[2696] | 1 | SUBROUTINE INTEGRATE( NSENSIT, Y, TIN, TOUT ) |
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| 2 | |
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| 3 | INCLUDE 'KPP_ROOT_Parameters.h' |
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| 4 | INCLUDE 'KPP_ROOT_Global.h' |
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| 5 | |
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| 6 | C TIN - Start Time |
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| 7 | REAL*8 TIN |
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| 8 | C TOUT - End Time |
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| 9 | REAL*8 TOUT |
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| 10 | C Concentrations and Sensitivities |
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| 11 | REAL*8 Y(NVAR,NSENSIT+1), PARAMS(NSENSIT) |
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| 12 | C --- Note: Y contains: (1:NVAR) concentrations, followed by |
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| 13 | C --- (1:NVAR) sensitivities w.r.t. first parameter, followed by |
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| 14 | C --- etc., followed by |
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| 15 | C --- (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
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| 16 | INTEGER i |
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| 17 | |
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| 18 | INTEGER LIW, LRW |
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| 19 | C PARAMETER (LRW = 22 + 8*(NSENSIT+1)*NVAR + NVAR**2 + NVAR) |
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| 20 | C PARAMETER (LIW = 21 + NVAR + NSENSIT) |
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| 21 | C REAL*8 RWORK(LRW) |
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| 22 | C INTEGER IWORK(LIW) |
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| 23 | C Note: the following dynamic allocation is not standard F77 and may not work on |
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| 24 | C some systems. Declare LRW, LIW parameters as above with some upper bound used for NSENSIT |
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| 25 | REAL*8 RWORK(22 + 8*(NSENSIT+1)*NVAR + NVAR**2 + NVAR) |
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| 26 | INTEGER IWORK(21 + NVAR + NSENSIT) |
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| 27 | |
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| 28 | INTEGER IOPT(3), NEQ(2) |
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| 29 | |
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| 30 | EXTERNAL FUNC_CHEM,JAC,DFUNC_CHEMDPAR |
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| 31 | |
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| 32 | MF = 21 ! --- BDF plus user-supplied Jacobian |
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| 33 | |
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| 34 | LRW = 22 + 8*(NSENSIT+1)*NVAR + NVAR**2 + NVAR |
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| 35 | LIW = 21 + NVAR + NSENSIT |
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| 36 | |
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| 37 | NEQ(1) = NVAR ! --- No. of Variables |
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| 38 | NEQ(2) = NSENSIT ! --- No of parameters |
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| 39 | |
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| 40 | ITOL=1 ! --- 1=Scalar Tolerances; 4 = VECTOR TOLERANCES |
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| 41 | ITASK=1 ! --- Normal Output |
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| 42 | ISTATE=1 |
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| 43 | IOPT(1)=1 ! --- 0= No optional parameters, 1=Optional parameters |
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| 44 | IOPT(2)=1 ! --- 1=Perform sensitivity analysis; 0 if not |
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| 45 | IOPT(3)=1 ! --- 1 if DFUNC_CHEMDPAR supplied by the user; |
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| 46 | ! --- 0 if finite differences are to be used |
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| 47 | C --- Set optional parameters |
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| 48 | DO 10 i=1,LRW |
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| 49 | RWORK(i) = 0.0D0 |
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| 50 | 10 CONTINUE |
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| 51 | DO 20 i=1,LIW |
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| 52 | IWORK(i) = 0 |
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| 53 | 20 CONTINUE |
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| 54 | |
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| 55 | RWORK(5) = STEPMIN ! THE STEP SIZE TO BE ATTEMPTED ON THE FIRST STEP. |
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| 56 | RWORK(6) = STEPMAX ! THE MAXIMUM ABSOLUTE STEP SIZE ALLOWED. |
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| 57 | RWORK(7) = 0.0D0 ! THE MINIMUM ABSOLUTE STEP SIZE ALLOWED. |
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| 58 | IWORK(6) = 5000 ! MAXIMUM NUMBER OF (INTERNALLY DEFINED) STEPS |
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| 59 | |
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| 60 | CALL KPP_ODESSA( FUNC_CHEM,DFUNC_CHEMDPAR,NEQ,Y,PARAMS,TIN,TOUT, |
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| 61 | & ITOL,RTOL,ATOL, |
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| 62 | 1 ITASK,ISTATE,IOPT,RWORK,LRW,IWORK,LIW, |
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| 63 | & JAC,MF) |
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| 64 | |
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| 65 | IF (ISTATE.LT.0) THEN |
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| 66 | print *,'KPP_ODESSA: Unsucessfull exit at T=', |
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| 67 | & TIN,' (ISTATE=',ISTATE,')' |
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| 68 | ENDIF |
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| 69 | |
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| 70 | RETURN |
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| 71 | END |
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| 72 | |
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| 73 | |
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| 74 | |
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| 75 | |
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| 76 | SUBROUTINE FUNC_CHEM (N, T, V, PARAMS, FCT) |
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| 77 | INCLUDE 'KPP_ROOT_Parameters.h' |
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| 78 | INCLUDE 'KPP_ROOT_Global.h' |
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| 79 | |
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| 80 | DIMENSION V(NVAR), PARAMS(*), FCT(NVAR) |
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| 81 | TOLD = TIME |
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| 82 | TIME = T |
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| 83 | CALL Update_SUN() |
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| 84 | CALL Update_RCONST() |
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| 85 | TIME = TOLD |
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| 86 | CALL Fun(V, FIX, RCONST, FCT) |
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| 87 | RETURN |
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| 88 | END |
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| 89 | |
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| 90 | SUBROUTINE DFUNC_CHEMDPAR (N, T, V, PARAMS, DFCT, JPAR) |
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| 91 | INCLUDE 'KPP_ROOT_Parameters.h' |
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| 92 | INCLUDE 'KPP_ROOT_Global.h' |
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| 93 | C --- NCOEFF = number of rate coefficients w.r.t. which we differentiate |
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| 94 | C (note that in some applications NCOEFF may be different than NSENSIT) |
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| 95 | C JCOEFF(1:NCOEFF) are the indices of rate coefficients w.r.t. which we differentiate |
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| 96 | INTEGER NCOEFF, JCOEFF(NREACT) |
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| 97 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
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| 98 | |
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| 99 | DIMENSION V(NVAR), PARAMS(*), DFCT(NVAR) |
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| 100 | INTEGER JPAR, i, JC(1) |
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| 101 | IF (DDMTYPE .EQ. 0) THEN |
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| 102 | C This setting is required for sensitivities w.r.t. initial conditions |
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| 103 | DO i=1,NVAR |
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| 104 | DFCT(i) = 0.d0 |
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| 105 | END DO |
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| 106 | ELSE |
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| 107 | C This setting is required for sensitivities w.r.t. rate coefficients |
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| 108 | C ... and should be changed by the user for other applications |
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| 109 | JC(1) = JCOEFF(JPAR) |
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| 110 | CALL dFun_dRcoeff(V, FIX, 1, JC, DFCT ) |
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| 111 | END IF |
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| 112 | RETURN |
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| 113 | END |
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| 114 | |
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| 115 | SUBROUTINE JAC (N, T, V, PARAMS, ML, MU, JS, NROWPD) |
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| 116 | INCLUDE 'KPP_ROOT_Parameters.h' |
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| 117 | INCLUDE 'KPP_ROOT_Sparse.h' |
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| 118 | |
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| 119 | REAL*8 V(NVAR), PARAMS(*), JS(LU_NONZERO) |
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| 120 | INTEGER ML, MU, NROWPD |
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| 121 | TOLD = TIME |
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| 122 | TIME = T |
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| 123 | CALL Update_SUN() |
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| 124 | CALL Update_RCONST() |
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| 125 | TIME = TOLD |
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| 126 | DO i=1,LU_NONZERO |
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| 127 | JS(i) = 0.0D0 |
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| 128 | END DO |
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| 129 | CALL Jac_SP(V, FIX, RCONST, JS) |
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| 130 | RETURN |
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| 131 | END |
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| 132 | |
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| 133 | |
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| 134 | C ALGORITHM 658, COLLECTED ALGORITHMS FROM ACM. |
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| 135 | C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, |
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| 136 | C VOL. 14, NO. 1, P.61. |
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| 137 | C----------------------------------------------------------------------- |
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| 138 | C THIS IS THE SEPTEMBER 1, 1986 VERSION OF ODESSA.. |
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| 139 | C AN ORDINARY DIFFERENTIAL EQUATION KppSolveR WITH EXPLICIT SIMULTANEOUS |
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| 140 | C SENSITIVITY ANALYSIS. |
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| 141 | C |
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| 142 | C THIS PACKAGE IS A MODIFICATION OF THE AUGUST 13, 1981 VERSION OF |
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| 143 | C LSODE.. LIVERMORE KppSolveR FOR ORDINARY DIFFERENTIAL EQUATIONS. |
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| 144 | C THIS VERSION IS IN DOUBLE PRECISION. |
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| 145 | C |
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| 146 | C ODESSA KppSolveS FOR THE FIRST-ORDER SENSITIVITY COEFFICIENTS.. |
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| 147 | C DY(I)/DP, FOR A SINGLE PARAMETER, OR, |
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| 148 | C DY(I)/DP(J), FOR MULTIPLE PARAMETERS, |
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| 149 | C ASSOCIATED WITH A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.. |
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| 150 | C DY/DT = F(Y,T;P). |
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| 151 | C----------------------------------------------------------------------- |
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| 152 | C REFERENCES... |
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| 153 | C |
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| 154 | C 1. JORGE R. LEIS AND MARK A. KRAMER, THE SIMULTANEOUS SOLUTION AND |
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| 155 | C EXPLICIT SENSITIVITY ANALYSIS OF SYSTEMS DESCRIBED BY ORDINARY |
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| 156 | C DIFFERENTIAL EQUATIONS. SUBMITTED TO ACM TRANS. MATH. SOFTWARE, |
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| 157 | C (1985). |
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| 158 | C |
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| 159 | C 2. JORGE R. LEIS AND MARK A. KRAMER, ODESSA - AN ORDINARY DIFFERENTIA |
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| 160 | C EQUATION KppSolveR WITH EXPLICIT SIMULTANEOUS SENSITIVITY ANALYSIS. |
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| 161 | C SUBMITTED TO ACM TRANS. MATH. SOFTWARE, (1985). |
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| 162 | C |
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| 163 | C 3. ALAN C. HINDMARSH, LSODE AND LSODI, TWO NEW INITIAL VALUE |
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| 164 | C ORDINARY DIFFERENTIAL EQUATION KppSolveRS, ACM-SIGNUM NEWSLETTER, |
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| 165 | C VOL. 15, NO. 4 (1980), PP. 10-11. |
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| 166 | C----------------------------------------------------------------------- |
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| 167 | C PROBLEM STATEMENT.. |
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| 168 | C |
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| 169 | C THE ODESSA MODIFICATION OF THE LSODE PACKAGE PROVIDES THE OPTION TO |
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| 170 | C CALCULATE FIRST-ORDER SENSITIVITY COEFFICIENTS FOR A SYSTEM OF STIFF |
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| 171 | C OR NON-STIFF EXPLICIT ORDINARY DIFFERENTIAL EQUATIONS OF THE GENERAL |
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| 172 | C FORM : |
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| 173 | C |
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| 174 | C DY/DT = F(Y,T;P) (1) |
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| 175 | C |
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| 176 | C WHERE Y IS AN N-DIMENSIONAL DEPENDENT VARIABLE VECTOR, T IS THE |
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| 177 | C INDEPENDENT INTEGRATION VARIABLE, AND P IS AN NPAR-DIMENSIONAL |
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| 178 | C CONSTANT VECTOR. THE GOVERNING EQUATIONS FOR THE FIRST-ORDER |
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| 179 | C SENSITIVITY COEFFICIENTS ARE GIVEN BY : |
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| 180 | C |
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| 181 | C S'(T) = J(T)*S(T) + DF/DP (2) |
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| 182 | C |
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| 183 | C WHERE |
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| 184 | C |
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| 185 | C S(T) = DY(T)/DP (= SENSITIVITY FUNCTIONS) |
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| 186 | C S'(T) = D(DY(T)/DP)/DT |
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| 187 | C J(T) = DF(Y,T;P)/DY(T) (= JACOBIAN MATRIX) |
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| 188 | C AND DF/DP = DF(Y,T;P)/DP (= INHOMOGENEITY MATRIX) |
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| 189 | C |
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| 190 | C SOLUTION OF EQUATIONS (1) AND (2) PROCEEDS SIMULTANEOUSLY VIA AN |
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| 191 | C EXTENSION OF THE LSODE PACKAGE AS DESCRIBED IN [1]. |
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| 192 | C---------------------------------------------------------------------- |
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| 193 | C ACKNOWLEDGEMENT : THE FOLLOWING ODESSA PACKAGE DOCUMENTATION IS A |
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| 194 | C MODIFICATION OF THE LSODE DOCUMENTATION WHICH |
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| 195 | C ACCOMPANIES THE LSODE PACKAGE CODE. |
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| 196 | C---------------------------------------------------------------------- |
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| 197 | C SUMMARY OF USAGE. |
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| 198 | C |
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| 199 | C COMMUNICATION BETWEEN THE USER AND THE ODESSA PACKAGE, FOR NORMAL |
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| 200 | C SITUATIONS, IS SUMMARIZED HERE. THIS SUMMARY DESCRIBES ONLY A SUBSET |
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| 201 | C OF THE FULL SET OF OPTIONS AVAILABLE. SEE THE FULL DESCRIPTION FOR |
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| 202 | C DETAILS, INCLUDING OPTIONAL COMMUNICATION, NONSTANDARD OPTIONS, |
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| 203 | C AND INSTRUCTIONS FOR SPECIAL SITUATIONS. SEE ALSO THE EXAMPLE |
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| 204 | C PROBLEM (WITH PROGRAM AND OUTPUT) FOLLOWING THIS SUMMARY. |
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| 205 | C |
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| 206 | C A. FIRST PROVIDE A SUBROUTINE OF THE FORM.. |
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| 207 | C SUBROUTINE F (N, T, Y, PAR, YDOT) |
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| 208 | C DOUBLE PRECISION T, Y, PAR, YDOT |
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| 209 | C DIMENSION Y(N), YDOT(N), PAR(NPAR) |
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| 210 | C WHICH SUPPLIES THE VECTOR FUNCTION F BY LOADING YDOT(I) WITH F(I). |
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| 211 | C N IS THE NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS IN THE |
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| 212 | C ABOVE MODEL. NPAR IS THE NUMBER OF MODEL PARAMETERS FOR WHICH |
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| 213 | C VECTOR SENSITIVITY FUNCTIONS ARE DESIRED. YOU ARE ALSO ENCOURAGED |
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| 214 | C TO PROVIDE A SUBROUTINE OF THE FORM.. |
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| 215 | C SUBROUTINE DF (N, T, Y, PAR, DFDP, JPAR) |
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| 216 | C DOUBLE PRECISION T, Y, PAR, DFDP |
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| 217 | C DIMENSION Y(N), PAR(NPAR), DFDP(N) |
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| 218 | C GO TO (1,...,NPAR) JPAR |
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| 219 | C 1 DFDP(1) = DF(1)/DP(1) |
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| 220 | C . |
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| 221 | C DFDP(I) = DF(I)/DP(1) |
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| 222 | C . |
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| 223 | C DFDP(N) = DF(N)/DP(1) |
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| 224 | C RETURN |
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| 225 | C 2 DFDP(1) = DF(1)/DP(2) |
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| 226 | C . |
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| 227 | C DFDP(I) = DF(I)/DP(2) |
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| 228 | C . |
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| 229 | C DFDP(N) = DF(N)/DP(2) |
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| 230 | C RETURN |
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| 231 | C . . |
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| 232 | C . . |
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| 233 | C RETURN |
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| 234 | C NPAR DFDP(1) = DF(1)/DP(NPAR) |
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| 235 | C . |
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| 236 | C DFDP(I) = DF(I)/DP(NPAR) |
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| 237 | C . |
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| 238 | C DFDP(N) = DF(N)/DP(NPAR) |
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| 239 | C RETURN |
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| 240 | C END |
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| 241 | C ONLY NONZERO ELEMENTS NEED BE LOADED. IF THIS IS NOT FEASIBLE, |
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| 242 | C ODESSA WILL GENERATE THIS MATRIX INTERNALLY BY DIFFERENCE QUOTIENTS. |
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| 243 | C |
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| 244 | C B. NEXT DETERMINE (OR GUESS) WHETHER OR NOT THE PROBLEM IS STIFF. |
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| 245 | C STIFFNESS OCCURS WHEN THE JACOBIAN MATRIX DF/DY HAS AN EIGENVALUE |
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| 246 | C WHOSE REAL PART IS NEGATIVE AND LARGE IN MAGNITUDE, COMPARED TO THE |
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| 247 | C RECIPROCAL OF THE T SPAN OF INTEREST. IF THE PROBLEM IS NONSTIFF, |
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| 248 | C USE METH = 10. IF IT IS STIFF, USE METH = 20. THE USER IS REQUIRED |
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| 249 | C TO INPUT THE METHOD FLAG MF = 10*METH + MITER. THERE ARE FOUR |
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| 250 | C STANDARD CHOICES FOR MITER WHEN A SENSITIVITY ANALYSIS IS DESIRED, |
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| 251 | C AND ODESSA REQUIRES THE JACOBIAN MATRIX IN SOME FORM. |
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| 252 | C THIS MATRIX IS REGARDED EITHER AS FULL (MITER = 1 OR 2), |
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| 253 | C OR BANDED (MITER = 4 OR 5). IN THE BANDED CASE, ODESSA REQUIRES TWO |
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| 254 | C HALF-BANDWIDTH PARAMETERS ML AND MU. THESE ARE, RESPECTIVELY, THE |
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| 255 | C WIDTHS OF THE LOWER AND UPPER PARTS OF THE BAND, EXCLUDING THE MAIN |
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| 256 | C DIAGONAL. THUS THE BAND CONSISTS OF THE LOCATIONS (I,J) WITH |
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| 257 | C I-ML .LE. J .LE. I+MU, AND THE FULL BANDWIDTH IS ML+MU+1. |
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| 258 | C |
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| 259 | C C. YOU ARE ENCOURAGED TO SUPPLY THE JACOBIAN DIRECTLY (MF = 11, 14, |
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| 260 | C 21, OR 24), BUT IF THIS IS NOT FEASIBLE, ODESSA WILL COMPUTE IT |
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| 261 | C INTERNALLY BY DIFFERENCE QUOTIENTS (MF = 12, 15, 22, OR 25). IF YOU |
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| 262 | C ARE SUPPLYING THE JACOBIAN, PROVIDE A SUBROUTINE OF THE FORM.. |
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| 263 | C SUBROUTINE JAC (NEQ, T, Y, PAR, ML, MU, PD, NROWPD) |
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| 264 | C DOUBLE PRECISION T, Y, PAR, PD |
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| 265 | C DIMENSION Y(N), PD(NROWPD,N), PAR(NPAR) |
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| 266 | C WHICH SUPPLIES DF/DY BY LOADING PD AS FOLLOWS.. |
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| 267 | C FOR A FULL JACOBIAN (MF = 11, OR 21), LOAD PD(I,J) WITH DF(I)/DY(J), |
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| 268 | C THE PARTIAL DERIVATIVE OF F(I) WITH RESPECT TO Y(J). (IGNORE THE |
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| 269 | C ML AND MU ARGUMENTS IN THIS CASE.) |
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| 270 | C FOR A BANDED JACOBIAN (MF = 14, OR 24), LOAD PD(I-J+MU+1,J) WITH |
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| 271 | C DF(I)/DY(J), I.E. LOAD THE DIAGONAL LINES OF DF/DY INTO THE ROWS OF |
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| 272 | C PD FROM THE TOP DOWN. |
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| 273 | C IN EITHER CASE, ONLY NONZERO ELEMENTS NEED BE LOADED. |
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| 274 | C |
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| 275 | C D. WRITE A MAIN PROGRAM WHICH CALLS SUBROUTINE ODESSA ONCE FOR |
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| 276 | C EACH POINT AT WHICH ANSWERS ARE DESIRED. THIS SHOULD ALSO PROVIDE |
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| 277 | C FOR POSSIBLE USE OF LOGICAL UNIT 6 FOR OUTPUT OF ERROR MESSAGES BY |
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| 278 | C ODESSA. ON THE FIRST CALL TO ODESSA, SUPPLY ARGUMENTS AS FOLLOWS.. |
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| 279 | C F = NAME OF SUBROUTINE FOR RIGHT-HAND SIDE VECTOR F (MODEL). |
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| 280 | C THIS NAME MUST BE DECLARED EXTERNAL IN CALLING PROGRAM. |
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| 281 | C DF = NAME OF SUBROUTINE FOR INHOMOGENEITY MATRIX DF/DP. |
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| 282 | C IF USED (IDF = 1), THIS NAME MUST BE DECLARED EXTERNAL IN |
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| 283 | C CALLING PROGRAM. IF NOT USED (IDF = 0), PASS A DUMMY NAME. |
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| 284 | C N = NUMBER OF FIRST ORDER ODE-S IN MODEL; LOAD INTO NEQ(1). |
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| 285 | C NPAR = NUMBER OF MODEL PARAMETERS OF INTEREST; LOAD INTO NEQ(2). |
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| 286 | C Y = AN (N) BY (NPAR+1) REAL ARRAY OF INITIAL VALUES.. |
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| 287 | C Y(I,1) , I = 1,N , CONTAIN THE STATE, OR MODEL, DEPENDENT |
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| 288 | C VARIABLES, |
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| 289 | C Y(I,J) , J = 2,NPAR , CONTAIN THE DEPENDENT SENSITIVITY |
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| 290 | C COEFFICIENTS. |
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| 291 | C PAR = A REAL ARRAY OF LENGTH NPAR CONTAINING MODEL PARAMETERS |
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| 292 | C OF INTEREST. |
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| 293 | C T = THE INITIAL VALUE OF THE INDEPENDENT VARIABLE. |
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| 294 | C TOUT = FIRST POINT WHERE OUTPUT IS DESIRED (.NE. T). |
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| 295 | C ITOL = 1, 2, 3, OR 4 ACCORDING AS RTOL, ATOL (BELOW) ARE SCALARS |
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| 296 | C OR ARRAYS. |
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| 297 | C RTOL = RELATIVE TOLERANCE PARAMETER (SCALAR OR (N) BY (NPAR+1) |
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| 298 | C ARRAY). |
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| 299 | C ATOL = ABSOLUTE TOLERANCE PARAMETER (SCALAR OR (N) BY (NPAR+1) |
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| 300 | C ARRAY). |
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| 301 | C THE ESTIMATED LOCAL ERROR IN Y(I,J) WILL BE CONTROLLED SO AS |
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| 302 | C TO BE ROUGHLY LESS (IN MAGNITUDE) THAN |
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| 303 | C EWT(I,J) = RTOL*ABS(Y(I,J)) + ATOL IF ITOL = 1, |
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| 304 | C EWT(I,J) = RTOL*ABS(Y(I,J)) + ATOL(I,J) IF ITOL = 2, |
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| 305 | C EWT(I,J) = RTOL(I,J)*ABS(Y(I,J) + ATOL IF ITOL = 3, OR |
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| 306 | C EWT(I,J) = RTOL(I,J)*ABS(Y(I,J) + ATOL(I,J) IF ITOL = 4. |
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| 307 | C THUS THE LOCAL ERROR TEST PASSES IF, IN EACH COMPONENT, |
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| 308 | C EITHER THE ABSOLUTE ERROR IS LESS THAN ATOL (OR ATOL(I,J)), |
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| 309 | C OR THE RELATIVE ERROR IS LESS THAN RTOL (OR RTOL(I,J)). |
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| 310 | C USE RTOL = 0.0 FOR PURE ABSOLUTE ERROR CONTROL, AND |
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| 311 | C USE ATOL = 0.0 FOR PURE RELATIVE ERROR CONTROL. |
