Expr SpectralPreprocessor::takeDeriv(const Expr& f, const MultiIndex& mi)
{
TEUCHOS_TEST_FOR_EXCEPT(mi.order() > 1);
const SpectralExpr* se
= dynamic_cast<const SpectralExpr*>(f.ptr().get());
Expr d = new Derivative(mi.firstOrderDirection());
int n = se->getSpectralBasis().nterms();
if (se)
{
Array<Expr> c(n);
for (int i=0; i<n; i++)
{
c[i] = d*se->getCoeff(i);
}
return new SpectralExpr(se->getSpectralBasis(), c);
}
else
{
return d*f;
}
}
void EdgeLocalizedBasis::evalOnTriangle(const Point& pt,
const MultiIndex& deriv,
Array<double>& result) const
{
ADReal x = ADReal(pt[0], 0, 2);
ADReal y = ADReal(pt[1], 1, 2);
ADReal one(1.0, 2);
ADReal zero(0.0, 2);
Array<ADReal> tmp;
SUNDANCE_OUT(this->verb() > 3, "x=" << x.value() << " y="
<< y.value());
result.resize(3);
tmp.resize(3);
bool onEdge2 = std::fabs(pt[1]) < 1.0e-14;
bool onEdge0 = std::fabs(1.0-pt[0]-pt[1]) < 1.0e-14;
bool onEdge1 = std::fabs(pt[0]) < 1.0e-14;
TEUCHOS_TEST_FOR_EXCEPTION(!(onEdge0 || onEdge1 || onEdge2),
std::runtime_error,
"EdgeLocalizedBasis should not be evaluated at points not on edges");
TEUCHOS_TEST_FOR_EXCEPTION((onEdge0 && onEdge1) || (onEdge1 && onEdge2)
|| (onEdge2 && onEdge0), std::runtime_error,
"Ambiguous edge in EdgeLocalizedBasis::evalOnTriangle()");
if (onEdge0)
{
tmp[0] = one;
tmp[1] = zero;
tmp[2] = zero;
}
if (onEdge1)
{
tmp[0] = zero;
tmp[1] = one;
tmp[2] = zero;
}
if (onEdge2)
{
tmp[0] = zero;
tmp[1] = zero;
tmp[2] = one;
}
for (int i=0; i<tmp.length(); i++)
{
SUNDANCE_OUT(this->verb() > 3,
"tmp[" << i << "]=" << tmp[i].value()
<< " grad=" << tmp[i].gradient());
if (deriv.order()==0) result[i] = tmp[i].value();
else
result[i] = tmp[i].gradient()[deriv.firstOrderDirection()];
}
}
void CubicHermite::evalOnTriangle(const Point& pt,
const MultiIndex& deriv,
Array<double>& result) const
{
result.resize(10);
ADReal x = ADReal(pt[0], 0, 2);
ADReal y = ADReal(pt[1], 1, 2);
ADReal one(1.0, 2);
Array<ADReal> tmp(10);
SUNDANCE_OUT(this->verb() > 3, "x=" << x.value() << " y="
<< y.value());
tmp[0] = 1 - 3*x*x + 2 * x*x*x - 13*x*y + 13*x*x*y - 3*y*y + 13 *x*y*y + 2 *y*y*y;
tmp[1] = x - 2 *x*x + x*x*x - 3*x*y + 3*x*x*y + 2*x*y*y;
tmp[2] = y - 3 *x *y + 2* x*x* y - 2* y*y + 3* x*y*y + y*y*y;
tmp[3] = 3 * x*x - 2* x*x*x - 7* x* y + 7* x*x *y + 7* x*y*y;
tmp[4] = -x*x + x*x*x + 2*x *y - 2* x*x* y - 2* x* y*y;
tmp[5] = -x* y + 2* x*x* y + x* y*y;
tmp[6] = -7* x* y + 7* x*x*y + 3* y*y + 7* x* y*y - 2* y*y*y;
tmp[7] = -x *y + x*x* y + 2* x* y*y;
tmp[8] = 2 *x *y - 2* x*x* y - y*y - 2* x* y*y + y*y*y;
tmp[9] = 27* x *y - 27* x*x* y - 27* x* y*y;
for (int i=0; i<tmp.length(); i++)
{
if (deriv.order()==0) result[i] = tmp[i].value();
else
result[i] = tmp[i].gradient()[deriv.firstOrderDirection()];
}
}
void Bernstein::evalOnTet(const Point& pt,
const MultiIndex& deriv,
Array<double>& result) const
{
ADReal x = ADReal(pt[0], 0, 3);
ADReal y = ADReal(pt[1], 1, 3);
