! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! Hessian File ! ! Generated by KPP-2.2.3 symbolic chemistry Kinetics PreProcessor ! (http://www.cs.vt.edu/~asandu/Software/KPP) ! KPP is distributed under GPL, the general public licence ! (http://www.gnu.org/copyleft/gpl.html) ! (C) 1995-1997, V. Damian & A. Sandu, CGRER, Univ. Iowa ! (C) 1997-2005, A. Sandu, Michigan Tech, Virginia Tech ! With important contributions from: ! M. Damian, Villanova University, USA ! R. Sander, Max-Planck Institute for Chemistry, Mainz, Germany ! ! File : cbm_Hessian.f90 ! Time : Fri Mar 15 14:04:58 2013 ! Working directory : /home/sandu/kpp-2.2.3/examples/Cbm_fortran ! Equation file : cbm.kpp ! Output root filename : cbm ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ MODULE cbm_Hessian USE cbm_Parameters USE cbm_HessianSP IMPLICIT NONE CONTAINS ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! Hessian - function for Hessian (Jac derivative w.r.t. variables) ! Arguments : ! V - Concentrations of variable species (local) ! F - Concentrations of fixed species (local) ! RCT - Rate constants (local) ! HESS - Hessian of Var (i.e. the 3-tensor d Jac / d Var) ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE Hessian ( V, F, RCT, HESS ) ! V - Concentrations of variable species (local) REAL(kind=dp) :: V(NVAR) ! F - Concentrations of fixed species (local) REAL(kind=dp) :: F(NFIX) ! RCT - Rate constants (local) REAL(kind=dp) :: RCT(NREACT) ! HESS - Hessian of Var (i.e. the 3-tensor d Jac / d Var) REAL(kind=dp) :: HESS(NHESS) ! -------------------------------------------------------- ! Note: HESS is represented in coordinate sparse format: ! HESS(m) = d^2 f_i / dv_j dv_k = d Jac_{i,j} / dv_k ! where i = IHESS_I(m), j = IHESS_J(m), k = IHESS_K(m). ! -------------------------------------------------------- ! Note: d^2 f_i / dv_j dv_k = d^2 f_i / dv_k dv_j, ! therefore only the terms d^2 f_i / dv_j dv_k ! with j <= k are computed and stored in HESS. ! -------------------------------------------------------- ! Local variables ! D2A - Second derivatives of equation rates REAL(kind=dp) :: D2A(59) ! Computation of the second derivatives of equation rates ! D2A(1) = d^2 A(3) / dV(25)dV(31) D2A(1) = RCT(3) ! D2A(2) = d^2 A(4) / dV(26)dV(29) D2A(2) = 9.3e-12 ! D2A(3) = d^2 A(5) / dV(26)dV(29) D2A(3) = RCT(5) ! D2A(4) = d^2 A(6) / dV(29)dV(31) D2A(4) = RCT(6) ! D2A(5) = d^2 A(7) / dV(25)dV(26) D2A(5) = RCT(7) ! D2A(6) = d^2 A(12) / dV(25)dV(27) D2A(6) = RCT(12) ! D2A(7) = d^2 A(13) / dV(25)dV(28) D2A(7) = RCT(13) ! D2A(8) = d^2 A(15) / dV(30)dV(31) D2A(8) = RCT(15) ! D2A(9) = d^2 A(16) / dV(26)dV(30) D2A(9) = RCT(16) ! D2A(10) = d^2 A(17) / dV(26)dV(30) D2A(10) = RCT(17) ! D2A(11) = d^2 A(20)/{dV(31)dV(31)} D2A(11) = RCT(20)*2 ! D2A(12) = d^2 A(21) / dV(26)dV(31) D2A(12) = 4.39999e-40*F(1) ! D2A(13) = d^2 A(22) / dV(27)dV(31) D2A(13) = RCT(22) ! D2A(14) = d^2 A(24) / dV(9)dV(27) D2A(14) = 6.6e-12 ! D2A(15) = d^2 A(25)/{dV(9)dV(9)} D2A(15) = 1e-20*2 ! D2A(16) = d^2 A(26) / dV(26)dV(27) D2A(16) = RCT(26) ! D2A(17) = d^2 A(27) / dV(12)dV(27) D2A(17) = RCT(27) ! D2A(18) = d^2 A(28) / dV(28)dV(31) D2A(18) = RCT(28) ! D2A(19) = d^2 A(29) / dV(26)dV(28) D2A(19) = RCT(29) ! D2A(20) = d^2 A(31) / dV(10)dV(27) D2A(20) = RCT(31) ! D2A(21) = d^2 A(32)/{dV(28)dV(28)} D2A(21) = RCT(32)*2 ! D2A(22) = d^2 A(33)/{dV(28)dV(28)} D2A(22) = RCT(33)*2*F(1) ! D2A(23) = d^2 A(35) / dV(2)dV(27) D2A(23) = RCT(35) ! D2A(24) = d^2 A(36) / dV(16)dV(27) D2A(24) = 2.2e-13 ! D2A(25) = d^2 A(37) / dV(21)dV(27) D2A(25) = 1e-11 ! D2A(26) = d^2 A(40) / dV(21)dV(29) D2A(26) = RCT(40) ! D2A(27) = d^2 A(41) / dV(21)dV(30) D2A(27) = 6.3e-16 ! D2A(28) = d^2 A(42) / dV(24)dV(29) D2A(28) = RCT(42) ! D2A(29) = d^2 A(43) / dV(24)dV(27) D2A(29) = RCT(43) ! D2A(30) = d^2 A(44) / dV(24)dV(30) D2A(30) = 2.5e-15 ! D2A(31) = d^2 A(46) / dV(31)dV(32) D2A(31) = RCT(46) ! D2A(32) = d^2 A(47) / dV(26)dV(32) D2A(32) = RCT(47) ! D2A(33) = d^2 A(49)/{dV(32)dV(32)} D2A(33) = 2e-12*2 ! D2A(34) = d^2 A(50) / dV(28)dV(32) D2A(34) = 6.5e-12 ! D2A(35) = d^2 A(52) / dV(20)dV(27) D2A(35) = 8.1e-13 ! D2A(36) = d^2 A(55) / dV(13)dV(26) D2A(36) = 1.5e-11 ! D2A(37) = d^2 A(56) / dV(23)dV(29) D2A(37) = RCT(56) ! D2A(38) = d^2 A(57) / dV(23)dV(27) D2A(38) = RCT(57) ! D2A(39) = d^2 A(58) / dV(23)dV(25) D2A(39) = RCT(58) ! D2A(40) = d^2 A(59) / dV(23)dV(30) D2A(40) = 7.7e-15 ! D2A(41) = d^2 A(60) / dV(17)dV(29) D2A(41) = RCT(60) ! D2A(42) = d^2 A(61) / dV(17)dV(27) D2A(42) = RCT(61) ! D2A(43) = d^2 A(62) / dV(17)dV(25) D2A(43) = RCT(62) ! D2A(44) = d^2 A(63) / dV(5)dV(27) D2A(44) = RCT(63) ! D2A(45) = d^2 A(64) / dV(11)dV(31) D2A(45) = 8.1e-12 ! D2A(46) = d^2 A(66) / dV(14)dV(27) D2A(46) = 4.1e-11 ! D2A(47) = d^2 A(67) / dV(14)dV(30) D2A(47) = 2.2e-11 ! D2A(48) = d^2 A(68) / dV(4)dV(26) D2A(48) = 1.4e-11 ! D2A(49) = d^2 A(69) / dV(7)dV(27) D2A(49) = RCT(69) ! D2A(50) = d^2 A(70) / dV(19)dV(27) D2A(50) = 3e-11 ! D2A(51) = d^2 A(72) / dV(19)dV(25) D2A(51) = RCT(72) ! D2A(52) = d^2 A(73) / dV(15)dV(27) D2A(52) = 1.7e-11 ! D2A(53) = d^2 A(75) / dV(22)dV(29) D2A(53) = 1.8e-11 ! D2A(54) = d^2 A(76) / dV(22)dV(27) D2A(54) = 9.6e-11 ! D2A(55) = d^2 A(77) / dV(22)dV(25) D2A(55) = 1.2e-17 ! D2A(56) = d^2 A(78) / dV(22)dV(30) D2A(56) = 3.2e-13 ! D2A(57) = d^2 A(79) / dV(18)dV(31) D2A(57) = 8.1e-12 ! D2A(58) = d^2 A(80)/{dV(18)dV(18)} D2A(58) = RCT(80)*2 ! D2A(59) = d^2 A(81) / dV(8)dV(31) D2A(59) = 6.8e-13 ! Computation of the Jacobian derivative ! HESS(1) = d^2 Vdot(2)/{dV(2)dV(27)} = d^2 Vdot(2)/{dV(27)dV(2)} HESS(1) = -D2A(23) ! HESS(2) = d^2 Vdot(2)/{dV(28)dV(28)} = d^2 Vdot(2)/{dV(28)dV(28)} HESS(2) = D2A(21)+D2A(22) ! HESS(3) = d^2 Vdot(3)/{dV(26)dV(32)} = d^2 Vdot(3)/{dV(32)dV(26)} HESS(3) = D2A(32) ! HESS(4) = d^2 Vdot(4)/{dV(4)dV(26)} = d^2 Vdot(4)/{dV(26)dV(4)} HESS(4) = -D2A(48) ! HESS(5) = d^2 Vdot(4)/{dV(14)dV(27)} = d^2 Vdot(4)/{dV(27)dV(14)} HESS(5) = 0.4*D2A(46) ! HESS(6) = d^2 Vdot(4)/{dV(14)dV(30)} = d^2 Vdot(4)/{dV(30)dV(14)} HESS(6) = D2A(47) ! HESS(7) = d^2 Vdot(5)/{dV(5)dV(27)} = d^2 Vdot(5)/{dV(27)dV(5)} HESS(7) = -D2A(44) ! HESS(8) = d^2 Vdot(6)/{dV(26)dV(30)} = d^2 Vdot(6)/{dV(30)dV(26)} HESS(8) = D2A(10) ! HESS(9) = d^2 Vdot(7)/{dV(7)dV(27)} = d^2 Vdot(7)/{dV(27)dV(7)} HESS(9) = -D2A(49) ! HESS(10) = d^2 Vdot(8)/{dV(8)dV(31)} = d^2 Vdot(8)/{dV(31)dV(8)} HESS(10) = -D2A(59) ! HESS(11) = d^2 Vdot(8)/{dV(20)dV(27)} = d^2 Vdot(8)/{dV(27)dV(20)} HESS(11) = 0.13*D2A(35) ! HESS(12) = d^2 Vdot(8)/{dV(22)dV(27)} = d^2 Vdot(8)/{dV(27)dV(22)} HESS(12) = 0.13*D2A(54) ! HESS(13) = d^2 Vdot(8)/{dV(22)dV(30)} = d^2 Vdot(8)/{dV(30)dV(22)} HESS(13) = D2A(56) ! HESS(14) = d^2 Vdot(8)/{dV(23)dV(29)} = d^2 Vdot(8)/{dV(29)dV(23)} HESS(14) = 0.02*D2A(37) ! HESS(15) = d^2 Vdot(8)/{dV(23)dV(30)} = d^2 Vdot(8)/{dV(30)dV(23)} HESS(15) = 0.09*D2A(40) ! HESS(16) = d^2 Vdot(9)/{dV(9)dV(9)} = d^2 Vdot(9)/{dV(9)dV(9)} HESS(16) = -2*D2A(15) ! HESS(17) = d^2 Vdot(9)/{dV(9)dV(27)} = d^2 Vdot(9)/{dV(27)dV(9)} HESS(17) = -D2A(14) ! HESS(18) = d^2 Vdot(9)/{dV(26)dV(31)} = d^2 Vdot(9)/{dV(31)dV(26)} HESS(18) = 2*D2A(12) ! HESS(19) = d^2 Vdot(9)/{dV(27)dV(31)} = d^2 Vdot(9)/{dV(31)dV(27)} HESS(19) = D2A(13) ! HESS(20) = d^2 Vdot(10)/{dV(10)dV(27)} = d^2 Vdot(10)/{dV(27)dV(10)} HESS(20) = -D2A(20) ! HESS(21) = d^2 