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| 312 | C CAUTION.. ACTUAL (GLOBAL) ERRORS MAY EXCEED THESE LOCAL |
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| 313 | C TOLERANCES, SO CHOOSE THEM CONSERVATIVELY. |
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| 314 | C ITASK = 1 FOR NORMAL COMPUTATION OF OUTPUT VALUES OF Y AT T = TOUT. |
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| 315 | C ISTATE = INTEGER FLAG (INPUT AND OUTPUT). SET ISTATE = 1. |
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| 316 | C IOPT = 0, TO INDICATE NO OPTIONAL INPUTS FOR INTEGRATION; |
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| 317 | C LOAD INTO IOPT(1). |
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| 318 | C ISOPT = 1, TO INDICATE SENSITIVITY ANALYSIS, = 0, TO INDICATE |
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| 319 | C NO SENSITIVITY ANALYSIS; LOAD INTO IOPT(2). |
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| 320 | C IDF = 1, IF SUBROUTINE DF (ABOVE) IS SUPPLIED BY THE USER, |
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| 321 | C = 0, OTHERWISE; LOAD INTO IOPT(3). |
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| 322 | C RWORK = REAL WORK ARRAY OF LENGTH AT LEAST.. |
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| 323 | C 22 + 16*N + N**2 FOR MF = 11 OR 12, |
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| 324 | C 22 + 17*N + (2*ML + MU)*N FOR MF = 14 OR 15, |
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| 325 | C 22 + 9*N + N**2 FOR MF = 21 OR 22, |
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| 326 | C 22 + 10*N + (2*ML + MU)*N FOR MF = 24 OR 25, |
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| 327 | C IF ISOPT = 0, OR.. |
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| 328 | C 22 + 15*(NPAR+1)*N + N**2 + N FOR MF = 11 OR 12, |
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| 329 | C 24 + 15*(NPAR+1)*N + (2*ML+MU+2)*N + N FOR MF = 14 OR 15, |
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| 330 | C 22 + 8*(NPAR+1)*N + N**2 + N FOR MF = 21 OR 22, |
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| 331 | C 24 + 8*(NPAR+1)*N + (2*ML+MU+2)*N + N FOR MF = 24 OR 25, |
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| 332 | C IF ISOPT = 1. |
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| 333 | C LRW = DECLARED LENGTH OF RWORK (IN USER-S DIMENSION STATEMENT). |
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| 334 | C IWORK = INTEGER WORK ARRAY OF LENGTH AT LEAST.. |
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| 335 | C 20 + N IF ISOPT = 0, |
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| 336 | C 21 + N + NPAR IF ISOPT = 1. |
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| 337 | C IF MITER = 4 OR 5, INPUT IN IWORK(1),IWORK(2) THE LOWER |
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| 338 | C AND UPPER HALF-BANDWIDTHS ML,MU (EXCLUDING MAIN DIAGONAL). |
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| 339 | C LIW = DECLARED LENGTH OF IWORK (IN USER-S DIMENSION STATEMENT). |
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| 340 | C JAC = NAME OF SUBROUTINE FOR JACOBIAN MATRIX. |
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| 341 | C IF USED, THIS NAME MUST BE DECLARED EXTERNAL IN CALLING |
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| 342 | C PROGRAM. IF NOT USED, PASS A DUMMY NAME. |
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| 343 | C MF = METHOD FLAG. STANDARD VALUES FOR ISOPT = 0 ARE.. |
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| 344 | C 10 FOR NONSTIFF (ADAMS) METHOD, NO JACOBIAN USED. |
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| 345 | C 21 FOR STIFF (BDF) METHOD, USER-SUPPLIED FULL JACOBIAN. |
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| 346 | C 22 FOR STIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. |
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| 347 | C 24 FOR STIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. |
---|
| 348 | C 25 FOR STIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. |
---|
| 349 | C IF ISOPT = 1, MF = 10 IS ILLEGAL AND CAN BE REPLACED BY.. |
---|
| 350 | C 11 FOR NONSTIFF METHOD, USER-SUPPLIED FULL JACOBIAN. |
---|
| 351 | C 12 FOR NONSTIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. |
---|
| 352 | C 14 FOR NONSTIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. |
---|
| 353 | C 15 FOR NONSTIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. |
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| 354 | C NOTE THAT THE MAIN PROGRAM MUST DECLARE ARRAYS Y, RWORK, IWORK, AND |
---|
| 355 | C POSSIBLY ATOL AND RTOL, AS WELL AS NEQ, IOPT, AND PAR IF ISOPT = 1. |
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| 356 | C |
---|
| 357 | C E. THE OUTPUT FROM THE FIRST CALL (OR ANY CALL) IS.. |
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| 358 | C Y = ARRAY OF COMPUTED VALUES OF Y(T) VECTOR. |
---|
| 359 | C T = CORRESPONDING VALUE OF INDEPENDENT VARIABLE (NORMALLY TOUT). |
---|
| 360 | C ISTATE = 2 IF ODESSA WAS SUCCESSFUL, NEGATIVE OTHERWISE. |
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| 361 | C -1 MEANS EXCESS WORK DONE ON THIS CALL (PERHAPS WRONG MF). |
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| 362 | C -2 MEANS EXCESS ACCURACY REQUESTED (TOLERANCES TOO SMALL). |
---|
| 363 | C -3 MEANS ILLEGAL INPUT DETECTED (SEE PRINTED MESSAGE). |
---|
| 364 | C -4 MEANS REPEATED ERROR TEST FAILURES (CHECK ALL INPUTS). |
---|
| 365 | C -5 MEANS REPEATED CONVERGENCE FAILURES (PERHAPS BAD JACOBIAN |
---|
| 366 | C SUPPLIED OR WRONG CHOICE OF MF OR TOLERANCES). |
---|
| 367 | C -6 MEANS ERROR WEIGHT BECAME ZERO DURING PROBLEM. (SOLUTION |
---|
| 368 | C COMPONENT I,J VANISHED, AND ATOL OR ATOL(I,J) = 0.0) |
---|
| 369 | C |
---|
| 370 | C F. TO CONTINUE THE INTEGRATION AFTER A SUCCESSFUL RETURN, SIMPLY |
---|
| 371 | C RESET TOUT AND CALL ODESSA AGAIN. NO OTHER PARAMETERS NEED BE RESET. |
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| 372 | C---------------------------------------------------------------------- |
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| 373 | C EXAMPLE PROBLEM. |
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| 374 | C |
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| 375 | C THE FOLLOWING IS A SIMPLE EXAMPLE PROBLEM, WITH THE CODING |
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| 376 | C NEEDED FOR ITS SOLUTION BY ODESSA. THE PROBLEM IS FROM CHEMICAL |
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| 377 | C KINETICS, AND CONSISTS OF THE FOLLOWING THREE RATE EQUATIONS.. |
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| 378 | C DY1/DT = -PAR(1)*Y1 + PAR(2)*Y2*Y3 ; PAR(1) = .04, PAR(2) = 1.E4 |
---|
| 379 | C DY2/DT = PAR(1)*Y1 - PAR(2)*Y2*Y3 - PAR(3)*Y2**2 ; PAR(3) = 3.E7 |
---|
| 380 | C DY3/DT = PAR(3)*Y2**2 |
---|
| 381 | C ON THE INTERVAL FROM T = 0.0 TO T = 4.E10, WITH INITIAL CONDITIONS |
---|
| 382 | C Y1 = 1.0, Y2 = Y3 = 0, AND S(I,J) = 0, I = 1,3, J = 1,3. |
---|
| 383 | C THE PROBLEM IS STIFF. |
---|
| 384 | C |
---|
| 385 | C THE FOLLOWING CODING KppSolveS THIS PROBLEM WITH ODESSA, USING |
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| 386 | C MF = 21 AND PRINTING RESULTS AT T = .4, 4., ..., 4.E10. |
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| 387 | C IT USES ITOL = 4 AND ATOL MUCH SMALLER FOR Y2 THAN Y1 OR Y3, |
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| 388 | C BECAUSE Y2 HAS MUCH SMALLER VALUES. LESS STRINGENT TOLERANCES |
---|
| 389 | C ARE ASSIGNED FOR THE SENSITIVITIES TO ACHIEVE GREATER EFFICIENCY. |
---|
| 390 | C AT THE END OF THE RUN, STATISTICAL QUANTITIES OF INTEREST ARE |
---|
| 391 | C PRINTED (SEE OPTIONAL OUTPUTS IN THE FULL DESCRIPTION BELOW). |
---|
| 392 | C |
---|
| 393 | C DOUBLE PRECISION ATOL, RWORK, RTOL, T, TOUT, Y, PAR |
---|
| 394 | C EXTERNAL FEX, JEX, DFEX |
---|
| 395 | C DIMENSION Y(3,4), PAR(3), ATOL(3,4), RTOL(3,4), RWORK(130), |
---|
| 396 | C 1 IWORK(27), NEQ(2), IOPT(3) |
---|
| 397 | C N = 3 |
---|
| 398 | C NPAR = 3 |
---|
| 399 | C NEQ(1) = N |
---|
| 400 | C NEQ(2) = NPAR |
---|
| 401 | C NSV = NPAR+1 |
---|
| 402 | C DO 10 I = 1,N |
---|
| 403 | C DO 10 J = 1,NSV |
---|
| 404 | C 10 Y(I,J) = 0.0D0 |
---|
| 405 | C Y(1,1) = 1.0D0 |
---|
| 406 | C PAR(1) = 0.04D0 |
---|
| 407 | C PAR(2) = 1.0D4 |
---|
| 408 | C PAR(3) = 3.0D7 |
---|
| 409 | C T = 0.D0 |
---|
| 410 | C TOUT = .4D0 |
---|
| 411 | C ITOL = 4 |
---|
| 412 | C ATOL(1,1) = 1.D-6 |
---|
| 413 | C ATOL(2,1) = 1.D-10 |
---|
| 414 | C ATOL(3,1) = 1.D-6 |
---|
| 415 | C DO 20 I = 1,N |
---|
| 416 | C RTOL(I,1) = 1.D-4 |
---|
| 417 | C DO 15 J = 2,NSV |
---|
| 418 | C RTOL(I,J) = 1.D-3 |
---|
| 419 | C 15 ATOL(I,J) = 1.D2 * ATOL(I,1) |
---|
| 420 | C 20 CONTINUE |
---|
| 421 | C ITASK = 1 |
---|
| 422 | C ISTATE = 1 |
---|
| 423 | C IOPT(1) = 0 |
---|
| 424 | C IOPT(2) = 1 |
---|
| 425 | C IOPT(3) = 1 |
---|
| 426 | C LRW = 130 |
---|
| 427 | C LIW = 27 |
---|
| 428 | C MF = 21 |
---|
| 429 | C DO 60 IOUT = 1,12 |
---|
| 430 | C CALL ODESSA(FEX,DFEX,NEQ,Y,PAR,T,TOUT,ITOL,RTOL,ATOL, |
---|
| 431 | C 1 ITASK,ISTATE, IOPT,RWORK,LRW,IWORK,LIW,JEX,MF) |
---|
| 432 | C WRITE(6,30)T,Y(1,1),Y(2,1),Y(3,1) |
---|
| 433 | C 30 FORMAT(1X,7H AT T =,E12.4,6H Y =,3E14.6) |
---|
| 434 | C DO 50 J = 2,NSV |
---|
| 435 | C JPAR = J-1 |
---|
| 436 | C WRITE(6,40)JPAR,Y(1,J),Y(2,J),Y(3,J) |
---|
| 437 | C 40 FORMAT(20X,2HS(,I1,3H) =,3E14.6) |
---|
| 438 | C 50 CONTINUE |
---|
| 439 | C IF (ISTATE .LT. 0) GO TO 80 |
---|
| 440 | C 60 TOUT = TOUT*10.D0 |
---|
| 441 | C WRITE(6,70)IWORK(11),IWORK(12),IWORK(13),IWORK(19) |
---|
| 442 | C 70 FORMAT(1X,/,12H NO. STEPS =,I4,11H NO. F-S =,I4,11H NO. J-S =, |
---|
| 443 | C 1 I4,12H NO. DF-S =,I4) |
---|
| 444 | C STOP |
---|
| 445 | C 80 WRITE(6,90)ISTATE |
---|
| 446 | C 90 FORMAT(///22H ERROR HALT.. ISTATE =,I3) |
---|
| 447 | C STOP |
---|
| 448 | C END |
---|
| 449 | C |
---|
| 450 | C SUBROUTINE FEX (NEQ, T, Y, PAR, YDOT) |
---|
| 451 | C DOUBLE PRECISION T, Y, YDOT, PAR |
---|
| 452 | C DIMENSION Y(3), YDOT(3), PAR(3) |
---|
| 453 | C YDOT(1) = -PAR(1)*Y(1) + PAR(2)*Y(2)*Y(3) |
---|
| 454 | C YDOT(3) = PAR(3)*Y(2)*Y(2) |
---|
| 455 | C YDOT(2) = -YDOT(1) - YDOT(3) |
---|
| 456 | C RETURN |
---|
| 457 | C END |
---|
| 458 | C |
---|
| 459 | C SUBROUTINE JEX (NEQ, T, Y, PAR, ML, MU, PD, NRPD) |
---|
| 460 | C DOUBLE PRECISION PD, T, Y, PAR |
---|
| 461 | C DIMENSION Y(3), PD(NRPD,3), PAR(3) |
---|
| 462 | C PD(1,1) = -PAR(1) |
---|
| 463 | C PD(1,2) = PAR(2)*Y(3) |
---|
| 464 | C PD(1,3) = PAR(2)*Y(2) |
---|
| 465 | C PD(2,1) = PAR(1) |
---|
| 466 | C PD(2,3) = -PD(1,3) |
---|
| 467 | C PD(3,2) = 2.D0*PAR(3)*Y(2) |
---|
| 468 | C PD(2,2) = -PD(1,2) - PD(3,2) |
---|
| 469 | C RETURN |
---|
| 470 | C END |
---|
| 471 | C |
---|
| 472 | C SUBROUTINE DFEX (NEQ, T, Y, PAR, DFDP, JPAR) |
---|
| 473 | C DOUBLE PRECISION T, Y, PAR, DFDP |
---|
| 474 | C DIMENSION Y(3), PAR(3), DFDP(3) |
---|
| 475 | C GO TO (1,2,3), JPAR |
---|
| 476 | C 1 DFDP(1) = -Y(1) |
---|
| 477 | C DFDP(2) = Y(1) |
---|
| 478 | C RETURN |
---|
| 479 | C 2 DFDP(1) = Y(2)*Y(3) |
---|
| 480 | C DFDP(2) = -Y(2)*Y(3) |
---|
| 481 | C RETURN |
---|
| 482 | C 3 DFDP(2) = -Y(2)*Y(2) |
---|
| 483 | C DFDP(3) = Y(2)*Y(2) |
---|
| 484 | C RETURN |
---|
| 485 | C END |
---|
| 486 | C |
---|
| 487 | C THE OUTPUT OF THIS PROGRAM (ON A DATA GENERAL MV-8000 IN |
---|
| 488 | C DOUBLE PRECISION IS AS FOLLOWS: |
---|
| 489 | C |
---|
| 490 | C AT T = .4000E+00 Y = .985173E+00 .338641E-04 .147930E-01 |
---|
| 491 | C S(1) = -.355914E+00 .390261E-03 .355524E+00 |
---|
| 492 | C S(2) = .955150E-07 -.213065E-09 -.953019E-07 |
---|
| 493 | C S(3) = -.158466E-10 -.529012E-12 .163756E-10 |
---|
| 494 | C AT T = .4000E+01 Y = .905516E+00 .224044E-04 .944615E-01 |
---|
| 495 | C S(1) = -.187621E+01 .179197E-03 .187603E+01 |
---|
| 496 | C S(2) = .296093E-05 -.583104E-09 -.296034E-05 |
---|
| 497 | C S(3) = -.493267E-09 -.276246E-12 .493544E-09 |
---|
| 498 | C AT T = .4000E+02 Y = .715848E+00 .918628E-05 .284143E+00 |
---|
| 499 | C S(1) = -.424730E+01 .459360E-04 .424726E+01 |
---|
| 500 | C S(2) = .137294E-04 -.235815E-09 -.137291E-04 |
---|
| 501 | C S(3) = -.228818E-08 -.113803E-12 .228829E-08 |
---|
| 502 | C AT T = .4000E+03 Y = .450526E+00 .322299E-05 .549471E+00 |
---|
| 503 | C S(1) = -.595837E+01 .354310E-05 .595836E+01 |
---|
| 504 | C S(2) = .227380E-04 -.226041E-10 -.227380E-04 |
---|
| 505 | C S(3) = -.378971E-08 -.499501E-13 .378976E-08 |
---|
| 506 | C AT T = .4000E+04 Y = .183185E+00 .894131E-06 .816814E+00 |
---|
| 507 | C S(1) = -.475006E+01 -.599504E-05 .475007E+01 |
---|
| 508 | C S(2) = .188089E-04 .231330E-10 -.188089E-04 |
---|
| 509 | C S(3) = -.313478E-08 -.187575E-13 .313480E-08 |
---|
| 510 | C AT T = .4000E+05 Y = .389733E-01 .162133E-06 .961027E+00 |
---|
| 511 | C S(1) = -.157477E+01 -.276199E-05 .157477E+01 |
---|
| 512 | C S(2) = .628668E-05 .110026E-10 -.628670E-05 |
---|
| 513 | C S(3) = -.104776E-08 -.453588E-14 .104776E-08 |
---|
| 514 | C AT T = .4000E+06 Y = .493609E-02 .198411E-07 .995064E+00 |
---|
| 515 | C S(1) = -.236244E+00 -.458262E-06 .236244E+00 |
---|
| 516 | C S(2) = .944669E-06 .183193E-11 -.944671E-06 |
---|
| 517 | C S(3) = -.157441E-09 -.635990E-15 .157442E-09 |
---|
| 518 | C AT T = .4000E+07 Y = .516087E-03 .206540E-08 .999484E+00 |
---|
| 519 | C S(1) = -.256277E-01 -.509808E-07 .256278E-01 |
---|
| 520 | C S(2) = .102506E-06 .203905E-12 -.102506E-06 |
---|
| 521 | C S(3) = -.170825E-10 -.684002E-16 .170826E-10 |
---|
| 522 | C AT T = .4000E+08 Y = .519314E-04 .207736E-09 .999948E+00 |
---|
| 523 | C S(1) = -.259316E-02 -.518029E-08 .259316E-02 |
---|
| 524 | C S(2) = .103726E-07 .207209E-13 -.103726E-07 |
---|
| 525 | C S(3) = -.172845E-11 -.691450E-17 .172845E-11 |
---|
| 526 | C AT T = .4000E+09 Y = .544710E-05 .217885E-10 .999995E+00 |
---|
| 527 | C S(1) = -.271637E-03 -.541849E-09 .271638E-03 |
---|
| 528 | C S(2) = .108655E-08 .216739E-14 -.108655E-08 |
---|
| 529 | C S(3) = -.180902E-12 -.723615E-18 .180902E-12 |
---|
| 530 | C AT T = .4000E+10 Y = .446748E-06 .178699E-11 .100000E+01 |
---|
| 531 | C S(1) = -.322322E-04 -.842541E-10 .322323E-04 |
---|
| 532 | C S(2) = .128929E-09 .337016E-15 -.128929E-09 |
---|
| 533 | C S(3) = -.209715E-13 -.838859E-19 .209715E-13 |
---|
| 534 | C AT T = .4000E+11 Y = -.363960E-07 -.145584E-12 .100000E+01 |
---|
| 535 | C S(1) = -.164109E-06 -.429604E-11 .164113E-06 |
---|
| 536 | C S(2) = .656436E-12 .171842E-16 -.656451E-12 |
---|
| 537 | C S(3) = -.689361E-15 -.275745E-20 .689363E-15 |
---|
| 538 | C |
---|
| 539 | C NO. STEPS = 340 NO. F-S = 412 NO. J-S = 343 NO. DF-S =1023 |
---|
| 540 | C---------------------------------------------------------------------- |
---|
| 541 | C FULL DESCRIPTION OF USER INTERFACE TO ODESSA. |
---|
| 542 | C |
---|
| 543 | C THE USER INTERFACE TO ODESSA CONSISTS OF THE FOLLOWING PARTS. |
---|
| 544 | C |
---|
| 545 | C I. THE CALL SEQUENCE TO SUBROUTINE ODESSA, WHICH IS A DRIVER |
---|
| 546 | C ROUTINE FOR THE KppSolveR. THIS INCLUDES DESCRIPTIONS OF BOTH |
---|
| 547 | C THE CALL SEQUENCE ARGUMENTS AND OF USER-SUPPLIED ROUTINES. |
---|
| 548 | C FOLLOWING THESE DESCRIPTIONS IS A DESCRIPTION OF |
---|
| 549 | C OPTIONAL INPUTS AVAILABLE THROUGH THE CALL SEQUENCE, AND THEN |
---|
| 550 | C A DESCRIPTION OF OPTIONAL OUTPUTS (IN THE WORK ARRAYS). |
---|
| 551 | C |
---|
| 552 | C II. DESCRIPTIONS OF OTHER ROUTINES IN THE ODESSA PACKAGE THAT MAY |
---|
| 553 | C BE (OPTIONALLY) CALLED BY THE USER. THESE PROVIDE THE ABILITY |
---|
| 554 | C TO ALTER ERROR MESSAGE HANDLING, SAVE AND RESTORE THE INTERNAL |
---|
| 555 | C COMMON, AND OBTAIN SPECIFIED DERIVATIVES OF THE SOLUTION Y(T). |
---|
| 556 | C |
---|
| 557 | C III. DESCRIPTIONS OF COMMON BLOCKS TO BE DECLARED IN OVERLAY |
---|
| 558 | C OR SIMILAR ENVIRONMENTS, OR TO BE SAVED WHEN DOING AN INTERRUPT |
---|
| 559 | C OF THE PROBLEM AND CONTINUED SOLUTION LATER. |
---|
| 560 | C |
---|
| 561 | C IV. DESCRIPTION OF TWO SUBROUTINES IN THE ODESSA PACKAGE, EITHER OF |
---|
| 562 | C WHICH THE USER MAY REPLACE WITH HIS OWN VERSION, IF DESIRED. |
---|
| 563 | C THESE RELATE TO THE MEASUREMENT OF ERRORS. |
---|
| 564 | C |
---|
| 565 | C V. GENERAL REMARKS WHICH HIGHLIGHT DIFFERENCES BETWEEN THE LSODE |
---|
| 566 | C PACKAGE AND THE ODESSA PACKAGE. |
---|
| 567 | C---------------------------------------------------------------------- |
---|
| 568 | C PART I. CALL SEQUENCE. |
---|
| 569 | C |
---|
| 570 | C THE CALL SEQUENCE PARAMETERS USED FOR INPUT ONLY ARE.. |
---|
| 571 | C F, DF, NEQ, PAR, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, |
---|
| 572 | C JAC, MF, |
---|
| 573 | C AND THOSE USED FOR BOTH INPUT AND OUTPUT ARE |
---|
| 574 | C Y, T, ISTATE. |
---|
| 575 | C THE WORK ARRAYS RWORK AND IWORK ARE ALSO USED FOR CONDITIONAL AND |
---|
| 576 | C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. (THE TERM OUTPUT HERE REFERS |
---|
| 577 | C TO THE RETURN FROM SUBROUTINE ODESSA TO THE USER-S CALLING PROGRAM.) |
---|
| 578 | C |
---|
| 579 | C THE LEGALITY OF INPUT PARAMETERS WILL BE THOROUGHLY CHECKED ON THE |
---|
| 580 | C INITIAL CALL FOR THE PROBLEM, BUT NOT CHECKED THEREAFTER UNLESS A |
---|
| 581 | C CHANGE IN INPUT PARAMETERS IS FLAGGED BY ISTATE = 3 ON INPUT. |
---|
| 582 | C |
---|
| 583 | C THE DESCRIPTIONS OF THE CALL ARGUMENTS ARE AS FOLLOWS. |
---|
| 584 | C |
---|
| 585 | C F = THE NAME OF THE USER-SUPPLIED SUBROUTINE DEFINING THE |
---|
| 586 | C ODE MODEL. THIS SYSTEM MUST BE PUT IN THE FIRST-ORDER |
---|
| 587 | C FORM DY/DT = F(Y,T;P), WHERE F IS A VECTOR-VALUED FUNCTION |
---|
| 588 | C OF THE SCALAR T AND VECTORS Y, AND PAR. SUBROUTINE F IS TO |
---|
| 589 | C COMPUTE THE FUNCTION F. IT IS TO HAVE THE FORM.. |
---|
| 590 | C SUBROUTINE F (NEQ, T, Y, PAR, YDOT) |
---|
| 591 | C DOUBLE PRECISION T, Y, PAR, YDOT |
---|
| 592 | C DIMENSION Y(1), PAR(1), YDOT(1) |
---|
| 593 | C WHERE NEQ, T, Y, AND PAR ARE INPUT, AND YDOT = F(Y,T;P) |
---|
| 594 | C IS OUTPUT. Y AND YDOT ARE ARRAYS OF LENGTH N (= NEQ(1)). |
---|
| 595 | C (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY |
---|
| 596 | C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) |
---|
| 597 | C F SHOULD NOT ALTER ARRAY Y, OR PAR(1),...,PAR(NPAR). |
---|
| 598 | C F MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. |
---|
| 599 | C |
---|
| 600 | C SUBROUTINE F MAY ACCESS USER-DEFINED QUANTITIES IN |
---|
| 601 | C NEQ(2),... AND PAR(NPAR+1),... IF NEQ IS AN ARRAY |
---|
| 602 | C (DIMENSIONED IN F) AND PAR HAS LENGTH EXCEEDING NPAR. |
---|
| 603 | C SEE THE DESCRIPTIONS OF NEQ AND PAR BELOW. |
---|
| 604 | C |
---|
| 605 | C DF = THE NAME OF THE USER-SUPPLIED ROUTINE (IDF = 1) TO COMPUTE |
---|
| 606 | C THE INHOMOGENEITY MATRIX, DF/DP, AS A FUNCTION OF THE SCALAR |
---|
| 607 | C T, AND THE VECTORS Y, AND PAR. IT IS TO HAVE THE FORM |
---|
| 608 | C SUBROUTINE DF (NEQ, T, Y, PAR, DFDP, JPAR) |
---|
| 609 | C DOUBLE PRECISION T, Y, PAR, DFDP |
---|
| 610 | C DIMENSION Y(1), PAR(1), DFDP(1) |
---|
| 611 | C GO TO (1,2,...,NPAR) JPAR |
---|
| 612 | C 1 DFDP(1) = DF(1)/DP(1) |
---|
| 613 | C . |
---|
| 614 | C DFDP(I) = DF(I)/DP(1) |
---|
| 615 | C . |
---|
| 616 | C DFDP(N) = DF(N)/DP(1) |
---|
| 617 | C RETURN |
---|
| 618 | C 2 DFDP(1) = DF(1)/DP(2) |
---|
| 619 | C . |
---|
| 620 | C DFDP(I) = DF(I)/DP(2) |
---|
| 621 | C . |
---|
| 622 | C DFDP(N) = DF(N)/DP(2) |
---|
| 623 | C . |
---|
| 624 | C RETURN |
---|
| 625 | C . . |
---|
| 626 | C . . |
---|
| 627 | C NPAR DFDP(1) = DF(1)/DP(NPAR) |
---|
| 628 | C . |
---|
| 629 | C DFDP(I) = DF(I)/DP(NPAR) |
---|
| 630 | C . |
---|
| 631 | C DFDP(N) = DF(N)/DP(NPAR) |
---|
| 632 | C RETURN |
---|
| 633 | C END |
---|
| 634 | C WHERE NEQ, T, Y, PAR, AND JPAR ARE INPUT AND THE VECTOR |
---|
| 635 | C DFDP(*,JPAR) IS TO BE LOADED WITH THE PARTIAL DERIVATIVES |
---|
| 636 | C DF(Y,T;PAR)/DP(JPAR) ON OUTPUT. ONLY NONZERO ELEMENTS NEED |
---|
| 637 | C BE LOADED. T, Y, AND PAR HAVE THE SAME MEANING AS IN |
---|
| 638 | C SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A DUMMY |
---|
| 639 | C DIMENSION.. IT CAN BE REPLACED BY ANY VALUE). |
---|
| 640 | C |
---|
| 641 | C DFDP(*,JPAR) IS PRESET TO ZERO BY THE KppSolveR, SO THAT ONLY |
---|
| 642 | C THE NONZERO ELEMENTS NEED BE LOADED BY DF. SUBROUTINE DF |
---|
| 643 | C MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM IF USED. |
---|
| 644 | C IF IDF = 0 (OR ISOPT = 0), A DUMMY ARGUMENT CAN BE USED. |
---|
| 645 | C |
---|
| 646 | C SUBROUTINE DF MAY ACCESS USER-DEFINED QUANTITIES IN |
---|
| 647 | C NEQ(2),... AND PAR(NPAR+1),... IF NEQ IS AN ARRAY |
---|
| 648 | C (DIMENSIONED IN DF) AND PAR HAS A LENGTH EXCEEDING NPAR. |
---|
| 649 | C SEE THE DESCRIPTIONS OF NEQ AND PAR (BELOW). |
---|
| 650 | C |
---|
| 651 | C NEQ = THE SIZE OF THE ODE SYSTEM (NUMBER OF FIRST ORDER ORDINARY |
---|
| 652 | C DIFFERENTIAL EQUATIONS (N) IN THE MODEL). USED ONLY FOR |
---|
| 653 | C INPUT. NEQ MAY NOT BE CHANGED DURING THE PROBLEM. |
---|
| 654 | C |
---|
| 655 | C FOR ISOPT = 0, NEQ IS NORMALLY A SCALAR. HOWEVER, NEQ MAY |
---|
| 656 | C BE AN ARRAY, WITH NEQ(1) SET TO THE SYSTEM SIZE (N), IN WHICH |
---|
| 657 | C CASE THE ODESSA PACKAGE ACCESSES ONLY NEQ(1). HOWEVER, |
---|
| 658 | C THIS PARAMETER IS PASSED AS THE NEQ ARGUMENT IN ALL CALLS |
---|
| 659 | C TO F, DF, AND JAC. HENCE, IF IT IS AN ARRAY, LOCATIONS |
---|
| 660 | C NEQ(2),... MAY BE USED TO STORE OTHER INTEGER DATA AND PASS |
---|
| 661 | C IT TO F, DF, AND/OR JAC. FOR ISOPT = 1, NPAR MUST BE LOADED |
---|
| 662 | C INTO NEQ(2), AND IS NOT ALLOWED TO CHANGE DURING THE PROBLEM. |
---|
| 663 | C IN THESE CASES, SUBROUTINES F, DF, AND/OR JAC MUST INCLUDE |
---|
| 664 | C NEQ IN A DIMENSION STATEMENT. |
---|
| 665 | C |
---|
| 666 | C Y = A REAL ARRAY FOR THE VECTOR OF DEPENDENT VARIABLES, OF |
---|
| 667 | C DIMENSION (N) BY (NPAR+1). USED FOR BOTH INPUT AND |
---|
| 668 | C OUTPUT ON THE FIRST CALL (ISTATE = 1), AND ONLY FOR |
---|
| 669 | C OUTPUT ON OTHER CALLS. ON THE FIRST CALL, Y MUST CONTAIN |
---|
| 670 | C THE VECTORS OF INITIAL VALUES. ON OUTPUT, Y CONTAINS THE |
---|
| 671 | C COMPUTED SOLUTION VECTORS, EVALUATED AT T. |
---|
| 672 | C |
---|
| 673 | C PAR = A REAL ARRAY FOR THE VECTOR OF CONSTANT MODEL PARAMETERS |
---|
| 674 | C OF INTEREST IN THE SENSITIVITY ANALYSIS, OF LENGTH NPAR |
---|
| 675 | C OR MORE. PAR IS PASSED AS AN ARGUMENT IN ALL CALLS TO F, |
---|
| 676 | C DF, AND JAC. HENCE LOCATIONS PAR(NPAR+1),... MAY BE USED |
---|
| 677 | C TO STORE OTHER REAL DATA AND PASS IT TO F, DF, AND/OR JAC. |
---|
| 678 | C LOCATIONS PAR(1),...,PAR(NPAR) ARE USED AS INPUT ONLY, |
---|
| 679 | C AND MUST NOT BE CHANGED DURING THE PROBLEM. |
---|
| 680 | C |
---|
| 681 | C T = THE INDEPENDENT VARIABLE. ON INPUT, T IS USED ONLY ON THE |
---|
| 682 | C FIRST CALL, AS THE INITIAL POINT OF THE INTEGRATION. |
---|
| 683 | C ON OUTPUT, AFTER EACH CALL, T IS THE VALUE AT WHICH A |
---|
| 684 | C COMPUTED SOLUTION Y IS EVALUATED (USUALLY THE SAME AS TOUT). |
---|
| 685 | C ON AN ERROR RETURN, T IS THE FARTHEST POINT REACHED. |
---|
| 686 | C |
---|
| 687 | C TOUT = THE NEXT VALUE OF T AT WHICH A COMPUTED SOLUTION IS DESIRED. |
---|
| 688 | C USED ONLY FOR INPUT. |
---|
| 689 | C |
---|
| 690 | C WHEN STARTING THE PROBLEM (ISTATE = 1), TOUT MAY BE EQUAL |
---|
| 691 | C TO T FOR ONE CALL, THEN SHOULD .NE. T FOR THE NEXT CALL. |
---|
| 692 | C FOR THE INITIAL T, AN INPUT VALUE OF TOUT .NE. T IS USED |
---|
| 693 | C IN ORDER TO DETERMINE THE DIRECTION OF THE INTEGRATION |
---|
| 694 | C (I.E. THE ALGEBRAIC SIGN OF THE STEP SIZES) AND THE ROUGH |
---|
| 695 | C SCALE OF THE PROBLEM. INTEGRATION IN EITHER DIRECTION |
---|
| 696 | C (FORWARD OR BACKWARD IN T) IS PERMITTED. |
---|
| 697 | C |
---|
| 698 | C IF ITASK = 2 OR 5 (ONE-STEP MODES), TOUT IS IGNORED AFTER |
---|
| 699 | C THE FIRST CALL (I.E. THE FIRST CALL WITH TOUT .NE. T). |
---|
| 700 | C OTHERWISE, TOUT IS REQUIRED ON EVERY CALL. |
---|
| 701 | C |
---|
| 702 | C IF ITASK = 1, 3, OR 4, THE VALUES OF TOUT NEED NOT BE |
---|
| 703 | C MONOTONE, BUT A VALUE OF TOUT WHICH BACKS UP IS LIMITED |
---|
| 704 | C TO THE CURRENT INTERNAL T INTERVAL, WHOSE ENDPOINTS ARE |
---|
| 705 | C TCUR - HU AND TCUR (SEE OPTIONAL OUTPUTS, BELOW, FOR |
---|
| 706 | C TCUR AND HU). |
---|
| 707 | C |
---|
| 708 | C ITOL = AN INDICATOR FOR THE TYPE OF ERROR CONTROL. SEE |
---|
| 709 | C DESCRIPTION BELOW UNDER ATOL. USED ONLY FOR INPUT. |
---|
| 710 | C |
---|
| 711 | C RTOL = A RELATIVE ERROR TOLERANCE PARAMETER, EITHER A SCALAR OR |
---|
| 712 | C AN ARRAY OF SPACE (N) BY (NPAR+1). SEE DESCRIPTION BELOW |
---|
| 713 | C UNDER ATOL. INPUT ONLY. |
---|
| 714 | C |
---|
| 715 | C ATOL = AN ABSOLUTE ERROR TOLERANCE PARAMETER, EITHER A SCALAR OR |
---|
| 716 | C AN ARRAY OF SPACE (N) BY (NPAR+1). INPUT ONLY. |
---|
| 717 | C |
---|
| 718 | C THE INPUT PARAMETERS ITOL, RTOL, AND ATOL DETERMINE |
---|
| 719 | C THE ERROR CONTROL PERFORMED BY THE KppSolveR. THE KppSolveR WILL |
---|
| 720 | C CONTROL THE VECTOR E = (E(I,J)) OF ESTIMATED LOCAL ERRORS |
---|
| 721 | C IN Y, ACCORDING TO AN INEQUALITY OF THE FORM |
---|
| 722 | C RMS-NORM OF ( E(I,J)/EWT(I,J) ) .LE. 1, |
---|
| 723 | C WHERE EWT(I,J) = RTOL(I,J)*ABS(Y(I,J)) + ATOL(I,J), |
---|
| 724 | C AND THE RMS-NORM (ROOT-MEAN-SQUARE NORM) HERE IS |
---|
| 725 | C RMS-NORM(V) = SQRT ( (1/N) * SUM (V(I,J)**2) ); I =1,...,N. |
---|
| 726 | C HERE EWT = (EWT(I,J)) IS A VECTOR OF WEIGHTS WHICH MUST |
---|
| 727 | C ALWAYS BE POSITIVE, AND THE VALUES OF RTOL AND ATOL SHOULD |
---|
| 728 | C ALL BE NON-NEGATIVE. THE FOLLOWING TABLE GIVES THE TYPES |
---|
| 729 | C (SCALAR/ARRAY) OF RTOL AND ATOL, AND THE CORRESPONDING FORM |
---|
| 730 | C OF EWT(I,J). |
---|
| 731 | C |
---|
| 732 | C ITOL RTOL ATOL EWT(I,J) |
---|
| 733 | C 1 SCALAR SCALAR RTOL*ABS(Y(I,J)) + ATOL |
---|
| 734 | C 2 SCALAR ARRAY RTOL*ABS(Y(I,J)) + ATOL(I,J) |
---|
| 735 | C 3 ARRAY SCALAR RTOL(I,J)*ABS(Y(I,J)) + ATOL |
---|
| 736 | C 4 ARRAY ARRAY RTOL(I,J)*ABS(Y(I,J)) + ATOL(I,J) |
---|
| 737 | C |
---|
| 738 | C WHEN EITHER OF THESE PARAMETERS IS A SCALAR, IT NEED NOT |
---|
| 739 | C BE DIMENSIONED IN THE USER-S CALLING PROGRAM. |
---|
| 740 | C |
---|
| 741 | C THE TOTAL NUMBER OF ERROR TEST FAILURES DUE TO THE SENSITIVITY |
---|
| 742 | C ANALYSIS, AND WHICH REQUIRE AN INTEGRATION STEP TO BE |
---|
| 743 | C REPEATED, ARE ACCUMULATED IN THE LAST NPAR+1 LOCATIONS OF THE |
---|
| 744 | C INTEGER WORK ARRAY IWORK (SEE OPTIONAL OUTPUTS BELOW). |
---|
| 745 | C THIS INFORMATION MAY BE OF VALUE IN DETERMINING APPROPRIATE |
---|
| 746 | C ERROR TOLERANCES TO BE APPLIED TO THE SENSITIVITY FUNCTIONS. |
---|
| 747 | C |
---|
| 748 | C IF NONE OF THE ABOVE CHOICES (WITH ITOL, RTOL, AND ATOL |
---|
| 749 | C FIXED THROUGHOUT THE PROBLEM) IS SUITABLE, MORE GENERAL |
---|
| 750 | C ERROR CONTROLS CAN BE OBTAINED BY SUBSTITUTING |
---|
| 751 | C USER-SUPPLIED ROUTINES FOR THE SETTING OF EWT AND/OR FOR |
---|
| 752 | C THE NORM CALCULATION. SEE PART IV BELOW. |
---|
| 753 | C |
---|
| 754 | C IF GLOBAL ERRORS ARE TO BE ESTIMATED BY MAKING A REPEATED |
---|
| 755 | C RUN ON THE SAME PROBLEM WITH SMALLER TOLERANCES, THEN ALL |
---|
| 756 | C COMPONENTS OF RTOL AND ATOL (I.E. OF EWT) SHOULD BE SCALED |
---|
| 757 | C DOWN UNIFORMLY. |
---|
| 758 | C |
---|
| 759 | C ITASK = AN INDEX SPECIFYING THE TASK TO BE PERFORMED. |
---|
| 760 | C INPUT ONLY. ITASK HAS THE FOLLOWING VALUES AND MEANINGS. |
---|
| 761 | C 1 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT |
---|
| 762 | C T = TOUT (BY OVERSHOOTING AND INTERPOLATING). |
---|
| 763 | C 2 MEANS TAKE ONE STEP ONLY AND RETURN. |
---|
| 764 | C 3 MEANS STOP AT THE FIRST INTERNAL MESH POINT AT OR |
---|
| 765 | C BEYOND T = TOUT AND RETURN. |
---|
| 766 | C 4 MEANS NORMAL COMPUTATION OF OUTPUT VALUES OF Y(T) AT |
---|
| 767 | C T = TOUT BUT WITHOUT OVERSHOOTING T = TCRIT. |
---|
| 768 | C TCRIT MUST BE INPUT AS RWORK(1). TCRIT MAY BE EQUAL TO |
---|
| 769 | C OR BEYOND TOUT, BUT NOT BEHIND IT IN THE DIRECTION OF |
---|
| 770 | C INTEGRATION. THIS OPTION IS USEFUL IF THE PROBLEM |
---|
| 771 | C HAS A SINGULARITY AT OR BEYOND T = TCRIT. |
---|
| 772 | C 5 MEANS TAKE ONE STEP, WITHOUT PASSING TCRIT, AND RETURN. |
---|
| 773 | C TCRIT MUST BE INPUT AS RWORK(1). |
---|
| 774 | C |
---|
| 775 | C NOTE.. IF ITASK = 4 OR 5 AND THE KppSolveR REACHES TCRIT |
---|
| 776 | C (WITHIN ROUNDOFF), IT WILL RETURN T = TCRIT (EXACTLY) TO |
---|
| 777 | C INDICATE THIS (UNLESS ITASK = 4 AND TOUT COMES BEFORE TCRIT, |
---|
| 778 | C IN WHICH CASE ANSWERS AT T = TOUT ARE RETURNED FIRST). |
---|
| 779 | C |
---|
| 780 | C ISTATE = AN INDEX USED FOR INPUT AND OUTPUT TO SPECIFY THE |
---|
| 781 | C THE STATE OF THE CALCULATION. |
---|
| 782 | C |
---|
| 783 | C ON INPUT, THE VALUES OF ISTATE ARE AS FOLLOWS. |
---|
| 784 | C 1 MEANS THIS IS THE FIRST CALL FOR THE PROBLEM |
---|
| 785 | C (INITIALIZATIONS WILL BE DONE). SEE NOTE BELOW. |
---|
| 786 | C 2 MEANS THIS IS NOT THE FIRST CALL, AND THE CALCULATION |
---|
| 787 | C IS TO CONTINUE NORMALLY, WITH NO CHANGE IN ANY INPUT |
---|
| 788 | C PARAMETERS EXCEPT POSSIBLY TOUT AND ITASK. |
---|
| 789 | C (IF ITOL, RTOL, AND/OR ATOL ARE CHANGED BETWEEN CALLS |
---|
| 790 | C WITH ISTATE = 2, THE NEW VALUES WILL BE USED BUT NOT |
---|
| 791 | C TESTED FOR LEGALITY.) |
---|
| 792 | C 3 MEANS THIS IS NOT THE FIRST CALL, AND THE |
---|
| 793 | C CALCULATION IS TO CONTINUE NORMALLY, BUT WITH |
---|
| 794 | C A CHANGE IN INPUT PARAMETERS OTHER THAN |
---|
| 795 | C TOUT AND ITASK. CHANGES ARE ALLOWED IN |
---|
| 796 | C ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, |
---|
| 797 | C AND ANY OF THE OPTIONAL INPUTS EXCEPT H0. |
---|
| 798 | C (SEE IWORK DESCRIPTION FOR ML AND MU.) |
---|
| 799 | C NOTE.. A PRELIMINARY CALL WITH TOUT = T IS NOT COUNTED |
---|
| 800 | C AS A FIRST CALL HERE, AS NO INITIALIZATION OR CHECKING OF |
---|
| 801 | C INPUT IS DONE. (SUCH A CALL IS SOMETIMES USEFUL FOR THE |
---|
| 802 | C PURPOSE OF OUTPUTTING THE INITIAL CONDITIONS.) |
---|
| 803 | C THUS THE FIRST CALL FOR WHICH TOUT .NE. T REQUIRES |
---|
| 804 | C ISTATE = 1 ON INPUT. |
---|
| 805 | C |
---|
| 806 | C ON OUTPUT, ISTATE HAS THE FOLLOWING VALUES AND MEANINGS. |
---|
| 807 | C 1 MEANS NOTHING WAS DONE, AS TOUT WAS EQUAL TO T WITH |
---|
| 808 | C ISTATE = 1 ON INPUT. (HOWEVER, AN INTERNAL COUNTER WAS |
---|
| 809 | C SET TO DETECT AND PREVENT REPEATED CALLS OF THIS TYPE.) |
---|
| 810 | C 2 MEANS THE INTEGRATION WAS PERFORMED SUCCESSFULLY. |
---|
| 811 | C -1 MEANS AN EXCESSIVE AMOUNT OF WORK (MORE THAN MXSTEP |
---|
| 812 | C STEPS) WAS DONE ON THIS CALL, BEFORE COMPLETING THE |
---|
