1
subroutine lsodar2(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.
499
c -1 means an excessive amount of work (more than mxstep
500
c steps) was done on this call, before completing the
501
c requested task, but the integration was otherwise
502
c successful as far as t. (mxstep is an optional input
503
c and is normally 500.) to continue, the user may
504
c simply reset istate to a value .gt. 1 and call again
505
c (the excess work step counter will be reset to 0).
506
c in addition, the user may increase mxstep to avoid
507
c this error return (see below on optional inputs).
508
c -2 means too much accuracy was requested for the precision
509
c of the machine being used. this was detected before
510
c completing the requested task, but the integration
511
c was successful as far as t. to continue, the tolerance
512
c parameters must be reset, and istate must be set
513
c to 3. the optional output tolsf may be used for this
514
c purpose. (note.. if this condition is detected before
515
c taking any steps, then an illegal input return
516
c (istate = -3) occurs instead.)
517
c -3 means illegal input was detected, before taking any
518
c integration steps. see written message for details.
519
c note.. if the solver detects an infinite loop of calls
520
c to the solver with illegal input, it will cause
522
c -4 means there were repeated error test failures on
523
c one attempted step, before completing the requested
524
c task, but the integration was successful as far as t.
525
c the problem may have a singularity, or the input
526
c may be inappropriate.
527
c -5 means there were repeated convergence test failures on
528
c one attempted step, before completing the requested
529
c task, but the integration was successful as far as t.
530
c this may be caused by an inaccurate jacobian matrix,
531
c if one is being used.
532
c -6 means ewt(i) became zero for some i during the
533
c integration. pure relative error control (atol(i)=0.0)
534
c was requested on a variable which has now vanished.
535
c the integration was successful as far as t.
536
c -7 means the length of rwork and/or iwork was too small to
537
c proceed, but the integration was successful as far as t.
538
c this happens when lsodar chooses to switch methods
539
c but lrw and/or liw is too small for the new method.
541
c note.. since the normal output value of istate is 2,
542
c it does not need to be reset for normal continuation.
543
c also, since a negative input value of istate will be
544
c regarded as illegal, a negative output value requires the
545
c user to change it, and possibly other inputs, before
546
c calling the solver again.
548
c iopt = an integer flag to specify whether or not any optional
549
c inputs are being used on this call. input only.
550
c the optional inputs are listed separately below.
551
c iopt = 0 means no optional inputs are being used.
552
c default values will be used in all cases.
553
c iopt = 1 means one or more optional inputs are being used.
555
c rwork = a real array (double precision) for work space, and (in the
556
c first 20 words) for conditional and optional inputs and
558
c as lsodar switches automatically between stiff and nonstiff
559
c methods, the required length of rwork can change during the
560
c problem. thus the rwork array passed to lsodar can either
561
c have a static (fixed) length large enough for both methods,
562
c or have a dynamic (changing) length altered by the calling
563
c program in response to output from lsodar.
565
c --- fixed length case ---
566
c if the rwork length is to be fixed, it should be at least
568
c where lrn and lrs are the rwork lengths required when the
569
c current method is nonstiff or stiff, respectively.
571
c the separate rwork length requirements lrn and lrs are
573
c if neq is constant and the maximum method orders have
574
c their default values, then
575
c lrn = 20 + 16*neq + 3*ng,
576
c lrs = 22 + 9*neq + neq**2 + 3*ng (jt = 1 or 2),
577
c lrs = 22 + 10*neq + (2*ml+mu)*neq + 3*ng (jt = 4 or 5).
578
c under any other conditions, lrn and lrs are given by..
579
c lrn = 20 + nyh*(mxordn+1) + 3*neq + 3*ng,
580
c lrs = 20 + nyh*(mxords+1) + 3*neq + lmat + 3*ng,
582
c nyh = the initial value of neq,
583
c mxordn = 12, unless a smaller value is given as an
585
c mxords = 5, unless a smaller value is given as an
587
c lmat = length of matrix work space..
588
c lmat = neq**2 + 2 if jt = 1 or 2,
589
c lmat = (2*ml + mu + 1)*neq + 2 if jt = 4 or 5.
591
c --- dynamic length case ---
592
c if the length of rwork is to be dynamic, then it should
593
c be at least lrn or lrs, as defined above, depending on the
594
c current method. initially, it must be at least lrn (since
595
c lsodar starts with the nonstiff method). on any return
596
c from lsodar, the optional output mcur indicates the current
597
c method. if mcur differs from the value it had on the
598
c previous return, or if there has only been one call to
599
c lsodar and mcur is now 2, then lsodar has switched
600
c methods during the last call, and the length of rwork
601
c should be reset (to lrn if mcur = 1, or to lrs if
602
c mcur = 2). (an increase in the rwork length is required
603
c if lsodar returned istate = -7, but not otherwise.)
604
c after resetting the length, call lsodar with istate = 3
605
c to signal that change.
607
c lrw = the length of the array rwork, as declared by the user.
608
c (this will be checked by the solver.)
610
c iwork = an integer array for work space.
611
c as lsodar switches automatically between stiff and nonstiff
612
c methods, the required length of iwork can change during
614
c lis = 20 + neq and lin = 20,
615
c respectively. thus the iwork array passed to lsodar can
616
c either have a fixed length of at least 20 + neq, or have a
617
c dynamic length of at least lin or lis, depending on the
618
c current method. the comments on dynamic length under
619
c rwork above apply here. initially, this length need
620
c only be at least lin = 20.
622
c the first few words of iwork are used for conditional and
623
c optional inputs and optional outputs.
625
c the following 2 words in iwork are conditional inputs..
626
c iwork(1) = ml these are the lower and upper
627
c iwork(2) = mu half-bandwidths, respectively, of the
628
c banded jacobian, excluding the main diagonal.
629
c the band is defined by the matrix locations
630
c (i,j) with i-ml .le. j .le. i+mu. ml and mu
631
c must satisfy 0 .le. ml,mu .le. neq-1.
632
c these are required if jt is 4 or 5, and
633
c ignored otherwise. ml and mu may in fact be
634
c the band parameters for a matrix to which
635
c df/dy is only approximately equal.
637
c liw = the length of the array iwork, as declared by the user.
638
c (this will be checked by the solver.)
640
c note.. the base addresses of the work arrays must not be
641
c altered between calls to lsodar for the same problem.
642
c the contents of the work arrays must not be altered
643
c between calls, except possibly for the conditional and
644
c optional inputs, and except for the last 3*neq words of rwork.
645
c the latter space is used for internal scratch space, and so is
646
c available for use by the user outside lsodar between calls, if
647
c desired (but not for use by f, jac, or g).
649
c jac = the name of the user-supplied routine to compute the
650
c jacobian matrix, df/dy, if jt = 1 or 4. the jac routine
651
c is optional, but if the problem is expected to be stiff much
652
c of the time, you are encouraged to supply jac, for the sake
653
c of efficiency. (alternatively, set jt = 2 or 5 to have
654
c lsodar compute df/dy internally by difference quotients.)