ADReal z = ADReal(pt[2], 2, 3);
ADReal one(1.0, 3);
Array<ADReal> tmp(result.length());
if(order_==0)
{
tmp.resize(1);
result.resize(1);
tmp[0] = one;
}
else
{
}
for (int i=0; i<tmp.length(); i++)
{
if (deriv.order()==0) result[i] = tmp[i].value();
else
result[i] = tmp[i].gradient()[deriv.firstOrderDirection()];
}
}
Set<MultipleDeriv> Xx(const MultiIndex& x)
{
Set<MultipleDeriv> rtn;
TEUCHOS_TEST_FOR_EXCEPTION(x.order() < 0 || x.order() > 1, std::logic_error,
"invalid multiindex " << x << " in this context");
MultipleDeriv xmd = makeMultiDeriv(coordDeriv(x.firstOrderDirection()));
rtn.put(xmd);
return rtn;
}
void EdgeLocalizedBasis::evalOnLine(const Point& pt,
const MultiIndex& deriv,
Array<double>& result) const
{
ADReal one(1.0, 1);
result.resize(1);
Array<ADReal> tmp(result.length());
tmp[0] = one;
for (int i=0; i<tmp.length(); i++)
{
if (deriv.order()==0) result[i] = tmp[i].value();
else result[i] = tmp[i].gradient()[deriv.firstOrderDirection()];
}
}
double TestEvalMediator::evalDummyBasis(int m, const MultiIndex& mi) const
{
TEUCHOS_TEST_FOR_EXCEPTION(mi.order() > 1, std::runtime_error,
"TestEvalMediator::evalDummyBasis found multiindex "
"order > 1. The bad multiindex was " << mi.toString());
ADReal result = fields_[m].basis().evaluate(ADField::evalPoint());
SUNDANCE_MSG3(verb(), "basis.value() " << result.value());
SUNDANCE_MSG3(verb(), "basis.gradient() " << result.gradient());
if (mi.order()==0)
{
return result.value();
}
else
{
return result.gradient()[mi.firstOrderDirection()];
}
}
void Legendre::evalOnQuad(const Point& pt,
const MultiIndex& deriv,
Array<double>& result) const
{
result.resize( 4 + 4*nrDOF_edge_ + nrDOF_face_);
ADReal x = ADReal(pt[0], 0, 2);
ADReal y = ADReal(pt[1], 1, 2);
ADReal one(1.0, 2);
Array<ADReal> refAllx(7);
Array<ADReal> refAlly(7);
refAllx[0] = 1-x;
refAllx[1] = x;
refAllx[2] = 2.44948974278318 * ( (2*x-1)*(2*x-1) - 1 ) / 4;
refAllx[3] = 3.16227766016838 * ( (2*x-1)*(2*x-1) - 1 ) * (2*x-1) / 4;
refAllx[4] = 3.74165738677394 * ( 5*(2*x-1)*(2*x-1)*(2*x-1)*(2*x-1) - 6*(2*x-1)*(2*x-1) + 1) / 16;
refAllx[5] = 4.24264068711929 * (2*x-1) * (7*(2*x-1)*(2*x-1)*(2*x-1)*(2*x-1) - 10*(2*x-1)*(2*x-1) + 3) / 16;
refAllx[6] = 4.69041575982343 * (21*(2*x-1)*(2*x-1)*(2*x-1)*(2*x-1)*(2*x-1) -
35*(2*x-1)*(2*x-1)*(2*x-1)*(2*x-1) + 15*(2*x-1)*(2*x-1) - 1) / 32;
refAlly[0] = 1-y;
refAlly[1] = y;
refAlly[2] = 2.44948974278318 * ( (2*y-1)*(2*y-1) - 1 ) / 4;
refAlly[3] = 3.16227766016838 * ( (2*y-1)*(2*y-1) - 1 ) * (2*y-1) / 4;
refAlly[4] = 3.74165738677394 * ( 5*(2*y-1)*(2*y-1)*(2*y-1)*(2*y-1) - 6*(2*y-1)*(2*y-1) + 1) / 16;
refAlly[5] = 4.24264068711929 * (2*y-1) * (7*(2*y-1)*(2*y-1)*(2*y-1)*(2*y-1) - 10*(2*y-1)*(2*y-1) + 3) / 16;
refAlly[6] = 4.69041575982343 * (21*(2*y-1)*(2*y-1)*(2*y-1)*(2*y-1)*(2*y-1) -
35*(2*y-1)*(2*y-1)*(2*y-1)*(2*y-1) + 15*(2*y-1)*(2*y-1) - 1) / 32;
SUNDANCE_OUT(this->verb() > 3, "x=" << x.value() << " y="
