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* -----------------------------------------------------------------
* $Revision: 1.2 $
* $Date: 2010/12/01 23:08:49 $
* -----------------------------------------------------------------
* Programmer(s): Allan Taylor, Alan Hindmarsh and
* Radu Serban @ LLNL
* -----------------------------------------------------------------
*
* This example loops through the available iterative linear solvers:
* SPGMR, SPBCG and SPTFQMR.
*
* Example (serial):
*
* This example solves a nonlinear system that arises from a system
* of partial differential equations. The PDE system is a food web
* population model, with predator-prey interaction and diffusion
* on the unit square in two dimensions. The dependent variable
* vector is the following:
*
* 1 2 ns
* c = (c , c , ..., c ) (denoted by the variable cc)
*
* and the PDE's are as follows:
*
* i i
* 0 = d(i)*(c + c ) + f (x,y,c) (i=1,...,ns)
* xx yy i
*
* where
*
* i ns j
* f (x,y,c) = c * (b(i) + sum a(i,j)*c )
* i j=1
*
* The number of species is ns = 2 * np, with the first np being
* prey and the last np being predators. The number np is both the
* number of prey and predator species. The coefficients a(i,j),
* b(i), d(i) are:
*
* a(i,i) = -AA (all i)
* a(i,j) = -GG (i <= np , j > np)
* a(i,j) = EE (i > np, j <= np)
* b(i) = BB * (1 + alpha * x * y) (i <= np)
* b(i) =-BB * (1 + alpha * x * y) (i > np)
* d(i) = DPREY (i <= np)
* d(i) = DPRED ( i > np)
*
* The various scalar parameters are set using define's or in
* routine InitUserData.
*
* The boundary conditions are: normal derivative = 0, and the
* initial guess is constant in x and y, but the final solution
* is not.
*
* The PDEs are discretized by central differencing on an MX by
* MY mesh.
*
* The nonlinear system is solved by KINSOL using the method
* specified in local variable globalstrat.
*
* The preconditioner matrix is a block-diagonal matrix based on
* the partial derivatives of the interaction terms f only.
*
* Constraints are imposed to make all components of the solution
* positive.
* -----------------------------------------------------------------
* References:
*
* 1. Peter N. Brown and Youcef Saad,
* Hybrid Krylov Methods for Nonlinear Systems of Equations
* LLNL report UCRL-97645, November 1987.
*
* 2. Peter N. Brown and Alan C. Hindmarsh,
* Reduced Storage Matrix Methods in Stiff ODE systems,
* Lawrence Livermore National Laboratory Report UCRL-95088,
* Rev. 1, June 1987, and Journal of Applied Mathematics and
* Computation, Vol. 31 (May 1989), pp. 40-91. (Presents a
* description of the time-dependent version of this test
* problem.)
* -----------------------------------------------------------------
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <kinsol/kinsol.h>
#include <kinsol/kinsol_spgmr.h>
#include <kinsol/kinsol_spbcgs.h>
#include <kinsol/kinsol_sptfqmr.h>
#include <nvector/nvector_serial.h>
#include <sundials/sundials_dense.h>
#include <sundials/sundials_types.h>
#include <sundials/sundials_math.h>
/* Problem Constants */
#define NUM_SPECIES 6 /* must equal 2*(number of prey or predators)
number of prey = number of predators */
#define PI RCONST(3.1415926535898) /* pi */
#define MX 5 /* MX = number of x mesh points */
#define MY 5 /* MY = number of y mesh points */
#define NSMX (NUM_SPECIES * MX)
#define NEQ (NSMX * MY) /* number of equations in the system */
#define AA RCONST(1.0) /* value of coefficient AA in above eqns */
#define EE RCONST(10000.) /* value of coefficient EE in above eqns */
#define GG RCONST(0.5e-6) /* value of coefficient GG in above eqns */
#define BB RCONST(1.0) /* value of coefficient BB in above eqns */
#define DPREY RCONST(1.0) /* value of coefficient dprey above */
#define DPRED RCONST(0.5) /* value of coefficient dpred above */
#define ALPHA RCONST(1.0) /* value of coefficient alpha above */
#define AX RCONST(1.0) /* total range of x variable */
#define AY RCONST(1.0) /* total range of y variable */
#define FTOL RCONST(1.e-7) /* ftol tolerance */
#define STOL RCONST(1.e-13) /* stol tolerance */
#define THOUSAND RCONST(1000.0) /* one thousand */
#define ZERO RCONST(0.) /* 0. */
#define ONE RCONST(1.0) /* 1. */
#define TWO RCONST(2.0) /* 2. */
#define PREYIN RCONST(1.0) /* initial guess for prey concentrations. */
#define PREDIN RCONST(30000.0)/* initial guess for predator concs. */
/* Linear Solver Loop Constants */
#define USE_SPGMR 0
#define USE_SPBCG 1
#define USE_SPTFQMR 2
/* User-defined vector access macro: IJ_Vptr */
/* IJ_Vptr is defined in order to translate from the underlying 3D structure
of the dependent variable vector to the 1D storage scheme for an N-vector.