655
c if and when lsodar uses df/dy, if treats this neq by neq
656
c matrix either as full (jt = 1 or 2), or as banded (jt =
657
c 4 or 5) with half-bandwidths ml and mu (discussed under
658
c iwork above). in either case, if jt = 1 or 4, the jac
659
c routine must compute df/dy as a function of the scalar t
660
c and the vector y. it is to have the form
661
c subroutine jac (neq, t, y, ml, mu, pd, nrowpd)
662
c dimension y(1), pd(nrowpd,1)
663
c where neq, t, y, ml, mu, and nrowpd are input and the array
664
c pd is to be loaded with partial derivatives (elements of
665
c the jacobian matrix) on output. pd must be given a first
666
c dimension of nrowpd. t and y have the same meaning as in
667
c subroutine f. (in the dimension statement above, 1 is a
668
c dummy dimension.. it can be replaced by any value.)
669
c in the full matrix case (jt = 1), ml and mu are
670
c ignored, and the jacobian is to be loaded into pd in
671
c columnwise manner, with df(i)/dy(j) loaded into pd(i,j).
672
c in the band matrix case (jt = 4), the elements
673
c within the band are to be loaded into pd in columnwise
674
c manner, with diagonal lines of df/dy loaded into the rows
675
c of pd. thus df(i)/dy(j) is to be loaded into pd(i-j+mu+1,j).
676
c ml and mu are the half-bandwidth parameters (see iwork).
677
c the locations in pd in the two triangular areas which
678
c correspond to nonexistent matrix elements can be ignored
679
c or loaded arbitrarily, as they are overwritten by lsodar.
680
c jac need not provide df/dy exactly. a crude
681
c approximation (possibly with a smaller bandwidth) will do.
682
c in either case, pd is preset to zero by the solver,
683
c so that only the nonzero elements need be loaded by jac.
684
c each call to jac is preceded by a call to f with the same
685
c arguments neq, t, and y. thus to gain some efficiency,
686
c intermediate quantities shared by both calculations may be
687
c saved in a user common block by f and not recomputed by jac,
688
c if desired. also, jac may alter the y array, if desired.
689
c jac must be declared external in the calling program.
690
c subroutine jac may access user-defined quantities in
691
c neq(2),... and y(neq(1)+1),... if neq is an array
692
c (dimensioned in jac) and y has length exceeding neq(1).
693
c see the descriptions of neq and y above.
695
c jt = jacobian type indicator. used only for input.
696
c jt specifies how the jacobian matrix df/dy will be
697
c treated, if and when lsodar requires this matrix.
698
c jt has the following values and meanings..
699
c 1 means a user-supplied full (neq by neq) jacobian.
700
c 2 means an internally generated (difference quotient) full
701
c jacobian (using neq extra calls to f per df/dy value).
702
c 4 means a user-supplied banded jacobian.
703
c 5 means an internally generated banded jacobian (using
704
c ml+mu+1 extra calls to f per df/dy evaluation).
705
c if jt = 1 or 4, the user must supply a subroutine jac
706
c (the name is arbitrary) as described above under jac.
707
c if jt = 2 or 5, a dummy argument can be used.
709
c g = the name of subroutine for constraint functions, whose
710
c roots are desired during the integration. it is to have
712
c subroutine g (neq, t, y, ng, gout)
713
c dimension y(neq), gout(ng)
714
c where neq, t, y, and ng are input, and the array gout
715
c is output. neq, t, and y have the same meaning as in
716
c the f routine, and gout is an array of length ng.
717
c for i = 1,...,ng, this routine is to load into gout(i)
718
c the value at (t,y) of the i-th constraint function g(i).
719
c lsodar will find roots of the g(i) of odd multiplicity
720
c (i.e. sign changes) as they occur during the integration.
721
c g must be declared external in the calling program.
723
c caution.. because of numerical errors in the functions
724
c g(i) due to roundoff and integration error, lsodar may
725
c return false roots, or return the same root at two or more
726
c nearly equal values of t. if such false roots are
727
c suspected, the user should consider smaller error tolerances
728
c and/or higher precision in the evaluation of the g(i).
730
c if a root of some g(i) defines the end of the problem,
731
c the input to lsodar should nevertheless allow integration
732
c to a point slightly past that root, so that lsodar can
733
c locate the root by interpolation.
735
c subroutine g may access user-defined quantities in
736
c neq(2),... and y(neq(1)+1),... if neq is an array
737
c (dimensioned in g) and y has length exceeding neq(1).
738
c see the descriptions of neq and y above.
740
c ng = number of constraint functions g(i). if there are none,
741
c set ng = 0, and pass a dummy name for g.
743
c jroot = integer array of length ng. used only for output.
744
c on a return with istate = 3 (one or more roots found),
745
c jroot(i) = 1 if g(i) has a root at t, or jroot(i) = 0 if not.
746
c-----------------------------------------------------------------------
749
c the following is a list of the optional inputs provided for in the
750
c call sequence. (see also part ii.) for each such input variable,
751
c this table lists its name as used in this documentation, its
752
c location in the call sequence, its meaning, and the default value.
753
c the use of any of these inputs requires iopt = 1, and in that
754
c case all of these inputs are examined. a value of zero for any
755
c of these optional inputs will cause the default value to be used.
756
c thus to use a subset of the optional inputs, simply preload
757
c locations 5 to 10 in rwork and iwork to 0.0 and 0 respectively, and
758
c then set those of interest to nonzero values.
760
c name location meaning and default value
762
c h0 rwork(5) the step size to be attempted on the first step.
763
c the default value is determined by the solver.
765
c hmax rwork(6) the maximum absolute step size allowed.
766
c the default value is infinite.
768
c hmin rwork(7) the minimum absolute step size allowed.
769
c the default value is 0. (this lower bound is not
770
c enforced on the final step before reaching tcrit
771
c when itask = 4 or 5.)
773
c ixpr iwork(5) flag to generate extra printing at method switches.
774
c ixpr = 0 means no extra printing (the default).
775
c ixpr = 1 means print data on each switch.
776
c t, h, and nst will be printed on the same logical
777
c unit as used for error messages.
779
c mxstep iwork(6) maximum number of (internally defined) steps
780
c allowed during one call to the solver.
781
c the default value is 500.
783
c mxhnil iwork(7) maximum number of messages printed (per problem)
784
c warning that t + h = t on a step (h = step size).
785
c this must be positive to result in a non-default
786
c value. the default value is 10.
788
c mxordn iwork(8) the maximum order to be allowed for the nonstiff
789
c (adams) method. the default value is 12.
790
c if mxordn exceeds the default value, it will
791
c be reduced to the default value.
792
c mxordn is held constant during the problem.
794
c mxords iwork(9) the maximum order to be allowed for the stiff
795
c (bdf) method. the default value is 5.
796
c if mxords exceeds the default value, it will
797
c be reduced to the default value.
798
c mxords is held constant during the problem.
799
c-----------------------------------------------------------------------
802
c as optional additional output from lsodar, the variables listed
803
c below are quantities related to the performance of lsodar
804
c which are available to the user. these are communicated by way of
805
c the work arrays, but also have internal mnemonic names as shown.
806
c except where stated otherwise, all of these outputs are defined
807
c on any successful return from lsodar, and on any return with
808
c istate = -1, -2, -4, -5, or -6. on an illegal input return
809
c (istate = -3), they will be unchanged from their existing values
810
c (if any), except possibly for tolsf, lenrw, and leniw.
811
c on any error return, outputs relevant to the error will be defined,
814
c name location meaning
816
c hu rwork(11) the step size in t last used (successfully).
818
c hcur rwork(12) the step size to be attempted on the next step.
820
c tcur rwork(13) the current value of the independent variable
821
c which the solver has actually reached, i.e. the
822
c current internal mesh point in t. on output, tcur
823
c will always be at least as far as the argument
824
c t, but may be farther (if interpolation was done).
