DLSODIS solves the initial value problem for linearly implicit systems of first order ODEs,
A(t,y) * dy/dt = g(t,y), where A(t,y) is a square matrix,
or, in component form,
( a * ( dy / dt )) + ... + ( a * ( dy / dt )) =
i,1 1 i,NEQ NEQ
= g ( t, y, y ,..., y ) ( i = 1,...,NEQ )
i 1 2 NEQ
If A is singular, this is a differential-algebraic system.
DLSODIS is a variant version of the DLSODI package, and is intended for stiff problems in which the matrix A and the Jacobian matrix d(g - A*s)/dy have arbitrary sparse structures.
This version is in double precision.
Communication between the user and the DLSODIS package, for normal situations, is summarized here. This summary describes only a subset of the full set of options available. See the full description for details, including optional communication, nonstandard options, and instructions for special situations. See also the example problem (with program and output) following this summary.
A. First, provide a subroutine of the form:
SUBROUTINE RES (NEQ, T, Y, S, R, IRES)
DOUBLE PRECISION T, Y(*), S(*), R(*)
which computes the residual function
r = g(t,y) - A(t,y) * s ,
as a function of t and the vectors y and s. (s is an internally generated approximation to dy/dt.) The arrays Y and S are inputs to the RES routine and should not be altered. The residual vector is to be stored in the array R. The argument IRES should be ignored for casual use of DLSODIS. (For uses of IRES, see the paragraph on RES in the full description below.)
B. DLSODIS must deal internally with the matrices A and dr/dy, where r is the residual function defined above. DLSODIS generates a linear combination of these two matrices in sparse form. The matrix structure is communicated by a method flag, MF: MF = 21 or 22 when the user provides the structures of matrix A and dr/dy, MF = 121 or 222 when the user does not provide structure information, and MF = 321 or 422 when the user provides the structure of matrix A.
C. You must also provide a subroutine of the form:
SUBROUTINE ADDA (NEQ, T, Y, J, IAN, JAN, P)
DOUBLE PRECISION T, Y(*), P(*)
INTEGER IAN(*), JAN(*)
which adds the matrix A = A(t,y) to the contents of the array P. NEQ, T, Y, and J are input arguments and should not be altered. This routine should add the J-th column of matrix A to the array P (of length NEQ). I.e. add A(i,J) to P(i) for all relevant values of i. The arguments IAN and JAN should be ignored for normal situations. DLSODIS will call the ADDA routine with J = 1,2,…,NEQ.
D. For the sake of efficiency, you are encouraged to supply the Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s (s = a fixed vector) as above. If dr/dy is being supplied, use MF = 21, 121, or 321, and provide a subroutine of the form:
SUBROUTINE JAC (NEQ, T, Y, S, J, IAN, JAN, PDJ)
DOUBLE PRECISION T, Y(*), S(*), PDJ(*)
INTEGER IAN(*), JAN(*)
which computes dr/dy as a function of t, y, and s. Here NEQ, T, Y, S, and J are input arguments, and the JAC routine is to load the array PDJ (of length NEQ) with the J-th column of dr/dy. I.e. load PDJ(i) with dr(i)/dy(J) for all relevant values of i. The arguments IAN and JAN should be ignored for normal situations. DLSODIS will call the JAC routine with J = 1,2,…,NEQ.
Only nonzero elements need be loaded. A crude approximation to dr/dy, possibly with fewer nonzero elememts, will suffice. Note that if A is independent of y (or this dependence is weak enough to be ignored) then JAC is to compute dg/dy.
If it is not feasible to provide a JAC routine, use MF = 22, 222, or 422 and DLSODIS will compute an approximate Jacobian internally by difference quotients.
E. Next decide whether or not to provide the initial value of the derivative vector dy/dt. If the initial value of A(t,y) is nonsingular (and not too ill-conditioned), you may let DLSODIS compute this vector (ISTATE = 0). (DLSODIS will solve the system A*s = g for s, with initial values of A and g.) If A(t,y) is initially singular, then the system is a differential-algebraic system, and you must make use of the particular form of the system to compute the initial values of y and dy/dt. In that case, use ISTATE = 1 and load the initial value of dy/dt into the array YDOTI.
The input array YDOTI and the initial Y array must be consistent with the equations A*dy/dt = g. This implies that the initial residual r = g(t,y) - A(t,y)*YDOTI must be approximately zero.
F. Write a main program which calls Subroutine DLSODIS once for each point at which answers are desired. This should also provide for possible use of logical unit 6 for output of error messages by DLSODIS. On the first call to DLSODIS, supply arguments as follows:
name of user subroutine for residual function r.
name of user subroutine for computing and adding A(t,y).
name of user subroutine for Jacobian matrix dr/dy (MF = 121). If not used, pass a dummy name. Note: The names for the RES and ADDA routines and (if used) the
JAC routine must be declared External in the calling program.
number of scalar equations in the system.
array of initial values, of length NEQ.
array of length NEQ (containing initial dy/dt if ISTATE = 1).
the initial value of the independent variable.
first point where output is desired (.ne. T).
1 or 2 according as ATOL (below) is a scalar or array.
relative tolerance parameter (scalar).
absolute tolerance parameter (scalar or array). The estimated local error in y(i) will be controlled so as to be roughly less (in magnitude) than
EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or
EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2.
Thus the local error test passes if, in each component, either the absolute error is less than ATOL (or ATOL(i)), or the relative error is less than RTOL. Use RTOL = 0.0 for pure absolute error control, and use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error control. Caution: Actual (global) errors may exceed these local tolerances, so choose them conservatively.
1 for normal computation of output values of y at t = TOUT.
integer flag (input and output). Set ISTATE = 1 if the initial dy/dt is supplied, and 0 otherwise.
0 to indicate no optional inputs used.
real work array of length at least:
20 + (2 + 1./LENRAT)*NNZ + (11 + 9./LENRAT)*NEQ
where:
NNZ = the number of nonzero elements in the sparse
iteration matrix P = A - con\*dr/dy (con = scalar)
(If NNZ is unknown, use an estimate of it.)
LENRAT = the real to integer wordlength ratio (usually 1 in
single precision and 2 in double precision).
In any case, the required size of RWORK cannot generally be predicted in advance for any value of MF, and the value above is a rough estimate of a crude lower bound. Some experimentation with this size may be necessary. (When known, the correct required length is an optional output, available in IWORK(17).)
declared length of RWORK (in user’s dimension).
integer work array of length at least 30.
declared length of IWORK (in user’s dimension).
method flag. Standard values are:
121 for a user-supplied sparse Jacobian.
222 for an internally generated sparse Jacobian.
For other choices of MF, see the paragraph on MF in the full description below.
Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, and possibly ATOL.
G. The output from the first call, or any call, is:
array of computed values of y(t) vector.
corresponding value of independent variable (normally TOUT).
value and their meanings:
| value | descriptions |
|---|---|
| 2 | if DLSODIS was successful, negative otherwise. |
| -1 | means excess work done on this call (check all inputs). |
| -2 | means excess accuracy requested (tolerances too small). |
| -3 | means illegal input detected (see printed message). |
| -4 | means repeated error test failures (check all inputs). |
| -5 | means repeated convergence failures (perhaps bad Jacobian |
| supplied or wrong choice of tolerances). | |
| -6 | means error weight became zero during problem. (Solution |
| component i vanished, and ATOL or ATOL(i) = 0.) | |
| -7 | cannot occur in casual use. |
| -8 | means DLSODIS was unable to compute the initial dy/dt. |
| in casual use, this means A(t,y) is initially singular. | |
| Supply YDOTI and use ISTATE = 1 on the first call. | |
| -9 | means a fatal error return flag came from sparse solver |
| CDRV by way of DPRJIS or DSOLSS. Should never happen. |
A return with ISTATE = -1, -4, or -5, may result from using an inappropriate sparsity structure, one that is quite different from the initial structure. Consider calling DLSODIS again with ISTATE = 3 to force the structure to be reevaluated. See the full description of ISTATE below.
If DLSODIS returns ISTATE = -1, -4 or -5, then the output of DLSODIS also includes YDOTI = array containing residual vector r = g - A * dy/dt evaluated at the current t, y, and dy/dt.
H. To continue the integration after a successful return, simply reset TOUT and call DLSODIS again. No other parameters need be reset.
Example Problem.
The following is an example problem, with the coding needed for its solution by DLSODIS. The problem comes from the partial differential equation (the Burgers equation)
du/dt = - u * du/dx + eta * d**2 u/dx**2, eta = .05,
on -1 .le. x .le. 1. The boundary conditions are periodic:
u(-1,t) = u(1,t) and du/dx(-1,t) = du/dx(1,t)
The initial profile is a square wave,
u = 1 in ABS(x) .lt. .5, u = .5 at ABS(x) = .5, u = 0 elsewhere.
The PDE is discretized in x by a simplified Galerkin method,
using piecewise linear basis functions, on a grid of 40 intervals.
The result is a system A * dy/dt = g(y), of size NEQ = 40,
where y(i) is the approximation to u at x = x(i), with
x(i) = -1 + (i-1)*delx, delx = 2/NEQ = .05.
The individual equations in the system are (in order):
(1/6)dy(NEQ)/dt+(4/6)dy(1)/dt+(1/6)dy(2)/dt
= r4d*(y(NEQ)**2-y(2)**2)+eodsq*(y(2)-2*y(1)+y(NEQ))
for i = 2,3,...,nm1,
(1/6)dy(i-1)/dt+(4/6)dy(i)/dt+(1/6)dy(i+1)/dt
= r4d*(y(i-1)**2-y(i+1)**2)+eodsq*(y(i+1)-2*y(i)+y(i-1))
and finally
(1/6)dy(nm1)/dt+(4/6)dy(NEQ)/dt+(1/6)dy(1)/dt
= r4d*(y(nm1)**2-y(1)**2)+eodsq*(y(1)-2*y(NEQ)+y(nm1))
where r4d = 1/(4*delx), eodsq = eta/delx**2 and nm1 = NEQ-1.
The following coding solves the problem with MF = 121, with output of solution statistics at t = .1, .2, .3, and .4, and of the solution vector at t = .4. Optional outputs (run statistics) are also printed.
