1
subroutine lsodi (res, adda, jac, neq, y, ydoti, t, tout, itol,
2
1 rtol, atol, itask, istate, iopt, rwork, lrw, iwork, liw, mf )
3
external res, adda, jac
4
integer neq, itol, itask, istate, iopt, lrw, iwork, liw, mf
5
double precision y, ydoti, t, tout, rtol, atol, rwork
6
dimension neq(1), y(1), ydoti(1), rtol(1), atol(1), rwork(lrw),
8
c-----------------------------------------------------------------------
9
c this is the march 30, 1987 version of lsodi..
10
c livermore solver for ordinary differential equations (implicit form).
11
c this version is in double precision.
13
c lsodi solves the initial value problem for linearly implicit
14
c systems of first order ode-s,
15
c a(t,y) * dy/dt = g(t,y) , where a(t,y) is a square matrix,
16
c or, in component form,
17
c ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) =
20
c = g ( t, y , y ,..., y ) ( i = 1,...,neq )
23
c if a is singular, this is a differential-algebraic system.
25
c lsodi is a variant version of the lsode package.
26
c-----------------------------------------------------------------------
28
c alan c. hindmarsh, odepack, a systematized collection of ode
29
c solvers, in scientific computing, r. s. stepleman et al. (eds.),
30
c north-holland, amsterdam, 1983, pp. 55-64.
31
c-----------------------------------------------------------------------
32
c authors... jeffrey f. painter and
34
c computing and mathematics research division, l-316
35
c lawrence livermore national laboratory
36
c livermore, ca 94550.
38
c-----------------------------------------------------------------------
41
c communication between the user and the lsodi package, for normal
42
c situations, is summarized here. this summary describes only a subset
43
c of the full set of options available. see the full description for
44
c details, including optional communication, nonstandard options,
45
c and instructions for special situations. see also the example
46
c problem (with program and output) following this summary.
48
c a. first, provide a subroutine of the form..
49
c subroutine res (neq, t, y, s, r, ires)
50
c dimension y(neq), s(neq), r(neq)
51
c which computes the residual function
52
c r = g(t,y) - a(t,y) * s ,
53
c as a function of t and the vectors y and s. (s is an internally
54
c generated approximation to dy/dt.) the arrays y and s are inputs
55
c to the res routine and should not be altered. the residual
56
c vector is to be stored in the array r. the argument ires should be
57
c ignored for casual use of lsodi. (for uses of ires, see the
58
c paragraph on res in the full description below.)
60
c b. next, decide whether full or banded form is more economical
61
c for the storage of matrices. lsodi must deal internally with the
62
c matrices a and dr/dy, where r is the residual function defined above.
63
c lsodi generates a linear combination of these two matrices, and
64
c this is treated in either full or banded form.
65
c the matrix structure is communicated by a method flag mf,
66
c which is 21 or 22 for the full case, and 24 or 25 in the band case.
67
c in the banded case, lsodi requires two half-bandwidth
68
c parameters ml and mu. these are, respectively, the widths of the
69
c lower and upper parts of the band, excluding the main diagonal.
70
c thus the band consists of the locations (i,j) with
71
c i-ml .le. j .le. i+mu, and the full bandwidth is ml+mu+1.
72
c note that the band must accommodate the nonzero elements of
73
c a(t,y), dg/dy, and d(a*s)/dy (s fixed). alternatively, one
74
c can define a band that encloses only the elements that are relatively
75
c large in magnitude, and gain some economy in storage and possibly
76
c also efficiency, although the appropriate threshhold for
77
c retaining matrix elements is highly problem-dependent.
79
c c. you must also provide a subroutine of the form..
80
c subroutine adda (neq, t, y, ml, mu, p, nrowp)
81
c dimension y(neq), p(nrowp,neq)
82
c which adds the matrix a = a(t,y) to the contents of the array p.
83
c t and the y array are input and should not be altered.
84
c in the full matrix case, this routine should add elements of
85
c to p in the usual order. i.e., add a(i,j) to p(i,j). (ignore the
86
c ml and mu arguments in this case.)
87
c in the band matrix case, this routine should add element a(i,j)
88
c to p(i-j+mu+1,j). i.e., add the diagonal lines of a to the rows of
89
c p from the top down (the top line of a added to the first row of p).
91
c d. for the sake of efficiency, you are encouraged to supply the
92
c jacobian matrix dr/dy in closed form, where r = g(t,y) - a(t,y)*s
93
c (s = a fixed vector) as above. if dr/dy is being supplied,
94
c use mf = 21 or 24, and provide a subroutine of the form..
95
c subroutine jac (neq, t, y, s, ml, mu, p, nrowp)
96
c dimension y(neq), s(neq), p(nrowp,neq)
97
c which computes dr/dy as a function of t, y, and s. here t, y, and
98
c s are inputs, and the routine is to load dr/dy into p as follows..
99
c in the full matrix case (mf = 21), load p(i,j) with dr(i)/dy(j),
100
c the partial derivative of r(i) with respect to y(j). (ignore the
101
c ml and mu arguments in this case.)
102
c in the band matrix case (mf = 24), load p(i-j+mu+1,j) with
103
c dr(i)/dy(j), i.e. load the diagonal lines of dr/dy into the rows of
104
c p from the top down.
105
c in either case, only nonzero elements need be loaded, and the
106
c indexing of p is the same as in the adda routine.
107
c note that if a is independent of y (or this dependence
108
c is weak enough to be ignored) then jac is to compute dg/dy.
109
c if it is not feasible to provide a jac routine, use
110
c mf = 22 or 25, and lsodi will compute an approximate jacobian
111
c internally by difference quotients.
113
c e. next decide whether or not to provide the initial value of the
114
c derivative vector dy/dt. if the initial value of a(t,y) is
115
c nonsingular (and not too ill-conditioned), you may let lsodi compute
116
c this vector (istate = 0). (lsodi will solve the system a*s = g for
117
c s, with initial values of a and g.) if a(t,y) is initially
118
c singular, then the system is a differential-algebraic system, and
119
c you must make use of the particular form of the system to compute the
120
c initial values of y and dy/dt. in that case, use istate = 1 and
121
c load the initial value of dy/dt into the array ydoti.
122
c the input array ydoti and the initial y array must be consistent with
123
c the equations a*dy/dt = g. this implies that the initial residual
124
c r = g(t,y) - a(t,y)*ydoti must be approximately zero.
126
c f. write a main program which calls subroutine lsodi once for
127
c each point at which answers are desired. this should also provide
128
c for possible use of logical unit 6 for output of error messages
129
c by lsodi. on the first call to lsodi, supply arguments as follows..
130
c res = name of user subroutine for residual function r.
131
c adda = name of user subroutine for computing and adding a(t,y).
132
c jac = name of user subroutine for jacobian matrix dr/dy
133
c (mf = 21 or 24). if not used, pass a dummy name.
134
c note.. the names for the res and adda routines and (if used) the
135
c jac routine must be declared external in the calling program.
136
c neq = number of scalar equations in the system.
137
c y = array of initial values, of length neq.
138
c ydoti = array of length neq (containing initial dy/dt if istate = 1).
139
c t = the initial value of the independent variable.
140
c tout = first point where output is desired (.ne. t).
141
c itol = 1 or 2 according as atol (below) is a scalar or array.
142
c rtol = relative tolerance parameter (scalar).
143
c atol = absolute tolerance parameter (scalar or array).
144
c the estimated local error in y(i) will be controlled so as
145
c to be roughly less (in magnitude) than
146
c ewt(i) = rtol*abs(y(i)) + atol if itol = 1, or
147
c ewt(i) = rtol*abs(y(i)) + atol(i) if itol = 2.
148
c thus the local error test passes if, in each component,
149
c either the absolute error is less than atol (or atol(i)),
150
c or the relative error is less than rtol.
151
c use rtol = 0.0 for pure absolute error control, and
152
c use atol = 0.0 (or atol(i) = 0.0) for pure relative error
153
c control. caution.. actual (global) errors may exceed these
154
c local tolerances, so choose them conservatively.
155
c itask = 1 for normal computation of output values of y at t = tout.
156
c istate = integer flag (input and output). set istate = 1 if the
157
c initial dy/dt is supplied, and 0 otherwise.
158
c iopt = 0 to indicate no optional inputs used.
159
c rwork = real work array of length at least..
160
c 22 + 9*neq + neq**2 for mf = 21 or 22,
161
c 22 + 10*neq + (2*ml + mu)*neq for mf = 24 or 25.
162
c lrw = declared length of rwork (in user-s dimension).
163
c iwork = integer work array of length at least 20 + neq.
164
c if mf = 24 or 25, input in iwork(1),iwork(2) the lower
165
c and upper half-bandwidths ml,mu.
166
c liw = declared length of iwork (in user-s dimension).
167
c mf = method flag. standard values are..
168
c 21 for a user-supplied full jacobian.
169
c 22 for an internally generated full jacobian.
170
c 24 for a user-supplied banded jacobian.
171
c 25 for an internally generated banded jacobian.
172
c for other choices of mf, see the paragraph on mf in
173
c the full description below.
174
c note that the main program must declare arrays y, ydoti, rwork, iwork,
177
c g. the output from the first call (or any call) is..
178
c y = array of computed values of y(t) vector.
179
c t = corresponding value of independent variable (normally tout).
180
c istate = 2 if lsodi was successful, negative otherwise.
181
c -1 means excess work done on this call (check all inputs).
182
c -2 means excess accuracy requested (tolerances too small).
183
c -3 means illegal input detected (see printed message).
184
c -4 means repeated error test failures (check all inputs).
185
c -5 means repeated convergence failures (perhaps bad jacobian
186
c supplied or wrong choice of tolerances).
187
c -6 means error weight became zero during problem. (solution
188
c component i vanished, and atol or atol(i) = 0.)