826
c tolsf rwork(14) a tolerance scale factor, greater than 1.0,
827
c computed when a request for too much accuracy was
828
c detected (istate = -3 if detected at the start of
829
c the problem, istate = -2 otherwise). if itol is
830
c left unaltered but rtol and atol are uniformly
831
c scaled up by a factor of tolsf for the next call,
832
c then the solver is deemed likely to succeed.
833
c (the user may also ignore tolsf and alter the
834
c tolerance parameters in any other way appropriate.)
836
c tsw rwork(15) the value of t at the time of the last method
839
c nge iwork(10) the number of g evaluations for the problem so far.
841
c nst iwork(11) the number of steps taken for the problem so far.
843
c nfe iwork(12) the number of f evaluations for the problem so far.
845
c nje iwork(13) the number of jacobian evaluations (and of matrix
846
c lu decompositions) for the problem so far.
848
c nqu iwork(14) the method order last used (successfully).
850
c nqcur iwork(15) the order to be attempted on the next step.
852
c imxer iwork(16) the index of the component of largest magnitude in
853
c the weighted local error vector ( e(i)/ewt(i) ),
854
c on an error return with istate = -4 or -5.
856
c lenrw iwork(17) the length of rwork actually required, assuming
857
c that the length of rwork is to be fixed for the
858
c rest of the problem, and that switching may occur.
859
c this is defined on normal returns and on an illegal
860
c input return for insufficient storage.
862
c leniw iwork(18) the length of iwork actually required, assuming
863
c that the length of iwork is to be fixed for the
864
c rest of the problem, and that switching may occur.
865
c this is defined on normal returns and on an illegal
866
c input return for insufficient storage.
868
c mused iwork(19) the method indicator for the last successful step..
869
c 1 means adams (nonstiff), 2 means bdf (stiff).
871
c mcur iwork(20) the current method indicator..
872
c 1 means adams (nonstiff), 2 means bdf (stiff).
873
c this is the method to be attempted
874
c on the next step. thus it differs from mused
875
c only if a method switch has just been made.
877
c the following two arrays are segments of the rwork array which
878
c may also be of interest to the user as optional outputs.
879
c for each array, the table below gives its internal name,
880
c its base address in rwork, and its description.
882
c name base address description
884
c yh 21 + 3*ng the nordsieck history array, of size nyh by
885
c (nqcur + 1), where nyh is the initial value
886
c of neq. for j = 0,1,...,nqcur, column j+1
887
c of yh contains hcur**j/factorial(j) times
888
c the j-th derivative of the interpolating
889
c polynomial currently representing the solution,
890
c evaluated at t = tcur.
892
c acor lacor array of size neq used for the accumulated
893
c (from common corrections on each step, scaled on output
894
c as noted) to represent the estimated local error in y
895
c on the last step. this is the vector e in
896
c the description of the error control. it is
897
c defined only on a successful return from
898
c lsodar. the base address lacor is obtained by
899
c including in the user-s program the
900
c following 3 lines..
901
c double precision rls
902
c common /ls0001/ rls(219), ils(39)
905
c-----------------------------------------------------------------------
906
c part ii. other routines callable.
908
c the following are optional calls which the user may make to
909
c gain additional capabilities in conjunction with lsodar.
910
c (the routines xsetun and xsetf are designed to conform to the
911
c slatec error handling package.)
913
c form of call function
914
c call xsetun(lun) set the logical unit number, lun, for
915
c output of messages from lsodar, if
916
c the default is not desired.
917
c the default value of lun is 6.
919
c call xsetf(mflag) set a flag to control the printing of
920
c messages by lsodar.
921
c mflag = 0 means do not print. (danger..
922
c this risks losing valuable information.)
923
c mflag = 1 means print (the default).
925
c either of the above calls may be made at
926
c any time and will take effect immediately.
928
c call svcar (rsav, isav) store in rsav and isav the contents
929
c of the internal common blocks used by
930
c lsodar (see part iii below).
931
c rsav must be a real array of length 246
932
c or more, and isav must be an integer
933
c array of length 59 or more.
935
c call rscar (rsav, isav) restore, from rsav and isav, the contents
936
c of the internal common blocks used by
937
c lsodar. presumes a prior call to svcar
938
c with the same arguments.
940
c svcar and rscar are useful if
941
c interrupting a run and restarting
942
c later, or alternating between two or
943
c more problems solved with lsodar.
945
c call intdy(,,,,,) provide derivatives of y, of various
946
c (see below) orders, at a specified point t, if
947
c desired. it may be called only after
948
c a successful return from lsodar.
950
c the detailed instructions for using intdy are as follows.
951
c the form of the call is..
953
c call intdy (t, k, rwork(lyh), nyh, dky, iflag)
955
c the input parameters are..
957
c t = value of independent variable where answers are desired
958
c (normally the same as the t last returned by lsodar).
959
c for valid results, t must lie between tcur - hu and tcur.
960
c (see optional outputs for tcur and hu.)
961
c k = integer order of the derivative desired. k must satisfy
962
c 0 .le. k .le. nqcur, where nqcur is the current order
963
c (see optional outputs). the capability corresponding
964
c to k = 0, i.e. computing y(t), is already provided
965
c by lsodar directly. since nqcur .ge. 1, the first
966
c derivative dy/dt is always available with intdy.
967
c lyh = 21 + 3*ng = base address in rwork of the history array yh.
968
c nyh = column length of yh, equal to the initial value of neq.
970
c the output parameters are..
972
c dky = a real array of length neq containing the computed value
973
c of the k-th derivative of y(t).
974
c iflag = integer flag, returned as 0 if k and t were legal,
975
c -1 if k was illegal, and -2 if t was illegal.
976
c on an error return, a message is also written.
977
c-----------------------------------------------------------------------
978
c part iii. common blocks.
980
c if lsodar is to be used in an overlay situation, the user
981
c must declare, in the primary overlay, the variables in..
982
c (1) the call sequence to lsodar,
983
c (2) the four internal common blocks
984
c /ls0001/ of length 258 (219 double precision words
985
c followed by 39 integer words),
986
c /lsa001/ of length 31 (22 double precision words
987
c followed by 9 integer words),
988
c /lsr001/ of length 14 (5 double precision words
989
c followed by 9 integer words),
990
c /eh0001/ of length 2 (integer words).
992
c if lsodar is used on a system in which the contents of internal
993
c common blocks are not preserved between calls, the user should
994
c declare the above common blocks in his main program to insure
995
c that their contents are preserved.
997
c if the solution of a given problem by lsodar is to be interrupted
998
c and then later continued, such as when restarting an interrupted run
999
c or alternating between two or more problems, the user should save,
1000
c following the return from the last lsodar call prior to the
1001
c interruption, the contents of the call sequence variables and the
1002
c internal common blocks, and later restore these values before the
1003
c next lsodar call for that problem. to save and restore the common
1004
c blocks, use subroutines svcar and rscar (see part ii above).
1006
c-----------------------------------------------------------------------
1007
c part iv. optionally replaceable solver routines.
1009
c below is a description of a routine in the lsodar package which
1010
c relates to the measurement of errors, and can be
1011
c replaced by a user-supplied version, if desired. however, since such
1012
c a replacement may have a major impact on performance, it should be
1013
c done only when absolutely necessary, and only with great caution.
1014
c (note.. the means by which the package version of a routine is
1015
c superseded by the user-s version may be system-dependent.)
