1 | SUBROUTINE INTEGRATE( NSENSIT, Y, TIN, TOUT ) |
---|
2 | |
---|
3 | INCLUDE 'KPP_ROOT_params.h' |
---|
4 | INCLUDE 'KPP_ROOT_global.h' |
---|
5 | |
---|
6 | C TIN - Start Time |
---|
7 | KPP_REAL TIN |
---|
8 | C TOUT - End Time |
---|
9 | KPP_REAL TOUT |
---|
10 | C Y - Concentrations and Sensitivities |
---|
11 | KPP_REAL Y(NVAR*(NSENSIT+1)) |
---|
12 | C --- Note: Y contains: (1:NVAR) concentrations, followed by |
---|
13 | C --- (1:NVAR) sensitivities w.r.t. first parameter, followed by |
---|
14 | C --- etc., followed by |
---|
15 | C --- (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
---|
16 | |
---|
17 | INTEGER INFO(5) |
---|
18 | |
---|
19 | EXTERNAL FUNC_CHEM, JAC_CHEM |
---|
20 | |
---|
21 | INFO(1) = Autonomous |
---|
22 | |
---|
23 | CALL ROS4_DDM(NVAR,NSENSIT,TIN,TOUT,STEPMIN,STEPMAX, |
---|
24 | + STEPMIN,Y,ATOL,RTOL, |
---|
25 | + Info,FUNC_CHEM,JAC_CHEM) |
---|
26 | |
---|
27 | |
---|
28 | RETURN |
---|
29 | END |
---|
30 | |
---|
31 | |
---|
32 | |
---|
33 | |
---|
34 | SUBROUTINE ROS4_DDM(N,NSENSIT,T,Tnext,Hmin,Hmax,Hstart, |
---|
35 | + y,AbsTol,RelTol, |
---|
36 | + Info,FUNC_CHEM,JAC_CHEM) |
---|
37 | IMPLICIT NONE |
---|
38 | INCLUDE 'KPP_ROOT_params.h' |
---|
39 | INCLUDE 'KPP_ROOT_global.h' |
---|
40 | INCLUDE 'KPP_ROOT_sparse.h' |
---|
41 | C |
---|
42 | C Four Stages, Fourth Order L-stable Rosenbrock Method, |
---|
43 | C with embedded L-stable, third order method for error control |
---|
44 | C Simplified version of E. Hairer's atmros4; the coefficients are slightly different |
---|
45 | C |
---|
46 | C Direct decoupled computation of sensitivities. |
---|
47 | C The global variable DDMTYPE distinguishes between: |
---|
48 | C DDMTYPE = 0 : sensitivities w.r.t. initial values |
---|
49 | C DDMTYPE = 1 : sensitivities w.r.t. parameters |
---|
50 | C |
---|
51 | C INPUT ARGUMENTS: |
---|
52 | C y = Vector of: (1:NVAR) concentrations, followed by |
---|
53 | C (1:NVAR) sensitivities w.r.t. first parameter, followed by |
---|
54 | C etc., followed by |
---|
55 | C (1:NVAR) sensitivities w.r.t. NSENSIT's parameter |
---|
56 | C (y contains initial values at input, final values at output) |
---|
57 | C [T, Tnext] = the integration interval |
---|
58 | C Hmin, Hmax = lower and upper bounds for the selected step-size. |
---|
59 | C Note that for Step = Hmin the current computed |
---|
60 | C solution is unconditionally accepted by the error |
---|
61 | C control mechanism. |
---|
62 | C AbsTol, RelTol = (NVAR) dimensional vectors of |
---|
63 | C componentwise absolute and relative tolerances. |
---|
64 | C FUNC_CHEM = name of routine of derivatives. KPP syntax. |
---|
65 | C See the header below. |
---|
66 | C JAC_CHEM = name of routine that computes the Jacobian, in |
---|
67 | C sparse format. KPP syntax. See the header below. |
---|
68 | C Info(1) = 1 for Autonomous system |
---|
69 | C = 0 for nonAutonomous system |
---|
70 | C |
---|
71 | C OUTPUT ARGUMENTS: |
---|
72 | C y = the values of concentrations and sensitivities at Tend. |
---|
