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HYDC20LS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HYDC20LS
* Problem :
* *********
* The hydrocarbon-20 problem by Fletcher.
* This is a least-squares version of problem HYDCAR20.
* Source: Problem 2b in
* J.J. More',"A collection of nonlinear model problems"
* Proceedings of the AMS-SIAM Summer Seminar on the Computational
* Solution of Nonlinear Systems of Equations, Colorado, 1988.
* Argonne National Laboratory MCS-P60-0289, 1989.
* SIF input : N. Gould and Ph. Toint, Feb 1991.
* classification SUR2-AN-99-00
* Problem data
IE N 20
IE M 3
IE K 9
* Antoine constants, liquid and vapour enthalpies, etc
RE A1 9.647
RE B1 -2998.00
RE C1 230.66
RE A2 9.953
RE B2 -3448.10
RE C2 235.88
RE A3 9.466
RE B3 -3347.25
RE C3 215.31
RE AL1 0.0
RE AL'1 37.6
RE AL''1 0.0
RE AL2 0.0
RE AL'2 48.2
RE AL''2 0.0
RE AL3 0.0
RE AL'3 45.4
RE AL''3 0.0
RE BE1 8425.0
RE BE'1 24.2
RE BE''1 0.0
RE BE2 9395.0
RE BE'2 35.6
RE BE''2 0.0
RE BE3 10466.0
RE BE'3 31.9
RE BE''3 0.0
RE FL1 30.0
RE FL2 30.0
RE FL3 40.0
RE FV1 0.0
RE FV2 0.0
RE FV3 0.0
RE TF 100.0
RE B 40.0
RE D 60.0
RE Q 2500000.0
* Constants
IE 0 0
IE 1 1
* Computed parameters
IA N-1 N -1
IA N-2 N -2
IA K- K -1
IA K+ K 1
DO I 0 N-1
AE PI(I) 1.0
ND
VARIABLES
DO I 0 N-1
X T(I)
AD INVPI(I) PI(I) 1.0
DO J 1 M
X X(I,J)
ND
DO I 0 N-2
X V(I)
ND
GROUPS
DO J 1 M
ZN 2.1-(J) X(0,J) B
XN 2.1-(J) 'SCALE' 100.0
XN 2.3-(J) X(N-1,J) -1.0
DO I 1 N-2
XN 2.2-(I,J) 'SCALE' 100.0
ND
DO I 0 N-1
XN 2.7-(I)
ND
N 2.8 'SCALE' 100000.0
DO I 1 N-2
XN 2.9-(I) 'SCALE' 100000.0
ND
CONSTANTS
RE SMALLHF 0.0D+0
RE BIGHF 0.0D+0
DO J 1 M
Z HYDC20LS 2.2-(K,J) FL(J)
Z HYDC20LS 2.2-(K+,J) FV(J)
R* TFTF TF TF
A* TEMP1 TFTF AL''(J)
A* TEMP2 TF AL'(J)
R+ TEMP1 TEMP1 TEMP2
A+ TEMP1 TEMP1 AL(J)
A* TEMP1 TEMP1 FL(J)
R+ SMALLHF SMALLHF TEMP1
A* TEMP1 TFTF BE''(J)
A* TEMP2 TF BE'(J)
R+ TEMP1 TEMP1 TEMP2
A+ TEMP1 TEMP1 BE(J)
A* TEMP1 TEMP1 FV(J)
R+ BIGHF BIGHF TEMP1
ND
DO I 0 N-1
X HYDC20LS 2.7-(I) 1.0
ND
Z HYDC20LS 2.8 Q
Z HYDC20LS 2.9-(K) SMALLHF
Z HYDC20LS 2.9-(K+) BIGHF
BOUNDS
FR HYDC20LS 'DEFAULT'
START POINT
HYDC20LS X0,1 0.0
HYDC20LS X0,2 0.3
HYDC20LS X0,3 0.1
HYDC20LS X1,1 0.0
HYDC20LS X1,2 0.3
HYDC20LS X1,3 0.9
HYDC20LS X2,1 0.01
HYDC20LS X2,2 0.3
