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* -----------------------------------------------------------------
* $Revision: 1.3 $
* $Date: 2010/12/01 22:51:32 $
* -----------------------------------------------------------------
* Programmer(s): Scott D. Cohen, Alan C. Hindmarsh and
* Radu Serban @ LLNL
* --------------------------------------------------------------------
* Demonstration program for CVODE - Krylov linear solver.
* ODE system from ns-species interaction PDE in 2 dimensions.
*
* This program solves a stiff ODE 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:
*
* 1 2 ns
* c = (c , c , ..., c )
*
* and the PDEs are as follows:
*
* i i i
* dc /dt = 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 coefficients a(i,j), b(i),
* d(i) are:
*
* a(i,i) = -a (all i)
* a(i,j) = -g (i <= np, j > np)
* a(i,j) = e (i > np, j <= np)
* b(i) = b*(1 + alpha*x*y) (i <= np)
* b(i) = -b*(1 + alpha*x*y) (i > np)
* d(i) = Dprey (i <= np)
* d(i) = Dpred (i > np)
*
* The spatial domain is the unit square. The final time is 10.
* The boundary conditions are: normal derivative = 0.
* A polynomial in x and y is used to set the initial conditions.
*
* The PDEs are discretized by central differencing on an MX by MY mesh.
*
* The resulting ODE system is stiff.
*
* The ODE system is solved using Newton iteration and the CVSPGMR
* linear solver (scaled preconditioned GMRES).
*
* The preconditioner matrix used is the product of two matrices:
* (1) A matrix, only defined implicitly, based on a fixed number
* of Gauss-Seidel iterations using the diffusion terms only.
* (2) A block-diagonal matrix based on the partial derivatives
* of the interaction terms f only, using block-grouping (computing
* only a subset of the ns by ns blocks).
*
* Four different runs are made for this problem.
* The product preconditoner is applied on the left and on the
* right. In each case, both the modified and classical Gram-Schmidt
* options are tested.
* In the series of runs, CVodeInit and CVSpgmr are called only
* for the first run, whereas CVodeReInit and CVReInitSpgmr are
* called for each of the remaining three runs.
*
* A problem description, performance statistics at selected output
* times, and final statistics are written to standard output.
* On the first run, solution values are also printed at output
* times. Error and warning messages are written to standard error,
* but there should be no such messages.
*
* Note: This program requires the dense linear solver functions
* newDenseMat, newLintArray, denseAddIdentity, denseGETRF, denseGETRS,
* destroyMat and destroyArray.
*
* Note: This program assumes the sequential implementation for the
* type N_Vector and uses the NV_DATA_S macro to gain access to the
* contiguous array of components of an N_Vector.
* --------------------------------------------------------------------
* Reference: Peter N. Brown and Alan C. Hindmarsh, Reduced Storage
* Matrix Methods in Stiff ODE Systems, J. Appl. Math. & Comp., 31
* (1989), pp. 40-91. Also available as Lawrence Livermore National
* Laboratory Report UCRL-95088, Rev. 1, June 1987.
* --------------------------------------------------------------------
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <cvode/cvode.h> /* main integrator header file */
#include <cvode/cvode_spgmr.h> /* prototypes & constants for CVSPGMR solver */
#include <nvector/nvector_serial.h> /* serial N_Vector types, fct. and macros */
#include <sundials/sundials_dense.h> /* use generic DENSE solver in preconditioning */
#include <sundials/sundials_types.h> /* definition of realtype */
#include <sundials/sundials_math.h> /* contains the macros ABS and SQR */
/* Constants */
#define ZERO RCONST(0.0)
#define ONE RCONST(1.0)
/* Problem Specification Constants */
#define AA ONE /* AA = a */
#define EE RCONST(1.0e4) /* EE = e */
#define GG RCONST(0.5e-6) /* GG = g */
#define BB ONE /* BB = b */
#define DPREY ONE
#define DPRED RCONST(0.5)
#define ALPH ONE
#define NP 3
#define NS (2*NP)
/* Method Constants */
#define MX 6
#define MY 6
#define MXNS (MX*NS)
#define AX ONE
#define AY ONE
