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SAROMM.SIF
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NAME SAROMM
*
* A discrete-time optimal control problem.
* This problem is a min-max-reformulation of problem SARO, a solar
* heating system example (see SARO.SIF for more explanation). The aim is to
* find the minimal value of the maximal supplementary heat load required in
* addition to solar heat during one year of operation.
* The only changes to the formulation of problem SARO are in the
* linear part of the SIF specification.
* The value of the global solution is 57.4 kW. The difference to the
* maximal heat load of 88.3 kW on the coldest day in February can be covered
* by solar in this example. However, a local optimizer exists at 88.3 kW.
* Using HQP 1.3, both solutions can be obtained by varying the starting
* value for the maximal supplementary heat load PSMSTART (see below).
*
* SIF input: Ruediger Franke, TU Ilmenau, January 1998
*
* classification LOR1-MN-5120-5110
********************************************
* define starting point
RE PSMSTART 0.0 $ HQP 1.3 finds the global solution
*RE PSMSTART 100.0 $ HQP 1.3 finds a local optimizer
* define required integer constants
IE KMAX 366 $ number of communication points
IE NX 9 $ number of states
IE NU 2 $ number of controls
IE NG 2 $ constraints
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
IE 7 7
IE 8 8
IE 9 9
IA KMAX-1 KMAX -1 $ number of time steps
VARIABLES
DO K 1 KMAX-1
* maximal supplementary heat load
X PSM(K)
* discrete-time states
DO I 1 NX
X X(I,K)
OD I
* control parameters
DO I 1 NU
X U(I,K)
OD I
* slack variables
DO I 1 NG
X S(I,K)
OD I
OD K
* final states
X PSM(KMAX)
DO I 1 NX
X X(I,KMAX)
OD I
GROUPS
* objective function
* (final value of supplementary heat load)
XN OBJ PSM(KMAX) 1.0
* system equations and constraints
DO K 1 KMAX-1
IA K+1 K 1
XE FPSM(K) PSM(K) 1.0 PSM(K+1) -1.0
DO I 1 NX
XE F(I,K) X(I,K+1) -1.0
OD I
DO I 1 NG
XE G(I,K) S(I,K) -1.0
XG GPSM(I,K) PSM(K) 1.0 S(I,K) -1.0
OD I
OD K
BOUNDS
FR BNDS 'DEFAULT'
* initial states
XX BNDS X(1,1) 83.50
XX BNDS X(2,1) 83.42
XX BNDS X(3,1) 82.55
XX BNDS X(4,1) 81.00
XX BNDS X(5,1) 78.00
XX BNDS X(6,1) 68.37
XX BNDS X(7,1) 0.00
XX BNDS X(8,1) 0.00
XX BNDS X(9,1) 0.00
* final states
XX BNDS X(1,KMAX) 83.50
* control bounds
DO K 1 KMAX-1
DO I 1 NU
XL BNDS U(I,K) 0.0
XU BNDS U(I,K) 1.0
ND
* bounds on algebraic variables,
* i.e. supplementary heat power
DO K 1 KMAX-1
DO I 1 NG
XL BNDS S(I,K) 0.0
ND
START POINT
DO K 1 KMAX
Z SPOINT PSM(K) PSMSTART
X SPOINT X(1,K) 83.50
X SPOINT X(2,K) 83.42
X SPOINT X(3,K) 82.55
X SPOINT X(4,K) 81.00
X SPOINT X(5,K) 78.00
X SPOINT X(6,K) 68.37
ND
DO K 1 KMAX-1
DO I 1 NU
X SPOINT U(I,K) 0.5
ND
ELEMENT TYPE
* system equations and constraints
EP FTYPE RK RIDX
EV FTYPE X1 X2
EV FTYPE X3 X4
EV FTYPE X5 X6
EV FTYPE X7 X8
EV FTYPE X9
EV FTYPE U1 U2
EP GTYPE RK RIDX
EV GTYPE X1 X2
EV GTYPE X3 X4
EV GTYPE X5 X6
EV GTYPE X7 X8
EV GTYPE X9
EV GTYPE U1 U2
ELEMENT USES
* system equations and constraints
DO K 1 KMAX-1
RI RK K
DO I 1 NX
RI RIDX I
XT FE(I,K) FTYPE
ZP FE(I,K) RK RK
ZP FE(I,K) RIDX RIDX
ZV FE(I,K) X1 X(1,K)
ZV FE(I,K) X2 X(2,K)
ZV FE(I,K) X3 X(3,K)
ZV FE(I,K) X4 X(4,K)
ZV FE(I,K) X5 X(5,K)
ZV FE(I,K) X6 X(6,K)
ZV FE(I,K) X7 X(7,K)
ZV FE(I,K) X8 X(8,K)
ZV FE(I,K) X9 X(9,K)
ZV FE(I,K) U1 U(1,K)
ZV FE(I,K) U2 U(2,K)
OD I
DO I 1 NG
RI RIDX I
XT GE(I,K) GTYPE
ZP GE(I,K) RK RK
ZP GE(I,K) RIDX RIDX
ZV GE(I,K) X1 X(1,K)
ZV GE(I,K) X2 X(2,K)
ZV GE(I,K) X3 X(3,K)
ZV GE(I,K) X4 X(4,K)
ZV GE(I,K) X5 X(5,K)
ZV GE(I,K) X6 X(6,K)
ZV GE(I,K) X7 X(7,K)
ZV GE(I,K) X8 X(8,K)
ZV GE(I,K) X9 X(9,K)
ZV GE(I,K) U1 U(1,K)
ZV GE(I,K) U2 U(2,K)
OD I
OD K
GROUP USES
* system equations and constraints
DO K 1 KMAX-1
DO I 1 NX
XE F(I,K) FE(I,K)
OD I
DO I 1 NG
XE G(I,K) GE(I,K)
OD I
OD K
OBJECT BOUND
*LO SOLUTION 57.3506
ENDATA
*
* nonlinear elements
*
ELEMENTS SAROMM
TEMPORARIES
R SAROFN
F SAROFN
R SAROGN
F SAROGN
R F
R GX1
R GX2
R GX3
R GX4
R GX5
R GX6
R GX7
R GX8
R GX9
R GU1
R GU2
INDIVIDUALS
* system equations
T FTYPE
F SAROFN(RK, RIDX, .TRUE.,
F+ X1, X2, X3, X4, X5, X6, X7, X8, X9,
F+ U1, U2)
A F SAROGN(RK, RIDX, .TRUE.,
A+ X1, X2, X3, X4, X5, X6, X7, X8, X9,
A+ U1, U2,
A+ GX1, GX2, GX3, GX4, GX5, GX6, GX7,
A+ GX8, GX9, GU1, GU2)
G X1 GX1
G X2 GX2
G X3 GX3
G X4 GX4
G X5 GX5
G X6 GX6
G X7 GX7
G X8 GX8
G X9 GX9
G U1 GU1
G U2 GU2
* constraints
T GTYPE
F SAROFN(RK, RIDX, .FALSE.,
F+ X1, X2, X3, X4, X5, X6, X7, X8, X9,
F+ U1, U2)
A F SAROGN(RK, RIDX, .FALSE.,
A+ X1, X2, X3, X4, X5, X6, X7, X8, X9,
A+ U1, U2,
A+ GX1, GX2, GX3, GX4, GX5, GX6, GX7,
A+ GX8, GX9, GU1, GU2)
G X1 GX1
G X2 GX2
G X3 GX3
G X4 GX4
G X5 GX5
G X6 GX6
G X7 GX7
G X8 GX8
G X9 GX9
G U1 GU1
G U2 GU2
ENDATA
C
C FORTRAN ROUTINES
C
C
C CALCULATE FUNCTION VALUE OF DISCRETE TIME SYSTEM EQUATIONS AND CONSTRAINTS.
