void SBBox::SBBoxImpl::fillXValue(tmv::MatrixView<double> val,
double x0, double dx, int izero,
double y0, double dy, int jzero) const
{
dbg<<"SBBox fillXValue\n";
dbg<<"x = "<<x0<<" + i * "<<dx<<", izero = "<<izero<<std::endl;
dbg<<"y = "<<y0<<" + j * "<<dy<<", jzero = "<<jzero<<std::endl;
assert(val.stepi() == 1);
const int m = val.colsize();
const int n = val.rowsize();
typedef tmv::VIt<double,1,tmv::NonConj> It;
// It will be useful to do everything in units of dx,dy
x0 /= dx;
double wo2 = _wo2 / std::abs(dx);
y0 /= dy;
double ho2 = _ho2 / std::abs(dy);
xdbg<<"x0,y0 -> "<<x0<<','<<y0<<std::endl;
xdbg<<"width,height -> "<<wo2*2.<<','<<ho2*2.<<std::endl;
// Start by setting everything to zero
val.setZero();
// Then fill the interior with _norm:
// Fill pixels where:
// x0 + ix >= -width/2
// x0 + ix < width/2
// y0 + iy >= -width/2
// y0 + iy < width/2
int ix1 = std::max(0, int(std::ceil(-wo2 - x0)));
int ix2 = std::min(m, int(std::ceil(wo2 - x0)));
int iy1 = std::max(0, int(std::ceil(-ho2 - y0)));
int iy2 = std::min(n, int(std::ceil(ho2 - y0)));
if (ix1 < ix2 && iy1 < iy2)
val.subMatrix(ix1,ix2,iy1,iy2).setAllTo(_norm);
#if 0
// We used to implement this by making the pixels that cross the edge have a
// fractional flux value appropriate for the fraction of the box that goes through
// each pixel. However, this isn't actually correct. SBProfile objects are always
// rendered as the local surface brightness at the center of the pixel. To get
// the right flux, you need to convolve by a Pixel. So if someone renders a Box
// without convolving by a pixel, it is inconsistent to do this differently than we
// do all the other SBProfile types. However, since it was an involved calculation
// and someone might actually care to resurrect it in a different guise at some point,
// I'm leaving it here, just commented out.
// We need to make sure the pixels where the edges of the box fall only get
// a fraction of the flux.
//
// We divide up the range into 3 sections in x:
// left of the box where val = 0
// in the box where val = _norm
// right of the box where val = 0 again
//
// ... and 3 sections in y:
// below the box where val = 0
// in the box where val = _norm
// above the box where val = 0 again
//
// Furthermore, we have to calculate the correct values for the pixels on the border.
int ix_left, ix_right, iy_bottom, iy_top;
double x_left, x_right, y_bottom, y_top;
// Find the x edges:
double tmp = 0.5*width + 0.5;
ix_left = int(-tmp-x0+1);
ix_right = int(tmp-x0);
// If the box goes off the image, it's ok, but it will cause us problems
// later on if we don't change it. Just use ix_left = 0.
if (ix_left < 0) { ix_left = 0; x_left = 1.; }
// If the whole box is off the image, just zero and return.
else if (ix_left >= m) { val.setZero(); return; }
// Normal case: calculate the fractional flux in the edge
else x_left = tmp+x0+ix_left;
// Now the right side.
if (ix_right >= m) { ix_right = m-1; x_right = 1.; }
else if (ix_right < 0) { val.setZero(); return; }
else x_right = tmp-x0-ix_right;
xdbg<<"ix_left = "<<ix_left<<" with partial flux "<<x_left<<std::endl;
xdbg<<"ix_right = "<<ix_right<<" with partial flux "<<x_right<<std::endl;
// Repeat for y values
tmp = 0.5*height + 0.5;
iy_bottom = int(-tmp-y0+1);
iy_top = int(tmp-y0);
if (iy_bottom < 0) { iy_bottom = 0; y_bottom = 1.; }
else if (iy_bottom >= n) { val.setZero(); return; }
else y_bottom = tmp+y0+iy_bottom;
if (iy_top >= n) { iy_top = n-1; y_top = 1.; }
else if (iy_top < 0) { val.setZero(); return; }
else y_top = tmp-y0-iy_top;
xdbg<<"iy_bottom = "<<iy_bottom<<" with partial flux "<<y_bottom<<std::endl;
xdbg<<"iy_top = "<<iy_top<<" with partial flux "<<y_top<<std::endl;
xdbg<<"m,n = "<<m<<','<<n<<std::endl;
// Now we need to fill the matrix with the appropriate values in each section.