#define DX (AX/(realtype)(MX-1))
#define DY (AY/(realtype)(MY-1))
#define MP NS
#define MQ (MX*MY)
#define MXMP (MX*MP)
#define NGX 2
#define NGY 2
#define NGRP (NGX*NGY)
#define ITMAX 5
/* CVodeInit Constants */
#define NEQ (NS*MX*MY)
#define T0 ZERO
#define RTOL RCONST(1.0e-5)
#define ATOL RCONST(1.0e-5)
/* CVSpgmr Constants */
#define MAXL 0 /* => use default = MIN(NEQ, 5) */
#define DELT ZERO /* => use default = 0.05 */
/* Output Constants */
#define T1 RCONST(1.0e-8)
#define TOUT_MULT RCONST(10.0)
#define DTOUT ONE
#define NOUT 18
/* Note: The value for species i at mesh point (j,k) is stored in */
/* component number (i-1) + j*NS + k*NS*MX of an N_Vector, */
/* where 1 <= i <= NS, 0 <= j < MX, 0 <= k < MY. */
/* Structure for user data */
typedef struct {
realtype **P[NGRP];
long int *pivot[NGRP];
int ns, mxns;
int mp, mq, mx, my, ngrp, ngx, ngy, mxmp;
int jgx[NGX+1], jgy[NGY+1], jigx[MX], jigy[MY];
int jxr[NGX], jyr[NGY];
realtype acoef[NS][NS], bcoef[NS], diff[NS];
realtype cox[NS], coy[NS], dx, dy, srur;
realtype fsave[NEQ];
N_Vector rewt;
void *cvode_mem;
} *WebData;
/* Private Helper Functions */
static WebData AllocUserData(void);
static void InitUserData(WebData wdata);
static void SetGroups(int m, int ng, int jg[], int jig[], int jr[]);
static void CInit(N_Vector c, WebData wdata);
static void PrintIntro(void);
static void PrintHeader(int jpre, int gstype);
static void PrintAllSpecies(N_Vector c, int ns, int mxns, realtype t);
static void PrintOutput(void *cvode_mem, realtype t);
static void PrintFinalStats(void *cvode_mem);
static void FreeUserData(WebData wdata);
static void WebRates(realtype x, realtype y, realtype t, realtype c[],
realtype rate[], WebData wdata);
static void fblock (realtype t, realtype cdata[], int jx, int jy,
realtype cdotdata[], WebData wdata);
static void GSIter(realtype gamma, N_Vector z, N_Vector x,WebData wdata);
/* Small Vector Kernels */
static void v_inc_by_prod(realtype u[], realtype v[], realtype w[], int n);
static void v_sum_prods(realtype u[], realtype p[], realtype q[], realtype v[],
realtype w[], int n);
static void v_prod(realtype u[], realtype v[], realtype w[], int n);
static void v_zero(realtype u[], int n);
/* Functions Called By The Solver */
static int f(realtype t, N_Vector y, N_Vector ydot, void *user_data);
static int Precond(realtype tn, N_Vector c, N_Vector fc,
booleantype jok, booleantype *jcurPtr, realtype gamma,
void *user_data, N_Vector vtemp1, N_Vector vtemp2,
N_Vector vtemp3);
static int PSolve(realtype tn, N_Vector c, N_Vector fc,
N_Vector r, N_Vector z,
realtype gamma, realtype delta,
int lr, void *user_data, N_Vector vtemp);
/* Private function to check function return values */
static int check_flag(void *flagvalue, char *funcname, int opt);
/* Implementation */
int main()
{
realtype abstol=ATOL, reltol=RTOL, t, tout;
N_Vector c;
WebData wdata;
void *cvode_mem;
booleantype firstrun;
int jpre, gstype, flag;
int ns, mxns, iout;
c = NULL;
wdata = NULL;
cvode_mem = NULL;
/* Initializations */
c = N_VNew_Serial(NEQ);
if(check_flag((void *)c, "N_VNew_Serial", 0)) return(1);
wdata = AllocUserData();
if(check_flag((void *)wdata, "AllocUserData", 2)) return(1);
InitUserData(wdata);
ns = wdata->ns;
mxns = wdata->mxns;
/* Print problem description */
PrintIntro();
/* Loop over jpre and gstype (four cases) */
for (jpre = PREC_LEFT; jpre <= PREC_RIGHT; jpre++) {
for (gstype = MODIFIED_GS; gstype <= CLASSICAL_GS; gstype++) {
/* Initialize c and print heading */
CInit(c, wdata);
PrintHeader(jpre, gstype);
/* Call CVodeInit or CVodeReInit, then CVSpgmr to set up problem */
firstrun = (jpre == PREC_LEFT) && (gstype == MODIFIED_GS);
if (firstrun) {
cvode_mem = CVodeCreate(CV_BDF, CV_NEWTON);
if(check_flag((void *)cvode_mem, "CVodeCreate", 0)) return(1);
wdata->cvode_mem = cvode_mem;
flag = CVodeSetUserData(cvode_mem, wdata);
if(check_flag(&flag, "CVodeSetUserData", 1)) return(1);
flag = CVodeInit(cvode_mem, f, T0, c);
if(check_flag(&flag, "CVodeInit", 1)) return(1);
flag = CVodeSStolerances(cvode_mem, reltol, abstol);
if (check_flag(&flag, "CVodeSStolerances", 1)) return(1);
