PetscErrorCode SetRandomVectors(AppCtx *user)
{
PetscErrorCode ierr;
PetscInt i,n,count=0;
PetscScalar *w1,*w2,*Pv_p,*eta_p;
PetscFunctionBeginUser;
ierr = VecSetRandom(user->work1,NULL);CHKERRQ(ierr);
ierr = VecSetRandom(user->work2,NULL);CHKERRQ(ierr);
ierr = VecGetArray(user->work1,&w1);CHKERRQ(ierr);
ierr = VecGetArray(user->work2,&w2);CHKERRQ(ierr);
ierr = VecGetArray(user->Pv,&Pv_p);CHKERRQ(ierr);
ierr = VecGetArray(user->eta,&eta_p);CHKERRQ(ierr);
ierr = VecGetLocalSize(user->work1,&n);CHKERRQ(ierr);
for (i=0; i<n; i++) {
if (eta_p[i]>=0.8 || w1[i]>user->P_casc) Pv_p[i]=0;
else {
Pv_p[i]=w2[i]*user->VG;
count =count+1;
}
}
ierr = VecCopy(user->Pv,user->Pi);CHKERRQ(ierr);
ierr = VecScale(user->Pi,0.9);CHKERRQ(ierr);
ierr = VecPointwiseMult(user->Piv,user->Pi,user->Pv);CHKERRQ(ierr);
ierr = VecRestoreArray(user->work1,&w1);CHKERRQ(ierr);
ierr = VecRestoreArray(user->work2,&w2);CHKERRQ(ierr);
ierr = VecRestoreArray(user->Pv,&Pv_p);CHKERRQ(ierr);
ierr = VecRestoreArray(user->eta,&eta_p);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc, char **argv)
{
PetscErrorCode ierr;
Vec *V,t;
PetscInt i,j,reps,n=15,k=6;
PetscRandom rctx;
PetscScalar *val_dot,*val_mdot,*tval_dot,*tval_mdot;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-k",&k,NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Test with %D random vectors of length %D",k,n);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n",k,n);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&t);CHKERRQ(ierr);
ierr = VecSetSizes(t,n,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(t);CHKERRQ(ierr);
ierr = VecDuplicateVecs(t,k,&V);CHKERRQ(ierr);
ierr = VecSetRandom(t,rctx);CHKERRQ(ierr);
ierr = PetscMalloc1(k,&val_dot);CHKERRQ(ierr);
ierr = PetscMalloc1(k,&val_mdot);CHKERRQ(ierr);
ierr = PetscMalloc1(k,&tval_dot);CHKERRQ(ierr);
ierr = PetscMalloc1(k,&tval_mdot);CHKERRQ(ierr);
for (i=0; i<k; i++) { ierr = VecSetRandom(V[i],rctx);CHKERRQ(ierr); }
for (reps=0; reps<20; reps++) {
for (i=1; i<k; i++) {
ierr = VecMDot(t,i,V,val_mdot);CHKERRQ(ierr);
ierr = VecMTDot(t,i,V,tval_mdot);CHKERRQ(ierr);
for (j=0;j<i;j++) {
ierr = VecDot(t,V[j],&val_dot[j]);CHKERRQ(ierr);
ierr = VecTDot(t,V[j],&tval_dot[j]);CHKERRQ(ierr);
}
/* Check result */
for (j=0;j<i;j++) {
if (PetscAbsScalar(val_mdot[j] - val_dot[j])/PetscAbsScalar(val_dot[j]) > 1e-5) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "[TEST FAILED] i=%D, j=%D, val_mdot[j]=%g, val_dot[j]=%g\n",i,j,(double)PetscAbsScalar(val_mdot[j]), (double)PetscAbsScalar(val_dot[j]));CHKERRQ(ierr);
break;
}
if (PetscAbsScalar(tval_mdot[j] - tval_dot[j])/PetscAbsScalar(tval_dot[j]) > 1e-5) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "[TEST FAILED] i=%D, j=%D, tval_mdot[j]=%g, tval_dot[j]=%g\n",i,j,(double)PetscAbsScalar(tval_mdot[j]), (double)PetscAbsScalar(tval_dot[j]));CHKERRQ(ierr);
break;
}
}
}
}
ierr = PetscPrintf(PETSC_COMM_WORLD,"Test completed successfully!\n",k,n);CHKERRQ(ierr);
ierr = PetscFree(val_dot);CHKERRQ(ierr);
ierr = PetscFree(val_mdot);CHKERRQ(ierr);
ierr = PetscFree(tval_dot);CHKERRQ(ierr);
ierr = PetscFree(tval_mdot);CHKERRQ(ierr);
ierr = VecDestroyVecs(k,&V);CHKERRQ(ierr);
ierr = VecDestroy(&t);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
/*@
MatMultAddEqual - Compares matrix-vector products of two matrices.
Collective on Mat
Input Parameters:
+ A - the first matrix
- B - the second matrix
- n - number of random vectors to be tested
Output Parameter:
. flg - PETSC_TRUE if the products are equal; PETSC_FALSE otherwise.
Level: intermediate
Concepts: matrices^equality between
@*/
PetscErrorCode MatMultAddEqual(Mat A,Mat B,PetscInt n,PetscBool *flg)
{
PetscErrorCode ierr;
Vec x,y,s1,s2;
PetscRandom rctx;
PetscReal r1,r2,tol=1.e-10;
PetscInt am,an,bm,bn,k;
PetscScalar none = -1.0;
PetscFunctionBegin;
ierr = MatGetLocalSize(A,&am,&an);CHKERRQ(ierr);
ierr = MatGetLocalSize(B,&bm,&bn);CHKERRQ(ierr);
if (am != bm || an != bn) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat A,Mat B: local dim %D %D %D %D",am,bm,an,bn);
PetscCheckSameComm(A,1,B,2);
ierr = PetscRandomCreate(((PetscObject)A)->comm,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecCreate(((PetscObject)A)->comm,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,an,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecCreate(((PetscObject)A)->comm,&s1);CHKERRQ(ierr);
ierr = VecSetSizes(s1,am,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetFromOptions(s1);CHKERRQ(ierr);
ierr = VecDuplicate(s1,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(s1,&y);CHKERRQ(ierr);
*flg = PETSC_TRUE;
for (k=0; k<n; k++) {
ierr = VecSetRandom(x,rctx);CHKERRQ(ierr);
ierr = VecSetRandom(y,rctx);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(B,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_INFINITY,&r2);CHKERRQ(ierr);
if (r2 < tol){
ierr = VecNorm(s1,NORM_INFINITY,&r1);CHKERRQ(ierr);
} else {
ierr = VecAXPY(s2,none,s1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_INFINITY,&r1);CHKERRQ(ierr);
r1 /= r2;
}
if (r1 > tol) {
*flg = PETSC_FALSE;
ierr = PetscInfo2(A,"Error: %d-th MatMultAdd() %G\n",k,r1);CHKERRQ(ierr);
break;
}
}
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode SNESNEWTONLSCheckLocalMin_Private(SNES snes,Mat A,Vec F,PetscReal fnorm,PetscBool *ismin)
{
PetscReal a1;
PetscErrorCode ierr;
PetscBool hastranspose;
Vec W;
PetscFunctionBegin;
*ismin = PETSC_FALSE;
ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr);
ierr = VecDuplicate(F,&W);CHKERRQ(ierr);
if (hastranspose) {
/* Compute || J^T F|| */
ierr = MatMultTranspose(A,F,W);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_2,&a1);CHKERRQ(ierr);
ierr = PetscInfo1(snes,"|| J^T F|| %14.12e near zero implies found a local minimum\n",(double)(a1/fnorm));CHKERRQ(ierr);
if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE;
} else {
Vec work;
PetscScalar result;
PetscReal wnorm;
ierr = VecSetRandom(W,NULL);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_2,&wnorm);CHKERRQ(ierr);
ierr = VecDuplicate(W,&work);CHKERRQ(ierr);
ierr = MatMult(A,W,work);CHKERRQ(ierr);
ierr = VecDot(F,work,&result);CHKERRQ(ierr);
ierr = VecDestroy(&work);CHKERRQ(ierr);
a1 = PetscAbsScalar(result)/(fnorm*wnorm);
ierr = PetscInfo1(snes,"(F^T J random)/(|| F ||*||random|| %14.12e near zero implies found a local minimum\n",(double)a1);CHKERRQ(ierr);
if (a1 < 1.e-4) *ismin = PETSC_TRUE;
}
ierr = VecDestroy(&W);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
// Formulas from page 22 of Hundsdorfer & Verwer (2003). Interpretation here is
// to always generate 0.5 x 0.5 non-trivial patch in (0,L) x (0,L) domain.