189
c -7 cannot occur in casual use.
190
c -8 means lsodi was unable to compute the initial dy/dt.
191
c in casual use, this means a(t,y) is initially singular.
192
c supply ydoti and use istate = 1 on the first call.
194
c if lsodi returns istate = -1, -4, or -5, then the output of
195
c lsodi also includes ydoti = array containing residual vector
196
c r = g - a * dy/dt evaluated at the current t, y, and dy/dt.
198
c h. to continue the integration after a successful return, simply
199
c reset tout and call lsodi again. no other parameters need be reset.
202
c-----------------------------------------------------------------------
205
c the following is a simple example problem, with the coding
206
c needed for its solution by lsodi. the problem is from chemical
207
c kinetics, and consists of the following three equations..
208
c dy1/dt = -.04*y1 + 1.e4*y2*y3
209
c dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2
210
c 0. = y1 + y2 + y3 - 1.
211
c on the interval from t = 0.0 to t = 4.e10, with initial conditions
212
c y1 = 1.0, y2 = y3 = 0.
214
c the following coding solves this problem with lsodi, using mf = 21
215
c and printing results at t = .4, 4., ..., 4.e10. it uses
216
c itol = 2 and atol much smaller for y2 than y1 or y3 because
217
c y2 has much smaller values. dy/dt is supplied in ydoti. we had
218
c obtained the initial value of dy3/dt by differentiating the
219
c third equation and evaluating the first two at t=0.
220
c at the end of the run, statistical quantities of interest are
221
c printed (see optional outputs in the full description below).
223
c external resid, aplusp, dgbydy
224
c double precision atol, rtol, rwork, t, tout, y, ydoti
225
c dimension y(3), ydoti(3), atol(3), rwork(58), iwork(23)
247
c call lsodi(resid, aplusp, dgbydy, neq, y, ydoti, t, tout, itol,
248
c 1 rtol, atol, itask, istate, iopt, rwork, lrw, iwork, liw, mf)
249
c write (6,20) t, y(1), y(2), y(3)
250
c 20 format(' at t =',e12.4,' y =',3e14.6)
251
c if (istate .lt. 0 ) go to 80
252
c 40 tout = tout*10.d0
253
c write (6,60) iwork(11), iwork(12), iwork(13)
254
c 60 format(/' no. steps =',i4,' no. r-s =',i4,
257
c 80 write (6,90) istate
258
c 90 format(///' error halt.. istate =',i3)
262
c subroutine resid(neq, t, y, s, r, ires)
263
c double precision r, s, t, y
264
c dimension y(3), s(3), r(3)
265
c r(1) = -.04d0*y(1) + 1.d4*y(2)*y(3) - s(1)
266
c r(2) = .04d0*y(1) - 1.d4*y(2)*y(3) - 3.d7*y(2)*y(2) - s(2)
267
c r(3) = y(1) + y(2) + y(3) - 1.d0
271
c subroutine aplusp(neq, t, y, ml, mu, p, nrowp)
272
c double precision p, t, y
273
c dimension y(3), p(nrowp,3)
274
c p(1,1) = p(1,1) + 1.d0
275
c p(2,2) = p(2,2) + 1.d0
279
c subroutine dgbydy(neq, t, y, s, ml, mu, p, nrowp)
280
c double precision s, t, p, y
281
c dimension y(3), s(3), p(nrowp,3)
286
c p(2,2) = -1.d4*y(3) - 6.d7*y(2)
287
c p(2,3) = -1.d4*y(2)
294
c the output of this program (on a cdc-7600 in single precision)
297
c at t = 4.0000e-01 y = 9.851726e-01 3.386406e-05 1.479357e-02
298
c at t = 4.0000e+00 y = 9.055142e-01 2.240418e-05 9.446344e-02
299
c at t = 4.0000e+01 y = 7.158050e-01 9.184616e-06 2.841858e-01
300
c at t = 4.0000e+02 y = 4.504846e-01 3.222434e-06 5.495122e-01
301
c at t = 4.0000e+03 y = 1.831701e-01 8.940379e-07 8.168290e-01
302
c at t = 4.0000e+04 y = 3.897016e-02 1.621193e-07 9.610297e-01
303
c at t = 4.0000e+05 y = 4.935213e-03 1.983756e-08 9.950648e-01
304
c at t = 4.0000e+06 y = 5.159269e-04 2.064759e-09 9.994841e-01
305
c at t = 4.0000e+07 y = 5.306413e-05 2.122677e-10 9.999469e-01
306
c at t = 4.0000e+08 y = 5.494532e-06 2.197826e-11 9.999945e-01
307
c at t = 4.0000e+09 y = 5.129457e-07 2.051784e-12 9.999995e-01
308
c at t = 4.0000e+10 y = -7.170472e-08 -2.868188e-13 1.000000e+00
310
c no. steps = 330 no. r-s = 404 no. j-s = 69
311
c-----------------------------------------------------------------------
312
c full description of user interface to lsodi.
314
c the user interface to lsodi consists of the following parts.
316
c i. the call sequence to subroutine lsodi, which is a driver
317
c routine for the solver. this includes descriptions of both
318
c the call sequence arguments and of user-supplied routines.
319
c following these descriptions is a description of
320
c optional inputs available through the call sequence, and then
321
c a description of optional outputs (in the work arrays).
323
c ii. descriptions of other routines in the lsodi package that may be
324
c (optionally) called by the user. these provide the ability to
325
c alter error message handling, save and restore the internal
326
c common, and obtain specified derivatives of the solution y(t).
328
c iii. descriptions of common blocks to be declared in overlay
329
c or similar environments, or to be saved when doing an interrupt
330
c of the problem and continued solution later.
332
c iv. description of two routines in the lsodi package, either of
333
c which the user may replace with his own version, if desired.
334
c these relate to the measurement of errors.
336
c-----------------------------------------------------------------------
337
c part i. call sequence.
339
c the call sequence parameters used for input only are
340
c res, adda, jac, neq, tout, itol, rtol, atol, itask,
341
c iopt, lrw, liw, mf,
342
c and those used for both input and output are
343
c y, t, istate, ydoti.
344
c the work arrays rwork and iwork are also used for conditional and
345
c optional inputs and optional outputs. (the term output here refers
346
c to the return from subroutine lsodi to the user-s calling program.)
348
c the legality of input parameters will be thoroughly checked on the
349
c initial call for the problem, but not checked thereafter unless a
350
c change in input parameters is flagged by istate = 3 on input.
352
c the descriptions of the call arguments are as follows.
354
c res = the name of the user-supplied subroutine which supplies
355
c the residual vector for the ode system, defined by
356
c r = g(t,y) - a(t,y) * s
357
c as a function of the scalar t and the vectors
358
c s and y ( s approximates dy/dt ). this
359
c subroutine is to have the form
360
c subroutine res ( neq, t, y, s, r, ires )
361
c dimension y(1), s(1), r(1)
362
c where neq, t, y, s, and ires are input, and r and
363
c ires are output. y, s, and r are arrays of length neq.
364
c in dimension statements such as that above, 1 is a
365
c dummy dimension. it can be replaced by any value.
366
c on input, ires indicates how lsodi will use the
367
c returned array r, as follows..
368
c ires = 1 means that lsodi needs the full residual,
369
c r = g - a*s, exactly.
370
c ires = -1 means that lsodi is using r only to compute
371
c the jacobian dr/dy by difference quotients.
372
c the res routine can ignore ires, or it can omit some terms
373
c if ires = -1. if a does not depend on y, then res can
374
c just return r = g when ires = -1. if g - a*s contains other
375
c additive terms that are independent of y, these can also be
376
c dropped, if done consistently, when ires = -1.
377
c the subroutine should set the flag ires if it
378
c encounters a halt condition or illegal input.
379
c otherwise, it should not reset ires. on output,
380
c ires = 1 or -1 represents a normal return, and
381
c lsodi continues integrating the ode. leave ires
382
c unchanged from its input value.
383
c ires = 2 tells lsodi to immediately return control
384
c to the calling program, with istate = 3. this lets
385
c the calling program change parameters of the prob-
387
c ires = 3 represents an error condition (for example, an
388
c illegal value of y). lsodi tries to integrate the ode without
389
c getting ires = 3 from res. if it cannot, lsodi returns
390
c with istate = -7 or -1.
391
c on an lsodi return with istate = 3, -1, or -7, the values
392
c of t and y returned correspond to the last point reached
393
c successfully without getting the flag ires = 2 or 3.
394
c the flag values ires = 2 and 3 should not be used to
395
c handle switches or root-stop conditions. this is better
396
c done by calling lsodi in a one-step mode and checking the
397
c stopping function for a sign change at each step.
398
c if quantities computed in the res routine are needed
399
c externally to lsodi, an extra call to res should be made
400
c for this purpose, for consistent and accurate results.
401
c to get the current dy/dt for the s argument, use intdy.
402
c res must be declared external in the calling
403
c program. see note below for more about res.
405
c adda = the name of the user-supplied subroutine which adds
406
c the matrix a = a(t,y) to another matrix stored in the same
407
c form as a. the storage form is determined by miter (see
408
c mf). this subroutine is to have the form
409
c subroutine adda ( neq, t, y, ml, mu, p, nrowp )
410
c dimension y(1), p(nrowp,1)
411
c where neq, t, y, ml, mu, and nrowp are input and p is
412
c output. y is an array of length neq, and the matrix p is
413
c stored in an nrowp by neq array.
414
c in the full matrix case ( miter = 1 or 2 ) adda should
415
c add a to p(i,j). ml and mu are ignored.
417
c in the band matrix case ( miter = 4 or 5 ) adda should
418
c add a to p(i-j+mu+1,j).
420
c see jac for details on this band storage form.
421
c adda must be declared external in the calling program.
