bool CheckInverse(Tensor<DataMesh>& A, Tensor<DataMesh>& B){
//Make sure the tensor and inverse of the inverse are equal
for(int i=0;i<A.Dim();i++){
for(int j=0;j<B.Dim();j++){
for(int k=0;k<A(0).Size();k++){
double diff = A(i,j)[k] - B(i,j)[k];
REQUIRE(diff<1e-14 && diff>-1e-14, "Tensor and the inverse of its inverse are not equal");
}
}
}
return true;
}
bool checkInverse(Tensor<DataMesh>& A, Tensor<DataMesh>& B){
/**
Checks that a tensor and its inverse are equal to within roundoff
*/
for(int i=0;i<A.Dim();i++){
for(int j=0;j<B.Dim();j++){
for(int k=0;k<A(0).Size();k++){
double d = A(i,j)[k]-B(i,j)[k];
REQUIRE(d<1e-14 && d>-1e-14, "Tensor and it's inverse are not the same");
}
}
}
return true;
}
void ComputeItemRho::RecomputeData(const DataBoxAccess& box) const {
REQUIRE(l >= 0, "ERROR: l must be >= 0");
REQUIRE(abs(m) <= l, "ERROR: m must be between the values of -l and l");
const Tensor<DataMesh> rho_i=box.Get<Tensor<DataMesh> >(mInput);
REQUIRE(rho_i.Dim() == 3,
"ERROR: The Dimension of the Tensor<DataMesh> input must be 3");
REQUIRE(rho_i.Rank() == 0,
"ERROR: The Rank of the Tensor<DataMesh> input must be 0");
const MyVector<DataMesh>& coords=
box.Get<MyVector<DataMesh> >("GlobalCoords");
const Mesh mesh = box.Get<Mesh>("Mesh");
DataMesh theta(mesh);
DataMesh phi(mesh);
theta = acos(coords[2] / sqrt(coords[0]*coords[0] +
coords[1]*coords[1] + coords[2]*coords[2]));
phi = atan(coords[1] / coords[0]);
Tensor<DataMesh> SHY(SphericalHarmonicYTDM(l, m, theta, phi, mesh));
mResult.assign(0, "", rho_i()*SHY());
}
void TensorDeterminant(const Tensor<DataMesh>& t, DataMesh& det) {
ASSERT(t.Rank() == 2, "Not a matrix");
ASSERT(t.Dim() == 3, "Not 3D");
det
= t(0,0) * (t(1,1)*t(2,2) - t(1,2)*t(2,1))
+ t(0,1) * (t(1,2)*t(2,0) - t(1,0)*t(2,2))
+ t(0,2) * (t(1,0)*t(2,1) - t(1,1)*t(2,0));
}
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;
}
}
int ModeDim(int mode) { return prob_tensor->Dim(mode); }
int VarDim(int var) { return prob_tensor->Dim((*vars_to_modes)[var]); }
// multiply two tensors, store result in result_tensor which is assumed to be uninitialized
void Tensor::Multiply(Tensor& result_tensor, Tensor& t1, Tensor& t2, vector<int>& mult_modes1, vector<int>& mult_modes2)
{
assert(mult_modes1.size() == mult_modes2.size());
if (t1.Order() == mult_modes1.size() && t2.Order() == mult_modes2.size())
{
double val = InnerProduct(t1, t2);
vector<int> fake_dims;
result_tensor.Initialize(fake_dims);
result_tensor.Set(0, val);
return;
}
int numMultElements = 1;
vector<int> mult_dims(mult_modes1.size(), 0);
for (int i = 0; i < mult_modes1.size(); ++i)
{
assert(t1.Dim(mult_modes1[i]) == t2.Dim(mult_modes2[i]));
mult_dims[i] = t1.Dim(mult_modes1[i]);
numMultElements = numMultElements * mult_dims[i];
}
vector<int> mult_offsets;
ComputeOffsets(mult_offsets, mult_dims);
int result_order = t1.Order() + t2.Order() - mult_modes1.size() - mult_modes2.size();
if (result_order == 0)
assert(0);
vector<int> result_dims;
vector<int> free_modes1;
vector<int> free_modes2;
// find free indices from t1
for (int i = 0; i < t1.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modes1, i))
{
result_dims.push_back(t1.Dim(i));
free_modes1.push_back(i);
}
}
// find free indices from t2
for (int i = 0; i < t2.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modes2, i))
{
result_dims.push_back(t2.Dim(i));
free_modes2.push_back(i);
}
}
// initialize result_tensor
result_tensor.Initialize(result_dims);
// fill in elements from result tensor
FastIndexer result_indexer(result_dims);
for (int n = 0; n < result_tensor.NumElements(); ++n)
{
vector<int>& indices = result_indexer.GetNext();
vector<int> free_indices1;
vector<int> free_indices2;
// result_tensor.ComputeIndexArray(indices, n);
for (int i = 0; i < result_tensor.Order(); ++i)
{
if (i < free_modes1.size())
free_indices1.push_back(indices[i]);
else
free_indices2.push_back(indices[i]);
}
// sum over elementwise products of mult-mode elements
double temp_sum = 0;
FastIndexer mult_indexer(mult_dims);
for (int k = 0; k < numMultElements; ++k)
{
vector<int>& mult_indices = mult_indexer.GetNext();
// ComputeIndexArray(mult_indices, mult_offsets, k);
vector<int> indices1;
vector<int> indices2;
MergeIndices(indices1, mult_modes1, free_modes1, mult_indices, free_indices1);
MergeIndices(indices2, mult_modes2, free_modes2, mult_indices, free_indices2);
