[2696] | 1 | |
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| 2 | #define MAX(a,b) ( ((a) >= (b)) ? (a):(b) ) |
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| 3 | #define MIN(b,c) ( ((b) < (c)) ? (b):(c) ) |
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| 4 | #define ABS(x) ( ((x) >= 0 ) ? (x):(-x) ) |
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| 5 | #define SIGN(x,y)( ( (x*y) >= 0 ) ?(x):(-x) ) |
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| 6 | #define SQRT(d) ( pow((d),0.5) ) |
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| 7 | |
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| 8 | /* Numerical Constants */ |
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| 9 | #define ZERO (KPP_REAL)0.0 |
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| 10 | #define ONE (KPP_REAL)1.0 |
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| 11 | #define HALF (KPP_REAL)0.5 |
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| 12 | #define DeltaMin (KPP_REAL)1.0e-5 |
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| 13 | enum boolean { FALSE=0, TRUE=1 }; |
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| 14 | |
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| 15 | /*~~~> Statistics on the work performed by the SDIRK method */ |
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| 16 | enum statistics { Nfun=1, Njac=2, Nstp=3, Nacc=4, Nrej=5, Ndec=6, Nsol=7, |
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| 17 | Nsng=8, Ntexit=1, Nhexit=2, Nhnew=3 }; |
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| 18 | |
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| 19 | /*~~~> SDIRK method coefficients, up to 5 stages */ |
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| 20 | int Smax = 5; |
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| 21 | enum ros_Params { S2A=1, S2B=2, S3A=3, S4A=4, S4B=5 }; |
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| 22 | KPP_REAL rkGamma, rkA[5][5], rkB[5], rkC[5], rkD[5], rkE[5], |
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| 23 | rkBhat[5], rkELO, rkAlpha[5][5], rkTheta[5][5]; |
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| 24 | int sdMethod, rkS; /* The number of stages */ |
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| 25 | |
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| 26 | /*~~~> Checkpoints in memory buffers */ |
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| 27 | int stack_ptr = -1; /* last written entry in checkpoint */ |
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| 28 | KPP_REAL *chk_H, *chk_T; |
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| 29 | KPP_REAL **chk_Y; |
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| 30 | KPP_REAL ***chk_Z; |
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| 31 | int **chk_P; |
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| 32 | #ifdef FULL_ALGEBRA |
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| 33 | KPP_REAL ***chk_J; |
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| 34 | #else |
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| 35 | KPP_REAL **chk_J; |
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| 36 | #endif |
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| 37 | |
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| 38 | /* Function Headers */ |
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| 39 | void INTEGRATE_ADJ( int NADJ, KPP_REAL Y[], KPP_REAL Lambda[][NVAR], |
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| 40 | KPP_REAL TIN, KPP_REAL TOUT, KPP_REAL ATOL_adj[][NVAR], |
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| 41 | KPP_REAL RTOL_adj[][NVAR], int ICNTRL_U[], |
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| 42 | KPP_REAL RCNTRL_U[], int ISTATUS_U[], |
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| 43 | KPP_REAL RSTATUS_U[] ); |
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| 44 | int SDIRKADJ( int N, int NADJ, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
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| 45 | KPP_REAL Lambda[][NVAR], KPP_REAL RelTol[], KPP_REAL AbsTol[], |
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| 46 | KPP_REAL RelTol_adj[][NVAR], KPP_REAL AbsTol_adj[][NVAR], |
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| 47 | KPP_REAL RCNTRL[], int ICNTRL[], KPP_REAL RSTATUS[], |
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| 48 | int ISTATUS[]); |
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| 49 | int SDIRK_FwdInt( int N, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
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| 50 | KPP_REAL Hmax, KPP_REAL Hmin, KPP_REAL Hstart, |
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| 51 | KPP_REAL Roundoff, KPP_REAL AbsTol[], KPP_REAL RelTol[], |
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| 52 | int ISTATUS[], KPP_REAL RSTATUS[], int Max_no_steps, |
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| 53 | int NewtonMaxit, KPP_REAL NewtonTol, KPP_REAL ThetaMin, |
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| 54 | KPP_REAL FacSafe, KPP_REAL FacMin, KPP_REAL FacMax, |
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| 55 | KPP_REAL FacRej, KPP_REAL Qmin, KPP_REAL Qmax, int ITOL, |
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| 56 | int SaveLU ); |
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| 57 | int SDIRK_DadjInt( int N, int NADJ, KPP_REAL Lambda[][NVAR], int SaveLU, |
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| 58 | int ISTATUS[], int ITOL, KPP_REAL AbsTol_adj[][NVAR], |
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| 59 | KPP_REAL RelTol_adj[][NVAR], int NewtonMaxit, |
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| 60 | KPP_REAL ThetaMin, KPP_REAL NewtonTol, int DirectADJ ); |
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| 61 | void SDIRK_AllocBuffers( int Max_no_steps, int rkS, int SaveLU ); |
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| 62 | void SDIRK_FreeBuffers( int Max_no_steps, int SaveLU ); |
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| 63 | void SDIRK_Push( KPP_REAL T, KPP_REAL H, KPP_REAL Y[], KPP_REAL Z[][NVAR], |
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| 64 | KPP_REAL E[], int P[], int Max_no_steps, int SaveLU ); |
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| 65 | void SDIRK_Pop( KPP_REAL* T, KPP_REAL* H, KPP_REAL* Y, KPP_REAL* Z, |
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| 66 | KPP_REAL* E, int* P, int SaveLU ); |
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| 67 | void SDIRK_ErrorScale( int N, int ITOL, KPP_REAL AbsTol[], KPP_REAL RelTol[], |
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| 68 | KPP_REAL Y[],KPP_REAL SCAL[]); |
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| 69 | KPP_REAL SDIRK_ErrorNorm( int N, KPP_REAL Y[], KPP_REAL SCAL[] ); |
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| 70 | int SDIRK_ErrorMsg( int code, KPP_REAL T, KPP_REAL H ); |
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| 71 | void SDIRK_PrepareMatrix( KPP_REAL H, KPP_REAL T, KPP_REAL Y[], KPP_REAL FJAC[], |
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| 72 | int SkipJac, int SkipLU, KPP_REAL E[], int IP[], |
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| 73 | int Reject, int ISING, int ISTATUS[] ); |
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| 74 | void SDIRK_Solve ( char Transp, KPP_REAL H, int N, KPP_REAL E[], |
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| 75 | int IP[], int ISING, KPP_REAL RHS[], int ISTATUS[] ); |
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| 76 | void Sdirk4a(); |
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| 77 | void Sdirk4b(); |
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| 78 | void Sdirk2a(); |
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| 79 | void Sdirk2b(); |
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| 80 | void Sdirk3a(); |
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| 81 | void FUN_CHEM( KPP_REAL T, KPP_REAL Y[], KPP_REAL P[] ); |
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| 82 | void JAC_CHEM( KPP_REAL T, KPP_REAL Y[], KPP_REAL JV[] ); |
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| 83 | KPP_REAL WLAMCH( char C ); |
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| 84 | void Set2Zero( int N, KPP_REAL Y[] ); |
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| 85 | void WAXPY( int N, KPP_REAL Alpha, KPP_REAL X[], int incX, KPP_REAL Y[], |
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| 86 | int incY ); |
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| 87 | void WADD( int N, KPP_REAL Y[], KPP_REAL Z[], KPP_REAL TMP[] ); |
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| 88 | void WSCAL( int N, KPP_REAL Alpha, KPP_REAL X[], int incX ); |
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| 89 | void JacTR_SP_Vec( KPP_REAL Jac[], KPP_REAL Fcn[], KPP_REAL K[] ); |
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| 90 | void KppSolve( KPP_REAL A[], KPP_REAL b[] ); |
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| 91 | void KppSolveTR( KPP_REAL JVS[], KPP_REAL X[], KPP_REAL XX[] ); |
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| 92 | int KppDecomp( KPP_REAL A[] ); |
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| 93 | void Update_SUN(); |
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| 94 | void Update_RCONST(); |
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| 95 | void Fun( KPP_REAL Y[], KPP_REAL FIX[], KPP_REAL RCONST[], KPP_REAL Ydot[] ); |
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| 96 | void Jac_SP( KPP_REAL Y[], KPP_REAL FIX[], KPP_REAL RCONST[], KPP_REAL Ydot[] ); |
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| 97 | void Set2Zero( int N, KPP_REAL Y[] ); |
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| 98 | |
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| 99 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 100 | void INTEGRATE_ADJ( int NADJ, KPP_REAL Y[], KPP_REAL Lambda[][NVAR], |
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| 101 | KPP_REAL TIN, KPP_REAL TOUT, KPP_REAL ATOL_adj[][NVAR], |
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| 102 | KPP_REAL RTOL_adj[][NVAR], int ICNTRL_U[], |
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| 103 | KPP_REAL RCNTRL_U[], int ISTATUS_U[], |
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| 104 | KPP_REAL RSTATUS_U[] ) { |
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| 105 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 106 | |
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| 107 | //int Ntotal = 0; |
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| 108 | KPP_REAL RCNTRL[20], RSTATUS[20], T1, T2; |
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| 109 | int ICNTRL[20], ISTATUS[20], Ierr, i; |
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| 110 | |
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| 111 | for(i=0; i<20; i++) { |
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| 112 | ICNTRL[i] = 0; |
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| 113 | RCNTRL[i] = (KPP_REAL)0.0; |
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| 114 | ISTATUS[i] = 0; |
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| 115 | RSTATUS[i] = (KPP_REAL)0.0; |