C THIS FUNCTION PROVIDES AN INTERFACE TO SRFG.
C
DOUBLE PRECISION FUNCTION SAROFN(
1 RK, RIDX, SYSEQ,
2 X1, X2, X3, X4, X5, X6, X7, X8, X9,
3 U1, U2)
C
INTEGER NX, NU, NG
PARAMETER(NX = 9, NU = 2, NG = 2)
DOUBLE PRECISION RK, RIDX
LOGICAL SYSEQ
DOUBLE PRECISION X1, X2, X3, X4, X5, X6, X7, X8, X9
DOUBLE PRECISION U1, U2
INTEGER K, IDX
DOUBLE PRECISION X(NX), U(NU), F(NX), G(NG)
DOUBLE PRECISION RKZBAK
C
SAVE
C
DATA RKZBAK /-1.0D0/
C
IF ((RK .NE. RKZBAK)
* .OR. (X1 .NE. X(1))
* .OR. (X2 .NE. X(2))
* .OR. (X3 .NE. X(3))
* .OR. (X4 .NE. X(4))
* .OR. (X5 .NE. X(5))
* .OR. (X6 .NE. X(6))
* .OR. (X7 .NE. X(7))
* .OR. (X8 .NE. X(8))
* .OR. (X9 .NE. X(9))
* .OR. (U1 .NE. U(1))
* .OR. (U2 .NE. U(2))) THEN
C
X(1) = X1
X(2) = X2
X(3) = X3
X(4) = X4
X(5) = X5
X(6) = X6
X(7) = X7
X(8) = X8
X(9) = X9
C
U(1) = U1
U(2) = U2
C
K = RK
RKZBAK = RK
C
CALL SRFG(K, X, U, F, G)
END IF
C
IDX = RIDX
IF (SYSEQ) THEN
SAROFN = F(IDX)
ELSE
SAROFN = G(IDX)
END IF
C
RETURN
END
C
C
C CALCULATE JACOBIAN OF DISCRETE TIME SYSTEM EQUATIONS AND CONSTRAINTS.
C THIS FUNCTION PROVIDES AN INTERFACE TO GZSRFG THAT HAS BEEN DERIVED
C FROM SRFG USING ADIFOR.
C
DOUBLE PRECISION FUNCTION SAROGN(
1 RK, RIDX, SYSEQ,
2 X1, X2, X3, X4, X5, X6, X7, X8, X9,
3 U1, U2,
4 GX1, GX2, GX3, GX4, GX5, GX6, GX7, GX8, GX9,
5 GU1, GU2)
C
INTEGER NX, NU, NG, PMAX
PARAMETER(NX = 9, NU = 2, NG = 2, PMAX = 11)
DOUBLE PRECISION RK, RIDX
LOGICAL SYSEQ
DOUBLE PRECISION X1, X2, X3, X4, X5, X6, X7, X8, X9
DOUBLE PRECISION U1, U2
DOUBLE PRECISION GX1, GX2, GX3, GX4, GX5, GX6, GX7, GX8, GX9
DOUBLE PRECISION GU1, GU2
INTEGER I, J, K, IDX
DOUBLE PRECISION X(NX), U(NU), F(NX), G(NG)
DOUBLE PRECISION GZF(PMAX, NX), GZG(PMAX, NG)
DOUBLE PRECISION GZX(PMAX, NX), GZU(PMAX, NU)
DOUBLE PRECISION RKZBAK
C
SAVE
C
DATA RKZBAK /-1.0D0/
C
IF ((RK .NE. RKZBAK)
* .OR. (X1 .NE. X(1))
* .OR. (X2 .NE. X(2))
* .OR. (X3 .NE. X(3))
* .OR. (X4 .NE. X(4))
* .OR. (X5 .NE. X(5))
* .OR. (X6 .NE. X(6))
* .OR. (X7 .NE. X(7))
* .OR. (X8 .NE. X(8))
* .OR. (X9 .NE. X(9))
* .OR. (U1 .NE. U(1))
* .OR. (U2 .NE. U(2))) THEN
C
X(1) = X1
X(2) = X2
X(3) = X3
X(4) = X4
X(5) = X5
X(6) = X6
X(7) = X7
X(8) = X8
X(9) = X9
C
U(1) = U1
U(2) = U2
C
K = RK
RKZBAK = RK
C
DO 120 I = 1, PMAX
DO 100 J = 1, NX
GZX(I, J) = 0.0D0
100 CONTINUE
DO 110 J = 1, NU
GZU(I, J) = 0.0D0
110 CONTINUE
IF (I .LE. NX) THEN
GZX(I, I) = 1.0D0
ELSE
GZU(I, I - NX) = 1.0D0
END IF
120 CONTINUE
C
CALL GZSRFG(PMAX, K, X, GZX, PMAX, U, GZU, PMAX,
* F, GZF, PMAX, G, GZG, PMAX)
C
END IF
C
IDX = RIDX
C
IF (SYSEQ) THEN
GX1 = GZF(1,IDX)
GX2 = GZF(2,IDX)
GX3 = GZF(3,IDX)
GX4 = GZF(4,IDX)
GX5 = GZF(5,IDX)
GX6 = GZF(6,IDX)
GX7 = GZF(7,IDX)
GX8 = GZF(8,IDX)
GX9 = GZF(9,IDX)
C
GU1 = GZF(10,IDX)
GU2 = GZF(11,IDX)
C
SAROGN = F(IDX)
ELSE
GX1 = GZG(1,IDX)
GX2 = GZG(2,IDX)
GX3 = GZG(3,IDX)
GX4 = GZG(4,IDX)
GX5 = GZG(5,IDX)
GX6 = GZG(6,IDX)
GX7 = GZG(7,IDX)
GX8 = GZG(8,IDX)
GX9 = GZG(9,IDX)
C
GU1 = GZG(10,IDX)
GU2 = GZG(11,IDX)
C
SAROGN = G(IDX)
END IF
C
RETURN
END
C
C
C CALCULATE FUNCTION VALUES OF DISCRETE-TIME SYSTEM EQUATIONS AND CONSTRAINTS.
