##
#  Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
#
#  File :      sensitivity.py
#
#  Purpose :   To demonstrate how to perform sensitivity
#              analysis from the API on a small problem:
#
#              minimize
#
#              obj: +1 x11 + 2 x12 + 5 x23 + 2 x24 + 1 x31 + 2 x33 + 1 x34
#              st
#              c1:   +  x11 +   x12                                           <= 400
#              c2:                  +   x23 +   x24                           <= 1200
#              c3:                                  +   x31 +   x33 +   x34   <= 1000
#              c4:   +  x11                         +   x31                   = 800
#              c5:          +   x12                                           = 100
#              c6:                  +   x23                 +   x33           = 500
#              c7:                          +   x24                 +   x34   = 500
#
#              The example uses basis type sensitivity analysis.
##

import sys
import mosek

# Since the actual value of Infinity is ignores, we define it solely
# for symbolic purposes:
inf = 0.0

# Define a stream printer to grab output from MOSEK
def streamprinter(text):
    sys.stdout.write(text)
    sys.stdout.flush()


def main():
    # Create a task
    with mosek.Task() as task:
        # Attach a printer to the task
        task.set_Stream(mosek.streamtype.log, streamprinter)

        # Set up data
        bkc = [mosek.boundkey.up, mosek.boundkey.up,
               mosek.boundkey.up, mosek.boundkey.fx,
               mosek.boundkey.fx, mosek.boundkey.fx,
               mosek.boundkey.fx]
        blc = [-inf, -inf, -inf, 800., 100., 500., 500.]
        buc = [400., 1200., 1000., 800., 100., 500., 500.]

        bkx = [mosek.boundkey.lo, mosek.boundkey.lo,
               mosek.boundkey.lo, mosek.boundkey.lo,
               mosek.boundkey.lo, mosek.boundkey.lo,
               mosek.boundkey.lo]
        c = [1.0, 2.0, 5.0, 2.0, 1.0, 2.0, 1.0]
        blx = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
        bux = [inf, inf, inf, inf, inf, inf, inf]

        ptrb = [0, 2, 4, 6, 8, 10, 12]
        ptre = [2, 4, 6, 8, 10, 12, 14]
        sub = [0, 3, 0, 4, 1, 5, 1, 6, 2, 3, 2, 5, 2, 6]

        val = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
               1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]

        numcon = len(bkc)
        numvar = len(bkx)
        numanz = len(val)

        # Input linear data
        task.inputdata(numcon, numvar,
                       c, 0.0,
                       ptrb, ptre, sub, val,
                       bkc, blc, buc,
                       bkx, blx, bux)
        # Set objective sense
        task.putobjsense(mosek.objsense.minimize)

        # Optimize
        task.optimize()

        # Analyze upper bound on c1 and the equality constraint on c4
        subi = [0, 3]
        marki = [mosek.mark.up, mosek.mark.up]

        # Analyze lower bound on the variables x12 and x31
        subj = [1, 4]
        markj = [mosek.mark.lo, mosek.mark.lo]

        (leftpricei, rightpricei, leftrangei, rightrangei, 
         leftpricej, rightpricej, leftrangej, rightrangej) = task.primalsensitivity(subi,
                                                                                    marki,
                                                                                    subj,
                                                                                    markj)

        print('Results from sensitivity analysis on bounds:')
        print('\tleftprice  | rightprice | leftrange  | rightrange ')
        print('For constraints:')

        for i in range(2):
            print('\t%10f   %10f   %10f   %10f' % (leftpricei[i],
                                                   rightpricei[i],
                                                   leftrangei[i],
                                                   rightrangei[i]))

        print('For variables:')
        for i in range(2):
            print('\t%10f   %10f   %10f   %10f' % (leftpricej[i],
                                                   rightpricej[i],
                                                   leftrangej[i],
                                                   rightrangej[i]))

        subc = [2, 5]

        leftprice, rightprice, leftrange, rightrange = task.dualsensitivity(subc)

        print('Results from sensitivity analysis on objective coefficients:')

        for i in range(2):
            print('\t%10f   %10f   %10f   %10f' % (leftprice[i],
                                                   rightprice[i],
                                                   leftrange[i],
                                                   rightrange[i]))

    return None

# call the main function
try:
    main()
except mosek.MosekException as e:
    print("ERROR: %s" % str(e.errno))
    if e.msg is not None:
        print("\t%s" % e.msg)
    sys.exit(1)
except:
    import traceback
    traceback.print_exc()
    sys.exit(1)