/* collective on KSP */
PetscErrorCode KSPPlotEigenContours_Private(KSP ksp,PetscInt neig,const PetscReal *r,const PetscReal *c)
{
PetscErrorCode ierr;
PetscReal xmin,xmax,ymin,ymax,*xloc,*yloc,*value,px0,py0,rscale,iscale;
PetscInt M,N,i,j;
PetscMPIInt rank;
PetscViewer viewer;
PetscDraw draw;
PetscDrawAxis drawaxis;
PetscFunctionBegin;
ierr = MPI_Comm_rank(((PetscObject)ksp)->comm,&rank);CHKERRQ(ierr);
if (rank) PetscFunctionReturn(0);
M = 80;
N = 80;
xmin = r[0]; xmax = r[0];
ymin = c[0]; ymax = c[0];
for (i=1; i<neig; i++) {
xmin = PetscMin(xmin,r[i]);
xmax = PetscMax(xmax,r[i]);
ymin = PetscMin(ymin,c[i]);
ymax = PetscMax(ymax,c[i]);
}
ierr = PetscMalloc3(M,PetscReal,&xloc,N,PetscReal,&yloc,M*N,PetscReal,&value);CHKERRQ(ierr);
for (i=0; i<M; i++) xloc[i] = xmin - 0.1*(xmax-xmin) + 1.2*(xmax-xmin)*i/(M-1);
for (i=0; i<N; i++) yloc[i] = ymin - 0.1*(ymax-ymin) + 1.2*(ymax-ymin)*i/(N-1);
ierr = PolyEval(neig,r,c,0,0,&px0,&py0);CHKERRQ(ierr);
rscale = px0/(PetscSqr(px0)+PetscSqr(py0));
iscale = -py0/(PetscSqr(px0)+PetscSqr(py0));
for (j=0; j<N; j++) {
for (i=0; i<M; i++) {
PetscReal px,py,tx,ty,tmod;
ierr = PolyEval(neig,r,c,xloc[i],yloc[j],&px,&py);CHKERRQ(ierr);
tx = px*rscale - py*iscale;
ty = py*rscale + px*iscale;
tmod = PetscSqr(tx) + PetscSqr(ty); /* modulus of the complex polynomial */
if (tmod > 1) tmod = 1.0;
if (tmod > 0.5 && tmod < 1) tmod = 0.5;
if (tmod > 0.2 && tmod < 0.5) tmod = 0.2;
if (tmod > 0.05 && tmod < 0.2) tmod = 0.05;
if (tmod < 1e-3) tmod = 1e-3;
value[i+j*M] = PetscLogScalar(tmod) / PetscLogScalar(10.0);
}
}
ierr = PetscViewerDrawOpen(PETSC_COMM_SELF,0,"Iteratively Computed Eigen-contours",PETSC_DECIDE,PETSC_DECIDE,450,450,&viewer);CHKERRQ(ierr);
ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
ierr = PetscDrawTensorContour(draw,M,N,PETSC_NULL,PETSC_NULL,value);CHKERRQ(ierr);
if (0) {
ierr = PetscDrawAxisCreate(draw,&drawaxis);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLimits(drawaxis,xmin,xmax,ymin,ymax);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(drawaxis,"Eigen-counters","real","imag");CHKERRQ(ierr);
ierr = PetscDrawAxisDraw(drawaxis);CHKERRQ(ierr);
ierr = PetscDrawAxisDestroy(&drawaxis);CHKERRQ(ierr);
}
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = PetscFree3(xloc,yloc,value);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscDrawLG lg;
PetscErrorCode ierr;
PetscInt Mx = 100,i;
PetscReal x,hx = .1/Mx,pause,xx[3],yy[3];
PetscDraw draw;
const char *const legend[] = {"(1 - u^2)^2","1 - u^2","-(1 - u)log(1 - u)"};
PetscDrawAxis axis;
static PetscDrawViewPorts *ports = 0;
PetscFunctionBegin;
PetscInitialize(&argc,&argv,0,help);
ierr = PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1200,800);CHKERRQ(ierr);
ierr = PetscViewerDrawGetDrawLG(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),0,&lg);CHKERRQ(ierr);
ierr = PetscDrawLGGetDraw(lg,&draw);CHKERRQ(ierr);
ierr = PetscDrawCheckResizedWindow(draw);CHKERRQ(ierr);
if (!ports) {
ierr = PetscDrawViewPortsCreateRect(draw,1,2,&ports);CHKERRQ(ierr);
}
ierr = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
/*
Plot the energies
*/
ierr = PetscDrawLGSetDimension(lg,3);CHKERRQ(ierr);
