inline Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic>
wishart_rng(const double nu,
const Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic>& S,
RNG& rng) {
static const char* function = "stan::prob::wishart_rng(%1%)";
using stan::math::check_size_match;
using stan::math::check_positive;
check_positive(function,nu,"degrees of freedom",(double*)0);
check_size_match(function,
S.rows(), "Rows of scale parameter",
S.cols(), "columns of scale parameter",
(double*)0);
Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic> B(S.rows(), S.cols());
B.setZero();
for(int i = 0; i < S.cols(); i++) {
B(i,i) = std::sqrt(chi_square_rng(nu - i, rng));
for(int j = 0; j < i; j++)
B(j,i) = normal_rng(0,1,rng);
}
return stan::math::multiply_lower_tri_self_transpose(S.llt().matrixL() * B);
}
inline Eigen::Matrix<typename return_type<T1, T2>::type,
Eigen::Dynamic, Eigen::Dynamic>
append_col(const Eigen::Matrix<T1, R1, C1>& A,
const Eigen::Matrix<T2, R2, C2>& B) {
using Eigen::Dynamic;
using Eigen::Matrix;
using stan::math::check_size_match;
int Arows = A.rows();
int Brows = B.rows();
int Acols = A.cols();
int Bcols = B.cols();
check_size_match("append_col",
"rows of A", Arows,
"rows of B", Brows);
Matrix<typename return_type<T1, T2>::type, Dynamic, Dynamic>
result(Arows, Acols+Bcols);
for (int j = 0; j < Acols; j++)
for (int i = 0; i < Arows; i++)
result(i, j) = A(i, j);
for (int j = Acols, k = 0; k < Bcols; j++, k++)
for (int i = 0; i < Arows; i++)
result(i, j) = B(i, k);
return result;
}
inline
Eigen::Matrix<fvar<T>,R1,C2>
mdivide_right(const Eigen::Matrix<fvar<T>,R1,C1> &A,
const Eigen::Matrix<double,R2,C2> &b) {
using stan::math::multiply;
using stan::math::mdivide_right;
stan::math::check_square("mdivide_right(%1%)",b,"b",(double*)0);
stan::math::check_multiplicable("mdivide_right(%1%)",A,"A",
b,"b",(double*)0);
Eigen::Matrix<T,R2,C2> deriv_b_mult_inv_b(b.rows(),b.cols());
Eigen::Matrix<T,R1,C1> val_A(A.rows(),A.cols());
Eigen::Matrix<T,R1,C1> deriv_A(A.rows(),A.cols());
for (int j = 0; j < A.cols(); j++) {
for(int i = 0; i < A.rows(); i++) {
val_A(i,j) = A(i,j).val_;
deriv_A(i,j) = A(i,j).d_;
}
}
return stan::agrad::to_fvar(mdivide_right(val_A, b),
mdivide_right(deriv_A, b));
}
inline bool check_corr_matrix(const char* function,
const Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>& y,
const char* name,
T_result* result,
const Policy&) {
if (!check_size_match(function,
y.rows(), "Rows of correlation matrix",
y.cols(), "columns of correlation matrix",
result, Policy()))
return false;
if (!check_positive(function, y.rows(), "rows", result, Policy()))
return false;
if (!check_symmetric(function, y, "y", result, Policy()))
return false;
for (typename Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>::size_type
k = 0; k < y.rows(); ++k) {
if (fabs(y(k,k) - 1.0) > CONSTRAINT_TOLERANCE) {
std::ostringstream message;
message << name << " is not a valid correlation matrix. "
<< name << "(" << k << "," << k
<< ") is %1%, but should be near 1.0";
T_result tmp
= policies::raise_domain_error<T_y>(function,
message.str().c_str(),
y(k,k), Policy());
if (result != 0)
*result = tmp;
return false;
}
}
if (!check_pos_definite(function, y, "y", result, Policy()))
return false;
return true;
}
inline
fvar<T>
determinant(const Eigen::Matrix<fvar<T>, R, C>& m) {