module c_test1
implicit none
integer,parameter,private :: dp=kind(0.0d0)
real(kind=dp),public :: EODsq, R4D
integer,public :: NM1
end module c_test1
program dlsodis_ex
use m_odepack
use c_test1
implicit none
integer,parameter :: dp=kind(0.0d0)
external :: addasp
external :: jacsp
external :: resid
real(kind=dp),save :: atol,rtol
real(kind=dp) :: delx,t,tout
integer :: i,io,istate,nnzlu
integer,save :: iopt,itask,itol,liw,lrw,mf,neq
integer,dimension(30) :: iw
real(kind=dp),dimension(1409) :: rw
real(kind=dp),dimension(40) :: y,ydoti
data itol/1/,rtol/1.0D-3/,atol/1.0D-3/,itask/1/,iopt/0/
data neq/40/,lrw/1409/,liw/30/,mf/121/
delx = 2.0/neq
R4D = 0.25/delx
EODsq = 0.05/delx**2
NM1 = neq - 1
do i = 1,neq
y(i) = 0.0
enddo
y(11) = 0.5
do i = 12,30
y(i) = 1.0
enddo
y(31) = 0.5
t = 0.0
tout = 0.1
istate = 0
do io = 1,4
call dlsodis(resid,addasp,jacsp,[neq],y,ydoti,t,tout,itol,[rtol], &
& [atol],itask,istate,iopt,rw,lrw,iw,liw,mf)
write (6,99010) t,iw(11),rw(11)
99010 format (' At t =',f5.2,' No. steps =',i4,' Last step =', &
& d12.4)
if ( istate/=2 ) then
write (6,99020) istate
99020 format (///' Error halt.. ISTATE =',i3)
stop 1
else
tout = tout + 0.1
endif
enddo
write (6,99030) (y(i),i=1,neq)
99030 format (/' Final solution values..'/8(5D12.4/))
write (6,99040) iw(17),iw(18),iw(11),iw(12),iw(13)
99040 format (/' Required RW size =',i5,' IW size =', &
& i4/' No. steps =',i4,' No. r-s =',i4,' No. J-s =',i4)
nnzlu = iw(25) + iw(26) + neq
write (6,99050) iw(19),nnzlu
99050 format (' No. of nonzeros in P matrix =',i4, &
&' No. of nonzeros in LU =',i4)
end program dlsodis_ex
subroutine gfun(N,T,Y,G)
use c_test1
implicit none
integer,parameter :: dp=kind(0.0d0)
integer,intent(in) :: N
real(kind=dp) :: T
real(kind=dp),intent(in),dimension(N) :: Y
real(kind=dp),intent(out),dimension(N) :: G
integer :: i
G(1) = R4D*(Y(N)**2-Y(2)**2) + EODsq*(Y(2)-2.0*Y(1)+Y(N))
do i = 2,NM1
G(i) = R4D*(Y(i-1)**2-Y(i+1)**2) + EODsq*(Y(i+1)-2.0*Y(i)+Y(i-1))
enddo
G(N) = R4D*(Y(NM1)**2-Y(1)**2) + EODsq*(Y(1)-2.0*Y(N)+Y(NM1))
end subroutine gfun
subroutine resid(N,T,Y,S,R,Ires)
use c_test1
implicit none
integer,parameter :: dp=kind(0.0d0)
external :: gfun
integer :: N
real(kind=dp) :: T
real(kind=dp),dimension(N) :: Y
real(kind=dp),intent(in),dimension(N) :: S
real(kind=dp),intent(inout),dimension(N) :: R
integer :: Ires
integer :: i
call gfun(N,T,Y,R)
R(1) = R(1) - (S(N)+4.0*S(1)+S(2))/6.0
do i = 2,NM1
R(i) = R(i) - (S(i-1)+4.0*S(i)+S(i+1))/6.0
enddo
R(N) = R(N) - (S(NM1)+4.0*S(N)+S(1))/6.0
end subroutine resid
subroutine addasp(N,T,Y,J,Ip,Jp,P)
implicit none
integer,parameter :: dp=kind(0.0d0)
integer,intent(in) :: N
real(kind=dp) :: T
real(kind=dp),dimension(N) :: Y
integer,intent(in) :: J
integer,dimension(*) :: Ip
integer,dimension(*) :: Jp
real(kind=dp),intent(inout),dimension(N) :: P
integer :: jm1,jp1
jm1 = J - 1
jp1 = J + 1
if ( J==N ) jp1 = 1
if ( J==1 ) jm1 = N
P(J) = P(J) + (2.0/3.0)
P(jp1) = P(jp1) + (1.0/6.0)
P(jm1) = P(jm1) + (1.0/6.0)
end subroutine addasp
subroutine jacsp(N,T,Y,S,J,Ip,Jp,Pdj)
use c_test1
implicit none
integer,parameter :: dp=kind(0.0d0)
integer,intent(in) :: N
real(kind=dp) :: T
real(kind=dp),intent(in),dimension(N) :: Y
real(kind=dp),dimension(N) :: S
integer,intent(in) :: J
integer,dimension(*) :: Ip
integer,dimension(*) :: Jp
real(kind=dp),intent(out),dimension(N) :: Pdj
integer :: jm1,jp1
jm1 = J - 1
jp1 = J + 1
if ( J==1 ) jm1 = N
if ( J==N ) jp1 = 1
Pdj(jm1) = -2.0*R4D*Y(J) + EODsq
Pdj(J) = -2.0*EODsq
Pdj(jp1) = 2.0*R4D*Y(J) + EODsq
end subroutine jacsp
The output of this program (on a CDC-7600 in single precision) is as follows:
At t = 0.10 No. steps = 15 Last step = 1.6863e-02
At t = 0.20 No. steps = 19 Last step = 2.4101e-02
At t = 0.30 No. steps = 22 Last step = 4.3143e-02
At t = 0.40 No. steps = 24 Last step = 5.7819e-02
Final solution values..
1.8371e-02 1.3578e-02 1.5864e-02 2.3805e-02 3.7245e-02
5.6630e-02 8.2538e-02 1.1538e-01 1.5522e-01 2.0172e-01
2.5414e-01 3.1150e-01 3.7259e-01 4.3608e-01 5.0060e-01
5.6482e-01 6.2751e-01 6.8758e-01 7.4415e-01 7.9646e-01
8.4363e-01 8.8462e-01 9.1853e-01 9.4500e-01 9.6433e-01
9.7730e-01 9.8464e-01 9.8645e-01 9.8138e-01 9.6584e-01
9.3336e-01 8.7497e-01 7.8213e-01 6.5315e-01 4.9997e-01
3.4672e-01 2.1758e-01 1.2461e-01 6.6208e-02 3.3784e-02
Required RW size = 1409 IW size = 30
No. steps = 24 No. r-s = 33 No. J-s = 8
No. of nonzeros in P matrix = 120 No. of nonzeros in LU = 194
The user interface to DLSODIS consists of the following parts.
The call sequence to Subroutine DLSODIS, which is a driver routine for the solver. This includes descriptions of both the call sequence arguments and of user-supplied routines. Following these descriptions is a description of optional inputs available through the call sequence, and then a description of optional outputs (in the work arrays).
Descriptions of other routines in the DLSODIS package that may be (optionally) called by the user. These provide the ability to alter error message handling, save and restore the internal Common, and obtain specified derivatives of the solution y(t).
Descriptions of Common blocks to be declared in overlay or similar environments, or to be saved when doing an interrupt of the problem and continued solution later.
Description of two routines in the DLSODIS package, either of which the user may replace with his/her own version, if desired. These relate to the measurement of errors.
The call sequence parameters used for input only are RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, MF,
and those used for both input and output are Y, T, ISTATE, YDOTI.
The work arrays RWORK and IWORK are also used for conditional and optional inputs and optional outputs. (The term output here refers to the return from Subroutine DLSODIS to the user’s calling program.)
The legality of input parameters will be thoroughly checked on the initial call for the problem, but not checked thereafter unless a change in input parameters is flagged by ISTATE = 3 on input.
The descriptions of the call arguments are as follows.
the name of the user-supplied subroutine which supplies the residual vector for the ODE system, defined by
r = g(t,y) - A(t,y) * s
as a function of the scalar t and the vectors s and y (s approximates dy/dt). This subroutine is to have the form
SUBROUTINE RES (NEQ, T, Y, S, R, IRES)
DOUBLE PRECISION T, Y(*), S(*), R(*)
where NEQ, T, Y, S, and IRES are input, and R and IRES are output. Y, S, and R are arrays of length NEQ.
On input, IRES indicates how DLSODIS will use the returned array R, as follows:
IRES = 1 means that DLSODIS needs the full residual,
r = g - A\*s, exactly.
IRES = -1 means that DLSODIS is using R only to compute
the Jacobian dr/dy by difference quotients.
The RES routine can ignore IRES, or it can omit some terms if IRES = -1. If A does not depend on y, then RES can just return R = g when IRES = -1. If g - A*s contains other additive terms that are independent of y, these can also be dropped, if done consistently, when IRES = -1.
The subroutine should set the flag IRES if it encounters a halt condition or illegal input. Otherwise, it should not reset IRES. On output,
IRES = 1 or -1 represents a normal return, and DLSODIS continues integrating the ODE. Leave IRES unchanged from its input value.
IRES = 2 tells DLSODIS to immediately return control to the calling program, with ISTATE = 3. This lets the calling program change parameters of the problem if necessary.
IRES = 3 represents an error condition (for example, an illegal value of y). DLSODIS tries to integrate the system without getting IRES = 3 from RES. If it cannot, DLSODIS returns with ISTATE = -7 or -1.
On a return with ISTATE = 3, -1, or -7, the values of T and Y returned correspond to the last point reached successfully without getting the flag IRES = 2 or 3.
The flag values IRES = 2 and 3 should not be used to handle switches or root-stop conditions. This is better done by calling DLSODIS in a one-step mode and checking the stopping function for a sign change at each step.
If quantities computed in the RES routine are needed externally to DLSODIS, an extra call to RES should be made for this purpose, for consistent and accurate results. To get the current dy/dt for the S argument, use DINTDY.
RES must be declared External in the calling program. See note below for more about RES.
the name of the user-supplied subroutine which adds the matrix A = A(t,y) to another matrix stored in sparse form. This subroutine is to have the form
SUBROUTINE ADDA (NEQ, T, Y, J, IAN, JAN, P)
DOUBLE PRECISION T, Y(*), P(*)
INTEGER IAN(*), JAN(*)
where NEQ, T, Y, J, IAN, JAN, and P are input. This routine should add the J-th column of matrix A to the array P, of length NEQ. Thus a(i,J) is to be added to P(i) for all relevant values of i. Here T and Y have the same meaning as in Subroutine RES, and J is a column index (1 to NEQ). IAN and JAN are undefined in calls to ADDA for structure determination (MOSS .ne. 0). Otherwise, IAN and JAN are structure descriptors, as defined under optional outputs below, and so can be used to determine the relevant row indices i, if desired.
Calls to ADDA are made with J = 1,…,NEQ, in that order. ADDA must not alter its input arguments.
ADDA must be declared External in the calling program. See note below for more information about ADDA.
the name of the user-supplied subroutine which supplies the Jacobian matrix, dr/dy, where r = g - A*s. JAC is required if MITER = 1, or MOSS = 1 or 3. Otherwise a dummy name can be passed. This subroutine is to have the form
SUBROUTINE JAC (NEQ, T, Y, S, J, IAN, JAN, PDJ)
DOUBLE PRECISION T, Y(*), S(*), PDJ(*)
INTEGER IAN(*), JAN(*)
where NEQ, T, Y, S, J, IAN, and JAN are input. The array PDJ, of length NEQ, is to be loaded with column J of the Jacobian on output. Thus dr(i)/dy(J) is to be loaded into PDJ(i) for all relevant values of i.
Here T, Y, and S have the same meaning as in Subroutine RES, and J is a column index (1 to NEQ). IAN and JAN are undefined in calls to JAC for structure determination (MOSS .ne. 0). Otherwise, IAN and JAN are structure descriptors, as defined under optional outputs below, and so can be used to determine the relevant row indices i, if desired.
JAC need not provide dr/dy exactly. A crude approximation (possibly with greater sparsity) will do.
In any case, PDJ is preset to zero by the solver, so that only the nonzero elements need be loaded by JAC. Calls to JAC are made with J = 1,…,NEQ, in that order, and each such set of calls is preceded by a call to RES with the same arguments NEQ, T, Y, S, and IRES. Thus to gain some efficiency intermediate quantities shared by both calculations may be saved in a user Common block by RES and not recomputed by JAC, if desired. JAC must not alter its input arguments.
JAC must be declared External in the calling program.
See note below for more about JAC.
Note on RES, ADDA, and JAC:
These subroutines may access user-defined quantities in NEQ(2),… and/or in Y(NEQ(1)+1),… if NEQ is an array (dimensioned in the subroutines) and/or Y has length exceeding NEQ(1). However, these subroutines should not alter NEQ(1), Y(1),…,Y(NEQ) or any other input variables. See the descriptions of NEQ and Y below.
the size of the system (number of first order ordinary differential equations or scalar algebraic equations). Used only for input. NEQ may be decreased, but not increased, during the problem. If NEQ is decreased (with ISTATE = 3 on input), the remaining components of Y should be left undisturbed, if these are to be accessed in RES, ADDA, or JAC.
Normally, NEQ is a scalar, and it is generally referred to as a scalar in this user interface description. However, NEQ may be an array, with NEQ(1) set to the system size. (The DLSODIS package accesses only NEQ(1).) In either case, this parameter is passed as the NEQ argument in all calls to RES, ADDA, and JAC. Hence, if it is an array, locations NEQ(2),… may be used to store other integer data and pass it to RES, ADDA, or JAC. Each such subroutine must include NEQ in a Dimension statement in that case.
a real array for the vector of dependent variables, of length NEQ or more. Used for both input and output on the first call (ISTATE = 0 or 1), and only for output on other calls. On the first call, Y must contain the vector of initial values. On output, Y contains the computed solution vector, evaluated at T. If desired, the Y array may be used for other purposes between calls to the solver.
This array is passed as the Y argument in all calls to RES, ADDA, and JAC. Hence its length may exceed NEQ, and locations Y(NEQ+1),… may be used to store other real data and pass it to RES, ADDA, or JAC. (The DLSODIS package accesses only Y(1),…,Y(NEQ). )
a real array for the initial value of the vector dy/dt and for work space, of dimension at least NEQ.
On input:
If ISTATE = 0 then DLSODIS will compute the initial value of dy/dt, if A is nonsingular. Thus YDOTI will serve only as work space and may have any value.
