Stan Math Library  2.10.0
reverse mode automatic differentiation
wiener_log.hpp
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28 
29 #ifndef STAN_MATH_PRIM_MAT_PROB_WIENER_LOG_HPP
30 #define STAN_MATH_PRIM_MAT_PROB_WIENER_LOG_HPP
31 
42 #include <boost/math/distributions.hpp>
43 #include <cmath>
44 #include <algorithm> // for max
45 
46 namespace stan {
47 
48  namespace math {
49 
68  template <bool propto,
69  typename T_y, typename T_alpha, typename T_tau,
70  typename T_beta, typename T_delta>
71  typename return_type<T_y, T_alpha, T_tau, T_beta, T_delta>::type
72  wiener_log(const T_y& y, const T_alpha& alpha, const T_tau& tau,
73  const T_beta& beta, const T_delta& delta) {
74  static const char* function("stan::math::wiener_log(%1%)");
75 
76  using boost::math::tools::promote_args;
77  using boost::math::isinf;
79  using std::log;
80  using std::exp;
81  using std::pow;
82 
83  static const double WIENER_ERR = 0.000001;
84  static const double PI_TIMES_WIENER_ERR = pi() * WIENER_ERR;
85  static const double LOG_PI_LOG_WIENER_ERR =
86  LOG_PI + log(WIENER_ERR);
87  static const double
88  TWO_TIMES_SQRT_2_TIMES_SQRT_PI_TIMES_WIENER_ERR =
89  2.0 * SQRT_2_TIMES_SQRT_PI * WIENER_ERR;
90  static const double LOG_TWO_OVER_TWO_PLUS_LOG_SQRT_PI =
91  LOG_TWO / 2 + LOG_SQRT_PI;
92  static const double SQUARE_PI_OVER_TWO = square(pi()) * 0.5;
93  static const double TWO_TIMES_LOG_SQRT_PI = 2.0 * LOG_SQRT_PI;
94 
95  if (!(stan::length(y)
96  && stan::length(alpha)
97  && stan::length(beta)
98  && stan::length(tau)
99  && stan::length(delta)))
100  return 0.0;
101 
102  typedef typename return_type<T_y, T_alpha, T_tau,
103  T_beta, T_delta>::type T_return_type;
104  T_return_type lp(0.0);
105 
106  check_not_nan(function, "Random variable", y);
107  check_not_nan(function, "Boundary separation", alpha);
108  check_not_nan(function, "A-priori bias", beta);
109  check_not_nan(function, "Nondecision time", tau);
110  check_not_nan(function, "Drift rate", delta);
111  check_finite(function, "Boundary separation", alpha);
112  check_finite(function, "A-priori bias", beta);
113  check_finite(function, "Nondecision time", tau);
114  check_finite(function, "Drift rate", delta);
115  check_positive(function, "Random variable", y);
116  check_positive(function, "Boundary separation", alpha);
117  check_positive(function, "Nondecision time", tau);
118  check_bounded(function, "A-priori bias", beta , 0, 1);
119  check_consistent_sizes(function,
120  "Random variable", y,
121  "Boundary separation", alpha,
122  "A-priori bias", beta,
123  "Nondecision time", tau,
124  "Drift rate", delta);
125 
126  size_t N =
127  std::max(max_size(y, alpha, beta), max_size(tau, delta));
128  if (!N)
129  return 0.0;
130  VectorView<const T_y> y_vec(y);
131  VectorView<const T_alpha> alpha_vec(alpha);
132  VectorView<const T_beta> beta_vec(beta);
133  VectorView<const T_tau> tau_vec(tau);
134  VectorView<const T_delta> delta_vec(delta);
135 
136  if (!include_summand<propto, T_y, T_alpha, T_tau,
137  T_beta, T_delta>::value) {
138  return 0;
139  }
140 
141  for (size_t i = 0; i < N; i++)
142  if (y_vec[i] < tau_vec[i]) {
144  return lp;
145  }
146 
147  for (size_t i = 0; i < N; i++) {
148  typename scalar_type<T_beta>::type one_minus_beta
149  = 1.0 - beta_vec[i];
150  typename scalar_type<T_alpha>::type alpha2
151  = square(alpha_vec[i]);
152  T_return_type x = y_vec[i];
153  T_return_type kl, ks, tmp = 0;
154  T_return_type k, K;
155 
156 
157  x = x - tau_vec[i]; // remove non-decision time from x
158  x = x / alpha2; // convert t to normalized time tt
159  T_return_type sqrt_x = sqrt(x);
160  T_return_type log_x = log(x);
161  T_return_type one_over_pi_times_sqrt_x = 1.0 / pi() * sqrt_x;
162 
163  // calculate number of terms needed for large t:
164  // if error threshold is set low enough
165  if (PI_TIMES_WIENER_ERR * x < 1) {
166  // compute bound
167  kl = sqrt(-2.0 * SQRT_PI *
168  (LOG_PI_LOG_WIENER_ERR + log_x)) /
169  sqrt_x;
170  // ensure boundary conditions met
171  kl = (kl > one_over_pi_times_sqrt_x) ?
