TEST(AgradFwdLog1pExp,Fvar) {
using stan::agrad::fvar;
using stan::math::log1p_exp;
using std::exp;
fvar<double> x(0.5,1.0);
fvar<double> y(1.0,2.0);
fvar<double> z(2.0,3.0);
fvar<double> a = log1p_exp(x);
EXPECT_FLOAT_EQ(log1p_exp(0.5), a.val_);
EXPECT_FLOAT_EQ(exp(0.5) / (1 + exp(0.5)), a.d_);
fvar<double> b = log1p_exp(y);
EXPECT_FLOAT_EQ(log1p_exp(1.0), b.val_);
EXPECT_FLOAT_EQ(2.0 * exp(1.0) / (1 + exp(1.0)), b.d_);
fvar<double> a2 = log(1+exp(x));
EXPECT_FLOAT_EQ(a.d_, a2.d_);
fvar<double> b2 = log(1+exp(y));
EXPECT_FLOAT_EQ(b.d_, b2.d_);
}
TEST(AgradFwdLogDiffExp,Double_FvarFvarVar_1stDeriv) {
using stan::agrad::fvar;
using stan::agrad::var;
using stan::math::log_diff_exp;
using std::exp;
double x(9.0);
fvar<fvar<var> > y;
y.val_.val_ = 6.0;
y.d_.val_ = 1.0;
fvar<fvar<var> > a = log_diff_exp(x,y);
EXPECT_FLOAT_EQ(log_diff_exp(9.0,6.0), a.val_.val_.val());
EXPECT_FLOAT_EQ(0, a.val_.d_.val());
EXPECT_FLOAT_EQ(-exp(6.0) / (exp(9.0) - exp(6.0)), a.d_.val_.val());
EXPECT_FLOAT_EQ(0, a.d_.d_.val());
AVEC p = createAVEC(y.val_.val_);
VEC g;
a.val_.val_.grad(p,g);
EXPECT_FLOAT_EQ(-exp(6.0) / (exp(9.0) - exp(6.0)), g[0]);
}
TEST(AgradFvar, log1m_inv_logit){
using stan::agrad::fvar;
using stan::math::log1m_inv_logit;
using std::exp;
fvar<double> x(0.5);
fvar<double> y(-1.0);
fvar<double> z(0.0);
x.d_ = 1.0;
y.d_ = 2.0;
z.d_ = 3.0;
fvar<double> a = log1m_inv_logit(x);
EXPECT_FLOAT_EQ(log1m_inv_logit(0.5), a.val_);
EXPECT_FLOAT_EQ(-1.0 * exp(0.5) / (1 + exp(0.5)), a.d_);
fvar<double> b = log1m_inv_logit(y);
EXPECT_FLOAT_EQ(log1m_inv_logit(-1.0), b.val_);
EXPECT_FLOAT_EQ(-2.0 * exp(-1.0) / (1 + exp(-1.0)), b.d_);
fvar<double> c = log1m_inv_logit(z);
EXPECT_FLOAT_EQ(log1m_inv_logit(0.0), c.val_);
EXPECT_FLOAT_EQ(-3.0 * exp(0.0) / (1 + exp(0.0)), c.d_);
}
void test_exp(const int fuzzy_bits)
{
// Use at least 8 resolution bits.
// Use at least 7 range bits.
BOOST_STATIC_ASSERT(-FixedPointType::resolution >= 8);
BOOST_STATIC_ASSERT( FixedPointType::range >= 7);
const FixedPointType a1(+1L ); const FloatPointType b1(+1L );
const FixedPointType a2(+2L ); const FloatPointType b2(+2L );
const FixedPointType a3(+4.375L); const FloatPointType b3(+4.375L);
const FixedPointType a4(+1.125L); const FloatPointType b4(+1.125L);
const FixedPointType a5(-1.125L); const FloatPointType b5(-1.125L);
const FixedPointType a6(+0.875L); const FloatPointType b6(+0.875L);
const FixedPointType a7(FixedPointType( 1) / 3); const FloatPointType b7(FloatPointType( 1) / 3);
const FixedPointType a8(FixedPointType(11) / 10); const FloatPointType b8(FloatPointType(11) / 10);
const FixedPointType a9(boost::math::constants::phi<FixedPointType>()); const FloatPointType b9(boost::math::constants::phi<FloatPointType>());
using std::exp;
BOOST_CHECK_CLOSE_FRACTION(exp(a1), FixedPointType(exp(b1)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a2), FixedPointType(exp(b2)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a3), FixedPointType(exp(b3)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a4), FixedPointType(exp(b4)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a5), FixedPointType(exp(b5)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a6), FixedPointType(exp(b6)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a7), FixedPointType(exp(b7)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a8), FixedPointType(exp(b8)), tolerance_maker<FixedPointType>(fuzzy_bits));
BOOST_CHECK_CLOSE_FRACTION(exp(a9), FixedPointType(exp(b9)), tolerance_maker<FixedPointType>(fuzzy_bits));
}
inline fvar<T> expm1(const fvar<T>& x) {
using std::exp;
return fvar<T>(expm1(x.val_), x.d_ * exp(x.val_));
}
int test_cv_vib()
{
using std::exp;
const Scalar Mm_N = 14.008e-3; //in SI kg/mol
const Scalar Mm_O = 16e-3; //in SI kg/mol
const Scalar Mm_N2 = 2.L * Mm_N; //in SI kg/mol
const Scalar Mm_O2 = 2.L * Mm_O; //in SI kg/mol
const Scalar Mm_NO = Mm_O + Mm_N; //in SI kg/mol
std::vector<std::string> species_str_list;
const unsigned int n_species = 5;
species_str_list.reserve(n_species);
species_str_list.push_back( "N2" );
species_str_list.push_back( "O2" );
species_str_list.push_back( "N" );
species_str_list.push_back( "O" );
species_str_list.push_back( "NO" );
Antioch::ChemicalMixture<Scalar> chem_mixture( species_str_list );
// Can we instantiate it?
Antioch::StatMechThermodynamics<Scalar> sm_thermo( chem_mixture );
// Mass fractions
std::vector<Scalar> mass_fractions( 5, 0.2 );
mass_fractions[0] = 0.5;
mass_fractions[1] = 0.2;
mass_fractions[2] = 0.1;
mass_fractions[3] = 0.1;
mass_fractions[4] = 0.1;
const Scalar R_N2 = Antioch::Constants::R_universal<Scalar>() / Mm_N2;
const Scalar R_O2 = Antioch::Constants::R_universal<Scalar>() / Mm_O2;
const Scalar R_NO = Antioch::Constants::R_universal<Scalar>() / Mm_NO;
const Scalar th0_N2 = 3.39500e+03; // degeneracy = 1
const Scalar th0_O2 = 2.23900e+03; // degeneracy = 1
const Scalar th0_NO = 2.81700e+03; // degeneracy = 1
// Tv
const Scalar Tv = 1000.0;
const Scalar tol = std::numeric_limits<Scalar>::epsilon() * 2;
const Scalar ztol = std::numeric_limits<Scalar>::epsilon();
int return_flag = 0;
Scalar cv_vib_mix = 0.0;
// N2
{
Scalar cv_vib_N2 = sm_thermo.cv_vib (0, Tv);
const Scalar expv = exp(th0_N2/Tv);
const Scalar expvmi = expv - Scalar(1.0);
Scalar cv_vib_N2_true = R_N2*th0_N2*th0_N2*expv/expvmi/expvmi/Tv/Tv;
if( !test_relative(cv_vib_N2, cv_vib_N2_true, tol) )
{
std::cerr << std::scientific << std::setprecision(20);
std::cerr << "Error: Mismatch in cv_vib for N2."