// Start with the zeros:
if (0 < ix_left)
val.subMatrix(0,ix_left,iy_bottom,iy_top+1).setZero();
if (ix_right+1 < m)
val.subMatrix(ix_right+1,m,iy_bottom,iy_top+1).setZero();
if (0 < iy_bottom)
val.colRange(0,iy_bottom).setZero();
if (iy_top+1 < n)
val.colRange(iy_top+1,n).setZero();
// Then the interior:
if (ix_left+1 < ix_right && iy_bottom+1 < iy_top)
val.subMatrix(ix_left+1,ix_right,iy_bottom+1,iy_top).setAllTo(_norm);
// And now the edges:
if (ix_left+1 < ix_right) {
val.col(iy_bottom,ix_left+1,ix_right).setAllTo(y_bottom * _norm);
val.col(iy_top,ix_left+1,ix_right).setAllTo(y_top * _norm);
}
if (iy_bottom+1 < iy_top) {
val.row(ix_left,iy_bottom+1,iy_top).setAllTo(x_left * _norm);
val.row(ix_right,iy_bottom+1,iy_top).setAllTo(x_right * _norm);
}
// Finally the corners
val(ix_left,iy_bottom) = x_left * y_bottom * _norm;
val(ix_right,iy_bottom) = x_right * y_bottom * _norm;
val(ix_left,iy_top) = x_left * y_top * _norm;
val(ix_right,iy_top) = x_right * y_top * _norm;
#endif
}
void LVector::mBasis(
const tmv::ConstVectorView<double>& x, const tmv::ConstVectorView<double>& y,
const tmv::ConstVectorView<double>* invsig,
tmv::MatrixView<T> psi, int order, double sigma)
{
assert (y.size()==x.size());
assert (psi.nrows()==x.size() && psi.ncols()==PQIndex::size(order));
const int N=order;
const int npts_full = x.size();
// It's faster to build the psi matrix in blocks so that more of the matrix stays in
// L1 cache. For a (typical) 256 KB L2 cache size, this corresponds to 8 columns in the
// cache, which is pretty good, since we are usually working on 4 columns at a time,
// plus either X and Y or 3 Lq vectors.
const int BLOCKING_FACTOR=4096;
const int max_npts = std::max(BLOCKING_FACTOR,npts_full);
tmv::DiagMatrix<double> Rsq_full(max_npts);
tmv::Matrix<double> A_full(max_npts,2);
tmv::Matrix<double> tmp_full(max_npts,2);
tmv::DiagMatrix<double> Lmq_full(max_npts);
tmv::DiagMatrix<double> Lmqm1_full(max_npts);
tmv::DiagMatrix<double> Lmqm2_full(max_npts);
for (int ilo=0; ilo<npts_full; ilo+=BLOCKING_FACTOR) {
const int ihi = std::min(npts_full, ilo + BLOCKING_FACTOR);
const int npts = ihi-ilo;
// Cast arguments as diagonal matrices so we can access
// vectorized element-by-element multiplication
tmv::ConstDiagMatrixView<double> X = DiagMatrixViewOf(x.subVector(ilo,ihi));
tmv::ConstDiagMatrixView<double> Y = DiagMatrixViewOf(y.subVector(ilo,ihi));
// Get the appropriate portion of our temporary matrices.
tmv::DiagMatrixView<double> Rsq = Rsq_full.subDiagMatrix(0,npts);
tmv::MatrixView<double> A = A_full.rowRange(0,npts);
tmv::MatrixView<double> tmp = tmp_full.rowRange(0,npts);
// We need rsq values twice, so store them here.
