C++ Tensor::Dim方法代码示例

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));
		}
	}
}