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subroutine objfcn(n,x,f,nprob)
integer n,nprob
double precision f
double precision x(n)
c **********
c
c subroutine objfcn
c
c this subroutine defines the objective functions of eighteen
c nonlinear unconstrained minimization problems. the values
c of n for functions 1,2,3,4,5,10,11,12,16 and 17 are
c 3,6,3,2,3,2,4,3,2 and 4, respectively.
c for function 7, n may be 2 or greater but is usually 6 or 9.
c for functions 6,8,9,13,14,15 and 18 n may be variable,
c however it must be even for function 14, a multiple of 4 for
c function 15, and not greater than 50 for function 18.
c
c the subroutine statement is
c
c subroutine objfcn(n,x,f,nprob)
c
c where
c
c n is a positive integer input variable.
c
c x is an input array of length n.
c
c f is an output variable which contains the value of
c the nprob objective function evaluated at x.
c
c nprob is a positive integer input variable which defines the
c number of the problem. nprob must not exceed 18.
c
c subprograms called
c
c fortran-supplied ... dabs,datan,dcos,dexp,dlog,dsign,dsin,
c dsqrt
c
c argonne national laboratory. minpack project. march 1980.
c burton s. garbow, kenneth e. hillstrom, jorge j. more
c
c **********
integer i,iev,ivar,j
double precision ap,arg,c2pdm6,cp0001,cp1,cp2,cp25,cp5,c1p5,
* c2p25,c2p625,c3p5,c25,c29,c90,c100,c10000,
* c1pd6,d1,d2,eight,fifty,five,four,one,r,s1,s2,
* s3,t,t1,t2,t3,ten,th,three,tpi,two,zero
double precision fvec(50),y(15)
double precision dfloat
data zero,one,two,three,four,five,eight,ten,fifty
* /0.0d0,1.0d0,2.0d0,3.0d0,4.0d0,5.0d0,8.0d0,1.0d1,5.0d1/
data c2pdm6,cp0001,cp1,cp2,cp25,cp5,c1p5,c2p25,c2p625,c3p5,c25,
* c29,c90,c100,c10000,c1pd6
* /2.0d-6,1.0d-4,1.0d-1,2.0d-1,2.5d-1,5.0d-1,1.5d0,2.25d0,
* 2.625d0,3.5d0,2.5d1,2.9d1,9.0d1,1.0d2,1.0d4,1.0d6/
data ap /1.0d-5/
data y(1),y(2),y(3),y(4),y(5),y(6),y(7),y(8),y(9),y(10),y(11),
* y(12),y(13),y(14),y(15)
* /9.0d-4,4.4d-3,1.75d-2,5.4d-2,1.295d-1,2.42d-1,3.521d-1,
* 3.989d-1,3.521d-1,2.42d-1,1.295d-1,5.4d-2,1.75d-2,4.4d-3,
* 9.0d-4/
dfloat(ivar) = ivar
c
c function routine selector.
c
go to (10,20,40,60,70,90,110,150,170,200,210,230,250,280,300,
* 320,330,340), nprob
c
c helical valley function.
c
10 continue
tpi = eight*datan(one)
th = dsign(cp25,x(2))
if (x(1) .gt. zero) th = datan(x(2)/x(1))/tpi
if (x(1) .lt. zero) th = datan(x(2)/x(1))/tpi + cp5
arg = x(1)**2 + x(2)**2
r = dsqrt(arg)
t = x(3) - ten*th
f = c100*(t**2 + (r - one)**2) + x(3)**2
go to 390
c
c biggs exp6 function.
c
20 continue
f = zero
do 30 i = 1, 13
d1 = dfloat(i)/ten
d2 = dexp(-d1) - five*dexp(-ten*d1) + three*dexp(-four*d1)
s1 = dexp(-d1*x(1))
s2 = dexp(-d1*x(2))
s3 = dexp(-d1*x(5))
t = x(3)*s1 - x(4)*s2 + x(6)*s3 - d2
f = f + t**2
30 continue
go to 390
c
c gaussian function.
c
40 continue
f = zero
do 50 i = 1, 15
d1 = cp5*dfloat(i-1)
d2 = c3p5 - d1 - x(3)
arg = -cp5*x(2)*d2**2
r = dexp(arg)
t = x(1)*r - y(i)
f = f + t**2
50 continue
go to 390
c
c powell badly scaled function.
c
60 continue
t1 = c10000*x(1)*x(2) - one
s1 = dexp(-x(1))
s2 = dexp(-x(2))
t2 = s1 + s2 - one - cp0001
f = t1**2 + t2**2
go to 390
c
c box 3-dimensional function.
c
70 continue
f = zero
do 80 i = 1, 10
d1 = dfloat(i)
d2 = d1/ten
s1 = dexp(-d2*x(1))
s2 = dexp(-d2*x(2))
s3 = dexp(-d2) - dexp(-d1)
t = s1 - s2 - s3*x(3)
f = f + t**2
80 continue
go to 390
c
c variably dimensioned function.