PetscErrorCode InitialState(Vec Y, double noiselevel, PatternCtx* user) {
PetscErrorCode ierr;
DMDALocalInfo info;
int i,j;
double sx,sy;
const double ledge = (user->L - 0.5) / 2.0, // nontrivial initial values on
redge = user->L - ledge; // ledge < x,y < redge
DMDACoor2d **aC;
Field **aY;
ierr = VecSet(Y,0.0); CHKERRQ(ierr);
if (noiselevel > 0.0) {
// noise added to usual initial condition is uniform on [0,noiselevel],
// independently for each location and component
ierr = VecSetRandom(Y,NULL); CHKERRQ(ierr);
ierr = VecScale(Y,noiselevel); CHKERRQ(ierr);
}
ierr = DMDAGetLocalInfo(user->da,&info); CHKERRQ(ierr);
ierr = DMDAGetCoordinateArray(user->da,&aC); CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da,Y,&aY); CHKERRQ(ierr);
for (j = info.ys; j < info.ys+info.ym; j++) {
for (i = info.xs; i < info.xs+info.xm; i++) {
if ((aC[j][i].x >= ledge) && (aC[j][i].x <= redge)
&& (aC[j][i].y >= ledge) && (aC[j][i].y <= redge)) {
sx = sin(4.0 * PETSC_PI * aC[j][i].x);
sy = sin(4.0 * PETSC_PI * aC[j][i].y);
aY[j][i].v += 0.5 * sx * sx * sy * sy;
}
aY[j][i].u += 1.0 - 2.0 * aY[j][i].v;
}
}
ierr = DMDAVecRestoreArray(user->da,Y,&aY); CHKERRQ(ierr);
ierr = DMDARestoreCoordinateArray(user->da,&aC); CHKERRQ(ierr);
return 0;
}
PetscErrorCode computeMaxEigVal(Mat A, PetscInt its, PetscScalar *eig)
{
PetscErrorCode ierr;
PetscRandom rctx; /* random number generator context */
Vec x0, x, x_1, tmp;
PetscScalar lambda_its, lambda_its_1;
PetscInt i;
PetscFunctionBeginUser;
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = MatGetVecs(A, &x_1, &x);CHKERRQ(ierr);
ierr = VecSetRandom(x, rctx);CHKERRQ(ierr);
ierr = VecDuplicate(x, &x0);CHKERRQ(ierr);
ierr = VecCopy(x, x0);CHKERRQ(ierr);
ierr = MatMult(A, x, x_1);CHKERRQ(ierr);
for (i=0; i<its; i++) {
tmp = x; x = x_1; x_1 = tmp;
ierr = MatMult(A, x, x_1);CHKERRQ(ierr);
}
ierr = VecDot(x0, x, &lambda_its);CHKERRQ(ierr);
ierr = VecDot(x0, x_1, &lambda_its_1);CHKERRQ(ierr);
*eig = lambda_its_1/lambda_its;
ierr = VecDestroy(&x0);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&x_1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetInitialGuess(Vec X,AppCtx* user)
{
PetscErrorCode ierr;
PetscScalar *x,*u;
PetscInt n,i;
Vec rand;
PetscFunctionBegin;
/* u = -0.4 + 0.05*rand(N,1)*(rand(N,1) - 0.5) */
ierr = VecDuplicate(user->u,&rand);
ierr = VecSetRandom(rand,PETSC_NULL);
ierr = VecCopy(rand,user->u);
ierr = VecShift(rand,-0.5);CHKERRQ(ierr);
ierr = VecPointwiseMult(user->u,user->u,rand);CHKERRQ(ierr);
ierr = VecDestroy(&rand);CHKERRQ(ierr);
ierr = VecScale(user->u,0.05);CHKERRQ(ierr);
ierr = VecShift(user->u,-0.4);CHKERRQ(ierr);
ierr = VecGetLocalSize(X,&n);CHKERRQ(ierr);
ierr = VecGetArray(X,&x);CHKERRQ(ierr);
ierr = VecGetArray(user->u,&u);CHKERRQ(ierr);
/* Set initial guess, only set value for 2nd dof */
for(i=0;i<n/2;i++) {
x[2*i+1] = u[i];
}
ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(user->u,&u);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode generateVectorRandom(int size, Vec * v){
PetscErrorCode ierr;
ierr=PetscPrintf(PETSC_COMM_WORLD,"Generating Vector \n");CHKERRQ(ierr);
ierr=generateVector(size,v);CHKERRQ(ierr);
ierr=VecSetRandom(*v,PETSC_NULL);CHKERRQ(ierr);
PetscPrintf(PETSC_COMM_WORLD,"Generated Random Vector of size : %d\n",size);
return 0;
}
/*
MSA_InitialPoint - Calculates the initial guess in one of three ways.
Input Parameters:
. user - user-defined application context
. X - vector for initial guess
Output Parameters:
. X - newly computed initial guess
*/
static int MSA_InitialPoint(AppCtx * user, Vec X)
{
int info;
PetscInt start2=-1,i,j;
PetscReal start1=0;
PetscTruth flg1,flg2;
info = PetscOptionsGetReal(PETSC_NULL,"-start",&start1,&flg1); CHKERRQ(info);
info = PetscOptionsGetInt(PETSC_NULL,"-random",&start2,&flg2); CHKERRQ(info);
if (flg1){ /* The zero vector is reasonable */
info = VecSet(X, start1); CHKERRQ(info);
} else if (flg2 && start2>0){ /* Try a random start between -0.5 and 0.5 */
PetscRandom rctx; PetscScalar np5=-0.5;
info = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
CHKERRQ(info);
for (i=0; i<start2; i++){
info = VecSetRandom(X, rctx); CHKERRQ(info);
}
info = PetscRandomDestroy(rctx); CHKERRQ(info);
info = VecShift(X, np5); CHKERRQ(info);
} else { /* Take an average of the boundary conditions */
PetscInt xs,xm,ys,ym;
PetscInt mx=user->mx,my=user->my;
PetscScalar **x;
/* Get local mesh boundaries */
info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
/* Get pointers to vector data */
info = DAVecGetArray(user->da,X,(void**)&x);
/* Perform local computations */
for (j=ys; j<ys+ym; j++){
for (i=xs; i< xs+xm; i++){
x[j][i] = ( ((j+1)*user->bottom[i-xs+1]+(my-j+1)*user->top[i-xs+1])/(my+2)+
((i+1)*user->left[j-ys+1]+(mx-i+1)*user->right[j-ys+1])/(mx+2))/2.0;
}
}
/* Restore vectors */
info = DAVecRestoreArray(user->da,X,(void**)&x); CHKERRQ(info);
info = PetscLogFlops(9*xm*ym); CHKERRQ(info);
}
return 0;
}
void PetscVector::randomize( double alpha, double beta, double * /* ix */ )
{
int ierr;
PetscRandom rctx;
ierr = PetscRandomCreate(PETSC_COMM_WORLD,RANDOM_DEFAULT,&rctx);
assert(ierr == 0);
ierr = PetscRandomSetInterval(rctx, alpha, beta );
assert(ierr == 0);
ierr = VecSetRandom(pv, rctx);
assert(ierr == 0);
ierr = PetscRandomDestroy(rctx);
assert(ierr == 0);
}
PetscErrorCode PCApply_Noise(PC pc,Vec xin,Vec xout)
{
PetscErrorCode ierr;
PCNoise_Ctx *ctx;
PetscReal nrmin, nrmnoise;
PetscFunctionBeginUser;
ierr = PCShellGetContext(pc,(void**)&ctx);CHKERRQ(ierr);
/* xout is ||xin|| * ctx->eta* f, where f is a pseudorandom unit vector
(Note that this should always be combined additively with another PC) */
ierr = VecSetRandom(xout,ctx->random);CHKERRQ(ierr);
ierr = VecNorm(xin,NORM_2,&nrmin);CHKERRQ(ierr);
ierr = VecNorm(xout,NORM_2,&nrmnoise);CHKERRQ(ierr);
ierr = VecScale(xout,ctx->eta*(nrmin/nrmnoise));CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormInitialState(Vec X, AppCtx* user)
{
PetscErrorCode ierr;
PetscRandom R;
PetscFunctionBegin;
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &R);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(R);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(R, 0., 10.);CHKERRQ(ierr);
/*
* Initialize the state vector
*/
ierr = VecSetRandom(X, R);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&R);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* Computes the wind speed using Weibull distribution */
PetscErrorCode WindSpeeds(AppCtx *user)
{
PetscErrorCode ierr;
PetscScalar *x,*t,avg_dev,sum;
PetscInt i;
PetscFunctionBegin;
user->cw = 5;
user->kw = 2; /* Rayleigh distribution */
user->nsamples = 2000;
user->Tw = 0.2;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,PETSC_NULL,"Wind Speed Options","");CHKERRQ(ierr);
{
ierr = PetscOptionsReal("-cw","","",user->cw,&user->cw,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-kw","","",user->kw,&user->kw,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-nsamples","","",user->nsamples,&user->nsamples,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-Tw","","",user->Tw,&user->Tw,PETSC_NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&user->wind_data);CHKERRQ(ierr);
ierr = VecSetSizes(user->wind_data,PETSC_DECIDE,user->nsamples);CHKERRQ(ierr);
ierr = VecSetFromOptions(user->wind_data);CHKERRQ(ierr);
ierr = VecDuplicate(user->wind_data,&user->t_wind);CHKERRQ(ierr);
ierr = VecGetArray(user->t_wind,&t);CHKERRQ(ierr);
for(i=0;i < user->nsamples;i++) t[i] = (i+1)*tmax/user->nsamples;
ierr = VecRestoreArray(user->t_wind,&t);CHKERRQ(ierr);
/* Wind speed deviation = (-log(rand)/cw)^(1/kw) */
ierr = VecSetRandom(user->wind_data,PETSC_NULL);CHKERRQ(ierr);
ierr = VecLog(user->wind_data);CHKERRQ(ierr);
ierr = VecScale(user->wind_data,-1/user->cw);CHKERRQ(ierr);
ierr = VecGetArray(user->wind_data,&x);CHKERRQ(ierr);
for(i=0;i < user->nsamples;i++) {
x[i] = PetscPowScalar(x[i],(1/user->kw));
}
ierr = VecRestoreArray(user->wind_data,&x);CHKERRQ(ierr);
ierr = VecSum(user->wind_data,&sum);CHKERRQ(ierr);
avg_dev = sum/user->nsamples;
/* Wind speed (t) = (1 + wind speed deviation(t) - avg_dev)*average wind speed */
ierr = VecShift(user->wind_data,(1-avg_dev));CHKERRQ(ierr);
ierr = VecScale(user->wind_data,vwa);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode VecSetRandom_MultiVec(Vec x, PetscRandom rctx)
{
#if !defined(NDEBUG)
TBOX_ASSERT(x);
#endif
Vec_MultiVec* mx = static_cast<Vec_MultiVec*>(x->data);
#if !defined(NDEBUG)
TBOX_ASSERT(mx);
#endif
PetscErrorCode ierr;
for (PetscInt k = 0; k < mx->n; ++k)
{
ierr = VecSetRandom(mx->array[k], rctx);
CHKERRQ(ierr);
}
ierr = PetscObjectStateIncrease(reinterpret_cast<PetscObject>(x));
CHKERRQ(ierr);
PetscFunctionReturn(0);
} // VecSetRandom_MultiVec
PetscErrorCode SNESDiffParameterCreate_More(SNES snes,Vec x,void **outneP)
{
DIFFPAR_MORE *neP;
Vec w;
PetscRandom rctx; /* random number generator context */
PetscErrorCode ierr;
PetscBool flg;
char noise_file[PETSC_MAX_PATH_LEN];
PetscFunctionBegin;
ierr = PetscNewLog(snes,&neP);CHKERRQ(ierr);
neP->function_count = 0;
neP->fnoise_min = 1.0e-20;
neP->hopt_min = 1.0e-8;
neP->h_first_try = 1.0e-3;
neP->fnoise_resets = 0;
neP->hopt_resets = 0;
/* Create work vectors */
ierr = VecDuplicateVecs(x,3,&neP->workv);CHKERRQ(ierr);
w = neP->workv[0];
/* Set components of vector w to random numbers */
ierr = PetscRandomCreate(PetscObjectComm((PetscObject)snes),&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(w,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
/* Open output file */
ierr = PetscOptionsGetString(((PetscObject)snes)->prefix,"-snes_mf_noise_file",noise_file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
if (flg) neP->fp = fopen(noise_file,"w");
else neP->fp = fopen("noise.out","w");
if (!neP->fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_FILE_OPEN,"Cannot open file");
