1 subroutine lsodar (f, neq, y, t, tout, itol, rtol, atol, itask,
2 1 istate, iopt, rwork, lrw, iwork, liw, jac, jt,
5 integer neq, itol, itask, istate, iopt, lrw, iwork, liw, jt,
7 double precision y, t, tout, rtol, atol, rwork
8 dimension neq(*), y(*), rtol(*), atol(*), rwork(lrw), iwork(liw),
10 c-----------------------------------------------------------------------
11 c this is the may 7, 1982 version of
12 c lsodar.. livermore solver for ordinary differential equations, with
13 c automatic method switching for stiff and nonstiff problems,
14 c and with root-finding.
16 c This version has been modified by scilab group on Feb 97 following Dr
17 c Hindmarsh direction see Comments noted "cSCI"
19 c this version is in double precision.
21 c lsodar solves the initial value problem for stiff or nonstiff
22 c systems of first order ode-s,
23 c dy/dt = f(t,y) , or, in component form,
24 c dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(neq)) (i = 1,...,neq).
25 c at the same time, it locates the roots of any of a set of functions
26 c g(i) = g(i,t,y(1),...,y(neq)) (i = 1,...,ng).
28 c this a variant version of the lsode package. it differs from lsode
30 c (a) it switches automatically between stiff and nonstiff methods.
31 c this means that the user does not have to determine whether the
32 c problem is stiff or not, and the solver will automatically choose the
33 c appropriate method. it always starts with the nonstiff method.
34 c (b) it finds the root of at least one of a set of constraint
35 c functions g(i) of the independent and dependent variables.
36 c it finds only those roots for which some g(i), as a function
37 c of t, changes sign in the interval of integration.
38 c it then returns the solution at the root, if that occurs
39 c sooner than the specified stop condition, and otherwise returns
40 c the solution according the specified stop condition.
44 c applied mathematics division 8331
45 c sandia national laboratories
49 c mathematics and statistics division, l-316
50 c lawrence livermore national laboratory
51 c livermore, ca 94550.
54 c 1. alan c. hindmarsh, lsode and lsodi, two new initial value
55 c ordinary differential equation solvers,
56 c acm-signum newsletter, vol. 15, no. 4 (1980), pp. 10-11.
57 c 2. linda r. petzold, automatic selection of methods for solving
58 c stiff and nonstiff systems of ordinary differential equations,
59 c siam j. sci. stat. comput. 4 (1983), pp. 136-148.
60 c 3. kathie l. hiebert and lawrence f. shampine, implicitly defined
61 c output points for solutions of ode-s, sandia report sand80-0180,
63 c-----------------------------------------------------------------------
66 c communication between the user and the lsodar package, for normal
67 c situations, is summarized here. this summary describes only a subset
68 c of the full set of options available. see the full description for
69 c details, including alternative treatment of the jacobian matrix,
70 c optional inputs and outputs, nonstandard options, and
71 c instructions for special situations. see also the example
72 c problem (with program and output) following this summary.
74 c a. first provide a subroutine of the form..
75 c subroutine f (neq, t, y, ydot)
76 c dimension y(neq), ydot(neq)
77 c which supplies the vector function f by loading ydot(i) with f(i).
79 c b. provide a subroutine of the form..
80 c subroutine g (neq, t, y, ng, gout)
81 c dimension y(neq), gout(ng)
82 c which supplies the vector function g by loading gout(i) with
83 c g(i), the i-th constraint function whose root is sought.
85 c c. write a main program which calls subroutine lsodar once for
86 c each point at which answers are desired. this should also provide
87 c for possible use of logical unit 6 for output of error messages by
88 c lsodar. on the first call to lsodar, supply arguments as follows..
89 c f = name of subroutine for right-hand side vector f.
90 c this name must be declared external in calling program.
91 c neq = number of first order ode-s.
92 c y = array of initial values, of length neq.
93 c t = the initial value of the independent variable.
94 c tout = first point where output is desired (.ne. t).
95 c itol = 1 or 2 according as atol (below) is a scalar or array.
96 c rtol = relative tolerance parameter (scalar).
97 c atol = absolute tolerance parameter (scalar or array).
98 c the estimated local error in y(i) will be controlled so as
100 c ewt(i) = rtol*abs(y(i)) + atol if itol = 1, or
101 c ewt(i) = rtol*abs(y(i)) + atol(i) if itol = 2.
102 c thus the local error test passes if, in each component,
103 c either the absolute error is less than atol (or atol(i)),
104 c or the relative error is less than rtol.
105 c use rtol = 0.0 for pure absolute error control, and
106 c use atol = 0.0 (or atol(i) = 0.0) for pure relative error
107 c control. caution.. actual (global) errors may exceed these
108 c local tolerances, so choose them conservatively.
109 c itask = 1 for normal computation of output values of y at t = tout.
110 c istate = integer flag (input and output). set istate = 1.
111 c iopt = 0 to indicate no optional inputs used.
112 c rwork = real work array of length at least..
113 c 22 + neq * max(16, neq + 9) + 3*ng.
114 c see also paragraph f below.
115 c lrw = declared length of rwork (in user-s dimension).
116 c iwork = integer work array of length at least 20 + neq.
117 c liw = declared length of iwork (in user-s dimension).
118 c jac = name of subroutine for jacobian matrix.
119 c use a dummy name. see also paragraph f below.
120 c jt = jacobian type indicator. set jt = 2.
121 c see also paragraph f below.
122 c g = name of subroutine for constraint functions, whose
123 c roots are desired during the integration.
124 c this name must be declared external in calling program.
125 c ng = number of constraint functions g(i). if there are none,
126 c set ng = 0, and pass a dummy name for g.
127 c jroot = integer array of length ng for output of root information.
128 c see next paragraph.
129 c note that the main program must declare arrays y, rwork, iwork,
130 c jroot, and possibly atol.
132 c d. the output from the first call (or any call) is..
133 c y = array of computed values of y(t) vector.
134 c t = corresponding value of independent variable. this is
135 c tout if istate = 2, or the root location if istate = 3,
136 c or the farthest point reached if lsodar was unsuccessful.
137 c istate = 2 or 3 if lsodar was successful, negative otherwise.
138 c 2 means no root was found, and tout was reached as desired.
139 c 3 means a root was found prior to reaching tout.
140 c -1 means excess work done on this call (perhaps wrong jt).
141 c -2 means excess accuracy requested (tolerances too small).
142 c -3 means illegal input detected (see printed message).
143 c -4 means repeated error test failures (check all inputs).
144 c -5 means repeated convergence failures (perhaps bad jacobian
145 c supplied or wrong choice of jt or tolerances).
146 c -6 means error weight became zero during problem. (solution
147 c component i vanished, and atol or atol(i) = 0.)
148 c -7 means work space insufficient to finish (see messages).
149 c jroot = array showing roots found if istate = 3 on return.
150 c jroot(i) = 1 if g(i) has a root at t, or 0 otherwise.
152 c e. to continue the integration after a successful return, proceed
154 c (a) if istate = 2 on return, reset tout and call lsodar again.
155 c (b) if istate = 3 on return, reset istate to 2 and call lsodar again.
156 c in either case, no other parameters need be reset.
158 c f. note.. if and when lsodar regards the problem as stiff, and
159 c switches methods accordingly, it must make use of the neq by neq
160 c jacobian matrix, j = df/dy. for the sake of simplicity, the
161 c inputs to lsodar recommended in paragraph c above cause lsodar to
162 c treat j as a full matrix, and to approximate it internally by
163 c difference quotients. alternatively, j can be treated as a band
164 c matrix (with great potential reduction in the size of the rwork
165 c array). also, in either the full or banded case, the user can supply
166 c j in closed form, with a routine whose name is passed as the jac
167 c argument. these alternatives are described in the paragraphs on
168 c rwork, jac, and jt in the full description of the call sequence below.
170 c-----------------------------------------------------------------------
173 c the following is a simple example problem, with the coding
174 c needed for its solution by lsodar. the problem is from chemical
175 c kinetics, and consists of the following three rate equations..
176 c dy1/dt = -.04*y1 + 1.e4*y2*y3
177 c dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2
178 c dy3/dt = 3.e7*y2**2
179 c on the interval from t = 0.0 to t = 4.e10, with initial conditions
180 c y1 = 1.0, y2 = y3 = 0. the problem is stiff.
181 c in addition, we want to find the values of t, y1, y2, and y3 at which
182 c (1) y1 reaches the value 1.e-4, and
183 c (2) y3 reaches the value 1.e-2.
185 c the following coding solves this problem with lsodar,
186 c printing results at t = .4, 4., ..., 4.e10, and at the computed
187 c roots. it uses itol = 2 and atol much smaller for y2 than y1 or y3
188 c because y2 has much smaller values.
189 c at the end of the run, statistical quantities of interest are
190 c printed (see optional outputs in the full description below).
