Matrices and templated mathematical functions. More...

Namespaces
namespace	policies
	Extending boost functionality.

Classes
struct	EigenType
	This is a traits structure for Eigen matrix types. More...

Typedefs
typedef boost::math::policies::policy	default_policy
	Default error-handling policy from Boost.

typedef EigenType< double >::matrix	matrix_d
	Type for matrix of double values.

typedef EigenType< double >::vector	vector_d
	Type for (column) vector of double values.

typedef EigenType< double > ::row_vector	row_vector_d
	Type for (row) vector of double values.

Functions
template<typename T_y , typename T_result , class Policy >
bool	check_not_nan (const char function, const T_y &y, const char name, T_result *result, const Policy &)
	Checks if the variable y is nan.

template<typename T_y , typename T_result >
bool	check_not_nan (const char function, const T_y &y, const char name, T_result *result=0)
	Checks if the variable y is nan.

template<typename T >
bool	check_not_nan (const char function, const T &y, const char name)

template<typename T_y , typename T_result , class Policy >
bool	check_finite (const char function, const T_y &y, const char name, T_result *result, const Policy &)
	Checks if the variable y is finite.

template<typename T_y , typename T_result >
bool	check_finite (const char function, const T_y &y, const char name, T_result *result)

template<typename T >
bool	check_finite (const char function, const T &y, const char name)

template<typename T_y , typename T_low , typename T_result , class Policy >
bool	check_greater (const char function, const T_y &y, const T_low &low, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_low , typename T_result >
bool	check_greater (const char function, const T_y &y, const T_low &low, const char name, T_result *result)

template<typename T_y , typename T_low >
bool	check_greater (const char function, const T_y &y, const T_low &low, const char name)

template<typename T_y , typename T_low , typename T_result , class Policy >
bool	check_greater_or_equal (const char function, const T_y &y, const T_low &low, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_low , typename T_result >
bool	check_greater_or_equal (const char function, const T_y &y, const T_low &low, const char name, T_result *result)

template<typename T_y , typename T_low >
bool	check_greater_or_equal (const char function, const T_y &y, const T_low &low, const char name)

template<typename T_y , typename T_high , typename T_result , class Policy >
bool	check_less (const char function, const T_y &y, const T_high &high, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_high , typename T_result >
bool	check_less (const char function, const T_y &y, const T_high &high, const char name, T_result *result)

template<typename T_y , typename T_high >
bool	check_less (const char function, const T_y &y, const T_high &high, const char name)

template<typename T_y , typename T_high , typename T_result , class Policy >
bool	check_less_or_equal (const char function, const T_y &y, const T_high &high, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_high , typename T_result >
bool	check_less_or_equal (const char function, const T_y &y, const T_high &high, const char name, T_result *result)

template<typename T_y , typename T_high >
bool	check_less_or_equal (const char function, const T_y &y, const T_high &high, const char name)

template<typename T_y , typename T_low , typename T_high , typename T_result , class Policy >
bool	check_bounded (const char function, const T_y &y, const T_low &low, const T_high &high, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_low , typename T_high , typename T_result >
bool	check_bounded (const char function, const T_y &y, const T_low &low, const T_high &high, const char name, T_result *result)

template<typename T_y , typename T_low , typename T_high >
bool	check_bounded (const char function, const T_y &y, const T_low &low, const T_high &high, const char name)

template<typename T_y , typename T_result , class Policy >
bool	check_nonnegative (const char function, const T_y &y, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_result >
bool	check_nonnegative (const char function, const T_y &y, const char name, T_result *result)

template<typename T_y >
bool	check_nonnegative (const char function, const T_y &y, const char name)

template<typename T_y , typename T_result , class Policy >
bool	check_positive (const char function, const T_y &y, const char name, T_result *result, const Policy &)

template<typename T_x , typename T_result >
bool	check_positive (const char function, const T_x &x, const char name, T_result *result)

template<typename T >
bool	check_positive (const char function, const T &x, const char name)

template<typename T , typename T_result , class Policy >
bool	check_consistent_size (size_t max_size, const char function, const T &x, const char name, T_result *result, const Policy &)

template<typename T1 , typename T2 , typename T_result , class Policy >
bool	check_consistent_sizes (const char function, const T1 &x1, const T2 &x2, const char name1, const char name2, T_result result, const Policy &)

template<typename T1 , typename T2 , typename T_result >
bool	check_consistent_sizes (const char function, const T1 &x1, const T2 &x2, const char name1, const char name2, T_result result)

template<typename T1 , typename T2 , typename T3 , typename T_result , class Policy >
bool	check_consistent_sizes (const char function, const T1 &x1, const T2 &x2, const T3 &x3, const char name1, const char name2, const char name3, T_result *result, const Policy &)

template<typename T1 , typename T2 , typename T3 , typename T_result >
bool	check_consistent_sizes (const char function, const T1 &x1, const T2 &x2, const T3 &x3, const char name1, const char name2, const char name3, T_result *result)

template<typename T1 , typename T2 , typename T3 , typename T4 , typename T_result , class Policy >
bool	check_consistent_sizes (const char function, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const char name1, const char name2, const char name3, const char name4, T_result result, const Policy &)

template<typename T1 , typename T2 , typename T3 , typename T4 , typename T_result >
bool	check_consistent_sizes (const char function, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const char name1, const char name2, const char name3, const char name4, T_result result)

double	determinant (const matrix_d &m)
	Returns the determinant of the specified square matrix.

vector_d	add (const vector_d &v1, const vector_d &v2)
	Return the sum of the specified column vectors.

row_vector_d	add (const row_vector_d &rv1, const row_vector_d &rv2)
	Return the sum of the specified row vectors.

matrix_d	add (const matrix_d &m1, const matrix_d &m2)
	Return the sum of the specified matrices.

vector_d	subtract (const vector_d &v1, const vector_d &v2)
	Return the difference between the first specified column vector and the second.

row_vector_d	subtract (const row_vector_d &rv1, const row_vector_d &rv2)
	Return the difference between the first specified row vector and the second.

matrix_d	subtract (const matrix_d &m1, const matrix_d &m2)
	Return the difference between the first specified matrix and the second.

vector_d	minus (const vector_d &v)
	Return the negation of the specified column vector.

row_vector_d	minus (const row_vector_d &rv)
	Return the negation of the specified row vector.

matrix_d	minus (const matrix_d &m)
	Return the negation of the specified matrix.

vector_d	divide (const vector_d &v, double c)
	Return the division of the specified column vector by the specified scalar.

row_vector_d	divide (const row_vector_d &rv, double c)
	Return the division of the specified row vector by the specified scalar.

matrix_d	divide (const matrix_d &m, double c)
	Return the division of the specified matrix by the specified scalar.

vector_d	elt_multiply (const vector_d &v1, const vector_d &v2)
	Return the element-wise product of the specified vectors.

row_vector_d	elt_multiply (const row_vector_d &v1, const row_vector_d &v2)
	Return the element-wise product of the specified row vectors.

matrix_d	elt_multiply (const matrix_d &m1, const matrix_d &m2)
	Return the element-wise product of the specified matrices.

vector_d	elt_divide (const vector_d &v1, const vector_d &v2)
	Return the element-wise divsion of the specified vectors.

row_vector_d	elt_divide (const row_vector_d &v1, const row_vector_d &v2)
	Return the element-wise division of the specified row vectors.

matrix_d	elt_divide (const matrix_d &m1, const matrix_d &m2)
	Return the element-wise division of the specified matrices.

vector_d	multiply (const vector_d &v, double c)
	Return the product of the of the specified column vector and specified scalar.

row_vector_d	multiply (const row_vector_d &rv, double c)
	Return the product of the of the specified row vector and specified scalar.

matrix_d	multiply (const matrix_d &m, double c)
	Return the product of the of the specified matrix and specified scalar.

vector_d	multiply (double c, const vector_d &v)
	Return the product of the specified scalar and vector.

row_vector_d	multiply (double c, const row_vector_d &rv)
	Return the product of the specified scalar and row vector.

matrix_d	multiply (double c, const matrix_d &m)
	Return the product of the specified scalar and matrix.

row_vector_d	row (const matrix_d &m, size_t i)
	Return the specified row of the specified matrix, using start-at-1 indexing.

vector_d	col (const matrix_d &m, size_t j)
	Return the specified column of the specified matrix using start-at-1 indexing.

vector_d	diagonal (const matrix_d &m)
	Return a column vector of the diagonal elements of the specified matrix.

matrix_d	diag_matrix (const vector_d &v)
	Return a square diagonal matrix with the specified vector of coefficients as the diagonal values.

row_vector_d	transpose (const vector_d &v)
	Return the transposition of the specified column vector.

vector_d	transpose (const row_vector_d &rv)
	Return the transposition of the specified row vector.

matrix_d	transpose (const matrix_d &m)
	Return the transposition of the specified matrix.

matrix_d	inverse (const matrix_d &m)
	Returns the inverse of the specified matrix.

vector_d	softmax (const vector_d &y)
	Return the softmax of the specified vector.

vector_d	eigenvalues (const matrix_d &m)
	Return the real component of the eigenvalues of the specified matrix in descending order of magnitude.

matrix_d	eigenvectors (const matrix_d &m)
	Return a matrix whose columns are the real components of the eigenvectors of the specified matrix.

void	eigen_decompose (const matrix_d &m, vector_d &eigenvalues, matrix_d &eigenvectors)
	Assign the real components of the eigenvalues and eigenvectors of the specified matrix to the specified references.

vector_d	eigenvalues_sym (const matrix_d &m)
	Return the eigenvalues of the specified symmetric matrix in descending order of magnitude.

matrix_d	eigenvectors_sym (const matrix_d &m)
	Return a matrix whose rows are the real components of the eigenvectors of the specified symmetric matrix.

void	eigen_decompose_sym (const matrix_d &m, vector_d &eigenvalues, matrix_d &eigenvectors)
	Assign the real components of the eigenvalues and eigenvectors of the specified symmetric matrix to the specified references.

matrix_d	cholesky_decompose (const matrix_d &m)
	Return the lower-triangular Cholesky factor (i.e., matrix square root) of the specified square, symmetric matrix.

vector_d	singular_values (const matrix_d &m)
	Return the vector of the singular values of the specified matrix in decreasing order of magnitude.

void	svd (const matrix_d &m, matrix_d &u, matrix_d &v, vector_d &s)
	Assign the real components of a singular value decomposition of the specified matrix to the specified references.

template<typename T >
void	resize (T &x, std::vector< size_t > dims)
	Recursively resize the specified vector of vectors, which must bottom out at scalar values, Eigen vectors or Eigen matrices.

template<typename T >
T &	get_base1 (std::vector< T > &x, size_t i, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one index.

template<typename T >
T &	get_base1 (std::vector< std::vector< T > > &x, size_t i1, size_t i2, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
T &	get_base1 (std::vector< std::vector< std::vector< T > > > &x, size_t i1, size_t i2, size_t i3, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
T &	get_base1 (std::vector< std::vector< std::vector< std::vector< T > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
T &	get_base1 (std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
T &	get_base1 (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
T &	get_base1 (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
T &	get_base1 (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, size_t i8, const char *error_msg, size_t idx)
	Return a reference to the value of the specified vector at the specified base-one indexes.

template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic >	get_base1 (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, const char *error_msg, size_t idx)
	Return a copy of the row of the specified vector at the specified base-one row index.

template<typename T >
T &	get_base1 (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, size_t n, const char *error_msg, size_t idx)
	Return a reference to the value of the specified matrix at the specified base-one row and column indexes.

template<typename T >
T &	get_base1 (Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t m, const char *error_msg, size_t idx)
	Return a reference to the value of the specified column vector at the specified base-one index.

template<typename T >
T &	get_base1 (Eigen::Matrix< T, 1, Eigen::Dynamic > &x, size_t n, const char *error_msg, size_t idx)
	Return a reference to the value of the specified row vector at the specified base-one index.

size_t	rows (const vector_d &v)
	Return the number of rows in the specified column vector.

size_t	rows (const row_vector_d &rv)
	Return the number of rows in the specified row vector.

size_t	rows (const matrix_d &m)
	Return the number of rows in the specified matrix.

size_t	cols (const vector_d &v)
	Return the number of columns in the specified column vector.

size_t	cols (const row_vector_d &rv)
	Return the number of columns in the specified row vector.

size_t	cols (const matrix_d &m)
	Return the number of columns in the specified matrix.

template<typename T , int R, int C>
void	validate_column_index (const Eigen::Matrix< T, R, C > &m, size_t j, const char *msg)

template<typename T , int R, int C>
void	validate_row_index (const Eigen::Matrix< T, R, C > &m, size_t i, const char *msg)

template<typename T , int R, int C>
void	validate_square (const Eigen::Matrix< T, R, C > &x, const char *msg)

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
void	validate_matching_dims (const Eigen::Matrix< T1, R1, C1 > &x1, const Eigen::Matrix< T2, R2, C2 > &x2, const char *msg)

template<typename T1 , typename T2 >
void	validate_matching_sizes (const std::vector< T1 > &x1, const std::vector< T2 > &x2, const char *msg)

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
void	validate_matching_sizes (const Eigen::Matrix< T1, R1, C1 > &x1, const Eigen::Matrix< T2, R2, C2 > &x2, const char *msg)

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
void	validate_multiplicable (const Eigen::Matrix< T1, R1, C1 > &x1, const Eigen::Matrix< T2, R2, C2 > &x2, const char *msg)

template<typename T >
void	validate_nonzero_size (const T &x, const char *msg)

template<typename T , int R, int C>
void	validate_vector (const Eigen::Matrix< T, R, C > &x, const char *msg)

template<int R, int C>
double	dot_self (const Eigen::Matrix< double, R, C > &v)
	Returns the dot product of the specified vector with itself.