ierr = PetscInfo(snes,"Creating Jorge's differencing parameter context\n");CHKERRQ(ierr);
*outneP = neP;
PetscFunctionReturn(0);
}
Ensure(FFT, i_transform_is_inverse_of_transform)
{
Vec v;
PetscInt dim = 5;
DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,dim,2,1,NULL,&da);
DMCreateGlobalVector(da, &v);
PetscRandom rdm;
PetscRandomCreate(PETSC_COMM_WORLD, &rdm);
PetscRandomSetFromOptions(rdm);
VecSetRandom(v, rdm);
PetscRandomDestroy(&rdm);
Vec vIn;
VecDuplicate(v, &vIn);
VecCopy(v, vIn);
scFftCreate(da, &fft);
Vec x, y, z;
scFftCreateVecsFFTW(fft, &x, &y, &z);
int component = 0;
scFftTransform(fft, v, component, y);
scFftITransform(fft, v, component, y);
VecAXPY(v, -dim, vIn);
PetscReal error;
VecStrideNorm(v, component, NORM_INFINITY, &error);
assert_that(error < 1.0e-6, is_true);
VecDestroy(&x);
VecDestroy(&y);
VecDestroy(&z);
VecDestroy(&v);
VecDestroy(&vIn);
scFftDestroy(&fft);
DMDestroy(&da);
}
PetscErrorCode KSPSolve_Chebyshev(KSP ksp)
{
KSP_Chebyshev *cheb = (KSP_Chebyshev*)ksp->data;
PetscErrorCode ierr;
PetscInt k,kp1,km1,maxit,ktmp,i;
PetscScalar alpha,omegaprod,mu,omega,Gamma,c[3],scale;
PetscReal rnorm = 0.0;
Vec sol_orig,b,p[3],r;
Mat Amat,Pmat;
PetscBool diagonalscale;
PetscFunctionBegin;
ierr = PCGetDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr);
if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
if (cheb->kspest && !cheb->estimate_current) {
PetscReal max=0.0,min=0.0;
Vec X,B;
X = ksp->work[0];
if (cheb->random) {
B = ksp->work[1];
ierr = VecSetRandom(B,cheb->random);CHKERRQ(ierr);
} else {
B = ksp->vec_rhs;
}
ierr = KSPSolve(cheb->kspest,B,X);CHKERRQ(ierr);
if (ksp->guess_zero) {
ierr = VecZeroEntries(X);CHKERRQ(ierr);
}
ierr = KSPChebyshevComputeExtremeEigenvalues_Private(cheb->kspest,&min,&max);CHKERRQ(ierr);
cheb->emin = cheb->tform[0]*min + cheb->tform[1]*max;
cheb->emax = cheb->tform[2]*min + cheb->tform[3]*max;
cheb->estimate_current = PETSC_TRUE;
}
ksp->its = 0;
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
maxit = ksp->max_it;
/* These three point to the three active solutions, we
rotate these three at each solution update */
km1 = 0; k = 1; kp1 = 2;
sol_orig = ksp->vec_sol; /* ksp->vec_sol will be asigned to rotating vector p[k], thus save its address */
b = ksp->vec_rhs;
p[km1] = sol_orig;
p[k] = ksp->work[0];
p[kp1] = ksp->work[1];
r = ksp->work[2];
/* use scale*B as our preconditioner */
scale = 2.0/(cheb->emax + cheb->emin);
/* -alpha <= scale*lambda(B^{-1}A) <= alpha */
alpha = 1.0 - scale*(cheb->emin);
Gamma = 1.0;
mu = 1.0/alpha;
omegaprod = 2.0/alpha;
c[km1] = 1.0;
c[k] = mu;
if (!ksp->guess_zero) {
ierr = KSP_MatMult(ksp,Amat,p[km1],r);CHKERRQ(ierr); /* r = b - A*p[km1] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
} else {
ierr = VecCopy(b,r);CHKERRQ(ierr);
}
ierr = KSP_PCApply(ksp,r,p[k]);CHKERRQ(ierr); /* p[k] = scale B^{-1}r + p[km1] */
ierr = VecAYPX(p[k],scale,p[km1]);CHKERRQ(ierr);
for (i=0; i<maxit; i++) {
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its++;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
c[kp1] = 2.0*mu*c[k] - c[km1];
omega = omegaprod*c[k]/c[kp1];
ierr = KSP_MatMult(ksp,Amat,p[k],r);CHKERRQ(ierr); /* r = b - Ap[k] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
ierr = KSP_PCApply(ksp,r,p[kp1]);CHKERRQ(ierr); /* p[kp1] = B^{-1}r */
ksp->vec_sol = p[k];
/* calculate residual norm if requested */
if (ksp->normtype != KSP_NORM_NONE || ksp->numbermonitors) {
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(r,NORM_2,&rnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(p[kp1],NORM_2,&rnorm);CHKERRQ(ierr);
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = rnorm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = KSPLogResidualHistory(ksp,rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i,rnorm);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,i,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) break;
}
/* y^{k+1} = omega(y^{k} - y^{k-1} + Gamma*r^{k}) + y^{k-1} */
ierr = VecAXPBYPCZ(p[kp1],1.0-omega,omega,omega*Gamma*scale,p[km1],p[k]);CHKERRQ(ierr);
ktmp = km1;
km1 = k;
k = kp1;
kp1 = ktmp;
}
if (!ksp->reason) {
if (ksp->normtype != KSP_NORM_NONE) {
ierr = KSP_MatMult(ksp,Amat,p[k],r);CHKERRQ(ierr); /* r = b - Ap[k] */
ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
ierr = VecNorm(r,NORM_2,&rnorm);CHKERRQ(ierr);
} else {
ierr = KSP_PCApply(ksp,r,p[kp1]);CHKERRQ(ierr); /* p[kp1] = B^{-1}r */
ierr = VecNorm(p[kp1],NORM_2,&rnorm);CHKERRQ(ierr);
}
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = rnorm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->vec_sol = p[k];
ierr = KSPLogResidualHistory(ksp,rnorm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,i,rnorm);CHKERRQ(ierr);
}
if (ksp->its >= ksp->max_it) {
if (ksp->normtype != KSP_NORM_NONE) {
ierr = (*ksp->converged)(ksp,i,rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
} else ksp->reason = KSP_CONVERGED_ITS;
}
}
/* make sure solution is in vector x */
ksp->vec_sol = sol_orig;
if (k) {
ierr = VecCopy(p[k],sol_orig);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
Vec V,W;
MPI_Comm comm;
PetscScalar one=1,e=2.7181;
PetscReal nrm1,nrm2,nrm3,nrm4;
PetscInt ione=1;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscInitialize(&argc,&argv,0,help);CHKERRQ(ierr);
comm = MPI_COMM_SELF;
ierr = VecCreateSeq(comm,10,&V);CHKERRQ(ierr);
ierr = VecSetRandom(V,NULL);CHKERRQ(ierr);
ierr = VecAssemblyBegin(V);CHKERRQ(ierr);
ierr = VecAssemblyEnd(V);CHKERRQ(ierr);
/*
* Initial
*/
/* display norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Original: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display cached norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"cached: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Alter an element
*/
ierr = VecSetValues(V,1,&ione,&one,INSERT_VALUES);CHKERRQ(ierr);
/* display norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Altered: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display cached norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"recomputed: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Scale the vector a little
*/
ierr = VecScale(V,e);CHKERRQ(ierr);
/* display updated cached norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Scale: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display forced norm 1 & 2 */
ierr = PetscObjectStateIncrease((PetscObject)V);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"recompute: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Normalize the vector a little
*/
ierr = VecNormalize(V,&nrm1);CHKERRQ(ierr);
/* display updated cached norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Normalize: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display forced norm 1 & 2 */
ierr = PetscObjectStateIncrease((PetscObject)V);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"recompute: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Copy to another vector
*/
ierr = VecDuplicate(V,&W);CHKERRQ(ierr);
ierr = VecCopy(V,W);CHKERRQ(ierr);
/* display norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Original: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display cached norm 1 & 2 */
ierr = VecNorm(W,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"copied: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Copy while data is invalid
*/
ierr = VecSetValues(V,1,&ione,&one,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecCopy(V,W);CHKERRQ(ierr);
/* display norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Invalidated: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display norm 1 & 2 */
ierr = VecNorm(W,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"copied: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Constant vector
*/
ierr = VecSet(V,e);CHKERRQ(ierr);
/* display updated cached norm 1 & 2 */
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Constant: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* display forced norm 1 & 2 */
ierr = PetscObjectStateIncrease((PetscObject)V);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_2,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"recomputed: norm1=%e,norm2=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/*
* Swap vectors
*/
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_1,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Orig: norm_V=%e,norm_W=%e\n",(double)nrm1,(double)nrm2);CHKERRQ(ierr);
/* store inf norm */
ierr = VecNorm(V,NORM_INFINITY,&nrm3);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_INFINITY,&nrm4);CHKERRQ(ierr);
ierr = VecSwap(V,W);CHKERRQ(ierr);
ierr = PetscObjectStateIncrease((PetscObject)V);CHKERRQ(ierr);
ierr = PetscObjectStateIncrease((PetscObject)W);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_1,&nrm1);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_1,&nrm2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"swapped: norm_V=%e,norm_W=%e\n",(double)nrm2,(double)nrm1);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"orig: F-norm_V=%e,F-norm_W=%e\n",(double)nrm3,(double)nrm4);CHKERRQ(ierr);
ierr = VecNorm(V,NORM_INFINITY,&nrm3);CHKERRQ(ierr);
ierr = VecNorm(W,NORM_INFINITY,&nrm4);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"swapped: F-norm_V=%e,F-norm_W=%e\n",(double)nrm4,(double)nrm3);CHKERRQ(ierr);
ierr = VecDestroy(&V);CHKERRQ(ierr);
ierr = VecDestroy(&W);CHKERRQ(ierr);
PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
DM da; /* distributed array */
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscRandom rctx; /* random number generator context */
PetscReal norm; /* norm of solution error */
PetscInt i,j,its;
PetscErrorCode ierr;
PetscBool flg = PETSC_FALSE;
PetscLogStage stage;
DMDALocalInfo info;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
/*
Create distributed array to handle parallel distribution.