flag = CVSpgmr(cvode_mem, jpre, MAXL);
if(check_flag(&flag, "CVSpgmr", 1)) return(1);
flag = CVSpilsSetGSType(cvode_mem, gstype);
if(check_flag(&flag, "CVSpilsSetGSType", 1)) return(1);
flag = CVSpilsSetEpsLin(cvode_mem, DELT);
if(check_flag(&flag, "CVSpilsSetEpsLin", 1)) return(1);
flag = CVSpilsSetPreconditioner(cvode_mem, Precond, PSolve);
if(check_flag(&flag, "CVSpilsSetPreconditioner", 1)) return(1);
} else {
flag = CVodeReInit(cvode_mem, T0, c);
if(check_flag(&flag, "CVodeReInit", 1)) return(1);
flag = CVSpilsSetPrecType(cvode_mem, jpre);
check_flag(&flag, "CVSpilsSetPrecType", 1);
flag = CVSpilsSetGSType(cvode_mem, gstype);
if(check_flag(&flag, "CVSpilsSetGSType", 1)) return(1);
}
/* Print initial values */
if (firstrun) PrintAllSpecies(c, ns, mxns, T0);
/* Loop over output points, call CVode, print sample solution values. */
tout = T1;
for (iout = 1; iout <= NOUT; iout++) {
flag = CVode(cvode_mem, tout, c, &t, CV_NORMAL);
PrintOutput(cvode_mem, t);
if (firstrun && (iout % 3 == 0)) PrintAllSpecies(c, ns, mxns, t);
if(check_flag(&flag, "CVode", 1)) break;
if (tout > RCONST(0.9)) tout += DTOUT; else tout *= TOUT_MULT;
}
/* Print final statistics, and loop for next case */
PrintFinalStats(cvode_mem);
}
}
/* Free all memory */
CVodeFree(&cvode_mem);
N_VDestroy_Serial(c);
FreeUserData(wdata);
return(0);
}
static WebData AllocUserData(void)
{
int i, ngrp = NGRP;
long int ns = NS;
WebData wdata;
wdata = (WebData) malloc(sizeof *wdata);
for(i=0; i < ngrp; i++) {
(wdata->P)[i] = newDenseMat(ns, ns);
(wdata->pivot)[i] = newLintArray(ns);
}
wdata->rewt = N_VNew_Serial(NEQ);
return(wdata);
}
static void InitUserData(WebData wdata)
{
int i, j, ns;
realtype *bcoef, *diff, *cox, *coy, dx, dy;
realtype (*acoef)[NS];
acoef = wdata->acoef;
bcoef = wdata->bcoef;
diff = wdata->diff;
cox = wdata->cox;
coy = wdata->coy;
ns = wdata->ns = NS;
for (j = 0; j < NS; j++) { for (i = 0; i < NS; i++) acoef[i][j] = 0.; }
for (j = 0; j < NP; j++) {
for (i = 0; i < NP; i++) {
acoef[NP+i][j] = EE;
acoef[i][NP+j] = -GG;
}
acoef[j][j] = -AA;
acoef[NP+j][NP+j] = -AA;
bcoef[j] = BB;
bcoef[NP+j] = -BB;
diff[j] = DPREY;
diff[NP+j] = DPRED;
}
/* Set remaining problem parameters */
wdata->mxns = MXNS;
dx = wdata->dx = DX;
dy = wdata->dy = DY;
for (i = 0; i < ns; i++) {
cox[i] = diff[i]/SQR(dx);
coy[i] = diff[i]/SQR(dy);
}
/* Set remaining method parameters */
wdata->mp = MP;
wdata->mq = MQ;
wdata->mx = MX;
wdata->my = MY;
wdata->srur = SQRT(UNIT_ROUNDOFF);
wdata->mxmp = MXMP;
wdata->ngrp = NGRP;
wdata->ngx = NGX;
wdata->ngy = NGY;
SetGroups(MX, NGX, wdata->jgx, wdata->jigx, wdata->jxr);
SetGroups(MY, NGY, wdata->jgy, wdata->jigy, wdata->jyr);
}
/*
This routine sets arrays jg, jig, and jr describing
a uniform partition of (0,1,2,...,m-1) into ng groups.
The arrays set are:
jg = length ng+1 array of group boundaries.
Group ig has indices j = jg[ig],...,jg[ig+1]-1.
jig = length m array of group indices vs node index.
Node index j is in group jig[j].
jr = length ng array of indices representing the groups.
The index for group ig is j = jr[ig].
*/
static void SetGroups(int m, int ng, int jg[], int jig[], int jr[])
{
int ig, j, len1, mper, ngm1;
mper = m/ng; /* does integer division */
for (ig=0; ig < ng; ig++) jg[ig] = ig*mper;
jg[ng] = m;
ngm1 = ng - 1;
len1 = ngm1*mper;
for (j = 0; j < len1; j++) jig[j] = j/mper;
for (j = len1; j < m; j++) jig[j] = ngm1;
for (ig = 0; ig < ngm1; ig++) jr[ig] = ((2*ig+1)*mper-1)/2;
jr[ngm1] = (ngm1*mper+m-1)/2;
}
/* This routine computes and loads the vector of initial values. */
static void CInit(N_Vector c, WebData wdata)
{
int jx, jy, ns, mxns, ioff, iyoff, i, ici;
realtype argx, argy, x, y, dx, dy, x_factor, y_factor, *cdata;
cdata = NV_DATA_S(c);
ns = wdata->ns;
mxns = wdata->mxns;
dx = wdata->dx;
dy = wdata->dy;
x_factor = RCONST(4.0)/SQR(AX);
y_factor = RCONST(4.0)/SQR(AY);
for (jy = 0; jy < MY; jy++) {
y = jy*dy;
argy = SQR(y_factor*y*(AY-y));
iyoff = mxns*jy;
for (jx = 0; jx < MX; jx++) {
x = jx*dx;
argx = SQR(x_factor*x*(AX-x));
ioff = iyoff + ns*jx;
for (i = 1; i <= ns; i++) {
ici = ioff + i-1;
cdata[ici] = RCONST(10.0) + i*argx*argy;
