1#ifndef STAN_MATH_REV_FUN_POW_HPP
2#define STAN_MATH_REV_FUN_POW_HPP
68template <
typename Scal1,
typename Scal2,
69 require_any_st_var<Scal1, Scal2>* =
nullptr,
70 require_all_stan_scalar_t<Scal1, Scal2>* =
nullptr>
71inline var pow(
const Scal1& base,
const Scal2& exponent) {
73 if (exponent == 0.5) {
75 }
else if (exponent == 1.0) {
77 }
else if (exponent == 2.0) {
79 }
else if (exponent == -2.0) {
81 }
else if (exponent == -1.0) {
83 }
else if (exponent == -0.5) {
89 [base, exponent](
auto&& vi)
mutable {
93 const double vi_mul = vi.adj() * vi.val();
96 forward_as<var>(base).adj()
100 forward_as<var>(exponent).adj() += vi_mul * std::log(
value_of(base));
118template <
typename Mat1,
typename Mat2,
122inline auto pow(
const Mat1& base,
const Mat2& exponent) {
126 using val_type = std::conditional_t<
128 decltype(std::declval<expr_type>().eval()),
129 decltype(std::declval<expr_type>().matrix().eval())>;
143 const auto& ret_mul =
to_ref(ret.adj().array() * ret.val().array());
146 forward_as<base_var_arena_t>(arena_base).adj()
154 forward_as<exp_var_arena_t>(arena_exponent).adj()
155 += (are_vals_zero).
select(ret_mul *
value_of(arena_base).log(), 0);
158 return ret_type(ret);
171template <
typename Mat1,
typename Scal1,
175inline auto pow(
const Mat1& base,
const Scal1& exponent) {
179 if (exponent == 0.5) {
180 return ret_type(
sqrt(base));
181 }
else if (exponent == 1.0) {
182 return ret_type(base);
183 }
else if (exponent == 2.0) {
184 return ret_type(
square(base));
185 }
else if (exponent == -2.0) {
187 }
else if (exponent == -1.0) {
188 return ret_type(
inv(base));
189 }
else if (exponent == -0.5) {
199 const auto& are_vals_zero =
to_ref(
value_of(arena_base).array() != 0.0);
200 const auto& ret_mul =
to_ref(ret.adj().array() * ret.val().array());
202 forward_as<ret_type>(arena_base).adj().array()
209 forward_as<var>(exponent).adj()
216 return ret_type(ret);
236template <
typename Scal1,
typename Mat1,
240inline auto pow(Scal1 base,
const Mat1& exponent) {
250 const auto& ret_mul =
to_ref(ret.adj().array() * ret.val().array());
252 forward_as<var>(base).adj()
257 forward_as<ret_type>(arena_exponent).adj().array()
258 += ret_mul * std::log(
value_of(base));
261 return ret_type(ret);
283inline std::complex<var>
pow(
const std::complex<var>& x,
284 const std::complex<var>& y) {
296template <
typename T,
typename = require_arithmetic_t<T>>
297inline std::complex<var>
pow(
const std::complex<var>& x,
298 const std::complex<T> y) {
309inline std::complex<var>
pow(
const std::complex<var>& x,
const var& y) {
321template <
typename T,
typename = require_arithmetic_t<T>>
322inline std::complex<var>
pow(
const std::complex<var>& x, T y) {
334template <
typename T,
typename = require_arithmetic_t<T>>
335inline std::complex<var>
pow(std::complex<T> x,
const std::complex<var>& y) {
347template <
typename T,
typename = require_arithmetic_t<T>>
348inline std::complex<var>
pow(std::complex<T> x,
const var& y) {
359inline std::complex<var>
pow(
const var& x,
const std::complex<var>& y) {
371template <
typename T,
typename = require_arithmetic_t<T>>
372inline std::complex<var>
pow(
const var& x, std::complex<T> y) {
384template <
typename T,
typename = require_arithmetic_t<T>>
385inline std::complex<var>
pow(T x,
const std::complex<var>& y) {
400inline std::complex<var>
pow(
const std::complex<var>& x,
int y) {
require_any_t< container_type_check_base< is_matrix, scalar_type_t, TypeCheck, Check >... > require_any_matrix_st
Require any of the types satisfy is_matrix.
require_all_t< container_type_check_base< is_matrix, scalar_type_t, TypeCheck, Check >... > require_all_matrix_st
Require all of the types does not satisfy is_matrix.
select_< as_operation_cl_t< T_condition >, as_operation_cl_t< T_then >, as_operation_cl_t< T_else > > select(T_condition &&condition, T_then &&then, T_else &&els)
Selection operation on kernel generator expressions.
require_t< is_stan_scalar< std::decay_t< T > > > require_stan_scalar_t
Require type satisfies is_stan_scalar.
require_all_not_t< is_stan_scalar< std::decay_t< Types > >... > require_all_not_stan_scalar_t
Require none of the types satisfy is_stan_scalar.
require_all_t< is_var_or_arithmetic< scalar_type_t< std::decay_t< Types > > >... > require_all_st_var_or_arithmetic
Require all of the scalar types satisfy is_var_or_arithmetic.
complex_return_t< U, V > complex_pow(const U &x, const V &y)
Return the first argument raised to the power of the second argument.
T as_array_or_scalar(T &&v)
Returns specified input value.
fvar< T > inv_square(const fvar< T > &x)
typename promote_scalar_type< std::decay_t< T >, std::decay_t< S > >::type promote_scalar_t
var_value< plain_type_t< T > > make_callback_var(T &&value, F &&functor)
Creates a new var initialized with a callback_vari with a given value and reverse-pass callback funct...
void reverse_pass_callback(F &&functor)
Puts a callback on the autodiff stack to be called in reverse pass.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
void check_consistent_sizes(const char *)
Trivial no input case, this function is a no-op.
fvar< T > sqrt(const fvar< T > &x)
fvar< T > sum(const std::vector< fvar< T > > &m)
Return the sum of the entries of the specified standard vector.
ref_type_t< T && > to_ref(T &&a)
This evaluates expensive Eigen expressions.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > inv_sqrt(const fvar< T > &x)
fvar< T > inv(const fvar< T > &x)
fvar< T > square(const fvar< T > &x)
typename internal::arena_type_impl< std::decay_t< T > >::type arena_t
Determines a type that can be used in place of T that does any dynamic allocations on the AD stack.
std::conditional_t< is_any_var_matrix< ReturnType, Types... >::value, stan::math::var_value< stan::math::promote_scalar_t< double, plain_type_t< ReturnType > > >, stan::math::promote_scalar_t< stan::math::var_value< double >, plain_type_t< ReturnType > > > return_var_matrix_t
Given an Eigen type and several inputs, determine if a matrix should be var<Matrix> or Matrix<var>.
The lgamma implementation in stan-math is based on either the reentrant safe lgamma_r implementation ...
Metaprogramming struct to detect whether a given type is constant in the mathematical sense (not the ...
Check if a type is derived from Eigen::ArrayBase
Extends std::false_type when instantiated with zero or more template parameters, all of which extend ...