73 | C T = equals TENDon output. |
---|
74 | C Info(2) = # of FUNC_CHEM CALLs. |
---|
75 | C Info(3) = # of JAC_CHEM CALLs. |
---|
76 | C Info(4) = # of accepted steps. |
---|
77 | C Info(5) = # of rejected steps. |
---|
78 | C |
---|
79 | C Adrian Sandu, December 2001 |
---|
80 | C |
---|
81 | |
---|
82 | |
---|
83 | INTEGER NSENSIT |
---|
84 | KPP_REAL y(NVAR*(NSENSIT+1)), ynew(NVAR*(NSENSIT+1)) |
---|
85 | KPP_REAL K1(NVAR*(NSENSIT+1)) |
---|
86 | KPP_REAL K2(NVAR*(NSENSIT+1)) |
---|
87 | KPP_REAL K3(NVAR*(NSENSIT+1)) |
---|
88 | KPP_REAL K4(NVAR*(NSENSIT+1)) |
---|
89 | KPP_REAL Fv(NVAR), Hv(NVAR) |
---|
90 | KPP_REAL DFDT(NVAR*(NSENSIT+1)) |
---|
91 | KPP_REAL DFDP(NVAR*NSENSIT), DFDPDT(NVAR*NSENSIT) |
---|
92 | KPP_REAL DJDP(NVAR*NSENSIT) |
---|
93 | KPP_REAL JAC(LU_NONZERO), AJAC(LU_NONZERO) |
---|
94 | KPP_REAL DJDT(LU_NONZERO) |
---|
95 | KPP_REAL HESS(NHESS) |
---|
96 | KPP_REAL Hmin,Hmax,Hstart,ghinv,uround |
---|
97 | KPP_REAL AbsTol(NVAR), RelTol(NVAR) |
---|
98 | KPP_REAL T, Tnext, Tplus, H, Hnew, elo |
---|
99 | KPP_REAL ERR, factor, facmax, dround, tau |
---|
100 | KPP_REAL w, e, beta1, beta2, beta3, beta4 |
---|
101 | |
---|
102 | INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier |
---|
103 | INTEGER Info(5) |
---|
104 | LOGICAL IsReject, Autonomous |
---|
105 | EXTERNAL FUNC_CHEM, JAC_CHEM, HESS_CHEM |
---|
106 | |
---|
107 | |
---|
108 | C The method coefficients |
---|
109 | C DOUBLE PRECISION gamma, gamma2, gamma3, gamma4 |
---|
110 | C PARAMETER ( gamma = 0.57281606D0 ) |
---|
111 | C PARAMETER ( gamma2 = -1.769177067112013949170520D0 ) |
---|
112 | C PARAMETER ( gamma3 = 0.759293964293209853670967D0 ) |
---|
113 | C PARAMETER ( gamma4 = -0.104894621490955803206743D0 ) |
---|
114 | C DOUBLE PRECISION a21, a31, a32, a41, a42, a43 |
---|
115 | C PARAMETER ( a21 = 2.00000000000000000000000D0 ) |
---|
116 | C PARAMETER ( a31 = 1.86794814949823713234476D0 ) |
---|
117 | C PARAMETER ( a32 = 0.23444556851723885002322D0 ) |
---|
118 | C DOUBLE PRECISION alpha2, alpha3, alpha4 |
---|
119 | C PARAMETER ( alpha2 = 1.145632120D0 ) |
---|
120 | C PARAMETER ( alpha3 = 0.655214975973133829477748D0 ) |
---|
121 | C DOUBLE PRECISION c21, c31, c32, c41, c42, c43 |
---|
122 | C PARAMETER ( c21 = -7.137649943349979830369260D0 ) |
---|
123 | C PARAMETER ( c31 = 2.580923666509657714488050D0 ) |
---|
124 | C PARAMETER ( c32 = 0.651629887302032023387417D0 ) |
---|
125 | C PARAMETER ( c41 = -2.137115266506619116806370D0 ) |
---|
126 | C PARAMETER ( c42 = -0.321469531339951070769241D0 ) |
---|
127 | C PARAMETER ( c43 = -0.694966049282445225157329D0 ) |
---|
128 | C DOUBLE PRECISION m1, m2, m3, m4, mhat1, mhat2, mhat3, mhat4 |
---|
129 | C PARAMETER ( m1 = 2.255566228604565243728840D0 ) |
---|
130 | C PARAMETER ( m2 = 0.287055063194157607662630D0 ) |
---|
131 | C PARAMETER ( m3 = 0.435311963379983213402707D0 ) |
---|
132 | C PARAMETER ( m4 = 1.093507656403247803214820D0 ) |
---|
133 | C PARAMETER ( mhat1 = 2.068399160527583734258670D0 ) |
---|
134 | C PARAMETER ( mhat2 = 0.238681352067532797956493D0 ) |
