/* 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);
}
/*************
* DESCRIPTION: Return the number of sign changes in the Sturm sequence in
* sseq at the value a.
* INPUT: np
* sseq
* a
* OUTPUT: sign changes
*************/
static int NumChanges(int np, POLYNOMIAL *sseq, double a)
{
int changes;
double f, lf;
POLYNOMIAL *s;
changes = 0;
lf = PolyEval(a, sseq[0].ord, sseq[0].coef);
for (s = sseq + 1; s <= sseq + np; s++)
{
f = PolyEval(a, s->ord, s->coef);
if(lf == 0.0 || lf * f < 0)
changes++;
lf = f;
}
return changes;
}
/*************
* DESCRIPTION: Close in on a root by using regula-falsa
* INPUT: order
* coef
* a
* b
* val
* OUTPUT:
*************/
static int RegulaFalsa(int order, double *coef, double a, double b, double *val)
{
int its;
double fa, fb, x, fx, lfx;
fa = PolyEval(a, order, coef);
fb = PolyEval(b, order, coef);
if(fa * fb > 0.0)
return 0;
if(fabs(fa) < COEFF_LIMIT)
{
*val = a;
return 1;
}
if(fabs(fb) < COEFF_LIMIT)
{
*val = b;
return 1;
}
lfx = fa;
for(its = 0; its < MAX_ITERATIONS; its++)
{
x = (fb * a - fa * b) / (fb - fa);
fx = PolyEval(x, order, coef);
if(fabs(x) > EPSILON)
{
if (fabs(fx / x) < EPSILON)
{
*val = x;
return 1;
}
}
else
{
if(fabs(fx) < EPSILON)
{
*val = x;
return 1;
}
}
if(fa < 0)
{
if(fx < 0)
{
a = x;
fa = fx;
if((lfx * fx) > 0)
fb *= .5;
}
else
{
b = x;
fb = fx;
if((lfx * fx) > 0)
fa *= .5;
}
}
else
{
if(fx < 0)
{
b = x;
fb = fx;
if((lfx * fx) > 0)
fa *= .5;
}
else
{
a = x;
fa = fx;
if((lfx * fx) > 0)
fb *= .5;
}
}
// Check for underflow in the domain
if(fabs(b-a) < EPSILON)
{
*val = x;
return 1;
}
lfx = fx;
}
return 0;
}
