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METHANL8.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME METHANL8
* Problem:
* ********
* The methanol-8 problem by Fletcher.
* Source: Problem 2c 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-MN-31-31
IE N 8
IE M 2
IE K 2
IE 0 0
IE 1 1
IA N-1 N -1
IA N-2 N -2
IA K- K -1
IA K+ K 1
RE A1 18.5751
RE B1 -3632.649
RE C1 239.2
RE A2 18.3443
RE B2 -3841.2203
RE C2 228.0
RE AL1 0.0
RE AL'1 15.97
RE AL''1 0.0422
RE AL2 0.0
RE AL'2 18.1
RE AL''2 0.0
RE BE1 9566.67
RE BE'1 -1.59
RE BE''1 0.0422
RE BE2 10834.67
RE BE'2 8.74
RE BE''2 0.0
RE FL1 451.25
RE FL2 684.25
RE FV1 0.0
RE FV2 0.0
RE TF 89.0
RE B 693.37
RE D 442.13
RE Q 8386200.0
RE PI0 1210.0
RE PI1 1200.0
RE PI2 1190.0
RE PI3 1180.0
RE PI4 1170.0
RE PI5 1160.0
RE PI6 1150.0
RE PI7 1140.0
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 METHANL8 2.2-(K,J) FL(J)
Z METHANL8 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 METHANL8 2.7-(I) 1.0
ND
Z METHANL8 2.8 Q
Z METHANL8 2.9-(K) SMALLHF
Z METHANL8 2.9-(K+) BIGHF
BOUNDS
FR B1 'DEFAULT'
START POINT
METHANL8 X0,1 0.09203
METHANL8 X0,2 0.908
METHANL8 X1,1 0.1819
METHANL8 X1,2 0.8181
METHANL8 X2,1 0.284
METHANL8 X2,2 0.716
METHANL8 X3,1 0.3051
METHANL8 X3,2 0.6949
METHANL8 X4,1 0.3566
METHANL8 X4,2 0.6434
METHANL8 X5,1 0.468
METHANL8 X5,2 0.532
METHANL8 X6,1 0.6579
METHANL8 X6,2 0.3421
METHANL8 X7,1 0.8763
METHANL8 X7,2 0.1237
METHANL8 T0 120.0
METHANL8 T1 110.0
METHANL8 T2 100.0
METHANL8 T3 88.0
METHANL8 T4 86.0
METHANL8 T5 84.0
METHANL8 T6 80.0
METHANL8 T7 76.0
METHANL8 V0 886.37
METHANL8 V1 910.01
METHANL8 V2 922.52
METHANL8 V3 926.46
METHANL8 V4 935.56
METHANL8 V5 952.83
METHANL8 V6 975.73
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 METHANL8 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS METHANL8
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