/[MITgcm]/MITgcm/lsopt/cubic.F
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Revision 1.2 - (show annotations) (download)
Fri Nov 15 04:03:24 2002 UTC (21 years, 3 months ago) by heimbach
Branch: MAIN
CVS Tags: checkpoint51k_post, checkpoint62v, checkpoint47e_post, checkpoint57m_post, checkpoint52l_pre, checkpoint62u, hrcube4, hrcube5, checkpoint57g_pre, checkpoint47c_post, checkpoint62t, checkpoint50c_post, checkpoint57s_post, checkpoint58b_post, checkpoint57b_post, checkpoint52d_pre, checkpoint57g_post, checkpoint48e_post, checkpoint56b_post, checkpoint50c_pre, checkpoint57y_post, checkpoint52j_pre, checkpoint51o_pre, checkpoint65z, checkpoint65x, checkpoint65y, checkpoint54d_post, checkpoint65r, checkpoint65s, checkpoint65p, checkpoint65q, checkpoint65v, checkpoint65w, checkpoint65t, checkpoint65u, checkpoint65j, checkpoint65k, checkpoint65h, checkpoint65i, checkpoint65n, checkpoint54e_post, checkpoint65l, checkpoint65m, checkpoint65b, checkpoint65c, checkpoint65a, checkpoint65f, checkpoint65g, checkpoint65d, checkpoint65e, checkpoint62c, checkpoint51l_post, checkpoint48i_post, checkpoint57r_post, checkpoint57d_post, checkpoint57i_post, checkpoint50d_pre, checkpoint52k_post, checkpoint59, checkpoint58, checkpoint55, checkpoint54, checkpoint57, checkpoint56, checkpoint51, checkpoint50, checkpoint53, checkpoint52, checkpoint50d_post, checkpoint58f_post, checkpoint52f_post, checkpoint57n_post, checkpoint58d_post, checkpoint62s, checkpoint58a_post, checkpoint62r, checkpoint62q, checkpoint50b_pre, checkpoint62p, checkpoint57z_post, checkpoint54f_post, checkpoint51f_post, checkpoint62a, checkpoint62g, checkpoint62f, checkpoint62e, checkpoint62d, checkpoint62k, checkpoint62j, checkpoint62i, checkpoint62h, checkpoint62o, checkpoint62n, checkpoint62m, checkpoint62l, checkpoint62w, checkpoint62z, checkpoint62y, checkpoint62x, checkpoint58y_post, checkpoint48b_post, checkpoint51d_post, checkpoint48c_pre, checkpoint47d_pre, checkpoint51t_post, checkpoint58t_post, checkpoint51n_post, checkpoint55i_post, checkpoint58m_post, checkpoint57l_post, checkpoint52i_pre, hrcube_1, hrcube_2, hrcube_3, checkpoint51s_post, checkpoint47a_post, checkpoint57t_post, checkpoint55c_post, checkpoint48d_pre, checkpoint51j_post, checkpoint47i_post, checkpoint63g, checkpoint52e_pre, checkpoint57v_post, checkpoint57f_post, checkpoint52e_post, checkpoint51n_pre, checkpoint47d_post, checkpoint53d_post, checkpoint64, checkpoint65, checkpoint60, checkpoint61, checkpoint62, checkpoint63, checkpoint57a_post, checkpoint48d_post, checkpoint57h_pre, checkpoint66g, checkpoint66f, checkpoint66e, checkpoint66d, checkpoint66c, checkpoint66b, checkpoint66a, checkpoint66o, checkpoint66n, checkpoint66m, checkpoint66l, checkpoint66k, checkpoint66j, checkpoint66i, checkpoint66h, checkpoint48f_post, checkpoint52b_pre, checkpoint54b_post, checkpoint58w_post, checkpoint57h_post, checkpoint51l_pre, checkpoint52m_post, checkpoint57y_pre, checkpoint55g_post, checkpoint48h_post, checkpoint51q_post, checkpoint51b_pre, checkpoint47g_post, checkpoint52b_post, checkpoint52c_post, checkpoint51h_pre, checkpoint58o_post, checkpoint48a_post, checkpoint57c_post, checkpoint50f_post, checkpoint50a_post, checkpoint50f_pre, checkpoint58p_post, checkpoint58q_post, checkpoint52f_pre, checkpoint55d_post, checkpoint58e_post, checkpoint47j_post, checkpoint54a_pre, checkpoint63p, checkpoint63q, checkpoint63r, checkpoint63s, checkpoint63l, checkpoint63m, checkpoint63n, checkpoint63o, checkpoint63h, checkpoint63i, checkpoint63j, checkpoint63k, checkpoint63d, checkpoint63e, checkpoint63f, checkpoint53c_post, checkpoint63a, checkpoint63b, checkpoint63c, checkpoint55d_pre, checkpoint57c_pre, checkpoint58r_post, checkpoint55j_post, branch-exfmods-tag, branchpoint-genmake2, checkpoint54a_post, checkpoint55h_post, checkpoint58n_post, checkpoint51r_post, checkpoint48c_post, checkpoint51i_post, checkpoint57e_post, checkpoint55b_post, checkpoint51b_post, checkpoint51c_post, checkpoint53a_post, checkpoint65o, checkpoint47b_post, checkpoint59q, checkpoint59p, checkpoint59r, checkpoint59e, checkpoint59d, checkpoint59g, checkpoint59f, checkpoint59a, checkpoint55f_post, checkpoint59c, checkpoint59b, checkpoint59m, checkpoint59l, checkpoint59o, checkpoint59n, checkpoint59i, checkpoint59h, checkpoint59k, checkpoint52d_post, checkpoint53g_post, checkpoint57