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ANTWERP.SIF
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ANTWERP.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ANTWERP
* Problem :
* *********
* This problem arises in the determination of a synthetic population for
* Belgian municipalities. The question is to estimate the distribution in
* Antwerp that households of the following types:
* type F (a couple + 1 to 5 children + 0 to 2 additional adults)
* type W (a woman + 1 to 3 children + 0 to 2 additional adults)
* type M (a man + 1 to 3 children + 0 to 2 additional adults).
*
* The data consists in
*
* - the number of individuals in households with 3 to 8 members,
* - the number of F, W and N households according to their number of
* children
* - and the total number of adults and children.
*
* If we define the variables by
*
* p1F: probability for a F_household to have 1 child,
* p2F: probability for a F_household to have 2 children,
* p3F: probability for a F_household to have 3 children,
* p4F: probability for a F_household to have 4 children,
* p5F: probability for a F_household to have 5 children,
* p1W: probability for a W_household to have 1 child,
* p2W: probability for a W_household to have 2 children,
* p3W: probability for a W_household to have 3 children,
* p1M: probability for a M_household to have 1 child,
* p2M: probability for a M_household to have 2 children,
* p3M: probability for a M_household to have 3 children,
* q0F: probability for a F_household to have 1 additional adult,
* q1F: probability for a F_household to have 2 additional adults,
* q2F: probability for a F_household to have 3 additional adults,
* q0W: probability for a W_household to have 1 additional adult,
* q1W: probability for a W_household to have 2 additional adults,
* q2W: probability for a W_household to have 3 additional adults,
* q0M: probability for a M_household to have 1 additional adult,
* q1M: probability for a M_household to have 2 additional adults,
* q2M: probability for a M_household to have 3 additional adults,
* nF : number of F-households,
* nW : number of W-households,
* nM : number of N-households,
* nC2: number of individuals considered as children in age class 2
* nC3: number of individuals considered as children in age class 3,
* nA2: number of individuals considered as adults in age class 2,
* nA3: number of individuals considered as adults in age class 3,
*
* the derived predictions for the observed quantities are then given by
*
* 1) prediction of the number of individuals in household of size 3:
*
* p1F*q0F*nF + (p1W*q1W+p2W*q0W)*nW + (p1M*q1M+p2M*q0M)*nM = M3
*
* 2) prediction of the number of individuals in household of size 4:
*
* (p2F*q0F+p1F*q1F)*nF + (p1W*q2W+p2W*q1W+p3W*q0W)*nW
* + (p1M*q2M+p2M*q1M+p3M*q0M)*nM = M4
*
* 3) prediction of the number of individuals in household of size 5:
*
* (p3F*q0F+p2F*q1F+p1F*q2F)*nF + (p2W*q2W+p3W*q1W)*nW
* + (p2M*q2M+p3M*q1M)*nM = M5
*
* 4) prediction of the number of individuals in household of size 6:
*