422
c see note below for more information about adda.
424
c jac = the name of the user-supplied subroutine which supplies
425
c the jacobian matrix, dr/dy, where r = g-a*s. the form of the
426
c jacobian matrix is determined by miter. jac is required
427
c if miter = 1 or 4 -- otherwise a dummy name can be
428
c passed. this subroutine is to have the form
429
c subroutine jac ( neq, t, y, s, ml, mu, p, nrowp )
430
c dimension y(1), s(1), p(nrowp,1)
431
c where neq, t, y, s, ml, mu, and nrowp are input and p
432
c is output. y and s are arrays of length neq, and the
433
c matrix p is stored in an nrowp by neq array.
434
c p is to be loaded with partial derivatives ( elements
435
c of the jacobian matrix ) on output.
436
c in the full matrix case ( miter = 1 ), ml and mu
437
c are ignored and the jacobian is to be loaded into p
438
c by columns- i.e., dr(i)/dy(j) is loaded into p(i,j).
439
c in the band matrix case ( miter = 4 ), the ele-
440
c ments within the band are to be loaded into p by
441
c by columns, with diagonal lines of dr/dy loaded into
442
c the rows of p. thus dr(i)/dy(j) is to be loaded
443
c into p(i-j+mu+1,j). the locations in p in the two
444
c triangular areas which correspond to nonexistent matrix
445
c elements can be ignored or loaded arbitrarily, as they
446
c they are overwritten by lsodi. ml and mu are the half-
447
c bandwidth parameters ( see iwork ).
448
c in either case, p is preset to zero by the solver,
449
c so that only the nonzero elements need be loaded by jac.
450
c each call to jac is preceded by a call to res with the same
451
c arguments neq, t, y, and s. thus to gain some efficiency,
452
c intermediate quantities shared by both calculations may be
453
c saved in a user common block by res and not recomputed by jac
454
c if desired. also, jac may alter the y array, if desired.
455
c jac need not provide dr/dy exactly. a crude
456
c approximation (possibly with a smaller bandwidth) will do.
457
c jac must be declared external in the calling program.
458
c see note below for more about jac.
460
c note on res, adda, and jac-- these
461
c subroutines may access user-defined quantities in
462
c neq(2),... and/or in y(neq(1)+1),... if neq is an array
463
c (dimensioned in the subroutines) and/or y has length
464
c exceeding neq(1). however, these routines should not alter
465
c neq(1), y(1),...,y(neq) or any other input variables.
466
c see the descriptions of neq and y below.
468
c neq = the size of the system (number of first order ordinary
469
c differential equations or scalar algebraic equations).
470
c used only for input.
471
c neq may be decreased, but not increased, during the problem.
472
c if neq is decreased (with istate = 3 on input), the
473
c remaining components of y should be left undisturbed, if
474
c these are to be accessed in res, adda, or jac.
476
c normally, neq is a scalar, and it is generally referred to
477
c as a scalar in this user interface description. however,
478
c neq may be an array, with neq(1) set to the system size.
479
c (the lsodi package accesses only neq(1).) in either case,
480
c this parameter is passed as the neq argument in all calls
481
c to res, adda, and jac. hence, if it is an array,
482
c locations neq(2),... may be used to store other integer data
483
c and pass it to res, adda, or jac. each such subroutine
484
c must include neq in a dimension statement in that case.
486
c y = a real array for the vector of dependent variables, of
487
c length neq or more. used for both input and output on the
488
c first call (istate = 0 or 1), and only for output on other
489
c calls. on the first call, y must contain the vector of
490
c initial values. on output, y contains the computed solution
491
c vector, evaluated at t. if desired, the y array may be used
492
c for other purposes between calls to the solver.
494
c this array is passed as the y argument in all calls to res,
495
c adda, and jac. hence its length may exceed neq,
496
c and locations y(neq+1),... may be used to store other real
497
c data and pass it to res, adda, or jac. (the lsodi
498
c package accesses only y(1),...,y(neq). )
500
c ydoti = a real array for the initial value of the vector
501
c dy/dt and for work space, of dimension at least neq.
504
c if istate = 0 then lsodi will compute the initial value
505
c of dy/dt, if a is nonsingular. thus ydoti will
506
c serve only as work space and may have any value.
507
c if istate = 1 then ydoti must contain the initial value
509
c if istate = 2 or 3 (continuation calls) then ydoti
510
c may have any value.
511
c n.b.- if the initial value of a is singular, then
512
c lsodi cannot compute the initial value of dy/dt, so
513
c it must be provided in ydoti, with istate=1.
515
c on output, when lsodi terminates abnormally with istate =
516
c -1, -4, or -5, ydoti will contain the residual
517
c r = g(t,y) - a(t,y)*(dy/dt). if r is large, t is near
518
c its initial value, and ydoti is supplied with istate=1,
519
c there may have been an incorrect input value of
520
c ydoti = dy/dt or the problem ( as given to lsodi )
521
c may not have a solution.
523
c if desired, the ydoti array may be used for other
524
c purposes between calls to the solver.
526
c t = the independent variable. on input, t is used only on the
527
c first call, as the initial point of the integration.
528
c on output, after each call, t is the value at which a
529
c computed solution y is evaluated (usually the same as tout).
530
c on an error return, t is the farthest point reached.
532
c tout = the next value of t at which a computed solution is desired.
533
c used only for input.
535
c when starting the problem (istate = 0 or 1), tout may be
536
c equal to t for one call, then should .ne. t for the next
537
c call. for the initial t, an input value of tout .ne. t is
538
c used in order to determine the direction of the integration
539
c (i.e. the algebraic sign of the step sizes) and the rough
540
c scale of the problem. integration in either direction
541
c (forward or backward in t) is permitted.
543
c if itask = 2 or 5 (one-step modes), tout is ignored after
544
c the first call (i.e. the first call with tout .ne. t).
545
c otherwise, tout is required on every call.
547
c if itask = 1, 3, or 4, the values of tout need not be
548
c monotone, but a value of tout which backs up is limited
549
c to the current internal t interval, whose endpoints are
550
c tcur - hu and tcur (see optional outputs, below, for
553
c itol = an indicator for the type of error control. see
554
c description below under atol. used only for input.
556
c rtol = a relative error tolerance parameter, either a scalar or
557
c an array of length neq. see description below under atol.
560
c atol = an absolute error tolerance parameter, either a scalar or
561
c an array of length neq. input only.
563
c the input parameters itol, rtol, and atol determine
564
c the error control performed by the solver. the solver will
565
c control the vector e = (e(i)) of estimated local errors
566
c in y, according to an inequality of the form
567
c rms-norm of ( e(i)/ewt(i) ) .le. 1,
568
c where ewt(i) = rtol(i)*abs(y(i)) + atol(i),
569
c and the rms-norm (root-mean-square norm) here is
570
c rms-norm(v) = sqrt(sum v(i)**2 / neq). here ewt = (ewt(i))
571
c is a vector of weights which must always be positive, and
572
c the values of rtol and atol should all be non-negative.
573
c the following table gives the types (scalar/array) of
574
c rtol and atol, and the corresponding form of ewt(i).
576
c itol rtol atol ewt(i)
577
c 1 scalar scalar rtol*abs(y(i)) + atol
578
c 2 scalar array rtol*abs(y(i)) + atol(i)
579
c 3 array scalar rtol(i)*abs(y(i)) + atol
580
c 4 array scalar rtol(i)*abs(y(i)) + atol(i)
582
c when either of these parameters is a scalar, it need not
583
c be dimensioned in the user-s calling program.
585
c if none of the above choices (with itol, rtol, and atol
586
c fixed throughout the problem) is suitable, more general
587
c error controls can be obtained by substituting
588
c user-supplied routines for the setting of ewt and/or for
589
c the norm calculation. see part iv below.
591
c if global errors are to be estimated by making a repeated
592
c run on the same problem with smaller tolerances, then all
593
c components of rtol and atol (i.e. of ewt) should be scaled
596
c itask = an index specifying the task to be performed.
597
c input only. itask has the following values and meanings.
598
c 1 means normal computation of output values of y(t) at
599
c t = tout (by overshooting and interpolating).
600
c 2 means take one step only and return.
601
c 3 means stop at the first internal mesh point at or
602
c beyond t = tout and return.
603
c 4 means normal computation of output values of y(t) at
604
c t = tout but without overshooting t = tcrit.
605
c tcrit must be input as rwork(1). tcrit may be equal to
606
c or beyond tout, but not behind it in the direction of
607
c integration. this option is useful if the problem
608
c has a singularity at or beyond t = tcrit.
609
c 5 means take one step, without passing tcrit, and return.
610
c tcrit must be input as rwork(1).
612
c note.. if itask = 4 or 5 and the solver reaches tcrit
613
c (within roundoff), it will return t = tcrit (exactly) to
614
c indicate this (unless itask = 4 and tout comes before tcrit,
615
c in which case answers at t = tout are returned first).
617
c istate = an index used for input and output to specify the
618
c state of the calculation.
620
c on input, the values of istate are as follows.
621
c 0 means this is the first call for the problem, and
622
c lsodi is to compute the initial value of dy/dt
623
c (while doing other initializations). see note below.
624
c 1 means this is the first call for the problem, and
625
c the initial value of dy/dt has been supplied in
626
c ydoti (lsodi will do other initializations). see note
628
c 2 means this is not the first call, and the calculation
629
c is to continue normally, with no change in any input
630
c parameters except possibly tout and itask.
631
c (if itol, rtol, and/or atol are changed between calls
632
c with istate = 2, the new values will be used but not
633
c tested for legality.)
634
c 3 means this is not the first call, and the
635
c calculation is to continue normally, but with
636
c a change in input parameters other than
637
c tout and itask. changes are allowed in
638
c neq, itol, rtol, atol, iopt, lrw, liw, mf, ml, mu,
639
c and any of the optional inputs except h0.