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	columns_dot_self (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x)
	Returns the dot product of each column of a matrix with itself.

template<int R1, int C1, int R2, int C2>
double	dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
	Returns the dot product of the specified vectors.

double	dot_product (const double v1, const double v2, size_t length)
	Returns the dot product of the specified arrays of doubles.

double	dot_product (const std::vector< double > &v1, const std::vector< double > &v2)
	Returns the dot product of the specified arrays of doubles.

int	min (const std::vector< int > &x)
	Returns the minimum coefficient in the specified column vector.

template<typename T >
T	min (const std::vector< T > &x)
	Returns the minimum coefficient in the specified column vector.

template<typename T , int R, int C>
T	min (const Eigen::Matrix< T, R, C > &m)
	Returns the minimum coefficient in the specified matrix, vector, or row vector.

int	max (const std::vector< int > &x)
	Returns the maximum coefficient in the specified column vector.

template<typename T >
T	max (const std::vector< T > &x)
	Returns the maximum coefficient in the specified column vector.

template<typename T , int R, int C>
T	max (const Eigen::Matrix< T, R, C > &m)
	Returns the maximum coefficient in the specified vector, row vector, or matrix.

template<typename T >
boost::math::tools::promote_args < T >::type	mean (const std::vector< T > &v)
	Returns the sample mean (i.e., average) of the coefficients in the specified standard vector.

template<typename T , int R, int C>
boost::math::tools::promote_args < T >::type	mean (const Eigen::Matrix< T, R, C > &m)
	Returns the sample mean (i.e., average) of the coefficients in the specified vector, row vector, or matrix.

template<typename T >
boost::math::tools::promote_args < T >::type	variance (const std::vector< T > &v)
	Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vector.

template<typename T , int R, int C>
boost::math::tools::promote_args < T >::type	variance (const Eigen::Matrix< T, R, C > &m)
	Returns the sample variance (divide by length - 1) of the coefficients in the specified column vector.

template<typename T >
boost::math::tools::promote_args < T >::type	sd (const std::vector< T > &v)
	Returns the unbiased sample standard deviation of the coefficients in the specified column vector.

template<typename T , int R, int C>
boost::math::tools::promote_args < T >::type	sd (const Eigen::Matrix< T, R, C > &m)
	Returns the unbiased sample standard deviation of the coefficients in the specified vector, row vector, or matrix.

template<typename T >
T	sum (const std::vector< T > &xs)
	Return the sum of the values in the specified standard vector.

template<typename T , int R, int C>
double	sum (const Eigen::Matrix< T, R, C > &v)
	Returns the sum of the coefficients of the specified column vector.

template<typename T >
T	prod (const std::vector< T > &v)
	Returns the product of the coefficients of the specified standard vector.

template<typename T , int R, int C>
T	prod (const Eigen::Matrix< T, R, C > &v)
	Returns the product of the coefficients of the specified column vector.

template<typename T >
T	trace (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
	Returns the trace of the specified matrix.

template<typename T , int Rows, int Cols>
Eigen::Matrix< T, Rows, Cols >	log (const Eigen::Matrix< T, Rows, Cols > &m)
	Return the element-wise logarithm of the matrix or vector.

template<typename T , int Rows, int Cols>
Eigen::Matrix< T, Rows, Cols >	exp (const Eigen::Matrix< T, Rows, Cols > &m)
	Return the element-wise exponentiation of the matrix or vector.

template<int Rows, int Cols>
Eigen::Matrix< double, Rows, Cols >	add (const Eigen::Matrix< double, Rows, Cols > &m, const double &c)
	Return the sum of a matrix or vector and a scalar.

template<int Rows, int Cols>
Eigen::Matrix< double, Rows, Cols >	add (const double &c, const Eigen::Matrix< double, Rows, Cols > &m)
	Return the sum of a scalar and a matrix or vector.

template<int Rows, int Cols>
Eigen::Matrix< double, Rows, Cols >	subtract (const Eigen::Matrix< double, Rows, Cols > &m, double c)
	Return the difference between a matrix or vector and a scalar.

template<int Rows, int Cols>
Eigen::Matrix< double, Rows, Cols >	subtract (double c, const Eigen::Matrix< double, Rows, Cols > &m)
	Return the difference between a scalar and a matrix or vector.

template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	multiply (const Eigen::Matrix< double, R1, C1 > &m1, const Eigen::Matrix< double, R2, C2 > &m2)
	Return the product of the specified matrices.

template<int C1, int R2>
double	multiply (const Eigen::Matrix< double, 1, C1 > &rv, const Eigen::Matrix< double, R2, 1 > &v)
	Return the scalar product of the specified row vector and specified column vector.

matrix_d	multiply_lower_tri_self_transpose (const matrix_d &L)
	Returns the result of multiplying the lower triangular portion of the square input matrix by its own transpose.

matrix_d	tcrossprod (const matrix_d &M)
	Returns the result of post-multiplying a matrix by its own transpose.

matrix_d	crossprod (const matrix_d &M)
	Returns the result of pre-multiplying a matrix by its own transpose.

template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	mdivide_left_tri_low (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)

Eigen::MatrixXd	mdivide_left_tri_low (const Eigen::MatrixXd &A)

template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	mdivide_left_tri (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
	Returns the solution of the system Ax=b when A is triangular.

template<int TriView>
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	mdivide_left_tri (const Eigen::MatrixXd &A)
	Returns the solution of the system Ax=b when A is triangular and b=I.

template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	mdivide_right_tri (const Eigen::Matrix< double, R1, C1 > &b, const Eigen::Matrix< double, R2, C2 > &A)
	Returns the solution of the system Ax=b when A is triangular.

template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	mdivide_right_tri_low (const Eigen::Matrix< double, R1, C1 > &b, const Eigen::Matrix< double, R2, C2 > &A)
	Returns the solution of the system tri(A)x=b when tri(A) is a lower triangular view of the matrix A.

template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	mdivide_left (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
	Returns the solution of the system Ax=b.

template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 >	mdivide_right (const Eigen::Matrix< double, R1, C1 > &b, const Eigen::Matrix< double, R2, C2 > &A)
	Returns the solution of the system Ax=b.

template<typename T >
void	stan_print (std::ostream *o, const T &x)

template<typename T >
void	stan_print (std::ostream *o, const std::vector< T > &x)

template<typename T >
void	stan_print (std::ostream *o, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)

template<typename T >
void	stan_print (std::ostream *o, const Eigen::Matrix< T, 1, Eigen::Dynamic > &x)

template<typename T >
void	stan_print (std::ostream *o, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x)

template<typename T_size1 , typename T_size2 , typename T_result , class Policy >
bool	check_size_match (const char function, T_size1 i, T_size2 j, T_result result, const Policy &)

template<typename T_size1 , typename T_size2 , typename T_result >
bool	check_size_match (const char function, T_size1 i, T_size2 j, T_result result)

template<typename T_size1 , typename T_size2 >
bool	check_size_match (const char function, T_size1 i, T_size2 j, T_size1 result=0)

template<typename T_y , typename T_result , class Policy >
bool	check_symmetric (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result, const Policy &)
	Return `true` if the specified matrix is symmetric.

template<typename T_y , typename T_result >
bool	check_symmetric (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result)

template<typename T >
bool	check_symmetric (const char function, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T *result=0)

template<typename T_y , typename T_result , class Policy >
bool	check_pos_definite (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result, const Policy &)
	Return `true` if the specified matrix is positive definite.

template<typename T_y , typename T_result >
bool	check_pos_definite (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result)

template<typename T >
bool	check_pos_definite (const char function, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T *result=0)

template<typename T_y , typename T_result , class Policy >
bool	check_cov_matrix (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result, const Policy &)
	Return `true` if the specified matrix is a valid covariance matrix.

template<typename T_y , typename T_result >
bool	check_cov_matrix (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result)

template<typename T >
bool	check_cov_matrix (const char function, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T *result=0)

template<typename T_y , typename T_result , class Policy >
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 &)
	Return `true` if the specified matrix is a valid correlation matrix.

template<typename T_y , typename T_result >
bool	check_corr_matrix (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result)

template<typename T >
bool	check_corr_matrix (const char function, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T *result=0)

template<typename T_covar , typename T_result , class Policy >
bool	check_cov_matrix (const char function, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, T_result result, const Policy &)
	Return `true` if the specified matrix is a valid covariance matrix.

template<typename T_covar , typename T_result >
bool	check_cov_matrix (const char function, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, T_result result)

template<typename T >
bool	check_cov_matrix (const char function, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &Sigma, T result=0)

template<typename T_prob , typename T_result , class Policy >
bool	check_simplex (const char function, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const char name, T_result *result, const Policy &)
	Return `true` if the specified vector is simplex.

template<typename T_y , typename T_result >
bool	check_simplex (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &theta, const char name, T_result *result)

template<typename T >
bool	check_simplex (const char function, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &theta, const char name, T *result=0)

template<typename T_y , typename T_result , class Policy >
bool	check_ordered (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y, const char name, T_result *result, const Policy &)
	Return `true` if the specified vector is sorted into increasing order.

template<typename T_y , typename T_result >
bool	check_ordered (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y, const char name, T_result *result)

template<typename T >
bool	check_ordered (const char function, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, const char name, T *result=0)

template<typename T_y , typename T_result , class Policy >
bool	check_positive_ordered (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y, const char name, T_result *result, const Policy &)
	Return `true` if the specified vector contains only non-negative values and is sorted into increasing order.

template<typename T_y , typename T_result >
bool	check_positive_ordered (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y, const char name, T_result *result)

template<typename T >
bool	check_positive_ordered (const char function, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, const char name, T *result=0)

template<typename T_y , typename T_result , class Policy >
bool	check_not_nan (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result, const Policy &)

template<typename T_y , typename T_result >
bool	check_not_nan (const char function, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T_result *result)

template<typename T >
bool	check_not_nan (const char function, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y, const char name, T *result=0)

template<typename T >
boost::math::tools::promote_args < T >::type	exp2 (T y)
	Return the exponent base 2 of the specified argument (C99).

template<typename T1 , typename T2 >
boost::math::tools::promote_args < T1, T2 >::type	fdim (T1 a, T2 b)
	The positive difference function (C99).

template<typename T1 , typename T2 , typename T3 >
boost::math::tools::promote_args < T1, T2, T3 >::type	fma (T1 a, T2 b, T3 c)
	The fused multiply-add operation (C99).

template<typename T >
boost::math::tools::promote_args < T >::type	log2 (T a)
	Returns the base 2 logarithm of the argument (C99).