* (p4F*q0F+p3F*q1F+p2F*q2F)*nF + p3W*q2W*nW + p3M*q2M*nM = M6
*
* 5) prediction of the number of individuals in household of size 7:
*
* (p5F*q0F+p4F*q1F+p3F*q2F)*nF = M7
*
* 6) prediction of the number of individuals in household of size 8:
*
* (p5F*q1F+p4F*q2F)*nF = M8
*
* 7) prediction of the number of F-households with 1 child
*
* p1F*nF*(M1F+M2F+M3F) = M1F
*
* 8) prediction of the number of F-households with 2 children
*
* p2F*nF*(M1F+M2F+M3F) = M2F
*
* 9) prediction of the number of F-households with 3 children or more
*
* (p3F+p4F+p5F)*nF*(M1F+M2F+M3F) = M3F
*
* 10) prediction of the number of W-households with 1 child
*
* p1W*nW*(M1W+M2W+M3W) = M1W
*
* 11) prediction of the number of W-households with 2 children
*
* p2W*nW*(M1W+M2W+M3W) = M2W
*
* 12) prediction of the number of W-households with 3 children
*
* p3W*nW*(M1W+M2W+M3W) = M3W
*
* 13) prediction of the number of M-households with 1 child
*
* p1M*nM*(M1M+M2M+M3M) = M1M
*
* 14) prediction of the number of M-households with 2 children
*
* p2M*nM*(M1M+M2M+M3M) = M2M
*
* 14) prediction of the number of M-households with 3 children
*
* p3M*nM*(M1M+M2M+M3M) = M3M
*
* 15) prediction of the number of children
*
* (p1F+2*p2F+3*p3F+4*P4F+5*p5F)*NF + (p1W+2*p2W+3*p3W)*nW
* + (p1W+2*p2W+3*p3W)*nW - nC2 -nC3 = N0 + N1
*
* 16) prediction of the total number of adults
*
* (2*q0F+3*q1F+4*q2F)*nF + (q0W+2*q1W+3*q2W)*nW
* + (q0W+2*q1W+3*q2W)*nW - nA2 -nA3 = N4
*
* 17) composition of age class 2
*
* nC2 + nA2 = N2
*
* 18) composition of age class 3
*
* nC3 + nA3 = N3
*
* 19) prediction of the total number of individuals in F-households
*
* (p1F+2*p2F+3*p3F+4*P4F+5*p5F)*NF + (2*q0F+3*q1F+4*q2F)*nF = NINF
*
* 20) the piF are probabilities and sum up to 1
*
* p1F + p2F + p3F + p4F + p5F = 1
*
* 21) the qiF are probabilities and sum up to 1
*
* q0F + q1F + q2F = 1
*
* 22) the piW are probabilities and sum up to 1
*
* p1W + p2W + p3W = 1
*
* 23) the qiW are probabilities and sum up to 1
*
* q0W + q1W + q2W = 1
*
* 24) the piM are probabilities and sum up to 1
*
* p1M + p2M + p3M = 1
*
* 25) the qiM are probabilities and sum up to 1
*
* q0M + q1M + q2M = 1
*
* In addition, the following inequalities are imposed
*
* 26) the fraction of children in age class 2 exceeds that in age class 3
*
* nC2/N2 >= nC3/N3
*
* 27) there are more adults in age class 2 than children
*
* nA2 >= nC2
*
* 28) there are more adults in age class 3 than children
*
* nA3 >= nC3
*
* and the bounds on the variables are
*
* 0 <= piF <= 1 ( i = 1, 2, 3, 4, 5 )
*
* 0 <= qiF <= 1 ( i = 0, 1, 2 )
*
* 0 <= piW <= 1 ( i = 1, 2, 3 )
*
* 0 <= qiW <= 1 ( i = 0, 1, 2 )
*
* 0 <= piM <= 1 ( i = 1, 2, 3 )
*
* 0 <= qiM <= 1 ( i = 0, 1, 2 )
*
* nF >= 0, nW >= 0, nM >= 0
*
* 0 <= nC2 <= N2, 0 <= nA2 <= N2
*
* 0 <= nC3 <= N3, 0 <= nA3 <= N3
*
* The problem is solved as a linearly/bound constrained nonlinear least-squares
* problem in 27 variables. In the least-squares formulation,
* each equation is scaled in a proportion inverse to its right-hand side.
* The problem appears to be very ill-conditioned.
*
* SIF input: Ph. Toint, Apr 2006.