using stan::math::multiply;
using stan::math::inverse;
stan::math::check_square("determinant", "m", m);
Eigen::Matrix<T,R,C> m_deriv(m.rows(), m.cols());
Eigen::Matrix<T,R,C> m_val(m.rows(), m.cols());
for(size_type i = 0; i < m.rows(); i++) {
for(size_type j = 0; j < m.cols(); j++) {
m_deriv(i,j) = m(i,j).d_;
m_val(i,j) = m(i,j).val_;
}
}
Eigen::Matrix<T,R,C> m_inv = inverse<T>(m_val);
m_deriv = multiply(m_inv, m_deriv);
fvar<T> result;
result.val_ = m_val.determinant();
result.d_ = result.val_ * m_deriv.trace();
// FIXME: I think this will overcopy compared to retur fvar<T>(...);
return result;
}
inline int
categorical_rng(const Eigen::Matrix<double, Eigen::Dynamic, 1>& theta,
RNG& rng) {
using boost::variate_generator;
using boost::uniform_01;
static const char* function("categorical_rng");
check_simplex(function, "Probabilities parameter", theta);
variate_generator<RNG&, uniform_01<> >
uniform01_rng(rng, uniform_01<>());
Eigen::VectorXd index(theta.rows());
index.setZero();
for (int i = 0; i < theta.rows(); i++) {
for (int j = i; j < theta.rows(); j++)
index(j) += theta(i, 0);
}
double c = uniform01_rng();
int b = 0;
while (c > index(b, 0))
b++;
return b + 1;
}
typename boost::math::tools::promote_args<T_prob,T_prior_sample_size>::type
dirichlet_log(const Eigen::Matrix<T_prob,Eigen::Dynamic,1>& theta,
const Eigen::Matrix<T_prior_sample_size,Eigen::Dynamic,1>& alpha) {
static const char* function = "stan::prob::dirichlet_log(%1%)";
using boost::math::lgamma;
using boost::math::tools::promote_args;
using stan::math::check_consistent_sizes;
using stan::math::check_positive;
using stan::math::check_simplex;
using stan::math::multiply_log;
typename promote_args<T_prob,T_prior_sample_size>::type lp(0.0);
check_consistent_sizes(function, theta, alpha,
"probabilities", "prior sample sizes",
&lp);
check_positive(function, alpha, "prior sample sizes", &lp);
check_simplex(function, theta, "probabilities", &lp);
if (include_summand<propto,T_prior_sample_size>::value) {
lp += lgamma(alpha.sum());
for (int k = 0; k < alpha.rows(); ++k)
lp -= lgamma(alpha[k]);
}
if (include_summand<propto,T_prob,T_prior_sample_size>::value)
for (int k = 0; k < theta.rows(); ++k)
lp += multiply_log(alpha[k]-1, theta[k]);
return lp;
}
inline typename
boost::disable_if_c<boost::is_same<I1, index_uni>::value
|| boost::is_same<I2, index_uni>::value, void>::type
assign(Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>& x,
const cons_index_list<I1,
cons_index_list<I2, nil_index_list> >& idxs,
const Eigen::Matrix<U, Eigen::Dynamic, Eigen::Dynamic>& y,
const char* name = "ANON", int depth = 0) {
int x_idxs_rows = rvalue_index_size(idxs.head_, x.rows());
int x_idxs_cols = rvalue_index_size(idxs.tail_.head_, x.cols());
math::check_size_match("matrix[multi,multi] assign sizes",
"lhs", x_idxs_rows,
name, y.rows());
math::check_size_match("matrix[multi,multi] assign sizes",
"lhs", x_idxs_cols,
name, y.cols());
for (int j = 0; j < y.cols(); ++j) {
int n = rvalue_at(j, idxs.tail_.head_);
math::check_range("matrix[multi,multi] assign range", name,
x.cols(), n);
for (int i = 0; i < y.rows(); ++i) {
int m = rvalue_at(i, idxs.head_);
math::check_range("matrix[multi,multi] assign range", name,
x.rows(), m);
x(m - 1, n - 1) = y(i, j);
}
}
}