The problem size will default to 8 by 7, but this can be
changed using -da_grid_x M -da_grid_y N
*/
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-7,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix preallocated according to the DMDA, format AIJ by default.
To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
*/
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
/*
Set matrix elements for the 2-D, five-point stencil in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Rows and columns are specified by the stencil
- Entries are normalized for a domain [0,1]x[0,1]
*/
ierr = PetscLogStageRegister("Assembly", &stage);CHKERRQ(ierr);
ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
for (j=info.ys; j<info.ys+info.ym; j++) {
for (i=info.xs; i<info.xs+info.xm; i++) {
PetscReal hx = 1./info.mx,hy = 1./info.my;
MatStencil row = {0},col[5] = {{0}};
PetscScalar v[5];
PetscInt ncols = 0;
row.j = j; row.i = i;
col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
/* boundaries */
if (i>0) {col[ncols].j = j; col[ncols].i = i-1; v[ncols++] = -hy/hx;}
if (i<info.mx-1) {col[ncols].j = j; col[ncols].i = i+1; v[ncols++] = -hy/hx;}
if (j>0) {col[ncols].j = j-1; col[ncols].i = i; v[ncols++] = -hx/hy;}
if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i; v[ncols++] = -hx/hy;}
ierr = MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
/*
Create parallel vectors compatible with the DMDA.
*/
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
By default we use an exact solution of a vector with all
elements of 1.0; Alternatively, using the runtime option
-random_sol forms a solution vector with random components.
*/
ierr = PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,1.);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/*
View the exact solution vector if desired
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
These options will override those specified above as long as
KSPSetFromOptions() is called _after_ any other customization
routines.
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Check the error
*/
ierr = VecAXPY(x,-1.,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
/*
Print convergence information. PetscPrintf() produces a single
print statement from all processes that share a communicator.
An alternative is PetscFPrintf(), which prints to a file.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_summary).
*/
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=50,N1=20,N=N0*N1,DIM;
PetscRandom rdm;
PetscScalar a;
PetscReal enorm;
Vec x,y,z;
PetscBool view=PETSC_FALSE,use_interface=PETSC_TRUE;
ierr = PetscInitialize(&argc,&args,(char*)0,help);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex numbers");
#endif
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "FFTW Options", "ex143");CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the vectors", "ex143", view, &view, NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-use_FFTW_interface", "Use PETSc-FFTW interface", "ex143",use_interface, &use_interface, NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-use_FFTW_interface",&use_interface,NULL);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
if (!use_interface) {
/* Use mpi FFTW without PETSc-FFTW interface, 2D case only */
/*---------------------------------------------------------*/
fftw_plan fplan,bplan;
fftw_complex *data_in,*data_out,*data_out2;
ptrdiff_t alloc_local,local_n0,local_0_start;
DIM = 2;
if (!rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Use FFTW without PETSc-FFTW interface, DIM %D\n",DIM);CHKERRQ(ierr);
}
fftw_mpi_init();
N = N0*N1;
alloc_local = fftw_mpi_local_size_2d(N0,N1,PETSC_COMM_WORLD,&local_n0,&local_0_start);
data_in = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
data_out = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
data_out2 = (fftw_complex*)fftw_malloc(sizeof(fftw_complex)*alloc_local);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_in,&x);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real Space vector");CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_out,&y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = VecCreateMPIWithArray(PETSC_COMM_WORLD,1,(PetscInt)local_n0*N1,(PetscInt)N,(const PetscScalar*)data_out2,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
fplan = fftw_mpi_plan_dft_2d(N0,N1,data_in,data_out,PETSC_COMM_WORLD,FFTW_FORWARD,FFTW_ESTIMATE);
bplan = fftw_mpi_plan_dft_2d(N0,N1,data_out,data_out2,PETSC_COMM_WORLD,FFTW_BACKWARD,FFTW_ESTIMATE);
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
if (view) {ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
fftw_execute(fplan);
if (view) {ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
fftw_execute(bplan);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
a = 1.0/(PetscReal)N;
ierr = VecScale(z,a);CHKERRQ(ierr);
if (view) {ierr = VecView(z, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11 && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %g\n",(double)enorm);CHKERRQ(ierr);
}
/* Free spaces */
fftw_destroy_plan(fplan);
fftw_destroy_plan(bplan);
fftw_free(data_in); ierr = VecDestroy(&x);CHKERRQ(ierr);
fftw_free(data_out); ierr = VecDestroy(&y);CHKERRQ(ierr);
fftw_free(data_out2);ierr = VecDestroy(&z);CHKERRQ(ierr);
} else {
/* Use PETSc-FFTW interface */
/*-------------------------------------------*/
PetscInt i,*dim,k;
Mat A;
N=1;
for (i=1; i<5; i++) {
DIM = i;
ierr = PetscMalloc1(i,&dim);CHKERRQ(ierr);
for (k=0; k<i; k++) {
dim[k]=30;
}
N *= dim[i-1];
/* Create FFTW object */
if (!rank) printf("Use PETSc-FFTW interface...%d-DIM: %d\n",(int)DIM,(int)N);
ierr = MatCreateFFT(PETSC_COMM_WORLD,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
/* Create vectors that are compatible with parallel layout of A - must call MatCreateVecs()! */
ierr = MatCreateVecsFFTW(A,&x,&y,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* Set values of space vector x */
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
if (view) {ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
/* Apply FFTW_FORWARD and FFTW_BACKWARD */
ierr = MatMult(A,x,y);CHKERRQ(ierr);
if (view) {ierr = VecView(y,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
a = 1.0/(PetscReal)N;
ierr = VecScale(z,a);CHKERRQ(ierr);
if (view) {ierr = VecView(z,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-9 && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
}
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFree(dim);CHKERRQ(ierr);
}
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
typedef enum {RANDOM, CONSTANT, TANH, NUM_FUNCS} FuncType;
const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"};
PetscMPIInt size;
PetscInt n = 10,N,Ny,ndim=4,dim[4],DIM,i;
Vec x,y,z;
PetscScalar s;
PetscRandom rdm;
PetscReal enorm;
PetscInt func=RANDOM;
FuncType function = RANDOM;
PetscBool view = PETSC_FALSE;
PetscErrorCode ierr;
PetscScalar *x_array,*y_array,*z_array;
fftw_plan fplan,bplan;
const ptrdiff_t N0 = 20, N1 = 20;
ptrdiff_t alloc_local, local_n0, local_0_start;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires real numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
alloc_local=fftw_mpi_local_size_2d(N0, N1, PETSC_COMM_WORLD,
&local_n0, &local_0_start);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uniprocessor example only!");
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, PETSC_NULL, "FFTW Options", "ex142");CHKERRQ(ierr);
ierr = PetscOptionsEList("-function", "Function type", "ex142", funcNames, NUM_FUNCS, funcNames[function], &func, PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the functions", "ex112", view, &view, PETSC_NULL);CHKERRQ(ierr);
function = (FuncType) func;
ierr = PetscOptionsEnd();CHKERRQ(ierr);
for (DIM = 0; DIM < ndim; DIM++){
dim[DIM] = n; /* size of real space vector in DIM-dimension */
}
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
for (DIM = 1; DIM < 5; DIM++){
/* create vectors of length N=dim[0]*dim[1]* ...*dim[DIM-1] */
/*----------------------------------------------------------*/
N = Ny = 1;
for (i = 0; i < DIM-1; i++) {
N *= dim[i];
}
Ny = N; Ny *= 2*(dim[DIM-1]/2 + 1); /* add padding elements to output vector y */
N *= dim[DIM-1];
ierr = PetscPrintf(PETSC_COMM_SELF, "\n %d-D: FFTW on vector of size %d \n",DIM,N);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,N,&x);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,Ny,&y);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = VecDuplicate(x,&z);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* Set fftw plan */
/*----------------------------------*/
ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
ierr = VecGetArray(z,&z_array);CHKERRQ(ierr);
unsigned int flags = FFTW_ESTIMATE; //or FFTW_MEASURE
/* The data in the in/out arrays is overwritten during FFTW_MEASURE planning, so such planning
should be done before the input is initialized by the user. */
printf("DIM: %d, N %d, Ny %d\n",DIM,N,Ny);
switch (DIM){
case 1:
fplan = fftw_plan_dft_r2c_1d(dim[0], (double *)x_array, (fftw_complex*)y_array, flags);
bplan = fftw_plan_dft_c2r_1d(dim[0], (fftw_complex*)y_array, (double *)z_array, flags);
break;
case 2:
fplan = fftw_plan_dft_r2c_2d(dim[0],dim[1],(double *)x_array, (fftw_complex*)y_array,flags);
bplan = fftw_plan_dft_c2r_2d(dim[0],dim[1],(fftw_complex*)y_array,(double *)z_array,flags);
break;
case 3:
fplan = fftw_plan_dft_r2c_3d(dim[0],dim[1],dim[2],(double *)x_array, (fftw_complex*)y_array,flags);
bplan = fftw_plan_dft_c2r_3d(dim[0],dim[1],dim[2],(fftw_complex*)y_array,(double *)z_array,flags);
break;
default:
fplan = fftw_plan_dft_r2c(DIM,dim,(double *)x_array, (fftw_complex*)y_array,flags);
bplan = fftw_plan_dft_c2r(DIM,dim,(fftw_complex*)y_array,(double *)z_array,flags);
break;
}
ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
ierr = VecRestoreArray(z,&z_array);CHKERRQ(ierr);
/* Initialize Real space vector x:
The data in the in/out arrays is overwritten during FFTW_MEASURE planning, so planning
should be done before the input is initialized by the user.