template<typename T >
unsigned int	int_step (T y)
	The integer step, or Heaviside, function.

template<typename T >
int	step (T y)
	The step, or Heaviside, function.

template<typename T1 , typename T2 >
boost::math::tools::promote_args < T1, T2 >::type	lbeta (T1 a, T2 b)
	Return the log of the beta function applied to the specified arguments.

template<typename T_N , typename T_n >
boost::math::tools::promote_args < T_N, T_n >::type	binomial_coefficient_log (T_N N, T_n n)
	Return the log of the binomial coefficient for the specified arguments.

template<typename T >
boost::math::tools::promote_args < T >::type	inv_logit (T a)
	Returns the inverse logit function applied to the argument.

template<typename T >
boost::math::tools::promote_args < T >::type	logit (T a)
	Returns the logit function applied to the argument.

template<typename T >
boost::math::tools::promote_args < T >::type	Phi (T x)
	The unit normal cumulative distribution function.

template<typename T >
boost::math::tools::promote_args < T >::type	inv_cloglog (T x)
	The inverse complementary log-log function.

template<typename T >
boost::math::tools::promote_args < T >::type	binary_log_loss (int y, T y_hat)
	Returns the log loss function for binary classification with specified reference and response values.

template<typename Vector , typename Scalar >
void	softmax (const Vector &x, Vector &simplex)
	Write the values of the softmax transformed first argument into the second argument.

template<typename Vector >
void	inverse_softmax (const Vector &simplex, Vector &y)
	Writes the inverse softmax of the simplex argument into the second argument.

template<typename T >
boost::math::tools::promote_args < T >::type	log1p (T x)
	Return the natural logarithm of one plus the specified value.

template<typename T >
boost::math::tools::promote_args < T >::type	log1m (T x)
	Return the natural logarithm of one minus the specified value.

template<typename T >
boost::math::tools::promote_args < T >::type	lmgamma (unsigned int k, T x)
	Return the natural logarithm of the multivariate gamma function with the speciifed dimensions and argument.

double	if_else (bool c, double y_true, double y_false)
	Return the second argument if the first argument is true and otherwise return the second argument.

template<typename T >
T	square (T x)
	Return the square of the specified argument.

template<typename T_a , typename T_b >
boost::math::tools::promote_args < T_a, T_b >::type	multiply_log (T_a a, T_b b)

double	log1p_exp (const double &a)
	Calculates the log of 1 plus the exponential of the specified value without overflow.

double	log_sum_exp (const double &a, const double &b)
	Calculates the log sum of exponetials without overflow.

double	ibeta (const double &a, const double &b, const double &x)
	The normalized incomplete beta function of a, b, and x.

static double	log_sum_exp (const std::vector< double > &x)
	Return the log of the sum of the exponentiated values of the specified sequence of values.

template<typename T1 , typename T2 , typename T3 >
double	simple_var (double v, const T1 &, const T1 &, const T2 &, const T2 &, const T3 &, const T3 &)
	Return the scalar value and ignore the remaining arguments.

template<typename T >
double	value_of (T x)
	Return the value of the specified scalar argument converted to a double value.

template<>
double	value_of< double > (double x)
	Return the specified argument.

double	pi ()
	Return the value of pi.

double	e ()
	Return the base of the natural logarithm.

double	sqrt2 ()
	Return the square root of two.

double	log2 ()
	Return natural logarithm of two.

double	log10 ()
	Return natural logarithm of ten.

double	positive_infinity ()
	Return positive infinity.

double	negative_infinity ()
	Return negative infinity.

double	not_a_number ()
	Return (quiet) not-a-number.

double	epsilon ()
	Return minimum positive number representable.

double	negative_epsilon ()
	Return maximum negative number (i.e., negative number with smallest absolute value).

double	max (double a, double b)

double	max (std::vector< double > &x)

double	min (double a, double b)

double	dot (std::vector< double > &x, std::vector< double > &y)

double	dot_self (std::vector< double > &x)

void	scaled_add (std::vector< double > &x, std::vector< double > &y, double lambda)

void	sub (std::vector< double > &x, std::vector< double > &y, std::vector< double > &result)

double	dist (const std::vector< double > &x, const std::vector< double > &y)

double	sum (std::vector< double > &x)

Variables
const double	E = boost::math::constants::e<double>()
	The base of the natural logarithm, .

const double	SQRT_2 = std::sqrt(2.0)
	The value of the square root of 2, $\sqrt{2}$ .

const double	LOG_2 = std::log(2.0)
	The natural logarithm of 2, $\log 2$ .

const double	LOG_10 = std::log(10.0)
	The natural logarithm of 10, $\log 10$ .

const double	INFTY = std::numeric_limits<double>::infinity()
	Positive infinity.

const double	NEGATIVE_INFTY = - std::numeric_limits<double>::infinity()
	Negative infinity.

const double	NOT_A_NUMBER = std::numeric_limits<double>::quiet_NaN()
	(Quiet) not-a-number value.

const double	EPSILON = std::numeric_limits<double>::epsilon()
	Smallest positive value.

const double	NEGATIVE_EPSILON = - std::numeric_limits<double>::epsilon()
	Largest negative value (i.e., smallest absolute value).

const double	CONSTRAINT_TOLERANCE = 1E-8
	The tolerance for checking arithmetic bounds In rank and in simplexes.

Detailed Description

Matrices and templated mathematical functions.

Typedef Documentation

typedef boost::math::policies::policy stan::math::default_policy

Default error-handling policy from Boost.

Definition at line 30 of file error_handling.hpp.

typedef EigenType<double>::matrix stan::math::matrix_d

Type for matrix of double values.

Definition at line 70 of file matrix.hpp.

typedef EigenType<double>::row_vector stan::math::row_vector_d

Type for (row) vector of double values.

Definition at line 80 of file matrix.hpp.

typedef EigenType<double>::vector stan::math::vector_d

Type for (column) vector of double values.

Definition at line 75 of file matrix.hpp.

Function Documentation

vector_d stan::math::add	(	const vector_d &	v1,
		const vector_d &	v2
	)

Return the sum of the specified column vectors.

The two vectors must have the same size.

Parameters

v1	First vector.
v2	Second vector.

Returns: Sum of the two vectors.

Exceptions

std::domain_error if v1 and v2 are not the same size.

Definition at line 16 of file matrix.cpp.

row_vector_d stan::math::add	(	const row_vector_d &	rv1,
		const row_vector_d &	rv2
	)

Return the sum of the specified row vectors.

The two vectors must have the same size.

Parameters

rv1	First vector.
rv2	Second vector.

Returns: Sum of the two vectors.

Exceptions

std::domain_error if rv1 and rv2 are not the same size.

Definition at line 21 of file matrix.cpp.

matrix_d stan::math::add	(	const matrix_d &	m1,
		const matrix_d &	m2
	)

Return the sum of the specified matrices.

The two matrices must have the same dimensions.

Parameters

m1	First matrix.
m2	Second matrix.

Returns: Sum of the two vectors.

Exceptions

std::domain_error if m1 and m2 are not the same size.

Definition at line 26 of file matrix.cpp.

template<int Rows, int Cols>

Eigen::Matrix<double,Rows,Cols> stan::math::add	(	const Eigen::Matrix< double, Rows, Cols > &	m,
		const double &	c
	)

inline

Return the sum of a matrix or vector and a scalar.

Parameters

m	Matrix or vector.
c	Scalar.

Returns: The matrix or vector plus the scalar.

Definition at line 1130 of file matrix.hpp.

template<int Rows, int Cols>

Eigen::Matrix<double,Rows,Cols> stan::math::add	(	const double &	c,
		const Eigen::Matrix< double, Rows, Cols > &	m
	)

inline

Return the sum of a scalar and a matrix or vector.

Parameters

c	Scalar.
m	Matrix or vector.

Returns: Scalar plus the matrix or vector.

Definition at line 1140 of file matrix.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::binary_log_loss	(	int	y,
		T	y_hat
	)

inline

Returns the log loss function for binary classification with specified reference and response values.

The log loss function for prediction $\hat{y} \in [0, 1]$ given outcome $y \in \{ 0, 1 \}$ is

$\mbox{logloss}(1,\hat{y}) = -\log \hat{y}$ , and

$\mbox{logloss}(0,\hat{y}) = -\log (1 - \hat{y})$ .

Parameters

y	Reference value in { 0 , 1 }.
y_hat	Response value in [0,1].

Returns: Log loss for response given reference value.

Definition at line 292 of file special_functions.hpp.

template<typename T_N , typename T_n >

boost::math::tools::promote_args<T_N, T_n>::type stan::math::binomial_coefficient_log	(	T_N	N,
		T_n	n
	)

inline

Return the log of the binomial coefficient for the specified arguments.

The binomial coefficient, ${N \choose n}$ , read "N choose n", is defined for $0 \leq n \leq N$ by

${N \choose n} = \frac{N!}{n! (N-n)!}$ .

This function uses Gamma functions to define the log and generalize the arguments to continuous N and n.

$\log {N \choose n} = \log \ \Gamma(N+1) - \log \Gamma(n+1) - \log \Gamma(N-n+1)$ .

Parameters

N	total number of objects.
n	number of objects chosen.

Returns: log (N choose n).

Definition at line 176 of file special_functions.hpp.

template<typename T_y , typename T_low , typename T_high , typename T_result , class Policy >

bool stan::math::check_bounded	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const T_high &	high,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 604 of file error_handling.hpp.

template<typename T_y , typename T_low , typename T_high , typename T_result >

bool stan::math::check_bounded	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const T_high &	high,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 614 of file error_handling.hpp.

template<typename T_y , typename T_low , typename T_high >

bool stan::math::check_bounded	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const T_high &	high,
		const char *	name
	)

inline

Definition at line 623 of file error_handling.hpp.

template<typename T , typename T_result , class Policy >

bool stan::math::check_consistent_size	(	size_t	max_size,
		const char *	function,
		const T &	x,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 763 of file error_handling.hpp.

template<typename T1 , typename T2 , typename T_result , class Policy >

bool stan::math::check_consistent_sizes	(	const char *	function,
		const T1 &	x1,
		const T2 &	x2,
		const char *	name1,
		const char *	name2,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 782 of file error_handling.hpp.

template<typename T1 , typename T2 , typename T_result >

bool stan::math::check_consistent_sizes	(	const char *	function,
		const T1 &	x1,
		const T2 &	x2,
		const char *	name1,
		const char *	name2,
		T_result *	result
	)

inline

Definition at line 795 of file error_handling.hpp.

template<typename T1 , typename T2 , typename T3 , typename T_result , class Policy >

bool stan::math::check_consistent_sizes	(	const char *	function,
		const T1 &	x1,
		const T2 &	x2,
		const T3 &	x3,
		const char *	name1,
		const char *	name2,
		const char *	name3,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 807 of file error_handling.hpp.

template<typename T1 , typename T2 , typename T3 , typename T_result >

bool stan::math::check_consistent_sizes	(	const char *	function,
		const T1 &	x1,
		const T2 &	x2,
		const T3 &	x3,
		const char *	name1,
		const char *	name2,
		const char *	name3,
		T_result *	result
	)

inline

Definition at line 823 of file error_handling.hpp.

template<typename T1 , typename T2 , typename T3 , typename T4 , typename T_result , class Policy >

bool stan::math::check_consistent_sizes	(	const char *	function,
		const T1 &	x1,
		const T2 &	x2,
		const T3 &	x3,
		const T4 &	x4,
		const char *	name1,
		const char *	name2,
		const char *	name3,
		const char *	name4,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 837 of file error_handling.hpp.

template<typename T1 , typename T2 , typename T3 , typename T4 , typename T_result >

bool stan::math::check_consistent_sizes	(	const char *	function,
		const T1 &	x1,
		const T2 &	x2,
		const T3 &	x3,
		const T4 &	x4,
		const char *	name1,
		const char *	name2,
		const char *	name3,
		const char *	name4,
		T_result *	result
	)

inline

Definition at line 857 of file error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_corr_matrix	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Return true if the specified matrix is a valid correlation matrix.

A valid correlation matrix is symmetric, has a unit diagonal (all 1 values), and has all values between -1 and 1 (inclussive).