IJ_Vptr(vv,i,j) returns a pointer to the location in vv corresponding to
indices is = 0, jx = i, jy = j. */
#define IJ_Vptr(vv,i,j) (&NV_Ith_S(vv, i*NUM_SPECIES + j*NSMX))
/* Type : UserData
contains preconditioner blocks, pivot arrays, and problem constants */
typedef struct {
realtype **P[MX][MY];
long int *pivot[MX][MY];
realtype **acoef, *bcoef;
N_Vector rates;
realtype *cox, *coy;
realtype ax, ay, dx, dy;
realtype uround, sqruround;
int mx, my, ns, np;
} *UserData;
/* Functions Called by the KINSOL Solver */
static int func(N_Vector cc, N_Vector fval, void *user_data);
static int PrecSetupBD(N_Vector cc, N_Vector cscale,
N_Vector fval, N_Vector fscale,
void *user_data,
N_Vector vtemp1, N_Vector vtemp2);
static int PrecSolveBD(N_Vector cc, N_Vector cscale,
N_Vector fval, N_Vector fscale,
N_Vector vv, void *user_data,
N_Vector ftem);
/* Private Helper Functions */
static UserData AllocUserData(void);
static void InitUserData(UserData data);
static void FreeUserData(UserData data);
static void SetInitialProfiles(N_Vector cc, N_Vector sc);
static void PrintHeader(int globalstrategy, int maxl, int maxlrst,
realtype fnormtol, realtype scsteptol,
int linsolver);
static void PrintOutput(N_Vector cc);
static void PrintFinalStats(void *kmem, int linsolver);
static void WebRate(realtype xx, realtype yy, realtype *cxy, realtype *ratesxy,
void *user_data);
static realtype DotProd(int size, realtype *x1, realtype *x2);
static int check_flag(void *flagvalue, char *funcname, int opt);
/*
*--------------------------------------------------------------------
* MAIN PROGRAM
*--------------------------------------------------------------------
*/
int main(void)
{
int globalstrategy, linsolver;
realtype fnormtol, scsteptol;
N_Vector cc, sc, constraints;
UserData data;
int flag, maxl, maxlrst;
void *kmem;
cc = sc = constraints = NULL;
kmem = NULL;
data = NULL;
/* Allocate memory, and set problem data, initial values, tolerances */
globalstrategy = KIN_NONE;
data = AllocUserData();
if (check_flag((void *)data, "AllocUserData", 2)) return(1);
InitUserData(data);
/* Create serial vectors of length NEQ */
cc = N_VNew_Serial(NEQ);
if (check_flag((void *)cc, "N_VNew_Serial", 0)) return(1);
sc = N_VNew_Serial(NEQ);
if (check_flag((void *)sc, "N_VNew_Serial", 0)) return(1);
data->rates = N_VNew_Serial(NEQ);
if (check_flag((void *)data->rates, "N_VNew_Serial", 0)) return(1);
constraints = N_VNew_Serial(NEQ);
if (check_flag((void *)constraints, "N_VNew_Serial", 0)) return(1);
N_VConst(TWO, constraints);
SetInitialProfiles(cc, sc);
fnormtol=FTOL; scsteptol=STOL;