inline bool check_corr_matrix(const std::string& function,
const std::string& name,
const Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>& y) {
using Eigen::Dynamic;
using Eigen::Matrix;
using stan::math::index_type;
typedef typename index_type<Matrix<T_y,Dynamic,Dynamic> >::type size_t;
check_size_match(function,
"Rows of correlation matrix", y.rows(),
"columns of correlation matrix", y.cols());
check_positive(function, "rows", y.rows());
check_symmetric(function, "y", y);
for (size_t k = 0; k < y.rows(); ++k) {
if (!(fabs(y(k,k) - 1.0) <= CONSTRAINT_TOLERANCE)) {
std::ostringstream msg;
msg << "is not a valid correlation matrix. "
<< name << "(" << stan::error_index::value + k
<< "," << stan::error_index::value + k
<< ") is "; ;
dom_err(function, name, y(k,k),
msg.str(),
", but should be near 1.0");
return false;
}
}
stan::error_handling::check_pos_definite(function, "y", y);
return true;
}
void expect_matrix_eq(const Eigen::Matrix<T1,Eigen::Dynamic,Eigen::Dynamic>& a,
const Eigen::Matrix<T2,Eigen::Dynamic,Eigen::Dynamic>& b) {
EXPECT_EQ(a.rows(), b.rows());
EXPECT_EQ(a.cols(), b.cols());
for (int i = 0; i < a.rows(); ++i)
for (int j = 0; j < a.cols(); ++j)
EXPECT_FLOAT_EQ(value_of(a(i,j)), value_of(b(i,j)));
}
void vector_test(const Eigen::Matrix<Real, NbRows, NbCols>& A, const Eigen::Matrix<Real, NbRows, NbCols>& B, Accumulator& Result)
{
for(int i = 0, k = 0; i != A.rows() && k != B.rows(); ++i, ++k)
for(int j = 0, l = 0; j != A.cols() && l != B.cols(); ++j, ++l)
test(A(i, j), B(k, l), Result);
Result.exact(A.rows() == B.rows() && A.cols() == B.cols());
};
inline Eigen::Matrix<fvar<T>,R,1>
rows_dot_self(const Eigen::Matrix<fvar<T>,R,C>& x) {
Eigen::Matrix<fvar<T>,R,1> ret(x.rows(),1);
for (size_type i = 0; i < x.rows(); i++) {
Eigen::Matrix<fvar<T>,1,C> crow = x.row(i);
ret(i,0) = dot_self(crow);
}
return ret;
}
inline Eigen::Matrix<fvar<T>,R,C>
divide(const Eigen::Matrix<fvar<T>, R,C>& v, const fvar<T>& c) {
Eigen::Matrix<fvar<T>,R,C> res(v.rows(),v.cols());
for(int i = 0; i < v.rows(); i++) {
for(int j = 0; j < v.cols(); j++)
res(i,j) = v(i,j) / c;
}
return res;
}
inline Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R,C>
divide(const Eigen::Matrix<T1, R,C>& v, const fvar<T2>& c) {
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R,C> res(v.rows(),v.cols());
for(int i = 0; i < v.rows(); i++) {
for(int j = 0; j < v.cols(); j++)
res(i,j) = to_fvar(v(i,j)) / c;
}
return res;
}
inline
Eigen::Matrix<fvar<T>,R1,C1>
multiply(const Eigen::Matrix<fvar<T>, R1, C1>& m, const fvar<T>& c) {
Eigen::Matrix<fvar<T>,R1,C1> res(m.rows(),m.cols());
for(int i = 0; i < m.rows(); i++) {
for(int j = 0; j < m.cols(); j++)
res(i,j) = c * m(i,j);
}
return res;
}
inline Eigen::Matrix<double, R1, 1>
rows_dot_product(const Eigen::Matrix<double, R1, C1>& v1,
const Eigen::Matrix<double, R2, C2>& v2) {
validate_matching_sizes(v1,v2,"rows_dot_product");
Eigen::Matrix<double, R1, 1> ret(v1.rows(),1);
for (size_type j = 0; j < v1.rows(); ++j) {
ret(j) = v1.row(j).dot(v2.row(j));
}
return ret;
}
inline
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>, R2, C2>
multiply(const Eigen::Matrix<fvar<T1>, R2, C2>& m, const T2& c) {
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R2,C2> res(m.rows(),m.cols());
for(int i = 0; i < m.rows(); i++) {