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| 116 | } |
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| 117 | |
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| 118 | /*~~~> fine-tune the integrator: */ |
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| 119 | ICNTRL[4] = 8; /* Max no. of Newton iterations */ |
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| 120 | ICNTRL[6] = 1; /* Adjoint solution by: 0=Newton, 1=direct */ |
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| 121 | ICNTRL[7] = 1; /* Save fwd LU factorization: 0 = do *not* save, 1 = save */ |
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| 122 | |
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| 123 | /* If optional parameters are given, and if they are >0, |
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| 124 | then they overwrite default settings. */ |
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| 125 | //if(ICNTRL_U != NULL) { /* Check to see if ICNTRL_U is not NULL */ |
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| 126 | // for(i=0; i<20; i++) { |
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| 127 | // if(ICNTRL_U[i] > 0) |
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| 128 | // ICNTRL[i] = ICNTRL_U[i]; |
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| 129 | // } |
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| 130 | //} |
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| 131 | // |
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| 132 | //if(RCNTRL_U != NULL) { /* Check to see if RCNTRL_U is not NULL */ |
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| 133 | // for(i=0; i<20; i++) { |
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| 134 | // if(RCNTRL_U[i] > 0) |
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| 135 | // RCNTRL[i] = RCNTRL_U[i]; |
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| 136 | // } |
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| 137 | //} |
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| 138 | |
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| 139 | T1 = TIN; |
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| 140 | T2 = TOUT; |
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| 141 | Ierr = SDIRKADJ( NVAR, NADJ, T1, T2, Y, Lambda, RTOL, ATOL, ATOL_adj, |
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| 142 | RTOL_adj, RCNTRL, ICNTRL, RSTATUS, ISTATUS ); |
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| 143 | |
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| 144 | /*~~~> Debug option: number of steps */ |
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| 145 | // Ntotal = Ntotal + ISTATUS(Nstp) |
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| 146 | // printf( "NSTEP=%d Ntotal=%d O3=%e NO2=%e\n", ISTATUS(Nstp), Ntotal, |
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| 147 | // VAR(ind_O3), VAR(ind_NO2) ); |
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| 148 | |
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| 149 | if (Ierr < 0) |
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| 150 | printf("SDIRK: Unsuccessful exit at T=%f (Ierr=%d)\n", TIN, Ierr ); |
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| 151 | |
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| 152 | /* if optional parameters are given for output they to return information */ |
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| 153 | //if(ISTATUS_U != NULL) { /* Check to see if ISTATUS_U is not NULL */ |
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| 154 | // for(i=0; i<20; i++) |
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| 155 | // ISTATUS_U[i] = ISTATUS[i]; |
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| 156 | //} |
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| 157 | // |
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| 158 | //if(RSTATUS_U != NULL) { /* Check to see if RSTATUS_U is not NULL */ |
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| 159 | // for(i=0; i<20; i++) |
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| 160 | // RSTATUS_U[i] = RSTATUS[i]; |
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| 161 | //} |
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| 162 | // |
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| 163 | //Ierr_U = Ierr; |
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| 164 | |
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| 165 | } /* END of SUBROUTINE INTEGRATE_ADJ */ |
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| 166 | |
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| 167 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 168 | int SDIRKADJ( int N, int NADJ, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
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| 169 | KPP_REAL Lambda[][NVAR], KPP_REAL RelTol[], KPP_REAL AbsTol[], |
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| 170 | KPP_REAL RelTol_adj[][NVAR], KPP_REAL AbsTol_adj[][NVAR], |
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| 171 | KPP_REAL RCNTRL[], int ICNTRL[], KPP_REAL RSTATUS[], |
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| 172 | int ISTATUS[] ) { |
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| 173 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 174 | |
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| 175 | Solves the system y'=F(t,y) using a Singly-Diagonally-Implicit |
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| 176 | Runge-Kutta (SDIRK) method. |
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| 177 | |
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| 178 | This implementation is based on the book and the code Sdirk4: |
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| 179 | |
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| 180 | E. Hairer and G. Wanner |
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| 181 | "Solving ODEs II. Stiff and differential-algebraic problems". |
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| 182 | Springer series in computational mathematics, Springer-Verlag, 1996. |
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| 183 | This code is based on the SDIRK4 routine in the above book. |
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| 184 | |
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| 185 | Methods: |
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| 186 | * Sdirk 2a, 2b: L-stable, 2 stages, order 2 |
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| 187 | * Sdirk 3a: L-stable, 3 stages, order 2, adjoint-invariant |
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| 188 | * Sdirk 4a, 4b: L-stable, 5 stages, order 4 |
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| 189 | |
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| 190 | (C) Adrian Sandu, July 2005 |
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| 191 | Virginia Polytechnic Institute and State University |
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| 192 | Contact: sandu@cs.vt.edu |
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| 193 | Revised by Philipp Miehe and Adrian Sandu, May 2006 |
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| 194 | Translation F90 to C by Paul Eller, May 2007 |
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| 195 | This implementation is part of KPP - the Kinetic PreProcessor |
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| 196 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 197 | |
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| 198 | ~~~> INPUT ARGUMENTS: |
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| 199 | |
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| 200 | - Y[NVAR] = vector of initial conditions (at T=Tinitial) |
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| 201 | - [Tinitial,Tfinal] = time range of integration |
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| 202 | (if Tinitial>Tfinal the integration is performed backwards in time) |
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| 203 | - RelTol, AbsTol = user precribed accuracy |
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| 204 | - SUBROUTINE ode_Fun( T, Y, Ydot ) = ODE function, |
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| 205 | returns Ydot = Y' = F(T,Y) |
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| 206 | - SUBROUTINE ode_Fun( T, Y, Ydot ) = Jacobian of the ODE function, |
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| 207 | returns Jcb = dF/dY |
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| 208 | - ICNTRL[1:20] = integer inputs parameters |
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| 209 | - RCNTRL[1:20] = real inputs parameters |
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| 210 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 211 | |
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| 212 | ~~~> OUTPUT ARGUMENTS: |
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| 213 | |
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| 214 | - Y[NVAR] -> vector of final states (at T->Tfinal) |
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| 215 | - ISTATUS[0:19] -> integer output parameters |
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| 216 | - RSTATUS[0:19] -> real output parameters |
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| 217 | - Ierr -> job status upon return |
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| 218 | success (positive value) or |
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| 219 | failure (negative value) |
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| 220 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 221 | |
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| 222 | ~~~> INPUT PARAMETERS: |
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| 223 | |
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| 224 | Note: For input parameters equal to zero the default values of the |
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| 225 | corresponding variables are used. |
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| 226 | |
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| 227 | Note: For input parameters equal to zero the default values of the |
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| 228 | corresponding variables are used. |
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| 229 | ~~~> |
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| 230 | ICNTRL[0] = not used |
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| 231 | |
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| 232 | ICNTRL[1] = 0: AbsTol, RelTol are NVAR-dimensional vectors |
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| 233 | = 1: AbsTol, RelTol are scalars |
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| 234 | |
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| 235 | ICNTRL[2] = Method |
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| 236 | |
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| 237 | ICNTRL[3] -> maximum number of integration steps |
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| 238 | For ICNTRL[3]=0 the default value of 1500 is used |
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| 239 | Note: use a conservative estimate, since the checkpoint |