Parameters

function
y	Matrix to test.
name
result

Returns: true if the specified matrix is a valid correlation matrix.

Template Parameters

T	Type of scalar.

Definition at line 258 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_corr_matrix	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 292 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_corr_matrix	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T *	result = `0`
	)

inline

Definition at line 300 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_cov_matrix	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Return true if the specified matrix is a valid covariance matrix.

A valid covariance matrix must be square, symmetric, and positive definite.

Parameters

function
y	Matrix to test.
name
result

Returns: true if the matrix is a valid covariance matrix.

Template Parameters

T	Type of scalar.

Definition at line 206 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_cov_matrix	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 223 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_cov_matrix	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T *	result = `0`
	)

inline

Definition at line 232 of file matrix_error_handling.hpp.

template<typename T_covar , typename T_result , class Policy >

bool stan::math::check_cov_matrix	(	const char *	function,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		T_result *	result,
		const Policy &
	)

inline

Return true if the specified matrix is a valid covariance matrix.

A valid covariance matrix must be symmetric and positive definite.

Parameters

function
Sigma	Matrix to test.
result

Returns: true if the matrix is a valid covariance matrix.

Template Parameters

T	Type of scalar.

Definition at line 320 of file matrix_error_handling.hpp.

template<typename T_covar , typename T_result >

bool stan::math::check_cov_matrix	(	const char *	function,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		T_result *	result
	)

inline

Definition at line 334 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_cov_matrix	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		T *	result = `0`
	)

inline

Definition at line 341 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_finite	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Checks if the variable y is finite.

Definition at line 224 of file error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_finite	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 233 of file error_handling.hpp.

template<typename T >

bool stan::math::check_finite	(	const char *	function,
		const T &	y,
		const char *	name
	)

inline

Definition at line 241 of file error_handling.hpp.

template<typename T_y , typename T_low , typename T_result , class Policy >

bool stan::math::check_greater	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 298 of file error_handling.hpp.

template<typename T_y , typename T_low , typename T_result >

bool stan::math::check_greater	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 308 of file error_handling.hpp.

template<typename T_y , typename T_low >

bool stan::math::check_greater	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const char *	name
	)

inline

Definition at line 316 of file error_handling.hpp.

template<typename T_y , typename T_low , typename T_result , class Policy >

bool stan::math::check_greater_or_equal	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 373 of file error_handling.hpp.

template<typename T_y , typename T_low , typename T_result >

bool stan::math::check_greater_or_equal	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 382 of file error_handling.hpp.

template<typename T_y , typename T_low >

bool stan::math::check_greater_or_equal	(	const char *	function,
		const T_y &	y,
		const T_low &	low,
		const char *	name
	)

inline

Definition at line 391 of file error_handling.hpp.

template<typename T_y , typename T_high , typename T_result , class Policy >

bool stan::math::check_less	(	const char *	function,
		const T_y &	y,
		const T_high &	high,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 448 of file error_handling.hpp.

template<typename T_y , typename T_high , typename T_result >

bool stan::math::check_less	(	const char *	function,
		const T_y &	y,
		const T_high &	high,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 457 of file error_handling.hpp.

template<typename T_y , typename T_high >

bool stan::math::check_less	(	const char *	function,
		const T_y &	y,
		const T_high &	high,
		const char *	name
	)

inline

Definition at line 465 of file error_handling.hpp.

template<typename T_y , typename T_high , typename T_result , class Policy >

bool stan::math::check_less_or_equal	(	const char *	function,
		const T_y &	y,
		const T_high &	high,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 522 of file error_handling.hpp.

template<typename T_y , typename T_high , typename T_result >

bool stan::math::check_less_or_equal	(	const char *	function,
		const T_y &	y,
		const T_high &	high,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 531 of file error_handling.hpp.

template<typename T_y , typename T_high >

bool stan::math::check_less_or_equal	(	const char *	function,
		const T_y &	y,
		const T_high &	high,
		const char *	name
	)

inline

Definition at line 539 of file error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_nonnegative	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 674 of file error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_nonnegative	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 682 of file error_handling.hpp.

template<typename T_y >

bool stan::math::check_nonnegative	(	const char *	function,
		const T_y &	y,
		const char *	name
	)

inline

Definition at line 689 of file error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_not_nan	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Checks if the variable y is nan.

Parameters

function	Name of function being invoked.
y	Reference to variable being tested.
name	Name of variable being tested.
result	Pointer to resulting value after test.

Template Parameters

T_y	Type of variable being tested.
T_result	Type of result returned.
Policy	Error handling policy.

Definition at line 144 of file error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_not_nan	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result = `0`
	)

inline

Checks if the variable y is nan.

Parameters

function	Name of function being invoked.
y	Reference to variable being tested.
name	Name of variable being tested.
result	Pointer to resulting value after test.

Template Parameters

T_y	Type of variable being tested.
T_result	Type of result returned.
Policy	Error handling policy.

Definition at line 165 of file error_handling.hpp.

template<typename T >

bool stan::math::check_not_nan	(	const char *	function,
		const T &	y,
		const char *	name
	)

inline

Definition at line 173 of file error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_not_nan	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 570 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_not_nan	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 594 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_not_nan	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T *	result = `0`
	)

inline

Definition at line 601 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_ordered	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

Return true if the specified vector is sorted into increasing order.

There may be duplicate values. Otherwise, raise a domain error according to the specified policy.

Parameters

function
y	Vector to test.
name
result

Template Parameters

Policy Only the policy's type matters.

Returns: true if the vector has positive, ordered values.

Definition at line 452 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_ordered	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &	y,
		const char *	name,
		T_result *	result
	)

Definition at line 481 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_ordered	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	y,
		const char *	name,
		T *	result = `0`
	)

Definition at line 488 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_pos_definite	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Return true if the specified matrix is positive definite.

NOTE: symmetry is NOT checked by this function

Parameters

function
y	Matrix to test.
name
result

Returns: true if the matrix is positive definite.

Template Parameters

T	Type of scalar.

Definition at line 136 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_pos_definite	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 173 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_pos_definite	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T *	result = `0`
	)

inline

Definition at line 182 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_positive	(	const char *	function,
		const T_y &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 740 of file error_handling.hpp.

template<typename T_x , typename T_result >

bool stan::math::check_positive	(	const char *	function,
		const T_x &	x,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 748 of file error_handling.hpp.

template<typename T >

bool stan::math::check_positive	(	const char *	function,
		const T &	x,
		const char *	name
	)

inline

Definition at line 755 of file error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_positive_ordered	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

Return true if the specified vector contains only non-negative values and is sorted into increasing order.

There may be duplicate values. Otherwise, raise a domain error according to the specified policy.

Parameters

function
y	Vector to test.
name
result

Template Parameters

Policy Only the policy's type matters.

Returns: true if the vector has positive, ordered values.

Definition at line 510 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_positive_ordered	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &	y,
		const char *	name,
		T_result *	result
	)

Definition at line 551 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_positive_ordered	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	y,
		const char *	name,
		T *	result = `0`
	)

Definition at line 558 of file matrix_error_handling.hpp.

template<typename T_prob , typename T_result , class Policy >

bool stan::math::check_simplex	(	const char *	function,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta,
		const char *	name,
		T_result *	result,
		const Policy &
	)

Return true if the specified vector is simplex.

To be a simplex, all values must be greater than or equal to 0 and the values must sum to 1.

The test that the values sum to 1 is done to within the tolerance specified by CONSTRAINT_TOLERANCE.

Parameters

function
theta	Vector to test.
name
result

Returns: true if the vector is a simplex.

Definition at line 368 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_simplex	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &	theta,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 420 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_simplex	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	theta,
		const char *	name,
		T *	result = `0`
	)

inline

Definition at line 427 of file matrix_error_handling.hpp.

template<typename T_size1 , typename T_size2 , typename T_result , class Policy >

bool stan::math::check_size_match	(	const char *	function,
		T_size1	i,
		T_size2	j,
		T_result *	result,
		const Policy &
	)

inline

Definition at line 16 of file matrix_error_handling.hpp.

template<typename T_size1 , typename T_size2 , typename T_result >

bool stan::math::check_size_match	(	const char *	function,
		T_size1	i,
		T_size2	j,
		T_result *	result
	)

inline

Definition at line 39 of file matrix_error_handling.hpp.

template<typename T_size1 , typename T_size2 >

bool stan::math::check_size_match	(	const char *	function,
		T_size1	i,
		T_size2	j,
		T_size1 *	result = `0`
	)

inline

Definition at line 48 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result , class Policy >

bool stan::math::check_symmetric	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result,
		const Policy &
	)

inline

Return true if the specified matrix is symmetric.

NOTE: squareness is not checked by this function

Parameters

function
y	Matrix to test.
name
result

Returns: true if the matrix is symmetric.

Template Parameters

T	Type of scalar.

Definition at line 70 of file matrix_error_handling.hpp.

template<typename T_y , typename T_result >

bool stan::math::check_symmetric	(	const char *	function,
		const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T_result *	result
	)

inline

Definition at line 104 of file matrix_error_handling.hpp.

template<typename T >

bool stan::math::check_symmetric	(	const char *	function,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const char *	name,
		T *	result = `0`
	)

inline

Definition at line 112 of file matrix_error_handling.hpp.

matrix_d stan::math::cholesky_decompose ( const matrix_d & m )

Return the lower-triangular Cholesky factor (i.e., matrix square root) of the specified square, symmetric matrix.

The return value $L$ will be a lower-traingular matrix such that the original matrix $A$ is given by

$A = L \times L^T$ .

Parameters

m	Symmetrix matrix.

Returns: Square root of matrix.

Exceptions

std::domain_error if m is not a square matrix

Definition at line 233 of file matrix.cpp.

vector_d stan::math::col	(	const matrix_d &	m,
		size_t	j
	)

Return the specified column of the specified matrix using start-at-1 indexing.

This is equivalent to calling m.col(i - 1) and assigning the resulting template expression to a column vector.

Parameters

m	Matrix.
j	Column index.

Returns: Specified column of the matrix.

Definition at line 149 of file matrix.cpp.

size_t stan::math::cols ( const vector_d & v )

inline

Return the number of columns in the specified column vector.

The return value is always 1.

Parameters

v	Specified vector.

Returns: Number of columns in the vector.

Definition at line 568 of file matrix.hpp.

size_t stan::math::cols ( const row_vector_d & rv )

inline

Return the number of columns in the specified row vector.

Parameters

rv	Specified vector.

Returns: Number of columns in the vector.

Definition at line 577 of file matrix.hpp.

size_t stan::math::cols ( const matrix_d & m )

inline

Return the number of columns in the specified matrix.

Parameters

m	Specified matrix.

Returns: Number of columns in the matrix.

Definition at line 585 of file matrix.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::math::columns_dot_self ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & x )

inline

Returns the dot product of each column of a matrix with itself.

Parameters

x Matrix.

Template Parameters

T	scalar type

Definition at line 738 of file matrix.hpp.

matrix_d stan::math::crossprod ( const matrix_d & M )

inline

Returns the result of pre-multiplying a matrix by its own transpose.

Parameters

M	Matrix to multiply.

Returns: Transpose of M times M

Definition at line 1415 of file matrix.hpp.

double stan::math::determinant ( const matrix_d & m )

Returns the determinant of the specified square matrix.

Parameters

m	Specified matrix.

Returns: Determinant of the matrix.

Exceptions

std::domain_error if matrix is not square.

Definition at line 11 of file matrix.cpp.

matrix_d stan::math::diag_matrix ( const vector_d & v )

Return a square diagonal matrix with the specified vector of coefficients as the diagonal values.

Parameters

v	Specified vector.

Returns: Diagonal matrix with vector as diagonal values.

Definition at line 158 of file matrix.cpp.

vector_d stan::math::diagonal ( const matrix_d & m )

Return a column vector of the diagonal elements of the specified matrix.

The matrix is not required to be square.

Parameters

m	Specified matrix.

Returns: Diagonal of the matrix.

Definition at line 154 of file matrix.cpp.

double stan::math::dist	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)

inline

Definition at line 61 of file util.hpp.

vector_d stan::math::divide	(	const vector_d &	v,
		double	c
	)

Return the division of the specified column vector by the specified scalar.