1018
c the following subroutine is called just before each internal
1019
c integration step, and sets the array of error weights, ewt, as
1020
c described under itol/rtol/atol above..
1021
c subroutine ewset (neq, itol, rtol, atol, ycur, ewt)
1022
c where neq, itol, rtol, and atol are as in the lsodar call sequence,
1023
c ycur contains the current dependent variable vector, and
1024
c ewt is the array of weights set by ewset.
1026
c if the user supplies this subroutine, it must return in ewt(i)
1027
c (i = 1,...,neq) a positive quantity suitable for comparing errors
1028
c in y(i) to. the ewt array returned by ewset is passed to the
1029
c vmnorm routine, and also used by lsodar in the computation
1030
c of the optional output imxer, and the increments for difference
1031
c quotient jacobians.
1033
c in the user-supplied version of ewset, it may be desirable to use
1034
c the current values of derivatives of y. derivatives up to order nq
1035
c are available from the history array yh, described above under
1036
c optional outputs. in ewset, yh is identical to the ycur array,
1037
c extended to nq + 1 columns with a column length of nyh and scale
1038
c factors of h**j/factorial(j). on the first call for the problem,
1039
c given by nst = 0, nq is 1 and h is temporarily set to 1.0.
1040
c the quantities nq, nyh, h, and nst can be obtained by including
1041
c in ewset the statements..
1042
c double precision h, rls
1043
c common /ls0001/ rls(219),ils(39)
1048
c thus, for example, the current value of dy/dt can be obtained as
1049
c ycur(nyh+i)/h (i=1,...,neq) (and the division by h is
1050
c unnecessary when nst = 0).
1051
c-----------------------------------------------------------------------
1052
c-----------------------------------------------------------------------
1053
c other routines in the lsodar package.
1055
c in addition to subroutine lsodar, the lsodar package includes the
1056
c following subroutines and function routines..
1057
c rchek does preliminary checking for roots, and serves as an
1058
c interface between subroutine lsodar and subroutine roots.
1059
c roots finds the leftmost root of a set of functions.
1060
c intdy computes an interpolated value of the y vector at t = tout.
1061
c stoda is the core integrator, which does one step of the
1062
c integration and the associated error control.
1063
c cfode sets all method coefficients and test constants.
1064
c prja computes and preprocesses the jacobian matrix j = df/dy
1065
c and the newton iteration matrix p = i - h*l0*j.
1066
c solsy manages solution of linear system in chord iteration.
1067
c ewset sets the error weight vector ewt before each step.
1068
c vmnorm computes the weighted max-norm of a vector.
1069
c fnorm computes the norm of a full matrix consistent with the
1070
c weighted max-norm on vectors.
1071
c bnorm computes the norm of a band matrix consistent with the
1072
c weighted max-norm on vectors.
1073
c svcar and rscar are user-callable routines to save and restore,
1074
c respectively, the contents of the internal common blocks.
1075
c dgefa and dgesl are routines from linpack for solving full
1076
c systems of linear algebraic equations.
1077
c dgbfa and dgbsl are routines from linpack for solving banded
1079
c daxpy, dscal, idamax, ddot, and dcopy are basic linear algebra
1080
c modules (blas) used by the above linpack routines.
1081
c dlamch computes the unit roundoff in a machine-independent manner.
1082
c xerrwv, xsetun, and xsetf handle the printing of all error
1083
c messages and warnings. xerrwv is machine-dependent.
1084
c note.. vmnorm, fnorm, bnorm, idamax, ddot, and dlamch are function
1085
c routines. all the others are subroutines.
1087
c the intrinsic and external routines used by lsodar are..
1088
c dabs, dmax1, dmin1, dfloat, max0, min0, mod, dsign, dsqrt, and write.
1090
c a block data subprogram is also included with the package,
1091
c for loading some of the variables in internal common.
1093
c-----------------------------------------------------------------------
1094
c the following card is for optimized compilation on lll compilers.
1096
c-----------------------------------------------------------------------
1097
external prja, solsy
1098
integer illin, init, lyh, lewt, lacor, lsavf, lwm, liwm,
1099
1 mxstep, mxhnil, nhnil, ntrep, nslast, nyh, iowns
1100
integer icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
1101
1 maxord, maxcor, msbp, mxncf, n, nq, nst, nfe, nje, nqu
1102
integer insufr, insufi, ixpr, iowns2, jtyp, mused, mxordn, mxords
1103
integer lg0, lg1, lgx, iownr3, irfnd, itaskc, ngc, nge
1104
integer i, i1, i2, iflag, imxer, kgo, lf0,
1105
1 leniw, lenrw, lenwm, ml, mord, mu, mxhnl0, mxstp0
1106
integer len1, len1c, len1n, len1s, len2, leniwc,
1107
1 lenrwc, lenrwn, lenrws
1108
integer irfp, irt, lenyh, lyhnew
1109
double precision tret, rowns,
1110
1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround
1111
double precision tsw, rowns2, pdnorm
1112
double precision rownr3, t0, tlast, toutc
1113
double precision atoli, ayi, big, ewti, h0, hmax, hmx, rh, rtoli,
1114
1 tcrit, tdist, tnext, tol, tolsf, tp, size, sum, w0,
1118
c-----------------------------------------------------------------------
1119
c the following three internal common blocks contain
1120
c (a) variables which are local to any subroutine but whose values must
1121
c be preserved between calls to the routine (own variables), and
1122
c (b) variables which are communicated between subroutines.
1123
c the structure of each block is as follows.. all real variables are
1124
c listed first, followed by all integers. within each type, the
1125
c variables are grouped with those local to subroutine lsodar first,
1126
c then those local to subroutine roots or subroutine stoda
1127
c (no other routines have own variables), and finally those used
1128
c for communication. the block ls0001 is declared in subroutines
1129
c lsodar, intdy, stoda, prja, and solsy. the block lsa001 is declared
1130
c in subroutines lsodar, stoda, and prja. the block lsr001 is declared
1131
c in subroutines lsodar, rchek, and roots. groups of variables are
1132
c replaced by dummy arrays in the common declarations in routines
1133
c where those variables are not used.
1134
c-----------------------------------------------------------------------
1136
common /ierode/ iero
1137
common /ls0001/ tret, rowns(209),
1138
1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround,
1139
2 illin, init, lyh, lewt, lacor, lsavf, lwm, liwm,
1140
3 mxstep, mxhnil, nhnil, ntrep, nslast, nyh, iowns(6),
1141
4 icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
1142
5 maxord, maxcor, msbp, mxncf, n, nq, nst, nfe, nje, nqu
1143
common /lsa001/ tsw, rowns2(20), pdnorm,
1144
1 insufr, insufi, ixpr, iowns2(2), jtyp, mused, mxordn, mxords
1145
common /lsr001/ rownr3(2), t0, tlast, toutc,
1146
1 lg0, lg1, lgx, iownr3(2), irfnd, itaskc, ngc, nge
1148
data mord(1),mord(2)/12,5/, mxstp0/500/, mxhnl0/10/
1149
c-----------------------------------------------------------------------
1151
c this code block is executed on every call.
1152
c it tests istate and itask for legality and branches appropriately.
1153
c if istate .gt. 1 but the flag init shows that initialization has
1154
c not yet been done, an error return occurs.
1155
c if istate = 1 and tout = t, jump to block g and return immediately.