| 813 | C REQUESTED TASK, BUT THE INTEGRATION WAS OTHERWISE |
---|
| 814 | C SUCCESSFUL AS FAR AS T. (MXSTEP IS AN OPTIONAL INPUT |
---|
| 815 | C AND IS NORMALLY 500.) TO CONTINUE, THE USER MAY |
---|
| 816 | C SIMPLY RESET ISTATE TO A VALUE .GT. 1 AND CALL AGAIN |
---|
| 817 | C (THE EXCESS WORK STEP COUNTER WILL BE RESET TO 0). |
---|
| 818 | C IN ADDITION, THE USER MAY INCREASE MXSTEP TO AVOID |
---|
| 819 | C THIS ERROR RETURN (SEE BELOW ON OPTIONAL INPUTS). |
---|
| 820 | C -2 MEANS TOO MUCH ACCURACY WAS REQUESTED FOR THE PRECISION |
---|
| 821 | C OF THE MACHINE BEING USED. THIS WAS DETECTED BEFORE |
---|
| 822 | C COMPLETING THE REQUESTED TASK, BUT THE INTEGRATION |
---|
| 823 | C WAS SUCCESSFUL AS FAR AS T. TO CONTINUE, THE TOLERANCE |
---|
| 824 | C PARAMETERS MUST BE RESET, AND ISTATE MUST BE SET |
---|
| 825 | C TO 3. THE OPTIONAL OUTPUT TOLSF MAY BE USED FOR THIS |
---|
| 826 | C PURPOSE. (NOTE.. IF THIS CONDITION IS DETECTED BEFORE |
---|
| 827 | C TAKING ANY STEPS, THEN AN ILLEGAL INPUT RETURN |
---|
| 828 | C (ISTATE = -3) OCCURS INSTEAD.) |
---|
| 829 | C -3 MEANS ILLEGAL INPUT WAS DETECTED, BEFORE TAKING ANY |
---|
| 830 | C INTEGRATION STEPS. SEE WRITTEN MESSAGE FOR DETAILS. |
---|
| 831 | C NOTE.. IF THE KppSolveR DETECTS AN INFINITE LOOP OF CALLS |
---|
| 832 | C TO THE KppSolveR WITH ILLEGAL INPUT, IT WILL CAUSE |
---|
| 833 | C THE RUN TO STOP. |
---|
| 834 | C -4 MEANS THERE WERE REPEATED ERROR TEST FAILURES ON |
---|
| 835 | C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED |
---|
| 836 | C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. |
---|
| 837 | C THE PROBLEM MAY HAVE A SINGULARITY, OR THE INPUT |
---|
| 838 | C MAY BE INAPPROPRIATE. |
---|
| 839 | C -5 MEANS THERE WERE REPEATED CONVERGENCE TEST FAILURES ON |
---|
| 840 | C ONE ATTEMPTED STEP, BEFORE COMPLETING THE REQUESTED |
---|
| 841 | C TASK, BUT THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. |
---|
| 842 | C THIS MAY BE CAUSED BY AN INACCURATE JACOBIAN MATRIX, |
---|
| 843 | C IF ONE IS BEING USED. |
---|
| 844 | C -6 MEANS EWT(I,J) BECAME ZERO FOR SOME I,J DURING THE |
---|
| 845 | C INTEGRATION. PURE RELATIVE ERROR CONTROL (ATOL(I,J)=0.0) |
---|
| 846 | C WAS REQUESTED ON A VARIABLE WHICH HAS NOW VANISHED. |
---|
| 847 | C THE INTEGRATION WAS SUCCESSFUL AS FAR AS T. |
---|
| 848 | C |
---|
| 849 | C NOTE.. SINCE THE NORMAL OUTPUT VALUE OF ISTATE IS 2, |
---|
| 850 | C IT DOES NOT NEED TO BE RESET FOR NORMAL CONTINUATION. |
---|
| 851 | C ALSO, SINCE A NEGATIVE INPUT VALUE OF ISTATE WILL BE |
---|
| 852 | C REGARDED AS ILLEGAL, A NEGATIVE OUTPUT VALUE REQUIRES THE |
---|
| 853 | C USER TO CHANGE IT, AND POSSIBLY OTHER INPUTS, BEFORE |
---|
| 854 | C CALLING THE KppSolveR AGAIN. |
---|
| 855 | C |
---|
| 856 | C IOPT = AN INTEGER ARRAY FLAG TO SPECIFY WHETHER OR NOT ANY OPTIONAL |
---|
| 857 | C INPUTS ARE BEING USED ON THIS CALL. INPUT ONLY. |
---|
| 858 | C THE OPTIONAL INPUTS ARE LISTED SEPARATELY BELOW. |
---|
| 859 | C IOPT(1) = 0 MEANS NO OPTIONAL INPUTS FOR THE KppSolveR WILL BE |
---|
| 860 | C USED. DEFAULT VALUES WILL BE USED IN ALL CASES. |
---|
| 861 | C = 1 MEANS ONE OR MORE OPTIONAL INPUTS FOR THE |
---|
| 862 | C KppSolveR ARE BEING USED. |
---|
| 863 | C NOTE : IOPT(1) IS INDEPENDENT OF ISOPT AND IDF. |
---|
| 864 | C IOPT(2) = 0 MEANS NO SENSITIVITY ANALYSIS WILL BE PERFORMED. |
---|
| 865 | C = 1 MEANS A SENSITIVITY ANALYSIS WILL BE PERFORMED. |
---|
| 866 | C NOTE : IOPT(2) IS RENAMED TO ISOPT IN ODESSA. |
---|
| 867 | C = 0 MEANS DF/DP WILL BE CALCULATED BY FINITE |
---|
| 868 | C DIFFERENCE WITHIN ODESSA. |
---|
| 869 | C IOPT(3) = 1 MEANS DF/DP WILL BE CALCULATED BY A USER-SUPPLIED |
---|
| 870 | C ROUTINE. |
---|
| 871 | C NOTE : IOPT(3) IS RENAMED TO IDF IN ODESSA. |
---|
| 872 | C IF IDF = 1, THE USER MUST SUPPLY A |
---|
| 873 | C SUBROUTINE DF (THE NAME IS ARBITRARY) AS |
---|
| 874 | C DESCRIBED BELOW UNDER DF. FOR IDF = 0, |
---|
| 875 | C A DUMMY ARGUMENT CAN BE USED. |
---|
| 876 | C |
---|
| 877 | C RWORK = A REAL WORKING ARRAY (DOUBLE PRECISION). |
---|
| 878 | C FOR ISOPT = 0, THE LENGTH OF RWORK MUST BE AT LEAST.. |
---|
| 879 | C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM |
---|
| 880 | C FOR ISOPT = 1, THE LENGTH OF RWORK MUST BE AT LEAST.. |
---|
| 881 | C 20 + NYH*(MAXORD + 1) + 2*NYH + LWM + N |
---|
| 882 | C WHERE.. |
---|
| 883 | C NYH = THE TOTAL NUMBER OF DEPENDENT VARIABLES; |
---|
| 884 | C (= N IF ISOPT = 0, AND N*(NPAR+1) IF ISOPT = 1). |
---|
| 885 | C MAXORD = 12 (IF METH = 1) OR 5 (IF METH = 2) (UNLESS A |
---|
| 886 | C SMALLER VALUE IS GIVEN AS AN OPTIONAL INPUT), |
---|
| 887 | C LWM = 0 IF MITER = 0, |
---|
| 888 | C LWM = N**2 + 2 IF MITER IS 1 OR 2, |
---|
| 889 | C LWM = N + 2 IF MITER = 3, AND |
---|
| 890 | C LWM = (2*ML+MU+1)*N + 2 IF MITER IS 4 OR 5. |
---|
| 891 | C (SEE THE MF DESCRIPTION FOR METH AND MITER.) |
---|
| 892 | C |
---|
| 893 | C THE FIRST 20 WORDS OF RWORK ARE RESERVED FOR CONDITIONAL |
---|
| 894 | C AND OPTIONAL INPUTS AND OPTIONAL OUTPUTS. |
---|
| 895 | C |
---|
| 896 | C THE FOLLOWING WORD IN RWORK IS A CONDITIONAL INPUT.. |
---|
| 897 | C RWORK(1) = TCRIT = CRITICAL VALUE OF T WHICH THE KppSolveR |
---|
| 898 | C IS NOT TO OVERSHOOT. REQUIRED IF ITASK IS |
---|
| 899 | C 4 OR 5, AND IGNORED OTHERWISE. (SEE ITASK.) |
---|
| 900 | C |
---|
| 901 | C LRW = THE LENGTH OF THE ARRAY RWORK, AS DECLARED BY THE USER. |
---|
| 902 | C (THIS WILL BE CHECKED BY THE KppSolveR.) |
---|
| 903 | C |
---|
| 904 | C IWORK = AN INTEGER WORK ARRAY. THE LENGTH MUST BE AT LEAST.. |
---|
| 905 | C 20 IF MITER = 0 OR 3 (MF = 10, 13, 20, 23), OR |
---|
| 906 | C 20 + N OTHERWISE (MF = 11, 12, 14, 15, 21, 22, 24, 25). |
---|
| 907 | C FOR ISOPT = 0, OR.. |
---|
| 908 | C 21 + N + NPAR |
---|
| 909 | C FOR ISOPT = 1. |
---|
| 910 | C THE FIRST FEW WORDS OF IWORK ARE USED FOR CONDITIONAL AND |
---|
| 911 | C OPTIONAL INPUTS AND OPTIONAL OUTPUTS. |
---|
| 912 | C |
---|
| 913 | C THE FOLLOWING 2 WORDS IN IWORK ARE CONDITIONAL INPUTS.. |
---|
| 914 | C IWORK(1) = ML THESE ARE THE LOWER AND UPPER |
---|
| 915 | C IWORK(2) = MU HALF-BANDWIDTHS, RESPECTIVELY, OF THE |
---|
| 916 | C BANDED JACOBIAN, EXCLUDING THE MAIN DIAGONAL. |
---|
| 917 | C THE BAND IS DEFINED BY THE MATRIX LOCATIONS |
---|
| 918 | C (I,J) WITH I-ML .LE. J .LE. I+MU. ML AND MU |
---|
| 919 | C MUST SATISFY 0 .LE. ML,MU .LE. NEQ-1. |
---|
| 920 | C THESE ARE REQUIRED IF MITER IS 4 OR 5, AND |
---|
| 921 | C IGNORED OTHERWISE. ML AND MU MAY IN FACT BE |
---|
| 922 | C THE BAND PARAMETERS FOR A MATRIX TO WHICH |
---|
| 923 | C DF/DY IS ONLY APPROXIMATELY EQUAL. |
---|
| 924 | * |
---|
| 925 | C |
---|
| 926 | C LIW = THE LENGTH OF THE ARRAY IWORK, AS DECLARED BY THE USER. |
---|
| 927 | C (THIS WILL BE CHECKED BY THE KppSolveR.) |
---|
| 928 | C |
---|
| 929 | C NOTE.. THE WORK ARRAYS MUST NOT BE ALTERED BETWEEN CALLS TO ODESSA |
---|
| 930 | C FOR THE SAME PROBLEM, EXCEPT POSSIBLY FOR THE CONDITIONAL AND |
---|
| 931 | C OPTIONAL INPUTS, AND EXCEPT FOR THE LAST 2*NYH + N WORDS OF RWORK. |
---|
| 932 | C THE LATTER SPACE IS USED FOR INTERNAL SCRATCH SPACE, AND SO IS |
---|
| 933 | C AVAILABLE FOR USE BY THE USER OUTSIDE ODESSA BETWEEN CALLS, IF |
---|
| 934 | C DESIRED (BUT NOT FOR USE BY F, DF, OR JAC). |
---|
| 935 | C |
---|
| 936 | C JAC = THE NAME OF THE USER-SUPPLIED ROUTINE (MITER = 1 OR 4) TO |
---|
| 937 | C COMPUTE THE JACOBIAN MATRIX, DF/DY, AS A FUNCTION OF THE |
---|
| 938 | C SCALAR T AND THE VECTORS Y, AND PAR. IT IS TO HAVE THE FORM |
---|
| 939 | C SUBROUTINE JAC (NEQ, T, Y, PAR, ML, MU, PD, NROWPD) |
---|
| 940 | C DOUBLE PRECISION T, Y, PAR, PD |
---|
| 941 | C DIMENSION Y(1), PAR(1), PD(NROWPD,1) |
---|
| 942 | C WHERE NEQ, T, Y, PAR, ML, MU, AND NROWPD ARE INPUT AND THE |
---|
| 943 | C ARRAY PD IS TO BE LOADED WITH PARTIAL DERIVATIVES (ELEMENTS |
---|
| 944 | C OF THE JACOBIAN MATRIX) ON OUTPUT. PD MUST BE GIVEN A FIRST |
---|
| 945 | C DIMENSION OF NROWPD. T, Y, AND PAR HAVE THE SAME MEANING AS |
---|
| 946 | C IN SUBROUTINE F. (IN THE DIMENSION STATEMENT ABOVE, 1 IS A |
---|
| 947 | C DUMMY DIMENSION.. IT CAN BE REPLACED BY ANY VALUE.) |
---|
| 948 | C IN THE FULL MATRIX CASE (MITER = 1), ML AND MU ARE |
---|
| 949 | C IGNORED, AND THE JACOBIAN IS TO BE LOADED INTO PD IN |
---|
| 950 | C COLUMNWISE MANNER, WITH DF(I)/DY(J) LOADED INTO PD(I,J). |
---|
| 951 | C IN THE BAND MATRIX CASE (MITER = 4), THE ELEMENTS |
---|
| 952 | C WITHIN THE BAND ARE TO BE LOADED INTO PD IN COLUMNWISE |
---|
| 953 | C MANNER, WITH DIAGONAL LINES OF DF/DY LOADED INTO THE ROWS |
---|
| 954 | C OF PD. THUS DF(I)/DY(J) IS TO BE LOADED INTO PD(I-J+MU+1,J). |
---|
| 955 | C ML AND MU ARE THE HALF-BANDWIDTH PARAMETERS (SEE IWORK). |
---|
| 956 | C THE LOCATIONS IN PD IN THE TWO TRIANGULAR AREAS WHICH |
---|
| 957 | C CORRESPOND TO NONEXISTENT MATRIX ELEMENTS CAN BE IGNORED |
---|
| 958 | C OR LOADED ARBITRARILY, AS THEY ARE OVERWRITTEN BY ODESSA. |
---|
| 959 | C PD IS PRESET TO ZERO BY THE KppSolveR, SO THAT ONLY THE |
---|
| 960 | C NONZERO ELEMENTS NEED BE LOADED BY JAC. EACH CALL TO JAC IS |
---|
| 961 | C PRECEDED BY A CALL TO F WITH THE SAME ARGUMENTS NEQ, T, Y, |
---|
| 962 | C AND PAR. THUS TO GAIN SOME EFFICIENCY, INTERMEDIATE |
---|
| 963 | C QUANTITIES SHARED BY BOTH CALCULATIONS MAY BE SAVED IN A |
---|
| 964 | C USER COMMON BLOCK BY F AND NOT RECOMPUTED BY JAC, IF |
---|
| 965 | C DESIRED. ALSO, JAC MAY ALTER THE Y ARRAY, IF DESIRED. |
---|
| 966 | C JAC MUST BE DECLARED EXTERNAL IN THE CALLING PROGRAM. |
---|
| 967 | C SUBROUTINE JAC MAY ACCESS USER-DEFINED QUANTITIES IN |
---|
| 968 | C NEQ(2),... AND PAR(NPAR+1),.... SEE THE DESCRIPTIONS OF |
---|
| 969 | C NEQ (ABOVE) AND PAR (BELOW). |
---|
| 970 | C |
---|
| 971 | C MF = THE METHOD FLAG. USED ONLY FOR INPUT. THE LEGAL VALUES OF |
---|
| 972 | C MF ARE 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, AND 25. |
---|
| 973 | C MF HAS DECIMAL DIGITS METH AND MITER.. MF = 10*METH + MITER. |
---|
| 974 | C METH INDICATES THE BASIC LINEAR MULTISTEP METHOD.. |
---|
| 975 | C METH = 1 MEANS THE IMPLICIT ADAMS METHOD. |
---|
| 976 | * |
---|
| 977 | C METH = 2 MEANS THE METHOD BASED ON BACKWARD |
---|
| 978 | C DIFFERENTIATION FORMULAS (BDF-S). |
---|
| 979 | C MITER INDICATES THE CORRECTOR ITERATION METHOD.. |
---|
| 980 | C MITER = 0 MEANS FUNCTIONAL ITERATION (NO JACOBIAN MATRIX |
---|
| 981 | C IS INVOLVED). |
---|
| 982 | C MITER = 1 MEANS CHORD ITERATION WITH A USER-SUPPLIED |
---|
| 983 | C FULL (NEQ BY NEQ) JACOBIAN. |
---|
| 984 | C MITER = 2 MEANS CHORD ITERATION WITH AN INTERNALLY |
---|
| 985 | C GENERATED (DIFFERENCE QUOTIENT) FULL JACOBIAN |
---|
| 986 | C (USING NEQ EXTRA CALLS TO F PER DF/DY VALUE). |
---|
| 987 | C MITER = 3 MEANS CHORD ITERATION WITH AN INTERNALLY |
---|
| 988 | C GENERATED DIAGONAL JACOBIAN APPROXIMATION. |
---|
| 989 | C (USING 1 EXTRA CALL TO F PER DF/DY EVALUATION). |
---|
| 990 | C MITER = 4 MEANS CHORD ITERATION WITH A USER-SUPPLIED |
---|
| 991 | C BANDED JACOBIAN. |
---|
| 992 | C MITER = 5 MEANS CHORD ITERATION WITH AN INTERNALLY |
---|
| 993 | C GENERATED BANDED JACOBIAN (USING ML+MU+1 EXTRA |
---|
| 994 | C CALLS TO F PER DF/DY EVALUATION). |
---|
| 995 | C IF MITER = 1 OR 4, THE USER MUST SUPPLY A SUBROUTINE JAC |
---|
| 996 | C (THE NAME IS ARBITRARY) AS DESCRIBED ABOVE UNDER JAC. |
---|
| 997 | C FOR OTHER VALUES OF MITER, A DUMMY ARGUMENT CAN BE USED. |
---|
| 998 | C |
---|
| 999 | C IF A SENSITIVITY ANLYSIS IS DESIRED (ISOPT = 1), MITER = 0 |
---|
| 1000 | C AND 3 ARE DISALLOWED. IN THESE CASES, THE USER IS RECOMMENDED |
---|
| 1001 | C TO SUPPLY AN ANALYTICAL JACOBIAN (MITER = 1 OR 4) AND AN |
---|
| 1002 | C ANALYTICAL INHOMOGENEITY MATRIX (IDF = 1). |
---|
| 1003 | C---------------------------------------------------------------------- |
---|
| 1004 | C OPTIONAL INPUTS. |
---|
| 1005 | C |
---|
| 1006 | C THE FOLLOWING IS A LIST OF THE OPTIONAL INPUTS PROVIDED FOR IN THE |
---|
| 1007 | C CALL SEQUENCE. (SEE ALSO PART II.) FOR EACH SUCH INPUT VARIABLE, |
---|
| 1008 | C THIS TABLE LISTS ITS NAME AS USED IN THIS DOCUMENTATION, ITS |
---|
| 1009 | C LOCATION IN THE CALL SEQUENCE, ITS MEANING, AND THE DEFAULT VALUE. |
---|
| 1010 | C THE USE OF ANY OF THESE INPUTS REQUIRES IOPT(1) = 1, AND IN THAT |
---|
| 1011 | C CASE ALL OF THESE INPUTS ARE EXAMINED. A VALUE OF ZERO FOR ANY |
---|
| 1012 | C OF THESE OPTIONAL INPUTS WILL CAUSE THE DEFAULT VALUE TO BE USED. |
---|
| 1013 | C THUS TO USE A SUBSET OF THE OPTIONAL INPUTS, SIMPLY PRELOAD |
---|
| 1014 | C LOCATIONS 5 TO 10 IN RWORK AND IWORK TO 0.0 AND 0 RESPECTIVELY, AND |
---|
| 1015 | C THEN SET THOSE OF INTEREST TO NONZERO VALUES. |
---|
| 1016 | C |
---|
| 1017 | C NAME LOCATION MEANING AND DEFAULT VALUE |
---|
| 1018 | C |
---|
| 1019 | C H0 RWORK(5) THE STEP SIZE TO BE ATTEMPTED ON THE FIRST STEP. |
---|
| 1020 | C THE DEFAULT VALUE IS DETERMINED BY THE KppSolveR. |
---|
| 1021 | C |
---|
| 1022 | C HMAX RWORK(6) THE MAXIMUM ABSOLUTE STEP SIZE ALLOWED. |
---|
| 1023 | C THE DEFAULT VALUE IS INFINITE. |
---|
| 1024 | C |
---|
| 1025 | C HMIN RWORK(7) THE MINIMUM ABSOLUTE STEP SIZE ALLOWED. |
---|
| 1026 | C THE DEFAULT VALUE IS 0. (THIS LOWER BOUND IS NOT |
---|
| 1027 | C ENFORCED ON THE FINAL STEP BEFORE REACHING TCRIT |
---|
| 1028 | C WHEN ITASK = 4 OR 5.) |
---|
| 1029 | C |
---|
| 1030 | C MAXORD IWORK(5) THE MAXIMUM ORDER TO BE ALLOWED. THE DEFAULT |
---|
| 1031 | C VALUE IS 12 IF METH = 1, AND 5 IF METH = 2. |
---|
| 1032 | C IF MAXORD EXCEEDS THE DEFAULT VALUE, IT WILL |
---|
| 1033 | C BE REDUCED TO THE DEFAULT VALUE. |
---|
| 1034 | C IF MAXORD IS CHANGED DURING THE PROBLEM, IT MAY |
---|
| 1035 | C CAUSE THE CURRENT ORDER TO BE REDUCED. |
---|
| 1036 | C |
---|
| 1037 | C MXSTEP IWORK(6) MAXIMUM NUMBER OF (INTERNALLY DEFINED) STEPS |
---|
| 1038 | C ALLOWED DURING ONE CALL TO THE KppSolveR. |
---|
| 1039 | C THE DEFAULT VALUE IS 500. |
---|
| 1040 | C |
---|
| 1041 | C MXHNIL IWORK(7) MAXIMUM NUMBER OF MESSAGES PRINTED (PER PROBLEM) |
---|
| 1042 | C WARNING THAT T + H = T ON A STEP (H = STEP SIZE). |
---|
| 1043 | C THIS MUST BE POSITIVE TO RESULT IN A NON-DEFAULT |
---|
| 1044 | C VALUE. THE DEFAULT VALUE IS 10. |
---|
| 1045 | C---------------------------------------------------------------------- |
---|
| 1046 | C OPTIONAL OUTPUTS. |
---|
| 1047 | C |
---|
| 1048 | C AS OPTIONAL ADDITIONAL OUTPUT FROM ODESSA, THE VARIABLES LISTED |
---|
| 1049 | C BELOW ARE QUANTITIES RELATED TO THE PERFORMANCE OF ODESSA |
---|
| 1050 | C WHICH ARE AVAILABLE TO THE USER. THESE ARE COMMUNICATED BY WAY OF |
---|
| 1051 | C THE WORK ARRAYS, BUT ALSO HAVE INTERNAL MNEMONIC NAMES AS SHOWN. |
---|
| 1052 | C EXCEPT WHERE STATED OTHERWISE, ALL OF THESE OUTPUTS ARE DEFINED |
---|
| 1053 | C ON ANY SUCCESSFUL RETURN FROM ODESSA, AND ON ANY RETURN WITH |
---|
| 1054 | C ISTATE = -1, -2, -4, -5, OR -6. ON AN ILLEGAL INPUT RETURN |
---|
| 1055 | C (ISTATE = -3), THEY WILL BE UNCHANGED FROM THEIR EXISTING VALUES |
---|
| 1056 | C (IF ANY), EXCEPT POSSIBLY FOR TOLSF, LENRW, AND LENIW. |
---|
| 1057 | C ON ANY ERROR RETURN, OUTPUTS RELEVANT TO THE ERROR WILL BE DEFINED, |
---|
| 1058 | C AS NOTED BELOW. |
---|
| 1059 | C |
---|
| 1060 | C NAME LOCATION MEANING |
---|
| 1061 | C |
---|
| 1062 | C HU RWORK(11) THE STEP SIZE IN T LAST USED (SUCCESSFULLY). |
---|
| 1063 | C |
---|
| 1064 | C HCUR RWORK(12) THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. |
---|
| 1065 | C |
---|
| 1066 | C TCUR RWORK(13) THE CURRENT VALUE OF THE INDEPENDENT VARIABLE |
---|
| 1067 | C WHICH THE KppSolveR HAS ACTUALLY REACHED, I.E. THE |
---|
| 1068 | C CURRENT INTERNAL MESH POINT IN T. ON OUTPUT, TCUR |
---|
| 1069 | C WILL ALWAYS BE AT LEAST AS FAR AS THE ARGUMENT |
---|
| 1070 | C T, BUT MAY BE FARTHER (IF INTERPOLATION WAS DONE). |
---|
| 1071 | C |
---|
| 1072 | C TOLSF RWORK(14) A TOLERANCE SCALE FACTOR, GREATER THAN 1.0, |
---|
| 1073 | C COMPUTED WHEN A REQUEST FOR TOO MUCH ACCURACY WAS |
---|
| 1074 | C DETECTED (ISTATE = -3 IF DETECTED AT THE START OF |
---|
| 1075 | C THE PROBLEM, ISTATE = -2 OTHERWISE). IF ITOL IS |
---|
| 1076 | C LEFT UNALTERED BUT RTOL AND ATOL ARE UNIFORMLY |
---|
| 1077 | C SCALED UP BY A FACTOR OF TOLSF FOR THE NEXT CALL, |
---|
| 1078 | C THEN THE KppSolveR IS DEEMED LIKELY TO SUCCEED. |
---|
| 1079 | C (THE USER MAY ALSO IGNORE TOLSF AND ALTER THE |
---|
| 1080 | C TOLERANCE PARAMETERS IN ANY OTHER WAY APPROPRIATE.) |
---|
| 1081 | C |
---|
| 1082 | C NST IWORK(11) THE NUMBER OF STEPS TAKEN FOR THE PROBLEM SO FAR. |
---|
| 1083 | C |
---|
| 1084 | C NFE IWORK(12) THE NUMBER OF F EVALUATIONS FOR THE PROBLEM SO FAR. |
---|
| 1085 | C |
---|
| 1086 | C NJE IWORK(13) THE NUMBER OF JACOBIAN EVALUATIONS (AND OF MATRIX |
---|
| 1087 | C LU DECOMPOSITIONS IF ISOPT = 0) FOR THE PROBLEM SO |
---|
| 1088 | C FAR. IF ISOPT = 1, THE NUMBER OF LU DECOMPOSITIONS |
---|
| 1089 | C IS EQUAL TO NJE - NSPE (SEE BELOW). |
---|
| 1090 | C |
---|
| 1091 | C NQU IWORK(14) THE METHOD ORDER LAST USED (SUCCESSFULLY). |
---|
| 1092 | C |
---|
| 1093 | C NQCUR IWORK(15) THE ORDER TO BE ATTEMPTED ON THE NEXT STEP. |
---|
| 1094 | C |
---|
| 1095 | C IMXER IWORK(16) THE INDEX OF THE COMPONENT OF LARGEST MAGNITUDE IN |
---|
| 1096 | C THE WEIGHTED LOCAL ERROR VECTOR (E(I,J)/EWT(I,J)), |
---|
| 1097 | C ON AN ERROR RETURN WITH ISTATE = -4 OR -5. |
---|
| 1098 | C |
---|
| 1099 | C LENRW IWORK(17) THE LENGTH OF RWORK ACTUALLY REQUIRED. |
---|
| 1100 | C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL |
---|
| 1101 | C INPUT RETURN FOR INSUFFICIENT STORAGE. |
---|
| 1102 | C |
---|
| 1103 | C LENIW IWORK(18) THE LENGTH OF IWORK ACTUALLY REQUIRED. |
---|
| 1104 | C THIS IS DEFINED ON NORMAL RETURNS AND ON AN ILLEGAL |
---|
| 1105 | C INPUT RETURN FOR INSUFFICIENT STORAGE. |
---|
| 1106 | C |
---|
| 1107 | C NDFE IWORK(19) THE NUMBER OF DF/DP (VECTOR) EVALUATIONS. |
---|
| 1108 | C |
---|
| 1109 | C NSPE IWORK(20) THE NUMBER OF CALLS TO SUBROUTINE SPRIME. EACH CALL |
---|
| 1110 | C TO SPRIME REQUIRES A JACOBIAN EVALUATION, BUT NOT |
---|
| 1111 | C AN LU DECOMPOSITION. |
---|
| 1112 | C |
---|
| 1113 | C THE FOLLOWING ARRAYS ARE SEGMENTS OF THE RWORK AND IWORK ARRAYS |
---|
| 1114 | C WHICH MAY ALSO BE OF INTEREST TO THE USER AS OPTIONAL OUTPUTS. |
---|
| 1115 | C FOR EACH ARRAY, THE TABLE BELOW GIVES ITS INTERNAL NAME, ITS BASE |
---|
| 1116 | C ADDRESS IN RWORK OR IWORK, AND ITS DESCRIPTION. |
---|
| 1117 | C |
---|
| 1118 | C NAME BASE ADDRESS DESCRIPTION |
---|
| 1119 | C |
---|
| 1120 | C YH 21 IN RWORK THE NORDSIECK HISTORY ARRAY, OF SIZE NYH BY |
---|
| 1121 | C (NQCUR + 1). FOR J = 0,1,...,NQCUR, COLUMN J+1 |
---|
| 1122 | C OF YH CONTAINS HCUR**J/FACTORIAL(J) TIMES |
---|
| 1123 | C THE J-TH DERIVATIVE OF THE INTERPOLATING |
---|
| 1124 | C POLYNOMIAL CURRENTLY REPRESENTING THE SOLUTION, |
---|
| 1125 | C EVALUATED AT T = TCUR. |
---|
| 1126 | C |
---|
| 1127 | C ACOR LENRW-NYH+1 ARRAY OF SIZE NYH USED FOR THE ACCUMULATED |
---|
| 1128 | C IN RWORK CORRECTIONS ON EACH STEP, SCALED ON OUTPUT |
---|
| 1129 | C TO REPRESENT THE ESTIMATED LOCAL ERROR IN Y |
---|
| 1130 | C ON THE LAST STEP. THIS IS THE VECTOR E IN |
---|
| 1131 | C THE DESCRIPTION OF THE ERROR CONTROL. |
---|
| 1132 | C IT IS DEFINED ONLY ON A SUCCESSFUL RETURN |
---|
| 1133 | C FROM ODESSA. |
---|
| 1134 | C NRS LENIW-NPAR ARRAY OF SIZE NPAR+1, USED TO STORE THE |
---|
| 1135 | C IN IWORK ACCUMULATED NUMBER OF REPEATED STEPS DUE TO |
---|
| 1136 | C THE SENSITIVITY ANALYSIS.. |
---|
| 1137 | C NRS(1) = TOTAL NUMBER OF REPEATED STEPS, |
---|
| 1138 | C NRS(2),... = NUMBER OF REPEATED STEPS DUE TO |
---|
| 1139 | C MODEL PARAMETER 1,... |
---|
| 1140 | C |
---|
| 1141 | C---------------------------------------------------------------------- |
---|
| 1142 | C PART II. OTHER ROUTINES CALLABLE. |
---|
| 1143 | C |
---|
| 1144 | C THE FOLLOWING ARE OPTIONAL CALLS WHICH THE USER MAY MAKE TO |
---|
| 1145 | C GAIN ADDITIONAL CAPABILITIES IN CONJUNCTION WITH ODESSA. |
---|
| 1146 | C (THE ROUTINES XSETUN AND XSETF ARE DESIGNED TO CONFORM TO THE |
---|
| 1147 | C SLATEC ERROR HANDLING PACKAGE.) |
---|
| 1148 | C |
---|
| 1149 | C FORM OF CALL FUNCTION |
---|
| 1150 | C CALL XSETUN(LUN) SET THE LOGICAL UNIT NUMBER, LUN, FOR |
---|
| 1151 | C OUTPUT OF MESSAGES FROM ODESSA, IF |
---|
| 1152 | C THE DEFAULT IS NOT DESIRED. |
---|
| 1153 | C THE DEFAULT VALUE OF LUN IS 6. |
---|
| 1154 | C |
---|
| 1155 | C CALL XSETF(MFLAG) SET A FLAG TO CONTROL THE PRINTING OF |
---|
| 1156 | C MESSAGES BY ODESSA.. |
---|
| 1157 | C MFLAG = 0 MEANS DO NOT PRINT. (DANGER.. |
---|
| 1158 | C THIS RISKS LOSING VALUABLE INFORMATION.) |
---|
| 1159 | C MFLAG = 1 MEANS PRINT (THE DEFAULT). |
---|
| 1160 | C |
---|
| 1161 | C EITHER OF THE ABOVE CALLS MAY BE MADE AT |
---|
| 1162 | C ANY TIME AND WILL TAKE EFFECT IMMEDIATELY. |
---|
| 1163 | C |
---|
| 1164 | C CALL SVCOM (RSAV, ISAV) STORE IN RSAV AND ISAV THE CONTENTS |
---|
| 1165 | C OF THE INTERNAL COMMON BLOCKS USED BY |
---|
| 1166 | C ODESSA (SEE PART III BELOW). |
---|
| 1167 | C RSAV MUST BE A REAL ARRAY OF LENGTH 222 |
---|
| 1168 | C OR MORE, AND ISAV MUST BE AN INTEGER |
---|
| 1169 | C ARRAY OF LENGTH 54 OR MORE. |
---|
| 1170 | C |
---|
| 1171 | C CALL RSCOM (RSAV, ISAV) RESTORE, FROM RSAV AND ISAV, THE CONTENTS |
---|
| 1172 | C OF THE INTERNAL COMMON BLOCKS USED BY |
---|
| 1173 | C ODESSA. PRESUMES A PRIOR CALL TO SVCOM |
---|
| 1174 | C WITH THE SAME ARGUMENTS. |
---|
| 1175 | C |
---|
| 1176 | C SVCOM AND RSCOM ARE USEFUL IF |
---|
| 1177 | C INTERRUPTING A RUN AND RESTARTING |
---|
| 1178 | C LATER, OR ALTERNATING BETWEEN TWO OR |
---|
| 1179 | C MORE PROBLEMS KppSolveD WITH ODESSA. |
---|
| 1180 | C |
---|
| 1181 | C CALL INTDY(,,,,,) PROVIDE DERIVATIVES OF Y, OF VARIOUS |
---|
| 1182 | C (SEE BELOW) ORDERS, AT A SPECIFIED POINT T, IF |
---|
| 1183 | C DESIRED. IT MAY BE CALLED ONLY AFTER |
---|
| 1184 | C A SUCCESSFUL RETURN FROM ODESSA. |
---|
| 1185 | C |
---|
| 1186 | C THE DETAILED INSTRUCTIONS FOR USING INTDY ARE AS FOLLOWS. |
---|
| 1187 | C THE FORM OF THE CALL IS.. |
---|
| 1188 | C |
---|
| 1189 | C CALL INTDY (T, K, RWORK(21), NYH, DKY, IFLAG) |
---|
| 1190 | C |
---|
| 1191 | C THE INPUT PARAMETERS ARE.. |
---|
| 1192 | C |
---|
| 1193 | C T = VALUE OF INDEPENDENT VARIABLE WHERE ANSWERS ARE DESIRED |
---|
| 1194 | C (NORMALLY THE SAME AS THE T LAST RETURNED BY ODESSA). |
---|
| 1195 | C FOR VALID RESULTS, T MUST LIE BETWEEN TCUR - HU AND TCUR. |
---|
| 1196 | C (SEE OPTIONAL OUTPUTS FOR TCUR AND HU.) |
---|
| 1197 | C K = INTEGER ORDER OF THE DERIVATIVE DESIRED. K MUST SATISFY |
---|
| 1198 | C 0 .LE. K .LE. NQCUR, WHERE NQCUR IS THE CURRENT ORDER |
---|
| 1199 | C (SEE OPTIONAL OUTPUTS). THE CAPABILITY CORRESPONDING |
---|
| 1200 | C TO K = 0, I.E. COMPUTING Y(T), IS ALREADY PROVIDED |
---|
| 1201 | C BY ODESSA DIRECTLY. SINCE NQCUR .GE. 1, THE FIRST |
---|
| 1202 | C DERIVATIVE DY/DT IS ALWAYS AVAILABLE WITH INTDY. |
---|
| 1203 | C RWORK(21) = THE BASE ADDRESS OF THE HISTORY ARRAY YH. |
---|
| 1204 | C NYH = COLUMN LENGTH OF YH, EQUAL TO THE TOTAL NUMBER OF |
---|
| 1205 | C DEPENDENT VARIABLES. IF ISOPT = 0, NYH = N. IF ISOPT = 1, |
---|
| 1206 | C NYH = N * (NPAR + 1). |
---|
| 1207 | C |
---|
| 1208 | C THE OUTPUT PARAMETERS ARE.. |
---|
| 1209 | C |
---|
| 1210 | C DKY = A REAL ARRAY OF LENGTH NYH CONTAINING THE COMPUTED VALUE |
---|
| 1211 | C OF THE K-TH DERIVATIVE OF Y(T). |
---|
| 1212 | C IFLAG = INTEGER FLAG, RETURNED AS 0 IF K AND T WERE LEGAL, |
---|
| 1213 | C -1 IF K WAS ILLEGAL, AND -2 IF T WAS ILLEGAL. |
---|
| 1214 | C ON AN ERROR RETURN, A MESSAGE IS ALSO WRITTEN. |
---|
| 1215 | C---------------------------------------------------------------------- |
---|
| 1216 | C PART III. COMMON BLOCKS. |
---|
| 1217 | C |
---|
| 1218 | C IF ODESSA IS TO BE USED IN AN OVERLAY SITUATION, THE USER |
---|
| 1219 | C MUST DECLARE, IN THE PRIMARY OVERLAY, THE VARIABLES IN.. |
---|
| 1220 | C (1) THE CALL SEQUENCE TO ODESSA, |
---|
| 1221 | C (2) THE THREE INTERNAL COMMON BLOCKS |
---|
| 1222 | C /ODE001/ OF LENGTH 258 (219 DOUBLE PRECISION WORDS |
---|
| 1223 | C FOLLOWED BY 39 INTEGER WORDS), |
---|
| 1224 | C /ODE002/ OF LENGTH 14 (3 DOUBLE PRECISION WORDS FOLLOWED |
---|
| 1225 | C BY 11 INTEGER WORDS), |
---|
| 1226 | C /EH0001/ OF LENGTH 2 (INTEGER WORDS). |
---|
| 1227 | C |
---|
| 1228 | C IF ODESSA IS USED ON A SYSTEM IN WHICH THE CONTENTS OF INTERNAL |
---|
| 1229 | C COMMON BLOCKS ARE NOT PRESERVED BETWEEN CALLS, THE USER SHOULD |
---|
| 1230 | C DECLARE THE ABOVE THREE COMMON BLOCKS IN HIS MAIN PROGRAM TO INSURE |
---|
| 1231 | C THAT THEIR CONTENTS ARE PRESERVED. |
---|
| 1232 | C |
---|
| 1233 | C IF THE SOLUTION OF A GIVEN PROBLEM BY ODESSA IS TO BE INTERRUPTED |
---|
| 1234 | C AND THEN LATER CONTINUED, SUCH AS WHEN RESTARTING AN INTERRUPTED RUN |
---|
| 1235 | C OR ALTERNATING BETWEEN TWO OR MORE PROBLEMS, THE USER SHOULD SAVE, |
---|
| 1236 | C FOLLOWING THE RETURN FROM THE LAST ODESSA CALL PRIOR TO THE |
---|
| 1237 | C INTERRUPTION, THE CONTENTS OF THE CALL SEQUENCE VARIABLES AND THE |
---|
| 1238 | C INTERNAL COMMON BLOCKS, AND LATER RESTORE THESE VALUES BEFORE THE |
---|
| 1239 | C NEXT ODESSA CALL FOR THAT PROBLEM. TO SAVE AND RESTORE THE COMMON |
---|
| 1240 | C BLOCKS, USE SUBROUTINES SVCOM AND RSCOM (SEE PART II ABOVE). |
---|
| 1241 | C |
---|
| 1242 | C---------------------------------------------------------------------- |
---|
| 1243 | C PART IV. OPTIONALLY REPLACEABLE KppSolveR ROUTINES. |
---|
| 1244 | C |
---|
| 1245 | C BELOW ARE DESCRIPTIONS OF TWO ROUTINES IN THE ODESSA PACKAGE WHICH |
---|
| 1246 | C RELATE TO THE MEASUREMENT OF ERRORS. EITHER ROUTINE CAN BE |
---|
| 1247 | C REPLACED BY A USER-SUPPLIED VERSION, IF DESIRED. HOWEVER, SINCE SUCH |
---|
| 1248 | C A REPLACEMENT MAY HAVE A MAJOR IMPACT ON PERFORMANCE, IT SHOULD BE |
---|
| 1249 | C DONE ONLY WHEN ABSOLUTELY NECESSARY, AND ONLY WITH GREAT CAUTION. |
---|
| 1250 | C (NOTE.. THE MEANS BY WHICH THE PACKAGE VERSION OF A ROUTINE IS |
---|
| 1251 | C SUPERSEDED BY THE USER-S VERSION MAY BE SYSTEM-DEPENDENT.) |
---|
| 1252 | C |
---|
| 1253 | C (A) EWSET. |
---|
| 1254 | C THE FOLLOWING SUBROUTINE IS CALLED JUST BEFORE EACH INTERNAL |
---|
| 1255 | C INTEGRATION STEP, AND SETS THE ARRAY OF ERROR WEIGHTS, EWT, AS |
---|
| 1256 | C DESCRIBED UNDER ITOL/RTOL/ATOL ABOVE.. |
---|
| 1257 | C SUBROUTINE EWSET (NYH, ITOL, RTOL, ATOL, YCUR, EWT) |
---|
| 1258 | C WHERE NEQ, ITOL, RTOL, AND ATOL ARE AS IN THE ODESSA CALL SEQUENCE, |
---|
| 1259 | C YCUR CONTAINS THE CURRENT DEPENDENT VARIABLE VECTOR, AND |
---|
| 1260 | C EWT IS THE ARRAY OF WEIGHTS SET BY EWSET. |
---|
| 1261 | C |
---|
| 1262 | C IF THE USER SUPPLIES THIS SUBROUTINE, IT MUST RETURN IN EWT(I) |
---|
| 1263 | C (I = 1,...,NYH) A POSITIVE QUANTITY SUITABLE FOR COMPARING ERRORS |
---|
| 1264 | C IN Y(I) TO. THE EWT ARRAY RETURNED BY EWSET IS PASSED TO THE |
---|
| 1265 | C VNORM ROUTINE (SEE BELOW), AND ALSO USED BY ODESSA IN THE COMPUTATION |
---|
| 1266 | C OF THE OPTIONAL OUTPUT IMXER, THE DIAGONAL JACOBIAN APPROXIMATION, |
---|
| 1267 | C AND THE INCREMENTS FOR DIFFERENCE QUOTIENT JACOBIANS. |
---|
| 1268 | C |
---|
| 1269 | C IN THE USER-SUPPLIED VERSION OF EWSET, IT MAY BE DESIRABLE TO USE |
---|
| 1270 | C THE CURRENT VALUES OF DERIVATIVES OF Y. DERIVATIVES UP TO ORDER NQ |
---|
| 1271 | C ARE AVAILABLE FROM THE HISTORY ARRAY YH, DESCRIBED ABOVE UNDER |
---|
| 1272 | C OPTIONAL OUTPUTS. IN EWSET, YH IS IDENTICAL TO THE YCUR ARRAY, |
---|
| 1273 | C EXTENDED TO NQ + 1 COLUMNS WITH A COLUMN LENGTH OF NYH AND SCALE |
---|
| 1274 | C FACTORS OF H**J/FACTORIAL(J). ON THE FIRST CALL FOR THE PROBLEM, |
---|
| 1275 | C GIVEN BY NST = 0, NQ IS 1 AND H IS TEMPORARILY SET TO 1.0. |
---|
| 1276 | C THE QUANTITIES NQ, NYH, H, AND NST CAN BE OBTAINED BY INCLUDING |
---|
| 1277 | C IN EWSET THE STATEMENTS.. |
---|
| 1278 | C DOUBLE PRECISION H, RLS |
---|
| 1279 | C COMMON /ODE001/ RLS(219),ILS(39) |
---|
| 1280 | C NQ = ILS(35) |
---|
| 1281 | C NYH = ILS(14) |
---|
| 1282 | C NST = ILS(36) |
---|
| 1283 | C H = RLS(213) |
---|
| 1284 | C THUS, FOR EXAMPLE, THE CURRENT VALUE OF DY/DT CAN BE OBTAINED AS |
---|
| 1285 | C YCUR(NYH+I)/H (I=1,...,N) (AND THE DIVISION BY H IS |
---|
| 1286 | C UNNECESSARY WHEN NST = 0). |
---|
| 1287 | C |
---|
| 1288 | C (B) VNORM. |
---|
| 1289 | C THE FOLLOWING IS A REAL FUNCTION ROUTINE WHICH COMPUTES THE WEIGHTED |
---|
| 1290 | C ROOT-MEAN-SQUARE NORM OF A VECTOR V.. |
---|
| 1291 | C D = VNORM (LV, V, W) |
---|
| 1292 | C WHERE.. |
---|
| 1293 | C LV = THE LENGTH OF THE VECTOR, |
---|
| 1294 | C V = REAL ARRAY OF LENGTH N CONTAINING THE VECTOR, |
---|
| 1295 | C W = REAL ARRAY OF LENGTH N CONTAINING WEIGHTS, |
---|
| 1296 | C D = SQRT( (1/N) * SUM(V(I)*W(I))**2 ). |
---|
| 1297 | C VNORM IS CALLED WITH LV = N AND WITH W(I) = 1.0/EWT(I), WHERE |
---|
| 1298 | C EWT IS AS SET BY SUBROUTINE EWSET. |
---|
| 1299 | C |
---|
| 1300 | C IF THE USER SUPPLIES THIS FUNCTION, IT SHOULD RETURN A NON-NEGATIVE |
---|
| 1301 | C VALUE OF VNORM SUITABLE FOR USE IN THE ERROR CONTROL IN ODESSA. |
---|
| 1302 | C NONE OF THE ARGUMENTS SHOULD BE ALTERED BY VNORM. |
---|
| 1303 | C FOR EXAMPLE, A USER-SUPPLIED VNORM ROUTINE MIGHT.. |
---|
| 1304 | C -SUBSTITUTE A MAX-NORM OF (V(I)*W(I)) FOR THE RMS-NORM, OR |
---|
| 1305 | C -IGNORE SOME COMPONENTS OF V IN THE NORM, WITH THE EFFECT OF |
---|
| 1306 | C SUPPRESSING THE ERROR CONTROL ON THOSE COMPONENTS OF Y. |
---|
| 1307 | C---------------------------------------------------------------------- |
---|
| 1308 | C OTHER ROUTINES IN THE ODESSA PACKAGE. |
---|
| 1309 | C |
---|
| 1310 | C IN ADDITION TO SUBROUTINE ODESSA, THE ODESSA PACKAGE INCLUDES THE |
---|
| 1311 | C FOLLOWING SUBROUTINES AND FUNCTION ROUTINES.. |
---|
| 1312 | C INTDY COMPUTES AN INTERPOLATED VALUE OF THE Y VECTOR AT T = TOUT. |
---|
| 1313 | C STODE IS THE CORE INTEGRATOR, WHICH DOES ONE STEP OF THE |
---|
| 1314 | C INTEGRATION AND THE ASSOCIATED ERROR CONTROL. |
---|
| 1315 | C STESA MANAGES THE SOLUTION OF THE SENSITIVITY FUNCTIONS. |
---|
| 1316 | C CFODE SETS ALL METHOD COEFFICIENTS AND TEST CONSTANTS. |
---|
| 1317 | C PREPJ COMPUTES AND PREPROCESSES THE JACOBIAN MATRIX J = DF/DY |
---|
| 1318 | C AND THE NEWTON ITERATION MATRIX P = I - H*L0*J. |
---|
| 1319 | C IT IS ALSO CALLED BY SPRIME (WITH JOPT = 1) TO JUST |
---|
| 1320 | C COMPUTE THE JACOBIAN MATRIX. |
---|
| 1321 | C PREPDF COMPUTES THE INHOMOGENEITY MATRIX DF/DP. |
---|
| 1322 | C SPRIME DEFINES THE SYSTEM OF SENSITIVITY EQUATIONS. |
---|
| 1323 | C SOLSY MANAGES SOLUTION OF LINEAR SYSTEM IN CHORD ITERATION. |
---|
| 1324 | C EWSET SETS THE ERROR WEIGHT VECTOR EWT BEFORE EACH STEP. |
---|
| 1325 | C VNORM COMPUTES THE WEIGHTED R.M.S. NORM OF A VECTOR. |
---|
