Optpack Test problems | William Hager

C
C COLVILLE 1
C
REAL*8 Y(5),S,T
REAL*8 X(15),LE(50),LI(15),U(100),DF(15),BL(15),BU(15),W(100)
REAL*8 VF,CT,ER,ST
REAL*8 A(10,15),B(10),C(5,5),D(5),E(5),VALF
INTEGER IA(15),K,IO,IT
real zzz(2)
COMMON A,B,C,D,E,NF,NDF
EXTERNAL VALF,GRADF
DATA A/-16.D0,0.D0,-3.5D0,0.D0,0.D0,2.D0,-1.D0,-1.D0,1.D0,1.D0,
1 2.D0,-2.D0,0.D0,-2.D0,-9.D0,0.D0,-1.D0,-2.D0,2.D0,1.D0,
2 0.D0,0.D0,2.D0,0.D0,-2.D0,-4.D0,-1.D0,-3.D0,3.D0,1.D0,
3 1.D0,.4D0,0.D0,-4.D0,1.D0,0.D0,-1.D0,-2.D0,4.D0,1.D0,
4 0.D0,2.D0,0.D0,-1.D0,-2.8D0,0.D0,-1.D0,-1.D0,5.D0,1.D0,
5 -1.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
6 0.D0,-1.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
7 0.D0,0.D0,-1.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
8 0.D0,0.D0,0.D0,-1.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
9 0.D0,0.D0,0.D0,0.D0,-1.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
1 0.D0,0.D0,0.D0,0.D0,0.D0,-1.D0,0.D0,0.D0,0.D0,0.D0,
2 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,-1.D0,0.D0,0.D0,0.D0,
3 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,-1.D0,0.D0,0.D0,
4 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,-1.D0,0.D0,
5 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,-1.D0/
DATA B/-40.D0,-2.D0,-.25D0,-4.D0,-4.D0,-1.D0,-40.D0,
1 -60.D0,5.D0,1.D0/
DATA C/30.D0,-20.D0,-10.D0,32.D0,-10.D0,
1 -20.D0,39.D0,-6.D0,-31.D0,32.D0,
2 -10.D0,-6.D0,10.D0,-6.D0,-10.D0,
3 32.D0,-31.D0,-6.D0,39.D0,-20.D0,
4 -10.D0,32.D0,-10.D0,-20.D0,30.D0/
DATA D/4.D0,8.D0,10.D0,6.D0,2.D0/
DATA E/-15.D0,-27.D0,-36.D0,-18.D0,-12.D0/
DATA X/0.D0,0.D0,0.D0,0.D0,1.D0,40.D0,4.D0,.25D0,3.D0,
1 1.2D0,1.D0,39.D0,59.D0,0.D0,0.D0/
DATA BL/0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
1 0.D0,0.D0,0.D0,0.D0/
DATA BU/90.D0,90.D0,90.D0,90.D0,90.D0,90.D0,90.D0,90.D0,90.D0,
1 90.D0,90.D0,90.D0,90.D0,90.D0,90.D0/
NF = 0
NDF= 0
LA = 10
N = 15
ST = 0.
CT = 1.D-4
strt = etime(zzz)
CALL LMIN(X,LE,LI,U,IA,K,VF,DF,ER,IT,ST,IO,
1 4,1.D-6,500,A,10,10,15,B,BL,BU,CT,VALF,GRADF,W)
CALL ERR(IO)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
WRITE(6,*) ‘BINDERS:’
WRITE(6,*) (IA(I), I=1,N)
WRITE(6,*) ‘VALUE:’,VF
WRITE(6,*) ‘ITERATIONS:’,IT
WRITE(6,*) ‘FREE VARIABLES:’,K
WRITE(6,*) ‘NUMBER OF FUNCTION EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF GRADIENT EVALUATIONS:’,NDF
DATA Y/.3D0,.33346761D0,.4D0,.42831010D0,.22396487D0/
T = 0.
S = 0.
DO 10 I = 1,5
WRITE(6,*) I,Y(I),X(I)
T = T + (X(I)-Y(I))**2
S = S + Y(I)**2
10 CONTINUE
S = DSQRT(T/S)
WRITE(6,*) ‘RELATIVE ERROR:’,S
STOP
END
DOUBLE PRECISION FUNCTION VALF(X)
REAL*8 X(1),S,T
REAL*8 A(10,15),B(10),C(5,5),D(5),E(5)
COMMON A,B,C,D,E,NF,NDF
NF = NF + 1
T = 0.
DO 20 J = 1,5
S = 0.
DO 10 I = 1,5
10 S = S + C(I,J)*X(I)
20 T = T + E(J)*X(J) + D(J)*X(J)**3 + S*X(J)
VALF = T
RETURN
END
SUBROUTINE GRADF(DF,X)
REAL*8 DF(1),X(1),T
REAL*8 A(10,15),B(10),C(5,5),D(5),E(5)
COMMON A,B,C,D,E,NF,NDF
NDF = NDF + 1
DO 20 J = 1,5
T = 0.
