numeric Namespace Reference

Unit headers. More...

Namespaces
	alignment
	constants
	conversions
	coordinate_fitting
	crick_equations
	deriv
	expression_parser
	fourier
	geometry
	histograms
	interpolation
	kdtree
	kinematic_closure
	linear_algebra
	model_quality
	nls
	random
	statistics

Classes
class	AgglomerativeHierarchicalClusterer
class	AverageLinkClusterer
class	BodyPosition
	Rigid body 3-D position/transform. More...
class	Calculator
class	CalculatorParser
class	ClusteringTreeNode
class	ClusterOptions
class	ColPointers
class	ColsPointer
class	ColVectors
class	CompleteLinkClusterer
class	EulerAngles
	Euler angles 3-D orientation representation. More...
struct	FastRemainderSelector
	Fast remainder function selector class for non-integer types. More...
struct	FastRemainderSelector< T, true >
	Fast remainder function selector class for integer types. More...
class	HomogeneousTransform
class	HomogeneousTransform_Double
class	IntervalSet
class	IntervalSet_Double
struct	IOTraits
	Numerics input/output type traits. More...
struct	IOTraits< double >
	Numerics input/output type traits double specialization. More...
struct	IOTraits< float >
	Numerics input/output type traits float Specialization. More...
struct	IOTraits< int >
	Numerics input/output type traits int specialization. More...
struct	IOTraits< long double >
	Numerics input/output type traits long double specialization. More...
struct	IOTraits< long int >
	: Numerics input/output type traits long int specialization More...
struct	IOTraits< short int >
	Numerics input/output type traits short int specialization. More...
struct	IOTraits< unsigned int >
	: Numerics input/output type traits unsigned int specialization More...
struct	IOTraits< unsigned long int >
	Numerics input/output type traits unsigned long int specialization. More...
struct	IOTraits< unsigned short int >
	: Numerics input/output type traits unsigned short int specialization More...
class	MathMatrix
class	MathNTensor
class	MathTensor
class	MathVector
struct	ModSelector
	Mod function selector class for non-integer types. More...
struct	ModSelector< T, true >
	Mod function selector class for integer types. More...
struct	ModuloSelector
	Modulo function selector class for non-integer types. More...
struct	ModuloSelector< T, true >
	Modulo function selector class for integer types. More...
class	MultiDimensionalHistogram
	a class for accumulating a histogram of one or more numeric variables More...
struct	NearestSelector
	Nearest function selector class for R non-integer or T integer. More...
struct	NearestSelector< R, T, true >
	Nearest function selector class for R integer and T non-integer. More...
struct	NumericTraits
	NumericTraits: Numeric type traits. More...
struct	NumericTraits< double >
	NumericTraits: Numeric type traits double specialization. More...
struct	NumericTraits< float >
	NumericTraits: Numeric type traits float specialization. More...
struct	NumericTraits< long double >
	NumericTraits: Numeric type traits long double specialization. More...
class	Polynomial_1d
class	Py_xyzTransform_double
class	Quaternion
	Unit quaternion 3-D orientation representation. More...
struct	RemainderSelector
	Remainder function selector class for non-integer types. More...
struct	RemainderSelector< T, true >
	Remainder function selector class for integer types. More...
class	RocCurve
class	RocPoint
class	RowPointers
class	RowsPointer
class	RowVectors
class	SingleLinkClusterer
class	sphericalVector
	sphericalVector: Fast spherical-coordinate numeric vector More...
class	UniformRotationSampler
struct	urs_Quat
struct	XformHash32
struct	XformHash64
struct	Xforms
class	xyzMatrix
	xyzMatrix: Fast 3x3 xyz matrix template More...
class	xyzTransform
class	xyzTriple
	Fast (x,y,z)-coordinate vector container. More...
class	xyzVector
	xyzVector: Fast (x,y,z)-coordinate numeric vector More...

Typedefs
typedef BodyPosition< float >	BodyPosition_float
typedef BodyPosition< double >	BodyPosition_double
typedef BodyPosition< long double >	BodyPosition_longdouble
typedef utility::pointer::shared_ptr < Calculator >	CalculatorOP
typedef utility::pointer::shared_ptr < ClusteringTreeNode >	ClusteringTreeNodeOP
typedef utility::pointer::weak_ptr < ClusteringTreeNode >	ClusteringTreeNodeAP
typedef xyzVector< Real >	Vector
typedef Real	Length
typedef utility::pointer::shared_ptr < Polynomial_1d >	Polynomial_1dOP
typedef utility::pointer::shared_ptr < Polynomial_1d const >	Polynomial_1dCOP
typedef Quaternion< float >	Quaternion_float
typedef Quaternion< double >	Quaternion_double
typedef Quaternion< long double >	Quaternion_longdouble
typedef utility::pointer::shared_ptr < RocPoint >	RocPointOP
typedef utility::pointer::shared_ptr < RocCurve >	RocCurveOP
typedef double	Real
typedef platform::Size	Size
typedef platform::SSize	SSize
typedef utility::pointer::shared_ptr < UniformRotationSampler >	UniformRotationSamplerOP
typedef utility::pointer::shared_ptr < UniformRotationSampler const >	UniformRotationSamplerCOP
typedef xyzMatrix< bool >	xyzMatrix_bool
typedef xyzMatrix< short int >	xyzMatrix_short
typedef xyzMatrix< int >	xyzMatrix_int
typedef xyzMatrix< long int >	xyzMatrix_long
typedef xyzMatrix< unsigned short int >	xyzMatrix_ushort
typedef xyzMatrix< unsigned int >	xyzMatrix_uint
typedef xyzMatrix< unsigned long int >	xyzMatrix_ulong
typedef xyzMatrix< platform::Size >	xyzMatrix_Size
typedef xyzMatrix< platform::Size >	xyzMatrix_size_t
typedef xyzMatrix< platform::Size >	xyzMatrix_size
typedef xyzMatrix< float >	xyzMatrix_float
typedef xyzMatrix< double >	xyzMatrix_double
typedef xyzMatrix< long double >	xyzMatrix_longdouble
typedef xyzMatrix< char >	xyzMatrix_char
typedef xyzMatrix< unsigned char >	xyzMatrix_uchar
typedef xyzMatrix< signed char >	xyzMatrix_schar
typedef xyzTransform< float >	Xformf
typedef xyzTransform< double >	Xform
typedef xyzTransform < numeric::Real >	xyzTransform_Real
typedef xyzTransform< float >	xyzTransform_float
typedef xyzTransform< double >	xyzTransform_double
typedef xyzTriple< bool >	xyzTriple_bool
typedef xyzTriple< short int >	xyzTriple_short
typedef xyzTriple< int >	xyzTriple_int
typedef xyzTriple< long int >	xyzTriple_long
typedef xyzTriple< unsigned short int >	xyzTriple_ushort
typedef xyzTriple< unsigned int >	xyzTriple_uint
typedef xyzTriple< unsigned long int >	xyzTriple_ulong
typedef xyzTriple< std::size_t >	xyzTriple_size_t
typedef xyzTriple< std::size_t >	xyzTriple_size
typedef xyzTriple< float >	xyzTriple_float
typedef xyzTriple< double >	xyzTriple_double
typedef xyzTriple< long double >	xyzTriple_longdouble
typedef xyzTriple< char >	xyzTriple_char
typedef xyzTriple< unsigned char >	xyzTriple_uchar
typedef xyzTriple< signed char >	xyzTriple_schar
typedef xyzVector< bool >	xyzVector_bool
typedef xyzVector< short int >	xyzVector_short
typedef xyzVector< int >	xyzVector_int
typedef xyzVector< long int >	xyzVector_long
typedef xyzVector< unsigned short int >	xyzVector_ushort
typedef xyzVector< unsigned int >	xyzVector_uint
typedef xyzVector< unsigned long int >	xyzVector_ulong
typedef xyzVector< std::size_t >	xyzVector_size_t
typedef xyzVector< std::size_t >	xyzVector_size
typedef xyzVector< float >	xyzVector_float
typedef xyzVector< double >	xyzVector_double
typedef xyzVector< long double >	xyzVector_longdouble
typedef xyzVector< char >	xyzVector_char
typedef xyzVector< unsigned char >	xyzVector_uchar
typedef xyzVector< signed char >	xyzVector_schar

Enumerations
enum	RocStatus { true_positive, true_negative, false_positive, false_negative }

