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std::atan2(std::valarray)

Defined in header <valarray>
template< class T > 
std::valarray<T> atan2( const std::valarray<T>& y, const std::valarray<T>& x );
(1)
template< class T > 
std::valarray<T> atan2( const std::valarray<T>& y,
                        const typename std::valarray<T>::value_type& vx );
(2)
template< class T > 
std::valarray<T> atan2( const typename std::valarray<T>::value_type& vy,
                        const std::valarray<T>& x );
(3)

Computes the inverse tangent of y/x using the signs of arguments to correctly determine quadrant.

1) Computes the inverse tangent of each pair of corresponding values from y and x.

The behavior is undefined if x.size() != y.size().

2) Computes the inverse tangent of vx and each value in the numeric array y.
3) Computes the inverse tangent of vy and each value in the numeric array x.

Parameters

x, y - numeric arrays to compute inverse tangent of
vy, vx - values to compute inverse tangent of

Return value

A numeric array containing the results of computation of inverse tangent.

Notes

Unqualified function (atan2) is used to perform the computation. If such function is not available, std::atan2 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:

Example

#include <algorithm>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <valarray>
 
void show(char const* title, const std::valarray<double>& va) {
    std::cout << title << " ";
    std::for_each(std::begin(va), std::end(va), [](const double x) { 
        std::cout << " " << std::right << std::setw(4) << x << "°";
    });
    std::cout << '\n';
}
 
const double pi = std::acos(-1.0); // C++20: std::numbers::pi
 
int main()
{
    auto degrees_to_radians = [](double const& x) { return (pi * x / 180); };
    auto radians_to_degrees = [](double const& x) { return (180 * x / pi); };
 
    const std::valarray<double> degrees{-90, -60, -45, -30, 0, 30, 45, 60, 90};
    const std::valarray<double> radians = degrees.apply(degrees_to_radians);
 
    const auto sin = std::sin(radians);
    const auto cos = std::cos(radians);
 
    show("(1)", std::atan2(sin, cos).apply(radians_to_degrees));
    show("(2)", std::atan2(sin/cos, 1.0).apply(radians_to_degrees));
    show("(3)", std::atan2(1.0, cos/sin).apply(radians_to_degrees));
}

Output:

(1)   -90°  -60°  -45°  -30°    0°   30°   45°   60°   90°
(2)   -90°  -60°  -45°  -30°    0°   30°   45°   60°   90°
(3)    90°  120°  135°  150°    0°   30°   45°   60°   90°

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR Applied to Behavior as published Correct behavior
LWG 3074 C++98 T is deduced from both the scalar and the valarray for (2-3), disallowing mixed-type calls only deduce T from the valarray

See also

applies the function std::asin to each element of valarray
(function template)
applies the function std::acos to each element of valarray
(function template)
applies the function std::atan to each element of valarray
(function template)
(C++11)(C++11)
arc tangent, using signs to determine quadrants
(function)
returns the phase angle
(function template)

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https://en.cppreference.com/w/cpp/numeric/valarray/atan2