<< "\n Expected = " << cv_vib_N2_true
<< "\n Computed = " << cv_vib_N2
<< "\n Diff = " << cv_vib_N2_true - cv_vib_N2
<< std::endl;
return_flag += 1;
}
cv_vib_mix += mass_fractions[0]*cv_vib_N2_true;
}
// O2
{
Scalar cv_vib_O2 = sm_thermo.cv_vib (1, Tv);
const Scalar expv = exp(th0_O2/Tv);
const Scalar expvmi = expv - Scalar(1.0);
Scalar cv_vib_O2_true = R_O2*th0_O2*th0_O2*expv/expvmi/expvmi/Tv/Tv;
if( !test_relative(cv_vib_O2, cv_vib_O2_true, tol) )
{
std::cerr << std::scientific << std::setprecision(20);
std::cerr << "Error: Mismatch in cv_vib for O2."
<< "\n Expected = " << cv_vib_O2_true
<< "\n Computed = " << cv_vib_O2
<< "\n Diff = " << cv_vib_O2_true - cv_vib_O2
<< std::endl;
return_flag += 1;
}
cv_vib_mix += mass_fractions[1]*cv_vib_O2_true;
}
// O
{
Scalar cv_vib_O = sm_thermo.cv_vib (2, Tv);
if( !test_zero(cv_vib_O, ztol) )
{
std::cerr << std::scientific << std::setprecision(20);
std::cerr << "Error: Mismatch in cv_vib for O."
<< "\n Expected = " << Scalar(0.0)
<< "\n Computed = " << cv_vib_O
<< "\n Diff = " << cv_vib_O
<< std::endl;
return_flag += 1;
}
// cv_vib_mix += 0.0;
}
// N
{
Scalar cv_vib_N = sm_thermo.cv_vib (3, Tv);
if( !test_zero(cv_vib_N, ztol) )
{
std::cerr << std::scientific << std::setprecision(20);
std::cerr << "Error: Mismatch in cv_vib for N."
<< "\n Expected = " << Scalar(0.0)
<< "\n Computed = " << cv_vib_N
<< "\n Diff = " << cv_vib_N
<< std::endl;
return_flag += 1;
}
// cv_vib_mix += 0.0;
}
// NO
{
Scalar cv_vib_NO = sm_thermo.cv_vib (4, Tv);
const Scalar expv = exp(th0_NO/Tv);
const Scalar expvmi = expv - Scalar(1.0);
Scalar cv_vib_NO_true = R_NO*th0_NO*th0_NO*expv/expvmi/expvmi/Tv/Tv;
if( !test_relative(cv_vib_NO, cv_vib_NO_true, tol*4) )
{
std::cerr << std::scientific << std::setprecision(20);
std::cerr << "Error: Mismatch in cv_vib for NO."
<< "\n Expected = " << cv_vib_NO_true
<< "\n Computed = " << cv_vib_NO
<< "\n Diff = " << cv_vib_NO_true - cv_vib_NO
<< std::endl;
return_flag += 1;
}
cv_vib_mix += mass_fractions[4]*cv_vib_NO_true;
}
// mixture
{
Scalar cv = sm_thermo.cv_vib(Tv, mass_fractions);
if( !test_relative(cv, cv_vib_mix, tol) )
{
std::cerr << std::scientific << std::setprecision(20);
std::cerr << "Error: Mismatch in mixture cv_vib."
<< "\n Expected = " << cv_vib_mix
<< "\n Computed = " << cv
<< "\n Diff = " << cv - cv_vib_mix
<< std::endl;
return_flag += 1;
}
}
return return_flag;
}
typename return_type<T_y, T_loc, T_scale, T_shape>::type
skew_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
const T_shape& alpha) {
static const char* function("skew_normal_log");
typedef typename stan::partials_return_type<T_y, T_loc,
T_scale, T_shape>::type
T_partials_return;
using std::log;
using stan::is_constant_struct;
using std::exp;
if (!(stan::length(y)
&& stan::length(mu)
&& stan::length(sigma)
&& stan::length(alpha)))
return 0.0;
T_partials_return logp(0.0);
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_finite(function, "Shape parameter", alpha);
check_positive(function, "Scale parameter", sigma);
check_consistent_sizes(function,
"Random variable", y,
"Location parameter", mu,
"Scale parameter", sigma,
"Shape paramter", alpha);
if (!include_summand<propto, T_y, T_loc, T_scale, T_shape>::value)
return 0.0;
OperandsAndPartials<T_y, T_loc, T_scale, T_shape>
operands_and_partials(y, mu, sigma, alpha);
using std::log;
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
VectorView<const T_shape> alpha_vec(alpha);
size_t N = max_size(y, mu, sigma, alpha);
VectorBuilder<true, T_partials_return, T_scale> inv_sigma(length(sigma));
VectorBuilder<include_summand<propto, T_scale>::value,
T_partials_return, T_scale> log_sigma(length(sigma));
for (size_t i = 0; i < length(sigma); i++) {
inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
if (include_summand<propto, T_scale>::value)
log_sigma[i] = log(value_of(sigma_vec[i]));
}
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return y_minus_mu_over_sigma
= (y_dbl - mu_dbl) * inv_sigma[n];
const double pi_dbl = pi();
if (include_summand<propto>::value)
logp -= 0.5 * log(2.0 * pi_dbl);
if (include_summand<propto, T_scale>::value)
logp -= log(sigma_dbl);
if (include_summand<propto, T_y, T_loc, T_scale>::value)
logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
if (include_summand<propto, T_y, T_loc, T_scale, T_shape>::value)
logp += log(erfc(-alpha_dbl * y_minus_mu_over_sigma
/ std::sqrt(2.0)));
T_partials_return deriv_logerf
= 2.0 / std::sqrt(pi_dbl)
* exp(-alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0)
* alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0))
/ (1 + erf(alpha_dbl * y_minus_mu_over_sigma
/ std::sqrt(2.0)));
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n]
+= -y_minus_mu_over_sigma / sigma_dbl
+ deriv_logerf * alpha_dbl / (sigma_dbl * std::sqrt(2.0));
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n]
+= y_minus_mu_over_sigma / sigma_dbl
+ deriv_logerf * -alpha_dbl / (sigma_dbl * std::sqrt(2.0));
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n]
+= -1.0 / sigma_dbl
+ y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
- deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
/ (sigma_dbl * std::sqrt(2.0));
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x4[n]
+= deriv_logerf * y_minus_mu_over_sigma / std::sqrt(2.0);
}
return operands_and_partials.value(logp);
}
typename return_type<T_y, T_scale_succ, T_scale_fail>::type
beta_cdf_log(const T_y& y, const T_scale_succ& alpha,
const T_scale_fail& beta) {
typedef typename stan::partials_return_type<T_y, T_scale_succ,
T_scale_fail>::type
T_partials_return;
// Size checks
if ( !( stan::length(y) && stan::length(alpha)
&& stan::length(beta) ) )
return 0.0;
// Error checks
static const char* function("stan::math::beta_cdf");
using stan::math::check_positive_finite;
using stan::math::check_not_nan;
using stan::math::check_nonnegative;
using stan::math::check_less_or_equal;
using boost::math::tools::promote_args;
using stan::math::check_consistent_sizes;
using stan::math::value_of;
T_partials_return cdf_log(0.0);
check_positive_finite(function, "First shape parameter", alpha);