Functions
template<class T >
void	get_cluster_data (utility::vector1< T > &data_in, ClusteringTreeNodeOP cluster, utility::vector1< T > &data_out)
template<typename T >
T	principal_angle (T const &angle)
	Principal value of angle in radians on ( -pi, pi ]. More...
template<typename T >
T	principal_angle_radians (T const &angle)
	Principal value of angle in radians on ( -pi, pi ]. More...
template<typename T >
T	principal_angle_degrees (T const &angle)
	Principal value of angle in degrees on ( -180, 180 ]. More...
template<typename T >
T	nonnegative_principal_angle (T const &angle)
	Positive principal value of angle in radians on [ 0, 2*pi ) More...
template<typename T >
T	nonnegative_principal_angle_radians (T const &angle)
	Positive principal value of angle in radians on [ 0, 2*pi ) More...
template<typename T >
T	nonnegative_principal_angle_degrees (T const &angle)
	Positive principal value of angle in degrees on [ 0, 360 ) More...
template<typename T >
T	nearest_angle (T const &angle, T const &base_angle)
	Nearest periodic value of angle to a base angle in radians. More...
template<typename T >
T	nearest_angle_radians (T const &angle, T const &base_angle)
	Nearest periodic value of angle to a base angle in radians. More...
template<typename T >
T	nearest_angle_degrees (T const &angle, T const &base_angle)
	Nearest periodic value of angle to a base angle in degrees. More...
template<typename T >
bool	operator== (BodyPosition< T > const &p1, BodyPosition< T > const &p2)
	BodyPosition == BodyPosition. More...
template<typename T >
bool	operator!= (BodyPosition< T > const &p1, BodyPosition< T > const &p2)
	BodyPosition != BodyPosition. More...
template<typename T >
std::ostream &	operator<< (std::ostream &stream, BodyPosition< T > const &p)
	stream << BodyPosition output operator More...
template<typename T >
std::istream &	operator>> (std::istream &stream, BodyPosition< T > &p)
	stream >> BodyPosition input operator More...
template<typename T >
std::istream &	read_row (std::istream &stream, T &x, T &y, T &z, T &t)
	Read an BodyPosition row from a stream. More...
void	do_add_symbol (CalculatorParser &cp, std::string name, double value)
double	do_abs (double a)
double	do_pow (double a, double b)
double	do_exp (double a)
double	do_ln (double a)
double	do_log10 (double a)
double	do_log2 (double a)
double	do_log (double a, double b)
double	do_sqrt (double a)
double	do_sin (double a)
double	do_cos (double a)
double	do_tan (double a)
double	do_max (std::vector< double > a)
double	do_min (std::vector< double > a)
double	do_mean (std::vector< double > a)
double	do_median (std::vector< double > a)
numeric::xyzVector < platform::Real >	rgb_to_hsv (platform::Real r, platform::Real b, platform::Real g)
	convert an RGB color to HSV More...
numeric::xyzVector < platform::Real >	rgb_to_hsv (numeric::xyzVector< platform::Real > rgb_triplet)
	convert and RGB color to HSV More...
numeric::xyzVector < platform::Real >	hsv_to_rgb (platform::Real h, platform::Real s, platform::Real v)
	convert an HSV color to RGB More...
numeric::xyzVector < platform::Real >	hsv_to_rgb (numeric::xyzVector< platform::Real > hsv_triplet)
	convert an HSV color to RGB More...
void	ccd_angle (utility::vector1< xyzVector< Real > > const &F, utility::vector1< xyzVector< Real > > const &M, xyzVector< Real > const &axis_atom, xyzVector< Real > const &theta_hat, Real &alpha, Real &S)
template<typename T >
std::ostream &	operator<< (std::ostream &stream, HomogeneousTransform< T > const &ht)
std::ostream &	operator<< (std::ostream &stream, HomogeneousTransform< double > const &ht)
template<class Value >
double	linear_interpolate (Value start, Value stop, unsigned curr_stage, unsigned num_stages)
	Linearly interpolates a quantity from start to stop over (num_stages + 1) stages. More...
template<typename T >
std::ostream &	operator<< (std::ostream &output, const IntervalSet< T > &interval)
template<typename T >
MathMatrix< T > &	operator+= (MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	add one matrix to another More...
template<typename T >
MathMatrix< T > &	operator-= (MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	subtract one matrix from another More...
template<typename T >
MathMatrix< T > &	operator/= (MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &)
	divide one matrix by another More...
template<typename T >
MathMatrix< T > &	operator+= (MathMatrix< T > &MATRIX_LHS, const T &VALUE)
	add scalar to matrix More...
template<typename T >
MathMatrix< T > &	operator-= (MathMatrix< T > &MATRIX_LHS, const T &VALUE)
	subtract scalar from matrix More...
template<typename T >
MathMatrix< T > &	operator*= (MathMatrix< T > &MATRIX_LHS, const T &SCALAR)
	multiply matrix with scalar More...
template<typename T >
MathMatrix< T > &	operator/= (MathMatrix< T > &MATRIX_LHS, const T &SCALAR)
	divide matrix by scalar More...
template<typename T >
bool	operator== (const MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	compare to matricess for equality More...
template<typename T >
bool	operator!= (const MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	compare to matrices for inequality More...
template<typename T >
bool	operator== (const MathMatrix< T > &MATRIX_LHS, const T &VALUE_RHS)
	compare if all items in matrix are equal to a given VALUE More...
template<typename T >
bool	operator== (const T &VALUE_LHS, const MathMatrix< T > &MATRIX_RHS)
	compare if all items in matrix are equal to a given VALUE More...
template<typename T >
bool	operator!= (const MathMatrix< T > &MATRIX_LHS, const T &VALUE_RHS)
	compare if all items in matrix are not equal to a given VALUE More...
template<typename T >
bool	operator!= (const T &VALUE_LHS, const MathMatrix< T > &MATRIX_RHS)
	compare if all items in matrix are not equal to a given VALUE More...
template<typename T >
MathMatrix< T >	operator+ (const MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	sum two matrixs of equal size More...
template<typename T >
MathMatrix< T >	operator- (const MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	subtract two matrixs of equal size More...
template<typename T >
MathMatrix< T >	operator* (const MathMatrix< T > &MATRIX_LHS, const MathMatrix< T > &MATRIX_RHS)
	multiply two matrixs of equal size by building the inner product yielding the scalar product More...
template<typename T >
MathMatrix< T >	operator+ (const MathMatrix< T > &MATRIX_LHS, const T &VALUE_RHS)
	add value to matrix More...
template<typename T >
MathMatrix< T >	operator+ (const T &VALUE_LHS, const MathMatrix< T > &MATRIX_RHS)
	add matrix to value More...
template<typename T >
MathMatrix< T >	operator- (const MathMatrix< T > &MATRIX_LHS, const T &VALUE_RHS)
	subtract value from matrix More...
template<typename T >
MathMatrix< T >	operator- (const T &VALUE_LHS, const MathMatrix< T > &MATRIX_RHS)
	subtract matrix from value More...
template<typename T >
MathMatrix< T >	operator* (const T &SCALAR_LHS, const MathMatrix< T > &MATRIX_RHS)
	multiply scalar with matrix More...
template<typename T >
MathMatrix< T >	operator* (const MathMatrix< T > &MATRIX_LHS, const T &SCALAR_RHS)
	multiply matrix with scalar More...
template<typename T >
MathVector< T >	operator* (const MathMatrix< T > &MATRIX_LHS, const MathVector< T > &VECTOR_RHS)
	multiply matrix with vector More...
template<typename T >
MathMatrix< T >	operator/ (const MathMatrix< T > &MATRIX_LHS, const T &SCALAR_RHS)
	divide matrix with scalar More...
template<typename T >
MathMatrix< T >	operator/ (const T &SCALAR_LHS, const MathMatrix< T > &MATRIX_RHS)
	divide scalar by matrix More...
template<typename T >
T	distance (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
T	proj_angl (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B, MathVector< T > const &VECTOR_C, MathVector< T > const &VECTOR_D)
template<typename T >
T	proj_angl (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B, MathVector< T > const &VECTOR_C)
template<typename T >
T	proj_angl (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
T	scalar_product (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
MathVector< T >	MakeVector (T const &X)
template<typename T >
MathVector< T >	MakeVector (T const &X, T const &Y)
template<typename T >
MathVector< T >	MakeVector (T const &X, T const &Y, T const &Z)
template<typename T >
MathVector< T >	operator- (MathVector< T > const &VECTOR)
template<typename T >
MathVector< T >	operator+ (MathVector< T > const &VECTOR)
template<typename T >
bool	operator== (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
bool	operator!= (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
bool	operator== (MathVector< T > const &VECTOR, T const &X)
template<typename T >
bool	operator!= (MathVector< T > const &VECTOR, T const &X)
template<typename T >
bool	operator== (T const &X, MathVector< T > const &VECTOR)
template<typename T >
bool	operator!= (T const &X, MathVector< T > const &VECTOR)
template<typename T >
MathVector< T >	operator+ (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
MathVector< T >	operator- (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
MathVector< T >	operator+ (MathVector< T > const &VECTOR, T const &X)
template<typename T >
MathVector< T >	operator- (MathVector< T > const &VECTOR, T const &X)
template<typename T >
MathVector< T >	operator+ (T const &X, MathVector< T > const &VECTOR)
template<typename T >
MathVector< T >	operator- (T const &X, MathVector< T > const &VECTOR)
template<typename T >
T	operator* (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
MathVector< T >	operator* (T const &X, MathVector< T > const &VECTOR)
template<typename T >
MathVector< T >	operator* (MathVector< T > const &VECTOR, T const &X)
template<typename T >
MathVector< T >	operator/ (MathVector< T > const &VECTOR, T const &X)
template<typename T >
MathVector< T >	operator/ (MathVector< T > const &VECTOR_A, MathVector< T > const &VECTOR_B)
template<typename T >
MathVector< T >	operator/ (T const &X, MathVector< T > const &VECTOR)
template<typename T >
MathVector< T >	operator^ (T const &X, MathVector< T > const &VECTOR)
std::ostream &	operator<< (std::ostream &os, MultiDimensionalHistogram const &mdhist)
short int	min (short int const a, short int const b)
	min( short int, short int ) More...
int	min (int const a, int const b)
	min( int, int ) More...
long int	min (long int const a, long int const b)
	min( long int, long int ) More...
unsigned short int	min (unsigned short int const a, unsigned short int const b)
	min( unsigned short int, unsigned short int ) More...
unsigned int	min (unsigned int const a, unsigned int const b)
	min( unsigned int, unsigned int ) More...
unsigned long int	min (unsigned long int const a, unsigned long int const b)
	min( unsigned long int, unsigned long int ) More...
float	min (float const a, float const b)
	min( float, float ) More...
double	min (double const a, double const b)
	min( double, double ) More...
long double	min (long double const a, long double const b)
	min( long double, long double ) More...
template<typename T >
T const &	min (T const &a, T const &b, T const &c)
	min( a, b, c ) More...
template<typename T >
T const &	min (T const &a, T const &b, T const &c, T const &d)
	min( a, b, c, d ) More...
template<typename T >
T const &	min (T const &a, T const &b, T const &c, T const &d, T const &e)
	min( a, b, c, d, e ) More...
template<typename T >
T const &	min (T const &a, T const &b, T const &c, T const &d, T const &e, T const &f)
	min( a, b, c, d, e, f ) More...
short int	max (short int const a, short int const b)
	max( short int, short int ) More...
int	max (int const a, int const b)
	max( int, int ) More...
long int	max (long int const a, long int const b)
	max( long int, long int ) More...
unsigned short int	max (unsigned short int const a, unsigned short int const b)
	max( unsigned short int, unsigned short int ) More...
unsigned int	max (unsigned int const a, unsigned int const b)
	max( unsigned int, unsigned int ) More...
unsigned long int	max (unsigned long int const a, unsigned long int const b)
	max( unsigned long int, unsigned long int ) More...
float	max (float const a, float const b)
	max( float, float ) More...
double	max (double const a, double const b)
	max( double, double ) More...
long double	max (long double const a, long double const b)
	max( long double, long double ) More...
template<typename T >
T const &	max (T const &a, T const &b, T const &c)
	max( a, b, c ) More...
template<typename T >
T const &	max (T const &a, T const &b, T const &c, T const &d)
	max( a, b, c, d ) More...
template<typename T >
T const &	max (T const &a, T const &b, T const &c, T const &d, T const &e)
	max( a, b, c, d, e ) More...
template<typename T >
T const &	max (T const &a, T const &b, T const &c, T const &d, T const &e, T const &f)
	max( a, b, c, d, e, f ) More...
template<typename T >
T	square (T const &x)
	square( x ) == x^2 More...
template<typename T >
T	cube (T const &x)
	cube( x ) == x^3 More...
template<typename T >
int	sign (T const &x)
	sign( x ) More...
template<typename S , typename T >
T	sign_transfered (S const &sigma, T const &x)
	Sign transfered value. More...
template<typename T >
T	abs_difference (T const &a, T const &b)
	Absolute difference. More...
template<typename R , typename T >
R	nearest (T const &x)
	nearest< R >( x ): Nearest R More...
template<typename T >
std::size_t	nearest_size (T const &x)
	nearest_size( x ): Nearest std::size_t More...
template<typename T >
SSize	nearest_ssize (T const &x)
	nearest_ssize( x ): Nearest SSize More...
template<typename T >
int	nearest_int (T const &x)
	nearest_int( x ): Nearest int More...
template<typename T >
int	nint (T const &x)
	nint( x ): Nearest int More...
template<typename T >
T	mod (T const &x, T const &y)
	x(mod y) computational modulo returning magnitude < | y | and sign of x More...
template<typename T >
T	modulo (T const &x, T const &y)
	x(mod y) mathematical modulo returning magnitude < | y | and sign of y More...
template<typename T >
T	remainder (T const &x, T const &y)
	Remainder of x with respect to division by y that is of smallest magnitude. More...
template<typename T >
T	fast_remainder (T const &x, T const &y)
	Remainder of x with respect to division by y that is of smallest magnitude. More...
template<typename T , typename S >
T	remainder_conversion (T const &t, S &s)
	Remainder and result of conversion to a different type. More...
template<typename T >
T	gcd (T const &m, T const &n)
	Greatest common divisor. More...
template<typename T >
bool	eq_tol (T const &x, T const &y, T const &r_tol, T const &a_tol)
	Equal within specified relative and absolute tolerances? More...
template<typename T >
bool	lt_tol (T const &x, T const &y, T const &r_tol, T const &a_tol)
	Less than within specified relative and absolute tolerances? More...
template<typename T >
bool	le_tol (T const &x, T const &y, T const &r_tol, T const &a_tol)
	Less than or equal within specified relative and absolute tolerances? More...
template<typename T >
bool	ge_tol (T const &x, T const &y, T const &r_tol, T const &a_tol)
	Greater than or equal within specified relative and absolute tolerances? More...
template<typename T >
bool	gt_tol (T const &x, T const &y, T const &r_tol, T const &a_tol)
	Greater than within specified relative and absolute tolerances? More...
bool	is_a_finitenumber (double s, double a, double b)
template<typename T >
xyzVector< T >	first_principal_component (utility::vector1< xyzVector< T > > const &coords)
	return the first principal component of the given set of points More...
template<typename T >
xyzMatrix< T >	principal_components (utility::vector1< xyzVector< T > > const &coords)
	return a matrix containing the first 3 principal components of the given set of points. Matrix columns are principal components, first column is first component, etc. More...
template<typename T >
xyzVector< T >	principal_component_eigenvalues (utility::vector1< xyzVector< T > > const &coords)
	return a vector containing the eigenvalues corresponding to the first 3 principal components of the given set of points. More...
template<typename T >
std::pair< xyzMatrix< T > , xyzVector< T > >	principal_components_and_eigenvalues (utility::vector1< xyzVector< T > > const &coords)
	return a pair containing a matrix of the first 3 principal components and a vector of the corresponding eigenvalues of the given set of points. More...
std::pair< utility::vector1 < utility::vector1< Real > >, utility::vector1< Real > >	principal_components_and_eigenvalues_ndimensions (utility::vector1< utility::vector1< Real > > const &coords, bool const shift_center)
	Return a pair containing a matrix (vector of vectors) of all of the principal components and a vector of the corresponding eigenvalues of the given set of points in n-dimensional space. More...
ostream &	operator<< (ostream &out, const Polynomial_1d &poly)
void	read_probabilities_or_die (const std::string &filename, utility::vector1< double > *probs)
	Loads normalized, per-residue probabilities from filename, storing the result in probs. Assumes line i holds the probability of sampling residue i. There must be 1 line for each residue in the pose on which this data will be used. More...
void	print_probabilities (const utility::vector1< double > &probs, std::ostream &out)
	Writes probs to the specified ostream. More...
template<class InputIterator >
double	sum (InputIterator first, InputIterator last)
	Returns the sum of all elements on the range [first, last) More...
template<class InputIterator >
void	normalize (InputIterator first, InputIterator last)
	Normalizes elements on the range [first, last) More...
template<class RandomAccessIterator >
void	cumulative (RandomAccessIterator first, RandomAccessIterator last)
	Converts pdf to cdf. More...
template<class ForwardIterator >
void	product (ForwardIterator probs1_first, ForwardIterator probs1_last, ForwardIterator probs2_first, ForwardIterator probs2_last)
	Multiplies two probability vectors with one another. Probability vectors are assumed to have equal lengths. More...
template<typename T >
Quaternion< T >	operator* (Quaternion< T > const &q2, Quaternion< T > const &q1)
	Quaternion * Quaternion. More...
template<typename T >
Quaternion< T >	product (Quaternion< T > const &q2, Quaternion< T > const &q1, bool const precise)
	Product: Quaternion * Quaternion. More...
template<typename T >
bool	operator== (Quaternion< T > const &q1, Quaternion< T > const &q2)
	Quaternion == Quaternion. More...
template<typename T >
bool	operator!= (Quaternion< T > const &q1, Quaternion< T > const &q2)
	Quaternion != Quaternion. More...
template<typename T >
T	dot (Quaternion< T > const &q1, Quaternion< T > const &q2)
	Dot product. More...
template<typename T >
T	dot_product (Quaternion< T > const &q1, Quaternion< T > const &q2)
	Dot product. More...
template<typename T >
std::ostream &	operator<< (std::ostream &stream, Quaternion< T > const &q)
	stream << Quaternion output operator More...
template<typename T >
std::istream &	operator>> (std::istream &stream, Quaternion< T > &q)
	stream >> Quaternion input operator More...
template<typename T >
T	sec (T const &x)
	Secant. More...
template<typename T >
T	csc (T const &x)
	Cosecant. More...
template<typename T >
T	cot (T const &x)
	Cotangent. More...
template<typename T >
bool	in_sin_cos_range (T const &x, T const &tol=T(.001))
	Is a sine or cosine value within a specified tolerance of the valid [-1,1] range? More...
template<typename T >
T	sin_cos_range (T const &x, T const &tol=T(.001))
	Adjust a sine or cosine value to the valid [-1,1] range if within a specified tolerance or exit with an error. More...
template<typename T >
T	arccos (T const x)
	like std::acos but with range checking More...
double	urs_norm4 (double a, double b, double c, double d)
platform::Real	urs_R2ang (numeric::xyzMatrix< Real > R)
numeric::Real	median (utility::vector1< numeric::Real > const &values)
	Returns the median from a vector1 of Real values. More...
numeric::Real	mean (utility::vector1< numeric::Real > const &values)
template<typename Number >
Number	clamp (Number value, Number lower_bound, Number upper_bound)
	Clamps to the closed interval [lower_bound, upper_bound]. Templated type must implement operator<. More...
double	log (double x, double base)
	Computes log(x) in the given base. More...
template<typename T >
bool	isnan (T value)
	portable check to see if a value is NaN. More...
template<typename T >
bool	isinf (T value)
bool	equal_by_epsilon (numeric::Real value1, numeric::Real value2, numeric::Real epsilon)
	are two Real values are equal up to some epsilon More...
template<typename T >
T	max (utility::vector1< T > const &values)
template<typename T >
T	min (utility::vector1< T > const &values)
Real	boltzmann_accept_probability (Real const score_before, Real const score_after, Real const temperature)
	Calculates the acceptance probability of a given score-change at the given temperature, generally used in simulated annealing algorithms. Returns a value in the range (0-1). More...
template<typename T >
T	find_nearest_value (typename utility::vector1< T > const &input_list, T key, platform::Size min_index, platform::Size max_index)
	recursive binary search that finds the value closest to key. Call find_nearest_value(input_list,value) instead. It's the driver function for this function. This fails miserably (and silently!) on a non-sorted vector, so don't do that!. More...
template<typename T >
T	find_nearest_value (typename utility::vector1< T > const &input_list, T key)
	given a vector and an input value, return the value in the vector that is closest to the input This is a wrapper for find_nearest_value(input_list,key,min,max) and insures that you're sorted. More...
template<typename T >
T	wrap_2pi (T const &angle)
	Wrap the given angle in the range [0, 2 * pi). More...
template<typename T >
T	wrap_pi (T const &angle)
	Wrap the given angle in the range [-pi, pi). More...
template<typename T >
T	wrap_360 (T const &angle)
	Wrap the given angle in the range [0, 360). More...
template<typename T >
T	wrap_180 (T const &angle)
	Wrap the given angle in the range [-180, 180). More...
template<typename T >
xyzVector< T >	operator* (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector More...
template<typename T >
xyzVector< T >	product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector product More...
template<typename T >
xyzVector< T > &	inplace_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix * xyzVector in-place product More...
template<typename T >
xyzVector< T >	transpose_product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix^T * xyzVector product More...
template<typename T >
xyzVector< T > &	inplace_transpose_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix^T * xyzVector in-place transpose product More...
template<typename T >
xyzMatrix< T >	outer_product (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector xyzVector outer product More...
template<typename T >
xyzMatrix< T >	inverse (xyzMatrix< T > const &a)
template<typename T >
xyzMatrix< T >	projection_matrix (xyzVector< T > const &v)
	geometric center More...
template<typename T >
void	dihedral_radians (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4, T &angle)
	Dihedral (torsion) angle in radians: angle value passed. More...
template<typename T >
T	dihedral_radians (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4)
	Dihedral (torsion) angle in radians: angle value returned. More...
template<typename T >
void	dihedral_degrees (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4, T &angle)
	Dihedral (torsion) angle in degrees: angle value passed. More...
template<typename T >
T	dihedral_degrees (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4)
	Dihedral (torsion) angle in degrees: angle value returned. More...
template<typename T >
void	dihedral (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4, T &angle)
	Dihedral (torsion) angle in degrees: angle value passed. More...
template<typename T >
T	dihedral (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4)
	Dihedral (torsion) angle in degrees: angle value returned. More...
template<typename T >
xyzMatrix< T >	rotation_matrix (xyzVector< T > const &axis, T const &theta)
	Rotation matrix for rotation about an axis by an angle in radians. More...
template<typename T >
xyzVector< T >	rotation_axis (xyzMatrix< T > const &R, T &theta)
	Transformation from rotation matrix to helical axis of rotation. More...
template<typename T >
xyzVector< T >	eigenvalue_jacobi (xyzMatrix< T > const &a, T const &tol)
	Classic Jacobi algorithm for the eigenvalues of a real symmetric matrix. More...
template<typename T >
xyzVector< T >	eigenvector_jacobi (xyzMatrix< T > const &a, T const &tol, xyzMatrix< T > &J)
	Classic Jacobi algorithm for the eigenvalues and eigenvectors of a real symmetric matrix. More...
template<typename T >
void	jacobi_rotation (xyzMatrix< T > const &m, int const i, int const j, xyzMatrix< T > &r)
	Jacobi rotation. More...
template<typename T >
sphericalVector< T >	xyz_to_spherical (xyzVector< T > const &xyz)
template<typename T >
xyzVector< T >	spherical_to_xyz (sphericalVector< T > const &spherical)
template<typename T >
xyzVector< T >	closest_point_on_line (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &q)
	xyzMatrix * xyzVector More...
template<typename T >
xyzVector< T >	center_of_mass (utility::vector1< xyzVector< T > > const &coords)
	calculate center of mass for coordinates More...
template<typename T >
void	angle_radians (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, T &angle)
	Plane angle in radians: angle value passed. More...
template<typename T >
T	angle_radians (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3)
	Plane angle in radians: angle value returned. More...
double	angle_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3)
template<typename T >
T	angle_degrees (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3)
	Plane angle in degrees: angle value returned. More...
double	angle_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3)
template<typename T >
T	angle_radians (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4)
	Angle between two vectors in radians. More...
double	angle_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
template<typename T >
T	angle_degrees (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3, xyzVector< T > const &p4)
	Angle between two vectors in radians. More...
double	angle_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
void	dihedral_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4, double &angle)
double	dihedral_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
void	dihedral_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4, double &angle)
double	dihedral_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
void	dihedral_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4, double &angle)
double	dihedral_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
template<typename T >
xyzMatrix< T >	rotation_matrix (xyzVector< T > const &axis_angle)
template<typename T >
xyzMatrix< T >	rotation_matrix_radians (xyzVector< T > const &axis, T const &theta)
	Rotation matrix for rotation about an axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	rotation_matrix_degrees (xyzVector< T > const &axis, T const &theta)
	Rotation matrix for rotation about an axis by an angle in degrees. More...
template<typename T >
xyzMatrix< T >	x_rotation_matrix (T const &theta)
	Rotation matrix for rotation about the x axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	x_rotation_matrix_radians (T const &theta)
	Rotation matrix for rotation about the x axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	x_rotation_matrix_degrees (T const &theta)
	Rotation matrix for rotation about the x axis by an angle in degrees. More...
template<typename T >
xyzMatrix< T >	y_rotation_matrix (T const &theta)
	Rotation matrix for rotation about the y axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	y_rotation_matrix_radians (T const &theta)
	Rotation matrix for rotation about the y axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	y_rotation_matrix_degrees (T const &theta)
	Rotation matrix for rotation about the y axis by an angle in degrees. More...
template<typename T >
xyzMatrix< T >	z_rotation_matrix (T const &theta)
	Rotation matrix for rotation about the z axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	z_rotation_matrix_radians (T const &theta)
	Rotation matrix for rotation about the z axis by an angle in radians. More...
template<typename T >
xyzMatrix< T >	z_rotation_matrix_degrees (T const &theta)
	Rotation matrix for rotation about the z axis by an angle in degrees. More...
template<typename T >
xyzMatrix< T >	alignVectorSets (xyzVector< T > A1, xyzVector< T > B1, xyzVector< T > A2, xyzVector< T > B2)
	Helper function to find the rotation to optimally transform the vectors A1-B1 to vectors A2-B2. More...
template<typename T >
T	rotation_angle (xyzMatrix< T > const &R)
	Transformation from rotation matrix to magnitude of helical rotation. More...
template<typename T >
xyzVector< T >	rotation_axis_angle (xyzMatrix< T > const &R)
	Transformation from rotation matrix to compact axis-angle representation. More...
template<typename T >
xyzVector< T >	comma_seperated_string_to_xyz (std::string triplet)
	convert a string of comma separated values "0.2,0.4,0.3" to an xyzVector More...
template<typename T >
ObjexxFCL::FArray2D< T >	vector_of_xyzvectors_to_FArray (utility::vector1< xyzVector< T > > const &input)
	convert a vector1 of xyzVectors to an FArray2D More...
template<typename T >
utility::vector1< xyzVector< T > >	FArray_to_vector_of_xyzvectors (ObjexxFCL::FArray2D< T > const &input)
	convert an FArray2D to a vector of xyzVectors More...
template<typename T >
numeric::xyzMatrix< T >	FArray_to_xyzmatrix (ObjexxFCL::FArray2D< T > const &input)
	convert a 3x3 FArray 2D to an xyzMatrix More...
template<typename T >
ObjexxFCL::FArray2D< T >	xyzmatrix_to_FArray (numeric::xyzMatrix< T > const &input)
	convert an xyzMatrix to a 3x3 FArray 2D More...
template<typename T >
utility::json_spirit::Value	serialize (xyzVector< T > coords)
	Convert vector to a json_spirit Value. More...
template<typename T >
xyzVector< T >	deserialize (utility::json_spirit::mArray data)
template<typename T >
xyzMatrix< T >	operator+ (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix + xyzMatrix More...
template<typename T >
xyzMatrix< T >	operator+ (xyzMatrix< T > const &m, T const &t)
	xyzMatrix + T More...
template<typename T >
xyzMatrix< T >	operator+ (T const &t, xyzMatrix< T > const &m)
	T + xyzMatrix. More...
template<typename T >
xyzMatrix< T >	operator- (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix - xyzMatrix More...
template<typename T >
xyzMatrix< T >	operator- (xyzMatrix< T > const &m, T const &t)
	xyzMatrix - T More...
template<typename T >
xyzMatrix< T >	operator- (T const &t, xyzMatrix< T > const &m)
	T - xyzMatrix. More...
template<typename T >
xyzMatrix< T >	operator* (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix * xyzMatrix More...
template<typename T >
xyzMatrix< T >	operator* (xyzMatrix< T > const &m, T const &t)
	xyzMatrix * T More...
template<typename T >
xyzMatrix< T >	operator* (T const &t, xyzMatrix< T > const &m)
	T * xyzMatrix. More...
template<typename T >
xyzMatrix< T >	operator/ (xyzMatrix< T > const &m, T const &t)
	xyzMatrix / T More...
template<typename T >
bool	operator== (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix == xyzMatrix More...
template<typename T >
bool	operator!= (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix != xyzMatrix More...
template<typename T >
bool	operator< (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix < xyzMatrix More...
template<typename T >
bool	operator<= (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix <= xyzMatrix More...
template<typename T >
bool	operator>= (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix >= xyzMatrix More...
template<typename T >
bool	operator> (xyzMatrix< T > const &a, xyzMatrix< T > const &b)
	xyzMatrix > xyzMatrix More...
template<typename T >
bool	operator== (xyzMatrix< T > const &m, T const &t)
	xyzMatrix == T More...
template<typename T >
bool	operator!= (xyzMatrix< T > const &m, T const &t)
	xyzMatrix != T More...
template<typename T >
bool	operator< (xyzMatrix< T > const &m, T const &t)
	xyzMatrix < T More...
template<typename T >
bool	operator<= (xyzMatrix< T > const &m, T const &t)
	xyzMatrix <= T More...
template<typename T >
bool	operator>= (xyzMatrix< T > const &m, T const &t)
	xyzMatrix >= T More...
template<typename T >
bool	operator> (xyzMatrix< T > const &m, T const &t)
	xyzMatrix > T More...
template<typename T >
bool	operator== (T const &t, xyzMatrix< T > const &m)
	T == xyzMatrix. More...
template<typename T >
bool	operator!= (T const &t, xyzMatrix< T > const &m)
	T != xyzMatrix. More...
template<typename T >
bool	operator< (T const &t, xyzMatrix< T > const &m)
	T < xyzMatrix. More...
template<typename T >
bool	operator<= (T const &t, xyzMatrix< T > const &m)
	T <= xyzMatrix. More...
template<typename T >
bool	operator>= (T const &t, xyzMatrix< T > const &m)
	T >= xyzMatrix. More...
template<typename T >
bool	operator> (T const &t, xyzMatrix< T > const &m)
	T > xyzMatrix. More...
template<typename T >
std::ostream &	operator<< (std::ostream &stream, xyzMatrix< T > const &m)
	stream << xyzMatrix output operator More...
template<typename T >
std::istream &	read_row (std::istream &stream, T &x, T &y, T &z)
	Read an xyzMatrix row from a stream. More...
template<typename T >
std::istream &	operator>> (std::istream &stream, xyzMatrix< T > &m)
	stream >> xyzMatrix input operator More...
template<typename T , class OutputIterator >
void	expand_xforms (OutputIterator container, xyzTransform< T > const &G1, xyzTransform< T > const &G2, xyzTransform< T > const &, int N=5, Real r=9e9, xyzVector< T > const &test_point=xyzVector< T >(Real(1.0), Real(3.0), Real(10.0)))
template<typename T , class OutputIterator >
void	expand_xforms (OutputIterator container, xyzTransform< T > const &G1, xyzTransform< T > const &G2, int N=5, Real r=9e9, xyzVector< T > const &test_point=xyzVector< T >(Real(1.0), Real(3.0), Real(10.0)))
template<typename T >
std::ostream &	operator<< (std::ostream &stream, xyzTransform< T > const &m)
	stream << xyzTransform output operator More...
template<typename T >
std::istream &	operator>> (std::istream &stream, xyzTransform< T > &m)
	stream >> xyzTransform input operator More...
template<typename T >
xyzTriple< T >	operator+ (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple + xyzTriple More...
template<typename T >
xyzTriple< T >	operator+ (xyzTriple< T > const &v, T const &t)
	xyzTriple + T More...
template<typename T >
xyzTriple< T >	operator+ (T const &t, xyzTriple< T > const &v)
	T + xyzTriple. More...
template<typename T >
xyzTriple< T >	operator- (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple - xyzTriple More...
template<typename T >
xyzTriple< T >	operator- (xyzTriple< T > const &v, T const &t)
	xyzTriple - T More...
template<typename T >
xyzTriple< T >	operator- (T const &t, xyzTriple< T > const &v)
	T - xyzTriple. More...
template<typename T >
xyzTriple< T >	operator* (xyzTriple< T > const &v, T const &t)
	xyzTriple * T More...
template<typename T >
xyzTriple< T >	operator* (T const &t, xyzTriple< T > const &v)
	T * xyzTriple. More...
template<typename T >
xyzTriple< T >	operator/ (xyzTriple< T > const &v, T const &t)
	xyzTriple / T More...
template<typename T >
void	add (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > &r)
	Add: xyzTriple + xyzTriple. More...
template<typename T >
void	add (xyzTriple< T > const &v, T const &t, xyzTriple< T > &r)
	Add: xyzTriple + T. More...
template<typename T >
void	add (T const &t, xyzTriple< T > const &v, xyzTriple< T > &r)
	Add: T + xyzTriple. More...
template<typename T >
void	subtract (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > &r)
	Subtract: xyzTriple - xyzTriple. More...
template<typename T >
void	subtract (xyzTriple< T > const &v, T const &t, xyzTriple< T > &r)
	Subtract: xyzTriple - T. More...
template<typename T >
void	subtract (T const &t, xyzTriple< T > const &v, xyzTriple< T > &r)
	Subtract: T - xyzTriple. More...
template<typename T >
void	multiply (xyzTriple< T > const &v, T const &t, xyzTriple< T > &r)
	Multiply: xyzTriple * T. More...
template<typename T >
void	multiply (T const &t, xyzTriple< T > const &v, xyzTriple< T > &r)
	Multiply: T * xyzTriple. More...
template<typename T >
void	divide (xyzTriple< T > const &v, T const &t, xyzTriple< T > &r)
	Divide: xyzTriple / T. More...
template<typename T >
xyzTriple< T >	min (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple with min coordinates of two xyzTriples More...
template<typename T >
xyzTriple< T >	max (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple with max coordinates of two xyzTriples More...
template<typename T >
T	distance (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Distance. More...
template<typename T >
T	distance_squared (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Distance squared. More...
template<typename T >
T	dot (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Dot product. More...
template<typename T >
T	dot_product (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Dot product. More...
template<typename T >
T	inner_product (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Inner product ( == dot product ) More...
template<typename T >
xyzTriple< T >	cross (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Cross product. More...
template<typename T >
xyzTriple< T >	cross_product (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Cross product. More...
template<typename T >
void	cross (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename T >
void	cross_product (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename T >
xyzTriple< T >	midpoint (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Midpoint of 2 xyzTriples. More...
template<typename T >
void	midpoint (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > &m)
	Midpoint of 2 xyzTriples: Return via argument (slightly faster) More...
template<typename T >
xyzTriple< T >	center (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Center of 2 xyzTriples. More...
template<typename T >
void	center (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > &m)
	Center of 2 xyzTriples: Return via argument (slightly faster) More...
template<typename T >
xyzTriple< T >	center (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c)
	Center of 3 xyzTriples. More...
template<typename T >
void	center (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c, xyzTriple< T > &m)
	Center of 3 xyzTriples: Return via argument (slightly faster) More...
template<typename T >
xyzTriple< T >	center (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c, xyzTriple< T > const &d)
	Center of 4 xyzTriples. More...
template<typename T >
void	center (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c, xyzTriple< T > const &d, xyzTriple< T > &m)
	Center of 4 xyzTriples: Return via argument (slightly faster) More...
template<typename T >
T	angle_of (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Angle between two vectors (in radians on [ 0, pi ]) More...
template<typename T >
T	angle_of (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c)
	Angle formed by three consecutive points (in radians on [ 0, pi ]) More...
template<typename T >
T	cos_of (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Cosine of angle between two vectors. More...
template<typename T >
T	cos_of (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c)
	Cosine of angle formed by three consecutive points. More...
template<typename T >
T	sin_of (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Sine of angle between two vectors. More...
template<typename T >
T	sin_of (xyzTriple< T > const &a, xyzTriple< T > const &b, xyzTriple< T > const &c)
	Sine of angle formed by three consecutive points. More...
template<typename T >
bool	operator== (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple == xyzTriple More...
template<typename T >
bool	operator!= (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple != xyzTriple More...
template<typename T >
bool	operator< (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple < xyzTriple More...
template<typename T >
bool	operator<= (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple <= xyzTriple More...
template<typename T >
bool	operator>= (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple >= xyzTriple More...
template<typename T >
bool	operator> (xyzTriple< T > const &a, xyzTriple< T > const &b)
	xyzTriple > xyzTriple More...
template<typename T >
bool	operator== (xyzTriple< T > const &v, T const &t)
	xyzTriple == T More...
template<typename T >
bool	operator!= (xyzTriple< T > const &v, T const &t)
	xyzTriple != T More...
template<typename T >
bool	operator< (xyzTriple< T > const &v, T const &t)
	xyzTriple < T More...
template<typename T >
bool	operator<= (xyzTriple< T > const &v, T const &t)
	xyzTriple <= T More...
template<typename T >
bool	operator>= (xyzTriple< T > const &v, T const &t)
	xyzTriple >= T More...
template<typename T >
bool	operator> (xyzTriple< T > const &v, T const &t)
	xyzTriple > T More...
template<typename T >
bool	operator== (T const &t, xyzTriple< T > const &v)
	T == xyzTriple. More...
template<typename T >
bool	operator!= (T const &t, xyzTriple< T > const &v)
	T != xyzTriple. More...
template<typename T >
bool	operator< (T const &t, xyzTriple< T > const &v)
	T < xyzTriple. More...
template<typename T >
bool	operator<= (T const &t, xyzTriple< T > const &v)
	T <= xyzTriple. More...
template<typename T >
bool	operator>= (T const &t, xyzTriple< T > const &v)
	T >= xyzTriple. More...
template<typename T >
bool	operator> (T const &t, xyzTriple< T > const &v)
	T > xyzTriple. More...
template<typename T >
bool	equal_length (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Equal length? More...
template<typename T >
bool	not_equal_length (xyzTriple< T > const &a, xyzTriple< T > const &b)
	Not equal length? More...
template<typename U >
U	dot (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Dot product. More...
template<typename U >
U	dot_product (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Dot product. More...
template<typename U >
U	inner_product (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Inner product ( == dot product ) More...
template<typename U >
bool	equal_length (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Equal length? More...
template<typename U >
xyzTriple< U >	cross (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Cross product. More...
template<typename U >
xyzTriple< U >	cross_product (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Cross product. More...
template<typename U >
void	cross (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename U >
void	cross_product (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename U >
xyzTriple< U >	midpoint (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Midpoint of 2 xyzTriples. More...
template<typename U >
void	midpoint (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > &m)
	Midpoint of 2 xyzTriples: Return via argument (slightly faster) More...
template<typename U >
xyzTriple< U >	center (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Center of 2 xyzTriples. More...
template<typename U >
void	center (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > &m)
	Center of 2 xyzTriples: Return via argument (slightly faster) More...
template<typename U >
xyzTriple< U >	center (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c)
	Center of 3 xyzTriples. More...
template<typename U >
void	center (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c, xyzTriple< U > &m)
	Center of 3 xyzTriples: Return via argument (slightly faster) More...
template<typename U >
xyzTriple< U >	center (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c, xyzTriple< U > const &d)
	Center of 4 xyzTriples. More...
template<typename U >
void	center (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c, xyzTriple< U > const &d, xyzTriple< U > &m)
	Center of 4 xyzTriples: Return via argument (slightly faster) More...
template<typename U >
U	angle_of (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Angle between two vectors (in radians on [ 0, pi ]) More...
template<typename U >
U	angle_of (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c)
	Angle formed by three consecutive points (in radians on [ 0, pi ]) More...
template<typename U >
U	cos_of (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Cosine of angle between two vectors. More...
template<typename U >
U	cos_of (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c)
	Cosine of angle formed by three consecutive points. More...
template<typename U >
U	sin_of (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Sine of angle between two vectors. More...
template<typename U >
U	sin_of (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > const &c)
	Sine of angle formed by three consecutive points. More...
template<typename U >
U	distance_squared (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Distance squared. More...
template<typename U >
bool	not_equal_length (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Not equal length? More...
template<typename U >
void	add (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > &r)
	Add: xyzTriple + xyzTriple. More...
template<typename U >
void	add (xyzTriple< U > const &v, U const &t, xyzTriple< U > &r)
	Add: xyzTriple + Value. More...
template<typename U >
void	add (U const &t, xyzTriple< U > const &v, xyzTriple< U > &r)
	Add: Value + xyzTriple. More...
template<typename U >
void	subtract (xyzTriple< U > const &a, xyzTriple< U > const &b, xyzTriple< U > &r)
	Subtract: xyzTriple - xyzTriple. More...
template<typename U >
void	subtract (xyzTriple< U > const &v, U const &t, xyzTriple< U > &r)
	Subtract: xyzTriple - Value. More...
template<typename U >
void	subtract (U const &t, xyzTriple< U > const &v, xyzTriple< U > &r)
	Subtract: Value - xyzTriple. More...
template<typename U >
void	multiply (xyzTriple< U > const &v, U const &t, xyzTriple< U > &r)
	Multiply: xyzTriple * Value. More...
template<typename U >
void	multiply (U const &t, xyzTriple< U > const &v, xyzTriple< U > &r)
	Multiply: Value * xyzTriple. More...
template<typename U >
void	divide (xyzTriple< U > const &v, U const &t, xyzTriple< U > &r)
	Divide: xyzTriple / Value. More...
template<typename U >
xyzTriple< U >	min (xyzTriple< U > const &a, xyzTriple< U > const &b)
	xyzTriple with min coordinates of two xyzTriples More...
template<typename U >
xyzTriple< U >	max (xyzTriple< U > const &a, xyzTriple< U > const &b)
	xyzTriple with max coordinates of two xyzTriples More...
template<typename U >
U	distance (xyzTriple< U > const &a, xyzTriple< U > const &b)
	Distance. More...
template<typename T >
std::ostream &	operator<< (std::ostream &stream, xyzTriple< T > const &v)
	stream << xyzTriple output operator More...
template<typename T >
std::istream &	operator>> (std::istream &stream, xyzTriple< T > &v)
	stream >> xyzTriple input operator More...
template<typename T >
platform::Size	hash_value (xyzVector< T > const &v)
template<typename T >
xyzVector< T >	operator+ (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector + xyzVector More...
template<typename T >
xyzVector< T >	operator+ (xyzVector< T > const &v, T const &t)
	xyzVector + T More...
template<typename T >
xyzVector< T >	operator+ (T const &t, xyzVector< T > const &v)
	T + xyzVector. More...
template<typename T >
xyzVector< T >	operator- (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector - xyzVector More...
template<typename T >
xyzVector< T >	operator- (xyzVector< T > const &v, T const &t)
	xyzVector - T More...
template<typename T >
xyzVector< T >	operator- (T const &t, xyzVector< T > const &v)
	T - xyzVector. More...
template<typename T >
xyzVector< T >	operator* (xyzVector< T > const &v, T const &t)
	xyzVector * T More...
template<typename T >
xyzVector< T >	operator* (T const &t, xyzVector< T > const &v)
	T * xyzVector. More...
template<typename T >
xyzVector< T >	operator/ (xyzVector< T > const &v, T const &t)
	xyzVector / T More...
template<typename T >
void	add (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > &r)
	Add: xyzVector + xyzVector. More...
template<typename T >
void	add (xyzVector< T > const &v, T const &t, xyzVector< T > &r)
	Add: xyzVector + T. More...
template<typename T >
void	add (T const &t, xyzVector< T > const &v, xyzVector< T > &r)
	Add: T + xyzVector. More...
template<typename T >
void	subtract (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > &r)
	Subtract: xyzVector - xyzVector. More...
template<typename T >
void	subtract (xyzVector< T > const &v, T const &t, xyzVector< T > &r)
	Subtract: xyzVector - T. More...
template<typename T >
void	subtract (T const &t, xyzVector< T > const &v, xyzVector< T > &r)
	Subtract: T - xyzVector. More...
template<typename T >
void	multiply (xyzVector< T > const &v, T const &t, xyzVector< T > &r)
	Multiply: xyzVector * T. More...
template<typename T >
void	multiply (T const &t, xyzVector< T > const &v, xyzVector< T > &r)
	Multiply: T * xyzVector. More...
template<typename T >
void	divide (xyzVector< T > const &v, T const &t, xyzVector< T > &r)
	Divide: xyzVector / T. More...
template<typename T >
xyzVector< T >	min (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector with min coordinates of two xyzVectors More...
template<typename T >
xyzVector< T >	max (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector with max coordinates of two xyzVectors More...
template<typename T >
T	dot (xyzVector< T > const &a, xyzVector< T > const &b)
	Distance. More...
template<typename T >
T	dot_product (xyzVector< T > const &a, xyzVector< T > const &b)
	Dot product. More...
template<typename T >
T	inner_product (xyzVector< T > const &a, xyzVector< T > const &b)
	Inner product ( == dot product ) More...
template<typename T >
xyzVector< T >	cross (xyzVector< T > const &a, xyzVector< T > const &b)
	Cross product. More...
template<typename T >
xyzVector< T >	cross_product (xyzVector< T > const &a, xyzVector< T > const &b)
	Cross product. More...
template<typename T >
void	cross (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename T >
void	cross_product (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename T >
xyzVector< T >	midpoint (xyzVector< T > const &a, xyzVector< T > const &b)
	Midpoint of 2 xyzVectors. More...
template<typename T >
void	midpoint (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > &m)
	Midpoint of 2 xyzVectors: Return via argument (slightly faster) More...
template<typename T >
xyzVector< T >	center (xyzVector< T > const &a, xyzVector< T > const &b)
	Center of 2 xyzVectors. More...
template<typename T >
void	center (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > &m)
	Center of 2 xyzVectors: Return via argument (slightly faster) More...
template<typename T >
xyzVector< T >	center (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c)
	Center of 3 xyzVectors. More...
template<typename T >
void	center (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c, xyzVector< T > &m)
	Center of 3 xyzVectors: Return via argument (slightly faster) More...
template<typename T >
xyzVector< T >	center (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c, xyzVector< T > const &d)
	Center of 4 xyzVectors. More...
template<typename T >
void	center (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c, xyzVector< T > const &d, xyzVector< T > &m)
	Center of 4 xyzVectors: Return via argument (slightly faster) More...
template<typename T >
T	angle_of (xyzVector< T > const &a, xyzVector< T > const &b)
	Angle between two vectors (in radians on [ 0, pi ]) More...
template<typename T >
T	angle_of (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c)
	Angle formed by three consecutive points (in radians on [ 0, pi ]) More...
template<typename T >
T	cos_of (xyzVector< T > const &a, xyzVector< T > const &b)
	Cosine of angle between two vectors. More...
template<typename T >
T	cos_of (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c)
	Cosine of angle formed by three consecutive points. More...
template<typename T >
T	sin_of (xyzVector< T > const &a, xyzVector< T > const &b)
	Sine of angle between two vectors. More...
template<typename T >
T	sin_of (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c)
	Sine of angle formed by three consecutive points. More...
template<typename T >
bool	operator== (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector == xyzVector More...
template<typename T >
bool	operator!= (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector != xyzVector More...
template<typename T >
bool	operator< (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector < xyzVector More...
template<typename T >
bool	operator<= (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector <= xyzVector More...
template<typename T >
bool	operator>= (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector >= xyzVector More...
template<typename T >
bool	operator> (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector > xyzVector More...
template<typename T >
bool	operator== (xyzVector< T > const &v, T const &t)
	xyzVector == T More...
template<typename T >
bool	operator!= (xyzVector< T > const &v, T const &t)
	xyzVector != T More...
template<typename T >
bool	operator< (xyzVector< T > const &v, T const &t)
	xyzVector < T More...
template<typename T >
bool	operator<= (xyzVector< T > const &v, T const &t)
	xyzVector <= T More...
template<typename T >
bool	operator>= (xyzVector< T > const &v, T const &t)
	xyzVector >= T More...
template<typename T >
bool	operator> (xyzVector< T > const &v, T const &t)
	xyzVector > T More...
template<typename T >
bool	operator== (T const &t, xyzVector< T > const &v)
	T == xyzVector. More...
template<typename T >
bool	operator!= (T const &t, xyzVector< T > const &v)
	T != xyzVector. More...
template<typename T >
bool	operator< (T const &t, xyzVector< T > const &v)
	T < xyzVector. More...
template<typename T >
bool	operator<= (T const &t, xyzVector< T > const &v)
	T <= xyzVector. More...
template<typename T >
bool	operator>= (T const &t, xyzVector< T > const &v)
	T >= xyzVector. More...
template<typename T >
bool	operator> (T const &t, xyzVector< T > const &v)
	T > xyzVector. More...
template<typename T >
bool	equal_length (xyzVector< T > const &a, xyzVector< T > const &b)
	Equal length? More...
template<typename T >
bool	not_equal_length (xyzVector< T > const &a, xyzVector< T > const &b)
	Not equal length? More...
template<typename U >
void	subtract (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > &r)
	Subtract: xyzVector - xyzVector. More...
template<typename U >
void	subtract (xyzVector< U > const &v, U const &t, xyzVector< U > &r)
	Subtract: xyzVector - Value. More...
template<typename U >
void	subtract (U const &t, xyzVector< U > const &v, xyzVector< U > &r)
	Subtract: Value - xyzVector. More...
template<typename U >
void	multiply (xyzVector< U > const &v, U const &t, xyzVector< U > &r)
	Multiply: xyzVector * Value. More...
template<typename U >
void	multiply (U const &t, xyzVector< U > const &v, xyzVector< U > &r)
	Multiply: Value * xyzVector. More...
template<typename T >
xyzVector< T >	update_operation (xyzVector< T > const &a, xyzVector< T > const &b)
template<typename T >
xyzVector< T >	update_5way_operation (xyzVector< T > const &a, xyzVector< T > const &b, xyzVector< T > const &c, xyzVector< T > const &d, xyzVector< T > const &e)
template<typename U >
U	angle_of (xyzVector< U > const &a, xyzVector< U > const &b)
	Angle between two vectors (in radians on [ 0, pi ]) More...
template<typename U >
U	angle_of (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c)
	Angle formed by three consecutive points (in radians on [ 0, pi ]) More...
template<typename U >
U	cos_of (xyzVector< U > const &a, xyzVector< U > const &b)
	Cosine of angle between two vectors. More...
template<typename U >
U	cos_of (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c)
	Cosine of angle formed by three consecutive points. More...
template<typename U >
U	sin_of (xyzVector< U > const &a, xyzVector< U > const &b)
	Sine of angle between two vectors. More...
template<typename U >
U	sin_of (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c)
	Sine of angle formed by three consecutive points. More...
template<typename U >
xyzVector< U >	min (xyzVector< U > const &a, xyzVector< U > const &b)
	xyzVector with min coordinates of two xyzVectors More...
template<typename U >
xyzVector< U >	max (xyzVector< U > const &a, xyzVector< U > const &b)
	xyzVector with max coordinates of two xyzVectors More...
template<typename U >
xyzVector< U >	cross (xyzVector< U > const &a, xyzVector< U > const &b)
	Cross product. More...
template<typename U >
xyzVector< U >	cross_product (xyzVector< U > const &a, xyzVector< U > const &b)
	Cross product. More...
template<typename U >
void	cross (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename U >
void	cross_product (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > &c)
	Cross product: Return via argument (slightly faster) More...
template<typename U >
xyzVector< U >	midpoint (xyzVector< U > const &a, xyzVector< U > const &b)
	Midpoint of 2 xyzVectors. More...
template<typename U >
void	midpoint (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > &m)
	Midpoint of 2 xyzVectors: Return via argument (slightly faster) More...
template<typename U >
xyzVector< U >	center (xyzVector< U > const &a, xyzVector< U > const &b)
	Center of 2 xyzVectors. More...
template<typename U >
void	center (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > &m)
	Center of 2 xyzVectors: Return via argument (slightly faster) More...
template<typename U >
xyzVector< U >	center (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c)
	Center of 3 xyzVectors. More...
template<typename U >
void	center (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c, xyzVector< U > &m)
	Center of 3 xyzVectors: Return via argument (slightly faster) More...
template<typename U >
xyzVector< U >	center (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c, xyzVector< U > const &d)
	Center of 4 xyzVectors. More...
template<typename U >
void	center (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > const &c, xyzVector< U > const &d, xyzVector< U > &m)
	Center of 4 xyzVectors: Return via argument (slightly faster) More...
template<typename U >
void	add (xyzVector< U > const &a, xyzVector< U > const &b, xyzVector< U > &r)
	Add: xyzVector + xyzVector. More...
template<typename U >
void	add (xyzVector< U > const &v, U const &t, xyzVector< U > &r)
	Add: xyzVector + Value. More...
template<typename U >
void	add (U const &t, xyzVector< U > const &v, xyzVector< U > &r)
	Add: Value + xyzVector. More...
template<typename U >
bool	equal_length (xyzVector< U > const &a, xyzVector< U > const &b)
	Equal length? More...
template<typename U >
bool	not_equal_length (xyzVector< U > const &a, xyzVector< U > const &b)
	Not equal length? More...
template<typename U >
U	dot (xyzVector< U > const &a, xyzVector< U > const &b)
	Dot product. More...
template<typename U >
U	inner_product (xyzVector< U > const &a, xyzVector< U > const &b)
	Inner product ( == dot product ) More...
template<typename U >
void	divide (xyzVector< U > const &v, U const &t, xyzVector< U > &r)
	Divide: xyzVector / Value. More...
template<typename T >
std::ostream &	operator<< (std::ostream &stream, xyzVector< T > const &v)
	stream << xyzVector output operator More...
template<typename T >
std::istream &	operator>> (std::istream &stream, xyzVector< T > &v)
	stream >> xyzVector input operator More...
template<typename T >
std::string	truncate_and_serialize_xyz_vector (xyzVector< T > vector, Real precision)