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| 240 | buffers are allocated to hold Max_no_steps |
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| 241 | |
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| 242 | ICNTRL[4] -> maximum number of Newton iterations |
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| 243 | For ICNTRL[4]=0 the default value of 8 is used |
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| 244 | |
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| 245 | ICNTRL[5] -> starting values of Newton iterations: |
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| 246 | ICNTRL[5]=0 : starting values are interpolated (the default) |
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| 247 | ICNTRL[5]=1 : starting values are zero |
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| 248 | |
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| 249 | ICNTRL[6] -> method to solve ADJ equations: |
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| 250 | ICNTRL[6]=0 : modified Newton re-using LU (the default) |
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| 251 | ICNTRL[6]=1 : direct solution(additional one LU factorization per stage) |
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| 252 | |
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| 253 | ICNTRL[7] -> checkpointing the LU factorization at each step: |
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| 254 | ICNTRL[7]=0 : do *not* save LU factorization (the default) |
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| 255 | ICNTRL[7]=1 : save LU factorization |
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| 256 | Note: if ICNTRL[6]=1 the LU factorization is *not* saved |
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| 257 | |
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| 258 | ~~~> Real parameters |
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| 259 | |
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| 260 | RCNTRL[0] -> Hmin, lower bound for the integration step size |
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| 261 | It is strongly recommended to keep Hmin = ZERO |
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| 262 | RCNTRL[1] -> Hmax, upper bound for the integration step size |
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| 263 | RCNTRL[2] -> Hstart, starting value for the integration step size |
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| 264 | |
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| 265 | RCNTRL[3] -> FacMin, lower bound on step decrease factor (default=0.2) |
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| 266 | RCNTRL[4] -> FacMax, upper bound on step increase factor (default=6) |
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| 267 | RCNTRL[5] -> FacRej, step decrease factor after multiple rejections |
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| 268 | (default=0.1) |
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| 269 | RCNTRL[6] -> FacSafe, by which the new step is slightly smaller |
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| 270 | than the predicted value (default=0.9) |
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| 271 | RCNTRL[7] -> ThetaMin. If Newton convergence rate smaller |
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| 272 | than ThetaMin the Jacobian is not recomputed; |
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| 273 | (default=0.001) |
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| 274 | RCNTRL[8] -> NewtonTol, stopping criterion for Newton's method |
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| 275 | (default=0.03) |
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| 276 | RCNTRL[9] -> Qmin |
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| 277 | RCNTRL[10] -> Qmax. If Qmin < Hnew/Hold < Qmax, then the |
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| 278 | step size is kept constant and the LU factorization |
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| 279 | reused (default Qmin=1, Qmax=1.2) |
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| 280 | |
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| 281 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 282 | |
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| 283 | ~~~> OUTPUT PARAMETERS: |
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| 284 | |
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| 285 | Note: each call to Rosenbrock adds the current no. of fcn calls |
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| 286 | to previous value of ISTATUS[0], and similar for the other params. |
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| 287 | Set ISTATUS[1:10] = 0 before call to avoid this accumulation. |
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| 288 | |
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| 289 | ISTATUS[0] = No. of function calls |
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| 290 | ISTATUS[1] = No. of jacobian calls |
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| 291 | ISTATUS[2] = No. of steps |
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| 292 | ISTATUS[3] = No. of accepted steps |
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| 293 | ISTATUS[4] = No. of rejected steps (except at the beginning) |
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| 294 | ISTATUS[5] = No. of LU decompositions |
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| 295 | ISTATUS[6] = No. of forward/backward substitutions |
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| 296 | ISTATUS[7] = No. of singular matrix decompositions |
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| 297 | |
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| 298 | RSTATUS[0] -> Texit, the time corresponding to the |
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| 299 | computed Y upon return |
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| 300 | RSTATUS[1] -> Hexit,last accepted step before return |
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| 301 | RSTATUS[2] -> Hnew, last predicted step before return |
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| 302 | For multiple restarts, use Hnew as Hstart in the following run |
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| 303 | |
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| 304 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
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| 305 | |
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| 306 | /* Local variables */ |
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| 307 | KPP_REAL Hmin=0.0, Hmax=0.0, Hstart=0.0, Roundoff, FacMin=0.0, FacMax=0.0, |
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| 308 | FacSafe=0.0, FacRej=0.0, ThetaMin, NewtonTol,Qmin, Qmax; |
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| 309 | int SaveLU, DirectADJ; /* Boolean variables */ |
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| 310 | int ITOL, NewtonMaxit, Max_no_steps=0, i, Ierr=0; |
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| 311 | |
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| 312 | stack_ptr = -1; |
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| 313 | |
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| 314 | /*~~~> Initialize statistics */ |
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| 315 | for(i=0; i<20; i++) { |
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| 316 | ISTATUS[i] = 0; |
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| 317 | RSTATUS[i] = ZERO; |
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| 318 | } |
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| 319 | |
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| 320 | /*~~~> For Scalar tolerances (ICNTRL[1] != 0) the code uses AbsTol[0] |
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| 321 | and RelTol[0] |
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| 322 | For Vector tolerances (ICNTRL[1] == 0) the code uses AbsTol[0:NVAR-1] |
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| 323 | and RelTol[0:NVAR-1]*/ |
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| 324 | if (ICNTRL[1]==0) |
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| 325 | ITOL = 1; |
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| 326 | else |
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| 327 | ITOL = 0; |
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| 328 | |
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| 329 | /*~~~> ICNTRL(3) - method selection */ |
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| 330 | switch (ICNTRL[2]) { |
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| 331 | case 0: |
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| 332 | case 1: |
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| 333 | Sdirk2a(); |
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| 334 | break; |
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| 335 | case 2: |
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| 336 | Sdirk2b(); |
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| 337 | break; |
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| 338 | case 3: |
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| 339 | Sdirk3a(); |
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| 340 | break; |
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| 341 | case 4: |
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| 342 | Sdirk4a(); |
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| 343 | break; |
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| 344 | case 5: |
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| 345 | Sdirk4b(); |
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| 346 | break; |
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| 347 | default: |
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| 348 | Sdirk2a(); |
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| 349 | } |
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| 350 | |
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| 351 | /*~~~> The maximum number of time steps admitted */ |
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| 352 | if (ICNTRL[3] == 0) |
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| 353 | Max_no_steps = 200000; |
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| 354 | else if (ICNTRL[3] > 0) |
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| 355 | Max_no_steps = ICNTRL[3]; |
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| 356 | else { |
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| 357 | printf("User-selected ICNTRL(4)=%d", ICNTRL[3]); |
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| 358 | Ierr = SDIRK_ErrorMsg(-1,Tinitial,ZERO); |
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| 359 | } |
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| 360 | |
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| 361 | /*~~~>The maximum number of Newton iterations admitted */ |
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| 362 | if(ICNTRL[4]==0) |
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| 363 | NewtonMaxit = 8; |
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| 364 | else { |
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| 365 | NewtonMaxit=ICNTRL[4]; |