193 c double precision atol, rtol, rwork, t, tout, y
194 c dimension y(3), atol(3), rwork(76), iwork(23), jroot(2)
214 c 10 call lsodar(fex,neq,y,t,tout,itol,rtol,atol,itask,istate,
215 c 1 iopt,rwork,lrw,iwork,liw,jdum,jt,gex,ng,jroot)
216 c write(6,20)t,y(1),y(2),y(3)
217 c 20 format(7h at t =,e12.4,6h y =,3e14.6)
218 c if (istate .lt. 0) go to 80
219 c if (istate .eq. 2) go to 40
220 c write(6,30)jroot(1),jroot(2)
221 c 30 format(5x,35h the above line is a root, jroot =,2i5)
224 c 40 tout = tout*10.0d0
225 c write(6,60)iwork(11),iwork(12),iwork(13),iwork(10),
226 c 1 iwork(19),rwork(15)
227 c 60 format(/12h no. steps =,i4,11h no. f-s =,i4,11h no. j-s =,i4,
228 c 1 11h no. g-s =,i4/
229 c 2 19h method last used =,i2,25h last switch was at t =,e12.4)
231 c 80 write(6,90)istate
232 c 90 format(///22h error halt.. istate =,i3)
236 c subroutine fex (neq, t, y, ydot)
237 c double precision t, y, ydot
238 c dimension y(3), ydot(3)
239 c ydot(1) = -0.04d0*y(1) + 1.0d4*y(2)*y(3)
240 c ydot(3) = 3.0d7*y(2)*y(2)
241 c ydot(2) = -ydot(1) - ydot(3)
245 c subroutine gex (neq, t, y, ng, gout)
246 c double precision t, y, gout
247 c dimension y(3), gout(2)
248 c gout(1) = y(1) - 1.0d-4
249 c gout(2) = y(3) - 1.0d-2
253 c the output of this program (on a cdc-7600 in single precision)
256 c at t = 2.6400e-01 y = 9.899653e-01 3.470563e-05 1.000000e-02
257 c the above line is a root, jroot = 0 1
258 c at t = 4.0000e-01 y = 9.851712e-01 3.386380e-05 1.479493e-02
259 c at t = 4.0000e+00 y = 9.055333e-01 2.240655e-05 9.444430e-02
260 c at t = 4.0000e+01 y = 7.158403e-01 9.186334e-06 2.841505e-01
261 c at t = 4.0000e+02 y = 4.505250e-01 3.222964e-06 5.494717e-01
262 c at t = 4.0000e+03 y = 1.831975e-01 8.941774e-07 8.168016e-01
263 c at t = 4.0000e+04 y = 3.898730e-02 1.621940e-07 9.610125e-01
264 c at t = 4.0000e+05 y = 4.936363e-03 1.984221e-08 9.950636e-01
265 c at t = 4.0000e+06 y = 5.161831e-04 2.065786e-09 9.994838e-01
266 c at t = 2.0745e+07 y = 1.000000e-04 4.000395e-10 9.999000e-01
267 c the above line is a root, jroot = 1 0
268 c at t = 4.0000e+07 y = 5.179817e-05 2.072032e-10 9.999482e-01
269 c at t = 4.0000e+08 y = 5.283401e-06 2.113371e-11 9.999947e-01
270 c at t = 4.0000e+09 y = 4.659031e-07 1.863613e-12 9.999995e-01
271 c at t = 4.0000e+10 y = 1.404280e-08 5.617126e-14 1.000000e+00
273 c no. steps = 361 no. f-s = 693 no. j-s = 64 no. g-s = 390
274 c method last used = 2 last switch was at t = 6.0092e-03
275 c-----------------------------------------------------------------------
276 c full description of user interface to lsodar.
278 c the user interface to lsodar consists of the following parts.
280 c i. the call sequence to subroutine lsodar, which is a driver
281 c routine for the solver. this includes descriptions of both
282 c the call sequence arguments and of user-supplied routines.
283 c following these descriptions is a description of
284 c optional inputs available through the call sequence, and then
285 c a description of optional outputs (in the work arrays).
287 c ii. descriptions of other routines in the lsodar package that may be
288 c (optionally) called by the user. these provide the ability to
289 c alter error message handling, save and restore the internal
290 c common, and obtain specified derivatives of the solution y(t).
292 c iii. descriptions of common blocks to be declared in overlay
293 c or similar environments, or to be saved when doing an interrupt
294 c of the problem and continued solution later.
296 c iv. description of a subroutine in the lsodar package,
297 c which the user may replace with his own version, if desired.
298 c this relates to the measurement of errors.
300 c-----------------------------------------------------------------------
301 c part i. call sequence.
303 c the call sequence parameters used for input only are
304 c f, neq, tout, itol, rtol, atol, itask, iopt, lrw, liw, jac,
306 c that used only for output is jroot,
307 c and those used for both input and output are
309 c the work arrays rwork and iwork are also used for conditional and
310 c optional inputs and optional outputs. (the term output here refers
311 c to the return from subroutine lsodar to the user-s calling program.)
313 c the legality of input parameters will be thoroughly checked on the
314 c initial call for the problem, but not checked thereafter unless a
315 c change in input parameters is flagged by istate = 3 on input.
317 c the descriptions of the call arguments are as follows.
319 c f = the name of the user-supplied subroutine defining the
320 c ode system. the system must be put in the first-order
321 c form dy/dt = f(t,y), where f is a vector-valued function
322 c of the scalar t and the vector y. subroutine f is to
323 c compute the function f. it is to have the form
324 c subroutine f (neq, t, y, ydot)
325 c dimension y(1), ydot(1)
326 c where neq, t, and y are input, and the array ydot = f(t,y)
327 c is output. y and ydot are arrays of length neq.
328 c (in the dimension statement above, 1 is a dummy
329 c dimension.. it can be replaced by any value.)
330 c subroutine f should not alter y(1),...,y(neq).
331 c f must be declared external in the calling program.
333 c subroutine f may access user-defined quantities in
334 c neq(2),... and y(neq(1)+1),... if neq is an array
335 c (dimensioned in f) and y has length exceeding neq(1).
336 c see the descriptions of neq and y below.
338 c neq = the size of the ode system (number of first order
339 c ordinary differential equations). used only for input.
340 c neq may be decreased, but not increased, during the problem.
341 c if neq is decreased (with istate = 3 on input), the
342 c remaining components of y should be left undisturbed, if
343 c these are to be accessed in f and/or jac.
345 c normally, neq is a scalar, and it is generally referred to
346 c as a scalar in this user interface description. however,
347 c neq may be an array, with neq(1) set to the system size.
348 c (the lsodar package accesses only neq(1).) in either case,
349 c this parameter is passed as the neq argument in all calls
350 c to f, jac, and g. hence, if it is an array, locations
351 c neq(2),... may be used to store other integer data and pass
352 c it to f, jac, and g. each such subroutine must include
353 c neq in a dimension statement in that case.
355 c y = a real array for the vector of dependent variables, of
356 c length neq or more. used for both input and output on the
357 c first call (istate = 1), and only for output on other calls.
358 c on the first call, y must contain the vector of initial
359 c values. on output, y contains the computed solution vector,
360 c evaluated at t. if desired, the y array may be used
361 c for other purposes between calls to the solver.
363 c this array is passed as the y argument in all calls to f,
364 c jac, and g. hence its length may exceed neq, and locations
365 c y(neq+1),... may be used to store other real data and
366 c pass it to f, jac, and g. (the lsodar package accesses only
369 c t = the independent variable. on input, t is used only on the
370 c first call, as the initial point of the integration.
371 c on output, after each call, t is the value at which a
372 c computed solution y is evaluated (usually the same as tout).
373 c if a root was found, t is the computed location of the
374 c root reached first, on output.
375 c on an error return, t is the farthest point reached.
377 c tout = the next value of t at which a computed solution is desired.
378 c used only for input.
380 c when starting the problem (istate = 1), tout may be equal
381 c to t for one call, then should .ne. t for the next call.
382 c for the initial t, an input value of tout .ne. t is used
383 c in order to determine the direction of the integration
384 c (i.e. the algebraic sign of the step sizes) and the rough
385 c scale of the problem. integration in either direction
386 c (forward or backward in t) is permitted.
388 c if itask = 2 or 5 (one-step modes), tout is ignored after
389 c the first call (i.e. the first call with tout .ne. t).
390 c otherwise, tout is required on every call.
392 c if itask = 1, 3, or 4, the values of tout need not be
393 c monotone, but a value of tout which backs up is limited
394 c to the current internal t interval, whose endpoints are
395 c tcur - hu and tcur (see optional outputs, below, for
398 c itol = an indicator for the type of error control. see
399 c description below under atol. used only for input.
401 c rtol = a relative error tolerance parameter, either a scalar or
402 c an array of length neq. see description below under atol.
405 c atol = an absolute error tolerance parameter, either a scalar or
406 c an array of length neq. input only.
408 c the input parameters itol, rtol, and atol determine
409 c the error control performed by the solver. the solver will
410 c control the vector e = (e(i)) of estimated local errors
411 c in y, according to an inequality of the form
412 c max-norm of ( e(i)/ewt(i) ) .le. 1,
413 c where ewt = (ewt(i)) is a vector of positive error weights.
414 c the values of rtol and atol should all be non-negative.
415 c the following table gives the types (scalar/array) of
416 c rtol and atol, and the corresponding form of ewt(i).
418 c itol rtol atol ewt(i)
419 c 1 scalar scalar rtol*abs(y(i)) + atol
420 c 2 scalar array rtol*abs(y(i)) + atol(i)
421 c 3 array scalar rtol(i)*abs(y(i)) + atol
422 c 4 array array rtol(i)*abs(y(i)) + atol(i)
424 c when either of these parameters is a scalar, it need not
425 c be dimensioned in the user-s calling program.
427 c if none of the above choices (with itol, rtol, and atol
428 c fixed throughout the problem) is suitable, more general
429 c error controls can be obtained by substituting a
430 c user-supplied routine for the setting of ewt.
433 c if global errors are to be estimated by making a repeated
434 c run on the same problem with smaller tolerances, then all
435 c components of rtol and atol (i.e. of ewt) should be scaled
438 c itask = an index specifying the task to be performed.
439 c input only. itask has the following values and meanings.
440 c 1 means normal computation of output values of y(t) at
441 c t = tout (by overshooting and interpolating).
442 c 2 means take one step only and return.
443 c 3 means stop at the first internal mesh point at or
444 c beyond t = tout and return.
445 c 4 means normal computation of output values of y(t) at
446 c t = tout but without overshooting t = tcrit.
447 c tcrit must be input as rwork(1). tcrit may be equal to
448 c or beyond tout, but not behind it in the direction of
449 c integration. this option is useful if the problem
450 c has a singularity at or beyond t = tcrit.
451 c 5 means take one step, without passing tcrit, and return.
452 c tcrit must be input as rwork(1).
454 c note.. if itask = 4 or 5 and the solver reaches tcrit
455 c (within roundoff), it will return t = tcrit (exactly) to
456 c indicate this (unless itask = 4 and tout comes before tcrit,
457 c in which case answers at t = tout are returned first).