check_positive_finite(function, "Second shape parameter", beta);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_less_or_equal(function, "Random variable", y, 1);
check_consistent_sizes(function,
"Random variable", y,
"First shape parameter", alpha,
"Second shape parameter", beta);
// Wrap arguments in vectors
VectorView<const T_y> y_vec(y);
VectorView<const T_scale_succ> alpha_vec(alpha);
VectorView<const T_scale_fail> beta_vec(beta);
size_t N = max_size(y, alpha, beta);
OperandsAndPartials<T_y, T_scale_succ, T_scale_fail>
operands_and_partials(y, alpha, beta);
// Compute CDF and its gradients
using stan::math::inc_beta;
using stan::math::digamma;
using stan::math::lbeta;
using std::pow;
using std::exp;
using std::log;
using std::exp;
// Cache a few expensive function calls if alpha or beta is a parameter
VectorBuilder<contains_nonconstant_struct<T_scale_succ,
T_scale_fail>::value,
T_partials_return, T_scale_succ, T_scale_fail>
digamma_alpha_vec(max_size(alpha, beta));
VectorBuilder<contains_nonconstant_struct<T_scale_succ,
T_scale_fail>::value,
T_partials_return, T_scale_succ, T_scale_fail>
digamma_beta_vec(max_size(alpha, beta));
VectorBuilder<contains_nonconstant_struct<T_scale_succ,
T_scale_fail>::value,
T_partials_return, T_scale_succ, T_scale_fail>
digamma_sum_vec(max_size(alpha, beta));
if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value) {
for (size_t i = 0; i < N; i++) {
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
const T_partials_return beta_dbl = value_of(beta_vec[i]);
digamma_alpha_vec[i] = digamma(alpha_dbl);
digamma_beta_vec[i] = digamma(beta_dbl);
digamma_sum_vec[i] = digamma(alpha_dbl + beta_dbl);
}
}
// Compute vectorized CDFLog and gradient
for (size_t n = 0; n < N; n++) {
// Pull out values
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return beta_dbl = value_of(beta_vec[n]);
const T_partials_return betafunc_dbl = exp(lbeta(alpha_dbl, beta_dbl));
// Compute
const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
cdf_log += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += pow(1-y_dbl, beta_dbl-1)
* pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
T_partials_return g1 = 0;
T_partials_return g2 = 0;
if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value) {
stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
digamma_alpha_vec[n],
digamma_beta_vec[n], digamma_sum_vec[n],
betafunc_dbl);
}
if (!is_constant_struct<T_scale_succ>::value)
operands_and_partials.d_x2[n] += g1 / Pn;
if (!is_constant_struct<T_scale_fail>::value)
operands_and_partials.d_x3[n] += g2 / Pn;
}
return operands_and_partials.to_var(cdf_log, y, alpha, beta);
}
DualNumber<T> exp(DualNumber<T> x)
{
using std::exp;
return DualNumber<T>(exp(x.first), x.second * exp(x.first));
}
TEST(AgradFwdLogDiffExp,FvarVar_FvarVar_2ndDeriv) {
using stan::agrad::fvar;
using stan::agrad::var;
using stan::math::log_diff_exp;
using std::exp;
fvar<var> x(9.0,1.3);
fvar<var> z(6.0,1.0);
fvar<var> a = log_diff_exp(x,z);
AVEC y = createAVEC(x.val_,z.val_);
VEC g;
a.d_.grad(y,g);
EXPECT_FLOAT_EQ((1.3 * exp(9.0) * (exp(9.0) - exp(6.0)) - exp(9.0)
* (1.3 * exp(9.0) - exp(6.0))) / (exp(9.0) - exp(6.0))
/ (exp(9.0) - exp(6.0)) ,g[0]);
EXPECT_FLOAT_EQ((-exp(6.0) * (exp(9.0) - exp(6.0)) + exp(6.0)
* (1.3 * exp(9.0) - exp(6.0))) / (exp(9.0) - exp(6.0))
/ (exp(9.0) - exp(6.0)) ,g[1]);
}
typename return_type<T_prob>::type
binomial_cdf(const T_n& n, const T_N& N, const T_prob& theta) {
static const char* function("stan::prob::binomial_cdf");
typedef typename stan::partials_return_type<T_n,T_N,T_prob>::type
T_partials_return;
using stan::math::check_finite;
using stan::math::check_bounded;
using stan::math::check_nonnegative;
using stan::math::value_of;
using stan::math::check_consistent_sizes;
using stan::prob::include_summand;
// Ensure non-zero arguments lenghts
if (!(stan::length(n) && stan::length(N) && stan::length(theta)))
return 1.0;
T_partials_return P(1.0);
// Validate arguments
check_nonnegative(function, "Population size parameter", N);
check_finite(function, "Probability parameter", theta);
check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
check_consistent_sizes(function,
"Successes variable", n,
"Population size parameter", N,
"Probability parameter", theta);
// Wrap arguments in vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_N> N_vec(N);
VectorView<const T_prob> theta_vec(theta);
size_t size = max_size(n, N, theta);
// Compute vectorized CDF and gradient
using stan::math::value_of;
using stan::math::inc_beta;
using stan::math::lbeta;
using std::exp;
using std::pow;
agrad::OperandsAndPartials<T_prob> operands_and_partials(theta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) < 0)
return operands_and_partials.to_var(0.0,theta);
}
for (size_t i = 0; i < size; i++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
continue;
}
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return N_dbl = value_of(N_vec[i]);
const T_partials_return theta_dbl = value_of(theta_vec[i]);
const T_partials_return betafunc = exp(lbeta(N_dbl-n_dbl,n_dbl+1));
const T_partials_return Pi = inc_beta(N_dbl - n_dbl, n_dbl + 1,
1 - theta_dbl);
P *= Pi;
if (!is_constant_struct<T_prob>::value)
operands_and_partials.d_x1[i] -= pow(theta_dbl,n_dbl)
* pow(1-theta_dbl,N_dbl-n_dbl-1) / betafunc / Pi;
}
if (!is_constant_struct<T_prob>::value) {
for(size_t i = 0; i < stan::length(theta); ++i)
operands_and_partials.d_x1[i] *= P;
}
return operands_and_partials.to_var(P,theta);
}
typename return_type<T_y, T_dof>::type
inv_chi_square_cdf_log(const T_y& y, const T_dof& nu) {
typedef typename stan::partials_return_type<T_y, T_dof>::type
T_partials_return;
// Size checks
if ( !( stan::length(y) && stan::length(nu) ) ) return 0.0;
// Error checks
static const char* function("stan::math::inv_chi_square_cdf_log");
using stan::math::check_positive_finite;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using stan::math::check_nonnegative;
using boost::math::tools::promote_args;
using stan::math::value_of;
using std::exp;
T_partials_return P(0.0);
check_positive_finite(function, "Degrees of freedom parameter", nu);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_consistent_sizes(function,
"Random variable", y,
"Degrees of freedom parameter", nu);
