#  ___________________________________________________________________________
#
#  Pyomo: Python Optimization Modeling Objects
#  Copyright (c) 2008-2022
#  National Technology and Engineering Solutions of Sandia, LLC
#  Under the terms of Contract DE-NA0003525 with National Technology and
#  Engineering Solutions of Sandia, LLC, the U.S. Government retains certain
#  rights in this software.
#  This software is distributed under the 3-clause BSD License.
#  ___________________________________________________________________________

import os
import pyomo.common.unittest as unittest
import pyomo.environ as pyo
import math

from pyomo.contrib.pynumero.dependencies import (
    numpy as np, numpy_available, scipy, scipy_available
)
from pyomo.common.dependencies.scipy import sparse as spa

if not (numpy_available and scipy_available):
    raise unittest.SkipTest("Pynumero needs scipy and numpy to run NLP tests")

from pyomo.contrib.pynumero.asl import AmplInterface
if not AmplInterface.available():
    raise unittest.SkipTest(
        "Pynumero needs the ASL extension to run CyIpoptSolver tests")

from pyomo.contrib.pynumero.algorithms.solvers.cyipopt_solver import (
    CyIpoptSolver, CyIpoptNLP, cyipopt_available,
)

from pyomo.contrib.pynumero.interfaces.external_grey_box import ExternalGreyBoxModel, ExternalGreyBoxBlock
from pyomo.contrib.pynumero.interfaces.pyomo_nlp import PyomoGreyBoxNLP, PyomoNLP
from pyomo.contrib.pynumero.interfaces.pyomo_grey_box_nlp import PyomoNLPWithGreyBoxBlocks

from pyomo.contrib.pynumero.interfaces.tests.compare_utils import check_vectors_specific_order, check_sparse_matrix_specific_order

def create_pyomo_model(A1, A2, c1, c2, N, dt):
    m = pyo.ConcreteModel()
    
    # timesteps
    m.T = pyo.Set(initialize=list(range(N)), ordered=True)
    m.Tu = pyo.Set(initialize=list(range(N))[1:], ordered=True)
    
    # inputs (controls)
    m.F1 = pyo.Var(m.Tu, bounds=(0,None), initialize={t:1+0.1*t for t in m.Tu})
    m.F2 = pyo.Var(m.Tu, bounds=(0,None), initialize={t:2+0.1*t for t in m.Tu})

    # state variables
    m.h1 = pyo.Var(m.T, bounds=(0,None), initialize={t:3+0.1*t for t in m.T})
    m.h2 = pyo.Var(m.T, bounds=(0,None), initialize={t:4+0.1*t for t in m.T})

    # algebraics (outputs)
    m.F12 = pyo.Var(m.T, bounds=(0,None), initialize={t:5+0.1*t for t in m.T})
    m.Fo = pyo.Var(m.T, bounds=(0,None), initialize={t:6+0.1*t for t in m.T})

    @m.Constraint(m.Tu)
    def h1bal(m, t):
        return (m.h1[t] - m.h1[t-1]) - dt/A1 * (m.F1[t] - c1*pyo.sqrt(m.h1[t])) == 0

    @m.Constraint(m.Tu)
    def h2bal(m, t):
        return (m.h2[t] - m.h2[t-1]) - dt/A2 * (c1*pyo.sqrt(m.h1[t]) + m.F2[t] - c2*pyo.sqrt(m.h2[t])) == 0

    @m.Constraint(m.T)
    def F12con(m, t):
        return c1*pyo.sqrt(m.h1[t]) - m.F12[t] == 0

    @m.Constraint(m.T)
    def Focon(m, t):
        return c2*pyo.sqrt(m.h2[t]) - m.Fo[t] == 0

    @m.Constraint(m.Tu)
    def min_inflow(m, t):
        return 2 <= m.F1[t]