Vdot(10)/{dV(26)dV(28)} = d^2 Vdot(10)/{dV(28)dV(26)} HESS(21) = D2A(19) ! HESS(22) = d^2 Vdot(11)/{dV(5)dV(27)} = d^2 Vdot(11)/{dV(27)dV(5)} HESS(22) = 0.56*D2A(44) ! HESS(23) = d^2 Vdot(11)/{dV(7)dV(27)} = d^2 Vdot(11)/{dV(27)dV(7)} HESS(23) = 0.3*D2A(49) ! HESS(24) = d^2 Vdot(11)/{dV(11)dV(31)} = d^2 Vdot(11)/{dV(31)dV(11)} HESS(24) = -D2A(45) ! HESS(25) = d^2 Vdot(12)/{dV(12)dV(27)} = d^2 Vdot(12)/{dV(27)dV(12)} HESS(25) = -D2A(17) ! HESS(26) = d^2 Vdot(12)/{dV(14)dV(30)} = d^2 Vdot(12)/{dV(30)dV(14)} HESS(26) = D2A(47) ! HESS(27) = d^2 Vdot(12)/{dV(21)dV(30)} = d^2 Vdot(12)/{dV(30)dV(21)} HESS(27) = D2A(27) ! HESS(28) = d^2 Vdot(12)/{dV(24)dV(30)} = d^2 Vdot(12)/{dV(30)dV(24)} HESS(28) = D2A(30) ! HESS(29) = d^2 Vdot(12)/{dV(26)dV(27)} = d^2 Vdot(12)/{dV(27)dV(26)} HESS(29) = D2A(16) ! HESS(30) = d^2 Vdot(13)/{dV(13)dV(26)} = d^2 Vdot(13)/{dV(26)dV(13)} HESS(30) = -D2A(36) ! HESS(31) = d^2 Vdot(13)/{dV(20)dV(27)} = d^2 Vdot(13)/{dV(27)dV(20)} HESS(31) = 0.76*D2A(35) ! HESS(32) = d^2 Vdot(14)/{dV(5)dV(27)} = d^2 Vdot(14)/{dV(27)dV(5)} HESS(32) = 0.36*D2A(44) ! HESS(33) = d^2 Vdot(14)/{dV(7)dV(27)} = d^2 Vdot(14)/{dV(27)dV(7)} HESS(33) = 0.2*D2A(49) ! HESS(34) = d^2 Vdot(14)/{dV(14)dV(27)} = d^2 Vdot(14)/{dV(27)dV(14)} HESS(34) = -D2A(46) ! HESS(35) = d^2 Vdot(14)/{dV(14)dV(30)} = d^2 Vdot(14)/{dV(30)dV(14)} HESS(35) = -D2A(47) ! HESS(36) = d^2 Vdot(15)/{dV(7)dV(27)} = d^2 Vdot(15)/{dV(27)dV(7)} HESS(36) = 0.8*D2A(49) ! HESS(37) = d^2 Vdot(15)/{dV(15)dV(27)} = d^2 Vdot(15)/{dV(27)dV(15)} HESS(37) = -D2A(52) ! HESS(38) = d^2 Vdot(15)/{dV(19)dV(25)} = d^2 Vdot(15)/{dV(25)dV(19)} HESS(38) = 0.2*D2A(51) ! HESS(39) = d^2 Vdot(15)/{dV(22)dV(25)} = d^2 Vdot(15)/{dV(25)dV(22)} HESS(39) = 0.2*D2A(55) ! HESS(40) = d^2 Vdot(15)/{dV(22)dV(27)} = d^2 Vdot(15)/{dV(27)dV(22)} HESS(40) = 0.4*D2A(54) ! HESS(41) = d^2 Vdot(16)/{dV(16)dV(27)} = d^2 Vdot(16)/{dV(27)dV(16)} HESS(41) = -D2A(24) ! HESS(42) = d^2 Vdot(16)/{dV(17)dV(25)} = d^2 Vdot(16)/{dV(25)dV(17)} HESS(42) = 0.42*D2A(43) ! HESS(43) = d^2 Vdot(16)/{dV(17)dV(29)} = d^2 Vdot(16)/{dV(29)dV(17)} HESS(43) = D2A(41) ! HESS(44) = d^2 Vdot(16)/{dV(19)dV(25)} = d^2 Vdot(16)/{dV(25)dV(19)} HESS(44) = 0.69*D2A(51) ! HESS(45) = d^2 Vdot(16)/{dV(19)dV(27)} = d^2 Vdot(16)/{dV(27)dV(19)} HESS(45) = 2*D2A(50) ! HESS(46) = d^2 Vdot(16)/{dV(21)dV(27)} = d^2 Vdot(16)/{dV(27)dV(21)} HESS(46) = D2A(25) ! HESS(47) = d^2 Vdot(16)/{dV(21)dV(29)} = d^2 Vdot(16)/{dV(29)dV(21)} HESS(47) = D2A(26) ! HESS(48) = d^2 Vdot(16)/{dV(21)dV(30)} = d^2 Vdot(16)/{dV(30)dV(21)} HESS(48) = D2A(27) ! HESS(49) = d^2 Vdot(16)/{dV(22)dV(25)} = d^2 Vdot(16)/{dV(25)dV(22)} HESS(49) = 0.06*D2A(55) ! HESS(50) = d^2 Vdot(16)/{dV(22)dV(29)} = d^2 Vdot(16)/{dV(29)dV(22)} HESS(50) = 0.5*D2A(53) ! HESS(51) = d^2 Vdot(16)/{dV(23)dV(25)} = d^2 Vdot(16)/{dV(25)dV(23)} HESS(51) = 0.33*D2A(39) ! HESS(52) = d^2 Vdot(16)/{dV(23)dV(29)} = d^2 Vdot(16)/{dV(29)dV(23)} HESS(52) = 0.3*D2A(37) ! HESS(53) = d^2 Vdot(17)/{dV(17)dV(25)} = d^2 Vdot(17)/{dV(25)dV(17)} HESS(53) = -D2A(43) ! HESS(54) = d^2 Vdot(17)/{dV(17)dV(27)} = d^2 Vdot(17)/{dV(27)dV(17)} HESS(54) = -D2A(42) ! HESS(55) = d^2 Vdot(17)/{dV(17)dV(29)} = d^2 Vdot(17)/{dV(29)dV(17)} HESS(55) = -D2A(41) ! HESS(56) = d^2 Vdot(17)/{dV(22)dV(25)} = d^2 Vdot(17)/{dV(25)dV(22)} HESS(56) = 0.55*D2A(55) ! HESS(57) = d^2 Vdot(17)/{dV(22)dV(27)} = d^2 Vdot(17)/{dV(27)dV(22)} HESS(57) = D2A(54) ! HESS(58) = d^2 Vdot(17)/{dV(22)dV(29)} = d^2 Vdot(17)/{dV(29)dV(22)} HESS(58) = 0.45*D2A(53) ! HESS(59) = d^2 Vdot(18)/{dV(5)dV(27)} = d^2 Vdot(18)/{dV(27)dV(5)} HESS(59) = 0.08*D2A(44) ! HESS(60) = d^2 Vdot(18)/{dV(7)dV(27)} = d^2 Vdot(18)/{dV(27)dV(7)} HESS(60) = 0.5*D2A(49) ! HESS(61) = d^2 Vdot(18)/{dV(14)dV(27)} = d^2 Vdot(18)/{dV(27)dV(14)} HESS(61) = 0.6*D2A(46) ! HESS(62) = d^2 Vdot(18)/{dV(15)dV(27)} = d^2 Vdot(18)/{dV(27)dV(15)} HESS(62) = D2A(52) ! HESS(63) = d^2 Vdot(18)/{dV(17)dV(27)} = d^2 Vdot(18)/{dV(27)dV(17)} HESS(63) = D2A(42) ! HESS(64) = d^2 Vdot(18)/{dV(17)dV(29)} = d^2 Vdot(18)/{dV(29)dV(17)} HESS(64) = 0.7*D2A(41) ! HESS(65) = d^2 Vdot(18)/{dV(18)dV(18)} = d^2 Vdot(18)/{dV(18)dV(18)} HESS(65) = -2*D2A(58) ! HESS(66) = d^2 Vdot(18)/{dV(18)dV(31)} = d^2 Vdot(18)/{dV(31)dV(18)} HESS(66) = -D2A(57) ! HESS(67) = d^2 Vdot(18)/{dV(19)dV(25)} = d^2 Vdot(18)/{dV(25)dV(19)} HESS(67) = 0.03*D2A(51) ! HESS(68) = d^2 Vdot(18)/{dV(19)dV(27)} = d^2 Vdot(18)/{dV(27)dV(19)} HESS(68) = D2A(50) ! HESS(69) = d^2 Vdot(18)/{dV(20)dV(27)} = d^2 Vdot(18)/{dV(27)dV(20)} HESS(69) = 0.87*D2A(35) ! HESS(70) = d^2 Vdot(18)/{dV(22)dV(27)} = d^2 Vdot(18)/{dV(27)dV(22)} HESS(70) = D2A(54) ! HESS(71) = d^2 Vdot(18)/{dV(22)dV(29)} = d^2 Vdot(18)/{dV(29)dV(22)} HESS(71) = 0.5*D2A(53) ! HESS(72) = d^2 Vdot(18)/{dV(23)dV(25)} = d^2 Vdot(18)/{dV(25)dV(23)} HESS(72) = 0.22*D2A(39) ! HESS(73) = d^2 Vdot(18)/{dV(23)dV(27)} = d^2 Vdot(18)/{dV(27)dV(23)} HESS(73) = D2A(38) ! HESS(74) = d^2 Vdot(18)/{dV(23)dV(29)} = d^2 Vdot(18)/{dV(29)dV(23)} HESS(74) = 0.28*D2A(37) ! HESS(75) = d^2 Vdot(18)/{dV(23)dV(30)} = d^2 Vdot(18)/{dV(30)dV(23)} HESS(75) = 0.91*D2A(40) ! HESS(76) = d^2 Vdot(18)/{dV(28)dV(32)} = d^2 Vdot(18)/{dV(32)dV(28)} HESS(76) = 0.79*D2A(34) ! HESS(77) = d^2 Vdot(18)/{dV(31)dV(32)} = d^2 Vdot(18)/{dV(32)dV(31)} HESS(77) = D2A(31) ! HESS(78) = d^2 Vdot(18)/{dV(32)dV(32)} = d^2 Vdot(18)/{dV(32)dV(32)} HESS(78) = 2*D2A(33) ! HESS(79) = d^2 Vdot(19)/{dV(11)dV(31)} = d^2 Vdot(19)/{dV(31)dV(11)} HESS(79) = 0.9*D2A(45) ! HESS(80) = d^2 Vdot(19)/{dV(14)dV(27)} = d^2 Vdot(19)/{dV(27)dV(14)} HESS(80) = 0.3*D2A(46) ! HESS(81) = d^2 Vdot(19)/{dV(19)dV(25)} = d^2 Vdot(19)/{dV(25)dV(19)} HESS(81) = -D2A(51) ! HESS(82) = d^2 Vdot(19)/{dV(19)dV(27)} = d^2 Vdot(19)/{dV(27)dV(19)} HESS(82) = -D2A(50) ! HESS(83) = d^2 Vdot(20)/{dV(7)dV(27)} = d^2 Vdot(20)/{dV(27)dV(7)} HESS(83) = 1.1*D2A(49) ! HESS(84) = d^2 Vdot(20)/{dV(20)dV(27)} = d^2 Vdot(20)/{dV(27)dV(20)} HESS(84) = -1.11*D2A(35) ! HESS(85) = d^2 Vdot(20)/{dV(22)dV(25)} = d^2 Vdot(20)/{dV(25)dV(22)} HESS(85) = 0.1*D2A(55) ! HESS(86) = d^2 Vdot(20)/{dV(22)dV(29)} = d^2 Vdot(20)/{dV(29)dV(22)} HESS(86) = 0.9*D2A(53) ! HESS(87) = d^2 Vdot(20)/{dV(23)dV(25)} = d^2 Vdot(20)/{dV(25)dV(23)} HESS(87) = -D2A(39) ! HESS(88) = d^2 Vdot(20)/{dV(23)dV(27)} = d^2 Vdot(20)/{dV(27)dV(23)} HESS(88) = -D2A(38) ! HESS(89) = d^2 Vdot(20)/{dV(23)dV(29)} = d^2 Vdot(20)/{dV(29)dV(23)} HESS(89) = 0.22*D2A(37) ! HESS(90) = d^2 Vdot(20)/{dV(23)dV(30)} = d^2 Vdot(20)/{dV(30)dV(23)} HESS(90) = -D2A(40) ! HESS(91) = d^2 Vdot(21)/{dV(17)dV(25)} = d^2 Vdot(21)/{dV(25)dV(17)} HESS(91) = D2A(43) ! HESS(92) = d^2 Vdot(21)/{dV(17)dV(27)} = d^2 Vdot(21)/{dV(27)dV(17)} HESS(92) = 1.56*D2A(42) ! HESS(93) = d^2 Vdot(21)/{dV(17)dV(29)} = d^2 Vdot(21)/{dV(29)dV(17)} HESS(93) = D2A(41) ! HESS(94) = d^2 Vdot(21)/{dV(19)dV(25)} = d^2 Vdot(21)/{dV(25)dV(19)} HESS(94) = 0.7*D2A(51) ! HESS(95) = d^2 Vdot(21)/{dV(19)dV(27)} = d^2 Vdot(21)/{dV(27)dV(19)} HESS(95) = D2A(50) ! HESS(96) = d^2 Vdot(21)/{dV(21)dV(27)} = d^2 Vdot(21)/{dV(27)dV(21)} HESS(96) = -D2A(25) ! HESS(97) = d^2 Vdot(21)/{dV(21)dV(29)} = d^2 Vdot(21)/{dV(29)dV(21)} HESS(97) = -D2A(26) ! HESS(98) = d^2 Vdot(21)/{dV(21)dV(30)} = d^2 Vdot(21)/{dV(30)dV(21)} HESS(98) = -D2A(27) ! HESS(99) = d^2 Vdot(21)/{dV(22)dV(25)} = d^2 Vdot(21)/{dV(25)dV(22)} HESS(99) = D2A(55) ! HESS(100) = d^2 Vdot(21)/{dV(22)dV(27)} = d^2 Vdot(21)/{dV(27)dV(22)} HESS(100) = D2A(54) ! HESS(101) = d^2 Vdot(21)/{dV(23)dV(25)} = d^2 Vdot(21)/{dV(25)dV(23)} HESS(101) = 0.74*D2A(39) ! HESS(102) = d^2 Vdot(21)/{dV(23)dV(27)} = d^2 Vdot(21)/{dV(27)dV(23)} HESS(102) = D2A(38) ! HESS(103) = d^2 Vdot(21)/{dV(23)dV(29)} = d^2 Vdot(21)/{dV(29)dV(23)} HESS(103) = 0.2*D2A(37) ! HESS(104) = d^2 Vdot(21)/{dV(23)dV(30)} = d^2 Vdot(21)/{dV(30)dV(23)} HESS(104) = D2A(40) ! HESS(105) = d^2 Vdot(21)/{dV(28)dV(32)} = d^2 Vdot(21)/{dV(32)dV(28)} HESS(105) = 0.79*D2A(34) ! HESS(106) = d^2 Vdot(21)/{dV(31)dV(32)} = d^2 Vdot(21)/{dV(32)dV(31)} HESS(106) = D2A(31) ! HESS(107) = d^2 Vdot(21)/{dV(32)dV(32)} = d^2 Vdot(21)/{dV(32)dV(32)} HESS(107) = 2*D2A(33) ! HESS(108) = d^2 Vdot(22)/{dV(22)dV(25)} = d^2 Vdot(22)/{dV(25)dV(22)} HESS(108) = -D2A(55) ! HESS(109) = d^2 Vdot(22)/{dV(22)dV(27)} = d^2 Vdot(22)/{dV(27)dV(22)} HESS(109) = -D2A(54) ! HESS(110) = d^2 Vdot(22)/{dV(22)dV(29)} = d^2 Vdot(22)/{dV(29)dV(22)} HESS(110) = -D2A(53) ! HESS(111) = d^2 Vdot(22)/{dV(22)dV(30)} = d^2 Vdot(22)/{dV(30)dV(22)} HESS(111) = -D2A(56) ! HESS(112) = d^2 Vdot(23)/{dV(22)dV(29)} = d^2 Vdot(23)/{dV(29)dV(22)} HESS(112) = 0.55*D2A(53) ! HESS(113) = d^2 Vdot(23)/{dV(23)dV(25)} = d^2 Vdot(23)/{dV(25)dV(23)} HESS(113) = -D2A(39) ! HESS(114) = d^2 Vdot(23)/{dV(23)dV(27)} = d^2 Vdot(23)/{dV(27)dV(23)} HESS(114) = -D2A(38) ! HESS(115) = d^2 Vdot(23)/{dV(23)dV(29)} = d^2 Vdot(23)/{dV(29)dV(23)} HESS(115) = -D2A(37) ! HESS(116) = d^2 Vdot(23)/{dV(23)dV(30)} = d^2 Vdot(23)/{dV(30)dV(23)} HESS(116) = -D2A(40) ! HESS(117) = d^2 Vdot(24)/{dV(17)dV(27)} = d^2 Vdot(24)/{dV(27)dV(17)} HESS(117) = 0.22*D2A(42) ! HESS(118) = d^2 Vdot(24)/{dV(19)dV(25)} = d^2 Vdot(24)/{dV(25)dV(19)} HESS(118) = 0.03*D2A(51) ! HESS(119) = d^2 Vdot(24)/{dV(20)dV(27)} = d^2 Vdot(24)/{dV(27)dV(20)} HESS(119) = 0.11*D2A(35) ! HESS(120) = d^2 Vdot(24)/{dV(22)dV(25)} = d^2 Vdot(24)/{dV(25)dV(22)} HESS(120) = 0.4*D2A(55) ! HESS(121) = d^2 Vdot(24)/{dV(22)dV(27)} = d^2 Vdot(24)/{dV(27)dV(22)} HESS(121) = 0.2*D2A(54) ! HESS(122) = d^2 Vdot(24)/{dV(22)dV(29)} = d^2 Vdot(24)/{dV(29)dV(22)} HESS(122) = 0.8*D2A(53) ! HESS(123) = d^2 Vdot(24)/{dV(23)dV(25)} = d^2 Vdot(24)/{dV(25)dV(23)} HESS(123) = 0.5*D2A(39) ! HESS(124) = d^2 Vdot(24)/{dV(23)dV(27)} = d^2 Vdot(24)/{dV(27)dV(23)} HESS(124) = D2A(38) ! HESS(125) = d^2 Vdot(24)/{dV(23)dV(29)} = d^2 Vdot(24)/{dV(29)dV(23)} HESS(125) = 0.63*D2A(37) ! HESS(126) = d^2 Vdot(24)/{dV(23)dV(30)} = d^2 Vdot(24)/{dV(30)dV(23)} HESS(126) = D2A(40) ! HESS(127) = d^2 Vdot(24)/{dV(24)dV(27)} = d^2 Vdot(24)/{dV(27)dV(24)} HESS(127) = -D2A(29) ! HESS(128) = d^2 Vdot(24)/{dV(24)dV(29)} = d^2 Vdot(24)/{dV(29)dV(24)} HESS(128) = -D2A(28) ! HESS(129) = d^2 Vdot(24)/{dV(24)dV(30)} = d^2 Vdot(24)/{dV(30)dV(24)} HESS(129) = -D2A(30) ! HESS(130) = d^2 Vdot(25)/{dV(17)dV(25)} = d^2 Vdot(25)/{dV(25)dV(17)} HESS(130) = -D2A(43) ! HESS(131) = d^2 Vdot(25)/{dV(19)dV(25)} = d^2 Vdot(25)/{dV(25)dV(19)} HESS(131) = -D2A(51) ! HESS(132) = d^2 Vdot(25)/{dV(22)dV(25)} = d^2 Vdot(25)/{dV(25)dV(22)} HESS(132) = -D2A(55) ! HESS(133) = d^2 Vdot(25)/{dV(23)dV(25)} = d^2 Vdot(25)/{dV(25)dV(23)} HESS(133) = -D2A(39) ! HESS(134) = d^2 Vdot(25)/{dV(25)dV(26)} = d^2 Vdot(25)/{dV(26)dV(25)} HESS(134) = -D2A(5) ! HESS(135) = d^2 Vdot(25)/{dV(25)dV(27)} = d^2 Vdot(25)/{dV(27)dV(25)} HESS(135) = -D2A(6) ! HESS(136) = d^2 Vdot(25)/{dV(25)dV(28)} = d^2 Vdot(25)/{dV(28)dV(25)} HESS(136) = -D2A(7) ! HESS(137) = d^2 Vdot(25)/{dV(25)dV(31)} = d^2 Vdot(25)/{dV(31)dV(25)} HESS(137) = -D2A(1) ! HESS(138) = d^2 Vdot(26)/{dV(4)dV(26)} = d^2 Vdot(26)/{dV(26)dV(4)} HESS(138) = -D2A(48) ! HESS(139) = d^2 Vdot(26)/{dV(9)dV(9)} = d^2 Vdot(26)/{dV(9)dV(9)} HESS(139) = D2A(15) ! HESS(140) = d^2 Vdot(26)/{dV(9)dV(27)} = d^2 Vdot(26)/{dV(27)dV(9)} HESS(140) = D2A(14) ! HESS(141) = d^2 Vdot(26)/{dV(10)dV(27)} = d^2 Vdot(26)/{dV(27)dV(10)} HESS(141) = D2A(20) ! HESS(142) = d^2 Vdot(26)/{dV(11)dV(31)} = d^2 Vdot(26)/{dV(31)dV(11)} HESS(142) = 0.9*D2A(45) ! HESS(143) = d^2 Vdot(26)/{dV(13)dV(26)} = d^2 Vdot(26)/{dV(26)dV(13)} HESS(143) = -D2A(36) ! HESS(144) = d^2 Vdot(26)/{dV(18)dV(31)} = d^2 Vdot(26)/{dV(31)dV(18)} HESS(144) = D2A(57) ! HESS(145) = d^2 Vdot(26)/{dV(23)dV(30)} = d^2 Vdot(26)/{dV(30)dV(23)} HESS(145) = D2A(40) ! HESS(146) = d^2 Vdot(26)/{dV(25)dV(26)} = d^2 Vdot(26)/{dV(26)dV(25)} HESS(146) = -D2A(5) ! HESS(147) = d^2 Vdot(26)/{dV(25)dV(31)} = d^2 Vdot(26)/{dV(31)dV(25)} HESS(147) = D2A(1) ! HESS(148) = d^2 Vdot(26)/{dV(26)dV(27)} = d^2 Vdot(26)/{dV(27)dV(26)} HESS(148) = -D2A(16) ! HESS(149) = d^2 Vdot(26)/{dV(26)dV(28)} = d^2 Vdot(26)/{dV(28)dV(26)} HESS(149) = -D2A(19) ! HESS(150) = d^2 Vdot(26)/{dV(26)dV(29)} = d^2 Vdot(26)/{dV(29)dV(26)} HESS(150) = -D2A(2)-D2A(3) ! HESS(151) = d^2 Vdot(26)/{dV(26)dV(30)} = d^2 Vdot(26)/{dV(30)dV(26)} HESS(151) = -D2A(10) ! HESS(152) = d^2 Vdot(26)/{dV(26)dV(31)} = d^2 Vdot(26)/{dV(31)dV(26)} HESS(152) = -D2A(12) ! HESS(153) = d^2 Vdot(26)/{dV(26)dV(32)} = d^2 Vdot(26)/{dV(32)dV(26)} HESS(153) = -D2A(32) ! HESS(154) = d^2 Vdot(26)/{dV(28)dV(31)} = d^2 Vdot(26)/{dV(31)dV(28)} HESS(154) = D2A(18) ! HESS(155) = d^2 Vdot(26)/{dV(29)dV(31)} = d^2 Vdot(26)/{dV(31)dV(29)} HESS(155) = D2A(4) ! HESS(156) = d^2 Vdot(26)/{dV(30)dV(31)} = d^2 Vdot(26)/{dV(31)dV(30)} HESS(156) = 2*D2A(8) ! HESS(157) = d^2 Vdot(26)/{dV(31)dV(31)} = d^2 Vdot(26)/{dV(31)dV(31)} HESS(157) = 2*D2A(11) ! HESS(158) = d^2 Vdot(26)/{dV(31)dV(32)} = d^2 Vdot(26)/{dV(32)dV(31)} HESS(158) = D2A(31) ! HESS(159) = d^2 Vdot(27)/{dV(2)dV(27)} = d^2 Vdot(27)/{dV(27)dV(2)} HESS(159) = -D2A(23) ! HESS(160) = d^2 Vdot(27)/{dV(5)dV(27)} = d^2 Vdot(27)/{dV(27)dV(5)} HESS(160) = -D2A(44) ! HESS(161) = d^2 Vdot(27)/{dV(7)dV(27)} = d^2 Vdot(27)/{dV(27)dV(7)} HESS(161) = -D2A(49) ! HESS(162) = d^2 Vdot(27)/{dV(9)dV(27)} = d^2 Vdot(27)/{dV(27)dV(9)} HESS(162) = -D2A(14) ! HESS(163) = d^2 Vdot(27)/{dV(10)dV(27)} = d^2 Vdot(27)/{dV(27)dV(10)} HESS(163) = -D2A(20) ! HESS(164) = d^2 Vdot(27)/{dV(12)dV(27)} = d^2 Vdot(27)/{dV(27)dV(12)} HESS(164) = -D2A(17) ! HESS(165) = d^2 Vdot(27)/{dV(14)dV(27)} = d^2 Vdot(27)/{dV(27)dV(14)} HESS(165) = -D2A(46) ! HESS(166) = d^2 Vdot(27)/{dV(15)dV(27)} = d^2 Vdot(27)/{dV(27)dV(15)} HESS(166) = -D2A(52) ! HESS(167) = d^2 Vdot(27)/{dV(16)dV(27)} = d^2 Vdot(27)/{dV(27)dV(16)} HESS(167) = -D2A(24) ! HESS(168) = d^2 Vdot(27)/{dV(17)dV(27)} = d^2 Vdot(27)/{dV(27)dV(17)} HESS(168) = -D2A(42) ! HESS(169) = d^2 Vdot(27)/{dV(17)dV(29)} = d^2 Vdot(27)/{dV(29)dV(17)} HESS(169) = 0.3*D2A(41) ! HESS(170) = d^2 Vdot(27)/{dV(19)dV(25)} = d^2 Vdot(27)/{dV(25)dV(19)} HESS(170) = 0.08*D2A(51) ! HESS(171) = d^2 Vdot(27)/{dV(19)dV(27)} = d^2 Vdot(27)/{dV(27)dV(19)} HESS(171) = -D2A(50) ! HESS(172) = d^2 Vdot(27)/{dV(20)dV(27)} = d^2 Vdot(27)/{dV(27)dV(20)} HESS(172) = -D2A(35) ! HESS(173) = d^2 Vdot(27)/{dV(21)dV(27)} = d^2 Vdot(27)/{dV(27)dV(21)} HESS(173) = -D2A(25) ! HESS(174) = d^2 Vdot(27)/{dV(21)dV(29)} = d^2 Vdot(27)/{dV(29)dV(21)} HESS(174) = D2A(26) ! HESS(175) = d^2 Vdot(27)/{dV(22)dV(25)} = d^2 Vdot(27)/{dV(25)dV(22)} HESS(175) = 0.1*D2A(55) ! HESS(176) = d^2 Vdot(27)/{dV(22)dV(27)} = d^2 Vdot(27)/{dV(27)dV(22)} HESS(176) = -D2A(54) ! HESS(177) = d^2 Vdot(27)/{dV(23)dV(25)} = d^2 