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* -----------------------------------------------------------------
* $Revision: 1.2 $
* $Date: 2010/12/01 22:51:32 $
* -----------------------------------------------------------------
* Programmer(s): Scott D. Cohen, Alan C. Hindmarsh and
* Radu Serban @ LLNL
* -----------------------------------------------------------------
* Example problem:
*
* The following is a simple example problem, with the coding
* needed for its solution by CVODE. The problem is from
* chemical kinetics, and consists of the following three rate
* equations:
* dy1/dt = -.04*y1 + 1.e4*y2*y3
* dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*(y2)^2
* dy3/dt = 3.e7*(y2)^2
* on the interval from t = 0.0 to t = 4.e10, with initial
* conditions: y1 = 1.0, y2 = y3 = 0. The problem is stiff.
* While integrating the system, we also use the rootfinding
* feature to find the points at which y1 = 1e-4 or at which
* y3 = 0.01. This program solves the problem with the BDF method,
* Newton iteration with the CVDENSE dense linear solver, and a
* user-supplied Jacobian routine.
* It uses a user-supplied function to compute the error weights
* required for the WRMS norm calculations.
* Output is printed in decades from t = .4 to t = 4.e10.
* Run statistics (optional outputs) are printed at the end.
* -----------------------------------------------------------------
*/
#include <stdio.h>
/* Header files with a description of contents used here */
#include <cvode/cvode.h> /* prototypes for CVODE fcts. and consts. */
#include <cvode/cvode_dense.h> /* prototype for CVDense */
#include <nvector/nvector_serial.h> /* serial N_Vector types, functions, and macros */
#include <sundials/sundials_dense.h> /* definitions DlsMat and DENSE_ELEM */
#include <sundials/sundials_types.h> /* definition of type realtype */
#include <sundials/sundials_math.h> /* definition of ABS */
/* User-defined vector and matrix accessor macros: Ith, IJth */
/* These macros are defined in order to write code which exactly matches
the mathematical problem description given above.
Ith(v,i) references the ith component of the vector v, where i is in
the range [1..NEQ] and NEQ is defined below. The Ith macro is defined
using the N_VIth macro in nvector.h. N_VIth numbers the components of
a vector starting from 0.
IJth(A,i,j) references the (i,j)th element of the dense matrix A, where
i and j are in the range [1..NEQ]. The IJth macro is defined using the
DENSE_ELEM macro in dense.h. DENSE_ELEM numbers rows and columns of a
dense matrix starting from 0. */
#define Ith(v,i) NV_Ith_S(v,i-1) /* Ith numbers components 1..NEQ */
#define IJth(A,i,j) DENSE_ELEM(A,i-1,j-1) /* IJth numbers rows,cols 1..NEQ */
/* Problem Constants */
#define NEQ 3 /* number of equations */
#define Y1 RCONST(1.0) /* initial y components */
#define Y2 RCONST(0.0)
#define Y3 RCONST(0.0)
#define RTOL RCONST(1.0e-4) /* scalar relative tolerance */
#define ATOL1 RCONST(1.0e-8) /* vector absolute tolerance components */
#define ATOL2 RCONST(1.0e-14)
#define ATOL3 RCONST(1.0e-6)
#define T0 RCONST(0.0) /* initial time */
#define T1 RCONST(0.4) /* first output time */
#define TMULT RCONST(10.0) /* output time factor */
#define NOUT 12 /* number of output times */
/* Functions Called by the Solver */
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data);
static int g(realtype t, N_Vector y, realtype *gout, void *user_data);
static int Jac(long int N, realtype t,
N_Vector y, N_Vector fy, DlsMat J, void *user_data,
N_Vector tmp1, N_Vector tmp2, N_Vector tmp3);
static int ewt(N_Vector y, N_Vector w, void *user_data);
/* Private functions to output results */
static void PrintOutput(realtype t, realtype y1, realtype y2, realtype y3);
static void PrintRootInfo(int root_f1, int root_f2);
/* Private function to print final statistics */
static void PrintFinalStats(void *cvode_mem);
/* Private function to check function return values */
static int check_flag(void *flagvalue, char *funcname, int opt);
/*
*-------------------------------
* Main Program
*-------------------------------
*/
int main()
{
realtype t, tout;
N_Vector y;
void *cvode_mem;
int flag, flagr, iout;
int rootsfound[2];
y = NULL;
cvode_mem = NULL;
/* Create serial vector of length NEQ for I.C. */
y = N_VNew_Serial(NEQ);
if (check_flag((void *)y, "N_VNew_Serial", 0)) return(1);
/* Initialize y */
Ith(y,1) = Y1;
Ith(y,2) = Y2;
Ith(y,3) = Y3;
/* Call CVodeCreate to create the solver memory and specify the
* Backward Differentiation Formula and the use of a Newton iteration */
cvode_mem = CVodeCreate(CV_BDF, CV_NEWTON);
if (check_flag((void *)cvode_mem, "CVodeCreate", 0)) return(1);
/* Call CVodeInit to initialize the integrator memory and specify the
* user's right hand side function in y'=f(t,y), the inital time T0, and
* the initial dependent variable vector y. */
flag = CVodeInit(cvode_mem, f, T0, y);
if (check_flag(&flag, "CVodeInit", 1)) return(1);
/* Use private function to compute error weights */
flag = CVodeWFtolerances(cvode_mem, ewt);
if (check_flag(&flag, "CVodeSetEwtFn", 1)) return(1);
/* Call CVodeRootInit to specify the root function g with 2 components */
flag = CVodeRootInit(cvode_mem, 2, g);
if (check_flag(&flag, "CVodeRootInit", 1)) return(1);
/* Call CVDense to specify the CVDENSE dense linear solver */
flag = CVDense(cvode_mem, NEQ);
if (check_flag(&flag, "CVDense", 1)) return(1);
/* Set the Jacobian routine to Jac (user-supplied) */
flag = CVDlsSetDenseJacFn(cvode_mem, Jac);
if (check_flag(&flag, "CVDlsSetDenseJacFn", 1)) return(1);
/* In loop, call CVode, print results, and test for error.
Break out of loop when NOUT preset output times have been reached. */
printf(" \n3-species kinetics problem\n\n");
iout = 0; tout = T1;
while(1) {
flag = CVode(cvode_mem, tout, y, &t, CV_NORMAL);
PrintOutput(t, Ith(y,1), Ith(y,2), Ith(y,3));
if (flag == CV_ROOT_RETURN) {
flagr = CVodeGetRootInfo(cvode_mem, rootsfound);
check_flag(&flagr, "CVodeGetRootInfo", 1);
PrintRootInfo(rootsfound[0],rootsfound[1]);
}
if (check_flag(&flag, "CVode", 1)) break;
if (flag == CV_SUCCESS) {
iout++;
tout *= TMULT;
}
if (iout == NOUT) break;
}
/* Print some final statistics */
PrintFinalStats(cvode_mem);
/* Free y vector */
N_VDestroy_Serial(y);
/* Free integrator memory */
CVodeFree(&cvode_mem);
return(0);
}
/*
*-------------------------------
* Functions called by the solver
*-------------------------------
*/
/*
* f routine. Compute function f(t,y).
*/
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data)
{
realtype y1, y2, y3, yd1, yd3;
y1 = Ith(y,1); y2 = Ith(y,2); y3 = Ith(y,3);
yd1 = Ith(ydot,1) = RCONST(-0.04)*y1 + RCONST(1.0e4)*y2*y3;
yd3 = Ith(ydot,3) = RCONST(3.0e7)*y2*y2;
Ith(ydot,2) = -yd1 - yd3;
return(0);
}
/*
* g routine. Compute functions g_i(t,y) for i = 0,1.
*/
static int g(realtype t, N_Vector y, realtype *gout, void *user_data)
{
realtype y1, y3;
y1 = Ith(y,1); y3 = Ith(y,3);
gout[0] = y1 - RCONST(0.0001);
gout[1] = y3 - RCONST(0.01);
return(0);
}
/*
* Jacobian routine. Compute J(t,y) = df/dy. *
*/
static int Jac(long int N, realtype t,
N_Vector y, N_Vector fy, DlsMat J, void *user_data,
N_Vector tmp1, N_Vector tmp2, N_Vector tmp3)
{
realtype y1, y2, y3;
y1 = Ith(y,1); y2 = Ith(y,2); y3 = Ith(y,3);
IJth(J,1,1) = RCONST(-0.04);
IJth(J,1,2) = RCONST(1.0e4)*y3;
IJth(J,1,3) = RCONST(1.0e4)*y2;
IJth(J,2,1) = RCONST(0.04);
IJth(J,2,2) = RCONST(-1.0e4)*y3-RCONST(6.0e7)*y2;
IJth(J,2,3) = RCONST(-1.0e4)*y2;
IJth(J,3,2) = RCONST(6.0e7)*y2;
return(0);
}
/*
* EwtSet function. Computes the error weights at the current solution.