--------------------------------------------------------*/
if (function == RANDOM) {
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
} else if (function == CONSTANT) {
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
} else if (function == TANH) {
ierr = VecGetArray(x, &x_array);CHKERRQ(ierr);
for (i = 0; i < N; ++i) {
x_array[i] = tanh((i - N/2.0)*(10.0/N));
}
ierr = VecRestoreArray(x, &x_array);CHKERRQ(ierr);
}
if (view) {
ierr = VecView(x, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* FFT - also test repeated transformation */
/*-------------------------------------------*/
ierr = VecGetArray(x,&x_array);CHKERRQ(ierr);
ierr = VecGetArray(y,&y_array);CHKERRQ(ierr);
ierr = VecGetArray(z,&z_array);CHKERRQ(ierr);
for (i=0; i<3; i++){
/* FFTW_FORWARD */
fftw_execute(fplan);
//printf("\n fout:\n");
//fftw_complex* fout = (fftw_complex*)y_array;
//for (i=0; i<N/2+1; i++) printf("%d (%g %g)\n",i,fout[i][0],fout[i][1]);
/* FFTW_BACKWARD: destroys its input array 'y_array' even for out-of-place transforms! */
fftw_execute(bplan);
}
ierr = VecRestoreArray(x,&x_array);CHKERRQ(ierr);
ierr = VecRestoreArray(y,&y_array);CHKERRQ(ierr);
ierr = VecRestoreArray(z,&z_array);CHKERRQ(ierr);
/* Compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
/*------------------------------------------------------------------*/
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
if (view) {ierr = VecView(x, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
if (view) {ierr = VecView(z, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %G\n",enorm);CHKERRQ(ierr);
}
/* free spaces */
fftw_destroy_plan(fplan);
fftw_destroy_plan(bplan);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* KSP context */
PetscErrorCode ierr;
PetscInt n = 10,its, dim,p = 1,use_random;
PetscScalar none = -1.0,pfive = 0.5;
PetscReal norm;
PetscRandom rctx;
TestType type;
PetscBool flg;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-p",&p,PETSC_NULL);CHKERRQ(ierr);
switch (p) {
case 1: type = TEST_1; dim = n; break;
case 2: type = TEST_2; dim = n; break;
case 3: type = TEST_3; dim = n; break;
case 4: type = HELMHOLTZ_1; dim = n*n; break;
case 5: type = HELMHOLTZ_2; dim = n*n; break;
default: type = TEST_1; dim = n;
}
/* Create vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
ierr = VecSetSizes(x,PETSC_DECIDE,dim);CHKERRQ(ierr);
ierr = VecSetFromOptions(x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);CHKERRQ(ierr);
use_random = 1;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-norandom",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
use_random = 0;
ierr = VecSet(u,pfive);CHKERRQ(ierr);
} else {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
}
/* Create and assemble matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = FormTestMatrix(A,n,type);CHKERRQ(ierr);
ierr = MatMult(A,u,b);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-printout",&flg,PETSC_NULL);CHKERRQ(ierr);
if (flg) {
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(b,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/* Create KSP context; set operators and options; solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
ierr = KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* Check error */
ierr = VecAXPY(x,none,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G,Iterations %D\n",norm,its);CHKERRQ(ierr);
/* Free work space */
ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
typedef enum {RANDOM, CONSTANT, TANH, NUM_FUNCS} FuncType;
const char *funcNames[NUM_FUNCS] = {"random", "constant", "tanh"};
Mat A;
PetscMPIInt size;
PetscInt n = 10,N,ndim=4,dim[4],DIM,i;
Vec x,y,z;
PetscScalar s;
PetscRandom rdm;
PetscReal enorm;
PetscInt func;
FuncType function = RANDOM;
PetscBool view = PETSC_FALSE;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uniprocessor example only!");
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, PETSC_NULL, "FFTW Options", "ex112");CHKERRQ(ierr);
ierr = PetscOptionsEList("-function", "Function type", "ex112", funcNames, NUM_FUNCS, funcNames[function], &func, PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-vec_view draw", "View the functions", "ex112", view, &view, PETSC_NULL);CHKERRQ(ierr);
function = (FuncType) func;
ierr = PetscOptionsEnd();CHKERRQ(ierr);
for (DIM = 0; DIM < ndim; DIM++){
dim[DIM] = n; /* size of transformation in DIM-dimension */
}
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
for (DIM = 1; DIM < 5; DIM++){
for (i = 0, N = 1; i < DIM; i++) N *= dim[i];
ierr = PetscPrintf(PETSC_COMM_SELF, "\n %d-D: FFTW on vector of size %d \n",DIM,N);CHKERRQ(ierr);
/* create FFTW object */
ierr = MatCreateFFT(PETSC_COMM_SELF,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
/* create vectors of length N=n^DIM */
ierr = MatGetVecs(A,&x,&y);CHKERRQ(ierr);
ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
/* set values of space vector x */
if (function == RANDOM) {
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
} else if (function == CONSTANT) {
ierr = VecSet(x, 1.0);CHKERRQ(ierr);
} else if (function == TANH) {
PetscScalar *a;
ierr = VecGetArray(x, &a);CHKERRQ(ierr);
for (i = 0; i < N; ++i) {
a[i] = tanh((i - N/2.0)*(10.0/N));
}
ierr = VecRestoreArray(x, &a);CHKERRQ(ierr);
}
if (view) {ierr = VecView(x, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
/* apply FFTW_FORWARD and FFTW_BACKWARD several times on same x, y, and z */
for (i=0; i<3; i++){
ierr = MatMult(A,x,y);CHKERRQ(ierr);
if (view && i == 0) {ierr = VecView(y, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
/* compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
if (view && i == 0) {ierr = VecView(z, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %G\n",enorm);CHKERRQ(ierr);
}
}
/* apply FFTW_FORWARD and FFTW_BACKWARD several times on different x */
for (i=0; i<3; i++){
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,N,&x);CHKERRQ(ierr);
ierr = VecSetRandom(x, rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
/* compare x and z. FFTW computes an unnormalized DFT, thus z = N*x */
s = 1.0/(PetscReal)N;
ierr = VecScale(z,s);CHKERRQ(ierr);
if (view && i == 0) {ierr = VecView(z, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);}
ierr = VecAXPY(z,-1.0,x);CHKERRQ(ierr);
ierr = VecNorm(z,NORM_1,&enorm);CHKERRQ(ierr);
if (enorm > 1.e-11){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of new |x - z| %G\n",enorm);CHKERRQ(ierr);
}
}
/* free spaces */
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
}
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
PetscMPIInt size;
PetscErrorCode ierr;
Vec x,y,b,s1,s2;
Mat A; /* linear system matrix */
Mat sA,sB,sC; /* symmetric part of the matrices */
PetscInt n,mbs=16,bs=1,nz=3,prob=1,i,j,k1,k2,col[3],lf,block, row,Ii,J,n1,inc;
PetscReal norm1,norm2,rnorm,tol=PETSC_SMALL;
PetscScalar neg_one = -1.0,four=4.0,value[3];
IS perm, iscol;
PetscRandom rdm;
PetscBool doIcc=PETSC_TRUE,equal;
MatInfo minfo1,minfo2;
MatFactorInfo factinfo;
MatType type;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!");
ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
n = mbs*bs;
ierr = MatCreate(PETSC_COMM_SELF,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATSEQBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSeqBAIJSetPreallocation(A,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_SELF,&sA);CHKERRQ(ierr);
ierr = MatSetSizes(sA,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(sA,MATSEQSBAIJ);CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
ierr = MatGetType(sA,&type);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)sA,MATSEQSBAIJ,&doIcc);CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,nz,NULL);CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_IGNORE_LOWER_TRIANGULAR,PETSC_TRUE);CHKERRQ(ierr);
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(sA,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetOwnershipRange() in MatSBAIJ format\n");CHKERRQ(ierr);
}
/* Assemble matrix */
if (bs == 1) {
ierr = PetscOptionsGetInt(NULL,"-test_problem",&prob,NULL);CHKERRQ(ierr);
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
value[0]= 0.1; value[1]=-1; value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0;
col[0] = n-1; col[1] = 1; col[2] = 0;
value[0] = 0.1; value[1] = -1.0; value[2] = 2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (PetscInt) (PetscSqrtReal((PetscReal)n) + 0.001);
if (n1*n1 - n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"sqrt(n) must be a positive interger!");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1; col[1] = i; col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
i = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
value[0]=-1.0; value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
i = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
value[0]=4.0; value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
col[0]=i; row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Test MatGetInfo() of A and sA */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sA,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("A matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("sA matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error (compare A and sA): MatGetInfo()\n");CHKERRQ(ierr);