1156
c-----------------------------------------------------------------------
1157
if (istate .lt. 1 .or. istate .gt. 3) go to 601
1158
if (itask .lt. 1 .or. itask .gt. 5) go to 602
1160
if (istate .eq. 1) go to 10
1161
if (init .eq. 0) go to 603
1162
if (istate .eq. 2) go to 200
1165
if (tout .eq. t) go to 430
1167
c-----------------------------------------------------------------------
1169
c the next code block is executed for the initial call (istate = 1),
1170
c or for a continuation call with parameter changes (istate = 3).
1171
c it contains checking of all inputs and various initializations.
1173
c first check legality of the non-optional inputs neq, itol, iopt,
1174
c jt, ml, mu, and ng.
1175
c-----------------------------------------------------------------------
1176
if (neq(1) .le. 0) go to 604
1177
if (istate .eq. 1) go to 25
1178
if (neq(1) .gt. n) go to 605
1180
if (itol .lt. 1 .or. itol .gt. 4) go to 606
1181
if (iopt .lt. 0 .or. iopt .gt. 1) go to 607
1182
if (jt .eq. 3 .or. jt .lt. 1 .or. jt .gt. 5) go to 608
1184
if (jt .le. 2) go to 30
1187
if (ml .lt. 0 .or. ml .ge. n) go to 609
1188
if (mu .lt. 0 .or. mu .ge. n) go to 610
1190
if (ng .lt. 0) go to 630
1191
if (istate .eq. 1) go to 35
1192
if (irfnd .eq. 0 .and. ng .ne. ngc) go to 631
1194
c next process and check the optional inputs. --------------------------
1195
if (iopt .eq. 1) go to 40
1201
if (istate .ne. 1) go to 60
1207
if (ixpr .lt. 0 .or. ixpr .gt. 1) go to 611
1209
if (mxstep .lt. 0) go to 612
1210
if (mxstep .eq. 0) mxstep = mxstp0
1212
if (mxhnil .lt. 0) go to 613
1213
if (mxhnil .eq. 0) mxhnil = mxhnl0
1214
if (istate .ne. 1) go to 50
1217
if (mxordn .lt. 0) go to 628
1218
if (mxordn .eq. 0) mxordn = 100
1219
mxordn = min0(mxordn,mord(1))
1221
if (mxords .lt. 0) go to 629
1222
if (mxords .eq. 0) mxords = 100
1223
mxords = min0(mxords,mord(2))
1224
if ((tout - t)*h0 .lt. 0.0d0) go to 614
1226
if (hmax .lt. 0.0d0) go to 615
1228
if (hmax .gt. 0.0d0) hmxi = 1.0d0/hmax
1230
if (hmin .lt. 0.0d0) go to 616
1231
c-----------------------------------------------------------------------
1232
c set work array pointers and check lengths lrw and liw.
1233
c if istate = 1, meth is initialized to 1 here to facilitate the
1234
c checking of work space lengths.
1235
c pointers to segments of rwork and iwork are named by prefixing l to
1236
c the name of the segment. e.g., the segment yh starts at rwork(lyh).
1237
c segments of rwork (in order) are denoted g0, g1, gx, yh, wm,
1239
c if the lengths provided are insufficient for the current method,
1240
c an error return occurs. this is treated as illegal input on the
1241
c first call, but as a problem interruption with istate = -7 on a
1242
c continuation call. if the lengths are sufficient for the current
1243
c method but not for both methods, a warning message is sent.
1244
c-----------------------------------------------------------------------
1245
60 if (istate .eq. 1) meth = 1
1246
if (istate .eq. 1) nyh = n
1251
if (istate .eq. 1) lyh = lyhnew
1252
if (lyhnew .eq. lyh) go to 62
1253
c if istate = 3 and ng was changed, shift yh to its new location. ------
1255
if (lrw .lt. lyhnew-1+lenyh) go to 62
1257
if (lyhnew .gt. lyh) i1 = -1
1258
call dcopy (lenyh, rwork(lyh), i1, rwork(lyhnew), i1)
1261
len1n = lyhnew - 1 + (mxordn + 1)*nyh
1262
len1s = lyhnew - 1 + (mxords + 1)*nyh
1264
if (jt .le. 2) lenwm = n*n + 2
1265
if (jt .ge. 4) lenwm = (2*ml + mu + 1)*n + 2
1266
len1s = len1s + lenwm
1268
if (meth .eq. 2) len1c = len1s
1269
len1 = max0(len1n,len1s)
1272
lenrwn = len1n + len2
1273
lenrws = len1s + len2
1274
lenrwc = len1c + len2
1278
c ----------------------------- masking ----------------
1280
c ----------------------------- masking ----------------
1282
if (meth .eq. 2) leniwc = leniw
1284
if (istate .eq. 1 .and. lrw .lt. lenrwc) go to 617
1285
if (istate .eq. 1 .and. liw .lt. leniwc) go to 618
1286
if (istate .eq. 3 .and. lrw .lt. lenrwc) go to 550
1287
if (istate .eq. 3 .and. liw .lt. leniwc) go to 555
1290
if (lrw .ge. lenrw) go to 65
1294
1 'lsodar- warning.. rwork length is sufficient for now, but ',
1295
1 60, 103, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1297
1 ' may not be later. integration will proceed anyway. ',
1298
1 60, 103, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1300
1 ' length needed is lenrw = i1, while lrw = i2.',
1301
1 50, 103, 1, 2, lenrw, lrw, 0, 0.0d0, 0.0d0)
1305
if (liw .ge. leniw) go to 70
1308
1 'lsodar- warning.. iwork length is sufficient for now, but ',
1309
1 60, 104, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1311
1 ' may not be later. integration will proceed anyway. ',
1312
1 60, 104, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1314
1 ' length needed is leniw = i1, while liw = i2.',
1315
1 50, 104, 1, 2, leniw, liw, 0, 0.0d0, 0.0d0)
1317
c check rtol and atol for legality. ------------------------------------
1321
if (itol .ge. 3) rtoli = rtol(i)
1322
if (itol .eq. 2 .or. itol .eq. 4) atoli = atol(i)
1323
if (rtoli .lt. 0.0d0) go to 619
1324
if (atoli .lt. 0.0d0) go to 620
1326
if (istate .eq. 1) go to 100
1327
c if istate = 3, set flag to signal parameter changes to stoda. --------
1329
if (n .eq. nyh) go to 200
1330
c neq was reduced. zero part of yh to avoid undefined references. -----
1332
i2 = lyh + (maxord + 1)*nyh - 1
1333
if (i1 .gt. i2) go to 200
1337
c-----------------------------------------------------------------------
1339
c the next block is for the initial call only (istate = 1).
1340
c it contains all remaining initializations, the initial call to f,
1341
c and the calculation of the initial step size.
1342
c the error weights in ewt are inverted after being loaded.
1343
c-----------------------------------------------------------------------
1344
100 uround = dlamch('p')
1348
if (itask .ne. 4 .and. itask .ne. 5) go to 110
1350
if ((tcrit - tout)*(tout - t) .lt. 0.0d0) go to 625
1351
if (h0 .ne. 0.0d0 .and. (t + h0 - tcrit)*h0 .gt. 0.0d0)
1366
c initial call to f. (lf0 points to yh(*,2).) -------------------------
1368
call f (neq, t, y, rwork(lf0))
1369
if(iero.gt.0) return
1371
c load the initial value vector in yh. ---------------------------------
1373
115 rwork(i+lyh-1) = y(i)
1374
c load and invert the ewt array. (h is temporarily set to 1.0.) -------
1377
call ewset (n, itol, rtol, atol, rwork(lyh), rwork(lewt))
1379
if (rwork(i+lewt-1) .le. 0.0d0) go to 621
1380
120 rwork(i+lewt-1) = 1.0d0/rwork(i+lewt-1)
1381
c-----------------------------------------------------------------------
1382
c the coding below computes the step size, h0, to be attempted on the
1383
c first step, unless the user has supplied a value for this.
