C ALGORITHM 765, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 23, NO. 1, March, 1997, P. 81--90. C #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # Doc # Drivers # Src # This archive created: Sat Apr 19 22:23:29 1997 export PATH; PATH=/bin:$PATH if test ! -d 'Doc' then mkdir 'Doc' fi cd 'Doc' if test -f 'stenmin_user_manual.ps' then echo shar: will not over-write existing file "'stenmin_user_manual.ps'" else cat << \SHAR_EOF > 'stenmin_user_manual.ps' %!PS-Adobe-2.0 %%Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %%Title: stenmin_2.dvi %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips stenmin_2 %DVIPSParameters: dpi=300, compressed, comments removed %DVIPSSource: TeX output 1996.07.03:2046 %%BeginProcSet: texc.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale 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Fi(f)5 b Fl(\()p Fi(x)p Fl(\))18 b(at)g(the)g(curren)o(t)h(p)q(oin)o(t)g Fj(X)p Fl(.)f Fj(USH)g Fl(m)o(ust)g(b)q(e)h(declared)h Fj(EXTERNAL)d Fl(in)j(the)e(user's)h(calling)h(program)59 951 y(and)15 b(m)o(ust)g(conform)g(to)f(the)i(usage)527 1045 y Fj(CALL)23 b(USH\(N,)g(X,)h(NZ,)f(LICN,)g(HESS,)g(IRN,)h(ICN\))59 1139 y Fl(where)14 b Fj(N)g Fl(is)g(the)g(dimension)h(of)e(the)h (problem,)g Fj(X)g Fl(is)g(a)g(v)o(ector)f(of)g(length)h Fj(N)p Fl(,)f Fj(HESS)h Fl(is)g(the)g(Hessian)g(matrix)f(at)59 1196 y Fj(X)p Fl(,)g Fj(LICN)g Fl(is)h(the)f(length)h(of)f Fj(HESS)p Fl(,)g Fj(NZ)g Fl(is)h(the)f(n)o(um)o(b)q(er)h(of)f(nonzeros) h(in)g(the)f(lo)o(w)o(er)g(or)g(upp)q(er)i(triangular)e(part)59 1252 y(of)g Fj(HESS)p Fl(,)g(and)g Fj(IRN)g Fl(and)h Fj(ICN)f Fl(are)g(the)h(ro)o(w)e(and)i(column)h(indices)g(of)e(the)h (nonzeros)f(in)i Fj(HESS)p Fl(.)d Fj(USH)h Fl(m)o(ust)g(not)59 1308 y(alter)18 b(the)f(v)m(alues)i(of)e Fj(N)p Fl(,)g Fj(X)p Fl(,)g(and)h Fj(LICN)p Fl(.)f(Only)i(the)e(lo)o(w)o(er)h(or)f (upp)q(er)h(triangular)g(part)f(of)g Fj(HESS)g Fl(should)i(b)q(e)59 1365 y(giv)o(en.)27 b(When)18 b(using)g(the)g(in)o(terface)f Fj(STUMCD)p Fl(,)g(if)h(no)f(analytic)h(Hessian)g(is)g(supplied)i(\()p Fj(HSNFLG)j(=)h(0)p Fl(\),)17 b(the)59 1421 y(user)e(m)o(ust)g(use)h (the)f(dumm)o(y)g(name)g Fj(STDUSH)p Fl(.)59 1534 y Fj(*TYPX)p Ff(!)p Fl(:)32 b(An)22 b(arra)o(y)e(of)h(length)h Fj(N)g Fl(in)g(whic)o(h)g(the)g(t)o(ypical)g(size)h(of)e(the)g(comp)q(onen)o (ts)h(of)f Fj(X)g Fl(are)g(sp)q(eci-)59 1591 y(\014ed.)f(The)13 b(t)o(ypical)h(comp)q(onen)o(t)g(sizes)g(should)g(b)q(e)g(p)q(ositiv)o (e)g(real)g(scalars.)19 b(If)14 b(a)e(negativ)o(e)i(v)m(alue)g(is)g(sp) q(eci\014ed,)59 1647 y(its)j(absolute)h(v)m(alue)h(will)f(b)q(e)g (used.)27 b(When)18 b(0.0)e(is)i(sp)q(eci\014ed,)h(1.0)d(will)j(b)q(e)f (used.)27 b(The)17 b(program)f(will)j(not)59 1704 y(ab)q(ort.)g(This)14 b(v)o(ector)e(is)i(used)g(b)o(y)f(the)g(the)g(pac)o(k)m(age)h(to)e (determine)j(the)e(scaling)h(matrix)f Fi(D)1633 1711 y Fd(x)1655 1704 y Fl(.)19 b(Although)14 b(the)59 1760 y(pac)o(k)m(age)k(ma)o(y)f(w)o(ork)g(reasonably)h(w)o(ell)h(in)g(a)e (large)h(n)o(um)o(b)q(er)g(of)g(instances)h(without)e(scaling,)j(it)e (ma)o(y)f(fail)59 1817 y(when)c(the)f(comp)q(onen)o(ts)h(of)f Fi(x)573 1824 y Fm(\003)605 1817 y Fl(are)g(of)g(radically)i (di\013eren)o(t)e(magnitude)h(and)g(scaling)g(is)g(not)f(in)o(v)o(ok)o (ed.)19 b(If)13 b(the)59 1873 y(sizes)j(of)f(the)h(parameters)e(are)h (kno)o(wn)g(to)g(di\013er)h(b)o(y)f(man)o(y)g(orders)g(of)g(magnitude,) g(then)h(the)f(scale)h(v)o(ector)59 1929 y Fj(TYPX)e Fl(should)h(de\014nitely)i(b)q(e)e(used.)20 b(Mo)q(dule)c Fj(STDFLT)d Fl(returns)i Fj(TYPX)f Fl(=)h(\(1.0,)p Fi(:)8 b(:)f(:)m Fl(,)14 b(1.0\).)19 b(F)l(or)13 b(example,)j(if)f(it)59 1986 y(is)h(an)o(ticipated)g(that)e(the)i(range)f(of)f(v)m(alues)j(for) d(the)h(iterates)g Fi(x)1164 1993 y Fd(k)1201 1986 y Fl(is)512 2080 y Fi(x)538 2087 y Fq(1)595 2080 y Ff(2)36 b Fl([)p Ff(\000)p Fl(10)755 2063 y Fq(10)816 2080 y Fi(;)31 b Fl(10)906 2063 y Fq(10)943 2080 y Fl(])512 2136 y Fi(x)538 2143 y Fq(2)595 2136 y Ff(2)36 b Fl([)p Ff(\000)p Fl(10)755 2120 y Fq(2)798 2136 y Fi(;)c Fl(10)889 2120 y Fq(4)908 2136 y Fl(])512 2193 y Fi(x)538 2200 y Fq(3)595 2193 y Ff(2)k Fl([)p Ff(\000)p Fl(6)10 b Ff(\002)h Fl(10)834 2176 y Fm(\000)p Fq(6)880 