Vdot(27)/{dV(25)dV(23)} HESS(177) = 0.1*D2A(39) ! HESS(178) = d^2 Vdot(27)/{dV(23)dV(27)} = d^2 Vdot(27)/{dV(27)dV(23)} HESS(178) = -D2A(38) ! HESS(179) = d^2 Vdot(27)/{dV(23)dV(29)} = d^2 Vdot(27)/{dV(29)dV(23)} HESS(179) = 0.2*D2A(37) ! HESS(180) = d^2 Vdot(27)/{dV(24)dV(27)} = d^2 Vdot(27)/{dV(27)dV(24)} HESS(180) = -D2A(29) ! HESS(181) = d^2 Vdot(27)/{dV(24)dV(29)} = d^2 Vdot(27)/{dV(29)dV(24)} HESS(181) = D2A(28) ! HESS(182) = d^2 Vdot(27)/{dV(25)dV(27)} = d^2 Vdot(27)/{dV(27)dV(25)} HESS(182) = -D2A(6) ! HESS(183) = d^2 Vdot(27)/{dV(25)dV(28)} = d^2 Vdot(27)/{dV(28)dV(25)} HESS(183) = D2A(7) ! HESS(184) = d^2 Vdot(27)/{dV(26)dV(27)} = d^2 Vdot(27)/{dV(27)dV(26)} HESS(184) = -D2A(16) ! HESS(185) = d^2 Vdot(27)/{dV(27)dV(31)} = d^2 Vdot(27)/{dV(31)dV(27)} HESS(185) = -D2A(13) ! HESS(186) = d^2 Vdot(27)/{dV(28)dV(31)} = d^2 Vdot(27)/{dV(31)dV(28)} HESS(186) = D2A(18) ! HESS(187) = d^2 Vdot(27)/{dV(28)dV(32)} = d^2 Vdot(27)/{dV(32)dV(28)} HESS(187) = 0.79*D2A(34) ! HESS(188) = d^2 Vdot(28)/{dV(2)dV(27)} = d^2 Vdot(28)/{dV(27)dV(2)} HESS(188) = D2A(23) ! HESS(189) = d^2 Vdot(28)/{dV(5)dV(27)} = d^2 Vdot(28)/{dV(27)dV(5)} HESS(189) = 0.44*D2A(44) ! HESS(190) = d^2 Vdot(28)/{dV(7)dV(27)} = d^2 Vdot(28)/{dV(27)dV(7)} HESS(190) = 0.7*D2A(49) ! HESS(191) = d^2 Vdot(28)/{dV(11)dV(31)} = d^2 Vdot(28)/{dV(31)dV(11)} HESS(191) = 0.9*D2A(45) ! HESS(192) = d^2 Vdot(28)/{dV(14)dV(27)} = d^2 Vdot(28)/{dV(27)dV(14)} HESS(192) = 0.6*D2A(46) ! HESS(193) = d^2 Vdot(28)/{dV(16)dV(27)} = d^2 Vdot(28)/{dV(27)dV(16)} HESS(193) = D2A(24) ! HESS(194) = d^2 Vdot(28)/{dV(17)dV(25)} = d^2 Vdot(28)/{dV(25)dV(17)} HESS(194) = 0.12*D2A(43) ! HESS(195) = d^2 Vdot(28)/{dV(17)dV(27)} = d^2 Vdot(28)/{dV(27)dV(17)} HESS(195) = D2A(42) ! HESS(196) = d^2 Vdot(28)/{dV(17)dV(29)} = d^2 Vdot(28)/{dV(29)dV(17)} HESS(196) = 1.7*D2A(41) ! HESS(197) = d^2 Vdot(28)/{dV(19)dV(25)} = d^2 Vdot(28)/{dV(25)dV(19)} HESS(197) = 0.76*D2A(51) ! HESS(198) = d^2 Vdot(28)/{dV(19)dV(27)} = d^2 Vdot(28)/{dV(27)dV(19)} HESS(198) = 2*D2A(50) ! HESS(199) = d^2 Vdot(28)/{dV(20)dV(27)} = d^2 Vdot(28)/{dV(27)dV(20)} HESS(199) = 0.11*D2A(35) ! HESS(200) = d^2 Vdot(28)/{dV(21)dV(27)} = d^2 Vdot(28)/{dV(27)dV(21)} HESS(200) = D2A(25) ! HESS(201) = d^2 Vdot(28)/{dV(21)dV(29)} = d^2 Vdot(28)/{dV(29)dV(21)} HESS(201) = D2A(26) ! HESS(202) = d^2 Vdot(28)/{dV(21)dV(30)} = d^2 Vdot(28)/{dV(30)dV(21)} HESS(202) = D2A(27) ! HESS(203) = d^2 Vdot(28)/{dV(22)dV(25)} = d^2 Vdot(28)/{dV(25)dV(22)} HESS(203) = 0.44*D2A(55) ! HESS(204) = d^2 Vdot(28)/{dV(22)dV(27)} = d^2 Vdot(28)/{dV(27)dV(22)} HESS(204) = 0.67*D2A(54) ! HESS(205) = d^2 Vdot(28)/{dV(22)dV(29)} = d^2 Vdot(28)/{dV(29)dV(22)} HESS(205) = 0.6*D2A(53) ! HESS(206) = d^2 Vdot(28)/{dV(23)dV(25)} = d^2 Vdot(28)/{dV(25)dV(23)} HESS(206) = 0.44*D2A(39) ! HESS(207) = d^2 Vdot(28)/{dV(23)dV(27)} = d^2 Vdot(28)/{dV(27)dV(23)} HESS(207) = D2A(38) ! HESS(208) = d^2 Vdot(28)/{dV(23)dV(29)} = d^2 Vdot(28)/{dV(29)dV(23)} HESS(208) = 0.38*D2A(37) ! HESS(209) = d^2 Vdot(28)/{dV(25)dV(27)} = d^2 Vdot(28)/{dV(27)dV(25)} HESS(209) = D2A(6) ! HESS(210) = d^2 Vdot(28)/{dV(25)dV(28)} = d^2 Vdot(28)/{dV(28)dV(25)} HESS(210) = -D2A(7) ! HESS(211) = d^2 Vdot(28)/{dV(26)dV(28)} = d^2 Vdot(28)/{dV(28)dV(26)} HESS(211) = -D2A(19) ! HESS(212) = d^2 Vdot(28)/{dV(28)dV(28)} = d^2 Vdot(28)/{dV(28)dV(28)} HESS(212) = -2*D2A(21)-2*D2A(22) ! HESS(213) = d^2 Vdot(28)/{dV(28)dV(31)} = d^2 Vdot(28)/{dV(31)dV(28)} HESS(213) = -D2A(18) ! HESS(214) = d^2 Vdot(28)/{dV(28)dV(32)} = d^2 Vdot(28)/{dV(32)dV(28)} HESS(214) = -0.21*D2A(34) ! HESS(215) = d^2 Vdot(28)/{dV(31)dV(32)} = d^2 Vdot(28)/{dV(32)dV(31)} HESS(215) = D2A(31) ! HESS(216) = d^2 Vdot(28)/{dV(32)dV(32)} = d^2 Vdot(28)/{dV(32)dV(32)} HESS(216) = 2*D2A(33) ! HESS(217) = d^2 Vdot(29)/{dV(17)dV(29)} = d^2 Vdot(29)/{dV(29)dV(17)} HESS(217) = -D2A(41) ! HESS(218) = d^2 Vdot(29)/{dV(21)dV(29)} = d^2 Vdot(29)/{dV(29)dV(21)} HESS(218) = -D2A(26) ! HESS(219) = d^2 Vdot(29)/{dV(22)dV(29)} = d^2 Vdot(29)/{dV(29)dV(22)} HESS(219) = -D2A(53) ! HESS(220) = d^2 Vdot(29)/{dV(23)dV(29)} = d^2 Vdot(29)/{dV(29)dV(23)} HESS(220) = -D2A(37) ! HESS(221) = d^2 Vdot(29)/{dV(24)dV(29)} = d^2 Vdot(29)/{dV(29)dV(24)} HESS(221) = -D2A(28) ! HESS(222) = d^2 Vdot(29)/{dV(26)dV(29)} = d^2 Vdot(29)/{dV(29)dV(26)} HESS(222) = -D2A(2)-D2A(3) ! HESS(223) = d^2 Vdot(29)/{dV(29)dV(31)} = d^2 Vdot(29)/{dV(31)dV(29)} HESS(223) = -D2A(4) ! HESS(224) = d^2 Vdot(30)/{dV(12)dV(27)} = d^2 Vdot(30)/{dV(27)dV(12)} HESS(224) = D2A(17) ! HESS(225) = d^2 Vdot(30)/{dV(14)dV(30)} = d^2 Vdot(30)/{dV(30)dV(14)} HESS(225) = -D2A(47) ! HESS(226) = d^2 Vdot(30)/{dV(21)dV(30)} = d^2 Vdot(30)/{dV(30)dV(21)} HESS(226) = -D2A(27) ! HESS(227) = d^2 Vdot(30)/{dV(22)dV(30)} = d^2 Vdot(30)/{dV(30)dV(22)} HESS(227) = -D2A(56) ! HESS(228) = d^2 Vdot(30)/{dV(23)dV(30)} = d^2 Vdot(30)/{dV(30)dV(23)} HESS(228) = -D2A(40) ! HESS(229) = d^2 Vdot(30)/{dV(24)dV(30)} = d^2 Vdot(30)/{dV(30)dV(24)} HESS(229) = -D2A(30) ! HESS(230) = d^2 Vdot(30)/{dV(25)dV(26)} = d^2 Vdot(30)/{dV(26)dV(25)} HESS(230) = D2A(5) ! HESS(231) = d^2 Vdot(30)/{dV(26)dV(29)} = d^2 Vdot(30)/{dV(29)dV(26)} HESS(231) = D2A(3) ! HESS(232) = d^2 Vdot(30)/{dV(26)dV(30)} = d^2 Vdot(30)/{dV(30)dV(26)} HESS(232) = -D2A(9)-D2A(10) ! HESS(233) = d^2 Vdot(30)/{dV(30)dV(31)} = d^2 Vdot(30)/{dV(31)dV(30)} HESS(233) = -D2A(8) ! HESS(234) = d^2 Vdot(31)/{dV(8)dV(31)} = d^2 Vdot(31)/{dV(31)dV(8)} HESS(234) = -D2A(59) ! HESS(235) = d^2 Vdot(31)/{dV(9)dV(9)} = d^2 Vdot(31)/{dV(9)dV(9)} HESS(235) = D2A(15) ! HESS(236) = d^2 Vdot(31)/{dV(11)dV(31)} = d^2 Vdot(31)/{dV(31)dV(11)} HESS(236) = -D2A(45) ! HESS(237) = d^2 Vdot(31)/{dV(18)dV(31)} = d^2 Vdot(31)/{dV(31)dV(18)} HESS(237) = -D2A(57) ! HESS(238) = d^2 Vdot(31)/{dV(25)dV(31)} = d^2 Vdot(31)/{dV(31)dV(25)} HESS(238) = -D2A(1) ! HESS(239) = d^2 Vdot(31)/{dV(26)dV(29)} = d^2 Vdot(31)/{dV(29)dV(26)} HESS(239) = D2A(2) ! HESS(240) = d^2 Vdot(31)/{dV(26)dV(30)} = d^2 Vdot(31)/{dV(30)dV(26)} HESS(240) = D2A(9) ! HESS(241) = d^2 Vdot(31)/{dV(26)dV(31)} = d^2 Vdot(31)/{dV(31)dV(26)} HESS(241) = -D2A(12) ! HESS(242) = d^2 Vdot(31)/{dV(27)dV(31)} = d^2 Vdot(31)/{dV(31)dV(27)} HESS(242) = -D2A(13) ! HESS(243) = d^2 Vdot(31)/{dV(28)dV(31)} = d^2 Vdot(31)/{dV(31)dV(28)} HESS(243) = -D2A(18) ! HESS(244) = d^2 Vdot(31)/{dV(29)dV(31)} = d^2 Vdot(31)/{dV(31)dV(29)} HESS(244) = -D2A(4) ! HESS(245) = d^2 Vdot(31)/{dV(30)dV(31)} = d^2 Vdot(31)/{dV(31)dV(30)} HESS(245) = -D2A(8) ! HESS(246) = d^2 Vdot(31)/{dV(31)dV(31)} = d^2 Vdot(31)/{dV(31)dV(31)} HESS(246) = -2*D2A(11) ! HESS(247) = d^2 Vdot(31)/{dV(31)dV(32)} = d^2 Vdot(31)/{dV(32)dV(31)} HESS(247) = -D2A(31) ! HESS(248) = d^2 Vdot(32)/{dV(15)dV(27)} = d^2 Vdot(32)/{dV(27)dV(15)} HESS(248) = D2A(52) ! HESS(249) = d^2 Vdot(32)/{dV(19)dV(25)} = d^2 Vdot(32)/{dV(25)dV(19)} HESS(249) = 0.62*D2A(51) ! HESS(250) = d^2 Vdot(32)/{dV(19)dV(27)} = d^2 Vdot(32)/{dV(27)dV(19)} HESS(250) = D2A(50) ! HESS(251) = d^2 Vdot(32)/{dV(22)dV(27)} = d^2 Vdot(32)/{dV(27)dV(22)} HESS(251) = 0.2*D2A(54) ! HESS(252) = d^2 Vdot(32)/{dV(24)dV(27)} = d^2 Vdot(32)/{dV(27)dV(24)} HESS(252) = D2A(29) ! HESS(253) = d^2 Vdot(32)/{dV(24)dV(29)} = d^2 Vdot(32)/{dV(29)dV(24)} HESS(253) = D2A(28) ! HESS(254) = d^2 Vdot(32)/{dV(24)dV(30)} = d^2 Vdot(32)/{dV(30)dV(24)} HESS(254) = D2A(30) ! HESS(255) = d^2 