459 c istate = an index used for input and output to specify the
460 c the state of the calculation.
462 c on input, the values of istate are as follows.
463 c 1 means this is the first call for the problem
464 c (initializations will be done). see note below.
465 c 2 means this is not the first call, and the calculation
466 c is to continue normally, with no change in any input
467 c parameters except possibly tout and itask.
468 c (if itol, rtol, and/or atol are changed between calls
469 c with istate = 2, the new values will be used but not
470 c tested for legality.)
471 c 3 means this is not the first call, and the
472 c calculation is to continue normally, but with
473 c a change in input parameters other than
474 c tout and itask. changes are allowed in
475 c neq, itol, rtol, atol, iopt, lrw, liw, jt, ml, mu,
476 c and any optional inputs except h0, mxordn, and mxords.
477 c (see iwork description for ml and mu.)
478 c in addition, immediately following a return with
479 c istate = 3 (root found), ng and g may be changed.
480 c (but changing ng from 0 to .gt. 0 is not allowed.)
481 c note.. a preliminary call with tout = t is not counted
482 c as a first call here, as no initialization or checking of
483 c input is done. (such a call is sometimes useful for the
484 c purpose of outputting the initial conditions.)
485 c thus the first call for which tout .ne. t requires
486 c istate = 1 on input.
488 c on output, istate has the following values and meanings.
489 c 1 means nothing was done, as tout was equal to t with
490 c istate = 1 on input. (however, an internal counter was
491 c set to detect and prevent repeated calls of this type.)
492 c 2 means the integration was performed successfully, and
493 c no roots were found.
494 c 3 means the integration was successful, and one or more
495 c roots were found before satisfying the stop condition
496 c specified by itask. see jroot.
497 c -1 means an excessive amount of work (more than mxstep
498 c steps) was done on this call, before completing the
499 c requested task, but the integration was otherwise
500 c successful as far as t. (mxstep is an optional input
501 c and is normally 500.) to continue, the user may
502 c simply reset istate to a value .gt. 1 and call again
503 c (the excess work step counter will be reset to 0).
504 c in addition, the user may increase mxstep to avoid
505 c this error return (see below on optional inputs).
506 c -2 means too much accuracy was requested for the precision
507 c of the machine being used. this was detected before
508 c completing the requested task, but the integration
509 c was successful as far as t. to continue, the tolerance
510 c parameters must be reset, and istate must be set
511 c to 3. the optional output tolsf may be used for this
512 c purpose. (note.. if this condition is detected before
513 c taking any steps, then an illegal input return
514 c (istate = -3) occurs instead.)
515 c -3 means illegal input was detected, before taking any
516 c integration steps. see written message for details.
517 c note.. if the solver detects an infinite loop of calls
518 c to the solver with illegal input, it will cause
520 c -4 means there were repeated error test failures on
521 c one attempted step, before completing the requested
522 c task, but the integration was successful as far as t.
523 c the problem may have a singularity, or the input
524 c may be inappropriate.
525 c -5 means there were repeated convergence test failures on
526 c one attempted step, before completing the requested
527 c task, but the integration was successful as far as t.
528 c this may be caused by an inaccurate jacobian matrix,
529 c if one is being used.
530 c -6 means ewt(i) became zero for some i during the
531 c integration. pure relative error control (atol(i)=0.0)
532 c was requested on a variable which has now vanished.
533 c the integration was successful as far as t.
534 c -7 means the length of rwork and/or iwork was too small to
535 c proceed, but the integration was successful as far as t.
536 c this happens when lsodar chooses to switch methods
537 c but lrw and/or liw is too small for the new method.
539 c note.. since the normal output value of istate is 2,
540 c it does not need to be reset for normal continuation.
541 c also, since a negative input value of istate will be
542 c regarded as illegal, a negative output value requires the
543 c user to change it, and possibly other inputs, before
544 c calling the solver again.
546 c iopt = an integer flag to specify whether or not any optional
547 c inputs are being used on this call. input only.
548 c the optional inputs are listed separately below.
549 c iopt = 0 means no optional inputs are being used.
550 c default values will be used in all cases.
551 c iopt = 1 means one or more optional inputs are being used.
553 c rwork = a real array (double precision) for work space, and (in the
554 c first 20 words) for conditional and optional inputs and
556 c as lsodar switches automatically between stiff and nonstiff
557 c methods, the required length of rwork can change during the
558 c problem. thus the rwork array passed to lsodar can either
559 c have a static (fixed) length large enough for both methods,
560 c or have a dynamic (changing) length altered by the calling
561 c program in response to output from lsodar.
563 c --- fixed length case ---
564 c if the rwork length is to be fixed, it should be at least
566 c where lrn and lrs are the rwork lengths required when the
567 c current method is nonstiff or stiff, respectively.
569 c the separate rwork length requirements lrn and lrs are
571 c if neq is constant and the maximum method orders have
572 c their default values, then
573 c lrn = 20 + 16*neq + 3*ng,
574 c lrs = 22 + 9*neq + neq**2 + 3*ng (jt = 1 or 2),
575 c lrs = 22 + 10*neq + (2*ml+mu)*neq + 3*ng (jt = 4 or 5).
576 c under any other conditions, lrn and lrs are given by..
577 c lrn = 20 + nyh*(mxordn+1) + 3*neq + 3*ng,
578 c lrs = 20 + nyh*(mxords+1) + 3*neq + lmat + 3*ng,
580 c nyh = the initial value of neq,
581 c mxordn = 12, unless a smaller value is given as an
583 c mxords = 5, unless a smaller value is given as an
585 c lmat = length of matrix work space..
586 c lmat = neq**2 + 2 if jt = 1 or 2,
587 c lmat = (2*ml + mu + 1)*neq + 2 if jt = 4 or 5.
589 c --- dynamic length case ---
590 c if the length of rwork is to be dynamic, then it should
591 c be at least lrn or lrs, as defined above, depending on the
592 c current method. initially, it must be at least lrn (since
593 c lsodar starts with the nonstiff method). on any return
594 c from lsodar, the optional output mcur indicates the current
595 c method. if mcur differs from the value it had on the
596 c previous return, or if there has only been one call to
597 c lsodar and mcur is now 2, then lsodar has switched
598 c methods during the last call, and the length of rwork
599 c should be reset (to lrn if mcur = 1, or to lrs if
600 c mcur = 2). (an increase in the rwork length is required
601 c if lsodar returned istate = -7, but not otherwise.)
602 c after resetting the length, call lsodar with istate = 3
603 c to signal that change.
605 c lrw = the length of the array rwork, as declared by the user.
606 c (this will be checked by the solver.)
608 c iwork = an integer array for work space.
609 c as lsodar switches automatically between stiff and nonstiff
610 c methods, the required length of iwork can change during
612 c lis = 20 + neq and lin = 20,
613 c respectively. thus the iwork array passed to lsodar can
614 c either have a fixed length of at least 20 + neq, or have a
615 c dynamic length of at least lin or lis, depending on the
616 c current method. the comments on dynamic length under
617 c rwork above apply here. initially, this length need
618 c only be at least lin = 20.
620 c the first few words of iwork are used for conditional and
621 c optional inputs and optional outputs.
623 c the following 2 words in iwork are conditional inputs..
624 c iwork(1) = ml these are the lower and upper
625 c iwork(2) = mu half-bandwidths, respectively, of the
626 c banded jacobian, excluding the main diagonal.
627 c the band is defined by the matrix locations
628 c (i,j) with i-ml .le. j .le. i+mu. ml and mu
629 c must satisfy 0 .le. ml,mu .le. neq-1.
630 c these are required if jt is 4 or 5, and
631 c ignored otherwise. ml and mu may in fact be
632 c the band parameters for a matrix to which
633 c df/dy is only approximately equal.
635 c liw = the length of the array iwork, as declared by the user.
636 c (this will be checked by the solver.)
638 c note.. the base addresses of the work arrays must not be
639 c altered between calls to lsodar for the same problem.
640 c the contents of the work arrays must not be altered
641 c between calls, except possibly for the conditional and
642 c optional inputs, and except for the last 3*neq words of rwork.
643 c the latter space is used for internal scratch space, and so is
644 c available for use by the user outside lsodar between calls, if
645 c desired (but not for use by f, jac, or g).
647 c jac = the name of the user-supplied routine to compute the
648 c jacobian matrix, df/dy, if jt = 1 or 4. the jac routine
649 c is optional, but if the problem is expected to be stiff much
650 c of the time, you are encouraged to supply jac, for the sake
651 c of efficiency. (alternatively, set jt = 2 or 5 to have
652 c lsodar compute df/dy internally by difference quotients.)
653 c if and when lsodar uses df/dy, if treats this neq by neq
654 c matrix either as full (jt = 1 or 2), or as banded (jt =
655 c 4 or 5) with half-bandwidths ml and mu (discussed under
656 c iwork above). in either case, if jt = 1 or 4, the jac
657 c routine must compute df/dy as a function of the scalar t
658 c and the vector y. it is to have the form
659 c subroutine jac (neq, t, y, ml, mu, pd, nrowpd)
660 c dimension y(1), pd(nrowpd,1)
661 c where neq, t, y, ml, mu, and nrowpd are input and the array
662 c pd is to be loaded with partial derivatives (elements of
663 c the jacobian matrix) on output. pd must be given a first
664 c dimension of nrowpd. t and y have the same meaning as in
665 c subroutine f. (in the dimension statement above, 1 is a
666 c dummy dimension.. it can be replaced by any value.)
667 c in the full matrix case (jt = 1), ml and mu are
668 c ignored, and the jacobian is to be loaded into pd in
669 c columnwise manner, with df(i)/dy(j) loaded into pd(i,j).
670 c in the band matrix case (jt = 4), the elements
671 c within the band are to be loaded into pd in columnwise
672 c manner, with diagonal lines of df/dy loaded into the rows
673 c of pd. thus df(i)/dy(j) is to be loaded into pd(i-j+mu+1,j).
674 c ml and mu are the half-bandwidth parameters (see iwork).