| 1326 | C SVCOM AND RSCOM ARE USER-CALLABLE ROUTINES TO SAVE AND RESTORE, |
---|
| 1327 | C RESPECTIVELY, THE CONTENTS OF THE INTERNAL COMMON BLOCKS. |
---|
| 1328 | C DGEFA AND DGESL ARE ROUTINES FROM LINPACK FOR SOLVING FULL |
---|
| 1329 | C SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. |
---|
| 1330 | C DGBFA AND DGBSL ARE ROUTINES FROM LINPACK FOR SOLVING BANDED |
---|
| 1331 | C LINEAR SYSTEMS. |
---|
| 1332 | C DAXPY, DSCAL, IDAMAX, AND DDOT ARE BASIC LINEAR ALGEBRA MODULES |
---|
| 1333 | C (BLAS) USED BY THE ABOVE LINPACK ROUTINES. |
---|
| 1334 | C D1MACH COMPUTES THE UNIT ROUNDOFF IN A MACHINE-INDEPENDENT MANNER. |
---|
| 1335 | C XERR, XSETUN, AND XSETF HANDLE THE PRINTING OF ALL ERROR |
---|
| 1336 | C MESSAGES AND WARNINGS. |
---|
| 1337 | C NOTE.. VNORM, IDAMAX, DDOT, AND D1MACH ARE FUNCTION ROUTINES. |
---|
| 1338 | C ALL THE OTHERS ARE SUBROUTINES. |
---|
| 1339 | C |
---|
| 1340 | C THE FORTRAN GENERIC INTRINSIC FUNCTIONS USED BY ODESSA ARE.. |
---|
| 1341 | C ABS, MAX, MIN, REAL, MOD, SIGN, SQRT, AND WRITE |
---|
| 1342 | C |
---|
| 1343 | C A BLOCK DATA SUBPROGRAM IS ALSO INCLUDED WITH THE PACKAGE, |
---|
| 1344 | C FOR LOADING SOME OF THE VARIABLES IN INTERNAL COMMON. |
---|
| 1345 | C |
---|
| 1346 | C---------------------------------------------------------------------- |
---|
| 1347 | C PART V. GENERAL REMARKS |
---|
| 1348 | C |
---|
| 1349 | C THIS SECTION HIGHLIGHTS THE BASIC DIFFERENCES BETWEEN THE ORIGINAL |
---|
| 1350 | C LSODE PACKAGE AND THE ODESSA MODIFICATION. THIS IS PROVIDED AS A |
---|
| 1351 | C SERVICE TO EXPERIENCED LSODE USERS TO EXPEDITE FAMILIARIZATION WITH |
---|
| 1352 | C ODESSA. |
---|
| 1353 | C |
---|
| 1354 | C (A). ORIGINAL SUBROUTINES AND FUNCTIONS. |
---|
| 1355 | C |
---|
| 1356 | C OF THE ORIGINAL 22 SUBROUTINES AND FUNCTIONS USED IN THE LSODE |
---|
| 1357 | C PACKAGE, ALL ARE USED BY ODESSA, WITH THE FOLLOWING HAVING BEEN |
---|
| 1358 | C MODIFIED.. |
---|
| 1359 | C |
---|
| 1360 | C LSODE THE ORIGINAL DRIVER SUBROUTINE FOR THE LSODE PACKAGE IS |
---|
| 1361 | C EXTENSIVELY MODIFIED AND RENAMED ODESSA, WHICH NOW |
---|
| 1362 | C CONTAINS A CALL TO SPRIME TO ESTABLISH INITIAL CONDITIONS |
---|
| 1363 | C FOR THE SENSITIVITY CALCULATIONS. |
---|
| 1364 | C |
---|
| 1365 | C STODE THE ONE STEP INTEGRATOR IS SLIGHTLY MODIFIED AND RETAINS |
---|
| 1366 | C ITS ORIGINAL NAME. IT NOW CONTAINS THE CALL TO STESA, |
---|
| 1367 | C AND ALSO CALLS SPRIME IF KFLAG .LE. -3. |
---|
| 1368 | C |
---|
| 1369 | C PREPJ ALSO NAMED PREPJ IN ODESSA IS SLIGHTLY MODIFIED TO ALLOW |
---|
| 1370 | C FOR THE CALCULATION OF JACOBIAN WITH NO PREPROCESSING |
---|
| 1371 | C (JOPT = 1). |
---|
| 1372 | C |
---|
| 1373 | C (B). NEW SUBROUTINES. |
---|
| 1374 | C |
---|
| 1375 | C IN ADDITION TO THE CHANGES NOTED ABOVE, THREE NEW SUBROUTINES |
---|
| 1376 | C HAVE BEEN INTRODUCED (SEE STESA, SPRIME, AND PREPDF AS DESCRIBED |
---|
| 1377 | C IN PART IV. ABOVE). |
---|
| 1378 | C |
---|
| 1379 | C (C). COMMON BLOCKS. |
---|
| 1380 | C |
---|
| 1381 | C /LS0001/ RETAINS THE SAME LENGTH AND IS RENAMED /ODE001/; |
---|
| 1382 | C HOWEVER THE REAL ARRAY ROWNS(209) IS SHORTENED TO A |
---|
| 1383 | C LENGTH OF (173) REAL WORDS, ALLOWING THE REMOVAL OF |
---|
| 1384 | C TESCO(3,12) WHICH IS NOW PASSED FROM STODE TO STESA. |
---|
| 1385 | C IN ADDITION, THE INTEGER ARRAY IOWNS(6) IS SHORTENED |
---|
| 1386 | C TO A LENGTH OF (4) INTEGER WORDS, ALLOWING THE REMOVAL |
---|
| 1387 | C OF IALTH AND LMAX WHICH ARE NOW PASSED FROM STODE TO |
---|
| 1388 | C STESA. |
---|
| 1389 | C |
---|
| 1390 | C /ODE002/ ADDED COMMON BLOCK FOR VARIABLES IMPORTANT TO |
---|
| 1391 | C SENSITIVITY ANALYSIS (SEE PART III. ABOVE). A BLOCK |
---|
| 1392 | C DATA PROGRAM IS NOT REQUIRED FOR THIS COMMON BLOCK. |
---|
| 1393 | C |
---|
| 1394 | C SVCOM,RSCOM THESE TWO SUBROUTINES ARE MODIFIED TO HANDLE |
---|
| 1395 | C COMMON BLOCK /ODE002/ AS WELL. |
---|
| 1396 | C |
---|
| 1397 | C (D). OPTIONAL INPUTS. |
---|
| 1398 | C |
---|
| 1399 | C THE FULL SET OF OPTIONAL INPUTS AVAILABLE IN LSODE IS ALSO |
---|
| 1400 | C AVAILABLE IN ODESSA, WITH THE EXCEPTION THAT THE NUMBER OF ODE'S |
---|
| 1401 | C IN THE MODEL (NEQ(1)), MAY NOT BE CHANGED DURING THE PROBLEM. |
---|
| 1402 | C IN ODESSA, NYH NOW REFERS TO THE TOTAL NUMBER OF FIRST-ORDER |
---|
| 1403 | C ODE'S (MODEL AND SENSITIVITY EQUATIONS) WHICH IS EQUAL TO |
---|
| 1404 | C NEQ(1) IF ISOPT = 0, OR NEQ(1)*(NEQ(2)+1) IF ISOPT = 1. |
---|
| 1405 | C NEQ(1), NEQ(2), AND NYH ARE NOT ALLOWED TO CHANGE DURING |
---|
| 1406 | C THE COURSE OF AN INTEGRATION. |
---|
| 1407 | C |
---|
| 1408 | C (E). OPTIONAL OUTPUTS. |
---|
| 1409 | C |
---|
| 1410 | C THE FULL SET OF OPTIONAL OUTPUTS AVAILABLE IN LSODE IS ALSO |
---|
| 1411 | C AVAILABLE IN ODESSA. IN ADDITION, IWORK(19) AND IWORK(20) ARE |
---|
| 1412 | C LOADED WITH NDFE AND NSPE, RESPECTIVELY, UPON OUTPUT. THE TOTAL |
---|
| 1413 | C NUMBER OF LU DECOMPOSITIONS OF THE PROCESSED JACOBIAN IS EQUAL |
---|
| 1414 | C TO NJE - NSPE. |
---|
| 1415 | C----------------------------------------------------------------------- |
---|
| 1416 | SUBROUTINE KPP_ODESSA (F, DF, NEQ, Y, PAR, T, TOUT, |
---|
| 1417 | 1 ITOL, RTOL, ATOL, |
---|
| 1418 | 1 ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) |
---|
| 1419 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 1420 | LOGICAL IHIT |
---|
| 1421 | EXTERNAL F, DF, JAC, PREPJ, SOLSY, PREPDF |
---|
| 1422 | DIMENSION NEQ(*), Y(*), PAR(*), RTOL(*), ATOL(*), IOPT(*), |
---|
| 1423 | 1 RWORK(LRW), IWORK(LIW), MORD(2) |
---|
| 1424 | C----------------------------------------------------------------------- |
---|
| 1425 | C THIS IS THE SEPTEMBER 1, 1986 VERSION OF ODESSA.. |
---|
| 1426 | C AN ORDINARY DIFFERENTIAL EQUATION KppSolveR WITH EXPLICIT SIMULTANEOUS |
---|
| 1427 | C SENSITIVITY ANALYSIS. |
---|
| 1428 | C |
---|
| 1429 | C THIS PACKAGE IS A MODIFICATION OF THE AUGUST 13, 1981 VERSION OF |
---|
| 1430 | C LSODE.. LIVERMORE KppSolveR FOR ORDINARY DIFFERENTIAL EQUATIONS. |
---|
| 1431 | C THIS VERSION IS IN DOUBLE PRECISION. |
---|
| 1432 | C |
---|
| 1433 | C ODESSA KppSolveS FOR THE FIRST-ORDER SENSITIVITY COEFFICIENTS.. |
---|
| 1434 | C DY(I)/DP, FOR A SINGLE PARAMETER, OR, |
---|
| 1435 | C DY(I)/DP(J), FOR MULTIPLE PARAMETERS, |
---|
| 1436 | C ASSOCIATED WITH A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS.. |
---|
| 1437 | C DY(T)/DT = F(Y,T;P). |
---|
| 1438 | C----------------------------------------------------------------------- |
---|
| 1439 | C REFERENCES... |
---|
| 1440 | C |
---|
| 1441 | C 1. JORGE R. LEIS AND MARK A. KRAMER, THE SIMULTANEOUS SOLUTION AND |
---|
| 1442 | C EXPLICIT SENSITIVITY ANALYSIS OF SYSTEMS DESCRIBED BY ORDINARY |
---|
| 1443 | C DIFFERENTIAL EQUATIONS, SUBMITTED TO ACM TRANS. MATH. SOFTWARE, |
---|
| 1444 | C (1985). |
---|
| 1445 | C |
---|
| 1446 | C 2. JORGE R. LEIS AND MARK A. KRAMER, ODESSA - AN ORDINARY |
---|
| 1447 | C DIFFERENTIAL EQUATION KppSolveR WITH EXPLICIT SIMULTANEOUS |
---|
| 1448 | C SENSITIVITY ANALYSIS, SUBMITTED TO ACM TRANS. MATH. SOFTWARE. |
---|
| 1449 | C (1985). |
---|
| 1450 | C |
---|
| 1451 | C 3. ALAN C. HINDMARSH, LSODE AND LSODI, TWO NEW INITIAL VALUE |
---|
| 1452 | C ORDINARY DIFFERENTIAL EQUATION KppSolveRS, ACM-SIGNUM NEWSLETTER, |
---|
| 1453 | C VOL. 15, NO. 4 (1980), PP. 10-11. |
---|
| 1454 | C----------------------------------------------------------------------- |
---|
| 1455 | C THE FOLLOWING INTERNAL COMMON BLOCKS CONTAIN |
---|
| 1456 | C (A) VARIABLES WHICH ARE LOCAL TO ANY SUBROUTINE BUT WHOSE VALUES MUST |
---|
| 1457 | C BE PRESERVED BETWEEN CALLS TO THE ROUTINE (OWN VARIABLES), AND |
---|
| 1458 | C (B) VARIABLES WHICH ARE COMMUNICATED BETWEEN SUBROUTINES. |
---|
| 1459 | C THE STRUCTURE OF THE BLOCKS ARE AS FOLLOWS.. ALL REAL VARIABLES ARE |
---|
| 1460 | C LISTED FIRST, FOLLOWED BY ALL INTEGERS. WITHIN EACH TYPE, THE |
---|
| 1461 | C VARIABLES ARE GROUPED WITH THOSE LOCAL TO SUBROUTINE ODESSA FIRST, |
---|
| 1462 | C THEN THOSE LOCAL TO SUBROUTINE STODE, AND FINALLY THOSE USED |
---|
| 1463 | C FOR COMMUNICATION. THE BLOCKS ARE DECLARED IN SUBROUTINES ODESSA |
---|
| 1464 | C INTDY, STODE, STESA, PREPJ, PREPDF, AND SOLSY. GROUPS OF VARIABLES |
---|
| 1465 | C ARE REPLACED BY DUMMY ARRAYS IN THE COMMON DECLARATIONS IN ROUTINES |
---|
| 1466 | C WHERE THOSE VARIABLES ARE NOT USED. |
---|
| 1467 | C----------------------------------------------------------------------- |
---|
| 1468 | COMMON /ODE001/ TRET, ROWNS(173), |
---|
| 1469 | 1 TESCO(3,12), CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, |
---|
| 1470 | 2 ILLIN, INIT, LYH, LEWT, LACOR, LSAVF, LWM, LIWM, |
---|
| 1471 | 3 MXSTEP, MXHNIL, NHNIL, NTREP, NSLAST, NYH, IOWNS(4), |
---|
| 1472 | 4 IALTH, LMAX, ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, |
---|
| 1473 | 5 MITER, MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU |
---|
| 1474 | COMMON /ODE002/ DUPS, DSMS, DDNS, |
---|
| 1475 | 1 NPAR, LDFDP, LNRS, |
---|
| 1476 | 2 ISOPT, NSV, NDFE, NSPE, IDF, IERSP, JOPT, KFLAGS |
---|
| 1477 | PARAMETER (ZERO=0.0D0,ONE=1.0D0,TWO=2.0D0,FOUR=4.0D0) |
---|
| 1478 | DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ |
---|
| 1479 | C----------------------------------------------------------------------- |
---|
| 1480 | C BLOCK A. |
---|
| 1481 | C THIS CODE BLOCK IS EXECUTED ON EVERY CALL. |
---|
| 1482 | C IT TESTS ISTATE AND ITASK FOR LEGALITY AND BRANCHES APPROPIATELY. |
---|
| 1483 | C IF ISTATE .GT. 1 BUT THE FLAG INIT SHOWS THAT INITIALIZATION HAS |
---|
| 1484 | C NOT YET BEEN DONE, AN ERROR RETURN OCCURS. |
---|
| 1485 | C IF ISTATE = 1 AND TOUT = T, JUMP TO BLOCK G AND RETURN IMMEDIATELY. |
---|
| 1486 | C----------------------------------------------------------------------- |
---|
| 1487 | IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 |
---|
| 1488 | IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 |
---|
| 1489 | IF (ISTATE .EQ. 1) GO TO 10 |
---|
| 1490 | IF (INIT .EQ. 0) GO TO 603 |
---|
| 1491 | IF (ISTATE .EQ. 2) GO TO 200 |
---|
| 1492 | GO TO 20 |
---|
| 1493 | 10 INIT = 0 |
---|
| 1494 | IF (TOUT .EQ. T) GO TO 430 |
---|
| 1495 | 20 NTREP = 0 |
---|
| 1496 | C----------------------------------------------------------------------- |
---|
| 1497 | C BLOCK B. |
---|
| 1498 | C THE NEXT CODE BLOCK IS EXECUTED FOR THE INITIAL CALL (ISTATE = 1), |
---|
| 1499 | C OR FOR A CONTINUATION CALL WITH PARAMETER CHANGES (ISTATE = 3). |
---|
| 1500 | C IT CONTAINS CHECKING OF ALL INPUTS AND VARIOUS INITIALIZATIONS. |
---|
| 1501 | C |
---|
| 1502 | C FIRST CHECK LEGALITY OF THE NON-OPTIONAL INPUTS NEQ, ITOL, IOPT, |
---|
| 1503 | C MF, ML, AND MU. |
---|
| 1504 | C----------------------------------------------------------------------- |
---|
| 1505 | IF (NEQ(1) .LE. 0) GO TO 604 |
---|
| 1506 | IF (ISTATE .EQ. 1) GO TO 25 |
---|
| 1507 | IF (NEQ(1) .NE. N) GO TO 605 |
---|
| 1508 | 25 N = NEQ(1) |
---|
| 1509 | IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 |
---|
| 1510 | DO 26 I = 1,3 |
---|
| 1511 | 26 IF (IOPT(I) .LT. 0 .OR. IOPT(I) .GT. 1) GO TO 607 |
---|
| 1512 | ISOPT = IOPT(2) |
---|
| 1513 | IDF = IOPT(3) |
---|
| 1514 | NYH = N |
---|
| 1515 | NSV = 1 |
---|
| 1516 | METH = MF/10 |
---|
| 1517 | MITER = MF - 10*METH |
---|
| 1518 | IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 |
---|
| 1519 | IF (MITER .LT. 0 .OR. MITER .GT. 5) GO TO 608 |
---|
| 1520 | IF (MITER .LE. 3) GO TO 30 |
---|
| 1521 | ML = IWORK(1) |
---|
| 1522 | MU = IWORK(2) |
---|
| 1523 | IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 |
---|
| 1524 | IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 |
---|
| 1525 | 30 IF (ISOPT .EQ. 0) GO TO 32 |
---|
| 1526 | C CHECK LEGALITY OF THE NON-OPTIONAL INPUTS ISOPT, NPAR. |
---|
| 1527 | C COMPUTE NUMBER OF SOLUTION VECTORS AND TOTAL NUMBER OF EQUATIONS. |
---|
| 1528 | IF (NEQ(2) .LE. 0) GO TO 628 |
---|
| 1529 | IF (ISTATE .EQ. 1) GO TO 31 |
---|
| 1530 | IF (NEQ(2) .NE. NPAR) GO TO 629 |
---|
| 1531 | 31 NPAR = NEQ(2) |
---|
| 1532 | NSV = NPAR + 1 |
---|
| 1533 | NYH = NSV * N |
---|
| 1534 | IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 630 |
---|
| 1535 | C NEXT PROCESS AND CHECK THE OPTIONAL INPUTS. -------------------------- |
---|
| 1536 | 32 IF (IOPT(1) .EQ. 1) GO TO 40 |
---|
| 1537 | MAXORD = MORD(METH) |
---|
| 1538 | MXSTEP = MXSTP0 |
---|
| 1539 | MXHNIL = MXHNL0 |
---|
| 1540 | IF (ISTATE .EQ. 1) H0 = ZERO |
---|
| 1541 | HMXI = ZERO |
---|
| 1542 | HMIN = ZERO |
---|
| 1543 | GO TO 60 |
---|
| 1544 | 40 MAXORD = IWORK(5) |
---|
| 1545 | IF (MAXORD .LT. 0) GO TO 611 |
---|
| 1546 | IF (MAXORD .EQ. 0) MAXORD = 100 |
---|
| 1547 | MAXORD = MIN(MAXORD,MORD(METH)) |
---|
| 1548 | MXSTEP = IWORK(6) |
---|
| 1549 | IF (MXSTEP .LT. 0) GO TO 612 |
---|
| 1550 | IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 |
---|
| 1551 | MXHNIL = IWORK(7) |
---|
| 1552 | IF (MXHNIL .LT. 0) GO TO 613 |
---|
| 1553 | IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 |
---|
| 1554 | IF (ISTATE .NE. 1) GO TO 50 |
---|
| 1555 | H0 = RWORK(5) |
---|
| 1556 | IF ((TOUT - T)*H0 .LT. ZERO) GO TO 614 |
---|
| 1557 | 50 HMAX = RWORK(6) |
---|
| 1558 | IF (HMAX .LT. ZERO) GO TO 615 |
---|
| 1559 | HMXI = ZERO |
---|
| 1560 | IF (HMAX .GT. ZERO) HMXI = ONE/HMAX |
---|
| 1561 | HMIN = RWORK(7) |
---|
| 1562 | IF (HMIN .LT. ZERO) GO TO 616 |
---|
| 1563 | C----------------------------------------------------------------------- |
---|
| 1564 | C SET WORK ARRAY POINTERS AND CHECK LENGTHS LRW AND LIW. |
---|
| 1565 | C POINTERS TO SEGMENTS OF RWORK AND IWORK ARE NAMED BY PREFIXING L TO |
---|
| 1566 | C THE NAME OF THE SEGMENT. E.G., THE SEGMENT YH STARTS AT RWORK(LYH). |
---|
| 1567 | C SEGMENTS OF RWORK (IN ORDER) ARE DENOTED YH, WM, EWT, SAVF, ACOR. |
---|
| 1568 | C WORK SPACE FOR DFDP IS CONTAINED IN ACOR. |
---|
| 1569 | C----------------------------------------------------------------------- |
---|
| 1570 | 60 LYH = 21 |
---|
| 1571 | LWM = LYH + (MAXORD + 1)*NYH |
---|
| 1572 | IF (MITER .EQ. 0) LENWM = 0 |
---|
| 1573 | IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LENWM = N*N + 2 |
---|
| 1574 | IF (MITER .EQ. 3) LENWM = N + 2 |
---|
| 1575 | IF (MITER .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 |
---|
| 1576 | LEWT = LWM + LENWM |
---|
| 1577 | LSAVF = LEWT + NYH |
---|
| 1578 | LACOR = LSAVF + N |
---|
| 1579 | LDFDP = LACOR + N |
---|
| 1580 | LENRW = LACOR + NYH - 1 |
---|
| 1581 | IWORK(17) = LENRW |
---|
| 1582 | LIWM = 1 |
---|
| 1583 | LENIW = 20 + N |
---|
| 1584 | IF (MITER .EQ. 0 .OR. MITER .EQ. 3) LENIW = 20 |
---|
| 1585 | LNRS = LENIW + LIWM |
---|
| 1586 | IF (ISOPT .EQ. 1) LENIW = LNRS + NPAR |
---|
| 1587 | IWORK(18) = LENIW |
---|
| 1588 | IF (LENRW .GT. LRW) GO TO 617 |
---|
| 1589 | IF (LENIW .GT. LIW) GO TO 618 |
---|
| 1590 | C CHECK RTOL AND ATOL FOR LEGALITY. ------------------------------------ |
---|
| 1591 | RTOLI = RTOL(1) |
---|
| 1592 | ATOLI = ATOL(1) |
---|
| 1593 | DO 70 I = 1,NYH |
---|
| 1594 | IF (ITOL .GE. 3) RTOLI = RTOL(I) |
---|
| 1595 | IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) |
---|
| 1596 | IF (RTOLI .LT. ZERO) GO TO 619 |
---|
| 1597 | IF (ATOLI .LT. ZERO) GO TO 620 |
---|
| 1598 | 70 CONTINUE |
---|
| 1599 | IF (ISTATE .EQ. 1) GO TO 100 |
---|
| 1600 | C IF ISTATE = 3, SET FLAG TO SIGNAL PARAMETER CHANGES TO STODE. -------- |
---|
| 1601 | JSTART = -1 |
---|
| 1602 | IF (NQ .LE. MAXORD) GO TO 90 |
---|
| 1603 | C MAXORD WAS REDUCED BELOW NQ. COPY YH(*,MAXORD+2) INTO SAVF. --------- |
---|
| 1604 | DO 80 I = 1,N |
---|
| 1605 | 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) |
---|
| 1606 | C RELOAD WM(1) = RWORK(LWM), SINCE LWM MAY HAVE CHANGED. --------------- |
---|
| 1607 | 90 IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) |
---|
| 1608 | GO TO 200 |
---|
| 1609 | C----------------------------------------------------------------------- |
---|
| 1610 | C BLOCK C. |
---|
| 1611 | C THE NEXT BLOCK IS FOR THE INITIAL CALL ONLY (ISTATE = 1). |
---|
| 1612 | C IT CONTAINS ALL REMAINING INITIALIZATIONS, THE INITIAL CALL TO F, |
---|
| 1613 | C THE INITIAL CALL TO SPRIME IF ISOPT = 1, |
---|
| 1614 | C AND THE CALCULATION OF THE INITIAL STEP SIZE. |
---|
| 1615 | C THE ERROR WEIGHTS IN EWT ARE INVERTED AFTER BEING LOADED. |
---|
| 1616 | C----------------------------------------------------------------------- |
---|
| 1617 | 100 UROUND = D1MACH(4) |
---|
| 1618 | TN = T |
---|
| 1619 | IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 105 |
---|
| 1620 | TCRIT = RWORK(1) |
---|
| 1621 | IF ((TCRIT - TOUT)*(TOUT - T) .LT. ZERO) GO TO 625 |
---|
| 1622 | IF (H0 .NE. ZERO .AND. (T + H0 - TCRIT)*H0 .GT. ZERO) |
---|
| 1623 | 1 H0 = TCRIT - T |
---|
| 1624 | 105 JSTART = 0 |
---|
| 1625 | IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) |
---|
| 1626 | NHNIL = 0 |
---|
| 1627 | NST = 0 |
---|
| 1628 | NJE = 0 |
---|
| 1629 | NSLAST = 0 |
---|
| 1630 | HU = ZERO |
---|
| 1631 | NQU = 0 |
---|
| 1632 | CCMAX = 0.3D0 |
---|
| 1633 | MAXCOR = 3 |
---|
| 1634 | IF (ISOPT .EQ. 1) MAXCOR = 4 |
---|
| 1635 | MSBP = 20 |
---|
| 1636 | MXNCF = 10 |
---|
| 1637 | C INITIAL CALL TO F. (LF0 POINTS TO YH(1,2) AND LOADS IN VALUES). |
---|
| 1638 | LF0 = LYH + NYH |
---|
| 1639 | CALL F (NEQ, T, Y, PAR, RWORK(LF0)) |
---|
| 1640 | NFE = 1 |
---|
| 1641 | DUPS = ZERO |
---|
| 1642 | DSMS = ZERO |
---|
| 1643 | DDNS = ZERO |
---|
| 1644 | NDFE = 0 |
---|
| 1645 | NSPE = 0 |
---|
| 1646 | IF (ISOPT .EQ. 0) GO TO 114 |
---|
| 1647 | C INITIALIZE COUNTS FOR REPEATED STEPS DUE TO SENSITIVITY ANALYSIS. |
---|
| 1648 | DO 110 J = 1,NSV |
---|
| 1649 | 110 IWORK(J + LNRS - 1) = 0 |
---|
| 1650 | C LOAD THE INITIAL VALUE VECTOR IN YH. --------------------------------- |
---|
| 1651 | 114 DO 115 I = 1,NYH |
---|
| 1652 | 115 RWORK(I+LYH-1) = Y(I) |
---|
| 1653 | C LOAD AND INVERT THE EWT ARRAY. (H IS TEMPORARILY SET TO ONE.) ------- |
---|
| 1654 | NQ = 1 |
---|
| 1655 | H = ONE |
---|
| 1656 | CALL EWSET (NYH, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) |
---|
| 1657 | DO 120 I = 1,NYH |
---|
| 1658 | IF (RWORK(I+LEWT-1) .LE. ZERO) GO TO 621 |
---|
| 1659 | 120 RWORK(I+LEWT-1) = ONE/RWORK(I+LEWT-1) |
---|
| 1660 | IF (ISOPT .EQ. 0) GO TO 125 |
---|
| 1661 | C CALL SPRIME TO LOAD FIRST-ORDER SENSITIVITY DERIVATIVES INTO |
---|
| 1662 | C REMAINING YH(*,2) POSITIONS. |
---|
| 1663 | CALL SPRIME (NEQ, Y, RWORK(LYH), NYH, N, NSV, RWORK(LWM), |
---|
| 1664 | 1 IWORK(LIWM), RWORK(LEWT), RWORK(LF0), RWORK(LACOR), |
---|
| 1665 | 2 RWORK(LDFDP), PAR, F, JAC, DF, PREPJ, PREPDF) |
---|
| 1666 | IF (IERSP .EQ. -1) GO TO 631 |
---|
| 1667 | IF (IERSP .EQ. -2) GO TO 632 |
---|
| 1668 | C----------------------------------------------------------------------- |
---|
| 1669 | C THE CODING BELOW COMPUTES THE STEP SIZE, H0, TO BE ATTEMPTED ON THE |
---|
| 1670 | C FIRST STEP, UNLESS THE USER HAS SUPPLIED A VALUE FOR THIS. |
---|
| 1671 | C FIRST CHECK THAT TOUT - T DIFFERS SIGNIFICANTLY FROM ZERO. |
---|
| 1672 | C A SCALAR TOLERANCE QUANTITY TOL IS COMPUTED, AS MAX(RTOL(I)) |
---|
| 1673 | C IF THIS IS POSITIVE, OR MAX(ATOL(I)/ABS(Y(I))) OTHERWISE, ADJUSTED |
---|
| 1674 | C SO AS TO BE BETWEEN 100*UROUND AND 1.0E-3. ONLY THE ORIGINAL |
---|
| 1675 | C SOLUTION VECTOR IS CONSIDERED IN THIS CALCULATION (ISOPT = 0 OR 1). |
---|
| 1676 | C THEN THE COMPUTED VALUE H0 IS GIVEN BY.. |
---|
| 1677 | C NEQ |
---|
| 1678 | C H0**2 = TOL / ( W0**-2 + (1/NEQ) * SUM ( F(I)/YWT(I) )**2 ) |
---|
| 1679 | C 1 |
---|
| 1680 | C WHERE W0 = MAX ( ABS(T), ABS(TOUT) ), |
---|
| 1681 | C F(I) = I-TH COMPONENT OF INITIAL VALUE OF F, |
---|
| 1682 | C YWT(I) = EWT(I)/TOL (A WEIGHT FOR Y(I)). |
---|
| 1683 | C THE SIGN OF H0 IS INFERRED FROM THE INITIAL VALUES OF TOUT AND T. |
---|
| 1684 | C----------------------------------------------------------------------- |
---|
| 1685 | 125 IF (H0 .NE. ZERO) GO TO 180 |
---|
| 1686 | TDIST = ABS(TOUT - T) |
---|
| 1687 | W0 = MAX(ABS(T),ABS(TOUT)) |
---|
| 1688 | IF (TDIST .LT. TWO*UROUND*W0) GO TO 622 |
---|
| 1689 | TOL = RTOL(1) |
---|
| 1690 | IF (ITOL .LE. 2) GO TO 140 |
---|
| 1691 | DO 130 I = 1,N |
---|
| 1692 | 130 TOL = MAX(TOL,RTOL(I)) |
---|
| 1693 | 140 IF (TOL .GT. ZERO) GO TO 160 |
---|
| 1694 | ATOLI = ATOL(1) |
---|
| 1695 | DO 150 I = 1,N |
---|
| 1696 | IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) |
---|
| 1697 | AYI = ABS(Y(I)) |
---|
| 1698 | IF (AYI .NE. ZERO) TOL = MAX(TOL,ATOLI/AYI) |
---|
| 1699 | 150 CONTINUE |
---|
| 1700 | 160 TOL = MAX(TOL,100.0D0*UROUND) |
---|
| 1701 | TOL = MIN(TOL,0.001D0) |
---|
| 1702 | SUM = VNORM (N, RWORK(LF0), RWORK(LEWT)) |
---|
| 1703 | SUM = ONE/(TOL*W0*W0) + TOL*SUM**2 |
---|
| 1704 | H0 = ONE/SQRT(SUM) |
---|
| 1705 | H0 = MIN(H0,TDIST) |
---|
| 1706 | H0 = SIGN(H0,TOUT-T) |
---|
| 1707 | C ADJUST H0 IF NECESSARY TO MEET HMAX BOUND. --------------------------- |
---|
| 1708 | 180 RH = ABS(H0)*HMXI |
---|
| 1709 | IF (RH .GT. ONE) H0 = H0/RH |
---|
| 1710 | C LOAD H WITH H0 AND SCALE YH(*,2) BY H0. ------------------------------ |
---|
| 1711 | H = H0 |
---|
| 1712 | DO 190 I = 1,NYH |
---|
| 1713 | 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) |
---|
| 1714 | GO TO 270 |
---|
| 1715 | C----------------------------------------------------------------------- |
---|
| 1716 | C BLOCK D. |
---|
| 1717 | C THE NEXT CODE BLOCK IS FOR CONTINUATION CALLS ONLY (ISTATE = 2 OR 3) |
---|
| 1718 | C AND IS TO CHECK STOP CONDITIONS BEFORE TAKING A STEP. |
---|
| 1719 | C----------------------------------------------------------------------- |
---|
| 1720 | 200 NSLAST = NST |
---|
| 1721 | GO TO (210, 250, 220, 230, 240), ITASK |
---|
| 1722 | 210 IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 |
---|
| 1723 | CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) |
---|
| 1724 | IF (IFLAG .NE. 0) GO TO 627 |
---|
| 1725 | T = TOUT |
---|
| 1726 | GO TO 420 |
---|
| 1727 | 220 TP = TN - HU*(ONE + 100.0D0*UROUND) |
---|
| 1728 | IF ((TP - TOUT)*H .GT. ZERO) GO TO 623 |
---|
| 1729 | IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 |
---|
| 1730 | GO TO 400 |
---|
| 1731 | 230 TCRIT = RWORK(1) |
---|
| 1732 | IF ((TN - TCRIT)*H .GT. ZERO) GO TO 624 |
---|
| 1733 | IF ((TCRIT - TOUT)*H .LT. ZERO) GO TO 625 |
---|
| 1734 | IF ((TN - TOUT)*H .LT. ZERO) GO TO 245 |
---|
| 1735 | CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) |
---|
| 1736 | IF (IFLAG .NE. 0) GO TO 627 |
---|
| 1737 | T = TOUT |
---|
| 1738 | GO TO 420 |
---|
| 1739 | 240 TCRIT = RWORK(1) |
---|
| 1740 | IF ((TN - TCRIT)*H .GT. ZERO) GO TO 624 |
---|
| 1741 | 245 HMX = ABS(TN) + ABS(H) |
---|
| 1742 | IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX |
---|
| 1743 | IF (IHIT) GO TO 400 |
---|
| 1744 | TNEXT = TN + H*(ONE + FOUR*UROUND) |
---|
| 1745 | IF ((TNEXT - TCRIT)*H .LE. ZERO) GO TO 250 |
---|
| 1746 | H = (TCRIT - TN)*(ONE - FOUR*UROUND) |
---|
| 1747 | IF (ISTATE .EQ. 2) JSTART = -2 |
---|
| 1748 | C----------------------------------------------------------------------- |
---|
| 1749 | C BLOCK E. |
---|
| 1750 | C THE NEXT BLOCK IS NORMALLY EXECUTED FOR ALL CALLS AND CONTAINS |
---|
| 1751 | C THE CALL TO THE ONE-STEP CORE INTEGRATOR STODE. |
---|
| 1752 | C |
---|
| 1753 | C THIS IS A LOOPING POINT FOR THE INTEGRATION STEPS. |
---|
| 1754 | C |
---|
| 1755 | C FIRST CHECK FOR TOO MANY STEPS BEING TAKEN, UPDATE EWT (IF NOT AT |
---|
| 1756 | C START OF PROBLEM), CHECK FOR TOO MUCH ACCURACY BEING REQUESTED, AND |
---|
| 1757 | C CHECK FOR H BELOW THE ROUNDOFF LEVEL IN T. |
---|
| 1758 | C TOLSF IS CALCULATED CONSIDERING ALL SOLUTION VECTORS. |
---|
| 1759 | C----------------------------------------------------------------------- |
---|
| 1760 | 250 CONTINUE |
---|
| 1761 | IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 |
---|
| 1762 | CALL EWSET (NYH, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) |
---|
| 1763 | DO 260 I = 1,NYH |
---|
| 1764 | IF (RWORK(I+LEWT-1) .LE. ZERO) GO TO 510 |
---|
| 1765 | 260 RWORK(I+LEWT-1) = ONE/RWORK(I+LEWT-1) |
---|
| 1766 | 270 TOLSF = UROUND*VNORM (NYH, RWORK(LYH), RWORK(LEWT)) |
---|
| 1767 | IF (TOLSF .LE. ONE) GO TO 280 |
---|
| 1768 | TOLSF = TOLSF*2.0D0 |
---|
| 1769 | IF (NST .EQ. 0) GO TO 626 |
---|
| 1770 | GO TO 520 |
---|
| 1771 | 280 IF (ADDX(TN,H) .NE. TN) GO TO 290 |
---|
| 1772 | NHNIL = NHNIL + 1 |
---|
| 1773 | IF (NHNIL .GT. MXHNIL) GO TO 290 |
---|
| 1774 | CALL XERR ('ODESSA - WARNING..INTERNAL T (=R1) AND H (=R2) ARE', |
---|
| 1775 | 1 101, 1, 0, 0, 0, 0, ZERO, ZERO) |
---|
| 1776 | CALL XERR ('SUCH THAT IN THE MACHINE, T + H = T ON THE NEXT STEP', |
---|
| 1777 | 1 101, 1, 0, 0, 0, 0, ZERO, ZERO) |
---|
| 1778 | CALL XERR ('(H = STEP SIZE). KppSolveR WILL CONTINUE ANYWAY', |
---|
| 1779 | 1 101, 1, 0, 0, 0, 2, TN, H) |
---|
| 1780 | IF (NHNIL .LT. MXHNIL) GO TO 290 |
---|
| 1781 | CALL XERR ('ODESSA - ABOVE WARNING HAS BEEN ISSUED I1 TIMES.', |
---|
| 1782 | 1 102, 1, 0, 0, 0, 0, ZERO, ZERO) |
---|
| 1783 | CALL XERR ('IT WILL NOT BE ISSUED AGAIN FOR THIS PROBLEM', |
---|
| 1784 | 1 102, 1, 1, MXHNIL, 0, 0, ZERO,ZERO) |
---|
| 1785 | 290 CONTINUE |
---|
| 1786 | C----------------------------------------------------------------------- |
---|
| 1787 | C CALL STODE(NEQ,Y,YH,NYH,YH,WM,IWM,EWT,SAVF,ACOR,PAR,NRS, |
---|
| 1788 | C 1 F,JAC,DF,PREPJ,PREPDF,SOLSY) |
---|
| 1789 | C----------------------------------------------------------------------- |
---|
| 1790 | CALL STODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LWM), |
---|
| 1791 | 1 IWORK(LIWM), RWORK(LEWT), RWORK(LSAVF), RWORK(LACOR), |
---|
| 1792 | 2 PAR, IWORK(LNRS), F, JAC, DF, PREPJ, PREPDF, SOLSY) |
---|
| 1793 | KGO = 1 - KFLAG |
---|
| 1794 | GO TO (300, 530, 540, 633), KGO |
---|
| 1795 | C----------------------------------------------------------------------- |
---|
| 1796 | C BLOCK F. |
---|
| 1797 | C THE FOLLOWING BLOCK HANDLES THE CASE OF A SUCCESSFUL RETURN FROM THE |
---|
| 1798 | C CORE INTEGRATOR (KFLAG = 0). TEST FOR STOP CONDITIONS. |
---|
| 1799 | C----------------------------------------------------------------------- |
---|
| 1800 | 300 INIT = 1 |
---|
| 1801 | GO TO (310, 400, 330, 340, 350), ITASK |
---|
| 1802 | C ITASK = 1. IF TOUT HAS BEEN REACHED, INTERPOLATE. ------------------- |
---|
| 1803 | 310 IF ((TN - TOUT)*H .LT. ZERO) GO TO 250 |
---|
| 1804 | CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) |
---|
| 1805 | T = TOUT |
---|
| 1806 | GO TO 420 |
---|
| 1807 | C ITASK = 3. JUMP TO EXIT IF TOUT WAS REACHED. ------------------------ |
---|
| 1808 | 330 IF ((TN - TOUT)*H .GE. ZERO) GO TO 400 |
---|
| 1809 | GO TO 250 |
---|
| 1810 | C ITASK = 4. SEE IF TOUT OR TCRIT WAS REACHED. ADJUST H IF NECESSARY. |
---|
| 1811 | 340 IF ((TN - TOUT)*H .LT. ZERO) GO TO 345 |
---|
| 1812 | CALL INTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) |
---|
| 1813 | T = TOUT |
---|
| 1814 | GO TO 420 |
---|
| 1815 | 345 HMX = ABS(TN) + ABS(H) |
---|
| 1816 | IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX |
---|
| 1817 | IF (IHIT) GO TO 400 |
---|
| 1818 | TNEXT = TN + H*(ONE + FOUR*UROUND) |
---|
| 1819 | IF ((TNEXT - TCRIT)*H .LE. ZERO) GO TO 250 |
---|
| 1820 | H = (TCRIT - TN)*(ONE - FOUR*UROUND) |
---|
| 1821 | JSTART = -2 |
---|
| 1822 | GO TO 250 |
---|
| 1823 | C ITASK = 5. SEE IF TCRIT WAS REACHED AND JUMP TO EXIT. --------------- |
---|
| 1824 | 350 HMX = ABS(TN) + ABS(H) |
---|
| 1825 | IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX |
---|
| 1826 | C----------------------------------------------------------------------- |
---|
| 1827 | C BLOCK G. |
---|
| 1828 | C THE FOLLOWING BLOCK HANDLES ALL SUCCESSFUL RETURNS FROM ODESSA. |
---|
| 1829 | C IF ITASK .NE. 1, Y IS LOADED FROM YH AND T IS SET ACCORDINGLY. |
---|
| 1830 | C ISTATE IS SET TO 2, THE ILLEGAL INPUT COUNTER IS ZEROED, AND THE |
---|
| 1831 | C OPTIONAL OUTPUTS ARE LOADED INTO THE WORK ARRAYS BEFORE RETURNING. |
---|
| 1832 | C IF ISTATE = 1 AND TOUT = T, THERE IS A RETURN WITH NO ACTION TAKEN, |
---|
| 1833 | C EXCEPT THAT IF THIS HAS HAPPENED REPEATEDLY, THE RUN IS TERMINATED. |
---|
| 1834 | C----------------------------------------------------------------------- |
---|
| 1835 | 400 DO 410 I = 1,NYH |
---|
| 1836 | 410 Y(I) = RWORK(I+LYH-1) |
---|
| 1837 | T = TN |
---|
| 1838 | IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 |
---|
| 1839 | IF (IHIT) T = TCRIT |
---|
| 1840 | 420 ISTATE = 2 |
---|
| 1841 | ILLIN = 0 |
---|
| 1842 | RWORK(11) = HU |
---|
| 1843 | RWORK(12) = H |
---|
| 1844 | RWORK(13) = TN |
---|
| 1845 | IWORK(11) = NST |
---|
| 1846 | IWORK(12) = NFE |
---|
| 1847 | IWORK(13) = NJE |
---|
| 1848 | IWORK(14) = NQU |
---|
| 1849 | IWORK(15) = NQ |
---|
| 1850 | IF (ISOPT .EQ. 0) RETURN |
---|
| 1851 | IWORK(19) = NDFE |
---|
| 1852 | IWORK(20) = NSPE |
---|
| 1853 | RETURN |
---|
| 1854 | 430 NTREP = NTREP + 1 |
---|
| 1855 | IF (NTREP .LT. 5) RETURN |
---|
| 1856 | CALL XERR ('ODESSA -- REPEATED CALLS WITH ISTATE = 1 AND |
---|
| 1857 | 1TOUT = T (=R1)', 301, 1, 0, 0, 0, 1, T, ZERO) |
---|
| 1858 | GO TO 800 |
---|
| 1859 | C----------------------------------------------------------------------- |
---|
| 1860 | C BLOCK H. |
---|
| 1861 | C THE FOLLOWING BLOCK HANDLES ALL UNSUCCESSFUL RETURNS OTHER THAN |
---|
| 1862 | C THOSE FOR ILLEGAL INPUT. FIRST THE ERROR MESSAGE ROUTINE IS CALLED. |
---|
| 1863 | C IF THERE WAS AN ERROR TEST OR CONVERGENCE TEST FAILURE, IMXER IS SET. |
---|
| 1864 | C THEN Y IS LOADED FROM YH, T IS SET TO TN, AND THE ILLEGAL INPUT |
---|
| 1865 | C COUNTER ILLIN IS SET TO 0. THE OPTIONAL OUTPUTS ARE LOADED INTO |
---|
| 1866 | C THE WORK ARRAYS BEFORE RETURNING. |
---|
| 1867 | C----------------------------------------------------------------------- |
---|
| 1868 | C THE MAXIMUM NUMBER OF STEPS WAS TAKEN BEFORE REACHING TOUT. ---------- |
---|
| 1869 | 500 CALL XERR ('ODESSA - AT CURRENT T (=R1), MXSTEP (=I1) STEPS', |
---|
| 1870 | 1 201, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 1871 | CALL XERR ('TAKEN ON THIS CALL BEFORE REACHING TOUT', |
---|
| 1872 | 1 201, 1, 1, MXSTEP, 0, 1, TN, ZERO) |
---|
| 1873 | ISTATE = -1 |
---|
| 1874 | GO TO 580 |
---|
| 1875 | C EWT(I) .LE. 0.0 FOR SOME I (NOT AT START OF PROBLEM). ---------------- |
---|
| 1876 | 510 EWTI = RWORK(LEWT+I-1) |
---|
| 1877 | CALL XERR ('ODESSA - AT T (=R1), EWT(I1) HAS BECOME R2 .LE. 0.', |
---|
| 1878 | 1 202, 1, 1, I, 0, 2, TN, EWTI) |
---|
| 1879 | ISTATE = -6 |
---|
| 1880 | GO TO 580 |
---|
| 1881 | C TOO MUCH ACCURACY REQUESTED FOR MACHINE PRECISION. ------------------- |
---|
| 1882 | 520 CALL XERR ('ODESSA - AT T (=R1), TOO MUCH ACCURACY REQUESTED', |
---|
| 1883 | 1 203, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 1884 | CALL XERR ('FOR PRECISION OF MACHINE.. SEE TOLSF (=R2)', |
---|