Detailed Description

Unit headers.

A collection of functions for working with probabilities.

Vector0's that can perform mathmatical functions.

construction/destructor of 3-D Matrix's with some functions

Mathmatical functions for the MathMatrix class.

construction/destructor of Matrix's with some functions

Tricubic spline for smoothly interpolating a function in 3 dimensions.

Polycubic spline for smoothly interpolating a function in n dimensions.

Cubic spline for all your evil desires.

Bicubic spline for all your hearts desires.

read the header file!

A 2D histogram based upon a map structure.

A 1D histogram based upon a map structure.

Boost headers.

Utility headers.

Core headers Utility headers C++ headers

Numeric headers Utility headers C++ headers

C++ headers

Very simple class for histograms based upon maps. You provide the key, which is templated, meaning that the key can be a string, real, size, enum. It will return a count, if you want it

Author

Steven Combs

Very simple class for histograms based upon maps. You provide the key, which is templated, meaning that the two keys can be strings, reals, sizes. It will return a count, if you want it

Author

Steven Combs

References:

Numerical Recipes in c++ 2nd edition Ralf Mueller

Author

Steven Combs, Ralf Mueller, Jens Meiler

This is an implementation of an algorithm from Numerical Recipes. It relies heavily on the implementation of the cubic spline (from Numerical Recipes), the MathMatrix, and the MathVector. You MUST USE the MathVector and MathMatrix implementations to use this function. The spline is very customizable and allows you to define the border behaviors (start/end of spline values). If you use the e_Natural (enum) BorderFlag, the start/end (border) of the spline will be linear. This may not be ideal for scoring functions as you want the a smoothing effect at the start/end (border) values. Instead, you probably want to use the e_FirstDeriv (enum) BorderFlag with the first derivate (private member value firstbe_) set to 0. This will cause a smoothing out of the start/end (border) of spline. If you want the splie to be continuous, you should use the e_Periodic (enum) BorderFlag.

To "train" the spline, use must provide the spline with a MathMatrix (numeric::MathMatrix). Lets look at an example. x values y 1__2__ 3 .1 | 1 2 3 | v .3 | 4 5 6 | a .5 | 7 8 9 | l |__________| u e s

Given the above Matrix (MathMatrix) You would want your start (START[2] private member value start_) values to be START[] = {1,.1}. You would then want to assign the delta (DELTA[2], private member value delta_) values to DELTA[] = {1,.2}. These delta values is the change between your x values and your y values. For example, the change between x1 and x2 is 1. Therefore, the delta for the x-values will be 1. For y values, you have y.1, y.3 which is a change of .2, therefore the delta will be .2. You do not have to specify an end because the algorithm will stop when it reaches the last value in the matrix.

Finally, the LinCont determins that if the argument x or y is outside the range decide if the spline should be continued linearly.

References:

Numerical Recipes in c++ 2nd edition Ralf Mueller

Author

Steven Combs, Ralf Mueller, Jens Meiler

The below comments are for the Bicubic spline but apply for the cubic spline. This is an implementation of an algorithm from Numerical Recipes. It relies heavily on the implementation of the cubic spline (from Numerical Recipes), the MathMatrix, and the MathVector. You MUST USE the MathVector and MathMatrix implementations to use this function. The spline is very customizable and allows you to define the border behaviors (start/end of spline values). If you use the e_Natural (enum) BorderFlag, the start/end (border) of the spline will be linear. This may not be ideal for scoring functions as you want the a smoothing effect at the start/end (border) values. Instead, you probably want to use the e_FirstDeriv (enum) BorderFlag with the first derivate (private member value firstbe_) set to 0. This will cause a smoothing out of the start/end (border) of spline. If you want the splie to be continuous, you should use the e_Periodic (enum) BorderFlag.