2193 y Fi(;)31 b Fl(9)10 b Ff(\002)h Fl(10)1049 2176 y Fm(\000)p Fq(6)1095 2193 y Fl(])59 2286 y(then)16 b(an)f(appropriate)g(c)o(hoice)h(will)h (b)q(e)f Fj(TYPX)e Fl(=)i(\(1.0)p Fj(E)p Fl(+10,)d(1.0)p Fj(E)p Fl(+3,)h(7.0)p Fj(E)p Fl(-6\).)59 2399 y Fj(FSCALE)p Ff(!)p Fl(:)29 b(A)20 b(p)q(ositiv)o(e)h(real)f(n)o(um)o(b)q(er)g (estimating)g(the)g(magnitude)h(of)e Fi(f)5 b Fl(\()p Fi(x)p Fl(\))20 b(near)g(the)g(minimizer)h Fi(x)1916 2406 y Fm(\003)1936 2399 y Fl(.)59 2456 y(It)16 b(is)h(used)f(in)h(the) f(gradien)o(t)g(stopping)h(condition)g(giv)o(en)g(b)q(elo)o(w.)23 b(If)16 b Fi(f)5 b Fl(\()p Fi(x)1344 2463 y Fq(0)1364 2456 y Fl(\))15 b(is)i(m)o(uc)o(h)f(greater)f(than)h Fi(f)5 b Fl(\()p Fi(x)1899 2463 y Fm(\003)1919 2456 y Fl(\),)59 2512 y Fj(FSCALE)15 b Fl(should)i(b)q(e)f(appro)o(ximately)g Fi(f)5 b Fl(\()p Fi(x)796 2519 y Fm(\003)815 2512 y Fl(\).)21 b(If)16 b(a)f(negativ)o(e)h(v)m(alue)h(is)f(sp)q(eci\014ed)i(for)d Fj(FSCALE)p Fl(,)g(its)g(absolute)59 2569 y(v)m(alue)h(is)g(used.)21 b(When)15 b(0.0)f(is)i(sp)q(eci\014ed,)h(1.0)d(will)j(b)q(e)f(used.)21 b(The)15 b(program)f(will)j(not)e(ab)q(ort.)993 2758 y(4)p eop %%Page: 5 5 5 4 bop 59 199 a Fj(GRADTL)p Ff(!)p Fl(:)33 b(P)o(ositiv)o(e)22 b(scalar)f(giving)i(the)f(tolerance)g(at)f(whic)o(h)i(the)f(scaled)h (gradien)o(t)f(of)f Fi(f)5 b Fl(\()p Fi(x)p Fl(\))21 b(is)h(con-)59 256 y(sidered)15 b(close)f(enough)f(to)g(zero)g(to)g (terminate)g(the)g(algorithm.)20 b(The)13 b(scaled)h(gradien)o(t)g(is)g (a)f(measure)g(of)g(the)59 312 y(relativ)o(e)18 b(c)o(hange)g(in)h Fi(f)j Fl(in)d(eac)o(h)f(direction)h Fi(x)855 319 y Fd(i)887 312 y Fl(divided)h(b)o(y)d(the)h(relativ)o(e)g(c)o(hange)g(in)h Fi(x)1595 319 y Fd(i)1609 312 y Fl(.)27 b(More)17 b(precisely)l(,)59 369 y(the)e(test)g(used)h(b)o(y)f(the)g(program)f(is)508 484 y(max)545 513 y Fd(i)600 425 y Fc(\032)657 454 y Ff(j)f(r)p Fi(f)5 b Fl(\()p Fi(x)p Fl(\))12 b Ff(j)835 461 y Fd(i)876 454 y Fl(max)p Ff(fj)g Fi(x)1035 461 y Fd(i)1061 454 y Ff(j)p Fi(;)c Fj(TYPX)1190 461 y Fd(i)1204 454 y Ff(g)p 657 474 570 2 v 756 515 a Fl(max)p Ff(fj)k Fi(f)18 b Ff(j)p Fi(;)8 b Fj(FSCALE)n Ff(g)1252 425 y Fc(\033)1296 484 y Ff(\024)13 b Fj(GRADTL)o Fi(:)59 610 y Fl(The)19 b(mo)q(dule)h Fj(STDFLT)d Fl(returns)i(the)g(v)m(alue)h Fi(\017)863 594 y Fq(1)p Fd(=)p Fq(3)918 610 y Fl(.)30 b(If)19 b(the)g(user)g(sp)q(eci\014es)h(a)e(negativ)o(e)h(v)m(alue,)h (the)f(default)59 667 y(v)m(alue)d(is)g(used)g(instead.)59 780 y Fj(STEPTL)p Ff(!)p Fl(:)31 b(A)22 b(p)q(ositiv)o(e)g(scalar)f (pro)o(viding)h(the)f(minim)o(um)h(allo)o(w)o(able)g(relativ)o(e)g (step)f(length.)39 b Fj(STEPTL)59 836 y Fl(should)16 b(b)q(e)f(at)g(least)g(as)f(small)i(as)e(10)701 820 y Fm(\000)p Fd(d)748 836 y Fl(,)h(where)g Fi(d)f Fl(is)i(the)e(n)o(um)o (b)q(er)i(of)e(accurate)h(digits)g(the)g(user)g(desires)h(in)59 892 y(the)f(solution)h Fi(x)335 899 y Fm(\003)355 892 y Fl(.)k(The)15 b(actual)h(test)e(used)i(is)617 1015 y(max)654 1044 y Fd(i)709 943 y Fc(\()817 987 y Ff(j)p Fi(x)856 994 y Fd(i)870 970 y(k)902 987 y Ff(\000)10 b Fi(x)973 994 y Fd(i)987 970 y(k)q Fm(\000)p Fq(1)1054 987 y Ff(j)p 769 1007 347 2 v 769 1049 a Fl(max)o Ff(fj)p Fi(x)915 1056 y Fd(i)929 1035 y(k)950 1049 y Fi(;)e Fj(TYPX)1066 1056 y Fd(i)1080 1049 y Ff(jg)1141 943 y Fc(\))1187 1015 y Ff(\024)13 b Fj(STEPTL)o Fi(;)59 1147 y Fl(where)21 b Fi(x)222 1131 y Fd(k)264 1147 y Fl(and)f Fi(x)383 1131 y Fd(k)q Fm(\000)p Fq(1)470 1147 y Fl(are)g(the)h(new)f(and)h(old)g (iterates,)g(resp)q(ectiv)o(ely)l(.)38 b(The)21 b(program)e(ma)o(y)h (terminate)59 1204 y(prematurely)c(if)h Fj(STEPTL)e Fl(is)i(to)q(o)e (large.)23 b(Mo)q(dule)17 b Fj(STDFLT)e Fl(returns)h(the)g(v)m(alue)h Fi(\017)1474 1187 y Fq(2)p Fd(=)p Fq(3)1530 1204 y Fl(.)22 b(If)17 b(the)f(user)g(sp)q(eci\014es)59 1260 y(a)f(negativ)o(e)g(v)m (alue,)h(then)g(the)f(default)h(v)m(alue)g(is)g(used)g(instead.)59 1373 y Fj(ILIM)p Ff(!)p Fl(:)29 b(P)o(ositiv)o(e)20 b(in)o(teger)g(sp)q (ecifying)i(the)e(maxim)o(um)f(iterations)h(to)f(b)q(e)i(p)q(erformed)f (b)q(efore)g(the)g(pro-)59 1430 y(gram)d(is)i(terminated.)30 b(Mo)q(dule)19 b Fj(STDFLT)e Fl(returns)h Fj(ILIM)24 b(=)f(500)p Fl(.)29 b(If)19 b(the)f(user)g(sp)q(eci\014es)j Fj(ILIM)c Ff(\024)h