printoptions = np.get_printoptions()
    np.set_printoptions(linewidth=500,
                        formatter={'float': lambda x: "{0: 12.4f}".format(x)})
    if status:
        print('--------- Simplex Early Exit -------\n'.format(nit))
        print('The simplex method exited early with status {0:d}'.format(status))
        print(message)
    elif complete:
        print('--------- Simplex Complete --------\n')
        print('Iterations required: {}'.format(nit))
    else:
        print('--------- Iteration {0:d}  ---------\n'.format(nit))

    if nit > 0:
        if phase == 1:
            print('Current Pseudo-Objective Value:')
        else:
            print('Current Objective Value:')
        print('f = ', fun)
        print()
        print('Current Solution Vector:')
        print('x = ', x)
        print()

    np.set_printoptions(**saved_printoptions)


def linprog_terse_callback(res):
    """
    A sample callback function demonstrating the linprog callback interface.
    This callback produces brief output to sys.stdout before each iteration
    and after the final iteration of the simplex algorithm.

    Parameters
    ----------
    res : A `scipy.optimize.OptimizeResult` consisting of the following fields:

        x : 1D array
            The independent variable vector which optimizes the linear
            programming problem.
        fun : float
            Value of the objective function.
        success : bool
            True if the algorithm succeeded in finding an optimal solution.
        slack : 1D array
            The values of the slack variables. Each slack variable corresponds
            to an inequality constraint. If the slack is zero, then the
            corresponding constraint is active.
        con : 1D array
            The (nominally zero) residuals of the equality constraints, that is,
            ``b - A_eq @ x``.
        phase : int
            The phase of the optimization being executed. In phase 1 a basic
            feasible solution is sought and the T has an additional row
            representing an alternate objective function.
        status : int
            An integer representing the exit status of the optimization::

                 0 : Optimization terminated successfully
                 1 : Iteration limit reached
                 2 : Problem appears to be infeasible
                 3 : Problem appears to be unbounded
                 4 : Serious numerical difficulties encountered

        nit : int
            The number of iterations performed.
        message : str
            A string descriptor of the exit status of the optimization.
    """
    nit = res['nit']
    x = res['x']

    if nit == 0:
        print("Iter:   X:")
    print("{0: <5d}   ".format(nit), end="")
    print(x)


def linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None,
            bounds=None, method='interior-point', callback=None,
            options=None, x0=None):
    r"""
    Linear programming: minimize a linear objective function subject to linear
    equality and inequality constraints.

    Linear programming solves problems of the following form:

    .. math::

        \min_x \ & c^T x \\
        \mbox{such that} \ & A_{ub} x \leq b_{ub},\\
        & A_{eq} x = b_{eq},\\
        & l \leq x \leq u ,

    where :math:`x` is a vector of decision variables; :math:`c`,
    :math:`b_{ub}`, :math:`b_{eq}`, :math:`l`, and :math:`u` are vectors; and
    :math:`A_{ub}` and :math:`A_{eq}` are matrices.

    Informally, that's:

    minimize::

        c @ x

    such that::

        A_ub @ x <= b_ub
        A_eq @ x == b_eq
        lb <= x <= ub

    Note that by default ``lb = 0`` and ``ub = None`` unless specified with
    ``bounds``.

    Parameters
    ----------
    c : 1D array
        The coefficients of the linear objective function to be minimized.
    A_ub : 2D array, optional
        The inequality constraint matrix. Each row of ``A_ub`` specifies the
        coefficients of a linear inequality constraint on ``x``.
    b_ub : 1D array, optional
        The inequality constraint vector. Each element represents an
        upper bound on the corresponding value of ``A_ub @ x``.
    A_eq : 2D array, optional
        The equality constraint matrix. Each row of ``A_eq`` specifies the
        coefficients of a linear equality constraint on ``x``.
    b_eq : 1D array, optional
        The equality constraint vector. Each element of ``A_eq @ x`` must equal
        the corresponding element of ``b_eq``.
    bounds : sequence, optional
        A sequence of ``(min, max)`` pairs for each element in ``x``, defining
        the minimum and maximum values of that decision variable. Use ``None`` to
        indicate that there is no bound. By default, bounds are ``(0, None)``
        (all decision variables are non-negative).
        If a single tuple ``(min, max)`` is provided, then ``min`` and
        ``max`` will serve as bounds for all decision variables.
    method : {'interior-point', 'revised simplex', 'simplex'}, optional
        The algorithm used to solve the standard form problem.
        :ref:`'interior-point' <optimize.linprog-interior-point>` (default),
        :ref:`'revised simplex' <optimize.linprog-revised_simplex>`, and
        :ref:`'simplex' <optimize.linprog-simplex>` (legacy)
        are supported.
    callback : callable, optional
        If a callback function is provided, it will be called at least once per
        iteration of the algorithm. The callback function must accept a single
        `scipy.optimize.OptimizeResult` consisting of the following fields:

