/*
ExactSolution - Computes the exact solution at a given time.
Input Parameters:
t - current time
solution - vector in which exact solution will be computed
appctx - user-defined application context
Output Parameter:
solution - vector with the newly computed exact solution
*/
PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
{
PetscScalar *s_localptr,h = appctx->h,ex1,ex2,sc1,sc2;
PetscInt i,mybase,myend;
PetscErrorCode ierr;
/*
Determine starting and ending points of each processor's
range of grid values
*/
ierr = VecGetOwnershipRange(solution,&mybase,&myend);CHKERRQ(ierr);
/*
Get a pointer to vector data.
*/
ierr = VecGetArray(solution,&s_localptr);CHKERRQ(ierr);
/*
Simply write the solution directly into the array locations.
Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
*/
ex1 = PetscExpReal(-36.*PETSC_PI*PETSC_PI*t); ex2 = PetscExpReal(-4.*PETSC_PI*PETSC_PI*t);
sc1 = PETSC_PI*6.*h; sc2 = PETSC_PI*2.*h;
for (i=mybase; i<myend; i++) s_localptr[i-mybase] = PetscSinScalar(sc1*(PetscReal)i)*ex1 + 3.*PetscSinScalar(sc2*(PetscReal)i)*ex2;
/*
Restore vector
*/
ierr = VecRestoreArray(solution,&s_localptr);CHKERRQ(ierr);
return 0;
}
/* Calculates the exact solution to problems that have one */
PetscErrorCode ExactSolution(Vec Y, void* s, PetscReal t, PetscBool *flag)
{
PetscErrorCode ierr;
char *p = (char*) s;
PetscScalar *y;
PetscFunctionBegin;
if (!strcmp(p,"hull1972a1")) {
ierr = VecGetArray(Y,&y);CHKERRQ(ierr);
y[0] = PetscExpReal(-t);
*flag = PETSC_TRUE;
ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr);
} else if (!strcmp(p,"hull1972a2")) {
ierr = VecGetArray(Y,&y);CHKERRQ(ierr);
y[0] = 1.0/PetscSqrtReal(t+1);
*flag = PETSC_TRUE;
ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr);
} else if (!strcmp(p,"hull1972a3")) {
ierr = VecGetArray(Y,&y);CHKERRQ(ierr);
y[0] = PetscExpReal(PetscSinReal(t));
*flag = PETSC_TRUE;
ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr);
} else if (!strcmp(p,"hull1972a4")) {
ierr = VecGetArray(Y,&y);CHKERRQ(ierr);
y[0] = 20.0/(1+19.0*PetscExpReal(-t/4.0));
*flag = PETSC_TRUE;
ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr);
} else {
ierr = VecSet(Y,0);CHKERRQ(ierr);
*flag = PETSC_FALSE;
}
PetscFunctionReturn(0);
}
/*
ExactSolution - Computes the exact solution at a given time.
Input Parameters:
t - current time
solution - vector in which exact solution will be computed
appctx - user-defined application context
Output Parameter:
solution - vector with the newly computed exact solution
*/
PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx)
{
PetscScalar *s_localptr, h = appctx->h, ex1, ex2, sc1, sc2;
PetscInt i;
PetscErrorCode ierr;
/*
Get a pointer to vector data.
*/
ierr = VecGetArray(solution,&s_localptr);CHKERRQ(ierr);
/*
Simply write the solution directly into the array locations.
Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
*/
ex1 = PetscExpReal(-36.*PETSC_PI*PETSC_PI*t); ex2 = PetscExpReal(-4.*PETSC_PI*PETSC_PI*t);
sc1 = PETSC_PI*6.*h; sc2 = PETSC_PI*2.*h;
for (i=0; i<appctx->m; i++) s_localptr[i] = PetscSinReal(PetscRealPart(sc1)*(PetscReal)i)*ex1 + 3.*PetscSinReal(PetscRealPart(sc2)*(PetscReal)i)*ex2;
/*
Restore vector
*/
ierr = VecRestoreArray(solution,&s_localptr);CHKERRQ(ierr);
return 0;
}
/*------------------------------------------------------------------------
Set exact solution
u(z,t) = sin(6*PI*z)*exp(-36.*PI*PI*t) + 3.*sin(2*PI*z)*exp(-4.*PI*PI*t)
--------------------------------------------------------------------------*/
PetscScalar exact(PetscScalar z,PetscReal t)
{
PetscScalar val, ex1, ex2;
ex1 = PetscExpReal(-36.*PETSC_PI*PETSC_PI*t);
ex2 = PetscExpReal(-4.*PETSC_PI*PETSC_PI*t);
val = PetscSinScalar(6*PETSC_PI*z)*ex1 + 3.*PetscSinScalar(2*PETSC_PI*z)*ex2;
return val;
}
/* ------------------------------------------------------------------- */
PetscErrorCode
FormInitialSolution(TS ts, Vec U, void * /*ptr*/)
{
DM da;
