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radau.f 70.64 KiB
SUBROUTINE RADAU(N,FCN,X,Y,XEND,H,
& RTOL,ATOL,ITOL,
& JAC ,IJAC,MLJAC,MUJAC,
& MAS ,IMAS,MLMAS,MUMAS,
& SOLOUT,IOUT,
& WORK,LWORK,IWORK,LIWORK,RPAR,IPAR,IDID)
C ----------------------------------------------------------
C NUMERICAL SOLUTION OF A STIFF (OR DIFFERENTIAL ALGEBRAIC)
C SYSTEM OF FIRST 0RDER ORDINARY DIFFERENTIAL EQUATIONS
C M*Y'=F(X,Y).
C THE SYSTEM CAN BE (LINEARLY) IMPLICIT (MASS-MATRIX M .NE. I)
C OR EXPLICIT (M=I).
C THE CODE IS BASED ON IMPLICIT RUNGE-KUTTA METHODS (RADAU IIA)
C WITH VARIABLE ORDER (5, 9, 13), WITH STEP SIZE CONTROL
C AND CONTINUOUS OUTPUT.
C
C AUTHORS: E. HAIRER AND G. WANNER
C UNIVERSITE DE GENEVE, DEPT. DE MATHEMATIQUES
C CH-1211 GENEVE 24, SWITZERLAND
C E-MAIL: Ernst.Hairer@math.unige.ch
C Gerhard.Wanner@math.unige.ch
C
C FOR A DESCRIPTION OF THE RELATED CODE RADAU5 SEE THE BOOK:
C E. HAIRER AND G. WANNER, SOLVING ORDINARY DIFFERENTIAL
C EQUATIONS II. STIFF AND DIFFERENTIAL-ALGEBRAIC PROBLEMS.
C SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS 14,
C SPRINGER-VERLAG 1991, SECOND EDITION 1996.
C
C PRELIMINARY VERSION OF APRIL 23, 1998
C (latest small correction: January 18, 2002)
C
C INPUT PARAMETERS
C ----------------
C N DIMENSION OF THE SYSTEM
C
C FCN NAME (EXTERNAL) OF SUBROUTINE COMPUTING THE
C VALUE OF F(X,Y):
C SUBROUTINE FCN(N,X,Y,F,RPAR,IPAR)
C DOUBLE PRECISION X,Y(N),F(N)
C F(1)=... ETC.
C RPAR, IPAR (SEE BELOW)
C
C X INITIAL X-VALUE
C
C Y(N) INITIAL VALUES FOR Y
C
C XEND FINAL X-VALUE (XEND-X MAY BE POSITIVE OR NEGATIVE)
C
C H INITIAL STEP SIZE GUESS;
C FOR STIFF EQUATIONS WITH INITIAL TRANSIENT,
C H=1.D0/(NORM OF F'), USUALLY 1.D-3 OR 1.D-5, IS GOOD.
C THIS CHOICE IS NOT VERY IMPORTANT, THE STEP SIZE IS
C QUICKLY ADAPTED. (IF H=0.D0, THE CODE PUTS H=1.D-6).
C
C RTOL,ATOL RELATIVE AND ABSOLUTE ERROR TOLERANCES. THEY
C CAN BE BOTH SCALARS OR ELSE BOTH VECTORS OF LENGTH N.
C
C ITOL SWITCH FOR RTOL AND ATOL:
C ITOL=0: BOTH RTOL AND ATOL ARE SCALARS.
C THE CODE KEEPS, ROUGHLY, THE LOCAL ERROR OF
C Y(I) BELOW RTOL*ABS(Y(I))+ATOL
C ITOL=1: BOTH RTOL AND ATOL ARE VECTORS.
C THE CODE KEEPS THE LOCAL ERROR OF Y(I) BELOW
C RTOL(I)*ABS(Y(I))+ATOL(I).
C
C JAC NAME (EXTERNAL) OF THE SUBROUTINE WHICH COMPUTES
C THE PARTIAL DERIVATIVES OF F(X,Y) WITH RESPECT TO Y
C (THIS ROUTINE IS ONLY CALLED IF IJAC=1; SUPPLY
C A DUMMY SUBROUTINE IN THE CASE IJAC=0).
C FOR IJAC=1, THIS SUBROUTINE MUST HAVE THE FORMC SUBROUTINE JAC(N,X,Y,DFY,LDFY,RPAR,IPAR)
C DOUBLE PRECISION X,Y(N),DFY(LDFY,N)
C DFY(1,1)= ...
C LDFY, THE COLUMN-LENGTH OF THE ARRAY, IS
C FURNISHED BY THE CALLING PROGRAM.
C IF (MLJAC.EQ.N) THE JACOBIAN IS SUPPOSED TO
C BE FULL AND THE PARTIAL DERIVATIVES ARE
C STORED IN DFY AS
C DFY(I,J) = PARTIAL F(I) / PARTIAL Y(J)
C ELSE, THE JACOBIAN IS TAKEN AS BANDED AND
C THE PARTIAL DERIVATIVES ARE STORED
C DIAGONAL-WISE AS
C DFY(I-J+MUJAC+1,J) = PARTIAL F(I) / PARTIAL Y(J).
C
C IJAC SWITCH FOR THE COMPUTATION OF THE JACOBIAN:
C IJAC=0: JACOBIAN IS COMPUTED INTERNALLY BY FINITE
C DIFFERENCES, SUBROUTINE "JAC" IS NEVER CALLED.
C IJAC=1: JACOBIAN IS SUPPLIED BY SUBROUTINE JAC.
C
C MLJAC SWITCH FOR THE BANDED STRUCTURE OF THE JACOBIAN:
C MLJAC=N: JACOBIAN IS A FULL MATRIX. THE LINEAR
C ALGEBRA IS DONE BY FULL-MATRIX GAUSS-ELIMINATION.
C 0<=MLJAC<N: MLJAC IS THE LOWER BANDWITH OF JACOBIAN
C MATRIX (>= NUMBER OF NON-ZERO DIAGONALS BELOW
C THE MAIN DIAGONAL).
C
C MUJAC UPPER BANDWITH OF JACOBIAN MATRIX (>= NUMBER OF NON-
C ZERO DIAGONALS ABOVE THE MAIN DIAGONAL).
C NEED NOT BE DEFINED IF MLJAC=N.
C
C ---- MAS,IMAS,MLMAS, AND MUMAS HAVE ANALOG MEANINGS -----
C ---- FOR THE "MASS MATRIX" (THE MATRIX "M" OF SECTION IV.8): -
C
C MAS NAME (EXTERNAL) OF SUBROUTINE COMPUTING THE MASS-
C MATRIX M.
C IF IMAS=0, THIS MATRIX IS ASSUMED TO BE THE IDENTITY
C MATRIX AND NEEDS NOT TO BE DEFINED;
C SUPPLY A DUMMY SUBROUTINE IN THIS CASE.
C IF IMAS=1, THE SUBROUTINE MAS IS OF THE FORM
C SUBROUTINE MAS(N,AM,LMAS,RPAR,IPAR)
C DOUBLE PRECISION AM(LMAS,N)
C AM(1,1)= ....
C IF (MLMAS.EQ.N) THE MASS-MATRIX IS STORED
C AS FULL MATRIX LIKE
C AM(I,J) = M(I,J)
C ELSE, THE MATRIX IS TAKEN AS BANDED AND STORED
C DIAGONAL-WISE AS
C AM(I-J+MUMAS+1,J) = M(I,J).
C
C IMAS GIVES INFORMATION ON THE MASS-MATRIX:
C IMAS=0: M IS SUPPOSED TO BE THE IDENTITY
C MATRIX, MAS IS NEVER CALLED.
C IMAS=1: MASS-MATRIX IS SUPPLIED.
C
C MLMAS SWITCH FOR THE BANDED STRUCTURE OF THE MASS-MATRIX:
C MLMAS=N: THE FULL MATRIX CASE. THE LINEAR
C ALGEBRA IS DONE BY FULL-MATRIX GAUSS-ELIMINATION.
C 0<=MLMAS<N: MLMAS IS THE LOWER BANDWITH OF THE
C MATRIX (>= NUMBER OF NON-ZERO DIAGONALS BELOW
C THE MAIN DIAGONAL).
C MLMAS IS SUPPOSED TO BE .LE. MLJAC.
C
C MUMAS UPPER BANDWITH OF MASS-MATRIX (>= NUMBER OF NON-
C ZERO DIAGONALS ABOVE THE MAIN DIAGONAL).
C NEED NOT BE DEFINED IF MLMAS=N.
C MUMAS IS SUPPOSED TO BE .LE. MUJAC.
C
C SOLOUT NAME (EXTERNAL) OF SUBROUTINE PROVIDING THE
C NUMERICAL SOLUTION DURING INTEGRATION.
C IF IOUT=1, IT IS CALLED AFTER EVERY SUCCESSFUL STEP.C SUPPLY A DUMMY SUBROUTINE IF IOUT=0.
C IT MUST HAVE THE FORM
C SUBROUTINE SOLOUT (NR,XOLD,X,Y,CONT,LRC,N,
C RPAR,IPAR,IRTRN)
C DOUBLE PRECISION X,Y(N),CONT(LRC)
C ....
C SOLOUT FURNISHES THE SOLUTION "Y" AT THE NR-TH
C GRID-POINT "X" (THEREBY THE INITIAL VALUE IS
C THE FIRST GRID-POINT).
C "XOLD" IS THE PRECEEDING GRID-POINT.
C "IRTRN" SERVES TO INTERRUPT THE INTEGRATION. IF IRTRN
C IS SET <0, RADAU RETURNS TO THE CALLING PROGRAM.
C
C ----- CONTINUOUS OUTPUT: -----
C DURING CALLS TO "SOLOUT", A CONTINUOUS SOLUTION
C FOR THE INTERVAL [XOLD,X] IS AVAILABLE THROUGH
C THE FUNCTION
C >>> CONTRA(I,S,CONT,LRC) <<<
C WHICH PROVIDES AN APPROXIMATION TO THE I-TH
C COMPONENT OF THE SOLUTION AT THE POINT S. THE VALUE
C S SHOULD LIE IN THE INTERVAL [XOLD,X].
C
C IOUT SWITCH FOR CALLING THE SUBROUTINE SOLOUT:
C IOUT=0: SUBROUTINE IS NEVER CALLED
C IOUT=1: SUBROUTINE IS AVAILABLE FOR OUTPUT.
C
C WORK ARRAY OF WORKING SPACE OF LENGTH "LWORK".
C WORK(1), WORK(2),.., WORK(20) SERVE AS PARAMETERS
C FOR THE CODE. FOR STANDARD USE OF THE CODE
C WORK(1),..,WORK(20) MUST BE SET TO ZERO BEFORE THE
C FIRST CALL. SEE BELOW FOR A MORE SOPHISTICATED USE.
C WORK(8),..,WORK(LWORK) SERVE AS WORKING SPACE
C FOR ALL VECTORS AND MATRICES.
C "LWORK" MUST BE AT LEAST
C N*(LJAC+LMAS+NSMAX*LE+3*NSMAX+3)+20
C WHERE
C NSMAX=IWORK(12) (SEE BELOW)
C AND
C LJAC=N IF MLJAC=N (FULL JACOBIAN)
C LJAC=MLJAC+MUJAC+1 IF MLJAC<N (BANDED JAC.)
C AND
C LMAS=0 IF IMAS=0
C LMAS=N IF IMAS=1 AND MLMAS=N (FULL)
C LMAS=MLMAS+MUMAS+1 IF MLMAS<N (BANDED MASS-M.)
C AND
C LE=N IF MLJAC=N (FULL JACOBIAN)
C LE=2*MLJAC+MUJAC+1 IF MLJAC<N (BANDED JAC.)
C
C IN THE USUAL CASE WHERE THE JACOBIAN IS FULL AND THE
C MASS-MATRIX IS THE INDENTITY (IMAS=0), THE MINIMUM
C STORAGE REQUIREMENT IS
C LWORK = (NSMAX+1)*N*N+(3*NSMAX+3)*N+20.
C IF IWORK(9)=M1>0 THEN "LWORK" MUST BE AT LEAST
C N*(LJAC+3*NSMAX+3)+(N-M1)*(LMAS+NSMAX*LE)+20
C WHERE IN THE DEFINITIONS OF LJAC, LMAS AND LE THE
C NUMBER N CAN BE REPLACED BY N-M1.