1384
c first check that tout - t differs significantly from zero.
1385
c a scalar tolerance quantity tol is computed, as max(rtol(i))
1386
c if this is positive, or max(atol(i)/abs(y(i))) otherwise, adjusted
1387
c so as to be between 100*uround and 1.0e-3.
1388
c then the computed value h0 is given by..
1390
c h0**(-2) = 1./(tol * w0**2) + tol * (norm(f))**2
1392
c where w0 = max ( abs(t), abs(tout) ),
1393
c f = the initial value of the vector f(t,y), and
1394
c norm() = the weighted vector norm used throughout, given by
1395
c the vmnorm function routine, and weighted by the
1396
c tolerances initially loaded into the ewt array.
1397
c the sign of h0 is inferred from the initial values of tout and t.
1398
c abs(h0) is made .le. abs(tout-t) in any case.
1399
c-----------------------------------------------------------------------
1400
if (h0 .ne. 0.0d0) go to 180
1401
tdist = dabs(tout - t)
1402
w0 = dmax1(dabs(t),dabs(tout))
1403
if (tdist .lt. 2.0d0*uround*w0) go to 622
1405
if (itol .le. 2) go to 140
1407
130 tol = dmax1(tol,rtol(i))
1408
140 if (tol .gt. 0.0d0) go to 160
1411
if (itol .eq. 2 .or. itol .eq. 4) atoli = atol(i)
1413
if (ayi .ne. 0.0d0) tol = dmax1(tol,atoli/ayi)
1415
160 tol = dmax1(tol,100.0d0*uround)
1416
tol = dmin1(tol,0.001d0)
1417
sum = vmnorm (n, rwork(lf0), rwork(lewt))
1418
sum = 1.0d0/(tol*w0*w0) + tol*sum**2
1419
h0 = 1.0d0/dsqrt(sum)
1420
h0 = dmin1(h0,tdist)
1421
h0 = dsign(h0,tout-t)
1422
c adjust h0 if necessary to meet hmax bound. ---------------------------
1423
180 rh = dabs(h0)*hmxi
1424
if (rh .gt. 1.0d0) h0 = h0/rh
1425
c load h with h0 and scale yh(*,2) by h0. ------------------------------
1428
190 rwork(i+lf0-1) = h0*rwork(i+lf0-1)
1430
c check for a zero of g at t. ------------------------------------------
1433
if (ngc .eq. 0) go to 270
1434
c --------------------- masking -----------------------
1435
call rchek2 (1, g, neq, y, rwork(lyh), nyh,
1436
1 rwork(lg0), rwork(lg1), rwork(lgx), jroot, irt,iwork)
1437
if (iero.gt.0) return
1438
if (irt .eq. 2) then
1442
if (irt .eq. 0) go to 270
1444
c-----------------------------------------------------------------------
1446
c the next code block is for continuation calls only (istate = 2 or 3)
1447
c and is to check stop conditions before taking a step.
1448
c first, rchek is called to check for a root within the last step
1449
c taken, other than the last root found there, if any.
1450
c if itask = 2 or 5, and y(tn) has not yet been returned to the user
1451
c because of an intervening root, return through block g.
1452
c-----------------------------------------------------------------------
1456
if (ngc .eq. 0) go to 205
1457
if (itask .eq. 1 .or. itask .eq. 4) toutc = tout
1458
c --------------------- masking -----------------------
1459
call rchek2 (2, g, neq, y, rwork(lyh), nyh,
1460
1 rwork(lg0), rwork(lg1), rwork(lgx), jroot, irt,iwork)
1461
c --------------------- masking -----------------------
1462
if(iero.gt.0) return
1463
if (irt .lt. 0) go to 632
1464
if (irt .ne. 1) go to 205
1471
if (irfp .eq. 1 .and. tlast .ne. tn .and. itask .eq. 2) go to 400
1473
go to (210, 250, 220, 230, 240), itask
1474
210 if ((tn - tout)*h .lt. 0.0d0) go to 250
1475
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1476
if (iflag .ne. 0) go to 627
1479
220 tp = tn - hu*(1.0d0 + 100.0d0*uround)
1480
if ((tp - tout)*h .gt. 0.0d0) go to 623
1481
if ((tn - tout)*h .lt. 0.0d0) go to 250
1484
230 tcrit = rwork(1)
1485
if ((tn - tcrit)*h .gt. 0.0d0) go to 624
1486
if ((tcrit - tout)*h .lt. 0.0d0) go to 625
1487
if ((tn - tout)*h .lt. 0.0d0) go to 245
1488
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1489
if (iflag .ne. 0) go to 627
1492
240 tcrit = rwork(1)
1493
if ((tn - tcrit)*h .gt. 0.0d0) go to 624
1494
245 hmx = dabs(tn) + dabs(h)
1495
ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1497
if (irfp .eq. 1 .and. tlast .ne. tn .and. itask .eq. 5) go to 400
1499
tnext = tn + h*(1.0d0 + 4.0d0*uround)
1500
if ((tnext - tcrit)*h .le. 0.0d0) go to 250
1501
h = (tcrit - tn)*(1.0d0 - 4.0d0*uround)
1503
cSCI if (istate .eq. 2) jstart = -2
1505
if (istate .eq. 2 .and. jstart .ge. 0) jstart = -2
1506
c-----------------------------------------------------------------------
1508
c the next block is normally executed for all calls and contains
1509
c the call to the one-step core integrator stoda.
1511
c this is a looping point for the integration steps.
1513
c first check for too many steps being taken, update ewt (if not at
1514
c start of problem), check for too much accuracy being requested, and
1515
c check for h below the roundoff level in t.
1516
c-----------------------------------------------------------------------
1518
if (meth .eq. mused) go to 255
1519
if (insufr .eq. 1) go to 550
1520
if (insufi .eq. 1) go to 555
1521
255 if ((nst-nslast) .ge. mxstep) go to 500
1522
call ewset (n, itol, rtol, atol, rwork(lyh), rwork(lewt))
1524
if (rwork(i+lewt-1) .le. 0.0d0) go to 510
1525
260 rwork(i+lewt-1) = 1.0d0/rwork(i+lewt-1)
1526
270 tolsf = uround*vmnorm (n, rwork(lyh), rwork(lewt))
1527
if (tolsf .le. 0.01d0) go to 280
1528
tolsf = tolsf*200.0d0
1529
if (nst .eq. 0) go to 626
1531
280 if ((tn + h) .ne. tn) go to 290
1533
if (nhnil .gt. mxhnil) go to 290
1534
call xerrwv('lsodar- warning..internal t (=r1) and h (=r2) are',
1535
1 50, 101, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1537
1 ' such that in the machine, t + h = t on the next step ',
1538
1 60, 101, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1539
call xerrwv(' (h = step size). solver will continue anyway',
1540
1 50, 101, 1, 0, 0, 0, 2, tn, h)
1541
if (nhnil .lt. mxhnil) go to 290
1542
call xerrwv('sodar- above warning has been issued i1 times. ',
1543
1 50, 102, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1544
call xerrwv(' it will not be issued again for this problem',
1545
1 50, 102, 1, 1, mxhnil, 0, 0, 0.0d0, 0.0d0)
1547
c-----------------------------------------------------------------------
1548
c call stoda(neq,y,yh,nyh,yh,ewt,savf,acor,wm,iwm,f,jac,prja,solsy)
1549
c-----------------------------------------------------------------------
1550
call stoda (neq, y, rwork(lyh), nyh, rwork(lyh), rwork(lewt),
1551
1 rwork(lsavf), rwork(lacor), rwork(lwm), iwork(liwm),
1552
2 f, jac, prja, solsy)
1553
if(iero.gt.0) return
1555
go to (300, 530, 540), kgo
1556
c-----------------------------------------------------------------------
1558
c the following block handles the case of a successful return from the
1559
c core integrator (kflag = 0).