}
/* Test MatDuplicate() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDuplicate()");
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_FROBENIUS,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS, NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_INFINITY,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&norm1);CHKERRQ(ierr);
ierr = MatNorm(sB,NORM_1,&norm2);CHKERRQ(ierr);
rnorm = PetscAbsReal(norm1-norm2)/norm2;
if (rnorm > tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_INFINITY(), NormA=%16.14e NormsB=%16.14e\n",norm1,norm2);CHKERRQ(ierr);
}
/* Test MatGetInfo(), MatGetSize(), MatGetBlockSize() */
ierr = MatGetInfo(A,MAT_LOCAL,&minfo1);CHKERRQ(ierr);
ierr = MatGetInfo(sB,MAT_LOCAL,&minfo2);CHKERRQ(ierr);
/*
printf("matrix nonzeros (BAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo1.nz_used,(int)minfo1.nz_allocated);
printf("matrix nonzeros(SBAIJ format) = %d, allocated nonzeros= %d\n", (int)minfo2.nz_used,(int)minfo2.nz_allocated);
*/
i = (int) (minfo1.nz_used - minfo2.nz_used);
j = (int) (minfo1.nz_allocated - minfo2.nz_allocated);
k1 = (int) (minfo1.nz_allocated - minfo1.nz_used);
k2 = (int) (minfo2.nz_allocated - minfo2.nz_used);
if (i < 0 || j < 0 || k1 < 0 || k2 < 0) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error(compare A and sB): MatGetInfo()\n");CHKERRQ(ierr);
}
ierr = MatGetSize(A,&Ii,&J);CHKERRQ(ierr);
ierr = MatGetSize(sB,&i,&j);CHKERRQ(ierr);
if (i-Ii || j-J) {
PetscPrintf(PETSC_COMM_SELF,"Error: MatGetSize()\n");CHKERRQ(ierr);
}
ierr = MatGetBlockSize(A, &Ii);CHKERRQ(ierr);
ierr = MatGetBlockSize(sB, &i);CHKERRQ(ierr);
if (i-Ii) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetBlockSize()\n");CHKERRQ(ierr);
}
ierr = PetscRandomCreate(PETSC_COMM_SELF,&rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,n,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
/* Test MatDiagonalScale(), MatGetDiagonal(), MatScale() */
#if !defined(PETSC_USE_COMPLEX)
/* Scaling matrix with complex numbers results non-spd matrix,
causing crash of MatForwardSolve() and MatBackwardSolve() */
ierr = MatDiagonalScale(A,x,x);CHKERRQ(ierr);
ierr = MatDiagonalScale(sB,x,x);CHKERRQ(ierr);
ierr = MatMultEqual(A,sB,10,&equal);CHKERRQ(ierr);
if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
ierr = MatGetDiagonal(A,s1);CHKERRQ(ierr);
ierr = MatGetDiagonal(sB,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,s1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm1);CHKERRQ(ierr);
if (norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetDiagonal(), ||s1-s2||=%G\n",norm1);CHKERRQ(ierr);
}
{
PetscScalar alpha=0.1;
ierr = MatScale(A,alpha);CHKERRQ(ierr);
ierr = MatScale(sB,alpha);CHKERRQ(ierr);
}
#endif
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sB,s2,NULL);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatGetRowMaxAbs() \n");CHKERRQ(ierr);
}
/* Test MatMult() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = MatMult(A,x,s1);CHKERRQ(ierr);
ierr = MatMult(sB,x,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatMult(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* MatMultAdd() */
for (i=0; i<40; i++) {
ierr = VecSetRandom(x,rdm);CHKERRQ(ierr);
ierr = VecSetRandom(y,rdm);CHKERRQ(ierr);
ierr = MatMultAdd(A,x,y,s1);CHKERRQ(ierr);
ierr = MatMultAdd(sB,x,y,s2);CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&norm1);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&norm2);CHKERRQ(ierr);
norm1 -= norm2;
if (norm1<-tol || norm1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error:MatMultAdd(), norm1-norm2: %G\n",norm1);CHKERRQ(ierr);
}
}
/* Test MatCholeskyFactor(), MatICCFactor() with natural ordering */
ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iscol);CHKERRQ(ierr);
ierr = ISDestroy(&iscol);CHKERRQ(ierr);
norm1 = tol;
inc = bs;
/* initialize factinfo */
ierr = PetscMemzero(&factinfo,sizeof(MatFactorInfo));CHKERRQ(ierr);
for (lf=-1; lf<10; lf += inc) {
if (lf==-1) { /* Cholesky factor of sB (duplicate sA) */
factinfo.fill = 5.0;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_CHOLESKY,&sC);CHKERRQ(ierr);
ierr = MatCholeskyFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
} else if (!doIcc) break;
else { /* incomplete Cholesky factor */
factinfo.fill = 5.0;
factinfo.levels = lf;
ierr = MatGetFactor(sB,MATSOLVERPETSC,MAT_FACTOR_ICC,&sC);CHKERRQ(ierr);
ierr = MatICCFactorSymbolic(sC,sB,perm,&factinfo);CHKERRQ(ierr);
}
ierr = MatCholeskyFactorNumeric(sC,sB,&factinfo);CHKERRQ(ierr);
/* MatView(sC, PETSC_VIEWER_DRAW_WORLD); */
/* test MatGetDiagonal on numeric factor */
/*
if (lf == -1) {
ierr = MatGetDiagonal(sC,s1);CHKERRQ(ierr);
printf(" in ex74.c, diag: \n");
ierr = VecView(s1,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
*/
ierr = MatMult(sB,x,b);CHKERRQ(ierr);
/* test MatForwardSolve() and MatBackwardSolve() */
if (lf == -1) {
ierr = MatForwardSolve(sC,b,s1);CHKERRQ(ierr);
ierr = MatBackwardSolve(sC,s1,s2);CHKERRQ(ierr);
ierr = VecAXPY(s2,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_2,&norm2);CHKERRQ(ierr);
if (10*norm1 < norm2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"MatForwardSolve and BackwardSolve: Norm of error=%G, bs=%d\n",norm2,bs);CHKERRQ(ierr);
}
}
/* test MatSolve() */
ierr = MatSolve(sC,b,y);CHKERRQ(ierr);
ierr = MatDestroy(&sC);CHKERRQ(ierr);
/* Check the error */
ierr = VecAXPY(y,neg_one,x);CHKERRQ(ierr);
ierr = VecNorm(y,NORM_2,&norm2);CHKERRQ(ierr);
/* printf("lf: %d, error: %G\n", lf,norm2); */
if (10*norm1 < norm2 && lf-inc != -1) {
ierr = PetscPrintf(PETSC_COMM_SELF,"lf=%D, %D, Norm of error=%G, %G\n",lf-inc,lf,norm1,norm2);CHKERRQ(ierr);
}
norm1 = norm2;
if (norm2 < tol && lf != -1) break;
}
ierr = ISDestroy(&perm);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&sB);CHKERRQ(ierr);
ierr = MatDestroy(&sA);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&s1);CHKERRQ(ierr);
ierr = VecDestroy(&s2);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Vec x,y,u,s1,s2;
Mat A,sA,sB;
PetscRandom rctx;
PetscReal r1,r2,rnorm,tol = PETSC_SQRT_MACHINE_EPSILON;
PetscScalar one=1.0, neg_one=-1.0, value[3], four=4.0,alpha=0.1;
PetscInt n,col[3],n1,block,row,i,j,i2,j2,Ii,J,rstart,rend,bs=1,mbs=16,d_nz=3,o_nz=3,prob=2;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscBool flg;
MatType type;
ierr = PetscInitialize(&argc,&args,(char*)0,help);
if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-mbs",&mbs,NULL);
CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,NULL,"-bs",&bs,NULL);
CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);
CHKERRQ(ierr);
n = mbs*bs;
/* Assemble MPISBAIJ matrix sA */
ierr = MatCreate(PETSC_COMM_WORLD,&sA);
CHKERRQ(ierr);
ierr = MatSetSizes(sA,PETSC_DECIDE,PETSC_DECIDE,n,n);
CHKERRQ(ierr);
ierr = MatSetType(sA,MATSBAIJ);
CHKERRQ(ierr);
ierr = MatSetFromOptions(sA);
CHKERRQ(ierr);
ierr = MatGetType(sA,&type);
CHKERRQ(ierr);
ierr = MatMPISBAIJSetPreallocation(sA,bs,d_nz,NULL,o_nz,NULL);
CHKERRQ(ierr);
ierr = MatSeqSBAIJSetPreallocation(sA,bs,d_nz,NULL);
CHKERRQ(ierr);
ierr = MatSetOption(sA,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
CHKERRQ(ierr);
if (bs == 1) {
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0;
value[1] = 2.0;
value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = n - 1;
col[0]=0;
col[1] = n - 2;
col[2] = n - 1;
value[0]= 0.1;
value[1]=-1;
value[2]=2;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0;
col[0] = 0;
col[1] = 1;
col[2]=n-1;
value[0] = 2.0;
value[1] = -1.0;
value[2]=0.1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (int) PetscSqrtReal((PetscReal)n);
if (n1*n1 != n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n must be a perfect square of n1");
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);
CHKERRQ(ierr);
}
}
}
/* end of if (bs == 1) */
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0;
value[1] = 4.0;
value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = bs - 1+block*bs;
col[0] = bs - 2+block*bs;
col[1] = bs - 1+block*bs;
value[0]=-1.0;
value[1]=4.0;
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0+block*bs;
col[0] = 0+block*bs;
col[1] = 1+block*bs;
value[0]=4.0;
value[1] = -1.0;
ierr = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
col[0]=i;
row=i+bs;
ierr = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/* Test MatView() */
ierr = MatCreateBAIJ(PETSC_COMM_WORLD,bs,PETSC_DECIDE,PETSC_DECIDE,n,n,d_nz,NULL,o_nz,NULL,&A);
CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
CHKERRQ(ierr);
if (bs == 1) {
if (prob == 1) { /* tridiagonal matrix */
value[0] = -1.0;
value[1] = 2.0;
value[2] = -1.0;
for (i=1; i<n-1; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = n - 1;
col[0]=0;
col[1] = n - 2;
col[2] = n - 1;
value[0]= 0.1;
value[1]=-1;
value[2]=2;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0;
col[0] = 0;
col[1] = 1;
col[2]=n-1;
value[0] = 2.0;
value[1] = -1.0;
value[2]=0.1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
} else if (prob ==2) { /* matrix for the five point stencil */
n1 = (int) PetscSqrtReal((PetscReal)n);