}
}
}
}
static void PrintIntro(void)
{
printf("\n\nDemonstration program for CVODE - CVSPGMR linear solver\n\n");
printf("Food web problem with ns species, ns = %d\n", NS);
printf("Predator-prey interaction and diffusion on a 2-D square\n\n");
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("Matrix parameters: a = %.2Lg e = %.2Lg g = %.2Lg\n",
AA, EE, GG);
printf("b parameter = %.2Lg\n", BB);
printf("Diffusion coefficients: Dprey = %.2Lg Dpred = %.2Lg\n",
DPREY, DPRED);
printf("Rate parameter alpha = %.2Lg\n\n", ALPH);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("Matrix parameters: a = %.2lg e = %.2lg g = %.2lg\n",
AA, EE, GG);
printf("b parameter = %.2lg\n", BB);
printf("Diffusion coefficients: Dprey = %.2lg Dpred = %.2lg\n",
DPREY, DPRED);
printf("Rate parameter alpha = %.2lg\n\n", ALPH);
#else
printf("Matrix parameters: a = %.2g e = %.2g g = %.2g\n",
AA, EE, GG);
printf("b parameter = %.2g\n", BB);
printf("Diffusion coefficients: Dprey = %.2g Dpred = %.2g\n",
DPREY, DPRED);
printf("Rate parameter alpha = %.2g\n\n", ALPH);
#endif
printf("Mesh dimensions (mx,my) are %d, %d. ", MX, MY);
printf("Total system size is neq = %d \n\n", NEQ);
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("Tolerances: reltol = %.2Lg, abstol = %.2Lg \n\n",
RTOL, ATOL);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("Tolerances: reltol = %.2lg, abstol = %.2lg \n\n",
RTOL, ATOL);
#else
printf("Tolerances: reltol = %.2g, abstol = %.2g \n\n",
RTOL, ATOL);
#endif
printf("Preconditioning uses a product of:\n");
printf(" (1) Gauss-Seidel iterations with ");
printf("itmax = %d iterations, and\n", ITMAX);
printf(" (2) interaction-only block-diagonal matrix ");
printf("with block-grouping\n");
printf(" Number of diagonal block groups = ngrp = %d", NGRP);
printf(" (ngx by ngy, ngx = %d, ngy = %d)\n", NGX, NGY);
printf("\n\n--------------------------------------------------------------");
printf("--------------\n");
}
static void PrintHeader(int jpre, int gstype)
{
if(jpre == PREC_LEFT)
printf("\n\nPreconditioner type is jpre = %s\n", "PREC_LEFT");
else
printf("\n\nPreconditioner type is jpre = %s\n", "PREC_RIGHT");
if(gstype == MODIFIED_GS)
printf("\nGram-Schmidt method type is gstype = %s\n\n\n", "MODIFIED_GS");
else
printf("\nGram-Schmidt method type is gstype = %s\n\n\n", "CLASSICAL_GS");
}
static void PrintAllSpecies(N_Vector c, int ns, int mxns, realtype t)
{
int i, jx ,jy;
realtype *cdata;
cdata = NV_DATA_S(c);
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("c values at t = %Lg:\n\n", t);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("c values at t = %lg:\n\n", t);
#else
printf("c values at t = %g:\n\n", t);
#endif
for (i=1; i <= ns; i++) {
printf("Species %d\n", i);
for (jy=MY-1; jy >= 0; jy--) {
for (jx=0; jx < MX; jx++) {
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("%-10.6Lg", cdata[(i-1) + jx*ns + jy*mxns]);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("%-10.6lg", cdata[(i-1) + jx*ns + jy*mxns]);
#else
printf("%-10.6g", cdata[(i-1) + jx*ns + jy*mxns]);
#endif
}
printf("\n");
}
printf("\n");
}
}
static void PrintOutput(void *cvode_mem, realtype t)
{
long int nst, nfe, nni;
int qu, flag;
realtype hu;
flag = CVodeGetNumSteps(cvode_mem, &nst);
check_flag(&flag, "CVodeGetNumSteps", 1);
flag = CVodeGetNumRhsEvals(cvode_mem, &nfe);
check_flag(&flag, "CVodeGetNumRhsEvals", 1);
flag = CVodeGetNumNonlinSolvIters(cvode_mem, &nni);
check_flag(&flag, "CVodeGetNumNonlinSolvIters", 1);
flag = CVodeGetLastOrder(cvode_mem, &qu);
check_flag(&flag, "CVodeGetLastOrder", 1);
flag = CVodeGetLastStep(cvode_mem, &hu);
check_flag(&flag, "CVodeGetLastStep", 1);
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf("t = %10.2Le nst = %ld nfe = %ld nni = %ld", t, nst, nfe, nni);
printf(" qu = %d hu = %11.2Le\n\n", qu, hu);
#elif defined(SUNDIALS_DOUBLE_PRECISION)
printf("t = %10.2le nst = %ld nfe = %ld nni = %ld", t, nst, nfe, nni);
printf(" qu = %d hu = %11.2le\n\n", qu, hu);
#else
printf("t = %10.2e nst = %ld nfe = %ld nni = %ld", t, nst, nfe, nni);
printf(" qu = %d hu = %11.2e\n\n", qu, hu);
#endif
}