C THIS SUBROUTINE DIVIDES EACH TIME STEP K INTO TWO SAMPLE PERIODS AND
C INTEGRATES CONTINUOUS-TIME SYSTEM EQUATIONS.
C
SUBROUTINE SRFG(K, X, U, F, G)
C
INTEGER NX, NU, NG, NP, NW
PARAMETER (NX = 9, NU = 2, NG = 2, NP = 1, NW = 1)
INTEGER K
DOUBLE PRECISION X(NX), U(NU), F(NX), G(NG)
INTEGER KK
DOUBLE PRECISION DT, FH(NX), P(NP), W(NW)
C
KK = 2 * (K - 1) + 1
DT = 12.0D0
C
P(1) = U(1)
CALL SRK4(KK, DT, X, P, FH, W)
G(1) = W(1)
C
P(1) = U(2)
CALL SRK4(KK + 1, DT, FH, P, F, W)
G(2) = W(1)
C
RETURN
END
C
C
C RUNGE KUTTA TYPE INTEGRATION PROCEDURE.
C
SUBROUTINE SRK4(KK, DT, X, P, F, W)
C
INTEGER NX, NP, NW
PARAMETER (NX = 9, NP = 1, NW = 1)
INTEGER KK
DOUBLE PRECISION DT, X(NX), P(NP), F(NX), W(NW)
INTEGER I
DOUBLE PRECISION DF(NX), XH(NX), W1(NW)
C
CALL SREQ(KK, X, P, DF, W)
DO 200 I = 1, NX
F(I) = X(I) + DT/6.0D0 * DF(I)
XH(I) = X(I) + DT/2.0D0 * DF(I)
200 CONTINUE
C
CALL SREQ(KK, XH, P, DF, W1)
DO 210 I = 1, NX
F(I) = F(I) + DT/3.0D0 * DF(I)
XH(I) = X(I) + DT/2.0D0 * DF(I)
210 CONTINUE
C
CALL SREQ(KK, XH, P, DF, W1)
DO 220 I = 1, NX
F(I) = F(I) + DT/3.0D0 * DF(I)
XH(I) = X(I) + DT * DF(I)
220 CONTINUE
C
CALL SREQ(KK, XH, P, DF, W1)
DO 230 I = 1, NX
F(I) = F(I) + DT/6.0D0 * DF(I)
230 CONTINUE
C
END
C
C
C CALCULATE RIGHT HAND SIDES OF THE ODES DEFINING THE SYSTEM.
C
SUBROUTINE SREQ(KK, X, P, DF, W)
C
INTEGER KMAX, NX, NP, NW
LOGICAL EXTU
PARAMETER (KMAX = 366, NX = 9, NP = 1, NW = 1, EXTU = .TRUE.)
INTEGER KK
DOUBLE PRECISION X(NX), P(NP), DF(NX), W(NW), V(199)
INTEGER K
DOUBLE PRECISION TAS(KMAX), TRSHS(KMAX), PSHS(KMAX)
DOUBLE PRECISION H0S(KMAX), H1S(KMAX), H2S(KMAX), H3S(KMAX)
DOUBLE PRECISION OP0S(KMAX), OP1S(KMAX), OP2S(KMAX), OP3S(KMAX)
COMMON /SARDAT/
1 TAS, TRSHS, PSHS, H0S, H1S, H2S, H3S, OP0S, OP1S, OP2S, OP3S
C
K = ((KK - 1) / 2) + 1
C
TA = TAS(K)
TRSH = TRSHS(K)
PSH = PSHS(K)
IF (2*(K-1) .EQ. (KK-1)) THEN
H0 = 2.0D0 * H0S(K)
H1 = 2.0D0 * H1S(K)
H2 = 2.0D0 * H2S(K)
H3 = 2.0D0 * H3S(K)
OP0 = 2.0D0 * OP0S(K)
OP1 = 2.0D0 * OP1S(K)
OP2 = 2.0D0 * OP2S(K)
OP3 = 2.0D0 * OP3S(K)
ELSE
H0 = 0.0D0
H1 = 0.0D0
H2 = 0.0D0
H3 = 0.0D0
OP0 = 0.0D0
OP1 = 0.0D0
OP2 = 0.0D0
OP3 = 0.0D0
END IF
C
C SORTED AND SOLVED EQUATIONS, GENERATED BY DYMOLA
C (POSTPROCESSED IN ORDER TO PLACE ALL TEMPORARY VARIABLES IN V)
C M.