Vdot(32)/{dV(26)dV(32)} = d^2 Vdot(32)/{dV(32)dV(26)} HESS(255) = -D2A(32) ! HESS(256) = d^2 Vdot(32)/{dV(28)dV(32)} = d^2 Vdot(32)/{dV(32)dV(28)} HESS(256) = -D2A(34) ! HESS(257) = d^2 Vdot(32)/{dV(31)dV(32)} = d^2 Vdot(32)/{dV(32)dV(31)} HESS(257) = -D2A(31) ! HESS(258) = d^2 Vdot(32)/{dV(32)dV(32)} = d^2 Vdot(32)/{dV(32)dV(32)} HESS(258) = -2*D2A(33) END SUBROUTINE Hessian ! End of Hessian function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! HessTR_Vec - Hessian transposed times user vectors ! Arguments : ! HESS - Hessian of Var (i.e. the 3-tensor d Jac / d Var) ! U1 - User vector ! U2 - User vector ! HTU - Transposed Hessian times user vectors: (Hess x U2)^T * U1 = [d (Jac^T*U1)/d Var] * U2 ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE HessTR_Vec ( HESS, U1, U2, HTU ) ! HESS - Hessian of Var (i.e. the 3-tensor d Jac / d Var) REAL(kind=dp) :: HESS(NHESS) ! U1 - User vector REAL(kind=dp) :: U1(NVAR) ! U2 - User vector REAL(kind=dp) :: U2(NVAR) ! HTU - Transposed Hessian times user vectors: (Hess x U2)^T * U1 = [d (Jac^T*U1)/d Var] * U2 REAL(kind=dp) :: HTU(NVAR) ! Compute the vector HTU =(Hess x U2)^T * U1 = d (Jac^T*U1)/d Var * U2 HTU(1) = 0 HTU(2) = HESS(1)*(U1(2)*U2(27))+HESS(159)*(U1(27)*U2(27))+HESS(188)*(U1(28)*U2(27)) HTU(3) = 0 HTU(4) = HESS(4)*(U1(4)*U2(26))+HESS(138)*(U1(26)*U2(26)) HTU(5) = HESS(7)*(U1(5)*U2(27))+HESS(22)*(U1(11)*U2(27))+HESS(32)*(U1(14)*U2(27))+HESS(59)*(U1(18)*U2(27))+HESS(160)& &*(U1(27)*U2(27))+HESS(189)*(U1(28)*U2(27)) HTU(6) = 0 HTU(7) = HESS(9)*(U1(7)*U2(27))+HESS(23)*(U1(11)*U2(27))+HESS(33)*(U1(14)*U2(27))+HESS(36)*(U1(15)*U2(27))+HESS(60)& &*(U1(18)*U2(27))+HESS(83)*(U1(20)*U2(27))+HESS(161)*(U1(27)*U2(27))+HESS(190)*(U1(28)*U2(27)) HTU(8) = HESS(10)*(U1(8)*U2(31))+HESS(234)*(U1(31)*U2(31)) HTU(9) = HESS(16)*(U1(9)*U2(9))+HESS(17)*(U1(9)*U2(27))+HESS(139)*(U1(26)*U2(9))+HESS(140)*(U1(26)*U2(27))+HESS(162)& &*(U1(27)*U2(27))+HESS(235)*(U1(31)*U2(9)) HTU(10) = HESS(20)*(U1(10)*U2(27))+HESS(141)*(U1(26)*U2(27))+HESS(163)*(U1(27)*U2(27)) HTU(11) = HESS(24)*(U1(11)*U2(31))+HESS(79)*(U1(19)*U2(31))+HESS(142)*(U1(26)*U2(31))+HESS(191)*(U1(28)*U2(31))& &+HESS(236)*(U1(31)*U2(31)) HTU(12) = HESS(25)*(U1(12)*U2(27))+HESS(164)*(U1(27)*U2(27))+HESS(224)*(U1(30)*U2(27)) HTU(13) = HESS(30)*(U1(13)*U2(26))+HESS(143)*(U1(26)*U2(26)) HTU(14) = HESS(5)*(U1(4)*U2(27))+HESS(6)*(U1(4)*U2(30))+HESS(26)*(U1(12)*U2(30))+HESS(34)*(U1(14)*U2(27))+HESS(35)& &*(U1(14)*U2(30))+HESS(61)*(U1(18)*U2(27))+HESS(80)*(U1(19)*U2(27))+HESS(165)*(U1(27)*U2(27))+HESS(192)& &*(U1(28)*U2(27))+HESS(225)*(U1(30)*U2(30)) HTU(15) = HESS(37)*(U1(15)*U2(27))+HESS(62)*(U1(18)*U2(27))+HESS(166)*(U1(27)*U2(27))+HESS(248)*(U1(32)*U2(27)) HTU(16) = HESS(41)*(U1(16)*U2(27))+HESS(167)*(U1(27)*U2(27))+HESS(193)*(U1(28)*U2(27)) HTU(17) = HESS(42)*(U1(16)*U2(25))+HESS(43)*(U1(16)*U2(29))+HESS(53)*(U1(17)*U2(25))+HESS(54)*(U1(17)*U2(27))+HESS(55)& &*(U1(17)*U2(29))+HESS(63)*(U1(18)*U2(27))+HESS(64)*(U1(18)*U2(29))+HESS(91)*(U1(21)*U2(25))+HESS(92)*(U1(21)& &*U2(27))+HESS(93)*(U1(21)*U2(29))+HESS(117)*(U1(24)*U2(27))+HESS(130)*(U1(25)*U2(25))+HESS(168)*(U1(27)& &*U2(27))+HESS(169)*(U1(27)*U2(29))+HESS(194)*(U1(28)*U2(25))+HESS(195)*(U1(28)*U2(27))+HESS(196)*(U1(28)& &*U2(29))+HESS(217)*(U1(29)*U2(29)) HTU(18) = HESS(65)*(U1(18)*U2(18))+HESS(66)*(U1(18)*U2(31))+HESS(144)*(U1(26)*U2(31))+HESS(237)*(U1(31)*U2(31)) HTU(19) = HESS(38)*(U1(15)*U2(25))+HESS(44)*(U1(16)*U2(25))+HESS(45)*(U1(16)*U2(27))+HESS(67)*(U1(18)*U2(25))+HESS(68)& &*(U1(18)*U2(27))+HESS(81)*(U1(19)*U2(25))+HESS(82)*(U1(19)*U2(27))+HESS(94)*(U1(21)*U2(25))+HESS(95)*(U1(21)& &*U2(27))+HESS(118)*(U1(24)*U2(25))+HESS(131)*(U1(25)*U2(25))+HESS(170)*(U1(27)*U2(25))+HESS(171)*(U1(27)& &*U2(27))+HESS(197)*(U1(28)*U2(25))+HESS(198)*(U1(28)*U2(27))+HESS(249)*(U1(32)*U2(25))+HESS(250)*(U1(32)& &*U2(27)) HTU(20) = HESS(11)*(U1(8)*U2(27))+HESS(31)*(U1(13)*U2(27))+HESS(69)*(U1(18)*U2(27))+HESS(84)*(U1(20)*U2(27))+HESS(119)& &*(U1(24)*U2(27))+HESS(172)*(U1(27)*U2(27))+HESS(199)*(U1(28)*U2(27)) HTU(21) = HESS(27)*(U1(12)*U2(30))+HESS(46)*(U1(16)*U2(27))+HESS(47)*(U1(16)*U2(29))+HESS(48)*(U1(16)*U2(30))+HESS(96)& &*(U1(21)*U2(27))+HESS(97)*(U1(21)*U2(29))+HESS(98)*(U1(21)*U2(30))+HESS(173)*(U1(27)*U2(27))+HESS(174)& &*(U1(27)*U2(29))+HESS(200)*(U1(28)*U2(27))+HESS(201)*(U1(28)*U2(29))+HESS(202)*(U1(28)*U2(30))+HESS(218)& &*(U1(29)*U2(29))+HESS(226)*(U1(30)*U2(30)) HTU(22) = HESS(12)*(U1(8)*U2(27))+HESS(13)*(U1(8)*U2(30))+HESS(39)*(U1(15)*U2(25))+HESS(40)*(U1(15)*U2(27))+HESS(49)& &*(U1(16)*U2(25))+HESS(50)*(U1(16)*U2(29))+HESS(56)*(U1(17)*U2(25))+HESS(57)*(U1(17)*U2(27))+HESS(58)*(U1(17)& &*U2(29))+HESS(70)*(U1(18)*U2(27))+HESS(71)*(U1(18)*U2(29))+HESS(85)*(U1(20)*U2(25))+HESS(86)*(U1(20)*U2(29))& &+HESS(99)*(U1(21)*U2(25))+HESS(100)*(U1(21)*U2(27))+HESS(108)*(U1(22)*U2(25))+HESS(109)*(U1(22)*U2(27))& &+HESS(110)*(U1(22)*U2(29))+HESS(111)*(U1(22)*U2(30))+HESS(112)*(U1(23)*U2(29))+HESS(120)*(U1(24)*U2(25))& &+HESS(121)*(U1(24)*U2(27))+HESS(122)*(U1(24)*U2(29))+HESS(132)*(U1(25)*U2(25))+HESS(175)*(U1(27)*U2(25))& &+HESS(176)*(U1(27)*U2(27))+HESS(203)*(U1(28)*U2(25))+HESS(204)*(U1(28)*U2(27))+HESS(205)*(U1(28)*U2(29))& &+HESS(219)*(U1(29)*U2(29))+HESS(227)*(U1(30)*U2(30))+HESS(251)*(U1(32)*U2(27)) HTU(23) = HESS(14)*(U1(8)*U2(29))+HESS(15)*(U1(8)*U2(30))+HESS(51)*(U1(16)*U2(25))+HESS(52)*(U1(16)*U2(29))+HESS(72)& &*(U1(18)*U2(25))+HESS(73)*(U1(18)*U2(27))+HESS(74)*(U1(18)*U2(29))+HESS(75)*(U1(18)*U2(30))+HESS(87)*(U1(20)& &*U2(25))+HESS(88)*(U1(20)*U2(27))+HESS(89)*(U1(20)*U2(29))+HESS(90)*(U1(20)*U2(30))+HESS(101)*(U1(21)*U2(25))& &+HESS(102)*(U1(21)*U2(27))+HESS(103)*(U1(21)*U2(29))+HESS(104)*(U1(21)*U2(30))+HESS(113)*(U1(23)*U2(25))& &+HESS(114)*(U1(23)*U2(27))+HESS(115)*(U1(23)*U2(29))+HESS(116)*(U1(23)*U2(30))+HESS(123)*(U1(24)*U2(25))& &+HESS(124)*(U1(24)*U2(27))+HESS(125)*(U1(24)*U2(29))+HESS(126)*(U1(24)*U2(30))+HESS(133)*(U1(25)*U2(25))& &+HESS(145)*(U1(26)*U2(30))+HESS(177)*(U1(27)*U2(25))+HESS(178)*(U1(27)*U2(27))+HESS(179)*(U1(27)*U2(29))& &+HESS(206)*(U1(28)*U2(25))+HESS(207)*(U1(28)*U2(27))+HESS(208)*(U1(28)*U2(29))+HESS(220)*(U1(29)*U2(29))& &+HESS(228)*(U1(30)*U2(30)) HTU(24) = HESS(28)*(U1(12)*U2(30))+HESS(127)*(U1(24)*U2(27))+HESS(128)*(U1(24)*U2(29))+HESS(129)*(U1(24)*U2(30))& &+HESS(180)*(U1(27)*U2(27))+HESS(181)*(U1(27)*U2(29))+HESS(221)*(U1(29)*U2(29))+HESS(229)*(U1(30)*U2(30))& &+HESS(252)*(U1(32)*U2(27))+HESS(253)*(U1(32)*U2(29))+HESS(254)*(U1(32)*U2(30)) HTU(25) = HESS(38)*(U1(15)*U2(19))+HESS(39)*(U1(15)*U2(22))+HESS(42)*(U1(16)*U2(17))+HESS(44)*(U1(16)*U2(19))+HESS(49)& &*(U1(16)*U2(22))+HESS(51)*(U1(16)*U2(23))+HESS(53)*(U1(17)*U2(17))+HESS(56)*(U1(17)*U2(22))+HESS(67)*(U1(18)& &*U2(19))+HESS(72)*(U1(18)*U2(23))+HESS(81)*(U1(19)*U2(19))+HESS(85)*(U1(20)*U2(22))+HESS(87)*(U1(20)*U2(23))& &+HESS(91)*(U1(21)*U2(17))+HESS(94)*(U1(21)*U2(19))+HESS(99)*(U1(21)*U2(22))+HESS(101)*(U1(21)*U2(23))& &+HESS(108)*(U1(22)*U2(22))+HESS(113)*(U1(23)*U2(23))+HESS(118)*(U1(24)*U2(19))+HESS(120)*(U1(24)*U2(22))& &+HESS(123)*(U1(24)*U2(23))+HESS(130)*(U1(25)*U2(17))+HESS(131)*(U1(25)*U2(19))+HESS(132)*(U1(25)*U2(22))& &+HESS(133)*(U1(25)*U2(23))+HESS(134)*(U1(25)*U2(26))+HESS(135)*(U1(25)*U2(27))+HESS(136)*(U1(25)*U2(28))& &+HESS(137