<< y.value());
int sideIndex[4][2] = { {0,0} , {1,0} , {0,1} , {1,1}};
int edgeIndex[4] = { 0 , 1 , 1 , 0};
int edgeMultI[4] = { 0 , 0 , 1 , 1};
int offs = 0;
Array<ADReal> tmp(4 + 4*nrDOF_edge_ + nrDOF_face_);
// loop over vertexes
for (int i=0; i < 4 ; i++, offs++){
tmp[offs] = refAllx[sideIndex[i][0]] * refAlly[sideIndex[i][1]];
}
// loop over edges
for (int i=0; i < 4 ; i++){
// loop over each DOF on the edge
if (edgeIndex[i] == 0){
for (int j = 0 ; j < nrDOF_edge_ ; j++ , offs++){
tmp[offs] = refAllx[2+j] * refAlly[edgeMultI[i]];
}
}
else
{
for (int j = 0 ; j < nrDOF_edge_ ; j++ , offs++){
tmp[offs] = refAllx[edgeMultI[i]] * refAlly[2+j];
}
}
}
// loop over all internal DOFs
if ( nrDOF_face_ > 0 ){
// loop for each hierarchical layer
for (int hierarch = 0 ; hierarch < order_ - 3 ; hierarch++)
{
//SUNDANCE_OUT( true , "Legendre::evalOnQuad hierarch:" << hierarch );
// for each layer add the basis function
for (int i=0 ; i < hierarch+1 ; i++ , offs++)
{
//SUNDANCE_OUT( true , "Legendre::evalOnQuad offs:" << offs << " 2+i:" << 2+i << " , 2+(hierarch-1-i):" << 2+(hierarch-i));
tmp[offs] = refAllx[2+i] * refAlly[2+(hierarch-i)];
}
}
}
// compute the results
for (int i=0; i<result.length(); i++)
{
if (deriv.order()==0) result[i] = tmp[i].value();
else
result[i] = tmp[i].gradient()[deriv.firstOrderDirection()];
}
//SUNDANCE_OUT( true , "Legendre::evalOnQuad result.length():" << result.length() );
}
void Bernstein::evalOnTriangle(const Point& pt,
const MultiIndex& deriv,
Array<double>& result) const
{
ADReal x = ADReal(pt[0], 0, 2);
ADReal y = ADReal(pt[1], 1, 2);
ADReal one(1.0, 2);
Array<ADReal> tmp;
SUNDANCE_OUT(this->verb() > 3, "x=" << x.value() << " y="
<< y.value());
if(order_==0) {
result.resize(1);
tmp.resize(1);
tmp[0] = one;
}
else {
int N = (order()+1)*(order()+2)/2;
result.resize(N);
tmp.resize(N);
// these are the barycentric coordinates
ADReal b1 = 1.0 - x - y;
ADReal b2 = x;
ADReal b3 = y;
// will hold \binom{n}{\alpha_1}
int bfcur = 0;
for (int alpha1=order();alpha1>=0;alpha1--)
{
for (int alpha2 = order()-alpha1;alpha2>=0;alpha2--)
{
int alpha3 = order() - alpha1 - alpha2;
tmp[bfcur] = one;
for (int i=0;i<alpha1;i++)
{
tmp[bfcur] *= b1;
}
for (int i=0;i<alpha2;i++)
{
tmp[bfcur] *= b2;
}
for (int i=0;i<alpha3;i++)
{
tmp[bfcur] *= b3;
}
for (int i=2;i<=order();i++)
{
tmp[bfcur] *= (double) i;
}
for (int i=2;i<=alpha1;i++)
{
tmp[bfcur] /= (double) i;
}
for (int i=2;i<=alpha2;i++)
{
tmp[bfcur] /= (double) i;
}
for (int i=2;i<=alpha3;i++)
{
tmp[bfcur] /= (double) i;
}
bfcur++;
}
}
}
for (int i=0; i<tmp.length(); i++)
{
if (deriv.order()==0) result[i] = tmp[i].value();
else
result[i] = tmp[i].gradient()[deriv.firstOrderDirection()];
}
}
DiffOp::DiffOp(const MultiIndex& op,
const RCP<ScalarExpr>& arg)
: UnaryExpr(arg), mi_(op), myCoordDeriv_(coordDeriv(op.firstOrderDirection())), requiredFunctions_(),
ignoreFuncTerms_(false)
{}