/usr/include/trilinos/Intrepid_OrthogonalBasesDef.hpp is in libtrilinos-dev 10.4.0.dfsg-1ubuntu2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 | namespace Intrepid {
template<class Scalar>
void OrthogonalBases::jrc(const Scalar &alpha , const Scalar &beta ,
const int &n ,
Scalar &an , Scalar &bn, Scalar &cn )
{
an = (2.0 * n + 1.0 + alpha + beta) * ( 2.0 * n + 2.0 + alpha + beta )
/ ( 2.0 * ( n + 1 ) * ( n + 1 + alpha + beta ) );
bn = (alpha*alpha-beta*beta)*(2.0*n+1.0+alpha+beta)
/ ( 2.0*(n+1.0)*(2.0*n+alpha+beta)*(n+1.0+alpha+beta) );
cn = (n+alpha)*(n+beta)*(2.0*n+2.0+alpha+beta)
/ ( (n+1.0)*(n+1.0+alpha+beta)*(2.0*n+alpha+beta) );
return;
}
template<class Scalar, class ScalarArray1, class ScalarArray2>
void OrthogonalBases::tabulateTriangle( const ScalarArray1& z ,
const int n ,
ScalarArray2 & poly_val )
{
const int np = z.dimension( 0 );
// 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)
// set up constant term
int idx_cur = OrthogonalBases::idxtri(0,0);
int idx_curp1,idx_curm1;
// set D^{0,0} = 1.0
for (int i=0;i<np;i++) {
poly_val(idx_cur,i) = 1.0;
}
Teuchos::Array<Scalar> f1(np),f2(np),f3(np);
for (int i=0;i<np;i++) {
f1[i] = 0.5 * (1.0+2.0*(2.0*z(i,0)-1.0)+(2.0*z(i,1)-1.0));
f2[i] = 0.5 * (1.0-(2.0*z(i,1)-1.0));
f3[i] = f2[i] * f2[i];
}
// set D^{1,0} = f1
idx_cur = OrthogonalBases::idxtri(1,0);
for (int i=0;i<np;i++) {
poly_val(idx_cur,i) = f1[i];
}
// recurrence in p
for (int p=1;p<n;p++) {
idx_cur = OrthogonalBases::idxtri(p,0);
idx_curp1 = OrthogonalBases::idxtri(p+1,0);
idx_curm1 = OrthogonalBases::idxtri(p-1,0);
Scalar a = (2.0*p+1.0)/(1.0+p);
Scalar b = p / (p+1.0);
for (int i=0;i<np;i++) {
poly_val(idx_curp1,i) = a * f1[i] * poly_val(idx_cur,i)
- b * f3[i] * poly_val(idx_curm1,i);
}
}
// D^{p,1}
for (int p=0;p<n;p++) {
int idxp0 = OrthogonalBases::idxtri(p,0);
int idxp1 = OrthogonalBases::idxtri(p,1);
for (int i=0;i<np;i++) {
poly_val(idxp1,i) = poly_val(idxp0,i)
*0.5*(1.0+2.0*p+(3.0+2.0*p)*(2.0*z(i,1)-1.0));
}
}
// recurrence in q
for (int p=0;p<n-1;p++) {
for (int q=1;q<n-p;q++) {
int idxpqp1=OrthogonalBases::idxtri(p,q+1);
int idxpq=OrthogonalBases::idxtri(p,q);
int idxpqm1=OrthogonalBases::idxtri(p,q-1);
Scalar a,b,c;
jrc((Scalar)(2*p+1),(Scalar)0,q,a,b,c);
for (int i=0;i<np;i++) {
poly_val(idxpqp1,i)
= (a*(2.0*z(i,1)-1.0)+b)*poly_val(idxpq,i)
- c*poly_val(idxpqm1,i);
}
}
}
return;
}
template<class Scalar, class ScalarArray1, class ScalarArray2>
void OrthogonalBases::tabulateTetrahedron(const ScalarArray1 &z ,
const int n ,
ScalarArray2 &poly_val )
{
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) );
f2[i] = pow( 0.5 * ( (2.0*z(i,1)-1.0) + (2.0*z(i,2)-1.0) ) , 2 );
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 = idxtet(0,0,0);
for (int i=0;i<np;i++) {
poly_val(idxcur,i) = 1.0;
}
// D^{1,0,0}
idxcur = idxtet(1,0,0);
for (int i=0;i<np;i++) {
poly_val(idxcur,i) = f1[i];
}
// p recurrence
for (int p=1;p<n;p++) {
Scalar a1 = (2.0 * p + 1.0) / ( p + 1.0);
Scalar a2 = p / ( p + 1.0 );
int idxp = idxtet(p,0,0);
int idxpp1 = idxtet(p+1,0,0);
int idxpm1 = idxtet(p-1,0,0);
//cout << idxpm1 << " " << idxp << " " << idxpp1 << endl;
for (int i=0;i<np;i++) {
poly_val(idxpp1,i) = a1 * f1[i] * poly_val(idxp,i) - a2 * f2[i] * poly_val(idxpm1,i);
}
}
// q = 1
for (int p=0;p<n;p++) {
int idx0 = idxtet(p,0,0);
int idx1 = idxtet(p,1,0);
for (int i=0;i<np;i++) {
poly_val(idx1,i) = poly_val(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<n-1;p++) {
for (int q=1;q<n-p;q++) {
Scalar aq,bq,cq;
jrc((Scalar)(2.0*p+1.0),(Scalar)(0),q,aq,bq,cq);
int idxpqp1 = idxtet(p,q+1,0);
int idxpq = idxtet(p,q,0);
int idxpqm1 = idxtet(p,q-1,0);
for (int i=0;i<np;i++) {
poly_val(idxpqp1,i) = ( aq * f3[i] + bq * f4[i] ) * poly_val(idxpq,i)
- ( cq * f5[i] ) * poly_val(idxpqm1,i);
}
}
}
// r = 1
for (int p=0;p<n;p++) {
for (int q=0;q<n-p;q++) {
int idxpq1 = idxtet(p,q,1);
int idxpq0 = idxtet(p,q,0);
for (int i=0;i<np;i++) {
poly_val(idxpq1,i) = poly_val(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<n-1;p++) {
for (int q=0;q<n-p-1;q++) {
for (int r=1;r<n-p-q;r++) {
Scalar ar,br,cr;
int idxpqrp1 = idxtet(p,q,r+1);
int idxpqr = idxtet(p,q,r);
int idxpqrm1 = idxtet(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++) {
poly_val(idxpqrp1,i) = (ar * (2.0*z(i,2)-1.0) + br) * poly_val( idxpqr , i ) - cr * poly_val(idxpqrm1,i);
}
}
}
}
return;
}
} // namespace Intrepid;
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