| Stan Math Library 2.6.3 probability, sampling & optimization

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math.hpp File Reference
`#include <stan/math/version.hpp>`
`#include <stan/math/prim/arr/meta/get.hpp>`
`#include <stan/math/prim/arr/meta/index_type.hpp>`
`#include <stan/math/prim/arr/meta/is_vector.hpp>`
`#include <stan/math/prim/arr/meta/length.hpp>`
`#include <stan/math/prim/mat/meta/get.hpp>`
`#include <stan/math/prim/mat/meta/index_type.hpp>`
`#include <stan/math/prim/mat/meta/is_vector.hpp>`
`#include <stan/math/prim/mat/meta/is_vector_like.hpp>`
`#include <stan/math/prim/mat/meta/length.hpp>`
`#include <stan/math/prim/mat/meta/seq_view.hpp>`
`#include <stan/math/prim/mat/meta/value_type.hpp>`
`#include <stan/math/prim/scal/meta/child_type.hpp>`
`#include <stan/math/prim/scal/meta/contains_fvar.hpp>`
`#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>`
`#include <stan/math/prim/scal/meta/contains_vector.hpp>`
`#include <stan/math/prim/scal/meta/error_index.hpp>`
`#include <stan/math/prim/scal/meta/get.hpp>`
`#include <stan/math/prim/scal/meta/include_summand.hpp>`
`#include <stan/math/prim/scal/meta/index_type.hpp>`
`#include <stan/math/prim/scal/meta/is_constant.hpp>`
`#include <stan/math/prim/scal/meta/is_constant_struct.hpp>`
`#include <stan/math/prim/scal/meta/is_fvar.hpp>`
`#include <stan/math/prim/scal/meta/is_var.hpp>`
`#include <stan/math/prim/scal/meta/is_var_or_arithmetic.hpp>`
`#include <stan/math/prim/scal/meta/is_vector.hpp>`
`#include <stan/math/prim/scal/meta/is_vector_like.hpp>`
`#include <stan/math/prim/scal/meta/length.hpp>`
`#include <stan/math/prim/scal/meta/length_mvt.hpp>`
`#include <stan/math/prim/scal/meta/likely.hpp>`
`#include <stan/math/prim/scal/meta/max_size.hpp>`
`#include <stan/math/prim/scal/meta/max_size_mvt.hpp>`
`#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>`
`#include <stan/math/prim/scal/meta/partials_return_type.hpp>`
`#include <stan/math/prim/scal/meta/partials_type.hpp>`
`#include <stan/math/prim/scal/meta/return_type.hpp>`
`#include <stan/math/prim/scal/meta/scalar_type.hpp>`
`#include <stan/math/prim/scal/meta/scalar_type_pre.hpp>`
`#include <stan/math/prim/scal/meta/size_of.hpp>`
`#include <stan/math/prim/scal/meta/value_type.hpp>`
`#include <stan/math/prim/scal/meta/VectorBuilder.hpp>`
`#include <stan/math/prim/scal/meta/VectorView.hpp>`
`#include <stan/math/prim/scal/meta/VectorViewMvt.hpp>`
`#include <stan/math/rev/scal/meta/is_var.hpp>`
`#include <stan/math/rev/scal/meta/partials_type.hpp>`
`#include <stan/math/prim/arr/fun/dist.hpp>`
`#include <stan/math/prim/arr/fun/dot.hpp>`
`#include <stan/math/prim/arr/fun/dot_self.hpp>`
`#include <stan/math/prim/arr/fun/log_sum_exp.hpp>`
`#include <stan/math/prim/arr/fun/rep_array.hpp>`
`#include <stan/math/prim/arr/fun/scaled_add.hpp>`
`#include <stan/math/prim/arr/fun/sub.hpp>`
`#include <stan/math/prim/arr/fun/sum.hpp>`
`#include <stan/math/prim/arr/functor/coupled_ode_observer.hpp>`
`#include <stan/math/prim/arr/functor/coupled_ode_system.hpp>`
`#include <stan/math/prim/arr/functor/integrate_ode.hpp>`
`#include <stan/math/prim/mat/err/check_cholesky_factor.hpp>`
`#include <stan/math/prim/mat/err/check_cholesky_factor_corr.hpp>`
`#include <stan/math/prim/mat/err/check_column_index.hpp>`
`#include <stan/math/prim/mat/err/check_corr_matrix.hpp>`
`#include <stan/math/prim/mat/err/check_cov_matrix.hpp>`
`#include <stan/math/prim/mat/err/check_ldlt_factor.hpp>`
`#include <stan/math/prim/mat/err/check_lower_triangular.hpp>`
`#include <stan/math/prim/mat/err/check_matching_dims.hpp>`
`#include <stan/math/prim/mat/err/check_matching_sizes.hpp>`
`#include <stan/math/prim/mat/err/check_multiplicable.hpp>`
`#include <stan/math/prim/mat/err/check_ordered.hpp>`
`#include <stan/math/prim/mat/err/check_pos_definite.hpp>`
`#include <stan/math/prim/mat/err/check_pos_semidefinite.hpp>`
`#include <stan/math/prim/mat/err/check_positive_ordered.hpp>`
`#include <stan/math/prim/mat/err/check_range.hpp>`
`#include <stan/math/prim/mat/err/check_row_index.hpp>`
`#include <stan/math/prim/mat/err/check_simplex.hpp>`
`#include <stan/math/prim/mat/err/check_spsd_matrix.hpp>`
`#include <stan/math/prim/mat/err/check_square.hpp>`
`#include <stan/math/prim/mat/err/check_std_vector_index.hpp>`
`#include <stan/math/prim/mat/err/check_symmetric.hpp>`
`#include <stan/math/prim/mat/err/check_unit_vector.hpp>`
