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Documentation for special functions of tensors added #170

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31 changes: 31 additions & 0 deletions doc/ublas/tensor/special_functions.adoc
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== Special Functions


=== [#Special Functions]#Special Functions used in tensor with their description#

==== Description

* The following free tensor functions are implemented in link:https://github.com/boostorg/ublas/blob/master/include/boost/numeric/ublas/tensor/functions.hpp[functions.hpp]
* Internally they call generic functions, defined in link:https://github.com/boostorg/ublas/blob/master/include/boost/numeric/ublas/tensor/multiplication.hpp[multiplication.hpp]
and link:https://github.com/boostorg/ublas/blob/master/include/boost/numeric/ublas/tensor/algorithms.hpp[algorithms.hpp],that are implemented in terms of pointers, strides and offsets.
* Note that the functions are evaluated immediately and no expression object is
generated and that you can combine entrywise and compare operations as well as computed assignments with these free functions.

==== Special functions and their examples

[cols=",,",]
|===
| Operations | Operators | Example
| Tensor Transposition | `trans()` |`auto Z = trans(X,{4,3,2})`
|k-mode Tensor-Times-Vector | `prod()` |`auto Z = prod(X,v,2);`
|k-mode Tensor-Times-Matrix | `prod()` |`auto Z = prod(X,A,2);`
|Tensor-Times-Tensor | `prod()` |`auto Z = prod(X,Y,{1,3});`, `auto Z =prod(X,Y,\{1,3},\{4,2});`
| Inner Product | `inner_prod()` |`auto a = inner_prod(X,Y);`
| Outer Product | `outer_prod()` |`auto Z = outer_prod(X,Y);`
| Frobenius Norm | `norm()` |`auto a = norm(X);`
|Extract Real Values | `real()` |`auto Y = real(X);`
| Extract Imaginary Values | `imag()` |`auto Y = imag(X);`
| Compute Complex Conjugate | `conj()` |`auto Y = conj(X);`
|===
Examples for the usage of special functions are given in the example file
link:https://github.com/boostorg/ublas/blob/master/examples/tensor/prod_expressions.cpp[prod_expressions.cpp]