| 1885 | 1 203, 1, 0, 0, 0, 2, TN, TOLSF) |
---|
| 1886 | RWORK(14) = TOLSF |
---|
| 1887 | ISTATE = -2 |
---|
| 1888 | GO TO 580 |
---|
| 1889 | C KFLAG = -1. ERROR TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ----- |
---|
| 1890 | 530 CALL XERR ('ODESSA - AT T(=R1) AND STEP SIZE H(=R2), THE ERROR', |
---|
| 1891 | 1 204, 1, 0, 0, 0, 0, ZERO, ZERO) |
---|
| 1892 | CALL XERR ('TEST FAILED REPEATEDLY OR WITH ABS(H) = HMIN', |
---|
| 1893 | 1 204, 1, 0, 0, 0, 2, TN, H) |
---|
| 1894 | ISTATE = -4 |
---|
| 1895 | GO TO 560 |
---|
| 1896 | C KFLAG = -2. CONVERGENCE FAILED REPEATEDLY OR WITH ABS(H) = HMIN. ---- |
---|
| 1897 | 540 CALL XERR ('ODESSA - AT T (=R1) AND STEP SIZE H (=R2), THE', |
---|
| 1898 | 1 205, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 1899 | CALL XERR ('CORRECTOR CONVERGENCE FAILED REPEATEDLY', |
---|
| 1900 | 1 205, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 1901 | CALL XERR ('OR WITH ABS(H) = HMIN', |
---|
| 1902 | 1 205, 1, 0, 0, 0, 2, TN, H) |
---|
| 1903 | ISTATE = -5 |
---|
| 1904 | C COMPUTE IMXER IF RELEVANT. ------------------------------------------- |
---|
| 1905 | 560 BIG = ZERO |
---|
| 1906 | IMXER = 1 |
---|
| 1907 | DO 570 I = 1,NYH |
---|
| 1908 | SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) |
---|
| 1909 | IF (BIG .GE. SIZE) GO TO 570 |
---|
| 1910 | BIG = SIZE |
---|
| 1911 | IMXER = I |
---|
| 1912 | 570 CONTINUE |
---|
| 1913 | IWORK(16) = IMXER |
---|
| 1914 | C SET Y VECTOR, T, ILLIN, AND OPTIONAL OUTPUTS. ------------------------ |
---|
| 1915 | 580 DO 590 I = 1,NYH |
---|
| 1916 | 590 Y(I) = RWORK(I+LYH-1) |
---|
| 1917 | T = TN |
---|
| 1918 | ILLIN = 0 |
---|
| 1919 | RWORK(11) = HU |
---|
| 1920 | RWORK(12) = H |
---|
| 1921 | RWORK(13) = TN |
---|
| 1922 | IWORK(11) = NST |
---|
| 1923 | IWORK(12) = NFE |
---|
| 1924 | IWORK(13) = NJE |
---|
| 1925 | IWORK(14) = NQU |
---|
| 1926 | IWORK(15) = NQ |
---|
| 1927 | IF (ISOPT .EQ. 0) RETURN |
---|
| 1928 | IWORK(19) = NDFE |
---|
| 1929 | IWORK(20) = NSPE |
---|
| 1930 | RETURN |
---|
| 1931 | C----------------------------------------------------------------------- |
---|
| 1932 | C BLOCK I. |
---|
| 1933 | C THE FOLLOWING BLOCK HANDLES ALL ERROR RETURNS DUE TO ILLEGAL INPUT |
---|
| 1934 | C (ISTATE = -3), AS DETECTED BEFORE CALLING THE CORE INTEGRATOR. |
---|
| 1935 | C FIRST THE ERROR MESSAGE ROUTINE IS CALLED. THEN IF THERE HAVE BEEN |
---|
| 1936 | C 5 CONSECUTIVE SUCH RETURNS JUST BEFORE THIS CALL TO THE KppSolveR, |
---|
| 1937 | C THE RUN IS HALTED. |
---|
| 1938 | C----------------------------------------------------------------------- |
---|
| 1939 | 601 CALL XERR ('ODESSA - ISTATE (=I1) ILLEGAL', |
---|
| 1940 | 1 1, 1, 1, ISTATE, 0, 0, ZERO,ZERO) |
---|
| 1941 | GO TO 700 |
---|
| 1942 | 602 CALL XERR ('ODESSA - ITASK (=I1) ILLEGAL', |
---|
| 1943 | 1 2, 1, 1, ITASK, 0, 0, ZERO,ZERO) |
---|
| 1944 | GO TO 700 |
---|
| 1945 | 603 CALL XERR ('ODESSA - ISTATE .GT. 1 BUT ODESSA NOT INITIALIZED', |
---|
| 1946 | 1 3, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 1947 | GO TO 700 |
---|
| 1948 | 604 CALL XERR ('ODESSA - NEQ (=I1) .LT. 1', |
---|
| 1949 | 1 4, 1, 1, NEQ(1), 0, 0, ZERO,ZERO) |
---|
| 1950 | GO TO 700 |
---|
| 1951 | 605 CALL XERR ('ODESSA - ISTATE = 3 AND NEQ CHANGED. (I1 TO I2)', |
---|
| 1952 | 1 5, 1, 2, N, NEQ(1), 0, ZERO,ZERO) |
---|
| 1953 | GO TO 700 |
---|
| 1954 | 606 CALL XERR ('ODESSA - ITOL (=I1) ILLEGAL', |
---|
| 1955 | 1 6, 1, 1, ITOL, 0, 0, ZERO,ZERO) |
---|
| 1956 | GO TO 700 |
---|
| 1957 | 607 CALL XERR ('ODESSA - IOPT (=I1) ILLEGAL', |
---|
| 1958 | 1 7, 1, 1, IOPT, 0, 0, ZERO,ZERO) |
---|
| 1959 | GO TO 700 |
---|
| 1960 | 608 CALL XERR('ODESSA - MF (=I1) ILLEGAL', |
---|
| 1961 | 1 8, 1, 1, MF, 0, 0, ZERO,ZERO) |
---|
| 1962 | GO TO 700 |
---|
| 1963 | 609 CALL XERR('ODESSA - ML (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', |
---|
| 1964 | 1 9, 1, 2, ML, NEQ(1), 0, ZERO,ZERO) |
---|
| 1965 | GO TO 700 |
---|
| 1966 | 610 CALL XERR('ODESSA - MU (=I1) ILLEGAL.. .LT.0 OR .GE.NEQ (=I2)', |
---|
| 1967 | 1 10, 1, 2, MU, NEQ(1), 0, ZERO,ZERO) |
---|
| 1968 | GO TO 700 |
---|
| 1969 | 611 CALL XERR('ODESSA - MAXORD (=I1) .LT. 0', |
---|
| 1970 | 1 11, 1, 1, MAXORD, 0, 0, ZERO,ZERO) |
---|
| 1971 | GO TO 700 |
---|
| 1972 | 612 CALL XERR('ODESSA - MXSTEP (=I1) .LT. 0', |
---|
| 1973 | 1 12, 1, 1, MXSTEP, 0, 0, ZERO,ZERO) |
---|
| 1974 | GO TO 700 |
---|
| 1975 | 613 CALL XERR('ODESSA - MXHNIL (=I1) .LT. 0', |
---|
| 1976 | 1 13, 1, 1, MXHNIL, 0, 0, ZERO,ZERO) |
---|
| 1977 | GO TO 700 |
---|
| 1978 | 614 CALL XERR('ODESSA - TOUT (=R1) BEHIND T (=R2)', |
---|
| 1979 | 1 14, 1, 0, 0, 0, 2, TOUT, T) |
---|
| 1980 | CALL XERR('INTEGRATION DIRECTION IS GIVEN BY H0 (=R1)', |
---|
| 1981 | 1 14, 1, 0, 0, 0, 1, H0, ZERO) |
---|
| 1982 | GO TO 700 |
---|
| 1983 | 615 CALL XERR('ODESSA - HMAX (=R1) .LT. 0.0', |
---|
| 1984 | 1 15, 1, 0, 0, 0, 1, HMAX, ZERO) |
---|
| 1985 | GO TO 700 |
---|
| 1986 | 616 CALL XERR('ODESSA - HMIN (=R1) .LT. 0.0', |
---|
| 1987 | 1 16, 1, 0, 0, 0, 1, HMIN, ZERO) |
---|
| 1988 | GO TO 700 |
---|
| 1989 | 617 CALL XERR('ODESSA - RWORK LENGTH NEEDED, LENRW (=I1), EXCEEDS |
---|
| 1990 | 1 LRW (=I2)', 17, 1, 2, LENRW, LRW, 0, ZERO,ZERO) |
---|
| 1991 | GO TO 700 |
---|
| 1992 | 618 CALL XERR('ODESSA - IWORK LENGTH NEEDED, LENIW (=I1), EXCEEDS |
---|
| 1993 | 1 LIW (=I2)', 18, 1, 2, LENIW, LIW, 0, ZERO,ZERO) |
---|
| 1994 | GO TO 700 |
---|
| 1995 | 619 CALL XERR('ODESSA - RTOL(I1) IS R1 .LT. 0.0', |
---|
| 1996 | 1 19, 1, 1, I, 0, 1, RTOLI, ZREO) |
---|
| 1997 | GO TO 700 |
---|
| 1998 | 620 CALL XERR('ODESSA - ATOL(I1) IS R1 .LT. 0.0', |
---|
| 1999 | 1 20, 1, 1, I, 0, 1, ATOLI, ZERO) |
---|
| 2000 | GO TO 700 |
---|
| 2001 | * |
---|
| 2002 | 621 EWTI = RWORK(LEWT+I-1) |
---|
| 2003 | CALL XERR('ODESSA - EWT(I1) IS R1 .LE. 0.0', |
---|
| 2004 | 1 21, 1, 1, I, 0, 1, EWTI, ZERO) |
---|
| 2005 | GO TO 700 |
---|
| 2006 | 622 CALL XERR('ODESSA - TOUT (=R1) TOO CLOSE TO T(=R2) TO START |
---|
| 2007 | 1 INTEGRATION', 22, 1, 0, 0, 0, 2, TOUT, T) |
---|
| 2008 | GO TO 700 |
---|
| 2009 | 623 CALL XERR('ODESSA - ITASK = I1 AND TOUT (=R1) BEHIND TCUR - HU |
---|
| 2010 | 1 (= R2)', 23, 1, 1, ITASK, 0, 2, TOUT, TP) |
---|
| 2011 | GO TO 700 |
---|
| 2012 | 624 CALL XERR('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TCUR |
---|
| 2013 | 1 (=R2)', 24, 1, 0, 0, 0, 2, TCRIT, TN) |
---|
| 2014 | GO TO 700 |
---|
| 2015 | 625 CALL XERR('ODESSA - ITASK = 4 OR 5 AND TCRIT (=R1) BEHIND TOUT |
---|
| 2016 | 1 (=R2)', 25, 1, 0, 0, 0, 2, TCRIT, TOUT) |
---|
| 2017 | GO TO 700 |
---|
| 2018 | 626 CALL XERR('ODESSA - AT START OF PROBLEM, TOO MUCH ACCURACY', |
---|
| 2019 | 1 26, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2020 | CALL XERR('REQUESTED FOR PRECISION OF MACHINE. SEE TOLSF (=R1)', |
---|
| 2021 | 1 26, 1, 0, 0, 0, 1, TOLSF, ZERO) |
---|
| 2022 | RWORK(14) = TOLSF |
---|
| 2023 | GO TO 700 |
---|
| 2024 | 627 CALL XERR('ODESSA - TROUBLE FROM INTDY. ITASK = I1, TOUT = R1', |
---|
| 2025 | 1 27, 1, 1, ITASK, 0, 1, TOUT, ZERO) |
---|
| 2026 | GO TO 700 |
---|
| 2027 | C ERROR STATEMENTS ASSOCIATED WITH SENSITIVITY ANALYSIS. |
---|
| 2028 | 628 CALL XERR('ODESSA - NPAR (=I1) .LT. 1', |
---|
| 2029 | 1 28, 1, 1, NPAR, 0, 0, ZERO,ZERO) |
---|
| 2030 | GO TO 700 |
---|
| 2031 | 629 CALL XERR('ODESSA - ISTATE = 3 AND NPAR CHANGED (I1 TO I2)', |
---|
| 2032 | 1 29, 1, 2, NP, NPAR, 0, ZERO,ZERO) |
---|
| 2033 | GO TO 700 |
---|
| 2034 | 630 CALL XERR('ODESSA - MITER (=I1) ILLEGAL', |
---|
| 2035 | 1 30, 1, 1, MITER, 0, 0, ZERO,ZERO) |
---|
| 2036 | GO TO 700 |
---|
| 2037 | 631 CALL XERR('ODESSA - TROUBLE IN SPRIME (IERPJ)', |
---|
| 2038 | 1 31, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2039 | GO TO 700 |
---|
| 2040 | 632 CALL XERR('ODESSA - TROUBLE IN SPRIME (MITER)', |
---|
| 2041 | 1 32, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2042 | GO TO 700 |
---|
| 2043 | 633 CALL XERR('ODESSA - FATAL ERROR IN STODE (KFLAG = -3)', |
---|
| 2044 | 1 33, 2, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2045 | GO TO 801 |
---|
| 2046 | C |
---|
| 2047 | 700 IF (ILLIN .EQ. 5) GO TO 710 |
---|
| 2048 | ILLIN = ILLIN + 1 |
---|
| 2049 | ISTATE = -3 |
---|
| 2050 | RETURN |
---|
| 2051 | 710 CALL XERR('ODESSA - REPEATED OCCURRENCES OF ILLEGAL INPUT', |
---|
| 2052 | 1 302, 1, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2053 | C |
---|
| 2054 | 800 CALL XERR('ODESSA - RUN ABORTED.. APPARENT INFINITE LOOP', |
---|
| 2055 | 1 303, 2, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2056 | RETURN |
---|
| 2057 | 801 CALL XERR('ODESSA - RUN ABORTED', |
---|
| 2058 | 1 304, 2, 0, 0, 0, 0, ZERO,ZERO) |
---|
| 2059 | RETURN |
---|
| 2060 | C-------------------- END OF SUBROUTINE ODESSA ------------------------- |
---|
| 2061 | END |
---|
| 2062 | DOUBLE PRECISION FUNCTION ADDX(A,B) |
---|
| 2063 | DOUBLE PRECISION A,B |
---|
| 2064 | C |
---|
| 2065 | C THIS FUNCTION IS NECESSARY TO FORCE OPTIMIZING COMPILERS TO |
---|
| 2066 | C EXECUTE AND STORE A SUM, FOR SUCCESSFUL EXECUTION OF THE |
---|
| 2067 | C TEST A + B = B. |
---|
| 2068 | C |
---|
| 2069 | ADDX = A + B |
---|
| 2070 | RETURN |
---|
| 2071 | C-------------------- END OF FUNCTION SUM ------------------------------ |
---|
| 2072 | END |
---|
| 2073 | SUBROUTINE SPRIME (NEQ, Y, YH, NYH, NROW, NCOL, WM, IWM, |
---|
| 2074 | 1 EWT, SAVF, FTEM, DFDP, PAR, F, JAC, DF, PJAC, PDF) |
---|
| 2075 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 2076 | DIMENSION NEQ(*), Y(*), YH(NROW,NCOL,*), WM(*), IWM(*), |
---|
| 2077 | 1 EWT(*), SAVF(*), FTEM(*), DFDP(NROW,*), PAR(*) |
---|
| 2078 | EXTERNAL F, JAC, DF, PJAC, PDF |
---|
| 2079 | PARAMETER (ONE=1.0D0,ZERO=0.0D0) |
---|
| 2080 | COMMON /ODE001/ ROWND, ROWNS(173), |
---|
| 2081 | 1 RDUM1(37),EL0, H, RDUM2(6), |
---|
| 2082 | 2 IOWND1(14), IOWNS(4), |
---|
| 2083 | 3 IDUM1(3), IERPJ, IDUM2(6), |
---|
| 2084 | 4 MITER, IDUM3(4), N, IDUM4(5) |
---|
| 2085 | COMMON /ODE002/ RDUM3(3), |
---|
| 2086 | 1 IOWND2(3), IDUM5, NSV, IDUM6, NSPE, IDUM7, IERSP, JOPT, IDUM8 |
---|
| 2087 | C----------------------------------------------------------------------- |
---|
| 2088 | C SPRIME IS CALLED BY ODESSA TO INITIALIZE THE YH ARRAY. IT IS ALSO |
---|
| 2089 | C CALLED BY STODE TO REEVALUATE FIRST ORDER DERIVATIVES WHEN KFLAG |
---|
| 2090 | C .LE. -3. SPRIME COMPUTES THE FIRST DERIVATIVES OF THE SENSITIVITY |
---|
| 2091 | C COEFFICIENTS WITH RESPECT TO THE INDEPENDENT VARIABLE T... |
---|
| 2092 | C |
---|
| 2093 | C SPRIME = D(DY/DP)/DT = JAC*DY/DP + DF/DP |
---|
| 2094 | C WHERE JAC = JACOBIAN MATRIX |
---|
| 2095 | C DY/DP = SENSITIVITY MATRIX |
---|
| 2096 | C DF/DP = INHOMOGENEITY MATRIX |
---|
| 2097 | C THIS ROUTINE USES THE COMMON VARIABLES EL0, H, IERPJ, MITER, N, |
---|
| 2098 | C NSV, NSPE, IERSP, JOPT |
---|
| 2099 | C----------------------------------------------------------------------- |
---|
| 2100 | C CALL PREPJ WITH JOPT = 1. |
---|
| 2101 | C IF MITER = 2 OR 5, EL0 IS TEMPORARILY SET TO -1.0 AND H IS |
---|
| 2102 | C TEMPORARILY SET TO 1.0D0. |
---|
| 2103 | C----------------------------------------------------------------------- |
---|
| 2104 | NSPE = NSPE + 1 |
---|
| 2105 | JOPT = 1 |
---|
| 2106 | IF (MITER .EQ. 1 .OR. MITER .EQ. 4) GO TO 10 |
---|
| 2107 | HTEMP = H |
---|
| 2108 | ETEMP = EL0 |
---|
| 2109 | H = ONE |
---|
| 2110 | EL0 = -ONE |
---|
| 2111 | 10 CALL PJAC (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, FTEM, |
---|
| 2112 | 1 PAR, F, JAC, JOPT) |
---|
| 2113 | IF (IERPJ .NE. 0) GO TO 300 |
---|
| 2114 | JOPT = 0 |
---|
| 2115 | IF (MITER .EQ. 1 .OR. MITER .EQ. 4) GO TO 20 |
---|
| 2116 | H = HTEMP |
---|
| 2117 | EL0 = ETEMP |
---|
| 2118 | C----------------------------------------------------------------------- |
---|
| 2119 | C CALL PREPDF AND LOAD DFDP(*,JPAR). |
---|
| 2120 | C----------------------------------------------------------------------- |
---|
| 2121 | 20 DO 30 J = 2,NSV |
---|
| 2122 | JPAR = J - 1 |
---|
| 2123 | CALL PDF (NEQ, Y, WM, SAVF, FTEM, DFDP(1,JPAR), PAR, |
---|
| 2124 | 1 F, DF, JPAR) |
---|
| 2125 | 30 CONTINUE |
---|
| 2126 | C----------------------------------------------------------------------- |
---|
| 2127 | C COMPUTE JAC*DY/DP AND STORE RESULTS IN YH(*,*,2). |
---|
| 2128 | C----------------------------------------------------------------------- |
---|
| 2129 | GO TO (40,40,310,100,100) MITER |
---|
| 2130 | C THE JACOBIAN IS FULL.------------------------------------------------ |
---|
| 2131 | C FOR EACH ROW OF THE JACOBIAN.. |
---|
| 2132 | C 40 DO 70 IROW = 1,N |
---|
| 2133 | C AND EACH COLUMN OF THE SENSITIVITY MATRIX.. |
---|
| 2134 | C DO 60 J = 2,NSV |
---|
| 2135 | C SUM = ZERO |
---|
| 2136 | C TAKE THE VECTOR DOT PRODUCT.. |
---|
| 2137 | C DO 50 I = 1,N |
---|
| 2138 | C IPD = IROW + N*(I-1) + 2 |
---|
| 2139 | C SUM = SUM + WM(IPD)*YH(I,J,1) |
---|
| 2140 | C 50 CONTINUE |
---|
| 2141 | C YH(IROW,J,2) = SUM |
---|
| 2142 | C 60 CONTINUE |
---|
| 2143 | C 70 CONTINUE |
---|
| 2144 | 40 CONTINUE |
---|
| 2145 | C FOR EACH COLUMN OF THE SENSITIVITY MATRIX.. |
---|
| 2146 | DO 60 J = 2,NSV |
---|
| 2147 | CALL Jac_SP_Vec( WM(3), YH(1,J,1), YH(1,J,2) ) |
---|
| 2148 | 60 CONTINUE |
---|
| 2149 | GO TO 200 |
---|
| 2150 | C THE JACOBIAN IS BANDED.----------------------------------------------- |
---|
| 2151 | 100 ML = IWM(1) |
---|
| 2152 | MU = IWM(2) |
---|
| 2153 | ICOUNT = 1 |
---|
| 2154 | MBAND = ML + MU + 1 |
---|
| 2155 | MEBAND = MBAND + ML |
---|
| 2156 | NMU = N - MU |
---|
| 2157 | ML1 = ML + 1 |
---|
| 2158 | C FOR EACH ROW OF THE JACOBIAN.. |
---|
| 2159 | DO 160 IROW = 1,N |
---|
| 2160 | IF (IROW .GT. ML1) GO TO 110 |
---|
| 2161 | IPD = MBAND + IROW + 1 |
---|
| 2162 | IYH = 1 |
---|
| 2163 | LBAND = MU + IROW |
---|
| 2164 | GO TO 120 |
---|
| 2165 | 110 ICOUNT = ICOUNT + 1 |
---|
| 2166 | IPD = ICOUNT*MEBAND + 2 |
---|
| 2167 | IYH = IYH + 1 |
---|
| 2168 | LBAND = LBAND - 1 |
---|
| 2169 | IF (IROW .LE. NMU) LBAND = MBAND |
---|
| 2170 | C AND EACH COLUMN OF THE SENSITIVITY MATRIX.. |
---|
| 2171 | 120 DO 150 J = 2,NSV |
---|
| 2172 | SUM = ZERO |
---|
| 2173 | I1 = IPD |
---|
| 2174 | I2 = IYH |
---|
| 2175 | C TAKE THE VECTOR DOT PRODUCT. |
---|
| 2176 | DO 140 I = 1,LBAND |
---|
| 2177 | SUM = SUM + WM(I1)*YH(I2,J,1) |
---|
| 2178 | I1 = I1 + MEBAND - 1 |
---|
| 2179 | I2 = I2 + 1 |
---|
| 2180 | 140 CONTINUE |
---|
| 2181 | YH(IROW,J,2) = SUM |
---|
| 2182 | 150 CONTINUE |
---|
| 2183 | 160 CONTINUE |
---|
| 2184 | C----------------------------------------------------------------------- |
---|
| 2185 | C ADD THE INHOMOGENEITY TERM, I.E., ADD DFDP(*,JPAR) TO YH(*,JPAR+1,2). |
---|
| 2186 | C----------------------------------------------------------------------- |
---|
| 2187 | 200 DO 220 J = 2,NSV |
---|
| 2188 | JPAR = J - 1 |
---|
| 2189 | DO 210 I = 1,N |
---|
| 2190 | YH(I,J,2) = YH(I,J,2) + DFDP(I,JPAR) |
---|
| 2191 | 210 CONTINUE |
---|
| 2192 | 220 CONTINUE |
---|
| 2193 | RETURN |
---|
| 2194 | C----------------------------------------------------------------------- |
---|
| 2195 | C ERROR RETURNS. |
---|
| 2196 | C----------------------------------------------------------------------- |
---|
| 2197 | 300 IERSP = -1 |
---|
| 2198 | RETURN |
---|
| 2199 | 310 IERSP = -2 |
---|
| 2200 | RETURN |
---|
| 2201 | C------------------------END OF SUBROUTINE SPRIME----------------------- |
---|
| 2202 | END |
---|
| 2203 | SUBROUTINE PREPJ (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, FTEM, |
---|
| 2204 | 1 PAR, FUNC_CHEM, JAC, JOPT) |
---|
| 2205 | C IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 2206 | INCLUDE 'KPP_ROOT_Parameters.h' |
---|
| 2207 | INCLUDE 'KPP_ROOT_Sparse.h' |
---|
| 2208 | DIMENSION NEQ(*), Y(*), YH(NYH,*), WM(*), IWM(*), EWT(*), |
---|
| 2209 | 1 SAVF(*), FTEM(*), PAR(*) |
---|
| 2210 | EXTERNAL FUNC_CHEM, JAC |
---|
| 2211 | PARAMETER (ZERO=0.0D0,ONE=1.0D0) |
---|
| 2212 | COMMON /ODE001/ ROWND, ROWNS(173), |
---|
| 2213 | 2 RDUM1(37), EL0, H, RDUM2(4), TN, UROUND, |
---|
| 2214 | 3 IOWND(14), IOWNS(4), |
---|
| 2215 | 4 IDUM1(3), IERPJ, IDUM2, JCUR, IDUM3(4), |
---|
| 2216 | 5 MITER, IDUM4(4), N, IDUM5(2), NFE, NJE, IDUM6 |
---|
| 2217 | C----------------------------------------------------------------------- |
---|
| 2218 | C PREPJ IS CALLED BY STODE TO COMPUTE AND PROCESS THE MATRIX |
---|
| 2219 | C P = I - H*EL(1)*J , WHERE J IS AN APPROXIMATION TO THE JACOBIAN. |
---|
| 2220 | C IF ISOPT = 1, PREPJ IS ALSO CALLED BY SPRIME WITH JOPT = 1. |
---|
| 2221 | C HERE J IS COMPUTED BY THE USER-SUPPLIED ROUTINE JAC IF |
---|
| 2222 | C MITER = 1 OR 4, OR BY FINITE DIFFERENCING IF MITER = 2, 3, OR 5. |
---|
| 2223 | C IF MITER = 3, A DIAGONAL APPROXIMATION TO J IS USED. |
---|
| 2224 | C J IS STORED IN WM AND REPLACED BY P. IF MITER .NE. 3, P IS THEN |
---|
| 2225 | C SUBJECTED TO LU DECOMPOSITION (JOPT = 0) IN PREPARATION FOR LATER |
---|
| 2226 | C SOLUTION OF LINEAR SYSTEMS WITH P AS COEFFICIENT MATRIX. THIS IS |
---|
| 2227 | C DONE BY DGEFA IF MITER = 1 OR 2, AND BY DGBFA IF MITER = 4 OR 5. |
---|
| 2228 | C |
---|
| 2229 | C IN ADDITION TO VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION |
---|
| 2230 | C WITH PREPJ USES THE FOLLOWING.. |
---|
| 2231 | C Y = ARRAY CONTAINING PREDICTED VALUES ON ENTRY. |
---|
| 2232 | C FTEM = WORK ARRAY OF LENGTH N (ACOR IN STODE). |
---|
| 2233 | C SAVF = ARRAY CONTAINING F EVALUATED AT PREDICTED Y. |
---|
| 2234 | C WM = REAL WORK SPACE FOR MATRICES. ON OUTPUT IT CONTAINS THE |
---|
| 2235 | C INVERSE DIAGONAL MATRIX IF MITER = 3 AND THE LU DECOMPOSITION |
---|
| 2236 | C OF P IF MITER IS 1, 2 , 4, OR 5. |
---|
| 2237 | C STORAGE OF MATRIX ELEMENTS STARTS AT WM(3). |
---|
| 2238 | C WM ALSO CONTAINS THE FOLLOWING MATRIX-RELATED DATA.. |
---|
| 2239 | C WM(1) = SQRT(UROUND), USED IN NUMERICAL JACOBIAN INCREMENTS. |
---|
| 2240 | C WM(2) = H*EL0, SAVED FOR LATER USE IF MITER = 3. |
---|
| 2241 | C IWM = INTEGER WORK SPACE CONTAINING PIVOT INFORMATION, STARTING AT |
---|
| 2242 | C IWM(21), IF MITER IS 1, 2, 4, OR 5. IWM ALSO CONTAINS BAND |
---|
| 2243 | C PARAMETERS ML = IWM(1) AND MU = IWM(2) IF MITER IS 4 OR 5. |
---|
| 2244 | C EL0 = EL(1) (INPUT). |
---|
| 2245 | C IERPJ = OUTPUT ERROR FLAG, = 0 IF NO TROUBLE, .GT. 0 IF |
---|
| 2246 | C P MATRIX FOUND TO BE SINGULAR. |
---|
| 2247 | C JCUR = OUTPUT FLAG = 1 TO INDICATE THAT THE JACOBIAN MATRIX |
---|
| 2248 | C (OR APPROXIMATION) IS NOW CURRENT. |
---|
| 2249 | C JOPT = INPUT JACOBIAN OPTION, = 1 IF JAC IS DESIRED ONLY. |
---|
| 2250 | C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, TN, UROUND, |
---|
| 2251 | C IERPJ, JCUR, MITER, N, NFE, AND NJE. |
---|
| 2252 | C----------------------------------------------------------------------- |
---|
| 2253 | NJE = NJE + 1 |
---|
| 2254 | IERPJ = 0 |
---|
| 2255 | JCUR = 1 |
---|
| 2256 | HL0 = H*EL0 |
---|
| 2257 | GO TO (100, 200, 300, 400, 500), MITER |
---|
| 2258 | C IF MITER = 1, CALL JAC AND MULTIPLY BY SCALAR. ----------------------- |
---|
| 2259 | C 100 LENP = N*N |
---|
| 2260 | 100 LENP = LU_NONZERO |
---|
| 2261 | DO 110 I = 1,LU_NONZERO |
---|
| 2262 | 110 WM(I+2) = ZERO |
---|
| 2263 | CALL JAC (NEQ, TN, Y, PAR, 0, 0, WM(3), N) |
---|
| 2264 | IF (JOPT .EQ. 1) RETURN |
---|
| 2265 | CON = -HL0 |
---|
| 2266 | DO 120 I = 1,LU_NONZERO |
---|
| 2267 | 120 WM(I+2) = WM(I+2)*CON |
---|
| 2268 | GO TO 240 |
---|
| 2269 | C IF MITER = 2, MAKE N CALLS TO F TO APPROXIMATE J. -------------------- |
---|
| 2270 | 200 FAC = VNORM (N, SAVF, EWT) |
---|
| 2271 | R0 = 1000.0D0*ABS(H)*UROUND*REAL(N)*FAC |
---|
| 2272 | IF (R0 .EQ. ZERO) R0 = ONE |
---|
| 2273 | SRUR = WM(1) |
---|
| 2274 | J1 = 2 |
---|
| 2275 | DO 230 J = 1,N |
---|
| 2276 | YJ = Y(J) |
---|
| 2277 | R = MAX(SRUR*ABS(YJ),R0/EWT(J)) |
---|
| 2278 | Y(J) = Y(J) + R |
---|
| 2279 | FAC = -HL0/R |
---|
| 2280 | CALL FUNC_CHEM (NEQ, TN, Y, PAR, FTEM) |
---|
| 2281 | DO 220 I = 1,N |
---|
| 2282 | 220 WM(I+J1) = (FTEM(I) - SAVF(I))*FAC |
---|
| 2283 | Y(J) = YJ |
---|
| 2284 | J1 = J1 + N |
---|
| 2285 | 230 CONTINUE |
---|
| 2286 | NFE = NFE + N |
---|
| 2287 | IF (JOPT .EQ. 1) RETURN |
---|
| 2288 | C ADD IDENTITY MATRIX. ------------------------------------------------- |
---|
| 2289 | 240 J = 3 |
---|
| 2290 | C DO 250 I = 1,N |
---|
| 2291 | C WM(J) = WM(J) + ONE |
---|
| 2292 | C 250 J = J + (N + 1) |
---|
| 2293 | DO 250 I = 1,NVAR |
---|
| 2294 | 250 WM(2+LU_DIAG(I)) = WM(2+LU_DIAG(I)) + ONE |
---|
| 2295 | C DO LU DECOMPOSITION ON P. -------------------------------------------- |
---|
| 2296 | C CALL DGEFA (WM(3), N, N, IWM(21), IER) |
---|
| 2297 | CALL KppDecomp (WM(3), IER) |
---|
| 2298 | IF (IER .NE. 0) THEN |
---|
| 2299 | IERPJ = 1 |
---|
| 2300 | PRINT*,"Singular Matrix" |
---|
| 2301 | STOP |
---|
| 2302 | END IF |
---|
| 2303 | RETURN |
---|
| 2304 | C IF MITER = 3, CONSTRUCT A DIAGONAL APPROXIMATION TO J AND P. --------- |
---|
| 2305 | 300 WM(2) = HL0 |
---|
| 2306 | R = EL0*0.1D0 |
---|
| 2307 | DO 310 I = 1,N |
---|
| 2308 | 310 Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2)) |
---|
| 2309 | CALL FUNC_CHEM (NEQ, TN, Y, PAR, WM(3)) |
---|
| 2310 | NFE = NFE + 1 |
---|
| 2311 | DO 320 I = 1,N |
---|
| 2312 | R0 = H*SAVF(I) - YH(I,2) |
---|
| 2313 | DI = 0.1D0*R0 - H*(WM(I+2) - SAVF(I)) |
---|
| 2314 | WM(I+2) = 1.0D0 |
---|
| 2315 | IF (ABS(R0) .LT. UROUND/EWT(I)) GO TO 320 |
---|
| 2316 | IF (ABS(DI) .EQ. ZERO) GO TO 330 |
---|
| 2317 | WM(I+2) = 0.1D0*R0/DI |
---|
| 2318 | 320 CONTINUE |
---|
| 2319 | RETURN |
---|
| 2320 | 330 IERPJ = 1 |
---|
| 2321 | RETURN |
---|
| 2322 | C IF MITER = 4, CALL JAC AND MULTIPLY BY SCALAR. ----------------------- |
---|
| 2323 | 400 ML = IWM(1) |
---|
| 2324 | MU = IWM(2) |
---|
| 2325 | ML3 = ML + 3 |
---|
| 2326 | MBAND = ML + MU + 1 |
---|
| 2327 | MEBAND = MBAND + ML |
---|
| 2328 | LENP = MEBAND*N |
---|
| 2329 | DO 410 I = 1,LENP |
---|
| 2330 | 410 WM(I+2) = ZERO |
---|
| 2331 | CALL JAC (NEQ, TN, Y, PAR, ML, MU, WM(ML3), MEBAND) |
---|
| 2332 | IF (JOPT .EQ. 1) RETURN |
---|
| 2333 | CON = -HL0 |
---|
| 2334 | DO 420 I = 1,LENP |
---|
| 2335 | 420 WM(I+2) = WM(I+2)*CON |
---|
| 2336 | GO TO 570 |
---|
| 2337 | C IF MITER = 5, MAKE MBAND CALLS TO F TO APPROXIMATE J. ---------------- |
---|
| 2338 | 500 ML = IWM(1) |
---|
| 2339 | MU = IWM(2) |
---|
| 2340 | MBAND = ML + MU + 1 |
---|
| 2341 | MBA = MIN(MBAND,N) |
---|
| 2342 | MEBAND = MBAND + ML |
---|
| 2343 | MEB1 = MEBAND - 1 |
---|
| 2344 | SRUR = WM(1) |
---|
| 2345 | FAC = VNORM (N, SAVF, EWT) |
---|
| 2346 | R0 = 1000.0D0*ABS(H)*UROUND*REAL(N)*FAC |
---|
| 2347 | IF (R0 .EQ. ZERO) R0 = ONE |
---|
| 2348 | DO 560 J = 1,MBA |
---|
| 2349 | DO 530 I = J,N,MBAND |
---|
| 2350 | YI = Y(I) |
---|
| 2351 | R = MAX(SRUR*ABS(YI),R0/EWT(I)) |
---|
| 2352 | 530 Y(I) = Y(I) + R |
---|
| 2353 | CALL FUNC_CHEM (NEQ, TN, Y, PAR, FTEM) |
---|
| 2354 | DO 550 JJ = J,N,MBAND |
---|
| 2355 | Y(JJ) = YH(JJ,1) |
---|
| 2356 | YJJ = Y(JJ) |
---|
| 2357 | R = MAX(SRUR*ABS(YJJ),R0/EWT(JJ)) |
---|
| 2358 | FAC = -HL0/R |
---|
| 2359 | I1 = MAX(JJ-MU,1) |
---|
| 2360 | I2 = MIN(JJ+ML,N) |
---|
| 2361 | II = JJ*MEB1 - ML + 2 |
---|
| 2362 | DO 540 I = I1,I2 |
---|
| 2363 | 540 WM(II+I) = (FTEM(I) - SAVF(I))*FAC |
---|
| 2364 | 550 CONTINUE |
---|
| 2365 | 560 CONTINUE |
---|
| 2366 | NFE = NFE + MBA |
---|
| 2367 | IF (JOPT .EQ. 1) RETURN |
---|
| 2368 | C ADD IDENTITY MATRIX. ------------------------------------------------- |
---|
| 2369 | 570 II = MBAND + 2 |
---|
| 2370 | DO 580 I = 1,N |
---|
| 2371 | WM(II) = WM(II) + ONE |
---|
| 2372 | 580 II = II + MEBAND |
---|
| 2373 | C DO LU DECOMPOSITION OF P. -------------------------------------------- |
---|
| 2374 | CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) |
---|
| 2375 | IF (IER .NE. 0) IERPJ = 1 |
---|
| 2376 | RETURN |
---|
| 2377 | C----------------------- END OF SUBROUTINE PREPJ ----------------------- |
---|
| 2378 | END |
---|
| 2379 | SUBROUTINE PREPDF (NEQ, Y, SRUR, SAVF, FTEM, DFDP, PAR, |
---|
| 2380 | 1 F, DF, JPAR) |
---|
| 2381 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 2382 | EXTERNAL F, DF |
---|
| 2383 | DIMENSION NEQ(*), Y(*), SAVF(*), FTEM(*), DFDP(*), PAR(*) |
---|
| 2384 | COMMON /ODE001/ ROWND, ROWNS(173), |
---|
| 2385 | 1 RDUM1(43), TN, RDUM2, |
---|
| 2386 | 2 IOWND1(14), IOWNS(4), |
---|
| 2387 | 3 IDUM1(10), MITER, IDUM2(4), N, IDUM3(2), NFE, IDUM4(2) |
---|
| 2388 | COMMON /ODE002/ RDUM3(3), |
---|
| 2389 | 1 IOWND2(3), IDUM5(2), NDFE, IDUM6, IDF, IDUM7(3) |
---|
| 2390 | C----------------------------------------------------------------------- |
---|
| 2391 | C PREPDF IS CALLED BY SPRIME AND STESA TO COMPUTE THE INHOMOGENEITY |
---|
| 2392 | C VECTORS DF(I)/DP(JPAR). HERE DF/DP IS COMPUTED BY THE USER-SUPPLIED |
---|
| 2393 | C ROUTINE DF IF IDF = 1, OR BY FINITE DIFFERENCING IF IDF = 0. |
---|
| 2394 | C |
---|
| 2395 | C IN ADDITION TO VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION WITH |
---|
| 2396 | C PREPDF USES THE FOLLOWING.. |
---|
| 2397 | C Y = REAL ARRAY OF LENGTH NYH CONTAINING DEPENDENT VARIABLES. |
---|
| 2398 | C PREPDF USES ONLY THE FIRST N ENTRIES OF Y(*). |
---|
| 2399 | C SRUR = SQRT(UROUND) (= WM(1)). |
---|
| 2400 | C SAVF = REAL ARRAY OF LENGTH N CONTAINING DERIVATIVES DY/DT. |
---|
| 2401 | C FTEM = REAL ARRAY OF LENGTH N USED TO TEMPORARILY STORE DY/DT FOR |
---|
| 2402 | C NUMERICAL DIFFERENTIATION. |
---|
| 2403 | C DFDP = REAL ARRAY OF LENGTH N USED TO STORE DF(I)/DP(JPAR), I = 1,N. |
---|
| 2404 | C PAR = REAL ARRAY OF LENGTH NPAR CONTAINING EQUATION PARAMETERS |
---|
| 2405 | C OF INTEREST. |
---|
| 2406 | C JPAR = INPUT PARAMETER, 2 .LE. JPAR .LE. NSV, DESIGNATING THE |
---|
| 2407 | C APPROPRIATE SOLUTION VECTOR CORRESPONDING TO PAR(JPAR). |
---|
| 2408 | C THIS ROUTINE ALSO USES THE COMMON VARIABLES TN, MITER, N, NFE, NDFE, |
---|
| 2409 | C AND IDF. |
---|
| 2410 | C----------------------------------------------------------------------- |
---|
| 2411 | NDFE = NDFE + 1 |
---|
| 2412 | IDF1 = IDF + 1 |
---|
| 2413 | GO TO (100, 200), IDF1 |
---|
| 2414 | C IDF = 0, CALL F TO APPROXIMATE DFDP. --------------------------------- |
---|
| 2415 | 100 RPAR = PAR(JPAR) |
---|
| 2416 | R = MAX(SRUR*ABS(RPAR),SRUR) |
---|
| 2417 | PAR(JPAR) = RPAR + R |
---|
| 2418 | FAC = 1.0D0/R |
---|
| 2419 | CALL F (NEQ, TN, Y, PAR, FTEM) |
---|
| 2420 | DO 110 I = 1,N |
---|
| 2421 | 110 DFDP(I) = (FTEM(I) - SAVF(I))*FAC |
---|
| 2422 | PAR(JPAR) = RPAR |
---|
| 2423 | NFE = NFE + 1 |
---|
| 2424 | RETURN |
---|
| 2425 | C IDF = 1, CALL USER SUPPLIED DF. -------------------------------------- |
---|
| 2426 | 200 DO 210 I = 1,N |
---|
| 2427 | 210 DFDP(I) = 0.0D0 |
---|
| 2428 | CALL DF (NEQ, TN, Y, PAR, DFDP, JPAR) |
---|
| 2429 | RETURN |
---|
| 2430 | C -------------------- END OF SUBROUTINE PREPDF ------------------------ |
---|
| 2431 | END |
---|
| 2432 | SUBROUTINE INTDY (T, K, YH, NYH, DKY, IFLAG) |
---|
| 2433 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 2434 | DIMENSION YH(NYH,1), DKY(1) |
---|
| 2435 | COMMON /ODE001/ ROWND, ROWNS(173), |
---|
| 2436 | 2 RDUM1(38),H, RDUM2(2), HU, RDUM3, TN, UROUND, |
---|
| 2437 | 3 IOWND(14), IOWNS(4), |
---|
| 2438 | 4 IDUM1(8), L, IDUM2, |
---|
| 2439 | 5 IDUM3(5), N, NQ, IDUM4(4) |
---|
| 2440 | C----------------------------------------------------------------------- |
---|
| 2441 | C INTDY COMPUTES INTERPOLATED VALUES OF THE K-TH DERIVATIVE OF THE |
---|
| 2442 | C DEPENDENT VARIABLE VECTOR Y, AND STORES IT IN DKY. THIS ROUTINE |
---|
| 2443 | C IS CALLED WITHIN THE PACKAGE WITH K = 0 AND T = TOUT, BUT MAY |
---|
| 2444 | C ALSO BE CALLED BY THE USER FOR ANY K UP TO THE CURRENT ORDER. |
---|
| 2445 | C (SEE DETAILED INSTRUCTIONS IN THE USAGE DOCUMENTATION.) |
---|
| 2446 | C----------------------------------------------------------------------- |
---|
| 2447 | C THE COMPUTED VALUES IN DKY ARE GOTTEN BY INTERPOLATION USING THE |
---|
| 2448 | C NORDSIECK HISTORY ARRAY YH. THIS ARRAY CORRESPONDS UNIQUELY TO A |
---|
| 2449 | C VECTOR-VALUED POLYNOMIAL OF DEGREE NQCUR OR LESS, AND DKY IS SET |
---|
| 2450 | C TO THE K-TH DERIVATIVE OF THIS POLYNOMIAL AT T. |
---|
| 2451 | C THE FORMULA FOR DKY IS.. |
---|
| 2452 | C Q |
---|
| 2453 | C DKY(I) = SUM C(J,K) * (T - TN)**(J-K) * H**(-J) * YH(I,J+1) |
---|
| 2454 | C J=K |
---|
| 2455 | C WHERE C(J,K) = J*(J-1)*...*(J-K+1), Q = NQCUR, TN = TCUR, H = HCUR. |
---|
| 2456 | C THE QUANTITIES NQ = NQCUR, L = NQ+1, N = NEQ, TN, AND H ARE |
---|
| 2457 | C COMMUNICATED BY COMMON. THE ABOVE SUM IS DONE IN REVERSE ORDER. |
---|
| 2458 | C IFLAG IS RETURNED NEGATIVE IF EITHER K OR T IS OUT OF BOUNDS. |
---|
| 2459 | C----------------------------------------------------------------------- |
---|
| 2460 | IFLAG = 0 |
---|
| 2461 | IF (K .LT. 0 .OR. K .GT. NQ) GO TO 80 |
---|
| 2462 | TP = TN - HU*(1.0D0 + 100.0D0*UROUND) |
---|
| 2463 | IF ((T-TP)*(T-TN) .GT. 0.0D0) GO TO 90 |
---|
| 2464 | C |
---|
| 2465 | S = (T - TN)/H |
---|
| 2466 | IC = 1 |
---|
| 2467 | IF (K .EQ. 0) GO TO 15 |
---|
| 2468 | JJ1 = L - K |
---|
| 2469 | DO 10 JJ = JJ1,NQ |
---|
| 2470 | 10 IC = IC*JJ |
---|
| 2471 | 15 C = REAL(IC) |
---|
| 2472 | DO 20 I = 1,NYH |
---|
| 2473 | 20 DKY(I) = C*YH(I,L) |
---|
| 2474 | IF (K .EQ. NQ) GO TO 55 |
---|
| 2475 | JB2 = NQ - K |
---|
| 2476 | DO 50 JB = 1,JB2 |
---|
| 2477 | J = NQ - JB |
---|
| 2478 | JP1 = J + 1 |
---|
| 2479 | IC = 1 |
---|
| 2480 | IF (K .EQ. 0) GO TO 35 |
---|
| 2481 | JJ1 = JP1 - K |
---|
| 2482 | DO 30 JJ = JJ1,J |
---|
| 2483 | 30 IC = IC*JJ |
---|
| 2484 | 35 C = REAL(IC) |
---|
| 2485 | DO 40 I = 1,NYH |
---|
| 2486 | 40 DKY(I) = C*YH(I,JP1) + S*DKY(I) |
---|
| 2487 | 50 CONTINUE |
---|
| 2488 | IF (K .EQ. 0) RETURN |
---|
| 2489 | 55 R = H**(-K) |
---|
| 2490 | DO 60 I = 1,NYH |
---|
| 2491 | 60 DKY(I) = R*DKY(I) |
---|
| 2492 | RETURN |
---|
| 2493 | C |
---|
| 2494 | 80 CALL XERR('INTDY-- K (=I1) ILLEGAL', |
---|
| 2495 | 1 51, 1, 1, K, 0, 0, ZERO,ZERO) |
---|
| 2496 | IFLAG = -1 |
---|
| 2497 | RETURN |
---|
| 2498 | 90 CALL XERR ('INTDY-- T (=R1) ILLEGAL', |
---|
| 2499 | 1 52, 1, 0, 0, 0, 1, T, ZERO) |
---|
| 2500 | CALL XERR('T NOT IN INTERVAL TCUR - HU (= R1) TO TCUR (=R2)', |
---|
| 2501 | 1 52, 1, 0, 0, 0, 2, TP, TN) |
---|
| 2502 | IFLAG = -2 |
---|
| 2503 | RETURN |
---|
| 2504 | C----------------------- END OF SUBROUTINE INTDY ----------------------- |
---|
| 2505 | END |
---|
| 2506 | SUBROUTINE STESA (NEQ, Y, NROW, NCOL, YH, WM, IWM, EWT, SAVF, |
---|
| 2507 | 1 ACOR, PAR, NRS, F, JAC, DF, PJAC, PDF, KppSolve) |
---|
| 2508 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 2509 | EXTERNAL F, JAC, DF, PJAC, PDF, KppSolve |
---|
| 2510 | DIMENSION NEQ(*), Y(NROW,*), YH(NROW,NCOL,*), WM(*), IWM(*), |
---|
| 2511 | 1 EWT(NROW,*), SAVF(*), ACOR(NROW,*), PAR(*), NRS(*) |
---|
