void Tensor::Slice(Tensor& result_tensor, int fixed_mode, int fixed_index)
{
vector<int> result_dims;
vector<int> free_modes;
vector<int> fixed_mode_vec = VectorPlus::CreateSingleton(fixed_mode);
vector<int> fixed_index_vec = VectorPlus::CreateSingleton(fixed_index);
VectorPlus::SetDiff(free_modes, *all_modes, fixed_mode_vec);
VectorPlus::Subset(result_dims, *dims, free_modes);
result_tensor.Initialize(result_dims);
if (result_tensor.NumElements() == 1)
{
assert(fixed_mode == 1);
result_tensor.Set(0, this->At(fixed_index));
return;
}
FastIndexer indexer(result_dims);
int i = 0;
while (indexer.HasNext())
// for (int i = 0; i < result_tensor.NumElements(); ++i)
{
vector<int>& indices = indexer.GetNext();
// vector<int> indices;
vector<int> total_indices;
// result_tensor.ComputeIndexArray(indices, i);
MergeIndices(total_indices, free_modes, fixed_mode_vec, indices, fixed_index_vec);
result_tensor.Set(i++, this->At(total_indices));
}
}
void Tensor::Divide(Tensor& result_tensor, Tensor& t1, double val)
{
result_tensor.Initialize(t1.Dims());
for (int i = 0; i < t1.NumElements(); ++i)
{
result_tensor.Set(i, t1.At(i) / val);
}
}
// add two tensors, store result in result_tensor which is assumed
// to be uninitialized
void Tensor::Add(Tensor& result_tensor, Tensor& t1, Tensor& t2)
{
assert(t1.NumElements() == t2.NumElements());
result_tensor.Initialize(t1.Dims());
for (int i = 0; i < result_tensor.NumElements(); ++i)
{
result_tensor.Set(i, t1.At(i) + t2.At(i));
}
}
void Tensor::Slice(Tensor& result_tensor, vector<int>& fixed_modes, vector<int>& fixed_indices)
{
vector<int> free_modes;
vector<int> free_dims;
VectorPlus::SetDiff(free_modes, *all_modes, fixed_modes);
VectorPlus::Subset(free_dims, *dims, free_modes);
result_tensor.Initialize(free_dims);
int i = 0;
FastIndexer indexer(free_dims);
while (indexer.HasNext())
// for (int i = 0; i < result_tensor.NumElements(); ++i)
{
// vector<int> result_indices;
// result_tensor.ComputeIndexArray(result_indices, i);
vector<int>& result_indices = indexer.GetNext();
vector<int> orig_indices;
MergeIndices(orig_indices, free_modes, fixed_modes, result_indices, fixed_indices);
result_tensor.Set(i++, this->At(orig_indices));
}
}
void Tensor::Rearrange(Tensor& result_tensor, Tensor& orig_tensor, vector<int>& old_to_new_modes)
{
vector<int> new_dims;
VectorPlus::Rearrange(new_dims, orig_tensor.Dims(), old_to_new_modes);
result_tensor.Initialize(new_dims);
int i = 0;
FastIndexer indexer(orig_tensor.Dims());
while (indexer.HasNext())
//for (int i = 0; i < orig_tensor.NumElements(); ++i)
{
vector<int>& orig_indices = indexer.GetNext();
// vector<int> orig_indices;
// orig_tensor.ComputeIndexArray(orig_indices, i);
vector<int> new_indices;
VectorPlus::Rearrange(new_indices, orig_indices, old_to_new_modes);
result_tensor.Set(new_indices, orig_tensor.At(i++));
}
}
void Tensor::Select(Tensor& result_tensor, vector<int>& fixed_modes, vector<int>& fixed_indices)
{
result_tensor.Initialize(*dims);
int i = 0;
FastIndexer indexer(*dims);
while (indexer.HasNext())
// for (int i = 0; i < result_tensor.NumElements(); ++i)
{
vector<int>& i_indices = indexer.GetNext();
// vector<int> i_indices;
// result_tensor.ComputeIndexArray(i_indices, i);
vector<int> fixed_i_indices;
VectorPlus::Subset(fixed_i_indices, i_indices, fixed_modes);
if (VectorPlus::Equals(fixed_i_indices, fixed_indices))
result_tensor.Set(i, this->At(i));
else
result_tensor.Set(i, 0);
i++;
}
}