* classification SBR2-RN-27-8-0-3-24-0-2-0-8-0-0-0
* Problem initial data
* Number of households according to their sizes
RE M3 23844.0
RE M4 16323.0
RE M5 6613.0
RE M6 2535.0
RE M7 1109.0
RE M8 1667.0
* Number of F-households according the number of children
RE M1F 16405.0
RE M2F 13647.0
RE M3F 9895.0
* Number of M-households according the number of children
RE M1M 4041.0
RE M2M 1634.0
RE M3M 637.0
* Number of W-households according the number of children
RE M1W 10966.0
RE M2W 4566.0
RE M3W 1921.0
* Number of children and adults in households of type F and N
RE N0 15866.0
RE N1 59832.0
RE N2 61929.0
RE N3 32321.0
RE N4 73650.0
* Number of individuals in F-households
RE NINF 180055.0
* Number of individuals in N-households
RE NINN 47677.0
* Initial total number of households of type F
R+ TMP M1F M2F
R+ SNF TMP M3F
* Initial total number of households of type M
R+ TMP M1M M2M
R+ SNM TMP M3M
* Initial total number of households of type W
R+ TMP M1W M2W
R+ SNW TMP M3W
* Partial age class sums
RM N2/2 N2 0.5
RM N3/2 N3 0.5
R+ N23/2 N2/2 N3/2
R+ N01 N0 N1
R+ N0123 N01 N23/2
R+ N234 N4 N23/2
* Compute starting values for easy probabilities
R/ SP1F M1F SNF
R/ SP2F M2F SNF
R/ SP1W M1W SNW
R/ SP2W M2W SNW
R/ SP3W M3W SNW
R/ SP1M M1M SNM
R/ SP2M M2M SNM
R/ SP3M M3M SNM
* Useful inverses
RD 1/N3 N3 1.0
RD -1/N2 N2 -1.0
VARIABLES
P1F
P2F
P3F
P4F
P5F
P1W
P2W
P3W
P1M
P2M
P3M
Q0F
Q1F
Q2F
Q0W
Q1W
Q2W
Q0M
Q1M
Q2M
NF
NW
NM
NC2
NA2
NC3
NA3
GROUPS
* Household of size 3 to 8: each of these constraints
* imposes that the total number of individuals in households
* of a given size is equal to the observed value.
ZN HSZ3 'SCALE' M3
ZN HSZ4 'SCALE' M4
ZN HSZ5 'SCALE' M5
ZN HSZ6 'SCALE' M6
ZN HSZ7 'SCALE' M7
ZN HSZ8 'SCALE' M8
* Household with 1,2 or 3+ children, for families (F), isolated woman (W) or
* isolated man (M)
ZN HST1F 'SCALE' M1F
ZN HST2F 'SCALE' M2F
ZN HST3F 'SCALE' M3F
ZN HST1W 'SCALE' M1W
ZN HST2W 'SCALE' M2W
ZN HST3W 'SCALE' M3W
ZN HST1M 'SCALE' M1M
ZN HST2M 'SCALE' M2M
ZN HST3M 'SCALE' M3M
* Number of children
RM WHCH N0123 100.0
ZN HCH 'SCALE' WHCH
XN HCH NC2 -1.0 NC3 -1.0
* Number of adults
RM WHAD N234 100.0
ZN HAD 'SCALE' WHAD
XN HAD NA2 -1.0 NA3 -1.0