// Wrap arguments in vectors
VectorView<const T_y> y_vec(y);
VectorView<const T_dof> nu_vec(nu);
size_t N = max_size(y, nu);
OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++)
if (value_of(y_vec[i]) == 0)
return operands_and_partials.to_var(stan::math::negative_infinity(),
y, nu);
// Compute cdf_log and its gradients
using stan::math::gamma_q;
using stan::math::digamma;
using boost::math::tgamma;
using std::exp;
using std::pow;
using std::log;
// Cache a few expensive function calls if nu is a parameter
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> gamma_vec(stan::length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> digamma_vec(stan::length(nu));
if (!is_constant_struct<T_dof>::value) {
for (size_t i = 0; i < stan::length(nu); i++) {
const T_partials_return nu_dbl = value_of(nu_vec[i]);
gamma_vec[i] = tgamma(0.5 * nu_dbl);
digamma_vec[i] = digamma(0.5 * nu_dbl);
}
}
// Compute vectorized cdf_log and gradient
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
continue;
}
// Pull out values
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return y_inv_dbl = 1.0 / y_dbl;
const T_partials_return nu_dbl = value_of(nu_vec[n]);
// Compute
const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += 0.5 * y_inv_dbl * y_inv_dbl
* exp(-0.5*y_inv_dbl) * pow(0.5*y_inv_dbl, 0.5*nu_dbl-1)
/ tgamma(0.5*nu_dbl) / Pn;
if (!is_constant_struct<T_dof>::value)
operands_and_partials.d_x2[n]
+= 0.5 * stan::math::grad_reg_inc_gamma(0.5 * nu_dbl,
0.5 * y_inv_dbl,
gamma_vec[n],
digamma_vec[n]) / Pn;
}
return operands_and_partials.to_var(P, y, nu);
}
typename return_type<T_y, T_dof, T_scale>::type
scaled_inv_chi_square_ccdf_log(const T_y& y, const T_dof& nu,
const T_scale& s) {
typedef typename stan::partials_return_type<T_y, T_dof, T_scale>::type
T_partials_return;
if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
return 0.0;
static const char* function("scaled_inv_chi_square_ccdf_log");
using std::exp;
T_partials_return P(0.0);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_positive_finite(function, "Degrees of freedom parameter", nu);
check_positive_finite(function, "Scale parameter", s);
check_consistent_sizes(function,
"Random variable", y,
"Degrees of freedom parameter", nu,
"Scale parameter", s);
VectorView<const T_y> y_vec(y);
VectorView<const T_dof> nu_vec(nu);
VectorView<const T_scale> s_vec(s);
size_t N = max_size(y, nu, s);
OperandsAndPartials<T_y, T_dof, T_scale>
operands_and_partials(y, nu, s);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) == 0)
return operands_and_partials.value(0.0);
}
using std::exp;
using std::pow;
using std::log;
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> gamma_vec(stan::length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> digamma_vec(stan::length(nu));
if (!is_constant_struct<T_dof>::value) {
for (size_t i = 0; i < stan::length(nu); i++) {
const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
gamma_vec[i] = tgamma(half_nu_dbl);
digamma_vec[i] = digamma(half_nu_dbl);
}
}
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
return operands_and_partials.value(negative_infinity());
}
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return y_inv_dbl = 1.0 / y_dbl;
const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
const T_partials_return s_dbl = value_of(s_vec[n]);
const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
* y_inv_dbl;
const T_partials_return half_nu_s2_overx_dbl
= 2.0 * half_nu_dbl * half_s2_overx_dbl;
const T_partials_return Pn = gamma_p(half_nu_dbl,
half_nu_s2_overx_dbl);
const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
* pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= half_nu_s2_overx_dbl * y_inv_dbl
* gamma_p_deriv / Pn;
if (!is_constant_struct<T_dof>::value)
operands_and_partials.d_x2[n]
-= (0.5 * grad_reg_inc_gamma(half_nu_dbl,
half_nu_s2_overx_dbl,
gamma_vec[n],
digamma_vec[n])
- half_s2_overx_dbl * gamma_p_deriv)
/ Pn;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] += 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
* gamma_p_deriv / Pn;
}
return operands_and_partials.value(P);
}
inline T0
operator()(const T0& arg1) const {
return exp(arg1);
}
TEST(AgradFwdExp,Fvar) {
using stan::math::fvar;
using std::exp;
fvar<double> x(0.5,1.0);
fvar<double> a = exp(x);
EXPECT_FLOAT_EQ(exp(0.5), a.val_);
EXPECT_FLOAT_EQ(exp(0.5), a.d_);
fvar<double> b = 2 * exp(x) + 4;
EXPECT_FLOAT_EQ(2 * exp(0.5) + 4, b.val_);
EXPECT_FLOAT_EQ(2 * exp(0.5), b.d_);
fvar<double> c = -exp(x) + 5;
EXPECT_FLOAT_EQ(-exp(0.5) + 5, c.val_);
EXPECT_FLOAT_EQ(-exp(0.5), c.d_);
fvar<double> d = -3 * exp(-x) + 5 * x;
EXPECT_FLOAT_EQ(-3 * exp(-0.5) + 5 * 0.5, d.val_);
EXPECT_FLOAT_EQ(3 * exp(-0.5) + 5, d.d_);
fvar<double> y(-0.5,1.0);
fvar<double> e = exp(y);
EXPECT_FLOAT_EQ(exp(-0.5), e.val_);
EXPECT_FLOAT_EQ(exp(-0.5), e.d_);
fvar<double> z(0.0,1.0);
fvar<double> f = exp(z);
EXPECT_FLOAT_EQ(exp(0.0), f.val_);
EXPECT_FLOAT_EQ(exp(0.0), f.d_);
}
double exact_soln(double x){
return 1.0 - (1.0-exp(-10.0))*x - exp(-10.0*x);
}
double f(double x){
// Source term or Inhomogeneous term
return 100.0 * exp(-10.0 * x);
}
const float phi1 = degreeToRadian(44.f); // 1st automecoic parallel
const float phi2 = degreeToRadian(49.f); // 2nd automecoic parallel
const float phi0 = degreeToRadian(46.5f);// latitude of origin
const float X0 = 700000; // x coordinate at origin
const float Y0 = 6600000; // y coordinate at origin
// Normals
const float gN1 = a/sqrt(1-e*e*sin(phi1)*sin(phi1));
const float gN2 = a/sqrt(1-e*e*sin(phi2)*sin(phi2));
// Isometric latitudes
const float gl1=log(tan(M_PI/4+phi1/2)*pow((1-e*sin(phi1))/(1+e*sin(phi1)),e/2));
const float gl2=log(tan(M_PI/4+phi2/2)*pow((1-e*sin(phi2))/(1+e*sin(phi2)),e/2));
const float gl0=log(tan(M_PI/4+phi0/2)*pow((1-e*sin(phi0))/(1+e*sin(phi0)),e/2));
// Projection exponent
const float n = (log((gN2*cos(phi2))/(gN1*cos(phi1))))/(gl1-gl2);
// Projection constant
const float c = ((gN1*cos(phi1))/n)*exp(n*gl1);
// Coordinate
const float ys = Y0 + c*exp(-n*gl0);
// Convert geographic coordinates (latitude, longitude in degrees) into
// cartesian coordinates (in kilometers) using the Lambert 93 projection.