DO 10 I = 1,5
10 T = T + C(I,J)*X(I)
20 DF(J) = E(J) + T + T + 3.*D(J)*X(J)*X(J)
DO 30 J = 6,15
30 DF(J) = 0.
RETURN
END
=======================
C
C COLVILLE 2
C
REAL*8 Y(15),SS,TT
REAL*8 X(25),LE(10),LI(25),U(300),G(5),DF(25),DG(5,25)
REAL*8 AA(10,25),BL(25),BU(25),W(200)
REAL*8 A(5,10),B(10),C(5,5),D(5),E(5)
REAL*8 CT,F,ER,PN,PNI,ST,TL,T,VALF
INTEGER IA(25),IO,IN,K,IT,L,LA,LG,LM,NL,N
real zzz(2)
COMMON A,B,C,D,E,NF,NG,NDF,NDG
EXTERNAL VALF,VALG,GRADF,GRADG
DATA A/-16.D0,2.D0,0.D0,1.D0,0.D0,
1 0.D0,-2.D0,0.D0,.4D0,2.D0,
2 -3.5D0,0.D0,2.D0,0.D0,0.D0,
3 0.D0,-2.D0,0.D0,-4.D0,-1.D0,
4 0.D0,-9.D0,-2.D0,1.D0,-2.8D0,
5 2.D0,0.D0,-4.D0,0.D0,0.D0,
6 -1.D0,-1.D0,-1.D0,-1.D0,-1.D0,
7 -1.D0,-2.D0,-3.D0,-2.D0,-1.D0,
8 1.D0,2.D0,3.D0,4.D0,5.D0,
9 1.D0,1.D0,1.D0,1.D0,1.D0/
DATA B/-40.D0,-2.D0,-.25D0,-4.D0,-4.D0,-1.D0,-40.D0,
1 -60.D0,5.D0,1.D0/
DATA C/30.D0,-20.D0,-10.D0,32.D0,-10.D0,
1 -20.D0,39.D0,-6.D0,-31.D0,32.D0,
2 -10.D0,-6.D0,10.D0,-6.D0,-10.D0,
3 32.D0,-31.D0,-6.D0,39.D0,-20.D0,
4 -10.D0,32.D0,-10.D0,-20.D0,30.D0/
DATA D/4.D0,8.D0,10.D0,6.D0,2.D0/
DATA E/-15.D0,-27.D0,-36.D0,-18.D0,-12.D0/
NF = 0
NG = 0
NDF = 0
NDG = 0
DO 10 I = 1,5
DO 10 J = 1,10
10 AA(I,J) = A(I,J)
DO 40 I = 1,5
DO 20 J = 11,15
20 AA(I,J) = -2*C(I,J-10)
DO 30 J = 16,25
30 AA(I,J) = 0.
AA(I,15+I) = -3*D(I)
AA(I,20+I) = 1
40 CONTINUE
DO 60 I = 1,5
DO 50 J = 1,25
50 DG(I,J) = 0.
DG(I,I+15) = 1
60 CONTINUE
DO 70 I = 21,25
70 DF(I) = 0.
DO 80 I = 1,25
BL(I) = 0.
80 BU(I) = 200.
DO 90 I = 16,20
90 BL(I) = -200.
C
C FEASIBLE STARTING GUESS
C
IN = 4
DO 100 I = 1,15
100 X(I) = 1.D-4
X(7) = 60.
DO 105 I = 1,5
105 X(I+15) = X(I+10)**2
DO 115 I = 1,5
T = E(I)
DO 110 J = 1,20
110 T = T – AA(I,J)*X(J)
X(I+20) = T
115 CONTINUE
C
C INFEASIBLE STARTING GUESS
C
C IN = 0
C DO 100 I = 1,10
C100 X(I) = B(I)
C DO 110 I = 11,25
C110 X(I) = 0.
C X(15) = 1
C X(20) = 1
TL = .0001
LM = 250
C
C ORIGINAL PENALTY WAS 40, THEN TRIED 10, 50, 250
C
PNI = 10
L = 5
N = 25
LA = 10
LG = 5
NL = 5
ST = 0
CT = 1.D-4
CALL NORM(AA,LA,L,N,E,W)
strt = etime(zzz)
CALL MIN(X,LE,LI,U,IA,K,F,G,DF,DG,ER,IT,ST,PN,IO,
1 IN,TL,LM,PNI,AA,LA,LG,L,NL,N,E,BL,BU,CT,VALF,VALG,GRADF,GRADG,W)
CALL ERR(IO)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
WRITE(6,*) ‘VALUE:’,F
WRITE(6,*) ‘LE MULTIPLIERS:’
J = L + NL
DO 120 I = 1,J
120 WRITE(6,*) I,LE(I)
WRITE(6,*) ‘LI MULTIPLIERS:’
DO 130 I = 1,N
130 WRITE(6,*) I,LI(I)
WRITE(6,*) ‘NUMBER OF F EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF G EVALUATIONS:’,NG
WRITE(6,*) ‘NUMBER OF DF EVALUATIONS:’,NDF
WRITE(6,*) ‘NUMBER OF DG EVALUATIONS:’,NDG
DATA Y/0.D0,0.D0,5.1740399D0,0.D0,3.0611083D0,11.8395453D0,
& 0.D0,0.D0,.10389602D0,0.D0,.3D0,.33346761D0,.4D0,
& .4283101D0,.22396487D0/
TT = 0.