*/
static int ewt(N_Vector y, N_Vector w, void *user_data)
{
int i;
realtype yy, ww, rtol, atol[3];
rtol = RTOL;
atol[0] = ATOL1;
atol[1] = ATOL2;
atol[2] = ATOL3;
for (i=1; i<=3; i++) {
yy = Ith(y,i);
ww = rtol * ABS(yy) + atol[i-1];
if (ww <= 0.0) return (-1);
Ith(w,i) = 1.0/ww;
}
return(0);
}
/*
*-------------------------------
* Private helper functions
*-------------------------------
*/
static void PrintOutput(realtype t, realtype y1, realtype y2, realtype y3)
{
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("At t = %0.4Le y =%14.6Le %14.6Le %14.6Le\n", t, y1, y2, y3);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("At t = %0.4le y =%14.6le %14.6le %14.6le\n", t, y1, y2, y3);
#else
printf("At t = %0.4e y =%14.6e %14.6e %14.6e\n", t, y1, y2, y3);
#endif
return;
}
static void PrintRootInfo(int root_f1, int root_f2)
{
printf(" rootsfound[] = %3d %3d\n", root_f1, root_f2);
return;
}
/*
* Get and print some final statistics
*/
static void PrintFinalStats(void *cvode_mem)
{
long int nst, nfe, nsetups, nje, nfeLS, nni, ncfn, netf, nge;
int flag;
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1);
flag = CVodeGetNumRhsEvals(cvode_mem, &nfe);
check_flag(&flag, "CVodeGetNumRhsEvals", 1);
flag = CVodeGetNumLinSolvSetups(cvode_mem, &nsetups);
check_flag(&flag, "CVodeGetNumLinSolvSetups", 1);
flag = CVodeGetNumErrTestFails(cvode_mem, &netf);
check_flag(&flag, "CVodeGetNumErrTestFails", 1);
flag = CVodeGetNumNonlinSolvIters(cvode_mem, &nni);
check_flag(&flag, "CVodeGetNumNonlinSolvIters", 1);
flag = CVodeGetNumNonlinSolvConvFails(cvode_mem, &ncfn);
check_flag(&flag, "CVodeGetNumNonlinSolvConvFails", 1);
flag = CVDlsGetNumJacEvals(cvode_mem, &nje);
check_flag(&flag, "CVDlsGetNumJacEvals", 1);
flag = CVDlsGetNumRhsEvals(cvode_mem, &nfeLS);
check_flag(&flag, "CVDlsGetNumRhsEvals", 1);
flag = CVodeGetNumGEvals(cvode_mem, &nge);
check_flag(&flag, "CVodeGetNumGEvals", 1);
printf("\nFinal Statistics:\n");
printf("nst = %-6ld nfe = %-6ld nsetups = %-6ld nfeLS = %-6ld nje = %ld\n",
nst, nfe, nsetups, nfeLS, nje);
printf("nni = %-6ld ncfn = %-6ld netf = %-6ld nge = %ld\n \n",
nni, ncfn, netf, nge);
}
/*
* Check function return value...
* opt == 0 means SUNDIALS function allocates memory so check if
* returned NULL pointer
* opt == 1 means SUNDIALS function returns a flag so check if
* flag >= 0
* opt == 2 means function allocates memory so check if returned
* NULL pointer
*/
static int check_flag(void *flagvalue, char *funcname, int opt)
{
int *errflag;
/* Check if SUNDIALS function returned NULL pointer - no memory allocated */
if (opt == 0 && flagvalue == NULL) {
fprintf(stderr, "\nSUNDIALS_ERROR: %s() failed - returned NULL pointer\n\n",
funcname);
return(1); }
/* Check if flag < 0 */
else if (opt == 1) {
errflag = (int *) flagvalue;
if (*errflag < 0) {
fprintf(stderr, "\nSUNDIALS_ERROR: %s() failed with flag = %d\n\n",
funcname, *errflag);
return(1); }}
/* Check if function returned NULL pointer - no memory allocated */
else if (opt == 2 && flagvalue == NULL) {
fprintf(stderr, "\nMEMORY_ERROR: %s() failed - returned NULL pointer\n\n",
funcname);
return(1); }
return(0);
}
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