If ISTATE = 1 then YDOTI must contain the initial value of dy/dt.
If ISTATE = 2 or 3 (continuation calls) then YDOTI may have any value.
Note: If the initial value of A is singular, then DLSODIS cannot compute the initial value of dy/dt, so it must be provided in YDOTI, with ISTATE = 1.
On output, when DLSODIS terminates abnormally with ISTATE = -1, -4, or -5, YDOTI will contain the residual r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near its initial value, and YDOTI is supplied with ISTATE = 1, there may have been an incorrect input value of YDOTI = dy/dt, or the problem (as given to DLSODIS) may not have a solution.
If desired, the YDOTI array may be used for other purposes between calls to the solver.
the independent variable. On input, T is used only on the first call, as the initial point of the integration. On output, after each call, T is the value at which a computed solution y is evaluated (usually the same as TOUT). On an error return, T is the farthest point reached.
the next value of t at which a computed solution is desired. Used only for input.
When starting the problem (ISTATE = 0 or 1), TOUT may be equal to T for one call, then should .ne. T for the next call. For the initial T, an input value of TOUT .ne. T is used in order to determine the direction of the integration (i.e. the algebraic sign of the step sizes) and the rough scale of the problem. Integration in either direction (forward or backward in t) is permitted.
If ITASK = 2 or 5 (one-step modes), TOUT is ignored after the first call (i.e. the first call with TOUT .ne. T). Otherwise, TOUT is required on every call.
If ITASK = 1, 3, or 4, the values of TOUT need not be monotone, but a value of TOUT which backs up is limited to the current internal T interval, whose endpoints are TCUR - HU and TCUR (see optional outputs, below, for TCUR and HU).
an indicator for the type of error control. See description below under ATOL. Used only for input.
a relative error tolerance parameter, either a scalar or an array of length NEQ. See description below under ATOL. Input only.
an absolute error tolerance parameter, either a scalar or an array of length NEQ. Input only.
The input parameters ITOL, RTOL, and ATOL determine the error control performed by the solver. The solver will control the vector E = (E(i)) of estimated local errors in y, according to an inequality of the form
RMS-norm of ( E(i)/EWT(i) ) .le. 1,
where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i),
and the RMS-norm (root-mean-square norm) here is RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) is a vector of weights which must always be positive, and the values of RTOL and ATOL should all be non-negative. The following table gives the types (scalar/array) of RTOL and ATOL, and the corresponding form of EWT(i).
| ITOL | RTOL | ATOL | EWT(i) |
|---|---|---|---|
| 1 | scalar | scalar | RTOL*ABS(Y(i)) + ATOL |
| 2 | scalar | array | RTOL*ABS(Y(i)) + ATOL(i) |
| 3 | array | scalar | RTOL(i)*ABS(Y(i)) + ATOL |
| 4 | array | scalar | RTOL(i)*ABS(Y(i)) + ATOL(i) |
When either of these parameters is a scalar, it need not be dimensioned in the user’s calling program.
If none of the above choices (with ITOL, RTOL, and ATOL fixed throughout the problem) is suitable, more general error controls can be obtained by substituting user-supplied routines for the setting of EWT and/or for the norm calculation. See Part 4 below.
If global errors are to be estimated by making a repeated run on the same problem with smaller tolerances, then all components of RTOL and ATOL (i.e. of EWT) should be scaled down uniformly.
an index specifying the task to be performed. Input only. ITASK has the following values and meanings.
| value | description |
|---|---|
| 1 | means normal computation of output values of y(t) at |
| t = TOUT (by overshooting and interpolating). | |
| 2 | means take one step only and return. |
| 3 | means stop at the first internal mesh point at or |
| beyond t = TOUT and return. | |
| 4 | means normal computation of output values of y(t) at |
| t = TOUT but without overshooting t = TCRIT. | |
| TCRIT must be input as RWORK(1). TCRIT may be equal to | |
| or beyond TOUT, but not behind it in the direction of | |
| integration. This option is useful if the problem | |
| has a singularity at or beyond t = TCRIT. | |
| 5 | means take one step, without passing TCRIT, and return. |
| TCRIT must be input as RWORK(1). |
Note: If ITASK = 4 or 5 and the solver reaches TCRIT (within roundoff), it will return T = TCRIT (exactly) to indicate this (unless ITASK = 4 and TOUT comes before TCRIT, in which case answers at t = TOUT are returned first).
an index used for input and output to specify the state of the calculation.
On input, the values of ISTATE are as follows.
| value | description |
|---|---|
| 0 | means this is the first call for the problem, and |
| DLSODIS is to compute the initial value of dy/dt | |
| (while doing other initializations). See note below. | |
| 1 | means this is the first call for the problem, and |
| the initial value of dy/dt has been supplied in | |
| YDOTI (DLSODIS will do other initializations). | |
| See note below. | |
| 2 | means this is not the first call, and the calculation |
| is to continue normally, with no change in any input | |
| parameters except possibly TOUT and ITASK. | |
| (If ITOL, RTOL, and/or ATOL are changed between calls | |
| with ISTATE = 2, the new values will be used but not | |
| tested for legality.) | |
| 3 | means this is not the first call, and the |
| calculation is to continue normally, but with | |
| a change in input parameters other than | |
| TOUT and ITASK. Changes are allowed in | |
| NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, | |
| the conditional inputs IA, JA, IC, and JC, | |
| and any of the optional inputs except H0. | |
| A call with ISTATE = 3 will cause the sparsity | |
| structure of the problem to be recomputed. | |
| (Structure information is reread from IA and JA if | |
| MOSS = 0, 3, or 4 and from IC and JC if MOSS = 0). |
Note: A preliminary call with TOUT = T is not counted as a first call here, as no initialization or checking of input is done. (Such a call is sometimes useful for the purpose of outputting the initial conditions.) Thus the first call for which TOUT .ne. T requires ISTATE = 0 or 1 on input.
On output, ISTATE has the following values and meanings.
| value | description |
|---|---|
| 0 or 1 | means nothing was done; TOUT = T and |
| ISTATE = 0 or 1 on input. | |
| 2 | means that the integration was performed successfully. |
| 3 | means that the user-supplied Subroutine RES signalled |
| DLSODIS to halt the integration and return (IRES = 2). | |
| Integration as far as T was achieved with no occurrence | |
| of IRES = 2, but this flag was set on attempting the | |
| next step. | |
| -1 | means an excessive amount of work (more than MXSTEP |
| steps) was done on this call, before completing the | |
| requested task, but the integration was otherwise | |
| successful as far as T. (MXSTEP is an optional input | |
| and is normally 500.) To continue, the user may | |
| simply reset ISTATE to a value .gt. 1 and call again | |
| (the excess work step counter will be reset to 0). | |
| In addition, the user may increase MXSTEP to avoid | |
| this error return (see below on optional inputs). | |
| -2 | means too much accuracy was requested for the precision |
| of the machine being used. This was detected before | |
| completing the requested task, but the integration | |
| was successful as far as T. To continue, the tolerance | |
| parameters must be reset, and ISTATE must be set | |
| to 3. The optional output TOLSF may be used for this | |
| purpose. (Note: If this condition is detected before | |
| taking any steps, then an illegal input return | |
| (ISTATE = -3) occurs instead.) | |
| -3 | means illegal input was detected, before taking any |
| integration steps. See written message for details. | |
| Note: If the solver detects an infinite loop of calls | |
| to the solver with illegal input, it will cause | |
| the run to stop. | |
| -4 | means there were repeated error test failures on |
| one attempted step, before completing the requested | |
| task, but the integration was successful as far as T. | |
| The problem may have a singularity, or the input | |
| may be inappropriate. | |
| -5 | means there were repeated convergence test failures on |
| one attempted step, before completing the requested | |
| task, but the integration was successful as far as T. | |
| This may be caused by an inaccurate Jacobian matrix. | |
| -6 | means EWT(i) became zero for some i during the |
| integration. Pure relative error control (ATOL(i) = 0.0) | |
| was requested on a variable which has now vanished. | |
| the integration was successful as far as T. | |
| -7 | means that the user-supplied Subroutine RES set |
| its error flag (IRES = 3) despite repeated tries by | |
| DLSODIS to avoid that condition. | |
| -8 | means that ISTATE was 0 on input but DLSODIS was unable |
| to compute the initial value of dy/dt. See the | |
| printed message for details. | |
| -9 | means a fatal error return flag came from the sparse |
| solver CDRV by way of DPRJIS or DSOLSS (numerical | |
| factorization or backsolve). This should never happen. | |
| The integration was successful as far as T. |
Note: An error return with ISTATE = -1, -4, or -5 may mean that the sparsity structure of the problem has changed significantly since it was last determined (or input). In that case, one can attempt to complete the integration by setting ISTATE = 3 on the next call, so that a new structure determination is done.
Note: Since the normal output value of ISTATE is 2, it does not need to be reset for normal continuation. similarly, ISTATE (= 3) need not be reset if RES told DLSODIS to return because the calling program must change the parameters of the problem. Also, since a negative input value of ISTATE will be regarded as illegal, a negative output value requires the user to change it, and possibly other inputs, before calling the solver again.
an integer flag to specify whether or not any optional inputs are being used on this call. Input only. The optional inputs are listed separately below.
IOPT = 0 means no optional inputs are being used.
Default values will be used in all cases.
IOPT = 1 means one or more optional inputs are being used.
a work array used for a mixture of real (double precision) and integer work space.
The length of RWORK (in real words) must be at least
20 + NYH*(MAXORD + 1) + 3*NEQ + LWM
where
NYH = the initial value of NEQ,
MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a
smaller value is given as an optional input),
LWM = 2*NNZ + 2*NEQ + (NNZ+9*NEQ)/LENRAT if MITER = 1,
LWM = 2*NNZ + 2*NEQ + (NNZ+10*NEQ)/LENRAT if MITER = 2.
in the above formulas,
NNZ = number of nonzero elements in the iteration matrix
P = A - con*J (con is a constant and J is the
Jacobian matrix dr/dy).
LENRAT = the real to integer wordlength ratio (usually 1 in
single precision and 2 in double precision).
(See the MF description for METH and MITER.)
Thus if MAXORD has its default value and NEQ is constant, the minimum length of RWORK is:
20 + 16*NEQ + LWM for MF = 11, 111, 311, 12, 212, 412,
20 + 9*NEQ + LWM for MF = 21, 121, 321, 22, 222, 422.
The above formula for LWM is only a crude lower bound. The required length of RWORK cannot be readily predicted in general, as it depends on the sparsity structure of the problem. Some experimentation may be necessary.
The first 20 words of RWORK are reserved for conditional and optional inputs and optional outputs.
The following word in RWORK is a conditional input:
RWORK(1) = TCRIT = critical value of t which the solver
is not to overshoot. Required if ITASK is
4 or 5, and ignored otherwise. (See ITASK.)
the length of the array RWORK, as declared by the user. (This will be checked by the solver.)
an integer work array. The length of IWORK must be at least
32 + 2*NEQ + NZA + NZC for MOSS = 0,
30 for MOSS = 1 or 2,
31 + NEQ + NZA for MOSS = 3 or 4.
(NZA is the number of nonzero elements in matrix A, and NZC is the number of nonzero elements in dr/dy.)
In DLSODIS, IWORK is used for conditional and optional inputs and optional outputs.
The following two blocks of words in IWORK are conditional inputs, required if MOSS = 0, 3, or 4, but not otherwise (see the description of MF for MOSS).
IWORK(30+j) = IA(j) (j=1,...,NEQ+1)
IWORK(31+NEQ+k) = JA(k) (k=1,...,NZA)
The two arrays IA and JA describe the sparsity structure to be assumed for the matrix A. JA contains the row indices where nonzero elements occur, reading in columnwise order, and IA contains the starting locations in JA of the descriptions of columns 1,…,NEQ, in that order, with IA(1) = 1. Thus, for each column index j = 1,…,NEQ, the values of the row index i in column j where a nonzero element may occur are given by
i = JA(k), where IA(j) .le. k .lt. IA(j+1).