1560
c if a method switch was just made, record tsw, reset maxord,
1561
c set jstart to -1 to signal stoda to complete the switch,
1562
c and do extra printing of data if ixpr = 1.
1563
c then call rchek to check for a root within the last step.
1564
c then, if no root was found, check for stop conditions.
1565
c-----------------------------------------------------------------------
1567
if (meth .eq. mused) go to 310
1570
if (meth .eq. 2) maxord = mxords
1571
if (meth .eq. 2) rwork(lwm) = dsqrt(uround)
1572
insufr = min0(insufr,1)
1573
insufi = min0(insufi,1)
1575
if (ixpr .eq. 0) go to 310
1576
if (meth .eq. 2) call xerrwv(
1577
1 'lsodar- a switch to the bdf (stiff) method has occurred ',
1578
1 60, 105, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1579
if (meth .eq. 1) call xerrwv(
1580
1 'lsodar- a switch to the adams (nonstiff) method has occurred',
1581
1 60, 106, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1583
1 ' at t = r1, tentative step size h = r2, step nst = i1 ',
1584
1 60, 107, 1, 1, nst, 0, 2, tn, h)
1587
if (ngc .eq. 0) go to 315
1588
c --------------------- masking -----------------------
1589
call rchek2 (3, g, neq, y, rwork(lyh), nyh,
1590
1 rwork(lg0), rwork(lg1), rwork(lgx), jroot, irt,iwork)
1591
c --------------------- masking -----------------------
1593
if(iero.gt.0) return
1602
if (irt .ne. 1) go to 315
1609
go to (320, 400, 330, 340, 350), itask
1610
c itask = 1. if tout has been reached, interpolate. -------------------
1611
320 if ((tn - tout)*h .lt. 0.0d0) go to 250
1612
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1615
c itask = 3. jump to exit if tout was reached. ------------------------
1616
330 if ((tn - tout)*h .ge. 0.0d0) go to 400
1618
c itask = 4. see if tout or tcrit was reached. adjust h if necessary.
1619
340 if ((tn - tout)*h .lt. 0.0d0) go to 345
1620
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1623
345 hmx = dabs(tn) + dabs(h)
1624
ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1626
tnext = tn + h*(1.0d0 + 4.0d0*uround)
1627
if ((tnext - tcrit)*h .le. 0.0d0) go to 250
1628
h = (tcrit - tn)*(1.0d0 - 4.0d0*uround)
1632
if (jstart .ge. 0) jstart = -2
1634
c itask = 5. see if tcrit was reached and jump to exit. ---------------
1635
350 hmx = dabs(tn) + dabs(h)
1636
ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1637
c-----------------------------------------------------------------------
1639
c the following block handles all successful returns from lsodar.
1640
c if itask .ne. 1, y is loaded from yh and t is set accordingly.
1641
c istate is set to 2, the illegal input counter is zeroed, and the
1642
c optional outputs are loaded into the work arrays before returning.
1643
c if istate = 1 and tout = t, there is a return with no action taken,
1644
c except that if this has happened repeatedly, the run is terminated.
1645
c-----------------------------------------------------------------------
1647
410 y(i) = rwork(i+lyh-1)
1649
if (itask .ne. 4 .and. itask .ne. 5) go to 420
1669
430 ntrep = ntrep + 1
1670
if (ntrep .lt. 5) return
1672
1 'lsodar- repeated calls with istate = 1 and tout = t (=r1) ',
1673
1 60, 301, 1, 0, 0, 0, 1, t, 0.0d0)
1675
c-----------------------------------------------------------------------
1677
c the following block handles all unsuccessful returns other than
1678
c those for illegal input. first the error message routine is called.
1679
c if there was an error test or convergence test failure, imxer is set.
1680
c then y is loaded from yh, t is set to tn, and the illegal input
1681
c counter illin is set to 0. the optional outputs are loaded into
1682
c the work arrays before returning.
1683
c-----------------------------------------------------------------------
1684
c the maximum number of steps was taken before reaching tout. ----------
1685
500 call xerrwv('lsodar- at current t (=r1), mxstep (=i1) steps' ,
1686
1 50, 201, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1687
call xerrwv(' taken on this call before reaching tout ',
1688
1 50, 201, 1, 1, mxstep, 0, 1, tn, 0.0d0)
1691
c ewt(i) .le. 0.0 for some i (not at start of problem). ----------------
1692
510 ewti = rwork(lewt+i-1)
1693
call xerrwv('lsodar- at t (=r1), ewt(i1) has become r2 .le. 0.',
1694
1 50, 202, 1, 1, i, 0, 2, tn, ewti)
1697
c too much accuracy requested for machine precision. -------------------
1698
520 call xerrwv('lsodar- at t (=r1), too much accuracy requested ',
1699
1 50, 203, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1700
call xerrwv(' for precision of machine.. see tolsf (=r2)',
1701
1 50, 203, 1, 0, 0, 0, 2, tn, tolsf)
1705
c kflag = -1. error test failed repeatedly or with abs(h) = hmin. -----
1706
530 call xerrwv('lsodar- at t(=r1) and step size h(=r2), the error',
1707
1 50, 204, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1708
call xerrwv(' test failed repeatedly or with abs(h) = hmin',
1709
1 50, 204, 1, 0, 0, 0, 2, tn, h)
1712
c kflag = -2. convergence failed repeatedly or with abs(h) = hmin. ----
1713
540 call xerrwv('lsodar- at t (=r1) and step size h (=r2), the ',
1714
1 50, 205, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1715
call xerrwv(' corrector convergence failed repeatedly ',
1716
1 50, 205, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1717
call xerrwv(' or with abs(h) = hmin ',
1718
1 30, 205, 1, 0, 0, 0, 2, tn, h)
1721
c rwork length too small to proceed. -----------------------------------
1722
550 call xerrwv('lsodar- at current t(=r1), rwork length too small',
1723
1 50, 206, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1725
1 ' to proceed. the integration was otherwise successful.',
1726
1 60, 206, 1, 0, 0, 0, 1, tn, 0.0d0)
1729
c iwork length too small to proceed. -----------------------------------
1730
555 call xerrwv('lsodar- at current t(=r1), iwork length too small',
1731
1 50, 207, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1733
1 ' to proceed. the integration was otherwise successful.',
1734
1 60, 207, 1, 0, 0, 0, 1, tn, 0.0d0)
1737
c compute imxer if relevant. -------------------------------------------
1741
size = dabs(rwork(i+lacor-1)*rwork(i+lewt-1))
1742
if (big .ge. size) go to 570
1747
c set y vector, t, illin, and optional outputs. ------------------------
1749
590 y(i) = rwork(i+lyh-1)
1766
c-----------------------------------------------------------------------
1768
c the following block handles all error returns due to illegal input
1769
c (istate = -3), as detected before calling the core integrator.