c
90 continue
t1 = zero
t2 = zero
do 100 j = 1, n
t1 = t1 + dfloat(j)*(x(j) - one)
t2 = t2 + (x(j) - one)**2
100 continue
f = t2 + t1**2*(one + t1**2)
go to 390
c
c watson function.
c
110 continue
f = zero
do 140 i = 1, 29
d1 = dfloat(i)/c29
s1 = zero
d2 = one
do 120 j = 2, n
s1 = s1 + dfloat(j-1)*d2*x(j)
d2 = d1*d2
120 continue
s2 = zero
d2 = one
do 130 j = 1, n
s2 = s2 + d2*x(j)
d2 = d1*d2
130 continue
t = s1 - s2**2 - one
f = f + t**2
140 continue
t1 = x(2) - x(1)**2 - one
f = f + x(1)**2 + t1**2
go to 390
c
c penalty function i.
c
150 continue
t1 = -cp25
t2 = zero
do 160 j = 1, n
t1 = t1 + x(j)**2
t2 = t2 + (x(j) - one)**2
160 continue
f = ap*t2 + t1**2
go to 390
c
c penalty function ii.
c
170 continue
t1 = -one
t2 = zero
t3 = zero
d1 = dexp(cp1)
d2 = one
do 190 j = 1, n
t1 = t1 + dfloat(n-j+1)*x(j)**2
s1 = dexp(x(j)/ten)
if (j .eq. 1) go to 180
s3 = s1 + s2 - d2*(d1 + one)
t2 = t2 + s3**2
t3 = t3 + (s1 - one/d1)**2
180 continue
s2 = s1
d2 = d1*d2
190 continue
f = ap*(t2 + t3) + t1**2 + (x(1) - cp2)**2
go to 390
c
c brown badly scaled function.
c
200 continue
t1 = x(1) - c1pd6
t2 = x(2) - c2pdm6
t3 = x(1)*x(2) - two
f = t1**2 + t2**2 + t3**2
go to 390
c
c brown and dennis function.
c
210 continue
f = zero
do 220 i = 1, 20
d1 = dfloat(i)/five
d2 = dsin(d1)
t1 = x(1) + d1*x(2) - dexp(d1)
t2 = x(3) + d2*x(4) - dcos(d1)
t = t1**2 + t2**2
f = f + t**2
220 continue
go to 390
c
c gulf research and development function.
c
230 continue
f = zero
d1 = two/three
do 240 i = 1, 99
arg = dfloat(i)/c100
r = (-fifty*dlog(arg))**d1 + c25 - x(2)
t1 = dabs(r)**x(3)/x(1)
t2 = dexp(-t1)
t = t2 - arg
f = f + t**2
240 continue
go to 390
c
c trigonometric function.
c
250 continue
s1 = zero
do 260 j = 1, n
s1 = s1 + dcos(x(j))
260 continue
f = zero
do 270 j = 1, n
t = dfloat(n+j) - dsin(x(j)) - s1 - dfloat(j)*dcos(x(j))
f = f + t**2
270 continue
go to 390
c
c extended rosenbrock function.
c
280 continue
f = zero
do 290 j = 1, n, 2
t1 = one - x(j)
t2 = ten*(x(j+1) - x(j)**2)
f = f + t1**2 + t2**2
290 continue
go to 390
c
c extended powell function.
c
300 continue
f = zero
do 310 j = 1, n, 4
t = x(j) + ten*x(j+1)
t1 = x(j+2) - x(j+3)
s1 = five*t1
t2 = x(j+1) - two*x(j+2)
s2 = t2**3
t3 = x(j) - x(j+3)
s3 = ten*t3**3
f = f + t**2 + s1*t1 + s2*t2 + s3*t3
310 continue
go to 390
c
c beale function.
c
320 continue
s1 = one - x(2)
t1 = c1p5 - x(1)*s1
s2 = one - x(2)**2
t2 = c2p25 - x(1)*s2
s3 = one - x(2)**3
t3 = c2p625 - x(1)*s3
f = t1**2 + t2**2 + t3**2
go to 390
c
c wood function.
c
330 continue
s1 = x(2) - x(1)**2
s2 = one - x(1)
s3 = x(2) - one
t1 = x(4) - x(3)**2
t2 = one - x(3)
t3 = x(4) - one
f = c100*s1**2 + s2**2 + c90*t1**2 + t2**2 + ten*(s3 + t3)**2
* + (s3 - t3)**2/ten
go to 390
c
c chebyquad function.
c
340 continue
do 350 i = 1, n
fvec(i) = zero
350 continue
do 370 j = 1, n
t1 = one
t2 = two*x(j) - one
t = two*t2
do 360 i = 1, n
fvec(i) = fvec(i) + t2
th = t*t2 - t1
t1 = t2
t2 = th
360 continue
370 continue
f = zero
d1 = one/dfloat(n)
iev = -1
do 380 i = 1, n
t = d1*fvec(i)
if (iev .gt. 0) t = t + one/(dfloat(i)**2 - one)
f = f + t**2
iev = -iev
380 continue
390 continue
return
c
c last card of subroutine objfcn.
c
end
|