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| 366 | if(NewtonMaxit <=0) { |
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| 367 | printf("User-selected ICNTRL(5)=%d", ICNTRL[4] ); |
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| 368 | Ierr = SDIRK_ErrorMsg(-2,Tinitial,ZERO); |
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| 369 | } |
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| 370 | } |
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| 371 | |
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| 372 | /*~~~> Solve ADJ equations directly or by Newton iterations */ |
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| 373 | DirectADJ = (ICNTRL[6] == 1); |
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| 374 | |
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| 375 | /*~~~> Save or not the forward LU factorization */ |
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| 376 | SaveLU = ((ICNTRL[7] != 0) && (DirectADJ == 0)); |
---|
| 377 | |
---|
| 378 | /*~~~> Unit roundoff (1+Roundoff>1) */ |
---|
| 379 | Roundoff = WLAMCH('E'); |
---|
| 380 | |
---|
| 381 | /*~~~> Lower bound on the step size: (positive value) */ |
---|
| 382 | if (RCNTRL[0] == ZERO) |
---|
| 383 | Hmin = ZERO; |
---|
| 384 | else if (RCNTRL[0] > ZERO) |
---|
| 385 | Hmin = RCNTRL[0]; |
---|
| 386 | else { |
---|
| 387 | printf("User-selected RCNTRL[0]=%f", RCNTRL[0]); |
---|
| 388 | Ierr = SDIRK_ErrorMsg(-3,Tinitial,ZERO); |
---|
| 389 | } |
---|
| 390 | |
---|
| 391 | /*~~~> Upper bound on the step size: (positive value) */ |
---|
| 392 | if (RCNTRL[1] == ZERO) |
---|
| 393 | Hmax = ABS(Tfinal-Tinitial); |
---|
| 394 | else if (RCNTRL[1] > ZERO) |
---|
| 395 | Hmax = MIN( ABS(RCNTRL[1]), ABS(Tfinal-Tinitial) ); |
---|
| 396 | else { |
---|
| 397 | printf("User-selected RCNTRL[1]=%f", RCNTRL[1]); |
---|
| 398 | Ierr = SDIRK_ErrorMsg(-3,Tinitial,ZERO); |
---|
| 399 | } |
---|
| 400 | |
---|
| 401 | /*~~~> Starting step size: (positive value) */ |
---|
| 402 | if (RCNTRL[2] == ZERO) |
---|
| 403 | Hstart = MAX( Hmin, Roundoff); |
---|
| 404 | else if (RCNTRL[2] > ZERO) |
---|
| 405 | Hstart = MIN( ABS(RCNTRL[2]), ABS(Tfinal-Tinitial) ); |
---|
| 406 | else { |
---|
| 407 | printf("User-selected Hstart: RCNTRL[2]=%f", RCNTRL[2]); |
---|
| 408 | Ierr = SDIRK_ErrorMsg(-3,Tinitial,ZERO); |
---|
| 409 | } |
---|
| 410 | |
---|
| 411 | /*~~~> Step size can be changed s.t. FacMin < Hnew/Hexit < FacMax */ |
---|
| 412 | if (RCNTRL[3] == ZERO) |
---|
| 413 | FacMin = (KPP_REAL)0.2; |
---|
| 414 | else if (RCNTRL[3] > ZERO) |
---|
| 415 | FacMin = RCNTRL[3]; |
---|
| 416 | else { |
---|
| 417 | printf("User-selected FacMin: RCNTRL[3]=%f", RCNTRL[3]); |
---|
| 418 | Ierr = SDIRK_ErrorMsg(-4,Tinitial,ZERO); |
---|
| 419 | } |
---|
| 420 | |
---|
| 421 | if (RCNTRL[4] == ZERO) |
---|
| 422 | FacMax = (KPP_REAL)10.0; |
---|
| 423 | else if (RCNTRL[4] > ZERO) |
---|
| 424 | FacMax = RCNTRL[4]; |
---|
| 425 | else { |
---|
| 426 | printf("User-selected FacMax: RCNTRL[4]=%f", RCNTRL[4]); |
---|
| 427 | Ierr = SDIRK_ErrorMsg(-4,Tinitial,ZERO); |
---|
| 428 | } |
---|
| 429 | |
---|
| 430 | /*~~~> FacRej: Factor to decrease step after 2 succesive rejections */ |
---|
| 431 | if (RCNTRL[5] == ZERO) |
---|
| 432 | FacRej = (KPP_REAL)0.1; |
---|
| 433 | else if (RCNTRL[5] > ZERO) |
---|
| 434 | FacRej = RCNTRL[5]; |
---|
| 435 | else { |
---|
| 436 | printf("User-selected FacRej: RCNTRL[5]=%f", RCNTRL[5]); |
---|
| 437 | Ierr = SDIRK_ErrorMsg(-4,Tinitial,ZERO); |
---|
| 438 | } |
---|
| 439 | |
---|
| 440 | /* ~~~> FacSafe: Safety Factor in the computation of new step size */ |
---|
| 441 | if (RCNTRL[6] == ZERO) |
---|
| 442 | FacSafe = (KPP_REAL)0.9; |
---|
| 443 | else if (RCNTRL[6] > ZERO) |
---|
| 444 | FacSafe = RCNTRL[6]; |
---|
| 445 | else { |
---|
| 446 | printf("User-selected FacSafe: RCNTRL[6]=%f", RCNTRL[6]); |
---|
| 447 | Ierr = SDIRK_ErrorMsg(-4,Tinitial,ZERO); |
---|
| 448 | } |
---|
| 449 | |
---|
| 450 | /*~~~> ThetaMin: decides whether the Jacobian should be recomputed */ |
---|
| 451 | if (RCNTRL[7] == ZERO) |
---|
| 452 | ThetaMin = (KPP_REAL)1.0e-03; |
---|
| 453 | else |
---|
| 454 | ThetaMin = RCNTRL[7]; |
---|
| 455 | |
---|
| 456 | /*~~~> Stopping criterion for Newton's method */ |
---|
| 457 | if (RCNTRL[8] == ZERO) |
---|
| 458 | NewtonTol = (KPP_REAL)3.0e-02; |
---|
| 459 | else |
---|
| 460 | NewtonTol = RCNTRL[8]; |
---|
| 461 | |
---|
| 462 | /* ~~~> Qmin, Qmax: IF Qmin < Hnew/Hold < Qmax, STEP SIZE = CONST. */ |
---|
| 463 | if (RCNTRL[9] == ZERO) |
---|
| 464 | Qmin = ONE; |
---|
| 465 | else |
---|
| 466 | Qmin = RCNTRL[9]; |
---|
| 467 | |
---|
| 468 | if (RCNTRL[10] == ZERO) |
---|
| 469 | Qmax = (KPP_REAL)1.2; |
---|
| 470 | else |
---|
| 471 | Qmax = RCNTRL [10]; |
---|
| 472 | |
---|
| 473 | /* ~~~> Check if tolerances are reasonable */ |
---|
| 474 | if (ITOL == 0) { |
---|
| 475 | if ((AbsTol[0]<=ZERO || RelTol[0])<=(((KPP_REAL)10.0)*Roundoff)) |
---|
| 476 | Ierr = SDIRK_ErrorMsg(-5,Tinitial,ZERO); |
---|
| 477 | } |
---|
| 478 | else { |
---|
| 479 | for (i = 0; i < N; i++) { |
---|
| 480 | if ((AbsTol[i]<=ZERO)||(RelTol[i]<=((KPP_REAL)10.0)*Roundoff)) |
---|
| 481 | Ierr = SDIRK_ErrorMsg(-5,Tinitial,ZERO); |
---|
| 482 | } |
---|
| 483 | } |
---|
| 484 | |
---|
| 485 | if (Ierr < 0) |
---|
| 486 | return Ierr; |
---|
| 487 | |
---|
| 488 | /*~~~> Allocate memory buffers */ |
---|
| 489 | SDIRK_AllocBuffers(Max_no_steps, rkS, SaveLU); |
---|
| 490 | |
---|
| 491 | /*~~~> Call forward integration */ |
---|
| 492 | Ierr = SDIRK_FwdInt( N, Tinitial, Tfinal, Y, Hmax, Hmin, Hstart, Roundoff, |
---|
| 493 | AbsTol, RelTol, ISTATUS, RSTATUS, Max_no_steps, |
---|
| 494 | NewtonMaxit, NewtonTol, ThetaMin, FacSafe, FacMin, |
---|
| 495 | FacMax, FacRej, Qmin, Qmax, ITOL, SaveLU ); |
---|
| 496 | |
---|
| 497 | /*~~~> Call adjoint integration */ |
---|
| 498 | Ierr = SDIRK_DadjInt( N, NADJ, Lambda, SaveLU, ISTATUS, ITOL, AbsTol_adj, |
---|
| 499 | RelTol_adj, NewtonMaxit, ThetaMin, NewtonTol, |
---|
| 500 | DirectADJ ); |
---|
| 501 | |
---|
| 502 | /*~~~> Free memory buffers */ |
---|
| 503 | SDIRK_FreeBuffers(Max_no_steps, SaveLU); |
---|
| 504 | |
---|
| 505 | return Ierr; |
---|
| 506 | |
---|
| 507 | } /* End of main SDIRK_ADJ */ |
---|
| 508 | |
---|
| 509 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 510 | int SDIRK_FwdInt( int N, KPP_REAL Tinitial, KPP_REAL Tfinal, KPP_REAL Y[], |
---|
| 511 | KPP_REAL Hmax, KPP_REAL Hmin, KPP_REAL Hstart, |
---|
| 512 | KPP_REAL Roundoff, KPP_REAL AbsTol[], KPP_REAL RelTol[], |
---|
| 513 | int ISTATUS[], KPP_REAL RSTATUS[], int Max_no_steps, |
---|
| 514 | int NewtonMaxit, KPP_REAL NewtonTol, KPP_REAL ThetaMin, |
---|
| 515 | KPP_REAL FacSafe, KPP_REAL FacMin, KPP_REAL FacMax, |
---|
| 516 | KPP_REAL FacRej, KPP_REAL Qmin, KPP_REAL Qmax, int ITOL, |
---|
| 517 | int SaveLU ) { |
---|
| 518 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 519 | |
---|
| 520 | /*~~~> Local variables: */ |
---|
| 521 | KPP_REAL Z[Smax][NVAR], G[NVAR], TMP[NVAR], NewtonRate, SCAL[NVAR], RHS[NVAR], |
---|
| 522 | T, H, Theta=0.0, Hratio, NewtonPredictedErr, Qnewton, Err, Fac, Hnew, |
---|
| 523 | Tdirection, NewtonIncrement, NewtonIncrementOld=0.0; |
---|
| 524 | int i, j, IER=0, istage, NewtonIter, IP[NVAR]; |
---|
| 525 | |
---|
| 526 | /*Boolean Variables*/ |
---|
| 527 | int Reject, FirstStep, SkipJac, SkipLU, NewtonDone, CycleTloop; |
---|
| 528 | |
---|
| 529 | #ifdef FULL_ALGEBRA |
---|
| 530 | KPP_REAL FJAC[NVAR][NVAR], E[NVAR][NVAR]; |
---|
| 531 | #else |
---|
| 532 | KPP_REAL FJAC[LU_NONZERO], E[LU_NONZERO]; |
---|
| 533 | #endif |
---|
| 534 | |
---|
| 535 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 536 | /*~~~~> Initializations */ |
---|
| 537 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 538 | T = Tinitial; |
---|
| 539 | Tdirection = SIGN(ONE, Tfinal-Tinitial); |
---|
| 540 | H = MAX(ABS(Hmin), ABS(Hstart)); |
---|
| 541 | if (ABS(H) <= ((KPP_REAL)10.0 * Roundoff)) |
---|
| 542 | H = (KPP_REAL)(1.0e-06); |
---|
| 543 | H = MIN(ABS(H), Hmax); |
---|
| 544 | H = SIGN(H, Tdirection); |
---|
| 545 | SkipLU = 0; |
---|
| 546 | SkipJac = 0; |
---|
| 547 | Reject = 0; |
---|
| 548 | FirstStep = 1; |
---|
| 549 | CycleTloop = 0; |
---|
| 550 | |
---|
| 551 | SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL); |
---|
| 552 | |
---|
| 553 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 554 | /*~~~> Time loop begins */ |
---|
| 555 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 556 | while((Tfinal-T)*Tdirection - Roundoff > ZERO) { /* Tloop */ |
---|
| 557 | |
---|
| 558 | /*~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition */ |
---|
| 559 | if (SkipLU == 0) { /* This time around skip the Jac update and LU */ |
---|
| 560 | SDIRK_PrepareMatrix( H, T, Y, FJAC, SkipJac, SkipLU, E, IP, |
---|
| 561 | Reject, IER, ISTATUS); |
---|
| 562 | if (IER != 0) |
---|
| 563 | return SDIRK_ErrorMsg(-8, T, H); |
---|
| 564 | } |
---|
| 565 | |
---|
| 566 | if (ISTATUS[Nstp] > Max_no_steps) |
---|
| 567 | return SDIRK_ErrorMsg(-6, T, H); |
---|
| 568 | |
---|
| 569 | if ((T + ((KPP_REAL)0.1) * H == T) || (ABS(H) <= Roundoff)) { |
---|
| 570 | return SDIRK_ErrorMsg(-7, T, H); |
---|
| 571 | } |
---|
| 572 | |
---|
| 573 | for (istage=0; istage < rkS; istage++) { /*stages*/ |
---|
| 574 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 575 | /*~~~> Simplified Newton iterations */ |
---|
| 576 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 577 | |
---|
| 578 | /*~~~> Starting values for Newton iterations */ |
---|
| 579 | Set2Zero(N, &Z[istage][0]); |
---|
| 580 | |
---|
| 581 | /*~~~> Prepare the loop-independent part of the right-hand side */ |
---|
| 582 | Set2Zero(N, G); |
---|
| 583 | if (istage > 0) { |
---|
| 584 | for (j=0; j < istage; j++) { |
---|
| 585 | /* Gj(:) = sum_j Theta(i,j)*Zj(:) = H * sum_j A(i,j)*Fun(Zj(:)) */ |
---|
| 586 | WAXPY(N, rkTheta[j][istage], &Z[j][0], 1, G, 1); |
---|
| 587 | /* Zi(:) = sum_j Alpha(i,j)*Zj(:) */ |
---|
| 588 | WAXPY(N, rkAlpha[j][istage],&Z[j][0], 1, &Z[istage][0], 1); |
---|
| 589 | } |
---|
| 590 | } |
---|
| 591 | |
---|
| 592 | /*~~~> Initializations for Newton iteration */ |
---|
| 593 | NewtonDone = 0; /* false */ |
---|
| 594 | Fac = (KPP_REAL)0.5; /* Step reduction factor */ |
---|
| 595 | |
---|
| 596 | for (NewtonIter=0; NewtonIter<NewtonMaxit; NewtonIter++ ) { /*NewtonLoop*/ |
---|
| 597 | /*~~~> Prepare the loop-dependent part of the right-hand side */ |
---|
| 598 | WADD(N, Y, &Z[istage][0], TMP); /* TMP <- Y + Zi */ |
---|
| 599 | FUN_CHEM(T+rkC[istage]*H, TMP, RHS); /* RHS <- Run(Y+Zi) */ |
---|
| 600 | ISTATUS[Nfun]++; |
---|
| 601 | /* RHS[0:N-1] = G[0:N-1] - Z[istage][0:N-1] + (H*rkGamma)*RHS[1:N] */ |
---|
| 602 | WSCAL(N, H*rkGamma, RHS, 1); |
---|
| 603 | WAXPY(N, -ONE, &Z[istage][0], 1, RHS, 1); |
---|
| 604 | WAXPY(N, ONE, G, 1, RHS, 1 ); |
---|
| 605 | |
---|
| 606 | /*~~~> Solve the linear system */ |
---|
| 607 | SDIRK_Solve('N', H, N, E, IP, IER, RHS, ISTATUS); |
---|
| 608 | |
---|
| 609 | /*~~~> Check convergence of Newton iterations */ |
---|
| 610 | NewtonIncrement = SDIRK_ErrorNorm(N, RHS, SCAL); |
---|
| 611 | if (NewtonIter == 0) { |
---|
| 612 | Theta = ABS(ThetaMin); |
---|
| 613 | NewtonRate = (KPP_REAL)2.0; |
---|
| 614 | } |
---|
| 615 | else { |
---|
| 616 | Theta = NewtonIncrement/NewtonIncrementOld; |
---|
| 617 | if (Theta < (KPP_REAL)0.99) { |
---|
| 618 | NewtonRate = Theta/(ONE-Theta); |
---|