`#include <stan/math/prim/mat/err/check_vector.hpp>`
`#include <stan/math/prim/mat/err/constraint_tolerance.hpp>`
`#include <stan/math/prim/mat/err/validate_non_negative_index.hpp>`
`#include <stan/math/prim/mat/fun/accumulator.hpp>`
`#include <stan/math/prim/mat/fun/add.hpp>`
`#include <stan/math/prim/mat/fun/append_col.hpp>`
`#include <stan/math/prim/mat/fun/append_row.hpp>`
`#include <stan/math/prim/mat/fun/array_builder.hpp>`
`#include <stan/math/prim/mat/fun/assign.hpp>`
`#include <stan/math/prim/mat/fun/autocorrelation.hpp>`
`#include <stan/math/prim/mat/fun/autocovariance.hpp>`
`#include <stan/math/prim/mat/fun/block.hpp>`
`#include <stan/math/prim/mat/fun/cholesky_corr_constrain.hpp>`
`#include <stan/math/prim/mat/fun/cholesky_corr_free.hpp>`
`#include <stan/math/prim/mat/fun/cholesky_decompose.hpp>`
`#include <stan/math/prim/mat/fun/cholesky_factor_constrain.hpp>`
`#include <stan/math/prim/mat/fun/cholesky_factor_free.hpp>`
`#include <stan/math/prim/mat/fun/col.hpp>`
`#include <stan/math/prim/mat/fun/cols.hpp>`
`#include <stan/math/prim/mat/fun/columns_dot_product.hpp>`
`#include <stan/math/prim/mat/fun/columns_dot_self.hpp>`
`#include <stan/math/prim/mat/fun/common_type.hpp>`
`#include <stan/math/prim/mat/fun/corr_matrix_constrain.hpp>`
`#include <stan/math/prim/mat/fun/corr_matrix_free.hpp>`
`#include <stan/math/prim/mat/fun/cov_matrix_constrain.hpp>`
`#include <stan/math/prim/mat/fun/cov_matrix_constrain_lkj.hpp>`
`#include <stan/math/prim/mat/fun/cov_matrix_free.hpp>`
`#include <stan/math/prim/mat/fun/cov_matrix_free_lkj.hpp>`
`#include <stan/math/prim/mat/fun/crossprod.hpp>`
`#include <stan/math/prim/mat/fun/cumulative_sum.hpp>`
`#include <stan/math/prim/mat/fun/determinant.hpp>`
`#include <stan/math/prim/mat/fun/diag_matrix.hpp>`
`#include <stan/math/prim/mat/fun/diag_post_multiply.hpp>`
`#include <stan/math/prim/mat/fun/diag_pre_multiply.hpp>`
`#include <stan/math/prim/mat/fun/diagonal.hpp>`
`#include <stan/math/prim/mat/fun/dims.hpp>`
`#include <stan/math/prim/mat/fun/distance.hpp>`
`#include <stan/math/prim/mat/fun/divide.hpp>`
`#include <stan/math/prim/mat/fun/dot_product.hpp>`
`#include <stan/math/prim/mat/fun/dot_self.hpp>`
`#include <stan/math/prim/mat/fun/Eigen.hpp>`
`#include <stan/math/prim/mat/fun/eigenvalues_sym.hpp>`
`#include <stan/math/prim/mat/fun/eigenvectors_sym.hpp>`
`#include <stan/math/prim/mat/fun/elt_divide.hpp>`
`#include <stan/math/prim/mat/fun/elt_multiply.hpp>`
`#include <stan/math/prim/mat/fun/exp.hpp>`
`#include <stan/math/prim/mat/fun/factor_cov_matrix.hpp>`
`#include <stan/math/prim/mat/fun/factor_U.hpp>`
`#include <stan/math/prim/mat/fun/fill.hpp>`
`#include <stan/math/prim/mat/fun/get_base1.hpp>`
`#include <stan/math/prim/mat/fun/get_base1_lhs.hpp>`
`#include <stan/math/prim/mat/fun/get_lp.hpp>`
`#include <stan/math/prim/mat/fun/head.hpp>`
`#include <stan/math/prim/mat/fun/initialize.hpp>`
`#include <stan/math/prim/mat/fun/inverse.hpp>`
`#include <stan/math/prim/mat/fun/inverse_spd.hpp>`
`#include <stan/math/prim/mat/fun/LDLT_factor.hpp>`
`#include <stan/math/prim/mat/fun/log.hpp>`
`#include <stan/math/prim/mat/fun/log_determinant.hpp>`
`#include <stan/math/prim/mat/fun/log_determinant_ldlt.hpp>`
`#include <stan/math/prim/mat/fun/log_determinant_spd.hpp>`
`#include <stan/math/prim/mat/fun/log_softmax.hpp>`
`#include <stan/math/prim/mat/fun/log_sum_exp.hpp>`
`#include <stan/math/prim/mat/fun/make_nu.hpp>`
`#include <stan/math/prim/mat/fun/max.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_left.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_left_ldlt.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_left_spd.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_left_tri.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_left_tri_low.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_right.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_right_ldlt.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_right_spd.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_right_tri.hpp>`
`#include <stan/math/prim/mat/fun/mdivide_right_tri_low.hpp>`
`#include <stan/math/prim/mat/fun/mean.hpp>`
`#include <stan/math/prim/mat/fun/min.hpp>`
`#include <stan/math/prim/mat/fun/minus.hpp>`
`#include <stan/math/prim/mat/fun/multiply.hpp>`
`#include <stan/math/prim/mat/fun/multiply_lower_tri_self_transpose.hpp>`
`#include <stan/math/prim/mat/fun/num_elements.hpp>`