    @m.Constraint(m.T)
    def max_outflow(m, t):
        return m.Fo[t] <= 4.5

    m.h10 = pyo.Constraint( expr=m.h1[m.T.first()] == 1.5 )
    m.h20 = pyo.Constraint( expr=m.h2[m.T.first()] == 0.5 )
    m.obj = pyo.Objective( expr= sum((m.h1[t]-1.0)**2  + (m.h2[t]-1.5)**2 for t in m.T) )
    
    return m


class TwoTanksSeries(ExternalGreyBoxModel):
    def __init__(self, A1, A2, c1, c2, N, dt):
        self._A1 = A1
        self._A2 = A2
        self._c1 = c1
        self._c2 = c2
        self._N = N
        self._dt = dt
        self._input_names = ['F1_{}'.format(t) for t in range(1,N)]
        self._input_names.extend(['F2_{}'.format(t) for t in range(1,N)])
        self._input_names.extend(['h1_{}'.format(t) for t in range(0,N)])
        self._input_names.extend(['h2_{}'.format(t) for t in range(0,N)])
        self._output_names = ['F12_{}'.format(t) for t in range(0,N)]
        self._output_names.extend(['Fo_{}'.format(t) for t in range(0,N)])
        self._equality_constraint_names = ['h1bal_{}'.format(t) for t in range(1,N)]
        self._equality_constraint_names.extend(['h2bal_{}'.format(t) for t in range(1,N)])

        # inputs
        self._F1 = np.zeros(N) # we don't use the first one
        self._F2 = np.zeros(N) # we don't use the first one
        self._h1 = np.zeros(N)
        self._h2 = np.zeros(N)

        # outputs
        self._F12 = np.zeros(N)
        self._Fo = np.zeros(N)

        # multipliers
        self._eq_con_mult_values = np.ones(2*(N-1))
        self._output_con_mult_values = np.ones(2*N)

    def input_names(self):
        return self._input_names

    def equality_constraint_names(self):
        return self._equality_constraint_names

    def output_names(self):
        return self._output_names

    def finalize_block_construction(self, pyomo_block):
        # initialize all variables to 1 and set bounds
        for k in pyomo_block.inputs:
            pyomo_block.inputs[k].setlb(0)
            pyomo_block.inputs[k].value = 1.0
        for k in pyomo_block.outputs:
            pyomo_block.outputs[k].setlb(0)
            pyomo_block.outputs[k].value = 1.0

    def set_input_values(self, input_values):
        N = self._N
        assert len(input_values) == 4*N-2
        self._F1[1:self._N] = np.copy(input_values[:N-1])
        self._F2[1:self._N] = np.copy(input_values[N-1:2*N-2])
        self._h1 = np.copy(input_values[2*N-2:3*N-2])
        self._h2 = np.copy(input_values[3*N-2:4*N-2])

    def set_equality_constraint_multipliers(self, eq_con_multiplier_values):
        assert len(eq_con_multiplier_values) == 2*(self._N-1)
        np.copyto(self._eq_con_mult_values, eq_con_multiplier_values)
        
    def set_output_constraint_multipliers(self, output_con_multiplier_values):
        assert len(output_con_multiplier_values) == 2*self._N
        np.copyto(self._output_con_mult_values, output_con_multiplier_values)

    def evaluate_equality_constraints(self):
        N = self._N
        F1 = self._F1
        F2 = self._F2
        h1 = self._h1
        h2 = self._h2
        
        resid = np.zeros(2*(N-1))

        for t in range(1,N):
            resid[t-1] = (h1[t]-h1[t-1]) - \
                self._dt/self._A1*(F1[t] - self._c1*math.sqrt(h1[t]))

        for t in range(1,N):
            resid[t-2+N] = (h2[t]-h2[t-1]) - \
                self._dt/self._A2*(self._c1*math.sqrt(h1[t]) + F2[t] - self._c2*math.sqrt(h2[t]))
        return resid

    def evaluate_outputs(self):
        N = self._N
        h1 = self._h1
        h2 = self._h2
        
        resid = np.zeros(2*N)

        for t in range(N):
            resid[t] = self._c1*math.sqrt(h1[t])

        for t in range(N):
            resid[t+N] = self._c2*math.sqrt(h2[t])

        return resid

    def evaluate_jacobian_equality_constraints(self):
        N = self._N
        F1 = self._F1
        F2 = self._F2
        h1 = self._h1
        h2 = self._h2
        A1 = self._A1
        A2 = self._A2
        c1 = self._c1
        c2 = self._c2
        dt = self._dt

