// l labels the position the vector index goes in.
// After that, indices are cyclic.
Tensor outerProduct(const DoubleVector &V, const DoubleMatrix & M, int l) {
Tensor temp;
int i, j, k;
for (i=1; i<=3; i++)
for (j=1; j<=3; j++)
for (k=1; k<=3; k++) {
switch(l) {
case 1: temp(i, j, k) = V.display(i) * M.display(j, k); break;
case 2: temp(i, j, k) = V.display(j) * M.display(k, i); break;
case 3: temp(i, j, k) = V.display(k) * M.display(i, j); break;
default:
ostringstream ii;
ii << "Trying to outer product " << l << "th element of tensor";
throw ii.str();
break;
}
}
return temp;
}
// T^kij=M^kl T^lij
Tensor Tensor::raise(const DoubleMatrix & M) const {
Tensor temp;
int i,k,j,l;
for(k=1; k<=3; k++)
for(i=1; i<=3; i++)
for(j=1; j<=3; j++)
for(l=1; l<=3; l++)
temp(k, i, j) += M.display(k, l) * this -> display(l, i, j);
return temp;
}
// T^kij = M_il T^klj
Tensor operator*(const DoubleMatrix &M, const Tensor &T) {
if (M.displayRows() !=3 || M.displayCols() != 3) {
ostringstream ii;
ii << "DoubleMatrix " << M << " * Tensor" << T << "of wrong size\n";
throw ii.str();
}
Tensor temp;
int i,j,k,l;
for(k=1; k<=3; k++)
for(i=1; i<=3; i++)
for(j=1; j<=3; j++)
for(l=1; l<=3; l++)
temp(k, i, j) += M.display(i, l) * T.display(k, l, j);
return temp;
}
// Does T^ijk = T^ljk M_li
Tensor Tensor::product(const DoubleMatrix & M) const {
if (M.displayRows() != 3 || M.displayCols() !=3) {
ostringstream ii;
ii << "Tensor " << *this << " * matrix" << M << "of wrong size.\n";
throw ii.str();
}
Tensor T;
int i,j,k,l;
for (i=1; i<=3; i++)
for (j=1; j<=3; j++)
for (k=1; k<=3; k++)
for (l=1; l<=3; l++)
T(i, j, k) = T(i, j, k) + display(l, j, k) * M.display(l, i);
return T;
}