Fl(0,)h(the)59 1486 y(default)d(v)m(alue)g(is)g (used)g(instead.)59 1599 y Fj(STEPMX)p Ff(!)p Fl(:)h(A)11 b(p)q(ositiv)o(e)g(scalar)f(pro)o(viding)i(the)e(maxim)o(um)h(allo)o(w) o(able)g(scaled)g(step)g(length)g Ff(jj)p Fi(D)1700 1606 y Fd(x)1721 1599 y Fl(\()p Fi(x)1765 1606 y Fq(+)1794 1599 y Ff(\000)q Fi(x)1856 1606 y Fd(c)1874 1599 y Fl(\))p Ff(jj)1918 1606 y Fq(2)1936 1599 y Fl(,)59 1655 y(where)19 b Fi(D)232 1662 y Fd(x)272 1655 y Fl(=)f Fi(diag)r Fl(\()p Fj(1/TYPX)575 1662 y Fq(1)592 1655 y Fj(,)p Fi(:)8 b(:)g(:)n Fj(,)24 b(1/TYPX)861 1662 y Fd(n)884 1655 y Fl(\).)29 b Fj(STEPMX)18 b Fl(is)h(used)g(to)f(prev)o(en)o(t)g(steps)h(that)f(w)o (ould)h(cause)59 1712 y(the)14 b(optimization)h(problem)f(to)g(o)o(v)o (er\015o)o(w,)e(to)h(prev)o(en)o(t)h(the)g(algorithm)g(from)f(lea)o (ving)i(the)f(area)f(of)h(in)o(terest)59 1768 y(in)19 b(parameter)e(space,)i(or)e(to)h(detect)g(div)o(ergence)h(in)g(the)f (algorithm.)28 b Fj(STEPMX)17 b Fl(should)i(b)q(e)g(c)o(hosen)f(small) 59 1825 y(enough)i(to)f(prev)o(en)o(t)h(these)g(o)q(ccurrences)h(but)e (should)i(b)q(e)g(larger)e(than)h(an)o(y)f(an)o(ticipated)i (\\reasonable")59 1881 y(step.)j(The)17 b(algorithm)f(will)i(halt)f (and)g(pro)o(vide)g(a)f(diagnostic)h(if)g(it)g(attempts)e(to)h(exceed)i Fj(STEPMX)d Fl(on)i(\014v)o(e)59 1938 y(successiv)o(e)f(iterations.)21 b(If)15 b(a)g(nonp)q(ositiv)o(e)h(v)m(alue)h(is)f(sp)q(eci\014ed)h(for) d Fj(STEPMX)p Fl(,)g(the)i(default)g(is)f(used.)21 b(Mo)q(dule)59 1994 y Fj(STDFLT)13 b Fl(returns)h(the)f(v)m(alue)i Fj(STEPMX)e Fl(=)h(max)p Ff(fjj)p Fi(x)930 2001 y Fq(0)949 1994 y Ff(jj)975 2001 y Fq(2)1001 1994 y Ff(\001)7 b Fl(10)1067 1978 y Fq(3)1086 1994 y Fi(;)h Fl(10)1153 1978 y Fq(3)1171 1994 y Ff(g)p Fl(,)13 b(where)h Fi(x)1376 2001 y Fq(0)1410 1994 y Fl(is)g(the)g(initial)i(appro)o(ximation)59 2051 y(pro)o(vided)g(b)o(y)f(the)g(user.)59 2164 y Fj(IPR)p Ff(!)p Fl(:)22 b(The)16 b(unit)h(on)f(whic)o(h)h(the)f(routine)g (outputs)g(information.)23 b Fj(STDFLT)15 b Fl(returns)h(the)g(v)m (alue)h(6,)f(whic)o(h)59 2220 y(is)g(the)f(standard)g Fj(FORTRAN)f Fl(unit)i(for)f(the)g(prin)o(ter.)59 2333 y Fj(METHOD)p Ff(!)p Fl(:)20 b(An)15 b(in)o(teger)g(\015ag)g (designating)h(whic)o(h)g(metho)q(d)g(to)e(use.)127 2386 y Ff(\017)23 b Fj(METHOD)14 b Fl(=)i(0)e(:)20 b(Use)c(Newton's)e(metho) q(d.)127 2444 y Ff(\017)23 b Fj(METHOD)14 b Fl(=)i(1)e(:)20 b(Use)c(the)f(tensor)g(metho)q(d.)59 2498 y(Mo)q(dule)k Fj(STDFLT)f Fl(returns)g(v)m(alue)i(1.)29 b(If)19 b(the)g(user)f(sp)q (eci\014es)j(an)d(illegal)j(v)m(alue,)f(mo)q(dule)f Fj(OPTCHK)f Fl(will)i(set)59 2555 y Fj(METHOD)14 b Fl(to)h(1;)f(the)i(program)e (will)j(not)d(ab)q(ort.)59 2667 y Fj(GRDFLG)p Ff(!)p Fl(:)j(In)o(teger)10 b(\015ag)h(designating)g(whether)f(or)g(not)g (analytic)i(Hessian)f(has)f(b)q(een)h(supplied)i(b)o(y)e(the)f(user.) 993 2758 y(5)p eop %%Page: 6 6 6 5 bop 127 199 a Ff(\017)23 b Fj(GRDFLG)14 b Fl(=)i(0)e(:)20 b(No)15 b(analytic)h(gradien)o(t)f(supplied.)127 260 y Ff(\017)23 b Fj(GRDFLG)10 b Fl(=)i(1)f(:)18 b(Analytic)13 b(gradien)o(t)e(supplied)j(\(will)e(b)q(e)h(c)o(hec)o(k)o(ed)e(against) g(\014nite)i(di\013erence)g(gradien)o(t.\))127 320 y Ff(\017)23 b Fj(GRDFLG)d Fl(=)h(2)g(:)31 b(Analytic)22 b(gradien)o(t)f(supplied)i(\(will)g(not)d(b)q(e)i(c)o(hec)o(k)o(ed)f (against)g(\014nite)h(di\013erence)173 376 y(gradien)o(t.\))59 437 y(When)16 b Fj(GRDFLG)e Fl(=)i(0,)f(the)g(gradien)o(t)h(is)g (obtained)g(b)o(y)f(forw)o(ard)f(\014nite)j(di\013erences.)k(When)16 b Fj(GRDFLG)e Fl(=)i(1)f(or)59 493 y(2,)h(the)g(name)h(of)e(the)i(user) f(supplied)j(routine)d(that)g(ev)m(aluates)h Ff(r)p Fi(f)5 b Fl(\()p Fi(x)p Fl(\))16 b(m)o(ust)f(b)q(e)i(supplied)i(in)e Fj(UGR)p Fl(.)e(When)59 549 y Fj(GRDFLG)g Fl(=)g(1,)g(the)h(program)e (compares)i(the)f(v)m(alue)i(of)e(the)g(user's)h(analytic)g(gradien)o (t)f(routine)h(at)f Fi(x)1825 556 y Fq(0)1860 549 y Fl(with)59 606 y(a)h(\014nite)g(di\013erence)h(estimate)f(and)g(ab)q(orts)f(if)h (the)g(relativ)o(e)g(di\013erence)h(b)q(et)o(w)o(een)g(an)o(y)e(t)o(w)o (o)f(comp)q(onen)o(ts)i(is)59 662 y(greater)d(than)g(0.01.)18 b(The)c(mo)q(dule)h Fj(STDFLT)e Fl(returns)g Fj(GRDFLG)g Fl(=)h(0.)19 b(If)14 b(the)f(user)h(sp)q(eci\014es)i(an)d(illegal)j(v)m (alue,)59 719 y(the)f(mo)q(dule)i Fj(OPTCHK)d Fl(supplies)j(the)f(v)m (alue)g(0.)59 832 y Fj(HSNFLG)p Ff(!)p Fl(:)h(In)o(teger)10 b(\015ag)h(designating)g(whether)f(or)g(not)g(analytic)i(Hessian)f(has) f(b)q(een)h(supplied)i(b)o(y)e(the)f(user.)127 892 y Ff(\017)23 b Fj(HSNFLG)14 b Fl(=)i(0)e(:)20 b(No)15 b(analytic)h (Hessian)g(supplied.)127 952 y Ff(\017)23 b Fj(HSNFLG)12 b Fl(=)i(1)f(:)19 b(Analytic)14 b(Hessian)g(supplied)i(\(will)f(b)q(e)f (c)o(hec)o(k)o(ed)g(against)f(\014nite)h(di\013erence)h(Hessian.