V(12) = 0.001D0*PSH
IF (EXTU) THEN
V(13) = P(1)
ELSE
IF (X(1) .GT. 60.0D0) THEN
V(199) = (60.0D0 - TRSH)/(X(1) -
1 TRSH)
ELSE
V(198) = EXP(15.0D0 - 20.0D0
1 *(X(1) - TRSH))
V(199) = 1.0D0/(1.0D0 + V(198))
END IF
V(13) = V(199)
END IF
V(6) = 1000.0D0*V(13)*V(12)/(
1 69666.6666666667D0 - 1161.11111111111D0*TRSH)
V(11) = 1.16111111111111D0*(X(1) - TRSH)*
1 V(6)
V(10) = V(12) - V(11)
DF(7) = 0.001D0*V(10)
V(19) = OP0 + (OP1 + (OP2 + OP3*X(6))*X(6))*
1 X(6)
V(14) = 740.0D0*V(19)
V(16) = 0.000277777777777778D0*V(14)
V(22) = - V(16)
V(26) = - V(16)
V(35) = - V(16)
V(43) = 3600.0D0*V(16)
V(18) = H0 + (H1 + (H2 + H3*X(6))*X(6))*
1 X(6)
V(46) = X(6) + V(18)/(1.16111111111111D-27
1 + 1161.11111111111D0*V(19))
V(8) = 0.000277777777777778D0*V(6)
V(24) = - V(8)
V(28) = - V(8)
V(123) = - V(8)
V(106) = - V(8)
V(89) = - V(8)
V(72) = - V(8)
V(55) = - V(8)
V(37) = - V(8)
V(48) = 3600.0D0*V(8)
V(166) = 47.5428571428572D0*(X(1) -
1 X(2))
V(157) = 10.1587301587302D0*(X(1) - TA)
V(40) = - (V(166) + V(157))
V(138) = 3.76619850066144D0*(X(1) - TA)
V(41) = - V(138)
DF(1) = 9.41985645933014D-06*(
1 1161.11111111111D0*V(43)*(V(46) -
1 X(1)) + 1161.11111111111D0*V(48)*(
1 X(2) - X(1)) + V(40) -
1 V(138))
V(53) = - V(16)
V(61) = 3600.0D0*V(16)
V(65) = 3600.0D0*V(8)
V(167) = - V(166)
V(170) = 39.6190476190476D0*(X(2) -
1 X(3))
V(58) = V(166) - V(170)
V(142) = 4.0D0 +
1 0.5D0*TA
V(141) = 5.64929775099216D0*(X(2) -
1 V(142))
V(59) = - V(141)
DF(2) = 6.27990430622009D-06*(
1 1161.11111111111D0*V(61)*(X(1) -
1 X(2)) + 1161.11111111111D0*V(65)*(
1 X(3) - X(2)) + V(58) -
1 V(141))
V(70) = - V(16)
V(78) = 3600.0D0*V(16)
V(82) = 3600.0D0*V(8)
V(172) = - V(170)
V(175) = 39.6190476190476D0*(X(3) -
1 X(4))
V(75) = V(170) - V(175)
V(145) = 5.64929775099216D0*X(3) -
1 45.1943820079373D0
V(76) = - V(145)
DF(3) = 6.27990430622009D-06*(
1 1161.11111111111D0*V(78)*(X(2) -
1 X(3)) + 1161.11111111111D0*V(82)*(
1 X(4) - X(3)) + V(75) -
1 V(145))
V(87) = - V(16)
V(95) = 3600.0D0*V(16)
V(99) = 3600.0D0*V(8)
V(177) = - V(175)
V(180) = 47.5428571428572D0*(X(4) -
1 X(5))
V(92) = V(175) - V(180)
V(148) = 5.64929775099216D0*X(4) -
1 45.1943820079373D0
V(93) = - V(148)
DF(4) = 6.27990430622009D-06*(
1 1161.11111111111D0*V(95)*(X(3) -
1 X(4)) + 1161.11111111111D0*V(99)*(
1 X(5) - X(4)) + V(92) -
1 V(148))
V(104) = - V(16)
V(112) = 3600.0D0*V(16)
V(116) = 3600.0D0*V(8)
V(182) = - V(180)
V(185) = 79.2380952380953D0*(X(5) -
1 X(6))
V(109) = V(180) - V(185)
V(151) = 3.76619850066144D0*X(5) -
1 30.1295880052915D0
V(110) = - V(151)
DF(5) = 9.41985645933014D-06*(
1 1161.11111111111D0*V(112)*(X(4) -
1 X(5)) + 1161.11111111111D0*V(116)*(
1 X(6) - X(5)) + V(109) -
1 V(151))
V(121) = - V(16)
V(129) = 3600.0D0*V(16)
V(133) = 3600.0D0*V(8)
V(187) = - V(185)
V(161) = 73.1428571428572D0*X(6) -
1 585.142857142857D0
V(126) = V(185) - V(161)
V(154) = 1.88309925033072D0*X(6) -
1 15.0647940026458D0
V(127) = - V(154)
DF(6) = 1.88397129186603D-05*(
1 1161.11111111111D0*V(129)*(X(5) -
1 X(6)) + 1161.11111111111D0*V(133)*(TRSH -
1 X(6)) + V(126) - V(154))
V(196) = 4180.0D0*(X(1) - TRSH)*V(8)
DF(8) = 0.001D0*V(196)
V(197) = 4180.0D0*(V(46) - X(6))*
1 V(16)
DF(9) = 0.001D0*V(197)
C END OF SORTED AND SOLVED EQUATIONS
C
W(1) = V(10)
C
RETURN
END
C
C
BLOCK DATA SARCOM
C
INTEGER NK1, NK2, NK3, NK4
PARAMETER (NK1 = 108, NK2 = 108, NK3 = 108, NK4 = 42)
