SLATEC Routines --- SDASTP ---

*DECK SDASTP
      SUBROUTINE SDASTP (X, Y, YPRIME, NEQ, RES, JAC, H, WT, JSTART,
     *   IDID, RPAR, IPAR, PHI, DELTA, E, WM, IWM, ALPHA, BETA, GAMMA,
     *   PSI, SIGMA, CJ, CJOLD, HOLD, S, HMIN, UROUND, IPHASE, JCALC, K,
     *   KOLD, NS, NONNEG, NTEMP)
C***BEGIN PROLOGUE  SDASTP
C***SUBSIDIARY
C***PURPOSE  Perform one step of the SDASSL integration.
C***LIBRARY   SLATEC (DASSL)
C***TYPE      SINGLE PRECISION (SDASTP-S, DDASTP-D)
C***AUTHOR  Petzold, Linda R., (LLNL)
C***DESCRIPTION
C-----------------------------------------------------------------------
C     SDASTP SOLVES A SYSTEM OF DIFFERENTIAL/
C     ALGEBRAIC EQUATIONS OF THE FORM
C     G(X,Y,YPRIME) = 0,  FOR ONE STEP (NORMALLY
C     FROM X TO X+H).
C
C     THE METHODS USED ARE MODIFIED DIVIDED
C     DIFFERENCE,FIXED LEADING COEFFICIENT
C     FORMS OF BACKWARD DIFFERENTIATION
C     FORMULAS. THE CODE ADJUSTS THE STEPSIZE
C     AND ORDER TO CONTROL THE LOCAL ERROR PER
C     STEP.
C
C
C     THE PARAMETERS REPRESENT
C     X  --        INDEPENDENT VARIABLE
C     Y  --        SOLUTION VECTOR AT X
C     YPRIME --    DERIVATIVE OF SOLUTION VECTOR
C                  AFTER SUCCESSFUL STEP
C     NEQ --       NUMBER OF EQUATIONS TO BE INTEGRATED
C     RES --       EXTERNAL USER-SUPPLIED SUBROUTINE
C                  TO EVALUATE THE RESIDUAL.  THE CALL IS
C                  CALL RES(X,Y,YPRIME,DELTA,IRES,RPAR,IPAR)
C                  X,Y,YPRIME ARE INPUT.  DELTA IS OUTPUT.
C                  ON INPUT, IRES=0.  RES SHOULD ALTER IRES ONLY
C                  IF IT ENCOUNTERS AN ILLEGAL VALUE OF Y OR A
C                  STOP CONDITION.  SET IRES=-1 IF AN INPUT VALUE
C                  OF Y IS ILLEGAL, AND SDASTP WILL TRY TO SOLVE
C                  THE PROBLEM WITHOUT GETTING IRES = -1.  IF
C                  IRES=-2, SDASTP RETURNS CONTROL TO THE CALLING
C                  PROGRAM WITH IDID = -11.
C     JAC --       EXTERNAL USER-SUPPLIED ROUTINE TO EVALUATE
C                  THE ITERATION MATRIX (THIS IS OPTIONAL)
C                  THE CALL IS OF THE FORM
C                  CALL JAC(X,Y,YPRIME,PD,CJ,RPAR,IPAR)
C                  PD IS THE MATRIX OF PARTIAL DERIVATIVES,
C                  PD=DG/DY+CJ*DG/DYPRIME
C     H --         APPROPRIATE STEP SIZE FOR NEXT STEP.
C                  NORMALLY DETERMINED BY THE CODE
C     WT --        VECTOR OF WEIGHTS FOR ERROR CRITERION.
C     JSTART --    INTEGER VARIABLE SET 0 FOR
C                  FIRST STEP, 1 OTHERWISE.
C     IDID --      COMPLETION CODE WITH THE FOLLOWING MEANINGS:
C                  IDID= 1 -- THE STEP WAS COMPLETED SUCCESSFULLY
C                  IDID=-6 -- THE ERROR TEST FAILED REPEATEDLY
C                  IDID=-7 -- THE CORRECTOR COULD NOT CONVERGE
C                  IDID=-8 -- THE ITERATION MATRIX IS SINGULAR
C                  IDID=-9 -- THE CORRECTOR COULD NOT CONVERGE.
C                             THERE WERE REPEATED ERROR TEST
C                             FAILURES ON THIS STEP.
C                  IDID=-10-- THE CORRECTOR COULD NOT CONVERGE
C                             BECAUSE IRES WAS EQUAL TO MINUS ONE
C                  IDID=-11-- IRES EQUAL TO -2 WAS ENCOUNTERED,
C                             AND CONTROL IS BEING RETURNED TO
C                             THE CALLING PROGRAM
C     RPAR,IPAR -- REAL AND INTEGER PARAMETER ARRAYS THAT
C                  ARE USED FOR COMMUNICATION BETWEEN THE
C                  CALLING PROGRAM AND EXTERNAL USER ROUTINES
C                  THEY ARE NOT ALTERED BY SDASTP
C     PHI --       ARRAY OF DIVIDED DIFFERENCES USED BY
C                  SDASTP. THE LENGTH IS NEQ*(K+1),WHERE
C                  K IS THE MAXIMUM ORDER
C     DELTA,E --   WORK VECTORS FOR SDASTP OF LENGTH NEQ
C     WM,IWM --    REAL AND INTEGER ARRAYS STORING
C                  MATRIX INFORMATION SUCH AS THE MATRIX
C                  OF PARTIAL DERIVATIVES,PERMUTATION
C                  VECTOR, AND VARIOUS OTHER INFORMATION.
C
C     THE OTHER PARAMETERS ARE INFORMATION
C     WHICH IS NEEDED INTERNALLY BY SDASTP TO
C     CONTINUE FROM STEP TO STEP.
C
C-----------------------------------------------------------------------
C***ROUTINES CALLED  SDAJAC, SDANRM, SDASLV, SDATRP
C***REVISION HISTORY  (YYMMDD)
C   830315  DATE WRITTEN
C   901009  Finished conversion to SLATEC 4.0 format (F.N.Fritsch)
C   901019  Merged changes made by C. Ulrich with SLATEC 4.0 format.
C   901026  Added explicit declarations for all variables and minor
C           cosmetic changes to prologue.  (FNF)
C***END PROLOGUE  SDASTP