To "train" the spline, use must provide the spline with a MathMatrix (numeric::MathMatrix). Lets look at an example. x values y 1__2__ 3 .1 | 1 2 3 | v .3 | 4 5 6 | a .5 | 7 8 9 | l |__________| u e s

Given the above Matrix (MathMatrix) You would want your start (START[2] private member value start_) values to be START[] = {1,.1}. You would then want to assign the delta (DELTA[2], private member value delta_) values to DELTA[] = {1,.2}. These delta values is the change between your x values and your y values. For example, the change between x1 and x2 is 1. Therefore, the delta for the x-values will be 1. For y values, you have y.1, y.3 which is a change of .2, therefore the delta will be .2. You do not have to specify an end because the algorithm will stop when it reaches the last value in the matrix.

Finally, the LinCont determins that if the argument x or y is outside the range decide if the spline should be continued linearly.

References:

Numerical Recipes in c++ 2nd edition Ralf Mueller

Author

Steven Combs, Ralf Mueller, Jens Meiler

References:

Numerical Recipes in c++ 2nd edition Ralf Mueller

Author

Steven Combs, Ralf Mueller, Jens Meiler ported to Rosetta by Andrew Leaver-Fay generalized to N dimensions by Andrew Watkins

References:

Numerical Recipes in c++ 2nd edition Ralf Mueller

Author

Steven Combs, Ralf Mueller, Jens Meiler ported to Rosetta by Andrew Leaver-Fay generalized to n dimensions by Andrew Watkins

References:

Numerical Recipes in c++ 2nd edition Ralf Mueller

Author

Steven Combs, Ralf Mueller, Jens Meiler ported to Rosetta by Andrew Leaver-Fay

This is an implementation of an algorithm that was taken from BCL (Jens Meiler) The Matrix is constructed out of arrays and places values into rows/columns based on however many columns/rows you specify. Actual operations of the MathMatrix are implemented in numeric/MathMatrix_operations.hh. To access specific values (elements), you must use the operator (). For example: to access row 5, column 3 of a matrix, you would use matrix(5,3). *****NOTE**** The MathMatrix class is indexed at 0!!!!

References:

Nils Woetzl Jens Meiler

Author

Steven Combs, Nils Woetzl, Jens Meiler

This is an implementation of an algorithm that was taken from BCL (Jens Meiler) The Matrix is construction is found in numeric/MathMatrix.hh. These are mathematical functions that can be used by the MathMatrix class. ***Note that these are outside of class, but having the operators take two arguments ensures that no one will use the functions unknowningly

References:

Nils Woetzl Jens Meiler

Author

Steven Combs, Nils Woetzl, Jens Meiler

This is an implementation of an algorithm that was taken from BCL (Jens Meiler) *****NOTE**** The MathTensor class is indexed at 0!!!!

References:

Nils Woetzl Jens Meiler

Author

Steven Combs, Nils Woetzl, Jens Meiler

ported to Rosetta by Andrew Leaver-Fay (aleav.nosp@m.erfa.nosp@m.y@gma.nosp@m.il.c.nosp@m.om)

generalized to N dimensions by Andrew Watkins

This is an implementation of an algorithm that was taken from BCL (Jens Meiler) *****NOTE**** The MathTensor class is indexed at 0!!!!

References:

Nils Woetzl Jens Meiler

Author

Steven Combs, Nils Woetzl, Jens Meiler

ported to Rosetta by Andrew Leaver-Fay (aleav.nosp@m.erfa.nosp@m.y@gma.nosp@m.il.c.nosp@m.om)

This is an implementation of an algorithm that was taken from BCL (Jens Meiler) The MathVector is constructed just like utility::vector0, however this class does not inherit from utility::vector0. It is implemented this way to avoid confusion. Most functions from the std::vector / utility::vector0 ARE NOT included. This is a vector that performs mathematical functions, not a "storage" vector. Actual mathematical functions found in numeric/MathVector_operations. To access specific values you must use the operator (). For example: vector(5), will give you the value at index 5. This is done to distinguish from utility::vector!

References:

Nils Woetzl Jens Meiler

Author

Steven Combs, Nils Woetzl, Jens Meiler

This is an implementation of an algorithm that was taken from BCL (Jens Meiler) The Matrix is construction is found in numeric/MathVector.hh. These are mathematical functions that can be used by the MathVector class. ***Note that these are outside of class, but having the operators take two arguments ensures that no one will use the functions unknowningly

References:

Nils Woetzl Jens Meiler

Author

Steven Combs, Nils Woetzl, Jens Meiler

Currently supported RG types: standard - build in C++ random generator ran3 - old generator from previos version of rosetta

Typedef Documentation

typedef BodyPosition< double > numeric::BodyPosition_double

typedef BodyPosition< float > numeric::BodyPosition_float

typedef BodyPosition< long double > numeric::BodyPosition_longdouble

typedef utility::pointer::shared_ptr<Calculator> numeric::CalculatorOP

typedef utility::pointer::weak_ptr<ClusteringTreeNode> numeric::ClusteringTreeNodeAP

typedef utility::pointer::shared_ptr<ClusteringTreeNode> numeric::ClusteringTreeNodeOP

typedef Real numeric::Length

typedef utility::pointer::shared_ptr< Polynomial_1d const > numeric::Polynomial_1dCOP

typedef utility::pointer::shared_ptr< Polynomial_1d > numeric::Polynomial_1dOP

typedef Quaternion< double > numeric::Quaternion_double

typedef Quaternion< float > numeric::Quaternion_float

typedef Quaternion< long double > numeric::Quaternion_longdouble

typedef double numeric::Real

typedef utility::pointer::shared_ptr<RocCurve> numeric::RocCurveOP

typedef utility::pointer::shared_ptr<RocPoint> numeric::RocPointOP

typedef platform::Size numeric::Size

typedef platform::SSize numeric::SSize

typedef utility::pointer::shared_ptr< UniformRotationSampler const > numeric::UniformRotationSamplerCOP

typedef utility::pointer::shared_ptr< UniformRotationSampler > numeric::UniformRotationSamplerOP

typedef xyzVector< Real > numeric::Vector

typedef xyzTransform< double > numeric::Xform

typedef xyzTransform< float > numeric::Xformf

typedef xyzMatrix< bool > numeric::xyzMatrix_bool

typedef xyzMatrix< char > numeric::xyzMatrix_char

typedef xyzMatrix< double > numeric::xyzMatrix_double

typedef xyzMatrix< float > numeric::xyzMatrix_float

typedef xyzMatrix< int > numeric::xyzMatrix_int

typedef xyzMatrix< long int > numeric::xyzMatrix_long

typedef xyzMatrix< long double > numeric::xyzMatrix_longdouble

typedef xyzMatrix< signed char > numeric::xyzMatrix_schar

typedef xyzMatrix< short int > numeric::xyzMatrix_short

typedef xyzMatrix< platform::Size > numeric::xyzMatrix_Size

typedef xyzMatrix< platform::Size > numeric::xyzMatrix_size

typedef xyzMatrix< platform::Size > numeric::xyzMatrix_size_t

typedef xyzMatrix< unsigned char > numeric::xyzMatrix_uchar

typedef xyzMatrix< unsigned int > numeric::xyzMatrix_uint

typedef xyzMatrix< unsigned long int > numeric::xyzMatrix_ulong

typedef xyzMatrix< unsigned short int > numeric::xyzMatrix_ushort

typedef xyzTransform< double > numeric::xyzTransform_double

typedef xyzTransform< float > numeric::xyzTransform_float

typedef xyzTransform< numeric::Real > numeric::xyzTransform_Real

typedef xyzTriple< bool > numeric::xyzTriple_bool

typedef xyzTriple< char > numeric::xyzTriple_char

typedef xyzTriple< double > numeric::xyzTriple_double

typedef xyzTriple< float > numeric::xyzTriple_float

typedef xyzTriple< int > numeric::xyzTriple_int

typedef xyzTriple< long int > numeric::xyzTriple_long

typedef xyzTriple< long double > numeric::xyzTriple_longdouble

typedef xyzTriple< signed char > numeric::xyzTriple_schar

typedef xyzTriple< short int > numeric::xyzTriple_short

typedef xyzTriple< std::size_t > numeric::xyzTriple_size

typedef xyzTriple< std::size_t > numeric::xyzTriple_size_t

typedef xyzTriple< unsigned char > numeric::xyzTriple_uchar

typedef xyzTriple< unsigned int > numeric::xyzTriple_uint

typedef xyzTriple< unsigned long int > numeric::xyzTriple_ulong

typedef xyzTriple< unsigned short int > numeric::xyzTriple_ushort

typedef xyzVector< bool > numeric::xyzVector_bool

typedef xyzVector< char > numeric::xyzVector_char

typedef xyzVector< double > numeric::xyzVector_double

typedef xyzVector< float > numeric::xyzVector_float

typedef xyzVector< int > numeric::xyzVector_int

typedef xyzVector< long int > numeric::xyzVector_long

typedef xyzVector< long double > numeric::xyzVector_longdouble

typedef xyzVector< signed char > numeric::xyzVector_schar

typedef xyzVector< short int > numeric::xyzVector_short

typedef xyzVector< std::size_t > numeric::xyzVector_size

typedef xyzVector< std::size_t > numeric::xyzVector_size_t

typedef xyzVector< unsigned char > numeric::xyzVector_uchar

typedef xyzVector< unsigned int > numeric::xyzVector_uint

typedef xyzVector< unsigned long int > numeric::xyzVector_ulong

typedef xyzVector< unsigned short int > numeric::xyzVector_ushort

Enumeration Type Documentation

enum numeric::RocStatus

Enumerator
true_positive
true_negative
false_positive
false_negative

Function Documentation

template<typename T >

T numeric::abs_difference ( T const &  a, T const &  b  )

inline

Absolute difference.

References max(), and min().

template<typename T >

void numeric::add	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > &	r
	)

Add: xyzTriple + xyzTriple.

Referenced by utility::json_spirit::Semantic_actions< Value_type, Iter_type >::add_to_current(), utility::split(), utility::split_to_list(), and utility::split_to_set().

template<typename T >

void numeric::add	(	xyzTriple< T > const &	v,
		T const &	t,
		xyzTriple< T > &	r
	)

Add: xyzTriple + T.

template<typename T >

void numeric::add	(	T const &	t,
		xyzTriple< T > const &	v,
		xyzTriple< T > &	r
	)

Add: T + xyzTriple.

template<typename T >

void numeric::add	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > &	r
	)

Add: xyzVector + xyzVector.

template<typename T >

void numeric::add	(	xyzVector< T > const &	v,
		T const &	t,
		xyzVector< T > &	r
	)

Add: xyzVector + T.

template<typename T >

void numeric::add	(	T const &	t,
		xyzVector< T > const &	v,
		xyzVector< T > &	r
	)

Add: T + xyzVector.

template<typename U >

void numeric::add ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > &  r  )

inline

Add: xyzTriple + xyzTriple.

template<typename U >

void numeric::add ( xyzTriple< U > const &  v, U const &  t, xyzTriple< U > &  r  )

inline

Add: xyzTriple + Value.

References basic::options::OptionKeys::in::file::t.

template<typename U >

void numeric::add ( U const &  t, xyzTriple< U > const &  v, xyzTriple< U > &  r  )

inline

Add: Value + xyzTriple.

template<typename U >

void numeric::add ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > &  r  )

inline

Add: xyzVector + xyzVector.

template<typename U >

void numeric::add ( xyzVector< U > const &  v, U const &  t, xyzVector< U > &  r  )

inline

Add: xyzVector + Value.

References basic::options::OptionKeys::in::file::t.

template<typename U >

void numeric::add ( U const &  t, xyzVector< U > const &  v, xyzVector< U > &  r  )

inline

Add: Value + xyzVector.

template<typename T >

xyzMatrix< T > numeric::alignVectorSets ( xyzVector< T >  A1, xyzVector< T >  B1, xyzVector< T >  A2, xyzVector< T >  B2  )

inline

Helper function to find the rotation to optimally transform the vectors A1-B1 to vectors A2-B2.

References numeric::xyzMatrix< typename >::identity(), inverse(), numeric::xyzVector< typename >::is_zero(), numeric::xyzVector< typename >::normalize(), numeric::xyzVector< typename >::normalize_or_zero(), test.T007_TracerIO::T, numeric::xyzMatrix< typename >::xx(), numeric::xyzMatrix< typename >::xy(), numeric::xyzMatrix< typename >::xz(), numeric::xyzMatrix< typename >::yx(), numeric::xyzMatrix< typename >::yy(), numeric::xyzMatrix< typename >::yz(), numeric::xyzMatrix< typename >::zx(), numeric::xyzMatrix< typename >::zy(), and numeric::xyzMatrix< typename >::zz().

template<typename T >

T numeric::angle_degrees ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3  )

inline

Plane angle in degrees: angle value returned.

Note

Given three positions in a chain ( p1, p2, p3 ), calculates the plane angle in degrees between the vectors p2->p1 and p2->p3

Angle returned is on [ 0, 180 ]

References basic::options::OptionKeys::hotspot::angle, angle_radians(), numeric::conversions::degrees(), and test.T007_TracerIO::T.

Referenced by angle_degrees_double().

template<typename T >

T numeric::angle_degrees ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4  )

inline

Angle between two vectors in radians.

Note

Given two vectors (p1->p2 & p3->p4), calculate the angle between them

Angle returned is on [ 0, pi ]

References basic::options::OptionKeys::hotspot::angle, angle_radians(), numeric::conversions::degrees(), and test.T007_TracerIO::T.

double numeric::angle_degrees_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3  )

inline

References angle_degrees().

double numeric::angle_degrees_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4  )

inline

References angle_degrees().

template<typename T >

T numeric::angle_of	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Angle between two vectors (in radians on [ 0, pi ])

Referenced by angle_of(), zinc2_homodimer_setup::filter_metal_geom(), zinc1_homodimer_design::setup_rollmoving(), and apps::public1::scenarios::chemically_conjugated_docking::ubq_ras_rotation_angle().

template<typename T >

T numeric::angle_of	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c
	)

Angle formed by three consecutive points (in radians on [ 0, pi ])

template<typename T >

T numeric::angle_of	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Angle between two vectors (in radians on [ 0, pi ])

template<typename T >

T numeric::angle_of	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c
	)

Angle formed by three consecutive points (in radians on [ 0, pi ])

template<typename U >

U numeric::angle_of ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Angle between two vectors (in radians on [ 0, pi ])

References sin_cos_range().

template<typename U >

U numeric::angle_of ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c  )

inline

Angle formed by three consecutive points (in radians on [ 0, pi ])

Note

For points a, b, c, the angle is the angle between the vectors a - b and c - b in other words, the positive angle about b from a to c

References angle_of().

template<typename U >

U numeric::angle_of ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Angle between two vectors (in radians on [ 0, pi ])

References sin_cos_range().

template<typename U >

U numeric::angle_of ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c  )

inline

Angle formed by three consecutive points (in radians on [ 0, pi ])

Note

For points a, b, c, the angle is the angle between the vectors a - b and c - b in other words, the positive angle about b from a to c

References angle_of().

template<typename T >

void numeric::angle_radians ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, T &  angle  )

inline

Plane angle in radians: angle value passed.

Note

Given thre positions in a chain ( p1, p2, p3 ), calculates the plane angle in radians between the vectors p2->p1 and p2->p3

Angle returned is on [ 0, pi ]

References basic::options::OptionKeys::score::fiber_diffraction::a, basic::options::OptionKeys::score::fiber_diffraction::b, dot(), and sin_cos_range().

Referenced by angle_degrees(), angle_radians(), and angle_radians_double().

template<typename T >

T numeric::angle_radians ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3  )

inline

Plane angle in radians: angle value returned.

Note

Given three positions in a chain ( p1, p2, p3 ), calculates the plane angle in radians between the vectors p2->p1 and p2->p3

Angle returned is on [ 0, pi ]

References basic::options::OptionKeys::hotspot::angle, angle_radians(), and test.T007_TracerIO::T.

template<typename T >

T numeric::angle_radians ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4  )

inline

Angle between two vectors in radians.

Note

Given two vectors (p1->p2 & p3->p4), calculate the angle between them

Angle returned is on [ 0, pi ]

References basic::options::OptionKeys::score::fiber_diffraction::a, basic::options::OptionKeys::hotspot::angle, basic::options::OptionKeys::score::fiber_diffraction::b, dot(), sin_cos_range(), and test.T007_TracerIO::T.

double numeric::angle_radians_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3  )

inline

References angle_radians().

double numeric::angle_radians_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4  )

inline

References angle_radians().

template<typename T >

T numeric::arccos ( T const  x )

inline

like std::acos but with range checking

References sin_cos_range().

Referenced by numeric::deriv::angle_p1_deriv(), numeric::deriv::angle_p1_p2_p3_deriv(), numeric::deriv::angle_p2_deriv(), and numeric::deriv::dihedral_deriv_second().

Real numeric::boltzmann_accept_probability ( Real const  score_before, Real const  score_after, Real const  temperature  )

inline

Calculates the acceptance probability of a given score-change at the given temperature, generally used in simulated annealing algorithms. Returns a value in the range (0-1).

References max(), and min().

void numeric::ccd_angle	(	utility::vector1< xyzVector< Real > > const &	F,
		utility::vector1< xyzVector< Real > > const &	M,
		xyzVector< Real > const &	axis_atom,
		xyzVector< Real > const &	theta_hat,
		Real &	alpha,
		Real &	S
	)

Parameters

<F>	the coordinates of the fixed target atoms
<M>	the coordinates of the moving positions to be overlapped with the target atoms
<theta_hat>	axis vector of the torsion angle
<alpha>	empty angle to be calculated
<S>	empty deviation to be calculated

The objective of an individual cyclic coordinate descent (CCD) move is to minimize the deviation between a set of points that should perfectly superimpose. The deviation squared (S) can be expressed as:

S = Sum(r^2 + f^2) - 2 Sum[r(f_vector dot r_hat)] cos theta - 2 Sum[r(f_vector dot s_hat)] sin theta

The derivative of S with respect to theta (the angle about the rotation axis):

dS/dtheta = 2 Sum[r(f_vector dot r_hat)] sin theta - 2 Sum[r(f_vector dot s_hat)] cos theta

Setting dS/dtheta to zero gives the minimal value of theta, which we call alpha:

tan alpha = Sum[r(f_vector dot s_hat] / Sum[r(f_vector dot r_hat]

If we define... a = Sum(r^2 + f^2) b = 2 Sum[r(f_vector dot r_hat)] c = 2 Sum[r(f_vector dot s_hat)] then S can be rewritten: S = a - b cos alpha - c sin alpha and we can express alpha as tan alpha = c / b

References basic::options::OptionKeys::mh::match::aa, ObjexxFCL::abs(), cross(), numeric::conversions::degrees(), dot(), ObjexxFCL::format::F(), numeric::xyzVector< typename >::is_unit(), numeric::xyzVector< typename >::length(), test.T007_TracerIO::M, min(), and numeric::xyzVector< typename >::normalized().

template<typename T >

xyzTriple< T > numeric::center	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Center of 2 xyzTriples.

Referenced by numeric::geometry::hashing::SixDCoordinateBinner::bin_center_point(), and numeric::alignment::QCP_Kernel< double >::remove_center_of_mass().

template<typename T >

void numeric::center	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > &	m
	)

Center of 2 xyzTriples: Return via argument (slightly faster)

template<typename T >

xyzTriple< T > numeric::center	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c
	)

Center of 3 xyzTriples.

template<typename T >

void numeric::center	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c,
		xyzTriple< T > &	m
	)

Center of 3 xyzTriples: Return via argument (slightly faster)

template<typename T >

xyzTriple< T > numeric::center	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c,
		xyzTriple< T > const &	d
	)

Center of 4 xyzTriples.

template<typename T >

void numeric::center	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c,
		xyzTriple< T > const &	d,
		xyzTriple< T > &	m
	)

Center of 4 xyzTriples: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::center	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Center of 2 xyzVectors.

template<typename T >

void numeric::center	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > &	m
	)

Center of 2 xyzVectors: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::center	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c
	)

Center of 3 xyzVectors.

template<typename T >

void numeric::center	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c,
		xyzVector< T > &	m
	)

Center of 3 xyzVectors: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::center	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c,
		xyzVector< T > const &	d
	)

Center of 4 xyzVectors.

template<typename T >

void numeric::center	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c,
		xyzVector< T > const &	d,
		xyzVector< T > &	m
	)

Center of 4 xyzVectors: Return via argument (slightly faster)

template<typename U >

xyzTriple<U> numeric::center ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Center of 2 xyzTriples.

template<typename U >

void numeric::center ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > &  m  )

inline

Center of 2 xyzTriples: Return via argument (slightly faster)

template<typename U >

xyzTriple<U> numeric::center ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c  )

inline

Center of 3 xyzTriples.

template<typename U >

void numeric::center ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c, xyzTriple< U > &  m  )

inline

Center of 3 xyzTriples: Return via argument (slightly faster)

template<typename U >

xyzTriple<U> numeric::center ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c, xyzTriple< U > const &  d  )

inline

Center of 4 xyzTriples.

template<typename U >

void numeric::center ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c, xyzTriple< U > const &  d, xyzTriple< U > &  m  )

inline

Center of 4 xyzTriples: Return via argument (slightly faster)

template<typename U >

xyzVector<U> numeric::center ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Center of 2 xyzVectors.

template<typename U >

void numeric::center ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > &  m  )

inline

Center of 2 xyzVectors: Return via argument (slightly faster)

template<typename U >

xyzVector<U> numeric::center ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c  )

inline

Center of 3 xyzVectors.

template<typename U >

void numeric::center ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c, xyzVector< U > &  m  )

inline

Center of 3 xyzVectors: Return via argument (slightly faster)

template<typename U >

xyzVector<U> numeric::center ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c, xyzVector< U > const &  d  )

inline

Center of 4 xyzVectors.

template<typename U >

void numeric::center ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c, xyzVector< U > const &  d, xyzVector< U > &  m  )

inline

Center of 4 xyzVectors: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::center_of_mass ( utility::vector1< xyzVector< T > > const &  coords )

inline

calculate center of mass for coordinates

Referenced by numeric::geometry::residual_squared_of_points_to_plane(), and numeric::geometry::vector_normal_to_ring_plane_of_best_fit().

template<typename Number >

Number numeric::clamp	(	Number	value,
		Number	lower_bound,
		Number	upper_bound
	)

Clamps to the closed interval [lower_bound, upper_bound]. Templated type must implement operator<.

