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;
}
int main(int /*argc*/, char** /*argv*/) {
//create Strahlkorper, SurfaceBasis, SurfaceBasisExt objects
int l=4;
//int m=2*l+1;
StrahlkorperMesh skm(l+1, 2*(l+1));
//print l,m
std::cout << "(l,m) should be ("<<l<<","<<l<<"); M->2M+1" << std::endl;
std::cout << "(l,m) = (" << skm.Basis().L() << "," << skm.Basis().M() << ")"<< std::endl;
SurfaceBasis sb(skm);
SurfaceBasisExt sbe(skm);
//copy surface coords into individual DataMeshes
DataMesh theta = skm.SurfaceCoords()(0);
DataMesh phi = skm.SurfaceCoords()(1);
//check theta, phi Dim
std::cout << "theta.Dim() = " << theta.Dim() << std::endl;
std::cout << "phi.Dim() = " << phi.Dim() << std::endl;
//check theta, phi extents
std::cout << "theta.Extents() = " << theta.Extents() << std::endl;
std::cout << "phi.Extents() = " << phi.Extents() << std::endl;
//initialize result, solution, and difference DataMeshes
DataMesh resultDm(theta);
DataMesh solutionDm(theta);
DataMesh differenceDm(theta);
DataMesh coefficientMeshDm(sbe.CoefficientMesh());
std::cout << "CoefficientMeshDm dimension is "
<< coefficientMeshDm.Dim() << std::endl;
//check resultDm Dim, Extents
std::cout << "resultDm.Dim() = " << resultDm.Dim() << std::endl;
std::cout << "resultDm.Extents() = " << resultDm.Extents() << std::endl;
//initialize result, solution, and difference Tensor<DataMesh>-es
Tensor<DataMesh> operandTDm(skm.SurfaceCoords());
Tensor<DataMesh> resultTDm(skm.SurfaceCoords());
Tensor<DataMesh> solutionTDm(skm.SurfaceCoords());
Tensor<DataMesh> differenceTDm(skm.SurfaceCoords());
//check resultTDm Rank, Dim
std::cout << "resultTDm.Rank() = " << resultTDm.Rank() << std::endl;
std::cout << "resultTDm.Dim() = " << resultTDm.Dim() << std::endl;
std::cout << "\n" << std::endl;
std::cout << "Test results for various functions. The printed results \n"
"show the L1Norm for the difference between the numerical \n"
"result and analytical solution. A successful test will \n"
"print out 0. \n"
<< std::endl;
//test VectorPhysToSpec function in SurfaceBasisExt
std::cout <<
"VectorPhysToSpec w/ SurfaceBasisExt, \n"
"f(theta,phi)=-sin(theta) thetaHat + sin(theta) phiHat\n"
<< std::endl;
operandTDm(0)=-sin(theta);
operandTDm(1)=sin(theta);
resultTDm(0)=0.0;
resultTDm(1)=0.0;
sbe.VectorPhysToSpec(operandTDm(0).Data(),
operandTDm(1).Data(),
1,
resultTDm(0).Data(),
resultTDm(1).Data(),
1 );
std::cout << "Result " << "\n"
<< resultTDm(0) << "\n "
<< resultTDm(1) << "\n "
<< std::endl;
//test VectorInterpAtPoint function in SurfaceBasisExt
std::cout <<
"VectorInterpAtPoint w/ SurfaceBasisExt, \n"
"f(0,0) = (0,0) \n"
<< std::endl;
MyVector<double> value1(MV::Size(2),0.0);
MyVector<double> value2 = sbe.VectorInterpAtPoint(operandTDm, value1, 0.,0.);
std::cout << "value1 " << value1 << "\n"
<< "value2 " << value2 << std::endl;
std::cout <<
"VectorInterpAtPoint w/ SurfaceBasisExt, \n"
"f(pi/2,pi/2) = (-1,1) \n"
<< std::endl;
value2 = sbe.VectorInterpAtPoint(operandTDm, value1, M_PI/2., M_PI/2.);
std::cout << "value1 " << value1 << "\n"
<< "value2 " << value2 << std::endl;
std::cout <<
"VectorInterpAtPoint w/ SurfaceBasisExt, \n"
"f(pi/4,pi/4) = (-sqrt(2)/2, sqrt(2)/2) \n"
<< std::endl;
value2 = sbe.VectorInterpAtPoint(operandTDm, value1, M_PI/4., M_PI/4.);
std::cout << "value1 " << value1 << "\n"
<< "value2 " << value2 << std::endl;
/**/
//Return success
//return u.NumberOfTestsFailed();
return EXIT_SUCCESS;
}
