      subroutine prepj (neq, y, yh, nyh, ewt, ftem, savf, wm, iwm,
     1   f, jac)
clll. optimize
      external f, jac
      integer neq, nyh, iwm
      integer iownd, iowns,
     1   icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
     2   maxord, maxcor, msbp, mxncf, n, nq, nst, nfe, nje, nqu
      integer i, i1, i2, ier, ii, j, j1, jj, lenp,
     1   mba, mband, meb1, meband, ml, ml3, mu, np1
      double precision y, yh, ewt, ftem, savf, wm
      double precision rowns,
     1   ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround
      double precision con, di, fac, hl0, r, r0, srur, yi, yj, yjj,
     1   vnorm
      dimension neq(1), y(1), yh(nyh,*), ewt(1), ftem(1), savf(1),
     1   wm(*), iwm(*)
      common /ls0001/ rowns(209),
     2   ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround,
     3   iownd(14), iowns(6),
     4   icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
     5   maxord, maxcor, msbp, mxncf, n, nq, nst, nfe, nje, nqu
c-----------------------------------------------------------------------
c prepj is called by stode to compute and process the matrix
c p = i - h*el(1)*j , where j is an approximation to the jacobian.
c here j is computed by the user-supplied routine jac if
c miter = 1 or 4, or by finite differencing if miter = 2, 3, or 5.
c if miter = 3, a diagonal approximation to j is used.
c j is stored in wm and replaced by p.  if miter .ne. 3, p is then
c subjected to lu decomposition in preparation for later solution
c of linear systems with p as coefficient matrix. this is done
c by dgefa if miter = 1 or 2, and by dgbfa if miter = 4 or 5.
c
c in addition to variables described previously, communication
c with prepj uses the following..
c y     = array containing predicted values on entry.
c ftem  = work array of length n (acor in stode).
c savf  = array containing f evaluated at predicted y.
c wm    = real work space for matrices.  on output it contains the
c         inverse diagonal matrix if miter = 3 and the lu decomposition
c         of p if miter is 1, 2 , 4, or 5.
c         storage of matrix elements starts at wm(3).
c         wm also contains the following matrix-related data..
c         wm(1) = sqrt(uround), used in numerical jacobian increments.
c         wm(2) = h*el0, saved for later use if miter = 3.
c iwm   = integer work space containing pivot information, starting at
c         iwm(21), if miter is 1, 2, 4, or 5.  iwm also contains band
c         parameters ml = iwm(1) and mu = iwm(2) if miter is 4 or 5.
c el0   = el(1) (input).
c ierpj = output error flag,  = 0 if no trouble, .gt. 0 if
c         p matrix found to be singular.
c jcur  = output flag = 1 to indicate that the jacobian matrix
c         (or approximation) is now current.
c this routine also uses the common variables el0, h, tn, uround,
c miter, n, nfe, and nje.
c-----------------------------------------------------------------------
      nje = nje + 1
      ierpj = 0
      jcur = 1
      hl0 = h*el0
      go to (100, 200, 300, 400, 500), miter
c if miter = 1, call jac and multiply by scalar. -----------------------
 100  lenp = n*n
      do 110 i = 1,lenp
 110    wm(i+2) = 0.0d0
      call jac (neq, tn, y, 0, 0, wm(3), n)
      con = -hl0
      do 120 i = 1,lenp
 120    wm(i+2) = wm(i+2)*con
      go to 240
c if miter = 2, make n calls to f to approximate j. --------------------
 200  fac = vnorm (n, savf, ewt)
      r0 = 1000.0d0*dabs(h)*uround*dfloat(n)*fac
      if (r0 .eq. 0.0d0) r0 = 1.0d0
      srur = wm(1)
      j1 = 2
      do 230 j = 1,n
        yj = y(j)
        r = dmax1(srur*dabs(yj),r0/ewt(j))
        y(j) = y(j) + r
        fac = -hl0/r
        call f (neq, tn, y, ftem)
        do 220 i = 1,n
 220      wm(i+j1) = (ftem(i) - savf(i))*fac
        y(j) = yj
        j1 = j1 + n
 230    continue
      nfe = nfe + n
c add identity matrix. -------------------------------------------------
 240  j = 3
      np1 = n + 1
      do 250 i = 1,n
        wm(j) = wm(j) + 1.0d0
 250    j = j + np1
c do lu decomposition on p. --------------------------------------------
      call dgefa (wm(3), n, n, iwm(21), ier)
      if (ier .ne. 0) ierpj = 1
      return
c if miter = 3, construct a diagonal approximation to j and p. ---------
 300  wm(2) = hl0
      r = el0*0.1d0
      do 310 i = 1,n
 310    y(i) = y(i) + r*(h*savf(i) - yh(i,2))
      call f (neq, tn, y, wm(3))
      nfe = nfe + 1
      do 320 i = 1,n
        r0 = h*savf(i) - yh(i,2)
        di = 0.1d0*r0 - h*(wm(i+2) - savf(i))
        wm(i+2) = 1.0d0
        if (dabs(r0) .lt. uround/ewt(i)) go to 320
        if (dabs(di) .eq. 0.0d0) go to 330
        wm(i+2) = 0.1d0*r0/di
 320    continue
      return
 330  ierpj = 1
      return
c if miter = 4, call jac and multiply by scalar. -----------------------
 400  ml = iwm(1)
      mu = iwm(2)
      ml3 = ml + 3
      mband = ml + mu + 1
      meband = mband + ml
      lenp = meband*n
      do 410 i = 1,lenp
 410    wm(i+2) = 0.0d0
      call jac (neq, tn, y, ml, mu, wm(ml3), meband)
      con = -hl0
      do 420 i = 1,lenp
 420    wm(i+2) = wm(i+2)*con
      go to 570
c if miter = 5, make mband calls to f to approximate j. ----------------
 500  ml = iwm(1)
      mu = iwm(2)
      mband = ml + mu + 1
      mba = min0(mband,n)
      meband = mband + ml
      meb1 = meband - 1
      srur = wm(1)
      fac = vnorm (n, savf, ewt)
      r0 = 1000.0d0*dabs(h)*uround*dfloat(n)*fac
      if (r0 .eq. 0.0d0) r0 = 1.0d0
      do 560 j = 1,mba
        do 530 i = j,n,mband
          yi = y(i)
          r = dmax1(srur*dabs(yi),r0/ewt(i))
 530      y(i) = y(i) + r
        call f (neq, tn, y, ftem)
        do 550 jj = j,n,mband
          y(jj) = yh(jj,1)
          yjj = y(jj)
          r = dmax1(srur*dabs(yjj),r0/ewt(jj))
          fac = -hl0/r
          i1 = max0(jj-mu,1)
          i2 = min0(jj+ml,n)
          ii = jj*meb1 - ml + 2
          do 540 i = i1,i2
 540        wm(ii+i) = (ftem(i) - savf(i))*fac
 550      continue
 560    continue
      nfe = nfe + mba
c add identity matrix. -------------------------------------------------
 570  ii = mband + 2
      do 580 i = 1,n
        wm(ii) = wm(ii) + 1.0d0
 580    ii = ii + meband
c do lu decomposition of p. --------------------------------------------
      call dgbfa (wm(3), meband, n, ml, mu, iwm(21), ier)
      if (ier .ne. 0) ierpj = 1
      return
c----------------------- end of subroutine prepj -----------------------
      end