C
C LWORK DECLARED LENGTH OF ARRAY "WORK".
C
C IWORK INTEGER WORKING SPACE OF LENGTH "LIWORK".
C IWORK(1),IWORK(2),...,IWORK(20) SERVE AS PARAMETERS
C FOR THE CODE. FOR STANDARD USE, SET IWORK(1),..,
C IWORK(20) TO ZERO BEFORE CALLING.
C IWORK(21),...,IWORK(LIWORK) SERVE AS WORKING AREA.
C "LIWORK" MUST BE AT LEAST
C (2+(NSMAX-1)/2)*N+20.
C
C LIWORK DECLARED LENGTH OF ARRAY "IWORK".
C
C RPAR, IPAR REAL AND INTEGER PARAMETERS (OR PARAMETER ARRAYS) WHICH C CAN BE USED FOR COMMUNICATION BETWEEN YOUR CALLING
C PROGRAM AND THE FCN, JAC, MAS, SOLOUT SUBROUTINES.
C
C ----------------------------------------------------------------------
C
C SOPHISTICATED SETTING OF PARAMETERS
C -----------------------------------
C SEVERAL PARAMETERS OF THE CODE ARE TUNED TO MAKE IT WORK
C WELL. THEY MAY BE DEFINED BY SETTING WORK(1),...
C AS WELL AS IWORK(1),... DIFFERENT FROM ZERO.
C FOR ZERO INPUT, THE CODE CHOOSES DEFAULT VALUES:
C
C IWORK(1) IF IWORK(1).NE.0, THE CODE TRANSFORMS THE JACOBIAN
C MATRIX TO HESSENBERG FORM. THIS IS PARTICULARLY
C ADVANTAGEOUS FOR LARGE SYSTEMS WITH FULL JACOBIAN.
C IT DOES NOT WORK FOR BANDED JACOBIAN (MLJAC<N)
C AND NOT FOR IMPLICIT SYSTEMS (IMAS=1).
C
C IWORK(2) THIS IS THE MAXIMAL NUMBER OF ALLOWED STEPS.
C THE DEFAULT VALUE (FOR IWORK(2)=0) IS 100000.
C
C IWORK(3) THE MAXIMUM NUMBER OF NEWTON ITERATIONS FOR THE
C SOLUTION OF THE IMPLICIT SYSTEM IN EACH STEP
C IWORK(3)+(NS-3)*2.5. DEFAULT VALUE (FOR IWORK(3)=0) IS 7.
C NS IS THE NUMBER OF STAGES (SEE IWORK(11)).
C
C IWORK(4) IF IWORK(4).EQ.0 THE EXTRAPOLATED COLLOCATION SOLUTION
C IS TAKEN AS STARTING VALUE FOR NEWTON'S METHOD.
C IF IWORK(4).NE.0 ZERO STARTING VALUES ARE USED.
C THE LATTER IS RECOMMENDED IF NEWTON'S METHOD HAS
C DIFFICULTIES WITH CONVERGENCE (THIS IS THE CASE WHEN
C NSTEP IS LARGER THAN NACCPT + NREJCT; SEE OUTPUT PARAM.).
C DEFAULT IS IWORK(4)=0.
C
C THE FOLLOWING 3 PARAMETERS ARE IMPORTANT FOR
C DIFFERENTIAL-ALGEBRAIC SYSTEMS OF INDEX > 1.
C THE FUNCTION-SUBROUTINE SHOULD BE WRITTEN SUCH THAT
C THE INDEX 1,2,3 VARIABLES APPEAR IN THIS ORDER.
C IN ESTIMATING THE ERROR THE INDEX 2 VARIABLES ARE
C MULTIPLIED BY H, THE INDEX 3 VARIABLES BY H**2.
C
C IWORK(5) DIMENSION OF THE INDEX 1 VARIABLES (MUST BE > 0). FOR
C ODE'S THIS EQUALS THE DIMENSION OF THE SYSTEM.
C DEFAULT IWORK(5)=N.
C
C IWORK(6) DIMENSION OF THE INDEX 2 VARIABLES. DEFAULT IWORK(6)=0.
C
C IWORK(7) DIMENSION OF THE INDEX 3 VARIABLES. DEFAULT IWORK(7)=0.
C
C IWORK(8) SWITCH FOR STEP SIZE STRATEGY
C IF IWORK(8).EQ.1 MOD. PREDICTIVE CONTROLLER (GUSTAFSSON)
C IF IWORK(8).EQ.2 CLASSICAL STEP SIZE CONTROL
C THE DEFAULT VALUE (FOR IWORK(8)=0) IS IWORK(8)=1.
C THE CHOICE IWORK(8).EQ.1 SEEMS TO PRODUCE SAFER RESULTS;
C FOR SIMPLE PROBLEMS, THE CHOICE IWORK(8).EQ.2 PRODUCES
C OFTEN SLIGHTLY FASTER RUNS
C
C IF THE DIFFERENTIAL SYSTEM HAS THE SPECIAL STRUCTURE THAT
C Y(I)' = Y(I+M2) FOR I=1,...,M1,
C WITH M1 A MULTIPLE OF M2, A SUBSTANTIAL GAIN IN COMPUTERTIME
C CAN BE ACHIEVED BY SETTING THE PARAMETERS IWORK(9) AND IWORK(10).
C E.G., FOR SECOND ORDER SYSTEMS P'=V, V'=G(P,V), WHERE P AND V ARE
C VECTORS OF DIMENSION N/2, ONE HAS TO PUT M1=M2=N/2.
C FOR M1>0 SOME OF THE INPUT PARAMETERS HAVE DIFFERENT MEANINGS:
C - JAC: ONLY THE ELEMENTS OF THE NON-TRIVIAL PART OF THE
C JACOBIAN HAVE TO BE STORED
C IF (MLJAC.EQ.N-M1) THE JACOBIAN IS SUPPOSED TO BE FULL
C DFY(I,J) = PARTIAL F(I+M1) / PARTIAL Y(J)
C FOR I=1,N-M1 AND J=1,N.
C ELSE, THE JACOBIAN IS BANDED ( M1 = M2 * MM )C DFY(I-J+MUJAC+1,J+K*M2) = PARTIAL F(I+M1) / PARTIAL Y(J+K*M2)
C FOR I=1,MLJAC+MUJAC+1 AND J=1,M2 AND K=0,MM.
C - MLJAC: MLJAC=N-M1: IF THE NON-TRIVIAL PART OF THE JACOBIAN IS FULL
C 0<=MLJAC<N-M1: IF THE (MM+1) SUBMATRICES (FOR K=0,MM)
C PARTIAL F(I+M1) / PARTIAL Y(J+K*M2), I,J=1,M2
C ARE BANDED, MLJAC IS THE MAXIMAL LOWER BANDWIDTH
C OF THESE MM+1 SUBMATRICES
C - MUJAC: MAXIMAL UPPER BANDWIDTH OF THESE MM+1 SUBMATRICES
C NEED NOT BE DEFINED IF MLJAC=N-M1
C - MAS: IF IMAS=0 THIS MATRIX IS ASSUMED TO BE THE IDENTITY AND
C NEED NOT BE DEFINED. SUPPLY A DUMMY SUBROUTINE IN THIS CASE.
C IT IS ASSUMED THAT ONLY THE ELEMENTS OF RIGHT LOWER BLOCK OF
C DIMENSION N-M1 DIFFER FROM THAT OF THE IDENTITY MATRIX.
C IF (MLMAS.EQ.N-M1) THIS SUBMATRIX IS SUPPOSED TO BE FULL
C AM(I,J) = M(I+M1,J+M1) FOR I=1,N-M1 AND J=1,N-M1.
C ELSE, THE MASS MATRIX IS BANDED
C AM(I-J+MUMAS+1,J) = M(I+M1,J+M1)
C - MLMAS: MLMAS=N-M1: IF THE NON-TRIVIAL PART OF M IS FULL
C 0<=MLMAS<N-M1: LOWER BANDWIDTH OF THE MASS MATRIX
C - MUMAS: UPPER BANDWIDTH OF THE MASS MATRIX
C NEED NOT BE DEFINED IF MLMAS=N-M1
C
C IWORK(9) THE VALUE OF M1. DEFAULT M1=0.
C
C IWORK(10) THE VALUE OF M2. DEFAULT M2=M1.
C
C IWORK(11) NSMIN, MINIMAL NUMBER OF STAGES NS (ORDER 2*NS-1)
C POSSIBLE VALUES ARE 1,3,5,7. DEFAULT NS=3.
C
C IWORK(12) NSMAX, MAXIMAL NUMBER OF STAGES NS.
C POSSIBLE VALUES ARE 1,3,5,7. DEFAULT NS=7.
C
C IWORK(13) VALUE OF NS FOR THE FIRST STEP (DEFAULT VALUE: NSMIN)
C
C ----------
C
C WORK(1) UROUND, THE ROUNDING UNIT, DEFAULT 1.D-16.
C
C WORK(2) THE SAFETY FACTOR IN STEP SIZE PREDICTION,
C DEFAULT 0.9D0.
C
C WORK(3) DECIDES WHETHER THE JACOBIAN SHOULD BE RECOMPUTED;
C INCREASE WORK(3), TO 0.1 SAY, WHEN JACOBIAN EVALUATIONS
C ARE COSTLY. FOR SMALL SYSTEMS WORK(3) SHOULD BE SMALLER
C (0.001D0, SAY). NEGATIV WORK(3) FORCES THE CODE TO
C COMPUTE THE JACOBIAN AFTER EVERY ACCEPTED STEP.
C DEFAULT 0.001D0.
C
C WORK(5) AND WORK(6) : IF WORK(5) < HNEW/HOLD < WORK(6), THEN THE
C STEP SIZE IS NOT CHANGED. THIS SAVES, TOGETHER WITH A
C LARGE WORK(3), LU-DECOMPOSITIONS AND COMPUTING TIME FOR
C LARGE SYSTEMS. FOR SMALL SYSTEMS ONE MAY HAVE
C WORK(5)=1.D0, WORK(6)=1.2D0, FOR LARGE FULL SYSTEMS
C WORK(5)=0.99D0, WORK(6)=2.D0 MIGHT BE GOOD.
C DEFAULTS WORK(5)=1.D0, WORK(6)=1.2D0 .
C
C WORK(7) MAXIMAL STEP SIZE, DEFAULT XEND-X.
C
C WORK(8), WORK(9) PARAMETERS FOR STEP SIZE SELECTION
C THE NEW STEP SIZE IS CHOSEN SUBJECT TO THE RESTRICTION
C WORK(8) <= HNEW/HOLD <= WORK(9)
C DEFAULT VALUES: WORK(8)=0.2D0, WORK(9)=8.D0
C
C WORK(10) ORDER IS INCREASED IF THE CONTRACTIVITY FACTOR IS
C SMALL THAN WORK(10), DEFAULT VALUE IS 0.002
C
C WORK(11) ORDER IS DECREASED IF THE CONTRACTIVITY FACTOR IS
C LARGER THAN WORK(11), DEFAULT VALUE IS 0.8
C
C WORK(12), WORK(13) ORDER IS DECREASED ONLY IF THE STEPSIZEC RATIO SATISFIES WORK(13).LE.HNEW/H.LE.WORK(12),
C DEFAULT VALUES ARE 1.2 AND 0.8
C
C-----------------------------------------------------------------------
C
C OUTPUT PARAMETERS
C -----------------
C X X-VALUE FOR WHICH THE SOLUTION HAS BEEN COMPUTED
C (AFTER SUCCESSFUL RETURN X=XEND).
C
C Y(N) NUMERICAL SOLUTION AT X
C
C H PREDICTED STEP SIZE OF THE LAST ACCEPTED STEP
C
C IDID REPORTS ON SUCCESSFULNESS UPON RETURN:
C IDID= 1 COMPUTATION SUCCESSFUL,
C IDID= 2 COMPUT. SUCCESSFUL (INTERRUPTED BY SOLOUT)
C IDID=-1 INPUT IS NOT CONSISTENT,
C IDID=-2 LARGER NMAX IS NEEDED,
C IDID=-3 STEP SIZE BECOMES TOO SMALL,
C IDID=-4 MATRIX IS REPEATEDLY SINGULAR.