References value.

template<typename T >

xyzVector< T > numeric::closest_point_on_line ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  q  )

inline

xyzMatrix * xyzVector

Note

Same as product( xyzMatrix, xyzVector ) return the point closest to point p3 that lies on the line defined by p1 and p2

References dot_product(), and numeric::xyzVector< typename >::magnitude_squared().

template<typename T >

xyzVector<T> numeric::comma_seperated_string_to_xyz ( std::string  triplet )

inline

convert a string of comma separated values "0.2,0.4,0.3" to an xyzVector

References utility::from_string(), runtime_assert, utility::string_split(), test.T007_TracerIO::T, and basic::options::OptionKeys::in::file::xyz.

template<typename T >

T numeric::cos_of	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Cosine of angle between two vectors.

Referenced by cos_of(), and sin_of().

template<typename T >

T numeric::cos_of	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c
	)

Cosine of angle formed by three consecutive points.

template<typename T >

T numeric::cos_of	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Cosine of angle between two vectors.

template<typename T >

T numeric::cos_of	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c
	)

Cosine of angle formed by three consecutive points.

template<typename U >

U numeric::cos_of ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Cosine of angle between two vectors.

References sin_cos_range().

template<typename U >

U numeric::cos_of ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c  )

inline

Cosine of angle formed by three consecutive points.

Note

For points a, b, c, the angle is the angle between the vectors a - b and c - b in other words, the positive angle about b from a to c.

References cos_of().

template<typename U >

U numeric::cos_of ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Cosine of angle between two vectors.

References sin_cos_range().

template<typename U >

U numeric::cos_of ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c  )

inline

Cosine of angle formed by three consecutive points.

Note

For points a, b, c, the angle is the angle between the vectors a - b and c - b in other words, the positive angle about b from a to c.

References cos_of().

template<typename T >

T numeric::cot ( T const &  x )

inline

Cotangent.

References test.T007_TracerIO::T.

template<typename T >

xyzTriple< T > numeric::cross	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Cross product.

Referenced by numeric::deriv::angle_p2_deriv(), ccd_angle(), numeric::deriv::dihedral_p1_cosine_deriv_first(), numeric::deriv::dihedral_p2_cosine_deriv_first(), dihedral_radians(), numeric::xyzTransform< numeric::Real >::from_four_points(), numeric::deriv::helper(), and numeric::deriv::p1_theta_deriv().

template<typename T >

void numeric::cross	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > &	c
	)

Cross product: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::cross	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Cross product.

template<typename T >

void numeric::cross	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > &	c
	)

Cross product: Return via argument (slightly faster)

template<typename U >

xyzTriple<U> numeric::cross ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Cross product.

template<typename U >

void numeric::cross ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > &  c  )

inline

Cross product: Return via argument (slightly faster)

template<typename U >

xyzVector<U> numeric::cross ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Cross product.

template<typename U >

void numeric::cross ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > &  c  )

inline

Cross product: Return via argument (slightly faster)

template<typename T >

xyzTriple< T > numeric::cross_product	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Cross product.

Referenced by zinc2_homodimer_setup::rollmove_to_inverse_C2_symmetry(), and zinc1_homodimer_design::setup_rollmoving().

template<typename T >

void numeric::cross_product	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > &	c
	)

Cross product: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::cross_product	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Cross product.

template<typename T >

void numeric::cross_product	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > &	c
	)

Cross product: Return via argument (slightly faster)

template<typename U >

xyzTriple<U> numeric::cross_product ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Cross product.

template<typename U >

void numeric::cross_product ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > &  c  )

inline

Cross product: Return via argument (slightly faster)

template<typename U >

xyzVector<U> numeric::cross_product ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Cross product.

template<typename U >

void numeric::cross_product ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > &  c  )

inline

Cross product: Return via argument (slightly faster)

template<typename T >

T numeric::csc ( T const &  x )

inline

Cosecant.

References test.T007_TracerIO::T.

Referenced by numeric::BodyPosition< typename >::BodyPosition().

template<typename T >

T numeric::cube ( T const &  x )

inline

cube( x ) == x^3

References x().

template<class RandomAccessIterator >

void numeric::cumulative	(	RandomAccessIterator	first,
		RandomAccessIterator	last
	)

Converts pdf to cdf.

References normalize().

template<typename T >

xyzVector<T> numeric::deserialize ( utility::json_spirit::mArray  data )

inline

References numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

void numeric::dihedral ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4, T &  angle  )

inline

Dihedral (torsion) angle in degrees: angle value passed.

Note

This is a Rosetta++ compatibility version that operates in degrees

References dihedral_radians(), and numeric::conversions::to_degrees().

Referenced by dihedral_double().

template<typename T >

T numeric::dihedral ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4  )

inline

Dihedral (torsion) angle in degrees: angle value returned.

Note

This is a Rosetta++ compatibility version that operates in degrees

References numeric::conversions::degrees(), and dihedral_radians().

template<typename T >

void numeric::dihedral_degrees ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4, T &  angle  )

inline

Dihedral (torsion) angle in degrees: angle value passed.

References dihedral_radians(), and numeric::conversions::to_degrees().

Referenced by dihedral_degrees_double(), and apps::public1::scenarios::chemically_conjugated_docking::ubq_ras_rotation_angle().

template<typename T >

T numeric::dihedral_degrees ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4  )

inline

Dihedral (torsion) angle in degrees: angle value returned.

References numeric::conversions::degrees(), and dihedral_radians().

void numeric::dihedral_degrees_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4, double &  angle  )

inline

References dihedral_degrees().

double numeric::dihedral_degrees_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4  )

inline

References dihedral_degrees().

void numeric::dihedral_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4, double &  angle  )

inline

References dihedral().

double numeric::dihedral_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4  )

inline

References dihedral().

template<typename T >

void numeric::dihedral_radians ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4, T &  angle  )

inline

Dihedral (torsion) angle in radians: angle value passed.

Note

Given four positions in a chain ( p1, p2, p3, p4 ), calculates the dihedral (torsion) angle in radians between the vectors p2->p1 and p3->p4 while sighting along the axis defined by the vector p2->p3 (positive indicates right handed twist)

Angle returned is on [ -pi, pi ]

Degenerate cases are handled and assigned a zero angle but assumed rare (wrt performance tuning)

For a reference on the determination of the dihedral angle formula see: http://www.math.fsu.edu/~quine/IntroMathBio_04/torsion_pdb/torsion_pdb.pdf

References basic::options::OptionKeys::score::fiber_diffraction::a, basic::options::OptionKeys::score::fiber_diffraction::b, cross(), dot(), test.T007_TracerIO::T, x(), and y().

Referenced by dihedral(), dihedral_degrees(), numeric::deriv::dihedral_deriv_second(), dihedral_radians(), dihedral_radians_double(), and minimize_test().

template<typename T >

T numeric::dihedral_radians ( xyzVector< T > const &  p1, xyzVector< T > const &  p2, xyzVector< T > const &  p3, xyzVector< T > const &  p4  )

inline

Dihedral (torsion) angle in radians: angle value returned.

Note

Given four positions in a chain ( p1, p2, p3, p4 ), calculates the dihedral (torsion) angle in radians between the vectors p2->p1 and p3->p4 while sighting along the axis defined by the vector p2->p3 (positive indicates right handed twist)

Angle returned is on [ -pi, pi ]

Degenerate cases are handled and assigned a zero angle but assumed rare (wrt performance tuning)

For a reference on the determination of the dihedral angle formula see: http://www.math.fsu.edu/~quine/IntroMathBio_04/torsion_pdb/torsion_pdb.pdf

References basic::options::OptionKeys::hotspot::angle, dihedral_radians(), and test.T007_TracerIO::T.

void numeric::dihedral_radians_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4, double &  angle  )

inline

References dihedral_radians().

double numeric::dihedral_radians_double ( xyzVector< double > const &  p1, xyzVector< double > const &  p2, xyzVector< double > const &  p3, xyzVector< double > const &  p4  )

inline

References dihedral_radians().

template<typename T >

T numeric::distance ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

distance between two MathVectors A->B

References numeric::kinematic_closure::norm().

Referenced by numeric::deriv::distance_f1_f2_deriv().

template<typename T >

T numeric::distance	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Distance.

template<typename U >

U numeric::distance ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Distance.

References square().

template<typename T >

T numeric::distance_squared	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Distance squared.

Referenced by HDmakerMover::bb_score(), ExposedStrandMover::bb_score(), pyrosetta::etable_atom_pair_energies(), and src::etable_atom_pair_energies().

template<typename U >

U numeric::distance_squared ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Distance squared.

References square().

template<typename T >

void numeric::divide	(	xyzTriple< T > const &	v,
		T const &	t,
		xyzTriple< T > &	r
	)

Divide: xyzTriple / T.

template<typename T >

void numeric::divide	(	xyzVector< T > const &	v,
		T const &	t,
		xyzVector< T > &	r
	)

Divide: xyzVector / T.

template<typename U >

void numeric::divide ( xyzTriple< U > const &  v, U const &  t, xyzTriple< U > &  r  )

inline

Divide: xyzTriple / Value.

template<typename U >

void numeric::divide ( xyzVector< U > const &  v, U const &  t, xyzVector< U > &  r  )

inline

Divide: xyzVector / Value.

double numeric::do_abs

(

double

a

)

References ObjexxFCL::abs().

Referenced by numeric::CalculatorParser::CalculatorParser().

void numeric::do_add_symbol	(	CalculatorParser &	cp,
		std::string	name,
		double	value
	)

References numeric::CalculatorParser::add_symbol().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_cos

(

double

a

)

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_exp

(

double

a

)

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_ln

(

double

a

)

References log().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_log	(	double	a,
		double	b
	)

References log().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_log10

(

double

a

)

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_log2

(

double

a

)

References log().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_max

(

std::vector< double >

a

)

References max().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_mean

(

std::vector< double >

a

)

References mean().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_median

(

std::vector< double >

a

)

References median().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_min

(

std::vector< double >

a

)

References min().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_pow	(	double	a,
		double	b
	)

References ObjexxFCL::pow().

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_sin

(

double

a

)

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_sqrt

(

double

a

)

Referenced by numeric::CalculatorParser::CalculatorParser().

double numeric::do_tan

(

double

a

)

Referenced by numeric::CalculatorParser::CalculatorParser().

template<typename T >

T numeric::dot	(	Quaternion< T > const &	q1,
		Quaternion< T > const &	q2
	)

Dot product.

Referenced by numeric::deriv::angle_p1_deriv(), numeric::deriv::angle_p1_p2_p3_deriv(), numeric::deriv::angle_p2_deriv(), angle_radians(), ccd_angle(), numeric::deriv::dihedral_p1_cosine_deriv_first(), numeric::deriv::dihedral_p2_cosine_deriv_first(), dihedral_radians(), numeric::xyzTransform< numeric::Real >::intersect3D_2Planes(), numeric::deriv::p1_theta_deriv(), and numeric::deriv::x_and_dtheta_dx().

template<typename T >

T numeric::dot	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Dot product.

template<typename T >

T numeric::dot	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Distance.

Distance squared Dot product

template<typename U >

U numeric::dot ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Dot product.

template<typename U >

U numeric::dot ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Dot product.

template<typename T >

T numeric::dot_product	(	Quaternion< T > const &	q1,
		Quaternion< T > const &	q2
	)

Dot product.

Referenced by closest_point_on_line().

template<typename T >

T numeric::dot_product	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Dot product.

template<typename T >

T numeric::dot_product ( xyzVector< T > const &  a, xyzVector< T > const &  b  )

inline

Dot product.

References numeric::xyzVector< typename >::x_, numeric::xyzVector< typename >::y_, and numeric::xyzVector< typename >::z_.

template<typename U >

U numeric::dot_product ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Dot product.

template<typename T >

xyzVector< T > numeric::eigenvalue_jacobi ( xyzMatrix< T > const &  a, T const &  tol  )

inline

Classic Jacobi algorithm for the eigenvalues of a real symmetric matrix.

Note

Use eigenvector_jacobi if eigenvectors are also desired

References ObjexxFCL::abs(), basic::options::OptionKeys::frags::j, jacobi_rotation(), numeric::xyzMatrix< typename >::left_multiply_by_transpose(), numeric::xyzMatrix< typename >::right_multiply_by(), test.T007_TracerIO::T, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by instantiate_numeric_functions().

template<typename T >

xyzVector< T > numeric::eigenvector_jacobi ( xyzMatrix< T > const &  a, T const &  tol, xyzMatrix< T > &  J  )

inline

Classic Jacobi algorithm for the eigenvalues and eigenvectors of a real symmetric matrix.

Note

Use eigenvalue_jacobi if eigenvectors are not desired

References ObjexxFCL::abs(), basic::options::OptionKeys::frags::j, jacobi_rotation(), numeric::xyzMatrix< typename >::left_multiply_by_transpose(), numeric::xyzMatrix< typename >::right_multiply_by(), test.T007_TracerIO::T, numeric::xyzMatrix< typename >::to_identity(), numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by numeric::model_quality::findUU(), instantiate_numeric_functions(), and principal_components_and_eigenvalues().

template<typename T >

bool numeric::eq_tol ( T const &  x, T const &  y, T const &  r_tol, T const &  a_tol  )

inline

Equal within specified relative and absolute tolerances?

References ObjexxFCL::abs(), max(), min(), and test.T007_TracerIO::T.

Referenced by numeric::interpolation::bilinearly_interpolated(), and numeric::interpolation::Histogram< typename, typename >::set_params().

bool numeric::equal_by_epsilon ( numeric::Real  value1, numeric::Real  value2, numeric::Real  epsilon  )

inline

are two Real values are equal up to some epsilon

implemented only for Reals, to prevent unsigned hassle (Barak 30/6/2009)

References basic::options::OptionKeys::pb_potential::epsilon.

template<typename T >

bool numeric::equal_length	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Equal length?

template<typename U >

bool numeric::equal_length ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Equal length?

template<typename T >

bool numeric::equal_length	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Equal length?

template<typename U >

bool numeric::equal_length ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Equal length?

template<typename T , class OutputIterator >

void numeric::expand_xforms	(	OutputIterator	container,
		xyzTransform< T > const &	G1,
		xyzTransform< T > const &	G2,
		xyzTransform< T > const &	,
		int	N = 5,
		Real	r = 9e9,
		xyzVector< T > const &	test_point = xyzVector<T>(Real(1.0),Real(3.0),Real(10.0))
	)

References ObjexxFCL::format::I(), app.pyrosetta_toolkit.window_modules.options_system.OptionSystemManager::test, and x().

Referenced by expand_xforms().

template<typename T , class OutputIterator >

void numeric::expand_xforms	(	OutputIterator	container,
		xyzTransform< T > const &	G1,
		xyzTransform< T > const &	G2,
		int	N = 5,
		Real	r = 9e9,
		xyzVector< T > const &	test_point = xyzVector<T>(Real(1.0),Real(3.0),Real(10.0))
	)

References expand_xforms().

template<typename T >

utility::vector1< xyzVector<T> > numeric::FArray_to_vector_of_xyzvectors ( ObjexxFCL::FArray2D< T > const &  input )

inline

convert an FArray2D to a vector of xyzVectors

References ObjexxFCL::index(), app.surface_docking.surface_docking::input, basic::options::OptionKeys::cp::output, ObjexxFCL::FArray2< T >::size1(), ObjexxFCL::FArray2D< typename >::size2(), x(), y(), and z().

Referenced by numeric::model_quality::findUU().

template<typename T >

numeric::xyzMatrix<T> numeric::FArray_to_xyzmatrix ( ObjexxFCL::FArray2D< T > const &  input )

inline

convert a 3x3 FArray 2D to an xyzMatrix

References app.surface_docking.surface_docking::input, numeric::xyzMatrix< typename >::rows(), ObjexxFCL::FArray2< T >::size1(), and ObjexxFCL::FArray2D< typename >::size2().

Referenced by numeric::model_quality::findUU().

template<typename T >

T numeric::fast_remainder ( T const &  x, T const &  y  )

inline

Remainder of x with respect to division by y that is of smallest magnitude.

Note

Emulates the C99 remainder function except for rounding halfway values to even multiples

Returns zero if y is zero

Return value has magnitude <= | y / 2 |

template<typename T >

T numeric::find_nearest_value	(	typename utility::vector1< T > const &	input_list,
		T	key,
		platform::Size	min_index,
		platform::Size	max_index
	)

recursive binary search that finds the value closest to key. Call find_nearest_value(input_list,value) instead. It's the driver function for this function. This fails miserably (and silently!) on a non-sorted vector, so don't do that!.

References ObjexxFCL::abs(), key, and test.T007_TracerIO::T.

template<typename T >

T numeric::find_nearest_value	(	typename utility::vector1< T > const &	input_list,
		T	key
	)

given a vector and an input value, return the value in the vector that is closest to the input This is a wrapper for find_nearest_value(input_list,key,min,max) and insures that you're sorted.

References key.

template<typename T >

xyzVector< T > numeric::first_principal_component ( utility::vector1< xyzVector< T > > const &  coords )

inline

return the first principal component of the given set of points

References numeric::xyzMatrix< typename >::col(), and principal_components().

template<typename T >

T numeric::gcd ( T const &  m, T const &  n  )

inline

Greatest common divisor.

References max(), min(), mod(), and test.T007_TracerIO::T.

template<typename T >

bool numeric::ge_tol ( T const &  x, T const &  y, T const &  r_tol, T const &  a_tol  )

inline

Greater than or equal within specified relative and absolute tolerances?

References ObjexxFCL::abs(), max(), min(), and test.T007_TracerIO::T.

template<class T >

void numeric::get_cluster_data	(	utility::vector1< T > &	data_in,
		ClusteringTreeNodeOP	cluster,
		utility::vector1< T > &	data_out
	)

template<typename T >

bool numeric::gt_tol ( T const &  x, T const &  y, T const &  r_tol, T const &  a_tol  )

inline

Greater than within specified relative and absolute tolerances?

References ObjexxFCL::abs(), max(), min(), and test.T007_TracerIO::T.

template<typename T >

platform::Size numeric::hash_value

(

xyzVector< T > const &

v

)

References numeric::xyzVector< typename >::x_, numeric::xyzVector< typename >::y_, and numeric::xyzVector< typename >::z_.

numeric::xyzVector< platform::Real > numeric::hsv_to_rgb	(	platform::Real	h,
		platform::Real	s,
		platform::Real	v
	)

convert an HSV color to RGB

numeric::xyzVector< platform::Real > numeric::hsv_to_rgb

(

numeric::xyzVector< platform::Real >

hsv_triplet

)

convert an HSV color to RGB

References demo.D060_Folding::f, basic::options::OptionKeys::score::fiber_diffraction::p, basic::options::OptionKeys::in::file::t, value, numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

bool numeric::in_sin_cos_range ( T const &  x, T const &  tol = T( .001 )  )

inline

Is a sine or cosine value within a specified tolerance of the valid [-1,1] range?

References test.T007_TracerIO::T, and loops_kic::tol.

template<typename T >

T numeric::inner_product	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Inner product ( == dot product )

Referenced by numeric::MathVector< Real >::square_norm().

template<typename T >

T numeric::inner_product	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Inner product ( == dot product )

template<typename U >

U numeric::inner_product ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Inner product ( == dot product )

template<typename U >

U numeric::inner_product ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Inner product ( == dot product )

template<typename T >

xyzVector< T > & numeric::inplace_product ( xyzMatrix< T > const &  m, xyzVector< T > &  v  )

inline

xyzMatrix * xyzVector in-place product

Note

Input xyzVector is modified

References test.T007_TracerIO::T, test.T850_SubClassing::v, x(), numeric::xyzVector< typename >::x_, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, y(), numeric::xyzVector< typename >::y_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzVector< typename >::z_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by instantiate_numeric_functions(), numeric::BodyPosition< typename >::invert(), numeric::BodyPosition< typename >::operator()(), and numeric::BodyPosition< typename >::transform().

template<typename T >

xyzVector< T > & numeric::inplace_transpose_product ( xyzMatrix< T > const &  m, xyzVector< T > &  v  )

inline

xyzMatrix^T * xyzVector in-place transpose product

Note

Input xyzVector is modified

References test.T007_TracerIO::T, test.T850_SubClassing::v, x(), numeric::xyzVector< typename >::x_, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, y(), numeric::xyzVector< typename >::y_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzVector< typename >::z_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by instantiate_numeric_functions(), and numeric::BodyPosition< typename >::inverse_transform().

template<typename T >

xyzMatrix< T > numeric::inverse ( xyzMatrix< T > const &  a )

inline

References numeric::xyzMatrix< typename >::det(), test.T007_TracerIO::T, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by alignVectorSets(), numeric::UniformRotationSampler::remove_redundant(), and slice_ellipsoid_envelope().

bool numeric::is_a_finitenumber ( double  s, double  a, double  b  )

inline

template<typename T >

bool numeric::isinf ( T  value )

inline

Referenced by compare_times::compare_times(), utility::is_inf(), and utility::is_undefined().

template<typename T >

bool numeric::isnan ( T  value )

inline

portable check to see if a value is NaN.

References value.

Referenced by compare_times::compare_times(), utility::is_nan(), and utility::is_undefined().

template<typename T >

void numeric::jacobi_rotation ( xyzMatrix< T > const &  m, int const  i, int const  j, xyzMatrix< T > &  r  )

inline

Jacobi rotation.

Note

Compute the orthogonal transformation used to zero out a pair of off-diagonal elements

References ObjexxFCL::abs(), basic::options::OptionKeys::in::file::s, test.T007_TracerIO::T, basic::options::OptionKeys::in::file::t, and numeric::xyzMatrix< typename >::to_identity().

Referenced by eigenvalue_jacobi(), eigenvector_jacobi(), and instantiate_numeric_functions().

template<typename T >

bool numeric::le_tol ( T const &  x, T const &  y, T const &  r_tol, T const &  a_tol  )

inline

Less than or equal within specified relative and absolute tolerances?

References ObjexxFCL::abs(), max(), min(), and test.T007_TracerIO::T.

template<class Value >

double numeric::linear_interpolate	(	Value	start,
		Value	stop,
		unsigned	curr_stage,
		unsigned	num_stages
	)

Linearly interpolates a quantity from start to stop over (num_stages + 1) stages.