        nnz = 3*(N-1)+ 4*(N-1)
        irow = np.zeros(nnz, dtype=np.int64)
        jcol = np.zeros(nnz, dtype=np.int64)
        data = np.zeros(nnz, dtype=np.float64)
        idx = 0
        # Jac h1bal
        for i in range(N-1):
            irow[idx] = i
            jcol[idx] = i
            data[idx] = -dt/A1
            idx += 1
            irow[idx] = i
            jcol[idx] = 2*(N-1)+i
            data[idx] = -1
            idx += 1
            irow[idx] = i
            jcol[idx] = 2*(N-1)+i+1
            data[idx] = 1+dt/A1*c1*1/2*(h1[i+1])**(-0.5)
            idx += 1
        # Jac h2bal
        for i in range(N-1):
            irow[idx] = i+(N-1)
            jcol[idx] = i+(N-1)
            data[idx] = -dt/A2
            idx += 1
            irow[idx] = i+(N-1)
            jcol[idx] = 2*(N-1)+i+1
            data[idx] = -dt/A2*c1*1/2*(h1[i+1])**(-0.5)
            idx += 1
            irow[idx] = i+(N-1)
            jcol[idx] = 2*(N-1)+N+i
            data[idx] = -1
            idx += 1
            irow[idx] = i+(N-1)
            jcol[idx] = 2*(N-1)+N+i+1
            data[idx] = 1+dt/A2*c2*1/2*(h2[i+1])**(-0.5)
            idx += 1

        assert idx == nnz
        return spa.coo_matrix( (data, (irow,jcol)), shape=(2*(N-1), 2*(N-1)+2*N) )

    def evaluate_jacobian_outputs(self):
        N = self._N
        F1 = self._F1
        F2 = self._F2
        h1 = self._h1
        h2 = self._h2
        A1 = self._A1
        A2 = self._A2
        c1 = self._c1
        c2 = self._c2
        dt = self._dt

        nnz = 2*N
        irow = np.zeros(nnz, dtype=np.int64)
        jcol = np.zeros(nnz, dtype=np.int64)
        data = np.zeros(nnz, dtype=np.float64)
        idx = 0
        # Jac F12
        for i in range(N):
            irow[idx] = i
            jcol[idx] = 2*(N-1)+i
            data[idx] = 1/2*c1*h1[i]**(-0.5)
            idx += 1
        for i in range(N):
            irow[idx] = N+i
            jcol[idx] = 2*(N-1)+N+i
            data[idx] = 1/2*c2*h2[i]**(-0.5)
            idx += 1

        assert idx == nnz
        return spa.coo_matrix( (data, (irow,jcol)), shape=(2*N, 2*(N-1)+2*N) )

    def evaluate_hessian_equality_constraints(self):
        N = self._N
        F1 = self._F1
        F2 = self._F2
        h1 = self._h1
        h2 = self._h2
        A1 = self._A1
        A2 = self._A2
        c1 = self._c1
        c2 = self._c2
        dt = self._dt
        lam = self._eq_con_mult_values
        
        nnz = 2*(N-1)
        irow = np.zeros(nnz, dtype=np.int64)
        jcol = np.zeros(nnz, dtype=np.int64)
        data = np.zeros(nnz, dtype=np.float64)
        idx = 0
        for i in range(N-1):
            irow[idx] = 2*(N-1)+i+1
            jcol[idx] = 2*(N-1)+i+1
            data[idx] = lam[i]*dt/A1*(-c1/4)*h1[i+1]**(-1.5) + lam[(N-1)+i]*dt/A2*(c1/4)*h1[i+1]**(-1.5)
            idx += 1
            irow[idx] = 2*(N-1)+N+i+1
            jcol[idx] = 2*(N-1)+N+i+1
            data[idx] = lam[(N-1)+i]*dt/A2*(-c2/4)*h2[i+1]**(-1.5)
            idx += 1

        assert idx == nnz
        hess =  spa.coo_matrix( (data, (irow,jcol)), shape=(2*(N-1)+2*N, 2*(N-1)+2*N) )
        return hess
    
    def evaluate_hessian_outputs(self):
        N = self._N
        F1 = self._F1
        F2 = self._F2
        h1 = self._h1
        h2 = self._h2
        A1 = self._A1
        A2 = self._A2
        c1 = self._c1
        c2 = self._c2
        dt = self._dt
        lam = self._output_con_mult_values
        
        nnz = 2*N
        irow = np.zeros(nnz, dtype=np.int64)
        jcol = np.zeros(nnz, dtype=np.int64)
        data = np.zeros(nnz, dtype=np.float64)
        idx = 0