for (i=0; i<n1; i++) {
for (j=0; j<n1; j++) {
Ii = j + n1*i;
if (i>0) {
J = Ii - n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<n1-1) {
J = Ii + n1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n1-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&neg_one,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatSetValues(A,1,&Ii,1,&Ii,&four,INSERT_VALUES);
CHKERRQ(ierr);
}
}
}
/* end of if (bs == 1) */
} else { /* bs > 1 */
for (block=0; block<n/bs; block++) {
/* diagonal blocks */
value[0] = -1.0;
value[1] = 4.0;
value[2] = -1.0;
for (i=1+block*bs; i<bs-1+block*bs; i++) {
col[0] = i-1;
col[1] = i;
col[2] = i+1;
ierr = MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
i = bs - 1+block*bs;
col[0] = bs - 2+block*bs;
col[1] = bs - 1+block*bs;
value[0]=-1.0;
value[1]=4.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
i = 0+block*bs;
col[0] = 0+block*bs;
col[1] = 1+block*bs;
value[0]=4.0;
value[1] = -1.0;
ierr = MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
/* off-diagonal blocks */
value[0]=-1.0;
for (i=0; i<(n/bs-1)*bs; i++) {
col[0]=i+bs;
ierr = MatSetValues(A,1,&i,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
col[0]=i;
row=i+bs;
ierr = MatSetValues(A,1,&row,1,col,value,INSERT_VALUES);
CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/* Test MatGetSize(), MatGetLocalSize() */
ierr = MatGetSize(sA, &i,&j);
CHKERRQ(ierr);
ierr = MatGetSize(A, &i2,&j2);
CHKERRQ(ierr);
i -= i2;
j -= j2;
if (i || j) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatGetSize()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatGetLocalSize(sA, &i,&j);
CHKERRQ(ierr);
ierr = MatGetLocalSize(A, &i2,&j2);
CHKERRQ(ierr);
i2 -= i;
j2 -= j;
if (i2 || j2) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatGetLocalSize()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* vectors */
/*--------------------*/
/* i is obtained from MatGetLocalSize() */
ierr = VecCreate(PETSC_COMM_WORLD,&x);
CHKERRQ(ierr);
ierr = VecSetSizes(x,i,PETSC_DECIDE);
CHKERRQ(ierr);
ierr = VecSetFromOptions(x);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&y);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&u);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&s1);
CHKERRQ(ierr);
ierr = VecDuplicate(x,&s2);
CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);
CHKERRQ(ierr);
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = VecSet(u,one);
CHKERRQ(ierr);
/* Test MatNorm() */
ierr = MatNorm(A,NORM_FROBENIUS,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_FROBENIUS,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatNorm_FROBENIUS(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_INFINITY,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_INFINITY,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: MatNorm_INFINITY(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
ierr = MatNorm(A,NORM_1,&r1);
CHKERRQ(ierr);
ierr = MatNorm(sA,NORM_1,&r2);
CHKERRQ(ierr);
rnorm = PetscAbsReal(r1-r2)/r2;
if (rnorm > tol && !rank) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: MatNorm_1(), Anorm=%16.14e, sAnorm=%16.14e bs=%D\n",r1,r2,bs);
CHKERRQ(ierr);
}
/* Test MatGetOwnershipRange() */
ierr = MatGetOwnershipRange(sA,&rstart,&rend);
CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&i2,&j2);
CHKERRQ(ierr);
i2 -= rstart;
j2 -= rend;
if (i2 || j2) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MaGetOwnershipRange()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* Test MatDiagonalScale() */
ierr = MatDiagonalScale(A,x,x);
CHKERRQ(ierr);
ierr = MatDiagonalScale(sA,x,x);
CHKERRQ(ierr);
ierr = MatMultEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NOTSAMETYPE,"Error in MatDiagonalScale");
/* Test MatGetDiagonal(), MatScale() */
ierr = MatGetDiagonal(A,s1);
CHKERRQ(ierr);
ierr = MatGetDiagonal(sA,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDiagonalScale() or MatGetDiagonal(), r1=%g \n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatScale(A,alpha);
CHKERRQ(ierr);
ierr = MatScale(sA,alpha);
CHKERRQ(ierr);
/* Test MatGetRowMaxAbs() */
ierr = MatGetRowMaxAbs(A,s1,NULL);
CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(sA,s2,NULL);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: MatGetRowMaxAbs() \n");
CHKERRQ(ierr);
}
/* Test MatMult(), MatMultAdd() */
ierr = MatMultEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMult() or MatScale()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatMultAddEqual(A,sA,10,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMultAdd()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
/* Test MatMultTranspose(), MatMultTransposeAdd() */
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = MatMultTranspose(A,x,s1);
CHKERRQ(ierr);
ierr = MatMultTranspose(sA,x,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMult() or MatScale(), err=%g\n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
}
for (i=0; i<10; i++) {
ierr = VecSetRandom(x,rctx);
CHKERRQ(ierr);
ierr = VecSetRandom(y,rctx);
CHKERRQ(ierr);
ierr = MatMultTransposeAdd(A,x,y,s1);
CHKERRQ(ierr);
ierr = MatMultTransposeAdd(sA,x,y,s2);
CHKERRQ(ierr);
ierr = VecNorm(s1,NORM_1,&r1);
CHKERRQ(ierr);
ierr = VecNorm(s2,NORM_1,&r2);
CHKERRQ(ierr);
r1 -= r2;
if (r1<-tol || r1>tol) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatMultAdd(), err=%g \n",rank,(double)r1);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
}
/* Test MatDuplicate() */
ierr = MatDuplicate(sA,MAT_COPY_VALUES,&sB);
CHKERRQ(ierr);
ierr = MatEqual(sA,sB,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscPrintf(PETSC_COMM_WORLD," Error in MatDuplicate(), sA != sB \n");
CHKERRQ(ierr);
CHKERRQ(ierr);
}
ierr = MatMultEqual(sA,sB,5,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDuplicate() or MatMult()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatMultAddEqual(sA,sB,5,&flg);
CHKERRQ(ierr);
if (!flg) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"[%d], Error: MatDuplicate() or MatMultAdd(()\n",rank);
CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
CHKERRQ(ierr);
}
ierr = MatDestroy(&sB);
CHKERRQ(ierr);
ierr = VecDestroy(&u);
CHKERRQ(ierr);
ierr = VecDestroy(&x);
CHKERRQ(ierr);
ierr = VecDestroy(&y);
CHKERRQ(ierr);
ierr = VecDestroy(&s1);
CHKERRQ(ierr);
ierr = VecDestroy(&s2);
CHKERRQ(ierr);
ierr = MatDestroy(&sA);
CHKERRQ(ierr);
ierr = MatDestroy(&A);
CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);
CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscReal norm; /* norm of solution error */
PetscInt dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
PetscErrorCode ierr;
PetscScalar v,none = -1.0,sigma2,pfive = 0.5,*xa;
PetscRandom rctx;
PetscReal h2,sigma1 = 100.0;
PetscBool flg = PETSC_FALSE;
PetscScalar a = 1.0+PETSC_i;
PetscInitialize(&argc,&args,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex numbers");
#endif
a=1.0+PETSC_i;
printf("%g+%gi\n",(double)PetscRealPart(a),(double)PetscImaginaryPart(a));
ierr = PetscOptionsGetReal(NULL,"-sigma1",&sigma1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
dim = n*n;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix, specifying only its global dimensions.
When using MatCreate(), the matrix format can be specified at
runtime. Also, the parallel partitioning of the matrix is
determined by PETSc at runtime.
*/
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
/*
Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors. Determine which
rows of the matrix are locally owned.
*/
ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
/*
Set matrix elements in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Always specify global rows and columns of matrix entries.
*/
ierr = PetscOptionsGetBool(NULL,"-norandom",&flg,NULL);CHKERRQ(ierr);
if (flg) use_random = 0;
else use_random = 1;
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = PetscRandomSetInterval(rctx,0.0,PETSC_i);CHKERRQ(ierr);
} else {
sigma2 = 10.0*PETSC_i;
}
h2 = 1.0/((n+1)*(n+1));
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0; i = Ii/n; j = Ii - i*n;
if (i>0) {
J = Ii-n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (i<n-1) {
J = Ii+n; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j>0) {
J = Ii-1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii+1; ierr = MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomGetValue(rctx,&sigma2);CHKERRQ(ierr);}
v = 4.0 - sigma1*h2 + sigma2*h2;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);CHKERRQ(ierr);
}
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Create parallel vectors.
- When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
we specify only the vector's global
dimension; the parallel partitioning is determined at runtime.
- Note: We form 1 vector from scratch and then duplicate as needed.
*/
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,dim);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
*/
if (use_random) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,pfive);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Print the first 3 entries of x; this demonstrates extraction of the
real and imaginary components of the complex vector, x.