`#include <stan/math/prim/mat/fun/ordered_constrain.hpp>`
`#include <stan/math/prim/mat/fun/ordered_free.hpp>`
`#include <stan/math/prim/mat/fun/positive_ordered_constrain.hpp>`
`#include <stan/math/prim/mat/fun/positive_ordered_free.hpp>`
`#include <stan/math/prim/mat/fun/prod.hpp>`
`#include <stan/math/prim/mat/fun/promote_common.hpp>`
`#include <stan/math/prim/mat/fun/promote_scalar.hpp>`
`#include <stan/math/prim/mat/fun/promote_scalar_type.hpp>`
`#include <stan/math/prim/mat/fun/promoter.hpp>`
`#include <stan/math/prim/mat/fun/qr_Q.hpp>`
`#include <stan/math/prim/mat/fun/qr_R.hpp>`
`#include <stan/math/prim/mat/fun/quad_form.hpp>`
`#include <stan/math/prim/mat/fun/quad_form_diag.hpp>`
`#include <stan/math/prim/mat/fun/quad_form_sym.hpp>`
`#include <stan/math/prim/mat/fun/rank.hpp>`
`#include <stan/math/prim/mat/fun/read_corr_L.hpp>`
`#include <stan/math/prim/mat/fun/read_corr_matrix.hpp>`
`#include <stan/math/prim/mat/fun/read_cov_L.hpp>`
`#include <stan/math/prim/mat/fun/read_cov_matrix.hpp>`
`#include <stan/math/prim/mat/fun/rep_matrix.hpp>`
`#include <stan/math/prim/mat/fun/rep_row_vector.hpp>`
`#include <stan/math/prim/mat/fun/rep_vector.hpp>`
`#include <stan/math/prim/mat/fun/resize.hpp>`
`#include <stan/math/prim/mat/fun/row.hpp>`
`#include <stan/math/prim/mat/fun/rows.hpp>`
`#include <stan/math/prim/mat/fun/rows_dot_product.hpp>`
`#include <stan/math/prim/mat/fun/rows_dot_self.hpp>`
`#include <stan/math/prim/mat/fun/sd.hpp>`
`#include <stan/math/prim/mat/fun/segment.hpp>`
`#include <stan/math/prim/mat/fun/simplex_constrain.hpp>`
`#include <stan/math/prim/mat/fun/simplex_free.hpp>`
`#include <stan/math/prim/mat/fun/singular_values.hpp>`
`#include <stan/math/prim/mat/fun/size.hpp>`
`#include <stan/math/prim/mat/fun/softmax.hpp>`
`#include <stan/math/prim/mat/fun/sort.hpp>`
`#include <stan/math/prim/mat/fun/sort_indices.hpp>`
`#include <stan/math/prim/mat/fun/sort_indices_asc.hpp>`
`#include <stan/math/prim/mat/fun/sort_indices_desc.hpp>`
`#include <stan/math/prim/mat/fun/squared_distance.hpp>`
`#include <stan/math/prim/mat/fun/stan_print.hpp>`
`#include <stan/math/prim/mat/fun/sub_col.hpp>`
`#include <stan/math/prim/mat/fun/sub_row.hpp>`
`#include <stan/math/prim/mat/fun/subtract.hpp>`
`#include <stan/math/prim/mat/fun/sum.hpp>`
`#include <stan/math/prim/mat/fun/tail.hpp>`
`#include <stan/math/prim/mat/fun/tcrossprod.hpp>`
`#include <stan/math/prim/mat/fun/to_array_1d.hpp>`
`#include <stan/math/prim/mat/fun/to_array_2d.hpp>`
`#include <stan/math/prim/mat/fun/to_matrix.hpp>`
`#include <stan/math/prim/mat/fun/to_row_vector.hpp>`
`#include <stan/math/prim/mat/fun/to_vector.hpp>`
`#include <stan/math/prim/mat/fun/trace.hpp>`
`#include <stan/math/prim/mat/fun/trace_gen_inv_quad_form_ldlt.hpp>`
`#include <stan/math/prim/mat/fun/trace_gen_quad_form.hpp>`
`#include <stan/math/prim/mat/fun/trace_inv_quad_form_ldlt.hpp>`
`#include <stan/math/prim/mat/fun/trace_quad_form.hpp>`
`#include <stan/math/prim/mat/fun/transpose.hpp>`
`#include <stan/math/prim/mat/fun/typedefs.hpp>`
`#include <stan/math/prim/mat/fun/unit_vector_constrain.hpp>`
`#include <stan/math/prim/mat/fun/unit_vector_free.hpp>`
`#include <stan/math/prim/mat/fun/value_of.hpp>`
`#include <stan/math/prim/mat/fun/value_of_rec.hpp>`
`#include <stan/math/prim/mat/fun/variance.hpp>`
`#include <stan/math/prim/mat/fun/welford_covar_estimator.hpp>`
`#include <stan/math/prim/mat/fun/welford_var_estimator.hpp>`
`#include <stan/math/prim/mat/prob/categorical_log.hpp>`
`#include <stan/math/prim/mat/prob/categorical_logit_log.hpp>`
`#include <stan/math/prim/mat/prob/categorical_rng.hpp>`
`#include <stan/math/prim/mat/prob/dirichlet_log.hpp>`
`#include <stan/math/prim/mat/prob/dirichlet_rng.hpp>`
`#include <stan/math/prim/mat/prob/gaussian_dlm_obs_log.hpp>`
`#include <stan/math/prim/mat/prob/inv_wishart_log.hpp>`
`#include <stan/math/prim/mat/prob/inv_wishart_rng.hpp>`
`#include <stan/math/prim/mat/prob/lkj_corr_cholesky_log.hpp>`
`#include <stan/math/prim/mat/prob/lkj_corr_cholesky_rng.hpp>`
`#include <stan/math/prim/mat/prob/lkj_corr_log.hpp>`
`#include <stan/math/prim/mat/prob/lkj_corr_rng.hpp>`
`#include <stan/math/prim/mat/prob/lkj_cov_log.hpp>`
`#include <stan/math/prim/mat/prob/matrix_normal_prec_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_gp_cholesky_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_gp_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_normal_cholesky_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_normal_cholesky_rng.hpp>`