If NZA is the total number of nonzero locations assumed, then the length of the JA array is NZA, and IA(NEQ+1) must be NZA + 1. Duplicate entries are not allowed. The following additional blocks of words are required if MOSS = 0, but not otherwise. If LC = 31 + NEQ + NZA, then
IWORK(LC+j) = IC(j) (j=1,...,NEQ+1), and
IWORK(LC+NEQ+1+k) = JC(k) (k=1,...,NZC)
The two arrays IC and JC describe the sparsity structure to be assumed for the Jacobian matrix dr/dy. They are used in the same manner as the above IA and JA arrays. If NZC is the number of nonzero locations assumed, then the length of the JC array is NZC, and IC(NEQ+1) must be NZC + 1. Duplicate entries are not allowed.
the length of the array IWORK, as declared by the user. (This will be checked by the solver.)
Note: The work arrays must not be altered between calls to DLSODIS for the same problem, except possibly for the conditional and optional inputs, and except for the last 3*NEQ words of RWORK. The latter space is used for internal scratch space, and so is available for use by the user outside DLSODIS between calls, if desired (but not for use by RES, ADDA, or JAC).
the method flag. Used only for input. MF has three decimal digits– MOSS, METH, and MITER. For standard options:
MF = 100*MOSS + 10*METH + MITER.
MOSS indicates the method to be used to obtain the sparsity structure of the Jacobian matrix:
| MOSS | Description |
|---|---|
| 0 | means the user has supplied IA, JA, IC, and JC |
| (see descriptions under IWORK above). | |
| 1 | means the user has supplied JAC (see below) and |
| the structure will be obtained from NEQ initial | |
| calls to JAC and NEQ initial calls to ADDA. | |
| 2 | means the structure will be obtained from NEQ+1 |
| initial calls to RES and NEQ initial calls to ADDA | |
| 3 | like MOSS = 1, except user has supplied IA and JA. |
| 4 | like MOSS = 2, except user has supplied IA and JA. |
METH indicates the basic linear multistep method:
| METH | Description |
|---|---|
| 1 | means the implicit Adams method. |
| 2 | means the method based on Backward |
| Differentiation Formulas (BDFs). |
The BDF method is strongly preferred for stiff problems, while the Adams method is preferred when the problem is not stiff. If the matrix A(t,y) is nonsingular, stiffness here can be taken to mean that of the explicit ODE system dy/dt = A-inverse * g. If A is singular, the concept of stiffness is not well defined.
If you do not know whether the problem is stiff, we recommend using METH = 2. If it is stiff, the advantage of METH = 2 over METH = 1 will be great, while if it is not stiff, the advantage of METH = 1 will be slight. If maximum efficiency is important, some experimentation with METH may be necessary.
MITER indicates the corrector iteration method:
| METH | Description |
|---|---|
| 1 | means chord iteration with a user-supplied |
| sparse Jacobian, given by Subroutine JAC. | |
| 2 | means chord iteration with an internally |
| generated (difference quotient) sparse | |
| Jacobian (using NGP extra calls to RES per | |
| dr/dy value, where NGP is an optional | |
| output described below.) |
If MITER = 1 or MOSS = 1 or 3 the user must supply a Subroutine JAC (the name is arbitrary) as described above under JAC. Otherwise, a dummy argument can be used.
The standard choices for MF are:
| MF | Description |
|---|---|
| 21 or 22 | for a stiff problem with IA/JA and IC/JC |
| supplied, | |
| 121 | for a stiff problem with JAC supplied, but not |
| IA/JA or IC/JC, | |
| 222 | for a stiff problem with neither IA/JA, IC/JC/, |
| nor JAC supplied, | |
| 321 | for a stiff problem with IA/JA and JAC supplied, |
| but not IC/JC, | |
| 422 | for a stiff problem with IA/JA supplied, but not |
| IC/JC or JAC. |
The sparseness structure can be changed during the problem by making a call to DLSODIS with ISTATE = 3.
Optional Inputs.
The following is a list of the optional inputs provided for in the call sequence. (See also Part 2.) For each such input variable, this table lists its name as used in this documentation, its location in the call sequence, its meaning, and the default value. The use of any of these inputs requires IOPT = 1, and in that case all of these inputs are examined. A value of zero for any of these optional inputs will cause the default value to be used. Thus to use a subset of the optional inputs, simply preload locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and then set those of interest to nonzero values.
| Name | Location | Meaning and Default Value |
|---|---|---|
| H0 | RWORK(5) | the step size to be attempted on the first step. |
| The default value is determined by the solver. | ||
| HMAX | RWORK(6) | the maximum absolute step size allowed. |
| The default value is infinite. | ||
| HMIN | RWORK(7) | the minimum absolute step size allowed. |
| The default value is 0. (This lower bound is not | ||
| enforced on the final step before reaching TCRIT | ||
| when ITASK = 4 or 5.) | ||
| MAXORD | IWORK(5) | the maximum order to be allowed. The default |
| value is 12 if METH = 1, and 5 if METH = 2. | ||
| If MAXORD exceeds the default value, it will | ||
| be reduced to the default value. | ||
| If MAXORD is changed during the problem, it may | ||
| cause the current order to be reduced. | ||
| MXSTEP | IWORK(6) | maximum number of (internally defined) steps |
| allowed during one call to the solver. | ||
| The default value is 500. | ||
| MXHNIL | IWORK(7) | maximum number of messages printed (per problem) |
| warning that T + H = T on a step (H = step size). | ||
| This must be positive to result in a non-default | ||
| value. The default value is 10. |
As optional additional output from DLSODIS, the variables listed below are quantities related to the performance of DLSODIS which are available to the user. These are communicated by way of the work arrays, but also have internal mnemonic names as shown.
Except where stated otherwise, all of these outputs are defined on any successful return from DLSODIS, and on any return with ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal input) or -8, they will be unchanged from their existing values (if any), except possibly for TOLSF, LENRW, and LENIW.
On any error return, outputs relevant to the error will be defined, as noted below.
| Name | Location | Meaning |
|---|---|---|
| HU | RWORK(11) | the step size in t last used (successfully). |
| HCUR | RWORK(12) | the step size to be attempted on the next step. |
| TCUR | RWORK(13) | the current value of the independent variable |
| which the solver has actually reached, i.e. the | ||
| current internal mesh point in t. On output, TCUR | ||
| will always be at least as far as the argument | ||
| T, but may be farther (if interpolation was done). | ||
| TOLSF | RWORK(14) | a tolerance scale factor, greater than 1.0, |
| computed when a request for too much accuracy was | ||
| detected (ISTATE = -3 if detected at the start of | ||
| the problem, ISTATE = -2 otherwise). If ITOL is | ||
| left unaltered but RTOL and ATOL are uniformly | ||
| scaled up by a factor of TOLSF for the next call, | ||
| then the solver is deemed likely to succeed. | ||
| (The user may also ignore TOLSF and alter the | ||
| tolerance parameters in any other way appropriate.) | ||
| NST | IWORK(11) | the number of steps taken for the problem so far. |
| NRE | IWORK(12) | the number of residual evaluations (RES calls) |
| for the problem so far, excluding those for | ||
| structure determination (MOSS = 2 or 4). | ||
| NJE | IWORK(13) | the number of Jacobian evaluations (each involving |
| an evaluation of A and dr/dy) for the problem so | ||
| far, excluding those for structure determination | ||
| (MOSS = 1 or 3). This equals the number of calls | ||
| to ADDA and (if MITER = 1) JAC. | ||
| NQU | IWORK(14) | the method order last used (successfully). |
| NQCUR | IWORK(15) | the order to be attempted on the next step. |
| IMXER | IWORK(16) | the index of the component of largest magnitude in |
| the weighted local error vector ( E(i)/EWT(i) ), | ||
| on an error return with ISTATE = -4 or -5. | ||
| LENRW | IWORK(17) | the length of RWORK actually required. |
| This is defined on normal returns and on an illegal | ||
| input return for insufficient storage. | ||
| LENIW | IWORK(18) | the length of IWORK actually required. |
| This is defined on normal returns and on an illegal | ||
| input return for insufficient storage. | ||
| NNZ | IWORK(19) | the number of nonzero elements in the iteration |
| matrix P = A - con*J (con is a constant and | ||
| J is the Jacobian matrix dr/dy). | ||
| NGP | IWORK(20) | the number of groups of column indices, used in |
| difference quotient Jacobian aproximations if | ||
| MITER = 2. This is also the number of extra RES | ||
| evaluations needed for each Jacobian evaluation. | ||
| NLU | IWORK(21) | the number of sparse LU decompositions for the |
| problem so far. (Excludes the LU decomposition | ||
| necessary when ISTATE = 0.) | ||
| LYH | IWORK(22) | the base address in RWORK of the history array YH, |
| described below in this list. | ||
| IPIAN | IWORK(23) | the base address of the structure descriptor array |
| IAN, described below in this list. | ||
| IPJAN | IWORK(24) | the base address of the structure descriptor array |
| JAN, described below in this list. | ||
| NZL | IWORK(25) | the number of nonzero elements in the strict lower |
| triangle of the LU factorization used in the chord | ||
| iteration. | ||
| NZU | IWORK(26) | the number of nonzero elements in the strict upper |
| triangle of the LU factorization used in the chord | ||
| iteration. The total number of nonzeros in the | ||
| factorization is therefore NZL + NZU + NEQ. |
The following four arrays are segments of the RWORK array which may also be of interest to the user as optional outputs. For each array, the table below gives its internal name, its base address, and its description.
For YH and ACOR, the base addresses are in RWORK (a real array). The integer arrays IAN and JAN are to be obtained by declaring an integer array IWK and identifying IWK(1) with RWORK(21), using either an equivalence statement or a subroutine call. Then the base addresses IPIAN (of IAN) and IPJAN (of JAN) in IWK are to be obtained as optional outputs IWORK(23) and IWORK(24), respectively.
Thus IAN(1) is IWK(ipian), etc.
| Name | Base Address | Description |
|---|---|---|
| IAN | IPIAN (in IWK) | structure descriptor array of size NEQ + 1. |
| JAN | IPJAN (in IWK) | structure descriptor array of size NNZ. |
| (see above) | IAN and JAN together describe the sparsity | |
| structure of the iteration matrix | ||
| P = A - con*J, as used by DLSODIS. | ||
| JAN contains the row indices of the nonzero | ||
| locations, reading in columnwise order, and | ||
| IAN contains the starting locations in JAN of | ||
| the descriptions of columns 1,…,NEQ, in | ||
| that order, with IAN(1) = 1. Thus for each | ||
| j = 1,…,NEQ, the row indices i of the | ||
| nonzero locations in column j are | ||
| i = JAN(k), IAN(j) .le. k .lt. IAN(j+1). | ||
| Note that IAN(NEQ+1) = NNZ + 1. | ||
| YH | LYH | the Nordsieck history array, of size NYH by |
| (optional | (NQCUR + 1), where NYH is the initial value | |
| output) | of NEQ. For j = 0,1,…,NQCUR, column j+1 | |
| of YH contains HCUR**j/factorial(j) times | ||
| the j-th derivative of the interpolating | ||
| polynomial currently representing the solution, | ||
| evaluated at t = TCUR. The base address LYH | ||
| is another optional output, listed above. | ||
| ACOR | LENRW-NEQ+1 | array of size NEQ used for the accumulated |
| corrections on each step, scaled on output to | ||
| represent the estimated local error in y on the | ||
| last step. This is the vector E in the | ||
| description of the error control. It is defined | ||
| only on a return from DLSODIS with ISTATE = 2. |
The following are optional calls which the user may make to gain additional capabilities in conjunction with DLSODIS. (The routines XSETUN and XSETF are designed to conform to the SLATEC error handling package.)
| Form of Call | Function |
|---|---|
| CALL XSETUN(LUN) | Set the logical unit number, LUN, for |
| output of messages from DLSODIS, if | |
| The default is not desired. | |
| The default value of LUN is 6. | |
| CALL XSETF(MFLAG) | Set a flag to control the printing of |
| messages by DLSODIS. | |
| MFLAG = 0 means do not print. (Danger: | |
| This risks losing valuable information.) | |
| MFLAG = 1 means print (the default). | |
| Either of the above calls may be made at | |
| any time and will take effect immediately. | |
| CALL DSRCMS(RSAV,ISAV,JOB) | saves and restores the contents of |
| the internal Common blocks used by | |
| DLSODIS (see Part 3 below). | |
| RSAV must be a real array of length 224 | |
| or more, and ISAV must be an integer | |
| array of length 71 or more. | |
| JOB=1 means save into RSAV/ISAV. | |
| JOB=2 means restore from RSAV/ISAV. | |
| DSRCMS is useful if one is | |
| interrupting a run and restarting | |
| later, or alternating between two or | |
| more problems solved with DLSODIS. | |
| CALL DINTDY(,,,,,) | Provide derivatives of y, of various |
| (see below) | orders, at a specified point t, if |
| desired. It may be called only after | |
| a successful return from DLSODIS. |
The detailed instructions for using DINTDY are as follows. The form of the call is:
LYH = IWORK(22)
CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG)
The input parameters are:
value of independent variable where answers are desired (normally the same as the T last returned by DLSODIS). For valid results, T must lie between TCUR - HU and TCUR. (See optional outputs for TCUR and HU.)
integer order of the derivative desired. K must satisfy 0 .le. K .le. NQCUR, where NQCUR is the current order (see optional outputs). The capability corresponding to K = 0, i.e. computing y(t), is already provided by DLSODIS directly. Since NQCUR .ge. 1, the first derivative dy/dt is always available with DINTDY.
the base address of the history array YH, obtained as an optional output as shown above.
column length of YH, equal to the initial value of NEQ.
The output parameters are:
a real array of length NEQ containing the computed value of the K-th derivative of y(t).
integer flag, returned as 0 if K and T were legal, -1 if K was illegal, and -2 if T was illegal. On an error return, a message is also written.
If the solution of a given problem by DLSODIS is to be interrupted and then later continued, such as when restarting an interrupted run or alternating between two or more problems, the user should save, following the return from the last DLSODIS call prior to the interruption, the contents of the call sequence variables and the internal state variables, and later restore these values before the next DLSODIS call for that problem. To save and restore the program state, use Subroutines DSRCMS (see Part 2 above).
Below are descriptions of two routines in the DLSODIS package which relate to the measurement of errors. Either routine can be replaced by a user-supplied version, if desired. However, since such a replacement may have a major impact on performance, it should be done only when absolutely necessary, and only with great caution. (Note: The means by which the package version of a routine is superseded by the user’s version may be system-dependent.)
The following subroutine is called just before each internal integration step, and sets the array of error weights, EWT, as described under ITOL/RTOL/ATOL above:
SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT)
where NEQ, ITOL, RTOL, and ATOL are as in the DLSODIS call sequence, YCUR contains the current dependent variable vector, and EWT is the array of weights set by DEWSET.
If the user supplies this subroutine, it must return in EWT(i) (i = 1,…,NEQ) a positive quantity suitable for comparing errors in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM routine (see below), and also used by DLSODIS in the computation of the optional output IMXER, and the increments for difference quotient Jacobians.
In the user-supplied version of DEWSET, it may be desirable to use the current values of derivatives of y. Derivatives up to order NQ are available from the history array YH, described above under optional outputs. In DEWSET, YH is identical to the YCUR array, extended to NQ + 1 columns with a column length of NYH and scale factors of H**j/factorial(j). On the first call for the problem, given by NST = 0, NQ is 1 and H is temporarily set to 1.0. NYH is the initial value of NEQ. The quantities NQ, H, and NST can be obtained by including in DEWSET the statements:
DOUBLE PRECISION RLS
COMMON /DLS001/ RLS(218),ILS(37)
NQ = ILS(33)
NST = ILS(34)
H = RLS(212)
Thus, for example, the current value of dy/dt can be obtained as YCUR(NYH+i)/H (i=1,…,NEQ) (and the division by H is unnecessary when NST = 0).
The following is a real function routine which computes the weighted root-mean-square norm of a vector v:
D = DVNORM (N, V, W)
where:
N = the length of the vector,
V = real array of length N containing the vector,
W = real array of length N containing weights,
D = SQRT( (1/N) * sum(V(i)*W(i))**2 ).
DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where EWT is as set by Subroutine DEWSET.
If the user supplies this function, it should return a non-negative value of DVNORM suitable for use in the error control in DLSODIS. None of the arguments should be altered by DVNORM. For example, a user-supplied DVNORM routine might: - substitute a max-norm of (V(i)*w(I)) for the RMS-norm, or - ignore some components of V in the norm, with the effect of suppressing the error control on those components of y.
References: 1. M. K. Seager and S. Balsdon, LSODIS, A Sparse Implicit ODE Solver, in Proceedings of the IMACS 10th World Congress, Montreal, August 8-13, 1982.
Alan C. Hindmarsh, LSODE and LSODI, Two New Initial Value Ordinary Differential Equation Solvers, ACM-SIGNUM Newsletter, vol. 15, no. 4 (1980), pp. 10-11.
S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, Yale Sparse Matrix Package: I. The Symmetric Codes, Int. J. Num. Meth. Eng., vol. 18 (1982), pp. 1145-1151.
S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, Yale Sparse Matrix Package: II. The Nonsymmetric Codes, Research Report No. 114, Dept. of Computer Sciences, Yale University, 1977.
DLSODIS is derived from the 18 November 2003 version of Livermore Solver for Ordinary Differential Equations package ODEPACK, (Implicit form) with general Sparse Jacobian matrices.
Authors: Alan C. Hindmarsh Center for Applied Scientific Computing, L-561 Lawrence Livermore National Laboratory Livermore, CA 94551 and Sheila Balsdon Zycor, Inc. Austin, TX 78741
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real | :: | res | ||||
| real | :: | adda | ||||
| integer | :: | jac | ||||
| integer | :: | Neq(*) | ||||
| real(kind=dp) | :: | Y(*) | ||||
| real(kind=dp) | :: | Ydoti(*) | ||||
| real(kind=dp), | intent(inout) | :: | T | |||
| real(kind=dp), | intent(inout) | :: | Tout | |||
| integer | :: | Itol | ||||
| real(kind=dp) | :: | Rtol(*) | ||||
| real(kind=dp) | :: | Atol(*) | ||||
| integer | :: | Itask | ||||
| integer | :: | Istate | ||||
| integer | :: | Iopt | ||||
| real(kind=dp), | intent(inout) | :: | Rwork(Lrw) | |||
| integer | :: | Lrw | ||||
| integer, | intent(inout) | :: | Iwork(Liw) | |||
| integer | :: | Liw | ||||
| integer | :: | Mf |
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| real(kind=dp), | public | :: | atoli | ||||
| real(kind=dp), | public | :: | ayi | ||||
| real(kind=dp), | public | :: | big | ||||
| real(kind=dp), | public | :: | ewti | ||||
| real(kind=dp), | public | :: | h0 | ||||
| real(kind=dp), | public | :: | hmax | ||||
| real(kind=dp), | public | :: | hmx | ||||
| integer, | public | :: | i | ||||
| integer, | public | :: | i1 | ||||
| integer, | public | :: | i2 | ||||
| integer, | public | :: | ier | ||||
| integer, | public | :: | iflag | ||||
| integer, | public | :: | igo | ||||
| logical, | public | :: | ihit | ||||
| integer, | public | :: | imax | ||||
| integer, | public | :: | imul | ||||
| integer, | public | :: | imxer | ||||
| integer, | public | :: | ipflag | ||||
| integer, | public | :: | ipgo | ||||
| integer, | public | :: | irem | ||||
| integer, | public | :: | ires | ||||
| integer, | public | :: | j | ||||
| integer, | public | :: | kgo | ||||
| integer, | public | :: | leniw | ||||
| integer, | public, | save | :: | lenrat | |||
| integer, | public | :: | lenrw | ||||
| integer, | public | :: | lenyht | ||||
| integer, | public | :: | lia | ||||
| integer, | public | :: | lic | ||||
| integer, | public | :: | lja | ||||
| integer, | public | :: | ljc | ||||
| integer, | public | :: | lrtem | ||||
| integer, | public | :: | lwtem | ||||
| integer, | public | :: | lyd0 | ||||
| integer, | public | :: | lyhd | ||||
| integer, | public | :: | lyhn | ||||
| integer, | public | :: | mf1 | ||||
| integer, | public, | save | :: | mord(2) | |||
| character(len=60), | public | :: | msg | ||||
| integer, | public, | save | :: | mxhnl0 | |||
| integer, | public, | save | :: | mxstp0 | |||
| integer, | public | :: | ncolm | ||||
| real(kind=dp), | public | :: | rh | ||||
| real(kind=dp), | public | :: | rtoli | ||||
| real(kind=dp), | public | :: | size | ||||
| real(kind=dp), | public | :: | sum | ||||
| real(kind=dp), | public | :: | tcrit | ||||
| real(kind=dp), | public | :: | tdist | ||||
| real(kind=dp), | public | :: | tnext | ||||
| real(kind=dp), | public | :: | tol | ||||
| real(kind=dp), | public | :: | tolsf | ||||
| real(kind=dp), | public | :: | tp | ||||
| real(kind=dp), | public | :: | w0 |
subroutine dlsodis(res,adda,jac,Neq,Y,Ydoti,T,Tout,Itol,Rtol,Atol,Itask,Istate,Iopt,Rwork,Lrw,Iwork,Liw,Mf) external res external adda external jac integer :: Neq(*) real(kind=dp) :: Y(*) real(kind=dp) :: Ydoti(*) real(kind=dp), intent(inout) :: T real(kind=dp), intent(inout) :: Tout integer :: Itol real(kind=dp) :: Rtol(*) real(kind=dp) :: Atol(*) integer :: Itask integer :: Istate integer :: Iopt integer :: Lrw real(kind=dp),intent(inout) :: Rwork(Lrw) integer :: Liw integer,intent(inout) :: Iwork(Liw) integer :: Mf real(kind=dp) :: atoli, ayi, big, ewti, h0, hmax, hmx, rh, rtoli, size, sum, tcrit, tdist, tnext, tol, tolsf, tp, w0 integer :: i, i1, i2, ier, iflag, igo, imax, imul, imxer, ipflag, ipgo, irem, ires, j, kgo, leniw, lenrw, lenyht, & & lia, lic, lja, ljc, lrtem, lwtem, lyd0, lyhd, lyhn, mf1, ncolm logical :: ihit integer,save :: lenrat, mxhnl0, mxstp0 integer,save :: mord(2) character(60) :: msg ! ! ----------------------------------------------------------------------- ! The following two internal Common blocks contain ! (a) variables which are local to any subroutine but whose values must ! be preserved between calls to the routine ("own" variables), and ! (b) variables which are communicated between subroutines. ! The block DLS001 is declared in subroutines DLSODIS, DIPREPI, DPREPI, ! DINTDY, DSTODI, DPRJIS, and DSOLSS. ! The block DLSS01 is declared in subroutines DLSODIS, DAINVGS, ! DIPREPI, DPREPI, DPRJIS, and DSOLSS. ! Groups of variables are replaced by dummy arrays in the Common ! declarations in routines where those variables are not used. ! ----------------------------------------------------------------------- data mord(1), mord(2)/12, 5/, mxstp0/500/, mxhnl0/10/ ! ----------------------------------------------------------------------- ! In the Data statement below, set LENRAT equal to the ratio of ! the wordlength for a real number to that for an integer. Usually, ! LENRAT = 1 for single precision and 2 for double precision. If the ! true ratio is not an integer, use the next smaller integer (.ge. 1), ! ----------------------------------------------------------------------- data lenrat/2/ ! ----------------------------------------------------------------------- ! Block A. ! This code block is executed on every call. ! It tests ISTATE and ITASK for legality and branches appropirately. ! If ISTATE .gt. 1 but the flag INIT shows that initialization has ! not yet been done, an error return occurs. ! If ISTATE = 0 or 1 and TOUT = T, return immediately. ! ----------------------------------------------------------------------- ihit=.false. if ( Istate<0 .or. Istate>3 ) then ! ----------------------------------------------------------------------- ! Block I. ! The following block handles all error returns due to illegal input ! (ISTATE = -3), as detected before calling the core integrator. ! First the error message routine is called. If the illegal input ! is a negative ISTATE, the run is aborted (apparent infinite loop). ! ----------------------------------------------------------------------- msg = 'DLSODIS- ISTATE (=I1) illegal.' call xerrwd(msg,30,1,0,1,Istate,0,0,0.0D0,0.0D0) if ( Istate>=0 ) goto 2300 ! msg = 'DLSODIS- Run aborted.. apparent infinite loop. ' call xerrwd(msg,50,303,2,0,0,0,0,0.0D0,0.0D0) goto 99999 else if ( Itask<1 .or. Itask>5 ) then msg = 'DLSODIS- ITASK (=I1) illegal. ' call xerrwd(msg,30,2,0,1,Itask,0,0,0.0D0,0.0D0) goto 2300 else if ( Istate<=1 ) then dls1%init = 0 if ( Tout==T ) return elseif ( dls1%init==0 ) then msg = 'DLSODIS-ISTATE .gt. 1 but DLSODIS not initialized.' call xerrwd(msg,50,3,0,0,0,0,0,0.0D0,0.0D0) goto 2300 elseif ( Istate==2 ) then goto 50 endif ! ----------------------------------------------------------------------- ! Block B. ! The next code block is executed for the initial call (ISTATE = 0 or 1) ! or for a continuation call with parameter changes (ISTATE = 3). ! It contains checking of all inputs and various initializations. ! If ISTATE = 0 or 1, the final setting of work space pointers, the ! matrix preprocessing, and other initializations are done in Block C. ! ! First check legality of the non-optional inputs NEQ, ITOL, IOPT, and ! MF. ! ----------------------------------------------------------------------- if ( Neq(1)<=0 ) then msg = 'DLSODIS- NEQ (=I1) .lt. 1 ' call xerrwd(msg,30,4,0,1,Neq(1),0,0,0.0D0,0.0D0) goto 2300 else if ( Istate>1 ) then if ( Neq(1)>dls1%n ) then msg = 'DLSODIS- ISTATE = 3 and NEQ increased (I1 to I2). ' call xerrwd(msg,50,5,0,2,dls1%n,Neq(1),0,0.0D0,0.0D0) goto 2300 endif endif dls1%n = Neq(1) if ( Itol<1 .or. Itol>4 ) then msg = 'DLSODIS- ITOL (=I1) illegal. ' call xerrwd(msg,30,6,0,1,Itol,0,0,0.0D0,0.0D0) goto 2300 elseif ( Iopt<0 .or. Iopt>1 ) then msg = 'DLSODIS- IOPT (=I1) illegal. ' call xerrwd(msg,30,7,0,1,Iopt,0,0,0.0D0,0.0D0) goto 2300 else dlss%moss = Mf/100 mf1 = Mf - 100*dlss%moss dls1%meth = mf1/10 dls1%miter = mf1 - 10*dls1%meth if ( dlss%moss<0 .or. dlss%moss>4 ) goto 900 if ( dls1%miter==2 .and. dlss%moss==1 ) dlss%moss = dlss%moss + 1 if ( dls1%miter==2 .and. dlss%moss==3 ) dlss%moss = dlss%moss + 1 if ( dls1%miter==1 .and. dlss%moss==2 ) dlss%moss = dlss%moss - 1 if ( dls1%miter==1 .and. dlss%moss==4 ) dlss%moss = dlss%moss - 1 if ( dls1%meth<1 .or. dls1%meth>2 ) goto 900 if ( dls1%miter<1 .or. dls1%miter>2 ) goto 900 ! Next process and check the optional inputs. -------------------------- if ( Iopt==1 ) then dls1%maxord = Iwork(5) if ( dls1%maxord<0 ) then msg = 'DLSODIS- MAXORD (=I1) .lt. 0 ' call xerrwd(msg,30,11,0,1,dls1%maxord,0,0,0.0D0,0.0D0) goto 2300 else if ( dls1%maxord==0 ) dls1%maxord = 100 dls1%maxord = min(dls1%maxord,mord(dls1%meth)) dls1%mxstep = Iwork(6) if ( dls1%mxstep<0 ) then msg = 'DLSODIS- MXSTEP (=I1) .lt. 0 ' call xerrwd(msg,30,12,0,1,dls1%mxstep,0,0,0.0D0,0.0D0) goto 2300 else if ( dls1%mxstep==0 ) dls1%mxstep = mxstp0 dls1%mxhnil = Iwork(7) if ( dls1%mxhnil<0 ) then msg = 'DLSODIS- MXHNIL (=I1) .lt. 0 ' call xerrwd(msg,30,13,0,1,dls1%mxhnil,0,0,0.0D0,0.0D0) goto 2300 else if ( dls1%mxhnil==0 ) dls1%mxhnil = mxhnl0 if ( Istate<=1 ) then h0 = Rwork(5) if ( (Tout-T)*h0<0.0D0 ) then msg = 'DLSODIS- TOUT (=R1) behind T (=R2) ' call xerrwd(msg,40,14,0,0,0,0,2,Tout,T) msg = ' Integration direction is given by H0 (=R1) ' call xerrwd(msg,50,14,0,0,0,0,1,h0,0.0D0) goto 2300 endif endif hmax = Rwork(6) if ( hmax<0.0D0 ) then msg = 'DLSODIS- HMAX (=R1) .lt. 0.0 ' call xerrwd(msg,30,15,0,0,0,0,1,hmax,0.0D0) goto 2300 else dls1%hmxi = 0.0D0 if ( hmax>0.0D0 ) dls1%hmxi = 1.0D0/hmax dls1%hmin = Rwork(7) if ( dls1%hmin<0.0D0 ) then msg = 'DLSODIS- HMIN (=R1) .lt. 0.0 ' call xerrwd(msg,30,16,0,0,0,0,1,dls1%hmin,0.0D0) goto 2300 endif endif endif endif endif else dls1%maxord = mord(dls1%meth) dls1%mxstep = mxstp0 dls1%mxhnil = mxhnl0 if ( Istate<=1 ) h0 = 0.0D0 dls1%hmxi = 0.0D0 dls1%hmin = 0.0D0 endif ! Check RTOL and ATOL for legality. ------------------------------------ rtoli = Rtol(1) atoli = Atol(1) do i = 1, dls1%n if ( Itol>=3 ) rtoli = Rtol(i) if ( Itol==2 .or. Itol==4 ) atoli = Atol(i) if ( rtoli<0.0D0 ) then msg = 'DLSODIS- RTOL(=I1) is R1 .lt. 0.0 ' call xerrwd(msg,40,19,0,1,i,0,1,rtoli,0.0D0) goto 2300 elseif ( atoli<0.0D0 ) then msg = 'DLSODIS- ATOL(=I1) is R1 .lt. 0.0 ' call xerrwd(msg,40,20,0,1,i,0,1,atoli,0.0D0) goto 2300 endif enddo ! ----------------------------------------------------------------------- ! Compute required work array lengths, as far as possible, and test ! these against LRW and LIW. Then set tentative pointers for work ! arrays. Pointers to RWORK/IWORK segments are named by prefixing L to ! the name of the segment. E.g., the segment YH starts at RWORK(LYH). ! Segments of RWORK (in order) are denoted WM, YH, SAVR, EWT, ACOR. ! The required length of the matrix work space WM is not yet known, ! and so a crude minimum value is used for the initial tests of LRW ! and LIW, and YH is temporarily stored as far to the right in RWORK ! as possible, to leave the maximum amount of space for WM for matrix ! preprocessing. Thus if MOSS .ne. 2 or 4, some of the segments of ! RWORK are temporarily omitted, as they are not needed in the ! preprocessing. These omitted segments are: ACOR if ISTATE = 1, ! EWT and ACOR if ISTATE = 3 and MOSS = 1, and SAVR, EWT, and ACOR if ! ISTATE = 3 and MOSS = 0. ! ----------------------------------------------------------------------- dlss%lrat = lenrat if ( Istate<=1 ) dls1%nyh = dls1%n if ( dls1%miter==1 ) dlss%lwmin = 4*dls1%n + 10*dls1%n/dlss%lrat if ( dls1%miter==2 ) dlss%lwmin = 4*dls1%n + 11*dls1%n/dlss%lrat dlss%lenyh = (dls1%maxord+1)*dls1%nyh dlss%lrest = dlss%lenyh + 3*dls1%n lenrw = 20 + dlss%lwmin + dlss%lrest Iwork(17) = lenrw leniw = 30 if ( dlss%moss/=1 .and. dlss%moss/=2 ) leniw = leniw + dls1%n + 1 Iwork(18) = leniw if ( lenrw>Lrw ) goto 1000 if ( leniw>Liw ) goto 1100 lia = 31 if ( dlss%moss/=1 .and. dlss%moss/=2 ) leniw = leniw + Iwork(lia+dls1%n) - 1 Iwork(18) = leniw if ( leniw>Liw ) goto 1100 lja = lia + dls1%n + 1 lia = min(lia,Liw) lja = min(lja,Liw) lic = leniw + 1 if ( dlss%moss==0 ) leniw = leniw + dls1%n + 1 Iwork(18) = leniw if ( leniw>Liw ) goto 1100 if ( dlss%moss==0 ) leniw = leniw + Iwork(lic+dls1%n) - 1 Iwork(18) = leniw if ( leniw>Liw ) goto 1100 ljc = lic + dls1%n + 1 lic = min(lic,Liw) ljc = min(ljc,Liw) dls1%lwm = 21 if ( Istate<=1 ) dls1%nq = Istate ncolm = min(dls1%nq+1,dls1%maxord+2) dlss%lenyhm = ncolm*dls1%nyh lenyht = dlss%lenyhm imul = 2 if ( Istate==3 ) imul = dlss%moss if ( Istate==3 .and. dlss%moss==3 ) imul = 1 if ( dlss%moss==2 .or. dlss%moss==4 ) imul = 3 lrtem = lenyht + imul*dls1%n lwtem = Lrw - 20 - lrtem dlss%lenwk = lwtem lyhn = dls1%lwm + lwtem dls1%lsavf = lyhn + lenyht dls1%lewt = dls1%lsavf + dls1%n dls1%lacor = dls1%lewt + dls1%n dlss%istatc = Istate if ( Istate<=1 ) then ! ----------------------------------------------------------------------- ! Block C. ! The next block is for the initial call only (ISTATE = 0 or 1). ! It contains all remaining initializations, the call to DAINVGS ! (if ISTATE = 0), the sparse matrix preprocessing, and the ! calculation if the initial step size. ! The error weights in EWT are inverted after being loaded. ! ----------------------------------------------------------------------- dls1%lyh = lyhn Iwork(22) = dls1%lyh dls1%tn = T dls1%nst = 0 dls1%nfe = 0 dls1%h = 1.0D0 dlss%nnz = 0 dlss%ngp = 0 dlss%nzl = 0 dlss%nzu = 0 ! Load the initial value vector in YH.---------------------------------- do i = 1, dls1%n Rwork(i+dls1%lyh-1) = Y(i) enddo if ( Istate==1 ) then ! Initial dy/dt was supplied. Load it into YH (LYD0 points to YH(*,2).) lyd0 = dls1%lyh + dls1%nyh do i = 1, dls1%n Rwork(i+lyd0-1) = Ydoti(i) enddo endif ! Load and invert the EWT array. (H is temporarily set to 1.0.)-------- call dewset(dls1%n,Itol,Rtol,Atol,Rwork(dls1%lyh),Rwork(dls1%lewt)) do i = 1, dls1%n if ( Rwork(i+dls1%lewt-1)<=0.0D0 ) goto 1200 Rwork(i+dls1%lewt-1) = 1.0D0/Rwork(i+dls1%lewt-1) enddo ! Call DIPREPI and DPREPI to do sparse matrix preprocessing.------------ dls1%lacor = min(dls1%lacor,Lrw) call diprepi(Neq,Y,Ydoti,Rwork,Iwork(lia),Iwork(lja),Iwork(lic),Iwork(ljc),ipflag,res,jac,adda) lenrw = dls1%lwm - 1 + dlss%lenwk + dlss%lrest Iwork(17) = lenrw if ( ipflag/=-1 ) Iwork(23) = dlss%ipian if ( ipflag/=-1 ) Iwork(24) = dlss%ipjan ipgo = -ipflag + 1 select case (ipgo) case (2) goto 1600 case (3) goto 1700 case (4) goto 1800 case (5) goto 1900 case (6) goto 2000 case (7) goto 2100 case (8,9) goto 2200 case default Iwork(22) = dls1%lyh if ( lenrw>Lrw ) goto 1000 ! Compute initial dy/dt, if necessary, and load it into YH.------------- lyd0 = dls1%lyh + dls1%n if ( Istate==0 ) then call dainvgs(Neq(1),T,Y,Rwork(dls1%lwm),Rwork(dls1%lwm),Rwork(dls1%lacor),Rwork(lyd0),ier,res,adda) dls1%nfe = dls1%nfe + 1 igo = ier + 1 select case (igo) case (2) ! DAINVGS failed because RES set IRES to 2 or 3. ----------------------- msg = 'DLSODIS- Attempt to initialize dy/dt failed ' call xerrwd(msg,50,209,0,0,0,0,0,0.0D0,0.0D0) msg = ' because residual routine set its error flag ' call xerrwd(msg,50,209,0,0,0,0,0,0.0D0,0.0D0) msg = ' to IRES = (I1)' call xerrwd(msg,20,209,0,1,ier,0,0,0.0D0,0.0D0) Istate = -8 return case (3,4) ! DAINVGS failed because matrix A was singular. ------------------------ msg = 'DLSODIS- Attempt to initialize dy/dt failed because matrix A' call xerrwd(msg,60,208,0,0,0,0,0,0.0D0,0.0D0) msg = ' was singular. CDRV returned zero pivot error flag. ' call xerrwd(msg,60,208,0,0,0,0,0,0.0D0,0.0D0) msg = 'DAINVGS set its error flag to IER = (I1)' call xerrwd(msg,40,208,0,1,ier,0,0,0.0D0,0.0D0) Istate = -8 return case default endselect endif ! Check TCRIT for legality (ITASK = 4 or 5). --------------------------- if ( Itask==4 .or. Itask==5 ) then tcrit = Rwork(1) if ( (tcrit-Tout)*(Tout-T)<0.0D0 ) goto 1400 if ( h0/=0.0D0 .and. (T+h0-tcrit)*h0>0.0D0 ) h0 = tcrit - T endif ! Initialize all remaining parameters. --------------------------------- dls1%uround = epsilon(0.0d0) dls1%jstart = 0 Rwork(dls1%lwm) = sqrt(dls1%uround) dls1%nhnil = 0 dls1%nje = 0 dlss%nlu = 0 dls1%nslast = 0 dls1%hu = 0.0D0 dls1%nqu = 0 dls1%ccmax = 0.3D0 dls1%maxcor = 3 dls1%msbp = 20 dls1%mxncf = 10 ! ----------------------------------------------------------------------- ! The coding below computes the step size, H0, to be attempted on the ! first step, unless the user has supplied a value for this. ! First check that TOUT - T differs significantly from zero. ! A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) ! if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted ! so as to be between 100*UROUND and 1.0E-3. ! Then the computed value H0 is given by.. ! NEQ ! H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) ! 1 ! where w0 = MAX ( ABS(T), ABS(TOUT) ), ! YDOT(i) = i-th component of initial value of dy/dt, ! ywt(i) = EWT(i)/TOL (a weight for y(i)). ! The sign of H0 is inferred from the initial values of TOUT and T. ! ----------------------------------------------------------------------- if ( h0==0.0D0 ) then tdist = abs(Tout-T) w0 = max(abs(T),abs(Tout)) if ( tdist<2.0D0*dls1%uround*w0 ) then msg = 'DLSODIS- TOUT(=R1) too close to T(=R2) to start integration.' call xerrwd(msg,60,22,0,0,0,0,2,Tout,T) goto 2300 else tol = Rtol(1) if ( Itol>2 ) then do i = 1, dls1%n tol = max(tol,Rtol(i)) enddo endif if ( tol<=0.0D0 ) then atoli = Atol(1) do i = 1, dls1%n if ( Itol==2 .or. Itol==4 ) atoli = Atol(i) ayi = abs(Y(i)) if ( ayi/=0.0D0 ) tol = max(tol,atoli/ayi) enddo endif tol = max(tol,100.0D0*dls1%uround) tol = min(tol,0.001D0) sum = dvnorm(dls1%n,Rwork(lyd0),Rwork(dls1%lewt)) sum = 1.0D0/(tol*w0*w0) + tol*sum**2 h0 = 1.0D0/sqrt(sum) h0 = min(h0,tdist) h0 = sign(h0,Tout-T) endif endif ! Adjust H0 if necessary to meet HMAX bound. --------------------------- rh = abs(h0)*dls1%hmxi if ( rh>1.0D0 ) h0 = h0/rh ! Load H with H0 and scale YH(*,2) by H0. ------------------------------ dls1%h = h0 do i = 1, dls1%n Rwork(i+lyd0-1) = h0*Rwork(i+lyd0-1) enddo goto 200 endselect else ! ----------------------------------------------------------------------- ! ISTATE = 3. Move YH to its new location. ! Note that only the part of YH needed for the next step, namely ! MIN(NQ+1,MAXORD+2) columns, is actually moved. ! A temporary error weight array EWT is loaded if MOSS = 2 or 4. ! Sparse matrix processing is done in DIPREPI/DPREPI. ! If MAXORD was reduced below NQ, then the pointers are finally set ! so that SAVR is identical to (YH*,MAXORD+2) ! ----------------------------------------------------------------------- lyhd = dls1%lyh - lyhn imax = lyhn - 1 + dlss%lenyhm ! Move YH. Move right if LYHD < 0; move left if LYHD > 0. ------------- if ( lyhd<0 ) then do i = lyhn, imax j = imax + lyhn - i Rwork(j) = Rwork(j+lyhd) enddo endif if ( lyhd>0 ) then do i = lyhn, imax Rwork(i) = Rwork(i+lyhd) enddo endif dls1%lyh = lyhn Iwork(22) = dls1%lyh if ( dlss%moss==2 .or. dlss%moss==4 ) then ! Temporarily load EWT if MOSS = 2 or 4. call dewset(dls1%n,Itol,Rtol,Atol,Rwork(dls1%lyh),Rwork(dls1%lewt)) do i = 1, dls1%n if ( Rwork(i+dls1%lewt-1)<=0.0D0 ) goto 1200 Rwork(i+dls1%lewt-1) = 1.0D0/Rwork(i+dls1%lewt-1) enddo endif ! DIPREPI and DPREPI do sparse matrix preprocessing. ------------------- dls1%lsavf = min(dls1%lsavf,Lrw) dls1%lewt = min(dls1%lewt,Lrw) dls1%lacor = min(dls1%lacor,Lrw) call diprepi(Neq,Y,Ydoti,Rwork,Iwork(lia),Iwork(lja),Iwork(lic),Iwork(ljc),ipflag,res,jac,adda) lenrw = dls1%lwm - 1 + dlss%lenwk + dlss%lrest Iwork(17) = lenrw if ( ipflag/=-1 ) Iwork(23) = dlss%ipian if ( ipflag/=-1 ) Iwork(24) = dlss%ipjan ipgo = -ipflag + 1 select case (ipgo) case (2) goto 1600 case (3) goto 1700 case (4) goto 1800 case (5) goto 1900 case (6) goto 2000 case (7) goto 2100 case (8,9) goto 2200 case default Iwork(22) = dls1%lyh lyd0 = dls1%lyh + dls1%n if ( lenrw>Lrw ) goto 1000 ! Set flag to signal changes to DSTODI.--------------------------------- dls1%jstart = -1 if ( dls1%nq>dls1%maxord ) then ! MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI. -------- do i = 1, dls1%n Ydoti(i) = Rwork(i+dls1%lsavf-1) enddo endif if ( dls1%n/=dls1%nyh ) then ! NEQ was reduced. Zero part of YH to avoid undefined references. ----- i1 = dls1%lyh + dls1%l*dls1%nyh i2 = dls1%lyh + (dls1%maxord+1)*dls1%nyh - 1 if ( i1<=i2 ) then do i = i1, i2 Rwork(i) = 0.0D0 enddo endif endif endselect endif endif endif endif ! ----------------------------------------------------------------------- ! Block D. ! The next code block is for continuation calls only (ISTATE = 2 or 3) ! and is to check stop conditions before taking a step. ! ----------------------------------------------------------------------- 50 continue dls1%nslast = dls1%nst select case (Itask) case (2) goto 100 case (3) tp = dls1%tn - dls1%hu*(1.0D0+100.0D0*dls1%uround) if ( (tp-Tout)*dls1%h>0.0D0 ) then msg = 'DLSODIS- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' call xerrwd(msg,60,23,0,1,Itask,0,2,Tout,tp) goto 2300 else if ( (dls1%tn-Tout)*dls1%h>=0.0D0 ) goto 300 goto 100 endif case (4) tcrit = Rwork(1) if ( (dls1%tn-tcrit)*dls1%h>0.0D0 ) goto 1300 if ( (tcrit-Tout)*dls1%h<0.0D0 ) goto 1400 if ( (dls1%tn-Tout)*dls1%h>=0.0D0 ) then call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) if ( iflag/=0 ) goto 1500 T = Tout goto 400 endif case (5) tcrit = Rwork(1) if ( (dls1%tn-tcrit)*dls1%h>0.0D0 ) goto 1300 case default if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) goto 100 call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) if ( iflag/=0 ) goto 1500 T = Tout goto 400 endselect hmx = abs(dls1%tn) + abs(dls1%h) ihit = abs(dls1%tn-tcrit)<=100.0D0*dls1%uround*hmx if ( ihit ) goto 300 tnext = dls1%tn + dls1%h*(1.0D0+4.0D0*dls1%uround) if ( (tnext-tcrit)*dls1%h>0.0D0 ) then dls1%h = (tcrit-dls1%tn)*(1.0D0-4.0D0*dls1%uround) if ( Istate==2 ) dls1%jstart = -2 endif endif ! ----------------------------------------------------------------------- ! Block E. ! The next block is normally executed for all calls and contains ! the call to the one-step core integrator DSTODI. ! ! This is a looping point for the integration steps. ! ! First check for too many steps being taken, update EWT (if not at ! start of problem), check for too much accuracy being requested, and ! check for H below the roundoff level in T. ! ----------------------------------------------------------------------- 100 continue if ( (dls1%nst-dls1%nslast)>=dls1%mxstep ) then ! ----------------------------------------------------------------------- ! Block H. ! The following block handles all unsuccessful returns other than ! those for illegal input. First the error message routine is called. ! If there was an error test or convergence test failure, IMXER is set. ! Then Y is loaded from YH and T is set to TN. ! The optional outputs are loaded into the work arrays before returning. ! ----------------------------------------------------------------------- ! The maximum number of steps was taken before reaching TOUT. ---------- msg = 'DLSODIS- At current T (=R1), MXSTEP (=I1) steps ' call xerrwd(msg,50,201,0,0,0,0,0,0.0D0,0.0D0) msg = ' taken on this call before reaching TOUT ' call xerrwd(msg,50,201,0,1,dls1%mxstep,0,1,dls1%tn,0.0D0) Istate = -1 goto 600 else call dewset(dls1%n,Itol,Rtol,Atol,Rwork(dls1%lyh),Rwork(dls1%lewt)) do i = 1, dls1%n if ( Rwork(i+dls1%lewt-1)<=0.0D0 ) then ! EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- ewti = Rwork(dls1%lewt+i-1) msg = 'DLSODIS- At T (=R1), EWT(I1) has become R2 .le. 0.' call xerrwd(msg,50,202,0,1,i,0,2,dls1%tn,ewti) Istate = -6 goto 700 else Rwork(i+dls1%lewt-1) = 1.0D0/Rwork(i+dls1%lewt-1) endif enddo endif 200 continue tolsf = dls1%uround*dvnorm(dls1%n,Rwork(dls1%lyh),Rwork(dls1%lewt)) if ( tolsf<=1.0D0 ) then if ( (dls1%tn+dls1%h)==dls1%tn ) then dls1%nhnil = dls1%nhnil + 1 if ( dls1%nhnil<=dls1%mxhnil ) then msg = 'DLSODIS- Warning..Internal T (=R1) and H (=R2) are' call xerrwd(msg,50,101,0,0,0,0,0,0.0D0,0.0D0) msg = ' such that in the machine, T + H = T on the next step ' call xerrwd(msg,60,101,0,0,0,0,0,0.0D0,0.0D0) msg = ' (H = step size). Solver will continue anyway.' call xerrwd(msg,50,101,0,0,0,0,2,dls1%tn,dls1%h) if ( dls1%nhnil>=dls1%mxhnil ) then msg = 'DLSODIS- Above warning has