static void PrintFinalStats(void *cvode_mem)
{
long int lenrw, leniw ;
long int lenrwLS, leniwLS;
long int nst, nfe, nsetups, nni, ncfn, netf;
long int nli, npe, nps, ncfl, nfeLS;
int flag;
realtype avdim;
flag = CVodeGetWorkSpace(cvode_mem, &lenrw, &leniw);
check_flag(&flag, "CVodeGetWorkSpace", 1);
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 = CVSpilsGetWorkSpace(cvode_mem, &lenrwLS, &leniwLS);
check_flag(&flag, "CVSpilsGetWorkSpace", 1);
flag = CVSpilsGetNumLinIters(cvode_mem, &nli);
check_flag(&flag, "CVSpilsGetNumLinIters", 1);
flag = CVSpilsGetNumPrecEvals(cvode_mem, &npe);
check_flag(&flag, "CVSpilsGetNumPrecEvals", 1);
flag = CVSpilsGetNumPrecSolves(cvode_mem, &nps);
check_flag(&flag, "CVSpilsGetNumPrecSolves", 1);
flag = CVSpilsGetNumConvFails(cvode_mem, &ncfl);
check_flag(&flag, "CVSpilsGetNumConvFails", 1);
flag = CVSpilsGetNumRhsEvals(cvode_mem, &nfeLS);
check_flag(&flag, "CVSpilsGetNumRhsEvals", 1);
printf("\n\n Final statistics for this run:\n\n");
printf(" CVode real workspace length = %4ld \n", lenrw);
printf(" CVode integer workspace length = %4ld \n", leniw);
printf(" CVSPGMR real workspace length = %4ld \n", lenrwLS);
printf(" CVSPGMR integer workspace length = %4ld \n", leniwLS);
printf(" Number of steps = %4ld \n", nst);
printf(" Number of f-s = %4ld \n", nfe);
printf(" Number of f-s (SPGMR) = %4ld \n", nfeLS);
printf(" Number of f-s (TOTAL) = %4ld \n", nfe + nfeLS);
printf(" Number of setups = %4ld \n", nsetups);
printf(" Number of nonlinear iterations = %4ld \n", nni);
printf(" Number of linear iterations = %4ld \n", nli);
printf(" Number of preconditioner evaluations = %4ld \n", npe);
printf(" Number of preconditioner solves = %4ld \n", nps);
printf(" Number of error test failures = %4ld \n", netf);
printf(" Number of nonlinear conv. failures = %4ld \n", ncfn);
printf(" Number of linear convergence failures = %4ld \n", ncfl);
avdim = (nni > 0) ? ((realtype)nli)/((realtype)nni) : ZERO;
#if defined(SUNDIALS_EXTENDED_PRECISION)
printf(" Average Krylov subspace dimension = %.3Lf \n", avdim);
#else
printf(" Average Krylov subspace dimension = %.3f \n", avdim);
#endif
printf("\n\n--------------------------------------------------------------");
printf("--------------\n");
printf( "--------------------------------------------------------------");
printf("--------------\n");
}
static void FreeUserData(WebData wdata)
{
int i, ngrp;
ngrp = wdata->ngrp;
for(i=0; i < ngrp; i++) {
destroyMat((wdata->P)[i]);
destroyArray((wdata->pivot)[i]);
}
N_VDestroy_Serial(wdata->rewt);
free(wdata);
}
/*
This routine computes the right-hand side of the ODE system and
returns it in cdot. The interaction rates are computed by calls to WebRates,
and these are saved in fsave for use in preconditioning.
*/
static int f(realtype t, N_Vector c, N_Vector cdot,void *user_data)
{
int i, ic, ici, idxl, idxu, jx, ns, mxns, iyoff, jy, idyu, idyl;
realtype dcxli, dcxui, dcyli, dcyui, x, y, *cox, *coy, *fsave, dx, dy;
realtype *cdata, *cdotdata;
WebData wdata;
wdata = (WebData) user_data;
cdata = NV_DATA_S(c);
cdotdata = NV_DATA_S(cdot);
mxns = wdata->mxns;
ns = wdata->ns;
fsave = wdata->fsave;
cox = wdata->cox;
coy = wdata->coy;
mxns = wdata->mxns;
dx = wdata->dx;
dy = wdata->dy;
for (jy = 0; jy < MY; jy++) {
y = jy*dy;
iyoff = mxns*jy;
idyu = (jy == MY-1) ? -mxns : mxns;
idyl = (jy == 0) ? -mxns : mxns;
for (jx = 0; jx < MX; jx++) {
x = jx*dx;
ic = iyoff + ns*jx;
/* Get interaction rates at one point (x,y). */
WebRates(x, y, t, cdata+ic, fsave+ic, wdata);
idxu = (jx == MX-1) ? -ns : ns;
idxl = (jx == 0) ? -ns : ns;
for (i = 1; i <= ns; i++) {
ici = ic + i-1;
/* Do differencing in y. */
dcyli = cdata[ici] - cdata[ici-idyl];
dcyui = cdata[ici+idyu] - cdata[ici];
/* Do differencing in x. */
dcxli = cdata[ici] - cdata[ici-idxl];
dcxui = cdata[ici+idxu] - cdata[ici];
/* Collect terms and load cdot elements. */
cdotdata[ici] = coy[i-1]*(dcyui - dcyli) + cox[i-1]*(dcxui - dcxli) +
fsave[ici];
}
}
}
return(0);
}
/*
This routine computes the interaction rates for the species
c_1, ... ,c_ns (stored in c[0],...,c[ns-1]), at one spatial point
and at time t.