HYDC20LS X2,3 0.9
HYDC20LS X3,1 0.02
HYDC20LS X3,2 0.4
HYDC20LS X3,3 0.8
HYDC20LS X4,1 0.05
HYDC20LS X4,2 0.4
HYDC20LS X4,3 0.8
HYDC20LS X5,1 0.07
HYDC20LS X5,2 0.45
HYDC20LS X5,3 0.8
HYDC20LS X6,1 0.09
HYDC20LS X6,2 0.5
HYDC20LS X6,3 0.7
HYDC20LS X7,1 0.1
HYDC20LS X7,2 0.5
HYDC20LS X7,3 0.7
HYDC20LS X8,1 0.15
HYDC20LS X8,2 0.5
HYDC20LS X8,3 0.6
HYDC20LS X9,1 0.2
HYDC20LS X9,2 0.5
HYDC20LS X9,3 0.6
HYDC20LS X10,1 0.25
HYDC20LS X10,2 0.6
HYDC20LS X10,3 0.5
HYDC20LS X11,1 0.3
HYDC20LS X11,2 0.6
HYDC20LS X11,3 0.5
HYDC20LS X12,1 0.35
HYDC20LS X12,2 0.6
HYDC20LS X12,3 0.5
HYDC20LS X13,1 0.4
HYDC20LS X13,2 0.6
HYDC20LS X13,3 0.4
HYDC20LS X14,1 0.4
HYDC20LS X14,2 0.7
HYDC20LS X14,3 0.4
HYDC20LS X15,1 0.42
HYDC20LS X15,2 0.7
HYDC20LS X15,3 0.3
HYDC20LS X16,1 0.45
HYDC20LS X16,2 0.75
HYDC20LS X16,3 0.3
HYDC20LS X17,1 0.45
HYDC20LS X17,2 0.75
HYDC20LS X17,3 0.2
HYDC20LS X18,1 0.5
HYDC20LS X18,2 0.8
HYDC20LS X18,3 0.1
HYDC20LS X19,1 0.5
HYDC20LS X19,2 0.8
HYDC20LS X19,3 0.0
DO I 0 N-1
X HYDC20LS T(I) 100.0
ND
DO I 0 N-2
X HYDC20LS V(I) 300.0
ND
ELEMENT TYPE
EV 2PROD V1 V2
EP 2PROD P1 P2
EV POLY1PRD V1 V2
EP POLY1PRD P1
EP POLY1PRD P6 P7
EP POLY1PRD P8
EV POLY2PRD V1 V2
EV POLY2PRD V3
EP POLY2PRD P1 P2
EP POLY2PRD P6 P7
EP POLY2PRD P8
EV EXP2PROD V2 V3
EP EXP2PROD P1 P2
EP EXP2PROD P3 P4
EP EXP2PROD P5
EV EXP3PROD V1 V2
EV EXP3PROD V3
EP EXP3PROD P1 P2
EP EXP3PROD P3 P4
EP EXP3PROD P5
EV EXP4PROD V1 V2
EV EXP4PROD V3
EP EXP4PROD P1 P2
EP EXP4PROD P3 P4
EP EXP4PROD P5 P6
EP EXP4PROD P7 P8
ELEMENT USES
RM -D D -1.0
DO J 1 M
XT E11-(J) 2PROD
ZV E11-(J) V1 X(1,J)
ZV E11-(J) V2 V(0)
XP E11-(J) P1 -1.0
ZP E11-(J) P2 B
XT E12-(J) EXP3PROD
ZV E12-(J) V1 V(0)
ZV E12-(J) V2 X(0,J)
ZV E12-(J) V3 T(0)
XP E12-(J) P1 1.0
ZP E12-(J) P2 INVPI(0)
ZP E12-(J) P3 A(J)
ZP E12-(J) P4 B(J)
ZP E12-(J) P5 C(J)
DO I 1 N-2
IA I-1 I -1
IA I+1 I 1
XT E21-(I,J) 2PROD
ZV E21-(I,J) V1 X(I+1,J)
ZV E21-(I,J) V2 V(I)
XP E21-(I,J) P1 -1.0
XT E22-(I,J) EXP3PROD
ZV E22-(I,J) V1 V(I-1)
ZV E22-(I,J) V2 X(I-1,J)
ZV E22-(I,J) V3 T(I-1)
XP E22-(I,J) P1 -1.0
ZP E22-(I,J) P2 INVPI(I-1)
ZP E22-(I,J) P3 A(J)
ZP E22-(I,J) P4 B(J)
ZP E22-(I,J) P5 C(J)
XT E23-(I,J) 2PROD
ZV E23-(I,J) V1 X(I,J)
ZV E23-(I,J) V2 V(I-1)
XP E23-(I,J) P1 1.0
XT E24-(I,J) EXP3PROD