675 c the locations in pd in the two triangular areas which
676 c correspond to nonexistent matrix elements can be ignored
677 c or loaded arbitrarily, as they are overwritten by lsodar.
678 c jac need not provide df/dy exactly. a crude
679 c approximation (possibly with a smaller bandwidth) will do.
680 c in either case, pd is preset to zero by the solver,
681 c so that only the nonzero elements need be loaded by jac.
682 c each call to jac is preceded by a call to f with the same
683 c arguments neq, t, and y. thus to gain some efficiency,
684 c intermediate quantities shared by both calculations may be
685 c saved in a user common block by f and not recomputed by jac,
686 c if desired. also, jac may alter the y array, if desired.
687 c jac must be declared external in the calling program.
688 c subroutine jac may access user-defined quantities in
689 c neq(2),... and y(neq(1)+1),... if neq is an array
690 c (dimensioned in jac) and y has length exceeding neq(1).
691 c see the descriptions of neq and y above.
693 c jt = jacobian type indicator. used only for input.
694 c jt specifies how the jacobian matrix df/dy will be
695 c treated, if and when lsodar requires this matrix.
696 c jt has the following values and meanings..
697 c 1 means a user-supplied full (neq by neq) jacobian.
698 c 2 means an internally generated (difference quotient) full
699 c jacobian (using neq extra calls to f per df/dy value).
700 c 4 means a user-supplied banded jacobian.
701 c 5 means an internally generated banded jacobian (using
702 c ml+mu+1 extra calls to f per df/dy evaluation).
703 c if jt = 1 or 4, the user must supply a subroutine jac
704 c (the name is arbitrary) as described above under jac.
705 c if jt = 2 or 5, a dummy argument can be used.
707 c g = the name of subroutine for constraint functions, whose
708 c roots are desired during the integration. it is to have
710 c subroutine g (neq, t, y, ng, gout)
711 c dimension y(neq), gout(ng)
712 c where neq, t, y, and ng are input, and the array gout
713 c is output. neq, t, and y have the same meaning as in
714 c the f routine, and gout is an array of length ng.
715 c for i = 1,...,ng, this routine is to load into gout(i)
716 c the value at (t,y) of the i-th constraint function g(i).
717 c lsodar will find roots of the g(i) of odd multiplicity
718 c (i.e. sign changes) as they occur during the integration.
719 c g must be declared external in the calling program.
721 c caution.. because of numerical errors in the functions
722 c g(i) due to roundoff and integration error, lsodar may
723 c return false roots, or return the same root at two or more
724 c nearly equal values of t. if such false roots are
725 c suspected, the user should consider smaller error tolerances
726 c and/or higher precision in the evaluation of the g(i).
728 c if a root of some g(i) defines the end of the problem,
729 c the input to lsodar should nevertheless allow integration
730 c to a point slightly past that root, so that lsodar can
731 c locate the root by interpolation.
733 c subroutine g may access user-defined quantities in
734 c neq(2),... and y(neq(1)+1),... if neq is an array
735 c (dimensioned in g) and y has length exceeding neq(1).
736 c see the descriptions of neq and y above.
738 c ng = number of constraint functions g(i). if there are none,
739 c set ng = 0, and pass a dummy name for g.
741 c jroot = integer array of length ng. used only for output.
742 c on a return with istate = 3 (one or more roots found),
743 c jroot(i) = 1 if g(i) has a root at t, or jroot(i) = 0 if not.
744 c-----------------------------------------------------------------------
747 c the following is a list of the optional inputs provided for in the
748 c call sequence. (see also part ii.) for each such input variable,
749 c this table lists its name as used in this documentation, its
750 c location in the call sequence, its meaning, and the default value.
751 c the use of any of these inputs requires iopt = 1, and in that
752 c case all of these inputs are examined. a value of zero for any
753 c of these optional inputs will cause the default value to be used.
754 c thus to use a subset of the optional inputs, simply preload
755 c locations 5 to 10 in rwork and iwork to 0.0 and 0 respectively, and
756 c then set those of interest to nonzero values.
758 c name location meaning and default value
760 c h0 rwork(5) the step size to be attempted on the first step.
761 c the default value is determined by the solver.
763 c hmax rwork(6) the maximum absolute step size allowed.
764 c the default value is infinite.
766 c hmin rwork(7) the minimum absolute step size allowed.
767 c the default value is 0. (this lower bound is not
768 c enforced on the final step before reaching tcrit
769 c when itask = 4 or 5.)
771 c ixpr iwork(5) flag to generate extra printing at method switches.
772 c ixpr = 0 means no extra printing (the default).
773 c ixpr = 1 means print data on each switch.
774 c t, h, and nst will be printed on the same logical
775 c unit as used for error messages.
777 c mxstep iwork(6) maximum number of (internally defined) steps
778 c allowed during one call to the solver.
779 c the default value is 500.
781 c mxhnil iwork(7) maximum number of messages printed (per problem)
782 c warning that t + h = t on a step (h = step size).
783 c this must be positive to result in a non-default
784 c value. the default value is 10.
786 c mxordn iwork(8) the maximum order to be allowed for the nonstiff
787 c (adams) method. the default value is 12.
788 c if mxordn exceeds the default value, it will
789 c be reduced to the default value.
790 c mxordn is held constant during the problem.
792 c mxords iwork(9) the maximum order to be allowed for the stiff
793 c (bdf) method. the default value is 5.
794 c if mxords exceeds the default value, it will
795 c be reduced to the default value.
796 c mxords is held constant during the problem.
797 c-----------------------------------------------------------------------
800 c as optional additional output from lsodar, the variables listed
801 c below are quantities related to the performance of lsodar
802 c which are available to the user. these are communicated by way of
803 c the work arrays, but also have internal mnemonic names as shown.
804 c except where stated otherwise, all of these outputs are defined
805 c on any successful return from lsodar, and on any return with
806 c istate = -1, -2, -4, -5, or -6. on an illegal input return
807 c (istate = -3), they will be unchanged from their existing values
808 c (if any), except possibly for tolsf, lenrw, and leniw.
809 c on any error return, outputs relevant to the error will be defined,
812 c name location meaning
814 c hu rwork(11) the step size in t last used (successfully).
816 c hcur rwork(12) the step size to be attempted on the next step.
818 c tcur rwork(13) the current value of the independent variable
819 c which the solver has actually reached, i.e. the
820 c current internal mesh point in t. on output, tcur
821 c will always be at least as far as the argument
822 c t, but may be farther (if interpolation was done).
824 c tolsf rwork(14) a tolerance scale factor, greater than 1.0,
825 c computed when a request for too much accuracy was
826 c detected (istate = -3 if detected at the start of
827 c the problem, istate = -2 otherwise). if itol is
828 c left unaltered but rtol and atol are uniformly
829 c scaled up by a factor of tolsf for the next call,
830 c then the solver is deemed likely to succeed.
831 c (the user may also ignore tolsf and alter the
832 c tolerance parameters in any other way appropriate.)
834 c tsw rwork(15) the value of t at the time of the last method
837 c nge iwork(10) the number of g evaluations for the problem so far.
839 c nst iwork(11) the number of steps taken for the problem so far.
841 c nfe iwork(12) the number of f evaluations for the problem so far.
843 c nje iwork(13) the number of jacobian evaluations (and of matrix
844 c lu decompositions) for the problem so far.
846 c nqu iwork(14) the method order last used (successfully).
848 c nqcur iwork(15) the order to be attempted on the next step.
850 c imxer iwork(16) the index of the component of largest magnitude in
851 c the weighted local error vector ( e(i)/ewt(i) ),
852 c on an error return with istate = -4 or -5.
854 c lenrw iwork(17) the length of rwork actually required, assuming
855 c that the length of rwork is to be fixed for the
856 c rest of the problem, and that switching may occur.
857 c this is defined on normal returns and on an illegal
858 c input return for insufficient storage.
860 c leniw iwork(18) the length of iwork actually required, assuming
861 c that the length of iwork is to be fixed for the
862 c rest of the problem, and that switching may occur.
863 c this is defined on normal returns and on an illegal
864 c input return for insufficient storage.
866 c mused iwork(19) the method indicator for the last successful step..
867 c 1 means adams (nonstiff), 2 means bdf (stiff).
869 c mcur iwork(20) the current method indicator..
870 c 1 means adams (nonstiff), 2 means bdf (stiff).
871 c this is the method to be attempted
872 c on the next step. thus it differs from mused
873 c only if a method switch has just been made.
875 c the following two arrays are segments of the rwork array which
876 c may also be of interest to the user as optional outputs.
877 c for each array, the table below gives its internal name,
878 c its base address in rwork, and its description.
880 c name base address description
882 c yh 21 + 3*ng the nordsieck history array, of size nyh by
883 c (nqcur + 1), where nyh is the initial value
884 c of neq. for j = 0,1,...,nqcur, column j+1
885 c of yh contains hcur**j/factorial(j) times
886 c the j-th derivative of the interpolating
887 c polynomial currently representing the solution,
888 c evaluated at t = tcur.
890 c acor lacor array of size neq used for the accumulated
891 c (from common corrections on each step, scaled on output
892 c as noted) to represent the estimated local error in y
893 c on the last step. this is the vector e in
894 c the description of the error control. it is
895 c defined only on a successful return from
896 c lsodar. the base address lacor is obtained by
897 c including in the user-s program the
898 c following 3 lines..
899 c double precision rls
900 c common /ls0001/ rls(219), ils(39)
903 c-----------------------------------------------------------------------
904 c part ii. other routines callable.
906 c the following are optional calls which the user may make to
907 c gain additional capabilities in conjunction with lsodar.
908 c (the routines xsetun and xsetf are designed to conform to the
909 c slatec error handling package.)
911 c form of call function
912 c call xsetun(lun) set the logical unit number, lun, for
913 c output of messages from lsodar, if
914 c the default is not desired.
915 c the default value of lun is 6.
917 c call xsetf(mflag) set a flag to control the printing of
918 c messages by lsodar.
919 c mflag = 0 means do not print. (danger..