`#include <stan/math/prim/mat/prob/multi_normal_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_normal_prec_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_normal_rng.hpp>`
`#include <stan/math/prim/mat/prob/multi_student_t_log.hpp>`
`#include <stan/math/prim/mat/prob/multi_student_t_rng.hpp>`
`#include <stan/math/prim/mat/prob/multinomial_log.hpp>`
`#include <stan/math/prim/mat/prob/multinomial_rng.hpp>`
`#include <stan/math/prim/mat/prob/ordered_logistic_log.hpp>`
`#include <stan/math/prim/mat/prob/ordered_logistic_rng.hpp>`
`#include <stan/math/prim/mat/prob/wishart_log.hpp>`
`#include <stan/math/prim/mat/prob/wishart_rng.hpp>`
`#include <stan/math/prim/scal/err/check_bounded.hpp>`
`#include <stan/math/prim/scal/err/check_consistent_size.hpp>`
`#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>`
`#include <stan/math/prim/scal/err/check_equal.hpp>`
`#include <stan/math/prim/scal/err/check_finite.hpp>`
`#include <stan/math/prim/scal/err/check_greater.hpp>`
`#include <stan/math/prim/scal/err/check_greater_or_equal.hpp>`
`#include <stan/math/prim/scal/err/check_less.hpp>`
`#include <stan/math/prim/scal/err/check_less_or_equal.hpp>`
`#include <stan/math/prim/scal/err/check_nonnegative.hpp>`
`#include <stan/math/prim/scal/err/check_nonzero_size.hpp>`
`#include <stan/math/prim/scal/err/check_not_nan.hpp>`
`#include <stan/math/prim/scal/err/check_positive.hpp>`
`#include <stan/math/prim/scal/err/check_positive_finite.hpp>`
`#include <stan/math/prim/scal/err/check_positive_size.hpp>`
`#include <stan/math/prim/scal/err/check_size_match.hpp>`
`#include <stan/math/prim/scal/err/domain_error.hpp>`
`#include <stan/math/prim/scal/err/domain_error_vec.hpp>`
`#include <stan/math/prim/scal/err/invalid_argument.hpp>`
`#include <stan/math/prim/scal/err/invalid_argument_vec.hpp>`
`#include <stan/math/prim/scal/err/out_of_range.hpp>`
`#include <stan/math/prim/scal/fun/abs.hpp>`
`#include <stan/math/prim/scal/fun/as_bool.hpp>`
`#include <stan/math/prim/scal/fun/bessel_first_kind.hpp>`
`#include <stan/math/prim/scal/fun/bessel_second_kind.hpp>`
`#include <stan/math/prim/scal/fun/binary_log_loss.hpp>`
`#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>`
`#include <stan/math/prim/scal/fun/constants.hpp>`
`#include <stan/math/prim/scal/fun/corr_constrain.hpp>`
`#include <stan/math/prim/scal/fun/corr_free.hpp>`
`#include <stan/math/prim/scal/fun/digamma.hpp>`
`#include <stan/math/prim/scal/fun/divide.hpp>`
`#include <stan/math/prim/scal/fun/exp2.hpp>`
`#include <stan/math/prim/scal/fun/F32.hpp>`
`#include <stan/math/prim/scal/fun/falling_factorial.hpp>`
`#include <stan/math/prim/scal/fun/fdim.hpp>`
`#include <stan/math/prim/scal/fun/gamma_p.hpp>`
`#include <stan/math/prim/scal/fun/gamma_q.hpp>`
`#include <stan/math/prim/scal/fun/grad_2F1.hpp>`
`#include <stan/math/prim/scal/fun/grad_F32.hpp>`
`#include <stan/math/prim/scal/fun/grad_inc_beta.hpp>`
`#include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>`
`#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>`
`#include <stan/math/prim/scal/fun/ibeta.hpp>`
`#include <stan/math/prim/scal/fun/identity_constrain.hpp>`
`#include <stan/math/prim/scal/fun/identity_free.hpp>`
`#include <stan/math/prim/scal/fun/if_else.hpp>`
`#include <stan/math/prim/scal/fun/inc_beta.hpp>`
`#include <stan/math/prim/scal/fun/int_step.hpp>`
`#include <stan/math/prim/scal/fun/inv.hpp>`
`#include <stan/math/prim/scal/fun/inv_cloglog.hpp>`
`#include <stan/math/prim/scal/fun/inv_logit.hpp>`
`#include <stan/math/prim/scal/fun/inv_sqrt.hpp>`
`#include <stan/math/prim/scal/fun/inv_square.hpp>`
`#include <stan/math/prim/scal/fun/inverse_softmax.hpp>`
`#include <stan/math/prim/scal/fun/is_inf.hpp>`
`#include <stan/math/prim/scal/fun/is_nan.hpp>`
`#include <stan/math/prim/scal/fun/is_uninitialized.hpp>`
`#include <stan/math/prim/scal/fun/lb_constrain.hpp>`
`#include <stan/math/prim/scal/fun/lb_free.hpp>`
`#include <stan/math/prim/scal/fun/lbeta.hpp>`
`#include <stan/math/prim/scal/fun/lgamma.hpp>`
`#include <stan/math/prim/scal/fun/lmgamma.hpp>`
`#include <stan/math/prim/scal/fun/log1m.hpp>`
`#include <stan/math/prim/scal/fun/log1m_exp.hpp>`
`#include <stan/math/prim/scal/fun/log1m_inv_logit.hpp>`
`#include <stan/math/prim/scal/fun/log1p.hpp>`
`#include <stan/math/prim/scal/fun/log1p_exp.hpp>`
`#include <stan/math/prim/scal/fun/log2.hpp>`