PetscReal c = -30.0;
PetscErrorCode ierr;
PetscInt i, j, xs, ys, xm, ym, Mx, My;
PetscScalar ** u;
PetscReal hx, hy, x, y, r;
PetscFunctionBeginUser;
ierr = TSGetDM(ts, &da);
CHKERRQ(ierr);
ierr = DMDAGetInfo(da,
PETSC_IGNORE,
&Mx,
&My,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE,
PETSC_IGNORE);
CHKERRQ(ierr);
hx = 1.0 / (PetscReal)(Mx - 1);
hy = 1.0 / (PetscReal)(My - 1);
/* Get pointers to vector data */
ierr = DMDAVecGetArray(da, U, &u);
CHKERRQ(ierr);
/* Get local grid boundaries */
ierr = DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);
CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (j = ys; j < ys + ym; j++)
{
y = j * hy;
for (i = xs; i < xs + xm; i++)
{
x = i * hx;
r = PetscSqrtReal((x - .5) * (x - .5) + (y - .5) * (y - .5));
if (r < .125)
u[j][i] = PetscExpReal(c * r * r * r);
else
u[j][i] = 0.0;
}
}
/* Restore vectors */
ierr = DMDAVecRestoreArray(da, U, &u);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* the initial function */
PetscReal f_ini(PetscReal x,PetscReal y)
{
PetscReal f;
f=PetscExpReal(-20.0*(PetscPowRealInt(x-0.5,2)+PetscPowRealInt(y-0.5,2)));
return f;
}
PetscScalar k1(AppCtx *ctx,PetscReal t)
{
PetscReal th = t/3600.0;
PetscReal barth = th - 24.0*floor(th/24.0);
if (((((PetscInt)th) % 24) < 4) || ((((PetscInt)th) % 24) >= 20)) return(1.0e-40);
else return(ctx->k1*PetscExpReal(7.0*PetscPowReal(PetscSinReal(.0625*PETSC_PI*(barth - 4.0)),.2)));
}
static PetscErrorCode CESolution(PetscReal t,Vec X,void *ctx)
{
PetscReal l = ((CECtx*)ctx)->lambda;
PetscErrorCode ierr;
PetscScalar *x;
PetscFunctionBeginUser;
ierr = VecGetArray(X,&x);CHKERRQ(ierr);
x[0] = l/(l*l+1)*(l*PetscCosReal(t)+PetscSinReal(t)) - l*l/(l*l+1)*PetscExpReal(-l*t);
ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormFunction(SNES snes, Vec x, Vec F, void *ctx) {
PetscErrorCode ierr;
const double b = 2.0, *ax;
double *aF;
ierr = VecGetArrayRead(x,&ax);CHKERRQ(ierr);
ierr = VecGetArray(F,&aF);CHKERRQ(ierr);
aF[0] = (1.0 / b) * PetscExpReal(b * ax[0]) - ax[1];
aF[1] = ax[0] * ax[0] + ax[1] * ax[1] - 1.0;
ierr = VecRestoreArrayRead(x,&ax);CHKERRQ(ierr);
ierr = VecRestoreArray(F,&aF);CHKERRQ(ierr);
return 0;
}
/*
Defines the DAE passed to the time solver
*/
static PetscErrorCode IFunctionSemiExplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,Vec F,void *ctx)
{
PetscErrorCode ierr;
const PetscScalar *y,*ydot;
PetscScalar *f;
PetscFunctionBegin;
/* The next three lines allow us to access the entries of the vectors directly */
ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr);
ierr = VecGetArray(F,&f);CHKERRQ(ierr);
f[0]=-400* PetscSinReal(200*PETSC_PI*t) + 1000*y[3] + ydot[0];
f[1]=0.5 - 1/(2.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.)) + (500*y[1])/9. + ydot[1];
f[2]=-222.5522222222222 + 33/(100.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.)) + (1000*y[4])/27. + ydot[2];
f[3]=0.0006666766666666667 - 1/(1.e8* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.)) + PetscSinReal(200*PETSC_PI*t)/2500. + y[0]/4500. - (11*y[3])/9000.;
f[4]=0.0006676566666666666 - 99/(1.e8* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.)) + y[2]/9000. - y[4]/4500.;
ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr);
ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Defines the DAE passed to the time solver
*/
static PetscErrorCode IFunctionImplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,Vec F,void *ctx)
{
PetscErrorCode ierr;
const PetscScalar *y,*ydot;
PetscScalar *f;
PetscFunctionBegin;
/* The next three lines allow us to access the entries of the vectors directly */
ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr);
ierr = VecGetArray(F,&f);CHKERRQ(ierr);
f[0]= PetscSinReal(200*PETSC_PI*t)/2500. - y[0]/1000. - ydot[0]/1.e6 + ydot[1]/1.e6;
f[1]=0.0006666766666666667 - PetscExpReal((500*(y[1] - y[2]))/13.)/1.e8 - y[1]/4500. + ydot[0]/1.e6 - ydot[1]/1.e6;