\))127 1013 y Ff(\017)23 b Fj(HSNFLG)e Fl(=)h(2)f(:)33 b(Analytic)23 b(Hessian)g(supplied)h(\(will)f(not)f(b)q(e)g(c)o(hec)o(k)o(ed)g (against)g(\014nite)h(di\013erence)173 1069 y(Hessian.\))59 1129 y(When)13 b Fj(HSNFLG)e Fl(=)i(0,)g(the)f(Hessian)h(v)m(alues)h (are)e(computed)h(b)o(y)f(forw)o(ard)f(\014nite)j(di\013erences)f (based)g(on)g(gradi-)59 1186 y(en)o(t)g(v)m(alues.)20 b(When)13 b Fj(HSNFLG)f Fl(=)h(1)g(or)f(2,)h(the)g(name)f(of)h(the)g (user{supplied)i(routine)e(that)f(ev)m(aluates)i Ff(r)1841 1169 y Fq(2)1860 1186 y Fi(f)5 b Fl(\()p Fi(x)p Fl(\))59 1242 y(m)o(ust)14 b(b)q(e)i(supplied)h(in)e Fj(USH)p Fl(.)f(When)h Fj(HSNFLG)f Fl(=)h(1,)g(the)f(program)g(compares)g(the)h (v)m(alue)h(of)f(the)g(user's)f(ana-)59 1299 y(lytic)j(Hessian)f (routine)g(at)f Fi(x)567 1306 y Fq(0)603 1299 y Fl(with)g(a)h(\014nite) g(di\013erence)h(estimate)f(and)g(ab)q(orts)f(if)h(the)f(relativ)o(e)i (di\013erence)59 1355 y(b)q(et)o(w)o(een)f(an)o(y)f(t)o(w)o(o)g(comp)q (onen)o(ts)g(is)i(greater)d(than)i(0.01.)k(The)c(mo)q(dule)h Fj(STDFLT)d Fl(returns)i Fj(HSNFLG)f Fl(=)h(0.)21 b(If)59 1412 y(the)15 b(user)h(sp)q(eci\014es)h(an)e(illegal)i(v)m(alue,)f(the) f(mo)q(dule)i Fj(OPTCHK)d Fl(supplies)j(the)f(v)m(alue)g(0.)59 1524 y Fj(NDIGIT)p Ff(!)p Fl(:)31 b(In)o(teger)21 b(estimating)h(the)f (n)o(um)o(b)q(er)g(of)g(accurate)g(digits)h(on)f(the)g(ob)s(jectiv)o(e) g(function)h Fi(f)5 b Fl(\()p Fi(x)p Fl(\).)59 1581 y Fj(STDFLT)12 b Fl(returns)h(the)g(v)m(alue)h(-)p Fj(LOG)648 1588 y Fq(10)685 1581 y Fl(\()p Fi(\017)p Fl(\),)f(where)g Fi(\017)g Fl(is)h(mac)o(hine)f(precision.)21 b(If)13 b Fj(NDIGIT)f Ff(\024)h Fl(0)g(then)g(the)g(default)59 1637 y(v)m(alue)j(is)g(used)g(instead.)59 1750 y Fj(*MSG)p Ff( )-8 b(!)p Fl(:)34 b(An)23 b(in)o(teger)f(v)m(ariable)h(that)f(the)g (user)g(ma)o(y)f(set)h(on)g(input)h(to)f(inhibit)i(certain)e(automatic) 59 1807 y(c)o(hec)o(ks)e(or)g(o)o(v)o(erride)g(certain)g(default)h(c)o (haracteristics)f(of)g(the)g(pac)o(k)m(age.)34 b(Curren)o(tly)l(,)22 b(three)e(\\message")59 1863 y(features)15 b(can)g(b)q(e)h(used)g (individuall)q(y)i(or)d(in)h(com)o(bination.)127 1924 y Ff(\017)23 b Fj(MSG)14 b Fl(=)i(0)f(:)20 b(No)15 b(output)g(will)h(b) q(e)g(pro)q(duced.)127 1984 y Ff(\017)23 b Fj(MSG)14 b Fl(=)i(1)f(:)20 b(Prin)o(t)15 b(the)g(input)h(state,)e(the)i(\014nal) g(results,)f(and)g(the)g(stopping)h(conditions.)127 2044 y Ff(\017)23 b Fj(MSG)11 b Fl(=)h(2)g(:)18 b(Prin)o(t)12 b(the)g(in)o(termediate)h(results,)g(that)e(is,)i(the)f(input)h(state,) e(the)h(v)m(alues)h(of)f(the)g(ob)s(jectiv)o(e)173 2100 y(function)23 b(and)f(the)g(scaled)h(gradien)o(t)f(at)g(eac)o(h)g (iteration,)i(and)e(the)g(\014nal)h(results)g(including)i(the)173 2157 y(stopping)15 b(conditions)i(and)e(the)g(n)o(um)o(b)q(er)h(of)f (function,)g(gradien)o(t,)g(and)h(Hessian)f(ev)m(aluations.)59 2221 y(The)h(mo)q(dule)g Fj(STDFLT)e Fl(returns)h(a)g(v)m(alue)i(of)d (1.)20 b(On)c(output,)e(if)i(the)f(program)f(has)i(terminated)f(b)q (ecause)h(of)59 2277 y(erroneous)f(input,)h Fj(MSG)f Fl(con)o(tains)g(an)g(error)g(co)q(de)g(indicating)j(the)d(reason:)127 2338 y Ff(\017)23 b Fj(MSG)14 b Fl(=)i(-1)f(:)20 b(Illegal)d(dimension) g Fj(N)p Fl(;)d Fj(N)h Ff(\024)e Fl(0.)20 b(The)15 b(program)f(ab)q (orts.)127 2398 y Ff(\017)23 b Fj(MSG)14 b Fl(=)i(-2)f(:)20 b(Illegal)d(length)f(of)f Fj(LIRN)f Fl(or)h Fj(LICN)p Fl(;)f Fj(LIRN)h Ff(\024)e Fl(0)i(or)f Fj(LICN)h Ff(\024)e Fl(0.)19 b(The)d(program)e(ab)q(orts.)127 2458 y Ff(\017)23 b Fj(MSG)15 b Fl(=)h(-3)f(:)21 b(Illegal)d(length)e(of)g Fj(LIWRK)f Fl(or)g Fj(LWRK)p Fl(;)f Fj(LIWRK)h Fi(<)h Fj(2*LIRN+12*N+2)e Fl(or)i Fj(LWRK)f Fi(<)h Fj(7*N)p Fl(.)f(The)173 2514 y(program)f(ab)q(orts.)127 