        # Hess F12_t
        for i in range(N):
            irow[idx] = 2*(N-1)+i
            jcol[idx] = 2*(N-1)+i
            data[idx] = lam[i]*c1*(-1/4)*h1[i]**(-1.5)
            idx += 1
        # Hess Fo_t
        for i in range(N):
            irow[idx] = 2*(N-1)+N+i
            jcol[idx] = 2*(N-1)+N+i
            data[idx] = lam[N+i]*c2*(-1/4)*h2[i]**(-1.5)
            idx += 1

        assert idx == nnz
        hess = spa.coo_matrix( (data, (irow,jcol)), shape=(2*(N-1)+2*N, 2*(N-1)+2*N) )
        return hess

def create_pyomo_external_grey_box_model(A1, A2, c1, c2, N, dt):
    m2 = pyo.ConcreteModel()
    m2.T = pyo.Set(initialize=list(range(N)), ordered=True)
    m2.Tu = pyo.Set(initialize=list(range(N))[1:], ordered=True)
    m2.egb = ExternalGreyBoxBlock()
    m2.egb.set_external_model(TwoTanksSeries(A1, A2, c1, c2, N, dt))

    # initialize the same as the pyomo model
    for t in m2.Tu:
        m2.egb.inputs['F1_{}'.format(t)].value = 1+0.1*t
        m2.egb.inputs['F2_{}'.format(t)].value = 2+0.1*t
    for t in m2.T:
        m2.egb.inputs['h1_{}'.format(t)].value = 3+0.1*t
        m2.egb.inputs['h2_{}'.format(t)].value = 4+0.1*t
        m2.egb.outputs['F12_{}'.format(t)].value = 5+0.1*t
        m2.egb.outputs['Fo_{}'.format(t)].value = 6+0.1*t

    @m2.Constraint(m2.Tu)
    def min_inflow(m, t):
        F1_t = m.egb.inputs['F1_{}'.format(t)]
        return 2 <= F1_t

    @m2.Constraint(m2.T)
    def max_outflow(m, t):
        Fo_t = m.egb.outputs['Fo_{}'.format(t)]
        return Fo_t <= 4.5

    m2.h10 = pyo.Constraint( expr=m2.egb.inputs['h1_0'] == 1.5 )
    m2.h20 = pyo.Constraint( expr=m2.egb.inputs['h2_0'] == 0.5 )
    m2.obj = pyo.Objective( expr= sum((m2.egb.inputs['h1_{}'.format(t)]-1.0)**2  + (m2.egb.inputs['h2_{}'.format(t)]-1.5)**2 for t in m2.T) )

    return m2


class TestGreyBoxModel(unittest.TestCase):

    @unittest.skipIf(
        not pyo.SolverFactory('ipopt').available(exception_flag=False),
        "Ipopt needed to run tests with solve")
    def test_compare_evaluations(self):
        A1 = 5
        A2 = 10
        c1 = 3
        c2 = 4
        N = 6
        dt = 1

        m = create_pyomo_model(A1, A2, c1, c2, N, dt)
        solver = pyo.SolverFactory('ipopt')
        solver.options['linear_solver'] = 'mumps'
        status = solver.solve(m, tee=False)
        m_nlp = PyomoNLP(m)

        mex = create_pyomo_external_grey_box_model(A1, A2, c1, c2, N, dt)
        # mex_nlp = PyomoGreyBoxNLP(mex)
        mex_nlp = PyomoNLPWithGreyBoxBlocks(mex)

        # get the variable and constraint order and create the maps
        # reliable order independent comparisons
        m_x_order = m_nlp.primals_names()
        m_c_order = m_nlp.constraint_names()
        mex_x_order = mex_nlp.primals_names()
        mex_c_order = mex_nlp.constraint_names()
        