)*(U1(25)*U2(31))+HESS(146)*(U1(26)*U2(26))+HESS(147)*(U1(26)*U2(31))+HESS(170)*(U1(27)*U2(19))& &+HESS(175)*(U1(27)*U2(22))+HESS(177)*(U1(27)*U2(23))+HESS(182)*(U1(27)*U2(27))+HESS(183)*(U1(27)*U2(28))& &+HESS(194)*(U1(28)*U2(17))+HESS(197)*(U1(28)*U2(19))+HESS(203)*(U1(28)*U2(22))+HESS(206)*(U1(28)*U2(23))& &+HESS(209)*(U1(28)*U2(27))+HESS(210)*(U1(28)*U2(28))+HESS(230)*(U1(30)*U2(26))+HESS(238)*(U1(31)*U2(31))& &+HESS(249)*(U1(32)*U2(19)) HTU(26) = HESS(3)*(U1(3)*U2(32))+HESS(4)*(U1(4)*U2(4))+HESS(8)*(U1(6)*U2(30))+HESS(18)*(U1(9)*U2(31))+HESS(21)*(U1(10)& &*U2(28))+HESS(29)*(U1(12)*U2(27))+HESS(30)*(U1(13)*U2(13))+HESS(134)*(U1(25)*U2(25))+HESS(138)*(U1(26)*U2(4))& &+HESS(143)*(U1(26)*U2(13))+HESS(146)*(U1(26)*U2(25))+HESS(148)*(U1(26)*U2(27))+HESS(149)*(U1(26)*U2(28))& &+HESS(150)*(U1(26)*U2(29))+HESS(151)*(U1(26)*U2(30))+HESS(152)*(U1(26)*U2(31))+HESS(153)*(U1(26)*U2(32))& &+HESS(184)*(U1(27)*U2(27))+HESS(211)*(U1(28)*U2(28))+HESS(222)*(U1(29)*U2(29))+HESS(230)*(U1(30)*U2(25))& &+HESS(231)*(U1(30)*U2(29))+HESS(232)*(U1(30)*U2(30))+HESS(239)*(U1(31)*U2(29))+HESS(240)*(U1(31)*U2(30))& &+HESS(241)*(U1(31)*U2(31))+HESS(255)*(U1(32)*U2(32)) HTU(27) = HESS(1)*(U1(2)*U2(2))+HESS(5)*(U1(4)*U2(14))+HESS(7)*(U1(5)*U2(5))+HESS(9)*(U1(7)*U2(7))+HESS(11)*(U1(8)& &*U2(20))+HESS(12)*(U1(8)*U2(22))+HESS(17)*(U1(9)*U2(9))+HESS(19)*(U1(9)*U2(31))+HESS(20)*(U1(10)*U2(10))& &+HESS(22)*(U1(11)*U2(5))+HESS(23)*(U1(11)*U2(7))+HESS(25)*(U1(12)*U2(12))+HESS(29)*(U1(12)*U2(26))+HESS(31)& &*(U1(13)*U2(20))+HESS(32)*(U1(14)*U2(5))+HESS(33)*(U1(14)*U2(7))+HESS(34)*(U1(14)*U2(14))+HESS(36)*(U1(15)& &*U2(7))+HESS(37)*(U1(15)*U2(15))+HESS(40)*(U1(15)*U2(22))+HESS(41)*(U1(16)*U2(16))+HESS(45)*(U1(16)*U2(19))& &+HESS(46)*(U1(16)*U2(21))+HESS(54)*(U1(17)*U2(17))+HESS(57)*(U1(17)*U2(22))+HESS(59)*(U1(18)*U2(5))+HESS(60)& &*(U1(18)*U2(7))+HESS(61)*(U1(18)*U2(14))+HESS(62)*(U1(18)*U2(15))+HESS(63)*(U1(18)*U2(17))+HESS(68)*(U1(18)& &*U2(19))+HESS(69)*(U1(18)*U2(20))+HESS(70)*(U1(18)*U2(22))+HESS(73)*(U1(18)*U2(23))+HESS(80)*(U1(19)*U2(14))& &+HESS(82)*(U1(19)*U2(19))+HESS(83)*(U1(20)*U2(7))+HESS(84)*(U1(20)*U2(20))+HESS(88)*(U1(20)*U2(23))+HESS(92)& &*(U1(21)*U2(17))+HESS(95)*(U1(21)*U2(19))+HESS(96)*(U1(21)*U2(21))+HESS(100)*(U1(21)*U2(22))+HESS(102)& &*(U1(21)*U2(23))+HESS(109)*(U1(22)*U2(22))+HESS(114)*(U1(23)*U2(23))+HESS(117)*(U1(24)*U2(17))+HESS(119)& &*(U1(24)*U2(20))+HESS(121)*(U1(24)*U2(22))+HESS(124)*(U1(24)*U2(23))+HESS(127)*(U1(24)*U2(24))+HESS(135)& &*(U1(25)*U2(25))+HESS(140)*(U1(26)*U2(9))+HESS(141)*(U1(26)*U2(10))+HESS(148)*(U1(26)*U2(26))+HESS(159)& &*(U1(27)*U2(2))+HESS(160)*(U1(27)*U2(5))+HESS(161)*(U1(27)*U2(7))+HESS(162)*(U1(27)*U2(9))+HESS(163)*(U1(27)& &*U2(10))+HESS(164)*(U1(27)*U2(12))+HESS(165)*(U1(27)*U2(14))+HESS(166)*(U1(27)*U2(15))+HESS(167)*(U1(27)& &*U2(16))+HESS(168)*(U1(27)*U2(17))+HESS(171)*(U1(27)*U2(19))+HESS(172)*(U1(27)*U2(20))+HESS(173)*(U1(27)& &*U2(21))+HESS(176)*(U1(27)*U2(22))+HESS(178)*(U1(27)*U2(23))+HESS(180)*(U1(27)*U2(24))+HESS(182)*(U1(27)& &*U2(25))+HESS(184)*(U1(27)*U2(26))+HESS(185)*(U1(27)*U2(31))+HESS(188)*(U1(28)*U2(2))+HESS(189)*(U1(28)& &*U2(5))+HESS(190)*(U1(28)*U2(7))+HESS(192)*(U1(28)*U2(14))+HESS(193)*(U1(28)*U2(16))+HESS(195)*(U1(28)& &*U2(17))+HESS(198)*(U1(28)*U2(19))+HESS(199)*(U1(28)*U2(20))+HESS(200)*(U1(28)*U2(21))+HESS(204)*(U1(28)& &*U2(22))+HESS(207)*(U1(28)*U2(23))+HESS(209)*(U1(28)*U2(25))+HESS(224)*(U1(30)*U2(12))+HESS(242)*(U1(31)& &*U2(31))+HESS(248)*(U1(32)*U2(15))+HESS(250)*(U1(32)*U2(19))+HESS(251)*(U1(32)*U2(22))+HESS(252)*(U1(32)& &*U2(24)) HTU(28) = HESS(2)*(U1(2)*U2(28))+HESS(21)*(U1(10)*U2(26))+HESS(76)*(U1(18)*U2(32))+HESS(105)*(U1(21)*U2(32))+HESS(136)& &*(U1(25)*U2(25))+HESS(149)*(U1(26)*U2(26))+HESS(154)*(U1(26)*U2(31))+HESS(183)*(U1(27)*U2(25))+HESS(186)& &*(U1(27)*U2(31))+HESS(187)*(U1(27)*U2(32))+HESS(210)*(U1(28)*U2(25))+HESS(211)*(U1(28)*U2(26))+HESS(212)& &*(U1(28)*U2(28))+HESS(213)*(U1(28)*U2(31))+HESS(214)*(U1(28)*U2(32))+HESS(243)*(U1(31)*U2(31))+HESS(256)& &*(U1(32)*U2(32)) HTU(29) = HESS(14)*(U1(8)*U2(23))+HESS(43)*(U1(16)*U2(17))+HESS(47)*(U1(16)*U2(21))+HESS(50)*(U1(16)*U2(22))+HESS(52)& &*(U1(16)*U2(23))+HESS(55)*(U1(17)*U2(17))+HESS(58)*(U1(17)*U2(22))+HESS(64)*(U1(18)*U2(17))+HESS(71)*(U1(18)& &*U2(22))+HESS(74)*(U1(18)*U2(23))+HESS(86)*(U1(20)*U2(22))+HESS(89)*(U1(20)*U2(23))+HESS(93)*(U1(21)*U2(17))& &+HESS(97)*(U1(21)*U2(21))+HESS(103)*(U1(21)*U2(23))+HESS(110)*(U1(22)*U2(22))+HESS(112)*(U1(23)*U2(22))& &+HESS(115)*(U1(23)*U2(23))+HESS(122)*(U1(24)*U2(22))+HESS(125)*(U1(24)*U2(23))+HESS(128)*(U1(24)*U2(24))& &+HESS(150)*(U1(26)*U2(26))+HESS(155)*(U1(26)*U2(31))+HESS(169)*(U1(27)*U2(17))+HESS(174)*(U1(27)*U2(21))& &+HESS(179)*(U1(27)*U2(23))+HESS(181)*(U1(27)*U2(24))+HESS(196)*(U1(28)*U2(17))+HESS(201)*(U1(28)*U2(21))& &+HESS(205)*(U1(28)*U2(22))+HESS(208)*(U1(28)*U2(23))+HESS(217)*(U1(29)*U2(17))+HESS(218)*(U1(29)*U2(21))& &+HESS(219)*(U1(29)*U2(22))+HESS(220)*(U1(29)*U2(23))+HESS(221)*(U1(29)*U2(24))+HESS(222)*(U1(29)*U2(26))& &+HESS(223)*(U1(29)*U2(31))+HESS(231)*(U1(30)*U2(26))+HESS(239)*(U1(31)*U2(26))+HESS(244)*(U1(31)*U2(31))& &+HESS(253)*(U1(32)*U2(24)) HTU(30) = HESS(6)*(U1(4)*U2(14))+HESS(8)*(U1(6)*U2(26))+HESS(13)*(U1(8)*U2(22))+HESS(15)*(U1(8)*U2(23))+HESS(26)& &*(U1(12)*U2(14))+HESS(27)*(U1(12)*U2(21))+HESS(28)*(U1(12)*U2(24))+HESS(35)*(U1(14)*U2(14))+HESS(48)*(U1(16)& &*U2(21))+HESS(75)*(U1(18)*U2(23))+HESS(90)*(U1(20)*U2(23))+HESS(98)*(U1(21)*U2(21))+HESS(104)*(U1(21)*U2(23))& &+HESS(111)*(U1(22)*U2(22))+HESS(116)*(U1(23)*U2(23))+HESS(126)*(U1(24)*U2(23))+HESS(129)*(U1(24)*U2(24))& &+HESS(145)*(U1(26)*U2(23))+HESS(151)*(U1(26)*U2(26))+HESS(156)*(U1(26)*U2(31))+HESS(202)*(U1(28)*U2(21))& &+HESS(225)*(U1(30)*U2(14))+HESS(226)*(U1(30)*U2(21))+HESS(227)*(U1(30)*U2(22))+HESS(228)*(U1(30)*U2(23))& &+HESS(229)*(U1(30)*U2(24))+HESS(232)*(U1(30)*U2(26))+HESS(233)*(U1(30)*U2(31))+HESS(240)*(U1(31)*U2(26))& &+HESS(245)*(U1(31)*U2(31))+HESS(254)*(U1(32)*U2(24)) HTU(31) = HESS(10)*(U1(8)*U2(8))+HESS(18)*(U1(9)*U2(26))+HESS(19)*(U1(9)*U2(27))+HESS(24)*(U1(11)*U2(11))+HESS(66)& &*(U1(18)*U2(18))+HESS(77)*(U1(18)*U2(32))+HESS(79)*(U1(19)*U2(11))+HESS(106)*(U1(21)*U2(32))+HESS(137)& &*(U1(25)*U2(25))+HESS(142)*(U1(26)*U2(11))+HESS(144)*(U1(26)*U2(18))+HESS(147)*(U1(26)*U2(25))+HESS(152)& &*(U1(26)*U2(26))+HESS(154)*(U1(26)*U2(28))+HESS(155)*(U1(26)*U2(29))+HESS(156)*(U1(26)*U2(30))+HESS(157)& &*(U1(26)*U2(31))+HESS(158)*(U1(26)*U2(32))+HESS(185)*(U1(27)*U2(27))+HESS(186)*(U1(27)*U2(28))+HESS(191)& &*(U1(28)*U2(11))+HESS(213)*(U1(28)*U2(28))+HESS(215)*(U1(28)*U2(32))+HESS(223)*(U1(29)*U2(29))+HESS(233)& &*(U1(30)*U2(30))+HESS(234)*(U1(31)*U2(8))+HESS(236)*(U1(31)*U2(11))+HESS(237)*(U1(31)*U2(18))+HESS(238)& &*(U1(31)*U2(25))+HESS(241)*(U1(31)*U2(26))+HESS(242)*(U1(31)*U2(27))+HESS(243)*(U1(31)*U2(28))+HESS(244)& &*(U1(31)*U2(29))+HESS(245)*(U1(31)*U2(30))+HESS(246)*(U1(31)*U2(31))+HESS(247)*(U1(31)*U2(32))+HESS(257)& &*(U1(32)*U2(32)) HTU(32) = HESS(3)*(U1(3)*U2(26))+HESS(76)*(U1(18)*U2(28))+HESS(77)*(U1(18)*U2(31))+HESS(78)*(U1(18)*U2(32))+HESS(105)& &*(U1(21)*U2(28))+HESS(106)*(U1(21)*U2(31))+HESS(107)*(U1(21)*U2(32))+HESS(153)*(U1(26)*U2(26))+HESS(158)& &*(U1(26)*U2(31))+HESS(187)*(U1(27)*U2(28))+HESS(214)*(U1(28)*U2(28))+HESS(215)*(U1(28)*U2(31))+HESS(216)& &*(U1(28)*U2(32))+HESS(247)*(U1(31)*U2(31))+HESS(255)*(U1(32)*U2(26))+HESS(256)*(U1(32)*U2(28))+HESS(257)& &*(U1(32)*U2(31))+HESS(258)*(U1(32)*U2(32)) END