2575 y Ff(\017)23 b Fj(MSG)14 b Fl(=)i(-4)f(:)20 b(Illegal)d(n)o(um)o(b)q(er)e (of)g(nonzeros)g Fj(NZ)p Fl(;)g Fj(NZ)g Ff(\024)e Fl(0.)19 b(The)d(program)e(ab)q(orts.)993 2758 y(6)p eop %%Page: 7 7 7 6 bop 127 184 a Ff(\017)23 b Fj(MSG)15 b Fl(=)i(-5)f(:)21 b(The)c Fj(K)p Fl(-th)f(elemen)o(t)h(of)e Fj(IRN)h Fl(or)f(the)i Fj(K)p Fl(-th)f(elemen)o(t)g(of)g Fj(ICN)g Fl(is)g(not)g(an)g(in)o (teger)g(b)q(et)o(w)o(een)173 241 y(1)h(and)h Fj(N)p Fl(;)f(\()p Fj(IRN\(K\))23 b Fi(<)h Fj(1)17 b Fl(or)g Fj(IRN\(K\))23 b Fi(>)h Fj(N)p Fl(\))18 b(or)f(\()p Fj(ICN\(K\))22 b Fi(<)j Fj(1)17 b Fl(or)g Fj(ICN\(K\))23 b Fi(>)h Fj(N)p Fl(\).)17 b(The)h(program)173 297 y(ab)q(orts.)127 358 y Ff(\017)23 b Fj(MSG)15 b Fl(=)g(-6)h(:)k(The)c Fj(K)p Fl(-th)f(diagonal)h(elemen)o(t)g(is)g(not)f(in)i(the)e(sparsit)o(y)g (pattern.)20 b(This)c(is)g(c)o(hec)o(k)o(ed)g(only)173 414 y(if)i Fj(HSNFLG)23 b(=)h(0)18 b Fl(b)q(ecause)h(the)f(\014nite)g (di\013erence)i(Hessian)e(appro)o(ximation)g(require)h(that)e(diagonal) 173 470 y(elemen)o(ts)f(b)q(e)f(in)h(the)g(sparsit)o(y)f(pattern.)k (The)c(program)f(ab)q(orts.)127 531 y Ff(\017)23 b Fj(MSG)f Fl(=)g(-7)g(:)34 b(Redundan)o(t)23 b(en)o(tries)g(in)g(sparsit)o(y)f (pattern)g(w)o(as)f(encoun)o(tered.)42 b(When)23 b Fj(HSNFLG)g(=)173 587 y(1)c Fl(or)g Fj(HSNFLG)k(=)h(2)p Fl(,)c(the)g(program)e(ab)q (orts.)32 b(When)20 b Fj(HSNFLG)j(=)h(0)p Fl(,)c(the)g(program)e (eliminates)k(the)173 644 y(redundan)o(t)15 b(en)o(tries)h(and)f(con)o (tin)o(ue)h(the)f(execution)i(\(no)d(error)h(message)g(is)g(rep)q (orted)h(in)g(this)f(case\).)127 704 y Ff(\017)23 b Fj(MSG)13 b Fl(=)h(-8)g(:)19 b(Probable)14 b(co)q(ding)h(error)f(in)g(the)g (user's)g(analytic)g(gradien)o(t)g(routine)h Fj(UGR)p Fl(.)e(Analytic)i(and)173 760 y(\014nite)20 b(di\013erence)h(gradien)o (t)e(do)g(not)g(agree)g(within)i(a)e(tolerance)h(of)f(0.01.)31 b(The)20 b(program)e(ab)q(orts.)173 817 y(\(This)d(c)o(hec)o(k)h(can)f (b)q(e)h(o)o(v)o(erridden)g(b)o(y)f(setting)g Fj(GRDFLG)f Fl(=)i(2.\))127 877 y Ff(\017)23 b Fj(MSG)14 b Fl(=)h(-9)g(:)k (Probable)c(co)q(ding)h(error)e(in)i(the)e(user's)h(analytic)g(Hessian) h(routine)f Fj(USH)p Fl(.)f(Analytic)i(and)173 934 y(\014nite)21 b(di\013erence)g(Hessian)g(do)f(not)g(agree)g(within)h(a)f(tolerance)h (of)f(0.01.)33 b(The)21 b(program)e(ab)q(orts.)173 990 y(\(This)c(c)o(hec)o(k)h(can)f(b)q(e)h(o)o(v)o(erridden)g(b)o(y)f (setting)g Fj(HSNFLG)f Fl(=)i(2.\))59 1107 y Fj(*XPLS)p Ff( )p Fl(:)28 b(An)20 b(arra)o(y)e(of)h(length)h Fj(N)f Fl(con)o(taining)h(the)g(b)q(est)f(appro)o(ximation)g(to)g(the)h (minimizer)h Fi(x)1810 1114 y Fm(\003)1849 1107 y Fl(up)q(on)59 1163 y(return.)f(\(If)15 b(the)g(algorithm)g(has)h(not)e(con)o(v)o (erged,)h(the)g(last)g(iterate)g(is)h(returned.\))59 1276 y Fj(*FPLS)p Ff( )p Fl(:)k(A)15 b(scalar)g(v)m(ariable)i(that)d (con)o(tains)h(the)h(function)g(v)m(alue)g(at)f(the)g(\014nal)h (iterate)f Fj(XPLS)p Fl(.)59 1389 y Fj(*GPLS)p Ff( )p Fl(:)20 b(An)15 b(arra)o(y)f(of)h(length)h Fj(N)f Fl(con)o(taining)h (the)f(gradien)o(t)g(v)m(alue)i(at)d Fj(XPLS)p Fl(.)59 1502 y Fj(HESS)p Ff( )-8 b(!)p Fl(:)32 b(An)21 b(arra)o(y)e(that)h(is)h (used)g(to)f(store)g(the)h(Hessian)h(matrix)e(at)g(eac)o(h)h (iteration.)36 b(It)21 b(needs)g(to)59 1558 y(b)q(e)d(at)f(least)g(of)g (dimension)i Fj(LICN)p Fl(.)e(Only)h(the)f(nonzeros)h(in)g(the)f(lo)o (w)o(er)g(or)g(upp)q(er)i(triangular)e(part)g(of)g(the)59 1615 y(Hessian)f(matrix)e(is)h(stored)f(in)i Fj(HESS)p Fl(.)e(On)h(en)o(try)l(,)f(these)h(nonzeros)g(ma)o(y)f(b)q(e)i(giv)o (en)f(in)h(an)o(y)e(order.)19 b(On)d(exit,)59 1671 y Fj(HESS)h Fl(con)o(tains)g(the)g(Hessian)h(matrix)f(at)f(the)i (minimizer)h Fi(x)1128 1678 y Fm(\003)1165 1671 y Fl(with)e(the)g (nonzeros)h(sorted)e(b)o(y)h(columns)h(if)59 1728 y Fj(HSNFLG)c Fl(w)o(as)h(set)g(to)f(0.)59 1841 y Fj(*WRK)p Ff(!)p Fl(:)19 b(An)c(arra)o(y)e(of)h(length)i Fj(LWRK)p Fl(.)d(This)i(is)g (used)g(as)f(w)o(orkspace)g(b)o(y)g(the)h(pac)o(k)m(age.)20 b(Its)14 b(length)h(m)o(ust)f(b)q(e)59 1897 y(at)h(least)g Fj(8*N)g Fl(if)g(the)h Fj(STUMSD)e Fl(in)o(terface)h(is)h(used)g(and)f (at)g(least)g Fj(7*N)g Fl(if)h(the)f Fj(STUMCD)f Fl(in)o(terface)i(is)f (used.)59 2010 y Fj(*LWRK)p Ff(!)p Fl(:)29 b(An)20 b(in)o(teger)g(v)m (ariable.)35 b(It)20 b(m)o(ust)f(b)q(e)i(set)f(b)o(y)f(the)h(user)g(to) f(the)h(length)h(of)e(arra)o(y)g Fj(WRK)g Fl(and)h(is)59 2066 y(not)15 b(altered)h(b)o(y)f(the)g(pac)o(k)m(age.)59 2179 y Fj(*IWRK)p Ff(!)p Fl(:)31 b(An)21 b(in)o(teger)h(arra)o(y)d(of)i (length)g Fj(LIWRK)p Fl(.)f(This)i(is)f(used)h(as)e(w)o(orkspace)h(b)o (y)g(the)g(pac)o(k)m(age.)37 b(Its)59 2236 y(length)16 b(m)o(ust)f(b)q(e)g(at)g(least)g Fj(2*LIRN+12*N+2)p Fl(.)59 2349 y Fj(*LIWRK)p Ff(!)p Fl(:)29 b(An)20 b(in)o(teger)g(v)m(ariable.) 