Stan Math Library  2.20.0
reverse mode automatic differentiation
matrix_exp_2x2.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_FUN_MATRIX_EXP_2X2_HPP
2 #define STAN_MATH_PRIM_MAT_FUN_MATRIX_EXP_2X2_HPP
3 
5 
6 namespace stan {
7 namespace math {
8 
18 template <typename Mtype>
19 Mtype matrix_exp_2x2(const Mtype& A) {
20  using T = typename Mtype::Scalar;
21  T a = A(0, 0), b = A(0, 1), c = A(1, 0), d = A(1, 1), delta;
22  delta = sqrt(square(a - d) + 4 * b * c);
23 
24  Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> B(2, 2);
25  T half_delta = 0.5 * delta;
26  T cosh_half_delta = cosh(half_delta);
27  T sinh_half_delta = sinh(half_delta);
28  T exp_half_a_plus_d = exp(0.5 * (a + d));
29  T Two_exp_sinh = 2 * exp_half_a_plus_d * sinh_half_delta;
30  T delta_cosh = delta * cosh_half_delta;
31  T ad_sinh_half_delta = (a - d) * sinh_half_delta;
32 
33  B(0, 0) = exp_half_a_plus_d * (delta_cosh + ad_sinh_half_delta);
34  B(0, 1) = b * Two_exp_sinh;
35  B(1, 0) = c * Two_exp_sinh;
36  B(1, 1) = exp_half_a_plus_d * (delta_cosh - ad_sinh_half_delta);
37 
38  return B / delta;
39 }
40 } // namespace math
41 } // namespace stan
42 #endif
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:13
fvar< T > cosh(const fvar< T > &x)
Definition: cosh.hpp:12
Mtype matrix_exp_2x2(const Mtype &A)
Return the matrix exponential of a 2x2 matrix.
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:12
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
fvar< T > sinh(const fvar< T > &x)
Definition: sinh.hpp:11

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