f[2]=-1.e-6 + PetscExpReal((500*(y[1] - y[2]))/13.)/1.e6 - y[2]/9000. - ydot[2]/500000.;
f[3]=0.0006676566666666666 - (99* PetscExpReal((500*(y[1] - y[2]))/13.))/1.e8 - y[3]/9000. - (3*ydot[3])/1.e6 + (3*ydot[4])/1.e6;
f[4]=-y[4]/9000. + (3*ydot[3])/1.e6 - (3*ydot[4])/1.e6;
ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr);
ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
TrueSolution() computes the true solution for the PDE
Input Parameter:
u - uninitialized solution vector (global)
appctx - user-defined application context
Output Parameter:
u - vector with solution at initial time (global)
*/
PetscErrorCode TrueSolution(TS ts, PetscReal t, Vec u,AppCtx *appctx)
{
PetscScalar *s;
const PetscScalar *xg;
PetscErrorCode ierr;
PetscInt i,xs,xn;
ierr = DMDAVecGetArray(appctx->da,u,&s);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(appctx->da,appctx->SEMop.grid,(void*)&xg);CHKERRQ(ierr);
ierr = DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);CHKERRQ(ierr);
for (i=xs; i<xs+xn; i++) {
s[i]=2.0*appctx->param.mu*PETSC_PI*PetscSinScalar(PETSC_PI*xg[i])*PetscExpReal(-appctx->param.mu*PETSC_PI*PETSC_PI*t)/(2.0+PetscCosScalar(PETSC_PI*xg[i])*PetscExpReal(-appctx->param.mu*PETSC_PI*PETSC_PI*t));
}
ierr = DMDAVecRestoreArray(appctx->da,u,&s);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(appctx->da,appctx->SEMop.grid,(void*)&xg);CHKERRQ(ierr);
return 0;
}
/*
Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
*/
static PetscErrorCode IJacobianImplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,PetscReal a,Mat A,Mat B,void *ctx)
{
PetscErrorCode ierr;
PetscInt rowcol[] = {0,1,2,3,4,5};
const PetscScalar *y,*ydot;
PetscScalar J[6][6];
PetscFunctionBegin;
ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr);
PetscMemzero(J,sizeof(J));
J[0][0]=-0.001 - a/1.e6;
J[0][1]=a/1.e6;
J[0][5]=(2*PETSC_PI* PetscCosReal(200*PETSC_PI*y[5]))/25.;
J[1][0]=a/1.e6;
J[1][1]=-0.00022222222222222223 - a/1.e6 - PetscExpReal((500*(y[1] - y[2]))/13.)/2.6e6;
J[1][2]= PetscExpReal((500*(y[1] - y[2]))/13.)/2.6e6;
J[2][1]= PetscExpReal((500*(y[1] - y[2]))/13.)/26000.;
J[2][2]=-0.00011111111111111112 - a/500000. - PetscExpReal((500*(y[1] - y[2]))/13.)/26000.;
J[3][1]=(-99* PetscExpReal((500*(y[1] - y[2]))/13.))/2.6e6;
J[3][2]=(99* PetscExpReal((500*(y[1] - y[2]))/13.))/2.6e6;
J[3][3]=-0.00011111111111111112 - (3*a)/1.e6;
J[3][4]=(3*a)/1.e6;
J[4][3]=(3*a)/1.e6;
J[4][4]=-0.00011111111111111112 - (3*a)/1.e6;
J[5][5]=a;
ierr = MatSetValues(B,6,rowcol,6,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (A != B) {
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PETSC_EXTERN PetscErrorCode MatGetOrdering_AWBM(Mat A, MatOrderingType type, IS *permR, IS *permC)
{
Vec *scalR, *scalC, scalRVec, scalCVec;
scalR = &scalRVec; scalC = &scalCVec;
/* EVERYTHING IS WRITTEN AS IF THE MATRIX WERE COLUMN-MAJOR */
Mat_SeqAIJ *aij = (Mat_SeqAIJ *) A->data;
PetscInt n = A->rmap->n; /* Number of local columns */
PetscInt m = A->cmap->n; /* Number of local rows */
PetscInt *match; /* The row matched to each column, and inverse column permutation */
PetscInt *matchR; /* The column matched to each row */
PetscInt *p; /* The column permutation */
const PetscInt *ia = aij->i;
const PetscInt *ja = aij->j;
const MatScalar *a = aij->a;
Vec colMax;
PetscScalar *a_j, *sr, *sc;
PetscReal *weights /* c_ij */, *u /* u_i */, *v /* v_j */, eps = PETSC_SQRT_MACHINE_EPSILON;
PetscInt debug = 0, r, c, r1, c1;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PetscOptionsGetInt(NULL, "-debug", &debug, NULL);CHKERRQ(ierr);
ierr = MatGetVecs(A, NULL, &colMax);CHKERRQ(ierr);
ierr = MatGetRowMaxAbs(A, colMax, NULL);CHKERRQ(ierr);
ierr = PetscMalloc2(n, &match, m, &matchR);CHKERRQ(ierr);
ierr = PetscMalloc1(n, &p);CHKERRQ(ierr);
ierr = PetscCalloc3(m, &u, n, &v, ia[n], &weights);CHKERRQ(ierr);
for (c = 0; c < n; ++c) match[c] = -1;
/* Compute weights */