ierr = PetscDrawViewPortsSet(ports,1);CHKERRQ(ierr);
x = .9;
for (i=0; i<Mx; i++) {
xx[0] = xx[1] = xx[2] = x;
yy[0] = (1.-x*x)*(1. - x*x);
yy[1] = (1. - x*x);
yy[2] = -(1.-x)*PetscLogScalar(1.-x);
ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
x += hx;
}
ierr = PetscDrawGetPause(draw,&pause);CHKERRQ(ierr);
ierr = PetscDrawSetPause(draw,0.0);CHKERRQ(ierr);
ierr = PetscDrawAxisSetLabels(axis,"Energy","","");CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(lg,legend);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
/*
Plot the forces
*/
ierr = PetscDrawViewPortsSet(ports,0);CHKERRQ(ierr);
ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
x = .9;
for (i=0; i<Mx; i++) {
xx[0] = xx[1] = xx[2] = x;
yy[0] = x*x*x - x;
yy[1] = -x;
yy[2] = 1.0 + PetscLogScalar(1. - x);
ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
x += hx;
}
ierr = PetscDrawAxisSetLabels(axis,"Derivative","","");CHKERRQ(ierr);
ierr = PetscDrawLGSetLegend(lg,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);
ierr = PetscDrawSetPause(draw,pause);CHKERRQ(ierr);
ierr = PetscDrawPause(draw);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. ts - the TS context
. X - input vector
. ptr - optional user-defined context, as set by SNESSetFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec Xdot,Vec F,void *ptr)
{
DM da;
PetscErrorCode ierr;
PetscInt i,Mx,xs,xm;
PetscReal hx,sx;
Field *x,*xdot,*f;
Vec localX,localXdot;
UserCtx *ctx = (UserCtx*)ptr;
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localXdot);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
/*
Scatter ghost points to local vector,using the 2-step process
DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,Xdot,INSERT_VALUES,localXdot);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,Xdot,INSERT_VALUES,localXdot);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localX,&x);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(da,localXdot,&xdot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
Compute function over the locally owned part of the grid
*/
for (i=xs; i<xs+xm; i++) {
f[i].w = x[i].w + ctx->kappa*(x[i-1].u + x[i+1].u - 2.0*x[i].u)*sx;
if (ctx->cahnhillard) {
switch (ctx->energy) {
case 1: /* double well */
f[i].w += -x[i].u*x[i].u*x[i].u + x[i].u;
break;
case 2: /* double obstacle */
f[i].w += x[i].u;
break;
case 3: /* logarithmic */
if (PetscRealPart(x[i].u) < -1.0 + 2.0*ctx->tol) f[i].w += .5*ctx->theta*(-PetscLogReal(ctx->tol) + PetscLogScalar((1.0-x[i].u)/2.0)) + ctx->theta_c*x[i].u;
else if (PetscRealPart(x[i].u) > 1.0 - 2.0*ctx->tol) f[i].w += .5*ctx->theta*(-PetscLogScalar((1.0+x[i].u)/2.0) + PetscLogReal(ctx->tol)) + ctx->theta_c*x[i].u;
else f[i].w += .5*ctx->theta*(-PetscLogScalar((1.0+x[i].u)/2.0) + PetscLogScalar((1.0-x[i].u)/2.0)) + ctx->theta_c*x[i].u;
break;
}
}
f[i].u = xdot[i].u - (x[i-1].w + x[i+1].w - 2.0*x[i].w)*sx;
}
/*
Restore vectors
*/
ierr = DMDAVecRestoreArrayRead(da,localXdot,&xdot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,localX,&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localXdot);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