References basic::options::OptionKeys::cutoutdomain::start.

double numeric::log ( double  x, double  base  )

inline

Computes log(x) in the given base.

Referenced by numeric::random::WeightedReservoirSampler< T >::consider_sample(), correct_dunbrack(), do_ln(), do_log(), do_log2(), numeric::random::RandomGenerator::gaussian(), numeric::statistics::kl_divergence(), main(), sigmoid_train(), and numeric::statistics::w().

template<typename T >

bool numeric::lt_tol ( T const &  x, T const &  y, T const &  r_tol, T const &  a_tol  )

inline

Less than within specified relative and absolute tolerances?

References ObjexxFCL::abs(), max(), min(), and test.T007_TracerIO::T.

template<typename T >

MathVector< T > numeric::MakeVector

(

T const &

X

)

References ObjexxFCL::format::X().

Referenced by numeric::interpolation::spline::BicubicSpline::F(), and numeric::interpolation::spline::BicubicSpline::FdF().

template<typename T >

MathVector< T > numeric::MakeVector ( T const &  X, T const &  Y  )

inline

Returns

construct MathVectors from two elements

References ObjexxFCL::format::X().

template<typename T >

MathVector< T > numeric::MakeVector ( T const &  X, T const &  Y, T const &  Z  )

inline

Returns

construct MathVectors from three elements

References ObjexxFCL::format::X().

template<typename T >

T numeric::max

(

utility::vector1< T > const &

values

)

References test.T200_Scoring::ii, max(), and test.T007_TracerIO::T.

short int numeric::max ( short int const  a, short int const  b  )

inline

max( short int, short int )

Referenced by abs_difference(), numeric::geometry::hashing::xyzStripeHash::clash(), numeric::geometry::hashing::xyzStripeHash::clash_amount(), numeric::geometry::hashing::xyzStripeHash::clash_check_ball(), numeric::geometry::hashing::xyzStripeHash::clash_not_resid(), numeric::geometry::hashing::xyzStripeHash::clash_raw(), numeric::CompleteLinkClusterer::comparator(), do_max(), eq_tol(), numeric::geometry::hashing::xyzStripeHash::fill_pairs(), gcd(), ge_tol(), gt_tol(), numeric::geometry::hashing::xyzStripeHash::init(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::init(), le_tol(), lt_tol(), max(), numeric::geometry::hashing::xyzStripeHash::nbcount(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::nbcount(), numeric::geometry::hashing::xyzStripeHash::nbcount_raw(), rotation_axis(), numeric::kinematic_closure::sbisect(), numeric::interpolation::Histogram< typename, typename >::set_params(), numeric::kinematic_closure::solve_sturm(), numeric::geometry::hashing::xyzStripeHash::visit(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::visit(), numeric::geometry::hashing::xyzStripeHash::visit_lax(), and numeric::geometry::hashing::xyzStripeHashWithMeta< float >::visit_lax().

int numeric::max ( int const  a, int const  b  )

inline

max( int, int )

long int numeric::max ( long int const  a, long int const  b  )

inline

max( long int, long int )

unsigned short int numeric::max ( unsigned short int const  a, unsigned short int const  b  )

inline

max( unsigned short int, unsigned short int )

unsigned int numeric::max ( unsigned int const  a, unsigned int const  b  )

inline

max( unsigned int, unsigned int )

unsigned long int numeric::max ( unsigned long int const  a, unsigned long int const  b  )

inline

max( unsigned long int, unsigned long int )

float numeric::max ( float const  a, float const  b  )

inline

max( float, float )

double numeric::max ( double const  a, double const  b  )

inline

max( double, double )

long double numeric::max ( long double const  a, long double const  b  )

inline

max( long double, long double )

template<typename T >

T const& numeric::max ( T const &  a, T const &  b, T const &  c  )

inline

max( a, b, c )

template<typename T >

T const& numeric::max ( T const &  a, T const &  b, T const &  c, T const &  d  )

inline

max( a, b, c, d )

References max().

template<typename T >

T const& numeric::max ( T const &  a, T const &  b, T const &  c, T const &  d, T const &  e  )

inline

max( a, b, c, d, e )

References max(), and max().

template<typename T >

T const& numeric::max ( T const &  a, T const &  b, T const &  c, T const &  d, T const &  e, T const &  f  )

inline

max( a, b, c, d, e, f )

References max(), and max().

template<typename T >

xyzTriple< T > numeric::max	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple with max coordinates of two xyzTriples

template<typename T >

xyzVector< T > numeric::max	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector with max coordinates of two xyzVectors

template<typename U >

xyzVector<U> numeric::max ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

xyzVector with max coordinates of two xyzVectors

template<typename U >

xyzTriple<U> numeric::max ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

xyzTriple with max coordinates of two xyzTriples

numeric::Real numeric::mean

(

utility::vector1< numeric::Real > const &

values

)

References basic::options::OptionKeys::cutoutdomain::end, and basic::options::OptionKeys::mp::mutate_relax::iter.

Referenced by do_mean().

numeric::Real numeric::median

(

utility::vector1< numeric::Real > const &

values

)

Returns the median from a vector1 of Real values.

Referenced by do_median().

template<typename T >

xyzTriple< T > numeric::midpoint	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Midpoint of 2 xyzTriples.

Referenced by HDmakerMover::apply(), HDmakerMover::find_midpoint(), and zinc2_homodimer_setup::rollmove_to_inverse_C2_symmetry().

template<typename T >

void numeric::midpoint	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > &	m
	)

Midpoint of 2 xyzTriples: Return via argument (slightly faster)

template<typename T >

xyzVector< T > numeric::midpoint	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Midpoint of 2 xyzVectors.

template<typename T >

void numeric::midpoint	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > &	m
	)

Midpoint of 2 xyzVectors: Return via argument (slightly faster)

template<typename U >

xyzTriple<U> numeric::midpoint ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Midpoint of 2 xyzTriples.

template<typename U >

void numeric::midpoint ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > &  m  )

inline

Midpoint of 2 xyzTriples: Return via argument (slightly faster)

template<typename U >

xyzVector<U> numeric::midpoint ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Midpoint of 2 xyzVectors.

template<typename U >

void numeric::midpoint ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > &  m  )

inline

Midpoint of 2 xyzVectors: Return via argument (slightly faster)

short int numeric::min ( short int const  a, short int const  b  )

inline

min( short int, short int )

Referenced by abs_difference(), ccd_angle(), numeric::geometry::hashing::xyzStripeHash::clash(), numeric::geometry::hashing::xyzStripeHash::clash_amount(), numeric::geometry::hashing::xyzStripeHash::clash_check_ball(), numeric::geometry::hashing::xyzStripeHash::clash_not_resid(), numeric::geometry::hashing::xyzStripeHash::clash_raw(), do_min(), eq_tol(), numeric::geometry::hashing::xyzStripeHash::fill_pairs(), gcd(), ge_tol(), gt_tol(), numeric::geometry::hashing::xyzStripeHash::init(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::init(), le_tol(), lt_tol(), min(), numeric::geometry::hashing::xyzStripeHash::nbcount(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::nbcount(), numeric::geometry::hashing::xyzStripeHash::nbcount_raw(), numeric::interpolation::Histogram< typename, typename >::set_params(), numeric::kinematic_closure::solve_sturm(), numeric::geometry::hashing::xyzStripeHash::visit(), numeric::geometry::hashing::xyzStripeHashWithMeta< float >::visit(), numeric::geometry::hashing::xyzStripeHash::visit_lax(), and numeric::geometry::hashing::xyzStripeHashWithMeta< float >::visit_lax().

int numeric::min ( int const  a, int const  b  )

inline

min( int, int )

long int numeric::min ( long int const  a, long int const  b  )

inline

min( long int, long int )

unsigned short int numeric::min ( unsigned short int const  a, unsigned short int const  b  )

inline

min( unsigned short int, unsigned short int )

unsigned int numeric::min ( unsigned int const  a, unsigned int const  b  )

inline

min( unsigned int, unsigned int )

template<typename T >

T numeric::min

(

utility::vector1< T > const &

values

)

References test.T200_Scoring::ii, min(), and test.T007_TracerIO::T.

unsigned long int numeric::min ( unsigned long int const  a, unsigned long int const  b  )

inline

min( unsigned long int, unsigned long int )

float numeric::min ( float const  a, float const  b  )

inline

min( float, float )

double numeric::min ( double const  a, double const  b  )

inline

min( double, double )

long double numeric::min ( long double const  a, long double const  b  )

inline

min( long double, long double )

template<typename T >

T const& numeric::min ( T const &  a, T const &  b, T const &  c  )

inline

min( a, b, c )

template<typename T >

T const& numeric::min ( T const &  a, T const &  b, T const &  c, T const &  d  )

inline

min( a, b, c, d )

References min().

template<typename T >

T const& numeric::min ( T const &  a, T const &  b, T const &  c, T const &  d, T const &  e  )

inline

min( a, b, c, d, e )

References min(), and min().

template<typename T >

T const& numeric::min ( T const &  a, T const &  b, T const &  c, T const &  d, T const &  e, T const &  f  )

inline

min( a, b, c, d, e, f )

References min(), and min().

template<typename T >

xyzTriple< T > numeric::min	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple with min coordinates of two xyzTriples

template<typename T >

xyzVector< T > numeric::min	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector with min coordinates of two xyzVectors

template<typename U >

xyzVector<U> numeric::min ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

xyzVector with min coordinates of two xyzVectors

template<typename U >

xyzTriple<U> numeric::min ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

xyzTriple with min coordinates of two xyzTriples

template<typename T >

T numeric::mod ( T const &  x, T const &  y  )

inline

x(mod y) computational modulo returning magnitude < | y | and sign of x

Note

When used with negative integer arguments this assumes integer division rounds towards zero (de facto and future official standard)

Referenced by gcd(), numeric::RemainderSelector< T, bool >::remainder(), and numeric::RemainderSelector< T, true >::remainder().

template<typename T >

T numeric::modulo ( T const &  x, T const &  y  )

inline

x(mod y) mathematical modulo returning magnitude < | y | and sign of y

Referenced by numeric::interpolation::periodic_range::full::bilinearly_interpolated(), numeric::interpolation::periodic_range::half::bilinearly_interpolated(), numeric::interpolation::periodic_range::half::bin(), numeric::interpolation::periodic_range::full::bin(), numeric::interpolation::Histogram< typename, typename >::bin_number(), numeric::interpolation::periodic_range::half::interpolated(), numeric::interpolation::periodic_range::full::interpolated(), nonnegative_principal_angle(), nonnegative_principal_angle_degrees(), and nonnegative_principal_angle_radians().

template<typename T >

void numeric::multiply	(	xyzTriple< T > const &	v,
		T const &	t,
		xyzTriple< T > &	r
	)

Multiply: xyzTriple * T.

template<typename T >

void numeric::multiply	(	T const &	t,
		xyzTriple< T > const &	v,
		xyzTriple< T > &	r
	)

Multiply: T * xyzTriple.

template<typename T >

void numeric::multiply	(	xyzVector< T > const &	v,
		T const &	t,
		xyzVector< T > &	r
	)

Multiply: xyzVector * T.

template<typename T >

void numeric::multiply	(	T const &	t,
		xyzVector< T > const &	v,
		xyzVector< T > &	r
	)

Multiply: T * xyzVector.

template<typename U >

void numeric::multiply ( xyzVector< U > const &  v, U const &  t, xyzVector< U > &  r  )

inline

Multiply: xyzVector * Value.

References basic::options::OptionKeys::in::file::t.

template<typename U >

void numeric::multiply ( U const &  t, xyzVector< U > const &  v, xyzVector< U > &  r  )

inline

Multiply: Value * xyzVector.

template<typename U >

void numeric::multiply ( xyzTriple< U > const &  v, U const &  t, xyzTriple< U > &  r  )

inline

Multiply: xyzTriple * Value.

References basic::options::OptionKeys::in::file::t.

template<typename U >

void numeric::multiply ( U const &  t, xyzTriple< U > const &  v, xyzTriple< U > &  r  )

inline

Multiply: Value * xyzTriple.

template<typename R , typename T >

R numeric::nearest ( T const &  x )

inline

nearest< R >( x ): Nearest R

Referenced by numeric::kdtree::nearest_neighbors().

template<typename T >

T numeric::nearest_angle ( T const &  angle, T const &  base_angle  )

inline

Nearest periodic value of angle to a base angle in radians.

References nearest_ssize(), and numeric::NumericTraits< T >::pi_2().

template<typename T >

T numeric::nearest_angle_degrees ( T const &  angle, T const &  base_angle  )

inline

Nearest periodic value of angle to a base angle in degrees.

References nearest_ssize(), and test.T007_TracerIO::T.

template<typename T >

T numeric::nearest_angle_radians ( T const &  angle, T const &  base_angle  )

inline

Nearest periodic value of angle to a base angle in radians.

References nearest_ssize(), and numeric::NumericTraits< T >::pi_2().

template<typename T >

int numeric::nearest_int ( T const &  x )

inline

nearest_int( x ): Nearest int

References sign(), and test.T007_TracerIO::T.

template<typename T >

std::size_t numeric::nearest_size ( T const &  x )

inline

nearest_size( x ): Nearest std::size_t

References sign(), and test.T007_TracerIO::T.

template<typename T >

SSize numeric::nearest_ssize ( T const &  x )

inline

nearest_ssize( x ): Nearest SSize

References sign(), and test.T007_TracerIO::T.

Referenced by numeric::interpolation::periodic_range::half::bin(), numeric::FastRemainderSelector< T, bool >::fast_remainder(), numeric::FastRemainderSelector< T, true >::fast_remainder(), nearest_angle(), nearest_angle_degrees(), nearest_angle_radians(), numeric::RemainderSelector< T, bool >::remainder(), and numeric::RemainderSelector< T, true >::remainder().

template<typename T >

int numeric::nint ( T const &  x )

inline

nint( x ): Nearest int

References sign(), and test.T007_TracerIO::T.

template<typename T >

T numeric::nonnegative_principal_angle ( T const &  angle )

inline

Positive principal value of angle in radians on [ 0, 2*pi )

References modulo().

template<typename T >

T numeric::nonnegative_principal_angle_degrees ( T const &  angle )

inline

Positive principal value of angle in degrees on [ 0, 360 )

References modulo(), and test.T007_TracerIO::T.

template<typename T >

T numeric::nonnegative_principal_angle_radians ( T const &  angle )

inline

Positive principal value of angle in radians on [ 0, 2*pi )

References modulo().

template<class InputIterator >

void numeric::normalize	(	InputIterator	first,
		InputIterator	last
	)

Normalizes elements on the range [first, last)

References assign_charges::first, and sum().

Referenced by cumulative(), and product().

template<typename T >

bool numeric::not_equal_length	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Not equal length?

template<typename T >

bool numeric::not_equal_length	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Not equal length?

template<typename U >

bool numeric::not_equal_length ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Not equal length?

template<typename U >

bool numeric::not_equal_length ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Not equal length?

template<typename T >

bool numeric::operator!= ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

operator != (Comparison) MathVectors

template<typename T >

bool numeric::operator!= ( MathVector< T > const &  VECTOR, T const &  X  )

inline

Returns

operator MathVector != X (Comparison with T value)

References ObjexxFCL::format::X().

template<typename T >

bool numeric::operator!= ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

operator X != MathVector(Comparison with T value)

References ObjexxFCL::format::X().

template<typename T >

bool numeric::operator!= ( const MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

compare to matrices for inequality

Parameters

MATRIX_LHS	lhs matrix
MATRIX_RHS	rhs matrix

Returns

!( MATRIX_LHS == MATRIX_RHS)

template<typename T >

bool numeric::operator!= ( const MathMatrix< T > &  MATRIX_LHS, const T &  VALUE_RHS  )

inline

compare if all items in matrix are not equal to a given VALUE

Parameters

MATRIX_LHS	matrix with values
VALUE_RHS	value that is compared against

Returns

false if matrix is empty are all elements in matrix are equal to given VALUE

References numeric::MathMatrix< T >::begin(), and numeric::MathMatrix< T >::end().

template<typename T >

bool numeric::operator!= ( const T &  VALUE_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

compare if all items in matrix are not equal to a given VALUE

Parameters

VALUE_LHS	value that is compared against
MATRIX_RHS	matrix with values

Returns

false if matrix is empty are all elements in matrix are equal to given VALUE

template<typename T >

bool numeric::operator!=	(	BodyPosition< T > const &	p1,
		BodyPosition< T > const &	p2
	)

BodyPosition != BodyPosition.

template<typename T >

bool numeric::operator!=	(	Quaternion< T > const &	q1,
		Quaternion< T > const &	q2
	)

Quaternion != Quaternion.

template<typename T >

bool numeric::operator!=	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple != xyzTriple

template<typename T >

bool numeric::operator!=	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple != T

template<typename T >

bool numeric::operator!=	(	T const &	t,
		xyzTriple< T > const &	v
	)

T != xyzTriple.

template<typename T >

bool numeric::operator!=	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector != xyzVector

template<typename T >

bool numeric::operator!=	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix != xyzMatrix

template<typename T >

bool numeric::operator!=	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector != T

template<typename T >

bool numeric::operator!=	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix != T

template<typename T >

bool numeric::operator!=	(	T const &	t,
		xyzVector< T > const &	v
	)

T != xyzVector.

template<typename T >

bool numeric::operator!=	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T != xyzMatrix.

template<typename T >

xyzVector< T > numeric::operator* ( xyzMatrix< T > const &  m, xyzVector< T > const &  v  )

inline

xyzMatrix * xyzVector

Note

Same as product( xyzMatrix, xyzVector )

References numeric::xyzVector< typename >::x_, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzVector< typename >::y_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzVector< typename >::z_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

template<typename T >

T numeric::operator* ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

operator MathVector * MathVector

References numeric::MathVector< T >::begin(), numeric::MathVector< T >::end(), and test.T007_TracerIO::T.

template<typename T >

MathVector< T > numeric::operator* ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

operator MathVector * MathVector

template<typename T >

MathVector< T > numeric::operator* ( MathVector< T > const &  VECTOR, T const &  X  )

inline

Returns

operator MathVector * MathVector

template<typename T >

MathMatrix< T> numeric::operator* ( const MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

multiply two matrixs of equal size by building the inner product yielding the scalar product

Parameters

MATRIX_LHS	lhs matrix
MATRIX_RHS	rhs matrix

Returns

scalar representing root of inner product of the two ranges

References numeric::MathMatrix< T >::get_number_cols(), numeric::MathMatrix< T >::get_number_rows(), and basic::options::OptionKeys::frags::j.

template<typename T >

MathMatrix< T> numeric::operator* ( const T &  SCALAR_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

multiply scalar with matrix

Parameters

SCALAR_LHS	lhs value to be multiplied
MATRIX_RHS	rhs matrix

Returns

matrix that has the values multiplied with the scalar

template<typename T >

MathMatrix< T> numeric::operator* ( const MathMatrix< T > &  MATRIX_LHS, const T &  SCALAR_RHS  )

inline

multiply matrix with scalar

Parameters

MATRIX_LHS	lhs matrix
SCALAR_RHS	rhs value to be multiplied

Returns

matrix that has the values multiplied with the scalar

template<typename T >

MathVector< T> numeric::operator* ( const MathMatrix< T > &  MATRIX_LHS, const MathVector< T > &  VECTOR_RHS  )

inline

multiply matrix with vector

Parameters

MATRIX_LHS	lhs matrix
VECTOR	vector to be multiplied

Returns

resulting vector

References numeric::MathMatrix< T >::get_number_cols(), numeric::MathMatrix< T >::get_number_rows(), and basic::options::OptionKeys::frags::j.

template<typename T >

Quaternion< T > numeric::operator*	(	Quaternion< T > const &	q2,
		Quaternion< T > const &	q1
	)

Quaternion * Quaternion.

template<typename T >

xyzTriple< T > numeric::operator*	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple * T

template<typename T >

xyzTriple< T > numeric::operator*	(	T const &	t,
		xyzTriple< T > const &	v
	)

T * xyzTriple.

template<typename T >

xyzVector< T > numeric::operator*	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector * T

template<typename T >

xyzVector< T > numeric::operator*	(	T const &	t,
		xyzVector< T > const &	v
	)

T * xyzVector.

template<typename T >

xyzMatrix< T > numeric::operator*	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix * xyzMatrix

template<typename T >

xyzMatrix< T > numeric::operator*	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix * T

template<typename T >

xyzMatrix< T > numeric::operator*	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T * xyzMatrix.

template<typename T >

MathMatrix< T>& numeric::operator*= ( MathMatrix< T > &  MATRIX_LHS, const T &  SCALAR  )

inline

multiply matrix with scalar

Parameters

MATRIX_LHS	matrix to multiply to
SCALAR	scalar to be multiplied

Returns

the changed lhs matrix

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and basic::options::OptionKeys::mp::transform::transform.

template<typename T >

MathVector< T > numeric::operator+ ( MathVector< T > const &  VECTOR )

inline

Returns

operator +MathVectors

template<typename T >

MathVector< T > numeric::operator+ ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

operator MathVector + MathVector

template<typename T >

MathVector< T > numeric::operator+ ( MathVector< T > const &  VECTOR, T const &  X  )

inline

Returns

operator MathVector + MathVector

template<typename T >

MathVector< T > numeric::operator+ ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

operator MathVector + MathVector

template<typename T >

MathMatrix< T> numeric::operator+ ( const MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

sum two matrixs of equal size

Parameters

MATRIX_LHS	lhs matrix
MATRIX_RHS	rhs matrix

Returns

matrix with all individual summed elements of lhs and rhs matrix

template<typename T >

MathMatrix< T> numeric::operator+ ( const MathMatrix< T > &  MATRIX_LHS, const T &  VALUE_RHS  )

inline

add value to matrix

Parameters

MATRIX_LHS	lhs matrix
VALUE_RHS	rhs value to be added

Returns

matrix that has the value added to each value of the lhs given matrix

template<typename T >

MathMatrix< T> numeric::operator+ ( const T &  VALUE_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

add matrix to value

Parameters

VALUE_LHS	lhs value to be added
MATRIX_RHS	rhs matrix

Returns

matrix that has the value added to each value of the lhs given matrix

template<typename T >

xyzTriple< T > numeric::operator+	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple + xyzTriple

template<typename T >

xyzTriple< T > numeric::operator+	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple + T

template<typename T >

xyzTriple< T > numeric::operator+	(	T const &	t,
		xyzTriple< T > const &	v
	)