C
C IWORK(14) NFCN NUMBER OF FUNCTION EVALUATIONS (THOSE FOR NUMERICAL
C EVALUATION OF THE JACOBIAN ARE NOT COUNTED)
C IWORK(15) NJAC NUMBER OF JACOBIAN EVALUATIONS (EITHER ANALYTICALLY
C OR NUMERICALLY)
C IWORK(16) NSTEP NUMBER OF COMPUTED STEPS
C IWORK(17) NACCPT NUMBER OF ACCEPTED STEPS
C IWORK(18) NREJCT NUMBER OF REJECTED STEPS (DUE TO ERROR TEST),
C (STEP REJECTIONS IN THE FIRST STEP ARE NOT COUNTED)
C IWORK(19) NDEC NUMBER OF LU-DECOMPOSITIONS OF THE MATRICES
C IWORK(20) NSOL NUMBER OF FORWARD-BACKWARD SUBSTITUTIONS, OF ALL
C SYSTEMS THAT HAVE TO BE SOLVED FOR ONE SIMPLIFIED
C NEWTON ITERATION; THE NSTEP (REAL) FORWARD-BACKWARD
C SUBSTITUTIONS, NEEDED FOR STEP SIZE SELECTION,
C ARE NOT COUNTED.
C-----------------------------------------------------------------------
C *** *** *** *** *** *** *** *** *** *** *** *** ***
C DECLARATIONS
C *** *** *** *** *** *** *** *** *** *** *** *** ***
USE omp_lib
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION Y(N),ATOL(*),RTOL(*),WORK(LWORK),IWORK(LIWORK)
DIMENSION RPAR(*),IPAR(*)
LOGICAL IMPLCT,JBAND,ARRET,STARTN,PRED
EXTERNAL FCN,JAC,MAS,SOLOUT
C *** *** *** *** *** *** ***
C SETTING THE PARAMETERS
C *** *** *** *** *** *** ***
NFCN=0
NJAC=0
NSTEP=0
NACCPT=0
NREJCT=0
NDEC=0
NSOL=0
ARRET=.FALSE.
C -------- NUMBER MAXIMAL AND MINIMAL OF STAGES NS
IF (IWORK(11).EQ.0) THEN
NSMIN=3
ELSE
NSMIN=MAX(1,IWORK(11))
IF (IWORK(11).GE.2) NSMIN=MAX(3,IWORK(11))
IF (IWORK(11).GE.4) NSMIN=MAX(5,IWORK(11))
IF (IWORK(11).GE.6) NSMIN=7
END IF
IF (IWORK(12).EQ.0) THEN
NSMAX=7
ELSE
NSMAX=MIN(7,IWORK(12)) IF (IWORK(12).LE.6) NSMAX=MIN(5,IWORK(12))
IF (IWORK(12).LE.4) NSMAX=MIN(3,IWORK(12))
IF (IWORK(12).LE.2) NSMAX=1
END IF
NS=NSMAX
IF (IWORK(13).EQ.0) THEN
NSUS=NSMIN
ELSE
NSUS=IWORK(13)
IF (NSUS.LE.0.OR.NS.GE.8.OR.NS.EQ.2.OR.NS.EQ.4.OR.NS.EQ.6) THEN
WRITE(6,*)' WRONG INPUT IWORK(13)=',IWORK(13)
ARRET=.TRUE.
END IF
END IF
C -------- NMAX , THE MAXIMAL NUMBER OF STEPS -----
IF (IWORK(2).EQ.0) THEN
NMAX=100000
ELSE
NMAX=IWORK(2)
IF (NMAX.LE.0) THEN
WRITE(6,*)' WRONG INPUT IWORK(2)=',IWORK(2)
ARRET=.TRUE.
END IF
END IF
C -------- NIT MAXIMAL NUMBER OF NEWTON ITERATIONS
IF (IWORK(3).EQ.0) THEN
NIT=7
ELSE
NIT=IWORK(3)
IF (NIT.LE.0.OR.NIT.GT.50) THEN
WRITE(6,*)' CURIOUS INPUT IWORK(3)=',IWORK(3)
ARRET=.TRUE.
END IF
END IF
C -------- STARTN SWITCH FOR STARTING VALUES OF NEWTON ITERATIONS
IF(IWORK(4).EQ.0)THEN
STARTN=.FALSE.
ELSE
STARTN=.TRUE.
END IF
C -------- PARAMETER FOR DIFFERENTIAL-ALGEBRAIC COMPONENTS
NIND1=IWORK(5)
NIND2=IWORK(6)
NIND3=IWORK(7)
IF (NIND1.EQ.0) NIND1=N
IF (NIND1+NIND2+NIND3.NE.N) THEN
WRITE(6,*)' CURIOUS INPUT FOR IWORK(5,6,7)=',NIND1,NIND2,NIND3
ARRET=.TRUE.
END IF
C -------- PRED STEP SIZE CONTROL
IF(IWORK(8).LE.1)THEN
PRED=.TRUE.
ELSE
PRED=.FALSE.
END IF
C -------- PARAMETER FOR SECOND ORDER EQUATIONS
M1=IWORK(9)
M2=IWORK(10)
NM1=N-M1
IF (M1.EQ.0) M2=N
IF (M2.EQ.0) M2=M1
IF (M1.LT.0.OR.M2.LT.0.OR.M1+M2.GT.N) THEN
WRITE(6,*)' CURIOUS INPUT FOR IWORK(9,10)=',M1,M2
ARRET=.TRUE.
END IF
C -------- UROUND SMALLEST NUMBER SATISFYING 1.0D0+UROUND>1.0D0
IF (WORK(1).EQ.0.0D0) THEN
UROUND=1.0D-16
ELSE
UROUND=WORK(1) IF (UROUND.LE.1.0D-19.OR.UROUND.GE.1.0D0) THEN
WRITE(6,*)' COEFFICIENTS HAVE 20 DIGITS, UROUND=',WORK(1)
ARRET=.TRUE.
END IF
END IF
C --------- CHECK IF TOLERANCES ARE O.K.
IF (ITOL.EQ.0) THEN
IF (ATOL(1).LE.0.D0.OR.RTOL(1).LE.10.D0*UROUND) THEN
WRITE (6,*) ' TOLERANCES ARE TOO SMALL'
ARRET=.TRUE.
END IF
ELSE
DO I=1,N
IF (ATOL(I).LE.0.D0.OR.RTOL(I).LE.10.D0*UROUND) THEN
WRITE (6,*) ' TOLERANCES(',I,') ARE TOO SMALL'
ARRET=.TRUE.
END IF
END DO
END IF
C --------- SAFE SAFETY FACTOR IN STEP SIZE PREDICTION
IF (WORK(2).EQ.0.0D0) THEN
SAFE=0.9D0
ELSE
SAFE=WORK(2)
IF (SAFE.LE.0.001D0.OR.SAFE.GE.1.0D0) THEN
WRITE(6,*)' CURIOUS INPUT FOR WORK(2)=',WORK(2)
ARRET=.TRUE.
END IF
END IF
C ------ THET DECIDES WHETHER THE JACOBIAN SHOULD BE RECOMPUTED;
IF (WORK(3).EQ.0.D0) THEN
THET=0.001D0
ELSE
THET=WORK(3)
IF (THET.GE.1.0D0) THEN
WRITE(6,*)' CURIOUS INPUT FOR WORK(3)=',WORK(3)
ARRET=.TRUE.
END IF
END IF
C --- QUOT1 AND QUOT2: IF QUOT1 < HNEW/HOLD < QUOT2, STEP SIZE = CONST.
IF (WORK(5).EQ.0.D0) THEN
QUOT1=1.D0
ELSE
QUOT1=WORK(5)
END IF
IF (WORK(6).EQ.0.D0) THEN
QUOT2=1.2D0
ELSE
QUOT2=WORK(6)
END IF
IF (QUOT1.GT.1.0D0.OR.QUOT2.LT.1.0D0) THEN
WRITE(6,*)' CURIOUS INPUT FOR WORK(5,6)=',QUOT1,QUOT2
ARRET=.TRUE.
END IF
C -------- MAXIMAL STEP SIZE
IF (WORK(7).EQ.0.D0) THEN
HMAX=XEND-X
ELSE
HMAX=WORK(7)
END IF
C ------- FACL,FACR PARAMETERS FOR STEP SIZE SELECTION
IF(WORK(8).EQ.0.D0)THEN
FACL=5.D0
ELSE
FACL=1.D0/WORK(8)
END IF
IF(WORK(9).EQ.0.D0)THEN
FACR=1.D0/8.0D0
ELSE
FACR=1.D0/WORK(9) END IF
IF (FACL.LT.1.0D0.OR.FACR.GT.1.0D0) THEN
WRITE(6,*)' CURIOUS INPUT WORK(8,9)=',WORK(8),WORK(9)
ARRET=.TRUE.
END IF
C -------- PARAMETERS FOR ORDER SELECTION STRATEGY
IF (WORK(10).EQ.0.D0) THEN
VITU=0.002D0
ELSE
VITU=WORK(10)
END IF
IF (WORK(11).EQ.0.D0) THEN
VITD=0.8D0
ELSE
VITD=WORK(11)
END IF
IF (WORK(12).EQ.0.D0) THEN
HHOU=1.2D0
ELSE
HHOU=WORK(12)
END IF
IF (WORK(13).EQ.0.D0) THEN
HHOD=0.8D0
ELSE
HHOD=WORK(13)
END IF
C *** *** *** *** *** *** *** *** *** *** *** *** ***
C COMPUTATION OF ARRAY ENTRIES
C *** *** *** *** *** *** *** *** *** *** *** *** ***
C ---- IMPLICIT, BANDED OR NOT ?
IMPLCT=IMAS.NE.0
JBAND=MLJAC.LT.NM1
C -------- COMPUTATION OF THE ROW-DIMENSIONS OF THE 2-ARRAYS ---
C -- JACOBIAN AND MATRICES E1, E2
IF (JBAND) THEN
LDJAC=MLJAC+MUJAC+1
LDE1=MLJAC+LDJAC
ELSE
MLJAC=NM1
MUJAC=NM1
LDJAC=NM1
LDE1=NM1
END IF
C -- MASS MATRIX
IF (IMPLCT) THEN
IF (MLMAS.NE.NM1) THEN
LDMAS=MLMAS+MUMAS+1
IF (JBAND) THEN
IJOB=4
ELSE
IJOB=3
END IF
ELSE
LDMAS=NM1
IJOB=5
END IF
C ------ BANDWITH OF "MAS" NOT SMALLER THAN BANDWITH OF "JAC"
IF (MLMAS.GT.MLJAC.OR.MUMAS.GT.MUJAC) THEN
WRITE (6,*) 'BANDWITH OF "MAS" NOT SMALLER THAN BANDWITH OF
& "JAC"'
ARRET=.TRUE.
END IF
ELSE
LDMAS=0
IF (JBAND) THEN
IJOB=2
ELSE
IJOB=1
IF (N.GT.2.AND.IWORK(1).NE.0) IJOB=7
END IF END IF
LDMAS2=MAX(1,LDMAS)
C ------ HESSENBERG OPTION ONLY FOR EXPLICIT EQU. WITH FULL JACOBIAN
IF ((IMPLCT.OR.JBAND).AND.IJOB.EQ.7) THEN
WRITE(6,*)' HESSENBERG OPTION ONLY FOR EXPLICIT EQUATIONS WITH
&FULL JACOBIAN'
ARRET=.TRUE.
END IF
C ------- PREPARE THE ENTRY-POINTS FOR THE ARRAYS IN WORK -----
NNS=NS*N
NM1NS=NS*NM1
NMEE=(NS-1)*NM1
IEZZ=21
IEY0=IEZZ+NNS
IESCAL=IEY0+N
IEFF=IESCAL+N
IECON=IEFF+NNS
IEJAC=IECON+NNS+N
IEMAS=IEJAC+N*LDJAC
IEE1=IEMAS+NM1*LDMAS
IEE=IEE1+NM1*LDE1
C ------ TOTAL STORAGE REQUIREMENT -----------
ISTORE=IEE+NMEE*LDE1-1
IF(ISTORE.GT.LWORK)THEN
WRITE(6,*)' INSUFFICIENT STORAGE FOR WORK, MIN. LWORK=',ISTORE
ARRET=.TRUE.