| 619 | /* Predict error at the end of Newton process */ |
---|
| 620 | NewtonPredictedErr = (NewtonIncrement*pow(Theta, |
---|
| 621 | (NewtonMaxit - (NewtonIter+1))/(ONE - Theta))); |
---|
| 622 | if(NewtonPredictedErr >= NewtonTol) { |
---|
| 623 | /* Non-convergence of Newton: predicted error too large*/ |
---|
| 624 | Qnewton = MIN((KPP_REAL)10.0, NewtonPredictedErr/NewtonTol); |
---|
| 625 | Fac = (KPP_REAL)0.8 * pow(Qnewton, (-ONE / (1 + NewtonMaxit - |
---|
| 626 | NewtonIter + 1))); |
---|
| 627 | break; |
---|
| 628 | } |
---|
| 629 | } |
---|
| 630 | else /* Non-convergence of Newton: Theta too large */ { |
---|
| 631 | break; |
---|
| 632 | } |
---|
| 633 | } |
---|
| 634 | |
---|
| 635 | NewtonIncrementOld = NewtonIncrement; |
---|
| 636 | |
---|
| 637 | /* Update solution: Z(:) <-- Z(:)+RHS(:) */ |
---|
| 638 | WAXPY(N, ONE, RHS, 1, &Z[istage][0], 1); |
---|
| 639 | |
---|
| 640 | /* Check error in Newton iterations */ |
---|
| 641 | NewtonDone=(NewtonRate*NewtonIncrement<=NewtonTol); |
---|
| 642 | if (NewtonDone == 1) |
---|
| 643 | break; |
---|
| 644 | } /* end NewtonLoop for */ |
---|
| 645 | |
---|
| 646 | if(NewtonDone == 0) { |
---|
| 647 | H = Fac*H; |
---|
| 648 | Reject = 1; |
---|
| 649 | SkipJac = 1; |
---|
| 650 | SkipLU = 0; |
---|
| 651 | CycleTloop = 1; |
---|
| 652 | } /* end if */ |
---|
| 653 | |
---|
| 654 | if (CycleTloop == 1) { |
---|
| 655 | CycleTloop=0; |
---|
| 656 | break; |
---|
| 657 | } |
---|
| 658 | /* End of implified Newton iterations */ |
---|
| 659 | } /* end stages for */ |
---|
| 660 | |
---|
| 661 | if (CycleTloop==0) { |
---|
| 662 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 663 | /*~~~> Error estimation */ |
---|
| 664 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 665 | ISTATUS[Nstp]++; |
---|
| 666 | Set2Zero(N, TMP); |
---|
| 667 | |
---|
| 668 | for (i=0; i<rkS; i++) { |
---|
| 669 | if (rkE[i] != ZERO) |
---|
| 670 | WAXPY(N, rkE[i], &Z[i][0], 1, TMP, 1); |
---|
| 671 | } |
---|
| 672 | |
---|
| 673 | SDIRK_Solve('N', H, N, E, IP, IER, TMP, ISTATUS); |
---|
| 674 | Err = SDIRK_ErrorNorm(N, TMP, SCAL); |
---|
| 675 | |
---|
| 676 | /*~~~~> Computation of new step size Hnew */ |
---|
| 677 | Fac = FacSafe * pow((Err), (-ONE/rkELO)); |
---|
| 678 | Fac = MAX(FacMin, MIN(FacMax, Fac)); |
---|
| 679 | Hnew = H*Fac; |
---|
| 680 | |
---|
| 681 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 682 | /*~~~> Accept/Reject step */ |
---|
| 683 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 684 | if (Err < ONE) { /*~~~> Step is accepted */ |
---|
| 685 | FirstStep = 0; /* false */ |
---|
| 686 | ISTATUS[Nacc]++; |
---|
| 687 | |
---|
| 688 | /* Checkpoint solution */ |
---|
| 689 | SDIRK_Push( T, H, Y, Z, E, IP, Max_no_steps, SaveLU ); |
---|
| 690 | |
---|
| 691 | /*~~~> Update time and solution */ |
---|
| 692 | T = T + H; |
---|
| 693 | /* Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) */ |
---|
| 694 | for(i=0; i<rkS; i++) { |
---|
| 695 | if(rkD[i] != ZERO) |
---|
| 696 | WAXPY(N, rkD[i], &Z[i][0], 1, Y, 1); |
---|
| 697 | } |
---|
| 698 | |
---|
| 699 | /*~~~> Update scaling coefficients */ |
---|
| 700 | SDIRK_ErrorScale(N, ITOL, AbsTol, RelTol, Y, SCAL); |
---|
| 701 | |
---|
| 702 | /*~~~> Next time step */ |
---|
| 703 | Hnew = Tdirection*MIN(ABS(Hnew), Hmax); |
---|
| 704 | |
---|
| 705 | /* Last T and H */ |
---|
| 706 | RSTATUS[Ntexit] = T; |
---|
| 707 | RSTATUS[Nhexit] = H; |
---|
| 708 | RSTATUS[Nhnew] = Hnew; |
---|
| 709 | |
---|
| 710 | /* No step increase after a rejection */ |
---|
| 711 | if (Reject==1) |
---|
| 712 | Hnew = Tdirection*MIN(ABS(Hnew), ABS(H)); |
---|
| 713 | Reject = 0; /* false */ |
---|
| 714 | if ((T+Hnew/Qmin-Tfinal)*Tdirection > ZERO) |
---|
| 715 | H = Tfinal-T; |
---|
| 716 | else { |
---|
| 717 | Hratio = Hnew/H; |
---|
| 718 | /* If step not changed too much keep Jacobian and reuse LU */ |
---|
| 719 | SkipLU = ((Theta <= ThetaMin) && (Hratio >= Qmin) |
---|
| 720 | && (Hratio <= Qmax)); |
---|
| 721 | if (SkipLU==0) |
---|
| 722 | H = Hnew; |
---|
| 723 | } |
---|
| 724 | |
---|
| 725 | /* If convergence is fast enough, do not update Jacobian */ |
---|
| 726 | /* SkipJac = (Theta <= ThetaMin); */ |
---|
| 727 | SkipJac = 0; |
---|
| 728 | } |
---|
| 729 | else { /*~~~> Step is rejected */ |
---|
| 730 | if ((FirstStep==1) || (Reject==1)) |
---|
| 731 | H = FacRej * H; |
---|
| 732 | else |
---|
| 733 | H = Hnew; |
---|
| 734 | |
---|
| 735 | Reject = 1; |
---|
| 736 | SkipJac = 1; |
---|
| 737 | SkipLU = 0; |
---|
| 738 | if (ISTATUS[Nacc] >=1) |
---|
| 739 | ISTATUS[Nrej]++; |
---|
| 740 | |
---|
| 741 | } |
---|
| 742 | } /* end CycleTloop if */ |
---|
| 743 | } /* end Tloop */ |
---|
| 744 | |
---|
| 745 | /* Successful return */ |
---|
| 746 | return 1; |
---|
| 747 | |
---|
| 748 | } /* end SDIRK_FwdInt */ |
---|
| 749 | |
---|
| 750 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 751 | int SDIRK_DadjInt( int N, int NADJ, KPP_REAL Lambda[][NVAR], int SaveLU, |
---|
| 752 | int ISTATUS[], int ITOL, KPP_REAL AbsTol_adj[][NVAR], |
---|
| 753 | KPP_REAL RelTol_adj[][NVAR], int NewtonMaxit, |
---|
| 754 | KPP_REAL ThetaMin, KPP_REAL NewtonTol, int DirectADJ) { |
---|
| 755 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 756 | |
---|
| 757 | /*~~~> Local variables: */ |
---|
| 758 | KPP_REAL Y[NVAR]; |
---|
| 759 | KPP_REAL Z[Smax][NVAR], U[Smax][NADJ][NVAR], TMP[NVAR], G[NVAR], NewtonRate, |
---|
| 760 | SCAL[NVAR], DU[NVAR], T, H, Theta, NewtonPredictedErr, NewtonIncrement, |
---|
| 761 | NewtonIncrementOld=0.0; |
---|
| 762 | int i, j, IER=0, istage, iadj, NewtonIter, IP[NVAR], IP_adj[NVAR]; |
---|
| 763 | int Reject=0, SkipJac, SkipLU, NewtonDone; /* Boolean */ |
---|
| 764 | |
---|
| 765 | #ifdef FULL_ALGEBRA |
---|
| 766 | KPP_REAL E[NVAR][NVAR], Jac[NVAR][NVAR], E_adj[NVAR][NVAR]; |
---|
| 767 | #else |
---|
| 768 | KPP_REAL E[LU_NONZERO], Jac[LU_NONZERO], E_adj[LU_NONZERO]; |
---|
| 769 | #endif |
---|
| 770 | |
---|
| 771 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 772 | ~~~> Time loop begins |
---|
| 773 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 774 | while ( stack_ptr > -1 ) { /* Tloop */ |
---|
| 775 | |
---|
| 776 | /*~~~> Recover checkpoints for stage values and vectors */ |
---|
| 777 | SDIRK_Pop( &T, &H, &Y[0], &Z[0][0], &E[0], &IP[0], SaveLU ); |
---|
| 778 | |
---|
| 779 | /*~~~> Compute E = 1/(h*gamma)-Jac and its LU decomposition */ |
---|
| 780 | if (!SaveLU) { |
---|
| 781 | SkipJac = FALSE; |
---|
| 782 | SkipLU = FALSE; |
---|
| 783 | SDIRK_PrepareMatrix ( H, T, Y, Jac, SkipJac, SkipLU, E, IP, Reject, IER, |
---|
| 784 | ISTATUS ); |
---|
| 785 | if (IER != 0) |
---|
| 786 | return SDIRK_ErrorMsg(-8,T,H); |
---|
| 787 | } |
---|
| 788 | |
---|
| 789 | for( istage = rkS-1; istage >=0; istage--) { /* Stages Loop */ |
---|
| 790 | /*~~~> Jacobian of the current stage solution */ |
---|
| 791 | for(i=0; i<N; i++) |
---|
| 792 | TMP[i] = Y[i] + Z[istage][i]; |
---|
| 793 | JAC_CHEM(T+rkC[istage]*H,TMP,Jac); |
---|
| 794 | ISTATUS[Njac]++; |
---|
| 795 | |
---|
| 796 | if (DirectADJ) { |
---|
| 797 | #ifdef FULL_ALGEBRA |
---|
| 798 | for(i=0; i<N; i++) { |
---|
| 799 | for(j=0; j<N; j++) |
---|
| 800 | E_adj[i][j] = -Jac[i][j]; |
---|
| 801 | } |
---|
| 802 | for(i=0; i<N; i++) |
---|
| 803 | E_adj[i][i] = E_adj[i][i] + ONE/(H*rkGamma); |
---|
| 804 | |
---|
| 805 | DGETRF( N, N, E_adj, N, IP_adj, IER ); |
---|
| 806 | #else |
---|
| 807 | for(i=0; i<LU_NONZERO; i++) |
---|
| 808 | E_adj[i] = -Jac[i]; |
---|
| 809 | for(i=0; i<NVAR; i++) { |
---|
| 810 | j = LU_DIAG[i]; |
---|
| 811 | E_adj[j] = E_adj[j] + ONE/(H*rkGamma); |
---|
| 812 | } |
---|
| 813 | IER = KppDecomp (E_adj); |
---|
| 814 | #endif |
---|
| 815 | ISTATUS[Ndec]++; |
---|
| 816 | if (IER != 0) { |
---|
| 817 | printf("At stage %d the matrix used in adjoint computation is " |
---|
| 818 | "singular\n", istage); |
---|
| 819 | return SDIRK_ErrorMsg(-8,T,H); |
---|
| 820 | } |
---|
| 821 | } |
---|
| 822 | |
---|
| 823 | for(iadj=0; iadj<NADJ; iadj++) { /* adj loop */ |
---|
| 824 | |
---|
| 825 | /*~~~> Update scaling coefficients */ |
---|
| 826 | for(i=0; i<NVAR; i++) |
---|
| 827 | SDIRK_ErrorScale(N, ITOL, &AbsTol_adj[iadj][i], &RelTol_adj[iadj][i], |
---|
| 828 | &Lambda[iadj][i], SCAL); |
---|
| 829 | |
---|
| 830 | /*~~~> Prepare the loop-independent part of the right-hand side |
---|
| 831 | G(:) = H*Jac^T*( B(i)*Lambda + sum_j A(j,i)*Uj(:) ) */ |
---|
| 832 | for(i=0; i<N; i++) |
---|
| 833 | G[i] = rkB[istage]*Lambda[iadj][i]; |
---|
| 834 | if (istage+1 < rkS) { |
---|
| 835 | for (j=istage+1; j<rkS; j++) |
---|
| 836 | WAXPY(N,rkA[istage][j],&U[j][iadj][0],1,G,1); |
---|
| 837 | } |
---|
| 838 | #ifdef FULL_ALGEBRA |
---|
| 839 | TMP = MATMUL(TRANSPOSE(Jac),G); /* DZ <- Jac(Y+Z)*Y_tlm */ |
---|
| 840 | #else |
---|
| 841 | JacTR_SP_Vec ( Jac, G, TMP ); |
---|
| 842 | #endif |
---|
| 843 | for(i=0; i<N; i++) |
---|
| 844 | G[i] = H*TMP[i]; |
---|
| 845 | |
---|
| 846 | if (DirectADJ) { |
---|
| 847 | SDIRK_Solve ( 'T', H, N, E_adj, IP_adj, IER, G, ISTATUS ); |
---|
| 848 | for(i=0; i<N; i++) |
---|
| 849 | U[istage][iadj][i] = G[i]; |
---|
| 850 | } else { |
---|
| 851 | /*~~~> Initializations for Newton iteration */ |
---|
| 852 | Set2Zero(N,&U[istage][iadj][0]); |
---|
| 853 | NewtonDone = FALSE; |
---|
| 854 | |
---|
| 855 | /* Newton Loop */ |
---|
| 856 | for( NewtonIter=0; NewtonIter<NewtonMaxit; NewtonIter++) { |
---|
| 857 | |
---|
| 858 | /*~~~> Prepare the loop-dependent part of the right-hand side */ |
---|
| 859 | #ifdef FULL_ALGEBRA |
---|
| 860 | for(i=0; i<N; i++) |
---|
| 861 | TMP = MATMUL(TRANSPOSE(Jac),U[istage][iadj][i]); |
---|
| 862 | #else |
---|
| 863 | for(i=0; i<N; i++) |
---|
| 864 | JacTR_SP_Vec ( Jac, &U[istage][iadj][i], TMP ); |
---|
| 865 | #endif |
---|
| 866 | for(i=0; i<N; i++) |
---|
| 867 | DU[i] = U[istage][iadj][i] - (H*rkGamma)*TMP[i] - G[i]; |
---|
| 868 | |
---|
| 869 | /*~~~> Solve the linear system */ |
---|
| 870 | SDIRK_Solve ( 'T', H, N, E, IP, IER, DU, ISTATUS ); |
---|
| 871 | |
---|
| 872 | /*~~~> Check convergence of Newton iterations */ |
---|
| 873 | NewtonIncrement = SDIRK_ErrorNorm(N, DU, SCAL); |
---|
| 874 | if ( NewtonIter == 0 ) { |
---|
| 875 | Theta = ABS(ThetaMin); |
---|
| 876 | NewtonRate = (KPP_REAL)2.0; |
---|
| 877 | } |
---|
| 878 | else { |
---|
| 879 | Theta = NewtonIncrement/NewtonIncrementOld; |
---|
| 880 | if (Theta < (KPP_REAL)0.99) { |
---|
| 881 | NewtonRate = Theta/(ONE-Theta); |
---|
| 882 | /* Predict error at the end of Newton process */ |
---|
| 883 | NewtonPredictedErr = NewtonIncrement* |
---|
| 884 | pow(Theta,(NewtonMaxit-NewtonIter)) / (ONE-Theta); |
---|
| 885 | /* Non-convergence of Newton: predicted error too large */ |
---|
| 886 | if (NewtonPredictedErr >= NewtonTol) |
---|
| 887 | break; /* Exit NewtonLoop */ |
---|
| 888 | } else { /* Non-convergence of Newton: Theta too large */ |
---|
| 889 | break; |
---|
| 890 | } |
---|
| 891 | } |
---|
| 892 | NewtonIncrementOld = NewtonIncrement; |
---|
| 893 | /* Update solution */ |
---|
| 894 | for(i=0; i<N; i++) |
---|
| 895 | U[istage][iadj][i] -= DU[i]; |
---|
| 896 | |
---|
| 897 | /* Check error in Newton iterations */ |
---|
| 898 | NewtonDone = (NewtonRate*NewtonIncrement <= NewtonTol); |
---|
| 899 | /* AbsTol is often inappropriate for adjoints - |
---|
| 900 | we do at least 4 Newton iterations to ensure convergence |
---|
| 901 | of all adjoint components */ |
---|
| 902 | if ((NewtonIter>=4) && NewtonDone) |
---|
| 903 | break; /* Exit Newton Loop */ |