DOUBLE PRECISION TA1(NK1), TA2(NK2), TA3(NK3), TA4(NK4)
DOUBLE PRECISION TRSH1(NK1), TRSH2(NK2), TRSH3(NK3), TRSH4(NK4)
DOUBLE PRECISION PSH1(NK1), PSH2(NK2), PSH3(NK3), PSH4(NK4)
DOUBLE PRECISION H01(NK1), H02(NK2), H03(NK3), H04(NK4)
DOUBLE PRECISION H11(NK1), H12(NK2), H13(NK3), H14(NK4)
DOUBLE PRECISION H21(NK1), H22(NK2), H23(NK3), H24(NK4)
DOUBLE PRECISION H31(NK1), H32(NK2), H33(NK3), H34(NK4)
DOUBLE PRECISION OP01(NK1), OP02(NK2), OP03(NK3), OP04(NK4)
DOUBLE PRECISION OP11(NK1), OP12(NK2), OP13(NK3), OP14(NK4)
DOUBLE PRECISION OP21(NK1), OP22(NK2), OP23(NK3), OP24(NK4)
DOUBLE PRECISION OP31(NK1), OP32(NK2), OP33(NK3), OP34(NK4)
C
COMMON /SARDAT/
1 TA1, TA2, TA3, TA4, TRSH1, TRSH2, TRSH3, TRSH4,
2 PSH1, PSH2, PSH3, PSH4,
3 H01, H02, H03, H04, H11, H12, H13, H14,
4 H21, H22, H23, H24, H31, H32, H33, H34,
5 OP01, OP02, OP03, OP04, OP11, OP12, OP13, OP14,
6 OP21, OP22, OP23, OP24, OP31, OP32, OP33, OP34
C
DATA TA1/
1 1.52D+01, 1.60D+01, 1.67D+01, 1.77D+01, 1.54D+01, 1.14D+01,
2 9.10D+00, 1.23D+01, 1.21D+01, 1.46D+01, 1.28D+01, 9.44D+00,
3 1.25D+01, 1.53D+01, 1.51D+01, 1.37D+01, 1.18D+01, 1.26D+01,
4 1.31D+01, 1.36D+01, 1.25D+01, 1.25D+01, 1.14D+01, 1.33D+01,
5 1.35D+01, 1.18D+01, 9.37D+00, 7.50D+00, 8.75D+00, 1.25D+01,
6 1.03D+01, 9.90D+00, 7.45D+00, 1.10D+01, 1.17D+01, 1.14D+01,
7 7.96D+00, 1.34D+01, 1.25D+01, 8.81D+00, 1.14D+01, 1.12D+01,
8 1.04D+01, 1.12D+01, 1.06D+01, 1.07D+01, 9.89D+00, 7.89D+00,
9 5.32D+00, 2.33D-01,-7.92D-02, 2.34D+00, 1.65D+00, 4.45D+00,
1 4.46D+00, 6.70D+00, 6.65D+00, 6.72D+00, 6.22D+00, 5.08D+00,
2 4.08D+00, 4.65D+00, 7.82D+00, 8.24D+00, 6.96D+00, 5.36D+00,
3 4.56D+00, 7.21D+00, 6.74D+00, 4.94D+00, 1.10D+00, 5.45D+00,
4 6.33D+00, 5.92D+00, 5.50D+00, 3.67D+00, 2.60D+00, 1.38D+00,
5 1.59D+00,-2.08D-01,-4.81D+00,-1.77D+00, 6.08D+00, 7.07D+00,
6 6.96D+00, 6.12D+00, 4.92D+00, 5.89D+00, 6.32D+00, 6.60D+00,
7 5.90D+00, 4.59D+00, 4.70D+00, 5.61D+00, 5.00D+00,-5.21D-01,
8 1.70D+00,-1.49D+00,-4.02D+00, 1.21D+00, 1.83D+00, 1.73D+00,
9 1.83D+00, 1.73D+00, 1.83D+00, 1.73D+00, 3.66D+00, 4.05D+00/
DATA TA2/
1 4.98D+00, 4.32D+00, 3.55D+00, 4.17D+00, 4.33D-01, 5.30D+00,
2 -5.08D-01,-2.08D+00, 4.50D+00,-8.17D-01, 3.60D+00, 5.70D+00,
3 3.45D+00,-6.00D-01, 3.83D+00, 3.46D+00, 3.83D+00, 3.46D+00,
4 4.36D+00, 3.72D+00, 3.65D+00, 3.16D+00, 3.56D+00, 4.45D+00,
5 3.87D+00, 1.90D+00,-3.90D+00,-2.36D+00, 4.08D-01, 3.92D-01,
6 -1.97D+00, 3.83D-01, 3.92D-01, 2.60D+00, 2.95D+00,-3.21D-01,
7 3.31D+00, 6.00D-01, 2.40D+00,-1.42D-01,-1.93D+00,-1.48D+00,
8 -2.29D+00,-3.65D+00,-4.23D+00,-5.12D+00,-3.84D+00,-3.91D+00,
9 -5.16D+00,-4.20D+00,-4.86D+00,-4.05D+00,-2.55D+00,-2.36D+00,
1 -2.08D+00,-2.38D+00,-2.43D+00,-5.47D+00,-6.94D+00,-7.25D+00,
2 -4.92D+00,-2.78D+00,-3.52D+00,-4.62D-01, 4.42D-01, 9.37D-01,
3 1.97D+00, 2.65D+00, 3.95D+00, 2.75D+00,-5.33D-01,-3.28D+00,
4 -2.62D+00, 1.12D+00, 1.26D+00, 6.00D-01, 1.45D+00, 8.13D-01,
5 2.48D+00, 2.80D+00, 3.57D+00, 3.33D+00, 2.89D+00, 4.14D+00,
6 3.61D+00, 1.89D+00, 4.30D+00, 4.69D+00, 3.46D+00, 4.04D+00,
7 4.72D+00, 4.74D+00, 4.92D+00, 4.01D+00, 4.04D+00, 3.16D+00,
8 2.78D+00, 3.49D+00, 6.55D+00, 6.41D+00, 2.83D+00, 3.03D+00,
9 4.19D+00, 2.69D+00, 5.51D+00, 6.39D+00, 6.08D+00, 4.89D+00/
DATA TA3/
1 7.48D+00, 7.07D+00, 5.88D+00, 5.92D+00, 4.61D+00, 6.31D+00,