END IF
C ------- ENTRY POINTS FOR INTEGER WORKSPACE -----
IEIP1=21
IEIP2=IEIP1+NM1
IEIPH=IEIP2+NM1*(NS-1)/2
C --------- TOTAL REQUIREMENT ---------------
ISTORE=IEIPH+NM1-1
IF (ISTORE.GT.LIWORK) THEN
WRITE(6,*)' INSUFF. STORAGE FOR IWORK, MIN. LIWORK=',ISTORE
ARRET=.TRUE.
END IF
C ------ WHEN A FAIL HAS OCCURED, WE RETURN WITH IDID=-1
IF (ARRET) THEN
IDID=-1
RETURN
END IF
C -------- CALL TO CORE INTEGRATOR ------------
CALL RADCOV(N,FCN,X,Y,XEND,HMAX,H,RTOL,ATOL,ITOL,NSUS,
& JAC,IJAC,MLJAC,MUJAC,MAS,MLMAS,MUMAS,SOLOUT,IOUT,IDID,
& NMAX,UROUND,SAFE,THET,QUOT1,QUOT2,NIT,IJOB,STARTN,
& NIND1,NIND2,NIND3,PRED,FACL,FACR,M1,M2,NM1,NSMIN,NS,NNS,NM1NS,
& NMEE,IMPLCT,JBAND,LDJAC,LDE1,LDMAS2,WORK(IEZZ),WORK(IEY0),
& WORK(IESCAL),WORK(IEFF),WORK(IEJAC),WORK(IEE1),WORK(IEE),
& WORK(IEMAS),WORK(IECON),IWORK(IEIP1),IWORK(IEIP2),
& IWORK(IEIPH),VITU,VITD,HHOU,HHOD,NFCN,NJAC,NSTEP,NACCPT,
& NREJCT,NDEC,NSOL,RPAR,IPAR)
IWORK(13)=NSUS
IWORK(14)=NFCN
IWORK(15)=NJAC
IWORK(16)=NSTEP
IWORK(17)=NACCPT
IWORK(18)=NREJCT
IWORK(19)=NDEC
IWORK(20)=NSOL
C ----------- RETURN -----------
RETURN
END
C
C END OF SUBROUTINE RADAU
C
C ***********************************************************
C
SUBROUTINE RADCOV(N,FCN,X,Y,XEND,HMAX,H,RTOL,ATOL,ITOL,NS,
& JAC,IJAC,MLJAC,MUJAC,MAS,MLMAS,MUMAS,SOLOUT,IOUT,IDID, & NMAX,UROUND,SAFE,THET,QUOT1,QUOT2,NIT1,IJOB,STARTN,NIND1,
& NIND2,NIND3,PRED,FACL,FACR,M1,M2,NM1,NSMIN,NSMAX,NNMS,NM1NS,
& NMEE,IMPLCT,BANDED,LDJAC,LDE1,LDMAS,ZZ,Y0,SCAL,FF,FJAC,
& E1,EE2,FMAS,CONT,IP1,IP2,IPHES,VITU,VITD,HHOU,HHOD,
& NFCN,NJAC,NSTEP,NACCPT,NREJCT,NDEC,NSOL,RPAR,IPAR)
C ----------------------------------------------------------
C CORE INTEGRATOR FOR RADAU
C PARAMETERS SAME AS IN RADAU WITH WORKSPACE ADDED
C ----------------------------------------------------------
C DECLARATIONS
C ----------------------------------------------------------
USE omp_lib
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
PARAMETER (NSDIM=7)
C --- THIS PARAMETER HAS TO BE CHANGED IF NUMBER OF STAGES IS >=7
DIMENSION Y(N),ZZ(NNMS),FF(NNMS),Y0(N),SCAL(N)
DIMENSION FJAC(LDJAC,N),FMAS(LDMAS,NM1),CONT(NNMS+N)
DIMENSION ATOL(1),RTOL(1),RPAR(*),IPAR(*)
DIMENSION E1(LDE1,NM1),EE2(LDE1,NMEE)
DIMENSION ALPH(NSDIM),BETA(NSDIM),DD(NSDIM)
DIMENSION ALPHN(NSDIM),BETAN(NSDIM)
INTEGER IP1(NM1),IP2(NMEE/2),IPHES(NM1)
COMMON/WEIGHT/NN,NSCON,XSOL,HSOL,C(0:NSDIM)
!$OMP THREADPRIVATE(/WEIGHT/)
COMMON/LINAL/MLE,MUE,MBJAC,MBB,MDIAG,MDIFF,MBDIAG
!$OMP THREADPRIVATE(/LINAL/)
COMMON /COE3/ T311,T312,T313,T321,T322,T323,T331,
* TI311,TI312,TI313,TI321,TI322,TI323,TI331,TI332,TI333
!$OMP THREADPRIVATE(/COE3/)
COMMON /COE5/ T511,T512,T513,T514,T515,T521,T522,T523,T524,T525,
* T531,T532,T533,T534,T535,T541,T542,T543,T544,T545,T551,
* TI511,TI512,TI513,TI514,TI515,TI521,TI522,TI523,TI524,TI525,
* TI531,TI532,TI533,TI534,TI535,TI541,TI542,TI543,TI544,TI545,
* TI551,TI552,TI553,TI554,TI555
!$OMP THREADPRIVATE(/COE5/)
COMMON /COE7/ T711,T712,T713,T714,T715,T716,T717,
* T721,T722,T723,T724,T725,T726,T727,
* T731,T732,T733,T734,T735,T736,T737,
* T741,T742,T743,T744,T745,T746,T747,
* T751,T752,T753,T754,T755,T756,T757,
* T761,T762,T763,T764,T765,T766,T767,T771,
* TI711,TI712,TI713,TI714,TI715,TI716,TI717,
* TI721,TI722,TI723,TI724,TI725,TI726,TI727,
* TI731,TI732,TI733,TI734,TI735,TI736,TI737,
* TI741,TI742,TI743,TI744,TI745,TI746,TI747,
* TI751,TI752,TI753,TI754,TI755,TI756,TI757,
* TI761,TI762,TI763,TI764,TI765,TI766,TI767,
* TI771,TI772,TI773,TI774,TI775,TI776,TI777
!$OMP THREADPRIVATE(/COE7/)
LOGICAL REJECT,FIRST,IMPLCT,BANDED,CALJAC,STARTN,CALHES
LOGICAL INDEX1,INDEX2,INDEX3,LAST,PRED,CHANGE,UNEXP,UNEXN,VARIAB
EXTERNAL FCN,JAC
C *** *** *** *** *** *** ***
C INITIALISATIONS
C *** *** *** *** *** *** ***
C -------- CHECK THE INDEX OF THE PROBLEM -----
INDEX1=NIND1.NE.0
INDEX2=NIND2.NE.0
INDEX3=NIND3.NE.0
C ------- COMPUTE MASS MATRIX FOR IMPLICIT CASE ----------
IF (IMPLCT) CALL MAS(NM1,FMAS,LDMAS,RPAR,IPAR)
VARIAB=NSMIN.LT.NSMAX
C ---------- CONSTANTS ---------
EXPO=1.D0/(NS+1.D0)
SQ6=DSQRT(6.D0)
C31=(4.D0-SQ6)/10.D0
C32=(4.D0+SQ6)/10.D0
C31M1=C31-1.D0
C32M1=C32-1.D0
C31MC2=C31-C32 DD1=-(13.D0+7.D0*SQ6)/3.D0
DD2=(-13.D0+7.D0*SQ6)/3.D0
DD3=-1.D0/3.D0
N2=2*N
N3=3*N
N4=4*N
N5=5*N
N6=6*N
UNEXP=.FALSE.
UNEXN=.FALSE.
CHANGE=.FALSE.
IKEEP=0
ICHAN=0
THETA=0.0D0
THETAT=0.0D0
NN=N
NNS=N*NS
NSCON=NS
LRC=NNS+N
CALL COERTV(NSMAX)
CALL COERCV(NS,C,DD,U1,ALPH,BETA)
IF (M1.GT.0) IJOB=IJOB+10
POSNEG=SIGN(1.D0,XEND-X)
HMAXN=MIN(ABS(HMAX),ABS(XEND-X))
IF (ABS(H).LE.10.D0*UROUND) H=1.0D-6
H=MIN(ABS(H),HMAXN)
H=SIGN(H,POSNEG)
HOLD=H
REJECT=.FALSE.
FIRST=.TRUE.
LAST=.FALSE.
IF ((X+H*1.0001D0-XEND)*POSNEG.GE.0.D0) THEN
H=XEND-X
LAST=.TRUE.
END IF
HOPT=H
FACCON=1.D0
NSING=0
XOLD=X
IF (IOUT.NE.0) THEN
IRTRN=1
NRSOL=1
XOSOL=XOLD
XSOL=X
DO I=1,N
CONT(I)=Y(I)
END DO
NSOLU=N
HSOL=HOLD
CALL SOLOUT(NRSOL,XOSOL,XSOL,Y,CONT,LRC,NSOLU,
& RPAR,IPAR,IRTRN)
IF (IRTRN.LT.0) GOTO 179
END IF
MLE=MLJAC
MUE=MUJAC
MBJAC=MLJAC+MUJAC+1
MBB=MLMAS+MUMAS+1
MDIAG=MLE+MUE+1
MDIFF=MLE+MUE-MUMAS
MBDIAG=MUMAS+1
EXPMNS=(NS+1.0D0)/(2.0D0*NS)
QUOTT=ATOL(1)/RTOL(1)
IF (ITOL.EQ.0) THEN
RTOL1=0.1D0*RTOL(1)**EXPMNS
ATOL1=RTOL1*QUOTT
DO I=1,N
SCAL(I)=ATOL1+RTOL1*ABS(Y(I))
END DO
ELSE
DO I=1,N QUOTT=ATOL(I)/RTOL(I)
RTOL1=0.1D0*RTOL(I)**EXPMNS
ATOL1=RTOL1*QUOTT
SCAL(I)=ATOL1+RTOL1*ABS(Y(I))
END DO
END IF
HHFAC=H
CALL FCN(N,X,Y,Y0,RPAR,IPAR)
NFCN=NFCN+1
C --- BASIC INTEGRATION STEP
10 CONTINUE
C --- pberndt XXX: Check for rejected step
DO I=1,N
IF (ISNAN(Y0(I))) GOTO 175
END DO
C *** *** *** *** *** *** ***
C COMPUTATION OF THE JACOBIAN
C *** *** *** *** *** *** ***
NJAC=NJAC+1
IF (IJAC.EQ.0) THEN
C --- COMPUTE JACOBIAN MATRIX NUMERICALLY
IF (BANDED) THEN
C --- JACOBIAN IS BANDED
MUJACP=MUJAC+1
MD=MIN(MBJAC,M2)
DO MM=1,M1/M2+1
DO K=1,MD
J=K+(MM-1)*M2
12 FF(J)=Y(J)
FF(J+N)=DSQRT(UROUND*MAX(1.D-5,ABS(Y(J))))
Y(J)=Y(J)+FF(J+N)
J=J+MD
IF (J.LE.MM*M2) GOTO 12
CALL FCN(N,X,Y,CONT,RPAR,IPAR)
J=K+(MM-1)*M2
J1=K
LBEG=MAX(1,J1-MUJAC)+M1
14 LEND=MIN(M2,J1+MLJAC)+M1
Y(J)=FF(J)
MUJACJ=MUJACP-J1-M1
DO L=LBEG,LEND
FJAC(L+MUJACJ,J)=(CONT(L)-Y0(L))/FF(J+N)
END DO
J=J+MD
J1=J1+MD
LBEG=LEND+1
IF (J.LE.MM*M2) GOTO 14
END DO
END DO
ELSE
C --- JACOBIAN IS FULL
DO I=1,N
YSAFE=Y(I)
DELT=DSQRT(UROUND*MAX(1.D-5,ABS(YSAFE)))
Y(I)=YSAFE+DELT
CALL FCN(N,X,Y,CONT,RPAR,IPAR)
DO J=M1+1,N
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(CONT(J))) GOTO 78
FJAC(J-M1,I)=(CONT(J)-Y0(J))/DELT
END DO
Y(I)=YSAFE
END DO
END IF
ELSE
C --- COMPUTE JACOBIAN MATRIX ANALYTICALLY
CALL JAC(N,X,Y,FJAC,LDJAC,RPAR,IPAR)
END IF
CALJAC=.TRUE.
