SLATEC Routines --- SDAINI ---

*DECK SDAINI
      SUBROUTINE SDAINI (X, Y, YPRIME, NEQ, RES, JAC, H, WT, IDID, RPAR,
     *   IPAR, PHI, DELTA, E, WM, IWM, HMIN, UROUND, NONNEG, NTEMP)
C***BEGIN PROLOGUE  SDAINI
C***SUBSIDIARY
C***PURPOSE  Initialization routine for SDASSL.
C***LIBRARY   SLATEC (DASSL)
C***TYPE      SINGLE PRECISION (SDAINI-S, DDAINI-D)
C***AUTHOR  Petzold, Linda R., (LLNL)
C***DESCRIPTION
C-----------------------------------------------------------------
C     SDAINI TAKES ONE STEP OF SIZE H OR SMALLER
C     WITH THE BACKWARD EULER METHOD, TO
C     FIND YPRIME.  X AND Y ARE UPDATED TO BE CONSISTENT WITH THE
C     NEW STEP.  A MODIFIED DAMPED NEWTON ITERATION IS USED TO
C     SOLVE THE CORRECTOR ITERATION.
C
C     THE INITIAL GUESS FOR YPRIME IS USED IN THE
C     PREDICTION, AND IN FORMING THE ITERATION
C     MATRIX, BUT IS NOT INVOLVED IN THE
C     ERROR TEST. THIS MAY HAVE TROUBLE
C     CONVERGING IF THE INITIAL GUESS IS NO
C     GOOD, OR IF G(X,Y,YPRIME) DEPENDS
C     NONLINEARLY ON YPRIME.
C
C     THE PARAMETERS REPRESENT:
C     X --         INDEPENDENT VARIABLE
C     Y --         SOLUTION VECTOR AT X
C     YPRIME --    DERIVATIVE OF SOLUTION VECTOR
C     NEQ --       NUMBER OF EQUATIONS
C     H --         STEPSIZE. IMDER MAY USE A STEPSIZE
C                  SMALLER THAN H.
C     WT --        VECTOR OF WEIGHTS FOR ERROR
C                  CRITERION
C     IDID --      COMPLETION CODE WITH THE FOLLOWING MEANINGS
C                  IDID= 1 -- YPRIME WAS FOUND SUCCESSFULLY
C                  IDID=-12 -- SDAINI FAILED TO FIND YPRIME
C     RPAR,IPAR -- REAL AND INTEGER PARAMETER ARRAYS
C                  THAT ARE NOT ALTERED BY SDAINI
C     PHI --       WORK SPACE FOR SDAINI
C     DELTA,E --   WORK SPACE FOR SDAINI
C     WM,IWM --    REAL AND INTEGER ARRAYS STORING
C                  MATRIX INFORMATION
C
C-----------------------------------------------------------------
C***ROUTINES CALLED  SDAJAC, SDANRM, SDASLV
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   901030  Minor corrections to declarations.  (FNF)
C***END PROLOGUE  SDAINI