subroutine prepji (neq, y, yh, nyh, ewt, rtem, savr, s, wm, iwm, 1 res, jac, adda) clll. optimize external res, jac, adda 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, nre, nje, nqu integer i, i1, i2, ier, ii, ires, j, j1, jj, lenp, 1 mba, mband, meb1, meband, ml, ml3, mu double precision y, yh, ewt, rtem, savr, s, wm double precision rowns, 1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround double precision con, fac, hl0, r, srur, yi, yj, yjj dimension neq(1), y(1), yh(nyh,*), ewt(1), rtem(1), 1 s(1), savr(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, nre, nje, nqu c----------------------------------------------------------------------- c prepji is called by stodi to compute and process the matrix c p = a - h*el(1)*j , where j is an approximation to the jacobian dr/dy, c where r = g(t,y) - a(t,y)*s. here j is computed by the user-supplied c routine jac if miter = 1 or 4, or by finite differencing if miter = c 2 or 5. j is stored in wm, rescaled, and adda is called to generate c p. p is then subjected to lu decomposition in preparation c for later solution of linear systems with p as coefficient c matrix. this is done by dgefa if miter = 1 or 2, and by c dgbfa if miter = 4 or 5. c c in addition to variables described previously, communication c with prepji uses the following.. c y = array containing predicted values on entry. c rtem = work array of length n (acor in stodi). c savr = array used for output only. on output it contains the c residual evaluated at current values of t and y. c s = array containing predicted values of dy/dt (savf in stodi). c wm = real work space for matrices. on output it contains the c lu decomposition of p. 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 iwm = integer work space containing pivot information, starting at c iwm(21). iwm also contains the band parameters c ml = iwm(1) and mu = iwm(2) if miter is 4 or 5. c el0 = el(1) (input). c ierpj = output error flag. c = 0 if no trouble occurred, c = 1 if the p matrix was found to be singular, c = ires (= 2 or 3) if res returned ires = 2 or 3. 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, nre, and nje. c----------------------------------------------------------------------- nje = nje + 1 hl0 = h*el0 ierpj = 0 jcur = 1 go to (100, 200, 300, 400, 500), miter c if miter = 1, call res, then jac, and multiply by scalar. ------------ 100 ires = 1 call res (neq, tn, y, s, savr, ires) nre = nre + 1 if (ires .gt. 1) go to 600 lenp = n*n do 110 i = 1,lenp 110 wm(i+2) = 0.0d0 call jac ( neq, tn, y, s, 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 + 1 calls to res to approximate j. -------------- 200 continue ires = -1 call res (neq, tn, y, s, savr, ires) nre = nre + 1 if (ires .gt. 1) go to 600 srur = wm(1) j1 = 2 do 230 j = 1,n yj = y(j) r = dmax1(srur*dabs(yj),0.01d0/ewt(j)) y(j) = y(j) + r fac = -hl0/r call res ( neq, tn, y, s, rtem, ires ) nre = nre + 1 if (ires .gt. 1) go to 600 do 220 i = 1,n 220 wm(i+j1) = (rtem(i) - savr(i))*fac y(j) = yj j1 = j1 + n 230 continue ires = 1 call res (neq, tn, y, s, savr, ires) nre = nre + 1 if (ires .gt. 1) go to 600 c add matrix a. -------------------------------------------------------- 240 continue call adda(neq, tn, y, 0, 0, wm(3), n) c do lu decomposition on p. -------------------------------------------- call dgefa (wm(3), n, n, iwm(21), ier) if (ier .ne. 0) ierpj = 1 return c dummy section for miter = 3 300 return c if miter = 4, call res, then jac, and multiply by scalar. ------------ 400 ires = 1 call res (neq, tn, y, s, savr, ires) nre = nre + 1 if (ires .gt. 1) go to 600 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, s, 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 ml + mu + 2 calls to res to approximate j. -------- 500 continue ires = -1 call res (neq, tn, y, s, savr, ires) nre = nre + 1 if (ires .gt. 1) go to 600 ml = iwm(1) mu = iwm(2) ml3 = ml + 3 mband = ml + mu + 1 mba = min0(mband,n) meband = mband + ml meb1 = meband - 1 srur = wm(1) do 560 j = 1,mba do 530 i = j,n,mband yi = y(i) r = dmax1(srur*dabs(yi),0.01d0/ewt(i)) 530 y(i) = y(i) + r call res ( neq, tn, y, s, rtem, ires) nre = nre + 1 if (ires .gt. 1) go to 600 do 550 jj = j,n,mband y(jj) = yh(jj,1) yjj = y(jj) r = dmax1(srur*dabs(yjj),0.01d0/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) = (rtem(i) - savr(i))*fac 550 continue 560 continue ires = 1 call res (neq, tn, y, s, savr, ires) nre = nre + 1 if (ires .gt. 1) go to 600 c add matrix a. -------------------------------------------------------- 570 continue call adda(neq, tn, y, ml, mu, wm(ml3), 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 error return for ires = 2 or ires = 3 return from res. --------------- 600 ierpj = ires return c----------------------- end of subroutine prepji ---------------------- end