`#include <stan/math/prim/scal/fun/log_diff_exp.hpp>`
`#include <stan/math/prim/scal/fun/log_falling_factorial.hpp>`
`#include <stan/math/prim/scal/fun/log_inv_logit.hpp>`
`#include <stan/math/prim/scal/fun/log_mix.hpp>`
`#include <stan/math/prim/scal/fun/log_rising_factorial.hpp>`
`#include <stan/math/prim/scal/fun/log_sum_exp.hpp>`
`#include <stan/math/prim/scal/fun/logical_and.hpp>`
`#include <stan/math/prim/scal/fun/logical_eq.hpp>`
`#include <stan/math/prim/scal/fun/logical_gt.hpp>`
`#include <stan/math/prim/scal/fun/logical_gte.hpp>`
`#include <stan/math/prim/scal/fun/logical_lt.hpp>`
`#include <stan/math/prim/scal/fun/logical_lte.hpp>`
`#include <stan/math/prim/scal/fun/logical_negation.hpp>`
`#include <stan/math/prim/scal/fun/logical_neq.hpp>`
`#include <stan/math/prim/scal/fun/logical_or.hpp>`
`#include <stan/math/prim/scal/fun/logit.hpp>`
`#include <stan/math/prim/scal/fun/lub_constrain.hpp>`
`#include <stan/math/prim/scal/fun/lub_free.hpp>`
`#include <stan/math/prim/scal/fun/modified_bessel_first_kind.hpp>`
`#include <stan/math/prim/scal/fun/modified_bessel_second_kind.hpp>`
`#include <stan/math/prim/scal/fun/modulus.hpp>`
`#include <stan/math/prim/scal/fun/multiply_log.hpp>`
`#include <stan/math/prim/scal/fun/owens_t.hpp>`
`#include <stan/math/prim/scal/fun/Phi.hpp>`
`#include <stan/math/prim/scal/fun/Phi_approx.hpp>`
`#include <stan/math/prim/scal/fun/positive_constrain.hpp>`
`#include <stan/math/prim/scal/fun/positive_free.hpp>`
`#include <stan/math/prim/scal/fun/primitive_value.hpp>`
`#include <stan/math/prim/scal/fun/prob_constrain.hpp>`
`#include <stan/math/prim/scal/fun/prob_free.hpp>`
`#include <stan/math/prim/scal/fun/promote_scalar.hpp>`
`#include <stan/math/prim/scal/fun/promote_scalar_type.hpp>`
`#include <stan/math/prim/scal/fun/rising_factorial.hpp>`
`#include <stan/math/prim/scal/fun/sign.hpp>`
`#include <stan/math/prim/scal/fun/square.hpp>`
`#include <stan/math/prim/scal/fun/step.hpp>`
`#include <stan/math/prim/scal/fun/trigamma.hpp>`
`#include <stan/math/prim/scal/fun/ub_constrain.hpp>`
`#include <stan/math/prim/scal/fun/ub_free.hpp>`
`#include <stan/math/prim/scal/fun/value_of.hpp>`
`#include <stan/math/prim/scal/fun/value_of_rec.hpp>`
`#include <stan/math/prim/scal/prob/bernoulli_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/bernoulli_cdf.hpp>`
`#include <stan/math/prim/scal/prob/bernoulli_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/bernoulli_log.hpp>`
`#include <stan/math/prim/scal/prob/bernoulli_logit_log.hpp>`
`#include <stan/math/prim/scal/prob/bernoulli_rng.hpp>`
`#include <stan/math/prim/scal/prob/beta_binomial_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/beta_binomial_cdf.hpp>`
`#include <stan/math/prim/scal/prob/beta_binomial_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/beta_binomial_log.hpp>`
`#include <stan/math/prim/scal/prob/beta_binomial_rng.hpp>`
`#include <stan/math/prim/scal/prob/beta_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/beta_cdf.hpp>`
`#include <stan/math/prim/scal/prob/beta_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/beta_log.hpp>`
`#include <stan/math/prim/scal/prob/beta_rng.hpp>`
`#include <stan/math/prim/scal/prob/binomial_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/binomial_cdf.hpp>`
`#include <stan/math/prim/scal/prob/binomial_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/binomial_log.hpp>`
`#include <stan/math/prim/scal/prob/binomial_logit_log.hpp>`
`#include <stan/math/prim/scal/prob/binomial_rng.hpp>`
`#include <stan/math/prim/scal/prob/cauchy_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/cauchy_cdf.hpp>`
`#include <stan/math/prim/scal/prob/cauchy_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/cauchy_log.hpp>`
`#include <stan/math/prim/scal/prob/cauchy_rng.hpp>`
`#include <stan/math/prim/scal/prob/chi_square_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/chi_square_cdf.hpp>`
`#include <stan/math/prim/scal/prob/chi_square_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/chi_square_log.hpp>`
`#include <stan/math/prim/scal/prob/chi_square_rng.hpp>`
`#include <stan/math/prim/scal/prob/double_exponential_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/double_exponential_cdf.hpp>`
`#include <stan/math/prim/scal/prob/double_exponential_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/double_exponential_log.hpp>`