---|
| 904 | } |
---|
| 905 | |
---|
| 906 | /*~~~> If Newton iterations fail employ the direct solution */ |
---|
| 907 | if (!NewtonDone) { |
---|
| 908 | printf("Problems with Newton Adjoint!!!\n"); |
---|
| 909 | #ifdef FULL_ALGEBRA |
---|
| 910 | for(i=0; i<N; i++) |
---|
| 911 | E_adj[i][j] = -Jac[i][j]; |
---|
| 912 | for(j=0; j<N; j++) |
---|
| 913 | E_adj[j][j] += ONE/(H*rkGamma); |
---|
| 914 | DGETRF( N, N, E_adj, N, IP_adj, IER ); |
---|
| 915 | #else |
---|
| 916 | for(i=0; i<LU_NONZERO; i++) |
---|
| 917 | E_adj[i] = -Jac[i]; |
---|
| 918 | for(i=0; i<NVAR; i++) { |
---|
| 919 | j = LU_DIAG[i]; |
---|
| 920 | E_adj[j] += ONE/(H*rkGamma); |
---|
| 921 | } |
---|
| 922 | IER = KppDecomp ( E_adj); |
---|
| 923 | #endif |
---|
| 924 | ISTATUS[Ndec]++; |
---|
| 925 | if (IER != 0) { |
---|
| 926 | printf("At stage %d the matrix used in adjoint computation is " |
---|
| 927 | "singular", istage); |
---|
| 928 | return SDIRK_ErrorMsg(-8,T,H); |
---|
| 929 | } |
---|
| 930 | SDIRK_Solve ( 'T', H, N, E_adj, IP_adj, IER, G, ISTATUS ); |
---|
| 931 | for(i=0; i<N; i++) |
---|
| 932 | U[istage][iadj][i] = G[i]; |
---|
| 933 | } |
---|
| 934 | |
---|
| 935 | /*~~~> End of implified Newton iterations */ |
---|
| 936 | } /* End of DirADJ */ |
---|
| 937 | |
---|
| 938 | } /* End of adj */ |
---|
| 939 | |
---|
| 940 | } /* End of stages */ |
---|
| 941 | |
---|
| 942 | /*~~~> Update adjoint solution |
---|
| 943 | Y(:) <-- Y(:) + Sum_j rkD(j)*Z_j(:) */ |
---|
| 944 | for (istage=0; istage<rkS; istage++) { |
---|
| 945 | for (iadj=0; iadj<NADJ; iadj++) { |
---|
| 946 | for(i=0; i<N; i++) |
---|
| 947 | Lambda[iadj][i] += U[istage][iadj][i]; |
---|
| 948 | } |
---|
| 949 | } |
---|
| 950 | } /* End of Tloop */ |
---|
| 951 | |
---|
| 952 | /* Successful return */ |
---|
| 953 | return 1; |
---|
| 954 | |
---|
| 955 | } /* End of SDIRK_DadjInt */ |
---|
| 956 | |
---|
| 957 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 958 | void SDIRK_AllocBuffers(int Max_no_steps, int rkS, int SaveLU) { |
---|
| 959 | /*~~~> Allocate buffer space for checkpointing |
---|
| 960 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 961 | int i,j; |
---|
| 962 | |
---|
| 963 | chk_H = (KPP_REAL*) malloc(Max_no_steps * sizeof(KPP_REAL)); |
---|
| 964 | if (chk_H == NULL) { |
---|
| 965 | printf("Failed allocation of buffer H\n"); |
---|
| 966 | exit(0); |
---|
| 967 | } |
---|
| 968 | |
---|
| 969 | chk_T = (KPP_REAL*) malloc(Max_no_steps * sizeof(KPP_REAL)); |
---|
| 970 | if (chk_T == NULL) { |
---|
| 971 | printf("Failed allocation of buffer T\n"); |
---|
| 972 | exit(0); |
---|
| 973 | } |
---|
| 974 | |
---|
| 975 | chk_Y = (KPP_REAL**) malloc(Max_no_steps * sizeof(KPP_REAL*)); |
---|
| 976 | if (chk_Y == NULL) { |
---|
| 977 | printf("Failed allocation of buffer Y\n"); |
---|
| 978 | exit(0); |
---|
| 979 | } |
---|
| 980 | for(i=0; i<Max_no_steps; i++) { |
---|
| 981 | chk_Y[i] = (KPP_REAL*) malloc(NVAR * sizeof(KPP_REAL)); |
---|
| 982 | if (chk_Y[i] == NULL) { |
---|
| 983 | printf("Failed allocation of buffer Y\n"); |
---|
| 984 | exit(0); |
---|
| 985 | } |
---|
| 986 | } |
---|
| 987 | |
---|
| 988 | chk_Z = (KPP_REAL***) malloc(Max_no_steps * sizeof(KPP_REAL**)); |
---|
| 989 | if (chk_Z == NULL) { |
---|
| 990 | printf("Failed allocation of buffer Z\n"); |
---|
| 991 | exit(0); |
---|
| 992 | } |
---|
| 993 | for(i=0; i<Max_no_steps; i++) { |
---|
| 994 | chk_Z[i] = (KPP_REAL**) malloc(rkS * sizeof(KPP_REAL*)); |
---|
| 995 | if (chk_Z[i] == NULL) { |
---|
| 996 | printf("Failed allocation of buffer Z\n"); |
---|
| 997 | exit(0); |
---|
| 998 | } |
---|
| 999 | for(j=0; j<rkS; j++) { |
---|
| 1000 | chk_Z[i][j] = (KPP_REAL*) malloc(NVAR * sizeof(KPP_REAL)); |
---|
| 1001 | if (chk_Z[i][j] == NULL) { |
---|
| 1002 | printf("Failed allocation of buffer Z\n"); |
---|
| 1003 | exit(0); |
---|
| 1004 | } |
---|
| 1005 | } |
---|
| 1006 | } |
---|
| 1007 | |
---|
| 1008 | if (SaveLU) { |
---|
| 1009 | #ifdef FULL_ALGEBRA |
---|
| 1010 | chk_J = (KPP_REAL***) malloc(Max_no_steps * sizeof(KPP_REAL**)); |
---|
| 1011 | if (chk_J == NULL) { |
---|
| 1012 | printf("Failed allocation of buffer J\n"); |
---|
| 1013 | exit(0); |
---|
| 1014 | } |
---|
| 1015 | for(i=0; i<Max_no_steps; i++) { |
---|
| 1016 | chk_J[i] = (KPP_REAL**) malloc(NVAR * sizeof(KPP_REAL*)); |
---|
| 1017 | if (chk_J[i] == NULL) { |
---|
| 1018 | printf("Failed allocation of buffer J\n"); |
---|
| 1019 | exit(0); |
---|
| 1020 | } |
---|
| 1021 | for(j=0; j<NVAR; j++) { |
---|
| 1022 | chk_J[i][j] = (KPP_REAL*) malloc(NVAR * sizeof(KPP_REAL)); |
---|
| 1023 | if (chk_J[i][j] == NULL) { |
---|
| 1024 | printf("Failed allocation of buffer J\n"); |
---|
| 1025 | exit(0); |
---|
| 1026 | } |
---|
| 1027 | } |
---|
| 1028 | } |
---|
| 1029 | #else |
---|
| 1030 | chk_J = (KPP_REAL**) malloc(Max_no_steps * sizeof(KPP_REAL*)); |
---|
| 1031 | if (chk_J == NULL) { |
---|
| 1032 | printf("Failed allocation of buffer J\n"); |
---|
| 1033 | exit(0); |
---|
| 1034 | } |
---|
| 1035 | for(i=0; i<Max_no_steps; i++) { |
---|
| 1036 | chk_J[i] = (KPP_REAL*) malloc(LU_NONZERO * sizeof(KPP_REAL)); |
---|
| 1037 | if (chk_J[i] == NULL) { |
---|
| 1038 | printf("Failed allocation of buffer J\n"); |
---|
| 1039 | exit(0); |
---|
| 1040 | } |
---|
| 1041 | } |
---|
| 1042 | #endif |
---|
| 1043 | |
---|
| 1044 | chk_P = (int**) malloc(Max_no_steps * sizeof(int*)); |
---|
| 1045 | if (chk_P == NULL) { |
---|
| 1046 | printf("Failed allocation of buffer P\n"); |
---|
| 1047 | exit(0); |
---|
| 1048 | } |
---|
| 1049 | for(i=0; i<Max_no_steps; i++) { |
---|
| 1050 | chk_P[i] = (int*) malloc(NVAR * sizeof(int)); |
---|
| 1051 | if (chk_P[i] == NULL) { |
---|
| 1052 | printf("Failed allocation of buffer P\n"); |
---|
| 1053 | exit(0); |
---|
| 1054 | } |
---|
| 1055 | } |
---|
| 1056 | } |
---|
| 1057 | } /* End of SDIRK_AllocBuffers */ |
---|
| 1058 | |
---|
| 1059 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1060 | void SDIRK_FreeBuffers(int Max_no_steps, int SaveLU) { |
---|
| 1061 | /*~~~> Deallocate buffer space for discrete adjoint |
---|
| 1062 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1063 | int i,j; |
---|
| 1064 | |
---|
| 1065 | free(chk_H); |
---|
| 1066 | free(chk_T); |
---|
| 1067 | |
---|
| 1068 | for(i=0; i<Max_no_steps; i++) |
---|
| 1069 | free(chk_Y[i]); |
---|
| 1070 | free(chk_Y); |
---|
| 1071 | |
---|
| 1072 | for(i=0; i<Max_no_steps; i++) { |
---|
| 1073 | for(j=0; j<rkS; j++) { |
---|
| 1074 | free(chk_Z[i][j]); |
---|
| 1075 | } |
---|
| 1076 | free(chk_Z[i]); |
---|
| 1077 | } |
---|
| 1078 | free(chk_Z); |
---|
| 1079 | |
---|
| 1080 | if(SaveLU) { |
---|
| 1081 | #ifdef FULL_ALGEBRA |
---|
| 1082 | for(i=0; i<Max_no_steps; i++) { |
---|
| 1083 | for(j=0; j<rkS; j++) { |
---|
| 1084 | free(chk_J[i][j]); |
---|
| 1085 | } |
---|
| 1086 | free(chk_J[i]); |
---|
| 1087 | } |
---|
| 1088 | free(chk_Z); |
---|
| 1089 | #else |
---|
| 1090 | for(i=0; i<Max_no_steps; i++) |
---|
| 1091 | free(chk_J[i]); |
---|
| 1092 | free(chk_J); |
---|
| 1093 | #endif |
---|
| 1094 | |
---|
| 1095 | for(i=0; i<Max_no_steps; i++) |
---|
| 1096 | free(chk_P[i]); |
---|
| 1097 | free(chk_P); |
---|
| 1098 | } |
---|
| 1099 | } /* End of SDIRK_FreeBuffers */ |
---|
| 1100 | |
---|
| 1101 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1102 | void SDIRK_Push( KPP_REAL T, KPP_REAL H, KPP_REAL Y[], KPP_REAL Z[][NVAR], |
---|
| 1103 | KPP_REAL E[], int P[], int Max_no_steps, int SaveLU ) { |
---|
| 1104 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1105 | ~~~> Saves the next trajectory snapshot for discrete adjoints |
---|
| 1106 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1107 | |
---|
| 1108 | int i,j; |
---|
| 1109 | |
---|
| 1110 | stack_ptr++; |
---|
| 1111 | if( stack_ptr > Max_no_steps ) { |
---|
| 1112 | printf( "Push failed: buffer overflow"); |
---|
| 1113 | exit(0); |
---|
| 1114 | } |
---|
| 1115 | |
---|
| 1116 | chk_H[ stack_ptr ] = H; |
---|
| 1117 | chk_T[ stack_ptr ] = T; |
---|
| 1118 | for(i=0; i<NVAR; i++) { |
---|
| 1119 | chk_Y[stack_ptr][i] = Y[i]; |
---|
| 1120 | for(j=0; j<rkS; j++) |
---|
| 1121 | chk_Z[stack_ptr][j][i] = Z[j][i]; |
---|
| 1122 | } |
---|
| 1123 | |
---|
| 1124 | if (SaveLU) { |
---|
| 1125 | #ifdef FULL_ALGEBRA |
---|
| 1126 | for(i=0; i<NVAR; i++) { |
---|
| 1127 | for(j=0; j<NVAR; j++) |
---|
| 1128 | chk_J[stack_ptr][i][j] = E[i][j]; |
---|
| 1129 | chk_P[stack_ptr][i] = P[i]; |
---|
| 1130 | } |
---|
| 1131 | #else |
---|
| 1132 | for(i=0; i<LU_NONZERO; i++) |
---|
| 1133 | chk_J[stack_ptr][i] = E[i]; |
---|
| 1134 | #endif |
---|
| 1135 | } |
---|
| 1136 | |
---|
| 1137 | } /* End of SDIRK_Push */ |
---|
| 1138 | |
---|
| 1139 | |
---|
| 1140 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1141 | void SDIRK_Pop( KPP_REAL* T, KPP_REAL* H, KPP_REAL* Y, KPP_REAL* Z, KPP_REAL* E, |
---|
| 1142 | int* P, int SaveLU ) { |
---|
| 1143 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1144 | ~~~> Retrieves the next trajectory snapshot for discrete adjoints |
---|
| 1145 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1146 | |
---|
| 1147 | int i,j; |
---|
| 1148 | |
---|
| 1149 | if ( stack_ptr < 0 ) { |
---|
| 1150 | printf( "Pop failed: empty buffer\n" ); |
---|
| 1151 | exit(0); |
---|
| 1152 | } |
---|
| 1153 | |
---|
| 1154 | *H = chk_H[ stack_ptr ]; |
---|
| 1155 | *T = chk_T[ stack_ptr ]; |
---|
| 1156 | for(i=0; i<NVAR; i++) { |
---|
| 1157 | Y[i] = chk_Y[stack_ptr][i]; |
---|
| 1158 | for(j=0; j<rkS; j++) |
---|
| 1159 | Z[(j * NVAR) + i] = chk_Z[stack_ptr][j][i]; |
---|
| 1160 | } |
---|
| 1161 | |
---|
| 1162 | if (SaveLU) { |
---|
| 1163 | #ifdef FULL_ALGEBRA |
---|
| 1164 | for(i=0; i<NVAR; i++) { |
---|
| 1165 | for(j=0; j<NVAR; j++) |
---|
| 1166 | E[(j*NVAR)+i] = chk_J[stack_ptr][j][i]; |
---|
| 1167 | P[i] = chk_P[stack_ptr][i]; |
---|
| 1168 | } |
---|
| 1169 | #else |
---|
| 1170 | for(i=0; i<LU_NONZERO; i++) |
---|
| 1171 | E[i] = chk_J[stack_ptr][i]; |
---|
| 1172 | #endif |
---|
| 1173 | } |
---|
| 1174 | |
---|
| 1175 | stack_ptr--; |
---|
| 1176 | |
---|
| 1177 | } /* End of SDIRK_Pop */ |
---|
| 1178 | |
---|
| 1179 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1180 | void SDIRK_ErrorScale( int N, int ITOL, KPP_REAL AbsTol[], KPP_REAL RelTol[], |
---|
| 1181 | KPP_REAL Y[], KPP_REAL SCAL[]) { |
---|
| 1182 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1183 | |
---|
| 1184 | int i; |
---|
| 1185 | if (ITOL == 0){ |
---|
| 1186 | for (i = 0; i < NVAR; i++) |
---|
| 1187 | SCAL[i] = ONE / (AbsTol[0]+RelTol[0]*ABS(Y[i]) ); |
---|
| 1188 | } |
---|
| 1189 | else { |
---|
| 1190 | for (i = 0; i < NVAR; i++) |
---|
| 1191 | SCAL[i] = ONE / (AbsTol[i]+RelTol[i]*ABS(Y[i]) ); |
---|
| 1192 | } |
---|
| 1193 | |
---|
| 1194 | } /* End of SDIRK_ErrorScale */ |
---|
| 1195 | |
---|
| 1196 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1197 | KPP_REAL SDIRK_ErrorNorm( int N, KPP_REAL Y[], KPP_REAL SCAL[] ) { |
---|
| 1198 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1199 | |
---|
| 1200 | int i; |
---|
| 1201 | KPP_REAL Err = ZERO; |
---|
| 1202 | |
---|
| 1203 | for (i = 0; i < N; i++) |
---|
| 1204 | Err = Err + pow( (Y[i]*SCAL[i]), 2); |
---|
| 1205 | Err = MAX( SQRT(Err/(KPP_REAL)N), (KPP_REAL)1.0e-10); |
---|
| 1206 | |
---|
| 1207 | return Err; |
---|
| 1208 | |
---|
| 1209 | } /* End of SDIRK_ErrorNorm */ |
---|
| 1210 | |
---|
| 1211 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1212 | int SDIRK_ErrorMsg(int code, KPP_REAL T, KPP_REAL H) { |
