#!/usr/bin/env python3
"``naginterfaces.library.opt.lsq_gencon_deriv`` Python Example."

# nAG Copyright 2018-2019.

# pylint: disable=invalid-name,too-many-arguments,too-many-locals

from math import exp

import numpy as np

from naginterfaces.library import opt

def main():
    """
    Example for :func:`naginterfaces.library.opt.lsq_gencon_deriv`.

    Minimum of a sum of squares, nonlinear constraints, dense, active-set SQP
    method, using function values and optionally first derivatives.

    >>> main()
    naginterfaces.library.opt.lsq_gencon_deriv Python Example Results.
    Minimizing Problem 57 from Hock and Schittkowski's
    'Test Examples for Nonlinear Scripting Codes'.
    Final function value is 1.42298348615e-02.
    """

    print(
        'naginterfaces.library.opt.lsq_gencon_deriv Python Example Results.'
    )
    print('Minimizing Problem 57 from Hock and Schittkowski\'s')
    print('\'Test Examples for Nonlinear Scripting Codes\'.')

    def cb_confun(mode, needc, x, cjac, nstate):
        "The nonlinear constraint and its first derivatives."

        if needc[0] <= 0 or mode == 1:
            c = [0.]*len(needc)
        elif mode in [0, 2]:
            c = [0.49*x[1] - x[0]*x[1]]

        if needc[0] <= 0:
            return c

        if mode in [1, 2]:
            cjac[0, 0] = -x[1]
            cjac[0, 1] = -x[0] + 0.49

        return c

    def cb_objfun(mode, needfi, x, fjac, nstate):
        """
        The (two-variable) sum of squares function to minimize,
        and its first derivatives.
        """

        # The set of 44 'a' data values:
        a = [
            8., 8., 10., 10., 10., 10., 12., 12., 12.,
            12., 14., 14., 14., 16., 16., 16., 18., 18.,
            20., 20., 20., 22.,
            22., 22., 24., 24., 24., 26., 26., 26., 28.,
            28., 30., 30., 30., 32., 32., 34., 36., 36.,
            38., 38., 40., 42.,
        ]
        m = fjac.shape[0]
        f = np.empty(m)

        for fi in range(m):
            exp_term = exp(-x[1]*(a[fi] - 8.))

            if needfi == fi + 1 or mode in [0, 2]:
                f[fi] = x[0] + (0.49 - x[0])*exp_term

                if needfi == fi + 1:
                    return f

            if mode in [1, 2]:
                fjac[fi, 0] = 1. - exp_term
                fjac[fi, 1] = -(0.49 - x[0])*(a[fi] - 8.)*exp_term

        return f

    # Initialize the communication structure:
    comm = opt.nlp1_init('lsq_gencon_deriv')

    # The configuration for this problem.
    # One nonlinear constraint (defined by confun):
    ncnln = 1
    # The linear constraints:
    a = [[1., 1.]]
    # The bounds on x and on the constraints:
    bl = [0.4, -4., 1., 0.09]
    # 'Infinite' upper bounds:
    bu = [1.e25]*len(bl)
    # The coefficients of the constant vector in the objective:
    y = [
        0.49, 0.49, 0.48, 0.47, 0.48, 0.47, 0.46, 0.46, 0.45, 0.43, 0.45,
        0.43, 0.43, 0.44, 0.43, 0.43, 0.46, 0.45, 0.42, 0.42, 0.43, 0.41,
        0.41, 0.40, 0.42, 0.40, 0.40, 0.41, 0.40, 0.41, 0.41, 0.40, 0.40,
        0.40, 0.38, 0.41, 0.40, 0.40, 0.41, 0.38, 0.40, 0.40, 0.39, 0.39
    ]
    # Initial estimate of the solution:
    x = [0.4, 0.]
    n = len(x)
    # Zero the initial nonlinear-constraint Jacobian, which has an effect
    # here because of the default setting of 'Derivative Level' (level 3):
    cjac = np.zeros((ncnln, n))

    # Solve the problem:
    objf = opt.lsq_gencon_deriv(
        bl, bu, y, cb_objfun, x, comm, a=a, confun=cb_confun, cjac=cjac,
    ).objf

    print('Final function value is {:.11e}.'.format(objf))

if __name__ == '__main__':
    main()
    import doctest
    import sys
    sys.exit(
        doctest.testmod(
            None, verbose=True, report=False,
            optionflags=doctest.ELLIPSIS | doctest.REPORT_NDIFF,
        ).failed
    )