Line data    Source code

       1            1 : // Distributed under the MIT License.
       2              : // See LICENSE.txt for details.
       3              : 
       4              : /// \file
       5              : /// Declares functions for solving quadratic equations
       6              : 
       7              : #pragma once
       8              : 
       9              : #include <array>
      10              : #include <optional>
      11              : 
      12              : /*!
      13              :  * \ingroup NumericalAlgorithmsGroup
      14              :  * \brief Returns the positive root of a quadratic equation \f$ax^2 +
      15              :  * bx + c = 0\f$
      16              :  * \returns The positive root of a quadratic equation.
      17              :  * \requires That there are two real roots, of which only one is positive.
      18              :  */
      19            1 : double positive_root(double a, double b, double c);
      20              : 
      21              : /*!
      22              :  * \ingroup NumericalAlgorithmsGroup
      23              :  * \brief Returns the smallest root of a quadratic equation \f$ax^2 +
      24              :  * bx + c = 0\f$ that is greater than the given value, within roundoff.
      25              :  * \returns A root of a quadratic equation.
      26              :  * \requires That there are two real roots.
      27              :  * \requires At least one root is greater than the given value, to roundoff.
      28              :  */
      29              : template <typename T>
      30            1 : T smallest_root_greater_than_value_within_roundoff(const T& a, const T& b,
      31              :                                                    const T& c, double value);
      32              : /*!
      33              :  * \ingroup NumericalAlgorithmsGroup
      34              :  * \brief Returns the largest root of a quadratic equation
      35              :  * \f$ax^2 + bx + c = 0\f$ that is between min_value and max_value,
      36              :  * within roundoff.
      37              :  * \returns A root of a quadratic equation.
      38              :  * \requires That there are two real roots.
      39              :  * \requires At least one root is between min_value and max_value, to roundoff.
      40              :  */
      41              : template <typename T>
      42            1 : T largest_root_between_values_within_roundoff(const T& a, const T& b,
      43              :                                               const T& c, double min_value,
      44              :                                               double max_value);
      45              : /*!
      46              :  * \ingroup NumericalAlgorithmsGroup
      47              :  * \brief Returns the two real roots of a quadratic equation \f$ax^2 +
      48              :  * bx + c = 0\f$ with the root closer to \f$-\infty\f$ first, or an
      49              :  * empty optional if there are no real roots.
      50              :  */
      51            1 : std::optional<std::array<double, 2>> real_roots(double a, double b, double c);