Rsq = X*X;
Rsq += Y*Y;
// This matrix will keep track of real & imag parts
// of prefactor * exp(-r^2/2) (x+iy)^m / sqrt(m!)
// Build the Gaussian factor
for (int i=0; i<npts; i++) A.ref(i,0) = std::exp(-0.5*Rsq(i));
mBasisHelper<T>::applyPrefactor(A.col(0),sigma);
A.col(1).setZero();
// Put 1/sigma factor into every point if doing a design matrix:
if (invsig) A.col(0) *= tmv::DiagMatrixViewOf(invsig->subVector(ilo,ihi));
// Assign the m=0 column first:
psi.col( PQIndex(0,0).rIndex(), ilo,ihi ) = A.col(0);
// Then ascend m's at q=0:
for (int m=1; m<=N; m++) {
int rIndex = PQIndex(m,0).rIndex();
// Multiply by (X+iY)/sqrt(m), including a factor 2 first time through
tmp = Y * A;
A = X * A;
A.col(0) += tmp.col(1);
A.col(1) -= tmp.col(0);
A *= m==1 ? 2. : 1./sqrtn(m);
psi.subMatrix(ilo,ihi,rIndex,rIndex+2) = mBasisHelper<T>::Asign(m%4) * A;
}
// Make three DiagMatrix to hold Lmq's during recurrence calculations
boost::shared_ptr<tmv::DiagMatrixView<double> > Lmq(
new tmv::DiagMatrixView<double>(Lmq_full.subDiagMatrix(0,npts)));
boost::shared_ptr<tmv::DiagMatrixView<double> > Lmqm1(
new tmv::DiagMatrixView<double>(Lmqm1_full.subDiagMatrix(0,npts)));
boost::shared_ptr<tmv::DiagMatrixView<double> > Lmqm2(
new tmv::DiagMatrixView<double>(Lmqm2_full.subDiagMatrix(0,npts)));
for (int m=0; m<=N; m++) {
PQIndex pq(m,0);
int iQ0 = pq.rIndex();
// Go to q=1:
pq.incN();
if (pq.pastOrder(N)) continue;
{ // q == 1
const int p = pq.getP();
const int q = pq.getQ();
const int iQ = pq.rIndex();
Lmqm1->setAllTo(1.); // This is Lm0.
*Lmq = Rsq - (p+q-1.);
*Lmq *= mBasisHelper<T>::Lsign(1.) / (sqrtn(p)*sqrtn(q));
if (m==0) {
psi.col(iQ,ilo,ihi) = (*Lmq) * psi.col(iQ0,ilo,ihi);
} else {
psi.subMatrix(ilo,ihi,iQ,iQ+2) = (*Lmq) * psi.subMatrix(ilo,ihi,iQ0,iQ0+2);
}
}
// do q=2,...
for (pq.incN(); !pq.pastOrder(N); pq.incN()) {
const int p = pq.getP();
const int q = pq.getQ();
const int iQ = pq.rIndex();
// cycle the Lmq vectors
// Lmqm2 <- Lmqm1
// Lmqm1 <- Lmq
// Lmq <- Lmqm2
Lmqm2.swap(Lmqm1);
Lmqm1.swap(Lmq);
double invsqrtpq = 1./sqrtn(p)/sqrtn(q);
*Lmq = Rsq - (p+q-1.);
*Lmq *= mBasisHelper<T>::Lsign(invsqrtpq) * *Lmqm1;
*Lmq -= (sqrtn(p-1)*sqrtn(q-1)*invsqrtpq) * (*Lmqm2);
if (m==0) {
psi.col(iQ,ilo,ihi) = (*Lmq) * psi.col(iQ0,ilo,ihi);
} else {
psi.subMatrix(ilo,ihi,iQ,iQ+2) = (*Lmq) * psi.subMatrix(ilo,ihi,iQ0,iQ0+2);
}
}
}
}
}