*/
static void WebRates(realtype x, realtype y, realtype t, realtype c[],
realtype rate[], WebData wdata)
{
int i, j, ns;
realtype fac, *bcoef;
realtype (*acoef)[NS];
ns = wdata->ns;
acoef = wdata->acoef;
bcoef = wdata->bcoef;
for (i = 0; i < ns; i++)
rate[i] = ZERO;
for (j = 0; j < ns; j++)
for (i = 0; i < ns; i++)
rate[i] += c[j] * acoef[i][j];
fac = ONE + ALPH*x*y;
for (i = 0; i < ns; i++)
rate[i] = c[i]*(bcoef[i]*fac + rate[i]);
}
/*
This routine generates the block-diagonal part of the Jacobian
corresponding to the interaction rates, multiplies by -gamma, adds
the identity matrix, and calls denseGETRF to do the LU decomposition of
each diagonal block. The computation of the diagonal blocks uses
the preset block and grouping information. One block per group is
computed. The Jacobian elements are generated by difference
quotients using calls to the routine fblock.
This routine can be regarded as a prototype for the general case
of a block-diagonal preconditioner. The blocks are of size mp, and
there are ngrp=ngx*ngy blocks computed in the block-grouping scheme.
*/
static int Precond(realtype t, N_Vector c, N_Vector fc,
booleantype jok, booleantype *jcurPtr, realtype gamma,
void *user_data, N_Vector vtemp1, N_Vector vtemp2,
N_Vector vtemp3)
{
realtype ***P;
int ier;
long int **pivot;
int i, if0, if00, ig, igx, igy, j, jj, jx, jy;
int *jxr, *jyr, ngrp, ngx, ngy, mxmp, flag;
long int mp;
realtype uround, fac, r, r0, save, srur;
realtype *f1, *fsave, *cdata, *rewtdata;
WebData wdata;
void *cvode_mem;
N_Vector rewt;
wdata = (WebData) user_data;
cvode_mem = wdata->cvode_mem;
cdata = NV_DATA_S(c);
rewt = wdata->rewt;
flag = CVodeGetErrWeights(cvode_mem, rewt);
if(check_flag(&flag, "CVodeGetErrWeights", 1)) return(1);
rewtdata = NV_DATA_S(rewt);
uround = UNIT_ROUNDOFF;
P = wdata->P;
pivot = wdata->pivot;
jxr = wdata->jxr;
jyr = wdata->jyr;
mp = wdata->mp;
srur = wdata->srur;
ngrp = wdata->ngrp;
ngx = wdata->ngx;
ngy = wdata->ngy;
mxmp = wdata->mxmp;
fsave = wdata->fsave;
/* Make mp calls to fblock to approximate each diagonal block of Jacobian.
Here, fsave contains the base value of the rate vector and
r0 is a minimum increment factor for the difference quotient. */
f1 = NV_DATA_S(vtemp1);
fac = N_VWrmsNorm (fc, rewt);
r0 = RCONST(1000.0)*ABS(gamma)*uround*NEQ*fac;
if (r0 == ZERO) r0 = ONE;
for (igy = 0; igy < ngy; igy++) {
jy = jyr[igy];
if00 = jy*mxmp;
for (igx = 0; igx < ngx; igx++) {
jx = jxr[igx];
if0 = if00 + jx*mp;
ig = igx + igy*ngx;
/* Generate ig-th diagonal block */
for (j = 0; j < mp; j++) {
/* Generate the jth column as a difference quotient */
jj = if0 + j;
save = cdata[jj];
r = MAX(srur*ABS(save),r0/rewtdata[jj]);
cdata[jj] += r;
fac = -gamma/r;
fblock (t, cdata, jx, jy, f1, wdata);
for (i = 0; i < mp; i++) {
P[ig][j][i] = (f1[i] - fsave[if0+i])*fac;
}
cdata[jj] = save;
}
}
}
/* Add identity matrix and do LU decompositions on blocks. */
for (ig = 0; ig < ngrp; ig++) {
denseAddIdentity(P[ig], mp);
ier = denseGETRF(P[ig], mp, mp, pivot[ig]);
if (ier != 0) return(1);
}
*jcurPtr = TRUE;
return(0);
}
/*
This routine computes one block of the interaction terms of the
system, namely block (jx,jy), for use in preconditioning.
Here jx and jy count from 0.
*/
static void fblock(realtype t, realtype cdata[], int jx, int jy,
realtype cdotdata[], WebData wdata)
{
int iblok, ic;
realtype x, y;
iblok = jx + jy*(wdata->mx);
y = jy*(wdata->dy);
x = jx*(wdata->dx);
ic = (wdata->ns)*(iblok);
WebRates(x, y, t, cdata+ic, cdotdata, wdata);
}
/*
This routine applies two inverse preconditioner matrices
to the vector r, using the interaction-only block-diagonal Jacobian
with block-grouping, denoted Jr, and Gauss-Seidel applied to the
diffusion contribution to the Jacobian, denoted Jd.
