/**
* Converts argument to an automatic differentiation variable.
*
* Returns a stan::math::var variable with the input value.
*
* @param[in] m A Matrix with scalars
* @return A Matrix with automatic differentiation variables
*/
inline matrix_v to_var(const stan::math::matrix_d& m) {
matrix_v m_v(m.rows(), m.cols());
for (int j = 0; j < m.cols(); ++j)
for (int i = 0; i < m.rows(); ++i)
m_v(i, j) = m(i, j);
return m_v;
}
std::vector<double> finite_differences(const size_t row, const size_t col,
const stan::math::matrix_d A,
const bool calc_A_partials,
const stan::math::matrix_d B,
const bool calc_B_partials) {
const double e = 1e-8;
std::vector<double> finite_diff;
stan::math::matrix_d C_plus, C_minus;
if (calc_A_partials) {
for (size_type j = 0; j < A.cols(); j++) {
for (size_type i = 0; i < A.rows(); i++) {
stan::math::matrix_d A_plus(A), A_minus(A);
A_plus(i,j) += e;
A_plus(j,i) = A_plus(i,j);
A_minus(i,j) -= e;
A_minus(j,i) = A_minus(i,j);
stan::math::LDLT_factor<double,-1,-1> ldlt_A_plus;
stan::math::LDLT_factor<double,-1,-1> ldlt_A_minus;
ldlt_A_plus.compute(A_plus);
ldlt_A_minus.compute(A_minus);
C_plus = stan::math::mdivide_left_ldlt(ldlt_A_plus, B);
C_minus = stan::math::mdivide_left_ldlt(ldlt_A_minus, B);
finite_diff.push_back((C_plus(row,col) - C_minus(row,col)) / (2*e));
}
}
}
if (calc_B_partials) {
stan::math::LDLT_factor<double,-1,-1> ldlt_A;
ldlt_A.compute(A);
for (size_type j = 0; j < B.cols(); j++) {
for (size_type i = 0; i < B.rows(); i++) {
stan::math::matrix_d B_plus(B);
stan::math::matrix_d B_minus(B);
B_plus(i,j) += e;
B_minus(i,j) -= e;
C_plus = stan::math::mdivide_left_ldlt(ldlt_A, B_plus);
C_minus = stan::math::mdivide_left_ldlt(ldlt_A, B_minus);
finite_diff.push_back((C_plus(row,col) - C_minus(row,col)) / (2*e));
}
}
}
return finite_diff;
}
