fmcTitle ("tp068r3"): # Source version 4 # FMCMAP post processor version 1.1 # FMC's first native input language. # The Hock & Schittkowski test problem #68. # This is the formulation of #68 to obtain the reference values for # tp068r2, i.e., tp068r3 is equivalent to tp068r2 down to the last detail. a := 0.0001: b := 1: d := 1: n := 24: ubx2hs := 100: # phi0(x[2] = 6) > 9.8*10^(-10) # phi0(x[2] = 5) > 2.8*10^( -7) ubx2r := 4: # phi0(x[2] = 4) > 3.1*10^( -5) # phi0(x[2] = 3) > 1.3*10^( -3) # phi0(x[2] = 2) > 2.2*10^( -2) ubx2 := ubx2r: iv[1] := 1: slb[1] := 0.0001: sub[1] := 100: iv[2] := 1: slb[2] := 0: sub[2] := ubx2: iv[3] := 1: slb[3] := 0: sub[3] := 2: iv[4] := 1: slb[4] := 0: sub[4] := 2: for i from 1 to 4 do fmcInitialValue (nprintf ("x%d", i), iv[i]): fmcStrongLowerBound (nprintf ("x%d", i), slb[i]): fmcStrongUpperBound (nprintf ("x%d", i), sub[i]): od: argn := (-1) * x2 - d * sqrt (n): arg0 := (-1) * x2: argp := (-1) * x2 + d * sqrt (n): argnerfc := (-1) * argn / sqrt (2): arg0erfc := (-1) * arg0 / sqrt (2): argperfc := (-1) * argp / sqrt (2): phin := (1/2) * myerfc (fmc_ident_tcb, argnerfc): phi0 := (1/2) * myerfc (fmc_ident_tcb, arg0erfc): phip := (1/2) * myerfc (fmc_ident_tcb, argperfc): c[1] := x3 - 2 * phi0: c[2] := x4 - phip - phin: # phin may vanish but not phip num := b * (exp (x1) - 1) - x3: den := exp (x1) - 1 + x4: mf := (a * n - (num / den) * x4) / x1: for j from 1 to 2 do fmcEquality (nprintf ("ce%d", j), c[j]): od: myminfun := mf: fmcMinimum (myminfun): fmcFunctionDiffHint ([ myerfc, 0, myerfcd (fmcFunctionArg1, fmcFunctionArg2) ]): fmcExternalCodePath ("../../doc/RevisedHockSchittkowski/src/tp068r3x.c"): fmcEscortFloat ('argnerfc', argnerfc): fmcEscortFloat ('arg0erfc', arg0erfc): fmcEscortFloat ('argperfc', argperfc): fmcEscortFloat (derfcn, myerfc (fmc_ident_tcb, argnerfc) - erfc (argnerfc)): fmcEscortFloat (derfc0, myerfc (fmc_ident_tcb, arg0erfc) - erfc (arg0erfc)): fmcEscortFloat (derfcp, myerfc (fmc_ident_tcb, argperfc) - erfc (argperfc)): fmcEscortFloat ('phin', phin): fmcEscortFloat ('phi0', phi0): fmcEscortFloat ('phip', phip): # argnerfc = 6.042362036830880 # arg0erfc = 2.578260421693126 # argperfc = -0.8858411934446289 # derfcn = 2.9*10^(-17) # derfc0 = -1.4*10^(-17) # derfcp = -4.5*10^(-18) # phin = 2.1*10^(-17) # phi0 = 0.0001330678126076933 # phip = 0.8948550393735502 myownabs := proc (x::algebraic) local y: y := fmc_m_abs (x): RETURN (y): end: myabsdevnod0_0 := myownabs (myminfun + 0.9204250036397504): myreldevnod0_0 := myownabs (myminfun/0.9204250036397504 + 1): myabsdevnod0_1 := myownabs (x1 - 0.06785857708551205): myreldevnod0_1 := myownabs (x1/0.06785857708551205 - 1): myabsdevnod0_2 := myownabs (x2 - 3.646210855688194): myreldevnod0_2 := myownabs (x2/3.646210855688194 - 1): myabsdevnod0_3 := myownabs (x3 - 0.0002661356252153867): myreldevnod0_3 := myownabs (x3/0.0002661356252153867 - 1): myabsdevnod0_4 := myownabs (x4 - 0.8948550393735502): myreldevnod0_4 := myownabs (x4/0.8948550393735502 - 1): myabsdevnod1_0 := (1/2)*(myownabs (myabsdevnod0_0 - myabsdevnod0_1) + (myabsdevnod0_0 + myabsdevnod0_1)): myreldevnod1_0 := (1/2)*(myownabs (myreldevnod0_0 - myreldevnod0_1) + (myreldevnod0_0 + myreldevnod0_1)): myabsdevnod1_2 := (1/2)*(myownabs (myabsdevnod0_2 - myabsdevnod0_3) + (myabsdevnod0_2 + myabsdevnod0_3)): myreldevnod1_2 := (1/2)*(myownabs (myreldevnod0_2 - myreldevnod0_3) + (myreldevnod0_2 + myreldevnod0_3)): myabsdevnod1_4 := myabsdevnod0_4: myreldevnod1_4 := myreldevnod0_4: myabsdevnod2_0 := (1/2)*(myownabs (myabsdevnod1_0 - myabsdevnod1_2) + (myabsdevnod1_0 + myabsdevnod1_2)): myreldevnod2_0 := (1/2)*(myownabs (myreldevnod1_0 - myreldevnod1_2) + (myreldevnod1_0 + myreldevnod1_2)): myabsdevnod2_4 := myabsdevnod1_4: myreldevnod2_4 := myreldevnod1_4: myabsdevnod3_0 := (1/2)*(myownabs (myabsdevnod2_0 - myabsdevnod2_4) + (myabsdevnod2_0 + myabsdevnod2_4)): myreldevnod3_0 := (1/2)*(myownabs (myreldevnod2_0 - myreldevnod2_4) + (myreldevnod2_0 + myreldevnod2_4)): zmyabsdevmax := myabsdevnod3_0: zmyreldevmax := myreldevnod3_0: fmcEscortFloat ('x1', x1): fmcEscortFloat ('x2', x2): fmcEscortFloat ('x3', x3): fmcEscortFloat ('x4', x4): fmcEscortFloat ('myminfun', myminfun): fmcEscortFloat ('zmyabsdevmax', zmyabsdevmax): fmcEscortFloat ('zmyreldevmax', zmyreldevmax):