ierr = VecGetArray(colMax, &a_j);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
for (r = ia[c]; r < ia[c+1]; ++r) {
PetscReal ar = PetscAbsScalar(a[r]);
if (ar == 0.0) weights[r] = PETSC_MAX_REAL;
else weights[r] = log(a_j[c]/ar);
}
}
/* Compute local row weights */
for (r = 0; r < m; ++r) u[r] = PETSC_MAX_REAL;
for (c = 0; c < n; ++c) {
for (r = ia[c]; r < ia[c+1]; ++r) {
u[ja[r]] = PetscMin(u[ja[r]], weights[r]);
}
}
/* Compute local column weights */
for (c = 0; c < n; ++c) {
v[c] = PETSC_MAX_REAL;
for (r = ia[c]; r < ia[c+1]; ++r) {
v[c] = PetscMin(v[c], weights[r] - u[ja[r]]);
}
}
for (r = 0; r < m; ++r) matchR[r] = -1;
/* Match columns */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
/* if (match[c] >= 0) continue; */
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Row %d\n Weights:", c);CHKERRQ(ierr);}
for (r = ia[c]; r < ia[c+1]; ++r) {
PetscReal weight = weights[r] - u[ja[r]] - v[c];
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, " %g", weight);CHKERRQ(ierr);}
if ((weight <= eps) && (matchR[ja[r]] < 0)) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Matched %d -- %d\n", c, ja[r]);CHKERRQ(ierr);}
match[c] = ja[r];
matchR[ja[r]] = c;
break;
}
}
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "\n");CHKERRQ(ierr);}
}
/* Deal with unmatched columns */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] >= 0) continue;
for (r = ia[c]; r < ia[c+1]; ++r) {
PetscReal weight = weights[r] - u[ja[r]] - v[c];
if (weight > eps) continue;
/* \bar c_ij = 0 and (r, j1) \in M */
c1 = matchR[ja[r]];
for (r1 = ia[c1]; r1 < ia[c1+1]; ++r1) {
PetscReal weight1 = weights[r1] - u[ja[r1]] - v[c1];
if ((matchR[ja[r1]] < 0) && (weight1 <= eps)) {
/* (r, c1) in M is replaced by (r, c) and (r1, c1) */
if (debug) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Replaced match %d -- %d\n", c1, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c1, ja[r1]);CHKERRQ(ierr);
}
match[c] = ja[r];
matchR[ja[r]] = c;
match[c1] = ja[r1];
matchR[ja[r1]] = c1;
break;
}
}
if (match[c] >= 0) break;
}
}
/* Allow matching with non-optimal rows */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] >= 0) continue;
for (r = ia[c]; r < ia[c+1]; ++r) {
if (matchR[ja[r]] < 0) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Matched non-opt %d -- %d\n", c, ja[r]);CHKERRQ(ierr);}
match[c] = ja[r];
matchR[ja[r]] = c;
break;
}
}
}
/* Deal with non-optimal unmatched columns */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] >= 0) continue;
for (r = ia[c]; r < ia[c+1]; ++r) {
/* \bar c_ij = 0 and (r, j1) \in M */
c1 = matchR[ja[r]];
for (r1 = ia[c1]; r1 < ia[c1+1]; ++r1) {
if (matchR[ja[r1]] < 0) {
/* (r, c1) in M is replaced by (r, c) and (r1, c1) */
if (debug) {
ierr = PetscPrintf(PETSC_COMM_SELF, "Replaced match %d -- %d\n", c1, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c, ja[r]);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF, " Added match %d -- %d\n", c1, ja[r1]);CHKERRQ(ierr);
}
match[c] = ja[r];
matchR[ja[r]] = c;
match[c1] = ja[r1];
matchR[ja[r1]] = c1;
break;
}
}
if (match[c] >= 0) break;
}
}
/* Complete matching */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0, r = 0; c < n; ++c) {
if (match[c] >= n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Column %d matched to invalid row %d", c, match[c]);
if (match[c] < 0) {
for (; r < n; ++r) {
if (matchR[r] < 0) {
if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "Matched default %d -- %d\n", c, r);CHKERRQ(ierr);}
match[c] = r;
matchR[r] = c;
break;
}
}
}
}
/* Check matching */
ierr = CheckUnmatched(n, match, matchR);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
if (match[c] < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Column %d unmatched", c);
if (match[c] >= n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Column %d matched to invalid row %d", c, match[c]);
}
/* Make permutation */
for (c = 0; c < n; ++c) {p[match[c]] = c;}