SS = 0.
DO 200 I = 1,15
TT = TT + (X(I)-Y(I))**2
SS = SS + Y(I)**2
WRITE(6,*) I,Y(I),X(I)
200 CONTINUE
SS = DSQRT(TT/SS)
WRITE(6,*) ‘RELATIVE ERROR:’,SS
STOP
END
DOUBLE PRECISION FUNCTION VALF(X)
REAL*8 X(1),A(5,10),B(10),C(5,5),D(5),E(5),S,T
COMMON A,B,C,D,E,NF,NG,NDF,NDG
NF = NF + 1
T = 0.
DO 10 I = 1,10
10 T = T – B(I)*X(I)
DO 30 J = 1,5
S = 0.
DO 20 I = 1,5
20 S = S + C(I,J)*X(I+10)
30 T = T + S*X(J+10)
DO 40 I = 1,5
40 T = T + 2.*D(I)*X(I+10)*X(I+15)
VALF = T
RETURN
END
SUBROUTINE GRADF(DF,X)
REAL*8 DF(1),X(1),A(5,10),B(10),C(5,5),D(5),E(5),T
COMMON A,B,C,D,E,NF,NG,NDF,NDG
NDF = NDF + 1
DO 10 I = 1,10
10 DF(I) = -B(I)
DO 30 J = 1,5
T = 0.
DO 20 I = 1,5
20 T = T + C(I,J)*X(I+10)
30 DF(J+10) = T + T + 2.*D(J)*X(J+15)
DO 40 I = 16,20
40 DF(I) = 2.*D(I-15)*X(I-5)
RETURN
END
SUBROUTINE VALG(G,X)
REAL*8 G(1),X(1)
REAL*8 A(5,10),B(10),C(5,5),D(5),E(5)
COMMON A,B,C,D,E,NF,NG,NDF,NDG
NG = NG + 1
DO 10 I = 11,15
10 G(I-10) = X(I+5) – X(I)**2
RETURN
END
SUBROUTINE GRADG(DG,X)
REAL*8 DG(5,1),X(1)
REAL*8 A(5,10),B(10),C(5,5),D(5),E(5)
COMMON A,B,C,D,E,NF,NG,NDF,NDG
NDG = NDG + 1
DO 10 I = 1,5
DG(I,I+10) = -2.*X(I+10)
10 CONTINUE
RETURN
END
=====================
C
C COLVILLE 3
C
REAL*8 Y(5),SS,TT
REAL*8 X(8),LE(3),LI(8),G(3),DF(8),DG(3,8),W(200),U(100),A(3,8)
REAL*8 B(1),BL(8),BU(8),VALF
REAL*8 CT,E,F,ST,TL,PN,PNI
real zzz(2)
INTEGER IA(8),K
COMMON NF,NG,NDF,NDG
EXTERNAL VALF,VALG,GRADF,GRADG
DATA BL/78.D0,33.D0,27.D0,27.D0,27.D0,0.D0,90.D0,20.D0/
DATA BU/102.D0,45.D0,45.D0,45.D0,45.D0,92.D0,110.D0,25.D0/
NF = 0
NG = 0
NDF = 0
NDG = 0
N = 8
NL = 3
LG = 3
LA = 3
DO 10 J = 1,N
DO 10 I = 1,NL
10 DG(I,J) = 0.
DF(2) = 0.
DF(4) = 0.
DF(6) = 0.
DF(7) = 0.
DF(8) = 0.
C
C FEASIBLE STARTING GUESS
C
IN = 4
X(1) = 78.62D0
X(2) = 33.44D0
X(3) = 31.07D0
X(4) = 44.18D0
X(5) = 35.32D0
X(6) = 0.D0
X(7) = 0.D0
X(8) = 0.D0
CALL VALG(G,X)
X(6) = G(1)
X(7) = G(2)
X(8) = G(3)
C
C NONFEASIBLE STARTING GUESS
C
IN = 0
X(1) = 78.D0
X(2) = 33.D0
X(3) = 27.D0
X(4) = 27.D0
X(5) = 27.D0
X(6) = 0.D0
X(7) = 0.D0
X(8) = 0.D0
CALL VALG(G,X)
X(6) = G(1)
X(7) = G(2)
X(8) = G(3)
ST = 0.
PNI = 10.D0
TL = 1.D-6
CT = 1.D-4
strt = etime(zzz)
CALL MIN(X,LE,LI,U,IA,K,F,G,DF,DG,E,IT,ST,PN,IO,
1 IN,TL,500,PNI,A,LA,LG,0,NL,N,B,BL,BU,CT,VALF,VALG,GRADF,GRADG,W)
CALL ERR(IO)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
WRITE(6,*) ‘ERROR TOLERANCE:’,E
WRITE(6,*) ‘NUMBER OF ITERATIONS:’,IT
F = F – 40792.141D0
WRITE(6,*) ‘VALUE:’,F
WRITE(6,*) ‘NUMBER OF F EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF G EVALUATIONS:’,NG
WRITE(6,*) ‘NUMBER OF DF EVALUATIONS:’,NDF
WRITE(6,*) ‘NUMBER OF DG EVALUATIONS:’,NDG
DATA Y/78.D0,33.D0,29.995256025D0,45.D0,36.7758129058D0/
TT = 0.