| 2512 | PARAMETER (ONE=1.0D0,ZERO=0.0D0) |
---|
| 2513 | COMMON /ODE001/ ROWND, ROWNS(173), |
---|
| 2514 | 1 TESCO(3,12), RDUM1, EL0, H, RDUM2(4), TN, RDUM3, |
---|
| 2515 | 2 IOWND1(14), IOWNS(4), |
---|
| 2516 | 3 IALTH, LMAX, IDUM1, IERPJ, IERSL, JCUR, IDUM2, KFLAG, L, IDUM3, |
---|
| 2517 | 4 MITER, IDUM4(4), N, NQ, IDUM5, NFE, IDUM6(2) |
---|
| 2518 | COMMON /ODE002/ DUPS, DSMS, DDNS, |
---|
| 2519 | 1 IOWND2(3), IDUM7, NSV, IDUM8(2), IDF, IDUM9, JOPT, KFLAGS |
---|
| 2520 | C----------------------------------------------------------------------- |
---|
| 2521 | C STESA IS CALLED BY STODE TO PERFORM AN EXPLICIT CALCULATION FOR THE |
---|
| 2522 | C FIRST-ORDER SENSITIVITY COEFFICIENTS DY(I)/DP(J), I = 1,N; J = 1,NPAR. |
---|
| 2523 | C |
---|
| 2524 | C IN ADDITION TO THE VARIABLES DESCRIBED PREVIOUSLY, COMMUNICATION |
---|
| 2525 | C WITH STESA USES THE FOLLOWING.. |
---|
| 2526 | C Y = AN NROW (=N) BY NCOL (=NSV) REAL ARRAY CONTAINING THE |
---|
| 2527 | C CORRECTED DEPENDENT VARIABLES ON OUTPUT.. |
---|
| 2528 | C Y(I,1) , I = 1,N = STATE VARIABLES (INPUT); |
---|
| 2529 | C Y(I,J) , I = 1,N , J = 2,NSV , |
---|
| 2530 | C = SENSITIVITY COEFFICIENTS, DY(I)/DP(J). |
---|
| 2531 | C YH = AN N BY NSV BY LMAX REAL ARRAY CONTAINING THE PREDICTED |
---|
| 2532 | C DEPENDENT VARIABLES AND THEIR APPROXIMATE SCALED DERIVATIVES. |
---|
| 2533 | C SAVF = A REAL ARRAY OF LENGTH N USED TO STORE FIRST DERIVATIVES |
---|
| 2534 | C OF DEPENDENT VARIABLES IF MITER = 2 OR 5. |
---|
| 2535 | C PAR = A REAL ARRAY OF LENGTH NPAR CONTAINING THE EQUATION |
---|
| 2536 | C PARAMETERS OF INTEREST. |
---|
| 2537 | C NRS = AN INTEGER ARRAY OF LENGTH NPAR + 1 CONTAINING THE NUMBER |
---|
| 2538 | C OF REPEATED STEPS (KFLAGS .LT. 0) DUE TO THE SENSITIVITY |
---|
| 2539 | C CALCULATIONS.. |
---|
| 2540 | C NRS(1) = TOTAL NUMBER OF REPEATED STEPS |
---|
| 2541 | C NRS(I) , I = 2,NPAR = NUMBER OF REPEATED STEPS DUE |
---|
| 2542 | C TO PARAMETER I. |
---|
| 2543 | C NSV = NUMBER OF SOLUTION VECTORS = NPAR + 1. |
---|
| 2544 | C KFLAGS = LOCAL ERROR TEST FLAG, = 0 IF TEST PASSES, .LT. 0 IF TEST |
---|
| 2545 | C FAILS, AND STEP NEEDS TO BE REPEATED. ERROR TEST IS APPLIED |
---|
| 2546 | C TO EACH SOLUTION VECTOR INDEPENDENTLY. |
---|
| 2547 | C DUPS, DSMS, DDNS = REAL SCALARS USED FOR COMPUTING RHUP, RHSM, RHDN, |
---|
| 2548 | C ON RETURN TO STODE (IALTH .EQ. 1). |
---|
| 2549 | C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, TN, IALTH, LMAX, |
---|
| 2550 | C IERPJ, IERSL, JCUR, KFLAG, L, MITER, N, NQ, NFE, AND JOPT. |
---|
| 2551 | C----------------------------------------------------------------------- |
---|
| 2552 | DUPS = ZERO |
---|
| 2553 | DSMS = ZERO |
---|
| 2554 | DDNS = ZERO |
---|
| 2555 | HL0 = H*EL0 |
---|
| 2556 | EL0I = ONE/EL0 |
---|
| 2557 | TI2 = ONE/TESCO(2,NQ) |
---|
| 2558 | TI3 = ONE/TESCO(3,NQ) |
---|
| 2559 | C IF MITER = 2 OR 5 (OR IDF = 0), SUPPLY DERIVATIVES AT CORRECTED |
---|
| 2560 | C Y(*,1) VALUES FOR NUMERICAL DIFFERENTIATION IN PJAC AND/OR PDF. |
---|
| 2561 | IF (MITER .EQ. 2 .OR. MITER .EQ. 5 .OR. IDF .EQ. 0) GO TO 10 |
---|
| 2562 | GO TO 15 |
---|
| 2563 | 10 CALL F (NEQ, TN, Y, PAR, SAVF) |
---|
| 2564 | NFE = NFE + 1 |
---|
| 2565 | C IF JCUR = 0, UPDATE THE JACOBIAN MATRIX. |
---|
| 2566 | C IF MITER = 5, LOAD CORRECTED Y(*,1) VALUES INTO Y(*,2). |
---|
| 2567 | 15 IF (JCUR .EQ. 1) GO TO 30 |
---|
| 2568 | IF (MITER .NE. 5) GO TO 25 |
---|
| 2569 | DO 20 I = 1,N |
---|
| 2570 | 20 Y(I,2) = Y(I,1) |
---|
| 2571 | 25 CALL PJAC (NEQ, Y, Y(1,2), N, WM, IWM, EWT, SAVF, ACOR(1,2), |
---|
| 2572 | 1 PAR, F, JAC, JOPT) |
---|
| 2573 | IF (IERPJ .NE. 0) RETURN |
---|
| 2574 | C----------------------------------------------------------------------- |
---|
| 2575 | C THIS IS A LOOPING POINT FOR THE SENSITIVITY CALCULATIONS. |
---|
| 2576 | C----------------------------------------------------------------------- |
---|
| 2577 | C FOR EACH PARAMETER PAR(*), A SENSITIVITY SOLUTION VECTOR IS COMPUTED |
---|
| 2578 | C USING THE SAME STEP SIZE (H) AND ORDER (NQ) AS IN STODE. |
---|
| 2579 | C A LOCAL ERROR TEST IS APPLIED INDEPENDENTLY TO EACH SOLUTION VECTOR. |
---|
| 2580 | C----------------------------------------------------------------------- |
---|
| 2581 | 30 DO 100 J = 2,NSV |
---|
| 2582 | JPAR = J - 1 |
---|
| 2583 | C EVALUATE INHOMOGENEITY TERM, TEMPORARILY LOAD INTO Y(*,JPAR+1). ------ |
---|
| 2584 | CALL PDF(NEQ, Y, WM, SAVF, ACOR(1,J), Y(1,J), PAR, |
---|
| 2585 | 1 F, DF, JPAR) |
---|
| 2586 | C----------------------------------------------------------------------- |
---|
| 2587 | C LOAD RHS OF SENSITIVITY SOLUTION (CORRECTOR) EQUATION.. |
---|
| 2588 | C |
---|
| 2589 | C RHS = DY/DP - EL(1)*H*D(DY/DP)/DT + EL(1)*H*DF/DP |
---|
| 2590 | C |
---|
| 2591 | C----------------------------------------------------------------------- |
---|
| 2592 | DO 40 I = 1,N |
---|
| 2593 | 40 Y(I,J) = YH(I,J,1) - EL0*YH(I,J,2) + HL0*Y(I,J) |
---|
| 2594 | C----------------------------------------------------------------------- |
---|
| 2595 | C KppSolve CORRECTOR EQUATION: THE SOLUTIONS ARE LOCATED IN Y(*,JPAR+1). |
---|
| 2596 | C THE EXPLICIT FORMULA IS.. |
---|
| 2597 | C |
---|
| 2598 | C (I - EL(1)*H*JAC) * DY/DP(CORRECTED) = RHS |
---|
| 2599 | C |
---|
| 2600 | C----------------------------------------------------------------------- |
---|
| 2601 | CALL KppSolve (WM, IWM, Y(1,J), DUM) |
---|
| 2602 | IF (IERSL .NE. 0) RETURN |
---|
| 2603 | C ESTIMATE LOCAL TRUNCATION ERROR. ------------------------------------- |
---|
| 2604 | DO 50 I = 1,N |
---|
| 2605 | 50 ACOR(I,J) = (Y(I,J) - YH(I,J,1))*EL0I |
---|
| 2606 | ERR = VNORM(N, ACOR(1,J), EWT(1,J))*TI2 |
---|
| 2607 | IF (ERR .GT. ONE) GO TO 200 |
---|
| 2608 | C----------------------------------------------------------------------- |
---|
| 2609 | C LOCAL ERROR TEST PASSED. SET KFLAGS TO 0 TO INDICATE THIS. |
---|
| 2610 | C IF IALTH = 1, COMPUTE DSMS, DDNS, AND DUPS (IF L .LT. LMAX). |
---|
| 2611 | C----------------------------------------------------------------------- |
---|
| 2612 | KFLAGS = 0 |
---|
| 2613 | IF (IALTH .GT. 1) GO TO 100 |
---|
| 2614 | IF (L .EQ. LMAX) GO TO 70 |
---|
| 2615 | DO 60 I= 1,N |
---|
| 2616 | 60 Y(I,J) = ACOR(I,J) - YH(I,J,LMAX) |
---|
| 2617 | DUPS = MAX(DUPS,VNORM(N,Y(1,J),EWT(1,J))*TI3) |
---|
| 2618 | 70 DSMS = MAX(DSMS,ERR) |
---|
| 2619 | 100 CONTINUE |
---|
| 2620 | RETURN |
---|
| 2621 | C----------------------------------------------------------------------- |
---|
| 2622 | C THIS SECTION IS REACHED IF THE ERROR TOLERANCE FOR SENSITIVITY |
---|
| 2623 | C SOLUTION VECTOR JPAR HAS BEEN VIOLATED. KFLAGS IS MADE NEGATIVE TO |
---|
| 2624 | C INDICATE THIS. IF KFLAGS = -1, SET KFLAG EQUAL TO ZERO SO THAT KFLAG |
---|
| 2625 | C IS SET TO -1 ON RETURN TO STODE BEFORE REPEATING THE STEP. |
---|
| 2626 | C INCREMENT NRS(1) (= TOTAL NUMBER OF REPEATED STEPS DUE TO ALL |
---|
| 2627 | C SENSITIVITY SOLUTION VECTORS) BY ONE. |
---|
| 2628 | C INCREMENT NRS(JPAR+1) (= TOTAL NUMBER OF REPEATED STEPS DUE TO |
---|
| 2629 | C SOLUTION VECTOR JPAR+1) BY ONE. |
---|
| 2630 | C LOAD DSMS FOR RH CALCULATION IN STODE. |
---|
| 2631 | C----------------------------------------------------------------------- |
---|
| 2632 | 200 KFLAGS = KFLAGS - 1 |
---|
| 2633 | IF (KFLAGS .EQ. -1) KFLAG = 0 |
---|
| 2634 | NRS(1) = NRS(1) + 1 |
---|
| 2635 | NRS(J) = NRS(J) + 1 |
---|
| 2636 | DSMS = ERR |
---|
| 2637 | RETURN |
---|
| 2638 | C------------------------ END OF SUBROUTINE STESA ---------------------- |
---|
| 2639 | END |
---|
| 2640 | SUBROUTINE STODE (NEQ, Y, YH, NYH, YH1, WM, IWM, EWT, SAVF, ACOR, |
---|
| 2641 | 1 PAR, NRS, F, JAC, DF, PJAC, PDF, SLVS) |
---|
| 2642 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 2643 | EXTERNAL F, JAC, DF, PJAC, PDF, SLVS |
---|
| 2644 | DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), WM(*), IWM(*), EWT(*), |
---|
| 2645 | 1 SAVF(*), ACOR(*), PAR(*), NRS(*) |
---|
| 2646 | PARAMETER (ONE=1.0D0,ZERO=0.0D0) |
---|
| 2647 | COMMON /ODE001/ ROWND, |
---|
| 2648 | 1 CONIT, CRATE, EL(13), ELCO(13,12), HOLD, RMAX, |
---|
| 2649 | 2 TESCO(3,12), CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, |
---|
| 2650 | 3 IOWND1(14), IPUP, MEO, NQNYH, NSLP, |
---|
| 2651 | 4 IALTH, LMAX, ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, |
---|
| 2652 | 5 MITER, MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU |
---|
| 2653 | COMMON /ODE002/ DUPS, DSMS, DDNS, |
---|
| 2654 | 1 IOWND2(3), ISOPT, NSV, NDFE, NSPE, IDF, IERSP, JOPT, KFLAGS |
---|
| 2655 | C----------------------------------------------------------------------- |
---|
| 2656 | C STODE PERFORMS ONE STEP OF THE INTEGRATION OF AN INITIAL VALUE |
---|
| 2657 | C PROBLEM FOR A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS. |
---|
| 2658 | C NOTE.. STODE IS INDEPENDENT OF THE VALUE OF THE ITERATION METHOD |
---|
| 2659 | C INDICATOR MITER, WHEN THIS IS .NE. 0, AND HENCE IS INDEPENDENT |
---|
| 2660 | C OF THE TYPE OF CHORD METHOD USED, OR THE JACOBIAN STRUCTURE. |
---|
| 2661 | C FOR ISOPT = 1, STODE CALLS STESA FOR SENSITIVITY CALCULATIONS. |
---|
| 2662 | C VARIABLES USED FOR COMMUNICATION WITH STESA ARE DESCRIBED IN STESA. |
---|
| 2663 | C COMMUNICATION WITH STODE IS DONE WITH THE FOLLOWING VARIABLES.. |
---|
| 2664 | C |
---|
| 2665 | C NEQ = INTEGER ARRAY CONTAINING PROBLEM SIZE IN NEQ(1), AND |
---|
| 2666 | C NUMBER OF PARAMETERS TO BE CONSIDERED IN THE SENSITIVITY |
---|
| 2667 | C ANALYSIS NEQ(2) (FOR ISOPT = 1), AND PASSED AS THE |
---|
| 2668 | C NEQ ARGUMENT IN ALL CALLS TO F, JAC, AND DF. |
---|
| 2669 | C Y = AN ARRAY OF LENGTH .GE. N USED AS THE Y ARGUMENT IN |
---|
| 2670 | C ALL CALLS TO F, JAC, AND DF. |
---|
| 2671 | C YH = AN NYH BY LMAX ARRAY CONTAINING THE DEPENDENT VARIABLES |
---|
| 2672 | C AND THEIR APPROXIMATE SCALED DERIVATIVES, WHERE |
---|
| 2673 | C LMAX = MAXORD + 1. YH(I,J+1) CONTAINS THE APPROXIMATE |
---|
| 2674 | C J-TH DERIVATIVE OF Y(I), SCALED BY H**J/FACTORIAL(J) |
---|
| 2675 | C (J = 0,1,...,NQ). ON ENTRY FOR THE FIRST STEP, THE FIRST |
---|
| 2676 | C TWO COLUMNS OF YH MUST BE SET FROM THE INITIAL VALUES. |
---|
| 2677 | C NYH = A CONSTANT INTEGER .GE. N, THE FIRST DIMENSION OF YH. |
---|
| 2678 | C THE TOTAL NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS.. |
---|
| 2679 | C NYH = N, ISOPT = 0, |
---|
| 2680 | C NYH = N * (NPAR + 1), ISOPT = 1 |
---|
| 2681 | C YH1 = A ONE-DIMENSIONAL ARRAY OCCUPYING THE SAME SPACE AS YH. |
---|
| 2682 | C EWT = AN ARRAY OF LENGTH NYH CONTAINING MULTIPLICATIVE WEIGHTS |
---|
| 2683 | C FOR LOCAL ERROR MEASUREMENTS. LOCAL ERRORS IN Y(I) ARE |
---|
| 2684 | C COMPARED TO 1.0/EWT(I) IN VARIOUS ERROR TESTS. |
---|
| 2685 | C SAVF = AN ARRAY OF WORKING STORAGE, OF LENGTH N. |
---|
| 2686 | C ALSO USED FOR INPUT OF YH(*,MAXORD+2) WHEN JSTART = -1 |
---|
| 2687 | C AND MAXORD .LT. THE CURRENT ORDER NQ. |
---|
| 2688 | C ACOR = A WORK ARRAY OF LENGTH NYH, USED FOR THE ACCUMULATED |
---|
| 2689 | C CORRECTIONS. ON A SUCCESSFUL RETURN, ACOR(I) CONTAINS |
---|
| 2690 | C THE ESTIMATED ONE-STEP LOCAL ERROR IN Y(I). |
---|
| 2691 | C WM,IWM = REAL AND INTEGER WORK ARRAYS ASSOCIATED WITH MATRIX |
---|
| 2692 | C OPERATIONS IN CHORD ITERATION (MITER .NE. 0). |
---|
| 2693 | C PJAC = NAME OF ROUTINE TO EVALUATE AND PREPROCESS JACOBIAN MATRIX |
---|
| 2694 | C AND P = I - H*EL0*JAC, IF A CHORD METHOD IS BEING USED. |
---|
| 2695 | C IF ISOPT = 1, PJAC CAN BE CALLED TO CALCULATE JAC BY |
---|
| 2696 | C SETTING JOPT = 1. |
---|
| 2697 | C SLVS = NAME OF ROUTINE TO KppSolve LINEAR SYSTEM IN CHORD ITERATION. |
---|
| 2698 | C CCMAX = MAXIMUM RELATIVE CHANGE IN H*EL0 BEFORE PJAC IS CALLED. |
---|
| 2699 | C H = THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. |
---|
| 2700 | C H IS ALTERED BY THE ERROR CONTROL ALGORITHM DURING THE |
---|
| 2701 | C PROBLEM. H CAN BE EITHER POSITIVE OR NEGATIVE, BUT ITS |
---|
| 2702 | C SIGN MUST REMAIN CONSTANT THROUGHOUT THE PROBLEM. |
---|
| 2703 | C HMIN = THE MINIMUM ABSOLUTE VALUE OF THE STEP SIZE H TO BE USED. |
---|
| 2704 | C HMXI = INVERSE OF THE MAXIMUM ABSOLUTE VALUE OF H TO BE USED. |
---|
| 2705 | C HMXI = 0.0 IS ALLOWED AND CORRESPONDS TO AN INFINITE HMAX. |
---|
| 2706 | C HMIN AND HMXI MAY BE CHANGED AT ANY TIME, BUT WILL NOT |
---|
| 2707 | C TAKE EFFECT UNTIL THE NEXT CHANGE OF H IS CONSIDERED. |
---|
| 2708 | C TN = THE INDEPENDENT VARIABLE. TN IS UPDATED ON EACH STEP TAKEN. |
---|
| 2709 | C JSTART = AN INTEGER USED FOR INPUT ONLY, WITH THE FOLLOWING |
---|
| 2710 | C VALUES AND MEANINGS.. |
---|
| 2711 | C 0 PERFORM THE FIRST STEP. |
---|
| 2712 | C .GT.0 TAKE A NEW STEP CONTINUING FROM THE LAST. |
---|
| 2713 | C -1 TAKE THE NEXT STEP WITH A NEW VALUE OF H, MAXORD, |
---|
| 2714 | C N, METH, OR MITER. |
---|
| 2715 | C -2 TAKE THE NEXT STEP WITH A NEW VALUE OF H, |
---|
| 2716 | C BUT WITH OTHER INPUTS UNCHANGED. |
---|
| 2717 | C ON RETURN, JSTART IS SET TO 1 TO FACILITATE CONTINUATION. |
---|
| 2718 | C KFLAG = A COMPLETION CODE WITH THE FOLLOWING MEANINGS.. |
---|
| 2719 | C 0 THE STEP WAS SUCCESFUL. |
---|
| 2720 | C -1 THE REQUESTED ERROR COULD NOT BE ACHIEVED. |
---|
| 2721 | C -2 CORRECTOR CONVERGENCE COULD NOT BE ACHIEVED. |
---|
| 2722 | C -3 FATAL ERROR IN PJAC, OR SLVS, (OR STESA). |
---|
| 2723 | C A RETURN WITH KFLAG = -1 OR -2 MEANS EITHER |
---|
| 2724 | C ABS(H) = HMIN OR 10 CONSECUTIVE FAILURES OCCURRED. |
---|
| 2725 | C ON A RETURN WITH KFLAG NEGATIVE, THE VALUES OF TN AND |
---|
| 2726 | C THE YH ARRAY ARE AS OF THE BEGINNING OF THE LAST |
---|
| 2727 | C STEP, AND H IS THE LAST STEP SIZE ATTEMPTED. |
---|
| 2728 | C MAXORD = THE MAXIMUM ORDER OF INTEGRATION METHOD TO BE ALLOWED. |
---|
| 2729 | C MAXCOR = THE MAXIMUM NUMBER OF CORRECTOR ITERATIONS ALLOWED. |
---|
| 2730 | C (= 3, IF ISOPT = 0) |
---|
| 2731 | C (= 4, IF ISOPT = 1) |
---|
| 2732 | C MSBP = MAXIMUM NUMBER OF STEPS BETWEEN PJAC CALLS (MITER .GT. 0). |
---|
| 2733 | C IF ISOPT = 1, PJAC IS CALLED AT LEAST ONCE EVERY STEP. |
---|
| 2734 | C MXNCF = MAXIMUM NUMBER OF CONVERGENCE FAILURES ALLOWED. |
---|
| 2735 | C METH/MITER = THE METHOD FLAGS. SEE DESCRIPTION IN DRIVER. |
---|
| 2736 | C N = THE NUMBER OF FIRST-ORDER MODEL DIFFERENTIAL EQUATIONS. |
---|
| 2737 | C----------------------------------------------------------------------- |
---|
| 2738 | KFLAG = 0 |
---|
| 2739 | KFLAGS = 0 |
---|
| 2740 | TOLD = TN |
---|
| 2741 | NCF = 0 |
---|
| 2742 | IERPJ = 0 |
---|
| 2743 | IERSL = 0 |
---|
| 2744 | JCUR = 0 |
---|
| 2745 | ICF = 0 |
---|
| 2746 | IF (JSTART .GT. 0) GO TO 200 |
---|
| 2747 | IF (JSTART .EQ. -1) GO TO 100 |
---|
| 2748 | IF (JSTART .EQ. -2) GO TO 160 |
---|
| 2749 | C----------------------------------------------------------------------- |
---|
| 2750 | C ON THE FIRST CALL, THE ORDER IS SET TO 1, AND OTHER VARIABLES ARE |
---|
| 2751 | C INITIALIZED. RMAX IS THE MAXIMUM RATIO BY WHICH H CAN BE INCREASED |
---|
| 2752 | C IN A SINGLE STEP. IT IS INITIALLY 1.E4 TO COMPENSATE FOR THE SMALL |
---|
| 2753 | C INITIAL H, BUT THEN IS NORMALLY EQUAL TO 10. IF A FAILURE |
---|
| 2754 | C OCCURS (IN CORRECTOR CONVERGENCE OR ERROR TEST), RMAX IS SET AT 2 |
---|
| 2755 | C FOR THE NEXT INCREASE. |
---|
| 2756 | C THESE COMPUTATIONS CONSIDER ONLY THE ORIGINAL SOLUTION VECTOR. |
---|
| 2757 | C THE SENSITIVITY SOLUTION VECTORS ARE CONSIDERED IN STESA (ISOPT = 1). |
---|
| 2758 | C----------------------------------------------------------------------- |
---|
| 2759 | LMAX = MAXORD + 1 |
---|
| 2760 | NQ = 1 |
---|
| 2761 | L = 2 |
---|
| 2762 | IALTH = 2 |
---|
| 2763 | RMAX = 10000.0D0 |
---|
| 2764 | RC = ZERO |
---|
| 2765 | EL0 = ONE |
---|
| 2766 | CRATE = 0.7D0 |
---|
| 2767 | DELP = ZERO |
---|
| 2768 | HOLD = H |
---|
| 2769 | MEO = METH |
---|
| 2770 | NSLP = 0 |
---|
| 2771 | IPUP = MITER |
---|
| 2772 | IRET = 3 |
---|
| 2773 | GO TO 140 |
---|
| 2774 | C----------------------------------------------------------------------- |
---|
| 2775 | C THE FOLLOWING BLOCK HANDLES PRELIMINARIES NEEDED WHEN JSTART = -1. |
---|
| 2776 | C IPUP IS SET TO MITER TO FORCE A MATRIX UPDATE. |
---|
| 2777 | C IF AN ORDER INCREASE IS ABOUT TO BE CONSIDERED (IALTH = 1), |
---|
| 2778 | C IALTH IS RESET TO 2 TO POSTPONE CONSIDERATION ONE MORE STEP. |
---|
| 2779 | C IF THE CALLER HAS CHANGED METH, CFODE IS CALLED TO RESET |
---|
| 2780 | C THE COEFFICIENTS OF THE METHOD. |
---|
| 2781 | C IF THE CALLER HAS CHANGED MAXORD TO A VALUE LESS THAN THE CURRENT |
---|
| 2782 | C ORDER NQ, NQ IS REDUCED TO MAXORD, AND A NEW H CHOSEN ACCORDINGLY. |
---|
| 2783 | C IF H IS TO BE CHANGED, YH MUST BE RESCALED. |
---|
| 2784 | C IF H OR METH IS BEING CHANGED, IALTH IS RESET TO L = NQ + 1 |
---|
| 2785 | C TO PREVENT FURTHER CHANGES IN H FOR THAT MANY STEPS. |
---|
| 2786 | C----------------------------------------------------------------------- |
---|
| 2787 | 100 IPUP = MITER |
---|
| 2788 | LMAX = MAXORD + 1 |
---|
| 2789 | IF (IALTH .EQ. 1) IALTH = 2 |
---|
| 2790 | IF (METH .EQ. MEO) GO TO 110 |
---|
| 2791 | CALL CFODE (METH, ELCO, TESCO) |
---|
| 2792 | MEO = METH |
---|
| 2793 | IF (NQ .GT. MAXORD) GO TO 120 |
---|
| 2794 | IALTH = L |
---|
| 2795 | IRET = 1 |
---|
| 2796 | GO TO 150 |
---|
| 2797 | 110 IF (NQ .LE. MAXORD) GO TO 160 |
---|
| 2798 | 120 NQ = MAXORD |
---|
| 2799 | L = LMAX |
---|
| 2800 | DO 125 I = 1,L |
---|
| 2801 | 125 EL(I) = ELCO(I,NQ) |
---|
| 2802 | NQNYH = NQ*NYH |
---|
| 2803 | RC = RC*EL(1)/EL0 |
---|
| 2804 | EL0 = EL(1) |
---|
| 2805 | CONIT = 0.5D0/REAL(NQ+2) |
---|
| 2806 | DDN = VNORM (N, SAVF, EWT)/TESCO(1,L) |
---|
| 2807 | EXDN = ONE/REAL(L) |
---|
| 2808 | RHDN = ONE/(1.3D0*DDN**EXDN + 0.0000013D0) |
---|
| 2809 | RH = MIN(RHDN,ONE) |
---|
| 2810 | IREDO = 3 |
---|
| 2811 | IF (H .EQ. HOLD) GO TO 170 |
---|
| 2812 | RH = MIN(RH,ABS(H/HOLD)) |
---|
| 2813 | H = HOLD |
---|
| 2814 | GO TO 175 |
---|
| 2815 | C----------------------------------------------------------------------- |
---|
| 2816 | C CFODE IS CALLED TO GET ALL THE INTEGRATION COEFFICIENTS FOR THE |
---|
| 2817 | C CURRENT METH. THEN THE EL VECTOR AND RELATED CONSTANTS ARE RESET |
---|
| 2818 | C WHENEVER THE ORDER NQ IS CHANGED, OR AT THE START OF THE PROBLEM. |
---|
| 2819 | C----------------------------------------------------------------------- |
---|
| 2820 | 140 CALL CFODE (METH, ELCO, TESCO) |
---|
| 2821 | 150 DO 155 I = 1,L |
---|
| 2822 | 155 EL(I) = ELCO(I,NQ) |
---|
| 2823 | NQNYH = NQ*NYH |
---|
| 2824 | RC = RC*EL(1)/EL0 |
---|
| 2825 | EL0 = EL(1) |
---|
| 2826 | CONIT = 0.5D0/REAL(NQ+2) |
---|
| 2827 | GO TO (160, 170, 200), IRET |
---|
| 2828 | C----------------------------------------------------------------------- |
---|
| 2829 | C IF H IS BEING CHANGED, THE H RATIO RH IS CHECKED AGAINST |
---|
| 2830 | C RMAX, HMIN, AND HMXI, AND THE YH ARRAY RESCALED. IALTH IS SET TO |
---|
| 2831 | C L = NQ + 1 TO PREVENT A CHANGE OF H FOR THAT MANY STEPS, UNLESS |
---|
| 2832 | C FORCED BY A CONVERGENCE OR ERROR TEST FAILURE. |
---|
| 2833 | C----------------------------------------------------------------------- |
---|
| 2834 | 160 IF (H .EQ. HOLD) GO TO 200 |
---|
| 2835 | RH = H/HOLD |
---|
| 2836 | H = HOLD |
---|
| 2837 | IREDO = 3 |
---|
| 2838 | GO TO 175 |
---|
| 2839 | 170 RH = MAX(RH,HMIN/ABS(H)) |
---|
| 2840 | 175 RH = MIN(RH,RMAX) |
---|
| 2841 | RH = RH/MAX(ONE,ABS(H)*HMXI*RH) |
---|
| 2842 | R = ONE |
---|
| 2843 | DO 180 J = 2,L |
---|
| 2844 | R = R*RH |
---|
| 2845 | DO 180 I = 1,NYH |
---|
| 2846 | 180 YH(I,J) = YH(I,J)*R |
---|
| 2847 | H = H*RH |
---|
| 2848 | RC = RC*RH |
---|
| 2849 | IALTH = L |
---|
| 2850 | IF (IREDO .EQ. 0) GO TO 690 |
---|
| 2851 | C----------------------------------------------------------------------- |
---|
| 2852 | C THIS SECTION COMPUTES THE PREDICTED VALUES BY EFFECTIVELY |
---|
| 2853 | C MULTIPLYING THE YH ARRAY BY THE PASCAL TRIANGLE MATRIX. |
---|
| 2854 | C RC IS THE RATIO OF NEW TO OLD VALUES OF THE COEFFICIENT H*EL(1). |
---|
| 2855 | C WHEN RC DIFFERS FROM 1 BY MORE THAN CCMAX, IPUP IS SET TO MITER |
---|
| 2856 | C TO FORCE PJAC TO BE CALLED, IF A JACOBIAN IS INVOLVED. |
---|
| 2857 | C IN ANY CASE, PJAC IS CALLED AT LEAST EVERY MSBP STEPS FOR ISOPT = 0, |
---|
| 2858 | C AND AT LEAST ONCE EVERY STEP FOR ISOPT = 1. |
---|
| 2859 | C----------------------------------------------------------------------- |
---|
| 2860 | 200 IF (ABS(RC-ONE) .GT. CCMAX) IPUP = MITER |
---|
| 2861 | IF (NST .GE. NSLP+MSBP) IPUP = MITER |
---|
| 2862 | TN = TN + H |
---|
| 2863 | I1 = NQNYH + 1 |
---|
| 2864 | DO 215 JB = 1,NQ |
---|
| 2865 | I1 = I1 - NYH |
---|
| 2866 | DO 210 I = I1,NQNYH |
---|
| 2867 | 210 YH1(I) = YH1(I) + YH1(I+NYH) |
---|
| 2868 | 215 CONTINUE |
---|
| 2869 | C----------------------------------------------------------------------- |
---|
| 2870 | C UP TO MAXCOR CORRECTOR ITERATIONS ARE TAKEN. (= 3, FOR ISOPT = 0; |
---|
| 2871 | C = 4, FOR ISOPT = 1). A CONVERGENCE TEST IS MADE ON THE R.M.S. NORM |
---|
| 2872 | C OF EACH CORRECTION, WEIGHTED BY THE ERROR WEIGHT VECTOR EWT. THE SUM |
---|
| 2873 | C OF THE CORRECTIONS IS ACCUMULATED IN THE VECTOR ACOR(I), I = 1,N. |
---|
| 2874 | C (ACOR(I), I = N+1,NYH IS LOADED IN SUBROUTINE STESA (ISOPT = 1).) |
---|
| 2875 | C THE YH ARRAY IS NOT ALTERED IN THE CORRECTOR LOOP. |
---|
| 2876 | C----------------------------------------------------------------------- |
---|
| 2877 | 220 M = 0 |
---|
| 2878 | DO 230 I = 1,N |
---|
| 2879 | 230 Y(I) = YH(I,1) |
---|
| 2880 | CALL F (NEQ, TN, Y, PAR, SAVF) |
---|
| 2881 | NFE = NFE + 1 |
---|
| 2882 | IF (IPUP .LE. 0) GO TO 250 |
---|
| 2883 | C----------------------------------------------------------------------- |
---|
| 2884 | C IF INDICATED, THE MATRIX P = I - H*EL(1)*J IS REEVALUATED AND |
---|
| 2885 | C PREPROCESSED BEFORE STARTING THE CORRECTOR ITERATION. IPUP IS SET |
---|
| 2886 | C TO 0 AS AN INDICATOR THAT THIS HAS BEEN DONE. |
---|
| 2887 | C----------------------------------------------------------------------- |
---|
| 2888 | IPUP = 0 |
---|
| 2889 | RC = ONE |
---|
| 2890 | NSLP = NST |
---|
| 2891 | CRATE = 0.7D0 |
---|
| 2892 | CALL PJAC (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, ACOR, PAR, |
---|
| 2893 | 1 F, JAC, JOPT) |
---|
| 2894 | IF (IERPJ .NE. 0) GO TO 430 |
---|
| 2895 | 250 DO 260 I = 1,N |
---|
| 2896 | 260 ACOR(I) = ZERO |
---|
| 2897 | 270 IF (MITER .NE. 0) GO TO 350 |
---|
| 2898 | C----------------------------------------------------------------------- |
---|
| 2899 | C IN THE CASE OF FUNCTIONAL ITERATION, UPDATE Y DIRECTLY FROM |
---|
| 2900 | C THE RESULT OF THE LAST FUNCTION EVALUATION. |
---|
| 2901 | C (IF ISOPT = 1, FUNCTIONAL ITERATION IS NOT ALLOWED.) |
---|
| 2902 | C----------------------------------------------------------------------- |
---|
| 2903 | DO 290 I = 1,N |
---|
| 2904 | SAVF(I) = H*SAVF(I) - YH(I,2) |
---|
| 2905 | 290 Y(I) = SAVF(I) - ACOR(I) |
---|
| 2906 | DEL = VNORM (N, Y, EWT) |
---|
| 2907 | DO 300 I = 1,N |
---|
| 2908 | Y(I) = YH(I,1) + EL(1)*SAVF(I) |
---|
| 2909 | 300 ACOR(I) = SAVF(I) |
---|
| 2910 | GO TO 400 |
---|
| 2911 | C----------------------------------------------------------------------- |
---|
| 2912 | C IN THE CASE OF THE CHORD METHOD, COMPUTE THE CORRECTOR ERROR, |
---|
| 2913 | C AND KppSolve THE LINEAR SYSTEM WITH THAT AS RIGHT-HAND SIDE AND |
---|
| 2914 | C P AS COEFFICIENT MATRIX. |
---|
| 2915 | C----------------------------------------------------------------------- |
---|
| 2916 | 350 DO 360 I = 1,N |
---|
| 2917 | 360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) |
---|
| 2918 | CALL SLVS (WM, IWM, Y, SAVF) |
---|
| 2919 | IF (IERSL .LT. 0) GO TO 430 |
---|
| 2920 | IF (IERSL .GT. 0) GO TO 410 |
---|
| 2921 | DEL = VNORM (N, Y, EWT) |
---|
| 2922 | DO 380 I = 1,N |
---|
| 2923 | ACOR(I) = ACOR(I) + Y(I) |
---|
| 2924 | 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) |
---|
| 2925 | C----------------------------------------------------------------------- |
---|
| 2926 | C TEST FOR CONVERGENCE. IF M.GT.0, AN ESTIMATE OF THE CONVERGENCE |
---|
| 2927 | C RATE CONSTANT IS STORED IN CRATE, AND THIS IS USED IN THE TEST. |
---|
| 2928 | C----------------------------------------------------------------------- |
---|
| 2929 | 400 IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) |
---|
| 2930 | DCON = DEL*MIN(ONE,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) |
---|
| 2931 | IF (DCON .LE. ONE) GO TO 450 |
---|
| 2932 | M = M + 1 |
---|
| 2933 | IF (M .EQ. MAXCOR) GO TO 410 |
---|
| 2934 | IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 |
---|
| 2935 | DELP = DEL |
---|
| 2936 | CALL F (NEQ, TN, Y, PAR, SAVF) |
---|
| 2937 | NFE = NFE + 1 |
---|
| 2938 | GO TO 270 |
---|
| 2939 | C----------------------------------------------------------------------- |
---|
| 2940 | C THE CORRECTOR ITERATION FAILED TO CONVERGE IN MAXCOR TRIES. |
---|
| 2941 | C IF MITER .NE. 0 AND THE JACOBIAN IS OUT OF DATE, PJAC IS CALLED FOR |
---|
| 2942 | C THE NEXT TRY. OTHERWISE THE YH ARRAY IS RETRACTED TO ITS VALUES |
---|
| 2943 | C BEFORE PREDICTION, AND H IS REDUCED, IF POSSIBLE. IF H CANNOT BE |
---|
| 2944 | C REDUCED OR MXNCF FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -2. |
---|
| 2945 | C----------------------------------------------------------------------- |
---|
| 2946 | 410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430 |
---|
| 2947 | ICF = 1 |
---|
| 2948 | IPUP = MITER |
---|
| 2949 | GO TO 220 |
---|
| 2950 | 430 ICF = 2 |
---|
| 2951 | NCF = NCF + 1 |
---|
| 2952 | RMAX = 2.0D0 |
---|
| 2953 | TN = TOLD |
---|
| 2954 | I1 = NQNYH + 1 |
---|
| 2955 | DO 445 JB = 1,NQ |
---|
| 2956 | I1 = I1 - NYH |
---|
| 2957 | DO 440 I = I1,NQNYH |
---|
| 2958 | 440 YH1(I) = YH1(I) - YH1(I+NYH) |
---|
| 2959 | 445 CONTINUE |
---|
| 2960 | IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 |
---|
| 2961 | IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 |
---|
| 2962 | IF (NCF .EQ. MXNCF) GO TO 670 |
---|
| 2963 | RH = 0.25D0 |
---|
| 2964 | IPUP = MITER |
---|
| 2965 | IREDO = 1 |
---|
| 2966 | GO TO 170 |
---|
| 2967 | C----------------------------------------------------------------------- |
---|
| 2968 | C THE CORRECTOR HAS CONVERGED. |
---|
| 2969 | C THE LOCAL ERROR TEST IS MADE AND CONTROL PASSES TO STATEMENT 500 |
---|
| 2970 | C IF IT FAILS. OTHERWISE, STESA IS CALLED (ISOPT = 1) TO PERFORM |
---|
| 2971 | C SENSITIVITY CALCULATIONS AT CURRENT STEP SIZE AND ORDER. |
---|
| 2972 | C----------------------------------------------------------------------- |
---|
| 2973 | 450 CONTINUE |
---|
| 2974 | IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) |
---|
| 2975 | IF (M .GT. 0) DSM = VNORM (N, ACOR, EWT)/TESCO(2,NQ) |
---|
| 2976 | IF (DSM .GT. ONE) GO TO 500 |
---|
| 2977 | C |
---|
| 2978 | IF (ISOPT .EQ. 0) GO TO 460 |
---|
| 2979 | C----------------------------------------------------------------------- |
---|
| 2980 | C CALL STESA TO PERFORM EXPLICIT SENSITIVITY ANALYSIS. |
---|
| 2981 | C IF THE LOCAL ERROR TEST FAILS (WITHIN STESA) FOR ANY SOLUTION VECTOR, |
---|
| 2982 | C KFLAGS IS SET .LT. 0 AND CONTROL PASSES TO STATEMENT 500 UPON RETURN. |
---|
| 2983 | C IN EITHER CASE, JCUR IS SET TO ZERO TO SIGNAL THAT THE JACOBIAN MAY |
---|
| 2984 | C NEED UPDATING LATER. |
---|
| 2985 | C----------------------------------------------------------------------- |
---|
| 2986 | CALL STESA (NEQ, Y, N, NSV, YH, WM, IWM, EWT, SAVF, ACOR, |
---|
| 2987 | 1 PAR, NRS, F, JAC, DF, PJAC, PDF, SLVS) |
---|
| 2988 | IF (IERPJ .NE. 0 .OR. IERSL .NE. 0) GO TO 680 |
---|
| 2989 | IF (KFLAGS .LT. 0) GO TO 500 |
---|
| 2990 | C----------------------------------------------------------------------- |
---|
| 2991 | C AFTER A SUCCESSFUL STEP, UPDATE THE YH ARRAY. |
---|
| 2992 | C CONSIDER CHANGING H IF IALTH = 1. OTHERWISE DECREASE IALTH BY 1. |
---|
| 2993 | C IF IALTH IS THEN 1 AND NQ .LT. MAXORD, THEN ACOR IS SAVED FOR |
---|
| 2994 | C USE IN A POSSIBLE ORDER INCREASE ON THE NEXT STEP. |
---|
| 2995 | C IF A CHANGE IN H IS CONSIDERED, AN INCREASE OR DECREASE IN ORDER |
---|
| 2996 | C BY ONE IS CONSIDERED ALSO. A CHANGE IN H IS MADE ONLY IF IT IS BY A |
---|
| 2997 | C FACTOR OF AT LEAST 1.1. IF NOT, IALTH IS SET TO 3 TO PREVENT |
---|
| 2998 | C TESTING FOR THAT MANY STEPS. |
---|
| 2999 | C----------------------------------------------------------------------- |
---|
| 3000 | 460 JCUR = 0 |
---|
| 3001 | KFLAG = 0 |
---|
| 3002 | IREDO = 0 |
---|
| 3003 | NST = NST + 1 |
---|
| 3004 | HU = H |
---|
| 3005 | NQU = NQ |
---|
| 3006 | DO 470 J = 1,L |
---|
| 3007 | DO 470 I = 1,NYH |
---|
| 3008 | 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) |
---|
| 3009 | IALTH = IALTH - 1 |
---|
| 3010 | IF (IALTH .EQ. 0) GO TO 520 |
---|
| 3011 | IF (IALTH .GT. 1) GO TO 700 |
---|
| 3012 | IF (L .EQ. LMAX) GO TO 700 |
---|
| 3013 | DO 490 I = 1,NYH |
---|
| 3014 | 490 YH(I,LMAX) = ACOR(I) |
---|
| 3015 | GO TO 700 |
---|
| 3016 | C----------------------------------------------------------------------- |
---|
| 3017 | C THE ERROR TEST FAILED IN EITHER STODE OR STESA. |
---|
| 3018 | C KFLAG KEEPS TRACK OF MULTIPLE FAILURES. |
---|
| 3019 | C RESTORE TN AND THE YH ARRAY TO THEIR PREVIOUS VALUES, AND PREPARE |
---|
| 3020 | C TO TRY THE STEP AGAIN. COMPUTE THE OPTIMUM STEP SIZE FOR THIS OR |
---|
| 3021 | C ONE LOWER ORDER. AFTER 2 OR MORE FAILURES, H IS FORCED TO DECREASE |
---|
| 3022 | C BY A FACTOR OF 0.2 OR LESS. |
---|
| 3023 | C----------------------------------------------------------------------- |
---|
| 3024 | 500 KFLAG = KFLAG - 1 |
---|
| 3025 | JCUR = 0 |
---|
| 3026 | TN = TOLD |
---|
| 3027 | I1 = NQNYH + 1 |
---|
| 3028 | DO 515 JB = 1,NQ |
---|
| 3029 | I1 = I1 - NYH |
---|
| 3030 | DO 510 I = I1,NQNYH |
---|
| 3031 | 510 YH1(I) = YH1(I) - YH1(I+NYH) |
---|
| 3032 | 515 CONTINUE |
---|
| 3033 | RMAX = 2.0D0 |
---|
| 3034 | IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 |
---|
| 3035 | IF (KFLAG .LE. -3) GO TO 640 |
---|
| 3036 | IREDO = 2 |
---|
| 3037 | RHUP = ZERO |
---|
| 3038 | GO TO 540 |
---|
| 3039 | C----------------------------------------------------------------------- |
---|
| 3040 | * |
---|
| 3041 | C REGARDLESS OF THE SUCCESS OR FAILURE OF THE STEP, FACTORS |
---|
| 3042 | C RHDN, RHSM, AND RHUP ARE COMPUTED, BY WHICH H COULD BE MULTIPLIED |
---|
| 3043 | C AT ORDER NQ - 1, ORDER NQ, OR ORDER NQ + 1, RESPECTIVELY. |
---|
| 3044 | C IN THE CASE OF FAILURE, RHUP = 0.0 TO AVOID AN ORDER INCREASE. |
---|
| 3045 | C THE LARGEST OF THESE IS DETERMINED AND THE NEW ORDER CHOSEN |
---|
| 3046 | C ACCORDINGLY. IF THE ORDER IS TO BE INCREASED, WE COMPUTE ONE |
---|
| 3047 | C ADDITIONAL SCALED DERIVATIVE. |
---|
| 3048 | C FOR ISOPT = 1, DUPS AND DSMS ARE LOADED WITH THE LARGEST RMS-NORMS |
---|