640
c (see iwork description for ml and mu.)
641
c note.. a preliminary call with tout = t is not counted
642
c as a first call here, as no initialization or checking of
643
c input is done. (such a call is sometimes useful for the
644
c purpose of outputting the initial conditions.)
645
c thus the first call for which tout .ne. t requires
646
c istate = 0 or 1 on input.
648
c on output, istate has the following values and meanings.
649
c 0 or 1 means nothing was done, as tout was equal to t with
650
c istate = 0 or 1 on input. (however, an internal counter
651
c was set to detect and prevent repeated calls of this
653
c 2 means that the integration was performed successfully.
654
c 3 means that the user-supplied subroutine res signalled
655
c lsodi to halt the integration and return (ires=2).
656
c integration as far as t was achieved with no occurrence
657
c of ires=2, but this flag was set on attempting the next
659
c -1 means an excessive amount of work (more than mxstep
660
c steps) was done on this call, before completing the
661
c requested task, but the integration was otherwise
662
c successful as far as t. (mxstep is an optional input
663
c and is normally 500.) to continue, the user may
664
c simply reset istate to a value .gt. 1 and call again
665
c (the excess work step counter will be reset to 0).
666
c in addition, the user may increase mxstep to avoid
667
c this error return (see below on optional inputs).
668
c -2 means too much accuracy was requested for the precision
669
c of the machine being used. this was detected before
670
c completing the requested task, but the integration
671
c was successful as far as t. to continue, the tolerance
672
c parameters must be reset, and istate must be set
673
c to 3. the optional output tolsf may be used for this
674
c purpose. (note.. if this condition is detected before
675
c taking any steps, then an illegal input return
676
c (istate = -3) occurs instead.)
677
c -3 means illegal input was detected, before taking any
678
c integration steps. see written message for details.
679
c note.. if the solver detects an infinite loop of calls
680
c to the solver with illegal input, it will cause
682
c -4 means there were repeated error test failures on
683
c one attempted step, before completing the requested
684
c task, but the integration was successful as far as t.
685
c the problem may have a singularity, or the input
686
c may be inappropriate.
687
c -5 means there were repeated convergence test failures on
688
c one attempted step, before completing the requested
689
c task, but the integration was successful as far as t.
690
c this may be caused by an inaccurate jacobian matrix.
691
c -6 means ewt(i) became zero for some i during the
692
c integration. pure relative error control (atol(i)=0.0)
693
c was requested on a variable which has now vanished.
694
c the integration was successful as far as t.
695
c -7 means that the user-supplied subroutine res set
696
c its error flag (ires = 3) despite repeated tries by
697
c lsodi to avoid that condition.
698
c -8 means that istate was 0 on input but lsodi was unable
699
c to compute the initial value of dy/dt. see the
700
c printed message for details.
702
c note.. since the normal output value of istate is 2,
703
c it does not need to be reset for normal continuation.
704
c similarly, istate need not be reset if res told lsodi
705
c to return because the calling program must change
706
c the parameters of the problem.
707
c also, since a negative input value of istate will be
708
c regarded as illegal, a negative output value requires the
709
c user to change it, and possibly other inputs, before
710
c calling the solver again.
712
c iopt = an integer flag to specify whether or not any optional
713
c inputs are being used on this call. input only.
714
c the optional inputs are listed separately below.
715
c iopt = 0 means no optional inputs are being used.
716
c default values will be used in all cases.
717
c iopt = 1 means one or more optional inputs are being used.
719
c rwork = a real working array (double precision).
720
c the length of rwork must be at least
721
c 20 + nyh*(maxord + 1) + 3*neq + lenwm where
722
c nyh = the initial value of neq,
723
c maxord = 12 (if meth = 1) or 5 (if meth = 2) (unless a
724
c smaller value is given as an optional input),
725
c lenwm = neq**2 + 2 if miter is 1 or 2, and
726
c lenwm = (2*ml+mu+1)*neq + 2 if miter is 4 or 5.
727
c (see mf description for the definition of meth and miter.)
728
c thus if maxord has its default value and neq is constant,
730
c 22 + 16*neq + neq**2 for mf = 11 or 12,
731
c 22 + 17*neq + (2*ml+mu)*neq for mf = 14 or 15,
732
c 22 + 9*neq + neq**2 for mf = 21 or 22,
733
c 22 + 10*neq + (2*ml+mu)*neq for mf = 24 or 25.
734
c the first 20 words of rwork are reserved for conditional
735
c and optional inputs and optional outputs.
737
c the following word in rwork is a conditional input..
738
c rwork(1) = tcrit = critical value of t which the solver
739
c is not to overshoot. required if itask is
740
c 4 or 5, and ignored otherwise. (see itask.)
742
c lrw = the length of the array rwork, as declared by the user.
743
c (this will be checked by the solver.)
745
c iwork = an integer work array. the length of iwork must be at least
746
c 20 + neq . the first few words of iwork are used for
747
c conditional and optional inputs and optional outputs.
749
c the following 2 words in iwork are conditional inputs..
750
c iwork(1) = ml these are the lower and upper
751
c iwork(2) = mu half-bandwidths, respectively, of the
752
c matrices in the problem-- the jacobian dr/dy
753
c and the left-hand side matrix a. these half-
754
c bandwidths exclude the main diagonal, so
755
c the total bandwidth is ml + mu + 1 .
756
c the band is defined by the matrix locations
757
c (i,j) with i-ml .le. j .le. i+mu. ml and mu
758
c must satisfy 0 .le. ml,mu .le. neq-1.
759
c these are required if miter is 4 or 5, and
761
c ml and mu may in fact be the band parameters for
762
c matrices to which dr/dy and a are only
763
c approximately equal.
765
c liw = the length of the array iwork, as declared by the user.
766
c (this will be checked by the solver.)
768
c note.. the work arrays must not be altered between calls to lsodi
769
c for the same problem, except possibly for the conditional and
770
c optional inputs, and except for the last 3*neq words of rwork.
771
c the latter space is used for internal scratch space, and so is
772
c available for use by the user outside lsodi between calls, if
773
c desired (but not for use by res, adda, or jac).
775
c mf = the method flag. used only for input. the legal values of
776
c mf are 11, 12, 14, 15, 21, 22, 24, and 25.
777
c mf has decimal digits meth and miter.. mf = 10*meth + miter.
778
c meth indicates the basic linear multistep method..
779
c meth = 1 means the implicit adams method.
780
c meth = 2 means the method based on backward
781
c differentiation formulas (bdf-s).
782
c the bdf method is strongly preferred for stiff prob-
783
c lems, while the adams method is preferred when the prob-
784
c lem is not stiff. if the matrix a(t,y) is nonsingular,
785
c stiffness here can be taken to mean that of the explicit
786
c ode system dy/dt = a**(-1) * g. if a is singular, the
787
c concept of stiffness is not well defined.
788
c if you do not know whether the problem is stiff, we
789
c recommend using meth = 2. if it is stiff, the advan-
790
c tage of meth = 2 over 1 will be great, while if it is
791
c not stiff, the advantage of meth = 1 will be slight.
792
c if maximum efficiency is important, some experimentation
793
c with meth may be necessary.
794
c miter indicates the corrector iteration method..
795
c miter = 1 means chord iteration with a user-supplied
796
c full (neq by neq) jacobian.
797
c miter = 2 means chord iteration with an internally
798
c generated (difference quotient) full jacobian.
799
c this uses neq+1 extra calls to res per dr/dy
801
c miter = 4 means chord iteration with a user-supplied
803
c miter = 5 means chord iteration with an internally
804
c generated banded jacobian (using ml+mu+2
805
c extra calls to res per dr/dy evaluation).
806
c if miter = 1 or 4, the user must supply a subroutine jac
807
c (the name is arbitrary) as described above under jac.
808
c for other values of miter, a dummy argument can be used.
809
c-----------------------------------------------------------------------
812
c the following is a list of the optional inputs provided for in the
813
c call sequence. (see also part ii.) for each such input variable,
814
c this table lists its name as used in this documentation, its
815
c location in the call sequence, its meaning, and the default value.
816
c the use of any of these inputs requires iopt = 1, and in that
817
c case all of these inputs are examined. a value of zero for any
818
c of these optional inputs will cause the default value to be used.
819
c thus to use a subset of the optional inputs, simply preload
820
c locations 5 to 10 in rwork and iwork to 0.0 and 0 respectively, and
821
c then set those of interest to nonzero values.
823
c name location meaning and default value
825
c h0 rwork(5) the step size to be attempted on the first step.
826
c the default value is determined by the solver.
828
c hmax rwork(6) the maximum absolute step size allowed.
829
c the default value is infinite.
831
c hmin rwork(7) the minimum absolute step size allowed.
832
c the default value is 0. (this lower bound is not
833
c enforced on the final step before reaching tcrit
834
c when itask = 4 or 5.)
836
c maxord iwork(5) the maximum order to be allowed. the default
837
c value is 12 if meth = 1, and 5 if meth = 2.
838
c if maxord exceeds the default value, it will
839
c be reduced to the default value.
840
c if maxord is changed during the problem, it may
841
c cause the current order to be reduced.
843
c mxstep iwork(6) maximum number of (internally defined) steps
844
c allowed during one call to the solver.
845
c the default value is 500.
847
c mxhnil iwork(7) maximum number of messages printed (per problem)
848
c warning that t + h = t on a step (h = step size).
849
c this must be positive to result in a non-default
850
c value. the default value is 10.
851
c-----------------------------------------------------------------------
854
c as optional additional output from lsodi, the variables listed
855
c below are quantities related to the performance of lsodi
856
c which are available to the user. these are communicated by way of
857
c the work arrays, but also have internal mnemonic names as shown.