/* Call KINCreate/KINInit to initialize KINSOL:
nvSpec is the nvSpec pointer used in the serial version
A pointer to KINSOL problem memory is returned and stored in kmem. */
kmem = KINCreate();
if (check_flag((void *)kmem, "KINCreate", 0)) return(1);
/* Vector cc passed as template vector. */
flag = KINInit(kmem, func, cc);
if (check_flag(&flag, "KINInit", 1)) return(1);
flag = KINSetUserData(kmem, data);
if (check_flag(&flag, "KINSetUserData", 1)) return(1);
flag = KINSetConstraints(kmem, constraints);
if (check_flag(&flag, "KINSetConstraints", 1)) return(1);
flag = KINSetFuncNormTol(kmem, fnormtol);
if (check_flag(&flag, "KINSetFuncNormTol", 1)) return(1);
flag = KINSetScaledStepTol(kmem, scsteptol);
if (check_flag(&flag, "KINSetScaledStepTol", 1)) return(1);
/* We no longer need the constraints vector since KINSetConstraints
creates a private copy for KINSOL to use. */
N_VDestroy_Serial(constraints);
/* START: Loop through SPGMR, SPBCG and SPTFQMR linear solver modules */
for (linsolver = 0; linsolver < 3; ++linsolver) {
/* Re-initialize user data */
if (linsolver != 0) SetInitialProfiles(cc, sc);
/* Attach a linear solver module */
switch(linsolver) {
/* (a) SPGMR */
case(USE_SPGMR):
/* Print header */
printf(" -------");
printf(" \n| SPGMR |\n");
printf(" -------\n");
/* Call KINSpgmr to specify the linear solver KINSPGMR with preconditioner
routines PrecSetupBD and PrecSolveBD, and the pointer to the user block data. */
maxl = 15;
maxlrst = 2;
flag = KINSpgmr(kmem, maxl);
if (check_flag(&flag, "KINSpgmr", 1)) return(1);
flag = KINSpilsSetMaxRestarts(kmem, maxlrst);
if (check_flag(&flag, "KINSpilsSetMaxRestarts", 1)) return(1);
break;
/* (b) SPBCG */
case(USE_SPBCG):
/* Print header */
printf(" -------");
printf(" \n| SPBCG |\n");
printf(" -------\n");
/* Call KINSpbcg to specify the linear solver KINSPBCG with preconditioner
routines PrecSetupBD and PrecSolveBD, and the pointer to the user block data. */
maxl = 15;
flag = KINSpbcg(kmem, maxl);
if (check_flag(&flag, "KINSpbcg", 1)) return(1);
break;
/* (c) SPTFQMR */
case(USE_SPTFQMR):
/* Print header */
printf(" ---------");
printf(" \n| SPTFQMR |\n");
printf(" ---------\n");
/* Call KINSptfqmr to specify the linear solver KINSPTFQMR with preconditioner
routines PrecSetupBD and PrecSolveBD, and the pointer to the user block data. */
maxl = 25;
flag = KINSptfqmr(kmem, maxl);
if (check_flag(&flag, "KINSptfqmr", 1)) return(1);
break;
}
/* Set preconditioner functions */
flag = KINSpilsSetPreconditioner(kmem,
PrecSetupBD,
PrecSolveBD);
if (check_flag(&flag, "KINSpilsSetPreconditioner", 1)) return(1);