36 b(It)20 b(m)o(ust)f(b)q(e)i(set)f(b)o(y)g(the)g(user)g(to)f(the)h (length)h(of)f(arra)o(y)e Fj(IWRK)i Fl(and)59 2405 y(is)c(not)f (altered)g(b)o(y)g(the)h(pac)o(k)m(age.)59 2518 y Fj(*TERMCD)p Ff( )p Fl(:)j(An)d(in)o(teger)f(that)g(sp)q(eci\014es)i(the)e(reason)g (wh)o(y)g(the)g(algorithm)g(has)g(terminated.)127 2579 y Ff(\017)23 b Fj(TERMCD)14 b Fl(=)i(1)e(:)20 b(The)c(scaled)g(gradien) o(t)f(at)f(the)i(\014nal)g(iterate)f(w)o(as)f(less)i(than)f Fj(GRADTL)p Fl(.)127 2639 y Ff(\017)23 b Fj(TERMCD)14 b Fl(=)i(2)e(:)20 b(The)c(length)g(of)e(the)i(last)f(step)g(w)o(as)f (less)i(than)f Fj(STEPTL)p Fl(.)993 2758 y(7)p eop %%Page: 8 8 8 7 bop 127 199 a Ff(\017)23 b Fj(TERMCD)17 b Fl(=)h(3)f(:)26 b(Last)17 b(global)i(step)f(failed)h(to)e(lo)q(cate)h(a)g(p)q(oin)o(t)g (lo)o(w)o(er)g(than)g Fj(XPLS)p Fl(.)f(It)g(is)i(lik)o(ely)g(that)173 256 y(either)d Fj(XPLS)e Fl(is)i(an)f(appro)o(ximate)g(solution)h(of)f (the)g(function)h(or)f Fj(STEPTL)f Fl(is)i(to)q(o)e(large.)127 316 y Ff(\017)23 b Fj(TERMCD)14 b Fl(=)i(4)e(:)20 b(The)c(iteration)f (limit)i(has)e(b)q(een)h(exceeded.)127 376 y Ff(\017)23 b Fj(TERMCD)14 b 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y(CALL)g(STDFLT\(N,TYPX,FSCALE,GR)o(ADTL,ST)o(EPTL,IL)o(IM,STEPM)o (X,)178 2006 y(*)287 b(IPR,METHOD,GRDFLG,HSNFL)o(G,NDIGI)o(T,INFORM)o (,MSG\))59 2119 y(CD)95 b(GRADTL)23 b(=)h(1.0D-5)59 2175 y(CS)95 b(GRADTL)23 b(=)h(1.0E-3)202 2232 y(GRDFLG)f(=)h(2)59 2345 y(C)48 b(CALL)23 b(THE)g(SPARSE)g(OPTIMIZER.)59 2457 y(CD)95 b(CALL)24 b(STUMCD\(N,X,NZ,IRN,LIRN,)o(ICN,LIC)o(N,DODCF)o (,DODCG,)59 2514 y(CS)95 b(CALL)24 b(STUMCS\(N,X,NZ,IRN,LIRN,)o (ICN,LIC)o(N,DODCF)o(,DODCG,S)o(TDUSH,)178 2570 y(*)287 b(TYPX,FSCALE,GRADTL,STEP)o(TL,ILIM)o(,STEPMX,)o(IPR,)178 2627 y(*)g(METHOD,GRDFLG,HSNFLG,ND)o(IGIT,MS)o(G,XPLS,F)o(PLS,GPL)o(S,) 981 2758 y Fl(16)p eop %%Page: 17 17 17 16 bop 178 199 a Fj(*)287 b(HESS,WRK,LWRK,IWRK,LIWR)o(K,TERMC)o (D,HTV,IN)o(FORM\))202 312 y(STOP)202 369 y(END)209 502 y Fl(Figure)15 b(A.1:)k(Co)q(de)d(to)e(solv)o(e)i(the)f(optimal)h (design)g(with)f(comp)q(osite)h(materials)f(problem)59 616 y(If)g(w)o(e)f(use)h(the)g(double{precision)i(v)o(ersion)e(of)f 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272 a %%BeginDocument: odc_last.eps % MathWorks dictionary /MathWorks 150 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef currentdict end def MathWorks begin 0 cap 0 setlinejoin end MathWorks begin bpage bplot /dpi2point 12 def portraitMode 0216 7344 csm 513 340 6135 4486 MR c np 76 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef /Helvetica /ISOLatin1Encoding 144 FMSR c1 0 0 6914 5184 PR 6 w DO 4 w SO 6 w c0 3224 4612 mt 6256 3792 L 3224 4612 mt 898 3543 L 898 3543 mt 898 1208 L 3224 4612 mt 3296 4645 L 3327 4793 mt (0) s 3730 4475 mt 3801 4508 L 3832 4656 mt (20) s 4235 4339 mt 4306 4371 L 4338 4520 mt (40) s 4740 4202 mt 4812 4235 L 4843 4383 mt (60) s 5245 4065 mt 5317 4098 L 5348 4246 mt (80) s 5751 3928 mt 5822 3961 L 5853 4110 mt (100) s 6256 3792 mt 6327 3824 L 6359 3973 mt (120) s 3224 4612 mt 3149 4633 L 3035 4776 mt (0) s 2449 4256 mt 2373 4276 L 2180 4419 mt (50) s 1673 3899 mt 1598 3920 L 1324 4063 mt (100) s 898 3543 mt 822 3563 L 549 3706 mt (150) s 898 3543 mt 827 3510 L 715 3549 mt (0) s 898 3209 mt 827 3177 L 515 3215 mt (0.05) s 898 2876 mt 827 2843 L 595 2882 mt (0.1) s 898 2542 mt 827 2510 L 515 2548 mt (0.15) s 898 2209 mt 827 2176 L 595 2215 mt (0.2) s 898 1875 mt 827 1843 L 515 1881 mt (0.25) s 898 1542 mt 827 1509 L 595 1548 mt (0.3) s 898 1208 mt 827 1176 L 515 1214 mt (0.35) s gs 898 388 5359 4225 MR c np 16 -110 25 111 -16 29 4210 3048 4 MP gs /c8 { 