# Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
#
# File:      diet.py
#
# Purpose: Solving Stigler's Nutrition model (DIET,SEQ=7)
#
# Source: GAMS Model library,
#           Dantzig, G B, Chapter 27.1. In Linear Programming and Extensions.
#           Princeton University Press, Princeton, New Jersey, 1963.
#
# Given a set of nutrients, foods with associated nutrient values, allowance of
# nutrients per day, the model will find the cheapest combination of foods
# which will provide the necessary nutrients.

from mosek.fusion import Model, Matrix, Domain, Expr, ObjectiveSense, Set
import numpy

##
#  Arguments for construction:
#  name      - Model name.
#  foods     - List of M names of the foods.
#  nutrients - List of N names of the nutrients.
#  daily_allowance - List of N floats denoting the daily allowance of each
#              nutrient.
#  nutritive_value - Two-dimensional MxN array of floats where each row
#              denotes the nutrient values for a single food per $ spent.
def DietModel(name,
              foods,
              nutrients,
              daily_allowance,
              nutritive_value):
    with Model() as DM:
        dailyAllowance = numpy.array(daily_allowance, float)
        nutrientValue = Matrix.dense(nutritive_value).transpose()

        M = len(foods)
        N = len(nutrients)
        if len(dailyAllowance) != N:
            raise ValueError("Length of daily_allowance does not match "
                             "the number of nutrients")
        if nutrientValue.numColumns() != M:
            raise ValueError("Number of rows in nutrient_value does not "
                             "match the number of foods")
        if nutrientValue.numRows() != N:
            raise ValueError("Number of columns in nutrient_value does "
                             "not match the number of nutrients")

        dailyPurchase = DM.variable(
            'Daily Purchase',
            [M],
            Domain.greaterThan(0.0).withNamesOnAxis(foods,0))
        dailyNutrients = DM.constraint(
            'Nutrient Balance',
            Expr.mul(nutrientValue,
                     dailyPurchase),
            Domain.greaterThan(dailyAllowance).withNamesOnAxis(nutrients,0))
        DM.objective(ObjectiveSense.Minimize,
                    Expr.sum(dailyPurchase))

        DM.solve()
        DM.writeTask("diet.ptf")

        return dailyPurchase.level(),dailyNutrients.level()

# class DietModel(Model):

#     def __init__(self, name,
#                  foods,
#                  nutrients,
#                  daily_allowance,
#                  nutritive_value):
#         Model.__init__(self, name)
#         finished = False
#         try:
#             self.foods = numpy.array([str(f) for f in foods],dtype=numpy.dtype(object))
#             print(self.foods,len(numpy.array(self.foods,dtype=numpy.dtype(object))))
#             self.nutrients = [str(n) for n in nutrients]
#             self.dailyAllowance = numpy.array(daily_allowance, float)
#             self.nutrientValue = Matrix.dense(nutritive_value).transpose()

#             M = len(self.foods)
#             N = len(self.nutrients)
#             if len(self.dailyAllowance) != N:
#                 raise ValueError("Length of daily_allowance does not match "
#                                  "the number of nutrients")
#             if self.nutrientValue.numColumns() != M:
#                 raise ValueError("Number of rows in nutrient_value does not "
#                                  "match the number of foods")
#             if self.nutrientValue.numRows() != N:
#                 raise ValueError("Number of columns in nutrient_value does "
#                                  "not match the number of nutrients")

#             self.__dailyPurchase = self.variable('Daily Purchase',
#                                                  [M],
#                                                  Domain.greaterThan(0.0).withNamesOnAxis(self.foods,0))
#             self.__dailyNutrients = \
#                 self.constraint('Nutrient Balance',
#                                 Expr.mul(self.nutrientValue,
#                                          self.__dailyPurchase),
#                                 Domain.greaterThan(self.dailyAllowance).withNamesOnAxis(self.nutrients,0))
#             self.objective(ObjectiveSense.Minimize,
#                            Expr.sum(self.__dailyPurchase))
#             finished = True
#         finally:
#             if not finished:
#                 self.__del__()

