************************************************************************* * chebyquad 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 integer m2 double precision coeff common /PARAM1/ coeff, m2 save /PARAM1/ logical lf, lj integer na, nb, nc, nd, nt, nh integer i, i2, j double precision dn1 double precision s, s0, s1, t, t0, t1, tj, u double precision ddot intrinsic dble double precision zero, one, two, four parameter (zero = 0.d0, one = 1.d0, two = 2.d0) parameter (four = 4.d0) *======================================================================= if (mode .eq. 0) goto 20 if (mode .eq. -1) goto 10 if (mode .eq. -2) goto 30 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 = 10 m = n m2 = m/2 coeff = one / dble(n) if (nout .gt. 0) write( nout, 9999) n, m return *----------------------------------------------------------------------- 20 continue dn1 = one / dble(n+1) do 21 i = 1, n x(i) = dble(i) * dn1 21 continue return *----------------------------------------------------------------------- 30 continue ftf = 4.77271d-3 return *----------------------------------------------------------------------- 100 continue call dcopy( m, zero, 0, f, 1) do 110 i = 1, m2 i2 = 2*i f(i2) = one / dble((i2*i2) - 1) 110 continue do 125 j = 1, n t0 = one t1 = two * x(j) - one tj = t1 f(1) = f(1) + coeff*t1 do 120 i = 2, m t = two*tj*t1 - t0 f(i) = f(i) + coeff*t t0 = t1 t1 = t 120 continue 125 continue if (nb .ne. 0) ftf = ddot( m, f, 1, f, 1) return 200 continue do 225 j = 1, n t0 = one s0 = zero s1 = two t1 = two * x(j) - one tj = t1 fj( 1, j) = coeff*s1 do 220 i = 2, m u = two * tj t = u*t1 - t0 s = four*t1 + u*s1 - s0 fj( i, j) = coeff*s t0 = t1 t1 = t s0 = s1 s1 = s 220 continue 225 continue return 300 continue call dcopy( m, zero, 0, f, 1) do 310 i = 1, m2 i2 = 2*i f(i2) = one / dble((i2*i2) - 1) 310 continue do 325 j = 1, n t0 = one s0 = zero s1 = two t1 = two * x(j) - one tj = t1 f(1) = f(1) + coeff*t1 fj( 1, j) = coeff*s1 do 320 i = 2, m u = two*tj t = u*t1 - t0 s = four*t1 + u*s1 - s0 f(i) = f(i) + coeff*t fj( i, j) = coeff*s t0 = t1 t1 = t s0 = s1 s1 = s 320 continue 325 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('=')//, *' chebyquad 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 r, r0, r1, s, s0, s1, t, t0, t1, tk, u integer m2 double precision coeff common /PARAM1/ coeff, m2 save /PARAM1/ double precision zero, one, two, four, eight parameter (zero = 0.d0, one = 1.d0, two = 2.d0) parameter (four = 4.d0, eight = 8.d0) *======================================================================= do 100 j = 1, n nonzro(j) = 0 call dcopy( m, zero, 0, dfj( 1, j), 1) 100 continue nonzro(k) = 1 t0 = one s0 = zero s1 = two r0 = zero r1 = zero t1 = two * x(k) - one tk = t1 dfj( 1, k) = zero do 200 i = 2, m u = two*tk t = u*t1 - t0 s = four*t1 + u*s1 - s0 r = eight*s1 + u*r1 - r0 dfj( i, k) = coeff*r t0 = t1 t1 = t s0 = s1 s1 = s r0 = r1 r1 = r 200 continue 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) integer j double precision r, r0, r1, s, s0, s1, t, t0, t1, tj, u integer m2 double precision coeff common /PARAM1/ coeff, m2 save /PARAM1/ double precision zero, one, two, four, eight parameter (zero = 0.d0, one = 1.d0, two = 2.d0) parameter (four = 4.d0, eight = 8.d0) *======================================================================= do 100 j = 1, n call dcopy( n, zero, 0, hess( 1, j), 1) 100 continue if (k .eq. 1) linear = .true. if (k .eq. 1) return linear = .false. do 220 j = 1, n t0 = one s0 = zero s1 = two r0 = zero r1 = zero t1 = two * x(j) - one tj = t1 do 210 i = 2, k u = two*tj t = u*t1 - t0 s = four*t1 + u*s1 - s0 r = eight*s1 + u*r1 - r0 t0 = t1 t1 = t s0 = s1 s1 = s r0 = r1 r1 = r 210 continue hess( j, j) = coeff*r 220 continue return end