for(int j = 0; j < m.cols(); j++)
res(i,j) = to_fvar(c) * m(i,j);
}
return res;
}
void validate_row_index(const Eigen::Matrix<T,R,C>& m,
size_t i,
const char* msg) {
if (i > 0 && i <= static_cast<size_t>(m.rows())) return;
std::stringstream ss;
ss << "require 0 < row index <= number of rows in" << msg;
ss << " found rows()=" << m.rows()
<< "; index i=" << i;
throw std::domain_error(ss.str());
}
inline
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R1,C1>
multiply(const Eigen::Matrix<T1, R1, C1>& m, const fvar<T2>& c) {
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R1,C1> res(m.rows(),m.cols());
for(int i = 0; i < m.rows(); i++) {
for(int j = 0; j < m.cols(); j++)
res(i,j) = c * to_fvar(m(i,j));
}
return res;
}
inline bool check_cov_matrix(const std::string& function,
const std::string& name,
const Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>& y) {
check_size_match(function,
"Rows of covariance matrix", y.rows(),
"columns of covariance matrix", y.cols());
check_positive(function, "rows", y.rows());
check_symmetric(function, name, y);
check_pos_definite(function, name, y);
return true;
}
inline
Eigen::Matrix<T,Eigen::Dynamic,1>
segment(const Eigen::Matrix<T,Eigen::Dynamic,1>& v,
size_t i, size_t n) {
stan::math::check_greater("segment(%1%)",i,0.0,"n",(double*)0);
stan::math::check_less_or_equal("segment(%1%)",i,static_cast<size_t>(v.rows()),"n",(double*)0);
if (n != 0) {
stan::math::check_greater("segment(%1%)",i+n-1,0.0,"n",(double*)0);
stan::math::check_less_or_equal("segment(%1%)",i+n-1,static_cast<size_t>(v.rows()),"n",(double*)0);
}
return v.segment(i-1,n);
}
Eigen::Matrix<fvar<T>,Eigen::Dynamic,Eigen::Dynamic>
qr_Q(const Eigen::Matrix<fvar<T>,Eigen::Dynamic,Eigen::Dynamic>& m) {
typedef Eigen::Matrix<fvar<T>,Eigen::Dynamic,Eigen::Dynamic> matrix_fwd_t;
stan::math::check_nonzero_size("qr_Q", "m", m);
stan::math::check_greater_or_equal("qr_Q", "m.rows()", m.rows(), m.cols());
Eigen::HouseholderQR< matrix_fwd_t > qr(m.rows(), m.cols());
qr.compute(m);
matrix_fwd_t Q = qr.householderQ();
for (int i=0; i<m.cols(); i++)
if (qr.matrixQR()(i,i) < 0.0)
Q.col(i) *= -1.0;
return Q;
}
inline bool check_cov_matrix(const char* function,
const Eigen::Matrix<T_y,Eigen::Dynamic,Eigen::Dynamic>& y,
const char* name,
T_result* result) {
check_size_match(function,
y.rows(), "Rows of covariance matrix",
y.cols(), "columns of covariance matrix",
result);
check_positive(function, y.rows(), "rows", result);
check_symmetric(function, y, name, result);
check_pos_definite(function, y, name, result);
return true;
}
std::string Gaussian<ScalarType>::toJSONString(bool styledWriter) const
{
DEBUG_OUT("saving gaussian as JSON", 40);
//uses Jsoncpp as library. Jsoncpp is licensed as MIT, so we may use it without restriction.
Json::Value root;
Json::Writer* writer=NULL;
if (styledWriter)
writer = new Json::StyledWriter();
else
writer = new Json::FastWriter();
//output the weight
root["weight"] = getWeight();
//output the mean as array of doubles
Json::Value mean(Json::arrayValue);
Eigen::Matrix<ScalarType, Eigen::Dynamic, 1> gMean = getMean();
for (int i=0; i<gMean.size(); i++)
mean.append(Json::Value(gMean[i]));
root["mean"] = mean;
//output the variance as array of double. only save the lower
//triangular, as the other values are mirrored.