temp_sum += t1.At(indices1) * t2.At(indices2);
}
result_tensor.Set(n, temp_sum);
}
}
void Tensor::ElementwiseMultiply(Tensor& result_tensor, Tensor& t1, Tensor& t2, vector<int>& mult_modes1, vector<int>& mult_modes2)
{
assert(mult_modes1.size() == mult_modes2.size());
int numMultElements = 1;
vector<int> mult_dims(mult_modes1.size(), 0);
for (int i = 0; i < mult_modes1.size(); ++i)
{
assert(t1.Dim(mult_modes1[i]) == t2.Dim(mult_modes2[i]));
mult_dims[i] = t1.Dim(mult_modes1[i]);
numMultElements = numMultElements * mult_dims[i];
}
vector<int> mult_offsets;
ComputeOffsets(mult_offsets, mult_dims);
int result_order = t1.Order() + t2.Order() - mult_modes2.size();
if (result_order == 0)
assert(0);
vector<int> result_dims;
vector<int> free_modes1;
vector<int> free_modes2;
// find free indices from t1
for (int i = 0; i < t1.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modes1, i))
{
free_modes1.push_back(i);
}
}
// find free indices from t2
for (int i = 0; i < t2.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modes2, i))
{
free_modes2.push_back(i);
}
}
int curr_index = 0;
for (int i = 0; i < result_order; ++i)
{
if (i < t1.Order())
{
result_dims.push_back(t1.Dim(i));
}
else
{
result_dims.push_back(t2.Dim(free_modes2[curr_index++]));
}
}
// initialize result_tensor
result_tensor.Initialize(result_dims);
// fill in elements from result tensor
FastIndexer indexer(result_dims);
int n = 0;
while (indexer.HasNext())
{
vector<int>& indices = indexer.GetNext();
vector<int> indices1(t1.Order(), 0);
vector<int> free_indices2;
// result_tensor.ComputeIndexArray(indices, n);
for (int i = 0; i < result_tensor.Order(); ++i)
{
if (i < t1.Order())
indices1[i] = indices[i];
else
free_indices2.push_back(indices[i]);
}
vector<int> mult_indices;
VectorPlus::Subset(mult_indices, indices1, mult_modes1);
vector<int> indices2;
MergeIndices(indices2, mult_modes2, free_modes2, mult_indices, free_indices2);
double val = 0;
double val1 = t1.At(indices1);
if (val1 != 0)
{
val = val1 * t2.At(indices2);
}
result_tensor.Set(n++, val);
}
}
void Tensor::CreateLinearSystem(vector<double>& B_vec, Matrix& A_matrix,
Tensor& X, Tensor& A, Tensor& B,
vector<int>& mult_modesX, vector<int>& mult_modesA)
{
// fake multiply x and A together to create B, creating the linear system in the process
assert(mult_modesX.size() == mult_modesA.size());
if (X.Order() == mult_modesX.size() && A.Order() == mult_modesA.size())
{
assert(0);
}
int numMultElements = 1;
vector<int> mult_dims(mult_modesX.size(), 0);
for (int i = 0; i < mult_modesX.size(); ++i)
{
assert(X.Dim(mult_modesX[i]) == A.Dim(mult_modesA[i]));
mult_dims[i] = X.Dim(mult_modesX[i]);
numMultElements = numMultElements * mult_dims[i];
}
vector<int> mult_offsets;
ComputeOffsets(mult_offsets, mult_dims);
int result_order = X.Order() + A.Order() - mult_modesX.size() - mult_modesA.size();
if (result_order == 0)
assert(0);
vector<int> result_dims;
vector<int> free_modesX;
vector<int> free_modesA;
// find free indices from X
for (int i = 0; i < X.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modesX, i))
{
free_modesX.push_back(i);
}
}
// find free indices from A
for (int i = 0; i < A.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modesA, i))
{
free_modesA.push_back(i);
}
}
vector<int> a_mat_dims = VectorPlus::CreatePair(B.NumElements(), X.NumElements());
A_matrix.Initialize(a_mat_dims);
B_vec.reserve(B.NumElements());
// fill in elements from result tensor
FastIndexer B_indexer(B.Dims());
for (int n = 0; n < B.NumElements(); ++n)
{
B_vec.push_back(B.At(n));
vector<int>& indices = B_indexer.GetNext();
vector<int> free_indicesX;
vector<int> free_indicesA;
// B.ComputeIndexArray(indices, n);
for (int i = 0; i < B.Order(); ++i)
{
if (!VectorPlus::Contains(mult_modesX, i))
free_indicesX.push_back(indices[i]);
else
free_indicesA.push_back(indices[i]);
}
// sum over elementwise products of mult-mode elements
double temp_sum = 0;
FastIndexer mult_indexer(mult_dims);
for (int k = 0; k < numMultElements; ++k)
{
vector<int>& mult_indices = mult_indexer.GetNext();
// ComputeIndexArray(mult_indices, mult_offsets, k);
vector<int> indicesX;
vector<int> indicesA;
MergeIndices(indicesX, mult_modesX, free_modesX, mult_indices, free_indicesX);
MergeIndices(indicesA, mult_modesA, free_modesA, mult_indices, free_indicesA);
A_matrix.Set(n, X.ComputeIndex(indicesX), A.At(indicesA));
}
}
}