ZV E24-(I,J) V1 V(I)
ZV E24-(I,J) V2 X(I,J)
ZV E24-(I,J) V3 T(I)
XP E24-(I,J) P1 1.0
ZP E24-(I,J) P2 INVPI(I)
ZP E24-(I,J) P3 A(J)
ZP E24-(I,J) P4 B(J)
ZP E24-(I,J) P5 C(J)
OD I
DO I 1 K-
ZP E21-(I,J) P2 B
ZP E23-(I,J) P2 B
OD I
ZP E21-(K,J) P2 -D
ZP E23-(K,J) P2 B
DO I K+ N-2
ZP E21-(I,J) P2 -D
ZP E23-(I,J) P2 -D
OD I
XT E31-(J) EXP2PROD
ZV E31-(J) V2 X(N-2,J)
ZV E31-(J) V3 T(N-2)
XP E31-(J) P1 1.0
ZP E31-(J) P2 INVPI(N-2)
ZP E31-(J) P3 A(J)
ZP E31-(J) P4 B(J)
ZP E31-(J) P5 C(J)
ND
DO J 1 M
DO I 0 N-1
XT E71-(I,J) EXP2PROD
ZV E71-(I,J) V2 X(I,J)
ZV E71-(I,J) V3 T(I)
XP E71-(I,J) P1 1.0
ZP E71-(I,J) P2 INVPI(I)
ZP E71-(I,J) P3 A(J)
ZP E71-(I,J) P4 B(J)
ZP E71-(I,J) P5 C(J)
ND
DO J 1 M
XT E81-(J) EXP4PROD
ZV E81-(J) V1 V(0)
ZV E81-(J) V2 X(0,J)
ZV E81-(J) V3 T(0)
XP E81-(J) P1 1.0
ZP E81-(J) P2 INVPI(0)
ZP E81-(J) P3 A(J)
ZP E81-(J) P4 B(J)
ZP E81-(J) P5 C(J)
ZP E81-(J) P6 BE(J)
ZP E81-(J) P7 BE'(J)
ZP E81-(J) P8 BE''(J)
XT E82-(J) POLY1PRD
ZV E82-(J) V1 X(0,J)
ZV E82-(J) V2 T(0)
ZP E82-(J) P1 B
ZP E82-(J) P6 AL(J)
ZP E82-(J) P7 AL'(J)
ZP E82-(J) P8 AL''(J)
XT E83-(J) POLY2PRD
ZV E83-(J) V1 X(1,J)
ZV E83-(J) V2 V(0)
ZV E83-(J) V3 T(1)
XP E83-(J) P1 -1.0
ZP E83-(J) P2 B
ZP E83-(J) P6 AL(J)
ZP E83-(J) P7 AL'(J)
ZP E83-(J) P8 AL''(J)
DO I 1 N-2
IA I-1 I -1
IA I+1 I 1
XT E91-(I,J) EXP4PROD
ZV E91-(I,J) V1 V(I)
ZV E91-(I,J) V2 X(I,J)
ZV E91-(I,J) V3 T(I)
XP E91-(I,J) P1 1.0
ZP E91-(I,J) P2 INVPI(I)
ZP E91-(I,J) P3 A(J)
ZP E91-(I,J) P4 B(J)
ZP E91-(I,J) P5 C(J)
ZP E91-(I,J) P6 BE(J)
ZP E91-(I,J) P7 BE'(J)
ZP E91-(I,J) P8 BE''(J)
XT E92-(I,J) POLY2PRD
ZV E92-(I,J) V1 X(I,J)
ZV E92-(I,J) V2 V(I-1)
ZV E92-(I,J) V3 T(I)
XP E92-(I,J) P1 1.0
ZP E92-(I,J) P6 AL(J)
ZP E92-(I,J) P7 AL'(J)
ZP E92-(I,J) P8 AL''(J)
XT E93-(I,J) EXP4PROD
ZV E93-(I,J) V1 V(I-1)
ZV E93-(I,J) V2 X(I-1,J)
ZV E93-(I,J) V3 T(I-1)
XP E93-(I,J) P1 -1.0
ZP E93-(I,J) P2 INVPI(I-1)
ZP E93-(I,J) P3 A(J)
ZP E93-(I,J) P4 B(J)
ZP E93-(I,J) P5 C(J)
ZP E93-(I,J) P6 BE(J)
ZP E93-(I,J) P7 BE'(J)
ZP E93-(I,J) P8 BE''(J)
XT E94-(I,J) POLY2PRD
ZV E94-(I,J) V1 X(I+1,J)
ZV E94-(I,J) V2 V(I)
ZV E94-(I,J) V3 T(I+1)
XP E94-(I,J) P1 -1.0
ZP E94-(I,J) P6 AL(J)
ZP E94-(I,J) P7 AL'(J)
ZP E94-(I,J) P8 AL''(J)
OD I
DO I 1 K-
ZP E92-(I,J) P2 B
ZP E94-(I,J) P2 B
OD I
ZP E92-(K,J) P2 B