pair<float,float> geoToLambert93(float latitude,float longitude)
{
float phi = degreeToRadian(latitude);
float l = degreeToRadian(longitude);
float gl = log(tan(M_PI/4+phi/2)*pow((1-e*sin(phi))/(1+e*sin(phi)),e/2));
float x93 = X0 + c*exp(-n*gl)*sin(n*(l-lc));
float y93 = ys - c*exp(-n*gl)*cos(n*(l-lc));
return make_pair(x93/1000,y93/1000);
}
void FunctionsTest::testWeightedModifiedBesselFunctions() {
BOOST_TEST_MESSAGE("Testing weighted modified Bessel functions...");
Real nu = -5.0;
while (nu <= 5.0) {
Real x = 0.1;
while (x <= 15.0) {
const Real calculated_i =
modifiedBesselFunction_i_exponentiallyWeighted(nu, x);
const Real expected_i =
modifiedBesselFunction_i(nu, x) * exp(-x);
const Real calculated_k =
modifiedBesselFunction_k_exponentiallyWeighted(nu, x);
const Real expected_k =
M_PI_2 * (modifiedBesselFunction_i(-nu,x) -
modifiedBesselFunction_i(nu,x)) * exp(-x) / std::sin(M_PI*nu);
const Real tol_i = 1e3 * QL_EPSILON *
std::fabs(expected_i) * std::max(exp(x), 1.0);
const Real tol_k = std::max(QL_EPSILON,
1e3 * QL_EPSILON *
std::fabs(expected_k) * std::max(exp(x), 1.0));
if (std::abs(expected_i - calculated_i) > tol_i) {
BOOST_ERROR("failed to verify exponentially weighted"
<< "modified Bessel function of first kind"
<< "\n order : " << nu << "\n argument : "
<< x << "\n calculated : " << calculated_i
<< "\n expected : " << expected_i);
}
if (std::abs(expected_k - calculated_k) > tol_k) {
BOOST_ERROR("failed to verify exponentially weighted"
<< "modified Bessel function of second kind"
<< "\n order : " << nu << "\n argument : "
<< x << "\n calculated : " << calculated_k
<< "\n expected : " << expected_k);
}
x += 0.5;
}
nu += 0.5;
}
nu = -5.0;
while (nu <= 5.0) {
Real x = -5.0;
while (x <= 5.0) {
Real y = -5.0;
while (y <= 5.0) {
const std::complex<Real> z(x, y);
const std::complex<Real> calculated_i =
modifiedBesselFunction_i_exponentiallyWeighted(nu, z);
const std::complex<Real> expected_i =
modifiedBesselFunction_i(nu, z) * exp(-z);
const std::complex<Real> calculated_k =
modifiedBesselFunction_k_exponentiallyWeighted(nu, z);
const std::complex<Real> expected_k =
M_PI_2 * (modifiedBesselFunction_i(-nu, z) * exp(-z) -
modifiedBesselFunction_i(nu, z) * exp(-z)) /
std::sin(M_PI * nu);
const Real tol_i = 1e3 * QL_EPSILON*std::abs(calculated_i);
const Real tol_k = 1e3 * QL_EPSILON*std::abs(calculated_k);
if (std::abs(calculated_i - expected_i) > tol_i) {
BOOST_ERROR("failed to verify exponentially weighted"
<< "modified Bessel function of first kind"
<< "\n order : " << nu
<< "\n argument : " << z <<
"\n calculated: "
<< calculated_i << "\n expected : " << expected_i);
}
if (std::abs(calculated_k - expected_k) > tol_k) {
BOOST_ERROR("failed to verify exponentially weighted"
<< "modified Bessel function of second kind"
<< "\n order : " << nu
<< "\n argument : " << z <<
"\n calculated: "
<< calculated_k << "\n expected : " << expected_k);
}
y += 0.5;
}
x += 0.5;
}
nu += 0.5;
}
}
int test_values(const Scalar & Cf, const Scalar & eta, const Scalar & Ea, const Scalar & D, const Scalar & Tref, const Scalar & R, const Antioch::KineticsType<Scalar> & rate_base)
{
using std::abs;
using std::exp;
using std::pow;
int return_flag = 0;
const Scalar tol = std::numeric_limits<Scalar>::epsilon() * 100;
for(Scalar T = 300.1L; T <= 2500.1L; T += 10.L)
{
const Scalar rate_exact = Cf*pow(T/Tref,eta)*exp(-Ea/(R*T) + D * T);
const Scalar derive_exact = exp(-Ea/(R*T) + D * T) * pow(T/Tref,eta) * Cf * (Ea/(R*T*T) + eta/T + D );
Antioch::KineticsConditions<Scalar> cond(T);
Scalar rate1 = rate_base(cond);
Scalar deriveRate1 = rate_base.derivative(cond);
Scalar rate;
Scalar deriveRate;
rate_base.compute_rate_and_derivative(cond,rate,deriveRate);
if( abs( (rate1 - rate_exact)/rate_exact ) > tol )
{
std::cerr << std::scientific << std::setprecision(16)
<< "Error: Mismatch in rate values." << std::endl
<< "T = " << T << " K" << std::endl
<< "rate(T) = " << rate1 << std::endl
<< "rate_exact = " << rate_exact << std::endl
<< "relative difference = " << abs( (rate1 - rate_exact)/rate_exact ) << std::endl
<< "tolerance = " << tol << std::endl
<< "on rate " << rate_base << std::endl << std::endl;
return_flag = 1;
}
if( abs( (rate - rate_exact)/rate_exact ) > tol )
{
std::cerr << std::scientific << std::setprecision(16)
<< "Error: Mismatch in rate values." << std::endl
<< "T = " << T << " K" << std::endl
<< "rate(T) = " << rate << std::endl
<< "rate_exact = " << rate_exact << std::endl
<< "relative difference = " << abs( (rate - rate_exact)/rate_exact ) << std::endl
<< "tolerance = " << tol << std::endl
<< "on rate " << rate_base << std::endl << std::endl;
return_flag = 1;
}
if( abs( (deriveRate1 - derive_exact)/derive_exact ) > tol )
{
std::cerr << std::scientific << std::setprecision(16)
<< "Error: Mismatch in rate derivative values." << std::endl
<< "T = " << T << " K" << std::endl
<< "drate_dT(T) = " << deriveRate1 << std::endl
<< "derive_exact = " << derive_exact << std::endl
<< "relative difference = " << abs( (deriveRate1 - derive_exact)/derive_exact ) << std::endl
<< "tolerance = " << tol << std::endl
<< "on rate " << rate_base << std::endl << std::endl;
return_flag = 1;
}
if( abs( (deriveRate - derive_exact)/derive_exact ) > tol )
{
std::cerr << std::scientific << std::setprecision(16)
<< "Error: Mismatch in rate derivative values." << std::endl
<< "T = " << T << " K" << std::endl
<< "drate_dT(T) = " << deriveRate << std::endl
<< "derive_exact = " << derive_exact << std::endl
<< "relative difference = " << abs( (deriveRate - derive_exact)/derive_exact ) << std::endl
<< "tolerance = " << tol << std::endl
<< "on rate " << rate_base << std::endl << std::endl;
return_flag = 1;
}
if(return_flag)break;
}
return return_flag;
}
typename return_type<T_y,T_dof>::type
chi_square_cdf(const T_y& y, const T_dof& nu) {
static const char* function("stan::prob::chi_square_cdf");
typedef typename stan::partials_return_type<T_y,T_dof>::type
T_partials_return;
using stan::math::check_positive_finite;
using stan::math::check_nonnegative;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using stan::math::value_of;
T_partials_return cdf(1.0);
// Size checks
if (!(stan::length(y) && stan::length(nu)))
return cdf;
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_positive_finite(function, "Degrees of freedom parameter", nu);
check_consistent_sizes(function,
"Random variable", y,
"Degrees of freedom parameter", nu);
// Wrap arguments in vectors
VectorView<const T_y> y_vec(y);
VectorView<const T_dof> nu_vec(nu);
size_t N = max_size(y, nu);
agrad::OperandsAndPartials<T_y, T_dof>
operands_and_partials(y, nu);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) == 0)
return operands_and_partials.to_var(0.0,y,nu);
}
// Compute CDF and its gradients
using stan::math::gamma_p;
using stan::math::digamma;
using boost::math::tgamma;
using std::exp;
using std::pow;
// Cache a few expensive function calls if nu is a parameter
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return, T_dof> gamma_vec(stan::length(nu));
VectorBuilder<!is_constant_struct<T_dof>::value,
T_partials_return,T_dof> digamma_vec(stan::length(nu));