`#include <stan/math/prim/scal/prob/double_exponential_rng.hpp>`
`#include <stan/math/prim/scal/prob/exp_mod_normal_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/exp_mod_normal_cdf.hpp>`
`#include <stan/math/prim/scal/prob/exp_mod_normal_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/exp_mod_normal_log.hpp>`
`#include <stan/math/prim/scal/prob/exp_mod_normal_rng.hpp>`
`#include <stan/math/prim/scal/prob/exponential_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/exponential_cdf.hpp>`
`#include <stan/math/prim/scal/prob/exponential_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/exponential_log.hpp>`
`#include <stan/math/prim/scal/prob/exponential_rng.hpp>`
`#include <stan/math/prim/scal/prob/frechet_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/frechet_cdf.hpp>`
`#include <stan/math/prim/scal/prob/frechet_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/frechet_log.hpp>`
`#include <stan/math/prim/scal/prob/frechet_rng.hpp>`
`#include <stan/math/prim/scal/prob/gamma_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/gamma_cdf.hpp>`
`#include <stan/math/prim/scal/prob/gamma_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/gamma_log.hpp>`
`#include <stan/math/prim/scal/prob/gamma_rng.hpp>`
`#include <stan/math/prim/scal/prob/gumbel_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/gumbel_cdf.hpp>`
`#include <stan/math/prim/scal/prob/gumbel_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/gumbel_log.hpp>`
`#include <stan/math/prim/scal/prob/gumbel_rng.hpp>`
`#include <stan/math/prim/scal/prob/hypergeometric_log.hpp>`
`#include <stan/math/prim/scal/prob/hypergeometric_rng.hpp>`
`#include <stan/math/prim/scal/prob/inv_chi_square_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/inv_chi_square_cdf.hpp>`
`#include <stan/math/prim/scal/prob/inv_chi_square_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/inv_chi_square_log.hpp>`
`#include <stan/math/prim/scal/prob/inv_chi_square_rng.hpp>`
`#include <stan/math/prim/scal/prob/inv_gamma_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/inv_gamma_cdf.hpp>`
`#include <stan/math/prim/scal/prob/inv_gamma_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/inv_gamma_log.hpp>`
`#include <stan/math/prim/scal/prob/inv_gamma_rng.hpp>`
`#include <stan/math/prim/scal/prob/logistic_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/logistic_cdf.hpp>`
`#include <stan/math/prim/scal/prob/logistic_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/logistic_log.hpp>`
`#include <stan/math/prim/scal/prob/logistic_rng.hpp>`
`#include <stan/math/prim/scal/prob/lognormal_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/lognormal_cdf.hpp>`
`#include <stan/math/prim/scal/prob/lognormal_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/lognormal_log.hpp>`
`#include <stan/math/prim/scal/prob/lognormal_rng.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_cdf.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_log_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_log_rng.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_2_rng.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_cdf.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_log.hpp>`
`#include <stan/math/prim/scal/prob/neg_binomial_rng.hpp>`
`#include <stan/math/prim/scal/prob/normal_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/normal_cdf.hpp>`
`#include <stan/math/prim/scal/prob/normal_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/normal_log.hpp>`
`#include <stan/math/prim/scal/prob/normal_rng.hpp>`
`#include <stan/math/prim/scal/prob/pareto_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/pareto_cdf.hpp>`
`#include <stan/math/prim/scal/prob/pareto_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/pareto_log.hpp>`
`#include <stan/math/prim/scal/prob/pareto_rng.hpp>`
`#include <stan/math/prim/scal/prob/pareto_type_2_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/pareto_type_2_cdf.hpp>`
`#include <stan/math/prim/scal/prob/pareto_type_2_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/pareto_type_2_log.hpp>`
`#include <stan/math/prim/scal/prob/pareto_type_2_rng.hpp>`
`#include <stan/math/prim/scal/prob/poisson_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/poisson_cdf.hpp>`
`#include <stan/math/prim/scal/prob/poisson_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/poisson_log.hpp>`
`#include <stan/math/prim/scal/prob/poisson_log_log.hpp>`