SS = 0.
DO 200 I = 1,5
TT = TT + (X(I)-Y(I))**2
SS = SS + Y(I)**2
WRITE(6,*) I,Y(I),X(I)
200 CONTINUE
SS = DSQRT(TT/SS)
WRITE(6,*) ‘RELATIVE ERROR:’,SS
STOP
END
DOUBLE PRECISION FUNCTION VALF(X)
REAL*8 X(1),T
COMMON NF,NG,NDF,NDG
NF = NF + 1
T = 5.3578547D0*X(3)*X(3)+.8356891D0*X(1)*X(5)+37.293239D0*X(1)
VALF = T
RETURN
END
SUBROUTINE GRADF(DF,X)
REAL*8 DF(1),X(1)
COMMON NF,NG,NDF,NDG
NDF = NDF + 1
DF(1) = 37.293239D0 + .8356891D0*X(5)
DF(3) = 10.7157094D0*X(3)
DF(5) = .8356891D0*X(1)
RETURN
END
SUBROUTINE VALG(G,X)
REAL*8 G(1),X(1),T
COMMON NF,NG,NDF,NDG
NG = NG + 1
T = 85.334407D0+.0056858D0*X(2)*X(5)+.0006262D0*X(1)*X(4)
G(1) = T – .0022053D0*X(3)*X(5) – X(6)
T = 80.51249D0+.0071317D0*X(2)*X(5)+.0029955D0*X(1)*X(2)
G(2) = T + .0021813D0*X(3)*X(3) – X(7)
T = (.0047026D0*X(5)+.0012547D0*X(1)+.0019085D0*X(4))*X(3)
G(3) = 9.300961D0 + T – X(8)
RETURN
END
SUBROUTINE GRADG(DG,X)
REAL*8 DG(3,1),X(1)
COMMON NF,NG,NDF,NDG
NDG = NDG + 1
DG(1,1) = .0006262D0*X(4)
DG(1,2) = .0056858D0*X(5)
DG(1,3) = -.0022053D0*X(5)
DG(1,4) = .0006262D0*X(1)
DG(1,5) = .0056858D0*X(2) – .0022053D0*X(3)
DG(1,6) = -1.D0
DG(2,1) = .0029955D0*X(2)
DG(2,2) = .0071317D0*X(5)+.0029955D0*X(1)
DG(2,3) = .0043626D0*X(3)
DG(2,5) = .0071317D0*X(2)
DG(2,7) = -1.D0
DG(3,1) = .0012547D0*X(3)
DG(3,3) = .0047026D0*X(5)+.0012547D0*X(1)+.0019085D0*X(4)
DG(3,4) = .0019085D0*X(3)
DG(3,5) = .0047026D0*X(3)
DG(3,8) = -1.D0
RETURN
END
=====================
C
C COLVILLE 4
C
REAL*8 Y(4),SS,TT
REAL*8 X(4),BL(4),BU(4),DF(4),W(200)
REAL*8 CT,E,VF,ST,TL,VALF
INTEGER IA(4),K,IO,IN,LM,N
real zzz(2)
COMMON NF,NDF
EXTERNAL VALF,GRADF
DATA X/-3.D0,-1.D0,-3.D0,-1.D0/
DATA BL/-10.D0,-10.D0,-10.D0,-10.D0/
DATA BU/10.D0,10.D0,10.D0,10.D0/
NF = 0
NDF = 0
N = 4
ST = 0.
TL = 1.D-6
CT = 1.D-4
IN = 0
LM = 500
strt = etime(zzz)
CALL BMIN(X,IA,K,VF,DF,E,IT,ST,IO,
& IN,TL,LM,N,BL,BU,CT,VALF,GRADF,W)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
CALL ERR(IO)
WRITE(6,*) ‘ERROR TOLERANCE:’,E
WRITE(6,*) ‘NUMBER OF ITERATIONS:’,IT
WRITE(6,*) ‘VALUE:’,VF
WRITE(6,*) ‘NUMBER OF F EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF DF EVALUATIONS:’,NDF
DATA Y/1.D0,1.D0,1.D0,1.D0/
TT = 0.
SS = 0.