2 9.54D+00, 1.11D+01, 1.11D+01, 9.06D+00, 6.74D+00, 6.02D+00,
3 2.68D+00, 1.36D+00, 1.01D+00, 1.67D+00, 2.49D+00, 3.35D+00,
4 4.59D+00, 4.76D+00, 6.83D+00, 4.51D+00, 6.67D+00, 8.83D+00,
5 7.94D+00, 8.48D+00, 5.20D+00, 7.71D+00, 6.14D+00, 5.75D+00,
6 7.69D+00, 7.78D+00, 7.82D+00, 8.29D+00, 8.85D+00, 8.78D+00,
7 8.93D+00, 1.03D+01, 9.17D+00, 9.85D+00, 8.28D+00, 9.65D+00,
8 8.20D+00, 9.11D+00, 9.03D+00, 1.06D+01, 1.10D+01, 1.09D+01,
9 9.14D+00, 8.81D+00, 9.72D+00, 1.01D+01, 1.17D+01, 1.15D+01,
1 1.18D+01, 1.47D+01, 1.40D+01, 1.11D+01, 1.04D+01, 7.71D+00,
2 7.31D+00, 9.96D+00, 1.05D+01, 1.12D+01, 1.08D+01, 1.16D+01,
3 1.33D+01, 1.22D+01, 1.14D+01, 1.28D+01, 1.13D+01, 1.25D+01,
4 1.16D+01, 1.25D+01, 9.95D+00, 1.19D+01, 1.18D+01, 1.29D+01,
5 1.34D+01, 1.41D+01, 1.39D+01, 1.47D+01, 1.40D+01, 1.43D+01,
6 1.44D+01, 1.23D+01, 1.35D+01, 1.51D+01, 1.73D+01, 1.95D+01,
7 2.03D+01, 2.09D+01, 2.11D+01, 2.11D+01, 2.18D+01, 1.93D+01,
8 1.71D+01, 1.74D+01, 1.80D+01, 1.74D+01, 1.68D+01, 1.66D+01,
9 1.55D+01, 1.63D+01, 1.65D+01, 1.55D+01, 1.67D+01, 1.68D+01/
DATA TA4/
1 1.83D+01, 1.55D+01, 1.66D+01, 1.73D+01, 1.72D+01, 1.69D+01,
2 1.69D+01, 1.72D+01, 2.07D+01, 2.22D+01, 2.24D+01, 2.17D+01,
3 2.00D+01, 1.89D+01, 1.86D+01, 1.75D+01, 1.94D+01, 1.88D+01,
4 1.67D+01, 1.79D+01, 1.68D+01, 1.55D+01, 1.65D+01, 1.66D+01,
5 1.70D+01, 1.66D+01, 1.47D+01, 1.46D+01, 1.59D+01, 1.62D+01,
6 1.65D+01, 1.74D+01, 1.86D+01, 1.58D+01, 1.61D+01, 1.49D+01,
7 1.45D+01, 1.46D+01, 1.45D+01, 1.69D+01, 1.53D+01, 1.52D+01/
C
DATA TRSH1/
1 3.03D+01, 3.02D+01, 3.10D+01, 3.11D+01, 3.11D+01, 3.01D+01,
2 3.19D+01, 3.11D+01, 3.16D+01, 3.08D+01, 3.07D+01, 3.21D+01,
3 2.97D+01, 3.09D+01, 3.01D+01, 3.02D+01, 3.08D+01, 3.07D+01,
4 3.07D+01, 2.93D+01, 3.10D+01, 3.02D+01, 3.04D+01, 3.08D+01,
5 3.06D+01, 3.09D+01, 3.09D+01, 3.28D+01, 3.15D+01, 3.02D+01,
6 3.11D+01, 3.15D+01, 3.30D+01, 3.01D+01, 3.08D+01, 2.98D+01,
7 3.24D+01, 3.15D+01, 3.12D+01, 3.14D+01, 3.09D+01, 3.12D+01,
8 3.04D+01, 3.04D+01, 3.15D+01, 3.08D+01, 3.14D+01, 3.18D+01,
9 3.32D+01, 3.58D+01, 3.64D+01, 3.56D+01, 3.55D+01, 3.43D+01,
1 3.36D+01, 3.27D+01, 3.21D+01, 3.21D+01, 3.32D+01, 3.35D+01,
2 3.37D+01, 3.35D+01, 3.23D+01, 3.10D+01, 3.18D+01, 3.35D+01,
3 3.35D+01, 3.20D+01, 3.24D+01, 3.34D+01, 3.50D+01, 3.25D+01,
4 3.28D+01, 3.27D+01, 3.31D+01, 3.38D+01, 3.45D+01, 3.46D+01,
5 3.48D+01, 3.65D+01, 3.97D+01, 3.83D+01, 3.28D+01, 3.21D+01,
6 3.14D+01, 3.23D+01, 3.34D+01, 3.29D+01, 3.27D+01, 3.25D+01,
7 3.27D+01, 3.30D+01, 3.30D+01, 3.34D+01, 3.37D+01, 3.67D+01,
8 3.53D+01, 3.72D+01, 3.86D+01, 3.49D+01, 3.52D+01, 3.51D+01,
9 3.49D+01, 3.50D+01, 3.50D+01, 3.45D+01, 3.38D+01, 3.42D+01/
DATA TRSH2/
1 3.33D+01, 3.36D+01, 3.39D+01, 3.37D+01, 3.54D+01, 3.28D+01,
2 3.69D+01, 3.80D+01, 3.34D+01, 3.71D+01, 3.47D+01, 3.21D+01,
3 3.40D+01, 3.71D+01, 3.37D+01, 3.42D+01, 3.38D+01, 3.43D+01,
4 3.36D+01, 3.33D+01, 3.33D+01, 3.40D+01, 3.41D+01, 3.34D+01,
5 3.42D+01, 3.53D+01, 3.82D+01, 3.73D+01, 3.55D+01, 3.60D+01,
6 3.72D+01, 3.61D+01, 3.58D+01, 3.38D+01, 3.38D+01, 3.66D+01,
7 3.45D+01, 3.56D+01, 3.49D+01, 3.61D+01, 3.67D+01, 3.64D+01,
8 3.75D+01, 3.86D+01, 3.88D+01, 3.98D+01, 3.85D+01, 3.80D+01,
9 3.94D+01, 3.87D+01, 3.95D+01, 3.90D+01, 3.78D+01, 3.73D+01,
1 3.64D+01, 3.71D+01, 3.73D+01, 3.97D+01, 4.12D+01, 4.14D+01,
2 3.91D+01, 3.71D+01, 3.81D+01, 3.60D+01, 3.55D+01, 3.53D+01,
