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. |
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348 | C 25 FOR STIFF METHOD, INTERNALLY GENERATED BANDED JACOBIAN. |
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349 | C IF ISOPT = 1, MF = 10 IS ILLEGAL AND CAN BE REPLACED BY.. |
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350 | C 11 FOR NONSTIFF METHOD, USER-SUPPLIED FULL JACOBIAN. |
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351 | C 12 FOR NONSTIFF METHOD, INTERNALLY GENERATED FULL JACOBIAN. |
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352 | C 14 FOR NONSTIFF METHOD, USER-SUPPLIED BANDED JACOBIAN. |
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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 |
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355 | C POSSIBLY ATOL AND RTOL, AS WELL AS NEQ, IOPT, AND PAR IF ISOPT = 1. |
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356 | C |
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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. |
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359 | C T = CORRESPONDING VALUE OF INDEPENDENT VARIABLE (NORMALLY TOUT). |
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360 | C ISTATE = 2 IF ODESSA WAS SUCCESSFUL, NEGATIVE OTHERWISE. |
---|
361 | C -1 MEANS EXCESS WORK DONE ON THIS CALL (PERHAPS WRONG MF). |
---|
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. |
---|
372 | C---------------------------------------------------------------------- |
---|
373 | C EXAMPLE PROBLEM. |
---|
374 | C |
---|
375 | C THE FOLLOWING IS A SIMPLE EXAMPLE PROBLEM, WITH THE CODING |
---|
376 | C NEEDED FOR ITS SOLUTION BY ODESSA. THE PROBLEM IS FROM CHEMICAL |
---|
377 | C KINETICS, AND CONSISTS OF THE FOLLOWING THREE RATE EQUATIONS.. |
---|
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 |
---|
386 | C MF = 21 AND PRINTING RESULTS AT T = .4, 4., ..., 4.E10. |
---|
387 | C IT USES ITOL = 4 AND ATOL MUCH SMALLER FOR Y2 THAN Y1 OR Y3, |
---|
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 |
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4361 | C routines are used in the single precision version. |
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4362 | C |
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4363 | C 4. There are four integer variables, in the two labeled COMMON |
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4364 | C blocks /ODE001/ and /EH0001/, which need to be loaded with DATA |
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4365 | C statements. They can vary during execution, and are in common to |
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4366 | C assure their retention between calls. This is legal in ANSI Fortran |
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4367 | C only if done in a BLOCK DATA subprogram, and this package has a |
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4368 | C BLOCK DATA for this purpose. However, BLOCK DATA subprograms can be |
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4369 | C difficult to install in libraries, and many compilers allow such DATA |
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4370 | C statements in subroutines. If your system allows this, the location |
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4371 | C of the DATA statements are just after the initial type and common |
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4372 | C declarations in subroutines ODESSA and XERR. In ODESSA, ILLIN and |
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4373 | C NTREP are DATA-loaded as 0. In XERR, MESFLG is loaded as 1 and |
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4374 | C LUNIT is loaded as the appropriate default logical unit number. |
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4375 | C |
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4376 | C 5. The ODESSA package contains subscript expressions which may not |
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4377 | C be accepted by some compilers. Subscripts of the form I + J, I - J, |
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4378 | C etc., occur in various routines. If any of these forms are |
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4379 | C unacceptable to your compiler, an extra line of code setting the |
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4380 | C subscript to a dummy integer value should be added for each subscipt. |
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4381 | C |
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4382 | C 6. User documentation is provided in a two-level structure |
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4383 | C to accommmodate both the casual and serious user. The novice or |
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4384 | C casual user should need to read only the Summary of Usage and the |
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4385 | C Example Problem located at the beginning of the documentation. More |
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4386 | C experienced users, requiring the full set of available options, |
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4387 | C should read the Full Description which follows the Example Problem. |
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4388 | C |
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4389 | C 7. The user documentation may need corrections in the following ways: |
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4390 | C a. If subroutine names have been changed to avoid conflicts between |
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4391 | C the LSODE and ODESSA packages, the corresponding name changes |
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4392 | C should be made in the documentation. |
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4393 | C b. In the Summary of Usage, and in the description of XSETUN under |
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4394 | C Part II of the Full Description, the default logical unit number |
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4395 | C should be corrected if it is not 6. |
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4396 | C c. In the Summary of Usage, users should be instructed to execute |
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4397 | C CALL XSETF(1) before the first CALL to ODESSA, if this is neces- |
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4398 | C sary for proper error message handling. (see note 2(e) above.) |
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4399 | C d. In the description of the subroutines DF and JAC in the Summary |
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4400 | C of Usage and in Part I of the Full Description, it is stated |
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4401 | C that dummy names may be passed if these two routines are not user |
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4402 | C supplied. Your system may require the user to supply a dummy |
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4403 | C subroutine instead. |
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4404 | C e. The ODESSA package treats the arguments NEQ, RTOL, and ATOL as |
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4405 | C arrays (possibly of length 1), while the usage documentation |
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4406 | C states that these arguments may be either arrays or scalars. |
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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 |
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4410 | C verification. |
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4411 | C |
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4412 | C |
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4413 | C Jorge R. Leis and Mark A. Kramer |
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4414 | C Department of Chemical Engineering |
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4415 | C Massachusetts Institute of Technology |
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4416 | C Cambridge, Massachusetts 02139 |
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4417 | C U.S.A. |
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4418 | C |
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4419 | C Current address of J.R. Leis (Jan. 1988): |
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4420 | C |
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4421 | C Shell Development Company |
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4422 | C Westhollow Research Center |
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4423 | C Houston, TX |
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4424 | C |
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4425 | C @ Adapted from 'Instructions for Installing LSODE', written by |
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4426 | C Alan C. Hindmarsh, Mathematics & Statistics Division, L-316, |
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4427 | C Lawrence Livermore National Laboratory, Livermore, CA. 94550 |
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