vec2r Fresnel::eval(real theta0, real kappa0, real a, real s)
{
real c1 = kappa0 / a;
real theta = theta0 - kappa0 * kappa0 / (rl(2.0) * a);
if (isnan(c1) || isinf(c1) || isnan(theta) || isinf(theta)) // This is a circle or a line
{
real r = rl(1) / kappa0;
if (isinf(r)) // This is a line
{
return vec2r(s * cos(theta0), s * sin(theta0));
}
else // This is a circle
{
// Note that negative kappa is handled magically by itself
real angle = s * kappa0;
vec2r result = { r * sin(angle), r - r * cos(angle) };
result.rot(theta0);
return result;
}
}
else // This is the normal case
{
real c0 = sqrt(abs(a) / PI);
real s0 = c0 * (s + c1);
real s1 = c0 * c1;
vec2r result = (eval(s0) - eval(s1)) / c0;
if (a < 0)
result.y = -result.y;
result.rot(theta0 - kappa0 * kappa0 / (rl(2.0) * a));
return result;
}
}
vec2r Fresnel::eval1(real a, real s)
{
const real c0 = sqrt(abs(a) / PI);
const real c1 = rl(1) / a;
if (isinf(c1)) // This is circle
return vec2r(sin(s), 1 - cos(s));
real s0 = c0 * (s + c1);
real s1 = c0 * c1;
vec2r result = (eval(s0) - eval(s1)) / c0;
if (a < 0)
result.y = -result.y;
result.rot(-rl(1) / (rl(2) * a));
return result;
}
static void testnsevdproblem(const ap::real_2d_array& a,
int n,
double& vecerr,
double& valonlydiff,
bool& wfailed)
{
double mx;
int i;
int j;
int k;
int vjob;
bool needl;
bool needr;
ap::real_1d_array wr0;
ap::real_1d_array wi0;
ap::real_1d_array wr1;
ap::real_1d_array wi1;
ap::real_1d_array wr0s;
ap::real_1d_array wi0s;
ap::real_1d_array wr1s;
ap::real_1d_array wi1s;
ap::real_2d_array vl;
ap::real_2d_array vr;
ap::real_1d_array vec1r;
ap::real_1d_array vec1i;
ap::real_1d_array vec2r;
ap::real_1d_array vec2i;
ap::real_1d_array vec3r;
ap::real_1d_array vec3i;
double curwr;
double curwi;
double vt;
double tmp;
vec1r.setbounds(0, n-1);
vec2r.setbounds(0, n-1);
vec3r.setbounds(0, n-1);
vec1i.setbounds(0, n-1);
vec2i.setbounds(0, n-1);
vec3i.setbounds(0, n-1);
wr0s.setbounds(0, n-1);
wr1s.setbounds(0, n-1);
wi0s.setbounds(0, n-1);
wi1s.setbounds(0, n-1);
mx = 0;
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-1; j++)
{
if( fabs(a(i,j))>mx )
{
mx = fabs(a(i,j));
}
}
}
if( mx==0 )
{
mx = 1;
}
//
// Load values-only
//
if( !rmatrixevd(a, n, 0, wr0, wi0, vl, vr) )
{
wfailed = false;
return;
}
//
// Test different jobs
//
for(vjob = 1; vjob <= 3; vjob++)
{
needr = vjob==1||vjob==3;
needl = vjob==2||vjob==3;
if( !rmatrixevd(a, n, vjob, wr1, wi1, vl, vr) )
{
wfailed = false;
return;
}
//
// Test values:
// 1. sort by real part
// 2. test
//
ap::vmove(&wr0s(0), &wr0(0), ap::vlen(0,n-1));
ap::vmove(&wi0s(0), &wi0(0), ap::vlen(0,n-1));
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-2-i; j++)
{
if( wr0s(j)>wr0s(j+1) )
{
tmp = wr0s(j);
wr0s(j) = wr0s(j+1);
wr0s(j+1) = tmp;
tmp = wi0s(j);
