void TensorInverse(const Tensor<DataMesh>& t, Tensor<DataMesh>& inv) {
ASSERT(t.Rank() == 2, "Not a matrix");
ASSERT(t.Dim() == 3, "Not 3D");
ASSERT(t.Structure() == inv.Structure(),
"Tensors have different structures");
DataMesh det = t(0,0);
TensorDeterminant(t, det);
for(int i=0;i<det.Size();i++) {
ASSERT(det[i] != 0, "Singular matrix");
}
for(TensorIter it(t);it;++it) {
IPoint ind = t.Structure().Indices(it.Index());
inv[it] = (t((ind[1]+1)%3,(ind[0]+1)%3) * t((ind[1]+2)%3,(ind[0]+2)%3)
- t((ind[1]+1)%3,(ind[0]+2)%3) * t((ind[1]+2)%3,(ind[0]+1)%3))
/ det;
}
}
Tensor<DataMesh> findInverse(const Tensor<DataMesh>& T){
/**
Compute the inverse of the given Tensor using a minor expansion.
*/
const Mesh m(T(0).Extents());
DataMesh det = computeDet(T);
for(int k=0;k<det.Size();k++){
REQUIRE(det[k]>1e-15 || det[k]<1e-15,"determinant is too close to zero!\n");
}
//The inverse of a symmetric matrix is symmetric:
Tensor<DataMesh> inverse(3,"aa",m,0.0);
inverse(0,0) = (T(1,1)*T(2,2)-T(1,2)*T(2,1))/det;
inverse(0,1) = -(T(1,0)*T(2,2)-T(1,2)*T(2,0))/det;
inverse(0,2) = (T(1,0)*T(2,1)-T(1,1)*T(2,0))/det;
inverse(1,1) = (T(0,0)*T(2,2)-T(0,2)*T(2,0))/det;
inverse(1,2) = -(T(0,0)*T(2,1)-T(0,1)*T(2,0))/det;
inverse(2,2) = (T(0,0)*T(1,1)-T(0,1)*T(1,0))/det;
return inverse;
}