#     def dailyPurchase(self):
#         return self.__dailyPurchase.level()

#     def dailyNutrients(self):
#         return self.__dailyNutrients.level()

if __name__ == '__main__':
    nutrient_unit = [
        "thousands", "grams", "grams",
        "milligrams", "thousand ius", "milligrams",
        "milligrams", "milligrams", "milligrams"]
    nutrients = [
        "calorie", "protein", "calcium",
        "iron", "vitamin a", "vitamin b1",
        "vitamin b2", "niacin", "vitamin c"]
    foods = [
        "wheat", "cornmeal", "cannedmilk", "margarine", "cheese",
        "peanut butter", "lard", "liver", "porkroast", "salmon",
        "greenbeans", "cabbage", "onions", "potatoes", "spinach",
        "sweet potatos", "peaches", "prunes", "limabeans", "navybeans"]
    nutritive_value = [
        #  calorie       calcium      vitamin a        vitamin b2      vitamin c
        #         protein        iron           vitamin b1      niacin
        [44.7, 1411, 2.0, 365, 0, 55.4, 33.3, 441, 0],  # wheat
        [36, 897, 1.7, 99, 30.9, 17.4, 7.9, 106, 0],  # cornmeal
        [8.4, 422, 15.1, 9, 26, 3, 23.5, 11, 60],  # cannedmilk
        [20.6, 17, .6, 6, 55.8, .2, 0, 0, 0],  # margarine
        [7.4, 448, 16.4, 19, 28.1, .8, 10.3, 4, 0],  # cheese
        [15.7, 661, 1, 48, 0, 9.6, 8.1, 471, 0],  # peanut butter
        [41.7, 0, 0, 0, .2, 0, .5, 5, 0],  # lard
        [2.2, 333, .2, 139, 169.2, 6.4, 50.8, 316, 525],  # liver
        [4.4, 249, .3, 37, 0, 18.2, 3.6, 79, 0],  # porkroast
        [5.8, 705, 6.8, 45, 3.5, 1, 4.9, 209, 0],  # salmon
        [2.4, 138, 3.7, 80, 69, 4.3, 5.8, 37, 862],  # greenbeans
        [2.6, 125, 4, 36, 7.2, 9, 4.5, 26, 5369],  # cabbage
        [5.8, 166, 3.8, 59, 16.6, 4.7, 5.9, 21, 1184],  # onions
        [14.3, 336, 1.8, 118, 6.7, 29.4, 7.1, 198, 2522],  # potatoes
        [1.1, 106, 0.0, 138, 918.4, 5.7, 13.8, 33, 2755],  # spinach
        [9.6, 138, 2.7, 54, 290.7, 8.4, 5.4, 83, 1912],  # sweet potatos
        [8.5, 87, 1.7, 173, 86.8, 1.2, 4.3, 55, 57],  # peaches
        [12.8, 99, 2.5, 154, 85.7, 3.9, 4.3, 65, 257],  # prunes
        [17.4, 1055, 3.7, 459, 5.1, 26.9, 38.2, 93, 0],  # limabeans
        [26.9, 1691, 11.4, 792, 0, 38.4, 24.6, 217, 0]] # navybeans

    daily_allowance = [
        3., 70., .8, 12., 5., 1.8, 2.7, 18., 75.]
    x,y = DietModel('Stinglers Diet Problem',
                    foods,
                    nutrients,
                    daily_allowance,
                    nutritive_value)

    # with DietModel('Stinglers Diet Problem',
    #                foods,
    #                nutrients,
    #                daily_allowance,
    #                nutritive_value) as M:
    #     M.solve()
    if True:
        print("Solution:")
        #x = M.dailyPurchase()
        for name, quantum in zip(foods, x):
            print("%20s : $%.4f " % (name, quantum))

        print("Nutrients:")
        #y = M.dailyNutrients()
        for name, quantum, unit, minval in zip(nutrients, y, nutrient_unit, daily_allowance):
            print("%20s : %7.2f %s (%.2f)" % (name, quantum, unit, minval))
