std::sqrt(std::valarray)(3)

NAME
std::sqrt(std::valarray) - std::sqrt(std::valarray)

Synopsis
   Defined in header <valarray>
   template< class T >
   valarray<T> sqrt( const valarray<T>& va );
   For each element in va computes the square root of the value of the element.

Parameters
   va - value array to apply the operation to

Return value
   Value array containing square roots of the values in va.

Notes
   Unqualified function (sqrt) is used to perform the computation. If such function is
   not available, std::sqrt 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.
              * All functions accepting an argument of type const std::valarray&
                except begin() and end()
                (since C++11) should also accept the replacement type.
              * All functions accepting two arguments of type const std::valarray&
                should accept every combination of const std::valarray& and the
                replacement type.
              * 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> sqrt( const valarray<T>& va )
   {
       valarray<T> other = va;
       for (T &i : other) {
           i = sqrt(i);
       }
       return other; // proxy object may be returned
   }

Example
   Finds real roots of multiple quadratic equations. // Run this code
 #include <cstddef>
 #include <valarray>
 #include <iostream>
 int main()
 {
     std::valarray<double> a(1, 8);
     std::valarray<double> b{1, 2, 3, 4, 5, 6, 7, 8};
     std::valarray<double> c = -b;
     // literals must also be of type T until LWG3074 (double in this case)
     std::valarray<double> d = std::sqrt(b * b - 4.0 * a * c);
     std::valarray<double> x1 = (-b - d) / (2.0 * a);
     std::valarray<double> x2 = (-b + d) / (2.0 * a);
     std::cout << "quadratic equation: root 1: root 2:\n";
     for (std::size_t i = 0; i < a.size(); ++i) {
         std::cout << a[i] << "\u00B7x\u00B2 + " << b[i] << "\u00B7x + "
                   << c[i] << " = 0 " << std::fixed << x1[i] << " "
                   << x2[i] << std::defaultfloat << '\n';
     }
 }

Output:
 quadratic equation: root 1: root 2:
 1·x² + 1·x + -1 = 0 -1.618034 0.618034
 1·x² + 2·x + -2 = 0 -2.732051 0.732051
 1·x² + 3·x + -3 = 0 -3.791288 0.791288
 1·x² + 4·x + -4 = 0 -4.828427 0.828427
 1·x² + 5·x + -5 = 0 -5.854102 0.854102
 1·x² + 6·x + -6 = 0 -6.872983 0.872983
 1·x² + 7·x + -7 = 0 -7.887482 0.887482
 1·x² + 8·x + -8 = 0 -8.898979 0.898979

See also
                      applies the function std::pow to two valarrays or a valarray and
   pow(std::valarray) a value
                      (function template)
   sqrt computes square root (\(\small{\sqrt{x} }\)
   sqrtf √
   sqrtl x)
   (C++11) (function)
   (C++11)
   sqrt(std::complex) complex square root in the range of the right half-plane
                      (function template)