3 3.47D+01, 3.42D+01, 3.26D+01, 3.39D+01, 3.62D+01, 3.81D+01,
4 3.77D+01, 3.53D+01, 3.49D+01, 3.46D+01, 3.46D+01, 3.50D+01,
5 3.44D+01, 3.42D+01, 3.41D+01, 3.40D+01, 3.33D+01, 3.31D+01,
6 3.38D+01, 3.47D+01, 3.33D+01, 3.35D+01, 3.38D+01, 3.28D+01,
7 3.28D+01, 3.31D+01, 3.35D+01, 3.37D+01, 3.39D+01, 3.41D+01,
8 3.35D+01, 3.40D+01, 3.33D+01, 3.30D+01, 3.45D+01, 3.53D+01,
9 3.37D+01, 3.38D+01, 3.21D+01, 3.24D+01, 3.31D+01, 3.35D+01/
DATA TRSH3/
1 3.26D+01, 3.26D+01, 3.20D+01, 3.20D+01, 3.36D+01, 3.36D+01,
2 3.17D+01, 3.24D+01, 3.17D+01, 3.09D+01, 3.20D+01, 3.26D+01,
3 3.50D+01, 3.55D+01, 3.60D+01, 3.57D+01, 3.43D+01, 3.36D+01,
4 3.38D+01, 3.44D+01, 3.30D+01, 3.40D+01, 3.30D+01, 3.13D+01,
5 3.15D+01, 3.20D+01, 3.34D+01, 3.20D+01, 3.33D+01, 3.27D+01,
6 3.10D+01, 3.16D+01, 3.31D+01, 3.29D+01, 3.26D+01, 3.30D+01,
7 3.14D+01, 3.02D+01, 3.04D+01, 3.15D+01, 3.21D+01, 3.11D+01,
8 3.23D+01, 3.20D+01, 3.14D+01, 3.02D+01, 3.11D+01, 3.14D+01,
9 3.15D+01, 3.23D+01, 3.17D+01, 3.10D+01, 3.01D+01, 3.19D+01,
1 3.14D+01, 3.06D+01, 3.15D+01, 3.08D+01, 3.06D+01, 3.18D+01,
2 3.26D+01, 3.16D+01, 3.13D+01, 3.13D+01, 3.09D+01, 2.99D+01,
3 2.97D+01, 3.11D+01, 3.08D+01, 3.03D+01, 3.08D+01, 3.12D+01,
4 3.03D+01, 2.98D+01, 3.20D+01, 3.06D+01, 3.09D+01, 3.00D+01,
5 3.08D+01, 2.95D+01, 3.04D+01, 3.05D+01, 2.98D+01, 3.16D+01,
6 3.18D+01, 3.05D+01, 2.96D+01, 2.76D+01, 3.07D+01, 3.23D+01,
7 3.05D+01, 3.07D+01, 3.09D+01, 2.98D+01, 2.98D+01, 3.09D+01,
8 3.37D+01, 3.12D+01, 3.22D+01, 3.14D+01, 2.97D+01, 2.86D+01,
9 3.12D+01, 3.11D+01, 3.23D+01, 3.25D+01, 3.16D+01, 2.98D+01/
DATA TRSH4/
1 2.95D+01, 3.09D+01, 3.07D+01, 3.06D+01, 2.93D+01, 3.05D+01,
2 3.00D+01, 2.98D+01, 3.06D+01, 3.11D+01, 3.12D+01, 2.92D+01,
3 3.11D+01, 3.03D+01, 3.03D+01, 3.12D+01, 3.11D+01, 3.12D+01,
4 2.92D+01, 3.12D+01, 3.03D+01, 3.02D+01, 3.11D+01, 3.09D+01,
5 3.11D+01, 2.92D+01, 3.09D+01, 3.01D+01, 3.02D+01, 3.10D+01,
6 3.09D+01, 3.10D+01, 2.92D+01, 3.09D+01, 3.02D+01, 3.04D+01,
7 3.12D+01, 3.10D+01, 3.12D+01, 2.92D+01, 3.09D+01, 3.03D+01/
C
DATA PSH1/
1 2.46D+04, 1.96D+04, 2.12D+04, 1.55D+04, 1.74D+04, 2.89D+04,
2 3.63D+04, 2.99D+04, 2.68D+04, 2.12D+04, 2.41D+04, 3.33D+04,
3 2.50D+04, 1.91D+04, 2.09D+04, 2.11D+04, 2.94D+04, 2.47D+04,
4 2.20D+04, 2.21D+04, 2.61D+04, 2.82D+04, 2.80D+04, 2.48D+04,
5 2.22D+04, 2.62D+04, 3.52D+04, 4.10D+04, 3.92D+04, 2.46D+04,
6 3.39D+04, 3.21D+04, 4.14D+04, 2.98D+04, 2.85D+04, 3.30D+04,
7 3.92D+04, 2.48D+04, 2.44D+04, 3.72D+04, 2.84D+04, 3.11D+04,
8 3.70D+04, 3.22D+04, 3.20D+04, 3.20D+04, 3.29D+04, 3.97D+04,
9 4.92D+04, 6.54D+04, 6.58D+04, 5.78D+04, 5.99D+04, 4.86D+04,
1 5.10D+04, 4.53D+04, 4.71D+04, 4.41D+04, 4.61D+04, 4.81D+04,
2 5.12D+04, 4.99D+04, 4.06D+04, 4.24D+04, 4.58D+04, 4.99D+04,
3 5.12D+04, 4.16D+04, 4.30D+04, 5.25D+04, 6.48D+04, 5.02D+04,
4 4.66D+04, 4.84D+04, 4.77D+04, 5.46D+04, 5.96D+04, 6.40D+04,
5 6.14D+04, 6.67D+04, 8.03D+04, 6.84D+04, 4.54D+04, 4.71D+04,
6 4.76D+04, 4.80D+04, 5.09D+04, 4.80D+04, 4.38D+04, 4.41D+04,
7 5.07D+04, 5.40D+04, 5.23D+04, 4.89D+04, 5.12D+04, 6.48D+04,
8 5.97D+04, 7.27D+04, 7.96D+04, 6.28D+04, 6.04D+04, 6.06D+04,
9 5.98D+04, 6.01D+04, 6.12D+04, 6.28D+04, 5.48D+04, 5.34D+04/
DATA PSH2/
1 5.09D+04, 5.34D+04, 5.46D+04, 5.46D+04, 6.66D+04, 5.02D+04,
2 6.65D+04, 7.16D+04, 5.43D+04, 6.62D+04, 5.51D+04, 5.13D+04,