DO 200 I = 1,4
TT = TT + (X(I)-Y(I))**2
SS = SS + Y(I)**2
WRITE(6,*) I,Y(I),X(I)
200 CONTINUE
SS = DSQRT(TT/SS)
WRITE(6,*) ‘RELATIVE ERROR:’,SS
STOP
END
DOUBLE PRECISION FUNCTION VALF(X)
REAL*8 X(1),T
COMMON NF,NDF
NF = NF + 1
T = 100*(X(2)-X(1)**2)**2 + (1-X(1))**2
T = T + 90*(X(4)-X(3)**2)**2 + (1-X(3))**2
T = T + 10.1D0*((X(2)-1)**2+(X(4)-1)**2)
T = T + 19.8D0*(X(2)-1)*(X(4)-1)
VALF = T
RETURN
END
SUBROUTINE GRADF(DF,X)
REAL*8 DF(1),X(1)
REAL*8 A,B
COMMON NF,NDF
NDF = NDF + 1
A = X(2) – X(1)**2
B = X(4) – X(3)**2
DF(1) = -400*A*X(1) – 2*(1-X(1))
DF(2) =20.2D0*(X(2)-1) + 200*A + 19.8D0*(X(4)-1)
DF(3) = -360*B*X(3) – 2*(1-X(3))
DF(4) = 180*B + 20.2D0*(X(4)-1) + 19.8D0*(X(2)-1)
RETURN
END
=====================
C
C COLVILLE 6
C
REAL*8 Y(6),SS,TT
REAL*8 X(6),LE(4),LI(6),U(300),G(4),DF(6),DG(4,6)
REAL*8 A(4,6),BL(6),BU(6),E(1),W(200)
REAL*8 CT,F,ER,PN,PNI,ST,TL,VALF
REAL*8 B,BB,C,D,CN,SN
real zzz(2)
INTEGER IA(6),IO,IN,K,IT,L,LA,LG,LM,NL,N
COMMON B,BB,C,D,CN,SN,NF,NG,NDF,NDG
EXTERNAL VALF,VALG,GRADF,GRADG
DATA BL/0.D0,0.D0,340.D0,340.D0,-1000.D0,0.D0/
DATA BU/400.D0,1000.D0,420.D0,420.D0,1000.D0,.5236D0/
DATA X/390.D0,1000.D0,419.5D0,340.5D0,198.175D0,.5D0/
NF = 0
NG = 0
NDF = 0
NDG = 0
B = 1.48477D0
C = 300
D = 200
BB = 1.D0/131.078D0
CN = (.90798D0*BB)*DCOS(B-.00889D0)
SN = (.90798D0*BB)*DSIN(B-.00889D0)
DF(3) = 0.
DF(4) = 0.
DF(5) = 0.
DF(6) = 0.
DG(1,1) = 1.
DG(1,2) = 0.
DG(1,5) = 0.
DG(2,1) = 0.
DG(2,2) = 1.
DG(2,5) = 0.
DG(3,1) = 0.
DG(3,2) = 0.
DG(3,5) = 0.
DG(4,1) = 0.
DG(4,2) = 0.
DG(4,5) = 1.
C
C NONFEASIBLE STARTING GUESS
C
IN = 0
TL = .000001
LM = 1000
PNI = 10
L = 0
N = 6
LA = 4
LG = 4
NL = 4
ST = 0.
CT = 1.D-4
strt = etime(zzz)
CALL MIN(X,LE,LI,U,IA,K,F,G,DF,DG,ER,IT,ST,PN,IO,
1 IN,TL,LM,PNI,A,LA,LG,L,NL,N,E,BL,BU,CT,VALF,VALG,GRADF,GRADG,W)
CALL ERR(IO)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
WRITE(6,*) ‘VALUE:’,F
WRITE(6,*) ‘NUMBER OF F EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF G EVALUATIONS:’,NG
WRITE(6,*) ‘NUMBER OF DF EVALUATIONS:’,NDF
WRITE(6,*) ‘NUMBER OF DG EVALUATIONS:’,NDG
DATA Y/107.8119312D0,196.3186138D0,373.8307277D0,420.D0,
& 21.307132490D0,.1532919593D0/
TT = 0.
SS = 0.
DO 200 I = 1,6
TT = TT + (X(I)-Y(I))**2
SS = SS + Y(I)**2
WRITE(6,*) I,Y(I),X(I)
200 CONTINUE
SS = DSQRT(TT/SS)
WRITE(6,*) ‘RELATIVE ERROR:’,SS
STOP
END
DOUBLE PRECISION FUNCTION VALF(X)
REAL*8 X(1),B,BB,C,D,CN,SN,T
COMMON B,BB,C,D,CN,SN,NF,NG,NDF,NDG
NF = NF + 1
T = 0.