ierr = ISCreateGeneral(PETSC_COMM_SELF, n, p, PETSC_OWN_POINTER, permR);CHKERRQ(ierr);
ierr = ISSetPermutation(*permR);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF, n, 0, 1, permC);CHKERRQ(ierr);
ierr = ISSetPermutation(*permC);CHKERRQ(ierr);
ierr = PetscFree2(match, matchR);CHKERRQ(ierr);
/* Make scaling */
ierr = VecCreateSeq(PETSC_COMM_SELF, n, scalR);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF, n, scalC);CHKERRQ(ierr);
ierr = VecGetArray(*scalR, &sr);CHKERRQ(ierr);
ierr = VecGetArray(*scalC, &sc);CHKERRQ(ierr);
for (c = 0; c < n; ++c) {
sr[c] = PetscExpReal(v[c])/a_j[c];
sc[c] = PetscExpReal(u[c]);
}
ierr = VecRestoreArray(*scalR, &sr);CHKERRQ(ierr);
ierr = VecRestoreArray(*scalC, &sc);CHKERRQ(ierr);
ierr = VecRestoreArray(colMax, &a_j);CHKERRQ(ierr);
ierr = VecDestroy(&colMax);CHKERRQ(ierr);
ierr = PetscFree3(u,v,weights);CHKERRQ(ierr);
ierr = VecDestroy(scalR);CHKERRQ(ierr);
ierr = VecDestroy(scalC);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static void func12(PetscReal x, PetscReal *val)
{
*val = PetscExpReal(1-1/x)/PetscSqrtReal(x*x*x-x*x*x*x);
}
static void func14(PetscReal x, PetscReal *val)
{
if (x == 0.0) *val = 0.0;
else if (x == 1.0) *val = 1.0;
else *val = PetscExpReal(1-1/x)*PetscCosReal(1/x-1)/(x*x);
}
/*
Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian.
*/
static PetscErrorCode IJacobianSemiExplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,PetscReal a,Mat A,Mat B,void *ctx)
{
PetscErrorCode ierr;
PetscInt rowcol[] = {0,1,2,3,4};
const PetscScalar *y,*ydot;
PetscScalar J[5][5];
PetscFunctionBegin;
ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr);
PetscMemzero(J,sizeof(J));
J[0][0]=a;
J[0][3]=1000;
J[1][0]=250/(13.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[1][1]=55.55555555555556 + a + 250/(13.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[1][3]=-250/(13.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[2][0]=-165/(13.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[2][1]=-165/(13.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[2][2]=a;
J[2][3]=165/(13.* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[2][4]=37.03703703703704;
J[3][0]=0.00022222222222222223 + 1/(2.6e6* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[3][1]=1/(2.6e6* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[3][3]=-0.0012222222222222222 - 1/(2.6e6* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[4][0]=99/(2.6e6* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[4][1]=99/(2.6e6* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[4][2]=0.00011111111111111112;
J[4][3]=-99/(2.6e6* PetscExpReal((500*(y[0] + y[1] - y[3]))/13.));
J[4][4]=-0.00022222222222222223;
ierr = MatSetValues(B,5,rowcol,5,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr);
ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (A != B) {
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static void func12(PetscReal x, PetscReal *val)
{
if (x == 0.0) *val = 0.0;
else if (x == 1.0) *val = PETSC_INFINITY;
else *val = PetscExpReal(1-1/x)/PetscSqrtReal(x*x*x-x*x*x*x);
}
static void func13(PetscReal x, PetscReal *val)
{
if (x == 0.0) *val = 0.0;
else if (x == 1.0) *val = 1.0;
else *val = PetscExpReal(-(1/x-1)*(1/x-1)/2)/(x*x);
}
static void func3(PetscReal x, PetscReal *val)
{
*val = PetscExpReal(x)*PetscCosReal(x);
}
int main(int argc,char **argv)
{
Mat A[NMAT]; /* problem matrices */
PEP pep; /* polynomial eigenproblem solver context */
PetscInt m=15,n,II,Istart,Iend,i,j,k;
PetscReal h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
PetscScalar alpha,beta,gamma;
PetscBool flg;
PetscErrorCode ierr;
SlepcInitialize(&argc,&argv,(char*)0,help);
#if !defined(PETSC_USE_COMPLEX)
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex scalars");
#endif
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
n = m*m;
h = PETSC_PI/(m+1);