172  kl : one_over_pi_times_sqrt_x;
173  } else { // if error threshold set too high
174  kl = one_over_pi_times_sqrt_x; // set to boundary condition
175  }
176  // calculate number of terms needed for small t:
177  // if error threshold is set low enough
178  T_return_type tmp_expr0
179  = TWO_TIMES_SQRT_2_TIMES_SQRT_PI_TIMES_WIENER_ERR * sqrt_x;
180  if (tmp_expr0 < 1) {
181  // compute bound
182  ks = 2.0 + sqrt_x * sqrt(-2 * log(tmp_expr0));
183  // ensure boundary conditions are met
184  T_return_type sqrt_x_plus_one = sqrt_x + 1.0;
185  ks = (ks > sqrt_x_plus_one) ? ks : sqrt_x_plus_one;
186  } else { // if error threshold was set too high
187  ks = 2.0; // minimal kappa for that case
188  }
189  // compute density: f(tt|0,1,w)
190  if (ks < kl) { // if small t is better (i.e., lambda<0)
191  K = ceil(ks); // round to smallest integer meeting error
192  T_return_type tmp_expr1 = (K - 1.0) / 2.0;
193  T_return_type tmp_expr2 = ceil(tmp_expr1);
194  for (k = -floor(tmp_expr1); k <= tmp_expr2; k++)
195  // increment sum
196  tmp += (one_minus_beta + 2.0 * k) *
197  exp(-(square(one_minus_beta + 2.0 * k)) * 0.5 / x);
198  // add constant term
199  tmp = log(tmp) -
200  LOG_TWO_OVER_TWO_PLUS_LOG_SQRT_PI - 1.5 * log_x;
201  } else { // if large t is better...
202  K = ceil(kl); // round to smallest integer meeting error
203  for (k = 1; k <= K; k++)
204  // increment sum
205  tmp += k * exp(-(square(k)) *
206  (SQUARE_PI_OVER_TWO * x)) *
207  sin(k * pi() * one_minus_beta);
208  tmp = log(tmp) +
209  TWO_TIMES_LOG_SQRT_PI; // add constant term
210  }
211 
212  // convert to f(t|v,a,w) and return result
213  lp += delta_vec[i] * alpha_vec[i] * one_minus_beta -
214  square(delta_vec[i]) * x * alpha2 / 2.0 -
215  log(alpha2) + tmp;
216  }
217 
218  return lp;
219  }
220 
221  template <typename T_y, typename T_alpha, typename T_tau,
222  typename T_beta, typename T_delta>
223  inline
225  wiener_log(const T_y& y, const T_alpha& alpha, const T_tau& tau,
226  const T_beta& beta, const T_delta& delta) {
227  return wiener_log<false>(y, alpha, tau, beta, delta);
228  }
229  }
230 }
231 #endif
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type wiener_log(const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
The log of the first passage time density function for a (Wiener) drift diffusion model for the given...
Definition: wiener_log.hpp:72
bool isfinite(const stan::math::var &v)
Checks if the given number has finite value.
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
const double LOG_PI
Definition: constants.hpp:170
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
const double LOG_SQRT_PI
Definition: constants.hpp:173
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
bool check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Return true if the value is between the low and high values, inclusively.
Metaprogram to calculate the base scalar return type resulting from promoting all the scalar types of...
Definition: return_type.hpp:19
scalar_type_helper< is_vector< T >::value, T >::type type
Definition: scalar_type.hpp:35
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
const double LOG_TWO
Definition: constants.hpp:177
const double SQRT_2_TIMES_SQRT_PI
Definition: constants.hpp:158
bool isinf(const stan::math::var &v)
Checks if the given number is infinite.
Definition: boost_isinf.hpp:22
fvar< T > sin(const fvar< T > &x)
Definition: sin.hpp:14
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
int max(const std::vector< int > &x)
Returns the maximum coefficient in the specified column vector.
Definition: max.hpp:21
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
fvar< T > floor(const fvar< T > &x)
Definition: floor.hpp:11
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
double pi()
Return the value of pi.
Definition: constants.hpp:86
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
const double SQRT_PI
Definition: constants.hpp:156
fvar< T > ceil(const fvar< T > &x)
Definition: ceil.hpp:11
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132

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