SUBROUTINE HessTR_Vec ! End of HessTR_Vec function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! Hess_Vec - Hessian times user vectors ! Arguments : ! HESS - Hessian of Var (i.e. the 3-tensor d Jac / d Var) ! U1 - User vector ! U2 - User vector ! HU - Hessian times user vectors: (Hess x U2) * U1 = [d (Jac*U1)/d Var] * U2 ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE Hess_Vec ( HESS, U1, U2, HU ) ! HESS - Hessian of Var (i.e. the 3-tensor d Jac / d Var) REAL(kind=dp) :: HESS(NHESS) ! U1 - User vector REAL(kind=dp) :: U1(NVAR) ! U2 - User vector REAL(kind=dp) :: U2(NVAR) ! HU - Hessian times user vectors: (Hess x U2) * U1 = [d (Jac*U1)/d Var] * U2 REAL(kind=dp) :: HU(NVAR) ! Compute the vector HU =(Hess x U2) * U1 = d (Jac*U1)/d Var * U2 HU(1) = 0 HU(2) = HESS(1)*(U1(2)*U2(27))+HESS(1)*(U1(27)*U2(2))+HESS(2)*(U1(28)*U2(28)) HU(3) = HESS(3)*(U1(26)*U2(32))+HESS(3)*(U1(32)*U2(26)) HU(4) = HESS(4)*(U1(4)*U2(26))+HESS(4)*(U1(26)*U2(4))+HESS(5)*(U1(14)*U2(27))+HESS(5)*(U1(27)*U2(14))+HESS(6)*(U1(14)& &*U2(30))+HESS(6)*(U1(30)*U2(14)) HU(5) = HESS(7)*(U1(5)*U2(27))+HESS(7)*(U1(27)*U2(5)) HU(6) = HESS(8)*(U1(26)*U2(30))+HESS(8)*(U1(30)*U2(26)) HU(7) = HESS(9)*(U1(7)*U2(27))+HESS(9)*(U1(27)*U2(7)) HU(8) = HESS(10)*(U1(8)*U2(31))+HESS(10)*(U1(31)*U2(8))+HESS(11)*(U1(20)*U2(27))+HESS(11)*(U1(27)*U2(20))+HESS(12)& &*(U1(22)*U2(27))+HESS(12)*(U1(27)*U2(22))+HESS(13)*(U1(22)*U2(30))+HESS(13)*(U1(30)*U2(22))+HESS(14)*(U1(23)& &*U2(29))+HESS(14)*(U1(29)*U2(23))+HESS(15)*(U1(23)*U2(30))+HESS(15)*(U1(30)*U2(23)) HU(9) = HESS(16)*(U1(9)*U2(9))+HESS(17)*(U1(9)*U2(27))+HESS(17)*(U1(27)*U2(9))+HESS(18)*(U1(26)*U2(31))+HESS(18)& &*(U1(31)*U2(26))+HESS(19)*(U1(27)*U2(31))+HESS(19)*(U1(31)*U2(27)) HU(10) = HESS(20)*(U1(10)*U2(27))+HESS(20)*(U1(27)*U2(10))+HESS(21)*(U1(26)*U2(28))+HESS(21)*(U1(28)*U2(26)) HU(11) = HESS(22)*(U1(5)*U2(27))+HESS(22)*(U1(27)*U2(5))+HESS(23)*(U1(7)*U2(27))+HESS(23)*(U1(27)*U2(7))+HESS(24)& &*(U1(11)*U2(31))+HESS(24)*(U1(31)*U2(11)) HU(12) = HESS(25)*(U1(12)*U2(27))+HESS(25)*(U1(27)*U2(12))+HESS(26)*(U1(14)*U2(30))+HESS(26)*(U1(30)*U2(14))+HESS(27)& &*(U1(21)*U2(30))+HESS(27)*(U1(30)*U2(21))+HESS(28)*(U1(24)*U2(30))+HESS(28)*(U1(30)*U2(24))+HESS(29)*(U1(26)& &*U2(27))+HESS(29)*(U1(27)*U2(26)) HU(13) = HESS(30)*(U1(13)*U2(26))+HESS(30)*(U1(26)*U2(13))+HESS(31)*(U1(20)*U2(27))+HESS(31)*(U1(27)*U2(20)) HU(14) = HESS(32)*(U1(5)*U2(27))+HESS(32)*(U1(27)*U2(5))+HESS(33)*(U1(7)*U2(27))+HESS(33)*(U1(27)*U2(7))+HESS(34)& &*(U1(14)*U2(27))+HESS(34)*(U1(27)*U2(14))+HESS(35)*(U1(14)*U2(30))+HESS(35)*(U1(30)*U2(14)) HU(15) = HESS(36)*(U1(7)*U2(27))+HESS(36)*(U1(27)*U2(7))+HESS(37)*(U1(15)*U2(27))+HESS(37)*(U1(27)*U2(15))+HESS(38)& &*(U1(19)*U2(25))+HESS(38)*(U1(25)*U2(19))+HESS(39)*(U1(22)*U2(25))+HESS(39)*(U1(25)*U2(22))+HESS(40)*(U1(22)& &*U2(27))+HESS(40)*(U1(27)*U2(22)) HU(16) = HESS(41)*(U1(16)*U2(27))+HESS(41)*(U1(27)*U2(16))+HESS(42)*(U1(17)*U2(25))+HESS(42)*(U1(25)*U2(17))+HESS(43)& &*(U1(17)*U2(29))+HESS(43)*(U1(29)*U2(17))+HESS(44)*(U1(19)*U2(25))+HESS(44)*(U1(25)*U2(19))+HESS(45)*(U1(19)& &*U2(27))+HESS(45)*(U1(27)*U2(19))+HESS(46)*(U1(21)*U2(27))+HESS(46)*(U1(27)*U2(21))+HESS(47)*(U1(21)*U2(29))& &+HESS(47)*(U1(29)*U2(21))+HESS(48)*(U1(21)*U2(30))+HESS(48)*(U1(30)*U2(21))+HESS(49)*(U1(22)*U2(25))+HESS(49)& &*(U1(25)*U2(22))+HESS(50)*(U1(22)*U2(29))+HESS(50)*(U1(29)*U2(22))+HESS(51)*(U1(23)*U2(25))+HESS(51)*(U1(25)& &*U2(23))+HESS(52)*(U1(23)*U2(29))+HESS(52)*(U1(29)*U2(23)) HU(17) = HESS(53)*(U1(17)*U2(25))+HESS(53)*(U1(25)*U2(17))+HESS(54)*(U1(17)*U2(27))+HESS(54)*(U1(27)*U2(17))+HESS(55)& &*(U1(17)*U2(29))+HESS(55)*(U1(29)*U2(17))+HESS(56)*(U1(22)*U2(25))+HESS(56)*(U1(25)*U2(22))+HESS(57)*(U1(22)& &*U2(27))+HESS(57)*(U1(27)*U2(22))+HESS(58)*(U1(22)*U2(29))+HESS(58)*(U1(29)*U2(22)) HU(18) = HESS(59)*(U1(5)*U2(27))+HESS(59)*(U1(27)*U2(5))+HESS(60)*(U1(7)*U2(27))+HESS(60)*(U1(27)*U2(7))+HESS(61)& &*(U1(14)*U2(27))+HESS(61)*(U1(27)*U2(14))+HESS(62)*(U1(15)*U2(27))+HESS(62)*(U1(27)*U2(15))+HESS(63)*(U1(17)& &*U2(27))+HESS(63)*(U1(27)*U2(17))+HESS(64)*(U1(17)*U2(29))+HESS(64)*(U1(29)*U2(17))+HESS(65)*(U1(18)*U2(18))& &+HESS(66)*(U1(18)*U2(31))+HESS(66)*(U1(31)*U2(18))+HESS(67)*(U1(19)*U2(25))+HESS(67)*(U1(25)*U2(19))+HESS(68)& &*(U1(19)*U2(27))+HESS(68)*(U1(27)*U2(19))+HESS(69)*(U1(20)*U2(27))+HESS(69)*(U1(27)*U2(20))+HESS(70)*(U1(22)& &*U2(27))+HESS(70)*(U1(27)*U2(22))+HESS(71)*(U1(22)*U2(29))+HESS(71)*(U1(29)*U2(22))+HESS(72)*(U1(23)*U2(25))& &+HESS(72)*(U1(25)*U2(23))+HESS(73)*(U1(23)*U2(27))+HESS(73)*(U1(27)*U2(23))+HESS(74)*(U1(23)*U2(29))+HESS(74)& &*(U1(29)*U2(23))+HESS(75)*(U1(23)*U2(30))+HESS(75)*(U1(30)*U2(23))+HESS(76)*(U1(28)*U2(32))+HESS(76)*(U1(32)& &*U2(28))+HESS(77)*(U1(31)*U2(32))+HESS(77)*(U1(32)*U2(31))+HESS(78)*(U1(32)*U2(32)) HU(19) = HESS(79)*(U1(11)*U2(31))+HESS(79)*(U1(31)*U2(11))+HESS(80)*(U1(14)*U2(27))+HESS(80)*(U1(27)*U2(14))+HESS(81)& &*(U1(19)*U2(25))+HESS(81)*(U1(25)*U2(19))+HESS(82)*(U1(19)*U2(27))+HESS(82)*(U1(27)*U2(19)) HU(20) = HESS(83)*(U1(7)*U2(27))+HESS(83)*(U1(27)*U2(7))+HESS(84)*(U1(20)*U2(27))+HESS(84)*(U1(27)*U2(20))+HESS(85)& &*(U1(22)*U2(25))+HESS(85)*(U1(25)*U2(22))+HESS(86)*(U1(22)*U2(29))+HESS(86)*(U1(29)*U2(22))+HESS(87)*(U1(23)& &*U2(25))+HESS(87)*(U1(25)*U2(23))+HESS(88)*(U1(23)*U2(27))+HESS(88)*(U1(27)*U2(23))+HESS(89)*(U1(23)*U2(29))& &+HESS(89)*(U1(29)*U2(23))+HESS(90)*(U1(23)*U2(30))+HESS(90)*(U1(30)*U2(23)) HU(21) = HESS(91)*(U1(17)*U2(25))+HESS(91)*(U1(25)*U2(17))+HESS(92)*(U1(17)*U2(27))+HESS(92)*(U1(27)*U2(17))+HESS(93)& &*(U1(17)*U2(29))+HESS(93)*(U1(29)*U2(17))+HESS(94)*(U1(19)*U2(25))+HESS(94)*(U1(25)*U2(19))+HESS(95)*(U1(19)& &*U2(27))+HESS(95)*(U1(27)*U2(19))+HESS(96)*(U1(21)*U2(27))+HESS(96)*(U1(27)*U2(21))+HESS(97)*(U1(21)*U2(29))& &+HESS(97)*(U1(29)*U2(21))+HESS(98)*(U1(21)*U2(30))+HESS(98)*(U1(30)*U2(21))+HESS(99)*(U1(22)*U2(25))+HESS(99)& &*(U1(25)*U2(22))+HESS(100)*(U1(22)*U2(27))+HESS(100)*(U1(27)*U2(22))+HESS(101)*(U1(23)*U2(25))+HESS(101)& &*(U1(25)*U2(23))+HESS(102)*(U1(23)*U2(27))+HESS(102)*(U1(27)*U2(23))+HESS(103)*(U1(23)*U2(29))+HESS(103)& &*(U1(29)*U2(23))+HESS(104)*(U1(23)*U2(30))+HESS(104)*(U1(30)*U2(23))+HESS(105)*(U1(28)*U2(32))+HESS(105)& &*(U1(32)*U2(28))+HESS(106)*(U1(31)*U2(32))+HESS(106)*(U1(32)*U2(31))+HESS(107)*(U1(32)*U2(32)) HU(22) = HESS(108)*(U1(22)*U2(25))+HESS(108)*(U1(25)*U2(22))+HESS(109)*(U1(22)*U2(27))+HESS(109)*(U1(27)*U2(22))& &+HESS(110)*(U1(22)*U2(29))+HESS(110)*(U1(29)*U2(22))+HESS(111)*(U1(22)*U2(30))+HESS(111)*(U1(30)*U2(22)) HU(23) = HESS(112)*(U1(22)*U2(29))+HESS(112)*(U1(29)*U2(22))+HESS(113)*(U1(23)*U2(25))+HESS(113)*(U1(25)*U2(23))& &+HESS(114)*(U1(23)*U2(27))+HESS(114)*(U1(27)*U2(23))+HESS(115)*(U1(23)*U2(29))+HESS(115)*(U1(29)*U2(23))& &+HESS(116)*(U1(23)*U2(30))+HESS(116)*(U1(30)*U2(23)) HU(24) = HESS(117)*(U1(17)*U2(27))+HESS(117)*(U1(27)*U2(17))+HESS(118)*(U1(19)*U2(25))+HESS(118)*(U1(25)*U2(19))& &+HESS(119)*(U1(20)*U2(27))+HESS(119)*(U1(27)*U2(20))+HESS(120)*(U1(22)*U2(25))+HESS(120)*(U1(25)*U2(22))& &+HESS(121)*(U1(22)*U2(27))+HESS(121)*(U1(27)*U2(22))+HESS(122)*(U1(22)*U2(29))+HESS(122)*(U1(29)*U2(22))& &+HESS(123)*(U1(23)*U2(25))+HESS(123)*(U1(25)*U2(23))+HESS(124)*(U1(23)*U2(27))+HESS(124)*(U1(27)*U2(23))& &+HESS(125)*(U1(23)*U2(29))+HESS(125)*(U1(29)*U2(23))+HESS(126)*(U1(23)*U2(30))+HESS(126)*(U1(30)*U2(23))& &+HESS(127)*(U1(24)*U2(27))+HESS(127)*(U1(27)*U2(24))+HESS(128)*(U1(24)*U2(29))+HESS(128)*(U1(29)*U2(24))& &+HESS(129)*(U1(24)*U2(30))+HESS(129)*(U1(30)*U2(24)) HU(25) = HESS(130)*(U1(17)*U2(25))+HESS(130)*(U1(25)*U2(17))+HESS(131)*(U1(19)*U2(25))+HESS(131)*(U1(25)*U2(19))& &+HESS(132)*(U1(22)*U2(25))+HESS(132)*(U1(25)*U2(22))+HESS(133)*(U1(23)*U2(25))+HESS(133)*(U1(25)*U2(23))& &+HESS(134)*(U1(25)*U2(26))+HESS(134)*(U1(26)*U2(25))+HESS(135)*(U1(25)*U2(27))+HESS(135)*(U1(27)*U2(25))& &+HESS(136)*(U1(25)*U2(28))+HESS(136)*(U1(28)*U2(25))+HESS(137)*(U1(25)*U2(31))+HESS(137)*(U1(31)*U2(25)) HU(26) = HESS(138)*(U1(4)*U2(26))+HESS(138)*(U1(26)*U2(4))+HESS(139)*(U1(9)*U2(9))+HESS(140)*(U1(9)*U2(27))+HESS(140)& &*(U1(27)*U2(9))+HESS(141)*(U1(10)*U2(27))+HESS(141)*(U1(27)*U2(10))+HESS(142)*(U1(11)*U2(31))+HESS(142)& &*(U1(31)*U2(11))+HESS(143)*(U1(13)*U2(26))+HESS(143)*(U1(26)*U2(13))+HESS(144)*(U1(18)*U2(31))+HESS(144)& &*(U1(31)*U2(18))+HESS(145)*(U1(23)*U2(30))+HESS(145)*(U1(30)*U2(23))+HESS(146)*(U1(25)*U2(26))+HESS(146)& &*(U1(26)*U2(25))+HESS(147)*(U1(25)*U2(31))+HESS(147)*(U1(31)*U2(25))+HESS(148)*(U1(26)*U2(27))+HESS(148)& &*(U1(27)*U2(26))+HESS(149)*(U1(26)*U2(28))+HESS(149)*(U1(28)*U2(26))+HESS(150)*(U1(26)*U2(29))+HESS(150)& &*(U1(29)*U2(26))+HESS(151)*(U1(26)*U2(30))+HESS(151)*(U1(30)*U2(26))+HESS(152)*(U1(26)*U2(31))+HESS(152)& &*(U1(31)*U2(26))+HESS(153)*(U1(26)*U2(32))+HESS(153)*(U1(32)*U2(26))+HESS(154)*(U1(28)*U2(31))+HESS(154)& &*(U1(31)*U2(28))+HESS(155)*(U1(29)*U2(31))+HESS(155)*(U1(31)*U2(29))+HESS(156)*(U1(30)*U2(31))+HESS(156)& &*(U1(31)*U2(30))+HESS(157)*(U1(31)*U2(31))+HESS(158)*(U1(31)*U2(32))+HESS(158)*(U1(32)*U2(31)) HU(27) = HESS(159)*(U1(2)*U2(27))+HESS(159)*(U1(27)*U2(2))+HESS(160)*(U1(5)*U2(27))+HESS(160)*(U1(27)*U2(5))+HESS(161)& &*(U1(7)*U2(27))+HESS(161)*(U1(27)*U2(7))+HESS(162)*(U1(9)*U2(27))+HESS(162)*(U1(27)*U2(9))+HESS(163)*(U1(10)& &*U2(27))+HESS(163)*(U1(27)*U2(10))+HESS(164)*(U1(12)*U2(27))+HESS(164)*(U1(27)*U2(12))+HESS(165)*(U1(14)& &*U2(27))+HESS(165)*(U1(27)*U2(14))+HESS(166)*(U1(15)*U2(27))+HESS(166)*(U1(27)*U2(15))+HESS(167)*(U1(16)& &*U2(27))+HESS(167)*(U1(27)*U2(16))+HESS(168)*(U1(17)*U2(27))+HESS(168)*(U1(27)*U2(17))+HESS(169)*(U1(17)& &*U2(29))+HESS(169)*(U1(29)*U2(17))+HESS(170)*(U1(19)*U2(25))+HESS(170)*(U1(25)*U2(19))+HESS(171)*(U1(19)& &*U2(27))+HESS(171)*(U1(27)*U2(19))+HESS(172)*(U1(20)*U2(27))+HESS(172)*(U1(27)*U2(20))+HESS(173)*(U1(21)& &*U2(27))+HESS(173)*(U1(27)*U2(21))+HESS(174)*(U1(21)*U2(29))+HESS(174)*(U1(29)*U2(21))+HESS(175)*(U1(22)& &*U2(25))+HESS(175)*(U1(25)*U2(22))+HESS(176)*(U1(22)*U2(27))+HESS(176)*(U1(27)*U2(22))+HESS(177)*(U1(23)& &*U2(25))+HESS(177)*(U1(25)*U2(23))+HESS(178)*(U1(23)*U2(27))+HESS(178)*(U1(27)*U2(23))+HESS(179)*(U1(23)& &*U2(29))+HESS(179)*(U1(29)*U2(23))+HESS(180)*(U1(24)*U2(27))+HESS(180)*(U1(27)*U2(24))+HESS(181)*(U1(24)& &*U2(29))+HESS(181)*(U1(29)*U2(24))+HESS(182)*(U1(25)*U2(27))+HESS(182)*(U1(27)*U2(25))+HESS(183)*(U1(25)& &*U2(28))+HESS(183)*(U1(28)*U2(25))+HESS(184)*(U1(26)*U2(27))+HESS(184)*(U1(27)*U2(26))+HESS(185)*(U1(27)& &*U2(31))+HESS(185)*(U1(31)*U2(27))+HESS(186)*(U1(28)*U2(31))+HESS(186)*(U1(31)*U2(28))+HESS(187)*(U1(28)& &*U2(32))+HESS(187)*(U1(32)*U2(28)) HU(28) = HESS(188)*(U1(2)*U2(27))+HESS(188)*(U1(27)*U2(2))+HESS(189)*(U1(5)*U2(27))+HESS(189)*(U1(27)*U2(5))+HESS(190)& &*(U1(7)*U2(27))+HESS(190)*(U1(27)*U2(7))+HESS(191)*(U1(11)*U2(31))+HESS(191)*(U1(31)*U2(11))+HESS(192)*(U1(14)& &*U2(27))+HESS(192)*(U1(27)*U2(14))+HESS(193)*(U1(16)*U2(27))+HESS(193)*(U1(27)*U2(16))+HESS(194)*(U1(17)& &*U2(25))+HESS(194)*(U1(25)*U2(17))+HESS(195)*(U1(17)*U2(27))+HESS(195)*(U1(27)*U2(17))+HESS(196)*(U1(17)& &*U2(29))+HESS(196)*(U1(29)*U2(17))+HESS(197)*(U1(19)*U2(25))+HESS(197)*(U1(25)*U2(19))+HESS(198)*(U1(19)& &*U2(27))+HESS(198)*(U1(27)*U2(19))+HESS(199)*(U1(20)*U2(27))+HESS(199)*(U1(27)*U2(20))+HESS(200)*(U1(21)& &*U2(27))+HESS(200)*(U1(27)*U2(21))+HESS(201)*(U1(21)*U2(29))+HESS(201)*(U1(29)*U2(21))+HESS(202)*(U1(21)& &*U2(30))+HESS(202)*(U1(30)*U2(21))+HESS(203)*(U1(22)*U2(25))+HESS(203)*(U1(25)*U2(22))+HESS(204)*(U1(22)& &*U2(27))+HESS(204)*(U1(27)*U2(22))+HESS(205)*(U1(22)*U2(29))+HESS(205)*(U1(29)*U2(22))+HESS(206)*(U1(23)& &*U2(25))+HESS(206)*(U1(25)*U2(23))+HESS(207)*(U1(23)*U2(27))+HESS(207)*(U1(27)*U2(23))+HESS(208)*(U1(23)& &*U2(29))+HESS(208)*(U1(29)*U2(23))+HESS(209)*(U1(25)*U2(27))+HESS(209)*(U1(27)*U2(25))+HESS(210)*(U1(25)& &*U2(28))+HESS(210)*(U1(28)*U2(25))+HESS(211)*(U1(26)*U2(28))+HESS(211)*(U1(28)*U2(26))+HESS(212)*(U1(28)& &*U2(28))+HESS(213)*(U1(28)*U2(31))+HESS(213)*(U1(31)*U2(28))+HESS(214)*(U1(28)*U2(32))+HESS(214)*(U1(32)& &*U2(28))+HESS(215)*(U1(31)*U2(32))+HESS(215)*(U1(32)*U2(31))+HESS(216)*(U1(32)*U2(32)) HU(29) = HESS(217)*(U1(17)*U2(29))+HESS(217)*(U1(29)*U2(17))+HESS(218)*(U1(21)*U2(29))+HESS(218)*(U1(29)*U2(21))& &+HESS(219)*(U1(22)*U2(29))+HESS(219)*(U1(29)*U2(22))+HESS(220)*(U1(23)*U2(29))+HESS(220)*(U1(29)*U2(23))& &+HESS(221)*(U1(24)*U2(29))+HESS(221)*(U1(29)*U2(24))+HESS(222)*(U1(26)*U2(29))+HESS(222)*(U1(29)*U2(26))& &+HESS(223)*(U1(29)*U2(31))+HESS(223)*(U1(31)*U2(29)) HU(30) = HESS(224)*(U1(12)*U2(27))+HESS(224)*(U1(27)*U2(12))+HESS(225)*(U1(14)*U2(30))+HESS(225)*(U1(30)*U2(14))& &+HESS(226)*(U1(21)*U2(30))+HESS(226)*(U1(30)*U2(21))+HESS(227)*(U1(22)*U2(30))+HESS(227)*(U1(30)*U2(22))& &+HESS(228)*(U1(23)*U2(30))+HESS(228)*(U1(30)*U2(23))+HESS(229)*(U1(24)*U2(30))+HESS(229)*(U1(30)*U2(24))& &+HESS(230)*(U1(25)*U2(26))+HESS(230)*(U1(26)*U2(25))+HESS(231)*(U1(26)*U2(29))+HESS(231)*(U1(29)*U2(26))& &+HESS(232)*(U1(26)*U2(30))+HESS(232)*(U1(30)*U2(26))+HESS(233)*(U1(30)*U2(31))+HESS(233)*(U1(31)*U2(30)) HU(31) = HESS(234)*(U1(8)*U2(31))+HESS(234)*(U1(31)*U2(8))+HESS(235)*(U1(9)*U2(9))+HESS(236)*(U1(11)*U2(31))+HESS(236)& &*(U1(31)*U2(11))+HESS(237)*(U1(18)*U2(31))+HESS(237)*(U1(31)*U2(18))+HESS(238)*(U1(25)*U2(31))+HESS(238)& &*(U1(31)*U2(25))+HESS(239)*(U1(26)*U2(29))+HESS(239)*(U1(29)*U2(26))+HESS(240)*(U1(26)*U2(30))+HESS(240)& &*(U1(30)*U2(26))+HESS(241)*(U1(26)*U2(31))+HESS(241)*(U1(31)*U2(26))+HESS(242)*(U1(27)*U2(31))+HESS(242)& &*(U1(31)*U2(27))+HESS(243)*(U1(28)*U2(31))+HESS(243)*(U1(31)*U2(28))+HESS(244)*(U1(29)*U2(31))+HESS(244)& &*(U1(31)*U2(29))+HESS(245)*(U1(30)*U2(31))+HESS(245)*(U1(31)*U2(30))+HESS(246)*(U1(31)*U2(31))+HESS(247)& &*(U1(31)*U2(32))+HESS(247)*(U1(32)*U2(31)) HU(32) = HESS(248)*(U1(15)*U2(27))+HESS(248)*(U1(27)*U2(15))+HESS(249)*(U1(19)*U2(25))+HESS(249)*(U1(25)*U2(19))& &+HESS(250)*(U1(19)*U2(27))+HESS(250)*(U1(27)*U2(19))+HESS(251)*(U1(22)*U2(27))+HESS(251)*(U1(27)*U2(22))& &+HESS(252)*(U1(24)*U2(27))+HESS(252)*(U1(27)*U2(24))+HESS(253)*(U1(24)*U2(29))+HESS(253)*(U1(29)*U2(24))& &+HESS(254)*(U1(24)*U2(30))+HESS(254)*(U1(30)*U2(24))+HESS(255)*(U1(26)*U2(32))+HESS(255)*(U1(32)*U2(26))& &+HESS(256)*(U1(28)*U2(32))+HESS(256)*(U1(32)*U2(28))+HESS(257)*(U1(31)*U2(32))+HESS(257)*(U1(32)*U2(31))& &+HESS(258)*(U1(32)*U2(32)) END SUBROUTINE Hess_Vec ! End of Hess_Vec function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ END MODULE cbm_Hessian