T + xyzTriple.

template<typename T >

xyzVector< T > numeric::operator+	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector + xyzVector

template<typename T >

xyzVector< T > numeric::operator+	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector + T

template<typename T >

xyzVector< T > numeric::operator+	(	T const &	t,
		xyzVector< T > const &	v
	)

T + xyzVector.

template<typename T >

xyzMatrix< T > numeric::operator+	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix + xyzMatrix

template<typename T >

xyzMatrix< T > numeric::operator+	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix + T

template<typename T >

xyzMatrix< T > numeric::operator+	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T + xyzMatrix.

template<typename T >

MathMatrix< T>& numeric::operator+= ( MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

add one matrix to another

Parameters

MATRIX_LHS	matrix to add to
MATRIX_RHS	matrix to add

Returns

the changed lhs matrix

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and basic::options::OptionKeys::mp::transform::transform.

template<typename T >

MathMatrix< T>& numeric::operator+= ( MathMatrix< T > &  MATRIX_LHS, const T &  VALUE  )

inline

add scalar to matrix

Parameters

MATRIX_LHS	matrix to add to
VALUE	scalar to be added

Returns

the changed lhs matrix

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and basic::options::OptionKeys::mp::transform::transform.

template<typename T >

MathVector< T > numeric::operator- ( MathVector< T > const &  VECTOR )

inline

Returns

operator -MathVectors

References test.T007_TracerIO::T.

template<typename T >

MathVector< T > numeric::operator- ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

operator MathVector - MathVector

template<typename T >

MathVector< T > numeric::operator- ( MathVector< T > const &  VECTOR, T const &  X  )

inline

Returns

operator MathVector - MathVector

template<typename T >

MathVector< T > numeric::operator- ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

operator MathVector - MathVector

template<typename T >

MathMatrix< T> numeric::operator- ( const MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

subtract two matrixs of equal size

Parameters

MATRIX_LHS	lhs matrix
MATRIX_RHS	rhs matrix

Returns

matrix with all individual subtracted elements of rhs from lhs matrix

template<typename T >

MathMatrix< T> numeric::operator- ( const MathMatrix< T > &  MATRIX_LHS, const T &  VALUE_RHS  )

inline

subtract value from matrix

Parameters

MATRIX_LHS	lhs matrix
VALUE_RHS	rhs value to be subtracted

Returns

matrix that has the value subtracted from each value of the lhs given matrix

template<typename T >

MathMatrix< T> numeric::operator- ( const T &  VALUE_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

subtract matrix from value

Parameters

VALUE_LHS	rhs value to be subtracted
MATRIX_RHS	lhs matrix

Returns

matrix that has the values in the matrix subtracted from the value

References numeric::MathMatrix< T >::size().

template<typename T >

xyzTriple< T > numeric::operator-	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple - xyzTriple

template<typename T >

xyzTriple< T > numeric::operator-	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple - T

template<typename T >

xyzTriple< T > numeric::operator-	(	T const &	t,
		xyzTriple< T > const &	v
	)

T - xyzTriple.

template<typename T >

xyzVector< T > numeric::operator-	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector - xyzVector

template<typename T >

xyzVector< T > numeric::operator-	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector - T

template<typename T >

xyzVector< T > numeric::operator-	(	T const &	t,
		xyzVector< T > const &	v
	)

T - xyzVector.

template<typename T >

xyzMatrix< T > numeric::operator-	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix - xyzMatrix

template<typename T >

xyzMatrix< T > numeric::operator-	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix - T

template<typename T >

xyzMatrix< T > numeric::operator-	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T - xyzMatrix.

template<typename T >

MathMatrix< T>& numeric::operator-= ( MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

subtract one matrix from another

Parameters

MATRIX_LHS	matrix to subtract from
MATRIX_RHS	matrix to subtract

Returns

the changed lhs matrix

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and basic::options::OptionKeys::mp::transform::transform.

template<typename T >

MathMatrix< T>& numeric::operator-= ( MathMatrix< T > &  MATRIX_LHS, const T &  VALUE  )

inline

subtract scalar from matrix

Parameters

MATRIX_LHS	matrix to subtract from
VALUE	scalar to be added

Returns

the changed lhs matrix

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and basic::options::OptionKeys::mp::transform::transform.

template<typename T >

MathVector< T > numeric::operator/ ( MathVector< T > const &  VECTOR, T const &  X  )

inline

Returns

operator MathVector / MathVector

template<typename T >

MathVector< T > numeric::operator/ ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

operator MathVector / MathVector ; divides each element by according argument element

template<typename T >

MathVector< T > numeric::operator/ ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

operator MathVector / MathVector = Value * Inverse( MathVector)

template<typename T >

MathMatrix< T> numeric::operator/ ( const MathMatrix< T > &  MATRIX_LHS, const T &  SCALAR_RHS  )

inline

divide matrix with scalar

Parameters

MATRIX_LHS	lhs matrix
SCALAR_RHS	rhs value to be divided by

Returns

matrix that has the values divided by the scalar

template<typename T >

MathMatrix< T> numeric::operator/ ( const T &  SCALAR_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

divide scalar by matrix

Parameters

SCALAR_LHS	lhs value to be divided
MATRIX_RHS	rhs matrix to be used to divide the scalar

Returns

matrix that has the values of scalar divided by each according value of the matrix

References numeric::MathMatrix< T >::size().

template<typename T >

xyzTriple< T > numeric::operator/	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple / T

template<typename T >

xyzVector< T > numeric::operator/	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector / T

template<typename T >

xyzMatrix< T > numeric::operator/	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix / T

template<typename T >

MathMatrix< T>& numeric::operator/= ( MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &    )

inline

divide one matrix by another

Parameters

MATRIX_LHS	matrix to divided
MATRIX_RHS	matrix to divide by

Returns

the changed lhs matrix

template<typename T >

MathMatrix< T>& numeric::operator/= ( MathMatrix< T > &  MATRIX_LHS, const T &  SCALAR  )

inline

divide matrix by scalar

Parameters

MATRIX_LHS	matrix to divide
SCALAR	scalar to divide by

Returns

the changed lhs matrix

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and basic::options::OptionKeys::mp::transform::transform.

template<typename T >

bool numeric::operator<	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple < xyzTriple

template<typename T >

bool numeric::operator<	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple < T

template<typename T >

bool numeric::operator<	(	T const &	t,
		xyzTriple< T > const &	v
	)

T < xyzTriple.

template<typename T >

bool numeric::operator<	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector < xyzVector

template<typename T >

bool numeric::operator<	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix < xyzMatrix

template<typename T >

bool numeric::operator<	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector < T

template<typename T >

bool numeric::operator<	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix < T

template<typename T >

bool numeric::operator<	(	T const &	t,
		xyzVector< T > const &	v
	)

T < xyzVector.

template<typename T >

bool numeric::operator<	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T < xyzMatrix.

std::ostream & numeric::operator<<	(	std::ostream &	os,
		MultiDimensionalHistogram const &	mdhist
	)

References numeric::MultiDimensionalHistogram::counts(), numeric::MultiDimensionalHistogram::dim_labels(), numeric::MultiDimensionalHistogram::end(), numeric::MultiDimensionalHistogram::label(), numeric::MultiDimensionalHistogram::num_bins(), numeric::MultiDimensionalHistogram::num_dimensions(), and numeric::MultiDimensionalHistogram::start().

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		xyzTransform< T > const &	m
	)

stream << xyzTransform output operator

References basic::options::OptionKeys::hotspot::angle, numeric::conversions::degrees(), ObjexxFCL::format::F(), BuildPackagedBindings::format, numeric::xyzVector< typename >::length(), rotation_axis(), test.T007_TracerIO::T, numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		Quaternion< T > const &	q
	)

stream << Quaternion output operator

References basic::options::OptionKeys::ufv::right, ObjexxFCL::uppercase(), numeric::statistics::w(), and basic::options::OptionKeys::mp::visualize::width.

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		xyzMatrix< T > const &	m
	)

stream << xyzMatrix output operator

References basic::options::OptionKeys::ufv::right, ObjexxFCL::uppercase(), numeric::statistics::w(), and basic::options::OptionKeys::mp::visualize::width.

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		xyzVector< T > const &	v
	)

stream << xyzVector output operator

References basic::options::OptionKeys::ufv::right, ObjexxFCL::uppercase(), test.T850_SubClassing::v, numeric::statistics::w(), and basic::options::OptionKeys::mp::visualize::width.

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		xyzTriple< T > const &	v
	)

stream << xyzTriple output operator

References basic::options::OptionKeys::ufv::right, ObjexxFCL::uppercase(), test.T850_SubClassing::v, numeric::statistics::w(), and basic::options::OptionKeys::mp::visualize::width.

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		BodyPosition< T > const &	p
	)

stream << BodyPosition output operator

References basic::options::OptionKeys::score::fiber_diffraction::p, basic::options::OptionKeys::ufv::right, basic::options::OptionKeys::in::file::t, ObjexxFCL::uppercase(), numeric::statistics::w(), and basic::options::OptionKeys::mp::visualize::width.

std::ostream & numeric::operator<<	(	ostream &	out,
		const Polynomial_1d &	poly
	)

References basic::options::OptionKeys::canonical_sampling::out::out, and numeric::Polynomial_1d::show().

template<typename T >

std::ostream& numeric::operator<< ( std::ostream &  output, const IntervalSet< T > &  interval  )

inline

References basic::options::OptionKeys::cp::output.

template<typename T >

std::ostream& numeric::operator<<	(	std::ostream &	stream,
		HomogeneousTransform< T > const &	ht
	)

std::ostream& numeric::operator<< ( std::ostream &  stream, HomogeneousTransform< double > const &  ht  )

inline

template<typename T >

bool numeric::operator<=	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple <= xyzTriple

template<typename T >

bool numeric::operator<=	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple <= T

template<typename T >

bool numeric::operator<=	(	T const &	t,
		xyzTriple< T > const &	v
	)

T <= xyzTriple.

template<typename T >

bool numeric::operator<=	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector <= xyzVector

template<typename T >

bool numeric::operator<=	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix <= xyzMatrix

template<typename T >

bool numeric::operator<=	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector <= T

template<typename T >

bool numeric::operator<=	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix <= T

template<typename T >

bool numeric::operator<=	(	T const &	t,
		xyzVector< T > const &	v
	)

T <= xyzVector.

template<typename T >

bool numeric::operator<=	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T <= xyzMatrix.

template<typename T >

bool numeric::operator== ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

operator == (Comparison) MathVectors

References numeric::MathVector< T >::begin(), numeric::MathVector< T >::end(), numeric::MathVector< T >::size(), and test.T007_TracerIO::T.

template<typename T >

bool numeric::operator== ( MathVector< T > const &  VECTOR, T const &  X  )

inline

Returns

operator MathVector == X (Comparison with T value) MathVectors

References numeric::MathVector< T >::begin(), numeric::MathVector< T >::end(), test.T007_TracerIO::T, and ObjexxFCL::format::X().

template<typename T >

bool numeric::operator== ( const MathMatrix< T > &  MATRIX_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

compare to matricess for equality

Parameters

MATRIX_LHS	lhs matrix
MATRIX_RHS	rhs matrix

Returns

true is they are equal in size and all pairs of items are equal

References numeric::MathMatrix< T >::begin(), numeric::MathMatrix< T >::end(), and ObjexxFCL::equal().

template<typename T >

bool numeric::operator== ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

operator X == MathVector(Comparison with T value)

template<typename T >

bool numeric::operator== ( const MathMatrix< T > &  MATRIX_LHS, const T &  VALUE_RHS  )

inline

compare if all items in matrix are equal to a given VALUE

Parameters

MATRIX_LHS	matrix with values
VALUE_RHS	value that is compared against

Returns

true if matrix is empty are all elements in matrix are equal to given VALUE

References numeric::MathMatrix< T >::begin(), and numeric::MathMatrix< T >::end().

template<typename T >

bool numeric::operator== ( const T &  VALUE_LHS, const MathMatrix< T > &  MATRIX_RHS  )

inline

compare if all items in matrix are equal to a given VALUE

Parameters

VALUE_LHS	value that is compared against
MATRIX_RHS	matrix with values

Returns

true if matrix is empty are all elements in matrix are equal to given VALUE

template<typename T >

bool numeric::operator==	(	BodyPosition< T > const &	p1,
		BodyPosition< T > const &	p2
	)

BodyPosition == BodyPosition.

template<typename T >

bool numeric::operator==	(	Quaternion< T > const &	q1,
		Quaternion< T > const &	q2
	)

Quaternion == Quaternion.

template<typename T >

bool numeric::operator==	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple == xyzTriple

template<typename T >

bool numeric::operator==	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple == T

template<typename T >

bool numeric::operator==	(	T const &	t,
		xyzTriple< T > const &	v
	)

T == xyzTriple.

template<typename T >

bool numeric::operator==	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector == xyzVector

template<typename T >

bool numeric::operator==	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix == xyzMatrix

template<typename T >

bool numeric::operator==	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector == T

template<typename T >

bool numeric::operator==	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix == T

template<typename T >

bool numeric::operator==	(	T const &	t,
		xyzVector< T > const &	v
	)

T == xyzVector.

template<typename T >

bool numeric::operator==	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T == xyzMatrix.

template<typename T >

bool numeric::operator>	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple > xyzTriple

template<typename T >

bool numeric::operator>	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple > T

template<typename T >

bool numeric::operator>	(	T const &	t,
		xyzTriple< T > const &	v
	)

T > xyzTriple.

template<typename T >

bool numeric::operator>	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector > xyzVector

template<typename T >

bool numeric::operator>	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix > xyzMatrix

template<typename T >

bool numeric::operator>	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector > T

template<typename T >

bool numeric::operator>	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix > T

template<typename T >

bool numeric::operator>	(	T const &	t,
		xyzVector< T > const &	v
	)

T > xyzVector.

template<typename T >

bool numeric::operator>	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T > xyzMatrix.

template<typename T >

bool numeric::operator>=	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

xyzTriple >= xyzTriple

template<typename T >

bool numeric::operator>=	(	xyzTriple< T > const &	v,
		T const &	t
	)

xyzTriple >= T

template<typename T >

bool numeric::operator>=	(	T const &	t,
		xyzTriple< T > const &	v
	)

T >= xyzTriple.

template<typename T >

bool numeric::operator>=	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

xyzVector >= xyzVector

template<typename T >

bool numeric::operator>=	(	xyzMatrix< T > const &	a,
		xyzMatrix< T > const &	b
	)

xyzMatrix >= xyzMatrix

template<typename T >

bool numeric::operator>=	(	xyzVector< T > const &	v,
		T const &	t
	)

xyzVector >= T

template<typename T >

bool numeric::operator>=	(	xyzMatrix< T > const &	m,
		T const &	t
	)

xyzMatrix >= T

template<typename T >

bool numeric::operator>=	(	T const &	t,
		xyzVector< T > const &	v
	)

T >= xyzVector.

template<typename T >

bool numeric::operator>=	(	T const &	t,
		xyzMatrix< T > const &	m
	)

T >= xyzMatrix.

template<typename T >

std::istream& numeric::operator>>	(	std::istream &	stream,
		xyzTransform< T > &	m
	)

stream >> xyzTransform input operator

Note

Reads row-ordered matrix elements from one or multiple lines

References numeric::xyzTransform< typename >::R, and numeric::xyzTransform< typename >::t.

template<typename T >

std::istream& numeric::operator>>	(	std::istream &	stream,
		Quaternion< T > &	q
	)

stream >> Quaternion input operator

Note

Supports whitespace-separated values with optional commas between values as long as whitespace is also present

Quaternion can optionally be enclosed in parentheses () or square brackets []

String or char values containing whitespace or commas or enclosed in quotes are not supported

References numeric::Quaternion< typename >::w(), numeric::Quaternion< typename >::x(), numeric::Quaternion< typename >::y(), and numeric::Quaternion< typename >::z().

template<typename T >

std::istream& numeric::operator>>	(	std::istream &	stream,
		xyzTriple< T > &	v
	)

stream >> xyzTriple input operator

Note

Supports whitespace-separated values with optional commas between values as long as whitespace is also present

Vector can optionally be enclosed in parentheses () or square brackets []

String or char values containing whitespace or commas or enclosed in quotes are not supported

References numeric::xyzTriple< typename >::x(), numeric::xyzTriple< typename >::y(), and numeric::xyzTriple< typename >::z().

template<typename T >

std::istream& numeric::operator>>	(	std::istream &	stream,
		xyzVector< T > &	v
	)

stream >> xyzVector input operator

Note

Supports whitespace-separated values with optional commas between values as long as whitespace is also present

Vector can optionally be enclosed in parentheses () or square brackets []

String or char values containing whitespace or commas or enclosed in quotes are not supported

References numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

std::istream& numeric::operator>>	(	std::istream &	stream,
		BodyPosition< T > &	p
	)

stream >> BodyPosition input operator

Note

Reads row-ordered matrix elements from one or multiple lines

References read_row(), basic::options::OptionKeys::in::file::t, numeric::xyzVector< typename >::x(), numeric::xyzMatrix< typename >::xx(), numeric::xyzMatrix< typename >::xy(), numeric::xyzMatrix< typename >::xz(), numeric::xyzVector< typename >::y(), numeric::xyzMatrix< typename >::yx(), numeric::xyzMatrix< typename >::yy(), numeric::xyzMatrix< typename >::yz(), numeric::xyzVector< typename >::z(), numeric::xyzMatrix< typename >::zx(), numeric::xyzMatrix< typename >::zy(), and numeric::xyzMatrix< typename >::zz().

template<typename T >

std::istream& numeric::operator>>	(	std::istream &	stream,
		xyzMatrix< T > &	m
	)

stream >> xyzMatrix input operator

Note

Reads row-ordered matrix elements from one or multiple lines

References read_row(), numeric::xyzMatrix< typename >::xx(), numeric::xyzMatrix< typename >::xy(), numeric::xyzMatrix< typename >::xz(), numeric::xyzMatrix< typename >::yx(), numeric::xyzMatrix< typename >::yy(), numeric::xyzMatrix< typename >::yz(), numeric::xyzMatrix< typename >::zx(), numeric::xyzMatrix< typename >::zy(), and numeric::xyzMatrix< typename >::zz().

template<typename T >

MathVector< T > numeric::operator^ ( T const &  X, MathVector< T > const &  VECTOR  )

inline

Returns

MathVector operator Value ^ MathVector

References numeric::MathVector< T >::begin(), numeric::MathVector< T >::end(), ObjexxFCL::pow(), and test.T007_TracerIO::T.

template<typename T >

xyzMatrix< T > numeric::outer_product ( xyzVector< T > const &  a, xyzVector< T > const &  b  )

inline

xyzVector xyzVector outer product

References numeric::xyzVector< typename >::x_, numeric::xyzVector< typename >::y_, and numeric::xyzVector< typename >::z_.

Referenced by instantiate_numeric_functions().

template<typename T >

T numeric::principal_angle ( T const &  angle )

inline

Principal value of angle in radians on ( -pi, pi ].

References remainder().

template<typename T >

T numeric::principal_angle_degrees ( T const &  angle )

inline

Principal value of angle in degrees on ( -180, 180 ].

References remainder(), and test.T007_TracerIO::T.

template<typename T >

T numeric::principal_angle_radians ( T const &  angle )

inline

Principal value of angle in radians on ( -pi, pi ].

References remainder().

template<typename T >

xyzVector< T > numeric::principal_component_eigenvalues ( utility::vector1< xyzVector< T > > const &  coords )

inline

return a vector containing the eigenvalues corresponding to the first 3 principal components of the given set of points.

References principal_components_and_eigenvalues().

template<typename T >

xyzMatrix< T > numeric::principal_components ( utility::vector1< xyzVector< T > > const &  coords )

inline

return a matrix containing the first 3 principal components of the given set of points. Matrix columns are principal components, first column is first component, etc.

References principal_components_and_eigenvalues().

Referenced by first_principal_component().

template<typename T >

std::pair<xyzMatrix<T>, xyzVector<T> > numeric::principal_components_and_eigenvalues ( utility::vector1< xyzVector< T > > const &  coords )

inline

return a pair containing a matrix of the first 3 principal components and a vector of the corresponding eigenvalues of the given set of points.

References numeric::xyzMatrix< typename >::col(), numeric::xyzMatrix< typename >::col_x(), eigenvector_jacobi(), assign_charges::first, basic::options::OptionKeys::frags::j, test.T007_TracerIO::T, numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

Referenced by principal_component_eigenvalues(), and principal_components().

std::pair<utility::vector1< utility::vector1< Real > >, utility::vector1< Real > > numeric::principal_components_and_eigenvalues_ndimensions ( utility::vector1< utility::vector1< Real > > const &  coords, bool const  shift_center  )

inline

Return a pair containing a matrix (vector of vectors) of all of the principal components and a vector of the corresponding eigenvalues of the given set of points in n-dimensional space.

Note that this does not assume that the input vectors are 3-dimensional. If shift_center=false, the mean vector is not subtracted by this function. (Failure to subtract mean vector prior to function call will produce odd results, however.)

Author

Vikram K. Mulligan (vmull.nosp@m.ig@u.nosp@m.w.edu)

References basic::options::OptionKeys::frags::j, runtime_assert_string_msg, and amino_acids::size.

void numeric::print_probabilities	(	const utility::vector1< double > &	probs,
		std::ostream &	out
	)

Writes probs to the specified ostream.

template<typename T >

xyzVector< T > numeric::product ( xyzMatrix< T > const &  m, xyzVector< T > const &  v  )

inline

xyzMatrix * xyzVector product

Note

Same as xyzMatrix * xyzVector

References numeric::xyzVector< typename >::x_, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzVector< typename >::y_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzVector< typename >::z_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

template<class ForwardIterator >

void numeric::product	(	ForwardIterator	probs1_first,
		ForwardIterator	probs1_last,
		ForwardIterator	probs2_first,
		ForwardIterator	probs2_last
	)

Multiplies two probability vectors with one another. Probability vectors are assumed to have equal lengths.

References basic::options::OptionKeys::frags::j, and normalize().