* Number of individuals in age class 2
XE AGE2 NC2 1.0 NA2 1.0
* Number of individuals in age class 3
XE AGE3 NC3 1.0 NA3 1.0
* Number of individuals in F-households
ZN HINF
* Number of individuals in N-households
ZN HINN
* Probability sums
E PSF P1F 1.0 P2F 1.0
E PSF P3F 1.0 P4F 1.0
E PSF P5F 1.0
E PSW P1W 1.0 P2W 1.0
E PSW P3W 1.0
E PSM P1M 1.0 P2M 1.0
E PSM P3M 1.0
E QSF Q0F 1.0 Q1F 1.0
E QSF Q2F 1.0
E QSM Q0M 1.0 Q1M 1.0
E QSM Q2M 1.0
E QSW Q0W 1.0 Q1W 1.0
E QSW Q2W 1.0
* ZL INEQ1 NC3 1/N3
* ZL INEQ1 NC2 -1/N2
L INEQ2 NC2 1.0 NA2 -1.0
L INEQ3 NC3 1.0 NA3 -1.0
CONSTANTS
Z ANTWERP HSZ3 M3
Z ANTWERP HSZ4 M4
Z ANTWERP HSZ5 M5
Z ANTWERP HSZ6 M6
Z ANTWERP HSZ7 M7
Z ANTWERP HSZ8 M8
Z ANTWERP HST1F M1F
Z ANTWERP HST2F M2F
Z ANTWERP HST3F M3F
Z ANTWERP HST1W M1W
Z ANTWERP HST2W M2W
Z ANTWERP HST3W M3W
Z ANTWERP HST1M M1M
Z ANTWERP HST2M M2M
Z ANTWERP HST3M M3M
Z ANTWERP HCH N01
Z ANTWERP HAD N4
Z ANTWERP HINF NINF
Z ANTWERP HINN NINN
Z ANTWERP AGE2 N2
Z ANTWERP AGE3 N3
ANTWERP PSF 1.0
ANTWERP PSM 1.0
ANTWERP PSW 1.0
ANTWERP QSF 1.0
ANTWERP QSM 1.0
ANTWERP QSW 1.0
BOUNDS
* FR ANTWERP 'DEFAULT'
LO ANTWERP 'DEFAULT' 0.0
UP ANTWERP 'DEFAULT' 1.0
PL ANTWERP NF
PL ANTWERP NM
PL ANTWERP NW
XL ANTWERP NC2 0.0
ZU ANTWERP NC2 N2
XL ANTWERP NA2 0.0
ZU ANTWERP NA2 N2
XL ANTWERP NC3 0.0
ZU ANTWERP NC3 N3
XL ANTWERP NA3 0.0
ZU ANTWERP NA3 N3
START POINT
Z ANTWERP P1F SP1F
Z ANTWERP P2F SP2F
ANTWERP P3F 0.15
ANTWERP P4F 0.10
ANTWERP P5F 0.05
Z ANTWERP P1W SP1W
Z ANTWERP P2W SP2W
Z ANTWERP P3W SP3W
Z ANTWERP P1M SP1M
Z ANTWERP P2M SP2M
Z ANTWERP P3M SP3M
ANTWERP Q0F 0.6
ANTWERP Q1F 0.3
ANTWERP Q2F 0.1
ANTWERP Q0M 0.6
ANTWERP Q1M 0.3
ANTWERP Q2M 0.1
ANTWERP Q0W 0.6
ANTWERP Q1W 0.3
ANTWERP Q2W 0.1
Z ANTWERP NF SNF
Z ANTWERP NW SNW
Z ANTWERP NM SNM
ANTWERP NC2 0.0
ANTWERP NC3 0.0
Z ANTWERP NA2 N2
Z ANTWERP NA3 N3
ELEMENT TYPE
EV 2PR V1 V2
EV 3PR V1 V2
EV 3PR V3
ELEMENT USES
* HSZ3
T P1FQ0FNF 3PR
V P1FQ0FNF V1 P1F
V P1FQ0FNF V2 Q0F
V P1FQ0FNF V3 NF
T P1WQ1WNW 3PR
V P1WQ1WNW V1 P1W
V P1WQ1WNW V2 Q1W
V P1WQ1WNW V3 NW
T P2WQ0WNW 3PR
V P2WQ0WNW V1 P2W
V P2WQ0WNW V2 Q0W
V P2WQ0WNW V3 NW
T P1MQ1MNM 3PR
V P1MQ1MNM V1 P1M
V P1MQ1MNM V2 Q1M
V P1MQ1MNM V3 NM