858
c except where stated otherwise, all of these outputs are defined
859
c on any successful return from lsodi, and on any return with
860
c istate = -1, -2, -4, -5, -6, or -7. on a return with -3 (illegal
861
c input) or -8, they will be unchanged from their existing values
862
c (if any), except possibly for tolsf, lenrw, and leniw.
863
c on any error return, outputs relevant to the error will be defined,
866
c name location meaning
868
c hu rwork(11) the step size in t last used (successfully).
870
c hcur rwork(12) the step size to be attempted on the next step.
872
c tcur rwork(13) the current value of the independent variable
873
c which the solver has actually reached, i.e. the
874
c current internal mesh point in t. on output, tcur
875
c will always be at least as far as the argument
876
c t, but may be farther (if interpolation was done).
878
c tolsf rwork(14) a tolerance scale factor, greater than 1.0,
879
c computed when a request for too much accuracy was
880
c detected (istate = -3 if detected at the start of
881
c the problem, istate = -2 otherwise). if itol is
882
c left unaltered but rtol and atol are uniformly
883
c scaled up by a factor of tolsf for the next call,
884
c then the solver is deemed likely to succeed.
885
c (the user may also ignore tolsf and alter the
886
c tolerance parameters in any other way appropriate.)
888
c nst iwork(11) the number of steps taken for the problem so far.
890
c nre iwork(12) the number of residual evaluations (res calls)
891
c for the problem so far.
893
c nje iwork(13) the number of jacobian evaluations (each involving
894
c an evaluation of a and dr/dy) for the problem so
895
c far. this equals the number of calls to adda and
896
c (if miter = 1 or 4) jac, and the number of matrix
897
c l-u decompositions.
899
c nqu iwork(14) the method order last used (successfully).
901
c nqcur iwork(15) the order to be attempted on the next step.
903
c imxer iwork(16) the index of the component of largest magnitude in
904
c the weighted local error vector ( e(i)/ewt(i) ),
905
c on an error return with istate = -4 or -5.
907
c lenrw iwork(17) the length of rwork actually required.
908
c this is defined on normal returns and on an illegal
909
c input return for insufficient storage.
911
c leniw iwork(18) the length of iwork actually required.
912
c this is defined on normal returns and on an illegal
913
c input return for insufficient storage.
916
c the following two arrays are segments of the rwork array which
917
c may also be of interest to the user as optional outputs.
918
c for each array, the table below gives its internal name,
919
c its base address in rwork, and its description.
921
c name base address description
923
c yh 21 the nordsieck history array, of size nyh by
924
c (nqcur + 1), where nyh is the initial value
925
c of neq. for j = 0,1,...,nqcur, column j+1
926
c of yh contains hcur**j/factorial(j) times
927
c the j-th derivative of the interpolating
928
c polynomial currently representing the solution,
929
c evaluated at t = tcur.
931
c acor lenrw-neq+1 array of size neq used for the accumulated
932
c corrections on each step, scaled on output to
933
c represent the estimated local error in y on the
934
c last step. this is the vector e in the descrip-
935
c tion of the error control. it is defined only
936
c on a return from lsodi with istate = 2.
938
c-----------------------------------------------------------------------
939
c part ii. other routines callable.
941
c the following are optional calls which the user may make to
942
c gain additional capabilities in conjunction with lsodi.
943
c (the routines xsetun and xsetf are designed to conform to the
944
c slatec error handling package.)
946
c form of call function
947
c call xsetun(lun) set the logical unit number, lun, for
948
c output of messages from lsodi, if
949
c the default is not desired.
950
c the default value of lun is 6.
952
c call xsetf(mflag) set a flag to control the printing of
954
c mflag = 0 means do not print. (danger..
955
c this risks losing valuable information.)
956
c mflag = 1 means print (the default).
958
c either of the above calls may be made at
959
c any time and will take effect immediately.
961
c call srcom(rsav,isav,job) saves and restores the contents of
962
c the internal common blocks used by
963
c lsodi (see part iii below).
964
c rsav must be a real array of length 218
965
c or more, and isav must be an integer
966
c array of length 41 or more.
967
c job=1 means save common into rsav/isav.
968
c job=2 means restore common from rsav/isav.
969
c srcom is useful if one is
970
c interrupting a run and restarting
971
c later, or alternating between two or
972
c more problems solved with lsodi.
974
c call intdy(,,,,,) provide derivatives of y, of various
975
c (see below) orders, at a specified point t, if
976
c desired. it may be called only after
977
c a successful return from lsodi.
979
c the detailed instructions for using intdy are as follows.
980
c the form of the call is..
982
c call intdy (t, k, rwork(21), nyh, dky, iflag)
984
c the input parameters are..
986
c t = value of independent variable where answers are desired
987
c (normally the same as the t last returned by lsodi).
988
c for valid results, t must lie between tcur - hu and tcur.
989
c (see optional outputs for tcur and hu.)
990
c k = integer order of the derivative desired. k must satisfy
991
c 0 .le. k .le. nqcur, where nqcur is the current order
992
c (see optional outputs). the capability corresponding
993
c to k = 0, i.e. computing y(t), is already provided
994
c by lsodi directly. since nqcur .ge. 1, the first
995
c derivative dy/dt is always available with intdy.
996
c rwork(21) = the base address of the history array yh.
997
c nyh = column length of yh, equal to the initial value of neq.
999
c the output parameters are..
1001
c dky = a real array of length neq containing the computed value
1002
c of the k-th derivative of y(t).
1003
c iflag = integer flag, returned as 0 if k and t were legal,
1004
c -1 if k was illegal, and -2 if t was illegal.
1005
c on an error return, a message is also written.
1006
c-----------------------------------------------------------------------
1007
c part iii. common blocks.
1009
c if lsodi is to be used in an overlay situation, the user
1010
c must declare, in the primary overlay, the variables in..
1011
c (1) the call sequence to lsodi,
1012
c (2) the two internal common blocks
1013
c /ls0001/ of length 257 (218 double precision words
1014
c followed by 39 integer words),
1015
c /eh0001/ of length 2 (integer words).
1017
c if lsodi is used on a system in which the contents of internal
1018
c common blocks are not preserved between calls, the user should
1019
c declare the above two common blocks in his main program to insure
1020
c that their contents are preserved.
1022
c if the solution of a given problem by lsodi is to be interrupted
1023
c and then later continued, such as when restarting an interrupted run
1024
c or alternating between two or more problems, the user should save,
1025
c following the return from the last lsodi call prior to the
1026
c interruption, the contents of the call sequence variables and the
1027
c internal common blocks, and later restore these values before the
1028
c next lsodi call for that problem. to save and restore the common
1029
c blocks, use subroutine srcom (see part ii above).
1031
c-----------------------------------------------------------------------
1032
c part iv. optionally replaceable solver routines.
1034
c below are descriptions of two routines in the lsodi package which
1035
c relate to the measurement of errors. either routine can be
1036
c replaced by a user-supplied version, if desired. however, since such
1037
c a replacement may have a major impact on performance, it should be
1038
c done only when absolutely necessary, and only with great caution.
1039
c (note.. the means by which the package version of a routine is
1040
c superseded by the user-s version may be system-dependent.)
1043
c the following subroutine is called just before each internal
1044
c integration step, and sets the array of error weights, ewt, as
1045
c described under itol/rtol/atol above..
1046
c subroutine ewset (neq, itol, rtol, atol, ycur, ewt)
1047
c where neq, itol, rtol, and atol are as in the lsodi call sequence,
1048
c ycur contains the current dependent variable vector, and
1049
c ewt is the array of weights set by ewset.
1051
c if the user supplies this subroutine, it must return in ewt(i)
1052
c (i = 1,...,neq) a positive quantity suitable for comparing errors
1053
c in y(i) to. the ewt array returned by ewset is passed to the
1054
c vnorm routine (see below), and also used by lsodi in the computation
1055
c of the optional output imxer, the diagonal jacobian approximation,
1056
c and the increments for difference quotient jacobians.
1058
c in the user-supplied version of ewset, it may be desirable to use
1059
c the current values of derivatives of y. derivatives up to order nq
1060
c are available from the history array yh, described above under
1061
c optional outputs. in ewset, yh is identical to the ycur array,
1062
c extended to nq + 1 columns with a column length of nyh and scale
1063
c factors of h**j/factorial(j). on the first call for the problem,
1064
c given by nst = 0, nq is 1 and h is temporarily set to 1.0.
1065
c the quantities nq, nyh, h, and nst can be obtained by including
1066
c in ewset the statements..
1067
c double precision h, rls
1068
c common /ls0001/ rls(218),ils(39)
1073
c thus, for example, the current value of dy/dt can be obtained as
1074
c ycur(nyh+i)/h (i=1,...,neq) (and the division by h is
1075
c unnecessary when nst = 0).
1078
c the following is a real function routine which computes the weighted
1079
c root-mean-square norm of a vector v..
1080
c d = vnorm (n, v, w)
1082
c n = the length of the vector,
1083
c v = real array of length n containing the vector,
1084
c w = real array of length n containing weights,
1085
c d = sqrt( (1/n) * sum(v(i)*w(i))**2 ).
1086
c vnorm is called with n = neq and with w(i) = 1.0/ewt(i), where
1087
c ewt is as set by subroutine ewset.
1089
c if the user supplies this function, it should return a non-negative
1090
c value of vnorm suitable for use in the error control in lsodi.
1091
c none of the arguments should be altered by vnorm.
1092
c for example, a user-supplied vnorm routine might..
1093
c -substitute a max-norm of (v(i)*w(i)) for the rms-norm, or
1094
c -ignore some components of v in the norm, with the effect of
1095
c suppressing the error control on those components of y.
1096
c-----------------------------------------------------------------------
1097
c-----------------------------------------------------------------------
1098
c other routines in the lsodi package.