if (!is_constant_struct<T_dof>::value) {
for (size_t i = 0; i < stan::length(nu); i++) {
const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
gamma_vec[i] = tgamma(alpha_dbl);
digamma_vec[i] = digamma(alpha_dbl);
}
}
// Compute vectorized CDF and gradient
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
continue;
// Pull out values
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
const T_partials_return beta_dbl = 0.5;
// Compute
const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
cdf *= Pn;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
* pow(beta_dbl * y_dbl,alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
if (!is_constant_struct<T_dof>::value)
operands_and_partials.d_x2[n]
-= 0.5 * stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
* y_dbl, gamma_vec[n],
digamma_vec[n]) / Pn;
}
if (!is_constant_struct<T_y>::value)
for (size_t n = 0; n < stan::length(y); ++n)
operands_and_partials.d_x1[n] *= cdf;
if (!is_constant_struct<T_dof>::value)
for (size_t n = 0; n < stan::length(nu); ++n)
operands_and_partials.d_x2[n] *= cdf;
return operands_and_partials.to_var(cdf,y,nu);
}
typename return_type<T_size1,T_size2>::type
beta_binomial_ccdf_log(const T_n& n, const T_N& N, const T_size1& alpha,
const T_size2& beta) {
static const char* function("stan::prob::beta_binomial_ccdf_log");
typedef typename stan::partials_return_type<T_n,T_N,T_size1,
T_size2>::type
T_partials_return;
using stan::math::check_positive_finite;
using stan::math::check_nonnegative;
using stan::math::value_of;
using stan::math::check_consistent_sizes;
using stan::prob::include_summand;
// Ensure non-zero argument lengths
if (!(stan::length(n) && stan::length(N) && stan::length(alpha)
&& stan::length(beta)))
return 0.0;
T_partials_return P(0.0);
// Validate arguments
check_nonnegative(function, "Population size parameter", N);
check_positive_finite(function, "First prior sample size parameter", alpha);
check_positive_finite(function, "Second prior sample size parameter", beta);
check_consistent_sizes(function,
"Successes variable", n,
"Population size parameter", N,
"First prior sample size parameter", alpha,
"Second prior sample size parameter", beta);
// Wrap arguments in vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_N> N_vec(N);
VectorView<const T_size1> alpha_vec(alpha);
VectorView<const T_size2> beta_vec(beta);
size_t size = max_size(n, N, alpha, beta);
// Compute vectorized cdf_log and gradient
using stan::math::lgamma;
using stan::math::lbeta;
using stan::math::digamma;
using std::exp;
agrad::OperandsAndPartials<T_size1, T_size2>
operands_and_partials(alpha, beta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as neg infinity
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) <= 0)
return operands_and_partials.to_var(0.0,alpha,beta);
}
for (size_t i = 0; i < size; i++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(n_vec[i]) >= value_of(N_vec[i])) {
return operands_and_partials.to_var(stan::math::negative_infinity(),
alpha,beta);
}
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return N_dbl = value_of(N_vec[i]);
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
const T_partials_return beta_dbl = value_of(beta_vec[i]);
const T_partials_return mu = alpha_dbl + n_dbl + 1;
const T_partials_return nu = beta_dbl + N_dbl - n_dbl - 1;
const T_partials_return F = stan::math::F32((T_partials_return)1, mu,
-N_dbl + n_dbl + 1,
n_dbl + 2, 1 - nu,
(T_partials_return)1);
T_partials_return C = lgamma(nu) - lgamma(N_dbl - n_dbl);
C += lgamma(mu) - lgamma(n_dbl + 2);
C += lgamma(N_dbl + 2) - lgamma(N_dbl + alpha_dbl + beta_dbl);
C = exp(C);
C *= F / exp(lbeta(alpha_dbl, beta_dbl));
C /= N_dbl + 1;
const T_partials_return Pi = C;
P += log(Pi);
T_partials_return dF[6];
T_partials_return digammaOne = 0;
T_partials_return digammaTwo = 0;
if (contains_nonconstant_struct<T_size1,T_size2>::value) {
digammaOne = digamma(mu + nu);
digammaTwo = digamma(alpha_dbl + beta_dbl);
stan::math::grad_F32(dF, (T_partials_return)1, mu, -N_dbl + n_dbl + 1,
n_dbl + 2, 1 - nu, (T_partials_return)1);
}
if (!is_constant_struct<T_size1>::value) {
const T_partials_return g
= - C * (digamma(mu) - digammaOne + dF[1] / F
- digamma(alpha_dbl) + digammaTwo);
operands_and_partials.d_x1[i] -= g / Pi;
}
if (!is_constant_struct<T_size2>::value) {
const T_partials_return g
= - C * (digamma(nu) - digammaOne - dF[4] / F - digamma(beta_dbl)
+ digammaTwo);
operands_and_partials.d_x2[i] -= g / Pi;
}
}
return operands_and_partials.to_var(P,alpha,beta);
}
int vectester(const PairScalars& example)
{
using std::abs;
using std::exp;
typedef typename Antioch::value_type<PairScalars>::type Scalar;
const Scalar Cf = 1.4;
const Scalar D = -2.5;
Antioch::BerthelotRate<Scalar> berthelot_rate(Cf,D);
// Construct from example to avoid resizing issues
PairScalars T = example;
T[0] = 1500.1;
T[1] = 1600.1;
const Scalar rate_exact0 = Cf*exp(D*1500.1);
const Scalar rate_exact1 = Cf*exp(D*1600.1);
const Scalar derive_exact0 = D * Cf * exp(D*Scalar(1500.1));
const Scalar derive_exact1 = D * Cf * exp(D*Scalar(1600.1));
int return_flag = 0;
const PairScalars rate = berthelot_rate(T);
const PairScalars deriveRate = berthelot_rate.derivative(T);
const Scalar tol = std::numeric_limits<Scalar>::epsilon()*10;
if( abs( (rate[0] - rate_exact0)/rate_exact0 ) > tol )
{
std::cout << "Error: Mismatch in rate values." << std::endl
<< "rate(T0) = " << rate[0] << std::endl
<< "rate_exact = " << rate_exact0 << std::endl
<< "difference = " << rate[0] - rate_exact0 << std::endl;
return_flag = 1;
}
if( abs( (rate[1] - rate_exact1)/rate_exact1 ) > tol )
{
std::cout << "Error: Mismatch in rate values." << std::endl
<< "rate(T1) = " << rate[1] << std::endl
<< "rate_exact = " << rate_exact1 << std::endl
<< "difference = " << rate[1] - rate_exact1 << std::endl;
return_flag = 1;
}
if( abs( (deriveRate[0] - derive_exact0)/derive_exact0 ) > tol )
{
std::cout << std::scientific << std::setprecision(16)
<< "Error: Mismatch in rate derivative values." << std::endl
<< "drate_dT(T0) = " << deriveRate[0] << std::endl
<< "derive_exact = " << derive_exact0 << std::endl;
return_flag = 1;
}
if( abs( (deriveRate[1] - derive_exact1)/derive_exact1 ) > tol )
{
std::cout << std::scientific << std::setprecision(16)
<< "Error: Mismatch in rate derivative values." << std::endl
<< "drate_dT(T1) = " << deriveRate[1] << std::endl
<< "derive_exact = " << derive_exact1 << std::endl;
return_flag = 1;
}
std::cout << "Berthelot rate: " << berthelot_rate << std::endl;
return return_flag;
}
typename return_type<T_y, T_loc, T_scale>::type
normal_ccdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
static const char* function("stan::math::normal_ccdf_log");
typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
T_partials_return;
using stan::math::check_positive;
using stan::math::check_finite;
using stan::math::check_not_nan;
using stan::math::check_consistent_sizes;
using stan::math::value_of;
using stan::math::INV_SQRT_2;
using std::log;
using std::exp;
T_partials_return ccdf_log(0.0);
// check if any vectors are zero length