---|
135 | C PARAMETER ( mhat3 = 0.363373345435391708261747D0 ) |
---|
136 | C PARAMETER ( mhat4 = 0.366557127936155144309163D0 ) |
---|
137 | C DOUBLE PRECISION e1, e2, e3, e4 |
---|
138 | c PARAMETER ( e1 = 1.8716706807698191283861888D-01 ) |
---|
139 | c PARAMETER ( e2 = 4.8373711126624835410225955D-02 ) |
---|
140 | c PARAMETER ( e3 = 7.1938617944591554120847832D-02 ) |
---|
141 | c PARAMETER ( e4 = 7.2695052846709262706070831D-01 ) |
---|
142 | C PARAMETER ( e1 = -0.2815431932141155D+00 ) |
---|
143 | C PARAMETER ( e2 = -0.7276199124938920D-01 ) |
---|
144 | C PARAMETER ( e3 = -0.1082196201495311D+00 ) |
---|
145 | C PARAMETER ( e4 = -0.1093502252409163D+01 ) |
---|
146 | C The method coefficients |
---|
147 | DOUBLE PRECISION gamma, gamma2, gamma3, gamma4 |
---|
148 | PARAMETER ( gamma = 0.5728200000000000D+00 ) |
---|
149 | PARAMETER ( gamma2 = -0.1769193891319233D+01 ) |
---|
150 | PARAMETER ( gamma3 = 0.7592633437920482D+00 ) |
---|
151 | PARAMETER ( gamma4 = -0.1049021087100450D+00 ) |
---|
152 | DOUBLE PRECISION a21, a31, a32, a41, a42, a43 |
---|
153 | PARAMETER ( a21 = 0.2000000000000000D+01 ) |
---|
154 | PARAMETER ( a31 = 0.1867943637803922D+01 ) |
---|
155 | PARAMETER ( a32 = 0.2344449711399156D+00 ) |
---|
156 | DOUBLE PRECISION alpha2, alpha3 |
---|
157 | PARAMETER ( alpha2 = 0.1145640000000000D+01 ) |
---|
158 | PARAMETER ( alpha3 = 0.6552168638155900D+00 ) |
---|
159 | DOUBLE PRECISION c21, c31, c32, c41, c42, c43 |
---|
160 | PARAMETER ( c21 = -0.7137615036412310D+01 ) |
---|
161 | PARAMETER ( c31 = 0.2580708087951457D+01 ) |
---|
162 | PARAMETER ( c32 = 0.6515950076447975D+00 ) |
---|
163 | PARAMETER ( c41 = -0.2137148994382534D+01 ) |
---|
164 | PARAMETER ( c42 = -0.3214669691237626D+00 ) |
---|
165 | PARAMETER ( c43 = -0.6949742501781779D+00 ) |
---|
166 | DOUBLE PRECISION b1, b2, b3, b4 |
---|
167 | PARAMETER ( b1 = 0.2255570073418735D+01 ) |
---|
168 | PARAMETER ( b2 = 0.2870493262186792D+00 ) |
---|
169 | PARAMETER ( b3 = 0.4353179431840180D+00 ) |
---|
170 | PARAMETER ( b4 = 0.1093502252409163D+01 ) |
---|
171 | DOUBLE PRECISION d1, d2, d3, d4 |
---|
172 | PARAMETER ( d1 = -0.2815431932141155D+00 ) |
---|
173 | PARAMETER ( d2 = -0.7276199124938920D-01 ) |
---|
174 | PARAMETER ( d3 = -0.1082196201495311D+00 ) |
---|
175 | PARAMETER ( d4 = -0.1093502252409163D+01 ) |
---|
176 | |
---|
177 | |
---|
178 | c Initialization of counters, etc. |
---|
179 | Autonomous = Info(1) .EQ. 1 |
---|
180 | uround = 1.d-15 |
---|
181 | dround = DSQRT(uround) |
---|
182 | IF (Hmax.le.0.D0) THEN |
---|
183 | Hmax = DABS(Tnext-T) |
---|
184 | END IF |
---|
185 | H = DMAX1(1.d-8, Hstart) |
---|
186 | Tplus = T |
---|
187 | IsReject = .false. |
---|
188 | Naccept = 0 |
---|
189 | Nreject = 0 |
---|
190 | Nfcn = 0 |
---|
191 | Njac = 0 |
---|
192 | |
---|
193 | C === Starting the time loop === |
---|
194 | 10 CONTINUE |
---|
195 | |
---|
196 | Tplus = T + H |
---|
197 | IF ( Tplus .gt. Tnext ) THEN |
---|
198 | H = Tnext - T |
---|
199 | Tplus = Tnext |
---|
200 | END IF |
---|
201 | |
---|
202 | C Initial Function, Jacobian, and Hessian Values |
---|
203 | CALL FUNC_CHEM(NVAR, T, y, Fv) |
---|
204 | CALL JAC_CHEM(NVAR, T, y, JAC) |
---|
205 | CALL HESS_CHEM( NVAR, T, y, HESS ) |
---|
206 | IF (DDMTYPE .EQ. 1) THEN |
---|
207 | CALL DFUNDPAR(NVAR, NSENSIT, T, y, DFDP) |
---|
208 | END IF |
---|
209 | |
---|
210 | C The time derivatives for non-Autonomous case |
---|
211 | IF (.not. Autonomous) THEN |
---|
212 | tau = DSIGN(dround*DMAX1( 1.0d0, DABS(T) ), T) |
---|
213 | CALL FUNC_CHEM(NVAR, T+tau, y, K2) |
---|
214 | CALL JAC_CHEM(NVAR, T+tau, y, AJAC) |
---|
215 | nfcn=nfcn+1 |
---|
216 | DO 20 j = 1,NVAR |
---|
217 | DFDT(j) = ( K2(j)-Fv(j) )/tau |
---|
218 | 20 CONTINUE |
---|
219 | DO 30 j = 1,LU_NONZERO |
---|
220 | DJDT(j) = ( AJAC(j)-JAC(j) )/tau |
---|
221 | 30 CONTINUE |
---|
222 | DO 35 i=1,NSENSIT |
---|
223 | CALL Jac_SP_Vec (DJDT,y(i*NVAR+1),DFDT(i*NVAR+1)) |
---|
224 | 35 CONTINUE |
---|
225 | END IF |
---|
226 | |
---|
227 | 11 CONTINUE ! From here we restart after a rejected step |
---|
228 | |
---|
229 | C Form the Prediction matrix and compute its LU factorization |
---|
230 | Njac = Njac+1 |
---|
231 | ghinv = 1.0d0/(gamma*H) |
---|
232 | DO 40 j=1,LU_NONZERO |
---|
233 | AJAC(j) = -JAC(j) |
---|
234 | 40 CONTINUE |
---|
235 | DO 50 j=1,NVAR |
---|
236 | AJAC(LU_DIAG(j)) = AJAC(LU_DIAG(j)) + ghinv |
---|
237 | 50 CONTINUE |
---|
238 | CALL KppDecomp (AJAC, ier) |
---|
239 | C |
---|
240 | IF (ier.ne.0) THEN |
---|
241 | IF ( H.gt.Hmin) THEN |
---|
242 | H = 5.0d-1*H |
---|
243 | GO TO 10 |
---|
244 | ELSE |
---|
245 | PRINT *,'ROS4: Singular factorization at T=',T,'; H=',H |
---|
246 | STOP |
---|
247 | END IF |
---|
248 | END IF |
---|
249 | |
---|
250 | C ------------ STAGE 1------------------------- |
---|
251 | DO 60 j = 1,NVAR |
---|
252 | K1(j) = Fv(j) |
---|
253 | 60 CONTINUE |
---|
254 | IF (.NOT. Autonomous) THEN |
---|
255 | beta1 = H*gamma |
---|
256 | DO 70 j=1,NVAR |
---|
257 | K1(j) = K1(j) + beta1*DFDT(j) |
---|
258 | 70 CONTINUE |
---|
259 | END IF |
---|
260 | CALL KppSolve (AJAC, K1) |
---|
261 | C --- If derivative w.r.t. parameters |
---|
262 | IF (DDMTYPE .EQ. 1) THEN |
---|
263 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K1(1), DJDP) |
---|
264 | END IF |
---|
265 | C --- End of derivative w.r.t. parameters |
---|
266 | |
---|
267 | DO 100 i=1,NSENSIT |
---|
268 | CALL Jac_SP_Vec (JAC,y(i*NVAR+1),K1(i*NVAR+1)) |
---|
269 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K1(1), Hv ) |
---|
270 | DO 80 j=1,NVAR |
---|
271 | K1(i*NVAR+j) = K1(i*NVAR+j) + Hv(j) |
---|
272 | 80 CONTINUE |
---|
273 | IF (.NOT. Autonomous) THEN |
---|
274 | DO 90 j=1,NVAR |
---|
275 | K1(i*NVAR+j) = K1(i*NVAR+j) + beta1*DFDT(i*NVAR+j) |
---|
276 | 90 CONTINUE |
---|
277 | END IF |
---|
278 | C --- If derivative w.r.t. parameters |
---|
279 | IF (DDMTYPE .EQ. 1) THEN |
---|
280 | DO 95 j = 1,NVAR |
---|
281 | K1(i*NVAR+j) = K1(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
---|
282 | & + DJDP((i-1)*NVAR+j) |
---|
283 | 95 CONTINUE |
---|
284 | END IF |
---|
285 | C --- End of derivative w.r.t. parameters |
---|
286 | CALL KppSolve (AJAC, K1(i*NVAR+1)) |
---|
287 | 100 CONTINUE |
---|
288 | |
---|
289 | C ----------- STAGE 2 ------------------------- |
---|
290 | DO 110 j = 1,NVAR*(NSENSIT+1) |
---|
291 | ynew(j) = y(j) + a21*K1(j) |
---|
292 | 110 CONTINUE |
---|
293 | CALL FUNC_CHEM(NVAR, T+alpha2*H, ynew, Fv) |
---|
294 | IF (DDMTYPE .EQ. 1) THEN |
---|
295 | CALL DFUNDPAR(NVAR, NSENSIT, T+alpha2*H, ynew, DFDP) |
---|
296 | END IF |
---|
297 | nfcn=nfcn+1 |
---|
298 | beta1 = c21/H |
---|
299 | DO 120 j = 1,NVAR |
---|
300 | K2(j) = Fv(j) + beta1*K1(j) |
---|
301 | 120 CONTINUE |
---|
302 | IF (.NOT. Autonomous) THEN |
---|
303 | beta2 = H*gamma2 |
---|
304 | DO 130 j=1,NVAR |
---|
305 | K2(j) = K2(j) + beta2*DFDT(j) |
---|
306 | 130 CONTINUE |
---|
307 | END IF |
---|
308 | CALL KppSolve (AJAC, K2) |
---|
309 | C --- If derivative w.r.t. parameters |
---|
310 | IF (DDMTYPE .EQ. 1) THEN |
---|
311 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K2(1), DJDP) |
---|
312 | END IF |
---|
313 | C --- End of derivative w.r.t. parameters |
---|
314 | |
---|
315 | CALL JAC_CHEM(NVAR, T+alpha2*H, ynew, JAC) |
---|
316 | njac=njac+1 |
---|
317 | DO 160 i=1,NSENSIT |
---|
318 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K2(i*NVAR+1)) |
---|
319 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K2(1), Hv ) |
---|
320 | DO 140 j = 1,NVAR |
---|
321 | K2(i*NVAR+j) = K2(i*NVAR+j) + beta1*K1(i*NVAR+j) |
---|
322 | & + Hv(j) |
---|
323 | 140 CONTINUE |
---|
324 | IF (.NOT. Autonomous) THEN |
---|
325 | DO 150 j=1,NVAR |
---|
326 | K2(i*NVAR+j) = K2(i*NVAR+j) + beta2*DFDT(i*NVAR+j) |
---|
327 | 150 CONTINUE |
---|
328 | END IF |
---|
329 | C --- If derivative w.r.t. parameters |
---|
330 | IF (DDMTYPE .EQ. 1) THEN |
---|
331 | DO 155 j = 1,NVAR |
---|
332 | K2(i*NVAR+j) = K2(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
---|
333 | & + DJDP((i-1)*NVAR+j) |
---|
334 | 155 CONTINUE |
---|
335 | END IF |
---|
336 | C --- End of derivative w.r.t. parameters |
---|
337 | CALL KppSolve (AJAC, K2(i*NVAR+1)) |
---|
338 | 160 CONTINUE |
---|
339 | |
---|
340 | |
---|
341 | C ------------ STAGE 3 ------------------------- |
---|
342 | DO 170 j = 1,NVAR*(NSENSIT+1) |
---|
343 | ynew(j) = y(j) + a31*K1(j) + a32*K2(j) |
---|
344 | 170 CONTINUE |
---|
345 | CALL FUNC_CHEM(NVAR, T+alpha3*H, ynew, Fv) |
---|
346 | IF (DDMTYPE .EQ. 1) THEN |
---|
347 | CALL DFUNDPAR(NVAR, NSENSIT, T+alpha3*H, ynew, DFDP) |
---|
348 | END IF |
---|
349 | nfcn=nfcn+1 |
---|
350 | beta1 = c31/H |
---|
351 | beta2 = c32/H |
---|
352 | DO 180 j = 1,NVAR |
---|
353 | K3(j) = Fv(j) + beta1*K1(j) + beta2*K2(j) |
---|
354 | 180 CONTINUE |
---|
355 | IF (.NOT. Autonomous) THEN |
---|
356 | beta3 = H*gamma3 |
---|
357 | DO 190 j=1,NVAR |
---|
358 | K3(j) = K3(j) + beta3*DFDT(j) |
---|
359 | 190 CONTINUE |
---|
360 | END IF |
---|
361 | CALL KppSolve (AJAC, K3) |
---|
362 | C --- If derivative w.r.t. parameters |
---|
363 | IF (DDMTYPE .EQ. 1) THEN |
---|
364 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K3(1), DJDP) |
---|
365 | END IF |
---|
366 | C --- End of derivative w.r.t. parameters |
---|
367 | |
---|
368 | CALL JAC_CHEM(NVAR, T+alpha3*H, ynew, JAC) |
---|
369 | njac=njac+1 |
---|
370 | DO 220 i=1,NSENSIT |
---|
371 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K3(i*NVAR+1)) |
---|
372 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K3(1), Hv ) |
---|
373 | DO 200 j = 1,NVAR |
---|
374 | K3(i*NVAR+j) = K3(i*NVAR+j) + beta1*K1(i*NVAR+j) |
---|
375 | & + beta2*K2(i*NVAR+j) + Hv(j) |
---|
376 | 200 CONTINUE |
---|
377 | IF (.NOT. Autonomous) THEN |
---|
378 | DO 210 j=1,NVAR |
---|
379 | K3(i*NVAR+j) = K3(i*NVAR+j) + beta3*DFDT(i*NVAR+j) |
---|
380 | 210 CONTINUE |
---|
381 | END IF |
---|
382 | C --- If derivative w.r.t. parameters |
---|
383 | IF (DDMTYPE .EQ. 1) THEN |
---|
384 | DO 215 j = 1,NVAR |
---|
385 | K3(i*NVAR+j) = K3(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
---|
386 | & + DJDP((i-1)*NVAR+j) |
---|
387 | 215 CONTINUE |
---|
388 | END IF |
---|
389 | C --- End of derivative w.r.t. parameters |
---|
390 | CALL KppSolve (AJAC, K3(i*NVAR+1)) |
---|
391 | 220 CONTINUE |
---|
392 | |
---|
393 | C ------------ STAGE 4 ------------------------- |
---|
394 | C Note: uses the same function values as stage 3 |
---|
395 | beta1 = c41/H |
---|
396 | beta2 = c42/H |
---|
397 | beta3 = c43/H |
---|
398 | DO 230 j = 1,NVAR |
---|
399 | K4(j) = Fv(j) + beta1*K1(j) + beta2*K2(j) + beta3*K3(j) |
---|
400 | 230 CONTINUE |
---|
401 | IF (.NOT. Autonomous) THEN |
---|
402 | beta4 = H*gamma4 |
---|
403 | DO 240 j=1,NVAR |
---|
404 | K4(j) = K4(j) + beta4*DFDT(j) |
---|
405 | 240 CONTINUE |
---|
406 | END IF |
---|
407 | CALL KppSolve (AJAC, K4) |
---|
408 | C --- If derivative w.r.t. parameters |
---|
409 | IF (DDMTYPE .EQ. 1) THEN |
---|
410 | CALL DJACDPAR(NVAR, NSENSIT, T, y, K4(1), DJDP) |
---|
411 | END IF |
---|
412 | C --- End of derivative w.r.t. parameters |
---|
413 | |
---|
414 | njac=njac+1 |
---|
415 | DO 270 i=1,NSENSIT |
---|
416 | CALL Jac_SP_Vec (JAC,ynew(i*NVAR+1),K4(i*NVAR+1)) |
---|
417 | CALL Hess_Vec ( HESS, y(i*NVAR+1), K4(1), Hv ) |
---|
418 | DO 250 j = 1,NVAR |
---|
419 | K4(i*NVAR+j) = K4(i*NVAR+j) + beta1*K1(i*NVAR+j) |
---|
420 | & + beta2*K2(i*NVAR+j) + beta3*K3(i*NVAR+j) |
---|
421 | & + Hv(j) |
---|
422 | 250 CONTINUE |
---|
423 | IF (.NOT. Autonomous) THEN |
---|
424 | DO 260 j=1,NVAR |
---|
425 | K4(i*NVAR+j) = K4(i*NVAR+j) + beta4*DFDT(i*NVAR+j) |
---|
426 | 260 CONTINUE |
---|
427 | END IF |
---|
428 | C --- If derivative w.r.t. parameters |
---|
429 | IF (DDMTYPE .EQ. 1) THEN |
---|
430 | DO 265 j = 1,NVAR |
---|
431 | K4(i*NVAR+j) = K4(i*NVAR+j) + DFDP((i-1)*NVAR+j) |
---|
432 | & + DJDP((i-1)*NVAR+j) |
---|
433 | 265 CONTINUE |
---|
434 | END IF |
---|
435 | CALL KppSolve (AJAC, K4(i*NVAR+1)) |
---|
436 | 270 CONTINUE |
---|
437 | |
---|
438 | |
---|
439 | C ---- The Solution --- |
---|
440 | DO 280 j = 1,NVAR*(NSENSIT+1) |
---|
441 | ynew(j) = y(j) + b1*K1(j) + b2*K2(j) + b3*K3(j) + b4*K4(j) |
---|
442 | 280 CONTINUE |
---|
443 | |
---|
444 | |
---|
445 | C ====== Error estimation -- can be extended to control sensitivities too ======== |
---|
446 | |
---|
447 | ERR = 0.d0 |
---|
448 | DO 290 i=1,NVAR |
---|
449 | w = AbsTol(i) + RelTol(i)*DMAX1(DABS(ynew(i)),DABS(y(i))) |
---|
450 | e = d1*K1(i) + d2*K2(i) + d3*K3(i) + d4*K4(i) |
---|
451 | ERR = ERR + ( e/w )**2 |
---|
452 | 290 CONTINUE |
---|
453 | ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) |
---|
454 | |
---|
455 | C ======= Choose the stepsize =============================== |
---|
456 | |
---|
457 | elo = 4.0D0 ! estimator local order |
---|
458 | factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) |
---|
459 | Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) |
---|
460 | |
---|
461 | C ======= Rejected/Accepted Step ============================ |
---|
462 | |
---|
463 | IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN |
---|
464 | IsReject = .true. |
---|
465 | H = DMIN1(H/10,Hnew) |
---|
466 | Nreject = Nreject+1 |
---|
467 | ELSE |
---|
468 | DO 300 i=1,NVAR*(NSENSIT+1) |
---|
469 | y(i) = ynew(i) |
---|
470 | 300 CONTINUE |
---|
471 | T = Tplus |
---|
472 | IF (.NOT.IsReject) THEN |
---|
473 | H = Hnew ! Do not increase stepsize if previos step was rejected |
---|
474 | END IF |
---|
475 | IsReject = .false. |
---|
476 | Naccept = Naccept+1 |
---|
477 | END IF |
---|
478 | |
---|
479 | C ======= End of the time loop =============================== |
---|
480 | IF ( T .lt. Tnext ) GO TO 10 |
---|
481 | |
---|
482 | |
---|
483 | |
---|
484 | C ======= Output Information ================================= |
---|
485 | Info(2) = Nfcn |
---|
486 | Info(3) = Njac |
---|
487 | Info(4) = Naccept |
---|
488 | Info(5) = Nreject |
---|
489 | Hstart = H |
---|
490 | |
---|
491 | RETURN |
---|
492 | END |
---|
493 | |
---|
494 | |
---|
495 | |
---|
496 | SUBROUTINE FUNC_CHEM(N, T, Y, P) |
---|
497 | INCLUDE 'KPP_ROOT_params.h' |
---|
498 | INCLUDE 'KPP_ROOT_global.h' |
---|
499 | KPP_REAL T, Told |
---|
500 | KPP_REAL Y(NVAR), P(NVAR) |
---|
501 | Told = TIME |
---|
502 | TIME = T |
---|
503 | CALL Update_SUN() |
---|
504 | CALL Update_RCONST() |
---|
505 | CALL Fun( Y, FIX, RCONST, P ) |
---|
506 | TIME = Told |
---|
507 | RETURN |
---|
508 | END |
---|
509 | |
---|
510 | |
---|
511 | SUBROUTINE DFUNDPAR(N, NSENSIT, T, Y, P) |
---|
512 | C --- Computes the partial derivatives of FUNC_CHEM w.r.t. parameters |
---|
513 | INCLUDE 'KPP_ROOT_params.h' |
---|
514 | INCLUDE 'KPP_ROOT_global.h' |
---|
515 | C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients |
---|
516 | INTEGER NCOEFF, JCOEFF(NREACT) |
---|
517 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
---|
518 | |
---|
519 | KPP_REAL T, Told |
---|
520 | KPP_REAL Y(NVAR), P(NVAR*NSENSIT) |
---|
521 | Told = TIME |
---|
522 | TIME = T |
---|
523 | CALL Update_SUN() |
---|
524 | CALL Update_RCONST() |
---|
525 | C |
---|
526 | IF (DDMTYPE .EQ. 0) THEN |
---|
527 | C --- Note: the values below are for sensitivities w.r.t. initial values; |
---|
528 | C --- they may have to be changed for other applications |
---|
529 | DO j=1,NSENSIT |
---|
530 | DO i=1,NVAR |
---|
531 | P(i+NVAR*(j-1)) = 0.0D0 |
---|
532 | END DO |
---|
533 | END DO |
---|
534 | ELSE |
---|
535 | C --- Example: the call below is for sensitivities w.r.t. rate coefficients; |
---|
536 | C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients |
---|
537 | C --- w.r.t. which one differentiates |
---|
538 | CALL dFun_dRcoeff( Y, FIX, NCOEFF, JCOEFF, P ) |
---|
539 | END IF |
---|
540 | TIME = Told |
---|
541 | RETURN |
---|
542 | END |
---|
543 | |
---|
544 | SUBROUTINE JAC_CHEM(N, T, Y, J) |
---|
545 | INCLUDE 'KPP_ROOT_params.h' |
---|
546 | INCLUDE 'KPP_ROOT_global.h' |
---|
547 | INTEGER N |
---|
548 | KPP_REAL Told, T |
---|
549 | KPP_REAL Y(NVAR), J(LU_NONZERO) |
---|
550 | Told = TIME |
---|
551 | TIME = T |
---|
552 | CALL Update_SUN() |
---|
553 | CALL Update_RCONST() |
---|
554 | CALL Jac_SP( Y, FIX, RCONST, J ) |
---|
555 | TIME = Told |
---|
556 | RETURN |
---|
557 | END |
---|
558 | |
---|
559 | |
---|
560 | SUBROUTINE DJACDPAR(N, NSENSIT, T, Y, U, P) |
---|
561 | C --- Computes the partial derivatives of JAC w.r.t. parameters times user vector U |
---|
562 | INCLUDE 'KPP_ROOT_params.h' |
---|
563 | INCLUDE 'KPP_ROOT_global.h' |
---|
564 | C --- NCOEFF, JCOEFF useful for derivatives w.r.t. rate coefficients |
---|
565 | INTEGER N |
---|
566 | INTEGER NCOEFF, JCOEFF(NREACT) |
---|
567 | COMMON /DDMRCOEFF/ NCOEFF, JCOEFF |
---|
568 | |
---|
569 | KPP_REAL T, Told |
---|
570 | KPP_REAL Y(NVAR), U(NVAR) |
---|
571 | KPP_REAL P(NVAR*NSENSIT) |
---|
572 | Told = TIME |
---|
573 | TIME = T |
---|
574 | CALL Update_SUN() |
---|
575 | CALL Update_RCONST() |
---|
576 | C |
---|
577 | IF (DDMTYPE .EQ. 0) THEN |
---|
578 | C --- Note: the values below are for sensitivities w.r.t. initial values; |
---|
579 | C --- they may have to be changed for other applications |
---|
580 | DO j=1,NSENSIT |
---|
581 | DO i=1,NVAR |
---|
582 | P(i+NVAR*(j-1)) = 0.0D0 |
---|
583 | END DO |
---|
584 | END DO |
---|
585 | ELSE |
---|
586 | C --- Example: the call below is for sensitivities w.r.t. rate coefficients; |
---|
587 | C --- JCOEFF(1:NSENSIT) are the indices of the NSENSIT rate coefficients |
---|
588 | C --- w.r.t. which one differentiates |
---|
589 | CALL dJac_dRcoeff( Y, FIX, U, NCOEFF, JCOEFF, P ) |
---|
590 | END IF |
---|
591 | TIME = Told |
---|
592 | RETURN |
---|
593 | END |
---|
594 | |
---|
595 | |
---|
596 | SUBROUTINE HESS_CHEM(N, T, Y, HESS) |
---|
597 | INCLUDE 'KPP_ROOT_params.h' |
---|
598 | INCLUDE 'KPP_ROOT_global.h' |
---|
599 | INTEGER N |
---|
600 | KPP_REAL Told, T |
---|
601 | KPP_REAL Y(NVAR), HESS(NHESS) |
---|
602 | Told = TIME |
---|
603 | TIME = T |
---|
604 | CALL Update_SUN() |
---|
605 | CALL Update_RCONST() |
---|
606 | CALL Hessian( Y, FIX, RCONST, HESS ) |
---|
607 | TIME = Told |
---|
608 | RETURN |
---|
609 | END |
---|
610 | |
---|
611 | |
---|
612 | |
---|
613 | |
---|
614 | |
---|
615 | |
---|