T P2MQ0MNM 3PR
V P2MQ0MNM V1 P2M
V P2MQ0MNM V2 Q0M
V P2MQ0MNM V3 NM
* HSZ4
T P2FQ0FNF 3PR
V P2FQ0FNF V1 P2F
V P2FQ0FNF V2 Q0F
V P2FQ0FNF V3 NF
T P1FQ1FNF 3PR
V P1FQ1FNF V1 P1F
V P1FQ1FNF V2 Q1F
V P1FQ1FNF V3 NF
T P1WQ2WNW 3PR
V P1WQ2WNW V1 P1W
V P1WQ2WNW V2 Q2W
V P1WQ2WNW V3 NW
T P2WQ1WNW 3PR
V P2WQ1WNW V1 P2W
V P2WQ1WNW V2 Q1W
V P2WQ1WNW V3 NW
T P3WQ0WNW 3PR
V P3WQ0WNW V1 P3W
V P3WQ0WNW V2 Q0W
V P3WQ0WNW V3 NW
T P1MQ2MNM 3PR
V P1MQ2MNM V1 P1M
V P1MQ2MNM V2 Q2M
V P1MQ2MNM V3 NM
T P2MQ1MNM 3PR
V P2MQ1MNM V1 P2M
V P2MQ1MNM V2 Q1M
V P2MQ1MNM V3 NM
T P3MQ0MNM 3PR
V P3MQ0MNM V1 P3M
V P3MQ0MNM V2 Q0M
V P3MQ0MNM V3 NM
* HSZ5
T P3FQ0FNF 3PR
V P3FQ0FNF V1 P3F
V P3FQ0FNF V2 Q0F
V P3FQ0FNF V3 NF
T P2FQ1FNF 3PR
V P2FQ1FNF V1 P2F
V P2FQ1FNF V2 Q1F
V P2FQ1FNF V3 NF
T P1FQ2FNF 3PR
V P1FQ2FNF V1 P1F
V P1FQ2FNF V2 Q2F
V P1FQ2FNF V3 NF
T P2WQ2WNW 3PR
V P2WQ2WNW V1 P2W
V P2WQ2WNW V2 Q2W
V P2WQ2WNW V3 NW
T P3WQ1WNW 3PR
V P3WQ1WNW V1 P3W
V P3WQ1WNW V2 Q1W
V P3WQ1WNW V3 NW
T P2MQ2MNM 3PR
V P2MQ2MNM V1 P2M
V P2MQ2MNM V2 Q2M
V P2MQ2MNM V3 NM
T P3MQ1MNM 3PR
V P3MQ1MNM V1 P3M
V P3MQ1MNM V2 Q1M
V P3MQ1MNM V3 NM
* HSZ6
T P4FQ0FNF 3PR
V P4FQ0FNF V1 P4F
V P4FQ0FNF V2 Q0F
V P4FQ0FNF V3 NF
T P3FQ1FNF 3PR
V P3FQ1FNF V1 P3F
V P3FQ1FNF V2 Q1F
V P3FQ1FNF V3 NF
T P2FQ2FNF 3PR
V P2FQ2FNF V1 P2F
V P2FQ2FNF V2 Q2F
V P2FQ2FNF V3 NF
T P3WQ2WNW 3PR
V P3WQ2WNW V1 P3W
V P3WQ2WNW V2 Q2W
V P3WQ2WNW V3 NW
T P3MQ2MNM 3PR
V P3MQ2MNM V1 P3M
V P3MQ2MNM V2 Q2M
V P3MQ2MNM V3 NM
* HSZ7
T P5FQ0FNF 3PR
V P5FQ0FNF V1 P5F
V P5FQ0FNF V2 Q0F
V P5FQ0FNF V3 NF
T P4FQ1FNF 3PR
V P4FQ1FNF V1 P4F
V P4FQ1FNF V2 Q1F
V P4FQ1FNF V3 NF
T P3FQ2FNF 3PR
V P3FQ2FNF V1 P3F
V P3FQ2FNF V2 Q2F
V P3FQ2FNF V3 NF
* HSZ8
T P5FQ1FNF 3PR
V P5FQ1FNF V1 P5F
V P5FQ1FNF V2 Q1F
V P5FQ1FNF V3 NF
T P4FQ2FNF 3PR
V P4FQ2FNF V1 P4F
V P4FQ2FNF V2 Q2F
V P4FQ2FNF V3 NF
* HST1F
T P1FNF 2PR
V P1FNF V1 P1F
V P1FNF V2 NF
* HST2F
T P2FNF 2PR
V P2FNF V1 P2F
V P2FNF V2 NF
* HST3F
T P3FNF 2PR
V P3FNF V1 P3F
V P3FNF V2 NF
T P4FNF 2PR
V P4FNF V1 P4F
V P4FNF V2 NF
T P5FNF 2PR
V P5FNF V1 P5F
V P5FNF V2 NF
* HST1W
T P1WNW 2PR
V P1WNW V1 P1W
V P1WNW V2 NW
* HST2W
T P2WNW 2PR
V P2WNW V1 P2W
V P2WNW V2 NW
* HST3W
T P3WNW 2PR
V P3WNW V1 P3W
V P3WNW V2 NW