---|
| 1213 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1214 | Handles all error messages |
---|
| 1215 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */ |
---|
| 1216 | |
---|
| 1217 | printf("\nForced exit from Sdirk due to the following error:\n"); |
---|
| 1218 | |
---|
| 1219 | switch (code) { |
---|
| 1220 | case -1: |
---|
| 1221 | printf("--> Improper value for maximal no of steps\n"); |
---|
| 1222 | break; |
---|
| 1223 | case -2: |
---|
| 1224 | printf("--> Selected Rosenbrock method not implemented\n"); |
---|
| 1225 | break; |
---|
| 1226 | case -3: |
---|
| 1227 | printf("--> Hmin/Hmax/Hstart must be positive\n"); |
---|
| 1228 | break; |
---|
| 1229 | case -4: |
---|
| 1230 | printf("--> FacMin/FacMax/FacRej must be positive\n"); |
---|
| 1231 | break; |
---|
| 1232 | case -5: |
---|
| 1233 | printf("--> Improper tolerance values\n"); |
---|
| 1234 | break; |
---|
| 1235 | case -6: |
---|
| 1236 | printf("--> No of steps exceeds maximum bound\n"); |
---|
| 1237 | break; |
---|
| 1238 | case -7: |
---|
| 1239 | printf("--> Step size too small T + 10*H = T or H < Roundoff\n"); |
---|
| 1240 | break; |
---|
| 1241 | case -8: |
---|
| 1242 | printf("--> Matrix is repeatedly singular\n"); |
---|
| 1243 | break; |
---|
| 1244 | default: /* causing an error */ |
---|
| 1245 | printf("Unknown Error code: %d\n", code); |
---|
| 1246 | } |
---|
| 1247 | |
---|
| 1248 | printf("\nTime = %f and H = %f\n", T, H ); |
---|
| 1249 | return code; |
---|
| 1250 | |
---|
| 1251 | } /* end SDIRK_ErrorMsg */ |
---|
| 1252 | |
---|
| 1253 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1254 | void SDIRK_PrepareMatrix ( KPP_REAL H, KPP_REAL T, KPP_REAL Y[], |
---|
| 1255 | KPP_REAL FJAC[], int SkipJac, int SkipLU, |
---|
| 1256 | KPP_REAL E[], int IP[], int Reject, int ISING, |
---|
| 1257 | int ISTATUS[] ) { |
---|
| 1258 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1259 | ~~~> Compute the matrix E = 1/(H*GAMMA)*Jac, and its decomposition |
---|
| 1260 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1261 | |
---|
| 1262 | KPP_REAL HGammaInv; |
---|
| 1263 | int i, j, ConsecutiveSng = 0; |
---|
| 1264 | |
---|
| 1265 | ISING = 1; |
---|
| 1266 | |
---|
| 1267 | while (ISING != 0) { |
---|
| 1268 | HGammaInv = ONE/(H*rkGamma); |
---|
| 1269 | |
---|
| 1270 | /*~~~> Compute the Jacobian */ |
---|
| 1271 | if (SkipJac==0) { |
---|
| 1272 | JAC_CHEM(T,Y,FJAC); |
---|
| 1273 | ISTATUS[Njac]++; |
---|
| 1274 | } |
---|
| 1275 | |
---|
| 1276 | #ifdef FULL_ALGEBRA |
---|
| 1277 | for(j=0; j<NVAR; j++) { |
---|
| 1278 | for(i=0; i<NVAR; i++) |
---|
| 1279 | E[j][i] = -FJAC[j][i]; |
---|
| 1280 | E[j][j] = E[j][j] + HGammaInv; |
---|
| 1281 | } |
---|
| 1282 | DGETRF(NVAR, NVAR, E, NVAR, IP, ISING); |
---|
| 1283 | #else |
---|
| 1284 | for(i=0; i<LU_NONZERO; i++) |
---|
| 1285 | E[i] = -FJAC[i]; |
---|
| 1286 | for(i=0; i<NVAR; i++) { |
---|
| 1287 | j = LU_DIAG[i]; |
---|
| 1288 | E[j]=E[j] + HGammaInv; |
---|
| 1289 | } |
---|
| 1290 | |
---|
| 1291 | ISING = KppDecomp(E); |
---|
| 1292 | IP[0] = 1; |
---|
| 1293 | #endif |
---|
| 1294 | |
---|
| 1295 | ISTATUS[Ndec]++; |
---|
| 1296 | |
---|
| 1297 | if (ISING != 0) { |
---|
| 1298 | printf("MATRIX IS SINGULAR, ISING=%d T=%e H=%e\n", ISING, T, H); |
---|
| 1299 | ISTATUS[Nsng]++; |
---|
| 1300 | ConsecutiveSng++; |
---|
| 1301 | if (ConsecutiveSng >= 6) |
---|
| 1302 | return; /* Failure */ |
---|
| 1303 | H = (KPP_REAL)(0.5)*H; |
---|
| 1304 | SkipJac = 0; /* False */ |
---|
| 1305 | SkipLU = 0; /* False */ |
---|
| 1306 | Reject = 1; /* True */ |
---|
| 1307 | } |
---|
| 1308 | } |
---|
| 1309 | } /* End of SDIRK_PrepareMatrix */ |
---|
| 1310 | |
---|
| 1311 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1312 | void SDIRK_Solve ( char Transp, KPP_REAL H, int N, KPP_REAL E[], int IP[], |
---|
| 1313 | int ISING, KPP_REAL RHS[], int ISTATUS[] ) { |
---|
| 1314 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
---|
| 1315 | ~~~> Solves the system (H*Gamma-Jac)*x = R |
---|
| 1316 | using the LU decomposition of E = I - 1/(H*Gamma)*Jac |
---|
| 1317 | ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1318 | |
---|
| 1319 | KPP_REAL HGammaInv; |
---|
| 1320 | |
---|
| 1321 | HGammaInv = ONE/(H*rkGamma); |
---|
| 1322 | WSCAL(N,HGammaInv,RHS,1); |
---|
| 1323 | switch (Transp) { |
---|
| 1324 | case 'N': |
---|
| 1325 | #ifdef FULL_ALGEBRA |
---|
| 1326 | DGETRS( 'N', N, 1, E, N, IP, RHS, N, ISING ); |
---|
| 1327 | #else |
---|
| 1328 | KppSolve(E, RHS); |
---|
| 1329 | #endif |
---|
| 1330 | break; |
---|
| 1331 | case 'T': |
---|
| 1332 | #ifdef FULL_ALGEBRA |
---|
| 1333 | DGETRS( 'T', N, 1, E, N, IP, RHS, N, ISING ); |
---|
| 1334 | #else |
---|
| 1335 | KppSolveTR(E, RHS, RHS); |
---|
| 1336 | #endif |
---|
| 1337 | break; |
---|
| 1338 | default: |
---|
| 1339 | printf("Error in SDIRK_Solve. Unknown Transp argument: %c\n", Transp); |
---|
| 1340 | exit(0); |
---|
| 1341 | } |
---|
| 1342 | ISTATUS[Nsol]++; |
---|
| 1343 | } /* End of SDIRK_Solve */ |
---|
| 1344 | |
---|
| 1345 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1346 | void Sdirk4a() |
---|
| 1347 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1348 | { |
---|
| 1349 | sdMethod = S4A; |
---|
| 1350 | |
---|
| 1351 | /* Number of stages */ |
---|
| 1352 | rkS = 5; |
---|
| 1353 | |
---|
| 1354 | /* Method Coefficients */ |
---|
| 1355 | rkGamma = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1356 | |
---|
| 1357 | rkA[0][0] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1358 | rkA[0][1] = (KPP_REAL)0.5000000000000000000000000000000000; |
---|
| 1359 | rkA[1][1] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1360 | rkA[0][2] = (KPP_REAL)0.3541539528432732316227461858529820; |
---|
| 1361 | rkA[1][2] = (KPP_REAL)(-0.5415395284327323162274618585298197e-01); |
---|
| 1362 | rkA[2][2] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1363 | rkA[0][3] = (KPP_REAL)0.8515494131138652076337791881433756e-01; |
---|
| 1364 | rkA[1][3] = (KPP_REAL)(-0.6484332287891555171683963466229754e-01); |
---|
| 1365 | rkA[2][3] = (KPP_REAL)0.7915325296404206392428857585141242e-01; |
---|
| 1366 | rkA[3][3] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1367 | rkA[0][4] = (KPP_REAL)2.100115700566932777970612055999074; |
---|
| 1368 | rkA[1][4] = (KPP_REAL)(-0.7677800284445976813343102185062276); |
---|
| 1369 | rkA[2][4] = (KPP_REAL)2.399816361080026398094746205273880; |
---|
| 1370 | rkA[3][4] = (KPP_REAL)(-2.998818699869028161397714709433394); |
---|
| 1371 | rkA[4][4] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1372 | rkB[0] = (KPP_REAL)2.100115700566932777970612055999074; |
---|
| 1373 | rkB[1] = (KPP_REAL)(-0.7677800284445976813343102185062276); |
---|
| 1374 | rkB[2] = (KPP_REAL)2.399816361080026398094746205273880; |
---|
| 1375 | rkB[3] = (KPP_REAL)(-2.998818699869028161397714709433394); |
---|
| 1376 | rkB[4] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1377 | |
---|
| 1378 | rkBhat[0] = (KPP_REAL)2.885264204387193942183851612883390; |
---|
| 1379 | rkBhat[1] = (KPP_REAL)(-0.1458793482962771337341223443218041); |
---|
| 1380 | rkBhat[2] = (KPP_REAL)2.390008682465139866479830743628554; |
---|
| 1381 | rkBhat[3] = (KPP_REAL)(-4.129393538556056674929560012190140); |
---|
| 1382 | rkBhat[4] = ZERO; |
---|
| 1383 | |
---|
| 1384 | rkC[0] = (KPP_REAL)0.2666666666666666666666666666666667; |
---|
| 1385 | rkC[1] = (KPP_REAL)0.7666666666666666666666666666666667; |
---|
| 1386 | rkC[2] = (KPP_REAL)0.5666666666666666666666666666666667; |
---|
| 1387 | rkC[3] = (KPP_REAL)0.3661315380631796996374935266701191; |
---|
| 1388 | rkC[4] = ONE; |
---|
| 1389 | |
---|
| 1390 | /* Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1391 | rkD[0] = ZERO; |
---|
| 1392 | rkD[1] = ZERO; |
---|
| 1393 | rkD[2] = ZERO; |
---|
| 1394 | rkD[3] = ZERO; |
---|
| 1395 | rkD[4] = ONE; |
---|
| 1396 | |
---|
| 1397 | /* Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1398 | rkE[0] = (KPP_REAL)(-0.6804000050475287124787034884002302); |
---|
| 1399 | rkE[1] = (KPP_REAL)(1.558961944525217193393931795738823); |
---|
| 1400 | rkE[2] = (KPP_REAL)(-13.55893003128907927748632408763868); |
---|
| 1401 | rkE[3] = (KPP_REAL)(15.48522576958521253098585004571302); |
---|
| 1402 | rkE[4] = ONE; |
---|
| 1403 | |
---|
| 1404 | /* Local order of Err estimate */ |
---|
| 1405 | rkELO = 4; |
---|
| 1406 | |
---|
| 1407 | /* h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1408 | rkTheta[0][1] = (KPP_REAL)1.875000000000000000000000000000000; |
---|
| 1409 | rkTheta[0][2] = (KPP_REAL)1.708847304091539528432732316227462; |
---|
| 1410 | rkTheta[1][2] = (KPP_REAL)(-0.2030773231622746185852981969486824); |
---|
| 1411 | rkTheta[0][3] = (KPP_REAL)0.2680325578937783958847157206823118; |
---|
| 1412 | rkTheta[1][3] = (KPP_REAL)(-0.1828840955527181631794050728644549); |
---|
| 1413 | rkTheta[2][3] = (KPP_REAL)0.2968246986151577397160821594427966; |
---|
| 1414 | rkTheta[0][4] = (KPP_REAL)0.9096171815241460655379433581446771; |
---|
| 1415 | rkTheta[1][4] = (KPP_REAL)(-3.108254967778352416114774430509465); |
---|
| 1416 | rkTheta[2][4] = (KPP_REAL)12.33727431701306195581826123274001; |
---|
| 1417 | rkTheta[3][4] = (KPP_REAL)(-11.24557012450885560524143016037523); |
---|
| 1418 | |
---|
| 1419 | /* Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} */ |
---|
| 1420 | rkAlpha[0][1] = (KPP_REAL)2.875000000000000000000000000000000; |
---|
| 1421 | rkAlpha[0][2] = (KPP_REAL)0.8500000000000000000000000000000000; |
---|
| 1422 | rkAlpha[1][2] = (KPP_REAL)0.4434782608695652173913043478260870; |
---|
| 1423 | rkAlpha[0][3] = (KPP_REAL)0.7352046091658870564637910527807370; |
---|
| 1424 | rkAlpha[1][3] = (KPP_REAL)(-0.9525565003057343527941920657462074e-01); |
---|
| 1425 | rkAlpha[2][3] = (KPP_REAL)0.4290111305453813852259481840631738; |
---|
| 1426 | rkAlpha[0][4] = (KPP_REAL)(-16.10898993405067684831655675112808); |
---|
| 1427 | rkAlpha[1][4] = (KPP_REAL)6.559571569643355712998131800797873; |
---|
| 1428 | rkAlpha[2][4] = (KPP_REAL)(-15.90772144271326504260996815012482); |
---|
| 1429 | rkAlpha[3][4] = (KPP_REAL)25.34908987169226073668861694892683; |
---|
| 1430 | |
---|
| 1431 | rkELO = (KPP_REAL)4.0; |
---|
| 1432 | |
---|
| 1433 | } /* end Sdirk4a */ |
---|
| 1434 | |
---|
| 1435 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1436 | void Sdirk4b() { |
---|
| 1437 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1438 | |
---|
| 1439 | sdMethod = S4B; |
---|
| 1440 | |
---|
| 1441 | /* Number of stages */ |
---|
| 1442 | rkS = 5; |
---|
| 1443 | |
---|
| 1444 | /* Method coefficients */ |
---|
| 1445 | rkGamma = (KPP_REAL)0.25; |
---|
| 1446 | |
---|
| 1447 | rkA[0][0] = (KPP_REAL)0.25; |
---|
| 1448 | rkA[0][1] = (KPP_REAL)0.5; |
---|
| 1449 | rkA[1][1] = (KPP_REAL)0.25; |
---|
| 1450 | rkA[0][2] = (KPP_REAL)0.34; |
---|
| 1451 | rkA[1][2] = (KPP_REAL)(-0.40e-01); |
---|
| 1452 | rkA[2][2] = (KPP_REAL)0.25; |
---|
| 1453 | rkA[0][3] = (KPP_REAL)0.2727941176470588235294117647058824; |
---|
| 1454 | rkA[1][3] = (KPP_REAL)(-0.5036764705882352941176470588235294e-01); |
---|
| 1455 | rkA[2][3] = (KPP_REAL)0.2757352941176470588235294117647059e-01; |
---|
| 1456 | rkA[3][3] = (KPP_REAL)0.25; |
---|
| 1457 | rkA[0][4] = (KPP_REAL)1.041666666666666666666666666666667; |
---|
| 1458 | rkA[1][4] = (KPP_REAL)(-1.020833333333333333333333333333333); |
---|
| 1459 | rkA[2][4] = (KPP_REAL)7.812500000000000000000000000000000; |
---|
| 1460 | rkA[3][4] = (KPP_REAL)(-7.083333333333333333333333333333333); |