Referenced by instantiate_numeric_functions(), numeric::HomogeneousTransform< double >::operator*(), and numeric::BodyPosition< typename >::transformed().

template<typename T >

Quaternion< T > numeric::product	(	Quaternion< T > const &	q2,
		Quaternion< T > const &	q1,
		bool const	precise
	)

Product: Quaternion * Quaternion.

template<typename T >

T numeric::proj_angl ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B, MathVector< T > const &  VECTOR_C, MathVector< T > const &  VECTOR_D  )

inline

Returns

projection angle between four MathVectors A->B and C->D

References test.T400_Refinement::ab, basic::options::OptionKeys::hotspot::angle, max(), min(), numeric::MathVector< T >::norm(), and test.T007_TracerIO::T.

Referenced by proj_angl().

template<typename T >

T numeric::proj_angl ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B, MathVector< T > const &  VECTOR_C  )

inline

Returns

projection angle between three MathVectors A->B and A->C

References proj_angl().

template<typename T >

T numeric::proj_angl ( MathVector< T > const &  VECTOR_A, MathVector< T > const &  VECTOR_B  )

inline

Returns

projection angle between two MathVectors 0->A and 0->B

References proj_angl().

template<typename T >

xyzMatrix< T > numeric::projection_matrix ( xyzVector< T > const &  v )

inline

geometric center

Note

compute the geometric center of a list of points Projection matrix onto the line through a vector

References numeric::xyzVector< typename >::length_squared(), numeric::xyzVector< typename >::x_, numeric::xyzVector< typename >::y_, and numeric::xyzVector< typename >::z_.

Referenced by instantiate_numeric_functions(), and rotation_matrix().

void numeric::read_probabilities_or_die	(	const std::string &	filename,
		utility::vector1< double > *	probs
	)

Loads normalized, per-residue probabilities from filename, storing the result in probs. Assumes line i holds the probability of sampling residue i. There must be 1 line for each residue in the pose on which this data will be used.

References basic::options::OptionKeys::in::in, basic::options::OptionKeys::score::fiber_diffraction::p, and utility_exit_with_message.

template<typename T >

std::istream& numeric::read_row	(	std::istream &	stream,
		T &	x,
		T &	y,
		T &	z
	)

Read an xyzMatrix row from a stream.

Note

Supports whitespace-separated values with optional commas between values as long as whitespace is also present

Rows can optionally be enclosed in parentheses () or square brackets []

String or char values containing whitespace or commas or enclosed in quotes are not supported

References x(), y(), and z().

template<typename T >

std::istream& numeric::read_row	(	std::istream &	stream,
		T &	x,
		T &	y,
		T &	z,
		T &	t
	)

Read an BodyPosition row from a stream.

Note

Supports whitespace-separated values with optional commas between values as long as whitespace is also present

Rows can optionally be enclosed in parentheses () or square brackets []

String or char values containing whitespace or commas or enclosed in quotes are not supported

References basic::options::OptionKeys::in::file::t, x(), y(), and z().

Referenced by operator>>().

template<typename T >

T numeric::remainder ( T const &  x, T const &  y  )

inline

Remainder of x with respect to division by y that is of smallest magnitude.

Note

Emulates the C99 remainder function but also supports integer arguments

Returns zero if y is zero

Return value has magnitude <= | y / 2 |

If | n - ( x / y ) | == .5 the nearest even n is used

Referenced by zlib_stream::basic_zip_streambuf< Elem, Tr, ElemA, ByteT, ByteAT >::flush(), principal_angle(), principal_angle_degrees(), principal_angle_radians(), and zlib_stream::basic_zip_streambuf< Elem, Tr, ElemA, ByteT, ByteAT >::zip_to_stream().

template<typename T , typename S >

T numeric::remainder_conversion ( T const &  t, S &  s  )

inline

Remainder and result of conversion to a different type.

References basic::options::OptionKeys::in::file::s.

numeric::xyzVector< platform::Real > numeric::rgb_to_hsv	(	platform::Real	r,
		platform::Real	g,
		platform::Real	b
	)

convert an RGB color to HSV

numeric::xyzVector< platform::Real > numeric::rgb_to_hsv

(

numeric::xyzVector< platform::Real >

rgb_triplet

)

convert and RGB color to HSV

References numeric::xyzVector< typename >::maximum_value(), numeric::xyzVector< typename >::minimum_value(), numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

T numeric::rotation_angle ( xyzMatrix< T > const &  R )

inline

Transformation from rotation matrix to magnitude of helical rotation.

Note

Input matrix must be orthogonal

Orientation of axis chosen so that the angle of rotation is non-negative [0,pi]

References ObjexxFCL::abs(), numeric::NumericTraits< T >::pi(), sin_cos_range(), test.T007_TracerIO::T, basic::options::OptionKeys::loops::ccd::tolerance, and numeric::xyzMatrix< typename >::trace().

Referenced by numeric::EulerAngles< typename >::angular_distance_between(), and instantiate_numeric_functions().

template<typename T >

xyzVector< T > numeric::rotation_axis ( xyzMatrix< T > const &  R, T &  theta  )

inline

Transformation from rotation matrix to helical axis of rotation.

Note

Input matrix must be orthogonal

Angle of rotation is also returned

Orientation of axis chosen so that the angle of rotation is non-negative [0,pi]

References ObjexxFCL::abs(), max(), numeric::NumericTraits< T >::pi(), sin_cos_range(), test.T007_TracerIO::T, basic::options::OptionKeys::loops::ccd::tolerance, numeric::xyzMatrix< typename >::trace(), x(), numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, y(), numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, z(), numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by instantiate_numeric_functions(), operator<<(), numeric::random::random_rotation_angle(), and rotation_axis_angle().

template<typename T >

xyzVector< T > numeric::rotation_axis_angle ( xyzMatrix< T > const &  R )

inline

Transformation from rotation matrix to compact axis-angle representation.

Note

Input matrix must be orthogonal

Orientation of axis chosen so that the angle of rotation is non-negative [0,pi]

References rotation_axis(), and test.T007_TracerIO::T.

Referenced by instantiate_numeric_functions().

template<typename T >

xyzMatrix< T > numeric::rotation_matrix ( xyzVector< T > const &  axis, T const &  theta  )

inline

Rotation matrix for rotation about an axis by an angle in radians.

References numeric::xyzVector< typename >::normalized(), projection_matrix(), test.T007_TracerIO::T, numeric::xyzVector< typename >::x_, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzVector< typename >::y_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzVector< typename >::z_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by numeric::xyzTransform< numeric::Real >::align(), instantiate_numeric_functions(), numeric::xyzTransform< numeric::Real >::rot(), rotation_matrix(), rotation_matrix_degrees(), rotation_matrix_radians(), zinc1_homodimer_design::setup_rollmoving(), and slice_ellipsoid_envelope().

template<typename T >

xyzMatrix< T > numeric::rotation_matrix ( xyzVector< T > const &  axis_angle )

inline

References numeric::xyzVector< typename >::magnitude(), and rotation_matrix().

template<typename T >

xyzMatrix< T > numeric::rotation_matrix_degrees ( xyzVector< T > const &  axis, T const &  theta  )

inline

Rotation matrix for rotation about an axis by an angle in degrees.

References numeric::conversions::radians(), and rotation_matrix().

Referenced by numeric::random::gaussian_random_xform(), instantiate_numeric_functions(), and numeric::xyzTransform< numeric::Real >::rot_deg().

template<typename T >

xyzMatrix< T > numeric::rotation_matrix_radians ( xyzVector< T > const &  axis, T const &  theta  )

inline

Rotation matrix for rotation about an axis by an angle in radians.

References rotation_matrix().

Referenced by instantiate_numeric_functions().

template<typename T >

T numeric::scalar_product	(	MathVector< T > const &	VECTOR_A,
		MathVector< T > const &	VECTOR_B
	)

Returns

scalar product of two MathVectors

template<typename T >

T numeric::sec ( T const &  x )

inline

Secant.

References test.T007_TracerIO::T.

template<typename T >

utility::json_spirit::Value numeric::serialize ( xyzVector< T >  coords )

inline

Convert vector to a json_spirit Value.

Note

Format is a list in the form [x,y,z]

References utility::tools::make_vector(), x(), numeric::xyzVector< typename >::x(), y(), numeric::xyzVector< typename >::y(), z(), and numeric::xyzVector< typename >::z().

template<typename T >

int numeric::sign ( T const &  x )

inline

sign( x )

References test.T007_TracerIO::T.

Referenced by numeric::NearestSelector< R, T, true >::nearest(), nearest_int(), nearest_size(), nearest_ssize(), nint(), and urs_R2ang().

template<typename S , typename T >

T numeric::sign_transfered ( S const &  sigma, T const &  x  )

inline

Sign transfered value.

References ObjexxFCL::abs().

Referenced by numeric::model_quality::rmsfitca2(), and numeric::model_quality::rmsfitca3().

template<typename T >

T numeric::sin_cos_range ( T const &  x, T const &  tol = T( .001 )  )

inline

Adjust a sine or cosine value to the valid [-1,1] range if within a specified tolerance or exit with an error.

Note

The = on the first <= and >= else if conditions were added to work-around optimization register passing bugs where x can be passed by a register with a float value of +/-1.0f but where x has a full register precision value slightly different from +/-1.0f/ The first else if cases were failing but with the = added these if conditions will succeed. The alternative fix of declaring "volatile float const x" is slower for most calls. DON'T REMOVE THESE = EVEN THOUGH THEY APPEAR TO BE SUPERFLUOUS!!!

References utility::io::oc::cerr, utility::io::oc::cout, test.T007_TracerIO::T, loops_kic::tol, utility_exit, and x().

Referenced by angle_of(), angle_radians(), arccos(), cos_of(), numeric::xyzTransform< numeric::Real >::euler_angles_rad(), numeric::HomogeneousTransform< double >::euler_angles_rad(), numeric::EulerAngles< typename >::from_rotation_matrix(), rotation_angle(), rotation_axis(), numeric::xyzTransform< numeric::Real >::rotation_cosine(), and numeric::xyzTransform< numeric::Real >::rotation_sine().

template<typename T >

T numeric::sin_of	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b
	)

Sine of angle between two vectors.

Referenced by sin_of().

template<typename T >

T numeric::sin_of	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > const &	c
	)

Sine of angle formed by three consecutive points.

template<typename T >

T numeric::sin_of	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b
	)

Sine of angle between two vectors.

template<typename T >

T numeric::sin_of	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > const &	c
	)

Sine of angle formed by three consecutive points.

template<typename U >

U numeric::sin_of ( xyzTriple< U > const &  a, xyzTriple< U > const &  b  )

inline

Sine of angle between two vectors.

References cos_of(), and square().

template<typename U >

U numeric::sin_of ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > const &  c  )

inline

Sine of angle formed by three consecutive points.

Note

For points a, b, c, the angle is the angle between the vectors a - b and c - b in other words, the positive angle about b from a to c

References sin_of().

template<typename U >

U numeric::sin_of ( xyzVector< U > const &  a, xyzVector< U > const &  b  )

inline

Sine of angle between two vectors.

References cos_of(), and square().

template<typename U >

U numeric::sin_of ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > const &  c  )

inline

Sine of angle formed by three consecutive points.

Note

For points a, b, c, the angle is the angle between the vectors a - b and c - b in other words, the positive angle about b from a to c

References sin_of().

template<typename T >

xyzVector< T > numeric::spherical_to_xyz ( sphericalVector< T > const &  spherical )

inline

References numeric::sphericalVector< typename >::phi(), numeric::constants::f::pi_over_180, numeric::sphericalVector< typename >::radius(), numeric::sphericalVector< typename >::theta(), numeric::xyzVector< typename >::x(), basic::options::OptionKeys::in::file::xyz, numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

T numeric::square ( T const &  x )

inline

square( x ) == x^2

References x().

Referenced by distance(), distance_squared(), numeric::model_quality::maxsub(), run_pep_prep(), sin_of(), numeric::fourier::SHT::so3_correlate(), and numeric::fourier::SHT::sph_standardize().

template<typename T >

void numeric::subtract	(	xyzTriple< T > const &	a,
		xyzTriple< T > const &	b,
		xyzTriple< T > &	r
	)

Subtract: xyzTriple - xyzTriple.

template<typename T >

void numeric::subtract	(	xyzTriple< T > const &	v,
		T const &	t,
		xyzTriple< T > &	r
	)

Subtract: xyzTriple - T.

template<typename T >

void numeric::subtract	(	T const &	t,
		xyzTriple< T > const &	v,
		xyzTriple< T > &	r
	)

Subtract: T - xyzTriple.

template<typename T >

void numeric::subtract	(	xyzVector< T > const &	a,
		xyzVector< T > const &	b,
		xyzVector< T > &	r
	)

Subtract: xyzVector - xyzVector.

template<typename T >

void numeric::subtract	(	xyzVector< T > const &	v,
		T const &	t,
		xyzVector< T > &	r
	)

Subtract: xyzVector - T.

template<typename T >

void numeric::subtract	(	T const &	t,
		xyzVector< T > const &	v,
		xyzVector< T > &	r
	)

Subtract: T - xyzVector.

template<typename U >

void numeric::subtract ( xyzVector< U > const &  a, xyzVector< U > const &  b, xyzVector< U > &  r  )

inline

Subtract: xyzVector - xyzVector.

template<typename U >

void numeric::subtract ( xyzVector< U > const &  v, U const &  t, xyzVector< U > &  r  )

inline

Subtract: xyzVector - Value.

References basic::options::OptionKeys::in::file::t.

template<typename U >

void numeric::subtract ( U const &  t, xyzVector< U > const &  v, xyzVector< U > &  r  )

inline

Subtract: Value - xyzVector.

template<typename U >

void numeric::subtract ( xyzTriple< U > const &  a, xyzTriple< U > const &  b, xyzTriple< U > &  r  )

inline

Subtract: xyzTriple - xyzTriple.

template<typename U >

void numeric::subtract ( xyzTriple< U > const &  v, U const &  t, xyzTriple< U > &  r  )

inline

Subtract: xyzTriple - Value.

References basic::options::OptionKeys::in::file::t.

template<typename U >

void numeric::subtract ( U const &  t, xyzTriple< U > const &  v, xyzTriple< U > &  r  )

inline

Subtract: Value - xyzTriple.

template<class InputIterator >

double numeric::sum	(	InputIterator	first,
		InputIterator	last
	)

Returns the sum of all elements on the range [first, last)

References assign_charges::first.

Referenced by numeric::nls::lm_lmdif(), numeric::nls::lm_lmpar(), numeric::nls::lm_qrfac(), numeric::nls::lm_qrsolv(), and normalize().

template<typename T >

xyzVector< T > numeric::transpose_product ( xyzMatrix< T > const &  m, xyzVector< T > const &  v  )

inline

xyzMatrix^T * xyzVector product

References numeric::xyzVector< typename >::x_, numeric::xyzMatrix< typename >::xx_, numeric::xyzMatrix< typename >::xy_, numeric::xyzMatrix< typename >::xz_, numeric::xyzVector< typename >::y_, numeric::xyzMatrix< typename >::yx_, numeric::xyzMatrix< typename >::yy_, numeric::xyzMatrix< typename >::yz_, numeric::xyzVector< typename >::z_, numeric::xyzMatrix< typename >::zx_, numeric::xyzMatrix< typename >::zy_, and numeric::xyzMatrix< typename >::zz_.

Referenced by instantiate_numeric_functions(), numeric::BodyPosition< typename >::inverse_transformed(), and numeric::BodyPosition< typename >::inverse_translation().

template<typename T >

std::string numeric::truncate_and_serialize_xyz_vector	(	xyzVector< T >	vector,
		Real	precision
	)

References basic::options::OptionKeys::optE::fixed, numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

xyzVector<T> numeric::update_5way_operation ( xyzVector< T > const &  a, xyzVector< T > const &  b, xyzVector< T > const &  c, xyzVector< T > const &  d, xyzVector< T > const &  e  )

inline

References numeric::xyzVector< typename >::x_, numeric::xyzVector< typename >::y_, and numeric::xyzVector< typename >::z_.

template<typename T >

xyzVector<T> numeric::update_operation ( xyzVector< T > const &  a, xyzVector< T > const &  b  )

inline

References numeric::xyzVector< typename >::x_, numeric::xyzVector< typename >::y_, and numeric::xyzVector< typename >::z_.

double numeric::urs_norm4 ( double  a, double  b, double  c, double  d  )

inline

Referenced by urs_R2ang().

platform::Real numeric::urs_R2ang ( numeric::xyzMatrix< Real >  R )

inline

References basic::options::OptionKeys::hotspot::angle, numeric::conversions::degrees(), sign(), and urs_norm4().

Referenced by numeric::UniformRotationSampler::remove_redundant().

template<typename T >

ObjexxFCL::FArray2D<T> numeric::vector_of_xyzvectors_to_FArray ( utility::vector1< xyzVector< T > > const &  input )

inline

convert a vector1 of xyzVectors to an FArray2D

References ObjexxFCL::index(), app.surface_docking.surface_docking::input, basic::options::OptionKeys::cp::output, x(), y(), and z().

template<typename T >

T numeric::wrap_180 ( T const &  angle )

inline

Wrap the given angle in the range [-180, 180).

No conversion to degrees is implied.

template<typename T >

T numeric::wrap_2pi ( T const &  angle )

inline

Wrap the given angle in the range [0, 2 * pi).

No conversion to radians is implied.

References basic::options::OptionKeys::hotspot::angle, and numeric::NumericTraits< T >::pi_2().

Referenced by numeric::kinematic_closure::radians::torsion().

template<typename T >

T numeric::wrap_360 ( T const &  angle )

inline

Wrap the given angle in the range [0, 360).

No conversion to degrees is implied.

References basic::options::OptionKeys::hotspot::angle.

template<typename T >

T numeric::wrap_pi ( T const &  angle )

inline

Wrap the given angle in the range [-pi, pi).

No conversion to radians is implied.

References numeric::NumericTraits< T >::pi().

template<typename T >

xyzMatrix< T > numeric::x_rotation_matrix ( T const &  theta )

inline

Rotation matrix for rotation about the x axis by an angle in radians.

References numeric::xyzMatrix< typename >::rows(), and test.T007_TracerIO::T.

Referenced by instantiate_numeric_functions(), x_rotation_matrix_degrees(), and x_rotation_matrix_radians().

template<typename T >

xyzMatrix< T > numeric::x_rotation_matrix_degrees ( T const &  theta )

inline

Rotation matrix for rotation about the x axis by an angle in degrees.

References numeric::conversions::radians(), and x_rotation_matrix().

Referenced by instantiate_numeric_functions(), numeric::random::random_rotation_angle(), and numeric::HomogeneousTransform< double >::set_xaxis_rotation_deg().

template<typename T >

xyzMatrix< T > numeric::x_rotation_matrix_radians ( T const &  theta )

inline

Rotation matrix for rotation about the x axis by an angle in radians.

References x_rotation_matrix().

Referenced by instantiate_numeric_functions(), main(), and numeric::HomogeneousTransform< double >::set_xaxis_rotation_rad().

template<typename T >

sphericalVector< T > numeric::xyz_to_spherical ( xyzVector< T > const &  xyz )

inline

References numeric::sphericalVector< typename >::phi(), numeric::constants::f::pi_over_180, numeric::sphericalVector< typename >::radius(), numeric::sphericalVector< typename >::theta(), numeric::xyzVector< typename >::x(), numeric::xyzVector< typename >::y(), and numeric::xyzVector< typename >::z().

template<typename T >

ObjexxFCL::FArray2D<T> numeric::xyzmatrix_to_FArray ( numeric::xyzMatrix< T > const &  input )

inline

convert an xyzMatrix to a 3x3 FArray 2D

References basic::options::OptionKeys::cp::output, numeric::xyzMatrix< typename >::xx(), numeric::xyzMatrix< typename >::xy(), numeric::xyzMatrix< typename >::xz(), numeric::xyzMatrix< typename >::yx(), numeric::xyzMatrix< typename >::yy(), numeric::xyzMatrix< typename >::yz(), numeric::xyzMatrix< typename >::zx(), numeric::xyzMatrix< typename >::zy(), and numeric::xyzMatrix< typename >::zz().

template<typename T >

xyzMatrix< T > numeric::y_rotation_matrix ( T const &  theta )

inline

Rotation matrix for rotation about the y axis by an angle in radians.

References numeric::xyzMatrix< typename >::rows(), and test.T007_TracerIO::T.

Referenced by instantiate_numeric_functions(), y_rotation_matrix_degrees(), and y_rotation_matrix_radians().

template<typename T >

xyzMatrix< T > numeric::y_rotation_matrix_degrees ( T const &  theta )

inline

Rotation matrix for rotation about the y axis by an angle in degrees.

References numeric::conversions::radians(), and y_rotation_matrix().

Referenced by instantiate_numeric_functions(), numeric::random::random_rotation_angle(), and numeric::HomogeneousTransform< double >::set_yaxis_rotation_deg().

template<typename T >

xyzMatrix< T > numeric::y_rotation_matrix_radians ( T const &  theta )

inline

Rotation matrix for rotation about the y axis by an angle in radians.

References y_rotation_matrix().

Referenced by instantiate_numeric_functions(), main(), and numeric::HomogeneousTransform< double >::set_yaxis_rotation_rad().

template<typename T >

xyzMatrix< T > numeric::z_rotation_matrix ( T const &  theta )

inline

Rotation matrix for rotation about the z axis by an angle in radians.

References numeric::xyzMatrix< typename >::rows(), and test.T007_TracerIO::T.

Referenced by instantiate_numeric_functions(), zinc1_homodimer_design::setup_rollmoving(), z_rotation_matrix_degrees(), and z_rotation_matrix_radians().

template<typename T >

xyzMatrix< T > numeric::z_rotation_matrix_degrees ( T const &  theta )

inline

Rotation matrix for rotation about the z axis by an angle in degrees.

References numeric::conversions::radians(), and z_rotation_matrix().

Referenced by instantiate_numeric_functions(), numeric::random::random_rotation_angle(), and numeric::HomogeneousTransform< double >::set_zaxis_rotation_deg().

template<typename T >

xyzMatrix< T > numeric::z_rotation_matrix_radians ( T const &  theta )

inline

Rotation matrix for rotation about the z axis by an angle in radians.

References z_rotation_matrix().

Referenced by instantiate_numeric_functions(), main(), and numeric::HomogeneousTransform< double >::set_zaxis_rotation_rad().