/* Print out the problem size, solution parameters, initial guess. */
PrintHeader(globalstrategy, maxl, maxlrst, fnormtol, scsteptol, linsolver);
/* Call KINSol and print output concentration profile */
flag = KINSol(kmem, /* KINSol memory block */
cc, /* initial guess on input; solution vector */
globalstrategy, /* global stragegy choice */
sc, /* scaling vector, for the variable cc */
sc); /* scaling vector for function values fval */
if (check_flag(&flag, "KINSol", 1)) return(1);
printf("\n\nComputed equilibrium species concentrations:\n");
PrintOutput(cc);
/* Print final statistics and free memory */
PrintFinalStats(kmem, linsolver);
} /* END: Loop through SPGMR, SPBCG and SPTFQMR linear solver modules */
N_VDestroy_Serial(cc);
N_VDestroy_Serial(sc);
KINFree(&kmem);
FreeUserData(data);
return(0);
}
/* Readability definitions used in other routines below */
#define acoef (data->acoef)
#define bcoef (data->bcoef)
#define cox (data->cox)
#define coy (data->coy)
/*
*--------------------------------------------------------------------
* FUNCTIONS CALLED BY KINSOL
*--------------------------------------------------------------------
*/
/*
* System function for predator-prey system
*/
static int func(N_Vector cc, N_Vector fval, void *user_data)
{
realtype xx, yy, delx, dely, *cxy, *rxy, *fxy, dcyli, dcyui, dcxli, dcxri;
int jx, jy, is, idyu, idyl, idxr, idxl;
UserData data;
data = (UserData)user_data;
delx = data->dx;
dely = data->dy;
/* Loop over all mesh points, evaluating rate array at each point*/
for (jy = 0; jy < MY; jy++) {
yy = dely*jy;
/* Set lower/upper index shifts, special at boundaries. */
idyl = (jy != 0 ) ? NSMX : -NSMX;
idyu = (jy != MY-1) ? NSMX : -NSMX;
for (jx = 0; jx < MX; jx++) {
xx = delx*jx;
/* Set left/right index shifts, special at boundaries. */
idxl = (jx != 0 ) ? NUM_SPECIES : -NUM_SPECIES;
idxr = (jx != MX-1) ? NUM_SPECIES : -NUM_SPECIES;
cxy = IJ_Vptr(cc,jx,jy);
rxy = IJ_Vptr(data->rates,jx,jy);
fxy = IJ_Vptr(fval,jx,jy);
/* Get species interaction rate array at (xx,yy) */
WebRate(xx, yy, cxy, rxy, user_data);
for(is = 0; is < NUM_SPECIES; is++) {
/* Differencing in x direction */
dcyli = *(cxy+is) - *(cxy - idyl + is) ;
dcyui = *(cxy + idyu + is) - *(cxy+is);
/* Differencing in y direction */
dcxli = *(cxy+is) - *(cxy - idxl + is);
dcxri = *(cxy + idxr +is) - *(cxy+is);
/* Compute the total rate value at (xx,yy) */
fxy[is] = (coy)[is] * (dcyui - dcyli) +
(cox)[is] * (dcxri - dcxli) + rxy[is];
} /* end of is loop */
} /* end of jx loop */
} /* end of jy loop */
return(0);
}
/*
* Preconditioner setup routine. Generate and preprocess P.