1100
c in addition to subroutine lsodi, the lsodi package includes the
1101
c following subroutines and function routines..
1102
c ainvg computes the initial value of the vector
1103
c dy/dt = inverse(a) * g
1104
c intdy computes an interpolated value of the y vector at t = tout.
1105
c stodi is the core integrator, which does one step of the
1106
c integration and the associated error control.
1107
c cfode sets all method coefficients and test constants.
1108
c prepji computes and preprocesses the jacobian matrix
1109
c and the newton iteration matrix p.
1110
c solsy manages solution of linear system in chord iteration.
1111
c ewset sets the error weight vector ewt before each step.
1112
c vnorm computes the weighted r.m.s. norm of a vector.
1113
c srcom is a user-callable routine to save and restore
1114
c the contents of the internal common blocks.
1115
c dgefa and dgesl are routines from linpack for solving full
1116
c systems of linear algebraic equations.
1117
c dgbfa and dgbsl are routines from linpack for solving banded
1119
c daxpy, dscal, idamax, and ddot are basic linear algebra modules
1120
c (blas) used by the above linpack routines.
1121
c d1mach computes the unit roundoff in a machine-independent manner.
1122
c xerrwv, xsetun, and xsetf handle the printing of all error
1123
c messages and warnings. xerrwv is machine-dependent.
1124
c note.. vnorm, idamax, ddot, and d1mach are function routines.
1125
c all the others are subroutines.
1127
c the intrinsic and external routines used by lsodi are.. dabs,
1128
c dmax1, dmin1, dfloat, iabs, max0, min0, mod, dsign, dsqrt, and write.
1130
c a block data subprogram is also included with the package,
1131
c for loading some of the variables in internal common.
1133
c-----------------------------------------------------------------------
1134
c the following card is for optimized compilation on llnl compilers.
1136
c-----------------------------------------------------------------------
1137
external prepji, solsy
1138
integer illin, init, lyh, lewt, lacor, lsavr, lwm, liwm,
1139
1 mxstep, mxhnil, nhnil, ntrep, nslast, nyh, iowns
1140
integer icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
1141
1 maxord, maxcor, msbp, mxncf, n, nq, nst, nre, nje, nqu
1142
integer i, i1, i2, ier, iflag, imxer, ires, kgo,
1143
1 leniw, lenrw, lenwm, lp, lyd0, ml, mord, mu, mxhnl0, mxstp0
1144
double precision rowns,
1145
1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround
1146
double precision atoli, ayi, big, ewti, h0, hmax, hmx, rh, rtoli,
1147
1 tcrit, tdist, tnext, tol, tolsf, tp, size, sum, w0,
1151
c-----------------------------------------------------------------------
1152
c the following internal common block contains
1153
c (a) variables which are local to any subroutine but whose values must
1154
c be preserved between calls to the routine (own variables), and
1155
c (b) variables which are communicated between subroutines.
1156
c common block ls0001 is shared by the lsodi and lsode packages.
1157
c the structure of ls0001 is as follows.. all real variables are
1158
c listed first, followed by all integers. within each type, the
1159
c variables are grouped with those local to subroutine lsodi first,
1160
c then those local to subroutine stodi, and finally those used
1161
c for communication. the block is declared in subroutines
1162
c lsodi, intdy, stodi, prepji, and solsy. groups of variables are
1163
c replaced by dummy arrays in the common declarations in routines
1164
c where those variables are not used.
1165
c-----------------------------------------------------------------------
1166
common /ls0001/ rowns(209),
1167
1 ccmax, el0, h, hmin, hmxi, hu, rc, tn, uround,
1168
2 illin, init, lyh, lewt, lacor, lsavr, lwm, liwm,
1169
3 mxstep, mxhnil, nhnil, ntrep, nslast, nyh, iowns(6),
1170
4 icf, ierpj, iersl, jcur, jstart, kflag, l, meth, miter,
1171
5 maxord, maxcor, msbp, mxncf, n, nq, nst, nre, nje, nqu
1173
data mord(1),mord(2)/12,5/, mxstp0/500/, mxhnl0/10/
1174
c-----------------------------------------------------------------------
1176
c this code block is executed on every call.
1177
c it tests istate and itask for legality and branches appropriately.
1178
c if istate .gt. 1 but the flag init shows that initialization has
1179
c not yet been done, an error return occurs.
1180
c if istate = 0 or 1 and tout = t, jump to block g and return
1182
c-----------------------------------------------------------------------
1183
if (istate .lt. 0 .or. istate .gt. 3) go to 601
1184
if (itask .lt. 1 .or. itask .gt. 5) go to 602
1185
if (istate .le. 1) go to 10
1186
if (init .eq. 0) go to 603
1187
if (istate .eq. 2) go to 200
1190
if (tout .eq. t) go to 430
1192
c-----------------------------------------------------------------------
1194
c the next code block is executed for the initial call (istate = 0 or 1)
1195
c or for a continuation call with parameter changes (istate = 3).
1196
c it contains checking of all inputs and various initializations.
1198
c first check legality of the non-optional inputs neq, itol, iopt,
1200
c-----------------------------------------------------------------------
1201
if (neq(1) .le. 0) go to 604
1202
if (istate .le. 1) go to 25
1203
if (neq(1) .gt. n) go to 605
1205
if (itol .lt. 1 .or. itol .gt. 4) go to 606
1206
if (iopt .lt. 0 .or. iopt .gt. 1) go to 607
1208
miter = mf - 10*meth
1209
if (meth .lt. 1 .or. meth .gt. 2) go to 608
1210
if (miter .le. 0 .or. miter .gt. 5) go to 608
1211
if (miter .eq. 3) go to 608
1212
if (miter .lt. 3) go to 30
1215
if (ml .lt. 0 .or. ml .ge. n) go to 609
1216
if (mu .lt. 0 .or. mu .ge. n) go to 610
1218
c next process and check the optional inputs. --------------------------
1219
if (iopt .eq. 1) go to 40
1223
if (istate .le. 1) h0 = 0.0d0
1227
40 maxord = iwork(5)
1228
if (maxord .lt. 0) go to 611
1229
if (maxord .eq. 0) maxord = 100
1230
maxord = min0(maxord,mord(meth))
1232
if (mxstep .lt. 0) go to 612
1233
if (mxstep .eq. 0) mxstep = mxstp0
1235
if (mxhnil .lt. 0) go to 613
1236
if (mxhnil .eq. 0) mxhnil = mxhnl0
1237
if (istate .gt. 1) go to 50
1239
if ((tout - t)*h0 .lt. 0.0d0) go to 614
1241
if (hmax .lt. 0.0d0) go to 615
1243
if (hmax .gt. 0.0d0) hmxi = 1.0d0/hmax
1245
if (hmin .lt. 0.0d0) go to 616
1246
c-----------------------------------------------------------------------
1247
c set work array pointers and check lengths lrw and liw.
1248
c pointers to segments of rwork and iwork are named by prefixing l to
1249
c the name of the segment. e.g., the segment yh starts at rwork(lyh).
1250
c segments of rwork (in order) are denoted yh, wm, ewt, savr, acor.
1251
c-----------------------------------------------------------------------
1253
if (istate .le. 1) nyh = n
1254
lwm = lyh + (maxord + 1)*nyh
1255
if (miter .le. 2) lenwm = n*n + 2
1256
if (miter .ge. 4) lenwm = (2*ml + mu + 1)*n + 2
1260
lenrw = lacor + n - 1
1265
if (lenrw .gt. lrw) go to 617
1266
if (leniw .gt. liw) go to 618
1267
c check rtol and atol for legality. ------------------------------------
1271
if (itol .ge. 3) rtoli = rtol(i)
1272
if (itol .eq. 2 .or. itol .eq. 4) atoli = atol(i)
1273
if (rtoli .lt. 0.0d0) go to 619
1274
if (atoli .lt. 0.0d0) go to 620
1276
if (istate .le. 1) go to 100
1277
c if istate = 3, set flag to signal parameter changes to stodi. --------
1279
if (nq .le. maxord) go to 90
1280
c maxord was reduced below nq. copy yh(*,maxord+2) into ydoti.---------
1282
80 ydoti(i) = rwork(i+lwm-1)
1283
c reload wm(1) = rwork(lwm), since lwm may have changed. ---------------
1284
90 rwork(lwm) = dsqrt(uround)
1285
if (n .eq. nyh) go to 200
1286
c neq was reduced. zero part of yh to avoid undefined references. -----
1288
i2 = lyh + (maxord + 1)*nyh - 1
1289
if (i1 .gt. i2) go to 200
1293
c-----------------------------------------------------------------------
1295
c the next block is for the initial call only (istate = 0 or 1).
1296
c it contains all remaining initializations, the call to ainvg
1297
c (if istate = 1), and the calculation of the initial step size.
1298
c the error weights in ewt are inverted after being loaded.
1299
c-----------------------------------------------------------------------
1300
100 uround = d1mach(4)
1302
if (itask .ne. 4 .and. itask .ne. 5) go to 105
1304
if ((tcrit - tout)*(tout - t) .lt. 0.0d0) go to 625
1305
if (h0 .ne. 0.0d0 .and. (t + h0 - tcrit)*h0 .gt. 0.0d0)
1308
rwork(lwm) = dsqrt(uround)
1320
c compute initial dy/dt, if necessary, and load it and initial y into yh
1323
if (istate .eq. 1) go to 120
1324
c lsodi must compute initial dy/dt (lyd0 points to yh(*,2)). -----------
1325
call ainvg( res, adda, neq, t, y, rwork(lyd0), miter,
1326
1 ml, mu, rwork(lp), iwork(21), ier )
1328
if (ier.lt.0) go to 560
1329
if (ier.eq.0) go to 110
1333
115 rwork(i+lyh-1) = y(i)
1335
c initial dy/dt has been supplied. -------------------------------------
1337
rwork(i+lyh-1) = y(i)
1338
125 rwork(i+lyd0-1) = ydoti(i)
1339
c load and invert the ewt array. (h is temporarily set to 1.0.) -------
1343
call ewset (n, itol, rtol, atol, rwork(lyh), rwork(lewt))
1345
if (rwork(i+lewt-1) .le. 0.0d0) go to 621
1346
135 rwork(i+lewt-1) = 1.0d0/rwork(i+lewt-1)
1347
c-----------------------------------------------------------------------
1348
c the coding below computes the step size, h0, to be attempted on the
1349
c first step, unless the user has supplied a value for this.