Json::Value variance(Json::arrayValue);
Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic> gVariance = getCovarianceMatrix();
if (isDiagonal(gVariance))
{
DEBUG_OUT("save as diagonal covariance matrix", 45);
for (int i=0; i<gVariance.rows(); i++)
{
variance.append(Json::Value(gVariance(i, i)));
}
}
else
{
DEBUG_OUT("save as full covariance matrix", 45);
for (int i=0; i<gVariance.rows(); i++)
{
for (int j=i; j<gVariance.cols(); j++)
{
variance.append(Json::Value(gVariance(i, j)));
}
}
}
root["covariance"] = variance;
std::string str = writer->write(root);
delete writer;
return str;
}
inline var log_determinant_spd(const Eigen::Matrix<var,R,C>& m) {
using stan::math::domain_error;
using Eigen::Matrix;
math::check_square("log_determinant_spd", "m", m);
Matrix<double,R,C> m_d(m.rows(),m.cols());
for (int i = 0; i < m.size(); ++i)
m_d(i) = m(i).val();
Eigen::LDLT<Matrix<double,R,C> > ldlt(m_d);
if (ldlt.info() != Eigen::Success) {
double y = 0;
domain_error("log_determinant_spd",
"matrix argument", y,
"failed LDLT factorization");
}
// compute the inverse of A (needed for the derivative)
m_d.setIdentity(m.rows(), m.cols());
ldlt.solveInPlace(m_d);
if (ldlt.isNegative() || (ldlt.vectorD().array() <= 1e-16).any()) {
double y = 0;
domain_error("log_determinant_spd",
"matrix argument", y,
"matrix is negative definite");
}
double val = ldlt.vectorD().array().log().sum();
if (!boost::math::isfinite(val)) {
double y = 0;
domain_error("log_determinant_spd",
"matrix argument", y,
"log determininant is infinite");
}
vari** operands = ChainableStack::memalloc_
.alloc_array<vari*>(m.size());
for (int i = 0; i < m.size(); ++i)
operands[i] = m(i).vi_;
double* gradients = ChainableStack::memalloc_
.alloc_array<double>(m.size());
for (int i = 0; i < m.size(); ++i)
gradients[i] = m_d(i);
return var(new precomputed_gradients_vari(val,m.size(),operands,gradients));
}
inline void check_pos_definite(const char* function, const char* name,
const Eigen::Matrix<T_y, -1, -1>& y) {
check_symmetric(function, name, y);
check_positive_size(function, name, "rows", y.rows());
if (y.rows() == 1 && !(y(0, 0) > CONSTRAINT_TOLERANCE))
domain_error(function, name, "is not positive definite.", "");
Eigen::LDLT<Eigen::MatrixXd> cholesky = value_of_rec(y).ldlt();
if (cholesky.info() != Eigen::Success
|| !cholesky.isPositive()
|| (cholesky.vectorD().array() <= 0.0).any())
domain_error(function, name, "is not positive definite.", "");
check_not_nan(function, name, y);
}
inline Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>
append_col(const Eigen::Matrix<T, R1, C1>& A,
const Eigen::Matrix<T, R2, C2>& B) {
using Eigen::Matrix;
using Eigen::Dynamic;
check_size_match("append_col",
"rows of A", A.rows(),
"rows of B", B.rows());
Matrix<T, Dynamic, Dynamic> result(A.rows(), A.cols()+B.cols());
result << A, B;
return result;
}
inline
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R1,C2>
multiply(const Eigen::Matrix<fvar<T1>,R1,C1>& m1,
const Eigen::Matrix<T2,R2,C2>& m2) {
stan::math::validate_multiplicable(m1,m2,"multiply");
Eigen::Matrix<fvar<typename stan::return_type<T1,T2>::type>,R1,C2> result(m1.rows(),m2.cols());
for (size_type i = 0; i < m1.rows(); i++) {
Eigen::Matrix<fvar<T1>,1,C1> crow = m1.row(i);
for (size_type j = 0; j < m2.cols(); j++) {
Eigen::Matrix<T2,R2,1> ccol = m2.col(j);
result(i,j) = stan::agrad::dot_product(crow,ccol);
}
}
return result;
}
void write_stan(const Eigen::Matrix<double,
Eigen::Dynamic,Eigen::Dynamic>& x) {
typedef Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic>::Index Index;
out_ << "structure(c(";
std::vector<double> vals;
for (Index m = 0; m < x.cols(); ++m) {
for (Index n = 0; n < x.rows(); ++n) {
if (m > 0 || n > 0) out_ << ", ";
write_val(x(m,n));
}
}
out_ << "), .Dim = c(";
out_ << x.rows() << ", " << x.cols();
out_ << "))";
}
void eigen2cv( const Eigen::Matrix<_Tp, _rows, _cols, _options, _maxRows, _maxCols>& src, Mat& dst )
{
if( !(src.Flags & Eigen::RowMajorBit) )
{
Mat _src(src.cols(), src.rows(), DataType<_Tp>::type,
(void*)src.data(), src.stride()*sizeof(_Tp));
transpose(_src, dst);
}
else
{
Mat _src(src.rows(), src.cols(), DataType<_Tp>::type,
(void*)src.data(), src.stride()*sizeof(_Tp));
_src.copyTo(dst);
}
}