*/
static int PrecSetupBD(N_Vector cc, N_Vector cscale,
N_Vector fval, N_Vector fscale,
void *user_data,
N_Vector vtemp1, N_Vector vtemp2)
{
realtype r, r0, uround, sqruround, xx, yy, delx, dely, csave, fac;
realtype *cxy, *scxy, **Pxy, *ratesxy, *Pxycol, perturb_rates[NUM_SPECIES];
int i, j, jx, jy, ret;
UserData data;
data = (UserData) user_data;
delx = data->dx;
dely = data->dy;
uround = data->uround;
sqruround = data->sqruround;
fac = N_VWL2Norm(fval, fscale);
r0 = THOUSAND * uround * fac * NEQ;
if(r0 == ZERO) r0 = ONE;
/* Loop over spatial points; get size NUM_SPECIES Jacobian block at each */
for (jy = 0; jy < MY; jy++) {
yy = jy*dely;
for (jx = 0; jx < MX; jx++) {
xx = jx*delx;
Pxy = (data->P)[jx][jy];
cxy = IJ_Vptr(cc,jx,jy);
scxy= IJ_Vptr(cscale,jx,jy);
ratesxy = IJ_Vptr((data->rates),jx,jy);
/* Compute difference quotients of interaction rate fn. */
for (j = 0; j < NUM_SPECIES; j++) {
csave = cxy[j]; /* Save the j,jx,jy element of cc */
r = MAX(sqruround*ABS(csave), r0/scxy[j]);
cxy[j] += r; /* Perturb the j,jx,jy element of cc */
fac = ONE/r;
WebRate(xx, yy, cxy, perturb_rates, data);
/* Restore j,jx,jy element of cc */
cxy[j] = csave;
/* Load the j-th column of difference quotients */
Pxycol = Pxy[j];
for (i = 0; i < NUM_SPECIES; i++)
Pxycol[i] = (perturb_rates[i] - ratesxy[i]) * fac;
} /* end of j loop */
/* Do LU decomposition of size NUM_SPECIES preconditioner block */
ret = denseGETRF(Pxy, NUM_SPECIES, NUM_SPECIES, (data->pivot)[jx][jy]);
if (ret != 0) return(1);
} /* end of jx loop */
} /* end of jy loop */
return(0);
}
/*
* Preconditioner solve routine
*/
static int PrecSolveBD(N_Vector cc, N_Vector cscale,
N_Vector fval, N_Vector fscale,
N_Vector vv, void *user_data,
N_Vector ftem)
{
realtype **Pxy, *vxy;
long int *piv, jx, jy;
UserData data;
data = (UserData)user_data;
for (jx=0; jx<MX; jx++) {
for (jy=0; jy<MY; jy++) {
/* For each (jx,jy), solve a linear system of size NUM_SPECIES.
vxy is the address of the corresponding portion of the vector vv;
Pxy is the address of the corresponding block of the matrix P;
piv is the address of the corresponding block of the array pivot. */
vxy = IJ_Vptr(vv,jx,jy);
Pxy = (data->P)[jx][jy];
piv = (data->pivot)[jx][jy];
denseGETRS(Pxy, NUM_SPECIES, piv, vxy);
} /* end of jy loop */
} /* end of jx loop */
return(0);
}
/*
* Interaction rate function routine
*/
static void WebRate(realtype xx, realtype yy, realtype *cxy, realtype *ratesxy,
void *user_data)
{
int i;
realtype fac;
UserData data;
data = (UserData)user_data;
for (i = 0; i<NUM_SPECIES; i++)
ratesxy[i] = DotProd(NUM_SPECIES, cxy, acoef[i]);
fac = ONE + ALPHA * xx * yy;
for (i = 0; i < NUM_SPECIES; i++)
ratesxy[i] = cxy[i] * ( bcoef[i] * fac + ratesxy[i] );
}
/*
* Dot product routine for realtype arrays
*/
static realtype DotProd(int size, realtype *x1, realtype *x2)
{
int i;
realtype *xx1, *xx2, temp = ZERO;
xx1 = x1; xx2 = x2;
for (i = 0; i < size; i++) temp += (*xx1++) * (*xx2++);
return(temp);
}
/*
*--------------------------------------------------------------------
* PRIVATE FUNCTIONS
*--------------------------------------------------------------------
*/
/*
* Allocate memory for data structure of type UserData