920 c this risks losing valuable information.)
921 c mflag = 1 means print (the default).
923 c either of the above calls may be made at
924 c any time and will take effect immediately.
926 c call svcar (rsav, isav) store in rsav and isav the contents
927 c of the internal common blocks used by
928 c lsodar (see part iii below).
929 c rsav must be a real array of length 246
930 c or more, and isav must be an integer
931 c array of length 59 or more.
933 c call rscar (rsav, isav) restore, from rsav and isav, the contents
934 c of the internal common blocks used by
935 c lsodar. presumes a prior call to svcar
936 c with the same arguments.
938 c svcar and rscar are useful if
939 c interrupting a run and restarting
940 c later, or alternating between two or
941 c more problems solved with lsodar.
943 c call intdy(,,,,,) provide derivatives of y, of various
944 c (see below) orders, at a specified point t, if
945 c desired. it may be called only after
946 c a successful return from lsodar.
948 c the detailed instructions for using intdy are as follows.
949 c the form of the call is..
951 c call intdy (t, k, rwork(lyh), nyh, dky, iflag)
953 c the input parameters are..
955 c t = value of independent variable where answers are desired
956 c (normally the same as the t last returned by lsodar).
957 c for valid results, t must lie between tcur - hu and tcur.
958 c (see optional outputs for tcur and hu.)
959 c k = integer order of the derivative desired. k must satisfy
960 c 0 .le. k .le. nqcur, where nqcur is the current order
961 c (see optional outputs). the capability corresponding
962 c to k = 0, i.e. computing y(t), is already provided
963 c by lsodar directly. since nqcur .ge. 1, the first
964 c derivative dy/dt is always available with intdy.
965 c lyh = 21 + 3*ng = base address in rwork of the history array yh.
966 c nyh = column length of yh, equal to the initial value of neq.
968 c the output parameters are..
970 c dky = a real array of length neq containing the computed value
971 c of the k-th derivative of y(t).
972 c iflag = integer flag, returned as 0 if k and t were legal,
973 c -1 if k was illegal, and -2 if t was illegal.
974 c on an error return, a message is also written.
975 c-----------------------------------------------------------------------
976 c part iii. common blocks.
978 c if lsodar is to be used in an overlay situation, the user
979 c must declare, in the primary overlay, the variables in..
980 c (1) the call sequence to lsodar,
981 c (2) the four internal common blocks
982 c /ls0001/ of length 258 (219 double precision words
983 c followed by 39 integer words),
984 c /lsa001/ of length 31 (22 double precision words
985 c followed by 9 integer words),
986 c /lsr001/ of length 14 (5 double precision words
987 c followed by 9 integer words),
988 c /eh0001/ of length 2 (integer words).
990 c if lsodar is used on a system in which the contents of internal
991 c common blocks are not preserved between calls, the user should
992 c declare the above common blocks in his main program to insure
993 c that their contents are preserved.
995 c if the solution of a given problem by lsodar is to be interrupted
996 c and then later continued, such as when restarting an interrupted run
997 c or alternating between two or more problems, the user should save,
998 c following the return from the last lsodar call prior to the
999 c interruption, the contents of the call sequence variables and the
1000 c internal common blocks, and later restore these values before the
1001 c next lsodar call for that problem. to save and restore the common
1002 c blocks, use subroutines svcar and rscar (see part ii above).
1004 c-----------------------------------------------------------------------
1005 c part iv. optionally replaceable solver routines.
1007 c below is a description of a routine in the lsodar package which
1008 c relates to the measurement of errors, and can be
1009 c replaced by a user-supplied version, if desired. however, since such
1010 c a replacement may have a major impact on performance, it should be
1011 c done only when absolutely necessary, and only with great caution.
1012 c (note.. the means by which the package version of a routine is
1013 c superseded by the user-s version may be system-dependent.)
1016 c the following subroutine is called just before each internal
1017 c integration step, and sets the array of error weights, ewt, as
1018 c described under itol/rtol/atol above..
1019 c subroutine ewset (neq, itol, rtol, atol, ycur, ewt)
1020 c where neq, itol, rtol, and atol are as in the lsodar call sequence,
1021 c ycur contains the current dependent variable vector, and
1022 c ewt is the array of weights set by ewset.
1024 c if the user supplies this subroutine, it must return in ewt(i)
1025 c (i = 1,...,neq) a positive quantity suitable for comparing errors
1026 c in y(i) to. the ewt array returned by ewset is passed to the
1027 c vmnorm routine, and also used by lsodar in the computation
1028 c of the optional output imxer, and the increments for difference
1029 c quotient jacobians.
1031 c in the user-supplied version of ewset, it may be desirable to use
1032 c the current values of derivatives of y. derivatives up to order nq
1033 c are available from the history array yh, described above under
1034 c optional outputs. in ewset, yh is identical to the ycur array,
1035 c extended to nq + 1 columns with a column length of nyh and scale
1036 c factors of h**j/factorial(j). on the first call for the problem,
1037 c given by nst = 0, nq is 1 and h is temporarily set to 1.0.
1038 c the quantities nq, nyh, h, and nst can be obtained by including
1039 c in ewset the statements..
1040 c double precision h, rls
1041 c common /ls0001/ rls(219),ils(39)
1046 c thus, for example, the current value of dy/dt can be obtained as
1047 c ycur(nyh+i)/h (i=1,...,neq) (and the division by h is
1048 c unnecessary when nst = 0).
1049 c-----------------------------------------------------------------------
1050 c-----------------------------------------------------------------------
1051 c other routines in the lsodar package.
1053 c in addition to subroutine lsodar, the lsodar package includes the
1054 c following subroutines and function routines..
1055 c rchek does preliminary checking for roots, and serves as an
1056 c interface between subroutine lsodar and subroutine roots.
1057 c roots finds the leftmost root of a set of functions.
1058 c intdy computes an interpolated value of the y vector at t = tout.
1059 c stoda is the core integrator, which does one step of the
1060 c integration and the associated error control.
1061 c cfode sets all method coefficients and test constants.
1062 c prja computes and preprocesses the jacobian matrix j = df/dy
1063 c and the newton iteration matrix p = i - h*l0*j.
1064 c solsy manages solution of linear system in chord iteration.
1065 c ewset sets the error weight vector ewt before each step.
1066 c vmnorm computes the weighted max-norm of a vector.
1067 c fnorm computes the norm of a full matrix consistent with the
1068 c weighted max-norm on vectors.
1069 c bnorm computes the norm of a band matrix consistent with the
1070 c weighted max-norm on vectors.
1071 c svcar and rscar are user-callable routines to save and restore,
1072 c respectively, the contents of the internal common blocks.
1073 c dgefa and dgesl are routines from linpack for solving full
1074 c systems of linear algebraic equations.
1075 c dgbfa and dgbsl are routines from linpack for solving banded
1077 c daxpy, dscal, idamax, ddot, and dcopy are basic linear algebra
1078 c modules (blas) used by the above linpack routines.
1079 c dlamch computes the unit roundoff in a machine-independent manner.
1080 c xerrwv, xsetun, and xsetf handle the printing of all error
1081 c messages and warnings. xerrwv is machine-dependent.
1082 c note.. vmnorm, fnorm, bnorm, idamax, ddot, and dlamch are function
1083 c routines. all the others are subroutines.
1085 c the intrinsic and external routines used by lsodar are..
1086 c dabs, dmax1, dmin1, dfloat, max0, min0, mod, dsign, dsqrt, and write.
1088 c a block data subprogram is also included with the package,
1089 c for loading some of the variables in internal common.
1091 c-----------------------------------------------------------------------
1092 c the following card is for optimized compilation on lll compilers.
1094 c-----------------------------------------------------------------------
1098 external prja, solsy
1099 integer illin, init, lyh, lewt, lacor, lsavf, lwm, liwm,
1100 1 mxstep, mxhnil, nhnil, ntrep, nslast, nyh, iowns
1101 integer icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
1102 1 maxord, maxcor, msbp, mxncf, n, nq, nst, nfe, nje, nqu
1103 integer insufr, insufi, ixpr, iowns2, jtyp, mused, mxordn, mxords
1104 integer lg0, lg1, lgx, iownr3, irfnd, itaskc, ngc, nge
1105 integer i, i1, i2, iflag, imxer, kgo, lf0,
1106 1 leniw, lenrw, lenwm, ml, mord, mu, mxhnl0, mxstp0
1107 integer len1, len1c, len1n, len1s, len2, leniwc,
1108 1 lenrwc, lenrwn, lenrws
1109 integer irfp, irt, lenyh, lyhnew
1110 double precision tret, rowns,
1111 1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround
1112 double precision tsw, rowns2, pdnorm
1113 double precision rownr3, t0, tlast, toutc
1114 double precision atoli, ayi, big, ewti, h0, hmax, hmx, rh, rtoli,
1115 1 tcrit, tdist, tnext, tol, tolsf, tp, size, sum, w0,
1119 c-----------------------------------------------------------------------
1120 c the following three internal common blocks contain
1121 c (a) variables which are local to any subroutine but whose values must
1122 c be preserved between calls to the routine (own variables), and
1123 c (b) variables which are communicated between subroutines.
1124 c the structure of each block is as follows.. all real variables are
1125 c listed first, followed by all integers. within each type, the
1126 c variables are grouped with those local to subroutine lsodar first,
1127 c then those local to subroutine roots or subroutine stoda
1128 c (no other routines have own variables), and finally those used
1129 c for communication. the block ls0001 is declared in subroutines
1130 c lsodar, intdy, stoda, prja, and solsy. the block lsa001 is declared
1131 c in subroutines lsodar, stoda, and prja. the block lsr001 is declared
1132 c in subroutines lsodar, rchek, and roots. groups of variables are
1133 c replaced by dummy arrays in the common declarations in routines
1134 c where those variables are not used.