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-print_x3",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = VecGetArray(x,&xa);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");CHKERRQ(ierr);
for (i=0; i<3; i++) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));CHKERRQ(ierr);
}
ierr = VecRestoreArray(x,&xa);CHKERRQ(ierr);
}
/*
Check the error
*/
ierr = VecAXPY(x,none,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
if (use_random) {ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);}
ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr); ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=3,N1=3,N2=3,N=N0*N1*N2;
PetscRandom rdm;
PetscScalar a;
PetscReal enorm;
Vec x,y,z,input,output;
PetscBool view=PETSC_FALSE,use_interface=PETSC_TRUE;
Mat A;
PetscInt DIM, dim[3],vsize;
PetscReal fac;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires real numbers");
#endif
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&input);CHKERRQ(ierr);
ierr = VecSetSizes(input,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(input);CHKERRQ(ierr);
ierr = VecSetRandom(input,rdm);CHKERRQ(ierr);
ierr = VecDuplicate(input,&output);
// ierr = VecGetSize(input,&vsize);CHKERRQ(ierr);
// printf("Size of the input Vector is %d\n",vsize);
DIM = 3;
dim[0] = N0; dim[1] = N1; dim[2] = N2;
ierr = MatCreateFFT(PETSC_COMM_WORLD,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
ierr = MatGetVecs(A,&x,&y);CHKERRQ(ierr);
ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetSize(y,&vsize);CHKERRQ(ierr);
printf("The vector size from the main routine is %d\n",vsize);
ierr = InputTransformFFT(A,input,x);CHKERRQ(ierr);
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
ierr = OutputTransformFFT(A,z,output);CHKERRQ(ierr);
fac = 1.0/(PetscReal)N;
ierr = VecScale(output,fac);CHKERRQ(ierr);
ierr = VecAssemblyBegin(input);CHKERRQ(ierr);
ierr = VecAssemblyEnd(input);CHKERRQ(ierr);
ierr = VecAssemblyBegin(output);CHKERRQ(ierr);
ierr = VecAssemblyEnd(output);CHKERRQ(ierr);
ierr = VecView(input,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(output,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecAXPY(output,-1.0,input);CHKERRQ(ierr);
ierr = VecNorm(output,NORM_1,&enorm);CHKERRQ(ierr);
// if (enorm > 1.e-14){
if (!rank)
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
// }
// ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
// printf("Vector size from ex148 %d\n",vsize);
// ierr = PetscObjectSetName((PetscObject) x, "Real space vector");CHKERRQ(ierr);
// ierr = PetscObjectSetName((PetscObject) y, "Frequency space vector");CHKERRQ(ierr);
// ierr = PetscObjectSetName((PetscObject) z, "Reconstructed vector");CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscInt main(PetscInt argc,char **args)
{
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt N0=10,N1=10,N2=10,N3=10,N4=10,N=N0*N1*N2*N3*N4;
PetscRandom rdm;
PetscReal enorm;
Vec x,y,z,input,output;
Mat A;
PetscInt DIM, dim[5],vsize;
PetscReal fac;
ierr = PetscInitialize(&argc,&args,(char *)0,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
if (size!=1)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This is a uni-processor example only");
ierr = PetscRandomCreate(PETSC_COMM_SELF, &rdm);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rdm);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_SELF,&input);CHKERRQ(ierr);
ierr = VecSetSizes(input,N,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(input);CHKERRQ(ierr);
ierr = VecSetRandom(input,rdm);CHKERRQ(ierr);
ierr = VecDuplicate(input,&output);
DIM = 5; dim[0] = N0; dim[1] = N1; dim[2] = N2; dim[3] = N3; dim[4] = N4;
ierr = MatCreateFFT(PETSC_COMM_SELF,DIM,dim,MATFFTW,&A);CHKERRQ(ierr);
ierr = MatGetVecs(A,&x,&y);CHKERRQ(ierr);
ierr = MatGetVecs(A,&z,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetSize(x,&vsize);CHKERRQ(ierr);
printf("The vector size of input from the main routine is %d\n",vsize);
ierr = VecGetSize(z,&vsize);CHKERRQ(ierr);
printf("The vector size of output from the main routine is %d\n",vsize);
ierr = InputTransformFFT(A,input,x);CHKERRQ(ierr);
ierr = MatMult(A,x,y);CHKERRQ(ierr);
ierr = MatMultTranspose(A,y,z);CHKERRQ(ierr);
ierr = OutputTransformFFT(A,z,output);CHKERRQ(ierr);
fac = 1.0/(PetscReal)N;
ierr = VecScale(output,fac);CHKERRQ(ierr);
/*
ierr = VecAssemblyBegin(input);CHKERRQ(ierr);
ierr = VecAssemblyEnd(input);CHKERRQ(ierr);
ierr = VecAssemblyBegin(output);CHKERRQ(ierr);
ierr = VecAssemblyEnd(output);CHKERRQ(ierr);
ierr = VecView(input,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(output,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
*/
ierr = VecAXPY(output,-1.0,input);CHKERRQ(ierr);
ierr = VecNorm(output,NORM_1,&enorm);CHKERRQ(ierr);
// if (enorm > 1.e-14){
ierr = PetscPrintf(PETSC_COMM_SELF," Error norm of |x - z| %e\n",enorm);CHKERRQ(ierr);
// }
ierr = VecDestroy(&output);CHKERRQ(ierr);
ierr = VecDestroy(&input);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&y);CHKERRQ(ierr);
ierr = VecDestroy(&z);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rdm);CHKERRQ(ierr);
PetscFinalize();
return 0;
}
void PETSC_STDCALL vecsetrandom_(Vec x,PetscRandom rctx, int *__ierr ){
*__ierr = VecSetRandom(
(Vec)PetscToPointer((x) ),
(PetscRandom)PetscToPointer((rctx) ));
}
PetscErrorCode PCBDDCScalingSetUp(PC pc)
{
PC_IS* pcis=(PC_IS*)pc->data;
PC_BDDC* pcbddc=(PC_BDDC*)pc->data;
PetscErrorCode ierr;
PetscFunctionBegin;
PetscValidHeaderSpecific(pc,PC_CLASSID,1);
ierr = PetscLogEventBegin(PC_BDDC_Scaling[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
/* create work vector for the operator */
ierr = VecDestroy(&pcbddc->work_scaling);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_B,&pcbddc->work_scaling);CHKERRQ(ierr);
/* always rebuild pcis->D */
if (pcis->use_stiffness_scaling) {
PetscScalar *a;
PetscInt i,n;
ierr = MatGetDiagonal(pcbddc->local_mat,pcis->vec1_N);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->N_to_B,pcis->vec1_N,pcis->D,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecAbs(pcis->D);CHKERRQ(ierr);
ierr = VecGetLocalSize(pcis->D,&n);CHKERRQ(ierr);
ierr = VecGetArray(pcis->D,&a);CHKERRQ(ierr);
for (i=0;i<n;i++) if (PetscAbsScalar(a[i])<PETSC_SMALL) a[i] = 1.0;
ierr = VecRestoreArray(pcis->D,&a);CHKERRQ(ierr);
}
ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->D,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->D,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecPointwiseDivide(pcis->D,pcis->D,pcis->vec1_B);CHKERRQ(ierr);
/* now setup */
if (pcbddc->use_deluxe_scaling) {
if (!pcbddc->deluxe_ctx) {
ierr = PCBDDCScalingCreate_Deluxe(pc);CHKERRQ(ierr);
}
ierr = PCBDDCScalingSetUp_Deluxe(pc);CHKERRQ(ierr);
ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingRestriction_C",PCBDDCScalingRestriction_Deluxe);CHKERRQ(ierr);
ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingExtension_C",PCBDDCScalingExtension_Deluxe);CHKERRQ(ierr);
} else {
ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingRestriction_C",PCBDDCScalingRestriction_Basic);CHKERRQ(ierr);
ierr = PetscObjectComposeFunction((PetscObject)pc,"PCBDDCScalingExtension_C",PCBDDCScalingExtension_Basic);CHKERRQ(ierr);
}
/* test */
if (pcbddc->dbg_flag) {
Mat B0_B = NULL;
Vec B0_Bv = NULL, B0_Bv2 = NULL;
Vec vec2_global;
PetscViewer viewer = pcbddc->dbg_viewer;
PetscReal error;
/* extension -> from local to parallel */
ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
ierr = VecSetRandom(pcis->vec1_B,NULL);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecDuplicate(pcis->vec1_global,&vec2_global);CHKERRQ(ierr);
ierr = VecCopy(pcis->vec1_global,vec2_global);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
if (pcbddc->benign_n) {
IS is_dummy;
ierr = ISCreateStride(PETSC_COMM_SELF,pcbddc->benign_n,0,1,&is_dummy);CHKERRQ(ierr);
ierr = MatCreateSubMatrix(pcbddc->benign_B0,is_dummy,pcis->is_B_local,MAT_INITIAL_MATRIX,&B0_B);CHKERRQ(ierr);
ierr = ISDestroy(&is_dummy);CHKERRQ(ierr);
ierr = MatCreateVecs(B0_B,NULL,&B0_Bv);CHKERRQ(ierr);
ierr = VecDuplicate(B0_Bv,&B0_Bv2);CHKERRQ(ierr);
ierr = MatMult(B0_B,pcis->vec1_B,B0_Bv);CHKERRQ(ierr);
}
ierr = PCBDDCScalingExtension(pc,pcis->vec1_B,pcis->vec1_global);CHKERRQ(ierr);
if (pcbddc->benign_saddle_point) {
PetscReal errorl = 0.;
ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_global,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
if (pcbddc->benign_n) {
ierr = MatMult(B0_B,pcis->vec1_B,B0_Bv2);CHKERRQ(ierr);
ierr = VecAXPY(B0_Bv,-1.0,B0_Bv2);CHKERRQ(ierr);
ierr = VecNorm(B0_Bv,NORM_INFINITY,&errorl);CHKERRQ(ierr);
}
ierr = MPI_Allreduce(&errorl,&error,1,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)pc));CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Error benign extension %1.14e\n",error);CHKERRQ(ierr);
}
ierr = VecAXPY(pcis->vec1_global,-1.0,vec2_global);CHKERRQ(ierr);
ierr = VecNorm(pcis->vec1_global,NORM_INFINITY,&error);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Error scaling extension %1.14e\n",error);CHKERRQ(ierr);
ierr = VecDestroy(&vec2_global);CHKERRQ(ierr);
/* restriction -> from parallel to local */
ierr = VecSet(pcis->vec1_global,0.0);CHKERRQ(ierr);
ierr = VecSetRandom(pcis->vec1_B,NULL);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = PCBDDCScalingRestriction(pc,pcis->vec1_global,pcis->vec1_B);CHKERRQ(ierr);
ierr = VecScale(pcis->vec1_B,-1.0);CHKERRQ(ierr);
ierr = VecScatterBegin(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecScatterEnd(pcis->global_to_B,pcis->vec1_B,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
ierr = VecNorm(pcis->vec1_global,NORM_INFINITY,&error);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"Error scaling restriction %1.14e\n",error);CHKERRQ(ierr);
ierr = MatDestroy(&B0_B);CHKERRQ(ierr);
ierr = VecDestroy(&B0_Bv);CHKERRQ(ierr);
ierr = VecDestroy(&B0_Bv2);CHKERRQ(ierr);
}
ierr = PetscLogEventEnd(PC_BDDC_Scaling[pcbddc->current_level],pc,0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