CALHES=.TRUE. 20 CONTINUE
C --- CHANGE THE ORDER HERE IF NECESSARY
IF (VARIAB) THEN
NSNEW=NS
ICHAN=ICHAN+1
HQUOT=H/HOLD
THETAT=MIN(10.0D0,MAX(THETA,THETAT*0.5))
IF (NEWT.GT.1.AND.THETAT.LE.VITU.AND.
& HQUOT.LT.HHOU.AND.HQUOT.GT.HHOD) NSNEW=MIN(NSMAX,NS+2)
IF (THETAT.GE.VITD.OR.UNEXP) NSNEW=MAX(NSMIN,NS-2)
IF (ICHAN.GE.1.AND.UNEXN) NSNEW=MAX(NSMIN,NS-2)
IF (ICHAN.LE.10) NSNEW=MIN(NS,NSNEW)
CHANGE=NS.NE.NSNEW
UNEXN=.FALSE.
UNEXP=.FALSE.
IF (CHANGE) THEN
NS=NSNEW
ICHAN=1
NNS=N*NS
NSCON=NS
LRC=NNS+N
CALL COERCV(NS,C,DD,U1,ALPH,BETA)
EXPO=1.D0/(NS+1.D0)
EXPMNS=(NS+1.0D0)/(2.0D0*NS)
RTOL1=0.1D0*RTOL(1)**EXPMNS
ATOL1=RTOL1*QUOTT
IF (ITOL.EQ.0) THEN
DO I=1,N
SCAL(I)=ATOL1+RTOL1*ABS(Y(I))
END DO
ELSE
DO I=1,N
QUOTT=ATOL(I)/RTOL(I)
RTOL1=0.1D0*RTOL(I)**EXPMNS
ATOL1=RTOL1*QUOTT
SCAL(I)=ATOL1+RTOL1*ABS(Y(I))
END DO
END IF
END IF
END IF
C --- COMPUTE THE MATRICES E1 AND E2 AND THEIR DECOMPOSITIONS
FAC1=U1/H
CALL DECOMR(N,FJAC,LDJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,FAC1,E1,LDE1,IP1,IER,IJOB,CALHES,IPHES)
IF (IER.NE.0) GOTO 78
DO K=1,(NS-1)/2
ALPHN(K)=ALPH(K)/H
BETAN(K)=BETA(K)/H
IAD=(K-1)*2*NM1+1
CALL DECOMC(N,FJAC,LDJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,ALPHN(K),BETAN(K),EE2(1,IAD),EE2(1,IAD+NM1),
& LDE1,IP2((K-1)*NM1+1),IER,IJOB)
IF (IER.NE.0) GOTO 78
END DO
NDEC=NDEC+1
30 CONTINUE
IF (VARIAB.AND.IKEEP.EQ.1) THEN
ICHAN=ICHAN+1
IKEEP=0
IF (ICHAN.GE.10.AND.NS.LT.NSMAX) GOTO 20
END IF
NSTEP=NSTEP+1
IF (NSTEP.GT.NMAX) GOTO 178
IF (0.1D0*ABS(H).LE.ABS(X)*UROUND) GOTO 177
IF (INDEX2) THEN
DO I=NIND1+1,NIND1+NIND2
SCAL(I)=SCAL(I)/HHFAC
END DO
END IF
IF (INDEX3) THEN DO I=NIND1+NIND2+1,NIND1+NIND2+NIND3
SCAL(I)=SCAL(I)/(HHFAC*HHFAC)
END DO
END IF
XPH=X+H
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
IF (NS.EQ.3) THEN
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
IF (FIRST.OR.STARTN.OR.CHANGE) THEN
DO I=1,NNS
ZZ(I)=0.D0
FF(I)=0.D0
END DO
ELSE
HQUOT=H/HOLD
C3Q=HQUOT
C1Q=C31*C3Q
C2Q=C32*C3Q
DO I=1,N
AK1=CONT(I+N)
AK2=CONT(I+N2)
AK3=CONT(I+N3)
Z1I=C1Q*(AK1+(C1Q-C32M1)*(AK2+(C1Q-C31M1)*AK3))
Z2I=C2Q*(AK1+(C2Q-C32M1)*(AK2+(C2Q-C31M1)*AK3))
Z3I=C3Q*(AK1+(C3Q-C32M1)*(AK2+(C3Q-C31M1)*AK3))
ZZ(I)=Z1I
ZZ(I+N)=Z2I
ZZ(I+N2)=Z3I
FF(I)=TI311*Z1I+TI312*Z2I+TI313*Z3I
FF(I+N)=TI321*Z1I+TI322*Z2I+TI323*Z3I
FF(I+N2)=TI331*Z1I+TI332*Z2I+TI333*Z3I
END DO
END IF
C *** *** *** *** *** *** ***
C LOOP FOR THE SIMPLIFIED NEWTON ITERATION
C *** *** *** *** *** *** ***
NEWT=0
NIT=NIT1
EXPMI=1.0D0/EXPMNS
FNEWT=MAX(10*UROUND/RTOL1,MIN(0.03D0,RTOL1**(EXPMI-1.0D0)))
FACCON=MAX(FACCON,UROUND)**0.8D0
THETA=ABS(THET)
40 CONTINUE
IF (NEWT.GE.NIT) GOTO 78
C --- COMPUTE THE RIGHT-HAND SIDE
DO I=1,N
CONT(I)=Y(I)+ZZ(I)
END DO
CALL FCN(N,X+C31*H,CONT,ZZ,RPAR,IPAR)
DO I=1,N
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(ZZ(I))) GOTO 78
CONT(I)=Y(I)+ZZ(I+N)
END DO
CALL FCN(N,X+C32*H,CONT,ZZ(1+N),RPAR,IPAR)
DO I=1,N
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(ZZ(I))) GOTO 78
CONT(I)=Y(I)+ZZ(I+N2)
END DO
CALL FCN(N,XPH,CONT,ZZ(1+N2),RPAR,IPAR)
NFCN=NFCN+3
C --- SOLVE THE LINEAR SYSTEMS
DO I=1,N
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(ZZ(I))) GOTO 78
A1=ZZ(I)
A2=ZZ(I+N) A3=ZZ(I+N2)
ZZ(I)=TI311*A1+TI312*A2+TI313*A3
ZZ(I+N)=TI321*A1+TI322*A2+TI323*A3
ZZ(I+N2)=TI331*A1+TI332*A2+TI333*A3
END DO
CALL SLVRAD(N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,FAC1,ALPHN(1),BETAN(1),E1,EE2,EE2(1,1+NM1),LDE1,
& ZZ,ZZ(1+N),ZZ(1+N2),FF,FF(1+N),FF(1+N2),
& CONT,IP1,IP2,IPHES,IER,IJOB)
NSOL=NSOL+1
NEWT=NEWT+1
DYNO=0.D0
DO I=1,N
DENOM=SCAL(I)
DYNO=DYNO+(ZZ(I)/DENOM)**2+(ZZ(I+N)/DENOM)**2
& +(ZZ(I+N2)/DENOM)**2
END DO
DYNO=DSQRT(DYNO/NNS)
C --- BAD CONVERGENCE OR NUMBER OF ITERATIONS TO LARGE
IF (NEWT.GT.1.AND.NEWT.LT.NIT) THEN
THQ=DYNO/DYNOLD
IF (NEWT.EQ.2) THEN
THETA=THQ
ELSE
THETA=SQRT(THQ*THQOLD)
END IF
THQOLD=THQ
IF (THETA.LT.0.99D0) THEN
FACCON=THETA/(1.0D0-THETA)
DYTH=FACCON*DYNO*THETA**(NIT-1-NEWT)/FNEWT
IF (DYTH.GE.1.0D0) THEN
QNEWT=DMAX1(1.0D-4,DMIN1(20.0D0,DYTH))
HHFAC=0.8D0*QNEWT**(-1.0D0/(4.0D0+NIT-1-NEWT))
H=HHFAC*H
REJECT=.TRUE.
LAST=.FALSE.
IF (HHFAC.LE.0.5D0) UNEXN=.TRUE.
IF (CALJAC) GOTO 20
GOTO 10
END IF
ELSE
GOTO 78
END IF
END IF
DYNOLD=MAX(DYNO,UROUND)
DO I=1,N
IN=I+N
IN2=I+N2
F1I=FF(I)+ZZ(I)
F2I=FF(IN)+ZZ(IN)
F3I=FF(IN2)+ZZ(IN2)
FF(I)=F1I
FF(IN)=F2I
FF(IN2)=F3I
ZZ(I)=T311*F1I+T312*F2I+T313*F3I
ZZ(IN)=T321*F1I+T322*F2I+T323*F3I
ZZ(IN2)=T331*F1I+ F2I
END DO
IF (FACCON*DYNO.GT.FNEWT) GOTO 40
C --- ERROR ESTIMATION
CALL ESTRAD (N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& H,DD1,DD2,DD3,FCN,NFCN,Y0,Y,IJOB,X,M1,M2,NM1,
& E1,LDE1,ZZ,ZZ(1+N),ZZ(1+N2),CONT,FF,FF(1+N),IP1,
& IPHES,SCAL,ERR,FIRST,REJECT,FAC1,RPAR,IPAR)
C --- COMPUTE FINITE DIFFERENCES FOR DENSE OUTPUT
IF (ERR.LT.1.D0) THEN
DO I=1,N
Y(I)=Y(I)+ZZ(I+N2)
Z2I=ZZ(I+N)
Z1I=ZZ(I) CONT(I+N)=(Z2I-ZZ(I+N2))/C32M1
AK=(Z1I-Z2I)/C31MC2
ACONT3=Z1I/C31
ACONT3=(AK-ACONT3)/C32
CONT(I+N2)=(AK-CONT(I+N))/C31M1
CONT(I+N3)=CONT(I+N2)-ACONT3
END DO
END IF
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
ELSE
IF (NS.EQ.5) THEN
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
IF (FIRST.OR.STARTN.OR.CHANGE) THEN
DO I=1,NNS
ZZ(I)=0.D0
FF(I)=0.D0
END DO
ELSE
HQUOT=H/HOLD
DO K=1,NS
CCQ=C(K)*HQUOT
DO I=1,N
VAL=CONT(I+NS*N)
DO L=NS-1,1,-1
VAL=CONT(I+L*N)+(CCQ-C(NS-L)+1.D0)*VAL
END DO
ZZ(I+(K-1)*N)=CCQ*VAL
END DO
END DO
DO I=1,N
Z1I=ZZ(I)
Z2I=ZZ(I+N)
Z3I=ZZ(I+N2)
Z4I=ZZ(I+N3)
Z5I=ZZ(I+N4)
FF(I)=TI511*Z1I+TI512*Z2I+TI513*Z3I+TI514*Z4I+TI515*Z5I
FF(I+N)=TI521*Z1I+TI522*Z2I+TI523*Z3I+TI524*Z4I+TI525*Z5I
FF(I+N2)=TI531*Z1I+TI532*Z2I+TI533*Z3I+TI534*Z4I+TI535*Z5I
FF(I+N3)=TI541*Z1I+TI542*Z2I+TI543*Z3I+TI544*Z4I+TI545*Z5I
FF(I+N4)=TI551*Z1I+TI552*Z2I+TI553*Z3I+TI554*Z4I+TI555*Z5I
END DO
END IF
C *** *** *** *** *** *** ***
C LOOP FOR THE SIMPLIFIED NEWTON ITERATION
C *** *** *** *** *** *** ***
NEWT=0
NIT=NIT1+5
EXPMI=1.0D0/EXPMNS
FNEWT=MAX(10*UROUND/RTOL1,MIN(0.03D0,RTOL1**(EXPMI-1.0D0)))
FACCON=MAX(FACCON,UROUND)**0.8D0
THETA=ABS(THET)
140 CONTINUE
IF (NEWT.GE.NIT) GOTO 78
C --- COMPUTE THE RIGHT-HAND SIDE
DO K=0,NS-1
IADD=K*N
DO I=1,N
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(ZZ(IADD+I))) GOTO 78
CONT(I)=Y(I)+ZZ(IADD+I)
END DO
CALL FCN(N,X+C(K+1)*H,CONT,ZZ(IADD+1),RPAR,IPAR)
END DO
NFCN=NFCN+NS
C --- SOLVE THE LINEAR SYSTEMS
DO I=1,N
Z1I=ZZ(I)
Z2I=ZZ(I+N) Z3I=ZZ(I+N2)
Z4I=ZZ(I+N3)
Z5I=ZZ(I+N4)
ZZ(I)=TI511*Z1I+TI512*Z2I+TI513*Z3I+TI514*Z4I+TI515*Z5I
ZZ(I+N)=TI521*Z1I+TI522*Z2I+TI523*Z3I+TI524*Z4I+TI525*Z5I
ZZ(I+N2)=TI531*Z1I+TI532*Z2I+TI533*Z3I+TI534*Z4I+TI535*Z5I
ZZ(I+N3)=TI541*Z1I+TI542*Z2I+TI543*Z3I+TI544*Z4I+TI545*Z5I
ZZ(I+N4)=TI551*Z1I+TI552*Z2I+TI553*Z3I+TI554*Z4I+TI555*Z5I
END DO
CALL SLVRAR(N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,FAC1,E1,LDE1,ZZ,FF,IP1,IPHES,IER,IJOB)
DO K=1,2
IAD=(K-1)*2*NM1+1
CALL SLVRAI(N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,ALPHN(K),BETAN(K),EE2(1,IAD),EE2(1,IAD+NM1),LDE1,
& ZZ(1+(2*K-1)*N),ZZ(1+2*K*N),FF(1+(2*K-1)*N),
& FF(1+2*K*N),CONT,IP2((K-1)*NM1+1),IPHES,IER,IJOB)
END DO
NSOL=NSOL+1
NEWT=NEWT+1
DYNO=0.D0
DO I=1,N
DENOM=SCAL(I)
DO K=0,NS-1
DYNO=DYNO+(ZZ(I+K*N)/DENOM)**2
END DO
END DO
DYNO=DSQRT(DYNO/NNS)
C --- BAD CONVERGENCE OR NUMBER OF ITERATIONS TO LARGE
IF (NEWT.GT.1.AND.NEWT.LT.NIT) THEN
THQ=DYNO/DYNOLD
IF (NEWT.EQ.2) THEN
THETA=THQ
ELSE
THETA=SQRT(THQ*THQOLD)
END IF
THQOLD=THQ
IF (THETA.LT.0.99D0) THEN
FACCON=THETA/(1.0D0-THETA)
DYTH=FACCON*DYNO*THETA**(NIT-1-NEWT)/FNEWT
IF (DYTH.GE.1.0D0) THEN
QNEWT=DMAX1(1.0D-4,DMIN1(20.0D0,DYTH))
HHFAC=0.8D0*QNEWT**(-1.0D0/(4.0D0+NIT-1-NEWT))
H=HHFAC*H
REJECT=.TRUE.