| 3049 | C OBTAINED BY CONSIDERING SEPARATELY THE SENSITIVITY SOLUTION VECTORS. |
---|
| 3050 | C----------------------------------------------------------------------- |
---|
| 3051 | 520 RHUP = ZERO |
---|
| 3052 | IF (L .EQ. LMAX) GO TO 540 |
---|
| 3053 | DO 530 I = 1,N |
---|
| 3054 | 530 SAVF(I) = ACOR(I) - YH(I,LMAX) |
---|
| 3055 | DUP = VNORM (N, SAVF, EWT)/TESCO(3,NQ) |
---|
| 3056 | DUP = MAX(DUP,DUPS) |
---|
| 3057 | EXUP = ONE/REAL(L+1) |
---|
| 3058 | RHUP = ONE/(1.4D0*DUP**EXUP + 0.0000014D0) |
---|
| 3059 | 540 EXSM = ONE/REAL(L) |
---|
| 3060 | DSM = MAX(DSM,DSMS) |
---|
| 3061 | RHSM = ONE/(1.2D0*DSM**EXSM + 0.0000012D0) |
---|
| 3062 | RHDN = ZERO |
---|
| 3063 | IF (NQ .EQ. 1) GO TO 560 |
---|
| 3064 | JPOINT = 1 |
---|
| 3065 | DO 550 J = 1,NSV |
---|
| 3066 | DDN = VNORM (N, YH(JPOINT,L), EWT(JPOINT))/TESCO(1,NQ) |
---|
| 3067 | DDNS = MAX(DDNS,DDN) |
---|
| 3068 | JPOINT = JPOINT + N |
---|
| 3069 | 550 CONTINUE |
---|
| 3070 | DDN = DDNS |
---|
| 3071 | DDNS = ZERO |
---|
| 3072 | EXDN = ONE/REAL(NQ) |
---|
| 3073 | RHDN = ONE/(1.3D0*DDN**EXDN + 0.0000013D0) |
---|
| 3074 | 560 IF (RHSM .GE. RHUP) GO TO 570 |
---|
| 3075 | IF (RHUP .GT. RHDN) GO TO 590 |
---|
| 3076 | GO TO 580 |
---|
| 3077 | 570 IF (RHSM .LT. RHDN) GO TO 580 |
---|
| 3078 | NEWQ = NQ |
---|
| 3079 | RH = RHSM |
---|
| 3080 | GO TO 620 |
---|
| 3081 | 580 NEWQ = NQ - 1 |
---|
| 3082 | RH = RHDN |
---|
| 3083 | IF (KFLAG .LT. 0 .AND. RH .GT. ONE) RH = ONE |
---|
| 3084 | GO TO 620 |
---|
| 3085 | 590 NEWQ = L |
---|
| 3086 | RH = RHUP |
---|
| 3087 | IF (RH .LT. 1.1D0) GO TO 610 |
---|
| 3088 | R = EL(L)/REAL(L) |
---|
| 3089 | DO 600 I = 1,NYH |
---|
| 3090 | 600 YH(I,NEWQ+1) = ACOR(I)*R |
---|
| 3091 | GO TO 630 |
---|
| 3092 | 610 IALTH = 3 |
---|
| 3093 | GO TO 700 |
---|
| 3094 | 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 |
---|
| 3095 | IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) |
---|
| 3096 | C----------------------------------------------------------------------- |
---|
| 3097 | C IF THERE IS A CHANGE OF ORDER, RESET NQ, L, AND THE COEFFICIENTS. |
---|
| 3098 | C IN ANY CASE H IS RESET ACCORDING TO RH AND THE YH ARRAY IS RESCALED. |
---|
| 3099 | C THEN EXIT FROM 690 IF THE STEP WAS OK, OR REDO THE STEP OTHERWISE. |
---|
| 3100 | C----------------------------------------------------------------------- |
---|
| 3101 | IF (NEWQ .EQ. NQ) GO TO 170 |
---|
| 3102 | 630 NQ = NEWQ |
---|
| 3103 | L = NQ + 1 |
---|
| 3104 | IRET = 2 |
---|
| 3105 | GO TO 150 |
---|
| 3106 | C----------------------------------------------------------------------- |
---|
| 3107 | C CONTROL REACHES THIS SECTION IF 3 OR MORE FAILURES HAVE OCCURED. |
---|
| 3108 | C IF 10 FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -1. |
---|
| 3109 | C IT IS ASSUMED THAT THE DERIVATIVES THAT HAVE ACCUMULATED IN THE |
---|
| 3110 | C YH ARRAY HAVE ERRORS OF THE WRONG ORDER. HENCE THE FIRST |
---|
| 3111 | C DERIVATIVE IS RECOMPUTED, AND THE ORDER IS SET TO 1. THEN |
---|
| 3112 | C H IS REDUCED BY A FACTOR OF 10, AND THE STEP IS RETRIED, |
---|
| 3113 | C UNTIL IT SUCCEEDS OR H REACHES HMIN. |
---|
| 3114 | C----------------------------------------------------------------------- |
---|
| 3115 | 640 IF (KFLAG .EQ. -10) GO TO 660 |
---|
| 3116 | RH = 0.1D0 |
---|
| 3117 | RH = MAX(HMIN/ABS(H),RH) |
---|
| 3118 | H = H*RH |
---|
| 3119 | DO 645 I = 1,NYH |
---|
| 3120 | 645 Y(I) = YH(I,1) |
---|
| 3121 | CALL F (NEQ, TN, Y, PAR, SAVF) |
---|
| 3122 | NFE = NFE + 1 |
---|
| 3123 | IF (ISOPT .EQ. 0) GO TO 649 |
---|
| 3124 | CALL SPRIME (NEQ, Y, YH, NYH, N, NSV, WM, IWM, EWT, SAVF, ACOR, |
---|
| 3125 | 1 ACOR(N+1), PAR, F, JAC, DF, PJAC, PDF) |
---|
| 3126 | IF (IERSP .LT. 0) GO TO 680 |
---|
| 3127 | DO 646 I = N+1,NYH |
---|
| 3128 | 646 YH(I,2) = H*YH(I,2) |
---|
| 3129 | 649 DO 650 I = 1,N |
---|
| 3130 | 650 YH(I,2) = H*SAVF(I) |
---|
| 3131 | IPUP = MITER |
---|
| 3132 | IALTH = 5 |
---|
| 3133 | IF (NQ .EQ. 1) GO TO 200 |
---|
| 3134 | NQ = 1 |
---|
| 3135 | L = 2 |
---|
| 3136 | IRET = 3 |
---|
| 3137 | GO TO 150 |
---|
| 3138 | C----------------------------------------------------------------------- |
---|
| 3139 | C ALL RETURNS ARE MADE THROUGH THIS SECTION. H IS SAVED IN HOLD |
---|
| 3140 | C TO ALLOW THE CALLER TO CHANGE H ON THE NEXT STEP. |
---|
| 3141 | C----------------------------------------------------------------------- |
---|
| 3142 | 660 KFLAG = -1 |
---|
| 3143 | GO TO 720 |
---|
| 3144 | 670 KFLAG = -2 |
---|
| 3145 | GO TO 720 |
---|
| 3146 | 680 KFLAG = -3 |
---|
| 3147 | GO TO 720 |
---|
| 3148 | 690 RMAX = 10.0D0 |
---|
| 3149 | 700 R = ONE/TESCO(2,NQU) |
---|
| 3150 | DO 710 I = 1,NYH |
---|
| 3151 | 710 ACOR(I) = ACOR(I)*R |
---|
| 3152 | 720 HOLD = H |
---|
| 3153 | JSTART = 1 |
---|
| 3154 | RETURN |
---|
| 3155 | C----------------------- END OF SUBROUTINE STODE ----------------------- |
---|
| 3156 | END |
---|
| 3157 | SUBROUTINE CFODE (METH, ELCO, TESCO) |
---|
| 3158 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 3159 | DIMENSION ELCO(13,12), TESCO(3,12) |
---|
| 3160 | C----------------------------------------------------------------------- |
---|
| 3161 | C CFODE IS CALLED BY THE INTEGRATOR ROUTINE TO SET COEFFICIENTS |
---|
| 3162 | C NEEDED THERE. THE COEFFICIENTS FOR THE CURRENT METHOD, AS |
---|
| 3163 | C GIVEN BY THE VALUE OF METH, ARE SET FOR ALL ORDERS AND SAVED. |
---|
| 3164 | C THE MAXIMUM ORDER ASSUMED HERE IS 12 IF METH = 1 AND 5 IF METH = 2. |
---|
| 3165 | C (A SMALLER VALUE OF THE MAXIMUM ORDER IS ALSO ALLOWED.) |
---|
| 3166 | C CFODE IS CALLED ONCE AT THE BEGINNING OF THE PROBLEM, |
---|
| 3167 | C AND IS NOT CALLED AGAIN UNLESS AND UNTIL METH IS CHANGED. |
---|
| 3168 | C |
---|
| 3169 | C THE ELCO ARRAY CONTAINS THE BASIC METHOD COEFFICIENTS. |
---|
| 3170 | C THE COEFFICIENTS EL(I), 1 .LE. I .LE. NQ+1, FOR THE METHOD OF |
---|
| 3171 | C ORDER NQ ARE STORED IN ELCO(I,NQ). THEY ARE GIVEN BY A GENETRATING |
---|
| 3172 | C POLYNOMIAL, I.E., |
---|
| 3173 | C L(X) = EL(1) + EL(2)*X + ... + EL(NQ+1)*X**NQ. |
---|
| 3174 | C FOR THE IMPLICIT ADAMS METHODS, L(X) IS GIVEN BY |
---|
| 3175 | C DL/DX = (X+1)*(X+2)*...*(X+NQ-1)/FACTORIAL(NQ-1), L(-1) = 0. |
---|
| 3176 | C FOR THE BDF METHODS, L(X) IS GIVEN BY |
---|
| 3177 | C L(X) = (X+1)*(X+2)* ... *(X+NQ)/K, |
---|
| 3178 | C WHERE K = FACTORIAL(NQ)*(1 + 1/2 + ... + 1/NQ). |
---|
| 3179 | C |
---|
| 3180 | C THE TESCO ARRAY CONTAINS TEST CONSTANTS USED FOR THE |
---|
| 3181 | C LOCAL ERROR TEST AND THE SELECTION OF STEP SIZE AND/OR ORDER. |
---|
| 3182 | C AT ORDER NQ, TESCO(K,NQ) IS USED FOR THE SELECTION OF STEP |
---|
| 3183 | C SIZE AT ORDER NQ - 1 IF K = 1, AT ORDER NQ IF K = 2, AND AT ORDER |
---|
| 3184 | C NQ + 1 IF K = 3. |
---|
| 3185 | C----------------------------------------------------------------------- |
---|
| 3186 | DIMENSION PC(12) |
---|
| 3187 | PARAMETER (ONE=1.0D0,ZERO=0.0D0) |
---|
| 3188 | C |
---|
| 3189 | GO TO (100, 200), METH |
---|
| 3190 | C |
---|
| 3191 | 100 ELCO(1,1) = ONE |
---|
| 3192 | ELCO(2,1) = ONE |
---|
| 3193 | TESCO(1,1) = ZERO |
---|
| 3194 | TESCO(2,1) = 2.0D0 |
---|
| 3195 | TESCO(1,2) = ONE |
---|
| 3196 | TESCO(3,12) = ZERO |
---|
| 3197 | PC(1) = ONE |
---|
| 3198 | RQFAC = ONE |
---|
| 3199 | DO 140 NQ = 2,12 |
---|
| 3200 | C----------------------------------------------------------------------- |
---|
| 3201 | C THE PC ARRAY WILL CONTAIN THE COEFFICIENTS OF THE POLYNOMIAL |
---|
| 3202 | C P(X) = (X+1)*(X+2)*...*(X+NQ-1). |
---|
| 3203 | C INITIALLY, P(X) = 1. |
---|
| 3204 | C----------------------------------------------------------------------- |
---|
| 3205 | RQ1FAC = RQFAC |
---|
| 3206 | RQFAC = RQFAC/REAL(NQ) |
---|
| 3207 | NQM1 = NQ - 1 |
---|
| 3208 | FNQM1 = REAL(NQM1) |
---|
| 3209 | NQP1 = NQ + 1 |
---|
| 3210 | C FORM COEFFICIENTS OF P(X)*(X+NQ-1). ---------------------------------- |
---|
| 3211 | PC(NQ) = ZERO |
---|
| 3212 | DO 110 IB = 1,NQM1 |
---|
| 3213 | I = NQP1 - IB |
---|
| 3214 | 110 PC(I) = PC(I-1) + FNQM1*PC(I) |
---|
| 3215 | PC(1) = FNQM1*PC(1) |
---|
| 3216 | C COMPUTE INTEGRAL, -1 TO 0, OF P(X) AND X*P(X). ----------------------- |
---|
| 3217 | PINT = PC(1) |
---|
| 3218 | XPIN = PC(1)/2.0D0 |
---|
| 3219 | TSIGN = ONE |
---|
| 3220 | DO 120 I = 2,NQ |
---|
| 3221 | TSIGN = -TSIGN |
---|
| 3222 | PINT = PINT + TSIGN*PC(I)/REAL(I) |
---|
| 3223 | 120 XPIN = XPIN + TSIGN*PC(I)/REAL(I+1) |
---|
| 3224 | C STORE COEFFICIENTS IN ELCO AND TESCO. -------------------------------- |
---|
| 3225 | ELCO(1,NQ) = PINT*RQ1FAC |
---|
| 3226 | ELCO(2,NQ) = ONE |
---|
| 3227 | DO 130 I = 2,NQ |
---|
| 3228 | 130 ELCO(I+1,NQ) = RQ1FAC*PC(I)/REAL(I) |
---|
| 3229 | AGAMQ = RQFAC*XPIN |
---|
| 3230 | RAGQ = ONE/AGAMQ |
---|
| 3231 | TESCO(2,NQ) = RAGQ |
---|
| 3232 | IF (NQ .LT. 12) TESCO(1,NQP1) = RAGQ*RQFAC/REAL(NQP1) |
---|
| 3233 | TESCO(3,NQM1) = RAGQ |
---|
| 3234 | 140 CONTINUE |
---|
| 3235 | RETURN |
---|
| 3236 | C |
---|
| 3237 | 200 PC(1) = ONE |
---|
| 3238 | RQ1FAC = ONE |
---|
| 3239 | DO 230 NQ = 1,5 |
---|
| 3240 | C----------------------------------------------------------------------- |
---|
| 3241 | C THE PC ARRAY WILL CONTAIN THE COEFFICIENTS OF THE POLYNOMIAL |
---|
| 3242 | C P(X) = (X+1)*(X+2)*...*(X+NQ). |
---|
| 3243 | C INITIALLY, P(X) = 1. |
---|
| 3244 | C----------------------------------------------------------------------- |
---|
| 3245 | FNQ = REAL(NQ) |
---|
| 3246 | NQP1 = NQ + 1 |
---|
| 3247 | C FORM COEFFICIENTS OF P(X)*(X+NQ). ------------------------------------ |
---|
| 3248 | PC(NQP1) = ZERO |
---|
| 3249 | DO 210 IB = 1,NQ |
---|
| 3250 | I = NQ + 2 - IB |
---|
| 3251 | 210 PC(I) = PC(I-1) + FNQ*PC(I) |
---|
| 3252 | PC(1) = FNQ*PC(1) |
---|
| 3253 | C STORE COEFFICIENTS IN ELCO AND TESCO. -------------------------------- |
---|
| 3254 | DO 220 I = 1,NQP1 |
---|
| 3255 | 220 ELCO(I,NQ) = PC(I)/PC(2) |
---|
| 3256 | ELCO(2,NQ) = ONE |
---|
| 3257 | TESCO(1,NQ) = RQ1FAC |
---|
| 3258 | TESCO(2,NQ) = REAL(NQP1)/ELCO(1,NQ) |
---|
| 3259 | TESCO(3,NQ) = REAL(NQ+2)/ELCO(1,NQ) |
---|
| 3260 | RQ1FAC = RQ1FAC/FNQ |
---|
| 3261 | 230 CONTINUE |
---|
| 3262 | RETURN |
---|
| 3263 | C----------------------- END OF SUBROUTINE CFODE ----------------------- |
---|
| 3264 | END |
---|
| 3265 | SUBROUTINE SOLSY (WM, IWM, X, TEM) |
---|
| 3266 | C IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 3267 | INCLUDE 'KPP_ROOT_Parameters.h' |
---|
| 3268 | INCLUDE 'KPP_ROOT_Sparse.h' |
---|
| 3269 | DIMENSION WM(*), IWM(*), X(*), TEM(*) |
---|
| 3270 | PARAMETER (ZERO=0.0D0,ONE=1.0D0) |
---|
| 3271 | COMMON /ODE001/ ROWND, ROWNS(173), |
---|
| 3272 | 2 RDUM1(37), EL0, H, RDUM2(6), |
---|
| 3273 | 3 IOWND(14), IOWNS(4), |
---|
| 3274 | 4 IDUM1(4), IERSL, IDUM2(5), |
---|
| 3275 | 5 MITER, IDUM3(4), N, IDUM4(5) |
---|
| 3276 | C----------------------------------------------------------------------- |
---|
| 3277 | C THIS ROUTINE MANAGES THE SOLUTION OF THE LINEAR SYSTEM ARISING FROM |
---|
| 3278 | C A CHORD ITERATION. IT IS CALLED IF MITER .NE. 0. |
---|
| 3279 | C IF MITER IS 1 OR 2, IT CALLS DGESL TO ACCOMPLISH THIS. |
---|
| 3280 | C IF MITER = 3 IT UPDATES THE COEFFICIENT H*EL0 IN THE DIAGONAL |
---|
| 3281 | C MATRIX, AND THEN COMPUTES THE SOLUTION. |
---|
| 3282 | C IF MITER IS 4 OR 5, IT CALLS DGBSL. |
---|
| 3283 | C COMMUNICATION WITH SOLSY USES THE FOLLOWING VARIABLES.. |
---|
| 3284 | C WM = REAL WORK SPACE CONTAINING THE INVERSE DIAGONAL MATRIX IF |
---|
| 3285 | C MITER = 3 AND THE LU DECOMPOSITION OF THE MATRIX OTHERWISE. |
---|
| 3286 | C STORAGE OF MATRIX ELEMENTS STARTS AT WM(3). |
---|
| 3287 | C WM ALSO CONTAINS THE FOLLOWING MATRIX-RELATED DATA.. |
---|
| 3288 | C WM(1) = SQRT(UROUND) (NOT USED HERE), |
---|
| 3289 | C WM(2) = HL0, THE PREVIOUS VALUE OF H*EL0, USED IF MITER = 3. |
---|
| 3290 | C IWM = INTEGER WORK SPACE CONTAINING PIVOT INFORMATION, STARTING AT |
---|
| 3291 | C IWM(21), IF MITER IS 1, 2, 4, OR 5. IWM ALSO CONTAINS BAND |
---|
| 3292 | C PARAMETERS ML = IWM(1) AND MU = IWM(2) IF MITER IS 4 OR 5. |
---|
| 3293 | C X = THE RIGHT-HAND SIDE VECTOR ON INPUT, AND THE SOLUTION VECTOR |
---|
| 3294 | C ON OUTPUT, OF LENGTH N. |
---|
| 3295 | C TEM = VECTOR OF WORK SPACE OF LENGTH N, NOT USED IN THIS VERSION. |
---|
| 3296 | C IERSL = OUTPUT FLAG (IN COMMON). IERSL = 0 IF NO TROUBLE OCCURRED. |
---|
| 3297 | C IERSL = 1 IF A SINGULAR MATRIX AROSE WITH MITER = 3. |
---|
| 3298 | C THIS ROUTINE ALSO USES THE COMMON VARIABLES EL0, H, MITER, AND N. |
---|
| 3299 | C----------------------------------------------------------------------- |
---|
| 3300 | IERSL = 0 |
---|
| 3301 | GO TO (100, 100, 300, 400, 400), MITER |
---|
| 3302 | C 100 CALL DGESL (WM(3), N, N, IWM(21), X, 0) |
---|
| 3303 | 100 CALL KppSolve (WM(3), X) |
---|
| 3304 | RETURN |
---|
| 3305 | C |
---|
| 3306 | 300 PHL0 = WM(2) |
---|
| 3307 | HL0 = H*EL0 |
---|
| 3308 | WM(2) = HL0 |
---|
| 3309 | IF (HL0 .EQ. PHL0) GO TO 330 |
---|
| 3310 | R = HL0/PHL0 |
---|
| 3311 | DO 320 I = 1,N |
---|
| 3312 | DI = ONE - R*(ONE - ONE/WM(I+2)) |
---|
| 3313 | IF (ABS(DI) .EQ. ZERO) GO TO 390 |
---|
| 3314 | 320 WM(I+2) = ONE/DI |
---|
| 3315 | 330 DO 340 I = 1,N |
---|
| 3316 | 340 X(I) = WM(I+2)*X(I) |
---|
| 3317 | RETURN |
---|
| 3318 | 390 IERSL = 1 |
---|
| 3319 | RETURN |
---|
| 3320 | C |
---|
| 3321 | 400 ML = IWM(1) |
---|
| 3322 | MU = IWM(2) |
---|
| 3323 | MEBAND = 2*ML + MU + 1 |
---|
| 3324 | CALL DGBSL (WM(3), MEBAND, N, ML, MU, IWM(21), X, 0) |
---|
| 3325 | RETURN |
---|
| 3326 | C----------------------- END OF SUBROUTINE SOLSY ----------------------- |
---|
| 3327 | END |
---|
| 3328 | SUBROUTINE EWSET (N, ITOL, RTOL, ATOL, YCUR, EWT) |
---|
| 3329 | C----------------------------------------------------------------------- |
---|
| 3330 | C THIS SUBROUTINE SETS THE ERROR WEIGHT VECTOR EWT ACCORDING TO |
---|
| 3331 | C EWT(I) = RTOL(I)*ABS(YCUR(I)) + ATOL(I), I = 1,...,N, |
---|
| 3332 | C WITH THE SUBSCRIPT ON RTOL AND/OR ATOL POSSIBLY REPLACED BY 1 ABOVE, |
---|
| 3333 | C DEPENDING ON THE VALUE OF ITOL. |
---|
| 3334 | C----------------------------------------------------------------------- |
---|
| 3335 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 3336 | DIMENSION RTOL(*), ATOL(*), YCUR(N), EWT(N) |
---|
| 3337 | RTOLI = RTOL(1) |
---|
| 3338 | ATOLI = ATOL(1) |
---|
| 3339 | DO 10 I = 1,N |
---|
| 3340 | IF (ITOL .GE. 3) RTOLI = RTOL(I) |
---|
| 3341 | IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) |
---|
| 3342 | EWT(I) = RTOLI*ABS(YCUR(I)) + ATOLI |
---|
| 3343 | 10 CONTINUE |
---|
| 3344 | RETURN |
---|
| 3345 | C----------------------- END OF SUBROUTINE EWSET ----------------------- |
---|
| 3346 | END |
---|
| 3347 | DOUBLE PRECISION FUNCTION VNORM (N, V, W) |
---|
| 3348 | C----------------------------------------------------------------------- |
---|
| 3349 | C THIS FUNCTION ROUTINE COMPUTES THE WEIGHTED ROOT-MEAN-SQUARE NORM |
---|
| 3350 | C OF THE VECTOR OF LENGTH N CONTAINED IN THE ARRAY V, WITH WEIGHTS |
---|
| 3351 | C CONTAINED IN THE ARRAY W OF LENGTH N.. |
---|
| 3352 | C VNORM = SQRT( (1/N) * SUM( V(I)*W(I) )**2 ) |
---|
| 3353 | C PROTECTION FOR UNDERFLOW/OVERFLOW IS ACCOMPLISHED USING TWO |
---|
| 3354 | C CONSTANTS WHICH ARE HOPEFULLY APPLICABLE FOR ALL MACHINES. |
---|
| 3355 | C THESE ARE: |
---|
| 3356 | C CUTLO = maximum of SQRT(U/EPS) over all known machines |
---|
| 3357 | C CUTHI = minimum of SQRT(Z) over all known machines |
---|
| 3358 | C WHERE |
---|
| 3359 | C EPS = smallest number s.t. EPS + 1 .GT. 1 |
---|
| 3360 | C U = smallest positive number (underflow limit) |
---|
| 3361 | C Z = largest number (overflow limit) |
---|
| 3362 | C |
---|
| 3363 | C DETAILS OF THE ALGORITHM AND OF VALUES OF CUTLO AND CUTHI ARE |
---|
| 3364 | C FOUND IN THE BLAS ROUTINE SNRM2 (SEE ALSO ALGORITHM 539, TRANS. |
---|
| 3365 | C MATH. SOFTWARE, VOL. 5 NO. 3, 1979, 308-323. |
---|
| 3366 | C FOR SINGLE PRECISION, THE FOLLOWING VALUES SHOULD BE UNIVERSAL: |
---|
| 3367 | C DATA CUTLO,CUTHI /4.441E-16,1.304E19/ |
---|
| 3368 | C FOR DOUBLE PRECISION, USE |
---|
| 3369 | C DATA CUTLO,CUTHI /8.232D-11,1.304D19/ |
---|
| 3370 | C |
---|
| 3371 | C----------------------------------------------------------------------- |
---|
| 3372 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 3373 | INTEGER NEXT,I,J,N |
---|
| 3374 | DIMENSION V(N),W(N) |
---|
| 3375 | DATA CUTLO,CUTHI /8.232D-11,1.304D19/ |
---|
| 3376 | DATA ZERO,ONE/0.0D0,1.0D0/ |
---|
| 3377 | C BLAS ALGORITHM |
---|
| 3378 | NEXT = 1 |
---|
| 3379 | SUM = ZERO |
---|
| 3380 | I = 1 |
---|
| 3381 | 20 SX = V(I)*W(I) |
---|
| 3382 | GO TO (30,40,70,80),NEXT |
---|
| 3383 | 30 IF (ABS(SX).GT.CUTLO) GO TO 110 |
---|
| 3384 | NEXT = 2 |
---|
| 3385 | XMAX = ZERO |
---|
| 3386 | 40 IF (SX.EQ.ZERO) GO TO 130 |
---|
| 3387 | IF (ABS(SX).GT.CUTLO) GO TO 110 |
---|
| 3388 | NEXT = 3 |
---|
| 3389 | GO TO 60 |
---|
| 3390 | 50 I=J |
---|
| 3391 | NEXT = 4 |
---|
| 3392 | SUM = (SUM/SX)/SX |
---|
| 3393 | 60 XMAX = ABS(SX) |
---|
| 3394 | GO TO 90 |
---|
| 3395 | 70 IF(ABS(SX).GT.CUTLO) GO TO 100 |
---|
| 3396 | 80 IF(ABS(SX).LE.XMAX) GO TO 90 |
---|
| 3397 | SUM = ONE + SUM * (XMAX/SX)**2 |
---|
| 3398 | XMAX = ABS(SX) |
---|
| 3399 | GO TO 130 |
---|
| 3400 | 90 SUM = SUM + (SX/XMAX)**2 |
---|
| 3401 | GO TO 130 |
---|
| 3402 | 100 SUM = (SUM*XMAX)*XMAX |
---|
| 3403 | 110 HITEST = CUTHI/REAL(N) |
---|
| 3404 | DO 120 J = I,N |
---|
| 3405 | SX = V(J)*W(J) |
---|
| 3406 | IF(ABS(SX).GE.HITEST) GO TO 50 |
---|
| 3407 | SUM = SUM + SX**2 |
---|
| 3408 | 120 CONTINUE |
---|
| 3409 | VNORM = SQRT(SUM) |
---|
| 3410 | GO TO 140 |
---|
| 3411 | 130 CONTINUE |
---|
| 3412 | I = I + 1 |
---|
| 3413 | IF (I.LE.N) GO TO 20 |
---|
| 3414 | VNORM = XMAX * SQRT(SUM) |
---|
| 3415 | 140 CONTINUE |
---|
| 3416 | RETURN |
---|
| 3417 | C----------------------- END OF FUNCTION VNORM ------------------------- |
---|
| 3418 | END |
---|
| 3419 | SUBROUTINE SVCOM (RSAV, ISAV) |
---|
| 3420 | C----------------------------------------------------------------------- |
---|
| 3421 | C THIS ROUTINE STORES IN RSAV AND ISAV THE CONTENTS OF COMMON BLOCKS |
---|
| 3422 | C ODE001, ODE002 AND EH0001, WHICH ARE USED INTERNALLY IN THE ODESSA |
---|
| 3423 | C PACKAGE. |
---|
| 3424 | C RSAV = REAL ARRAY OF LENGTH 222 OR MORE. |
---|
| 3425 | C ISAV = INTEGER ARRAY OF LENGTH 52 OR MORE. |
---|
| 3426 | C----------------------------------------------------------------------- |
---|
| 3427 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 3428 | DIMENSION RSAV(*), ISAV(*) |
---|
| 3429 | COMMON /ODE001/ RODE1(219), IODE1(39) |
---|
| 3430 | COMMON /ODE002/ RODE2(3), IODE2(11) |
---|
| 3431 | COMMON /EH0001/ IEH(2) |
---|
| 3432 | DATA LRODE1/219/, LIODE1/39/, LRODE2/3/, LIODE2/11/ |
---|
| 3433 | C |
---|
| 3434 | DO 10 I = 1,LRODE1 |
---|
| 3435 | 10 RSAV(I) = RODE1(I) |
---|
| 3436 | DO 20 I = 1,LRODE2 |
---|
| 3437 | J = LRODE1 + I |
---|
| 3438 | 20 RSAV(J) = RODE2(I) |
---|
| 3439 | DO 30 I = 1,LIODE1 |
---|
| 3440 | 30 ISAV(I) = IODE1(I) |
---|
| 3441 | DO 40 I = 1,LIODE2 |
---|
| 3442 | J = LIODE1 + I |
---|
| 3443 | 40 ISAV(J) = IODE2(I) |
---|
| 3444 | ISAV(LIODE1+LIODE2+1) = IEH(1) |
---|
| 3445 | ISAV(LIODE1+LIODE2+2) = IEH(2) |
---|
| 3446 | RETURN |
---|
| 3447 | C----------------------- END OF SUBROUTINE SVCOM ----------------------- |
---|
| 3448 | END |
---|
| 3449 | SUBROUTINE RSCOM (RSAV, ISAV) |
---|
| 3450 | C----------------------------------------------------------------------- |
---|
| 3451 | C THIS ROUTINE RESTORES FROM RSAV AND ISAV THE CONTENTS OF COMMON BLOCKS |
---|
| 3452 | C ODE001, ODE002 AND EH0001, WHICH ARE USED INTERNALLY IN THE ODESSSA |
---|
| 3453 | C PACKAGE. THIS PRESUMES THAT RSAV AND ISAV WERE LOADED BY MEANS |
---|
| 3454 | C OF SUBROUTINE SVCOM OR THE EQUIVALENT. |
---|
| 3455 | C----------------------------------------------------------------------- |
---|
| 3456 | IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
---|
| 3457 | DIMENSION RSAV(*), ISAV(*) |
---|
| 3458 | COMMON /ODE001/ RODE1(219), IODE1(39) |
---|
| 3459 | COMMON /ODE002/ RODE2(3), IODE2(11) |
---|
| 3460 | COMMON /EH0001/ IEH(2) |
---|
| 3461 | DATA LRODE1/219/, LIODE1/39/, LRODE2/3/, LIODE2/11/ |
---|
| 3462 | C |
---|
| 3463 | DO 10 I = 1,LRODE1 |
---|
| 3464 | 10 RODE1(I) = RSAV(I) |
---|
| 3465 | DO 20 I = 1,LRODE2 |
---|
| 3466 | J = LRODE1 + I |
---|
| 3467 | 20 RODE2(I) = RSAV(J) |
---|
| 3468 | DO 30 I = 1,LIODE1 |
---|
| 3469 | 30 IODE1(I) = ISAV(I) |
---|
| 3470 | DO 40 I = 1,LODE2 |
---|
| 3471 | J = LIODE1 + I |
---|
| 3472 | 40 IODE2(I) = ISAV(J) |
---|
| 3473 | IEH(1) = ISAV(LIODE1+LIODE2+1) |
---|
| 3474 | IEH(2) = ISAV(LIODE1+LIODE2+2) |
---|
| 3475 | RETURN |
---|
| 3476 | C----------------------- END OF SUBROUTINE RSCOM ----------------------- |
---|
| 3477 | END |
---|
| 3478 | SUBROUTINE DGEFA(A,LDA,N,IPVT,INFO) |
---|
| 3479 | INTEGER LDA,N,IPVT(*),INFO |
---|
| 3480 | DOUBLE PRECISION A(LDA,*) |
---|
| 3481 | C |
---|
| 3482 | C DGEFA FACTORS A DOUBLE PRECISION MATRIX BY GAUSSIAN ELIMINATION. |
---|
| 3483 | C |
---|
| 3484 | C DGEFA IS USUALLY CALLED BY DGECO, BUT IT CAN BE CALLED |
---|
| 3485 | C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED. |
---|
| 3486 | C (TIME FOR DGECO) = (1 + 9/N)*(TIME FOR DGEFA) . |
---|
| 3487 | C |
---|
| 3488 | C ON ENTRY |
---|
| 3489 | C |
---|
| 3490 | C A DOUBLE PRECISION(LDA, N) |
---|
| 3491 | C THE MATRIX TO BE FACTORED. |
---|
| 3492 | C |
---|
| 3493 | C LDA INTEGER |
---|
| 3494 | C THE LEADING DIMENSION OF THE ARRAY A . |
---|
| 3495 | C |
---|
| 3496 | C N INTEGER |
---|
| 3497 | C THE ORDER OF THE MATRIX A . |
---|
| 3498 | C |
---|
| 3499 | C ON RETURN |
---|
| 3500 | C |
---|
| 3501 | C A AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS |
---|
| 3502 | C WHICH WERE USED TO OBTAIN IT. |
---|
| 3503 | C THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE |
---|
| 3504 | C L IS A PRODUCT OF PERMUTATION AND UNIT LOWER |
---|
| 3505 | C TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR. |
---|
| 3506 | C |
---|
| 3507 | C IPVT INTEGER(N) |
---|
| 3508 | C AN INTEGER VECTOR OF PIVOT INDICES. |
---|
| 3509 | C |
---|
| 3510 | C INFO INTEGER |
---|
| 3511 | C = 0 NORMAL VALUE. |
---|
| 3512 | C = K IF U(K,K) .EQ. 0.0 . THIS IS NOT AN ERROR |
---|
| 3513 | C CONDITION FOR THIS SUBROUTINE, BUT IT DOES |
---|
| 3514 | C INDICATE THAT DGESL OR DGEDI WILL DIVIDE BY ZERO |
---|
| 3515 | C IF CALLED. USE RCOND IN DGECO FOR A RELIABLE |
---|
| 3516 | C INDICATION OF SINGULARITY. |
---|
| 3517 | C |
---|
| 3518 | C LINPACK. THIS VERSION DATED 08/14/78 . |
---|
| 3519 | C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. |
---|
| 3520 | C |
---|
| 3521 | C SUBROUTINES AND FUNCTIONS |
---|
| 3522 | C |
---|
| 3523 | C BLAS DAXPY,DSCAL,IDAMAX |
---|
| 3524 | C |
---|
| 3525 | C INTERNAL VARIABLES |
---|
| 3526 | C |
---|
| 3527 | DOUBLE PRECISION T |
---|
| 3528 | INTEGER IDAMAX,J,K,KP1,L,NM1 |
---|
| 3529 | C |
---|
| 3530 | C |
---|
| 3531 | C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING |
---|
| 3532 | C |
---|
| 3533 | INFO = 0 |
---|
| 3534 | NM1 = N - 1 |
---|
| 3535 | IF (NM1 .LT. 1) GO TO 70 |
---|
| 3536 | DO 60 K = 1, NM1 |
---|
| 3537 | KP1 = K + 1 |
---|
| 3538 | C |
---|
| 3539 | C FIND L = PIVOT INDEX |
---|
| 3540 | C |
---|
| 3541 | L = IDAMAX(N-K+1,A(K,K),1) + K - 1 |
---|
| 3542 | IPVT(K) = L |
---|
| 3543 | C |
---|
| 3544 | C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED |
---|
| 3545 | C |
---|
| 3546 | IF (A(L,K) .EQ. 0.0D0) GO TO 40 |
---|
| 3547 | C |
---|
| 3548 | C INTERCHANGE IF NECESSARY |
---|
| 3549 | C |
---|
| 3550 | IF (L .EQ. K) GO TO 10 |
---|
| 3551 | T = A(L,K) |
---|
| 3552 | A(L,K) = A(K,K) |
---|
| 3553 | A(K,K) = T |
---|
| 3554 | 10 CONTINUE |
---|
| 3555 | C |
---|
| 3556 | C COMPUTE MULTIPLIERS |
---|
| 3557 | C |
---|
| 3558 | T = -1.0D0/A(K,K) |
---|
| 3559 | CALL DSCAL(N-K,T,A(K+1,K),1) |
---|
| 3560 | C |
---|
| 3561 | C ROW ELIMINATION WITH COLUMN INDEXING |
---|
| 3562 | C |
---|
| 3563 | DO 30 J = KP1, N |
---|
| 3564 | T = A(L,J) |
---|
| 3565 | IF (L .EQ. K) GO TO 20 |
---|
| 3566 | A(L,J) = A(K,J) |
---|
| 3567 | A(K,J) = T |
---|
| 3568 | 20 CONTINUE |
---|
| 3569 | CALL DAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1) |
---|
| 3570 | 30 CONTINUE |
---|
| 3571 | GO TO 50 |
---|
| 3572 | 40 CONTINUE |
---|
| 3573 | INFO = K |
---|
| 3574 | 50 CONTINUE |
---|
| 3575 | 60 CONTINUE |
---|
| 3576 | 70 CONTINUE |
---|
| 3577 | IPVT(N) = N |
---|
| 3578 | IF (A(N,N) .EQ. 0.0D0) INFO = N |
---|
| 3579 | RETURN |
---|
| 3580 | END |
---|
| 3581 | SUBROUTINE DGESL(A,LDA,N,IPVT,B,JOB) |
---|
| 3582 | INTEGER LDA,N,IPVT(*),JOB |
---|
| 3583 | DOUBLE PRECISION A(LDA,*),B(*) |
---|
| 3584 | C |
---|
| 3585 | C DGESL KppSolveS THE DOUBLE PRECISION SYSTEM |
---|
| 3586 | C A * X = B OR TRANS(A) * X = B |
---|
| 3587 | C USING THE FACTORS COMPUTED BY DGECO OR DGEFA. |
---|
| 3588 | C |
---|
| 3589 | C ON ENTRY |
---|
| 3590 | C |
---|
| 3591 | C A DOUBLE PRECISION(LDA, N) |
---|
| 3592 | C THE OUTPUT FROM DGECO OR DGEFA. |
---|
| 3593 | C |
---|
| 3594 | C LDA INTEGER |
---|
| 3595 | C THE LEADING DIMENSION OF THE ARRAY A . |
---|
| 3596 | C |
---|
| 3597 | C N INTEGER |
---|
| 3598 | C THE ORDER OF THE MATRIX A . |
---|
| 3599 | C |
---|
| 3600 | C IPVT INTEGER(N) |
---|
| 3601 | C THE PIVOT VECTOR FROM DGECO OR DGEFA. |
---|
| 3602 | C |
---|
| 3603 | C B DOUBLE PRECISION(N) |
---|
| 3604 | C THE RIGHT HAND SIDE VECTOR. |
---|
| 3605 | C |
---|
| 3606 | C JOB INTEGER |
---|
| 3607 | C = 0 TO KppSolve A*X = B , |
---|
| 3608 | C = NONZERO TO KppSolve TRANS(A)*X = B WHERE |
---|
| 3609 | C TRANS(A) IS THE TRANSPOSE. |
---|
| 3610 | C |
---|
| 3611 | C ON RETURN |
---|
| 3612 | C |
---|
| 3613 | C B THE SOLUTION VECTOR X . |
---|
| 3614 | C |
---|
| 3615 | C ERROR CONDITION |
---|
| 3616 | C |
---|
| 3617 | C A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS A |
---|
| 3618 | C ZERO ON THE DIAGONAL. TECHNICALLY THIS INDICATES SINGULARITY |
---|
| 3619 | C BUT IT IS OFTEN CAUSED BY IMPROPER ARGUMENTS OR IMPROPER |
---|
| 3620 | C SETTING OF LDA . IT WILL NOT OCCUR IF THE SUBROUTINES ARE |
---|
| 3621 | C CALLED CORRECTLY AND IF DGECO HAS SET RCOND .GT. 0.0 |
---|
| 3622 | C OR DGEFA HAS SET INFO .EQ. 0 . |
---|
| 3623 | C |
---|
| 3624 | C TO COMPUTE INVERSE(A) * C WHERE C IS A MATRIX |
---|
| 3625 | C WITH P COLUMNS |
---|
| 3626 | C CALL DGECO(A,LDA,N,IPVT,RCOND,Z) |
---|
| 3627 | C IF (RCOND IS TOO SMALL) GO TO ... |
---|
| 3628 | C DO 10 J = 1, P |
---|
| 3629 | C CALL DGESL(A,LDA,N,IPVT,C(1,J),0) |
---|
| 3630 | C 10 CONTINUE |
---|
| 3631 | C |
---|
| 3632 | C LINPACK. THIS VERSION DATED 08/14/78 . |
---|
| 3633 | C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. |
---|
| 3634 | C |
---|
| 3635 | C SUBROUTINES AND FUNCTIONS |
---|
| 3636 | C |
---|
| 3637 | C BLAS DAXPY,DDOT |
---|
| 3638 | C |
---|
| 3639 | C INTERNAL VARIABLES |
---|
| 3640 | C |
---|
| 3641 | DOUBLE PRECISION DDOT,T |
---|
| 3642 | INTEGER K,KB,L,NM1 |
---|
| 3643 | C |
---|
| 3644 | NM1 = N - 1 |
---|
| 3645 | IF (JOB .NE. 0) GO TO 50 |
---|
| 3646 | C |
---|
| 3647 | C JOB = 0 , KppSolve A * X = B |
---|
| 3648 | C FIRST KppSolve L*Y = B |
---|
| 3649 | C |
---|
| 3650 | IF (NM1 .LT. 1) GO TO 30 |
---|
| 3651 | DO 20 K = 1, NM1 |
---|
| 3652 | L = IPVT(K) |
---|
| 3653 | T = B(L) |
---|
| 3654 | IF (L .EQ. K) GO TO 10 |
---|
| 3655 | B(L) = B(K) |
---|
| 3656 | B(K) = T |
---|
| 3657 | 10 CONTINUE |
---|
| 3658 | CALL DAXPY(N-K,T,A(K+1,K),1,B(K+1),1) |
---|
| 3659 | 20 CONTINUE |
---|
| 3660 | 30 CONTINUE |
---|
| 3661 | C |
---|
| 3662 | C NOW KppSolve U*X = Y |
---|
| 3663 | C |
---|
| 3664 | DO 40 KB = 1, N |
---|
| 3665 | K = N + 1 - KB |
---|
| 3666 | B(K) = B(K)/A(K,K) |
---|
| 3667 | T = -B(K) |
---|
| 3668 | CALL DAXPY(K-1,T,A(1,K),1,B(1),1) |
---|
| 3669 | 40 CONTINUE |
---|
| 3670 | GO TO 100 |
---|
| 3671 | 50 CONTINUE |
---|
| 3672 | C |
---|
| 3673 | C JOB = NONZERO, KppSolve TRANS(A) * X = B |
---|
| 3674 | C FIRST KppSolve TRANS(U)*Y = B |
---|
| 3675 | C |
---|
| 3676 | DO 60 K = 1, N |
---|
| 3677 | T = DDOT(K-1,A(1,K),1,B(1),1) |
---|
| 3678 | B(K) = (B(K) - T)/A(K,K) |
---|
| 3679 | 60 CONTINUE |
---|
| 3680 | C |
---|
| 3681 | C NOW KppSolve TRANS(L)*X = Y |
---|
| 3682 | C |
---|
| 3683 | IF (NM1 .LT. 1) GO TO 90 |
---|
| 3684 | DO 80 KB = 1, NM1 |
---|
| 3685 | K = N - KB |
---|
| 3686 | B(K) = B(K) + DDOT(N-K,A(K+1,K),1,B(K+1),1) |
---|
| 3687 | L = IPVT(K) |
---|
| 3688 | IF (L .EQ. K) GO TO 70 |
---|
| 3689 | T = B(L) |
---|
| 3690 | B(L) = B(K) |
---|
| 3691 | B(K) = T |
---|
| 3692 | 70 CONTINUE |
---|
| 3693 | 80 CONTINUE |
---|
| 3694 | 90 CONTINUE |
---|
| 3695 | 100 CONTINUE |
---|
| 3696 | RETURN |
---|
| 3697 | END |
---|
| 3698 | SUBROUTINE DGBFA(ABD,LDA,N,ML,MU,IPVT,INFO) |
---|
| 3699 | INTEGER LDA,N,ML,MU,IPVT(*),INFO |
---|
| 3700 | DOUBLE PRECISION ABD(LDA,*) |
---|
| 3701 | C |
---|
| 3702 | C DGBFA FACTORS A DOUBLE PRECISION BAND MATRIX BY ELIMINATION. |
---|
| 3703 | C |
---|
| 3704 | C DGBFA IS USUALLY CALLED BY DGBCO, BUT IT CAN BE CALLED |
---|
| 3705 | C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED. |
---|
| 3706 | C |
---|
| 3707 | C ON ENTRY |
---|
| 3708 | C |
---|
| 3709 | C ABD DOUBLE PRECISION(LDA, N) |
---|
| 3710 | C CONTAINS THE MATRIX IN BAND STORAGE. THE COLUMNS |
---|
| 3711 | C OF THE MATRIX ARE STORED IN THE COLUMNS OF ABD AND |
---|
| 3712 | C THE DIAGONALS OF THE MATRIX ARE STORED IN ROWS |
---|
| 3713 | C ML+1 THROUGH 2*ML+MU+1 OF ABD . |
---|
| 3714 | C SEE THE COMMENTS BELOW FOR DETAILS. |
---|
| 3715 | C |
---|
| 3716 | C LDA INTEGER |
---|
| 3717 | C THE LEADING DIMENSION OF THE ARRAY ABD . |
---|
| 3718 | C LDA MUST BE .GE. 2*ML + MU + 1 . |
---|
| 3719 | C |
---|
| 3720 | C N INTEGER |
---|
| 3721 | C THE ORDER OF THE ORIGINAL MATRIX. |
---|
| 3722 | C |
---|
| 3723 | C ML INTEGER |
---|
| 3724 | C NUMBER OF DIAGONALS BELOW THE MAIN DIAGONAL. |
---|
| 3725 | C 0 .LE. ML .LT. N . |
---|
| 3726 | C |
---|
| 3727 | C MU INTEGER |
---|
| 3728 | C NUMBER OF DIAGONALS ABOVE THE MAIN DIAGONAL. |
---|
| 3729 | C 0 .LE. MU .LT. N . |
---|
| 3730 | C MORE EFFICIENT IF ML .LE. MU . |
---|
| 3731 | C ON RETURN |
---|
| 3732 | C |
---|
| 3733 | C ABD AN UPPER TRIANGULAR MATRIX IN BAND STORAGE AND |
---|
| 3734 | C THE MULTIPLIERS WHICH WERE USED TO OBTAIN IT. |
---|
| 3735 | C THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE |
---|
| 3736 | C L IS A PRODUCT OF PERMUTATION AND UNIT LOWER |
---|
| 3737 | C TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR. |
---|
| 3738 | C |
---|
| 3739 | C IPVT INTEGER(N) |
---|
| 3740 | C AN INTEGER VECTOR OF PIVOT INDICES. |
---|
| 3741 | C |
---|
| 3742 | C INFO INTEGER |
---|
| 3743 | C = 0 NORMAL VALUE. |
---|