1135 c-----------------------------------------------------------------------
1136 common /ls0001/ tret, rowns(209),
1137 1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround,
1138 2 illin, init, lyh, lewt, lacor, lsavf, lwm, liwm,
1139 3 mxstep, mxhnil, nhnil, ntrep, nslast, nyh, iowns(6),
1140 4 icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
1141 5 maxord, maxcor, msbp, mxncf, n, nq, nst, nfe, nje, nqu
1142 common /lsa001/ tsw, rowns2(20), pdnorm,
1143 1 insufr, insufi, ixpr, iowns2(2), jtyp, mused, mxordn, mxords
1144 common /lsr001/ rownr3(2), t0, tlast, toutc,
1145 1 lg0, lg1, lgx, iownr3(2), irfnd, itaskc, ngc, nge
1147 data mord(1),mord(2)/12,5/, mxstp0/500/, mxhnl0/10/
1148 c-----------------------------------------------------------------------
1150 c this code block is executed on every call.
1151 c it tests istate and itask for legality and branches appropriately.
1152 c if istate .gt. 1 but the flag init shows that initialization has
1153 c not yet been done, an error return occurs.
1154 c if istate = 1 and tout = t, jump to block g and return immediately.
1155 c-----------------------------------------------------------------------
1156 if (istate .lt. 1 .or. istate .gt. 3) go to 601
1157 if (itask .lt. 1 .or. itask .gt. 5) go to 602
1159 if (istate .eq. 1) go to 10
1160 if (init .eq. 0) go to 603
1161 if (istate .eq. 2) go to 200
1164 if (tout .eq. t) go to 430
1166 c-----------------------------------------------------------------------
1168 c the next code block is executed for the initial call (istate = 1),
1169 c or for a continuation call with parameter changes (istate = 3).
1170 c it contains checking of all inputs and various initializations.
1172 c first check legality of the non-optional inputs neq, itol, iopt,
1173 c jt, ml, mu, and ng.
1174 c-----------------------------------------------------------------------
1175 if (neq(1) .le. 0) go to 604
1176 if (istate .eq. 1) go to 25
1177 if (neq(1) .gt. n) go to 605
1179 if (itol .lt. 1 .or. itol .gt. 4) go to 606
1180 if (iopt .lt. 0 .or. iopt .gt. 1) go to 607
1181 if (jt .eq. 3 .or. jt .lt. 1 .or. jt .gt. 5) go to 608
1183 if (jt .le. 2) go to 30
1186 if (ml .lt. 0 .or. ml .ge. n) go to 609
1187 if (mu .lt. 0 .or. mu .ge. n) go to 610
1189 if (ng .lt. 0) go to 630
1190 if (istate .eq. 1) go to 35
1191 if (irfnd .eq. 0 .and. ng .ne. ngc) go to 631
1193 c next process and check the optional inputs. --------------------------
1194 if (iopt .eq. 1) go to 40
1200 if (istate .ne. 1) go to 60
1206 if (ixpr .lt. 0 .or. ixpr .gt. 1) go to 611
1208 if (mxstep .lt. 0) go to 612
1209 if (mxstep .eq. 0) mxstep = mxstp0
1211 if (mxhnil .lt. 0) go to 613
1212 if (mxhnil .eq. 0) mxhnil = mxhnl0
1213 if (istate .ne. 1) go to 50
1216 if (mxordn .lt. 0) go to 628
1217 if (mxordn .eq. 0) mxordn = 100
1218 mxordn = min0(mxordn,mord(1))
1220 if (mxords .lt. 0) go to 629
1221 if (mxords .eq. 0) mxords = 100
1222 mxords = min0(mxords,mord(2))
1223 if ((tout - t)*h0 .lt. 0.0d0) go to 614
1225 if (hmax .lt. 0.0d0) go to 615
1227 if (hmax .gt. 0.0d0) hmxi = 1.0d0/hmax
1229 if (hmin .lt. 0.0d0) go to 616
1230 c-----------------------------------------------------------------------
1231 c set work array pointers and check lengths lrw and liw.
1232 c if istate = 1, meth is initialized to 1 here to facilitate the
1233 c checking of work space lengths.
1234 c pointers to segments of rwork and iwork are named by prefixing l to
1235 c the name of the segment. e.g., the segment yh starts at rwork(lyh).
1236 c segments of rwork (in order) are denoted g0, g1, gx, yh, wm,
1238 c if the lengths provided are insufficient for the current method,
1239 c an error return occurs. this is treated as illegal input on the
1240 c first call, but as a problem interruption with istate = -7 on a
1241 c continuation call. if the lengths are sufficient for the current
1242 c method but not for both methods, a warning message is sent.
1243 c-----------------------------------------------------------------------
1244 60 if (istate .eq. 1) meth = 1
1245 if (istate .eq. 1) nyh = n
1250 if (istate .eq. 1) lyh = lyhnew
1251 if (lyhnew .eq. lyh) go to 62
1252 c if istate = 3 and ng was changed, shift yh to its new location. ------
1254 if (lrw .lt. lyhnew-1+lenyh) go to 62
1256 if (lyhnew .gt. lyh) i1 = -1
1257 call dcopy (lenyh, rwork(lyh), i1, rwork(lyhnew), i1)
1260 len1n = lyhnew - 1 + (mxordn + 1)*nyh
1261 len1s = lyhnew - 1 + (mxords + 1)*nyh
1263 if (jt .le. 2) lenwm = n*n + 2
1264 if (jt .ge. 4) lenwm = (2*ml + mu + 1)*n + 2
1265 len1s = len1s + lenwm
1267 if (meth .eq. 2) len1c = len1s
1268 len1 = max0(len1n,len1s)
1271 lenrwn = len1n + len2
1272 lenrws = len1s + len2
1273 lenrwc = len1c + len2
1278 if (meth .eq. 2) leniwc = leniw
1280 if (istate .eq. 1 .and. lrw .lt. lenrwc) go to 617
1281 if (istate .eq. 1 .and. liw .lt. leniwc) go to 618
1282 if (istate .eq. 3 .and. lrw .lt. lenrwc) go to 550
1283 if (istate .eq. 3 .and. liw .lt. leniwc) go to 555
1286 if (lrw .ge. lenrw) go to 65
1290 1 'lsodar- warning.. rwork length is sufficient for now, but ',
1291 1 60, 103, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1293 1 ' may not be later. integration will proceed anyway. ',
1294 1 60, 103, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1296 1 ' length needed is lenrw = i1, while lrw = i2.',
1297 1 50, 103, 1, 2, lenrw, lrw, 0, 0.0d0, 0.0d0)
1301 if (liw .ge. leniw) go to 70
1304 1 'lsodar- warning.. iwork length is sufficient for now, but ',
1305 1 60, 104, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1307 1 ' may not be later. integration will proceed anyway. ',
1308 1 60, 104, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1310 1 ' length needed is leniw = i1, while liw = i2.',
1311 1 50, 104, 1, 2, leniw, liw, 0, 0.0d0, 0.0d0)
1313 c check rtol and atol for legality. ------------------------------------
1317 if (itol .ge. 3) rtoli = rtol(i)
1318 if (itol .eq. 2 .or. itol .eq. 4) atoli = atol(i)
1319 if (rtoli .lt. 0.0d0) go to 619
1320 if (atoli .lt. 0.0d0) go to 620
1322 if (istate .eq. 1) go to 100
1323 c if istate = 3, set flag to signal parameter changes to stoda. --------
1325 if (n .eq. nyh) go to 200
1326 c neq was reduced. zero part of yh to avoid undefined references. -----
1328 i2 = lyh + (maxord + 1)*nyh - 1
1329 if (i1 .gt. i2) go to 200
1333 c-----------------------------------------------------------------------
1335 c the next block is for the initial call only (istate = 1).
1336 c it contains all remaining initializations, the initial call to f,
1337 c and the calculation of the initial step size.
1338 c the error weights in ewt are inverted after being loaded.
1339 c-----------------------------------------------------------------------
1340 100 uround = dlamch('p')
1344 if (itask .ne. 4 .and. itask .ne. 5) go to 110
1346 if ((tcrit - tout)*(tout - t) .lt. 0.0d0) go to 625
1347 if (h0 .ne. 0.0d0 .and. (t + h0 - tcrit)*h0 .gt. 0.0d0)
1362 c initial call to f. (lf0 points to yh(*,2).) -------------------------
1364 call f (neq, t, y, rwork(lf0))
1365 if(ierror.gt.0) return
1367 c load the initial value vector in yh. ---------------------------------
1369 115 rwork(i+lyh-1) = y(i)
1370 c load and invert the ewt array. (h is temporarily set to 1.0.) -------
1373 call ewset (n, itol, rtol, atol, rwork(lyh), rwork(lewt))
1375 if (rwork(i+lewt-1) .le. 0.0d0) go to 621
1376 120 rwork(i+lewt-1) = 1.0d0/rwork(i+lewt-1)
1377 c-----------------------------------------------------------------------
1378 c the coding below computes the step size, h0, to be attempted on the
1379 c first step, unless the user has supplied a value for this.
1380 c first check that tout - t differs significantly from zero.
1381 c a scalar tolerance quantity tol is computed, as max(rtol(i))
1382 c if this is positive, or max(atol(i)/abs(y(i))) otherwise, adjusted
1383 c so as to be between 100*uround and 1.0e-3.
1384 c then the computed value h0 is given by..
1386 c h0**(-2) = 1./(tol * w0**2) + tol * (norm(f))**2
1388 c where w0 = max ( abs(t), abs(tout) ),
1389 c f = the initial value of the vector f(t,y), and
1390 c norm() = the weighted vector norm used throughout, given by
1391 c the vmnorm function routine, and weighted by the
1392 c tolerances initially loaded into the ewt array.
1393 c the sign of h0 is inferred from the initial values of tout and t.
1394 c abs(h0) is made .le. abs(tout-t) in any case.