bool Tensor::Inverse(Tensor& Umat, Tensor& result_tensor, vector<int>& mult_modes, int nonzerovals)
{
int num_sing_vals = (int)pow((double)nonzerovals, (double)mult_modes.size());
vector<int> free_modes;
vector<int> mult_dims;
vector<int> free_dims;
vector<int> mult_offsets;
vector<int> free_offsets;
VectorPlus::SetDiff(free_modes, *all_modes, mult_modes);
VectorPlus::Subset(mult_dims, *dims, mult_modes);
VectorPlus::CSubset(free_dims, *dims, mult_modes);
ComputeOffsets(mult_offsets, mult_dims);
ComputeOffsets(free_offsets, free_dims);
vector<int> usmalldims(free_modes.size(), nonzerovals);
vector<int> udims;
vector<int> usmall_offsets;
ComputeOffsets(usmall_offsets, usmalldims);
VectorPlus::Concat(udims, free_dims, usmalldims);
Umat.Initialize(udims);
vector<int> result_dims;
VectorPlus::Concat(result_dims, free_dims, usmalldims);
result_tensor.Initialize(result_dims);
/* int numMultElements = VectorPlus::Product(mult_dims);
int numFreeElements = VectorPlus::Product(free_dims);
assert(numMultElements == numFreeElements);
Eigen::MatrixXd matricized_tensor(numFreeElements,numMultElements);
cout << "copy start 1\n";
for (int i = 0; i < numFreeElements; ++i)
{
vector<int> free_indices;
ComputeIndexArray(free_indices, free_offsets, i);
for (int j = 0; j < numMultElements; ++j)
{
vector<int> mult_indices;
ComputeIndexArray(mult_indices, mult_offsets, j);
vector<int> total_indices;
VectorPlus::Concat(total_indices, free_indices, mult_indices);
matricized_tensor(i,j) = this->At(total_indices);
}
}
cout << "copy end 1\n";
// MatrixXd matricized_inverse = matricized_tensor.inverse();
// cout << matricized_inverse;
// cout << "\n";
//compute pseudoinverse
cout << "svd start 1\n";
Eigen::JacobiSVD<Eigen::MatrixXd> svd(matricized_tensor, Eigen::ComputeFullU);
Eigen::MatrixXd U = svd.matrixU();
cout << "svd end 1\n";
Eigen::MatrixXd thinU = U.leftCols(num_sing_vals);
/* MatrixXd reduced_matrix = thinU.transpose() * matricized_tensor;
JacobiSVD<MatrixXd> svd2(reduced_matrix, ComputeFullU | ComputeFullV);
U = svd2.matrixU();
MatrixXd Uleft = U.leftCols(num_sing_vals);
MatrixXd V = svd2.matrixV();
MatrixXd Vleft = V.leftCols(num_sing_vals);
VectorXd s_vals = svd2.singularValues();
MatrixXd Sigma(num_sing_vals, num_sing_vals);
for (int i = 0; i < num_sing_vals; ++i)
{
for (int j = 0; j < num_sing_vals; ++j)
{
Sigma(i,j) = 0;
}
}
for (int s = 0; s < num_sing_vals; ++s)
{
cout << s_vals(s);
cout << "\n";
if (abs(s_vals(s)) < .00000000001)
assert(0);
Sigma(s,s) = 1.0 / s_vals(s);
}
MatrixXd pinverse_temp = Vleft * Sigma;
MatrixXd matricized_inverse = pinverse_temp * Uleft.transpose();
*/
// rearrange into tensor
/* vector<int> result_dims;
VectorPlus::Concat(result_dims, free_dims, usmalldims);
result_tensor.Initialize(result_dims);
/* for (int i = 0; i < matricized_inverse.rows(); ++i)
{
vector<int> left_indices;
ComputeIndexArray(left_indices, free_offsets, i);
for (int j = 0; j < matricized_inverse.cols(); ++j)
{
vector<int> right_indices;
ComputeIndexArray(right_indices, usmall_offsets, j);
vector<int> total_indices;
VectorPlus::Concat(total_indices, left_indices, right_indices);
result_tensor.Set(total_indices, matricized_inverse(i, j));
}
} */
/* VectorPlus::Concat(udims, free_dims, usmalldims);
Umat.Initialize(udims);
vector<int> semi_dims;
semi_dims.push_back(thinU.rows());
semi_dims.push_back(thinU.cols());
cout << "copy start 2 \n";
for (int i = 0; i < thinU.rows(); ++i)
{
vector<int> left_indices;
ComputeIndexArray(left_indices, free_offsets, i);
for (int j = 0; j < thinU.cols(); ++j)