1.000000 0.375000 0.000000 sr} bdef c8 PP gr c0 DP 16 -29 25 94 -15 2 4184 2981 4 MP gs /c9 { 1.000000 0.562500 0.000000 sr} bdef c9 PP gr c0 DP 15 -94 25 30 -15 67 4225 2981 4 MP gs c9 PP gr c0 DP 15 -67 26 67 -16 29 4200 2952 4 MP gs /c10 { 1.000000 0.656250 0.000000 sr} bdef c10 PP gr c0 DP 15 -2 25 84 -15 -8 4159 2907 4 MP gs /c11 { 1.000000 0.843750 0.000000 sr} bdef c11 PP gr c0 DP 16 -84 25 3 -16 73 4241 2908 4 MP gs c11 PP gr c0 DP 16 -29 25 74 -16 5 4175 2902 4 MP gs c11 PP gr c0 DP 16 -73 25 29 -15 50 4215 2902 4 MP gs c11 PP gr c0 DP 15 -50 25 50 -15 27 4190 2875 4 MP gs /c12 { 1.000000 0.937500 0.000000 sr} bdef c12 PP gr c0 DP 15 8 26 79 -16 -14 4134 2834 4 MP gs /c13 { 0.968750 1.000000 0.000000 sr} bdef c13 PP gr c0 DP 15 -78 25 -8 -15 73 4256 2835 4 MP gs c13 PP gr c0 DP 16 -5 25 73 -15 -10 4149 2844 4 MP gs c13 PP gr c0 DP 15 -73 26 6 -16 57 4231 2845 4 MP gs c13 PP gr c0 DP 15 -27 26 58 -16 8 4165 2836 4 MP gs c13 PP gr c0 DP 16 -57 25 27 -16 39 4206 2836 4 MP gs c13 PP gr c0 DP 16 14 25 78 -16 -19 4109 2761 4 MP gs /c14 { 0.781250 1.000000 0.000000 sr} bdef c14 PP gr c0 DP 16 -78 25 -13 -16 73 4272 2762 4 MP gs c14 PP gr c0 DP 16 -39 25 39 -15 22 4180 2814 4 MP gs /c15 { 0.875000 1.000000 0.000000 sr} bdef c15 PP gr c0 DP 15 10 25 73 -15 -23 4124 2784 4 MP gs c14 PP gr c0 DP 16 -73 25 -10 -15 60 4246 2785 4 MP gs c14 PP gr c0 DP 16 -8 25 60 -16 -7 4140 2791 4 MP gs c14 PP gr c0 DP 15 -60 25 9 -15 45 4221 2791 4 MP gs c14 PP gr c0 DP 15 -22 25 45 -15 7 4155 2784 4 MP gs c14 PP gr c0 DP 15 -45 26 22 -16 29 4196 2785 4 MP gs c14 PP gr c0 DP 16 19 25 85 -15 -26 4083 2683 4 MP gs /c16 { 0.500000 1.000000 0.000000 sr} bdef c16 PP gr c0 DP 15 23 26 78 -16 -42 4099 2725 4 MP gs /c17 { 0.593750 1.000000 0.000000 sr} bdef c17 PP gr c0 DP 15 -85 25 -18 -15 77 4287 2685 4 MP gs c16 PP gr c0 DP 15 -77 26 -23 -16 59 4262 2726 4 MP gs c17 PP gr c0 DP 16 7 25 59 -15 -21 4114 2746 4 MP gs /c18 { 0.687500 1.000000 0.000000 sr} bdef c18 PP gr c0 DP 16 -59 25 -6 -16 44 4237 2747 4 MP gs c18 PP gr c0 DP 16 -29 25 30 -16 15 4171 2769 4 MP gs c18 PP gr c0 DP 15 -7 26 45 -16 -6 4130 2752 4 MP gs c18 PP gr c0 DP 16 -44 25 6 -15 33 4211 2752 4 MP gs c18 PP gr c0 DP 16 -15 25 32 -15 5 4145 2747 4 MP gs c17 PP gr c0 DP 15 -33 25 16 -15 21 4186 2748 4 MP gs c17 PP gr c0 DP 15 21 25 44 -15 -25 4089 2706 4 MP gs c16 PP gr c0 DP 15 -43 25 -21 -15 40 4252 2707 4 MP gs c16 PP gr c0 DP 16 6 25 40 -16 -14 4105 2720 4 MP gs c16 PP gr c0 DP 16 42 25 84 -16 -82 4074 2681 4 MP gs c16 PP gr c0 DP 15 -40 26 -5 -16 31 4227 2721 4 MP gs c16 PP gr c0 DP 16 -84 25 -41 -15 43 4277 2683 4 MP gs c16 PP gr c0 DP 15 -21 26 22 -16 10 4161 2737 4 MP gs c17 PP gr c0 DP 15 -5 25 32 -15 -4 4120 2724 4 MP gs c16 PP gr c0 DP 16 -31 25 4 -16 23 4202 2725 4 MP gs c16 PP gr c0 DP 15 26 25 122 -15 -64 4058 2599 4 MP gs /c19 { 0.218750 1.000000 0.000000 sr} bdef c19 PP gr c0 DP 16 -122 25 -26 -16 84 4303 2601 4 MP gs c19 PP gr c0 DP 15 25 26 38 -16 -30 4064 2673 4 MP gs /c20 { 0.406250 1.000000 0.000000 sr} bdef c20 PP gr c0 DP 16 -10 25 23 -16 2 4136 2722 4 MP gs c16 PP gr c0 DP 16 -23 25 11 -15 14 4176 2723 4 MP gs c16 PP gr c0 DP 16 -38 25 -24 -16 32 4268 2675 4 MP gs c20 PP gr c0 DP 16 14 25 33 -15 -17 4079 2690 4 MP gs c20 PP gr c0 DP 16 -32 25 -14 -15 30 4242 2691 4 MP gs c20 PP gr c0 DP 15 4 26 30 -16 -10 4095 2700 4 MP gs c20 PP gr c0 DP 15 -30 25 -4 -15 24 4217 2701 4 MP gs c20 PP gr c0 DP 16 82 25 86 -15 -130 4048 2643 4 MP gs /c21 { 0.312500 1.000000 0.000000 sr} bdef c21 PP gr c0 DP 15 -14 25 15 -15 7 4151 2715 4 MP gs c16 PP gr c0 DP 15 -86 26 -82 -16 38 4293 2645 4 MP gs c21 PP gr c0 DP 16 -2 25 24 -15 -4 4110 2704 4 MP gs c20 PP gr c0 DP 15 -24 26 2 -16 18 4192 2705 4 MP gs c20 PP gr c0 DP 16 30 25 42 -16 -36 4039 2637 4 MP gs c21 PP gr c0 DP 15 17 25 36 -15 -24 4054 2661 4 MP gs c21 PP gr c0 DP 15 -42 25 -30 -15 37 4283 2638 4 MP gs c21 PP gr c0 DP 15 -37 26 -16 -16 29 4258 2662 4 MP gs c21 PP gr c0 DP 16 10 25 29 -16 -15 4070 2676 4 MP gs c20 PP gr c0 DP 15 -7 26 18 -16 4 4126 2700 4 MP gs c20 PP gr c0 DP 16 -18 25 8 -16 15 4167 2700 4 MP gs c20 PP gr c0 DP 16 -29 25 -10 -16 23 4233 2678 4 MP gs c20 PP gr c0 DP 15 4 25 24 -15 -5 