It first calls GSIter for a Gauss-Seidel approximation to
((I - gamma*Jd)-inverse)*r, and stores the result in z.
Then it computes ((I - gamma*Jr)-inverse)*z, using LU factors of the
blocks in P, and pivot information in pivot, and returns the result in z.
*/
static int PSolve(realtype tn, N_Vector c, N_Vector fc,
N_Vector r, N_Vector z,
realtype gamma, realtype delta,
int lr, void *user_data, N_Vector vtemp)
{
realtype ***P;
long int **pivot;
int jx, jy, igx, igy, iv, ig, *jigx, *jigy, mx, my, ngx;
long int mp;
WebData wdata;
wdata = (WebData) user_data;
N_VScale(ONE, r, z);
/* call GSIter for Gauss-Seidel iterations */
GSIter(gamma, z, vtemp, wdata);
/* Do backsolves for inverse of block-diagonal preconditioner factor */
P = wdata->P;
pivot = wdata->pivot;
mx = wdata->mx;
my = wdata->my;
ngx = wdata->ngx;
mp = wdata->mp;
jigx = wdata->jigx;
jigy = wdata->jigy;
iv = 0;
for (jy = 0; jy < my; jy++) {
igy = jigy[jy];
for (jx = 0; jx < mx; jx++) {
igx = jigx[jx];
ig = igx + igy*ngx;
denseGETRS(P[ig], mp, pivot[ig], &(NV_DATA_S(z)[iv]));
iv += mp;
}
}
return(0);
}
/*
This routine performs ITMAX=5 Gauss-Seidel iterations to compute an
approximation to (P-inverse)*z, where P = I - gamma*Jd, and
Jd represents the diffusion contributions to the Jacobian.
The answer is stored in z on return, and x is a temporary vector.
The dimensions below assume a global constant NS >= ns.
Some inner loops of length ns are implemented with the small
vector kernels v_sum_prods, v_prod, v_inc_by_prod.
*/
static void GSIter(realtype gamma, N_Vector z, N_Vector x, WebData wdata)
{
int jx, jy, mx, my, x_loc, y_loc;
int ns, mxns, i, iyoff, ic, iter;
realtype beta[NS], beta2[NS], cof1[NS], gam[NS], gam2[NS];
realtype temp, *cox, *coy, *xd, *zd;
xd = NV_DATA_S(x);
zd = NV_DATA_S(z);
ns = wdata->ns;
mx = wdata->mx;
my = wdata->my;
mxns = wdata->mxns;
cox = wdata->cox;
coy = wdata->coy;
/* Write matrix as P = D - L - U.
Load local arrays beta, beta2, gam, gam2, and cof1. */
for (i = 0; i < ns; i++) {
temp = ONE/(ONE + RCONST(2.0)*gamma*(cox[i] + coy[i]));
beta[i] = gamma*cox[i]*temp;
beta2[i] = RCONST(2.0)*beta[i];
gam[i] = gamma*coy[i]*temp;
gam2[i] = RCONST(2.0)*gam[i];
cof1[i] = temp;
}
/* Begin iteration loop.
Load vector x with (D-inverse)*z for first iteration. */
for (jy = 0; jy < my; jy++) {
iyoff = mxns*jy;
for (jx = 0; jx < mx; jx++) {
ic = iyoff + ns*jx;
v_prod(xd+ic, cof1, zd+ic, ns); /* x[ic+i] = cof1[i]z[ic+i] */
}
}
N_VConst(ZERO, z);
/* Looping point for iterations. */
for (iter=1; iter <= ITMAX; iter++) {
/* Calculate (D-inverse)*U*x if not the first iteration. */
if (iter > 1) {
for (jy=0; jy < my; jy++) {
iyoff = mxns*jy;
for (jx=0; jx < mx; jx++) { /* order of loops matters */
ic = iyoff + ns*jx;
x_loc = (jx == 0) ? 0 : ((jx == mx-1) ? 2 : 1);
y_loc = (jy == 0) ? 0 : ((jy == my-1) ? 2 : 1);
switch (3*y_loc+x_loc) {
case 0 :
/* jx == 0, jy == 0 */
/* x[ic+i] = beta2[i]x[ic+ns+i] + gam2[i]x[ic+mxns+i] */
v_sum_prods(xd+ic, beta2, xd+ic+ns, gam2, xd+ic+mxns, ns);
break;
case 1 :
/* 1 <= jx <= mx-2, jy == 0 */
/* x[ic+i] = beta[i]x[ic+ns+i] + gam2[i]x[ic+mxns+i] */
v_sum_prods(xd+ic, beta, xd+ic+ns, gam2, xd+ic+mxns, ns);
break;
case 2 :