LAST=.FALSE.
IF (HHFAC.LE.0.5D0) UNEXN=.TRUE.
IF (CALJAC) GOTO 20
GOTO 10
END IF
ELSE
GOTO 78
END IF
END IF
DYNOLD=MAX(DYNO,UROUND)
DO I=1,N
Z1I=FF(I)+ZZ(I)
Z2I=FF(I+N)+ZZ(I+N)
Z3I=FF(I+N2)+ZZ(I+N2)
Z4I=FF(I+N3)+ZZ(I+N3)
Z5I=FF(I+N4)+ZZ(I+N4)
FF(I)=Z1I
FF(I+N)=Z2I
FF(I+N2)=Z3I
FF(I+N3)=Z4I
FF(I+N4)=Z5I
ZZ(I)=T511*Z1I+T512*Z2I+T513*Z3I+T514*Z4I+T515*Z5I
ZZ(I+N)=T521*Z1I+T522*Z2I+T523*Z3I+T524*Z4I+T525*Z5I
ZZ(I+N2)=T531*Z1I+T532*Z2I+T533*Z3I+T534*Z4I+T535*Z5I
ZZ(I+N3)=T541*Z1I+T542*Z2I+T543*Z3I+T544*Z4I+T545*Z5I ZZ(I+N4)=T551*Z1I+ Z2I + Z4I
END DO
IF (FACCON*DYNO.GT.FNEWT) GOTO 140
C --- ERROR ESTIMATION
CALL ESTRAV (N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& H,DD,FCN,NFCN,Y0,Y,IJOB,X,M1,M2,NM1,NS,NNS,E1,LDE1,
& ZZ,CONT,FF,IP1,IPHES,SCAL,ERR,
& FIRST,REJECT,FAC1,RPAR,IPAR)
C --- COMPUTE FINITE DIFFERENCES FOR DENSE OUTPUT
IF (ERR.LT.1.D0) THEN
DO I=1,N
Y(I)=Y(I)+ZZ(I+N4)
CONT(I+N5)=ZZ(I)/C(1)
END DO
DO K=1,NS-1
FACT=1.D0/(C(NS-K)-C(NS-K+1))
DO I=1,N
CONT(I+K*N)=(ZZ(I+(NS-K-1)*N)-ZZ(I+(NS-K)*N))*FACT
END DO
END DO
DO J=2,NS
DO K=NS,J,-1
FACT=1.D0/(C(NS-K)-C(NS-K+J))
DO I=1,N
CONT(I+K*N)=(CONT(I+K*N)-CONT(I+(K-1)*N))*FACT
END DO
END DO
END DO
END IF
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
ELSE
IF (NS.EQ.7) THEN
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
IF (FIRST.OR.STARTN.OR.CHANGE) THEN
DO I=1,NNS
ZZ(I)=0.D0
FF(I)=0.D0
END DO
ELSE
HQUOT=H/HOLD
DO K=1,NS
CCQ=C(K)*HQUOT
DO I=1,N
VAL=CONT(I+NS*N)
DO L=NS-1,1,-1
VAL=CONT(I+L*N)+(CCQ-C(NS-L)+1.D0)*VAL
END DO
ZZ(I+(K-1)*N)=CCQ*VAL
END DO
END DO
DO I=1,N
Z1I=ZZ(I)
Z2I=ZZ(I+N)
Z3I=ZZ(I+N2)
Z4I=ZZ(I+N3)
Z5I=ZZ(I+N4)
Z6I=ZZ(I+N5)
Z7I=ZZ(I+N6)
FF(I)=TI711*Z1I+TI712*Z2I+TI713*Z3I+TI714*Z4I+TI715*Z5I
* +TI716*Z6I+TI717*Z7I
FF(I+N)=TI721*Z1I+TI722*Z2I+TI723*Z3I+TI724*Z4I+TI725*Z5I
* +TI726*Z6I+TI727*Z7I
FF(I+N2)=TI731*Z1I+TI732*Z2I+TI733*Z3I+TI734*Z4I+TI735*Z5I
* +TI736*Z6I+TI737*Z7I
FF(I+N3)=TI741*Z1I+TI742*Z2I+TI743*Z3I+TI744*Z4I+TI745*Z5I
* +TI746*Z6I+TI747*Z7I
FF(I+N4)=TI751*Z1I+TI752*Z2I+TI753*Z3I+TI754*Z4I+TI755*Z5I
* +TI756*Z6I+TI757*Z7I FF(I+N5)=TI761*Z1I+TI762*Z2I+TI763*Z3I+TI764*Z4I+TI765*Z5I
* +TI766*Z6I+TI767*Z7I
FF(I+N6)=TI771*Z1I+TI772*Z2I+TI773*Z3I+TI774*Z4I+TI775*Z5I
* +TI776*Z6I+TI777*Z7I
END DO
END IF
C *** *** *** *** *** *** ***
C LOOP FOR THE SIMPLIFIED NEWTON ITERATION
C *** *** *** *** *** *** ***
NEWT=0
NIT=NIT1+10
EXPMI=1.0D0/EXPMNS
FNEWT=MAX(10*UROUND/RTOL1,MIN(0.03D0,RTOL1**(EXPMI-1.0D0)))
FACCON=MAX(FACCON,UROUND)**0.8D0
THETA=ABS(THET)
240 CONTINUE
IF (NEWT.GE.NIT) GOTO 78
C --- COMPUTE THE RIGHT-HAND SIDE
DO K=0,NS-1
IADD=K*N
DO I=1,N
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(ZZ(IADD+I))) GOTO 78
CONT(I)=Y(I)+ZZ(IADD+I)
END DO
CALL FCN(N,X+C(K+1)*H,CONT,ZZ(IADD+1),RPAR,IPAR)
END DO
NFCN=NFCN+NS
C --- SOLVE THE LINEAR SYSTEMS
DO I=1,N
Z1I=ZZ(I)
Z2I=ZZ(I+N)
Z3I=ZZ(I+N2)
Z4I=ZZ(I+N3)
Z5I=ZZ(I+N4)
Z6I=ZZ(I+N5)
Z7I=ZZ(I+N6)
ZZ(I)=TI711*Z1I+TI712*Z2I+TI713*Z3I+TI714*Z4I+TI715*Z5I
* +TI716*Z6I+TI717*Z7I
ZZ(I+N)=TI721*Z1I+TI722*Z2I+TI723*Z3I+TI724*Z4I+TI725*Z5I
* +TI726*Z6I+TI727*Z7I
ZZ(I+N2)=TI731*Z1I+TI732*Z2I+TI733*Z3I+TI734*Z4I+TI735*Z5I
* +TI736*Z6I+TI737*Z7I
ZZ(I+N3)=TI741*Z1I+TI742*Z2I+TI743*Z3I+TI744*Z4I+TI745*Z5I
* +TI746*Z6I+TI747*Z7I
ZZ(I+N4)=TI751*Z1I+TI752*Z2I+TI753*Z3I+TI754*Z4I+TI755*Z5I
* +TI756*Z6I+TI757*Z7I
ZZ(I+N5)=TI761*Z1I+TI762*Z2I+TI763*Z3I+TI764*Z4I+TI765*Z5I
* +TI766*Z6I+TI767*Z7I
ZZ(I+N6)=TI771*Z1I+TI772*Z2I+TI773*Z3I+TI774*Z4I+TI775*Z5I
* +TI776*Z6I+TI777*Z7I
END DO
CALL SLVRAR(N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,FAC1,E1,LDE1,ZZ,FF,IP1,IPHES,IER,IJOB)
DO K=1,3
IAD=(K-1)*2*NM1+1
CALL SLVRAI(N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,ALPHN(K),BETAN(K),EE2(1,IAD),EE2(1,IAD+NM1),LDE1,
& ZZ(1+(2*K-1)*N),ZZ(1+2*K*N),FF(1+(2*K-1)*N),
& FF(1+2*K*N),CONT,IP2((K-1)*NM1+1),IPHES,IER,IJOB)
END DO
NSOL=NSOL+1
NEWT=NEWT+1
DYNO=0.D0
DO I=1,N
DENOM=SCAL(I)
DO K=0,NS-1
DYNO=DYNO+(ZZ(I+K*N)/DENOM)**2
END DO
END DO DYNO=DSQRT(DYNO/NNS)
C --- BAD CONVERGENCE OR NUMBER OF ITERATIONS TO LARGE
IF (NEWT.GT.1.AND.NEWT.LT.NIT) THEN
THQ=DYNO/DYNOLD
IF (NEWT.EQ.2) THEN
THETA=THQ
ELSE
THETA=SQRT(THQ*THQOLD)
END IF
THQOLD=THQ
IF (THETA.LT.0.99D0) THEN
FACCON=THETA/(1.0D0-THETA)
DYTH=FACCON*DYNO*THETA**(NIT-1-NEWT)/FNEWT
IF (DYTH.GE.1.0D0) THEN
QNEWT=DMAX1(1.0D-4,DMIN1(20.0D0,DYTH))
HHFAC=0.8D0*QNEWT**(-1.0D0/(4.0D0+NIT-1-NEWT))
H=HHFAC*H
REJECT=.TRUE.
LAST=.FALSE.
IF (HHFAC.LE.0.5D0) UNEXN=.TRUE.