{
vector<int> right_indices;
ComputeIndexArray(right_indices, usmall_offsets, j);
vector<int> indices;
VectorPlus::Concat(indices, left_indices, right_indices);
// Umat.Set(indices, rand_matrix.At(i,j));
Umat.Set(indices, thinU(i,j));
if (thinU.rows() == thinU.cols())
{
if (VectorPlus::Equals(left_indices, right_indices))
{
Umat.Set(indices, 1);
}
else
{
Umat.Set(indices, 0);
}
}
}
}
cout << "copy end 2 \n"; */
return true;
}
// 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);
}
}
bool Tensor::ComputeJointSVD(Tensor& Umat, vector<Tensor*>& extra_tensor_list, vector<int>& mult_modes, int nonzerovals)
{
int num_sing_vals = (int)pow((double)nonzerovals, (double)mult_modes.size());
vector<int> free_modes;
vector<int> mult_dims;
vector<int> free_dims;
vector<int> mult_offsets;
vector<int> free_offsets;
Tensor& temp_tensor = *(extra_tensor_list.at(0));
VectorPlus::SetDiff(free_modes, temp_tensor.Modes(), mult_modes);
VectorPlus::Subset(mult_dims, temp_tensor.Dims(), mult_modes);
VectorPlus::CSubset(free_dims, temp_tensor.Dims(), mult_modes);
ComputeOffsets(mult_offsets, mult_dims);
ComputeOffsets(free_offsets, free_dims);
vector<int> usmalldims(free_modes.size(), nonzerovals);
vector<int> udims;
vector<int> usmall_offsets;
ComputeOffsets(usmall_offsets, usmalldims);
int numMultElements = VectorPlus::Product(mult_dims);
int numFreeElements = VectorPlus::Product(free_dims);
assert(numMultElements == numFreeElements);
Eigen::MatrixXd matricized_tensor(numFreeElements,extra_tensor_list.size() * numMultElements);
//cout << "copy start 1\n";
for (int z = 0; z < extra_tensor_list.size(); ++z)
{
int z_offset = z * numMultElements;
FastIndexer i_indexer(free_dims);
for (int i = 0; i < numFreeElements; ++i)
{
vector<int>& free_indices = i_indexer.GetNext();
// ComputeIndexArray(free_indices, free_offsets, i);
FastIndexer j_indexer(mult_dims);
for (int j = 0; j < numMultElements; ++j)
{
vector<int>& mult_indices = j_indexer.GetNext();
// ComputeIndexArray(mult_indices, mult_offsets, j);
vector<int> total_indices;
VectorPlus::Concat(total_indices, free_indices, mult_indices);
matricized_tensor(i,z_offset + j) = extra_tensor_list.at(z)->At(total_indices);
}
}
}
// cout << "copy end 1\n";
// MatrixXd matricized_inverse = matricized_tensor.inverse();
// cout << matricized_inverse;
// cout << "\n";
//compute pseudoinverse
//cout << "svd start 1\n";
Eigen::JacobiSVD<Eigen::MatrixXd> svd(matricized_tensor, Eigen::ComputeFullU);
Eigen::MatrixXd U = svd.matrixU();
// cout << "svd end 1\n";
Eigen::MatrixXd thinU = U.leftCols(num_sing_vals);
VectorPlus::Concat(udims, free_dims, usmalldims);
Umat.Initialize(udims);
vector<int> semi_dims;
semi_dims.push_back(thinU.rows());
semi_dims.push_back(thinU.cols());
// cout << "copy start 2 \n";
FastIndexer i_indexer(free_dims);
for (int i = 0; i < thinU.rows(); ++i)
{
vector<int>& left_indices = i_indexer.GetNext();
// ComputeIndexArray(left_indices, free_offsets, i);
FastIndexer j_indexer(usmalldims);
for (int j = 0; j < thinU.cols(); ++j)
{
vector<int>& right_indices = j_indexer.GetNext();
// ComputeIndexArray(right_indices, usmall_offsets, j);
vector<int> indices;
VectorPlus::Concat(indices, left_indices, right_indices);
// Umat.Set(indices, rand_matrix.At(i,j));
Umat.Set(indices, thinU(i,j));
if (thinU.rows() == thinU.cols())
{
if (VectorPlus::Equals(left_indices, right_indices))
{
Umat.Set(indices, 1);
}
else
{
Umat.Set(indices, 0);
}
}
}
}
// cout << "copy end 2 \n";
return true;
}