        x1list = ['h1[0]', 'h1[1]', 'h1[2]', 'h1[3]', 'h1[4]', 'h1[5]', 'h2[0]', 'h2[1]', 'h2[2]', 'h2[3]', 'h2[4]', 'h2[5]', 'F1[1]', 'F1[2]', 'F1[3]', 'F1[4]', 'F1[5]', 'F2[1]', 'F2[2]', 'F2[3]', 'F2[4]', 'F2[5]', 'F12[0]', 'F12[1]', 'F12[2]', 'F12[3]', 'F12[4]', 'F12[5]', 'Fo[0]', 'Fo[1]', 'Fo[2]', 'Fo[3]', 'Fo[4]', 'Fo[5]']
        x2list = ['egb.inputs[h1_0]', 'egb.inputs[h1_1]', 'egb.inputs[h1_2]', 'egb.inputs[h1_3]', 'egb.inputs[h1_4]', 'egb.inputs[h1_5]', 'egb.inputs[h2_0]', 'egb.inputs[h2_1]', 'egb.inputs[h2_2]', 'egb.inputs[h2_3]', 'egb.inputs[h2_4]', 'egb.inputs[h2_5]', 'egb.inputs[F1_1]', 'egb.inputs[F1_2]', 'egb.inputs[F1_3]', 'egb.inputs[F1_4]', 'egb.inputs[F1_5]', 'egb.inputs[F2_1]', 'egb.inputs[F2_2]', 'egb.inputs[F2_3]', 'egb.inputs[F2_4]', 'egb.inputs[F2_5]', 'egb.outputs[F12_0]', 'egb.outputs[F12_1]', 'egb.outputs[F12_2]', 'egb.outputs[F12_3]', 'egb.outputs[F12_4]', 'egb.outputs[F12_5]', 'egb.outputs[Fo_0]', 'egb.outputs[Fo_1]', 'egb.outputs[Fo_2]', 'egb.outputs[Fo_3]', 'egb.outputs[Fo_4]', 'egb.outputs[Fo_5]']
        x1_x2_map = dict(zip(x1list, x2list))
        x1idx_x2idx_map = {i: mex_x_order.index(x1_x2_map[m_x_order[i]]) for i in range(len(m_x_order))}

        c1list = ['h1bal[1]', 'h1bal[2]', 'h1bal[3]', 'h1bal[4]',
                  'h1bal[5]', 'h2bal[1]', 'h2bal[2]', 'h2bal[3]', 'h2bal[4]',
                  'h2bal[5]', 'F12con[0]', 'F12con[1]', 'F12con[2]',
                  'F12con[3]', 'F12con[4]', 'F12con[5]', 'Focon[0]', 'Focon[1]',
                  'Focon[2]', 'Focon[3]', 'Focon[4]', 'Focon[5]',
                  'min_inflow[1]', 'min_inflow[2]', 'min_inflow[3]',
                  'min_inflow[4]', 'min_inflow[5]', 'max_outflow[0]',
                  'max_outflow[1]', 'max_outflow[2]', 'max_outflow[3]',
                  'max_outflow[4]', 'max_outflow[5]', 'h10', 'h20']
        c2list = ['egb.h1bal_1', 'egb.h1bal_2', 'egb.h1bal_3',
                  'egb.h1bal_4', 'egb.h1bal_5', 'egb.h2bal_1', 'egb.h2bal_2',
                  'egb.h2bal_3', 'egb.h2bal_4', 'egb.h2bal_5',
                  'egb.output_constraints[F12_0]',
                  'egb.output_constraints[F12_1]',
                  'egb.output_constraints[F12_2]',
                  'egb.output_constraints[F12_3]',
                  'egb.output_constraints[F12_4]',
                  'egb.output_constraints[F12_5]',
                  'egb.output_constraints[Fo_0]',
                  'egb.output_constraints[Fo_1]',
                  'egb.output_constraints[Fo_2]',
                  'egb.output_constraints[Fo_3]',
                  'egb.output_constraints[Fo_4]',
                  'egb.output_constraints[Fo_5]', 'min_inflow[1]',
                  'min_inflow[2]', 'min_inflow[3]', 'min_inflow[4]',
                  'min_inflow[5]', 'max_outflow[0]', 'max_outflow[1]',
                  'max_outflow[2]', 'max_outflow[3]', 'max_outflow[4]',
                  'max_outflow[5]', 'h10', 'h20']
        c1_c2_map = dict(zip(c1list, c2list))
        c1idx_c2idx_map = {i: mex_c_order.index(c1_c2_map[m_c_order[i]]) for i in range(len(m_c_order))}

        # get the primals from m and put them in the correct order for mex
        m_x = m_nlp.get_primals()
        mex_x = np.zeros(len(m_x))
        for i in range(len(m_x)):
            mex_x[x1idx_x2idx_map[i]] = m_x[i]