gamma = PetscExpScalar(PETSC_i*c[6]);
gamma = gamma/PetscAbsScalar(gamma);
k = 7;
ierr = PetscOptionsGetRealArray(NULL,"-c",c,&k,&flg);CHKERRQ(ierr);
if (flg && k!=7) SETERRQ1(PETSC_COMM_WORLD,1,"The number of parameters -c should be 7, you provided %D",k);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%D (m=%D)\n\n",n,m);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the polynomial matrices
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* initialize matrices */
for (i=0;i<NMAT;i++) {
ierr = MatCreate(PETSC_COMM_WORLD,&A[i]);CHKERRQ(ierr);
ierr = MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
ierr = MatSetFromOptions(A[i]);CHKERRQ(ierr);
ierr = MatSetUp(A[i]);CHKERRQ(ierr);
}
ierr = MatGetOwnershipRange(A[0],&Istart,&Iend);CHKERRQ(ierr);
/* A[1] has a pattern similar to the 2D Laplacian */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
xi = (i+1)*h; xj = (j+1)*h;
alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
ierr = MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES);CHKERRQ(ierr);
if (j>0) { ierr = MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
if (j<m-1) { ierr = MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
if (i>0) { ierr = MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
if (i<m-1) { ierr = MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES);CHKERRQ(ierr); }
}
/* A[0] and A[2] are diagonal */
for (II=Istart;II<Iend;II++) {
i = II/m; j = II-i*m;
xi = (i+1)*h; xj = (j+1)*h;
alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
beta = c[4]+c[5]*xj*(PETSC_PI-xj);
ierr = MatSetValue(A[0],II,II,alpha,INSERT_VALUES);CHKERRQ(ierr);
ierr = MatSetValue(A[2],II,II,beta,INSERT_VALUES);CHKERRQ(ierr);
}
/* assemble matrices */
for (i=0;i<NMAT;i++) {
ierr = MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
for (i=0;i<NMAT;i++) {
ierr = MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the eigensolver and solve the problem
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);
ierr = PEPSetOperators(pep,NMAT,A);CHKERRQ(ierr);
ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);
ierr = PEPSolve(pep);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Display solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PEPPrintSolution(pep,NULL);CHKERRQ(ierr);
ierr = PEPDestroy(&pep);CHKERRQ(ierr);
for (i=0;i<NMAT;i++) {
ierr = MatDestroy(&A[i]);CHKERRQ(ierr);
}
ierr = SlepcFinalize();CHKERRQ(ierr);
return 0;
}
PetscReal mcVal(PetscReal St, PetscReal r, PetscReal vol, PetscReal dt, PetscReal eps)
{
return (St * PetscExpReal((r-0.5*vol*vol)*dt + vol*PetscSqrtReal(dt)*eps));
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
DS ds;
FN f1,f2,f3,funs[3];
PetscScalar *Id,*A,*B,*wr,*wi,coeffs[2];
PetscReal tau=0.001,h,a=20,xi,re,im;
PetscInt i,n=10,ld,nev;
PetscViewer viewer;
PetscBool verbose;
SlepcInitialize(&argc,&argv,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-tau",&tau,NULL);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Solve a Dense System of type NEP - dimension %D, tau=%g.\n",n,(double)tau);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-verbose",&verbose);CHKERRQ(ierr);
/* Create DS object */
ierr = DSCreate(PETSC_COMM_WORLD,&ds);CHKERRQ(ierr);
ierr = DSSetType(ds,DSNEP);CHKERRQ(ierr);
ierr = DSSetFromOptions(ds);CHKERRQ(ierr);
/* Set functions (prior to DSAllocate) */
ierr = FNCreate(PETSC_COMM_WORLD,&f1);CHKERRQ(ierr);
ierr = FNSetType(f1,FNRATIONAL);CHKERRQ(ierr);
coeffs[0] = -1.0; coeffs[1] = 0.0;
ierr = FNSetParameters(f1,2,coeffs,0,NULL);CHKERRQ(ierr);
ierr = FNCreate(PETSC_COMM_WORLD,&f2);CHKERRQ(ierr);
ierr = FNSetType(f2,FNRATIONAL);CHKERRQ(ierr);
coeffs[0] = 1.0;
ierr = FNSetParameters(f2,1,coeffs,0,NULL);CHKERRQ(ierr);
ierr = FNCreate(PETSC_COMM_WORLD,&f3);CHKERRQ(ierr);
ierr = FNSetType(f3,FNEXP);CHKERRQ(ierr);
coeffs[0] = -tau;
ierr = FNSetParameters(f3,1,coeffs,0,NULL);CHKERRQ(ierr);
funs[0] = f1;