if (!(stan::length(y)
&& stan::length(mu)
&& stan::length(sigma)))
return ccdf_log;
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_not_nan(function, "Scale parameter", sigma);
check_positive(function, "Scale parameter", sigma);
check_consistent_sizes(function,
"Random variable", y,
"Location parameter", mu,
"Scale parameter", sigma);
OperandsAndPartials<T_y, T_loc, T_scale>
operands_and_partials(y, mu, sigma);
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
size_t N = max_size(y, mu, sigma);
double log_half = std::log(0.5);
const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return scaled_diff = (y_dbl - mu_dbl)
/ (sigma_dbl * SQRT_2);
T_partials_return one_m_erf;
if (scaled_diff < -37.5 * INV_SQRT_2)
one_m_erf = 2.0;
else if (scaled_diff < -5.0 * INV_SQRT_2)
one_m_erf = 2.0 - erfc(-scaled_diff);
else if (scaled_diff > 8.25 * INV_SQRT_2)
one_m_erf = 0.0;
else
one_m_erf = 1.0 - erf(scaled_diff);
// log ccdf
ccdf_log += log_half + log(one_m_erf);
// gradients
if (contains_nonconstant_struct<T_y, T_loc, T_scale>::value) {
const T_partials_return rep_deriv_div_sigma
= scaled_diff > 8.25 * INV_SQRT_2
? std::numeric_limits<double>::infinity()
: SQRT_TWO_OVER_PI * exp(-scaled_diff * scaled_diff)
/ one_m_erf / sigma_dbl;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= rep_deriv_div_sigma;
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n] += rep_deriv_div_sigma;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] += rep_deriv_div_sigma
* scaled_diff * stan::math::SQRT_2;
}
}
return operands_and_partials.value(ccdf_log);
}
typename return_type<T_y, T_scale, T_shape>::type
pareto_ccdf_log(const T_y& y, const T_scale& y_min,
const T_shape& alpha) {
typedef typename stan::partials_return_type<T_y, T_scale, T_shape>::type
T_partials_return;
// Size checks
if ( !( stan::length(y) && stan::length(y_min) && stan::length(alpha) ) )
return 0.0;
// Check errors
static const char* function("stan::math::pareto_ccdf_log");
using stan::math::check_positive_finite;
using stan::math::check_not_nan;
using stan::math::check_greater_or_equal;
using stan::math::check_consistent_sizes;
using stan::math::check_nonnegative;
using stan::math::value_of;
using std::log;
using std::exp;
T_partials_return P(0.0);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_positive_finite(function, "Scale parameter", y_min);
check_positive_finite(function, "Shape parameter", alpha);
check_consistent_sizes(function,
"Random variable", y,
"Scale parameter", y_min,
"Shape parameter", alpha);
// Wrap arguments in vectors
VectorView<const T_y> y_vec(y);
VectorView<const T_scale> y_min_vec(y_min);
VectorView<const T_shape> alpha_vec(alpha);
size_t N = max_size(y, y_min, alpha);
OperandsAndPartials<T_y, T_scale, T_shape>
operands_and_partials(y, y_min, alpha);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) < value_of(y_min_vec[i]))
return operands_and_partials.to_var(0.0, y, y_min, alpha);
}
// Compute vectorized cdf_log and its gradients
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
return operands_and_partials.to_var(stan::math::negative_infinity(),
y, y_min, alpha);
}
// Pull out values
const T_partials_return log_dbl = log(value_of(y_min_vec[n])
/ value_of(y_vec[n]));
const T_partials_return y_min_inv_dbl = 1.0 / value_of(y_min_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
P += alpha_dbl * log_dbl;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= alpha_dbl * y_min_inv_dbl
* exp(log_dbl);
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x2[n] += alpha_dbl * y_min_inv_dbl;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x3[n] += log_dbl;
}
return operands_and_partials.to_var(P, y, y_min, alpha);
}
typename return_type<T_y, T_loc, T_scale>::type
double_exponential_cdf(const T_y& y,
const T_loc& mu, const T_scale& sigma) {
static const char* function("stan::math::double_exponential_cdf");
typedef typename stan::partials_return_type<T_y, T_loc, T_scale>::type
T_partials_return;
// Size checks
if ( !( stan::length(y) && stan::length(mu)
&& stan::length(sigma) ) )
return 1.0;
using stan::math::value_of;
using stan::math::check_finite;
using stan::math::check_positive_finite;
using stan::math::check_not_nan;
using boost::math::tools::promote_args;
using std::exp;
T_partials_return cdf(1.0);
check_not_nan(function, "Random variable", y);
check_finite(function, "Location parameter", mu);
check_positive_finite(function, "Scale parameter", sigma);
OperandsAndPartials<T_y, T_loc, T_scale>
operands_and_partials(y, mu, sigma);
VectorView<const T_y> y_vec(y);
VectorView<const T_loc> mu_vec(mu);
VectorView<const T_scale> sigma_vec(sigma);
size_t N = max_size(y, mu, sigma);
// cdf
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
const T_partials_return exp_scaled_diff = exp(scaled_diff);
if (y_dbl < mu_dbl)
cdf *= exp_scaled_diff * 0.5;
else
cdf *= 1.0 - 0.5 / exp_scaled_diff;
}
// gradients
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return mu_dbl = value_of(mu_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
const T_partials_return exp_scaled_diff = exp(scaled_diff);
const T_partials_return inv_sigma = 1.0 / sigma_dbl;
if (y_dbl < mu_dbl) {
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += inv_sigma * cdf;
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n] -= inv_sigma * cdf;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] -= scaled_diff * inv_sigma * cdf;
} else {
const T_partials_return rep_deriv = cdf * inv_sigma
/ (2.0 * exp_scaled_diff - 1.0);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += rep_deriv;
if (!is_constant_struct<T_loc>::value)
operands_and_partials.d_x2[n] -= rep_deriv;
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff;
}
}
return operands_and_partials.value(cdf);
}
typename return_type<T_y, T_shape, T_scale>::type
weibull_cdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
typedef typename stan::partials_return_type<T_y, T_shape, T_scale>::type
T_partials_return;
static const char* function("stan::math::weibull_cdf");
using stan::math::check_positive_finite;
using stan::math::check_nonnegative;
using boost::math::tools::promote_args;
using stan::math::value_of;
using std::log;
using std::exp;
// check if any vectors are zero length
if (!(stan::length(y)
&& stan::length(alpha)
&& stan::length(sigma)))
return 1.0;
T_partials_return cdf(1.0);
check_nonnegative(function, "Random variable", y);
check_positive_finite(function, "Shape parameter", alpha);
check_positive_finite(function, "Scale parameter", sigma);
OperandsAndPartials<T_y, T_shape, T_scale>
operands_and_partials(y, alpha, sigma);
VectorView<const T_y> y_vec(y);
VectorView<const T_scale> sigma_vec(sigma);
VectorView<const T_shape> alpha_vec(alpha);
size_t N = max_size(y, sigma, alpha);
for (size_t n = 0; n < N; n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return pow_ = pow(y_dbl / sigma_dbl, alpha_dbl);
const T_partials_return exp_ = exp(-pow_);
const T_partials_return cdf_ = 1.0 - exp_;
// cdf
cdf *= cdf_;
// gradients