IF ( X(1) .GT. 300 ) GOTO 10
T = T + 30*X(1)
GOTO 20
10 T = 9000 + 31*(X(1)-300)
20 IF ( X(2) .GT. 100 ) GOTO 30
T = T + 28*X(2)
GOTO 50
30 IF ( X(2) .GT. 200 ) GOTO 40
T = T + 2800 + 29*(X(2)-100)
GOTO 50
40 T = T + 5700 + 30*(X(2)-200)
50 VALF = T
RETURN
END
SUBROUTINE GRADF(DF,X)
REAL*8 DF(1),X(1)
REAL*8 B,BB,C,D,CN,SN
COMMON B,BB,C,D,CN,SN,NF,NG,NDF,NDG
NDF = NDF + 1
DF(1) = 30
IF ( X(1) .GT. 300 ) DF(1) = 31
DF(2) = 28
IF ( X(2) .GT. 100 ) DF(2) = 29
IF ( X(2) .GT. 200 ) DF(2) = 30
RETURN
END
SUBROUTINE VALG(G,X)
REAL*8 G(1),X(1)
REAL*8 B,BB,C,D,CN,SN
COMMON B,BB,C,D,CN,SN,NF,NG,NDF,NDG
NG = NG + 1
G(1) = X(1) – C + BB*X(3)*X(4)*DCOS(B-X(6)) – CN*X(3)**2
G(2) = X(2) + BB*X(3)*X(4)*DCOS(B+X(6)) – CN*X(4)**2
G(3) = D – BB*X(3)*X(4)*DSIN(B-X(6)) + SN*X(3)**2
G(4) = X(5) + BB*X(3)*X(4)*DSIN(B+X(6)) – SN*X(4)**2
RETURN
END
SUBROUTINE GRADG(DG,X)
REAL*8 DG(4,1),X(1)
REAL*8 B,BB,C,D,CN,SN
COMMON B,BB,C,D,CN,SN,NF,NG,NDF,NDG
NDG = NDG + 1
DG(1,3) = BB*X(4)*DCOS(B-X(6)) – 2*CN*X(3)
DG(1,4) = BB*X(3)*DCOS(B-X(6))
DG(1,6) = BB*X(3)*X(4)*DSIN(B-X(6))
DG(2,3) = BB*X(4)*DCOS(B+X(6))
DG(2,4) = BB*X(3)*DCOS(B+X(6)) – 2*CN*X(4)
DG(2,6) = -BB*X(3)*X(4)*DSIN(B+X(6))
DG(3,3) = -BB*X(4)*DSIN(B-X(6)) + 2*SN*X(3)
DG(3,4) = -BB*X(3)*DSIN(B-X(6))
DG(3,6) = BB*X(3)*X(4)*DCOS(B-X(6))
DG(4,3) = BB*X(4)*DSIN(B+X(6))
DG(4,4) = BB*X(3)*DSIN(B+X(6)) – 2*SN*X(4)
DG(4,6) = BB*X(3)*X(4)*DCOS(B+X(6))
RETURN
END
=====================
C
C COLVILLE 7
C
REAL*8 Y(16),SS,TT
REAL*8 X(16),LE(8),LI(16),DF(16),W(200),A(8,16),B(8),BL(16),BU(16)
REAL*8 U(200),CT,ST,E,VF,VALUE
INTEGER IA(16),IR(30),IC(30)
real zzz(2)
COMMON IR,IC,N,NF,NDF
EXTERNAL VALUE,GRAD
DATA A/ 0.22, -1.46, 1.29, -1.10, 0.00, 0.00, 1.12, 0.00,
1 0.20, 0.00, -0.89, -1.06, 0.00, -1.72, 0.00, 0.45,
2 0.19, -1.30, 0.00, 0.95, 0.00, -0.33, 0.00, 0.26,
3 0.25, 1.82, 0.00, -0.54, -1.43, 0.00, 0.31, -1.10,
4 0.15, -1.15, -1.16, 0.00, 1.51, 1.62, 0.00, 0.58,
5 0.11, 0.00, -0.96, -1.78, 0.59, 1.24, 0.00, 0.00,
6 0.12, 0.80, 0.00, -0.41, -0.33, 0.21, 1.12, -1.03,
7 0.13, 0.00, -0.49, 0.00, -0.43, -0.26, 0.00, 0.10,
8 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, -0.36, 0.00,
9 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00,
1 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00,
2 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00,
3 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00,
4 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00,
5 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00,
6 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00/
DATA B/2.5D0,1.1D0,-3.1D0,-3.5D0,1.3D0,2.1D0,2.3D0,-1.5D0/
DATA BU/5.D0,5.D0,5.D0,5.D0,5.D0,5.D0,5.D0,5.D0,5.D0,5.D0,
1 5.D0,5.D0,5.D0,5.D0,5.D0,5.D0/
DATA BL/0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,
1 0.D0,0.D0,0.D0,0.D0,0.D0,0.D0/
DATA X/.0D0,.0D0,.0D0,.0D0,.0D0,.0D0,.0D0,.0D0,.0D0,
1 .0D0,.0D0,.0D0,.0D0,.0D0,.0D0,.0D0/
DATA IR/1,1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,7,7,8,8,9,9,
1 10,11,12,13/
DATA IC/4,7,8,16,3,7,10,7,9,10,14,7,11,15,6,10,12,16,8,15,11,13,
1 10,15,12,16,14,13,14,14/
NF = 0
NG = 0
NDF = 0
NDG = 0
LA = 8
N = 16
M = 8
ST = 0
CT = 1.D-4
strt = etime(zzz)
CALL LMIN(X,LE,LI,U,IA,K,VF,DF,E,IT,ST,IO,
1 0,1.D-6,500,A,LA,M,N,B,BL,BU,CT,VALUE,GRAD,W)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
WRITE(6,*) ‘OPTIMAL VALUE:’,VF
WRITE(6,*) ‘ERROR:’,E
WRITE(6,*) ‘ITERATIONS:’,IT
WRITE(6,*) ‘NUMBER OF F EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF DF EVALUATIONS:’,NDF
DATA Y/.039847371D0,.7919831688D0,.2028703277D0,.84435796726D0,
& 1.2699065D0,.9347386775D0,1.6819619415D0,.1553008715D0,
& 1.5678703159D0,0.D0,0.D0,0.D0,.660204085777D0,0.D0,
& .67425591386D0,0.D0/
TT = 0.
SS = 0.