1350
c first check that tout - t differs significantly from zero.
1351
c a scalar tolerance quantity tol is computed, as max(rtol(i))
1352
c if this is positive, or max(atol(i)/abs(y(i))) otherwise, adjusted
1353
c so as to be between 100*uround and 1.0e-3.
1354
c then the computed value h0 is given by..
1356
c h0**2 = tol / ( w0**-2 + (1/neq) * sum ( ydot(i)/ywt(i) )**2 )
1358
c where w0 = max ( abs(t), abs(tout) ),
1359
c ydot(i) = i-th component of initial value of dy/dt,
1360
c ywt(i) = ewt(i)/tol (a weight for y(i)).
1361
c the sign of h0 is inferred from the initial values of tout and t.
1362
c-----------------------------------------------------------------------
1363
if (h0 .ne. 0.0d0) go to 180
1364
tdist = dabs(tout - t)
1365
w0 = dmax1(dabs(t),dabs(tout))
1366
if (tdist .lt. 2.0d0*uround*w0) go to 622
1368
if (itol .le. 2) go to 145
1370
140 tol = dmax1(tol,rtol(i))
1371
145 if (tol .gt. 0.0d0) go to 160
1374
if (itol .eq. 2 .or. itol .eq. 4) atoli = atol(i)
1376
if (ayi .ne. 0.0d0) tol = dmax1(tol,atoli/ayi)
1378
160 tol = dmax1(tol,100.0d0*uround)
1379
tol = dmin1(tol,0.001d0)
1380
sum = vnorm (n, rwork(lyd0), rwork(lewt))
1381
sum = 1.0d0/(tol*w0*w0) + tol*sum**2
1382
h0 = 1.0d0/dsqrt(sum)
1383
h0 = dmin1(h0,tdist)
1384
h0 = dsign(h0,tout-t)
1385
c adjust h0 if necessary to meet hmax bound. ---------------------------
1386
180 rh = dabs(h0)*hmxi
1387
if (rh .gt. 1.0d0) h0 = h0/rh
1388
c load h with h0 and scale yh(*,2) by h0. ------------------------------
1391
190 rwork(i+lyd0-1) = h0*rwork(i+lyd0-1)
1393
c-----------------------------------------------------------------------
1395
c the next code block is for continuation calls only (istate = 2 or 3)
1396
c and is to check stop conditions before taking a step.
1397
c-----------------------------------------------------------------------
1399
go to (210, 250, 220, 230, 240), itask
1400
210 if ((tn - tout)*h .lt. 0.0d0) go to 250
1401
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1402
if (iflag .ne. 0) go to 627
1405
220 tp = tn - hu*(1.0d0 + 100.0d0*uround)
1406
if ((tp - tout)*h .gt. 0.0d0) go to 623
1407
if ((tn - tout)*h .lt. 0.0d0) go to 250
1409
230 tcrit = rwork(1)
1410
if ((tn - tcrit)*h .gt. 0.0d0) go to 624
1411
if ((tcrit - tout)*h .lt. 0.0d0) go to 625
1412
if ((tn - tout)*h .lt. 0.0d0) go to 245
1413
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1414
if (iflag .ne. 0) go to 627
1417
240 tcrit = rwork(1)
1418
if ((tn - tcrit)*h .gt. 0.0d0) go to 624
1419
245 hmx = dabs(tn) + dabs(h)
1420
ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1422
tnext = tn + h*(1.0d0 + 4.0d0*uround)
1423
if ((tnext - tcrit)*h .le. 0.0d0) go to 250
1424
h = (tcrit - tn)*(1.0d0 - 4.0d0*uround)
1425
if (istate .eq. 2) jstart = -2
1426
c-----------------------------------------------------------------------
1428
c the next block is normally executed for all calls and contains
1429
c the call to the one-step core integrator stodi.
1431
c this is a looping point for the integration steps.
1433
c first check for too many steps being taken, update ewt (if not at
1434
c start of problem), check for too much accuracy being requested, and
1435
c check for h below the roundoff level in t.
1436
c-----------------------------------------------------------------------
1438
if ((nst-nslast) .ge. mxstep) go to 500
1439
call ewset (n, itol, rtol, atol, rwork(lyh), rwork(lewt))
1441
if (rwork(i+lewt-1) .le. 0.0d0) go to 510
1442
260 rwork(i+lewt-1) = 1.0d0/rwork(i+lewt-1)
1443
270 tolsf = uround*vnorm (n, rwork(lyh), rwork(lewt))
1444
if (tolsf .le. 1.0d0) go to 280
1446
if (nst .eq. 0) go to 626
1448
280 if ((tn + h) .ne. tn) go to 290
1450
if (nhnil .gt. mxhnil) go to 290
1451
call xerrwv('lsodi-- warning..internal t (=r1) and h (=r2) are',
1452
1 50, 101, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1454
1 ' such that in the machine, t + h = t on the next step ',
1455
1 60, 101, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1456
call xerrwv(' (h = step size). solver will continue anyway',
1457
1 50, 101, 0, 0, 0, 0, 2, tn, h)
1458
if (nhnil .lt. mxhnil) go to 290
1459
call xerrwv('lsodi-- above warning has been issued i1 times. ',
1460
1 50, 102, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1461
call xerrwv(' it will not be issued again for this problem',
1462
1 50, 102, 0, 1, mxhnil, 0, 0, 0.0d0, 0.0d0)
1464
c-----------------------------------------------------------------------
1465
c call stodi(neq,y,yh,nyh,yh1,ewt,savf,savr,acor,wm,iwm,res,
1466
c adda,jac,prepji,solsy)
1467
c note... savf in stodi occupies the same space as ydoti in lsodi.
1468
c-----------------------------------------------------------------------
1469
call stodi (neq, y, rwork(lyh), nyh, rwork(lyh), rwork(lewt),
1470
1 ydoti, rwork(lsavr), rwork(lacor), rwork(lwm),
1471
2 iwork(liwm), res, adda, jac, prepji, solsy )
1473
go to (300, 530, 540, 400, 550), kgo
1475
c kgo = 1,success. 2,error test failure. 3,convergence failure.
1476
c 4,res ordered return. 5,res returned error.
1477
c-----------------------------------------------------------------------
1479
c the following block handles the case of a successful return from the
1480
c core integrator (kflag = 0). test for stop conditions.
1481
c-----------------------------------------------------------------------
1483
go to (310, 400, 330, 340, 350), itask
1484
c itask = 1. if tout has been reached, interpolate. -------------------
1485
310 if ((tn - tout)*h .lt. 0.0d0) go to 250
1486
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1489
c itask = 3. jump to exit if tout was reached. ------------------------
1490
330 if ((tn - tout)*h .ge. 0.0d0) go to 400
1492
c itask = 4. see if tout or tcrit was reached. adjust h if necessary.
1493
340 if ((tn - tout)*h .lt. 0.0d0) go to 345
1494
call intdy (tout, 0, rwork(lyh), nyh, y, iflag)
1497
345 hmx = dabs(tn) + dabs(h)
1498
ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1500
tnext = tn + h*(1.0d0 + 4.0d0*uround)
1501
if ((tnext - tcrit)*h .le. 0.0d0) go to 250
1502
h = (tcrit - tn)*(1.0d0 - 4.0d0*uround)
1505
c itask = 5. see if tcrit was reached and jump to exit. ---------------
1506
350 hmx = dabs(tn) + dabs(h)
1507
ihit = dabs(tn - tcrit) .le. 100.0d0*uround*hmx
1508
c-----------------------------------------------------------------------
1510
c the following block handles all successful returns from lsodi.
1511
c if itask .ne. 1, y is loaded from yh and t is set accordingly.
1512
c istate is set to 2, the illegal input counter is zeroed, and the
1513
c optional outputs are loaded into the work arrays before returning. if
1514
c istate = 0 or 1 and tout = t, there is a return with no action taken,
1515
c except that if this has happened repeatedly, the run is terminated.
1516
c-----------------------------------------------------------------------
1518
410 y(i) = rwork(i+lyh-1)
1520
if (itask .ne. 4 .and. itask .ne. 5) go to 420
1523
if (kflag .eq. -3) istate = 3
1535
430 ntrep = ntrep + 1
1536
if (ntrep .lt. 5) return
1538
1 'lsodi-- repeated calls with istate= 0 or 1 and tout= t(=r1)',
1539
1 60, 301, 0, 0, 0, 0, 1, t, 0.0d0)
1541
c-----------------------------------------------------------------------
1543
c the following block handles all unsuccessful returns other than
1544
c those for illegal input. first the error message routine is called.
1545
c if there was an error test or convergence test failure, imxer is set.
1546
c then y is loaded from yh, t is set to tn, and the illegal input
1547
c counter illin is set to 0. the optional outputs are loaded into
1548
c the work arrays before returning.
