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C/MEMBR ADD NAME=PRJA,SSI=0
subroutine prja (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 iownd2, iowns2, jtyp, mused, mxordn, mxords
integer i, i1, i2, ier, ii, j, j1, jj, lenp,
1 mba, mband, meb1, meband, ml, ml3, mu
double precision y, yh, ewt, ftem, savf, wm
double precision rownd, rowns,
1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround
double precision rownd2, rowns2, pdnorm
double precision con, fac, hl0, r, r0, srur, yi, yj, yjj,
1 vmnorm, fnorm, bnorm
dimension neq(*), y(*), yh(nyh,*), ewt(*), ftem(*), savf(*),
1 wm(*), iwm(*)
integer iero
common /ierode/ iero
common /ls0001/ rownd, 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
common /lsa001/ rownd2, rowns2(20), pdnorm,
1 iownd2(3), iowns2(2), jtyp, mused, mxordn, mxords
c-----------------------------------------------------------------------
c%purpose
c prja is called by stoda 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 or 5.
c j, scaled by -h*el(1), is stored in wm. then the norm of j (the
c matrix norm consistent with the weighted max-norm on vectors given
c by vmnorm) is computed, and j is overwritten by p. 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%additional parameters
c in addition to variables described previously, communication
c with prja uses the following..
c y = array containing predicted values on entry.
c ftem = work array of length n (acor in stoda).
c savf = array containing f evaluated at predicted y.
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 pdnorm= norm of jacobian matrix. (output).
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!
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) = 0.0d+0
call jac (neq, tn, y, 0, 0, wm(3), n)
if(iero.gt.0) return
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 = vmnorm (n, savf, ewt)
r0 = 1000.0d+0*abs(h)*uround*dble(n)*fac
if (r0 .eq. 0.0d+0) r0 = 1.0d+0
srur = wm(1)
j1 = 2
do 230 j = 1,n
yj = y(j)
r = max(srur*abs(yj),r0/ewt(j))
y(j) = y(j) + r
fac = -hl0/r
call f (neq, tn, y, ftem)
if(iero.gt.0) return
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
240 continue
c compute norm of jacobian. --------------------------------------------
pdnorm = fnorm (n, wm(3), ewt)/abs(hl0)
c add identity matrix. -------------------------------------------------
j = 3
do 250 i = 1,n
wm(j) = wm(j) + 1.0d+0
250 j = j + (n + 1)
c do lu decomposition on p. --------------------------------------------
call dgefa (wm(3), n, n, iwm(21), ier)
if (ier .ne. 0) ierpj = 1
return
c dummy block only, since miter is never 3 in this routine. ------------
300 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) = 0.0d+0
call jac (neq, tn, y, ml, mu, wm(ml3), meband)
if(iero.gt.0) return
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 = min(mband,n)
meband = mband + ml
meb1 = meband - 1
srur = wm(1)
fac = vmnorm (n, savf, ewt)
r0 = 1000.0d+0*abs(h)*uround*dble(n)*fac
if (r0 .eq. 0.0d+0) r0 = 1.0d+0
do 560 j = 1,mba
do 530 i = j,n,mband
yi = y(i)
r = max(srur*abs(yi),r0/ewt(i))
530 y(i) = y(i) + r
call f (neq, tn, y, ftem)
if(iero.gt.0) return
do 550 jj = j,n,mband
y(jj) = yh(jj,1)
yjj = y(jj)
r = max(srur*abs(yjj),r0/ewt(jj))
fac = -hl0/r
i1 = max(jj-mu,1)
i2 = min(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
570 continue
c compute norm of jacobian. --------------------------------------------
pdnorm = bnorm (n, wm(3), meband, ml, mu, ewt)/abs(hl0)
c add identity matrix. -------------------------------------------------
ii = mband + 2
do 580 i = 1,n
wm(ii) = wm(ii) + 1.0d+0
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 prja ------------------------
end
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