*/
static UserData AllocUserData(void)
{
int jx, jy;
UserData data;
data = (UserData) malloc(sizeof *data);
for (jx=0; jx < MX; jx++) {
for (jy=0; jy < MY; jy++) {
(data->P)[jx][jy] = newDenseMat(NUM_SPECIES, NUM_SPECIES);
(data->pivot)[jx][jy] = newLintArray(NUM_SPECIES);
}
}
acoef = newDenseMat(NUM_SPECIES, NUM_SPECIES);
bcoef = (realtype *)malloc(NUM_SPECIES * sizeof(realtype));
cox = (realtype *)malloc(NUM_SPECIES * sizeof(realtype));
coy = (realtype *)malloc(NUM_SPECIES * sizeof(realtype));
return(data);
}
/*
* Load problem constants in data
*/
static void InitUserData(UserData data)
{
int i, j, np;
realtype *a1,*a2, *a3, *a4, dx2, dy2;
data->mx = MX;
data->my = MY;
data->ns = NUM_SPECIES;
data->np = NUM_SPECIES/2;
data->ax = AX;
data->ay = AY;
data->dx = (data->ax)/(MX-1);
data->dy = (data->ay)/(MY-1);
data->uround = UNIT_ROUNDOFF;
data->sqruround = SQRT(data->uround);
/* Set up the coefficients a and b plus others found in the equations */
np = data->np;
dx2=(data->dx)*(data->dx); dy2=(data->dy)*(data->dy);
for (i = 0; i < np; i++) {
a1= &(acoef[i][np]);
a2= &(acoef[i+np][0]);
a3= &(acoef[i][0]);
a4= &(acoef[i+np][np]);
/* Fill in the portion of acoef in the four quadrants, row by row */
for (j = 0; j < np; j++) {
*a1++ = -GG;
*a2++ = EE;
*a3++ = ZERO;
*a4++ = ZERO;
}
/* and then change the diagonal elements of acoef to -AA */
acoef[i][i]=-AA;
acoef[i+np][i+np] = -AA;
bcoef[i] = BB;
bcoef[i+np] = -BB;
cox[i]=DPREY/dx2;
cox[i+np]=DPRED/dx2;
coy[i]=DPREY/dy2;
coy[i+np]=DPRED/dy2;
}
}
/*
* Free data memory
*/
static void FreeUserData(UserData data)
{
int jx, jy;
for (jx=0; jx < MX; jx++) {
for (jy=0; jy < MY; jy++) {
destroyMat((data->P)[jx][jy]);
destroyArray((data->pivot)[jx][jy]);
}
}
destroyMat(acoef);
free(bcoef);
free(cox);
free(coy);
N_VDestroy_Serial(data->rates);
free(data);
}
/*
* Set initial conditions in cc
*/
static void SetInitialProfiles(N_Vector cc, N_Vector sc)
{
int i, jx, jy;
realtype *cloc, *sloc;
realtype ctemp[NUM_SPECIES], stemp[NUM_SPECIES];
/* Initialize arrays ctemp and stemp used in the loading process */
for (i = 0; i < NUM_SPECIES/2; i++) {
ctemp[i] = PREYIN;
stemp[i] = ONE;
}
for (i = NUM_SPECIES/2; i < NUM_SPECIES; i++) {
ctemp[i] = PREDIN;
stemp[i] = RCONST(0.00001);
}
/* Load initial profiles into cc and sc vector from ctemp and stemp. */
for (jy = 0; jy < MY; jy++) {
for (jx = 0; jx < MX; jx++) {
cloc = IJ_Vptr(cc,jx,jy);
sloc = IJ_Vptr(sc,jx,jy);
for (i = 0; i < NUM_SPECIES; i++) {
cloc[i] = ctemp[i];
sloc[i] = stemp[i];
}
}
}
}
/*
* Print first lines of output (problem description)
*/
static void PrintHeader(int globalstrategy, int maxl, int maxlrst,
realtype fnormtol, realtype scsteptol,
int linsolver)
{
printf("\nPredator-prey test problem -- KINSol (serial version)\n\n");
printf("Mesh dimensions = %d X %d\n", MX, MY);
printf("Number of species = %d\n", NUM_SPECIES);
printf("Total system size = %d\n\n", NEQ);
printf("Flag globalstrategy = %d (0 = None, 1 = Linesearch)\n",
globalstrategy);
switch(linsolver) {
case(USE_SPGMR):
printf("Linear solver is SPGMR with maxl = %d, maxlrst = %d\n",
maxl, maxlrst);
break;
case(USE_SPBCG):