Parameters

v	Specified vector.
c	Specified scalar.

Returns: Vector divided by the scalar.

Definition at line 58 of file matrix.cpp.

row_vector_d stan::math::divide	(	const row_vector_d &	rv,
		double	c
	)

Return the division of the specified row vector by the specified scalar.

Parameters

rv	Specified vector.
c	Specified scalar.

Returns: Vector divided by the scalar.

Definition at line 62 of file matrix.cpp.

matrix_d stan::math::divide	(	const matrix_d &	m,
		double	c
	)

Return the division of the specified matrix by the specified scalar.

Parameters

m	Specified matrix.
c	Specified scalar.

Returns: Matrix divided by the scalar.

Definition at line 66 of file matrix.cpp.

double stan::math::dot	(	std::vector< double > &	x,
		std::vector< double > &	y
	)

inline

Definition at line 30 of file util.hpp.

template<int R1, int C1, int R2, int C2>

double stan::math::dot_product	(	const Eigen::Matrix< double, R1, C1 > &	v1,
		const Eigen::Matrix< double, R2, C2 > &	v2
	)

inline

Returns the dot product of the specified vectors.

Parameters

v1	First vector.
v2	Second vector.

Returns: Dot product of the vectors.

Exceptions

std::domain_error If the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 752 of file matrix.hpp.

double stan::math::dot_product	(	const double *	v1,
		const double *	v2,
		size_t	length
	)

inline

Returns the dot product of the specified arrays of doubles.

Parameters

v1	First array.
v2	Second array.
length	Length of both arrays.

Definition at line 768 of file matrix.hpp.

double stan::math::dot_product	(	const std::vector< double > &	v1,
		const std::vector< double > &	v2
	)

inline

Returns the dot product of the specified arrays of doubles.

Parameters

v1	First array.
v2	Second array.

Exceptions

std::domain_error if the vectors are not the same size.

Definition at line 781 of file matrix.hpp.

double stan::math::dot_self ( std::vector< double > & x )

inline

Definition at line 39 of file util.hpp.

template<int R, int C>

double stan::math::dot_self ( const Eigen::Matrix< double, R, C > & v )

inline

Returns the dot product of the specified vector with itself.

Parameters

v Vector.

Template Parameters

R	number of rows or `Eigen::Dynamic` for dynamic
C	number of rows or `Eigen::Dyanmic` for dynamic

Exceptions

std::domain_error If v is not vector dimensioned.

Definition at line 723 of file matrix.hpp.

double stan::math::e ( )

inline

Return the base of the natural logarithm.

Returns: Base of natural logarithm.

Definition at line 682 of file special_functions.hpp.

void stan::math::eigen_decompose	(	const matrix_d &	m,
		vector_d &	eigenvalues,
		matrix_d &	eigenvectors
	)

Assign the real components of the eigenvalues and eigenvectors of the specified matrix to the specified references.

Given an input matrix $A$ , the eigenvalues will be found in $D$ in descending order of magnitude. The eigenvectors will be written into the columns of $V$ . If $A$ is invertible, then

$A = V \times \mbox{\rm diag}(D) \times V^{-1}$ , where $ $\mbox{\rm diag}(D)$ is the square diagonal matrix with diagonal elements $D$ and $V^{-1}$ is the inverse of $V$ .

Parameters

m	Specified matrix.
eigenvalues	Column vector reference into which eigenvalues are written.
eigenvectors	Matrix reference into which eigenvectors are written.

Definition at line 202 of file matrix.cpp.

void stan::math::eigen_decompose_sym	(	const matrix_d &	m,
		vector_d &	eigenvalues,
		matrix_d &	eigenvectors
	)

Assign the real components of the eigenvalues and eigenvectors of the specified symmetric matrix to the specified references.

See eigen_decompose() for more information on the values.

Parameters

m	Symmetric matrix. This function is more efficient than the general decomposition method for symmetric matrices.
eigenvalues	Column vector reference into which eigenvalues are written.
eigenvectors	Matrix reference into which eigenvectors are written.

Definition at line 225 of file matrix.cpp.

vector_d stan::math::eigenvalues ( const matrix_d & m )

Return the real component of the eigenvalues of the specified matrix in descending order of magnitude.

See eigen_decompose() for more information.

Parameters

m	Specified matrix.

Returns: Eigenvalues of matrix.

Definition at line 187 of file matrix.cpp.

vector_d stan::math::eigenvalues_sym ( const matrix_d & m )

Return the eigenvalues of the specified symmetric matrix in descending order of magnitude.

This function is more efficient than the general eigenvalues function for symmetric matrices.

See eigen_decompose() for more information.

Parameters

m	Specified matrix.

Returns: Eigenvalues of matrix.

Definition at line 210 of file matrix.cpp.

matrix_d stan::math::eigenvectors ( const matrix_d & m )

Return a matrix whose columns are the real components of the eigenvectors of the specified matrix.

See eigen_decompose() for more information.

Parameters

m	Specified matrix.

Returns: Eigenvectors of matrix.

Definition at line 195 of file matrix.cpp.

matrix_d stan::math::eigenvectors_sym ( const matrix_d & m )

Return a matrix whose rows are the real components of the eigenvectors of the specified symmetric matrix.

This function is more efficient than the general eigenvectors function for symmetric matrices.

See eigen_decompose() for more information.

Parameters

m	Symmetric matrix.

Returns: Eigenvectors of matrix.

Definition at line 218 of file matrix.cpp.

vector_d stan::math::elt_divide	(	const vector_d &	v1,
		const vector_d &	v2
	)

Return the element-wise divsion of the specified vectors.

Parameters

v1	First vector.
v2	Second vector.

Returns: Elementwise division of the vectors.

Definition at line 95 of file matrix.cpp.

row_vector_d stan::math::elt_divide	(	const row_vector_d &	v1,
		const row_vector_d &	v2
	)

Return the element-wise division of the specified row vectors.

Parameters

v1	First row vector.
v2	Second row vector.

Returns: Elementwise division of the vectors.

Definition at line 103 of file matrix.cpp.

matrix_d stan::math::elt_divide	(	const matrix_d &	m1,
		const matrix_d &	m2
	)

Return the element-wise division of the specified matrices.

Parameters

m1	First matrix.
m2	Second matrix.

Returns: Elementwise division of the matrices.

Definition at line 111 of file matrix.cpp.

vector_d stan::math::elt_multiply	(	const vector_d &	v1,
		const vector_d &	v2
	)

Return the element-wise product of the specified vectors.

Parameters

v1	First vector.
v2	Second vector.

Returns: Elementwise product of the vectors.

Definition at line 70 of file matrix.cpp.

row_vector_d stan::math::elt_multiply	(	const row_vector_d &	v1,
		const row_vector_d &	v2
	)

Return the element-wise product of the specified row vectors.

Parameters

v1	First row vector.
v2	Second row vector.

Returns: Elementwise product of the vectors.

Definition at line 78 of file matrix.cpp.

matrix_d stan::math::elt_multiply	(	const matrix_d &	m1,
		const matrix_d &	m2
	)

Return the element-wise product of the specified matrices.

Parameters

m1	First matrix.
m2	Second matrix.

Returns: Elementwise product of the matrices.

Definition at line 86 of file matrix.cpp.

double stan::math::epsilon ( )

inline

Return minimum positive number representable.

Returns: Minimum positive number.

Definition at line 745 of file special_functions.hpp.

template<typename T , int Rows, int Cols>

Eigen::Matrix<T,Rows,Cols> stan::math::exp ( const Eigen::Matrix< T, Rows, Cols > & m )

inline

Return the element-wise exponentiation of the matrix or vector.

Parameters

m	The matrix or vector.

Returns: ret(i,j) = exp(m(i,j))

Definition at line 1086 of file matrix.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::exp2 ( T y )

inline

Return the exponent base 2 of the specified argument (C99).

The exponent base 2 function is defined by

exp2(y) = pow(2.0,y).

Parameters

y Value.

Template Parameters

T	Type of scalar.

Returns: Exponent base 2 of value.

Definition at line 34 of file special_functions.hpp.

template<typename T1 , typename T2 >

boost::math::tools::promote_args<T1, T2>::type stan::math::fdim	(	T1	a,
		T2	b
	)

inline

The positive difference function (C99).

The function is defined by

fdim(a,b) = (a > b) ? (a - b) : 0.0.

Parameters

a	First value.
b	Second value.

Returns: Returns min(a - b, 0.0).

Definition at line 52 of file special_functions.hpp.

template<typename T1 , typename T2 , typename T3 >

boost::math::tools::promote_args<T1,T2,T3>::type stan::math::fma	(	T1	a,
		T2	b,
		T3	c
	)

inline

The fused multiply-add operation (C99).

The function is defined by

fma(a,b,c) = (a * b) + c.

Parameters

a	First value.
b	Second value.
c	Third value.

Returns: Product of the first two values plust the third.

Definition at line 70 of file special_functions.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< T > &	x,
		size_t	i,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i	Index into vector plus 1.
error_msg	Error message if the index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at i - 1

Template Parameters

T	type of value.

Definition at line 188 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< T > > &	x,
		size_t	i1,
		size_t	i2,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 213 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< std::vector< T > > > &	x,
		size_t	i1,
		size_t	i2,
		size_t	i3,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
i3	Third index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 240 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< std::vector< std::vector< T > > > > &	x,
		size_t	i1,
		size_t	i2,
		size_t	i3,
		size_t	i4,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
i3	Third index plus 1.
i4	Fourth index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 269 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &	x,
		size_t	i1,
		size_t	i2,
		size_t	i3,
		size_t	i4,
		size_t	i5,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
i3	Third index plus 1.
i4	Fourth index plus 1.
i5	Fifth index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 300 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &	x,
		size_t	i1,
		size_t	i2,
		size_t	i3,
		size_t	i4,
		size_t	i5,
		size_t	i6,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
i3	Third index plus 1.
i4	Fourth index plus 1.
i5	Fifth index plus 1.
i6	Sixth index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 333 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &	x,
		size_t	i1,
		size_t	i2,
		size_t	i3,
		size_t	i4,
		size_t	i5,
		size_t	i6,
		size_t	i7,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
i3	Third index plus 1.
i4	Fourth index plus 1.
i5	Fifth index plus 1.
i6	Sixth index plus 1.
i7	Seventh index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 369 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &	x,
		size_t	i1,
		size_t	i2,
		size_t	i3,
		size_t	i4,
		size_t	i5,
		size_t	i6,
		size_t	i7,
		size_t	i8,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Vector from which to get a value.
i1	First index plus 1.
i2	Second index plus 1.
i3	Third index plus 1.
i4	Fourth index plus 1.
i5	Fifth index plus 1.
i6	Sixth index plus 1.
i7	Seventh index plus 1.
i8	Eigth index plus 1.
error_msg	Error message if an index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of vector at indexes.

Template Parameters

T	type of value.

Definition at line 407 of file matrix.hpp.

template<typename T >

Eigen::Matrix<T,1,Eigen::Dynamic> stan::math::get_base1	(	Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	x,
		size_t	m,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a copy of the row of the specified vector at the specified base-one row index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Warning: Because a copy is involved, it is inefficient to access element of matrices by first using this method to get a row then using a second call to get the value at a specified column.

Parameters

x	Matrix from which to get a row
m	Index into matrix plus 1.
error_msg	Error message if the index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Row of matrix at i - 1.

Template Parameters

T	type of value.

Definition at line 446 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	x,
		size_t	m,
		size_t	n,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified matrix at the specified base-one row and column indexes.

If either index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Matrix from which to get a row
m	Row index plus 1.
n	Column index plus 1.
error_msg	Error message if either index is out of range.
idx	Nested index level to report in error message if either index is out of range.

Returns: Value of matrix at row m - 1 and column n - 1.

Template Parameters

T	type of value.

Definition at line 472 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		size_t	m,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified column vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Column vector from which to get a value.
m	Row index plus 1.
error_msg	Error message if the index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of column vector at row m - 1.

Template Parameters

T	type of value.