3 5.83D+04, 6.71D+04, 5.63D+04, 5.50D+04, 5.60D+04, 5.48D+04,
4 5.29D+04, 5.79D+04, 5.73D+04, 5.83D+04, 5.48D+04, 5.42D+04,
5 5.33D+04, 6.11D+04, 8.12D+04, 7.50D+04, 6.66D+04, 6.38D+04,
6 7.31D+04, 6.38D+04, 6.66D+04, 6.14D+04, 6.00D+04, 6.81D+04,
7 5.53D+04, 6.54D+04, 5.78D+04, 6.85D+04, 7.54D+04, 7.28D+04,
8 7.47D+04, 7.60D+04, 8.03D+04, 8.04D+04, 7.96D+04, 8.29D+04,
9 8.39D+04, 8.00D+04, 8.04D+04, 7.93D+04, 7.33D+04, 7.54D+04,
1 7.78D+04, 7.59D+04, 7.52D+04, 8.23D+04, 8.83D+04, 8.78D+04,
2 8.28D+04, 7.96D+04, 7.95D+04, 7.00D+04, 6.58D+04, 6.37D+04,
3 6.15D+04, 6.07D+04, 6.00D+04, 6.21D+04, 7.14D+04, 7.72D+04,
4 7.57D+04, 6.29D+04, 6.53D+04, 7.02D+04, 6.58D+04, 6.72D+04,
5 5.95D+04, 5.83D+04, 5.67D+04, 5.87D+04, 6.28D+04, 5.65D+04,
6 5.82D+04, 6.11D+04, 5.40D+04, 5.21D+04, 5.81D+04, 5.94D+04,
7 5.46D+04, 5.35D+04, 5.12D+04, 5.46D+04, 5.37D+04, 5.89D+04,
8 6.32D+04, 5.80D+04, 4.77D+04, 4.63D+04, 5.94D+04, 5.59D+04,
9 5.55D+04, 6.28D+04, 5.20D+04, 4.83D+04, 4.71D+04, 5.26D+04/
DATA PSH3/
1 4.25D+04, 4.67D+04, 5.17D+04, 5.08D+04, 5.38D+04, 4.57D+04,
2 3.86D+04, 3.20D+04, 3.48D+04, 4.23D+04, 4.80D+04, 5.00D+04,
3 5.71D+04, 6.36D+04, 6.18D+04, 6.15D+04, 6.14D+04, 5.81D+04,
4 5.42D+04, 5.11D+04, 4.70D+04, 5.17D+04, 4.58D+04, 4.24D+04,
5 4.34D+04, 4.21D+04, 5.00D+04, 4.46D+04, 4.62D+04, 4.81D+04,
6 4.60D+04, 4.42D+04, 4.15D+04, 4.09D+04, 4.09D+04, 3.66D+04,
7 4.09D+04, 3.76D+04, 3.97D+04, 3.52D+04, 4.06D+04, 3.90D+04,
8 3.92D+04, 4.04D+04, 4.10D+04, 3.72D+04, 3.19D+04, 3.29D+04,
9 4.04D+04, 3.73D+04, 3.88D+04, 3.79D+04, 3.32D+04, 3.08D+04,
1 3.00D+04, 2.66D+04, 2.34D+04, 3.11D+04, 3.70D+04, 4.28D+04,
2 4.41D+04, 3.57D+04, 3.16D+04, 3.04D+04, 3.60D+04, 3.35D+04,
3 2.75D+04, 2.91D+04, 3.07D+04, 2.53D+04, 3.03D+04, 2.84D+04,
4 3.16D+04, 2.82D+04, 3.38D+04, 2.70D+04, 2.82D+04, 2.38D+04,
5 2.39D+04, 2.53D+04, 2.05D+04, 2.21D+04, 2.15D+04, 2.13D+04,
6 2.30D+04, 2.56D+04, 2.23D+04, 1.88D+04, 1.82D+04, 1.37D+04,
7 1.49D+04, 1.52D+04, 1.53D+04, 1.78D+04, 1.73D+04, 1.57D+04,
8 1.43D+04, 1.70D+04, 1.66D+04, 1.53D+04, 1.83D+04, 1.73D+04,
9 1.65D+04, 1.78D+04, 1.56D+04, 1.93D+04, 1.86D+04, 1.97D+04/
DATA PSH4/
1 1.59D+04, 1.83D+04, 1.88D+04, 1.79D+04, 1.75D+04, 1.89D+04,
2 1.99D+04, 1.85D+04, 1.93D+04, 1.55D+04, 1.44D+04, 1.60D+04,
3 1.68D+04, 1.92D+04, 1.69D+04, 1.77D+04, 1.55D+04, 1.46D+04,
4 1.71D+04, 1.65D+04, 1.90D+04, 1.74D+04, 1.79D+04, 1.65D+04,
5 1.49D+04, 1.61D+04, 1.98D+04, 2.33D+04, 1.76D+04, 1.92D+04,
6 1.69D+04, 1.70D+04, 1.72D+04, 1.84D+04, 2.11D+04, 2.08D+04,
7 2.41D+04, 2.19D+04, 2.03D+04, 1.60D+04, 2.10D+04, 2.46D+04/
C
DATA H01/
1 1.42D+02, 1.41D+02, 1.32D+02, 1.06D+02, 1.25D+02, 9.71D+01,
2 1.42D+02, 1.29D+02, 1.38D+02, 5.90D+00, 6.94D+01, 1.32D+02,
3 3.47D+01, 8.86D+01, 4.85D+01, 9.46D+01, 3.61D-02, 7.08D+00,
4 8.88D+01, 8.90D+01, 9.93D+01, 1.75D+00, 4.35D+01, 3.80D+01,
5 7.91D+01, 3.42D+01, 6.91D+01, 9.25D+01, 2.79D+01, 2.77D-01,
6 2.70D+01, 8.50D+01, 3.14D+01, 8.66D+01, 1.11D+01, 5.27D+01,
7 9.15D+01, 6.29D+01, 7.95D+01, 7.48D+01, 6.86D+01, 6.56D+01,
8 7.80D+01, 1.42D+01, 8.35D+00, 8.31D+00, 1.23D+01, 4.96D+00,
9 1.65D+00, 7.48D+01, 5.86D+01, 5.72D+01, 7.01D+01, 6.03D+01,
1 3.95D-01, 2.63D+01, 3.31D+01, 3.17D+01, 3.69D+01, 5.00D+01,
2 1.11D-03, 1.17D+00, 7.22D-02, 4.00D-04, 3.79D+01, 6.36D+00,
3 4.14D+01, 3.84D+01, 2.42D+01, 4.97D+01, 5.26D+01, 6.96D-01,