4085 2681 4 MP gs c21 PP gr c0 DP 16 -23 25 -4 -15 23 4207 2682 4 MP gs c21 PP gr c0 DP 15 64 26 133 -16 -111 4033 2513 4 MP gs /c22 { 0.031250 1.000000 0.000000 sr} bdef c22 PP gr c0 DP 15 -132 25 -64 -15 86 4318 2515 4 MP gs c22 PP gr c0 DP 15 24 26 37 -16 -32 4029 2632 4 MP gs c19 PP gr c0 DP 15 130 26 82 -16 -170 4023 2601 4 MP gs c19 PP gr c0 DP 16 -36 25 -24 -15 29 4273 2633 4 MP gs c19 PP gr c0 DP 16 36 25 50 -15 -49 4013 2600 4 MP gs /c23 { 0.125000 1.000000 0.000000 sr} bdef c23 PP gr c0 DP 16 -82 25 -130 -15 42 4308 2603 4 MP gs c19 PP gr c0 DP 16 15 25 29 -15 -14 4044 2646 4 MP gs c19 PP gr c0 DP 16 -15 25 15 -15 77 4141 2623 4 MP gs c19 PP gr c0 DP 15 -29 25 -16 -15 30 4248 2648 4 MP gs c19 PP gr c0 DP 16 -49 25 -35 -16 36 4299 2602 4 MP gs c23 PP gr c0 DP 16 -4 25 23 -16 63 4101 2618 4 MP gs c23 PP gr c0 DP 15 -23 25 5 -15 81 4182 2619 4 MP gs c23 PP gr c0 DP 15 5 26 30 -16 42 4060 2604 4 MP gs c23 PP gr c0 DP 15 -30 26 -4 -16 77 4223 2605 4 MP gs c23 PP gr c0 DP 16 32 25 40 -15 -36 4003 2596 4 MP gs c23 PP gr c0 DP 15 -40 26 -31 -16 35 4289 2598 4 MP gs c23 PP gr c0 DP 15 14 26 36 -16 14 4019 2582 4 MP gs c22 PP gr c0 DP 16 -35 25 -15 -16 64 4264 2584 4 MP gs c22 PP gr c0 DP 15 49 26 62 -16 -71 3988 2560 4 MP gs c22 PP gr c0 DP 15 -62 25 -48 -15 40 4314 2562 4 MP gs c22 PP gr c0 DP 16 170 25 80 -16 -200 3998 2551 4 MP gs c22 PP gr c0 DP 15 -79 26 -170 -16 49 4324 2554 4 MP gs c22 PP gr c0 DP 16 111 25 122 -15 -151 4007 2431 4 MP gs /c24 { 0.000000 1.000000 0.250000 sr} bdef c24 PP gr c0 DP 16 -123 25 -110 -16 82 4334 2433 4 MP gs c24 PP gr c0 DP 15 -77 25 82 -15 173 4116 2445 4 MP gs /c25 { 0.000000 1.000000 0.343750 sr} bdef c25 PP gr c0 DP 15 -81 26 77 -16 177 4157 2446 4 MP gs c25 PP gr c0 DP 16 -63 25 77 -15 149 4075 2455 4 MP gs c25 PP gr c0 DP 16 -77 25 63 -16 163 4198 2456 4 MP gs c25 PP gr c0 DP 15 36 25 45 -15 -26 3978 2541 4 MP gs /c26 { 0.000000 1.000000 0.062500 sr} bdef c26 PP gr c0 DP 16 -44 25 -36 -15 55 4304 2543 4 MP gs c26 PP gr c0 DP 16 -42 25 64 -16 112 4035 2470 4 MP gs c24 PP gr c0 DP 16 -64 25 43 -15 133 4238 2472 4 MP gs c24 PP gr c0 DP 16 71 25 79 -16 -105 3963 2515 4 MP gs c26 PP gr c0 DP 16 -14 25 55 -16 62 3994 2479 4 MP gs c24 PP gr c0 DP 15 -55 25 14 -15 103 4279 2481 4 MP gs c24 PP gr c0 DP 16 -79 25 -70 -16 44 4330 2518 4 MP gs c26 PP gr c0 DP 16 200 25 78 -15 -216 3972 2489 4 MP gs /c27 { 0.000000 1.000000 0.156250 sr} bdef c27 PP gr c0 DP 16 -78 25 -200 -15 62 4339 2492 4 MP gs c27 PP gr c0 DP 15 26 26 58 -16 -3 3953 2460 4 MP gs c24 PP gr c0 DP 15 -58 26 -25 -16 80 4320 2463 4 MP gs c24 PP gr c0 DP 15 151 25 107 -15 -178 3982 2351 4 MP gs /c28 { 0.000000 1.000000 0.437500 sr} bdef c28 PP gr c0 DP 15 -106 25 -151 -15 79 4349 2354 4 MP gs c28 PP gr c0 DP 16 105 25 87 -15 -134 3937 2457 4 MP gs c24 PP gr c0 DP 15 -86 25 -105 -15 58 4345 2460 4 MP gs c24 PP gr c0 DP 16 -112 25 103 -15 138 4009 2341 4 MP gs /c29 { 0.000000 1.000000 0.625000 sr} bdef c29 PP gr c0 DP 15 -103 26 112 -16 130 4254 2342 4 MP gs c29 PP gr c0 DP 16 -62 25 81 -15 94 3968 2366 4 MP gs /c30 { 0.000000 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MP gs c29 PP gr c0 DP 15 -94 25 96 -15 95 3943 2269 4 MP gs /c33 { 0.000000 1.000000 0.906250 sr} bdef c33 PP gr c0 DP 15 -138 26 113 -16 116 3984 2250 4 MP gs c33 PP gr c0 DP 15 -96 25 95 -15 97 4310 2271 4 MP gs c33 PP gr c0 DP 16 -113 25 139 -15 90 4269 2252 4 MP gs c33 PP gr c0 DP 15 -157 26 129 -16 105 4025 2236 4 MP gs c7 PP gr c0 DP 16 -130 25 158 -16 77 4229 2237 4 MP gs c7 PP gr c0 DP 16 179 25 43 -16 -146 3932 2197 4 MP gs c33 PP gr c0 DP 16 -12 25 105 -15 3 3902 2268 4 MP gs c33 PP gr c0 DP 16 -160 25 142 -16 83 4066 2230 4 MP gs c7 PP gr c0 DP 15 -142 26 161 -16 64 4188 2231 4 MP gs c7 PP gr c0 DP 15 -43 25 -179 -15 76 4380 2200 4 MP gs c33 PP gr c0 DP 15 -105 26 12 -16 96 4351 2271 4 MP gs c33 PP gr c0 DP 16 -157 25 150 -15 66 4106 2229 4 MP gs c7 PP gr c0 DP 15 -151 25 158 -15 59 4147 2229 4 MP gs c7 PP gr c0 DP 15 140 26 84 -16 -119 3887 2271 4 MP gs c32 PP gr c0 DP 15 -83 25 -140 -15 105 4376 2274 4 MP gs c32 PP gr c0 DP 16 197 25 58 -16 -168 3897 2236 4 MP gs c33 PP gr 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