******************************************************************************* * 2 by 2 matrix square root problem (hammarling) ******************************************************************************* 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 double precision x1, x2, x3, x4 double precision ddot double precision a common /PARAM1/ a(2,2) save /PARAM1/ double precision zero, one, two parameter (zero = 0.d0, one = 1.d0, two = 2.d0) *======================================================================= if (mode .eq. 0) goto 20 if (mode .eq. -1) goto 10 if (mode .lt. -1) goto 30 x1 = x(1) x2 = x(2) x3 = x(3) x4 = x(4) 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 100 if (lf) goto 100 if (lj) goto 200 *----------------------------------------------------------------------- 10 continue numbr = 1 nprobs = 1 nstrts = 1 na = 2 n = 4 m = 4 if (nout .gt. 0) write( nout, 9999) numbr, na, n a(1,1) = 1.0d-4 a(1,2) = one a(2,1) = zero a(2,2) = 1.0d-4 return *----------------------------------------------------------------------- 20 continue x(1) = 1.0d+0 x(2) = 0.0d+0 x(3) = 0.0d+0 x(4) = 1.0d+0 return *----------------------------------------------------------------------- 30 continue ftf = zero x(1) = 1.0d-2 x(2) = 5.0d+1 x(3) = 0.0d+0 x(4) = 1.0d-2 return *----------------------------------------------------------------------- 100 continue f(1) = (x1*x1 + x2*x3) - a(1,1) f(2) = (x1*x2 + x2*x4) - a(1,2) f(3) = (x3*x1 + x4*x3) - a(2,1) f(4) = (x3*x2 + x4*x4) - a(2,2) if (nb .ne. 0) ftf = ddot( m, f, 1, f, 1) if (.not. lj) return 200 continue fj( 1, 1) = two*x1 fj( 1, 2) = x3 fj( 1, 3) = x2 fj( 1, 4) = zero fj( 2, 1) = x2 fj( 2, 2) = x1 + x4 fj( 2, 3) = zero fj( 2, 4) = x2 fj( 3, 1) = x3 fj( 3, 2) = zero fj( 3, 3) = x1 + x4 fj( 3, 4) = x3 fj( 4, 1) = zero fj( 4, 2) = x3 fj( 4, 3) = x2 fj( 4, 4) = two*x4 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('=')//, *' matrix square root problem (hammarling) ', i4//, *' rows in matrix = ', i4/, *' # variables = # matrix entries = # constraints =', i4//, * ' ',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 j double precision zero, one, two parameter (zero = 0.d0, one = 1.d0, two = 2.d0) *======================================================================= do 10 j = 1, n nonzro(j) = 1 call dcopy( m, zero, 0, dfj( 1, j), 1) 10 continue goto ( 100, 200, 300, 400), k 100 continue nonzro(4) = 0 dfj( 1, 1) = two dfj( 2, 2) = one dfj( 3, 3) = one return 200 continue nonzro(2) = 0 dfj( 1, 3) = one dfj( 2, 1) = one dfj( 2, 4) = one dfj( 4, 3) = one return 300 continue nonzro(3) = 0 dfj( 1, 2) = one dfj( 3, 1) = one dfj( 3, 4) = one dfj( 4, 2) = one return 400 continue nonzro(1) = 0 dfj( 2, 2) = one dfj( 3, 3) = one dfj( 4, 4) = two 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 zero, one, two parameter (zero = 0.d0, one = 1.d0, two = 2.d0) *======================================================================= do 10 j = 1, n call dcopy( n, zero, 0, hess( 1, j), 1) 10 continue linear = .false. goto ( 100, 200, 300, 400), k 100 continue hess(1,1) = two hess(2,3) = one hess(3,2) = one return 200 continue hess(1,2) = one hess(2,1) = one hess(2,4) = one hess(4,2) = one return 300 continue hess(1,3) = one hess(3,1) = one hess(3,4) = one hess(4,3) = one return 400 continue hess(2,3) = one hess(3,2) = one hess(4,4) = two return end