std::tanh(std::valarray)

Defined in header `<valarray>`
template< class T > valarray<T> tanh( const valarray<T>& va );

For each element in va computes hyperbolic tangent of the value of the element.

Parameters

value array to apply the operation to

Return value

Value array containing hyperbolic tangent of the values in va.

Notes

Unqualified function (tanh) is used to perform the computation. If such function is not available, std::tanh is used due to argument-dependent lookup.

The function can be implemented with the return type different from std::valarray. In this case, the replacement type has the following properties:

All const member functions of std::valarray are provided.
std::valarray, std::slice_array, std::gslice_array, std::mask_array and std::indirect_array can be constructed from the replacement type.
For every function taking a conststd::valarray<T>& except begin() and end()(since C++11), identical functions taking the replacement types shall be added;
For every function taking two conststd::valarray<T>& arguments, identical functions taking every combination of conststd::valarray<T>& and replacement types shall be added.
The return type does not add more than two levels of template nesting over the most deeply-nested argument type.

Possible implementation

template<class T>
valarray<T> tanh(const valarray<T>& va)
{
    valarray<T> other = va;
    for (T& i : other)
        i = tanh(i);

    return other; // proxy object may be returned
}

Example

#include <cmath>
#include <iostream>
#include <valarray>

auto show = [](char const* title, const std::valarray<double>& va)
{
    std::cout << title << " :";
    for (auto x : va)
        std::cout << "  " << std::fixed << x;
    std::cout << '\n';
};

int main()
{
    const std::valarray<double> x = {.0, .1, .2, .3};
    const std::valarray<double> sinh = std::sinh(x);
    const std::valarray<double> cosh = std::cosh(x);
    const std::valarray<double> tanh = std::tanh(x);
    const std::valarray<double> tanh_by_def = sinh / cosh;
    const std::valarray<double> tanh_2x = std::tanh(2.0 * x);
    const std::valarray<double> tanh_2x_by_def = 
        (2.0 * tanh) / (1.0 + std::pow(tanh, 2.0));

    show("x              ", x);
    show("tanh(x)        ", tanh);
    show("tanh(x) (def)  ", tanh_by_def);
    show("tanh(2*x)      ", tanh_2x);
    show("tanh(2*x) (def)", tanh_2x_by_def);
}

Output:

x               :  0.000000  0.100000  0.200000  0.300000
tanh(x)         :  0.000000  0.099668  0.197375  0.291313
tanh(x) (def)   :  0.000000  0.099668  0.197375  0.291313
tanh(2*x)       :  0.000000  0.197375  0.379949  0.537050
tanh(2*x) (def) :  0.000000  0.197375  0.379949  0.537050