1395 c-----------------------------------------------------------------------
1396 if (h0 .ne. 0.0d0) go to 180
1397 tdist = dabs(tout - t)
1398 w0 = dmax1(dabs(t),dabs(tout))
1399 if (tdist .lt. 2.0d0*uround*w0) go to 622
1401 if (itol .le. 2) go to 140
1403 130 tol = dmax1(tol,rtol(i))
1404 140 if (tol .gt. 0.0d0) go to 160
1407 if (itol .eq. 2 .or. itol .eq. 4) atoli = atol(i)
1409 if (ayi .ne. 0.0d0) tol = dmax1(tol,atoli/ayi)
1411 160 tol = dmax1(tol,100.0d0*uround)
1412 tol = dmin1(tol,0.001d0)
1413 sum = vmnorm (n, rwork(lf0), rwork(lewt))
1414 sum = 1.0d0/(tol*w0*w0) + tol*sum**2
1415 h0 = 1.0d0/dsqrt(sum)
1416 h0 = dmin1(h0,tdist)
1417 h0 = dsign(h0,tout-t)
1418 c adjust h0 if necessary to meet hmax bound. ---------------------------
1419 180 rh = dabs(h0)*hmxi
1420 if (rh .gt. 1.0d0) h0 = h0/rh
1421 c load h with h0 and scale yh(*,2) by h0. ------------------------------
1424 190 rwork(i+lf0-1) = h0*rwork(i+lf0-1)
1426 c check for a zero of g at t. ------------------------------------------
1429 if (ngc .eq. 0) go to 270
1430 call rchek (1, g, neq, y, rwork(lyh), nyh,
1431 1 rwork(lg0), rwork(lg1), rwork(lgx), jroot, irt)
1432 if(ierror.gt.0) return
1433 if (irt .eq. 0) go to 270
1435 c-----------------------------------------------------------------------
1437 c the next code block is for continuation calls only (istate = 2 or 3)
1438 c and is to check stop conditions before taking a step.
1439 c first, rchek is called to check for a root within the last step
1440 c taken, other than the last root found there, if any.
1441 c if itask = 2 or 5, and y(tn) has not yet been returned to the user
1442 c because of an intervening root, return through block g.
1443 c-----------------------------------------------------------------------
1447 if (ngc .eq. 0) go to 205
1448 if (itask .eq. 1 .or. itask .eq. 4) toutc = tout
1449 call rchek (2, g, neq, y, rwork(lyh), nyh,
1450 1 rwork(lg0), rwork(lg1), rwork(lgx), jroot, irt)
1451 if(ierror.gt.0) return
1452 if (irt .lt. 0) go to 632
1453 if (irt .ne. 1) go to 205
1460 if (irfp .eq. 1 .and. tlast .ne. tn .and. itask .eq. 2) go to 400
1462 go to (210, 250, 220, 230, 240), itask
1463 210 if ((tn - tout)*h .lt. 0.0d0) go to 250
1464 call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1465 if (iflag .ne. 0) go to 627
1468 220 tp = tn - hu*(1.0d0 + 100.0d0*uround)
1469 if ((tp - tout)*h .gt. 0.0d0) go to 623
1470 if ((tn - tout)*h .lt. 0.0d0) go to 250
1473 230 tcrit = rwork(1)
1474 if ((tn - tcrit)*h .gt. 0.0d0) go to 624
1475 if ((tcrit - tout)*h .lt. 0.0d0) go to 625
1476 if ((tn - tout)*h .lt. 0.0d0) go to 245
1477 call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1478 if (iflag .ne. 0) go to 627
1481 240 tcrit = rwork(1)
1482 if ((tn - tcrit)*h .gt. 0.0d0) go to 624
1483 245 hmx = dabs(tn) + dabs(h)
1484 ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1486 if (irfp .eq. 1 .and. tlast .ne. tn .and. itask .eq. 5) go to 400
1488 tnext = tn + h*(1.0d0 + 4.0d0*uround)
1489 if ((tnext - tcrit)*h .le. 0.0d0) go to 250
1490 h = (tcrit - tn)*(1.0d0 - 4.0d0*uround)
1492 cSCI if (istate .eq. 2) jstart = -2
1494 if (istate .eq. 2 .and. jstart .ge. 0) jstart = -2
1495 c-----------------------------------------------------------------------
1497 c the next block is normally executed for all calls and contains
1498 c the call to the one-step core integrator stoda.
1500 c this is a looping point for the integration steps.
1502 c first check for too many steps being taken, update ewt (if not at
1503 c start of problem), check for too much accuracy being requested, and
1504 c check for h below the roundoff level in t.
1505 c-----------------------------------------------------------------------
1507 if (meth .eq. mused) go to 255
1508 if (insufr .eq. 1) go to 550
1509 if (insufi .eq. 1) go to 555
1510 255 if ((nst-nslast) .ge. mxstep) go to 500
1511 call ewset (n, itol, rtol, atol, rwork(lyh), rwork(lewt))
1513 if (rwork(i+lewt-1) .le. 0.0d0) go to 510
1514 260 rwork(i+lewt-1) = 1.0d0/rwork(i+lewt-1)
1515 270 tolsf = uround*vmnorm (n, rwork(lyh), rwork(lewt))
1516 if (tolsf .le. 0.01d0) go to 280
1517 tolsf = tolsf*200.0d0
1518 if (nst .eq. 0) go to 626
1520 280 if ((tn + h) .ne. tn) go to 290
1522 if (nhnil .gt. mxhnil) go to 290
1523 call xerrwv('lsodar- warning..internal t (=r1) and h (=r2) are',
1524 1 50, 101, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1526 1 ' such that in the machine, t + h = t on the next step ',
1527 1 60, 101, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1528 call xerrwv(' (h = step size). solver will continue anyway',
1529 1 50, 101, 1, 0, 0, 0, 2, tn, h)
1530 if (nhnil .lt. mxhnil) go to 290
1531 call xerrwv('sodar- above warning has been issued i1 times. ',
1532 1 50, 102, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1533 call xerrwv(' it will not be issued again for this problem',
1534 1 50, 102, 1, 1, mxhnil, 0, 0, 0.0d0, 0.0d0)
1536 c-----------------------------------------------------------------------
1537 c call stoda(neq,y,yh,nyh,yh,ewt,savf,acor,wm,iwm,f,jac,prja,solsy)
1538 c-----------------------------------------------------------------------
1539 call stoda (neq, y, rwork(lyh), nyh, rwork(lyh), rwork(lewt),
1540 1 rwork(lsavf), rwork(lacor), rwork(lwm), iwork(liwm),
1541 2 f, jac, prja, solsy)
1542 if(ierror.gt.0) return
1544 go to (300, 530, 540), kgo
1545 c-----------------------------------------------------------------------
1547 c the following block handles the case of a successful return from the
1548 c core integrator (kflag = 0).
1549 c if a method switch was just made, record tsw, reset maxord,
1550 c set jstart to -1 to signal stoda to complete the switch,
1551 c and do extra printing of data if ixpr = 1.
1552 c then call rchek to check for a root within the last step.
1553 c then, if no root was found, check for stop conditions.
1554 c-----------------------------------------------------------------------
1556 if (meth .eq. mused) go to 310
1559 if (meth .eq. 2) maxord = mxords
1560 if (meth .eq. 2) rwork(lwm) = dsqrt(uround)
1561 insufr = min0(insufr,1)
1562 insufi = min0(insufi,1)
1564 if (ixpr .eq. 0) go to 310
1565 if (meth .eq. 2) call xerrwv(
1566 1 'lsodar- a switch to the bdf (stiff) method has occurred ',
1567 1 60, 105, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1568 if (meth .eq. 1) call xerrwv(
1569 1 'lsodar- a switch to the adams (nonstiff) method has occurred',
1570 1 60, 106, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1572 1 ' at t = r1, tentative step size h = r2, step nst = i1 ',
1573 1 60, 107, 1, 1, nst, 0, 2, tn, h)
1576 if (ngc .eq. 0) go to 315
1577 call rchek (3, g, neq, y, rwork(lyh), nyh,
1578 1 rwork(lg0), rwork(lg1), rwork(lgx), jroot, irt)
1579 if(ierror.gt.0) return
1580 if (irt .ne. 1) go to 315
1587 go to (320, 400, 330, 340, 350), itask
1588 c itask = 1. if tout has been reached, interpolate. -------------------
1589 320 if ((tn - tout)*h .lt. 0.0d0) go to 250
1590 call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1593 c itask = 3. jump to exit if tout was reached. ------------------------
1594 330 if ((tn - tout)*h .ge. 0.0d0) go to 400
1596 c itask = 4. see if tout or tcrit was reached. adjust h if necessary.
1597 340 if ((tn - tout)*h .lt. 0.0d0) go to 345
1598 call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1601 345 hmx = dabs(tn) + dabs(h)
1602 ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1604 tnext = tn + h*(1.0d0 + 4.0d0*uround)
1605 if ((tnext - tcrit)*h .le. 0.0d0) go to 250
1606 h = (tcrit - tn)*(1.0d0 - 4.0d0*uround)
1610 if (jstart .ge. 0) jstart = -2
1612 c itask = 5. see if tcrit was reached and jump to exit. ---------------
1613 350 hmx = dabs(tn) + dabs(h)
1614 ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1615 c-----------------------------------------------------------------------
1617 c the following block handles all successful returns from lsodar.
1618 c if itask .ne. 1, y is loaded from yh and t is set accordingly.
1619 c istate is set to 2, the illegal input counter is zeroed, and the
1620 c optional outputs are loaded into the work arrays before returning.
1621 c if istate = 1 and tout = t, there is a return with no action taken,
1622 c except that if this has happened repeatedly, the run is terminated.
1623 c-----------------------------------------------------------------------
1625 410 y(i) = rwork(i+lyh-1)
1627 if (itask .ne. 4 .and. itask .ne. 5) go to 420
1647 430 ntrep = ntrep + 1
1648 if (ntrep .lt. 5) return
1650 1 'lsodar- repeated calls with istate = 1 and tout = t (=r1) ',
1651 1 60, 301, 1, 0, 0, 0, 1, t, 0.0d0)
1653 c-----------------------------------------------------------------------
1655 c the following block handles all unsuccessful returns other than
1656 c those for illegal input. first the error message routine is called.
1657 c if there was an error test or convergence test failure, imxer is set.
1658 c then y is loaded from yh, t is set to tn, and the illegal input
1659 c counter illin is set to 0. the optional outputs are loaded into
1660 c the work arrays before returning.
1661 c-----------------------------------------------------------------------
1662 c the maximum number of steps was taken before reaching tout. ----------
1663 500 call xerrwv('lsodar- at current t (=r1), mxstep (=i1) steps' ,
1664 1 50, 201, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1665 call xerrwv(' taken on this call before reaching tout ',
1666 1 50, 201, 1, 1, mxstep, 0, 1, tn, 0.0d0)
1669 c ewt(i) .le. 0.0 for some i (not at start of problem). ----------------
1670 510 ewti = rwork(lewt+i-1)
1671 call xerrwv('lsodar- at t (=r1), ewt(i1) has become r2 .le. 0.',
1672 1 50, 202, 1, 1, i, 0, 2, tn, ewti)
1675 c too much accuracy requested for machine precision. -------------------
1676 520 call xerrwv('lsodar- at t (=r1), too much accuracy requested ',
1677 1 50, 203, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1678 call xerrwv(' for precision of machine.. see tolsf (=r2)',
1679 1 50, 203, 1, 0, 0, 0, 2, tn, tolsf)
1683 c kflag = -1. error test failed repeatedly or with abs(h) = hmin. -----
1684 530 call xerrwv('lsodar- at t(=r1) and step size h(=r2), the error',
1685 1 50, 204, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1686 call xerrwv(' test failed repeatedly or with abs(h) = hmin',
1687 1 50, 204, 1, 0, 0, 0, 2, tn, h)
1690 c kflag = -2. convergence failed repeatedly or with abs(h) = hmin. ----
1691 540 call xerrwv('lsodar- at t (=r1) and step size h (=r2), the ',
1692 1 50, 205, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1693 call xerrwv(' corrector convergence failed repeatedly ',
1694 1 50, 205, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1695 call xerrwv(' or with abs(h) = hmin ',
1696 1 30, 205, 1, 0, 0, 0, 2, tn, h)
1699 c rwork length too small to proceed. -----------------------------------
1700 550 call xerrwv('lsodar- at current t(=r1), rwork length too small',
1701 1 50, 206, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1703 1 ' to proceed. the integration was otherwise successful.',
1704 1 60, 206, 1, 0, 0, 0, 1, tn, 0.0d0)
1707 c iwork length too small to proceed. -----------------------------------
1708 555 call xerrwv('lsodar- at current t(=r1), iwork length too small',
1709 1 50, 207, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1711 1 ' to proceed. the integration was otherwise successful.',
1712 1 60, 207, 1, 0, 0, 0, 1, tn, 0.0d0)
1715 c compute imxer if relevant. -------------------------------------------
1719 size = dabs(rwork(i+lacor-1)*rwork(i+lewt-1))
1720 if (big .ge. size) go to 570
1725 c set y vector, t, illin, and optional outputs. ------------------------
1727 590 y(i) = rwork(i+lyh-1)
1744 c-----------------------------------------------------------------------
1746 c the following block handles all error returns due to illegal input
1747 c (istate = -3), as detected before calling the core integrator.
1748 c first the error message routine is called. then if there have been
1749 c 5 consecutive such returns just before this call to the solver,
1750 c the run is halted.
1751 c-----------------------------------------------------------------------
1752 601 call xerrwv('lsodar- istate (=i1) illegal ',
1753 1 30, 1, 1, 1, istate, 0, 0, 0.0d0, 0.0d0)
1755 602 call xerrwv('lsodar- itask (=i1) illegal ',
1756 1 30, 2, 1, 1, itask, 0, 0, 0.0d0, 0.0d0)
1758 603 call xerrwv('lsodar- istate .gt. 1 but lsodar not initialized ',
1759 1 50, 3, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1761 604 call xerrwv('lsodar- neq (=i1) .lt. 1 ',
1762 1 30, 4, 1, 1, neq(1), 0, 0, 0.0d0, 0.0d0)
1764 605 call xerrwv('lsodar- istate = 3 and neq increased (i1 to i2) ',
1765 1 50, 5, 1, 2, n, neq(1), 0, 0.0d0, 0.0d0)
1767 606 call xerrwv('lsodar- itol (=i1) illegal ',
1768 1 30, 6, 1, 1, itol, 0, 0, 0.0d0, 0.0d0)
1770 607 call xerrwv('lsodar- iopt (=i1) illegal ',
1771 1 30, 7, 1, 1, iopt, 0, 0, 0.0d0, 0.0d0)
1773 608 call xerrwv('lsodar- jt (=i1) illegal ',
1774 1 30, 8, 1, 1, jt, 0, 0, 0.0d0, 0.0d0)
1776 609 call xerrwv('lsodar- ml (=i1) illegal.. .lt.0 or .ge.neq (=i2)',
1777 1 50, 9, 1, 2, ml, neq(1), 0, 0.0d0, 0.0d0)
1779 610 call xerrwv('lsodar- mu (=i1) illegal.. .lt.0 or .ge.neq (=i2)',
1780 1 50, 10, 1, 2, mu, neq(1), 0, 0.0d0, 0.0d0)
1782 611 call xerrwv('lsodar- ixpr (=i1) illegal ',
1783 1 30, 11, 1, 1, ixpr, 0, 0, 0.0d0, 0.0d0)
1785 612 call xerrwv('lsodar- mxstep (=i1) .lt. 0 ',
1786 1 30, 12, 1, 1, mxstep, 0, 0, 0.0d0, 0.0d0)
1788 613 call xerrwv('lsodar- mxhnil (=i1) .lt. 0 ',
1789 1 30, 13, 1, 1, mxhnil, 0, 0, 0.0d0, 0.0d0)
1791 614 call xerrwv('lsodar- tout (=r1) behind t (=r2) ',
1792 1 40, 14, 1, 0, 0, 0, 2, tout, t)
1793 call xerrwv(' integration direction is given by h0 (=r1) ',
1794 1 50, 14, 1, 0, 0, 0, 1, h0, 0.0d0)
1796 615 call xerrwv('lsodar- hmax (=r1) .lt. 0.0 ',
1797 1 30, 15, 1, 0, 0, 0, 1, hmax, 0.0d0)
1799 616 call xerrwv('lsodar- hmin (=r1) .lt. 0.0 ',
1800 1 30, 16, 1, 0, 0, 0, 1, hmin, 0.0d0)
1803 1 'lsodar- rwork length needed, lenrw (=i1), exceeds lrw (=i2)',
1804 1 60, 17, 1, 2, lenrw, lrw, 0, 0.0d0, 0.0d0)
1807 1 'lsodar- iwork length needed, leniw (=i1), exceeds liw (=i2)',
1808 1 60, 18, 1, 2, leniw, liw, 0, 0.0d0, 0.0d0)
1810 619 call xerrwv('lsodar- rtol(i1) is r1 .lt. 0.0 ',
1811 1 40, 19, 1, 1, i, 0, 1, rtoli, 0.0d0)
1813 620 call xerrwv('lsodar- atol(i1) is r1 .lt. 0.0 ',
1814 1 40, 20, 1, 1, i, 0, 1, atoli, 0.0d0)
1816 621 ewti = rwork(lewt+i-1)
1817 call xerrwv('lsodar- ewt(i1) is r1 .le. 0.0 ',
1818 1 40, 21, 1, 1, i, 0, 1, ewti, 0.0d0)
1821 1 'lsodar- tout (=r1) too close to t(=r2) to start integration',
1822 1 60, 22, 1, 0, 0, 0, 2, tout, t)
1825 1 'lsodar- itask = i1 and tout (=r1) behind tcur - hu (= r2) ',
1826 1 60, 23, 1, 1, itask, 0, 2, tout, tp)
1829 1 'lsodar- itask = 4 or 5 and tcrit (=r1) behind tcur (=r2) ',
1830 1 60, 24, 1, 0, 0, 0, 2, tcrit, tn)
1833 1 'lsodar- itask = 4 or 5 and tcrit (=r1) behind tout (=r2) ',
1834 1 60, 25, 1, 0, 0, 0, 2, tcrit, tout)
1836 626 call xerrwv('lsodar- at start of problem, too much accuracy ',
1837 1 50, 26, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1839 1 ' requested for precision of machine.. see tolsf (=r1) ',
1840 1 60, 26, 1, 0, 0, 0, 1, tolsf, 0.0d0)
1843 627 call xerrwv('lsodar- trouble from intdy. itask = i1, tout = r1',
1844 1 50, 27, 1, 1, itask, 0, 1, tout, 0.0d0)
1846 628 call xerrwv('lsodar- mxordn (=i1) .lt. 0 ',
1847 1 30, 28, 1, 1, mxordn, 0, 0, 0.0d0, 0.0d0)
1849 629 call xerrwv('lsodar- mxords (=i1) .lt. 0 ',
1850 1 30, 29, 1, 1, mxords, 0, 0, 0.0d0, 0.0d0)
1852 630 call xerrwv('lsodar- ng (=i1) .lt. 0 ',
1853 1 30, 30, 1, 1, ng, 0, 0, 0.0d0, 0.0d0)
1855 631 call xerrwv('lsodar- ng changed (from i1 to i2) illegally, ',
1856 1 50, 31, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1857 call xerrwv(' i.e. not immediately after a root was found ',
1858 1 50, 31, 1, 2, ngc, ng, 0, 0.0d0, 0.0d0)
1860 632 call xerrwv('lsodar- one or more components of g has a root ',
1861 1 50, 32, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1862 call xerrwv(' too near to the initial point ',
1863 1 40, 32, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1865 700 if (illin .eq. 5) go to 710
1870 710 call xerrwv('lsodar- repeated occurrences of illegal input ',
1871 1 50, 302, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1873 800 call xerrwv('lsodar- run aborted.. apparent infinite loop ',
1874 1 50, 303, 2, 0, 0, 0, 0, 0.0d0, 0.0d0)
1876 c----------------------- end of subroutine lsodar ----------------------