wi0s(j) = wi0s(j+1);
wi0s(j+1) = tmp;
}
}
}
ap::vmove(&wr1s(0), &wr1(0), ap::vlen(0,n-1));
ap::vmove(&wi1s(0), &wi1(0), ap::vlen(0,n-1));
for(i = 0; i <= n-1; i++)
{
for(j = 0; j <= n-2-i; j++)
{
if( wr1s(j)>wr1s(j+1) )
{
tmp = wr1s(j);
wr1s(j) = wr1s(j+1);
wr1s(j+1) = tmp;
tmp = wi1s(j);
wi1s(j) = wi1s(j+1);
wi1s(j+1) = tmp;
}
}
}
for(i = 0; i <= n-1; i++)
{
valonlydiff = ap::maxreal(valonlydiff, fabs(wr0s(i)-wr1s(i)));
valonlydiff = ap::maxreal(valonlydiff, fabs(wi0s(i)-wi1s(i)));
}
//
// Test right vectors
//
if( needr )
{
k = 0;
while(k<=n-1)
{
if( wi1(k)==0 )
{
ap::vmove(vec1r.getvector(0, n-1), vr.getcolumn(k, 0, n-1));
for(i = 0; i <= n-1; i++)
{
vec1i(i) = 0;
}
curwr = wr1(k);
curwi = 0;
}
if( wi1(k)>0 )
{
ap::vmove(vec1r.getvector(0, n-1), vr.getcolumn(k, 0, n-1));
ap::vmove(vec1i.getvector(0, n-1), vr.getcolumn(k+1, 0, n-1));
curwr = wr1(k);
curwi = wi1(k);
}
if( wi1(k)<0 )
{
ap::vmove(vec1r.getvector(0, n-1), vr.getcolumn(k-1, 0, n-1));
ap::vmoveneg(vec1i.getvector(0, n-1), vr.getcolumn(k, 0, n-1));
curwr = wr1(k);
curwi = wi1(k);
}
for(i = 0; i <= n-1; i++)
{
vt = ap::vdotproduct(&a(i, 0), &vec1r(0), ap::vlen(0,n-1));
vec2r(i) = vt;
vt = ap::vdotproduct(&a(i, 0), &vec1i(0), ap::vlen(0,n-1));
vec2i(i) = vt;
}
ap::vmove(&vec3r(0), &vec1r(0), ap::vlen(0,n-1), curwr);
ap::vsub(&vec3r(0), &vec1i(0), ap::vlen(0,n-1), curwi);
ap::vmove(&vec3i(0), &vec1r(0), ap::vlen(0,n-1), curwi);
ap::vadd(&vec3i(0), &vec1i(0), ap::vlen(0,n-1), curwr);
for(i = 0; i <= n-1; i++)
{
vecerr = ap::maxreal(vecerr, fabs(vec2r(i)-vec3r(i)));
vecerr = ap::maxreal(vecerr, fabs(vec2i(i)-vec3i(i)));
}
k = k+1;
}
}
//
// Test left vectors
//
if( needl )
{
k = 0;
while(k<=n-1)
{
if( wi1(k)==0 )
{
ap::vmove(vec1r.getvector(0, n-1), vl.getcolumn(k, 0, n-1));
for(i = 0; i <= n-1; i++)
{
vec1i(i) = 0;
}
curwr = wr1(k);
curwi = 0;
}
if( wi1(k)>0 )
{
ap::vmove(vec1r.getvector(0, n-1), vl.getcolumn(k, 0, n-1));
ap::vmove(vec1i.getvector(0, n-1), vl.getcolumn(k+1, 0, n-1));
curwr = wr1(k);
curwi = wi1(k);
}
if( wi1(k)<0 )
{
ap::vmove(vec1r.getvector(0, n-1), vl.getcolumn(k-1, 0, n-1));
ap::vmoveneg(vec1i.getvector(0, n-1), vl.getcolumn(k, 0, n-1));
curwr = wr1(k);
curwi = wi1(k);
}
for(j = 0; j <= n-1; j++)
{
vt = ap::vdotproduct(vec1r.getvector(0, n-1), a.getcolumn(j, 0, n-1));
vec2r(j) = vt;
vt = ap::vdotproduct(vec1i.getvector(0, n-1), a.getcolumn(j, 0, n-1));
vec2i(j) = -vt;
}
ap::vmove(&vec3r(0), &vec1r(0), ap::vlen(0,n-1), curwr);
ap::vadd(&vec3r(0), &vec1i(0), ap::vlen(0,n-1), curwi);
ap::vmove(&vec3i(0), &vec1r(0), ap::vlen(0,n-1), curwi);
ap::vsub(&vec3i(0), &vec1i(0), ap::vlen(0,n-1), curwr);
for(i = 0; i <= n-1; i++)
{
vecerr = ap::maxreal(vecerr, fabs(vec2r(i)-vec3r(i)));
vecerr = ap::maxreal(vecerr, fabs(vec2i(i)-vec3i(i)));
}
k = k+1;
}
}
}
}