const T_partials_return rep_deriv = exp_ * pow_ / cdf_;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += rep_deriv * alpha_dbl / y_dbl;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x2[n] += rep_deriv * log(y_dbl / sigma_dbl);
if (!is_constant_struct<T_scale>::value)
operands_and_partials.d_x3[n] -= rep_deriv * alpha_dbl / sigma_dbl;
}
if (!is_constant_struct<T_y>::value) {
for (size_t n = 0; n < stan::length(y); ++n)
operands_and_partials.d_x1[n] *= cdf;
}
if (!is_constant_struct<T_shape>::value) {
for (size_t n = 0; n < stan::length(alpha); ++n)
operands_and_partials.d_x2[n] *= cdf;
}
if (!is_constant_struct<T_scale>::value) {
for (size_t n = 0; n < stan::length(sigma); ++n)
operands_and_partials.d_x3[n] *= cdf;
}
return operands_and_partials.to_var(cdf, y, alpha, sigma);
}
typename return_type<T_y, T_shape, T_inv_scale>::type
gamma_ccdf_log(const T_y& y, const T_shape& alpha,
const T_inv_scale& beta) {
if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
return 0.0;
typedef typename stan::partials_return_type<T_y, T_shape,
T_inv_scale>::type
T_partials_return;
static const char* function("gamma_ccdf_log");
using boost::math::tools::promote_args;
using std::exp;
T_partials_return P(0.0);
check_positive_finite(function, "Shape parameter", alpha);
check_positive_finite(function, "Scale parameter", beta);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_consistent_sizes(function,
"Random variable", y,
"Shape parameter", alpha,
"Scale Parameter", beta);
VectorView<const T_y> y_vec(y);
VectorView<const T_shape> alpha_vec(alpha);
VectorView<const T_inv_scale> beta_vec(beta);
size_t N = max_size(y, alpha, beta);
OperandsAndPartials<T_y, T_shape, T_inv_scale>
operands_and_partials(y, alpha, beta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) == 0)
return operands_and_partials.value(0.0);
}
using boost::math::tgamma;
using std::exp;
using std::pow;
using std::log;
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape> gamma_vec(stan::length(alpha));
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape>
digamma_vec(stan::length(alpha));
if (!is_constant_struct<T_shape>::value) {
for (size_t i = 0; i < stan::length(alpha); i++) {
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
gamma_vec[i] = tgamma(alpha_dbl);
digamma_vec[i] = digamma(alpha_dbl);
}
}
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
return operands_and_partials.value(negative_infinity());
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return beta_dbl = value_of(beta_vec[n]);
const T_partials_return Pn = gamma_q(alpha_dbl, beta_dbl * y_dbl);
P += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] -= beta_dbl * exp(-beta_dbl * y_dbl)
* pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x2[n]
+= grad_reg_inc_gamma(alpha_dbl, beta_dbl
* y_dbl, gamma_vec[n],
digamma_vec[n]) / Pn;
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x3[n] -= y_dbl * exp(-beta_dbl * y_dbl)
* pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
}
return operands_and_partials.value(P);
}
typename return_type<T_log_rate>::type
poisson_log_log(const T_n& n, const T_log_rate& alpha) {
typedef typename stan::partials_return_type<T_n,T_log_rate>::type
T_partials_return;
static const char* function("stan::prob::poisson_log_log");
using boost::math::lgamma;
using stan::math::check_not_nan;
using stan::math::check_nonnegative;
using stan::math::value_of;
using stan::math::check_consistent_sizes;
using stan::prob::include_summand;
using std::exp;
// check if any vectors are zero length
if (!(stan::length(n)
&& stan::length(alpha)))
return 0.0;
// set up return value accumulator
T_partials_return logp(0.0);
// validate args
check_nonnegative(function, "Random variable", n);
check_not_nan(function, "Log rate parameter", alpha);
check_consistent_sizes(function,
"Random variable", n,
"Log rate parameter", alpha);
// check if no variables are involved and prop-to
if (!include_summand<propto,T_log_rate>::value)
return 0.0;
// set up expression templates wrapping scalars/vecs into vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_log_rate> alpha_vec(alpha);
size_t size = max_size(n, alpha);
// FIXME: first loop size of alpha_vec, second loop if-ed for size==1
for (size_t i = 0; i < size; i++)
if (std::numeric_limits<double>::infinity() == alpha_vec[i])
return LOG_ZERO;
for (size_t i = 0; i < size; i++)
if (-std::numeric_limits<double>::infinity() == alpha_vec[i]
&& n_vec[i] != 0)
return LOG_ZERO;
// return accumulator with gradients
agrad::OperandsAndPartials<T_log_rate> operands_and_partials(alpha);
// FIXME: cache value_of for alpha_vec? faster if only one?
VectorBuilder<include_summand<propto,T_log_rate>::value,
T_partials_return, T_log_rate>
exp_alpha(length(alpha));
for (size_t i = 0; i < length(alpha); i++)
if (include_summand<propto,T_log_rate>::value)
exp_alpha[i] = exp(value_of(alpha_vec[i]));
using stan::math::multiply_log;
for (size_t i = 0; i < size; i++) {
if (!(alpha_vec[i] == -std::numeric_limits<double>::infinity()
&& n_vec[i] == 0)) {
if (include_summand<propto>::value)
logp -= lgamma(n_vec[i] + 1.0);
if (include_summand<propto,T_log_rate>::value)
logp += n_vec[i] * value_of(alpha_vec[i]) - exp_alpha[i];
}
// gradients
if (!is_constant_struct<T_log_rate>::value)
operands_and_partials.d_x1[i] += n_vec[i] - exp_alpha[i];
}
return operands_and_partials.to_var(logp,alpha);
}
typename return_type<T_rate>::type
poisson_cdf_log(const T_n& n, const T_rate& lambda) {
static const char* function("stan::prob::poisson_cdf_log");
typedef typename stan::partials_return_type<T_n,T_rate>::type
T_partials_return;
using stan::math::check_not_nan;
using stan::math::check_nonnegative;
using stan::math::value_of;
using stan::math::check_consistent_sizes;
// Ensure non-zero argument slengths
if (!(stan::length(n) && stan::length(lambda)))
return 0.0;
T_partials_return P(0.0);
// Validate arguments
check_not_nan(function, "Rate parameter", lambda);
check_nonnegative(function, "Rate parameter", lambda);
check_consistent_sizes(function,
"Random variable", n,
"Rate parameter", lambda);
// Wrap arguments into vector views
VectorView<const T_n> n_vec(n);
VectorView<const T_rate> lambda_vec(lambda);
size_t size = max_size(n, lambda);
// Compute vectorized cdf_log and gradient
using stan::math::value_of;
using stan::math::gamma_q;
using boost::math::tgamma;
using std::exp;
using std::pow;
agrad::OperandsAndPartials<T_rate> operands_and_partials(lambda);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as neg infinity
for (size_t i = 0; i < stan::length(n); i++) {
if (value_of(n_vec[i]) < 0)
return operands_and_partials.to_var(stan::math::negative_infinity(),
lambda);
}
for (size_t i = 0; i < size; i++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(n_vec[i]) == std::numeric_limits<int>::max())
continue;
const T_partials_return n_dbl = value_of(n_vec[i]);
const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
const T_partials_return Pi = gamma_q(n_dbl+1, lambda_dbl);
P += log(Pi);
if (!is_constant_struct<T_rate>::value)
operands_and_partials.d_x1[i] -= exp(-lambda_dbl)
* pow(lambda_dbl,n_dbl) / tgamma(n_dbl+1) / Pi;
}
return operands_and_partials.to_var(P,lambda);
}