funs[1] = f2;
funs[2] = f3;
ierr = DSSetFN(ds,3,funs);CHKERRQ(ierr);
/* Set dimensions */
ld = n+2; /* test leading dimension larger than n */
ierr = DSAllocate(ds,ld);CHKERRQ(ierr);
ierr = DSSetDimensions(ds,n,0,0,0);CHKERRQ(ierr);
/* Set up viewer */
ierr = PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);CHKERRQ(ierr);
ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);CHKERRQ(ierr);
ierr = DSView(ds,viewer);CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
if (verbose) {
ierr = PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
}
/* Fill matrices */
ierr = DSGetArray(ds,DS_MAT_E0,&Id);CHKERRQ(ierr);
for (i=0;i<n;i++) Id[i+i*ld]=1.0;
ierr = DSRestoreArray(ds,DS_MAT_E0,&Id);CHKERRQ(ierr);
h = PETSC_PI/(PetscReal)(n+1);
ierr = DSGetArray(ds,DS_MAT_E1,&A);CHKERRQ(ierr);
for (i=0;i<n;i++) A[i+i*ld]=-2.0/(h*h)+a;
for (i=1;i<n;i++) {
A[i+(i-1)*ld]=1.0/(h*h);
A[(i-1)+i*ld]=1.0/(h*h);
}
ierr = DSRestoreArray(ds,DS_MAT_E1,&A);CHKERRQ(ierr);
ierr = DSGetArray(ds,DS_MAT_E2,&B);CHKERRQ(ierr);
for (i=0;i<n;i++) {
xi = (i+1)*h;
B[i+i*ld] = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
}
ierr = DSRestoreArray(ds,DS_MAT_E2,&B);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Initial - - - - - - - - -\n");CHKERRQ(ierr);
ierr = DSView(ds,viewer);CHKERRQ(ierr);
}
/* Solve */
ierr = PetscMalloc2(n,&wr,n,&wi);CHKERRQ(ierr);
ierr = DSSolve(ds,wr,wi);CHKERRQ(ierr);
if (verbose) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"After solve - - - - - - - - -\n");CHKERRQ(ierr);
ierr = DSView(ds,viewer);CHKERRQ(ierr);
}
/* Print first eigenvalue */
ierr = PetscPrintf(PETSC_COMM_WORLD,"Computed eigenvalue =\n",n);CHKERRQ(ierr);
nev = 1;
for (i=0;i<nev;i++) {
#if defined(PETSC_USE_COMPLEX)
re = PetscRealPart(wr[i]);
im = PetscImaginaryPart(wr[i]);
#else
re = wr[i];
im = wi[i];
#endif
if (PetscAbs(im)<1e-10) {
ierr = PetscViewerASCIIPrintf(viewer," %.5f\n",(double)re);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(viewer," %.5f%+.5fi\n",(double)re,(double)im);CHKERRQ(ierr);
}
}
ierr = PetscFree2(wr,wi);CHKERRQ(ierr);
ierr = FNDestroy(&f1);CHKERRQ(ierr);
ierr = FNDestroy(&f2);CHKERRQ(ierr);
ierr = FNDestroy(&f3);CHKERRQ(ierr);
ierr = DSDestroy(&ds);CHKERRQ(ierr);
ierr = SlepcFinalize();
return 0;
}
static void func13(PetscReal x, PetscReal *val)
{
*val = PetscExpReal(-(1/x-1)*(1/x-1)/2)/(x*x);
}
static void func14(PetscReal x, PetscReal *val)
{
*val = PetscExpReal(1-1/x)*PetscCosReal(1/x-1)/(x*x);
}
int main(int argc,char *argv[])
{
char mat_type[256] = "aij"; /* default matrix type */
PetscErrorCode ierr;
MPI_Comm comm;
PetscMPIInt rank,size;
DM slice;
PetscInt i,bs=1,N=5,n,m,rstart,ghosts[2],*d_nnz,*o_nnz,dfill[4]={1,0,0,1},ofill[4]={1,1,1,1};
PetscReal alpha =1,K=1,rho0=1,u0=0,sigma=0.2;
PetscBool useblock=PETSC_TRUE;
PetscScalar *xx;
Mat A;
Vec x,b,lf;
ierr = PetscInitialize(&argc,&argv,0,help);CHKERRQ(ierr);
comm = PETSC_COMM_WORLD;
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
ierr = PetscOptionsBegin(comm,0,"Options for DMSliced test",0);CHKERRQ(ierr);
{
ierr = PetscOptionsInt("-n","Global number of nodes","",N,&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsInt("-bs","Block size (1 or 2)","",bs,&bs,NULL);CHKERRQ(ierr);
if (bs != 1) {
if (bs != 2) SETERRQ(PETSC_COMM_WORLD,1,"Block size must be 1 or 2");
ierr = PetscOptionsReal("-alpha","Inverse time step for wave operator","",alpha,&alpha,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-K","Bulk modulus of compressibility","",K,&K,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-rho0","Reference density","",rho0,&rho0,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-u0","Reference velocity","",u0,&u0,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-sigma","Width of Gaussian density perturbation","",sigma,&sigma,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-block","Use block matrix assembly","",useblock,&useblock,NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsString("-sliced_mat_type","Matrix type to use (aij or baij)","",mat_type,mat_type,sizeof(mat_type),NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* Split ownership, set up periodic grid in 1D */
