***************************************************************************** * discrete integral 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 i, j double precision h2, bj, cj, oj, sj, ti, tj, xj double precision ddot intrinsic dble double precision h common /PARAM1/ h save /PARAM1/ double precision zero, half, one, two, three parameter (zero = 0.d0, half = .5d0, one = 1.d0) parameter (two = 2.d0, three = 3.d0) *======================================================================= if (mode .eq. 0) goto 20 if (mode .eq. -1) goto 10 if (mode .eq. -2) goto 30 na = mode / 1000 nh = mode - na*1000 nb = nh / 100 nt = nh - nb*100 nc = nt / 10 nd = nt - 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 = 10 m = n h = one / dble(n+1) h2 = half*h if (nout .gt. 0) write( nout, 9999) n, m return *----------------------------------------------------------------------- 20 continue do 21 j = 1, n tj = dble(j)*h x(j) = tj*(tj-one) 21 continue return *----------------------------------------------------------------------- 30 continue ftf = zero return *----------------------------------------------------------------------- 100 continue call dcopy( n, x, 1, f, 1) do 110 j = 1, n tj = dble(j)*h oj = one - tj cj = h2*(x(j) + tj + one)**3 do 110 i = 1, n ti = dble(i)*h oi = one - ti if (j .le. i) f(i) = f(i) + oi*tj*cj if (j .gt. i) f(i) = f(i) + ti*oj*cj 110 continue if (nb .ne. 0) ftf = ddot( m, f, 1, f, 1) return 200 continue do 210 j = 1, n tj = dble(j)*h oj = one - tj sj = three*h2*(x(j) + tj + one)**2 fj(j,j) = one + oj*tj*sj do 210 i = 1, n ti = dble(i)*h oi = one - ti if (j .lt. i) fj(i,j) = oi*tj*sj if (j .gt. i) fj(i,j) = ti*oj*sj 210 continue return 300 continue call dcopy( n, x, 1, f, 1) do 310 j = 1, n xj = x(j) tj = dble(j)*h oj = one - tj bj = (xj + tj + one) sj = h2*bj*bj cj = sj*bj sj = sj*three fj(j,j) = one + oj*tj*sj do 310 i = 1, n ti = dble(i)*h oi = one - ti if (j .le. i) f(i) = f(i) + oi*tj*cj if (j .gt. i) f(i) = f(i) + ti*oj*cj if (j .lt. i) fj(i,j) = oi*tj*sj if (j .gt. i) fj(i,j) = ti*oj*sj 310 continue 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('=')//, *' discrete integral function (more et al.)'//, *' number of variables =', i4,' (variable)'/, *' number of functions =', i4,' ( = n )'//, * ' ',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) integer i, j double precision ti, tk, xk intrinsic dble double precision h common /PARAM1/ h save /PARAM1/ double precision zero, one, three parameter (zero = 0.d0, one = 1.d0) parameter (three = 3.d0) *======================================================================= do 100 j = 1, n nonzro(j) = 0 call dcopy( m, zero, 0, dfj( 1, j), 1) 100 continue nonzro(k) = 1 tk = dble(k)*h xk = x(k) do 200 i = 1, n ti = dble(i)*h if (k .le. i) dfj(i,k) = * three*h*(one-ti)*tk*(xk+tk+one)**2 if (k .gt. i) dfj(i,k) = * three*h*ti*(one-tk)*(xk+tk+one)**2 200 continue return end ************************************************************************ ************************************************************************ subroutine dfkdij( k, x, n, lhess, hess, linear) implicit double precision (a-h,o-z) logical linear integer k, n, lhess double precision x(n), hess(lhess,n) integer j double precision tk, tj intrinsic dble double precision h common /PARAM1/ h save /PARAM1/ double precision zero, one, three parameter (zero = 0.d0, one = 1.d0) parameter (three = 3.d0) *======================================================================= do 100 j = 1, n call dcopy( n, zero, 0, hess( 1, j), 1) 100 continue linear = .false. tk = dble(k)*h do 200 j = 1, n tj = dble(j)*h if (j .le. k) hess(j,j) = three*h*(one-tk)*tj*(x(j)+tj+one)**2 if (j .gt. k) hess(j,j) = three*h*tk*(one-tj)*(x(j)+tj+one)**2 200 continue return end