1770
c first the error message routine is called. then if there have been
1771
c 5 consecutive such returns just before this call to the solver,
1772
c the run is halted.
1773
c-----------------------------------------------------------------------
1774
601 call xerrwv('lsodar- istate (=i1) illegal ',
1775
1 30, 1, 1, 1, istate, 0, 0, 0.0d0, 0.0d0)
1777
602 call xerrwv('lsodar- itask (=i1) illegal ',
1778
1 30, 2, 1, 1, itask, 0, 0, 0.0d0, 0.0d0)
1780
603 call xerrwv('lsodar- istate .gt. 1 but lsodar not initialized ',
1781
1 50, 3, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1783
604 call xerrwv('lsodar- neq (=i1) .lt. 1 ',
1784
1 30, 4, 1, 1, neq(1), 0, 0, 0.0d0, 0.0d0)
1786
605 call xerrwv('lsodar- istate = 3 and neq increased (i1 to i2) ',
1787
1 50, 5, 1, 2, n, neq(1), 0, 0.0d0, 0.0d0)
1789
606 call xerrwv('lsodar- itol (=i1) illegal ',
1790
1 30, 6, 1, 1, itol, 0, 0, 0.0d0, 0.0d0)
1792
607 call xerrwv('lsodar- iopt (=i1) illegal ',
1793
1 30, 7, 1, 1, iopt, 0, 0, 0.0d0, 0.0d0)
1795
608 call xerrwv('lsodar- jt (=i1) illegal ',
1796
1 30, 8, 1, 1, jt, 0, 0, 0.0d0, 0.0d0)
1798
609 call xerrwv('lsodar- ml (=i1) illegal.. .lt.0 or .ge.neq (=i2)',
1799
1 50, 9, 1, 2, ml, neq(1), 0, 0.0d0, 0.0d0)
1801
610 call xerrwv('lsodar- mu (=i1) illegal.. .lt.0 or .ge.neq (=i2)',
1802
1 50, 10, 1, 2, mu, neq(1), 0, 0.0d0, 0.0d0)
1804
611 call xerrwv('lsodar- ixpr (=i1) illegal ',
1805
1 30, 11, 1, 1, ixpr, 0, 0, 0.0d0, 0.0d0)
1807
612 call xerrwv('lsodar- mxstep (=i1) .lt. 0 ',
1808
1 30, 12, 1, 1, mxstep, 0, 0, 0.0d0, 0.0d0)
1810
613 call xerrwv('lsodar- mxhnil (=i1) .lt. 0 ',
1811
1 30, 13, 1, 1, mxhnil, 0, 0, 0.0d0, 0.0d0)
1813
614 call xerrwv('lsodar- tout (=r1) behind t (=r2) ',
1814
1 40, 14, 1, 0, 0, 0, 2, tout, t)
1815
call xerrwv(' integration direction is given by h0 (=r1) ',
1816
1 50, 14, 1, 0, 0, 0, 1, h0, 0.0d0)
1818
615 call xerrwv('lsodar- hmax (=r1) .lt. 0.0 ',
1819
1 30, 15, 1, 0, 0, 0, 1, hmax, 0.0d0)
1821
616 call xerrwv('lsodar- hmin (=r1) .lt. 0.0 ',
1822
1 30, 16, 1, 0, 0, 0, 1, hmin, 0.0d0)
1825
1 'lsodar- rwork length needed, lenrw (=i1), exceeds lrw (=i2)',
1826
1 60, 17, 1, 2, lenrw, lrw, 0, 0.0d0, 0.0d0)
1829
1 'lsodar- iwork length needed, leniw (=i1), exceeds liw (=i2)',
1830
1 60, 18, 1, 2, leniw, liw, 0, 0.0d0, 0.0d0)
1832
619 call xerrwv('lsodar- rtol(i1) is r1 .lt. 0.0 ',
1833
1 40, 19, 1, 1, i, 0, 1, rtoli, 0.0d0)
1835
620 call xerrwv('lsodar- atol(i1) is r1 .lt. 0.0 ',
1836
1 40, 20, 1, 1, i, 0, 1, atoli, 0.0d0)
1838
621 ewti = rwork(lewt+i-1)
1839
call xerrwv('lsodar- ewt(i1) is r1 .le. 0.0 ',
1840
1 40, 21, 1, 1, i, 0, 1, ewti, 0.0d0)
1843
1 'lsodar- tout (=r1) too close to t(=r2) to start integration',
1844
1 60, 22, 1, 0, 0, 0, 2, tout, t)
1847
1 'lsodar- itask = i1 and tout (=r1) behind tcur - hu (= r2) ',
1848
1 60, 23, 1, 1, itask, 0, 2, tout, tp)
1851
1 'lsodar- itask = 4 or 5 and tcrit (=r1) behind tcur (=r2) ',
1852
1 60, 24, 1, 0, 0, 0, 2, tcrit, tn)
1855
1 'lsodar- itask = 4 or 5 and tcrit (=r1) behind tout (=r2) ',
1856
1 60, 25, 1, 0, 0, 0, 2, tcrit, tout)
1858
626 call xerrwv('lsodar- at start of problem, too much accuracy ',
1859
1 50, 26, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1861
1 ' requested for precision of machine.. see tolsf (=r1) ',
1862
1 60, 26, 1, 0, 0, 0, 1, tolsf, 0.0d0)
1865
627 call xerrwv('lsodar- trouble from intdy. itask = i1, tout = r1',
1866
1 50, 27, 1, 1, itask, 0, 1, tout, 0.0d0)
1868
628 call xerrwv('lsodar- mxordn (=i1) .lt. 0 ',
1869
1 30, 28, 1, 1, mxordn, 0, 0, 0.0d0, 0.0d0)
1871
629 call xerrwv('lsodar- mxords (=i1) .lt. 0 ',
1872
1 30, 29, 1, 1, mxords, 0, 0, 0.0d0, 0.0d0)
1874
630 call xerrwv('lsodar- ng (=i1) .lt. 0 ',
1875
1 30, 30, 1, 1, ng, 0, 0, 0.0d0, 0.0d0)
1877
631 call xerrwv('lsodar- ng changed (from i1 to i2) illegally, ',
1878
1 50, 31, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1879
call xerrwv(' i.e. not immediately after a root was found ',
1880
1 50, 31, 1, 2, ngc, ng, 0, 0.0d0, 0.0d0)
1882
632 call xerrwv('lsodar- one or more components of g has a root ',
1883
1 50, 32, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1884
call xerrwv(' too near to the initial point ',
1885
1 40, 32, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1887
700 if (illin .eq. 5) go to 710
1892
710 call xerrwv('lsodar- repeated occurrences of illegal input ',
1893
1 50, 302, 1, 0, 0, 0, 0, 0.0d0, 0.0d0)
1895
800 call xerrwv('lsodar- run aborted.. apparent infinite loop ',
1896
1 50, 303, 2, 0, 0, 0, 0, 0.0d0, 0.0d0)
1898
c----------------------- end of subroutine lsodar ----------------------
added
removed
routines/integ/lsodar2.f