printf("Linear solver is SPBCG with maxl = %d\n", maxl);
break;
case(USE_SPTFQMR):
printf("Linear solver is SPTFQMR with maxl = %d\n", maxl);
break;
}
printf("Preconditioning uses interaction-only block-diagonal matrix\n");
printf("Positivity constraints imposed on all components \n");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("Tolerance parameters: fnormtol = %Lg scsteptol = %Lg\n",
fnormtol, scsteptol);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("Tolerance parameters: fnormtol = %lg scsteptol = %lg\n",
fnormtol, scsteptol);
#else
printf("Tolerance parameters: fnormtol = %g scsteptol = %g\n",
fnormtol, scsteptol);
#endif
printf("\nInitial profile of concentration\n");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("At all mesh points: %Lg %Lg %Lg %Lg %Lg %Lg\n",
PREYIN, PREYIN, PREYIN,
PREDIN, PREDIN, PREDIN);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("At all mesh points: %lg %lg %lg %lg %lg %lg\n",
PREYIN, PREYIN, PREYIN,
PREDIN, PREDIN, PREDIN);
#else
printf("At all mesh points: %g %g %g %g %g %g\n",
PREYIN, PREYIN, PREYIN,
PREDIN, PREDIN, PREDIN);
#endif
}
/*
* Print sampled values of current cc
*/
static void PrintOutput(N_Vector cc)
{
int is, jx, jy;
realtype *ct;
jy = 0; jx = 0;
ct = IJ_Vptr(cc,jx,jy);
printf("\nAt bottom left:");
/* Print out lines with up to 6 values per line */
for (is = 0; is < NUM_SPECIES; is++){
if ((is%6)*6 == is) printf("\n");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf(" %Lg",ct[is]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf(" %lg",ct[is]);
#else
printf(" %g",ct[is]);
#endif
}
jy = MY-1; jx = MX-1;
ct = IJ_Vptr(cc,jx,jy);
printf("\n\nAt top right:");
/* Print out lines with up to 6 values per line */
for (is = 0; is < NUM_SPECIES; is++) {
if ((is%6)*6 == is) printf("\n");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf(" %Lg",ct[is]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf(" %lg",ct[is]);
#else
printf(" %g",ct[is]);
#endif
}
printf("\n\n");
}
/*
* Print final statistics contained in iopt
*/
static void PrintFinalStats(void *kmem, int linsolver)
{
long int nni, nfe, nli, npe, nps, ncfl, nfeSG;
int flag;
flag = KINGetNumNonlinSolvIters(kmem, &nni);
check_flag(&flag, "KINGetNumNonlinSolvIters", 1);
flag = KINGetNumFuncEvals(kmem, &nfe);
check_flag(&flag, "KINGetNumFuncEvals", 1);
flag = KINSpilsGetNumLinIters(kmem, &nli);
check_flag(&flag, "KINSpilsGetNumLinIters", 1);
flag = KINSpilsGetNumPrecEvals(kmem, &npe);
check_flag(&flag, "KINSpilsGetNumPrecEvals", 1);
flag = KINSpilsGetNumPrecSolves(kmem, &nps);
check_flag(&flag, "KINSpilsGetNumPrecSolves", 1);
flag = KINSpilsGetNumConvFails(kmem, &ncfl);
check_flag(&flag, "KINSpilsGetNumConvFails", 1);
flag = KINSpilsGetNumFuncEvals(kmem, &nfeSG);
check_flag(&flag, "KINSpilsGetNumFuncEvals", 1);
printf("Final Statistics.. \n");
printf("nni = %5ld nli = %5ld\n", nni, nli);
printf("nfe = %5ld nfeSG = %5ld\n", nfe, nfeSG);
printf("nps = %5ld npe = %5ld ncfl = %5ld\n", nps, npe, ncfl);
if (linsolver < 2) printf("\n=========================================================\n\n");
}
/*
* 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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