DO 200 I = 1,16
TT = TT + (X(I)-Y(I))**2
SS = SS + Y(I)**2
WRITE(6,*) I,Y(I),X(I)
200 CONTINUE
SS = DSQRT(TT/SS)
WRITE(6,*) ‘RELATIVE ERROR:’,SS
STOP
END
DOUBLE PRECISION FUNCTION VALUE(X)
REAL*8 X(1),S,T
INTEGER IR(30),IC(30)
COMMON IR,IC,N,NF,NDF
NF = NF + 1
T = 0.
DO 10 I = 1,N
10 T = T + (X(I)*X(I)+X(I)+1)**2
DO 20 K = 1,30
I = IR(K)
J = IC(K)
S = (X(I)*X(I)+X(I)+1)*(X(J)*X(J)+X(J)+1)
T = T + S
20 CONTINUE
VALUE = T
RETURN
END
SUBROUTINE GRAD(G,X)
REAL*8 G(1),X(1),S,T
INTEGER IR(30),IC(30)
COMMON IR,IC,N,NF,NDF
NDF = NDF + 1
DO 10 I = 1,N
10 G(I) = 2*(X(I)*X(I)+X(I)+1)*(X(I)+X(I)+1)
DO 20 K = 1,30
I = IR(K)
J = IC(K)
S = (X(I)+X(I)+1)*(X(J)*X(J)+X(J)+1)
T = (X(J)+X(J)+1)*(X(I)*X(I)+X(I)+1)
G(I) = G(I) + S
G(J) = G(J) + T
20 CONTINUE
RETURN
END
=====================
C
C COLVILLE 8
C
REAL*8 Y(3),SS,TT
REAL*8 X(10),LE(7),LI(10),U(300),G(7),DF(10),DG(7,10)
REAL*8 A(7,10),B(1),BL(10),BU(10),W(200)
REAL*8 CT,F,ER,PN,PNI,ST,TL,VALF
real zzz(2)
INTEGER IA(10),IO,IN,K,IT,L,LA,LG,LM,NL,N
COMMON NF,NG,NDF,NDG
EXTERNAL VALF,VALG,GRADF,GRADG
DATA BL/0.D0,0.D0,0.D0,0.D0,0.D0,85.D0,90.D0,3.D0,.01D0,145.D0/
DATA BU/2000.,16000.D0,120.D0,5000.D0,2000.D0,93.D0,
& 95.D0,12.D0,4.D0,162.D0/
DATA X/1745D0,12000.D0,110.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0,0.D0/
DF(1) = 5.04D0
DF(2) = .035D0
DF(3) = 10.
DF(5) = 3.36D0
DF(6) = 0.
DF(8) = 0.
DF(9) = 0.
DF(10)= 0.
DO 20 I = 1,7
DO 10 J = 1,10
10 DG(I,J) = 0.
DG(I,3+I) = 1.
20 CONTINUE
NF = 0
NG = 0
NDF = 0
NDG = 0
C
C FEASIBLE STARTING GUESS
C
CALL VALG(G,X)
DO 30 I = 4,10
30 X(I) = -G(I-3)
NG = NG – 1
TL = .000001
LM = 250
PNI = 10
L = 0
N = 10
IN = 4
LA = 7
LG = 7
NL = 7
ST = 0
CT = 0.D-4
strt = etime(zzz)
CALL MIN(X,LE,LI,U,IA,K,F,G,DF,DG,ER,IT,ST,PN,IO,
1 IN,TL,LM,PNI,A,LA,LG,L,NL,N,B,BL,BU,CT,VALF,VALG,GRADF,GRADG,W)
CALL ERR(IO)
time = etime(zzz) – strt
write(6,*) ‘total time =’,time
WRITE(6,*) ‘VALUE:’,F
WRITE(6,*) ‘NUMBER OF F EVALUATIONS:’,NF
WRITE(6,*) ‘NUMBER OF G EVALUATIONS:’,NG
WRITE(6,*) ‘NUMBER OF DF EVALUATIONS:’,NDF
WRITE(6,*) ‘NUMBER OF DG EVALUATIONS:’,NDG
DATA Y/1728.371286d0,16000d0,98.14151402d0/
TT = 0.
SS = 0.
DO 200 I = 1,3
TT = TT + (X(I)-Y(I))**2
SS = SS + Y(I)**2
WRITE(6,*) I,Y(I),X(I)
200 CONTINUE
SS = DSQRT(TT/SS)
WRITE(6,*) ‘RELATIVE ERROR:’,SS
STOP
END
DOUBLE PRECISION FUNCTION VALF(X)
REAL*8 X(1),T
COMMON NF,NG,NDF,NDG
NF = NF + 1
T = 10.*X(3) + .035D0*X(2) + 3.36D0*X(5) + 5.04D0*X(1)
T = T – .063D0*X(4)*X(7)
VALF = T
RETURN
END
SUBROUTINE GRADF(DF,X)
REAL*8 DF(1),X(1)
COMMON NF,NG,NDF,NDG
NDF = NDF + 1
DF(4) = -.063D0*X(7)
DF(7) = -.063D0*X(4)
END
SUBROUTINE VALG(G,X)
REAL*8 G(1),X(1)
REAL*8 Y2,Y3,Y4,Y5,Y6,Y7,Y8,C2,C4
COMMON NF,NG,NDF,NDG
J1 = 0
J2 = 0
NG = NG + 1
Y2 = 1.6D0*X(1)
10 Y3 = 1.22D0*Y2 – X(1)
Y6 = (X(2)+Y3)/X(1)
C2 = X(1)*(1.12D0 + .13167D0*Y6-.6667D-2*Y6*Y6)