/* jx == mx-1, jy == 0 */
/* x[ic+i] = gam2[i]x[ic+mxns+i] */
v_prod(xd+ic, gam2, xd+ic+mxns, ns);
break;
case 3 :
/* jx == 0, 1 <= jy <= my-2 */
/* x[ic+i] = beta2[i]x[ic+ns+i] + gam[i]x[ic+mxns+i] */
v_sum_prods(xd+ic, beta2, xd+ic+ns, gam, xd+ic+mxns, ns);
break;
case 4 :
/* 1 <= jx <= mx-2, 1 <= jy <= my-2 */
/* x[ic+i] = beta[i]x[ic+ns+i] + gam[i]x[ic+mxns+i] */
v_sum_prods(xd+ic, beta, xd+ic+ns, gam, xd+ic+mxns, ns);
break;
case 5 :
/* jx == mx-1, 1 <= jy <= my-2 */
/* x[ic+i] = gam[i]x[ic+mxns+i] */
v_prod(xd+ic, gam, xd+ic+mxns, ns);
break;
case 6 :
/* jx == 0, jy == my-1 */
/* x[ic+i] = beta2[i]x[ic+ns+i] */
v_prod(xd+ic, beta2, xd+ic+ns, ns);
break;
case 7 :
/* 1 <= jx <= mx-2, jy == my-1 */
/* x[ic+i] = beta[i]x[ic+ns+i] */
v_prod(xd+ic, beta, xd+ic+ns, ns);
break;
case 8 :
/* jx == mx-1, jy == my-1 */
/* x[ic+i] = 0.0 */
v_zero(xd+ic, ns);
break;
}
}
}
} /* end if (iter > 1) */
/* Overwrite x with [(I - (D-inverse)*L)-inverse]*x. */
for (jy=0; jy < my; jy++) {
iyoff = mxns*jy;
for (jx=0; jx < mx; jx++) { /* order of loops matters */
ic = iyoff + ns*jx;
x_loc = (jx == 0) ? 0 : ((jx == mx-1) ? 2 : 1);
y_loc = (jy == 0) ? 0 : ((jy == my-1) ? 2 : 1);
switch (3*y_loc+x_loc) {
case 0 :
/* jx == 0, jy == 0 */
break;
case 1 :
/* 1 <= jx <= mx-2, jy == 0 */
/* x[ic+i] += beta[i]x[ic-ns+i] */
v_inc_by_prod(xd+ic, beta, xd+ic-ns, ns);
break;
case 2 :
/* jx == mx-1, jy == 0 */
/* x[ic+i] += beta2[i]x[ic-ns+i] */
v_inc_by_prod(xd+ic, beta2, xd+ic-ns, ns);
break;
case 3 :
/* jx == 0, 1 <= jy <= my-2 */
/* x[ic+i] += gam[i]x[ic-mxns+i] */
v_inc_by_prod(xd+ic, gam, xd+ic-mxns, ns);
break;
case 4 :
/* 1 <= jx <= mx-2, 1 <= jy <= my-2 */
/* x[ic+i] += beta[i]x[ic-ns+i] + gam[i]x[ic-mxns+i] */
v_inc_by_prod(xd+ic, beta, xd+ic-ns, ns);
v_inc_by_prod(xd+ic, gam, xd+ic-mxns, ns);
break;
case 5 :
/* jx == mx-1, 1 <= jy <= my-2 */
/* x[ic+i] += beta2[i]x[ic-ns+i] + gam[i]x[ic-mxns+i] */
v_inc_by_prod(xd+ic, beta2, xd+ic-ns, ns);
v_inc_by_prod(xd+ic, gam, xd+ic-mxns, ns);
break;
case 6 :
/* jx == 0, jy == my-1 */
/* x[ic+i] += gam2[i]x[ic-mxns+i] */
v_inc_by_prod(xd+ic, gam2, xd+ic-mxns, ns);
break;
case 7 :
/* 1 <= jx <= mx-2, jy == my-1 */
/* x[ic+i] += beta[i]x[ic-ns+i] + gam2[i]x[ic-mxns+i] */
v_inc_by_prod(xd+ic, beta, xd+ic-ns, ns);
v_inc_by_prod(xd+ic, gam2, xd+ic-mxns, ns);
break;
case 8 :
/* jx == mx-1, jy == my-1 */
/* x[ic+i] += beta2[i]x[ic-ns+i] + gam2[i]x[ic-mxns+i] */
v_inc_by_prod(xd+ic, beta2, xd+ic-ns, ns);
v_inc_by_prod(xd+ic, gam2, xd+ic-mxns, ns);
break;
}
}
}
/* Add increment x to z : z <- z+x */
N_VLinearSum(ONE, z, ONE, x, z);
}
}
static void v_inc_by_prod(realtype u[], realtype v[], realtype w[], int n)
{
int i;
for (i=0; i < n; i++) u[i] += v[i]*w[i];
}
static void v_sum_prods(realtype u[], realtype p[], realtype q[],
realtype v[], realtype w[], int n)
{
int i;
for (i=0; i < n; i++) u[i] = p[i]*q[i] + v[i]*w[i];
}
static void v_prod(realtype u[], realtype v[], realtype w[], int n)
{
int i;
for (i=0; i < n; i++) u[i] = v[i]*w[i];
}
static void v_zero(realtype u[], int n)
{
int i;
for (i=0; i < n; i++) u[i] = ZERO;
}
/* 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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