`#include <stan/math/prim/scal/prob/poisson_log_rng.hpp>`
`#include <stan/math/prim/scal/prob/poisson_rng.hpp>`
`#include <stan/math/prim/scal/prob/rayleigh_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/rayleigh_cdf.hpp>`
`#include <stan/math/prim/scal/prob/rayleigh_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/rayleigh_log.hpp>`
`#include <stan/math/prim/scal/prob/rayleigh_rng.hpp>`
`#include <stan/math/prim/scal/prob/scaled_inv_chi_square_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/scaled_inv_chi_square_cdf.hpp>`
`#include <stan/math/prim/scal/prob/scaled_inv_chi_square_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/scaled_inv_chi_square_log.hpp>`
`#include <stan/math/prim/scal/prob/scaled_inv_chi_square_rng.hpp>`
`#include <stan/math/prim/scal/prob/skew_normal_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/skew_normal_cdf.hpp>`
`#include <stan/math/prim/scal/prob/skew_normal_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/skew_normal_log.hpp>`
`#include <stan/math/prim/scal/prob/skew_normal_rng.hpp>`
`#include <stan/math/prim/scal/prob/student_t_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/student_t_cdf.hpp>`
`#include <stan/math/prim/scal/prob/student_t_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/student_t_log.hpp>`
`#include <stan/math/prim/scal/prob/student_t_rng.hpp>`
`#include <stan/math/prim/scal/prob/uniform_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/uniform_cdf.hpp>`
`#include <stan/math/prim/scal/prob/uniform_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/uniform_log.hpp>`
`#include <stan/math/prim/scal/prob/uniform_rng.hpp>`
`#include <stan/math/prim/scal/prob/von_mises_log.hpp>`
`#include <stan/math/prim/scal/prob/von_mises_rng.hpp>`
`#include <stan/math/prim/scal/prob/weibull_ccdf_log.hpp>`
`#include <stan/math/prim/scal/prob/weibull_cdf.hpp>`
`#include <stan/math/prim/scal/prob/weibull_cdf_log.hpp>`
`#include <stan/math/prim/scal/prob/weibull_log.hpp>`
`#include <stan/math/prim/scal/prob/weibull_rng.hpp>`
`#include <stan/math/prim/scal/prob/wiener_log.hpp>`
`#include <stan/math/rev/arr/fun/log_sum_exp.hpp>`
`#include <stan/math/rev/arr/functor/coupled_ode_system.hpp>`
`#include <stan/math/rev/core.hpp>`
`#include <stan/math/rev/mat/fun/columns_dot_product.hpp>`
`#include <stan/math/rev/mat/fun/columns_dot_self.hpp>`
`#include <stan/math/rev/mat/fun/crossprod.hpp>`
`#include <stan/math/rev/mat/fun/determinant.hpp>`
`#include <stan/math/rev/mat/fun/divide.hpp>`
`#include <stan/math/rev/mat/fun/dot_product.hpp>`
`#include <stan/math/rev/mat/fun/dot_self.hpp>`
`#include <stan/math/rev/mat/fun/Eigen_NumTraits.hpp>`
`#include <stan/math/rev/mat/fun/grad.hpp>`
`#include <stan/math/rev/mat/fun/initialize_variable.hpp>`
`#include <stan/math/rev/mat/fun/LDLT_alloc.hpp>`
`#include <stan/math/rev/mat/fun/LDLT_factor.hpp>`
`#include <stan/math/rev/mat/fun/log_determinant.hpp>`
`#include <stan/math/rev/mat/fun/log_determinant_ldlt.hpp>`
`#include <stan/math/rev/mat/fun/log_determinant_spd.hpp>`
`#include <stan/math/rev/mat/fun/log_softmax.hpp>`
`#include <stan/math/rev/mat/fun/log_sum_exp.hpp>`
`#include <stan/math/rev/mat/fun/mdivide_left.hpp>`
`#include <stan/math/rev/mat/fun/mdivide_left_ldlt.hpp>`
`#include <stan/math/rev/mat/fun/mdivide_left_spd.hpp>`
`#include <stan/math/rev/mat/fun/mdivide_left_tri.hpp>`
`#include <stan/math/rev/mat/fun/multiply.hpp>`
`#include <stan/math/rev/mat/fun/multiply_lower_tri_self_transpose.hpp>`
`#include <stan/math/rev/mat/fun/quad_form.hpp>`
`#include <stan/math/rev/mat/fun/quad_form_sym.hpp>`
`#include <stan/math/rev/mat/fun/rows_dot_product.hpp>`
`#include <stan/math/rev/mat/fun/sd.hpp>`
`#include <stan/math/rev/mat/fun/softmax.hpp>`
`#include <stan/math/rev/mat/fun/sort_asc.hpp>`
`#include <stan/math/rev/mat/fun/sort_desc.hpp>`
`#include <stan/math/rev/mat/fun/squared_distance.hpp>`
`#include <stan/math/rev/mat/fun/stan_print.hpp>`
`#include <stan/math/rev/mat/fun/sum.hpp>`
`#include <stan/math/rev/mat/fun/tcrossprod.hpp>`
`#include <stan/math/rev/mat/fun/to_var.hpp>`
`#include <stan/math/rev/mat/fun/trace_gen_inv_quad_form_ldlt.hpp>`
`#include <stan/math/rev/mat/fun/trace_gen_quad_form.hpp>`
`#include <stan/math/rev/mat/fun/trace_inv_quad_form_ldlt.hpp>`
`#include <stan/math/rev/mat/fun/trace_quad_form.hpp>`
`#include <stan/math/rev/mat/fun/typedefs.hpp>`