IF (CALJAC) GOTO 20
GOTO 10
END IF
ELSE
GOTO 78
END IF
END IF
DYNOLD=MAX(DYNO,UROUND)
DO I=1,N
Z1I=FF(I)+ZZ(I)
Z2I=FF(I+N)+ZZ(I+N)
Z3I=FF(I+N2)+ZZ(I+N2)
Z4I=FF(I+N3)+ZZ(I+N3)
Z5I=FF(I+N4)+ZZ(I+N4)
Z6I=FF(I+N5)+ZZ(I+N5)
Z7I=FF(I+N6)+ZZ(I+N6)
FF(I)=Z1I
FF(I+N)=Z2I
FF(I+N2)=Z3I
FF(I+N3)=Z4I
FF(I+N4)=Z5I
FF(I+N5)=Z6I
FF(I+N6)=Z7I
ZZ(I)=T711*Z1I+T712*Z2I+T713*Z3I+T714*Z4I+T715*Z5I
* +T716*Z6I+T717*Z7I
ZZ(I+N)=T721*Z1I+T722*Z2I+T723*Z3I+T724*Z4I+T725*Z5I
* +T726*Z6I+T727*Z7I
ZZ(I+N2)=T731*Z1I+T732*Z2I+T733*Z3I+T734*Z4I+T735*Z5I
* +T736*Z6I+T737*Z7I
ZZ(I+N3)=T741*Z1I+T742*Z2I+T743*Z3I+T744*Z4I+T745*Z5I
* +T746*Z6I+T747*Z7I
ZZ(I+N4)=T751*Z1I+T752*Z2I+T753*Z3I+T754*Z4I+T755*Z5I
* +T756*Z6I+T757*Z7I
ZZ(I+N5)=T761*Z1I+T762*Z2I+T763*Z3I+T764*Z4I+T765*Z5I
* +T766*Z6I+T767*Z7I
ZZ(I+N6)=T771*Z1I+Z2I+Z4I+Z6I
END DO
IF (FACCON*DYNO.GT.FNEWT) GOTO 240
C --- ERROR ESTIMATION
CALL ESTRAV (N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& H,DD,FCN,NFCN,Y0,Y,IJOB,X,M1,M2,NM1,NS,NNS,E1,LDE1,
& ZZ,CONT,FF,IP1,IPHES,SCAL,ERR,
& FIRST,REJECT,FAC1,RPAR,IPAR)
C --- COMPUTE FINITE DIFFERENCES FOR DENSE OUTPUT
IF (ERR.LT.1.D0) THEN
DO I=1,N
Y(I)=Y(I)+ZZ(I+(NS-1)*N)
CONT(I+NS*N)=ZZ(I)/C(1)
END DO
DO K=1,NS-1 FACT=1.D0/(C(NS-K)-C(NS-K+1))
DO I=1,N
CONT(I+K*N)=(ZZ(I+(NS-K-1)*N)-ZZ(I+(NS-K)*N))*FACT
END DO
END DO
DO J=2,NS
DO K=NS,J,-1
FACT=1.D0/(C(NS-K)-C(NS-K+J))
DO I=1,N
CONT(I+K*N)=(CONT(I+K*N)-CONT(I+(K-1)*N))*FACT
END DO
END DO
END DO
END IF
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
ELSE
CASE (NS.EQ.1)
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
IF (FIRST.OR.STARTN.OR.CHANGE) THEN
DO I=1,NS
ZZ(I)=0.D0
FF(I)=0.D0
END DO
ELSE
HQUOT=H/HOLD
DO I=1,N
Z1I=HQUOT*CONT(I+N)
ZZ(I)=Z1I
FF(I)=Z1I
END DO
END IF
C *** *** *** *** *** *** ***
C LOOP FOR THE SIMPLIFIED NEWTON ITERATION
C *** *** *** *** *** *** ***
NEWT=0
NIT=NIT1-3
EXPMI=1.0D0/EXPMNS
FNEWT=MAX(10*UROUND/RTOL1,0.03D0)
FACCON=MAX(FACCON,UROUND)**0.8D0
THETA=ABS(THET)
440 CONTINUE
IF (NEWT.GE.NIT) GOTO 78
C --- COMPUTE THE RIGHT-HAND SIDE
DO I=1,N
CONT(I)=Y(I)+ZZ(I)
END DO
CALL FCN(N,XPH,CONT,ZZ,RPAR,IPAR)
C --- pberndt XXX: Check if the rhs returned a NaN
DO I=1,N
IF (ISNAN(ZZ(I))) GOTO 78
END DO
NFCN=NFCN+1
C --- SOLVE THE LINEAR SYSTEMS
CALL SLVRAR(N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& M1,M2,NM1,FAC1,E1,LDE1,ZZ,FF,IP1,IPHES,IER,IJOB)
NSOL=NSOL+1
NEWT=NEWT+1
DYNO=0.D0
DO I=1,N
DENOM=SCAL(I)
DYNO=DYNO+(ZZ(I)/DENOM)**2
END DO
DYNO=DSQRT(DYNO/NNS)
C --- BAD CONVERGENCE OR NUMBER OF ITERATIONS TO LARGE
IF (NEWT.GT.1.AND.NEWT.LT.NIT) THEN
THQ=DYNO/DYNOLD
IF (NEWT.EQ.2) THEN
THETA=THQ ELSE
THETA=SQRT(THQ*THQOLD)
END IF
THQOLD=THQ
IF (THETA.LT.0.99D0) THEN
FACCON=THETA/(1.0D0-THETA)
DYTH=FACCON*DYNO*THETA**(NIT-1-NEWT)/FNEWT
IF (DYTH.GE.1.0D0) THEN
QNEWT=DMAX1(1.0D-4,DMIN1(20.0D0,DYTH))
HHFAC=0.8D0*QNEWT**(-1.0D0/(4.0D0+NIT-1-NEWT))
H=HHFAC*H
REJECT=.TRUE.
LAST=.FALSE.
IF (HHFAC.LE.0.5D0) UNEXN=.TRUE.
IF (CALJAC) GOTO 20
GOTO 10
END IF
ELSE
GOTO 78
END IF
END IF
DYNOLD=MAX(DYNO,UROUND)
DO I=1,N
F1I=FF(I)+ZZ(I)
FF(I)=F1I
ZZ(I)=F1I
C --- pberndt XXX: Check if the rhs returned a NaN
IF (ISNAN(ZZ(I))) GOTO 78
END DO
IF (FACCON*DYNO.GT.FNEWT) GOTO 440
C --- ERROR ESTIMATION
CALL ESTRAV (N,FJAC,LDJAC,MLJAC,MUJAC,FMAS,LDMAS,MLMAS,MUMAS,
& H,DD,FCN,NFCN,Y0,Y,IJOB,X,M1,M2,NM1,NS,NNS,E1,LDE1,
& ZZ,CONT,FF,IP1,IPHES,SCAL,ERR,
& FIRST,REJECT,FAC1,RPAR,IPAR)
C --- COMPUTE FINITE DIFFERENCES FOR DENSE OUTPUT
IF (ERR.LT.1.D0) THEN
DO I=1,N
Y(I)=Y(I)+ZZ(I)
CONT(I+N)=ZZ(I)
END DO
END IF
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
END IF
END IF
END IF
C --- pberndt XXX: Check if the Y update generated a NaN
DO I=1,N
IF (ISNAN(Y(I))) GOTO 78
END DO
C *** *** *** *** *** *** ***
C *** *** *** *** *** *** ***
C --- COMPUTATION OF HNEW
C --- WE REQUIRE .2<=HNEW/H<=8.
FAC=MIN(SAFE,(1+2*NIT)*SAFE/(NEWT+2*NIT))
QUOT=MAX(FACR,MIN(FACL,ERR**EXPO/FAC))
HNEW=H/QUOT
C *** *** *** *** *** *** ***
C IS THE ERROR SMALL ENOUGH ?
C *** *** *** *** *** *** ***
IF (ERR.LT.1.D0) THEN
C --- STEP IS ACCEPTED
FIRST=.FALSE.
NACCPT=NACCPT+1
IF (PRED.AND..NOT.CHANGE) THEN
C --- PREDICTIVE CONTROLLER OF GUSTAFSSON
IF (NACCPT.GT.1) THEN
FACGUS=(HACC/H)*(ERR**2/ERRACC)**EXPO/SAFE FACGUS=MAX(FACR,MIN(FACL,FACGUS))
QUOT=MAX(QUOT,FACGUS)
HNEW=H/QUOT
END IF
HACC=H
ERRACC=MAX(1.0D-2,ERR)
END IF
XOLD=X
HOLD=H
X=XPH
C --- UPDATE SCALING
IF (ITOL.EQ.0) THEN
DO I=1,N
SCAL(I)=ATOL1+RTOL1*ABS(Y(I))
END DO
ELSE
DO I=1,N
QUOTT=ATOL(I)/RTOL(I)
RTOL1=0.1D0*RTOL(I)**EXPMNS
ATOL1=RTOL1*QUOTT
SCAL(I)=ATOL1+RTOL1*ABS(Y(I))
END DO
END IF
IF (IOUT.NE.0) THEN
NRSOL=NACCPT+1
XSOL=X
XOSOL=XOLD
DO I=1,N
CONT(I)=Y(I)
END DO
NSOLU=N
HSOL=HOLD
CALL SOLOUT(NRSOL,XOSOL,XSOL,Y,CONT,LRC,NSOLU,
& RPAR,IPAR,IRTRN)
IF (IRTRN.LT.0) GOTO 179
END IF
CALJAC=.FALSE.
IF (LAST) THEN
H=HOPT
IDID=1
RETURN
END IF
CALL FCN(N,X,Y,Y0,RPAR,IPAR)
NFCN=NFCN+1
HNEW=POSNEG*MIN(ABS(HNEW),HMAXN)
HOPT=HNEW
HOPT=MIN(H,HNEW)
IF (REJECT) HNEW=POSNEG*MIN(ABS(HNEW),ABS(H))
REJECT=.FALSE.
IF ((X+HNEW/QUOT1-XEND)*POSNEG.GE.0.D0) THEN
H=XEND-X
LAST=.TRUE.
ELSE
QT=HNEW/H
HHFAC=H
IF (THETA.LE.THET.AND.QT.GE.QUOT1.AND.QT.LE.QUOT2) THEN
IKEEP=1
GOTO 30
END IF
H=HNEW
END IF
HHFAC=H
IF (THETA.LE.THET) GOTO 20
GOTO 10
ELSE
C --- STEP IS REJECTED
REJECT=.TRUE.
LAST=.FALSE.
IF (FIRST) THEN
H=H*0.1D0 HHFAC=0.1D0
ELSE
HHFAC=HNEW/H
H=HNEW
END IF
IF (NACCPT.GE.1) NREJCT=NREJCT+1
IF (CALJAC) GOTO 20
GOTO 10
END IF
C --- UNEXPECTED STEP-REJECTION
78 CONTINUE
UNEXP=.TRUE.
IF (IER.NE.0) THEN
NSING=NSING+1
IF (NSING.GE.5) GOTO 176
END IF
H=H*0.5D0
HHFAC=0.5D0
REJECT=.TRUE.
LAST=.FALSE.