Definition at line 498 of file matrix.hpp.

template<typename T >

T& stan::math::get_base1	(	Eigen::Matrix< T, 1, Eigen::Dynamic > &	x,
		size_t	n,
		const char *	error_msg,
		size_t	idx
	)

inline

Return a reference to the value of the specified row vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters

x	Row vector from which to get a value.
n	Column index plus 1.
error_msg	Error message if the index is out of range.
idx	Nested index level to report in error message if the index is out of range.

Returns: Value of row vector at column n - 1.

Template Parameters

T	type of value.

Definition at line 523 of file matrix.hpp.

double stan::math::ibeta	(	const double &	a,
		const double &	b,
		const double &	x
	)

inline

The normalized incomplete beta function of a, b, and x.

Used to compute the cumulative density function for the beta distribution.

Parameters

a	Shape parameter.
b	Shape parameter.
x	Random variate.

Returns: The normalized incomplete beta function.

Definition at line 572 of file special_functions.hpp.

double stan::math::if_else	(	bool	c,
		double	y_true,
		double	y_false
	)

inline

Return the second argument if the first argument is true and otherwise return the second argument.

This is just a convenience method to provide a function with the same behavior as the built-in ternary operator. In general, this function behaves as if defined by

if_else(c,y1,y0) = c ? y1 : y0.

Parameters

c	Boolean condition value.
y_true	Value to return if condition is true.
y_false	Value to return if condition is false.

Definition at line 489 of file special_functions.hpp.

template<typename T >

unsigned int stan::math::int_step ( T y )

The integer step, or Heaviside, function.

Parameters

y	Value to test.

Returns: 1 if value is greater than 0 and 0 otherwise

Template Parameters

T	Scalar argument type.

Definition at line 103 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::inv_cloglog ( T x )

inline

The inverse complementary log-log function.

The function is defined by

inv_cloglog(x) = -exp(-exp(x)).

This function can be used to implement the inverse link function for complenentary-log-log regression.

Parameters

x Argument.

Returns: Inverse complementary log-log of the argument.

Definition at line 270 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::inv_logit ( T a )

inline

Returns the inverse logit function applied to the argument.

The inverse logit function is defined by

$\mbox{logit}^{-1}(x) = \frac{1}{1 + \exp(-x)}$ .

This function can be used to implement the inverse link function for logistic regression.

The inverse to this function is stan::math::logit.

Parameters

a Argument.

Returns: Inverse logit of argument.

Definition at line 205 of file special_functions.hpp.

matrix_d stan::math::inverse ( const matrix_d & m )

Returns the inverse of the specified matrix.

Parameters

m	Specified matrix.

Returns: Inverse of the matrix.

Definition at line 174 of file matrix.cpp.

template<typename Vector >

void stan::math::inverse_softmax	(	const Vector &	simplex,
		Vector &	y
	)

Writes the inverse softmax of the simplex argument into the second argument.

See stan::math::softmax for the inverse function and a definition of the relation.

The inverse softmax function is defined by

$\mbox{inverse\_softmax}(x)[i] = \log x[i]$ .

This function defines the inverse of stan::math::softmax up to a scaling factor.

Because of the definition, values of 0.0 in the simplex are converted to negative infinity, and values of 1.0 are converted to 0.0.

There is no check that the input vector is a valid simplex vector.

Parameters

simplex	Simplex vector input.
y	Vector into which the inverse softmax is written.

Exceptions

std::invalid_argument if size of the input and output vectors differ.

Definition at line 397 of file special_functions.hpp.

template<typename T1 , typename T2 >

boost::math::tools::promote_args<T1,T2>::type stan::math::lbeta	(	T1	a,
		T2	b
	)

inline

Return the log of the beta function applied to the specified arguments.

The beta function is defined for $a > 0$ and $b > 0$ by

$\mbox{B}(a,b) = \frac{\Gamma(a) \Gamma(b)}{\Gamma(a+b)}$ .

This function returns its log,

$\log \mbox{B}(a,b) = \log \Gamma(a) + \log \Gamma(b) - \log \Gamma(a+b)$ .

See boost::math::lgamma() for the double-based and stan::agrad for the variable-based log Gamma function.

Parameters

a	First value
b	Second value

Returns: Log of the beta function applied to the two values.

Template Parameters

T1	Type of first value.
T2	Type of second value.

Definition at line 150 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::lmgamma	(	unsigned int	k,
		T	x
	)

inline

Return the natural logarithm of the multivariate gamma function with the speciifed dimensions and argument.

The multivariate gamma function $\Gamma_k(x)$ for dimensionality $k$ and argument $x$ is defined by

$\Gamma_k(x) = \pi^{k(k-1)/4} \, \prod_{j=1}^k \Gamma(x + (1 - j)/2)$ ,

where $\Gamma()$ is the gamma function.

Parameters

k	Number of dimensions.
x	Function argument.

Returns: Natural log of the multivariate gamma function.

Template Parameters

T	Type of scalar.

Definition at line 466 of file special_functions.hpp.

template<typename T , int Rows, int Cols>

Eigen::Matrix<T,Rows,Cols> stan::math::log ( const Eigen::Matrix< T, Rows, Cols > & m )

inline

Return the element-wise logarithm of the matrix or vector.

Parameters

m	The matrix or vector.

Returns: ret(i,j) = log(m(i,j))

Definition at line 1075 of file matrix.hpp.

double stan::math::log10 ( )

inline

Return natural logarithm of ten.

Returns: Natural logarithm of ten.

Definition at line 709 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::log1m ( T x )

inline

Return the natural logarithm of one minus the specified value.

The main use of this function is to cut down on intermediate values during algorithmic differentiation.

Parameters

x	Specified value.

Returns: Natural log of one minus x.

Definition at line 440 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::log1p ( T x )

inline

Return the natural logarithm of one plus the specified value.

The main use of this function is to cut down on intermediate values during algorithmic differentiation.

Parameters

x	Specified value.

Returns: Natural log of one plus x.

Definition at line 416 of file special_functions.hpp.

double stan::math::log1p_exp ( const double & a )

inline

Calculates the log of 1 plus the exponential of the specified value without overflow.

This function is related to other special functions by:

log_1p_exp(x)

= log1p(exp(a))

= log(1 + exp(x))

= log_sum_exp(0,x).

Definition at line 535 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::log2 ( T a )

inline

Returns the base 2 logarithm of the argument (C99).

The function is defined by:

log2(a) = log(a) / std::log(2.0).

Template Parameters

T	type of scalar

Parameters

a Value.

Returns: Base 2 logarithm of the value.

Definition at line 87 of file special_functions.hpp.

double stan::math::log2 ( )

inline

Return natural logarithm of two.

Returns: Natural logarithm of two.

Definition at line 700 of file special_functions.hpp.

double stan::math::log_sum_exp	(	const double &	a,
		const double &	b
	)

inline

Calculates the log sum of exponetials without overflow.

$\log (\exp(a) + \exp(b)) = m + \log(\exp(a-m) + \exp(b-m))$ ,

where $m = max(a,b)$ .

Parameters

a	the first variable
b	the second variable

Definition at line 553 of file special_functions.hpp.

static double stan::math::log_sum_exp ( const std::vector< double > & x )

static

Return the log of the sum of the exponentiated values of the specified sequence of values.

The function is defined as follows to prevent overflow in exponential calculations.

$\log \sum_{n=1}^N \exp(x_n) = \max(x) + \log \sum_{n=1}^N \exp(x_n - \max(x))$ .

Parameters

x	array of specified values

Definition at line 591 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::logit ( T a )

inline

Returns the logit function applied to the argument.

The logit function is defined as for $x \in [0,1]$ by returning the log odds of $x$ treated as a probability,

$\mbox{logit}(x) = \log \left( \frac{x}{1 - x} \right)$ .

The inverse to this function is stan::math::inv_logit.

Parameters

a Argument.

Returns: Logit of the argument.

Definition at line 226 of file special_functions.hpp.

double stan::math::max	(	double	a,
		double	b
	)

inline

Definition at line 12 of file util.hpp.

double stan::math::max ( std::vector< double > & x )

inline

Definition at line 16 of file util.hpp.

int stan::math::max ( const std::vector< int > & x )

inline

Returns the maximum coefficient in the specified column vector.

Parameters

v	Specified vector.

Returns: Maximum coefficient value in the vector.

Template Parameters

Type	of values being compared and returned

Exceptions

std::domain_error If the size of the vector is zero.

Definition at line 845 of file matrix.hpp.

template<typename T >

T stan::math::max ( const std::vector< T > & x )

inline

Returns the maximum coefficient in the specified column vector.

Parameters

v	Specified vector.

Returns: Maximum coefficient value in the vector.

Template Parameters

T	Type of values being compared and returned

Definition at line 863 of file matrix.hpp.

template<typename T , int R, int C>

T stan::math::max ( const Eigen::Matrix< T, R, C > & m )

inline

Returns the maximum coefficient in the specified vector, row vector, or matrix.

Parameters

v	Specified vector, row vector, or matrix.

Returns: Maximum coefficient value in the vector.

Definition at line 880 of file matrix.hpp.

template<int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::mdivide_left	(	const Eigen::Matrix< double, R1, C1 > &	A,
		const Eigen::Matrix< double, R2, C2 > &	b
	)

inline

Returns the solution of the system Ax=b.

Parameters

A	Matrix.
b	Right hand side matrix or vector.

Returns: x = A^-1 b, solution of the linear system.

Exceptions

std::domain_error if A is not square or the rows of b don't match the size of A.

Definition at line 1595 of file matrix.hpp.

template<int TriView, int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::mdivide_left_tri	(	const Eigen::Matrix< double, R1, C1 > &	A,
		const Eigen::Matrix< double, R2, C2 > &	b
	)

inline

Returns the solution of the system Ax=b when A is triangular.

Parameters

A	Triangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower.
b	Right hand side matrix or vector.

Returns: x = A^-1 b, solution of the linear system.

Exceptions

std::domain_error if A is not square or the rows of b don't match the size of A.

Definition at line 1527 of file matrix.hpp.

template<int TriView>

Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic> stan::math::mdivide_left_tri ( const Eigen::MatrixXd & A )

inline

Returns the solution of the system Ax=b when A is triangular and b=I.

Parameters

A	Triangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower.

Returns: x = A^-1 .

Exceptions

std::domain_error if A is not square

Definition at line 1543 of file matrix.hpp.

template<int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::mdivide_left_tri_low	(	const Eigen::Matrix< double, R1, C1 > &	A,
		const Eigen::Matrix< double, R2, C2 > &	b
	)

inline

Definition at line 1498 of file matrix.hpp.

Eigen::MatrixXd stan::math::mdivide_left_tri_low ( const Eigen::MatrixXd & A )

inline

Definition at line 1507 of file matrix.hpp.

template<int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::mdivide_right	(	const Eigen::Matrix< double, R1, C1 > &	b,
		const Eigen::Matrix< double, R2, C2 > &	A
	)

inline

Returns the solution of the system Ax=b.

Parameters

A	Matrix.
b	Right hand side matrix or vector.

Returns: x = A^-1 b, solution of the linear system.

Exceptions

std::domain_error if A is not square or the rows of b don't match the size of A.

Definition at line 1612 of file matrix.hpp.

template<int TriView, int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::mdivide_right_tri	(	const Eigen::Matrix< double, R1, C1 > &	b,
		const Eigen::Matrix< double, R2, C2 > &	A
	)

inline

Returns the solution of the system Ax=b when A is triangular.

Parameters

A	Triangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower.
b	Right hand side matrix or vector.

Returns: x = A^-1 b, solution of the linear system.

Exceptions

std::domain_error if A is not square or the rows of b don't match the size of A.

Definition at line 1562 of file matrix.hpp.

template<int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::mdivide_right_tri_low	(	const Eigen::Matrix< double, R1, C1 > &	b,
		const Eigen::Matrix< double, R2, C2 > &	A
	)

inline

Returns the solution of the system tri(A)x=b when tri(A) is a lower triangular view of the matrix A.

Parameters

A	Matrix.
b	Right hand side matrix or vector.

Returns: x = tri(A)^-1 b, solution of the linear system.

Exceptions

std::domain_error if A is not square or the rows of b don't match the size of A.

Definition at line 1580 of file matrix.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::mean ( const std::vector< T > & v )

inline

Returns the sample mean (i.e., average) of the coefficients in the specified standard vector.