n = PETSC_DECIDE;
ierr = PetscSplitOwnership(comm,&n,&N);CHKERRQ(ierr);
rstart = 0;
ierr = MPI_Scan(&n,&rstart,1,MPIU_INT,MPI_SUM,comm);CHKERRQ(ierr);
rstart -= n;
ghosts[0] = (N+rstart-1)%N;
ghosts[1] = (rstart+n)%N;
ierr = PetscMalloc2(n,&d_nnz,n,&o_nnz);CHKERRQ(ierr);
for (i=0; i<n; i++) {
if (size > 1 && (i==0 || i==n-1)) {
d_nnz[i] = 2;
o_nnz[i] = 1;
} else {
d_nnz[i] = 3;
o_nnz[i] = 0;
}
}
ierr = DMSlicedCreate(comm,bs,n,2,ghosts,d_nnz,o_nnz,&slice);CHKERRQ(ierr); /* Currently does not copy X_nnz so we can't free them until after DMSlicedGetMatrix */
if (!useblock) {ierr = DMSlicedSetBlockFills(slice,dfill,ofill);CHKERRQ(ierr);} /* Irrelevant for baij formats */
ierr = DMSetMatType(slice,mat_type);CHKERRQ(ierr);
ierr = DMCreateMatrix(slice,&A);CHKERRQ(ierr);
ierr = PetscFree2(d_nnz,o_nnz);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(slice,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&b);CHKERRQ(ierr);
ierr = VecGhostGetLocalForm(x,&lf);CHKERRQ(ierr);
ierr = VecGetSize(lf,&m);CHKERRQ(ierr);
if (m != (n+2)*bs) SETERRQ2(PETSC_COMM_SELF,1,"size of local form %D, expected %D",m,(n+2)*bs);
ierr = VecGetArray(lf,&xx);CHKERRQ(ierr);
for (i=0; i<n; i++) {
PetscInt row[2],col[9],im,ip;
PetscScalar v[12];
const PetscReal xref = 2.0*(rstart+i)/N - 1; /* [-1,1] */
const PetscReal h = 1.0/N; /* grid spacing */
im = (i==0) ? n : i-1;
ip = (i==n-1) ? n+1 : i+1;
switch (bs) {
case 1: /* Laplacian with periodic boundaries */
col[0] = im; col[1] = i; col[2] = ip;
v[0] = -h; v[1] = 2*h; v[2] = -h;
ierr = MatSetValuesLocal(A,1,&i,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
xx[i] = PetscSinReal(xref*PETSC_PI);
break;
case 2: /* Linear acoustic wave operator in variables [rho, u], central differences, periodic, timestep 1/alpha */
v[0] = -0.5*u0; v[1] = -0.5*K; v[2] = alpha; v[3] = 0; v[4] = 0.5*u0; v[5] = 0.5*K;
v[6] = -0.5/rho0; v[7] = -0.5*u0; v[8] = 0; v[9] = alpha; v[10] = 0.5/rho0; v[11] = 0.5*u0;
if (useblock) {
row[0] = i; col[0] = im; col[1] = i; col[2] = ip;
ierr = MatSetValuesBlockedLocal(A,1,row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
row[0] = 2*i; row[1] = 2*i+1;
col[0] = 2*im; col[1] = 2*im+1; col[2] = 2*i; col[3] = 2*ip; col[4] = 2*ip+1;
v[3] = v[4]; v[4] = v[5]; /* pack values in first row */
ierr = MatSetValuesLocal(A,1,row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
col[2] = 2*i+1;
v[8] = v[9]; v[9] = v[10]; v[10] = v[11]; /* pack values in second row */
ierr = MatSetValuesLocal(A,1,row+1,5,col,v+6,INSERT_VALUES);CHKERRQ(ierr);
}
/* Set current state (gaussian density perturbation) */
xx[2*i] = 0.2*PetscExpReal(-PetscSqr(xref)/(2*PetscSqr(sigma)));
xx[2*i+1] = 0;
break;
default: SETERRQ1(PETSC_COMM_SELF,1,"not implemented for block size %D",bs);
}
}
ierr = VecRestoreArray(lf,&xx);CHKERRQ(ierr);
ierr = VecGhostRestoreLocalForm(x,&lf);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatMult(A,x,b);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(b,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* Update the ghosted values, view the result on rank 0. */
ierr = VecGhostUpdateBegin(b,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecGhostUpdateEnd(b,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
if (!rank) {
ierr = VecGhostGetLocalForm(b,&lf);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(PETSC_VIEWER_STDOUT_SELF,"Local form of b on rank 0, last two nodes are ghost nodes\n");CHKERRQ(ierr);
ierr = VecView(lf,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = VecGhostRestoreLocalForm(b,&lf);CHKERRQ(ierr);
}
ierr = DMDestroy(&slice);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}