IF (CALJAC) GOTO 20
GOTO 10
C --- FAIL EXIT
175 CONTINUE
WRITE(9,979)X
WRITE(6,*) ' RHS EVALUATES TO NAN'
IDID=-42
RETURN
176 CONTINUE
WRITE(6,979)X
WRITE(6,*) ' MATRIX IS REPEATEDLY SINGULAR, IER=',IER
IDID=-4
RETURN
177 CONTINUE
WRITE(6,979)X
WRITE(6,*) ' STEP SIZE T0O SMALL, H=',H
IDID=-3
RETURN
178 CONTINUE
WRITE(6,979)X
WRITE(6,*) ' MORE THAN NMAX =',NMAX,'STEPS ARE NEEDED'
IDID=-2
RETURN
C --- EXIT CAUSED BY SOLOUT
179 CONTINUE
C WRITE(6,979)X
979 FORMAT(' EXIT OF RADAU AT X=',E18.4)
IDID=2
RETURN
END
C
C END OF SUBROUTINE RADCOV
C
C ***********************************************************
C
SUBROUTINE COERTV(NSMAX)
USE omp_lib
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
COMMON /COE3/ T311,T312,T313,T321,T322,T323,T331,
* TI311,TI312,TI313,TI321,TI322,TI323,TI331,TI332,TI333
!$OMP THREADPRIVATE(/COE3/)
COMMON /COE5/ T511,T512,T513,T514,T515,T521,T522,T523,T524,T525,
* T531,T532,T533,T534,T535,T541,T542,T543,T544,T545,T551,
* TI511,TI512,TI513,TI514,TI515,TI521,TI522,TI523,TI524,TI525,
* TI531,TI532,TI533,TI534,TI535,TI541,TI542,TI543,TI544,TI545,
* TI551,TI552,TI553,TI554,TI555
!$OMP THREADPRIVATE(/COE5/)
COMMON /COE7/ T711,T712,T713,T714,T715,T716,T717,
* T721,T722,T723,T724,T725,T726,T727,
* T731,T732,T733,T734,T735,T736,T737, * T741,T742,T743,T744,T745,T746,T747,
* T751,T752,T753,T754,T755,T756,T757,
* T761,T762,T763,T764,T765,T766,T767,T771,
* TI711,TI712,TI713,TI714,TI715,TI716,TI717,
* TI721,TI722,TI723,TI724,TI725,TI726,TI727,
* TI731,TI732,TI733,TI734,TI735,TI736,TI737,
* TI741,TI742,TI743,TI744,TI745,TI746,TI747,
* TI751,TI752,TI753,TI754,TI755,TI756,TI757,
* TI761,TI762,TI763,TI764,TI765,TI766,TI767,
* TI771,TI772,TI773,TI774,TI775,TI776,TI777
!$OMP THREADPRIVATE(/COE7/)
C ---
T311 = 0.9123239487089294279155D-01
T312 = -0.1412552950209542084280D+00
T313 = -0.3002919410514742449186D-01
T321 = 0.2417179327071070189575D+00
T322 = 0.2041293522937999319960D+00
T323 = 0.3829421127572619377954D+00
T331 = 0.9660481826150929361906D+00
TI311 = 0.4325579890063155351024D+01
TI312 = 0.3391992518158098695428D+00
TI313 = 0.5417705399358748711865D+00
TI321 = -0.4178718591551904727346D+01
TI322 = -0.3276828207610623870825D+00
TI323 = 0.4766235545005504519601D+00
TI331 = -0.5028726349457868759512D+00
TI332 = 0.2571926949855605429187D+01
TI333 = -0.5960392048282249249688D+00
IF (NSMAX.LE.3) RETURN
T511 = -0.1251758622050104589014D-01
T512 = -0.1024204781790882707009D-01
T513 = 0.4767387729029572386318D-01
T514 = -0.1147851525522951470794D-01
T515 = -0.1401985889287541028108D-01
T521 = -0.1491670151895382429004D-02
T522 = 0.5017286451737105816299D-01
T523 = -0.9433181918161143698066D-01
T524 = -0.7668830749180162885157D-02
T525 = 0.2470857842651852681253D-01
T531 = -0.7298187638808714862266D-01
T532 = -0.2305395340434179467214D+00
T533 = 0.1027030453801258997922D+00
T534 = 0.1939846399882895091122D-01
T535 = 0.8180035370375117083639D-01
T541 = -0.3800914400035681041264D+00
T542 = 0.3778939022488612495439D+00
T543 = 0.4667441303324943592896D+00
T544 = 0.4076011712801990666217D+00
T545 = 0.1996824278868025259365D+00
T551 = -0.9219789736812104884883D+00
TI511 = -0.3004156772154440162771D+02
TI512 = -0.1386510785627141316518D+02
TI513 = -0.3480002774795185561828D+01
TI514 = 0.1032008797825263422771D+01
TI515 = -0.8043030450739899174753D+00
TI521 = 0.5344186437834911598895D+01
TI522 = 0.4593615567759161004454D+01
TI523 = -0.3036360323459424298646D+01
TI524 = 0.1050660190231458863860D+01
TI525 = -0.2727786118642962705386D+00
TI531 = 0.3748059807439804860051D+01
TI532 = -0.3984965736343884667252D+01
TI533 = -0.1044415641608018792942D+01
TI534 = 0.1184098568137948487231D+01
TI535 = -0.4499177701567803688988D+00
TI541 = -0.3304188021351900000806D+02
TI542 = -0.1737695347906356701945D+02
TI543 = -0.1721290632540055611515D+00
TI544 = -0.9916977798254264258817D-01
TI545 = 0.5312281158383066671849D+00 TI551 = -0.8611443979875291977700D+01
TI552 = 0.9699991409528808231336D+01
TI553 = 0.1914728639696874284851D+01
TI554 = 0.2418692006084940026427D+01
TI555 = -0.1047463487935337418694D+01
IF (NSMAX.LE.5) RETURN
T711 = -0.2153754627310526422828D-02
T712 = 0.2156755135132077338691D-01
T713 = 0.8783567925144144407326D-02
T714 = -0.4055161452331023898198D-02
T715 = 0.4427232753268285479678D-02
T716 = -0.1238646187952874056377D-02
T717 = -0.2760617480543852499548D-02
T721 = 0.1600025077880428526831D-02
T722 = -0.3813164813441154669442D-01
T723 = -0.2152556059400687552385D-01
T724 = 0.8415568276559589237177D-02
T725 = -0.4031949570224549492304D-02
T726 = -0.6666635339396338181761D-04
T727 = 0.3185474825166209848748D-02
T731 = -0.4059107301947683091650D-02
T732 = 0.5739650893938171539757D-01
T733 = 0.5885052920842679105612D-01
T734 = -0.8560431061603432060177D-02
T735 = -0.6923212665023908924141D-02
T736 = -0.2352180982943338340535D-02
T737 = 0.4169077725297562691409D-03
T741 = -0.1575048807937684420346D-01
T742 = -0.3821469359696835048464D-01
T743 = -0.1657368112729438512412D+00
T744 = -0.3737124230238445741907D-01
T745 = 0.8239007298507719404499D-02
T746 = 0.3115071152346175252726D-02
T747 = 0.2511660491343882192836D-01
T751 = -0.1129776610242208076086D+00
T752 = -0.2491742124652636863308D+00
T753 = 0.2735633057986623212132D+00
T754 = 0.5366761379181770094279D-02
T755 = 0.1932111161012620144312D+00
T756 = 0.1017177324817151468081D+00
T757 = 0.9504502035604622821039D-01
T761 = -0.4583810431839315010281D+00
T762 = 0.5315846490836284292051D+00
T763 = 0.4863228366175728940567D+00
T764 = 0.5265742264584492629141D+00
T765 = 0.2755343949896258141929D+00
T766 = 0.5217519452747652852946D+00
T767 = 0.1280719446355438944141D+00
T771 = -0.8813915783538183763135D+00
TI711 = -0.2581319263199822292761D+03
TI712 = -0.1890737630813985089520D+03
TI713 = -0.4908731481793013119445D+02
TI714 = -0.4110647469661428418112D+01
TI715 = -0.4053447889315563304175D+01
TI716 = 0.3112755366607346076554D+01
TI717 = -0.1646774913558444650169D+01
TI721 = -0.3007390169451292131731D+01
TI722 = -0.1101586607876577132911D+02
TI723 = 0.1487799456131656281486D+01
TI724 = 0.2130388159559282459432D+01
TI725 = -0.1816141086817565624822D+01
TI726 = 0.1134325587895161100083D+01
TI727 = -0.4146990459433035319930D+00
TI731 = -0.8441963188321084681757D+01
TI732 = -0.6505252740575150028169D+00
TI733 = 0.6940670730369876478804D+01
TI734 = -0.3205047525597898431565D+01
TI735 = 0.1071280943546478589783D+01
TI736 = -0.3548507491216221879730D+00
TI737 = 0.9198549132786554154409D-01 TI741 = 0.7467833223502269977153D+02
TI742 = 0.8740858897990081640204D+02
TI743 = 0.4024158737379997877014D+01
TI744 = -0.3714806315158364186639D+01
TI745 = -0.3430093985982317350741D+01
TI746 = 0.2696604809765312378853D+01
TI747 = -0.9386927436075461933568D+00
TI751 = 0.5835652885190657724237D+02
TI752 = -0.1006877395780018096325D+02
TI753 = -0.3036638884256667120811D+02
TI754 = -0.1020020865184865985027D+01
TI755 = -0.1124175003784249621267D+00
TI756 = 0.1890640831000377622800D+01
TI757 = -0.9716486393831482282172D+00
TI761 = -0.2991862480282520966786D+03
TI762 = -0.2430407453687447911819D+03
TI763 = -0.4877710407803786921219D+02
TI764 = -0.2038671905741934405280D+01
TI765 = 0.1673560239861084944268D+01
TI766 = -0.1087374032057106164456D+01
TI767 = 0.9019382492960993738427D+00
TI771 = -0.9307650289743530591157D+02
TI772 = 0.2388163105628114427703D+02
TI773 = 0.3927888073081384382710D+02
TI774 = 0.1438891568549108006988D+02
TI775 = -0.3510438399399361221087D+01
TI776 = 0.4863284885566180701215D+01
TI777 = -0.2246482729591239916400D+01
RETURN
END
C
C END OF SUBROUTINE COERTV
C
C ***********************************************************
C
SUBROUTINE COERCV(NS,C,DD,U1,ALPH,BETA)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION C(0:NS),DD(NS),ALPH(NS),BETA(NS)
C(0)=0.D0
C(NS)=1.D0
GOTO (1,11,3,11,5,11,7) NS
11 CONTINUE
RETURN
1 CONTINUE
C(1)=1.0D0
U1=1.0D0
DD(1)=-1.0D0
RETURN
3 CONTINUE
SQ6=DSQRT(6.D0)
C(1)=(4.D0-SQ6)/10.D0
C(2)=(4.D0+SQ6)/10.D0
ST9=9.D0**(1.D0/3.D0)
U1=(6.D0+ST9*(ST9-1))/30.D0
ALP=(12.D0-ST9*(ST9-1))/60.D0
BET=ST9*(ST9+1)*DSQRT(3.D0)/60.D0
CNO=ALP**2+BET**2
U1=1.0D0/U1
ALPH(1)=ALP/CNO
BETA(1)=BET/CNO
RETURN
5 CONTINUE
C(1)= 0.5710419611451768219312D-01
C(2)= 0.2768430136381238276800D+00
C(3)= 0.5835904323689168200567D+00
C(4)= 0.8602401356562194478479D+00
DD(1)= -0.2778093394406463730479D+02
DD(2)= 0.3641478498049213152712D+01
DD(3)= -0.1252547721169118720491D+01
DD(4)= 0.5920031671845428725662D+00 DD(5)= -0.2000000000000000000000D+00
U1= 0.6286704751729276645173D+01
ALPH(1)= 0.3655694325463572258243D+01
BETA(1)= 0.6543736899360077294021D+01
ALPH(2)= 0.5700953298671789419170D+01
BETA(2)= 0.3210265600308549888425D+01
RETURN
7 CONTINUE
C(1)= 0.2931642715978489197205D-01
C(2)= 0.1480785996684842918500D+00
C(3)= 0.3369846902811542990971D+00
C(4)= 0.5586715187715501320814D+00
C(5)= 0.7692338620300545009169D+00
C(6)= 0.9269456713197411148519D+00
DD(1)= -0.5437443689412861451458D+02
DD(2)= 0.7000024004259186512041D+01
DD(3)= -0.2355661091987557192256D+01
DD(4)= 0.1132289066106134386384D+01
DD(5)= -0.6468913267673587118673D+00
DD(6)= 0.3875333853753523774248D+00
DD(7)= -0.1428571428571428571429D+00
U1= 0.8936832788405216337302D+01
ALPH(1)= 0.4378693561506806002523D+01
BETA(1)= 0.1016969328379501162732D+02
ALPH(2)= 0.7141055219187640105775D+01
BETA(2)= 0.6623045922639275970621D+01
ALPH(3)= 0.8511834825102945723051D+01
BETA(3)= 0.3281013624325058830036D+01
RETURN
END
C
C END OF SUBROUTINE COERCV
C
C ***********************************************************
C
DOUBLE PRECISION FUNCTION CONTRA(I,X,CONT,LRC)
USE omp_lib
C ----------------------------------------------------------
C THIS FUNCTION CAN BE USED FOR CONINUOUS OUTPUT. IT PROVIDES AN
C APPROXIMATION TO THE I-TH COMPONENT OF THE SOLUTION AT X.
C IT GIVES THE VALUE OF THE COLLOCATION POLYNOMIAL, DEFINED FOR
C THE LAST SUCCESSFULLY COMPUTED STEP (BY RADAU).
C ----------------------------------------------------------
PARAMETER (NSDIM=7)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION CONT(LRC)
COMMON/WEIGHT/NN,NS,XSOL,HSOL,C(0:NSDIM)
!$OMP THREADPRIVATE(/WEIGHT/)
S=(X-XSOL)/HSOL+1.D0
CONTRA=CONT(I+NS*NN)
DO K=NS-1,0,-1
CONTRA=CONT(I+K*NN)+(S-C(NS-K))*CONTRA
END DO
RETURN
END
C
C END OF FUNCTION CONTRA
C
C ***********************************************************