        # get the duals from m and put them in the correct order for mex
        m_lam = m_nlp.get_duals()
        mex_lam = np.zeros(len(m_lam))
        for i in range(len(m_x)):
            mex_lam[c1idx_c2idx_map[i]] = m_lam[i]

        mex_nlp.set_primals(mex_x)
        mex_nlp.set_duals(mex_lam)

        m_obj = m_nlp.evaluate_objective()
        mex_obj = mex_nlp.evaluate_objective()
        self.assertAlmostEqual(m_obj, mex_obj, places=4)

        m_gobj = m_nlp.evaluate_grad_objective()
        mex_gobj = mex_nlp.evaluate_grad_objective()
        check_vectors_specific_order(self, m_gobj, m_x_order, mex_gobj, mex_x_order, x1_x2_map)

        m_c = m_nlp.evaluate_constraints()
        mex_c = mex_nlp.evaluate_constraints()
        check_vectors_specific_order(self, m_c, m_c_order, mex_c, mex_c_order, c1_c2_map)

        m_j = m_nlp.evaluate_jacobian()
        mex_j = mex_nlp.evaluate_jacobian().todense()
        check_sparse_matrix_specific_order(self, m_j, m_c_order, m_x_order, mex_j, mex_c_order, mex_x_order, c1_c2_map, x1_x2_map)

        m_h = m_nlp.evaluate_hessian_lag()
        mex_h = mex_nlp.evaluate_hessian_lag()
        check_sparse_matrix_specific_order(self, m_h, m_x_order, m_x_order, mex_h, mex_x_order, mex_x_order, x1_x2_map, x1_x2_map)

        mex_h = 0*mex_h
        mex_nlp.evaluate_hessian_lag(out=mex_h)
        check_sparse_matrix_specific_order(self, m_h, m_x_order, m_x_order, mex_h, mex_x_order, mex_x_order, x1_x2_map, x1_x2_map)


    @unittest.skipIf(not cyipopt_available,
                     "CyIpopt needed to run tests with solve")
    def test_solve(self):
        A1 = 5
        A2 = 10
        c1 = 3
        c2 = 4
        N = 6
        dt = 1

        m = create_pyomo_model(A1, A2, c1, c2, N, dt)
        solver = pyo.SolverFactory('cyipopt')
        solver.config.options['linear_solver'] = 'mumps'
        status = solver.solve(m, tee=False)
                        
        mex = create_pyomo_external_grey_box_model(A1, A2, c1, c2, N, dt)
        solver = pyo.SolverFactory('cyipopt')
        solver.config.options['linear_solver'] = 'mumps'
        status = solver.solve(mex, tee=False)

        for k in m.F1:
            self.assertAlmostEqual(pyo.value(m.F1[k]), pyo.value(mex.egb.inputs['F1_{}'.format(k)]), places=3)
            self.assertAlmostEqual(pyo.value(m.F2[k]), pyo.value(mex.egb.inputs['F2_{}'.format(k)]), places=3)
        for k in m.h1:
            self.assertAlmostEqual(pyo.value(m.h1[k]), pyo.value(mex.egb.inputs['h1_{}'.format(k)]), places=3)
            self.assertAlmostEqual(pyo.value(m.h2[k]), pyo.value(mex.egb.inputs['h2_{}'.format(k)]), places=3)
        for k in m.F12:
            self.assertAlmostEqual(pyo.value(m.F12[k]), pyo.value(mex.egb.outputs['F12_{}'.format(k)]), places=3)
            self.assertAlmostEqual(pyo.value(m.Fo[k]), pyo.value(mex.egb.outputs['Fo_{}'.format(k)]), places=3)
        """
        self._input_names = ['F1_{}'.format(t) for t in range(1,N)]
        self._input_names.extend(['F2_{}'.format(t) for t in range(1,N)])
        self._input_names.extend(['h1_{}'.format(t) for t in range(0,N)])
        self._input_names.extend(['h2_{}'.format(t) for t in range(0,N)])
        self._output_names = ['F12_{}'.format(t) for t in range(0,N)]
        self._output_names.extend(['Fo_{}'.format(t) for t in range(0,N)])
        """

if __name__ == '__main__':
    t = TestGreyBoxModel()
    t.test_solve()
    