p_post, checkpint57u_post, checkpoint50g_post, checkpoint57q_post, eckpoint57e_pre, checkpoint58k_post, checkpoint52a_pre, checkpoint62b, checkpoint58v_post, checkpoint50h_post, checkpoint52i_post, checkpoint50e_pre, checkpoint50i_post, checkpoint51i_pre, checkpoint52h_pre, checkpoint56a_post, checkpoint64y, checkpoint64x, checkpoint58l_post, checkpoint64z, checkpoint53f_post, checkpoint64q, checkpoint64p, checkpoint64s, checkpoint64r, checkpoint64u, checkpoint64t, checkpoint64w, checkpoint64v, checkpoint64i, checkpoint64h, checkpoint64k, checkpoint64j, checkpoint64m, checkpoint64l, checkpoint64o, checkpoint64n, checkpoint64a, checkpoint64c, checkpoint64b, checkpoint64e, checkpoint64d, checkpoint64g, checkpoint64f, checkpoint57h_done, checkpoint52j_post, checkpoint47f_post, checkpoint50e_post, checkpoint57j_post, checkpoint57f_pre, checkpoint61f, checkpoint58g_post, branch-netcdf, checkpoint52l_post, checkpoint58x_post, checkpoint61n, checkpoint52n_post, checkpoint53b_pre, checkpoint59j, checkpoint58h_post, checkpoint56c_post, checkpoint58j_post, checkpoint51e_post, checkpoint57a_pre, checkpoint55a_post, checkpoint47, checkpoint48, checkpoint49, checkpoint57o_post, checkpoint51o_post, checkpoint61q, checkpoint57k_post, checkpoint51f_pre, checkpoint48g_post, checkpoint53b_post, checkpoint47h_post, checkpoint52a_post, checkpoint57w_post, checkpoint61e, checkpoint58i_post, checkpoint51g_post, ecco_c52_e35, checkpoint57x_post, checkpoint50b_post, checkpoint58c_post, checkpoint58u_post, checkpoint51m_post, checkpoint53d_pre, checkpoint58s_post, checkpoint55e_post, checkpoint61g, checkpoint61d, checkpoint54c_post, checkpoint61b, checkpoint61c, checkpoint61a, checkpoint51a_post, checkpoint61o, checkpoint61l, checkpoint61m, checkpoint61j, checkpoint61k, checkpoint61h, checkpoint61i, checkpoint61v, checkpoint61w, checkpoint61t, checkpoint61u, checkpoint61r, checkpoint61s, checkpoint61p, checkpoint51p_post, checkpoint61z, checkpoint61x, checkpoint61y, checkpoint51u_post, HEAD
Branch point for: branch-exfmods-curt, branch-genmake2, branch-nonh, tg2-branch, netcdf-sm0, checkpoint51n_branch
Changes since 1.1: +76 -0 lines
o Incorporating QNVS line search routines into MITgcm
  (this is separate code, not compiled with MITgcm,
  and therefore not under pkg)
  - lsopt/
  - optim/

1
2 subroutine cubic( t, f, fp, ta, fa, fpa, tlower, tupper )
3
4 c-----------------------------------------
5 c arguments
6 c-----------------------------------------
7 double precision t, f, fp, ta, fa, fpa, tlower, tupper
8
9 c-----------------------------------------
10 c local variables
11 c-----------------------------------------
12 double precision sign, den, anum
13 double precision z1, b, discri
14
15 c-----------------------------------------
16 c Using f and fp at t and ta,
17 c computes new t by cubic formula
18 c safeguarded inside [tlower,tupper].
19 c-----------------------------------------
20 z1 = dble(fp) + dble(fpa) - 3.d0*dble(fa-f)/dble(ta-t)
21 b = z1 + dble(fp)
22
23 c-----------------------------------------
24 c first compute the discriminant
25 c (without overflow)
26 c-----------------------------------------
27 if (abs(z1).le.1.) then
28 discri = z1*z1-dble(fp)*dble(fpa)
29 if (discri .lt. 0.d0) then
30 if (fp.lt.0.) t = tupper
31 if (fp.ge.0.) t = tlower
32 return
33 else
34 discri = dsqrt(discri)
35 end if
36 else
37 discri = dble(fp)/z1
38 discri = discri*dble(fpa)
39 discri = z1-discri
40 if (z1.ge.0.d0 .and. discri.ge.0.d0) then
41 discri = dsqrt(z1)*dsqrt(discri)
42 else if (z1.le.0.d0 .and. discri.le.0.d0) then
43 discri = dsqrt(-z1)*dsqrt(-discri)
44 else
45 if (fp.lt.0.) t = tupper
46 if (fp.ge.0.) t = tlower
47 return
48 end if
49 end if
50
51 c-----------------------------------------
52 c discriminant nonnegative,
53 c compute solution (without overflow)
54 c-----------------------------------------
55 if (t-ta .lt. 0.0) then
56 discri = -discri
57 end if
58
59 sign = (t-ta)/abs(t-ta)
60 if (sngl(b)*sign .gt. 0.0) then
61 t = t + fp*(ta-t)/sngl(b+discri)
62 else
63 den = sngl(z1+b+dble(fpa))
64 anum = sngl(b-discri)
65 if (abs((t-ta)*anum).lt.(tupper-tlower)*abs(den)) then
66 t = t + anum*(ta-t)/den
67 else
68 t = tupper
69 end if
70 end if
71
72 t = max( t, tlower )
73 t = min( t, tupper )
74
75 return
76 end

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