`#include <stan/math/rev/mat/fun/variance.hpp>`
`#include <stan/math/rev/mat/functor/gradient.hpp>`
`#include <stan/math/rev/mat/functor/jacobian.hpp>`
`#include <stan/math/rev/scal/fun/abs.hpp>`
`#include <stan/math/rev/scal/fun/acos.hpp>`
`#include <stan/math/rev/scal/fun/acosh.hpp>`
`#include <stan/math/rev/scal/fun/as_bool.hpp>`
`#include <stan/math/rev/scal/fun/asin.hpp>`
`#include <stan/math/rev/scal/fun/asinh.hpp>`
`#include <stan/math/rev/scal/fun/atan.hpp>`
`#include <stan/math/rev/scal/fun/atan2.hpp>`
`#include <stan/math/rev/scal/fun/atanh.hpp>`
`#include <stan/math/rev/scal/fun/bessel_first_kind.hpp>`
`#include <stan/math/rev/scal/fun/bessel_second_kind.hpp>`
`#include <stan/math/rev/scal/fun/binary_log_loss.hpp>`
`#include <stan/math/rev/scal/fun/boost_fpclassify.hpp>`
`#include <stan/math/rev/scal/fun/boost_isfinite.hpp>`
`#include <stan/math/rev/scal/fun/boost_isinf.hpp>`
`#include <stan/math/rev/scal/fun/boost_isnan.hpp>`
`#include <stan/math/rev/scal/fun/boost_isnormal.hpp>`
`#include <stan/math/rev/scal/fun/calculate_chain.hpp>`
`#include <stan/math/rev/scal/fun/cbrt.hpp>`
`#include <stan/math/rev/scal/fun/ceil.hpp>`
`#include <stan/math/rev/scal/fun/cos.hpp>`
`#include <stan/math/rev/scal/fun/cosh.hpp>`
`#include <stan/math/rev/scal/fun/digamma.hpp>`
`#include <stan/math/rev/scal/fun/erf.hpp>`
`#include <stan/math/rev/scal/fun/erfc.hpp>`
`#include <stan/math/rev/scal/fun/exp.hpp>`
`#include <stan/math/rev/scal/fun/exp2.hpp>`
`#include <stan/math/rev/scal/fun/expm1.hpp>`
`#include <stan/math/rev/scal/fun/fabs.hpp>`
`#include <stan/math/rev/scal/fun/falling_factorial.hpp>`
`#include <stan/math/rev/scal/fun/fdim.hpp>`
`#include <stan/math/rev/scal/fun/floor.hpp>`
`#include <stan/math/rev/scal/fun/fma.hpp>`
`#include <stan/math/rev/scal/fun/fmax.hpp>`
`#include <stan/math/rev/scal/fun/fmin.hpp>`
`#include <stan/math/rev/scal/fun/fmod.hpp>`
`#include <stan/math/rev/scal/fun/gamma_p.hpp>`
`#include <stan/math/rev/scal/fun/gamma_q.hpp>`
`#include <stan/math/rev/scal/fun/grad_inc_beta.hpp>`
`#include <stan/math/rev/scal/fun/hypot.hpp>`
`#include <stan/math/rev/scal/fun/ibeta.hpp>`
`#include <stan/math/rev/scal/fun/if_else.hpp>`
`#include <stan/math/rev/scal/fun/inc_beta.hpp>`
`#include <stan/math/rev/scal/fun/inv.hpp>`
`#include <stan/math/rev/scal/fun/inv_cloglog.hpp>`
`#include <stan/math/rev/scal/fun/inv_logit.hpp>`
`#include <stan/math/rev/scal/fun/inv_sqrt.hpp>`
`#include <stan/math/rev/scal/fun/inv_square.hpp>`
`#include <stan/math/rev/scal/fun/is_inf.hpp>`
`#include <stan/math/rev/scal/fun/is_nan.hpp>`
`#include <stan/math/rev/scal/fun/is_uninitialized.hpp>`
`#include <stan/math/rev/scal/fun/lgamma.hpp>`
`#include <stan/math/rev/scal/fun/lmgamma.hpp>`
`#include <stan/math/rev/scal/fun/log.hpp>`
`#include <stan/math/rev/scal/fun/log10.hpp>`
`#include <stan/math/rev/scal/fun/log1m.hpp>`
`#include <stan/math/rev/scal/fun/log1m_exp.hpp>`
`#include <stan/math/rev/scal/fun/log1p.hpp>`
`#include <stan/math/rev/scal/fun/log1p_exp.hpp>`
`#include <stan/math/rev/scal/fun/log2.hpp>`
`#include <stan/math/rev/scal/fun/log_diff_exp.hpp>`
`#include <stan/math/rev/scal/fun/log_falling_factorial.hpp>`
`#include <stan/math/rev/scal/fun/log_mix.hpp>`
`#include <stan/math/rev/scal/fun/log_rising_factorial.hpp>`
`#include <stan/math/rev/scal/fun/log_sum_exp.hpp>`
`#include <stan/math/rev/scal/fun/modified_bessel_first_kind.hpp>`
`#include <stan/math/rev/scal/fun/modified_bessel_second_kind.hpp>`
`#include <stan/math/rev/scal/fun/multiply_log.hpp>`
`#include <stan/math/rev/scal/fun/owens_t.hpp>`
`#include <stan/math/rev/scal/fun/Phi.hpp>`
`#include <stan/math/rev/scal/fun/Phi_approx.hpp>`
`#include <stan/math/rev/scal/fun/pow.hpp>`
`#include <stan/math/rev/scal/fun/primitive_value.hpp>`
`#include <stan/math/rev/scal/fun/rising_factorial.hpp>`
`#include <stan/math/rev/scal/fun/round.hpp>`
`#include <stan/math/rev/scal/fun/sin.hpp>`
`#include <stan/math/rev/scal/fun/sinh.hpp>`
`#include <stan/math/rev/scal/fun/sqrt.hpp>`
`#include <stan/math/rev/scal/fun/square.hpp>`
`#include <stan/math/rev/scal/fun/step.hpp>`
`#include <stan/math/rev/scal/fun/tan.hpp>`
`#include <stan/math/rev/scal/fun/tanh.hpp>`
`#include <stan/math/rev/scal/fun/tgamma.hpp>`
`#include <stan/math/rev/scal/fun/trunc.hpp>`
`#include <stan/math/rev/scal/fun/value_of.hpp>`
`#include <stan/math/rev/scal/fun/value_of_rec.hpp>`

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