Refuctoring Functional.h

By *horizontal* operations we mean vector expressions where we have one or more vectors as an input and a vector as an output. In TNL, this kind of operations is performed by the [Expression Templates](https://en.wikipedia.org/wiki/Expression_templates). It makes algebraic operations with vectors easy to do and very efficient at the same time. In some cases, one get even more efficient code compared to [Blas](https://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms) and [cuBlas](https://developer.nvidia.com/cublas). See the following example.

\include Expressions.cpp

\includelineno Expressions.cpp

Output is:

\include Expressions.out

Vector expressions work only with `VectorView` not with `Vector`. The expression is evaluated on the same device where the vectors are allocated, this is done automatically. One cannot, however, mix vectors from different devices in one expression. Vector expression may contain any common function like `min`, `max`, `abs`, `sin`, `cos`, `exp`, `log`, `sqrt`, `pow` etc.

Vector expressions work only with `VectorView` not with `Vector`. The expression is evaluated on the same device where the vectors are allocated, this is done automatically. One cannot, however, mix vectors from different devices in one expression. Vector expression may contain any common function like the following:

| \ref TNL::min     | Minimas of input vector expressions elements.               |

| \ref TNL::max     | Maximas of input vector expressions elements.               |

| \ref TNL::abs     | Absolute values of input vector expression elements.        |

| \ref TNL::sin     | Sine of input vector expression elements.                   |

| \ref TNL::cos     | Cosine of input vector expression elements.                 |

| \ref TNL::tan     | Tangent of input vector expression elements.                |

| \ref TNL::asin    | Arc sine of input vector expression elements.               |

| \ref TNL::acos    | Arc cosine of input vector expression elements.             |

| \ref TNL::atan    | Arc tangent of input vector expression elements.            |

| \ref TNL::sinh    | Hyperbolic sine of input vector expression elements.        |

| \ref TNL::cosh    | Hyperbolic cosine of input vector expression elements.      |

| \ref TNL::tanh    | Hyperbolic tangent of input vector expression elements.     |

| \ref TNL::asinh   | Arc hyperbolic sine of input vector expression elements.    |

| \ref TNL::acosh   | Arc hyperbolic cosine of input vector expression elements.  |

| \ref TNL::atanh   | Arc hyperbolic tangent of input vector expression elements. |

| \ref TNL::exp     | Exponential function of input vector expression elements.   |

| \ref TNL::log     | Natural logarithm of input vector expression elements.      |

| \ref TNL::log10   | Decadic logarithm of input vector expression elements.      |

| \ref TNL::log2    | Binary logarithm of input vector expression elements.       |

| \ref TNL::sqrt    | Square root of input vector expression elements.            |

| \ref TNL::cbrt    | Cubic root of input vector expression elements.             |

| \ref TNL::pow     | Power of of input vector expression elements.               |

| \ref TNL::floor   | Rounds downward input vector expression elements.           |

| \ref TNL::ceil    | Rounds upward of input vector expression elements.          |

| \ref TNL::sign    | Signum of input vector expression elements.                 |

### Vertical operations

By *vertical operations* we mean (parallel) reduction based operations where we have one vector expressions as an input and one value as an output. For example computing scalar product, vector norm or finding minimum or maximum of vector elements is based on reduction. See the following example.

\include Reduction.cpp

\includelineno Reduction.cpp

Output is:

\include Reduction.out

The following table shows vertical operations that can be used on vector expressions:

| \ref TNL::min        | Minimum of vector expression elements.                                    |

| \ref TNL::argMin     | Minimum of vector expression elements with index of the smallest element. |

| \ref TNL::max        | Maximum of vector expression elements.                                    |

| \ref TNL::argMax     | Minimum of vector expression elements with index of the smallest element. |

| \ref TNL::sum        | Sum of vector expression elements.                                        |

| \ref TNL::maxNorm    | Maximal norm of vector expression elements.                               |

| \ref TNL::l1Norm     | l1 norm of vector expression elements.                                    |

| \ref TNL::l2Norm     | l2 norm of vector expression elements.                                    |

| \ref TNL::lpNorm     | lp norm of vector expression elements. `p` is given as second argument.   |

| \ref TNL::product    | Product of vector expression elements.                                    |

| \ref TNL::logicalAnd | Logical AND of vector expression elements.                                |

| \ref TNL::logicalOr  | Logical OR of vector expression elements.                                 |

| \ref TNL::binaryAnd  | Binary AND of vector expression elements.                                 |

| \ref TNL::binaryOr   | Binary OR of vector expression elements.                                  |

## Static vectors

Static vectors are derived from static arrays and so they are allocated on the stack and can be created in CUDA kernels as well. Their size is fixed as well and it is given by a template parameter. Static vector is a templated class defined in namespace `TNL::Containers` having two template parameters: