void Fox(
int n /* in */,
GRID_INFO_T* grid /* in */,
LOCAL_MATRIX_T* local_A /* in */,
LOCAL_MATRIX_T* local_B /* in */,
LOCAL_MATRIX_T* local_C /* out */) {
LOCAL_MATRIX_T* temp_A; /* Storage for the sub- */
/* matrix of A used during */
/* the current stage */
int stage;
int bcast_root;
int n_bar; /* n/sqrt(p) */
int source;
int dest;
MPI_Status status;
n_bar = n/grid->q;
Set_to_zero(local_C);
/* Calculate addresses for circular shift of B */
source = (grid->my_row + 1) % grid->q;
dest = (grid->my_row + grid->q - 1) % grid->q;
/* Set aside storage for the broadcast block of A */
temp_A = Local_matrix_allocate(n_bar);
for (stage = 0; stage < grid->q; stage++) {
bcast_root = (grid->my_row + stage) % grid->q;
if (bcast_root == grid->my_col) {
MPI_Bcast(local_A, 1, local_matrix_mpi_t,
bcast_root, grid->row_comm);
Local_matrix_multiply(local_A, local_B,
local_C);
} else {
MPI_Bcast(temp_A, 1, local_matrix_mpi_t,
bcast_root, grid->row_comm);
Local_matrix_multiply(temp_A, local_B,
local_C);
}
MPI_Sendrecv_replace(local_B, 1, local_matrix_mpi_t,
dest, 0, source, 0, grid->col_comm, &status);
} /* for */
} /* Fox */
/************************************************
* Complex root search subroutine *
* --------------------------------------------- *
* This routine searches for the complex roots *
* of an analytical function by encircling the *
* zero and estimating where it is. The circle *
* is subsequently tightened by a factor e, and *
* a new estimate made. *
* The inputs to the subroutine are; *
* w initial radius of search circle *
* x0,y0 the initial guess *
* e factor by which circle is reduced *
* n maximum number of iterations *
* m evaluation points per quadrant *
* The routine returns Z=X+IY (X,Y), and the *
* number of iterations, k. *
************************************************/
void Zcircle(double w, double e, double x0, double y0, int n, int m,
double &xx, double &yy, dielectric &epsilon) {
//Labels: 50,100,200,250,300,310,320,330,340,350,400,450
// 460,470,500,510,520,521
int i,j,m3,m4;
double X[80],Y[80],U[80],V[80];
double a,b1,b2,PI,x1,x2,xm1,xm2;
double x3,y3,x4,y1,y2,y4,uu,vv;
int k;
double yy0;
m=m*4; k=1;
PI = 4*atan(1);
a=2*PI/m;
e50:for (i=1; i<m+1; i++) {
X[i]=w*cos(a*(i-1))+x0;
Y[i]=w*sin(a*(i-1))+yy0;
}
std::cout<<"Determine the corresponding U[i] and V[i]"<<std::endl;
for (i=1; i<m+1; i++) {
xx=X[i] ; yy=Y[i];
//Eval(xx,yy,&uu,&vv);
std::cout<<"Calling epsilon.determinant ..."<<std::endl;
std::cout<<k<<" "<<i<<" A kx_re: "<<xx<<" kx_im: "<<yy<<std::endl;
epsilon.determinant(xx,yy,&uu,&vv);
std::cout<<"B det_re: "<<uu<<" det_im: "<<vv<<std::endl;
U[i]=uu;
V[i]=vv;
}
std::cout<<"Find the position at which uu changes sign"<<std::endl;
// in the counterclockwise direction
i=1; uu=U[i];
e100: Auxilliary(m,&i,&j);
if (uu*U[i]<0) goto e200;
std::cout<<"Guard against infinite loop B"<<std::endl;
std::cout<<uu*U[i]<<std::endl;
if (i==1) Set_to_zero(&xx,&yy);
goto e100;
std::cout<<"Transition found"<<std::endl;
e200: xm1=i;
std::cout<<"Search for the other transition, starting"<<std::endl;
// on the other side of the circle
i=(int) xm1+m/2;
if (i>m) i=i-m;
j=i;
uu=U[i];
std::cout<<"Flip directions alternately"<<std::endl;
e250: Auxilliary(m,&i,&j);
if (uu*U[i]<0) goto e300;
if (uu*U[j]<0) goto e310;
std::cout<<"Guard against infinite loop C"<<std::endl;
if (i==xm1+(xm2/2)) Set_to_zero(&xx,&yy);
if (j==xm1+(xm2/2)) Set_to_zero(&xx,&yy);
goto e250;
std::cout<<"Transition found"<<std::endl;
e300: m3=i;
goto e320;
std::cout<<"Transition found"<<std::endl;
e310: if (j==m) j=0;
m3=j+1;
std::cout<<"xm1 and m3 have been determined, now for xm2 and m4"<<std::endl;
// now for the vv transitions
e320: i=(int) xm1+m/4;
if (i>m) i=i-m;
j=i; vv=V[i];
e330: Auxilliary(m,&i,&j);
if (vv*V[i]<0) goto e340;
if (vv*V[j]<0) goto e350;
std::cout<<"Guard against infinite loop A"<<std::endl;
if (i==xm1+m/4) Set_to_zero(&xx,&yy);
if (j==xm1+m/4) Set_to_zero(&xx,&yy);
goto e330;
std::cout<<"xm2 has been found"<<std::endl;
e340: xm2=i;
goto e400;
e350: if (j==m) j=0;
xm2=j+1;
std::cout<<"xm2 has been found, now for m4"<<std::endl;
e400: i=(int) xm2+m/2;
if (i>m) i=i-m;
j=i; vv=V[i];
e450: Auxilliary(m,&i,&j);
if (uu*V[i]<0) goto e460;
if (vv*V[j]<0) goto e470;
// Guard against infinite loop
if (i==xm2+m/2) Set_to_zero(&xx,&yy);
if (j==xm2+m/2) Set_to_zero(&xx,&yy);
goto e450;
e460: m4=i;
goto e500;
e470: if (j==m) j=0;
m4=j+1;
std::cout<<"All the intersections have been determinep"<<std::endl;
// Interpolate to find the four (x,y) coordinates
e500: i=(int) xm1;
Interpolation(m,i,j,X,Y,U,V,&xx,&yy);
x1=xx ; y1=yy ; i=(int) xm2;
Interpolation(m,i,j,X,Y,U,V,&xx,&yy);
x2=xx ; y2=yy ; i=m3;
Interpolation(m,i,j,X,Y,U,V,&xx,&yy);
x3=xx ; y3=yy ; i=m4;
Interpolation(m,i,j,X,Y,U,V,&xx,&yy);
x4=xx ; y4=yy;
std::cout<<"Calculate the intersection of the lines"<<std::endl;
// Guard against a divide by zero
if (x1!=x3) goto e510;
xx=x1; yy=(y1+y3)/2.0;
goto e520;
e510: xm1=(y3-y1)/(x3-x1);
if (x2!=x4) goto e520;
xm2=1e8;
goto e521;
e520: xm2=(y2-y4)/(x2-x4);
e521: b1=y1-xm1*x1;
b2=y2-xm2*x2;
xx=-(b1-b2)/(xm1-xm2);
yy=(xm1*b2+xm2*b1)/(xm1+xm2);
std::cout<<"is another iteration in order ?"<<std::endl;
if (k==n) return;
x0=xx ; yy0=yy ; k=k+1 ; w=w*e;
goto e50;
} // Zcircle
