*************************************************************************** * helical valley function * more, garbow, and hillstrom, acm toms vol. 7 no. 1 (march 1981) 17-41 *************************************************************************** subroutine getfun( x, n, f, m, ftf, fj, lfj, g, mode) implicit double precision (a-h,o-z) integer n, m, lfj, mode double precision x(n), f(m), ftf, fj(lfj,n), g(n) integer nprob, nprobs, nstart, nstrts common /PROBLM/ nprob, nprobs, nstart, nstrts integer nout common /IOUNIT/ nout logical lf, lj integer na, nb, nc, nd, nt, nh integer j double precision quo, theta intrinsic atan, atan2, sqrt double precision piinv common /PARAM1/ piinv save /PARAM1/ double precision zero, half, one, ten, fifty parameter (zero = 0.d0, half = .5d0, one = 1.d0) parameter (ten = 10.d0, fifty = 50.d0) *======================================================================= if (mode .eq. 0) goto 20 if (mode .eq. -1) goto 10 if (mode .eq. -2) goto 30 x1 = x(1) x2 = x(2) x3 = x(3) write( nu1, 2) x1 2 format(/' x1 = ', 1pe14.5) if (x1 .eq. zero) stop na = mode / 1000 nt = mode - na*1000 nb = nt / 100 nh = nt - nb*100 nc = nh / 10 nd = nh - nc*10 lf = (na .ne. 0) .or. (nb .ne. 0) .or. (nd .ne. 0) lj = (nc .ne. 0) .or. (nd .ne. 0) if (lf .and. lj) goto 300 if (lf) goto 100 if (lj) goto 200 *----------------------------------------------------------------------- 10 continue nprobs = 1 nstrts = 1 n = 3 m = 3 c piinv = one / acos(-one) piinv = .25d0 / atan(one) if (nout .gt. 0) write( nout, 9999) n, m return *----------------------------------------------------------------------- 20 continue x(1) = -one x(2) = zero x(3) = zero return *----------------------------------------------------------------------- 30 continue x(1) = one x(2) = zero x(3) = zero ftf = zero return *----------------------------------------------------------------------- 100 continue quo = x2 / x1 c theta = half*piinv*atan2(x2/x1) theta = half*piinv*atan(quo) if (x1 .lt. zero) theta = theta + half f(1) = ten*(x3 -ten*theta) f(2) = ten*(sqrt(x1*x1 + x2*x2) - one) f(3) = x3 if (nb .ne. 0) ftf = ddot( m, f, 1, f, 1) return 200 continue q = one / (x1*x1 + x2*x2) r = sqrt(q) fpq = fifty*piinv*q tr = ten*r fj(1,1) = fpq*x2 fj(1,2) = -fpq*x1 fj(1,3) = ten fj(2,1) = tr*x1 fj(2,2) = tr*x2 fj(2,3) = zero fj(3,1) = zero fj(3,2) = zero fj(3,3) = one return 300 continue quo = x2 / x1 c theta = half*piinv*atan2(x2,x1) theta = half*piinv*atan(quo) if (x1 .lt. zero) theta = theta + half t = x1*x1 + x2*x2 s = dsqrt(t) q = one / t r = dsqrt(q) f(1) = ten*(x3 -ten*theta) f(2) = ten*(s - one) f(3) = x3 fpq = fifty*piinv*q tr = ten*r fj(1,1) = fpq*x2 fj(1,2) = -fpq*x1 fj(1,3) = ten fj(2,1) = tr*x1 fj(2,2) = tr*x2 fj(2,3) = zero fj(3,1) = zero fj(3,2) = zero fj(3,3) = one if (nb .ne. 0) ftf = ddot( m, f, 1, f, 1) if (nd .eq. 0) return do 400 j = 1, n g(j) = ddot( m, fj( 1, j), 1, f, 1) 400 continue return 9999 format(/'1',70('=')//, *' helical valley function (more et al.)'//, *' number of variables =', i4, ' (3)'/, *' number of functions =', i4, ' (3)'//, * ' ',70('=')/) end ************************************************************************ ************************************************************************ subroutine dfjdxk ( k, x, n, dfj, ldfj, m, nonzro) implicit double precision (a-h,o-z) integer k, n, ldfj, m, nonzro(n) double precision x(n), dfj(ldfj,n) double precision piinv common /PARAM1/ piinv save /PARAM1/ double precision zero, one, two, ten, fifty parameter (zero = 0.d0, one = 1.d0, two = 2.d0) parameter (ten = 10.d0, fifty = 50.d0) *======================================================================= nonzro(3) = 0 dfj( 1, 3) = zero dfj( 2, 3) = zero dfj( 3, 1) = zero dfj( 3, 2) = zero dfj( 3, 3) = zero if (k .eq. 3) goto 230 x1 = x(1) x2 = x(2) x1sq = x1*x1 x2sq = x2*x2 x12 = x1*x2 nonzro(1) = 1 nonzro(2) = 1 q = one / (x1sq + x2sq) d = q*q fpq = fifty*piinv*d td = ten*dsqrt(q)*q goto ( 210, 220), k 210 continue dfj( 1, 1) = -two*fpq*x12 dfj( 1, 2) = fpq*(x1sq - x2sq) dfj( 2, 1) = td*x2sq dfj( 2, 2) = -td*x12 return 220 continue dfj( 1, 1) = fpq*(x1sq - x2sq) dfj( 1, 2) = two*fpq*x12 dfj( 2, 1) = -td*x12 dfj( 2, 2) = td*x1sq return 230 continue nonzro(1) = 0 nonzro(2) = 0 dfj( 1, 1) = zero dfj( 1, 2) = zero dfj( 2, 1) = zero dfj( 2, 2) = zero return end ************************************************************************ ************************************************************************ subroutine dfkdij ( k, x, n, hess, lhess, linear) implicit double precision (a-h,o-z) logical linear integer k, n, lhess double precision x(n), hess(lhess,n) double precision piinv common /PARAM1/ piinv save /PARAM1/ double precision zero, one, two, ten, fifty parameter (zero = 0.d0, one = 1.d0, two = 2.d0) parameter (ten = 10.d0, fifty = 50.d0) *======================================================================= goto ( 210, 220, 230), k 210 continue linear = .false. x1 = x(1) x2 = x(2) x1sq = x1*x1 x2sq = x2*x2 q = one / (x1sq + x2sq) d = q*q fpq = fifty*piinv*d tmp = two*fpq*x1*x2 hess( 1, 1) = -tmp hess( 1, 2) = fpq*(x1sq - x2sq) hess( 2, 1) = hess(1,2) hess( 1, 3) = zero hess( 3, 1) = zero hess( 2, 2) = tmp hess( 2, 3) = zero hess( 3, 2) = zero hess( 3, 3) = zero return 220 continue linear = .false. x1 = x(1) x2 = x(2) x1sq = x1*x1 x2sq = x2*x2 q = one / (x1sq + x2sq) d = q*q td = ten*dsqrt(q)*q hess( 1, 1) = td * x2sq hess( 1, 2) = -td * x1 * x2 hess( 2, 1) = hess(1,2) hess( 1, 3) = zero hess( 3, 1) = zero hess( 2, 2) = td * x1sq hess( 2, 3) = zero hess( 3, 2) = zero hess( 3, 3) = zero return 230 continue linear = .true. hess( 1, 1) = zero hess( 1, 2) = zero hess( 2, 1) = zero hess( 1, 3) = zero hess( 3, 1) = zero hess( 2, 2) = zero hess( 2, 3) = zero hess( 3, 2) = zero hess( 3, 3) = zero return end