| 3744 | C = K IF U(K,K) .EQ. 0.0 . THIS IS NOT AN ERROR |
---|
| 3745 | C CONDITION FOR THIS SUBROUTINE, BUT IT DOES |
---|
| 3746 | C INDICATE THAT DGBSL WILL DIVIDE BY ZERO IF |
---|
| 3747 | C CALLED. USE RCOND IN DGBCO FOR A RELIABLE |
---|
| 3748 | C INDICATION OF SINGULARITY. |
---|
| 3749 | C |
---|
| 3750 | C BAND STORAGE |
---|
| 3751 | C |
---|
| 3752 | C IF A IS A BAND MATRIX, THE FOLLOWING PROGRAM SEGMENT |
---|
| 3753 | C WILL SET UP THE INPUT. |
---|
| 3754 | C |
---|
| 3755 | C ML = (BAND WIDTH BELOW THE DIAGONAL) |
---|
| 3756 | C MU = (BAND WIDTH ABOVE THE DIAGONAL) |
---|
| 3757 | C M = ML + MU + 1 |
---|
| 3758 | C DO 20 J = 1, N |
---|
| 3759 | C I1 = MAX0(1, J-MU) |
---|
| 3760 | C I2 = MIN0(N, J+ML) |
---|
| 3761 | C DO 10 I = I1, I2 |
---|
| 3762 | C K = I - J + M |
---|
| 3763 | C ABD(K,J) = A(I,J) |
---|
| 3764 | C 10 CONTINUE |
---|
| 3765 | C 20 CONTINUE |
---|
| 3766 | C |
---|
| 3767 | C THIS USES ROWS ML+1 THROUGH 2*ML+MU+1 OF ABD . |
---|
| 3768 | C IN ADDITION, THE FIRST ML ROWS IN ABD ARE USED FOR |
---|
| 3769 | C ELEMENTS GENERATED DURING THE TRIANGULARIZATION. |
---|
| 3770 | C THE TOTAL NUMBER OF ROWS NEEDED IN ABD IS 2*ML+MU+1 . |
---|
| 3771 | C THE ML+MU BY ML+MU UPPER LEFT TRIANGLE AND THE |
---|
| 3772 | C ML BY ML LOWER RIGHT TRIANGLE ARE NOT REFERENCED. |
---|
| 3773 | C |
---|
| 3774 | C LINPACK. THIS VERSION DATED 08/14/78 . |
---|
| 3775 | C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. |
---|
| 3776 | C |
---|
| 3777 | C SUBROUTINES AND FUNCTIONS |
---|
| 3778 | C |
---|
| 3779 | C BLAS DAXPY,DSCAL,IDAMAX |
---|
| 3780 | C FORTRAN MAX0,MIN0 |
---|
| 3781 | C |
---|
| 3782 | C INTERNAL VARIABLES |
---|
| 3783 | C |
---|
| 3784 | DOUBLE PRECISION T |
---|
| 3785 | INTEGER I,IDAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1 |
---|
| 3786 | C |
---|
| 3787 | C |
---|
| 3788 | M = ML + MU + 1 |
---|
| 3789 | INFO = 0 |
---|
| 3790 | C |
---|
| 3791 | C ZERO INITIAL FILL-IN COLUMNS |
---|
| 3792 | C |
---|
| 3793 | J0 = MU + 2 |
---|
| 3794 | J1 = MIN0(N,M) - 1 |
---|
| 3795 | IF (J1 .LT. J0) GO TO 30 |
---|
| 3796 | DO 20 JZ = J0, J1 |
---|
| 3797 | I0 = M + 1 - JZ |
---|
| 3798 | DO 10 I = I0, ML |
---|
| 3799 | ABD(I,JZ) = 0.0D0 |
---|
| 3800 | 10 CONTINUE |
---|
| 3801 | 20 CONTINUE |
---|
| 3802 | 30 CONTINUE |
---|
| 3803 | JZ = J1 |
---|
| 3804 | JU = 0 |
---|
| 3805 | C |
---|
| 3806 | C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING |
---|
| 3807 | C |
---|
| 3808 | NM1 = N - 1 |
---|
| 3809 | IF (NM1 .LT. 1) GO TO 130 |
---|
| 3810 | DO 120 K = 1, NM1 |
---|
| 3811 | KP1 = K + 1 |
---|
| 3812 | C |
---|
| 3813 | C ZERO NEXT FILL-IN COLUMN |
---|
| 3814 | C |
---|
| 3815 | JZ = JZ + 1 |
---|
| 3816 | IF (JZ .GT. N) GO TO 50 |
---|
| 3817 | IF (ML .LT. 1) GO TO 50 |
---|
| 3818 | DO 40 I = 1, ML |
---|
| 3819 | ABD(I,JZ) = 0.0D0 |
---|
| 3820 | 40 CONTINUE |
---|
| 3821 | 50 CONTINUE |
---|
| 3822 | C |
---|
| 3823 | C FIND L = PIVOT INDEX |
---|
| 3824 | C |
---|
| 3825 | LM = MIN0(ML,N-K) |
---|
| 3826 | L = IDAMAX(LM+1,ABD(M,K),1) + M - 1 |
---|
| 3827 | IPVT(K) = L + K - M |
---|
| 3828 | C |
---|
| 3829 | C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED |
---|
| 3830 | C |
---|
| 3831 | IF (ABD(L,K) .EQ. 0.0D0) GO TO 100 |
---|
| 3832 | C |
---|
| 3833 | C INTERCHANGE IF NECESSARY |
---|
| 3834 | C |
---|
| 3835 | IF (L .EQ. M) GO TO 60 |
---|
| 3836 | T = ABD(L,K) |
---|
| 3837 | ABD(L,K) = ABD(M,K) |
---|
| 3838 | ABD(M,K) = T |
---|
| 3839 | 60 CONTINUE |
---|
| 3840 | C |
---|
| 3841 | C COMPUTE MULTIPLIERS |
---|
| 3842 | C |
---|
| 3843 | T = -1.0D0/ABD(M,K) |
---|
| 3844 | CALL DSCAL(LM,T,ABD(M+1,K),1) |
---|
| 3845 | C |
---|
| 3846 | C ROW ELIMINATION WITH COLUMN INDEXING |
---|
| 3847 | C |
---|
| 3848 | JU = MIN0(MAX0(JU,MU+IPVT(K)),N) |
---|
| 3849 | MM = M |
---|
| 3850 | IF (JU .LT. KP1) GO TO 90 |
---|
| 3851 | DO 80 J = KP1, JU |
---|
| 3852 | L = L - 1 |
---|
| 3853 | MM = MM - 1 |
---|
| 3854 | T = ABD(L,J) |
---|
| 3855 | IF (L .EQ. MM) GO TO 70 |
---|
| 3856 | ABD(L,J) = ABD(MM,J) |
---|
| 3857 | ABD(MM,J) = T |
---|
| 3858 | 70 CONTINUE |
---|
| 3859 | CALL DAXPY(LM,T,ABD(M+1,K),1,ABD(MM+1,J),1) |
---|
| 3860 | 80 CONTINUE |
---|
| 3861 | 90 CONTINUE |
---|
| 3862 | GO TO 110 |
---|
| 3863 | 100 CONTINUE |
---|
| 3864 | INFO = K |
---|
| 3865 | 110 CONTINUE |
---|
| 3866 | 120 CONTINUE |
---|
| 3867 | 130 CONTINUE |
---|
| 3868 | IPVT(N) = N |
---|
| 3869 | IF (ABD(M,N) .EQ. 0.0D0) INFO = N |
---|
| 3870 | RETURN |
---|
| 3871 | END |
---|
| 3872 | SUBROUTINE DGBSL(ABD,LDA,N,ML,MU,IPVT,B,JOB) |
---|
| 3873 | INTEGER LDA,N,ML,MU,IPVT(*),JOB |
---|
| 3874 | DOUBLE PRECISION ABD(LDA,*),B(*) |
---|
| 3875 | C |
---|
| 3876 | C DGBSL KppSolveS THE DOUBLE PRECISION BAND SYSTEM |
---|
| 3877 | C A * X = B OR TRANS(A) * X = B |
---|
| 3878 | C USING THE FACTORS COMPUTED BY DGBCO OR DGBFA. |
---|
| 3879 | C |
---|
| 3880 | C ON ENTRY |
---|
| 3881 | C |
---|
| 3882 | C ABD DOUBLE PRECISION(LDA, N) |
---|
| 3883 | C THE OUTPUT FROM DGBCO OR DGBFA. |
---|
| 3884 | C |
---|
| 3885 | C LDA INTEGER |
---|
| 3886 | C THE LEADING DIMENSION OF THE ARRAY ABD . |
---|
| 3887 | C |
---|
| 3888 | C N INTEGER |
---|
| 3889 | C THE ORDER OF THE ORIGINAL MATRIX. |
---|
| 3890 | C |
---|
| 3891 | C ML INTEGER |
---|
| 3892 | C NUMBER OF DIAGONALS BELOW THE MAIN DIAGONAL. |
---|
| 3893 | C |
---|
| 3894 | C MU INTEGER |
---|
| 3895 | C NUMBER OF DIAGONALS ABOVE THE MAIN DIAGONAL. |
---|
| 3896 | C |
---|
| 3897 | C IPVT INTEGER(N) |
---|
| 3898 | C THE PIVOT VECTOR FROM DGBCO OR DGBFA. |
---|
| 3899 | C |
---|
| 3900 | C B DOUBLE PRECISION(N) |
---|
| 3901 | C THE RIGHT HAND SIDE VECTOR. |
---|
| 3902 | C |
---|
| 3903 | C JOB INTEGER |
---|
| 3904 | C = 0 TO KppSolve A*X = B , |
---|
| 3905 | C = NONZERO TO KppSolve TRANS(A)*X = B , WHERE |
---|
| 3906 | C TRANS(A) IS THE TRANSPOSE. |
---|
| 3907 | C |
---|
| 3908 | C ON RETURN |
---|
| 3909 | C |
---|
| 3910 | C B THE SOLUTION VECTOR X . |
---|
| 3911 | C |
---|
| 3912 | C ERROR CONDITION |
---|
| 3913 | C |
---|
| 3914 | C A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS A |
---|
| 3915 | C ZERO ON THE DIAGONAL. TECHNICALLY THIS INDICATES SINGULARITY |
---|
| 3916 | C BUT IT IS OFTEN CAUSED BY IMPROPER ARGUMENTS OR IMPROPER |
---|
| 3917 | C SETTING OF LDA . IT WILL NOT OCCUR IF THE SUBROUTINES ARE |
---|
| 3918 | C CALLED CORRECTLY AND IF DGBCO HAS SET RCOND .GT. 0.0 |
---|
| 3919 | C OR DGBFA HAS SET INFO .EQ. 0 . |
---|
| 3920 | C |
---|
| 3921 | C TO COMPUTE INVERSE(A) * C WHERE C IS A MATRIX |
---|
| 3922 | C WITH P COLUMNS |
---|
| 3923 | C CALL DGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z) |
---|
| 3924 | C IF (RCOND IS TOO SMALL) GO TO ... |
---|
| 3925 | C DO 10 J = 1, P |
---|
| 3926 | C CALL DGBSL(ABD,LDA,N,ML,MU,IPVT,C(1,J),0) |
---|
| 3927 | C 10 CONTINUE |
---|
| 3928 | C |
---|
| 3929 | C LINPACK. THIS VERSION DATED 08/14/78 . |
---|
| 3930 | C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. |
---|
| 3931 | C |
---|
| 3932 | C SUBROUTINES AND FUNCTIONS |
---|
| 3933 | C |
---|
| 3934 | C BLAS DAXPY,DDOT |
---|
| 3935 | C FORTRAN MIN0 |
---|
| 3936 | C |
---|
| 3937 | C INTERNAL VARIABLES |
---|
| 3938 | C |
---|
| 3939 | DOUBLE PRECISION DDOT,T |
---|
| 3940 | INTEGER K,KB,L,LA,LB,LM,M,NM1 |
---|
| 3941 | C |
---|
| 3942 | M = MU + ML + 1 |
---|
| 3943 | NM1 = N - 1 |
---|
| 3944 | IF (JOB .NE. 0) GO TO 50 |
---|
| 3945 | C |
---|
| 3946 | C JOB = 0 , KppSolve A * X = B |
---|
| 3947 | C FIRST KppSolve L*Y = B |
---|
| 3948 | C |
---|
| 3949 | IF (ML .EQ. 0) GO TO 30 |
---|
| 3950 | IF (NM1 .LT. 1) GO TO 30 |
---|
| 3951 | DO 20 K = 1, NM1 |
---|
| 3952 | LM = MIN0(ML,N-K) |
---|
| 3953 | L = IPVT(K) |
---|
| 3954 | T = B(L) |
---|
| 3955 | IF (L .EQ. K) GO TO 10 |
---|
| 3956 | B(L) = B(K) |
---|
| 3957 | B(K) = T |
---|
| 3958 | 10 CONTINUE |
---|
| 3959 | CALL DAXPY(LM,T,ABD(M+1,K),1,B(K+1),1) |
---|
| 3960 | 20 CONTINUE |
---|
| 3961 | 30 CONTINUE |
---|
| 3962 | C |
---|
| 3963 | C NOW KppSolve U*X = Y |
---|
| 3964 | C |
---|
| 3965 | DO 40 KB = 1, N |
---|
| 3966 | K = N + 1 - KB |
---|
| 3967 | B(K) = B(K)/ABD(M,K) |
---|
| 3968 | LM = MIN0(K,M) - 1 |
---|
| 3969 | LA = M - LM |
---|
| 3970 | LB = K - LM |
---|
| 3971 | T = -B(K) |
---|
| 3972 | CALL DAXPY(LM,T,ABD(LA,K),1,B(LB),1) |
---|
| 3973 | 40 CONTINUE |
---|
| 3974 | GO TO 100 |
---|
| 3975 | 50 CONTINUE |
---|
| 3976 | C |
---|
| 3977 | C JOB = NONZERO, KppSolve TRANS(A) * X = B |
---|
| 3978 | C FIRST KppSolve TRANS(U)*Y = B |
---|
| 3979 | C |
---|
| 3980 | DO 60 K = 1, N |
---|
| 3981 | LM = MIN0(K,M) - 1 |
---|
| 3982 | LA = M - LM |
---|
| 3983 | LB = K - LM |
---|
| 3984 | T = DDOT(LM,ABD(LA,K),1,B(LB),1) |
---|
| 3985 | B(K) = (B(K) - T)/ABD(M,K) |
---|
| 3986 | 60 CONTINUE |
---|
| 3987 | C |
---|
| 3988 | C NOW KppSolve TRANS(L)*X = Y |
---|
| 3989 | C |
---|
| 3990 | IF (ML .EQ. 0) GO TO 90 |
---|
| 3991 | IF (NM1 .LT. 1) GO TO 90 |
---|
| 3992 | DO 80 KB = 1, NM1 |
---|
| 3993 | K = N - KB |
---|
| 3994 | LM = MIN0(ML,N-K) |
---|
| 3995 | B(K) = B(K) + DDOT(LM,ABD(M+1,K),1,B(K+1),1) |
---|
| 3996 | L = IPVT(K) |
---|
| 3997 | IF (L .EQ. K) GO TO 70 |
---|
| 3998 | T = B(L) |
---|
| 3999 | B(L) = B(K) |
---|
| 4000 | B(K) = T |
---|
| 4001 | 70 CONTINUE |
---|
| 4002 | 80 CONTINUE |
---|
| 4003 | 90 CONTINUE |
---|
| 4004 | 100 CONTINUE |
---|
| 4005 | RETURN |
---|
| 4006 | END |
---|
| 4007 | SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) |
---|
| 4008 | C |
---|
| 4009 | C CONSTANT TIMES A VECTOR PLUS A VECTOR. |
---|
| 4010 | C USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE. |
---|
| 4011 | C JACK DONGARRA, LINPACK, 3/11/78. |
---|
| 4012 | C |
---|
| 4013 | DOUBLE PRECISION DX(*),DY(*),DA |
---|
| 4014 | INTEGER I,INCX,INCY,IX,IY,M,MP1,N |
---|
| 4015 | C |
---|
| 4016 | IF(N.LE.0)RETURN |
---|
| 4017 | IF (DA .EQ. 0.0D0) RETURN |
---|
| 4018 | IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20 |
---|
| 4019 | C |
---|
| 4020 | C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS |
---|
| 4021 | C NOT EQUAL TO 1 |
---|
| 4022 | C |
---|
| 4023 | IX = 1 |
---|
| 4024 | IY = 1 |
---|
| 4025 | IF(INCX.LT.0)IX = (-N+1)*INCX + 1 |
---|
| 4026 | IF(INCY.LT.0)IY = (-N+1)*INCY + 1 |
---|
| 4027 | DO 10 I = 1,N |
---|
| 4028 | DY(IY) = DY(IY) + DA*DX(IX) |
---|
| 4029 | IX = IX + INCX |
---|
| 4030 | IY = IY + INCY |
---|
| 4031 | 10 CONTINUE |
---|
| 4032 | RETURN |
---|
| 4033 | C |
---|
| 4034 | C CODE FOR BOTH INCREMENTS EQUAL TO 1 |
---|
| 4035 | C |
---|
| 4036 | C |
---|
| 4037 | C CLEAN-UP LOOP |
---|
| 4038 | C |
---|
| 4039 | 20 M = MOD(N,4) |
---|
| 4040 | IF( M .EQ. 0 ) GO TO 40 |
---|
| 4041 | DO 30 I = 1,M |
---|
| 4042 | DY(I) = DY(I) + DA*DX(I) |
---|
| 4043 | 30 CONTINUE |
---|
| 4044 | IF( N .LT. 4 ) RETURN |
---|
| 4045 | 40 MP1 = M + 1 |
---|
| 4046 | DO 50 I = MP1,N,4 |
---|
| 4047 | DY(I) = DY(I) + DA*DX(I) |
---|
| 4048 | DY(I + 1) = DY(I + 1) + DA*DX(I + 1) |
---|
| 4049 | DY(I + 2) = DY(I + 2) + DA*DX(I + 2) |
---|
| 4050 | DY(I + 3) = DY(I + 3) + DA*DX(I + 3) |
---|
| 4051 | 50 CONTINUE |
---|
| 4052 | RETURN |
---|
| 4053 | END |
---|
| 4054 | SUBROUTINE DSCAL(N,DA,DX,INCX) |
---|
| 4055 | C |
---|
| 4056 | C SCALES A VECTOR BY A CONSTANT. |
---|
| 4057 | C USES UNROLLED LOOPS FOR INCREMENT EQUAL TO ONE. |
---|
| 4058 | C JACK DONGARRA, LINPACK, 3/11/78. |
---|
| 4059 | C |
---|
| 4060 | DOUBLE PRECISION DA,DX(*) |
---|
| 4061 | INTEGER I,INCX,M,MP1,N,NINCX |
---|
| 4062 | C |
---|
| 4063 | IF(N.LE.0)RETURN |
---|
| 4064 | IF(INCX.EQ.1)GO TO 20 |
---|
| 4065 | C |
---|
| 4066 | C CODE FOR INCREMENT NOT EQUAL TO 1 |
---|
| 4067 | * |
---|
| 4068 | C |
---|
| 4069 | NINCX = N*INCX |
---|
| 4070 | DO 10 I = 1,NINCX,INCX |
---|
| 4071 | DX(I) = DA*DX(I) |
---|
| 4072 | 10 CONTINUE |
---|
| 4073 | RETURN |
---|
| 4074 | C |
---|
| 4075 | C CODE FOR INCREMENT EQUAL TO 1 |
---|
| 4076 | C |
---|
| 4077 | C |
---|
| 4078 | C CLEAN-UP LOOP |
---|
| 4079 | C |
---|
| 4080 | 20 M = MOD(N,5) |
---|
| 4081 | IF( M .EQ. 0 ) GO TO 40 |
---|
| 4082 | DO 30 I = 1,M |
---|
| 4083 | DX(I) = DA*DX(I) |
---|
| 4084 | 30 CONTINUE |
---|
| 4085 | IF( N .LT. 5 ) RETURN |
---|
| 4086 | 40 MP1 = M + 1 |
---|
| 4087 | DO 50 I = MP1,N,5 |
---|
| 4088 | DX(I) = DA*DX(I) |
---|
| 4089 | DX(I + 1) = DA*DX(I + 1) |
---|
| 4090 | DX(I + 2) = DA*DX(I + 2) |
---|
| 4091 | DX(I + 3) = DA*DX(I + 3) |
---|
| 4092 | DX(I + 4) = DA*DX(I + 4) |
---|
| 4093 | 50 CONTINUE |
---|
| 4094 | RETURN |
---|
| 4095 | END |
---|
| 4096 | DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) |
---|
| 4097 | C |
---|
| 4098 | C FORMS THE DOT PRODUCT OF TWO VECTORS. |
---|
| 4099 | C USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE. |
---|
| 4100 | C JACK DONGARRA, LINPACK, 3/11/78. |
---|
| 4101 | C |
---|
| 4102 | DOUBLE PRECISION DX(*),DY(*),DTEMP |
---|
| 4103 | INTEGER I,INCX,INCY,IX,IY,M,MP1,N |
---|
| 4104 | C |
---|
| 4105 | DDOT = 0.0D0 |
---|
| 4106 | DTEMP = 0.0D0 |
---|
| 4107 | IF(N.LE.0)RETURN |
---|
| 4108 | IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20 |
---|
| 4109 | C |
---|
| 4110 | C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS |
---|
| 4111 | C NOT EQUAL TO 1 |
---|
| 4112 | C |
---|
| 4113 | IX = 1 |
---|
| 4114 | IY = 1 |
---|
| 4115 | IF(INCX.LT.0)IX = (-N+1)*INCX + 1 |
---|
| 4116 | IF(INCY.LT.0)IY = (-N+1)*INCY + 1 |
---|
| 4117 | DO 10 I = 1,N |
---|
| 4118 | DTEMP = DTEMP + DX(IX)*DY(IY) |
---|
| 4119 | IX = IX + INCX |
---|
| 4120 | IY = IY + INCY |
---|
| 4121 | 10 CONTINUE |
---|
| 4122 | DDOT = DTEMP |
---|
| 4123 | RETURN |
---|
| 4124 | C |
---|
| 4125 | C CODE FOR BOTH INCREMENTS EQUAL TO 1 |
---|
| 4126 | C |
---|
| 4127 | C |
---|
| 4128 | C CLEAN-UP LOOP |
---|
| 4129 | C |
---|
| 4130 | 20 M = MOD(N,5) |
---|
| 4131 | IF( M .EQ. 0 ) GO TO 40 |
---|
| 4132 | DO 30 I = 1,M |
---|
| 4133 | DTEMP = DTEMP + DX(I)*DY(I) |
---|
| 4134 | 30 CONTINUE |
---|
| 4135 | IF( N .LT. 5 ) GO TO 60 |
---|
| 4136 | 40 MP1 = M + 1 |
---|
| 4137 | DO 50 I = MP1,N,5 |
---|
| 4138 | DTEMP = DTEMP + DX(I)*DY(I) + DX(I + 1)*DY(I + 1) + |
---|
| 4139 | * DX(I + 2)*DY(I + 2) + DX(I + 3)*DY(I + 3) + DX(I + 4)*DY(I + 4) |
---|
| 4140 | 50 CONTINUE |
---|
| 4141 | 60 DDOT = DTEMP |
---|
| 4142 | RETURN |
---|
| 4143 | END |
---|
| 4144 | INTEGER FUNCTION IDAMAX(N,DX,INCX) |
---|
| 4145 | C |
---|
| 4146 | C FINDS THE INDEX OF ELEMENT HAVING MAX. ABSOLUTE VALUE. |
---|
| 4147 | C JACK DONGARRA, LINPACK, 3/11/78. |
---|
| 4148 | C |
---|
| 4149 | DOUBLE PRECISION DX(*),DMAX |
---|
| 4150 | INTEGER I,INCX,IX,N |
---|
| 4151 | C |
---|
| 4152 | IDAMAX = 0 |
---|
| 4153 | IF( N .LT. 1 ) RETURN |
---|
| 4154 | IDAMAX = 1 |
---|
| 4155 | IF(N.EQ.1)RETURN |
---|
| 4156 | IF(INCX.EQ.1)GO TO 20 |
---|
| 4157 | C |
---|
| 4158 | C CODE FOR INCREMENT NOT EQUAL TO 1 |
---|
| 4159 | C |
---|
| 4160 | IX = 1 |
---|
| 4161 | DMAX = DABS(DX(1)) |
---|
| 4162 | IX = IX + INCX |
---|
| 4163 | DO 10 I = 2,N |
---|
| 4164 | IF(DABS(DX(IX)).LE.DMAX) GO TO 5 |
---|
| 4165 | IDAMAX = I |
---|
| 4166 | DMAX = DABS(DX(IX)) |
---|
| 4167 | 5 IX = IX + INCX |
---|
| 4168 | 10 CONTINUE |
---|
| 4169 | RETURN |
---|
| 4170 | C |
---|
| 4171 | C CODE FOR INCREMENT EQUAL TO 1 |
---|
| 4172 | C |
---|
| 4173 | 20 DMAX = DABS(DX(1)) |
---|
| 4174 | DO 30 I = 2,N |
---|
| 4175 | IF(DABS(DX(I)).LE.DMAX) GO TO 30 |
---|
| 4176 | IDAMAX = I |
---|
| 4177 | DMAX = DABS(DX(I)) |
---|
| 4178 | 30 CONTINUE |
---|
| 4179 | RETURN |
---|
| 4180 | END |
---|
| 4181 | DOUBLE PRECISION FUNCTION D1MACH (IDUM) |
---|
| 4182 | INTEGER IDUM |
---|
| 4183 | C----------------------------------------------------------------------- |
---|
| 4184 | C THIS ROUTINE COMPUTES THE UNIT ROUNDOFF OF THE MACHINE IN DOUBLE |
---|
| 4185 | C PRECISION. THIS IS DEFINED AS THE SMALLEST POSITIVE MACHINE NUMBER |
---|
| 4186 | C U SUCH THAT 1.0D0 + U .NE. 1.0D0 (IN DOUBLE PRECISION). |
---|
| 4187 | C----------------------------------------------------------------------- |
---|
| 4188 | DOUBLE PRECISION U, COMP |
---|
| 4189 | U = 1.0D0 |
---|
| 4190 | 10 U = U*0.5D0 |
---|
| 4191 | COMP = 1.0D0 + U |
---|
| 4192 | IF (COMP .NE. 1.0D0) GO TO 10 |
---|
| 4193 | D1MACH = U*2.0D0 |
---|
| 4194 | RETURN |
---|
| 4195 | C----------------------- END OF FUNCTION D1MACH ------------------------ |
---|
| 4196 | END |
---|
| 4197 | SUBROUTINE XERR (MSG, NERR, IERT, NI, I1, I2, NR, R1, R2) |
---|
| 4198 | INTEGER NERR, IERT, NI, I1, I2, NR, |
---|
| 4199 | 1 LUN, LUNIT, MESFLG |
---|
| 4200 | DOUBLE PRECISION R1, R2 |
---|
| 4201 | CHARACTER*(*) MSG |
---|
| 4202 | C------------------------------------------------------------------- |
---|
| 4203 | C |
---|
| 4204 | C ALL ARGUMENTS ARE INPUT ARGUMENTS. |
---|
| 4205 | C |
---|
| 4206 | C MSG = THE MESSAGE (CHARACTER VARIABLE) |
---|
| 4207 | C NERR = THE ERROR NUMBER (NOT USED). |
---|
| 4208 | C IERT = THE ERROR TYPE.. |
---|
| 4209 | C 1 MEANS RECOVERABLE (CONTROL RETURNS TO CALLER). |
---|
| 4210 | C 2 MEANS FATAL (RUN IS ABORTED--SEE NOTE BELOW). |
---|
| 4211 | C NI = NUMBER OF INTEGERS (0, 1, OR 2) TO BE PRINTED WITH MESSAGE. |
---|
| 4212 | C I1,I2 = INTEGERS TO BE PRINTED, DEPENDING ON NI. |
---|
| 4213 | C NR = NUMBER OF REALS (0, 1, OR 2) TO BE PRINTED WITH MESSAGE. |
---|
| 4214 | C R1,R2 = REALS TO BE PRINTED, DEPENDING ON NR. |
---|
| 4215 | C |
---|
| 4216 | C NOTES: |
---|
| 4217 | C 1. THE DIMENSION OF MSG IS ASSUMED TO BE AT MOST 60. |
---|
| 4218 | C (MULTI-LINE MESSAGES ARE GENERATED BY REPEATED CALLS.) |
---|
| 4219 | C 2. IF IERT = 2, CONTROL PASSES TO THE STATEMENT STOP |
---|
| 4220 | C TO ABORT THE RUN. THIS STATEMENT MAY BE MACHINE-DEPENDENT. |
---|
| 4221 | C 3. R1 AND R2 ARE ASSUMED TO BE IN DOUBLE PRECISION AND ARE PRINTED |
---|
| 4222 | C IN D21.13 FORMAT. |
---|
| 4223 | C 4. THE COMMON BLOCK /EH0001/ BELOW IS DATA-LOADED (A MACHINE- |
---|
| 4224 | C DEPENDENT FEATURE) WITH DEFAULT VALUES. |
---|
| 4225 | C THIS BLOCK IS NEEDED FOR PROPER RETENTION OF PARAMETERS USED BY |
---|
| 4226 | C THIS ROUTINE WHICH THE USER CAN RESET BY CALLING XSETF OR XSETUN. |
---|
| 4227 | C THE VARIABLES IN THIS BLOCK ARE AS FOLLOWS.. |
---|
| 4228 | C MESFLG = PRINT CONTROL FLAG.. |
---|
| 4229 | C 1 MEANS PRINT ALL MESSAGES (THE DEFAULT). |
---|
| 4230 | C 0 MEANS NO PRINTING. |
---|
| 4231 | C LUNIT = LOGICAL UNIT NUMBER FOR MESSAGES. |
---|
| 4232 | C THE DEFAULT IS 6 (MACHINE-DEPENDENT). |
---|
| 4233 | C 5. TO CHANGE THE DEFAULT OUTPUT UNIT, CHANGE THE DATA STATEMENT |
---|
| 4234 | C IN THE BLOCK DATA SUBPROGRAM BELOW. |
---|
| 4235 | C |
---|
| 4236 | C FOR A DIFFERENT RUN-ABORT COMMAND, CHANGE THE STATEMENT FOLLOWING |
---|
| 4237 | C STATEMENT 100 AT THE END. |
---|
| 4238 | C----------------------------------------------------------------------- |
---|
| 4239 | COMMON /EH0001/ MESFLG, LUNIT |
---|
| 4240 | IF (MESFLG .EQ. 0) GO TO 100 |
---|
| 4241 | C GET LOGICAL UNIT NUMBER. --------------------------------------------- |
---|
| 4242 | LUN = LUNIT |
---|
| 4243 | C WRITE THE MESSAGE. --------------------------------------------------- |
---|
| 4244 | WRITE (LUN, 10) MSG |
---|
| 4245 | 10 FORMAT(1X,A) |
---|
| 4246 | C----------------------------------------------------------------------- |
---|
| 4247 | IF (NI .EQ. 1) WRITE (LUN, 20) I1 |
---|
| 4248 | 20 FORMAT(6X,'IN ABOVE MESSAGE, I1 = ',I10) |
---|
| 4249 | IF (NI .EQ. 2) WRITE (LUN, 30) I1,I2 |
---|
| 4250 | 30 FORMAT(6X,'IN ABOVE MESSAGE, I1 = ',I10,3X,'I2 = ',I10) |
---|
| 4251 | IF (NR .EQ. 1) WRITE (LUN, 40) R1 |
---|
| 4252 | 40 FORMAT(6X,'IN ABOVE MESSAGE, R1 = ',D21.13) |
---|
| 4253 | IF (NR .EQ. 2) WRITE (LUN, 50) R1,R2 |
---|
| 4254 | 50 FORMAT(6X,'IN ABOVE, R1 = ',D21.13,3X,'R2 = ',D21.13) |
---|
| 4255 | C ABORT THE RUN IF IERT = 2. ------------------------------------------- |
---|
| 4256 | 100 IF (IERT .NE. 2) RETURN |
---|
| 4257 | STOP |
---|
| 4258 | C----------------------- END OF SUBROUTINE XERR ---------------------- |
---|
| 4259 | END |
---|
| 4260 | SUBROUTINE XSETF (MFLAG) |
---|
| 4261 | C |
---|
| 4262 | C THIS ROUTINE RESETS THE PRINT CONTROL FLAG MFLAG. |
---|
| 4263 | C |
---|
| 4264 | INTEGER MFLAG, MESFLG, LUNIT |
---|
| 4265 | COMMON /EH0001/ MESFLG, LUNIT |
---|
| 4266 | C |
---|
| 4267 | IF (MFLAG .EQ. 0 .OR. MFLAG .EQ. 1) MESFLG = MFLAG |
---|
| 4268 | RETURN |
---|
| 4269 | C----------------------- END OF SUBROUTINE XSETF ----------------------- |
---|
| 4270 | END |
---|
| 4271 | SUBROUTINE XSETUN (LUN) |
---|
| 4272 | C |
---|
| 4273 | C THIS ROUTINE RESETS THE LOGICAL UNIT NUMBER FOR MESSAGES. |
---|
| 4274 | C |
---|
| 4275 | INTEGER LUN, MESFLG, LUNIT |
---|
| 4276 | COMMON /EH0001/ MESFLG, LUNIT |
---|
| 4277 | C |
---|
| 4278 | IF (LUN .GT. 0) LUNIT = LUN |
---|
| 4279 | RETURN |
---|
| 4280 | C----------------------- END OF SUBROUTINE XSETUN ---------------------- |
---|
| 4281 | END |
---|
| 4282 | BLOCK DATA |
---|
| 4283 | C----------------------------------------------------------------------- |
---|
| 4284 | C THIS DATA SUBPROGRAM LOADS VARIABLES INTO THE INTERNAL COMMON |
---|
| 4285 | C BLOCKS USED BY ODESSA AND ITS VARIANTS. THE VARIABLES ARE |
---|
| 4286 | C DEFINED AS FOLLOWS.. |
---|
| 4287 | C ILLIN = COUNTER FOR THE NUMBER OF CONSECUTIVE TIMES THE PACKAGE |
---|
| 4288 | C WAS CALLED WITH ILLEGAL INPUT. THE RUN IS STOPPED WHEN |
---|
| 4289 | C ILLIN REACHES 5. |
---|
| 4290 | C NTREP = COUNTER FOR THE NUMBER OF CONSECUTIVE TIMES THE PACKAGE |
---|
| 4291 | C WAS CALLED WITH ISTATE = 1 AND TOUT = T. THE RUN IS |
---|
| 4292 | C STOPPED WHEN NTREP REACHES 5. |
---|
| 4293 | C MESFLG = FLAG TO CONTROL PRINTING OF ERROR MESSAGES. 1 MEANS PRINT, |
---|
| 4294 | C 0 MEANS NO PRINTING. |
---|
| 4295 | C LUNIT = DEFAULT VALUE OF LOGICAL UNIT NUMBER FOR PRINTING OF ERROR |
---|
| 4296 | C MESSAGES. |
---|
| 4297 | C----------------------------------------------------------------------- |
---|
| 4298 | INTEGER ILLIN, IDUMA, NTREP, IDUMB, IOWNS, ICOMM, MESFLG, LUNIT |
---|
| 4299 | DOUBLE PRECISION ROWND, ROWNS, RCOMM |
---|
| 4300 | COMMON /ODE001/ ROWND, ROWNS(173), RCOMM(45), |
---|
| 4301 | 1 ILLIN, IDUMA(10), NTREP, IDUMB(2), IOWNS(4), ICOMM(21) |
---|
| 4302 | COMMON /EH0001/ MESFLG, LUNIT |
---|
| 4303 | DATA ILLIN/0/, NTREP/0/ |
---|
| 4304 | DATA MESFLG/1/, LUNIT/6/ |
---|
| 4305 | C |
---|
| 4306 | C------------------------ END OF BLOCK DATA ---------------------------- |
---|
| 4307 | END |
---|
| 4308 | C----------------------------------------------------------------------- |
---|
| 4309 | C INSTRUCTIONS FOR INSTALLING THE ODESSA PACKAGE. (see @ below.) |
---|
| 4310 | C |
---|
| 4311 | C ODESSA is an enhanced version of the widely disseminated ODE solver |
---|
| 4312 | C LSODE, and as such retains the same properties regarding portability. |
---|
| 4313 | C The notes below, adapted from the installation instructions for LSODE, |
---|
| 4314 | C are intended to facilitate the installation of the ODESSA package in |
---|
| 4315 | C the user's software library. |
---|
| 4316 | C |
---|
| 4317 | C 1. Both a single and a double precision version of ODESSA are |
---|
| 4318 | C provided in this release. It is expected that most users will |
---|
| 4319 | C utilize the double precision version, except in the case of |
---|
| 4320 | C extended word-length computers. Most routines used by ODESSA |
---|
| 4321 | C are named the same regardless of whether they are single or |
---|
| 4322 | C double precision. The exceptions are the LINPAK and BLAS |
---|
| 4323 | C routines that follow the LINPAK/BLAS naming conventions, i.e. |
---|
| 4324 | C D--- for a double precision routine, and S--- for a single |
---|
| 4325 | C precision routine. Thus, care should be taken if both single |
---|
| 4326 | C and double precision versions are stored in the same library. |
---|
| 4327 | C |
---|
| 4328 | C 2. Several routines in ODESSA have the same names as the LSODE |
---|
| 4329 | C routines from which they were derived, although they contain |
---|
| 4330 | C different code. These are: INTDY, STODE, PREPJ, SVCOM, and |
---|
| 4331 | C RSCOM. If ODESSA is added to a subroutine library of which |
---|
| 4332 | C LSODE is already a member, these routine names must be changed |
---|
| 4333 | C in one of the two programs. Also see the note regarding BLOCK |
---|
| 4334 | C DATA subroutines below. |
---|
| 4335 | C |
---|
| 4336 | C 3. In many cases, ODESSA uses unaltered LSODE routines and |
---|
| 4337 | C common library routines that may already reside on your system. |
---|
| 4338 | C The installation of ODESSA should be done so that identical routines |
---|
| 4339 | C are shared rather than kept as duplicate copies. |
---|
| 4340 | C a. Normally, the user calls only subroutine ODESSA, but for optional |
---|
| 4341 | C capabilities the user may also CALL XSETUN, XSETF, SVCOM, RSCOM, |
---|
| 4342 | C or INTDY, as described in Part II of the Full Description in the |
---|
| 4343 | C User Documentation (ODESSA.DOC, see below). Except for INTDY, |
---|
| 4344 | C none of these are called from within the package. |
---|
| 4345 | C b. Two routines, EWSET and VNORM, are optionally replaceable by the |
---|
| 4346 | C user if the package version is unsuitable. Hence, the install- |
---|
| 4347 | C ation of the package should be done so that the user's version |
---|
| 4348 | C for either routine overrides the package version. |
---|
| 4349 | C c. The function routine D1MACH is provided to compute the unit |
---|
| 4350 | C roundoff of the machine and precision in use, in a manner com- |
---|
| 4351 | C patible with machine parameter routines developed at Bell Lab- |
---|
| 4352 | C oratories. If such a routine has already been installed on |
---|
| 4353 | C your system, the version supplied here may be discarded. |
---|
| 4354 | C d. Linear algebraic systems are solved with routines from the |
---|
| 4355 | C LINPACK collection, in conjunction with routines from the Basic |
---|
| 4356 | C Linear Algebra module collection (BLAS). In double precision, |
---|
| 4357 | C the names are DGEFA, DGESL, DGBFA, and DGBSL (from LINPACK), and |
---|
| 4358 | C DAXPY, DSCAL, IDAMAX, and DDOT (from BLAS). If these routines |
---|
| 4359 | C have already been installed on your system, copies supplied with |
---|
| 4360 | C ODESSA may be discarded. The single precision versions of these |
---|
| 4361 | C routines are used in the single precision version. |
---|
| 4362 | C |
---|
| 4363 | C 4. There are four integer variables, in the two labeled COMMON |
---|
| 4364 | C blocks /ODE001/ and /EH0001/, which need to be loaded with DATA |
---|
| 4365 | C statements. They can vary during execution, and are in common to |
---|
| 4366 | C assure their retention between calls. This is legal in ANSI Fortran |
---|
| 4367 | C only if done in a BLOCK DATA subprogram, and this package has a |
---|
| 4368 | C BLOCK DATA for this purpose. However, BLOCK DATA subprograms can be |
---|
| 4369 | C difficult to install in libraries, and many compilers allow such DATA |
---|
| 4370 | C statements in subroutines. If your system allows this, the location |
---|
| 4371 | C of the DATA statements are just after the initial type and common |
---|
| 4372 | C declarations in subroutines ODESSA and XERR. In ODESSA, ILLIN and |
---|
| 4373 | C NTREP are DATA-loaded as 0. In XERR, MESFLG is loaded as 1 and |
---|
| 4374 | C LUNIT is loaded as the appropriate default logical unit number. |
---|
| 4375 | C |
---|
| 4376 | C 5. The ODESSA package contains subscript expressions which may not |
---|
| 4377 | C be accepted by some compilers. Subscripts of the form I + J, I - J, |
---|
| 4378 | C etc., occur in various routines. If any of these forms are |
---|
| 4379 | C unacceptable to your compiler, an extra line of code setting the |
---|
| 4380 | C subscript to a dummy integer value should be added for each subscipt. |
---|
| 4381 | C |
---|
| 4382 | C 6. User documentation is provided in a two-level structure |
---|
| 4383 | C to accommmodate both the casual and serious user. The novice or |
---|
| 4384 | C casual user should need to read only the Summary of Usage and the |
---|
| 4385 | C Example Problem located at the beginning of the documentation. More |
---|
| 4386 | C experienced users, requiring the full set of available options, |
---|
| 4387 | C should read the Full Description which follows the Example Problem. |
---|
| 4388 | C |
---|
| 4389 | C 7. The user documentation may need corrections in the following ways: |
---|
| 4390 | C a. If subroutine names have been changed to avoid conflicts between |
---|
| 4391 | C the LSODE and ODESSA packages, the corresponding name changes |
---|
| 4392 | C should be made in the documentation. |
---|
| 4393 | C b. In the Summary of Usage, and in the description of XSETUN under |
---|
| 4394 | C Part II of the Full Description, the default logical unit number |
---|
| 4395 | C should be corrected if it is not 6. |
---|
| 4396 | C c. In the Summary of Usage, users should be instructed to execute |
---|
| 4397 | C CALL XSETF(1) before the first CALL to ODESSA, if this is neces- |
---|
| 4398 | C sary for proper error message handling. (see note 2(e) above.) |
---|
| 4399 | C d. In the description of the subroutines DF and JAC in the Summary |
---|
| 4400 | C of Usage and in Part I of the Full Description, it is stated |
---|
| 4401 | C that dummy names may be passed if these two routines are not user |
---|
| 4402 | C supplied. Your system may require the user to supply a dummy |
---|
| 4403 | C subroutine instead. |
---|
| 4404 | C e. The ODESSA package treats the arguments NEQ, RTOL, and ATOL as |
---|
| 4405 | C arrays (possibly of length 1), while the usage documentation |
---|
| 4406 | C states that these arguments may be either arrays or scalars. |
---|
| 4407 | C If your system does not allow such a mismatch, then the |
---|
| 4408 | C documentation should be changed to reflect this. |
---|
| 4409 | C 8. A demonstration program is provided with the package for |
---|
| 4410 | C verification. |
---|
| 4411 | C |
---|
| 4412 | C |
---|
| 4413 | C Jorge R. Leis and Mark A. Kramer |
---|
| 4414 | C Department of Chemical Engineering |
---|
| 4415 | C Massachusetts Institute of Technology |
---|
| 4416 | C Cambridge, Massachusetts 02139 |
---|
| 4417 | C U.S.A. |
---|
| 4418 | C |
---|
| 4419 | C Current address of J.R. Leis (Jan. 1988): |
---|
| 4420 | C |
---|
| 4421 | C Shell Development Company |
---|
| 4422 | C Westhollow Research Center |
---|
| 4423 | C Houston, TX |
---|
| 4424 | C |
---|
| 4425 | C @ Adapted from 'Instructions for Installing LSODE', written by |
---|
| 4426 | C Alan C. Hindmarsh, Mathematics & Statistics Division, L-316, |
---|
| 4427 | C Lawrence Livermore National Laboratory, Livermore, CA. 94550 |
---|