* HST1M
T P1MNM 2PR
V P1MNM V1 P1M
V P1MNM V2 NM
* HST2M
T P2MNM 2PR
V P2MNM V1 P2M
V P2MNM V2 NM
* HST3M
T P3MNM 2PR
V P3MNM V1 P3M
V P3MNM V2 NM
* HNAD
T Q0FNF 2PR
V Q0FNF V1 Q0F
V Q0FNF V2 NF
T Q1FNF 2PR
V Q1FNF V1 Q1F
V Q1FNF V2 NF
T Q2FNF 2PR
V Q2FNF V1 Q2F
V Q2FNF V2 NF
T Q0WNW 2PR
V Q0WNW V1 Q0W
V Q0WNW V2 NW
T Q1WNW 2PR
V Q1WNW V1 Q1W
V Q1WNW V2 NW
T Q2WNW 2PR
V Q2WNW V1 Q2W
V Q2WNW V2 NW
T Q0MNM 2PR
V Q0MNM V1 Q0M
V Q0MNM V2 NM
T Q1MNM 2PR
V Q1MNM V1 Q1M
V Q1MNM V2 NM
T Q2MNM 2PR
V Q2MNM V1 Q2M
V Q2MNM V2 NM
GROUP TYPE
GV L2 GVAR
GROUP USES
T HSZ3 L2
E HSZ3 P1FQ0FNF P1WQ1WNW
E HSZ3 P2WQ0WNW P1MQ1MNM
E HSZ3 P2MQ0MNM
T HSZ4 L2
E HSZ4 P2FQ0FNF P1FQ1FNF
E HSZ4 P1WQ2WNW P2WQ1WNW
E HSZ4 P3WQ0WNW P1MQ2MNM
E HSZ4 P2MQ1MNM P3MQ0MNM
T HSZ5 L2
E HSZ5 P3FQ0FNF P2FQ1FNF
E HSZ5 P1FQ2FNF P2WQ2WNW
E HSZ5 P3WQ1WNW P2MQ2MNM
E HSZ5 P3MQ1MNM
T HSZ6 L2
E HSZ6 P4FQ0FNF P3FQ1FNF
E HSZ6 P2FQ2FNF P3WQ2WNW
E HSZ6 P3MQ2MNM
T HSZ7 L2
E HSZ7 P5FQ0FNF P4FQ1FNF
E HSZ7 P3FQ2FNF
T HSZ8 L2
E HSZ8 P5FQ1FNF P4FQ2FNF
T HST1F L2
E HST1F P1FNF
T HST2F L2
E HST2F P2FNF
T HST3F L2
E HST3F P3FNF P4FNF
E HST3F P5FNF
T HST1W L2
E HST1W P1WNW
T HST2W L2
E HST2W P2WNW
T HST3W L2
E HST3W P3WNW
T HST1M L2
E HST1M P1MNM
T HST2M L2
E HST2M P2MNM
T HST3M L2
E HST3M P3MNM
T HCH L2
E HCH P1FNF 1.0 P2FNF 2.0
E HCH P3FNF 3.0 P4FNF 4.0
E HCH P5FNF 5.0 P1MNM 1.0
E HCH P2MNM 2.0 P3MNM 3.0
E HCH P1WNW 1.0 P2WNW 2.0
E HCH P3WNW 3.0
T HAD L2
E HAD Q0FNF 2.0 Q1FNF 3.0
E HAD Q2FNF 4.0
E HAD Q0MNM
E HAD Q1MNM 2.0 Q2MNM 3.0
E HAD Q0WNW
E HAD Q1WNW 2.0 Q2WNW 3.0
T HINF L2
E HINF P1FNF 1.0 P2FNF 2.0
E HINF P3FNF 3.0 P4FNF 4.0
E HINF P5FNF 5.0 Q0FNF 2.0
E HINF Q1FNF 3.0 Q2FNF 4.0
T HINN L2
E HINN P1WNW 1.0 P2WNW 2.0
E HINN P3WNW 3.0 Q0WNW 1.0
E HINN Q1WNW 2.0 Q2WNW 3.0
E HINN P1MNM 1.0 P2MNM 2.0
E HINN P3MNM 3.0 Q0MNM 1.0
E HINN Q1MNM 2.0 Q2MNM 3.0
OBJECT BOUND
LO ANTWERP 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ANTWERP
INDIVIDUALS
T 2PR
F V1 * V2
G V1 V2
G V2 V1
H V1 V2 1.0
T 3PR
F V1 * V2 * V3
G V1 V2 * V3
G V2 V1 * V3
G V3 V1 * V2
H V1 V2 V3
H V1 V3 V2
H V2 V3 V1
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS ANTWERP
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA