Mercurial > octave
view libcruft/odessa/odessa_stode.f @ 3983:7a37caf6ed43
[project @ 2002-07-11 02:36:25 by jwe]
author | jwe |
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date | Thu, 11 Jul 2002 02:37:44 +0000 |
parents | |
children | 258c1d15ad78 |
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SUBROUTINE ODESSA_STODE (NEQ, Y, YH, NYH, YH1, WM, IWM, EWT, SAVF, 1 ACOR, PAR, NRS, F, JAC, DF, PJAC, PDF, SLVS) IMPLICIT DOUBLE PRECISION (A-H,O-Z) EXTERNAL F, JAC, DF, PJAC, PDF, SLVS DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), WM(*), IWM(*), EWT(*), 1 SAVF(*), ACOR(*), PAR(*), NRS(*) PARAMETER (ONE=1.0D0,ZERO=0.0D0) COMMON /ODE001/ ROWND, 1 CONIT, CRATE, EL(13), ELCO(13,12), HOLD, RMAX, 2 TESCO(3,12), CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, 3 IOWND1(14), IPUP, MEO, NQNYH, NSLP, 4 IALTH, LMAX, ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, METH, 5 MITER, MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU COMMON /ODE002/ DUPS, DSMS, DDNS, 1 IOWND2(3), ISOPT, NSV, NDFE, NSPE, IDF, IERSP, JOPT, KFLAGS C----------------------------------------------------------------------- C ODESSA_STODE PERFORMS ONE STEP OF THE INTEGRATION OF AN INITIAL VALUE C PROBLEM FOR A SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS. C NOTE.. ODESSA_STODE IS INDEPENDENT OF THE VALUE OF THE ITERATION METHOD C INDICATOR MITER, WHEN THIS IS .NE. 0, AND HENCE IS INDEPENDENT C OF THE TYPE OF CHORD METHOD USED, OR THE JACOBIAN STRUCTURE. C FOR ISOPT = 1, ODESSA_STODE CALLS ODESSA_STESA FOR SENSITIVITY CALCULATIONS. C VARIABLES USED FOR COMMUNICATION WITH ODESSA_STESA ARE DESCRIBED IN C ODESSA_STESA. COMMUNICATION WITH ODESSA_STODE IS DONE WITH THE C FOLLOWING VARIABLES.. C C NEQ = INTEGER ARRAY CONTAINING PROBLEM SIZE IN NEQ(1), AND C NUMBER OF PARAMETERS TO BE CONSIDERED IN THE SENSITIVITY C ANALYSIS NEQ(2) (FOR ISOPT = 1), AND PASSED AS THE C NEQ ARGUMENT IN ALL CALLS TO F, JAC, AND DF. C Y = AN ARRAY OF LENGTH .GE. N USED AS THE Y ARGUMENT IN C ALL CALLS TO F, JAC, AND DF. C YH = AN NYH BY LMAX ARRAY CONTAINING THE DEPENDENT VARIABLES C AND THEIR APPROXIMATE SCALED DERIVATIVES, WHERE C LMAX = MAXORD + 1. YH(I,J+1) CONTAINS THE APPROXIMATE C J-TH DERIVATIVE OF Y(I), SCALED BY H**J/FACTORIAL(J) C (J = 0,1,...,NQ). ON ENTRY FOR THE FIRST STEP, THE FIRST C TWO COLUMNS OF YH MUST BE SET FROM THE INITIAL VALUES. C NYH = A CONSTANT INTEGER .GE. N, THE FIRST DIMENSION OF YH. C THE TOTAL NUMBER OF FIRST-ORDER DIFFERENTIAL EQUATIONS.. C NYH = N, ISOPT = 0, C NYH = N * (NPAR + 1), ISOPT = 1 C YH1 = A ONE-DIMENSIONAL ARRAY OCCUPYING THE SAME SPACE AS YH. C EWT = AN ARRAY OF LENGTH NYH CONTAINING MULTIPLICATIVE WEIGHTS C FOR LOCAL ERROR MEASUREMENTS. LOCAL ERRORS IN Y(I) ARE C COMPARED TO 1.0/EWT(I) IN VARIOUS ERROR TESTS. C SAVF = AN ARRAY OF WORKING STORAGE, OF LENGTH N. C ALSO USED FOR INPUT OF YH(*,MAXORD+2) WHEN JSTART = -1 C AND MAXORD .LT. THE CURRENT ORDER NQ. C ACOR = A WORK ARRAY OF LENGTH NYH, USED FOR THE ACCUMULATED C CORRECTIONS. ON A SUCCESSFUL RETURN, ACOR(I) CONTAINS C THE ESTIMATED ONE-STEP LOCAL ERROR IN Y(I). C WM,IWM = REAL AND INTEGER WORK ARRAYS ASSOCIATED WITH MATRIX C OPERATIONS IN CHORD ITERATION (MITER .NE. 0). C PJAC = NAME OF ROUTINE TO EVALUATE AND PREPROCESS JACOBIAN MATRIX C AND P = I - H*EL0*JAC, IF A CHORD METHOD IS BEING USED. C IF ISOPT = 1, PJAC CAN BE CALLED TO CALCULATE JAC BY C SETTING JOPT = 1. C SLVS = NAME OF ROUTINE TO SOLVE LINEAR SYSTEM IN CHORD ITERATION. C CCMAX = MAXIMUM RELATIVE CHANGE IN H*EL0 BEFORE PJAC IS CALLED. C H = THE STEP SIZE TO BE ATTEMPTED ON THE NEXT STEP. C H IS ALTERED BY THE ERROR CONTROL ALGORITHM DURING THE C PROBLEM. H CAN BE EITHER POSITIVE OR NEGATIVE, BUT ITS C SIGN MUST REMAIN CONSTANT THROUGHOUT THE PROBLEM. C HMIN = THE MINIMUM ABSOLUTE VALUE OF THE STEP SIZE H TO BE USED. C HMXI = INVERSE OF THE MAXIMUM ABSOLUTE VALUE OF H TO BE USED. C HMXI = 0.0 IS ALLOWED AND CORRESPONDS TO AN INFINITE HMAX. C HMIN AND HMXI MAY BE CHANGED AT ANY TIME, BUT WILL NOT C TAKE EFFECT UNTIL THE NEXT CHANGE OF H IS CONSIDERED. C TN = THE INDEPENDENT VARIABLE. TN IS UPDATED ON EACH STEP TAKEN. C JSTART = AN INTEGER USED FOR INPUT ONLY, WITH THE FOLLOWING C VALUES AND MEANINGS.. C 0 PERFORM THE FIRST STEP. C .GT.0 TAKE A NEW STEP CONTINUING FROM THE LAST. C -1 TAKE THE NEXT STEP WITH A NEW VALUE OF H, MAXORD, C N, METH, OR MITER. C -2 TAKE THE NEXT STEP WITH A NEW VALUE OF H, C BUT WITH OTHER INPUTS UNCHANGED. C ON RETURN, JSTART IS SET TO 1 TO FACILITATE CONTINUATION. C KFLAG = A COMPLETION CODE WITH THE FOLLOWING MEANINGS.. C 0 THE STEP WAS SUCCESFUL. C -1 THE REQUESTED ERROR COULD NOT BE ACHIEVED. C -2 CORRECTOR CONVERGENCE COULD NOT BE ACHIEVED. C -3 FATAL ERROR IN PJAC, OR SLVS, (OR ODESSA_STESA). C A RETURN WITH KFLAG = -1 OR -2 MEANS EITHER C ABS(H) = HMIN OR 10 CONSECUTIVE FAILURES OCCURRED. C ON A RETURN WITH KFLAG NEGATIVE, THE VALUES OF TN AND C THE YH ARRAY ARE AS OF THE BEGINNING OF THE LAST C STEP, AND H IS THE LAST STEP SIZE ATTEMPTED. C MAXORD = THE MAXIMUM ORDER OF INTEGRATION METHOD TO BE ALLOWED. C MAXCOR = THE MAXIMUM NUMBER OF CORRECTOR ITERATIONS ALLOWED. C (= 3, IF ISOPT = 0) C (= 4, IF ISOPT = 1) C MSBP = MAXIMUM NUMBER OF STEPS BETWEEN PJAC CALLS (MITER .GT. 0). C IF ISOPT = 1, PJAC IS CALLED AT LEAST ONCE EVERY STEP. C MXNCF = MAXIMUM NUMBER OF CONVERGENCE FAILURES ALLOWED. C METH/MITER = THE METHOD FLAGS. SEE DESCRIPTION IN DRIVER. C N = THE NUMBER OF FIRST-ORDER MODEL DIFFERENTIAL EQUATIONS. C----------------------------------------------------------------------- KFLAG = 0 KFLAGS = 0 TOLD = TN NCF = 0 IERPJ = 0 IERSL = 0 JCUR = 0 ICF = 0 IF (JSTART .GT. 0) GO TO 200 IF (JSTART .EQ. -1) GO TO 100 IF (JSTART .EQ. -2) GO TO 160 C----------------------------------------------------------------------- C ON THE FIRST CALL, THE ORDER IS SET TO 1, AND OTHER VARIABLES ARE C INITIALIZED. RMAX IS THE MAXIMUM RATIO BY WHICH H CAN BE INCREASED C IN A SINGLE STEP. IT IS INITIALLY 1.E4 TO COMPENSATE FOR THE SMALL C INITIAL H, BUT THEN IS NORMALLY EQUAL TO 10. IF A FAILURE C OCCURS (IN CORRECTOR CONVERGENCE OR ERROR TEST), RMAX IS SET AT 2 C FOR THE NEXT INCREASE. C THESE COMPUTATIONS CONSIDER ONLY THE ORIGINAL SOLUTION VECTOR. C THE SENSITIVITY SOLUTION VECTORS ARE CONSIDERED IN ODESSA_STESA (ISOPT = 1). C----------------------------------------------------------------------- LMAX = MAXORD + 1 NQ = 1 L = 2 IALTH = 2 RMAX = 10000.0D0 RC = ZERO EL0 = ONE CRATE = 0.7D0 DELP = ZERO HOLD = H MEO = METH NSLP = 0 IPUP = MITER IRET = 3 GO TO 140 C----------------------------------------------------------------------- C THE FOLLOWING BLOCK HANDLES PRELIMINARIES NEEDED WHEN JSTART = -1. C IPUP IS SET TO MITER TO FORCE A MATRIX UPDATE. C IF AN ORDER INCREASE IS ABOUT TO BE CONSIDERED (IALTH = 1), C IALTH IS RESET TO 2 TO POSTPONE CONSIDERATION ONE MORE STEP. C IF THE CALLER HAS CHANGED METH, ODESSA_CFODE IS CALLED TO RESET C THE COEFFICIENTS OF THE METHOD. C IF THE CALLER HAS CHANGED MAXORD TO A VALUE LESS THAN THE CURRENT C ORDER NQ, NQ IS REDUCED TO MAXORD, AND A NEW H CHOSEN ACCORDINGLY. C IF H IS TO BE CHANGED, YH MUST BE RESCALED. C IF H OR METH IS BEING CHANGED, IALTH IS RESET TO L = NQ + 1 C TO PREVENT FURTHER CHANGES IN H FOR THAT MANY STEPS. C----------------------------------------------------------------------- 100 IPUP = MITER LMAX = MAXORD + 1 IF (IALTH .EQ. 1) IALTH = 2 IF (METH .EQ. MEO) GO TO 110 CALL ODESSA_CFODE (METH, ELCO, TESCO) MEO = METH IF (NQ .GT. MAXORD) GO TO 120 IALTH = L IRET = 1 GO TO 150 110 IF (NQ .LE. MAXORD) GO TO 160 120 NQ = MAXORD L = LMAX DO 125 I = 1,L 125 EL(I) = ELCO(I,NQ) NQNYH = NQ*NYH RC = RC*EL(1)/EL0 EL0 = EL(1) CONIT = 0.5D0/REAL(NQ+2) DDN = ODESSA_VNORM (N, SAVF, EWT)/TESCO(1,L) EXDN = ONE/REAL(L) RHDN = ONE/(1.3D0*DDN**EXDN + 0.0000013D0) RH = MIN(RHDN,ONE) IREDO = 3 IF (H .EQ. HOLD) GO TO 170 RH = MIN(RH,ABS(H/HOLD)) H = HOLD GO TO 175 C----------------------------------------------------------------------- C ODESSA_CFODE IS CALLED TO GET ALL THE INTEGRATION COEFFICIENTS FOR THE C CURRENT METH. THEN THE EL VECTOR AND RELATED CONSTANTS ARE RESET C WHENEVER THE ORDER NQ IS CHANGED, OR AT THE START OF THE PROBLEM. C----------------------------------------------------------------------- 140 CALL ODESSA_CFODE (METH, ELCO, TESCO) 150 DO 155 I = 1,L 155 EL(I) = ELCO(I,NQ) NQNYH = NQ*NYH RC = RC*EL(1)/EL0 EL0 = EL(1) CONIT = 0.5D0/REAL(NQ+2) GO TO (160, 170, 200), IRET C----------------------------------------------------------------------- C IF H IS BEING CHANGED, THE H RATIO RH IS CHECKED AGAINST C RMAX, HMIN, AND HMXI, AND THE YH ARRAY RESCALED. IALTH IS SET TO C L = NQ + 1 TO PREVENT A CHANGE OF H FOR THAT MANY STEPS, UNLESS C FORCED BY A CONVERGENCE OR ERROR TEST FAILURE. C----------------------------------------------------------------------- 160 IF (H .EQ. HOLD) GO TO 200 RH = H/HOLD H = HOLD IREDO = 3 GO TO 175 170 RH = MAX(RH,HMIN/ABS(H)) 175 RH = MIN(RH,RMAX) RH = RH/MAX(ONE,ABS(H)*HMXI*RH) R = ONE DO 180 J = 2,L R = R*RH DO 180 I = 1,NYH 180 YH(I,J) = YH(I,J)*R H = H*RH RC = RC*RH IALTH = L IF (IREDO .EQ. 0) GO TO 690 C----------------------------------------------------------------------- C THIS SECTION COMPUTES THE PREDICTED VALUES BY EFFECTIVELY C MULTIPLYING THE YH ARRAY BY THE PASCAL TRIANGLE MATRIX. C RC IS THE RATIO OF NEW TO OLD VALUES OF THE COEFFICIENT H*EL(1). C WHEN RC DIFFERS FROM 1 BY MORE THAN CCMAX, IPUP IS SET TO MITER C TO FORCE PJAC TO BE CALLED, IF A JACOBIAN IS INVOLVED. C IN ANY CASE, PJAC IS CALLED AT LEAST EVERY MSBP STEPS FOR ISOPT = 0, C AND AT LEAST ONCE EVERY STEP FOR ISOPT = 1. C----------------------------------------------------------------------- 200 IF (ABS(RC-ONE) .GT. CCMAX) IPUP = MITER IF (NST .GE. NSLP+MSBP) IPUP = MITER TN = TN + H I1 = NQNYH + 1 DO 215 JB = 1,NQ I1 = I1 - NYH DO 210 I = I1,NQNYH 210 YH1(I) = YH1(I) + YH1(I+NYH) 215 CONTINUE C----------------------------------------------------------------------- C UP TO MAXCOR CORRECTOR ITERATIONS ARE TAKEN. (= 3, FOR ISOPT = 0; C = 4, FOR ISOPT = 1). A CONVERGENCE TEST IS MADE ON THE R.M.S. NORM C OF EACH CORRECTION, WEIGHTED BY THE ERROR WEIGHT VECTOR EWT. THE SUM C OF THE CORRECTIONS IS ACCUMULATED IN THE VECTOR ACOR(I), I = 1,N. C (ACOR(I), I = N+1,NYH IS LOADED IN SUBROUTINE ODESSA_STESA (ISOPT = 1).) C THE YH ARRAY IS NOT ALTERED IN THE CORRECTOR LOOP. C----------------------------------------------------------------------- 220 M = 0 DO 230 I = 1,N 230 Y(I) = YH(I,1) CALL F (NEQ, TN, Y, PAR, SAVF) NFE = NFE + 1 IF (IPUP .LE. 0) GO TO 250 C----------------------------------------------------------------------- C IF INDICATED, THE MATRIX P = I - H*EL(1)*J IS REEVALUATED AND C PREPROCESSED BEFORE STARTING THE CORRECTOR ITERATION. IPUP IS SET C TO 0 AS AN INDICATOR THAT THIS HAS BEEN DONE. C----------------------------------------------------------------------- IPUP = 0 RC = ONE NSLP = NST CRATE = 0.7D0 CALL PJAC (NEQ, Y, YH, NYH, WM, IWM, EWT, SAVF, ACOR, PAR, 1 F, JAC, JOPT) IF (IERPJ .NE. 0) GO TO 430 250 DO 260 I = 1,N 260 ACOR(I) = ZERO 270 IF (MITER .NE. 0) GO TO 350 C----------------------------------------------------------------------- C IN THE CASE OF FUNCTIONAL ITERATION, UPDATE Y DIRECTLY FROM C THE RESULT OF THE LAST FUNCTION EVALUATION. C (IF ISOPT = 1, FUNCTIONAL ITERATION IS NOT ALLOWED.) C----------------------------------------------------------------------- DO 290 I = 1,N SAVF(I) = H*SAVF(I) - YH(I,2) 290 Y(I) = SAVF(I) - ACOR(I) DEL = ODESSA_VNORM (N, Y, EWT) DO 300 I = 1,N Y(I) = YH(I,1) + EL(1)*SAVF(I) 300 ACOR(I) = SAVF(I) GO TO 400 C----------------------------------------------------------------------- C IN THE CASE OF THE CHORD METHOD, COMPUTE THE CORRECTOR ERROR, C AND SOLVE THE LINEAR SYSTEM WITH THAT AS RIGHT-HAND SIDE AND C P AS COEFFICIENT MATRIX. C----------------------------------------------------------------------- 350 DO 360 I = 1,N 360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) CALL SLVS (WM, IWM, Y, SAVF) IF (IERSL .LT. 0) GO TO 430 IF (IERSL .GT. 0) GO TO 410 DEL = ODESSA_VNORM (N, Y, EWT) DO 380 I = 1,N ACOR(I) = ACOR(I) + Y(I) 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) C----------------------------------------------------------------------- C TEST FOR CONVERGENCE. IF M.GT.0, AN ESTIMATE OF THE CONVERGENCE C RATE CONSTANT IS STORED IN CRATE, AND THIS IS USED IN THE TEST. C----------------------------------------------------------------------- 400 IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) DCON = DEL*MIN(ONE,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) IF (DCON .LE. ONE) GO TO 450 M = M + 1 IF (M .EQ. MAXCOR) GO TO 410 IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 DELP = DEL CALL F (NEQ, TN, Y, PAR, SAVF) NFE = NFE + 1 GO TO 270 C----------------------------------------------------------------------- C THE CORRECTOR ITERATION FAILED TO CONVERGE IN MAXCOR TRIES. C IF MITER .NE. 0 AND THE JACOBIAN IS OUT OF DATE, PJAC IS CALLED FOR C THE NEXT TRY. OTHERWISE THE YH ARRAY IS RETRACTED TO ITS VALUES C BEFORE PREDICTION, AND H IS REDUCED, IF POSSIBLE. IF H CANNOT BE C REDUCED OR MXNCF FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -2. C----------------------------------------------------------------------- 410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430 ICF = 1 IPUP = MITER GO TO 220 430 ICF = 2 NCF = NCF + 1 RMAX = 2.0D0 TN = TOLD I1 = NQNYH + 1 DO 445 JB = 1,NQ I1 = I1 - NYH DO 440 I = I1,NQNYH 440 YH1(I) = YH1(I) - YH1(I+NYH) 445 CONTINUE IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 IF (NCF .EQ. MXNCF) GO TO 670 RH = 0.25D0 IPUP = MITER IREDO = 1 GO TO 170 C----------------------------------------------------------------------- C THE CORRECTOR HAS CONVERGED. C THE LOCAL ERROR TEST IS MADE AND CONTROL PASSES TO STATEMENT 500 C IF IT FAILS. OTHERWISE, ODESSA_STESA IS CALLED (ISOPT = 1) TO PERFORM C SENSITIVITY CALCULATIONS AT CURRENT STEP SIZE AND ORDER. C----------------------------------------------------------------------- 450 CONTINUE IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) IF (M .GT. 0) DSM = ODESSA_VNORM (N, ACOR, EWT)/TESCO(2,NQ) IF (DSM .GT. ONE) GO TO 500 C IF (ISOPT .EQ. 0) GO TO 460 C----------------------------------------------------------------------- C CALL ODESSA_STESA TO PERFORM EXPLICIT SENSITIVITY ANALYSIS. C IF THE LOCAL ERROR TEST FAILS (WITHIN ODESSA_STESA) FOR ANY SOLUTION C VECTOR, KFLAGS IS SET .LT. 0 AND CONTROL PASSES TO STATEMENT 500 UPON C RETURN. IN EITHER CASE, JCUR IS SET TO ZERO TO SIGNAL THAT THE C JACOBIAN MAY NEED UPDATING LATER. C----------------------------------------------------------------------- CALL ODESSA_STESA (NEQ, Y, N, NSV, YH, WM, IWM, EWT, SAVF, ACOR, 1 PAR, NRS, F, JAC, DF, PJAC, PDF, SLVS) IF (IERPJ .NE. 0 .OR. IERSL .NE. 0) GO TO 680 IF (KFLAGS .LT. 0) GO TO 500 C----------------------------------------------------------------------- C AFTER A SUCCESSFUL STEP, UPDATE THE YH ARRAY. C CONSIDER CHANGING H IF IALTH = 1. OTHERWISE DECREASE IALTH BY 1. C IF IALTH IS THEN 1 AND NQ .LT. MAXORD, THEN ACOR IS SAVED FOR C USE IN A POSSIBLE ORDER INCREASE ON THE NEXT STEP. C IF A CHANGE IN H IS CONSIDERED, AN INCREASE OR DECREASE IN ORDER C BY ONE IS CONSIDERED ALSO. A CHANGE IN H IS MADE ONLY IF IT IS BY A C FACTOR OF AT LEAST 1.1. IF NOT, IALTH IS SET TO 3 TO PREVENT C TESTING FOR THAT MANY STEPS. C----------------------------------------------------------------------- 460 JCUR = 0 KFLAG = 0 IREDO = 0 NST = NST + 1 HU = H NQU = NQ DO 470 J = 1,L DO 470 I = 1,NYH 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) IALTH = IALTH - 1 IF (IALTH .EQ. 0) GO TO 520 IF (IALTH .GT. 1) GO TO 700 IF (L .EQ. LMAX) GO TO 700 DO 490 I = 1,NYH 490 YH(I,LMAX) = ACOR(I) GO TO 700 C----------------------------------------------------------------------- C THE ERROR TEST FAILED IN EITHER ODESSA_STODE OR ODESSA_STESA. C KFLAG KEEPS TRACK OF MULTIPLE FAILURES. C RESTORE TN AND THE YH ARRAY TO THEIR PREVIOUS VALUES, AND PREPARE C TO TRY THE STEP AGAIN. COMPUTE THE OPTIMUM STEP SIZE FOR THIS OR C ONE LOWER ORDER. AFTER 2 OR MORE FAILURES, H IS FORCED TO DECREASE C BY A FACTOR OF 0.2 OR LESS. C----------------------------------------------------------------------- 500 KFLAG = KFLAG - 1 JCUR = 0 TN = TOLD I1 = NQNYH + 1 DO 515 JB = 1,NQ I1 = I1 - NYH DO 510 I = I1,NQNYH 510 YH1(I) = YH1(I) - YH1(I+NYH) 515 CONTINUE RMAX = 2.0D0 IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 IF (KFLAG .LE. -3) GO TO 640 IREDO = 2 RHUP = ZERO GO TO 540 C----------------------------------------------------------------------- * C REGARDLESS OF THE SUCCESS OR FAILURE OF THE STEP, FACTORS C RHDN, RHSM, AND RHUP ARE COMPUTED, BY WHICH H COULD BE MULTIPLIED C AT ORDER NQ - 1, ORDER NQ, OR ORDER NQ + 1, RESPECTIVELY. C IN THE CASE OF FAILURE, RHUP = 0.0 TO AVOID AN ORDER INCREASE. C THE LARGEST OF THESE IS DETERMINED AND THE NEW ORDER CHOSEN C ACCORDINGLY. IF THE ORDER IS TO BE INCREASED, WE COMPUTE ONE C ADDITIONAL SCALED DERIVATIVE. C FOR ISOPT = 1, DUPS AND DSMS ARE LOADED WITH THE LARGEST RMS-NORMS C OBTAINED BY CONSIDERING SEPARATELY THE SENSITIVITY SOLUTION VECTORS. C----------------------------------------------------------------------- 520 RHUP = ZERO IF (L .EQ. LMAX) GO TO 540 DO 530 I = 1,N 530 SAVF(I) = ACOR(I) - YH(I,LMAX) DUP = ODESSA_VNORM (N, SAVF, EWT)/TESCO(3,NQ) DUP = MAX(DUP,DUPS) EXUP = ONE/REAL(L+1) RHUP = ONE/(1.4D0*DUP**EXUP + 0.0000014D0) 540 EXSM = ONE/REAL(L) DSM = MAX(DSM,DSMS) RHSM = ONE/(1.2D0*DSM**EXSM + 0.0000012D0) RHDN = ZERO IF (NQ .EQ. 1) GO TO 560 JPOINT = 1 DO 550 J = 1,NSV DDN = ODESSA_VNORM (N, YH(JPOINT,L), EWT(JPOINT))/TESCO(1,NQ) DDNS = MAX(DDNS,DDN) JPOINT = JPOINT + N 550 CONTINUE DDN = DDNS DDNS = ZERO EXDN = ONE/REAL(NQ) RHDN = ONE/(1.3D0*DDN**EXDN + 0.0000013D0) 560 IF (RHSM .GE. RHUP) GO TO 570 IF (RHUP .GT. RHDN) GO TO 590 GO TO 580 570 IF (RHSM .LT. RHDN) GO TO 580 NEWQ = NQ RH = RHSM GO TO 620 580 NEWQ = NQ - 1 RH = RHDN IF (KFLAG .LT. 0 .AND. RH .GT. ONE) RH = ONE GO TO 620 590 NEWQ = L RH = RHUP IF (RH .LT. 1.1D0) GO TO 610 R = EL(L)/REAL(L) DO 600 I = 1,NYH 600 YH(I,NEWQ+1) = ACOR(I)*R GO TO 630 610 IALTH = 3 GO TO 700 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) C----------------------------------------------------------------------- C IF THERE IS A CHANGE OF ORDER, RESET NQ, L, AND THE COEFFICIENTS. C IN ANY CASE H IS RESET ACCORDING TO RH AND THE YH ARRAY IS RESCALED. C THEN EXIT FROM 690 IF THE STEP WAS OK, OR REDO THE STEP OTHERWISE. C----------------------------------------------------------------------- IF (NEWQ .EQ. NQ) GO TO 170 630 NQ = NEWQ L = NQ + 1 IRET = 2 GO TO 150 C----------------------------------------------------------------------- C CONTROL REACHES THIS SECTION IF 3 OR MORE FAILURES HAVE OCCURED. C IF 10 FAILURES HAVE OCCURRED, EXIT WITH KFLAG = -1. C IT IS ASSUMED THAT THE DERIVATIVES THAT HAVE ACCUMULATED IN THE C YH ARRAY HAVE ERRORS OF THE WRONG ORDER. HENCE THE FIRST C DERIVATIVE IS RECOMPUTED, AND THE ORDER IS SET TO 1. THEN C H IS REDUCED BY A FACTOR OF 10, AND THE STEP IS RETRIED, C UNTIL IT SUCCEEDS OR H REACHES HMIN. C----------------------------------------------------------------------- 640 IF (KFLAG .EQ. -10) GO TO 660 RH = 0.1D0 RH = MAX(HMIN/ABS(H),RH) H = H*RH DO 645 I = 1,NYH 645 Y(I) = YH(I,1) CALL F (NEQ, TN, Y, PAR, SAVF) NFE = NFE + 1 IF (ISOPT .EQ. 0) GO TO 649 CALL ODESSA_SPRIME (NEQ, Y, YH, NYH, N, NSV, WM, IWM, EWT, SAVF, 1 ACOR, ACOR(N+1), PAR, F, JAC, DF, PJAC, PDF) IF (IERSP .LT. 0) GO TO 680 DO 646 I = N+1,NYH 646 YH(I,2) = H*YH(I,2) 649 DO 650 I = 1,N 650 YH(I,2) = H*SAVF(I) IPUP = MITER IALTH = 5 IF (NQ .EQ. 1) GO TO 200 NQ = 1 L = 2 IRET = 3 GO TO 150 C----------------------------------------------------------------------- C ALL RETURNS ARE MADE THROUGH THIS SECTION. H IS SAVED IN HOLD C TO ALLOW THE CALLER TO CHANGE H ON THE NEXT STEP. C----------------------------------------------------------------------- 660 KFLAG = -1 GO TO 720 670 KFLAG = -2 GO TO 720 680 KFLAG = -3 GO TO 720 690 RMAX = 10.0D0 700 R = ONE/TESCO(2,NQU) DO 710 I = 1,NYH 710 ACOR(I) = ACOR(I)*R 720 HOLD = H JSTART = 1 RETURN C----------------------- END OF SUBROUTINE ODESSA_STODE ----------------------- END