---|
| 1461 | rkA[4][4] = (KPP_REAL)0.25; |
---|
| 1462 | |
---|
| 1463 | rkB[0] = (KPP_REAL)1.041666666666666666666666666666667; |
---|
| 1464 | rkB[1] = (KPP_REAL)(-1.020833333333333333333333333333333); |
---|
| 1465 | rkB[2] = (KPP_REAL)7.812500000000000000000000000000000; |
---|
| 1466 | rkB[3] = (KPP_REAL)(-7.083333333333333333333333333333333); |
---|
| 1467 | rkB[4] = (KPP_REAL)0.250000000000000000000000000000000; |
---|
| 1468 | |
---|
| 1469 | rkBhat[0] = (KPP_REAL)1.069791666666666666666666666666667; |
---|
| 1470 | rkBhat[1] = (KPP_REAL)(-0.894270833333333333333333333333333); |
---|
| 1471 | rkBhat[2] = (KPP_REAL)7.695312500000000000000000000000000; |
---|
| 1472 | rkBhat[3] = (KPP_REAL)(-7.083333333333333333333333333333333); |
---|
| 1473 | rkBhat[4] = (KPP_REAL)0.212500000000000000000000000000000; |
---|
| 1474 | |
---|
| 1475 | rkC[0] = (KPP_REAL)0.25; |
---|
| 1476 | rkC[1] = (KPP_REAL)0.75; |
---|
| 1477 | rkC[2] = (KPP_REAL)0.55; |
---|
| 1478 | rkC[3] = (KPP_REAL)0.5; |
---|
| 1479 | rkC[4] = ONE; |
---|
| 1480 | |
---|
| 1481 | /* Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1482 | rkD[0] = ZERO; |
---|
| 1483 | rkD[1] = ZERO; |
---|
| 1484 | rkD[2] = ZERO; |
---|
| 1485 | rkD[3] = ZERO; |
---|
| 1486 | rkD[4] = ONE; |
---|
| 1487 | |
---|
| 1488 | /* Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1489 | rkE[0] = (KPP_REAL)0.5750; |
---|
| 1490 | rkE[1] = (KPP_REAL)0.2125; |
---|
| 1491 | rkE[2] = (KPP_REAL)(-4.6875); |
---|
| 1492 | rkE[3] = (KPP_REAL)4.2500; |
---|
| 1493 | rkE[4] = (KPP_REAL)0.1500; |
---|
| 1494 | |
---|
| 1495 | /* Local order of Err estimate */ |
---|
| 1496 | rkELO = 4; |
---|
| 1497 | |
---|
| 1498 | /* h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1499 | rkTheta[0][1] = (KPP_REAL)2.0; |
---|
| 1500 | rkTheta[0][2] = (KPP_REAL)1.680000000000000000000000000000000; |
---|
| 1501 | rkTheta[1][2] = (KPP_REAL)(-0.1600000000000000000000000000000000); |
---|
| 1502 | rkTheta[0][3] = (KPP_REAL)1.308823529411764705882352941176471; |
---|
| 1503 | rkTheta[1][3] = (KPP_REAL)(-0.1838235294117647058823529411764706); |
---|
| 1504 | rkTheta[2][3] = (KPP_REAL)0.1102941176470588235294117647058824; |
---|
| 1505 | rkTheta[0][4] = (KPP_REAL)(-3.083333333333333333333333333333333); |
---|
| 1506 | rkTheta[1][4] = (KPP_REAL)(-4.291666666666666666666666666666667); |
---|
| 1507 | rkTheta[2][4] = (KPP_REAL)34.37500000000000000000000000000000; |
---|
| 1508 | rkTheta[3][4] = (KPP_REAL)(-28.3333333333333333333333333333); |
---|
| 1509 | |
---|
| 1510 | /* Starting value for Newton iterations: Z_i^0 = Sum_j {rkAlpha_ij*Z_j} */ |
---|
| 1511 | rkAlpha[0][1] = (KPP_REAL)3.0; |
---|
| 1512 | rkAlpha[0][2] = (KPP_REAL)0.8800000000000000000000000000000000; |
---|
| 1513 | rkAlpha[1][2] = (KPP_REAL)0.4400000000000000000000000000000000; |
---|
| 1514 | rkAlpha[0][3] = (KPP_REAL)0.1666666666666666666666666666666667; |
---|
| 1515 | rkAlpha[1][3] = (KPP_REAL)(-0.8333333333333333333333333333333333e-01); |
---|
| 1516 | rkAlpha[2][3] = (KPP_REAL)0.9469696969696969696969696969696970; |
---|
| 1517 | rkAlpha[0][4] = (KPP_REAL)(-6.0); |
---|
| 1518 | rkAlpha[1][4] = (KPP_REAL)9.0; |
---|
| 1519 | rkAlpha[2][4] = (KPP_REAL)(-56.81818181818181818181818181818182); |
---|
| 1520 | rkAlpha[3][4] = (KPP_REAL)54.0; |
---|
| 1521 | |
---|
| 1522 | } /* end Sdirk4b */ |
---|
| 1523 | |
---|
| 1524 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1525 | void Sdirk2a() { |
---|
| 1526 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1527 | |
---|
| 1528 | sdMethod = S2A; |
---|
| 1529 | |
---|
| 1530 | /* ~~~> Number of stages */ |
---|
| 1531 | rkS = 2; |
---|
| 1532 | |
---|
| 1533 | /* ~~~> Method coefficients */ |
---|
| 1534 | rkGamma = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1535 | rkA[0][0] = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1536 | rkA[0][1] = (KPP_REAL)0.7071067811865475244008443621048490; |
---|
| 1537 | rkA[1][1] = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1538 | rkB[0] = (KPP_REAL)0.7071067811865475244008443621048490; |
---|
| 1539 | rkB[1] = (KPP_REAL)0.2928932188134524755991556378951510; |
---|
| 1540 | rkBhat[0] = (KPP_REAL)0.6666666666666666666666666666666667; |
---|
| 1541 | rkBhat[1] = (KPP_REAL)0.3333333333333333333333333333333333; |
---|
| 1542 | rkC[0] = (KPP_REAL)0.292893218813452475599155637895151; |
---|
| 1543 | rkC[1] = ONE; |
---|
| 1544 | |
---|
| 1545 | /* ~~~> Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1546 | rkD[0] = ZERO; |
---|
| 1547 | rkD[1] = ONE; |
---|
| 1548 | |
---|
| 1549 | /* ~~~> Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1550 | rkE[0] = (KPP_REAL)0.4714045207910316829338962414032326; |
---|
| 1551 | rkE[1] = (KPP_REAL)(-0.1380711874576983496005629080698993); |
---|
| 1552 | |
---|
| 1553 | /* ~~~> Local order of Err estimate */ |
---|
| 1554 | rkELO = 2; |
---|
| 1555 | |
---|
| 1556 | /* ~~~> h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1557 | rkTheta[0][1] = (KPP_REAL)2.414213562373095048801688724209698; |
---|
| 1558 | |
---|
| 1559 | /* ~~~> Starting value for Newton iterations */ |
---|
| 1560 | rkAlpha[0][1] = (KPP_REAL)3.414213562373095048801688724209698; |
---|
| 1561 | |
---|
| 1562 | } /* end Sdirk2a */ |
---|
| 1563 | |
---|
| 1564 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1565 | void Sdirk2b() { |
---|
| 1566 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1567 | |
---|
| 1568 | sdMethod = S2B; |
---|
| 1569 | |
---|
| 1570 | /* ~~~> Number of stages */ |
---|
| 1571 | rkS = 2; |
---|
| 1572 | |
---|
| 1573 | /* ~~~> Method coefficients */ |
---|
| 1574 | rkGamma = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1575 | rkA[0][0] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1576 | rkA[0][1] = (KPP_REAL)(-0.707106781186547524400844362104849); |
---|
| 1577 | rkA[1][1] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1578 | rkB[0] = (KPP_REAL)(-0.707106781186547524400844362104849); |
---|
| 1579 | rkB[1] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1580 | rkBhat[0] = (KPP_REAL)0.6666666666666666666666666666666667; |
---|
| 1581 | rkBhat[1] = (KPP_REAL)0.3333333333333333333333333333333333; |
---|
| 1582 | rkC[0] = (KPP_REAL)1.707106781186547524400844362104849; |
---|
| 1583 | rkC[1] = ONE; |
---|
| 1584 | |
---|
| 1585 | /* ~~~> Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1586 | rkD[0] = ZERO; |
---|
| 1587 | rkD[1] = ONE; |
---|
| 1588 | |
---|
| 1589 | /* ~~~> Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1590 | rkE[0] = (KPP_REAL)(-0.4714045207910316829338962414032326); |
---|
| 1591 | rkE[1] = (KPP_REAL)0.8047378541243650162672295747365659; |
---|
| 1592 | |
---|
| 1593 | /* ~~~> Local order of Err estimate */ |
---|
| 1594 | rkELO = 2; |
---|
| 1595 | |
---|
| 1596 | /* ~~~> h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1597 | rkTheta[0][1] = (KPP_REAL)(-0.414213562373095048801688724209698); |
---|
| 1598 | |
---|
| 1599 | /* ~~~> Starting value for Newton iterations */ |
---|
| 1600 | rkAlpha[0][1] = (KPP_REAL)0.5857864376269049511983112757903019; |
---|
| 1601 | |
---|
| 1602 | } /* end Sdirk2b */ |
---|
| 1603 | |
---|
| 1604 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1605 | void Sdirk3a() { |
---|
| 1606 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1607 | |
---|
| 1608 | sdMethod = S3A; |
---|
| 1609 | |
---|
| 1610 | /* ~~~> Number of stages */ |
---|
| 1611 | rkS = 3; |
---|
| 1612 | |
---|
| 1613 | /* ~~~> Method coefficients */ |
---|
| 1614 | rkGamma = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1615 | rkA[0][0] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1616 | rkA[0][1] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1617 | rkA[1][1] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1618 | rkA[0][2] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1619 | rkA[1][2] = (KPP_REAL)0.5773502691896257645091487805019573; |
---|
| 1620 | rkA[2][2] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1621 | rkB[0] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1622 | rkB[1] = (KPP_REAL)0.5773502691896257645091487805019573; |
---|
| 1623 | rkB[2] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1624 | rkBhat[0]= (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1625 | rkBhat[1]= (KPP_REAL)0.6477918909913548037576239837516312; |
---|
| 1626 | rkBhat[2]= (KPP_REAL)0.1408832436034580784969504064993475; |
---|
| 1627 | rkC[0] = (KPP_REAL)0.2113248654051871177454256097490213; |
---|
| 1628 | rkC[1] = (KPP_REAL)0.4226497308103742354908512194980427; |
---|
| 1629 | rkC[2] = ONE; |
---|
| 1630 | |
---|
| 1631 | /* ~~~> Ynew = Yold + h*Sum_i {rkB_i*k_i} = Yold + Sum_i {rkD_i*Z_i} */ |
---|
| 1632 | rkD[0] = ZERO; |
---|
| 1633 | rkD[1] = ZERO; |
---|
| 1634 | rkD[2] = ONE; |
---|
| 1635 | |
---|
| 1636 | /* ~~~> Err = h * Sum_i {(rkB_i-rkBhat_i)*k_i} = Sum_i {rkE_i*Z_i} */ |
---|
| 1637 | rkE[0] = (KPP_REAL)0.9106836025229590978424821138352906; |
---|
| 1638 | rkE[1] = (KPP_REAL)(-1.244016935856292431175815447168624); |
---|
| 1639 | rkE[2] = (KPP_REAL)0.3333333333333333333333333333333333; |
---|
| 1640 | |
---|
| 1641 | /* ~~~> Local order of Err estimate */ |
---|
| 1642 | rkELO = 2; |
---|
| 1643 | |
---|
| 1644 | /* ~~~> h*Sum_j {rkA_ij*k_j} = Sum_j {rkTheta_ij*Z_j} */ |
---|
| 1645 | rkTheta[0][1] = ONE; |
---|
| 1646 | rkTheta[0][2] = (KPP_REAL)(-1.732050807568877293527446341505872); |
---|
| 1647 | rkTheta[1][2] = (KPP_REAL)2.732050807568877293527446341505872; |
---|
| 1648 | |
---|
| 1649 | /* ~~~> Starting value for Newton iterations */ |
---|
| 1650 | rkAlpha[0][1] = (KPP_REAL)2.0; |
---|
| 1651 | rkAlpha[0][2] = (KPP_REAL)(-12.92820323027550917410978536602349); |
---|
| 1652 | rkAlpha[1][2] = (KPP_REAL)8.83012701892219323381861585376468; |
---|
| 1653 | |
---|
| 1654 | } /* end Sdirk3a */ |
---|
| 1655 | |
---|
| 1656 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1657 | void FUN_CHEM(KPP_REAL T, KPP_REAL Y[], KPP_REAL P[]) |
---|
| 1658 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1659 | { |
---|
| 1660 | |
---|
| 1661 | KPP_REAL Told; |
---|
| 1662 | |
---|
| 1663 | Told = TIME; |
---|
| 1664 | TIME = T; |
---|
| 1665 | Update_SUN(); |
---|
| 1666 | Update_RCONST(); |
---|
| 1667 | Fun( Y, FIX, RCONST, P ); |
---|
| 1668 | TIME = Told; |
---|
| 1669 | |
---|
| 1670 | } /* end FUN_CHEM */ |
---|
| 1671 | |
---|
| 1672 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1673 | void JAC_CHEM(KPP_REAL T, KPP_REAL Y[], KPP_REAL JV[]) { |
---|
| 1674 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|
| 1675 | |
---|
| 1676 | KPP_REAL Told; |
---|
| 1677 | |
---|
| 1678 | #ifdef FULL_ALGEBRA |
---|
| 1679 | KPP_REAL JS[LU_NONZERO]; |
---|
| 1680 | int i,j; |
---|
| 1681 | #endif |
---|
| 1682 | |
---|
| 1683 | Told = TIME; |
---|
| 1684 | TIME = T; |
---|
| 1685 | Update_SUN(); |
---|
| 1686 | Update_RCONST(); |
---|
| 1687 | |
---|
| 1688 | #ifdef FULL_ALGEBRA |
---|
| 1689 | Jac_SP( Y, FIX, RCONST, JS); |
---|
| 1690 | |
---|
| 1691 | for(j=0; j<NVAR; j++) { |
---|
| 1692 | for(i=0; i<NVAR; i++) |
---|
| 1693 | JV[j][i] = (KPP_REAL)0.0; |
---|
| 1694 | } /* end for */ |
---|
| 1695 | |
---|
| 1696 | for(i=0; i<LU_NONZERO; i++) |
---|
| 1697 | JV[LU_ICOL[i]][LU_IROW[i]] = JS[i]; |
---|
| 1698 | #else |
---|
| 1699 | Jac_SP(Y, FIX, RCONST, JV); |
---|
| 1700 | #endif |
---|
| 1701 | |
---|
| 1702 | TIME = Told; |
---|
| 1703 | |
---|
| 1704 | } /* end JAC_CHEM */ |
---|
| 1705 | /*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/ |
---|