1 #ifndef STAN_MATH_REV_FUN_ATAN2_HPP
2 #define STAN_MATH_REV_FUN_ATAN2_HPP
3
4 #include <stan/math/rev/meta.hpp>
5 #include <stan/math/rev/core.hpp>
6 #include <cmath>
7
8 namespace stan {
9 namespace math {
10
11 /**
12 * Return the principal value of the arc tangent, in radians, of
13 * the first variable divided by the second (cmath).
14 *
15 * The partial derivatives are defined by
16 *
17 * \f$ \frac{\partial}{\partial x} \arctan \frac{x}{y} = \frac{y}{x^2 + y^2}\f$,
18 * and
19 *
20 * \f$ \frac{\partial}{\partial y} \arctan \frac{x}{y} = \frac{-x}{x^2 +
21 * y^2}\f$.
22 *
23 * @param a Numerator variable.
24 * @param b Denominator variable.
25 * @return The arc tangent of the fraction, in radians.
26 */
atan2(const var & a,const var & b)27 inline var atan2(const var& a, const var& b) {
28 return make_callback_var(
29 std::atan2(a.val(), b.val()), [a, b](const auto& vi) mutable {
30 double a_sq_plus_b_sq = (a.val() * a.val()) + (b.val() * b.val());
31 a.adj() += vi.adj_ * b.val() / a_sq_plus_b_sq;
32 b.adj() -= vi.adj_ * a.val() / a_sq_plus_b_sq;
33 });
34 }
35
36 /**
37 * Return the principal value of the arc tangent, in radians, of
38 * the first variable divided by the second scalar (cmath).
39 *
40 * The derivative with respect to the variable is
41 *
42 * \f$ \frac{d}{d x} \arctan \frac{x}{c} = \frac{c}{x^2 + c^2}\f$.
43 *
44 * @param a Numerator variable.
45 * @param b Denominator scalar.
46 * @return The arc tangent of the fraction, in radians.
47 */
atan2(const var & a,double b)48 inline var atan2(const var& a, double b) {
49 return make_callback_var(
50 std::atan2(a.val(), b), [a, b](const auto& vi) mutable {
51 double a_sq_plus_b_sq = (a.val() * a.val()) + (b * b);
52 a.adj() += vi.adj_ * b / a_sq_plus_b_sq;
53 });
54 }
55
56 /**
57 * Return the principal value of the arc tangent, in radians, of
58 * the first scalar divided by the second variable (cmath).
59 *
60 * The derivative with respect to the variable is
61 *
62 * \f$ \frac{\partial}{\partial y} \arctan \frac{c}{y} = \frac{-c}{c^2 +
63 y^2}\f$.
64 *
65 *
66 \f[
67 \mbox{atan2}(x, y) =
68 \begin{cases}
69 \arctan\left(\frac{x}{y}\right) & \mbox{if } -\infty\leq x \leq \infty,
70 -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or
71 } y = \textrm{NaN} \end{cases} \f]
72
73 \f[
74 \frac{\partial\, \mbox{atan2}(x, y)}{\partial x} =
75 \begin{cases}
76 \frac{y}{x^2+y^2} & \mbox{if } -\infty\leq x\leq \infty, -\infty\leq y \leq
77 \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN}
78 \end{cases}
79 \f]
80
81 \f[
82 \frac{\partial\, \mbox{atan2}(x, y)}{\partial y} =
83 \begin{cases}
84 -\frac{x}{x^2+y^2} & \mbox{if } -\infty\leq x\leq \infty, -\infty\leq y
85 \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y =
86 \textrm{NaN} \end{cases} \f]
87 *
88 * @param a Numerator scalar.
89 * @param b Denominator variable.
90 * @return The arc tangent of the fraction, in radians.
91 */
atan2(double a,const var & b)92 inline var atan2(double a, const var& b) {
93 return make_callback_var(
94 std::atan2(a, b.val()), [a, b](const auto& vi) mutable {
95 double a_sq_plus_b_sq = (a * a) + (b.val() * b.val());
96 b.adj() -= vi.adj_ * a / a_sq_plus_b_sq;
97 });
98 }
99
100 } // namespace math
101 } // namespace stan
102 #endif
103