Parameters

v	Specified vector.

Returns: Sample mean of vector coefficients.

Exceptions

std::domain_error if the size of the vector is less than 1.

Definition at line 897 of file matrix.hpp.

template<typename T , int R, int C>

boost::math::tools::promote_args<T>::type stan::math::mean ( const Eigen::Matrix< T, R, C > & m )

inline

Returns the sample mean (i.e., average) of the coefficients in the specified vector, row vector, or matrix.

Parameters

m	Specified vector, row vector, or matrix.

Returns: Sample mean of vector coefficients.

Definition at line 914 of file matrix.hpp.

double stan::math::min	(	double	a,
		double	b
	)

inline

Definition at line 25 of file util.hpp.

int stan::math::min ( const std::vector< int > & x )

inline

Returns the minimum coefficient in the specified column vector.

Parameters

v	Specified vector.

Returns: Minimum coefficient value in the vector.

Template Parameters

Type	of values being compared and returned

Definition at line 794 of file matrix.hpp.

template<typename T >

T stan::math::min ( const std::vector< T > & x )

inline

Returns the minimum coefficient in the specified column vector.

Parameters

v	Specified vector.

Returns: Minimum coefficient value in the vector.

Template Parameters

Type	of values being compared and returned

Definition at line 812 of file matrix.hpp.

template<typename T , int R, int C>

T stan::math::min ( const Eigen::Matrix< T, R, C > & m )

inline

Returns the minimum coefficient in the specified matrix, vector, or row vector.

Parameters

v	Specified matrix, vector, or row vector.

Returns: Minimum coefficient value in the vector.

Definition at line 829 of file matrix.hpp.

vector_d stan::math::minus ( const vector_d & v )

Return the negation of the specified column vector.

The result is the same as multiplying by the scalar -1.

Parameters

v	Specified vector.

Returns: The negation of the vector.

Definition at line 46 of file matrix.cpp.

row_vector_d stan::math::minus ( const row_vector_d & rv )

Return the negation of the specified row vector.

The result is the same as multiplying by the scalar -1.

Parameters

rv	Specified vector.

Returns: The negation of the vector.

Definition at line 50 of file matrix.cpp.

matrix_d stan::math::minus ( const matrix_d & m )

Return the negation of the specified matrix.

The result is the same as multiplying by the scalar -1.

Parameters

m	Specified matrix.

Returns: The negation of the matrix.

Definition at line 54 of file matrix.cpp.

vector_d stan::math::multiply	(	const vector_d &	v,
		double	c
	)

Return the product of the of the specified column vector and specified scalar.

Parameters

v	Specified vector.
c	Specified scalar.

Returns: Product of vector and scalar.

Definition at line 120 of file matrix.cpp.

row_vector_d stan::math::multiply	(	const row_vector_d &	rv,
		double	c
	)

Return the product of the of the specified row vector and specified scalar.

Parameters

rv	Specified vector.
c	Specified scalar.

Returns: Product of vector and scalar.

Definition at line 124 of file matrix.cpp.

matrix_d stan::math::multiply	(	const matrix_d &	m,
		double	c
	)

Return the product of the of the specified matrix and specified scalar.

Parameters

m	Matrix.
c	Scalar.

Returns: Product of matrix and scalar.

Definition at line 128 of file matrix.cpp.

vector_d stan::math::multiply	(	double	c,
		const vector_d &	v
	)

Return the product of the specified scalar and vector.

Parameters

c	Scalar.
v	Vector.

Returns: Product of scalar and vector.

Definition at line 132 of file matrix.cpp.

row_vector_d stan::math::multiply	(	double	c,
		const row_vector_d &	rv
	)

Return the product of the specified scalar and row vector.

Parameters

c	Scalar.
rv	Row vector.

Returns: Product of scalar and row vector.

Definition at line 136 of file matrix.cpp.

matrix_d stan::math::multiply	(	double	c,
		const matrix_d &	m
	)

Return the product of the specified scalar and matrix.

Parameters

c	Scalar.
m	Matrix

Returns: Product of scalar and matrix.

Definition at line 140 of file matrix.cpp.

template<int R1, int C1, int R2, int C2>

Eigen::Matrix<double,R1,C2> stan::math::multiply	(	const Eigen::Matrix< double, R1, C1 > &	m1,
		const Eigen::Matrix< double, R2, C2 > &	m2
	)

inline

Return the product of the specified matrices.

The number of columns in the first matrix must be the same as the number of rows in the second matrix.

Parameters

m1	First matrix.
m2	Second matrix.

Returns: The product of the first and second matrices.

Exceptions

std::domain_error if the number of columns of m1 does not match the number of rows of m2.

Definition at line 1321 of file matrix.hpp.

template<int C1, int R2>

double stan::math::multiply	(	const Eigen::Matrix< double, 1, C1 > &	rv,
		const Eigen::Matrix< double, R2, 1 > &	v
	)

inline

Return the scalar product of the specified row vector and specified column vector.

The return is the same as the dot product. The two vectors must be the same size.

Parameters

rv	Row vector.
v	Column vector.

Returns: Scalar result of multiplying row vector by column vector.

Exceptions

std::domain_error if rv and v are not the same size.

Definition at line 1338 of file matrix.hpp.

template<typename T_a , typename T_b >

boost::math::tools::promote_args<T_a,T_b>::type stan::math::multiply_log	(	T_a	a,
		T_b	b
	)

inline

Definition at line 514 of file special_functions.hpp.

matrix_d stan::math::multiply_lower_tri_self_transpose ( const matrix_d & L )

inline

Returns the result of multiplying the lower triangular portion of the square input matrix by its own transpose.

Parameters

L	Matrix to multiply.

Returns: The lower triangular values in L times their own transpose.

Exceptions

std::domain_error If the input matrix is not square.

Definition at line 1376 of file matrix.hpp.

double stan::math::negative_epsilon ( )

inline

Return maximum negative number (i.e., negative number with smallest absolute value).

Returns: Maximum negative number.

Definition at line 755 of file special_functions.hpp.

double stan::math::negative_infinity ( )

inline

Return negative infinity.

Returns: Negative infinity.

Definition at line 727 of file special_functions.hpp.

double stan::math::not_a_number ( )

inline

Return (quiet) not-a-number.

Returns: Quiet not-a-number.

Definition at line 736 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::Phi ( T x )

inline

The unit normal cumulative distribution function.

The return value for a specified input is the probability that a random unit normal variate is less than or equal to the specified value, defined by

$\Phi(x) = \int_{-\infty}^x \mbox{\sf Norm}(x|0,1) \ dx$

This function can be used to implement the inverse link function for probit regression.

Parameters

x Argument.

Returns: Probability random sample is less than or equal to argument.

Definition at line 250 of file special_functions.hpp.

double stan::math::pi ( )

inline

Return the value of pi.

Returns: Pi.

Definition at line 673 of file special_functions.hpp.

double stan::math::positive_infinity ( )

inline

Return positive infinity.

Returns: Positive infinity.

Definition at line 718 of file special_functions.hpp.

template<typename T >

T stan::math::prod ( const std::vector< T > & v )

inline

Returns the product of the coefficients of the specified standard vector.

Parameters

v	Specified vector.

Returns: Product of coefficients of vector.

Definition at line 1034 of file matrix.hpp.

template<typename T , int R, int C>

T stan::math::prod ( const Eigen::Matrix< T, R, C > & v )

inline

Returns the product of the coefficients of the specified column vector.

Parameters

v	Specified vector.

Returns: Product of coefficients of vector.

Definition at line 1049 of file matrix.hpp.

template<typename T >

void stan::math::resize	(	T &	x,
		std::vector< size_t >	dims
	)

inline

Recursively resize the specified vector of vectors, which must bottom out at scalar values, Eigen vectors or Eigen matrices.

Parameters

x	Array-like object to resize.
dims	New dimensions.

Template Parameters

T	Type of object being resized.

Definition at line 135 of file matrix.hpp.

row_vector_d stan::math::row	(	const matrix_d &	m,
		size_t	i
	)

Return the specified row of the specified matrix, using start-at-1 indexing.

This is equivalent to calling m.row(i - 1) and assigning the resulting template expression to a row vector.

Parameters

m	Matrix.
i	Row index.

Returns: Specified row of the matrix.

Definition at line 144 of file matrix.cpp.

size_t stan::math::rows ( const vector_d & v )

inline

Return the number of rows in the specified column vector.

Parameters

v	Specified vector.

Returns: Number of rows in the vector.

Definition at line 540 of file matrix.hpp.

size_t stan::math::rows ( const row_vector_d & rv )

inline

Return the number of rows in the specified row vector.

The return value is always 1.

Parameters

rv	Specified vector.

Returns: Number of rows in the vector.

Definition at line 549 of file matrix.hpp.

size_t stan::math::rows ( const matrix_d & m )

inline

Return the number of rows in the specified matrix.

Parameters

m	Specified matrix.

Returns: Number of rows in the vector.

Definition at line 558 of file matrix.hpp.

void stan::math::scaled_add	(	std::vector< double > &	x,
		std::vector< double > &	y,
		double	lambda
	)

inline

Definition at line 47 of file util.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::sd ( const std::vector< T > & v )

inline

Returns the unbiased sample standard deviation of the coefficients in the specified column vector.

Parameters

v	Specified vector.

Returns: Sample variance of vector.

Definition at line 977 of file matrix.hpp.

template<typename T , int R, int C>

boost::math::tools::promote_args<T>::type stan::math::sd ( const Eigen::Matrix< T, R, C > & m )

inline

Returns the unbiased sample standard deviation of the coefficients in the specified vector, row vector, or matrix.

Parameters

m	Specified vector, row vector or matrix.

Returns: Sample variance.

Definition at line 992 of file matrix.hpp.

template<typename T1 , typename T2 , typename T3 >

double stan::math::simple_var	(	double	v,
		const T1 &	,
		const T1 &	,
		const T2 &	,
		const T2 &	,
		const T3 &	,
		const T3 &
	)

inline

Return the scalar value and ignore the remaining arguments.

This function provides an overload of simple_var to use with primitive values for which the type and derivative type are the same. The other overloads are for stan::agrad::var arguments; the definitions can be found in stan/agrad/partials_vari.hpp.

Template Parameters

T1	Type of first dummy argument and derivative.
T2	Type of second dummy argument and derivative.
T3	Type of third dummy argument and derivative.

Parameters

v	Value to return.

Returns: Value.

Definition at line 626 of file special_functions.hpp.

vector_d stan::math::singular_values ( const matrix_d & m )

Return the vector of the singular values of the specified matrix in decreasing order of magnitude.

See the documentation for svd() for information on the signular values.

Parameters

m	Specified matrix.

Returns: Singular values of the matrix.

Definition at line 240 of file matrix.cpp.

vector_d stan::math::softmax ( const vector_d & y )

Return the softmax of the specified vector.

Parameters

y	Vector to transform

Returns: Unit simplex result of the softmax transform of the vector.

Definition at line 180 of file matrix.cpp.

template<typename Vector , typename Scalar >

void stan::math::softmax	(	const Vector &	x,
		Vector &	simplex
	)

Write the values of the softmax transformed first argument into the second argument.

Values in the first argument are unbounded and values in the output form a simplex.

The softmax transformed generalizes the inverse logistic function by transforming a vector $x$ of length $K$ as

$\mbox{softmax}(x)[i] = \frac{\exp(x[i])}{\sum_{k=1}^{K} \exp(x[k])}$ .

By construction, the result is a simplex, which means the values are all non-negative and sum to 1.0,

$\sum_{k=1}^{K} \mbox{softmax}(x)[k] = 1$ .

The type Vector is for a vector with values of type Scalar. Vectors x must support x.size() and return assignable references of type Scalar through x[int]. Variables a of type Scalar need to support division (in context x[i] /= a) and exponentiation (exp(a)). Conforming examples include

Vector = std::vector<double> and Scalar = double,

Vector = std::vector<stan::agrad::var> and Scalar = stan::agrad::var,

Vector = Eigen::Matrix<double,Eigen::Dynamic,1><double> and Scalar = double,

and so on.

The function stan::math::inverse_softmax provides an inverse of this operation up to an additive constant. Specifically, if x is a simplex argument, then

softmax(inv_softmax(x)) = x.

If y is an arbitrary vector, then we only have identification up to an additive constant c, as in

inv_softmax(softmax(y)) = y + c * I.

Parameters

x	Input vector of unbounded parameters.
simplex	Output vector of simplex values.

Exceptions

std::invalid_argument if size of the input and output vectors differ.

Definition at line 362 of file special_functions.hpp.

double stan::math::sqrt2 ( )

inline

Return the square root of two.

Returns: Square root of two.

Definition at line 691 of file special_functions.hpp.

template<typename T >

T stan::math::square ( T x )

inline

Return the square of the specified argument.

$\mbox{square}(x) = x^2$ .

The implementation of square(x) is just x * x. Given this, this method is mainly useful in cases where x is not a simple primitive type, particularly when it is an auto-dif type.

Parameters

x	Input to square.

Returns: Square of input.

Template Parameters

T	Type of scalar.

Definition at line 508 of file special_functions.hpp.

template<typename T >

void stan::math::stan_print	(	std::ostream *	o,
		const T &	x
	)

Definition at line 1742 of file matrix.hpp.

template<typename T >

void stan::math::stan_print	(	std::ostream *	o,
		const std::vector< T > &	x
	)

Definition at line 1747 of file matrix.hpp.

template<typename T >

void stan::math::stan_print	(	std::ostream *	o,
		const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x
	)

Definition at line 1757 of file matrix.hpp.

template<typename T >

void stan::math::stan_print	(	std::ostream *	o,
		const Eigen::Matrix< T, 1, Eigen::Dynamic > &	x
	)

Definition at line 1767 of file matrix.hpp.

template<typename T >

void stan::math::stan_print	(	std::ostream *	o,
		const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	x
	)

Definition at line 1777 of file matrix.hpp.

template<typename T >

int stan::math::step ( T y )

inline

The step, or Heaviside, function.

The function is defined by

step(y) = (y < 0.0) ? 0 : 1.

Parameters

y	Scalar argument.

Returns: 1 if the specified argument is greater than or equal to 0.0, and 0 otherwise.

Definition at line 120 of file special_functions.hpp.

void stan::math::sub	(	std::vector< double > &	x,
		std::vector< double > &	y,
		std::vector< double > &	result
	)

inline

Definition at line 54 of file util.hpp.

vector_d stan::math::subtract	(	const vector_d &	v1,
		const vector_d &	v2
	)

Return the difference between the first specified column vector and the second.

The two vectors must have the same size.

Parameters

v1	First vector.
v2	Second vector.

Returns: First vector minus the second vector.

Exceptions

std::domain_error if v1 and v2 are not the same size.

Definition at line 31 of file matrix.cpp.

row_vector_d stan::math::subtract	(	const row_vector_d &	rv1,
		const row_vector_d &	rv2
	)

Return the difference between the first specified row vector and the second.

The two vectors must have the same size.

Parameters

rv1	First vector.
rv2	Second vector.

Returns: First vector minus the second vector.

Exceptions

std::domain_error if rv1 and rv2 are not the same size.

Definition at line 36 of file matrix.cpp.

matrix_d stan::math::subtract	(	const matrix_d &	m1,
		const matrix_d &	m2
	)

Return the difference between the first specified matrix and the second.

The two matrices must have the same dimensions.

Parameters

m1	First matrix.
m2	Second matrix.

Returns: First matrix minus the second matrix.

Exceptions

std::domain_error if m1 and m2 are not the same size.

Definition at line 41 of file matrix.cpp.

template<int Rows, int Cols>

Eigen::Matrix<double,Rows,Cols> stan::math::subtract	(	const Eigen::Matrix< double, Rows, Cols > &	m,
		double	c
	)

inline

Return the difference between a matrix or vector and a scalar.

Parameters

m	Matrix or vector.
c	Scalar.

Returns: The matrix or vector minus the scalar.

Definition at line 1179 of file matrix.hpp.

template<int Rows, int Cols>

Eigen::Matrix<double,Rows,Cols> stan::math::subtract	(	double	c,
		const Eigen::Matrix< double, Rows, Cols > &	m
	)

inline

Return the difference between a scalar and a matrix or vector.

Parameters

c	Scalar.
m	Matrix or vector.

Returns: Scalar minus the matrix or vector.

Definition at line 1190 of file matrix.hpp.

double stan::math::sum ( std::vector< double > & x )

inline

Definition at line 71 of file util.hpp.

template<typename T >

T stan::math::sum ( const std::vector< T > & xs )

inline

Return the sum of the values in the specified standard vector.

Parameters

xs	Standard vector to sum.

Returns: Sum of elements.

Template Parameters

T	Type of elements summed.

Definition at line 1008 of file matrix.hpp.

template<typename T , int R, int C>

double stan::math::sum ( const Eigen::Matrix< T, R, C > & v )

inline

Returns the sum of the coefficients of the specified column vector.

Parameters

v	Specified vector.

Returns: Sum of coefficients of vector.

Definition at line 1023 of file matrix.hpp.

void stan::math::svd	(	const matrix_d &	m,
		matrix_d &	u,
		matrix_d &	v,
		vector_d &	s
	)

Assign the real components of a singular value decomposition of the specified matrix to the specified references.

Thesingular values $S$ are assigned to a vector in decreasing order of magnitude. The left singular vectors are found in the columns of $U$ and the right singular vectors in the columns of $V$ .

The original matrix is recoverable as

$A = U \times \mbox{\rm diag}(S) \times V^T$ , where $\mbox{\rm diag}(S)$ is the square diagonal matrix with diagonal elements $S$ .

If $A$ is an $M \times N$ matrix and $K = \mbox{\rm min}(M,N)$ , then $U$ is an $M \times K$ matrix, $S$ is a length $K$ column vector, and $V$ is an $N \times K$ matrix.

Parameters

m	Matrix to decompose.
u	Left singular vectors.
v	Right singular vectors.
s	Singular values.

Definition at line 245 of file matrix.cpp.

matrix_d stan::math::tcrossprod ( const matrix_d & M )

inline

Returns the result of post-multiplying a matrix by its own transpose.

Parameters

M	Matrix to multiply.

Returns: M times its transpose.

Definition at line 1398 of file matrix.hpp.

template<typename T >

T stan::math::trace ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & m )

inline

Returns the trace of the specified matrix.

The trace is defined as the sum of the elements on the diagonal. The matrix is not required to be square. Returns 0 if matrix is empty.

Parameters

[in] m Specified matrix.

Returns: Trace of the matrix.

Definition at line 1064 of file matrix.hpp.

row_vector_d stan::math::transpose ( const vector_d & v )

Return the transposition of the specified column vector.

Parameters

v	Specified vector.

Returns: Transpose of the vector.

Definition at line 162 of file matrix.cpp.

vector_d stan::math::transpose ( const row_vector_d & rv )

Return the transposition of the specified row vector.

Parameters

rv	Specified vector.

Returns: Transpose of the vector.

Definition at line 166 of file matrix.cpp.

matrix_d stan::math::transpose ( const matrix_d & m )

Return the transposition of the specified matrix.

Parameters

m	Specified matrix.

Returns: Transpose of the matrix.

Definition at line 170 of file matrix.cpp.

template<typename T , int R, int C>

void stan::math::validate_column_index	(	const Eigen::Matrix< T, R, C > &	m,
		size_t	j,
		const char *	msg
	)

Definition at line 590 of file matrix.hpp.

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>

void stan::math::validate_matching_dims	(	const Eigen::Matrix< T1, R1, C1 > &	x1,
		const Eigen::Matrix< T2, R2, C2 > &	x2,
		const char *	msg
	)

inline

Definition at line 626 of file matrix.hpp.

template<typename T1 , typename T2 >

void stan::math::validate_matching_sizes	(	const std::vector< T1 > &	x1,
		const std::vector< T2 > &	x2,
		const char *	msg
	)

inline

Definition at line 640 of file matrix.hpp.

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>

void stan::math::validate_matching_sizes	(	const Eigen::Matrix< T1, R1, C1 > &	x1,
		const Eigen::Matrix< T2, R2, C2 > &	x2,
		const char *	msg
	)

inline

Definition at line 652 of file matrix.hpp.

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>

void stan::math::validate_multiplicable	(	const Eigen::Matrix< T1, R1, C1 > &	x1,
		const Eigen::Matrix< T2, R2, C2 > &	x2,
		const char *	msg
	)

inline

Definition at line 667 of file matrix.hpp.

template<typename T >

void stan::math::validate_nonzero_size	(	const T &	x,
		const char *	msg
	)

inline

Definition at line 680 of file matrix.hpp.

template<typename T , int R, int C>

void stan::math::validate_row_index	(	const Eigen::Matrix< T, R, C > &	m,
		size_t	i,
		const char *	msg
	)

Definition at line 602 of file matrix.hpp.

template<typename T , int R, int C>

void stan::math::validate_square	(	const Eigen::Matrix< T, R, C > &	x,
		const char *	msg
	)

Definition at line 614 of file matrix.hpp.

template<typename T , int R, int C>

void stan::math::validate_vector	(	const Eigen::Matrix< T, R, C > &	x,
		const char *	msg
	)

inline

Definition at line 689 of file matrix.hpp.

template<typename T >

double stan::math::value_of ( T x )

inline

Return the value of the specified scalar argument converted to a double value.

This function is meant to cover the primitive types. For types requiring pass-by-reference, this template function should be specialized.

Template Parameters

T	Type of scalar.

Parameters

x	Scalar to convert to double.

Returns: Value of scalar cast to a double.

Definition at line 646 of file special_functions.hpp.

template<>

double stan::math::value_of< double > ( double x )

inline

Return the specified argument.

See value_of(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters

x	Specified value.

Returns: Specified value.

Definition at line 662 of file special_functions.hpp.

template<typename T >

boost::math::tools::promote_args<T>::type stan::math::variance ( const std::vector< T > & v )

inline

Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vector.

Parameters

v	Specified vector.

Returns: Sample variance of vector.

Exceptions

std::domain_error if the size of the vector is less than 1.

Definition at line 930 of file matrix.hpp.

template<typename T , int R, int C>

boost::math::tools::promote_args<T>::type stan::math::variance ( const Eigen::Matrix< T, R, C > & m )

inline

Returns the sample variance (divide by length - 1) of the coefficients in the specified column vector.

Parameters

v	Specified vector.

Returns: Sample variance of vector.

Definition at line 952 of file matrix.hpp.

Variable Documentation

const double stan::math::CONSTRAINT_TOLERANCE = 1E-8

The tolerance for checking arithmetic bounds In rank and in simplexes.

The default value is 1E-8.

Definition at line 24 of file error_handling.hpp.

const double stan::math::E = boost::math::constants::e<double>()

The base of the natural logarithm, $ e $ .

Definition at line 14 of file constants.hpp.

const double stan::math::EPSILON = std::numeric_limits<double>::epsilon()

Smallest positive value.

Definition at line 52 of file constants.hpp.

const double stan::math::INFTY = std::numeric_limits<double>::infinity()

Positive infinity.

Definition at line 37 of file constants.hpp.

const double stan::math::LOG_10 = std::log(10.0)

The natural logarithm of 10, $\log 10$ .

Definition at line 32 of file constants.hpp.

const double stan::math::LOG_2 = std::log(2.0)

The natural logarithm of 2, $\log 2$ .

Definition at line 26 of file constants.hpp.

const double stan::math::NEGATIVE_EPSILON = - std::numeric_limits<double>::epsilon()

Largest negative value (i.e., smallest absolute value).

Definition at line 57 of file constants.hpp.

const double stan::math::NEGATIVE_INFTY = - std::numeric_limits<double>::infinity()

Negative infinity.

Definition at line 42 of file constants.hpp.

const double stan::math::NOT_A_NUMBER = std::numeric_limits<double>::quiet_NaN()

(Quiet) not-a-number value.

Definition at line 47 of file constants.hpp.

const double stan::math::SQRT_2 = std::sqrt(2.0)

The value of the square root of 2, $\sqrt{2}$ .

Definition at line 20 of file constants.hpp.

Namespaces

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

Function Documentation

Variable Documentation