1549
c-----------------------------------------------------------------------
1550
c the maximum number of steps was taken before reaching tout. ----------
1551
500 call xerrwv('lsodi-- at current t (=r1), mxstep (=i1) steps ',
1552
1 50, 201, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1553
call xerrwv(' taken on this call before reaching tout ',
1554
1 50, 201, 0, 1, mxstep, 0, 1, tn, 0.0d0)
1557
c ewt(i) .le. 0.0 for some i (not at start of problem). ----------------
1558
510 ewti = rwork(lewt+i-1)
1559
call xerrwv('lsodi-- at t (=r1), ewt(i1) has become r2 .le. 0.',
1560
1 50, 202, 0, 1, i, 0, 2, tn, ewti)
1563
c too much accuracy requested for machine precision. -------------------
1564
520 call xerrwv('lsodi-- at t (=r1), too much accuracy requested ',
1565
1 50, 203, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1566
call xerrwv(' for precision of machine.. see tolsf (=r2) ',
1567
1 50, 203, 0, 0, 0, 0, 2, tn, tolsf)
1571
c kflag = -1. error test failed repeatedly or with abs(h) = hmin. -----
1572
530 call xerrwv('lsodi-- at t(=r1) and step size h(=r2), the error',
1573
1 50, 204, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1574
call xerrwv(' test failed repeatedly or with abs(h) = hmin',
1575
1 50, 204, 0, 0, 0, 0, 2, tn, h)
1578
c kflag = -2. convergence failed repeatedly or with abs(h) = hmin. ----
1579
540 call xerrwv('lsodi-- at t (=r1) and step size h (=r2), the ',
1580
1 50, 205, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1581
call xerrwv(' corrector convergence failed repeatedly ',
1582
1 50, 205, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1583
call xerrwv(' or with abs(h) = hmin ',
1584
1 30, 205, 0, 0, 0, 0, 2, tn, h)
1587
c ires = 3 returned by res, despite retries by stodi. ------------------
1588
550 call xerrwv('lsodi-- at t (=r1) residual routine returned ',
1589
1 50, 206, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1590
call xerrwv(' error ires = 3 repeatedly ',
1591
1 40, 206, 0, 0, 0, 0, 1, tn, 0.0d0)
1594
c ainvg failed because a-matrix was singular. --------------------------
1597
1 'lsodi-- attempt to initialize dy/dt failed.. matrix a is ',
1598
1 60, 207, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1599
call xerrwv(' singular. sgefa or sgbfa returned info=(i1)',
1600
2 50, 207, 0, 1, ier, 0, 0, 0.0d0, 0.0d0)
1603
c ainvg failed because res set ires to 2 or 3. -------------------------
1604
565 call xerrwv('lsodi-- attempt to initialize dy/dt failed ',
1605
1 50, 208, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1606
call xerrwv(' because residual routine set its error flag ',
1607
1 50, 208, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1608
call xerrwv(' to ires = (i1)',
1609
1 20, 208, 0, 1, ier, 0, 0, 0.0d0, 0.0d0)
1612
c compute imxer if relevant. -------------------------------------------
1616
size = dabs(rwork(i+lacor-1)*rwork(i+lewt-1))
1617
if (big .ge. size) go to 575
1622
c compute residual if relevant. ----------------------------------------
1623
580 lyd0 = lyh + nyh
1625
rwork(i+lsavr-1) = rwork(i+lyd0-1)/h
1626
585 y(i) = rwork(i+lyh-1)
1628
call res ( neq, tn, y, rwork(lsavr), ydoti, ires )
1630
if (ires .le. 1) go to 595
1631
call xerrwv('lsodi-- residual routine set its flag ires ',
1632
1 50, 210, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1633
call xerrwv(' to (i1) when called for final output. ',
1634
1 50, 210, 0, 1, ires, 0, 0, 0.0d0, 0.0d0)
1636
c set y vector, t, illin, and optional outputs. ------------------------
1638
592 y(i) = rwork(i+lyh-1)
1650
c-----------------------------------------------------------------------
1652
c the following block handles all error returns due to illegal input
1653
c (istate = -3), as detected before calling the core integrator.
1654
c first the error message routine is called. then if there have been
1655
c 5 consecutive such returns just before this call to the solver,
1656
c the run is halted.
1657
c-----------------------------------------------------------------------
1658
601 call xerrwv('lsodi-- istate (=i1) illegal ',
1659
1 30, 1, 0, 1, istate, 0, 0, 0.0d0, 0.0d0)
1661
602 call xerrwv('lsodi-- itask (=i1) illegal ',
1662
1 30, 2, 0, 1, itask, 0, 0, 0.0d0, 0.0d0)
1664
603 call xerrwv('lsodi-- istate .gt. 1 but lsodi not initialized ',
1665
1 50, 3, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1667
604 call xerrwv('lsodi-- neq (=i1) .lt. 1 ',
1668
1 30, 4, 0, 1, neq(1), 0, 0, 0.0d0, 0.0d0)
1670
605 call xerrwv('lsodi-- istate = 3 and neq increased (i1 to i2) ',
1671
1 50, 5, 0, 2, n, neq(1), 0, 0.0d0, 0.0d0)
1673
606 call xerrwv('lsodi-- itol (=i1) illegal ',
1674
1 30, 6, 0, 1, itol, 0, 0, 0.0d0, 0.0d0)
1676
607 call xerrwv('lsodi-- iopt (=i1) illegal ',
1677
1 30, 7, 0, 1, iopt, 0, 0, 0.0d0, 0.0d0)
1679
608 call xerrwv('lsodi-- mf (=i1) illegal ',
1680
1 30, 8, 0, 1, mf, 0, 0, 0.0d0, 0.0d0)
1682
609 call xerrwv('lsodi-- ml(=i1) illegal.. .lt. 0 or .ge. neq(=i2)',
1683
1 50, 9, 0, 2, ml, neq(1), 0, 0.0d0, 0.0d0)
1685
610 call xerrwv('lsodi-- mu(=i1) illegal.. .lt. 0 or .ge. neq(=i2)',
1686
1 50, 10, 0, 2, mu, neq(1), 0, 0.0d0, 0.0d0)
1688
611 call xerrwv('lsodi-- maxord (=i1) .lt. 0 ',
1689
1 30, 11, 0, 1, maxord, 0, 0, 0.0d0, 0.0d0)
1691
612 call xerrwv('lsodi-- mxstep (=i1) .lt. 0 ',
1692
1 30, 12, 0, 1, mxstep, 0, 0, 0.0d0, 0.0d0)
1694
613 call xerrwv('lsodi-- mxhnil (=i1) .lt. 0 ',
1695
1 30, 13, 0, 1, mxhnil, 0, 0, 0.0d0, 0.0d0)
1697
614 call xerrwv('lsodi-- tout (=r1) behind t (=r2) ',
1698
1 40, 14, 0, 0, 0, 0, 2, tout, t)
1699
call xerrwv(' integration direction is given by h0 (=r1) ',
1700
1 50, 14, 0, 0, 0, 0, 1, h0, 0.0d0)
1702
615 call xerrwv('lsodi-- hmax (=r1) .lt. 0.0 ',
1703
1 30, 15, 0, 0, 0, 0, 1, hmax, 0.0d0)
1705
616 call xerrwv('lsodi-- hmin (=r1) .lt. 0.0 ',
1706
1 30, 16, 0, 0, 0, 0, 1, hmin, 0.0d0)
1709
1 'lsodi-- rwork length needed, lenrw (=i1), exceeds lrw (=i2)',
1710
1 60, 17, 0, 2, lenrw, lrw, 0, 0.0d0, 0.0d0)
1713
1 'lsodi-- iwork length needed, leniw (=i1), exceeds liw (=i2)',
1714
1 60, 18, 0, 2, leniw, liw, 0, 0.0d0, 0.0d0)
1716
619 call xerrwv('lsodi-- rtol(=i1) is r1 .lt. 0.0 ',
1717
1 40, 19, 0, 1, i, 0, 1, rtoli, 0.0d0)
1719
620 call xerrwv('lsodi-- atol(=i1) is r1 .lt. 0.0 ',
1720
1 40, 20, 0, 1, i, 0, 1, atoli, 0.0d0)
1722
621 ewti = rwork(lewt+i-1)
1723
call xerrwv('lsodi-- ewt(=i1) is r1 .le. 0.0 ',
1724
1 40, 21, 0, 1, i, 0, 1, ewti, 0.0d0)
1727
1 'lsodi-- tout (=r1) too close to t(=r2) to start integration',
1728
1 60, 22, 0, 0, 0, 0, 2, tout, t)
1731
1 'lsodi-- itask = i1 and tout (=r1) behind tcur - hu (= r2) ',
1732
1 60, 23, 0, 1, itask, 0, 2, tout, tp)
1735
1 'lsodi-- itask = 4 or 5 and tcrit (=r1) behind tcur (=r2) ',
1736
1 60, 24, 0, 0, 0, 0, 2, tcrit, tn)
1739
1 'lsodi-- itask = 4 or 5 and tcrit (=r1) behind tout (=r2) ',
1740
1 60, 25, 0, 0, 0, 0, 2, tcrit, tout)
1742
626 call xerrwv('lsodi-- at start of problem, too much accuracy ',
1743
1 50, 26, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1745
1 ' requested for precision of machine.. see tolsf (=r1) ',
1746
1 60, 26, 0, 0, 0, 0, 1, tolsf, 0.0d0)
1749
627 call xerrwv('lsodi-- trouble from intdy. itask = i1, tout = r1',
1750
1 50, 27, 0, 1, itask, 0, 1, tout, 0.0d0)
1752
700 if (illin .eq. 5) go to 710
1756
710 call xerrwv('lsodi-- repeated occurrences of illegal input ',
1757
1 50, 302, 0, 0, 0, 0, 0, 0.0d0, 0.0d0)
1759
800 call xerrwv('lsodi-- run aborted.. apparent infinite loop ',
1760
1 50, 303, 2, 0, 0, 0, 0, 0.0d0, 0.0d0)
1762
c----------------------- end of subroutine lsodi -----------------------
added
removed
scipy/integrate/odepack/lsodi.f