ZP E94-(K,J) P2 -D
DO I K+ N-2
ZP E92-(I,J) P2 -D
ZP E94-(I,J) P2 -D
OD I
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO J 1 M
XE 2.1-(J) E11-(J) E12-(J)
XE 2.3-(J) E31-(J)
XE 2.8 E81-(J) E82-(J)
XE 2.8 E83-(J)
DO I 1 N-2
XE 2.2-(I,J) E21-(I,J) E22-(I,J)
XE 2.2-(I,J) E23-(I,J) E24-(I,J)
XE 2.9-(I) E91-(I,J) E92-(I,J)
XE 2.9-(I) E93-(I,J) E94-(I,J)
OD I
DO I 0 N-1
XE 2.7-(I) E71-(I,J)
OD I
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO HYCAR 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HYDC20LS
TEMPORARIES
R EXPROD
R F
R POLY
R DPOLY
R TERM
M EXP
INDIVIDUALS
T 2PROD
F P1 * V1 * ( V2 + P2 )
G V1 P1 * ( V2 + P2 )
G V2 P1 * V1
H V1 V2 P1
T POLY1PRD
A POLY P6 + P7 * V2 + P8 * V2 * V2
A DPOLY P7 + 2.0 * P8 * V2
F P1 * V1 * POLY
G V1 P1 * POLY
G V2 P1 * V1 * DPOLY
H V1 V2 P1 * DPOLY
H V2 V2 P1 * V1 * 2.0D+0 * P8
T POLY2PRD
A POLY P6 + P7 * V3 + P8 * V3 * V3
A DPOLY P7 + 2.0 * P8 * V3
F P1 * V1 * ( P2 + V2 ) * POLY
G V1 P1 * ( P2 + V2 ) * POLY
G V2 P1 * V1 * POLY
G V3 P1 * V1 * ( P2 + V2 ) * DPOLY
H V1 V2 P1 * POLY
H V1 V3 P1 * ( P2 + V2 ) * DPOLY
H V2 V3 P1 * V1 * DPOLY
H V3 V3 P1 * V1 * ( P2 + V2 ) * 2.0D+0 * P8
T EXP2PROD
A EXPROD P1 * P2 * EXP(P3 + (P4 / (V3 + P5)))
A F V2 * EXPROD
F F
G V2 EXPROD
G V3 - V2 * EXPROD * P4 / (P5 + V3)**2
H V2 V3 - EXPROD * P4 / (P5 + V3)**2
H V3 V3 F * (P4 / (P5 + V3)**2)**2
H+ + 2.0D+0 * F * P4 / (P5 + V3)**3
T EXP3PROD
A EXPROD P1 * P2 * EXP(P3 + (P4 / (V3 + P5)))
A F V1 * V2 * EXPROD
A TERM - P4 / (P5 + V3) ** 2
F F
G V1 V2 * EXPROD
G V2 V1 * EXPROD
G V3 F * TERM
H V1 V2 EXPROD
H V1 V3 V2 * EXPROD * TERM
H V2 V3 V1 * EXPROD * TERM
H V3 V3 F * ( TERM * TERM
H+ + 2.0D+0 * P4 / (P5 + V3)**3 )
T EXP4PROD
A EXPROD P1 * P2 * EXP(P3 + (P4 / (V3 + P5)))
A F V1 * V2 * EXPROD
A POLY P6 + P7 * V3 + P8 * V3 * V3
A DPOLY P7 + 2.0 * P8 * V3
A TERM DPOLY - POLY * P4 / (P5 + V3) ** 2
F F * POLY
G V1 V2 * EXPROD * POLY
G V2 V1 * EXPROD * POLY
G V3 F * TERM
H V1 V2 EXPROD * POLY
H V1 V3 V2 * EXPROD * TERM
H V2 V3 V1 * EXPROD * TERM
H V3 V3 F * ( - (P4 / (P5 + V3)**2) * TERM
H+ + 2.0 * P8 - DPOLY * P4 / (P5 + V3)**2
H+ + 2.0D+0 * POLY * P4 / (P5 + V3)**3 )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HYDC20LS
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA