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HYDCAR6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HYDCAR6
* Problem :
* *********
* The hydrocarbon-6 problem by Fletcher.
* Source: Problem 2a 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, Dec 1989
* classification NOR2-AN-29-29
IE 0 0
IE 1 1
IE N 6
IA N-1 N -1
IA N-2 N -2
IE M 3
IE K 2
IA K- K -1
IA K+ K 1
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
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
ZE 2.1-(J) X(0,J) B
XE 2.1-(J) 'SCALE' 100.0
XE 2.3-(J) X(N-1,J) -1.0
DO I 1 N-2
XE 2.2-(I,J) 'SCALE' 100.0
ND
DO I 0 N-1
XE 2.7-(I)
ND
E 2.8 'SCALE' 100000.0
DO I 1 N-2
XE 2.9-(I) 'SCALE' 100000.0
ND
CONSTANTS
RE SMALLHF 0.0D+0
RE BIGHF 0.0D+0
DO J 1 M
Z HYDCAR6 2.2-(K,J) FL(J)
Z HYDCAR6 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 HYDCAR6 2.7-(I) 1.0
ND
Z HYDCAR6 2.8 Q
Z HYDCAR6 2.9-(K) SMALLHF
Z HYDCAR6 2.9-(K+) BIGHF
BOUNDS
FR HYDCAR6 'DEFAULT'
START POINT
HYDCAR6 X0,1 0.0
HYDCAR6 X0,2 0.2
HYDCAR6 X0,3 0.9
HYDCAR6 X1,1 0.0
HYDCAR6 X1,2 0.2
HYDCAR6 X1,3 0.8
HYDCAR6 X2,1 0.05
HYDCAR6 X2,2 0.3
HYDCAR6 X2,3 0.8
HYDCAR6 X3,1 0.1
HYDCAR6 X3,2 0.3
HYDCAR6 X3,3 0.6
HYDCAR6 X4,1 0.3
HYDCAR6 X4,2 0.5
HYDCAR6 X4,3 0.3
HYDCAR6 X5,1 0.6
HYDCAR6 X5,2 0.6
HYDCAR6 X5,3 0.0
DO I 0 N-1
X HYDCAR6 T(I) 100.0
ND
DO I 0 N-2
X HYDCAR6 V(I) 300.0
ND
START2 X0,1 0.00547225
START2 X0,2 0.129537
START2 X0,3 0.864991
START2 X1,1 0.0200767
START2 X1,2 0.222556
START2 X1,3 0.757368
START2 X2,1 0.0645143
START2 X2,2 0.330253
START2 X2,3 0.605232
START2 X3,1 0.117201
START2 X3,2 0.442833
START2 X3,3 0.439966
START2 X4,1 0.249447
START2 X4,2 0.501568
START2 X4,3 0.248985
START2 X5,1 0.496352
START2 X5,2 0.413642
START2 X5,3 0.0900063
START2 T0 132.683
START2 T1 127.942
START2 T2 120.569
START2 T3 113.650
START2 T4 103.977
START2 T5 93.1902
START2 V0 288.902
START2 V1 288.558
START2 V2 288.669
START2 V3 293.339
START2 V4 303.021
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 USES
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 HYDCAR6
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