void TabulatorTet<Scalar,ArrayScalar,0>::tabulate( ArrayScalar &outputValues ,
const int deg ,
const ArrayScalar &z )
{
const int np = z.dimension( 0 );
int idxcur;
// each point needs to be transformed from Pavel's element
// z(i,0) --> (2.0 * z(i,0) - 1.0)
// z(i,1) --> (2.0 * z(i,1) - 1.0)
// z(i,2) --> (2.0 * z(i,2) - 1.0)
Teuchos::Array<Scalar> f1(np),f2(np),f3(np),f4(np),f5(np);
for (int i=0;i<np;i++) {
f1[i] = 0.5 * ( 2.0 + 2.0*(2.0*z(i,0)-1.0) + (2.0*z(i,1)-1.0) + (2.0*z(i,2)-1.0) );
Scalar foo = 0.5 * ( (2.0*z(i,1)-1.0) + (2.0*z(i,2)-1.0) );
f2[i] = foo * foo;
f3[i] = 0.5 * ( 1.0 + 2.0 * (2.0*z(i,1)-1.0) + (2.0*z(i,2)-1.0) );
f4[i] = 0.5 * ( 1.0 - (2.0*z(i,2)-1.0) );
f5[i] = f4[i] * f4[i];
}
// constant term
idxcur = TabulatorTet<Scalar,ArrayScalar,0>::idx(0,0,0);
for (int i=0;i<np;i++) {
outputValues(idxcur,i) = 1.0 + z(i,0) - z(i,0) + z(i,1) - z(i,1) + z(i,2) - z(i,2);
}
if (deg > 0) {
// D^{1,0,0}
idxcur = TabulatorTet<Scalar,ArrayScalar,0>::idx(1,0,0);
for (int i=0;i<np;i++) {
outputValues(idxcur,i) = f1[i];
}
// p recurrence
for (int p=1;p<deg;p++) {
Scalar a1 = (2.0 * p + 1.0) / ( p + 1.0);
Scalar a2 = p / ( p + 1.0 );
int idxp = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,0,0);
int idxpp1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p+1,0,0);
int idxpm1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p-1,0,0);
for (int i=0;i<np;i++) {
outputValues(idxpp1,i) = a1 * f1[i] * outputValues(idxp,i) - a2 * f2[i] * outputValues(idxpm1,i);
}
}
// q = 1
for (int p=0;p<deg;p++) {
int idx0 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,0,0);
int idx1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,1,0);
for (int i=0;i<np;i++) {
outputValues(idx1,i) = outputValues(idx0,i) * ( p * ( 1.0 + (2.0*z(i,1)-1.0) ) +
0.5 * ( 2.0 + 3.0 * (2.0*z(i,1)-1.0) + (2.0*z(i,2)-1.0) ) );
}
}
// q recurrence
for (int p=0;p<deg-1;p++) {
for (int q=1;q<deg-p;q++) {
Scalar aq,bq,cq;
TabulatorTet<Scalar,ArrayScalar,0>::jrc(2.0*p+1.0 ,0 ,q, aq, bq, cq);
int idxpqp1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q+1,0);
int idxpq = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,0);
int idxpqm1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q-1,0);
for (int i=0;i<np;i++) {
outputValues(idxpqp1,i) = ( aq * f3[i] + bq * f4[i] ) * outputValues(idxpq,i)
- ( cq * f5[i] ) * outputValues(idxpqm1,i);
}
}
}
// r = 1
for (int p=0;p<deg;p++) {
for (int q=0;q<deg-p;q++) {
int idxpq1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,1);
int idxpq0 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,0);
for (int i=0;i<np;i++) {
outputValues(idxpq1,i) = outputValues(idxpq0,i) * ( 1.0 + p + q + ( 2.0 + q +
p ) * (2.0*z(i,2)-1.0) );
}
}
}
// general r recurrence
for (int p=0;p<deg-1;p++) {
for (int q=0;q<deg-p-1;q++) {
for (int r=1;r<deg-p-q;r++) {
Scalar ar,br,cr;
int idxpqrp1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,r+1);
int idxpqr = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,r);
int idxpqrm1 = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,r-1);
jrc(2.0*p+2.0*q+2.0, 0.0, r, ar, br, cr);
for (int i=0;i<np;i++) {
outputValues(idxpqrp1,i) = (ar * (2.0*z(i,2)-1.0) + br) * outputValues( idxpqr , i ) - cr * outputValues(idxpqrm1,i);
}
}
}
}
}
// normalize
for (int p=0;p<=deg;p++) {
for (int q=0;q<=deg-p;q++) {
for (int r=0;r<=deg-p-q;r++) {
int idxcur = TabulatorTet<Scalar,ArrayScalar,0>::idx(p,q,r);
Scalar scal = sqrt( (p+0.5)*(p+q+1.0)*(p+q+r+1.5) );
for (int i=0;i<np;i++) {
outputValues(idxcur,i) *= scal;
}
}
}
}
return;
}
static void
jmpc(int op, ulong *dest)
{
ldbigc((ulong)dest, Rpic);
jrc(op, Rpic);
}