IF ( DABS(C2-Y2) .LE. .001D0 ) GOTO 20
Y2 = C2
J1 = J1 + 1
GOTO 10
20 Y4 = 93.
30 Y5 = 86.35D0 + 1.098D0*Y6 – .038D0*Y6*Y6 + .325D0*(Y4-89.)
Y8 = -133. + 3.*Y5
Y7 = 35.82D0 – .222D0*Y8
C4 = 98000.*X(3)/(Y2*Y7 + X(3)*1000)
IF ( DABS(C4-Y4) .LE. .0001D0 ) GOTO 40
Y4 = C4
J2 = J2 + 1
GOTO 30
40 G(1) = X(4) – Y2
G(2) = X(5) – Y3
G(3) = X(6) – Y4
G(4) = X(7) – Y5
G(5) = X(8) – Y6
G(6) = X(9) – Y7
G(7) = X(10) – Y8
c WRITE(6,*) ‘J1,J2’,J1,J2
RETURN
END
SUBROUTINE GRADG(DG,X)
REAL*8 DG(7,1),X(1)
REAL*8 Y2,Y3,Y4,Y5,Y6,Y7,Y8,C2,C4
REAL*8 Y21,Y31,Y41,Y51,Y61,Y71,Y81
REAL*8 Y22,Y32,Y42,Y52,Y62,Y72,Y82
REAL*8 Y23,Y33,Y43,Y53,Y63,Y73,Y83
COMMON NF,NG,NDF,NDG
NDG = NDG + 1
Y2 = 1.6D0*X(1)
Y21 = 1.6D0
Y22 = 0.
Y23 = 0.
10 Y3 = 1.22D0*Y2 – X(1)
Y31 = 1.22D0*Y21 – 1
Y32 = 1.22D0*Y22
Y33 = 1.22D0*Y23
Y6 = (X(2)+Y3)/X(1)
Y61 = -(X(2)+Y3)/X(1)**2 + Y31/X(1)
Y62 = (1.+Y32)/X(1)
Y63 = Y33/X(1)
C2 = X(1)*(1.12D0 + .13167D0*Y6-.6667D-2*Y6*Y6)
IF ( DABS(C2-Y2) .LE. .001D0 ) GOTO 20
Y2 = C2
Y21 = X(1)*(.13167D0*Y61 – 2*.6667D-2*Y6*Y61)
Y21 = Y21 + 1.12D0 + .13167D0*Y6 – .6667D-2*Y6*Y6
Y22 = X(1)*(.13167D0*Y62 – 2.*.6667D-2*Y6*Y62)
Y23 = X(1)*(.13167D0*Y63 – 2.*.6667D-2*Y6*Y63)
GOTO 10
20 Y4 = 93.
Y41 = 0.
Y42 = 0.
Y43 = 0.
30 Y5 = 86.35D0 + 1.098D0*Y6 – .038D0*Y6*Y6 + .325D0*(Y4-89.)
Y51 = (1.098D0 – 2.*.038D0*Y6)*Y61 + .325D0*Y41
Y52 = (1.098D0 – 2.*.038D0*Y6)*Y62 + .325D0*Y42
Y53 = (1.098D0 – 2.*.038D0*Y6)*Y63 + .325D0*Y43
Y8 = -133. + 3.*Y5
Y81 = 3.*Y51
Y82 = 3.*Y52
Y83 = 3.*Y53
Y7 = 35.82D0 – .222D0*Y8
Y71 = -.222D0*Y81
Y72 = -.222D0*Y82
Y73 = -.222D0*Y83
C4 = 98000.*X(3)/(Y2*Y7 + X(3)*1000)
IF ( DABS(C4-Y4) .LE. .0001D0 ) GOTO 40
Y4 = C4
Y41 = -98000.*X(3)*(Y21*Y7 + Y2*Y71)/(Y2*Y7+X(3)*1000.)**2
Y42 = -98000.*X(3)*(Y22*Y7 + Y2*Y72)/(Y2*Y7+X(3)*1000.)**2
Y43 = -98000.*X(3)*(Y23*Y7 + Y2*Y73 + 1000.)
Y43 = (Y43/(Y2*Y7+X(3)*1000.) + 98000.)/(Y2*Y7+X(3)*1000.)
GOTO 30
40 DG(1,1) = -Y21
DG(1,2) = -Y22
DG(1,3) = -Y23
DG(2,1) = -Y31
DG(2,2) = -Y32
DG(2,3) = -Y33
DG(3,1) = -Y41
DG(3,2) = -Y42
DG(3,3) = -Y43
DG(4,1) = -Y51
DG(4,2) = -Y52
DG(4,3) = -Y53
DG(5,1) = -Y61
DG(5,2) = -Y62
DG(5,3) = -Y63
DG(6,1) = -Y71
DG(6,2) = -Y72
DG(6,3) = -Y73
DG(7,1) = -Y81
DG(7,2) = -Y82
DG(7,3) = -Y83
RETURN
END