            x : 1D array
                The current solution vector.
            fun : float
                The current value of the objective function ``c @ x``.
            success : bool
                ``True`` when the algorithm has completed successfully.
            slack : 1D array
                The (nominally positive) values of the slack,
                ``b_ub - A_ub @ x``.
            con : 1D array
                The (nominally zero) residuals of the equality constraints,
                ``b_eq - A_eq @ x``.
            phase : int
                The phase of the algorithm being executed.
            status : int
                An integer representing the status of the algorithm.

                ``0`` : Optimization proceeding nominally.

                ``1`` : Iteration limit reached.

                ``2`` : Problem appears to be infeasible.

                ``3`` : Problem appears to be unbounded.

                ``4`` : Numerical difficulties encountered.

            nit : int
                The current iteration number.
            message : str
                A string descriptor of the algorithm status.

    options : dict, optional
        A dictionary of solver options. All methods accept the following
        options:

            maxiter : int
                Maximum number of iterations to perform.
            disp : bool
                Set to ``True`` to print convergence messages.

        For method-specific options, see
        :func:`show_options('linprog') <show_options>`.

    x0 : 1D array, optional
        Guess values of the decision variables, which will be refined by
        the optimization algorithm. This argument is currently used only by the
        'revised simplex' method, and can only be used if `x0` represents a
        basic feasible solution.


    Returns
    -------
    res : OptimizeResult
        A :class:`scipy.optimize.OptimizeResult` consisting of the fields:

            x : 1D array
                The values of the decision variables that minimizes the
                objective function while satisfying the constraints.
            fun : float
                The optimal value of the objective function ``c @ x``.
            slack : 1D array
                The (nominally positive) values of the slack variables,
                ``b_ub - A_ub @ x``.
            con : 1D array
                The (nominally zero) residuals of the equality constraints,
                ``b_eq - A_eq @ x``.
            success : bool
                ``True`` when the algorithm succeeds in finding an optimal
                solution.
            status : int
                An integer representing the exit status of the algorithm.

                ``0`` : Optimization terminated successfully.

                ``1`` : Iteration limit reached.

                ``2`` : Problem appears to be infeasible.

                ``3`` : Problem appears to be unbounded.

                ``4`` : Numerical difficulties encountered.

            nit : int
                The total number of iterations performed in all phases.
            message : str
                A string descriptor of the exit status of the algorithm.

    See Also
    --------
    show_options : Additional options accepted by the solvers.

    Notes
    -----
    This section describes the available solvers that can be selected by the
    'method' parameter.

    :ref:`'interior-point' <optimize.linprog-interior-point>` is the default
    as it is typically the fastest and most robust method.
    :ref:`'revised simplex' <optimize.linprog-revised_simplex>` is more
    accurate for the problems it solves.
    :ref:`'simplex' <optimize.linprog-simplex>` is the legacy method and is
    included for backwards compatibility and educational purposes.

    Method *interior-point* uses the primal-dual path following algorithm
    as outlined in [4]_. This algorithm supports sparse constraint matrices and
    is typically faster than the simplex methods, especially for large, sparse
    problems. Note, however, that the solution returned may be slightly less
    accurate than those of the simplex methods and will not, in general,
    correspond with a vertex of the polytope defined by the constraints.

    .. versionadded:: 1.0.0