Class tensor (o2scl)

O2scl : Class List

template<class data_t = double, class vec_t = std::vector<data_t>, class vec_size_t = std::vector<size_t>>
class o2scl::tensor

Tensor class with arbitrary dimensions.

The elements of a tensor are typically specified as a list of size_t numbers with length equal to the tensor rank. For a rank-4 tensor named t, the element t[1][2][0][3] can be obtained with something similar to

size_t ix[4]={1,2,0,3};
double x=t.get(ix);

Empty tensors have zero rank.

The type vec_t can be any vector type with operator[], size() and resize() methods. The type vec_size_t can be any integer-like vector type with operator[], size() and resize() methods.

For I/O with tensors, see o2scl_hdf::hdf_file::setd_ten() and o2scl_hdf::hdf_file::getd_ten() . See also the discussion in the sections tensor_subsect and vec_io_cont_subsect of the user’s guide.

The storage pattern is a generalization of row-major order. In the case of a 4-rank tensor, the location of a generic element is

\[ \left( \left( i_0 s_1 + i_1 \right) s_2 + i_2 \right) s_3 + i_3 \, . \]
In this case the distance between two elements \((i_0,i_1, i_2,i_3)\) and \( (i_0+1,i_1,i_2,i_3) \) is \( s_1 s_2 s_3 \), the distance between two elements \((i_0,i_1,i_2, i_3)\) and \( (i_0,i_1+1,i_2,i_3) \) is \( s_2 s_3 \), and the elements \((i_0,i_1,i_2,i_3)\) and \( (i_0,i_1,i_2,i_3+1) \) are adjacent.

Idea for Future:

Create an operator[] for tensor and not just tensor1?

Note

Slices of tensors are subsets obtained from fixing the index of several dimensions, while letting other dimensions vary. For a slice with one dimension not fixed, see vector_slice(). The o2scl::tensor::vector_slice() function should clearly work for uBlas vectors, and seems to work with std::vector objects also, but latter use has not been fully tested.

Idea for Future:

Could implement arithmetic operators + and - and some different products.

Idea for Future:

Implement copies to and from vector and matrices

Idea for Future:

Implement tensor contractions, i.e. tensor = tensor * tensor

Idea for Future:

Could be interesting to write an iterator for this class.

Method to check for valid object

void is_valid() const

Check that the o2scl::tensor object is valid.

Copy constructors

tensor(const tensor<data_t, vec_t, vec_size_t> &t)

Copy using operator()

tensor<data_t, vec_t, vec_size_t> &operator=(const tensor<data_t, vec_t, vec_size_t> &t)

Copy using operator=()

Clear method

void clear()

Clear the tensor of all data and free allocated memory.

Set functions

template<class size_vec_t>
void set(const size_vec_t &index, data_t val)

Set the element indexed by index to value val.

void set_all(data_t x)

Set all elements in a tensor to some fixed value.

void swap_data(vec_t &dat)

Swap the data vector.

Get functions

typedef boost::numeric::ublas::vector_slice<boost::numeric::ublas::vector<data_t>> ubvector_slice
typedef boost::numeric::ublas::slice slice
template<class size_vec_t>
data_t &get(const size_vec_t &index)

Get the element indexed by index.

template<class size_vec_t>
data_t const &get(const size_vec_t &index) const

Get a const reference to the element indexed by index.

Slice function

template<class size_vec_t>
ubvector_slice vector_slice(size_t ix, const size_vec_t &index)

Fix all but one index to create a vector.

This fixes all of the indices to the values given in index except for the index number ix, and returns the corresponding vector, whose length is equal to the size of the tensor in that index. The value index[ix] is ignored.

For example, for a rank 3 tensor allocated with

tensor t;
size_t dim[3]={3,4,5};
t.resize(3,dim);
the following code
size_t index[3]={1,0,3};
ubvector_view v=t.vector_slice(1,index);
Gives a vector v of length 4 which refers to the values t(1,0,3), t(1,1,3), t(1,2,3), and t(1,3,3).

Resize method

template<class size_vec_t>
void resize(size_t rank, const size_vec_t &dim)

Resize the tensor to rank rank with sizes given in dim.

The parameter dim must be a vector of sizes with a length equal to rank. This resize method is always destructive.

If the user requests any of the sizes to be zero, this function will call the error handler.

Size functions

size_t get_rank() const

Return the rank of the tensor.

size_t get_size(size_t i) const

Returns the size of the ith index.

const vec_size_t &get_size_arr() const

Return the full vector of sizes.

const vec_t &get_data() const

Return the full data vector.

size_t total_size() const

Returns the size of the tensor (the product of the sizes over every index)

Index manipulation

template<class size_vec_t>
size_t pack_indices(const size_vec_t &index)

Pack the indices into a single vector index.

template<class size_vec_t>
void unpack_index(size_t ix, size_vec_t &index)

Unpack the single vector index into indices.

Minimum, maximum, and sum

data_t min_value()

Compute the minimum value in the tensor.

void min_index(vec_size_t &index)

Compute the index of the minimum value in the tensor.

void min(vec_size_t &index, data_t &val)

Compute the index of the minimum value in the tensor and return the minimum.

data_t max_value()

Compute the maximum value in the tensor.

void max_index(vec_size_t &index)

Compute the index of the maximum value in the tensor.

void max(vec_size_t &index, data_t &val)

Compute the index and value of the maximum value in the tensor and return the maximum.

void minmax_value(data_t &min, data_t &max)

Compute the minimum and maximum values in the tensor.

void minmax_index(vec_size_t &index_min, vec_size_t &index_max)

Compute the indices of the minimum and maximum values in the tensor.

void minmax(vec_size_t &index, size_t &index_min, data_t &min, size_t &index_max, data_t &max)

Compute the indices and values of the maximum and minimum in the tensor.

double total_sum() const

Return the sum over every element in the tensor.

Slicing and converting to table3d objects

void convert_table3d_sum(size_t ix_x, size_t ix_y, table3d &tab, std::string x_name = "x", std::string y_name = "y", std::string slice_name = "z")

Convert to a o2scl::table3d object by summing over all but two indices.

tensor<data_t> rearrange_and_copy(std::vector<index_spec> spec, int verbose = 0, bool err_on_fail = true)

Rearrange, sum and copy current tensor to a new tensor.

Idea for Future:

Return a scalar if possible as a rank 1 tensor with 1 element.

Public Functions

tensor()

Create an empty tensor with zero rank.

template<class size_vec_t>
tensor(size_t rank, const size_vec_t &dim)

Create a tensor of rank rank with sizes given in dim.

The parameter dim must be a pointer to a vector of sizes with length rank. If the user requests any of the sizes to be zero, this constructor will call the error handler, create an empty tensor, and will allocate no memory.

~tensor()

Protected Attributes

vec_t data

The data.

vec_size_t size

A rank-sized vector of the sizes of each dimension.

size_t rk

Rank.