been issued I1 times. ' call xerrwd(msg,50,102,0,0,0,0,0,0.0D0,0.0D0) msg = ' It will not be issued again for this problem.' call xerrwd(msg,50,102,0,1,dls1%mxhnil,0,0,0.0D0,0.0D0) endif endif endif ! ----------------------------------------------------------------------- ! CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,WM,RES, ! ADDA,JAC,DPRJIS,DSOLSS) ! Note: SAVF in DSTODI occupies the same space as YDOTI in DLSODIS. ! ----------------------------------------------------------------------- call dstodi(Neq,Y,Rwork(dls1%lyh),dls1%nyh,Rwork(dls1%lyh),Rwork(dls1%lewt), & & Ydoti,Rwork(dls1%lsavf),Rwork(dls1%lacor), & & Rwork(dls1%lwm),Rwork(dls1%lwm),res,adda,jac,dprjis,dsolss) kgo = 1 - dls1%kflag select case (kgo) case (2) ! KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- msg = 'DLSODIS- At T (=R1) and step size H (=R2), the ' call xerrwd(msg,50,204,0,0,0,0,0,0.0D0,0.0D0) msg = ' error test failed repeatedly or with ABS(H) = HMIN ' call xerrwd(msg,60,204,0,0,0,0,2,dls1%tn,dls1%h) Istate = -4 goto 500 case (3) ! KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- msg = 'DLSODIS- At T (=R1) and step size H (=R2), the ' call xerrwd(msg,50,205,0,0,0,0,0,0.0D0,0.0D0) msg = ' corrector convergence failed repeatedly ' call xerrwd(msg,50,205,0,0,0,0,0,0.0D0,0.0D0) msg = ' or with ABS(H) = HMIN ' call xerrwd(msg,30,205,0,0,0,0,2,dls1%tn,dls1%h) Istate = -5 goto 500 case (4) case (5) ! IRES = 3 returned by RES, despite retries by DSTODI. ----------------- msg = 'DLSODIS- At T (=R1) residual routine returned ' call xerrwd(msg,50,206,0,0,0,0,0,0.0D0,0.0D0) msg = ' error IRES = 3 repeatedly.' call xerrwd(msg,30,206,1,0,0,0,0,dls1%tn,0.0D0) Istate = -7 goto 700 case (6) ! KFLAG = -5. Fatal error flag returned by DPRJIS or DSOLSS (CDRV). --- msg = 'DLSODIS- At T (=R1) and step size H (=R2), a fatal' call xerrwd(msg,50,207,0,0,0,0,0,0.0D0,0.0D0) msg = ' error flag was returned by CDRV (by way of ' call xerrwd(msg,50,207,0,0,0,0,0,0.0D0,0.0D0) msg = ' Subroutine DPRJIS or DSOLSS) ' call xerrwd(msg,40,207,0,0,0,0,2,dls1%tn,dls1%h) Istate = -9 goto 600 case default ! ! KGO = 1:success; 2:error test failure; 3:convergence failure; ! 4:RES ordered return; 5:RES returned error; ! 6:fatal error from CDRV via DPRJIS or DSOLSS. ! ----------------------------------------------------------------------- ! Block F. ! The following block handles the case of a successful return from the ! core integrator (KFLAG = 0). Test for stop conditions. ! ----------------------------------------------------------------------- dls1%init = 1 select case (Itask) case (2) case (3) ! ITASK = 3. Jump to exit if TOUT was reached. ------------------------ if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) goto 100 case (4) ! ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) then hmx = abs(dls1%tn) + abs(dls1%h) ihit = abs(dls1%tn-tcrit)<=100.0D0*dls1%uround*hmx if ( .not.(ihit) ) then tnext = dls1%tn + dls1%h*(1.0D0+4.0D0*dls1%uround) if ( (tnext-tcrit)*dls1%h>0.0D0 ) then dls1%h = (tcrit-dls1%tn)*(1.0D0-4.0D0*dls1%uround) dls1%jstart = -2 endif goto 100 endif else call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) T = Tout goto 400 endif case (5) ! ITASK = 5. See if TCRIT was reached and jump to exit. --------------- hmx = abs(dls1%tn) + abs(dls1%h) ihit = abs(dls1%tn-tcrit)<=100.0D0*dls1%uround*hmx case default ! ITASK = 1. If TOUT has been reached, interpolate. ------------------- if ( (dls1%tn-Tout)*dls1%h<0.0D0 ) goto 100 call dintdy(Tout,0,Rwork(dls1%lyh),dls1%nyh,Y,iflag) T = Tout goto 400 endselect endselect else tolsf = tolsf*2.0D0 if ( dls1%nst==0 ) then msg = 'DLSODIS- At start of problem, too much accuracy ' call xerrwd(msg,50,26,0,0,0,0,0,0.0D0,0.0D0) msg = ' requested for precision of machine.. See TOLSF (=R1) ' call xerrwd(msg,60,26,0,0,0,0,1,tolsf,0.0D0) Rwork(14) = tolsf goto 2300 else ! Too much accuracy requested for machine precision. ------------------- msg = 'DLSODIS- At T (=R1), too much accuracy requested ' call xerrwd(msg,50,203,0,0,0,0,0,0.0D0,0.0D0) msg = ' for precision of machine.. See TOLSF (=R2) ' call xerrwd(msg,50,203,0,0,0,0,2,dls1%tn,tolsf) Rwork(14) = tolsf Istate = -2 goto 700 endif endif ! ----------------------------------------------------------------------- ! Block G. ! The following block handles all successful returns from DLSODIS. ! if ITASK .ne. 1, Y is loaded from YH and T is set accordingly. ! ISTATE is set to 2, and the optional outputs are loaded into the ! work arrays before returning. ! ----------------------------------------------------------------------- 300 continue do i = 1, dls1%n Y(i) = Rwork(i+dls1%lyh-1) enddo T = dls1%tn if ( Itask==4 .or. Itask==5 ) then if ( ihit ) T = tcrit endif 400 continue Istate = 2 if ( dls1%kflag==-3 ) Istate = 3 Rwork(11) = dls1%hu Rwork(12) = dls1%h Rwork(13) = dls1%tn Iwork(11) = dls1%nst Iwork(12) = dls1%nfe Iwork(13) = dls1%nje Iwork(14) = dls1%nqu Iwork(15) = dls1%nq Iwork(19) = dlss%nnz Iwork(20) = dlss%ngp Iwork(21) = dlss%nlu Iwork(25) = dlss%nzl Iwork(26) = dlss%nzu return ! Compute IMXER if relevant. ------------------------------------------- 500 continue big = 0.0D0 imxer = 1 do i = 1, dls1%n size = abs(Rwork(i+dls1%lacor-1)*Rwork(i+dls1%lewt-1)) if ( big<size ) then big = size imxer = i endif enddo Iwork(16) = imxer ! Compute residual if relevant. ---------------------------------------- 600 continue lyd0 = dls1%lyh + dls1%nyh do i = 1, dls1%n Rwork(i+dls1%lsavf-1) = Rwork(i+lyd0-1)/dls1%h Y(i) = Rwork(i+dls1%lyh-1) enddo ires = 1 call res(Neq,dls1%tn,Y,Rwork(dls1%lsavf),Ydoti,ires) dls1%nfe = dls1%nfe + 1 if ( ires>1 ) then msg = 'DLSODIS- Residual routine set its flag IRES ' call xerrwd(msg,50,210,0,0,0,0,0,0.0D0,0.0D0) msg = ' to (I1) when called for final output. ' call xerrwd(msg,50,210,0,1,ires,0,0,0.0D0,0.0D0) endif goto 800 ! set y vector, t, and optional outputs. ------------------------------- 700 continue do i = 1, dls1%n Y(i) = Rwork(i+dls1%lyh-1) enddo 800 continue T = dls1%tn Rwork(11) = dls1%hu Rwork(12) = dls1%h Rwork(13) = dls1%tn Iwork(11) = dls1%nst Iwork(12) = dls1%nfe Iwork(13) = dls1%nje Iwork(14) = dls1%nqu Iwork(15) = dls1%nq Iwork(19) = dlss%nnz Iwork(20) = dlss%ngp Iwork(21) = dlss%nlu Iwork(25) = dlss%nzl Iwork(26) = dlss%nzu return 900 continue msg = 'DLSODIS- MF (=I1) illegal. ' call xerrwd(msg,30,8,0,1,Mf,0,0,0.0D0,0.0D0) goto 2300 1000 continue msg = 'DLSODIS- RWORK length is insufficient to proceed. ' call xerrwd(msg,50,17,0,0,0,0,0,0.0D0,0.0D0) msg = ' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' call xerrwd(msg,60,17,0,2,lenrw,Lrw,0,0.0D0,0.0D0) goto 2300 1100 continue msg = 'DLSODIS- IWORK length is insufficient to proceed. ' call xerrwd(msg,50,18,0,0,0,0,0,0.0D0,0.0D0) msg = ' Length needed is .ge. LENIW (=I1), exceeds LIW (=I2)' call xerrwd(msg,60,18,0,2,leniw,Liw,0,0.0D0,0.0D0) goto 2300 1200 continue ewti = Rwork(dls1%lewt+i-1) msg = 'DLSODIS- EWT(I1) is R1 .le. 0.0 ' call xerrwd(msg,40,21,0,1,i,0,1,ewti,0.0D0) goto 2300 1300 continue msg = 'DLSODIS- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' call xerrwd(msg,60,24,0,0,0,0,2,tcrit,dls1%tn) goto 2300 1400 continue msg = 'DLSODIS- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' call xerrwd(msg,60,25,0,0,0,0,2,tcrit,Tout) goto 2300 1500 continue msg = 'DLSODIS- Trouble in DINTDY. ITASK = I1, TOUT = R1' call xerrwd(msg,50,27,0,1,Itask,0,1,Tout,0.0D0) goto 2300 1600 continue msg = 'DLSODIS- RWORK length insufficient (for Subroutine DPREPI). ' call xerrwd(msg,60,28,0,0,0,0,0,0.0D0,0.0D0) msg = ' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' call xerrwd(msg,60,28,0,2,lenrw,Lrw,0,0.0D0,0.0D0) goto 2300 1700 continue msg = 'DLSODIS- RWORK length insufficient (for Subroutine JGROUP). ' call xerrwd(msg,60,29,0,0,0,0,0,0.0D0,0.0D0) msg = ' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' call xerrwd(msg,60,29,0,2,lenrw,Lrw,0,0.0D0,0.0D0) goto 2300 1800 continue msg = 'DLSODIS- RWORK length insufficient (for Subroutine ODRV). ' call xerrwd(msg,60,30,0,0,0,0,0,0.0D0,0.0D0) msg = ' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' call xerrwd(msg,60,30,0,2,lenrw,Lrw,0,0.0D0,0.0D0) goto 2300 1900 continue msg = 'DLSODIS- Error from ODRV in Yale Sparse Matrix Package. ' call xerrwd(msg,60,31,0,0,0,0,0,0.0D0,0.0D0) imul = (dlss%iys-1)/dls1%n irem = dlss%iys - imul*dls1%n msg = ' At T (=R1), ODRV returned error flag = I1*NEQ + I2. ' call xerrwd(msg,60,31,0,2,imul,irem,1,dls1%tn,0.0D0) goto 2300 2000 continue msg = 'DLSODIS- RWORK length insufficient (for Subroutine CDRV). ' call xerrwd(msg,60,32,0,0,0,0,0,0.0D0,0.0D0) msg = ' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' call xerrwd(msg,60,32,0,2,lenrw,Lrw,0,0.0D0,0.0D0) goto 2300 2100 continue msg = 'DLSODIS- Error from CDRV in Yale Sparse Matrix Package. ' call xerrwd(msg,60,33,0,0,0,0,0,0.0D0,0.0D0) imul = (dlss%iys-1)/dls1%n irem = dlss%iys - imul*dls1%n msg = ' At T (=R1), CDRV returned error flag = I1*NEQ + I2. ' call xerrwd(msg,60,33,0,2,imul,irem,1,dls1%tn,0.0D0) if ( imul==2 ) then msg = ' Duplicate entry in sparsity structure descriptors. ' call xerrwd(msg,60,33,0,0,0,0,0,0.0D0,0.0D0) endif if ( imul==3 .or. imul==6 ) then msg = ' Insufficient storage for NSFC (called by CDRV). ' call xerrwd(msg,60,33,0,0,0,0,0,0.0D0,0.0D0) endif goto 2300 2200 continue msg = 'DLSODIS- At T (=R1) residual routine (called by DPREPI) ' call xerrwd(msg,60,34,0,0,0,0,0,0.0D0,0.0D0) ier = -ipflag - 5 msg = ' returned error IRES (=I1)' call xerrwd(msg,30,34,0,1,ier,0,1,dls1%tn,0.0D0) ! 2300 continue Istate = -3 return 99999 continue end subroutine dlsodis