xyz.functions.hh File Reference

xyzVector and xyzMatrix functions More...

#include <numeric/conversions.hh>
#include <numeric/NumericTraits.hh>
#include <numeric/trig.functions.hh>
#include <numeric/xyzVector.hh>
#include <numeric/xyzMatrix.hh>
#include <numeric/sphericalVector.hh>
#include <utility/string_util.hh>
#include <utility/vector1.hh>
#include <cmath>
#include <cstdlib>
#include <vector>
#include <ObjexxFCL/FArray2D.hh>

Namespaces
	numeric
	Unit headers.

Functions
template<typename T >
xyzVector< T >	numeric::closest_point_on_line (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &q)
	xyzMatrix * xyzVector More...
template<typename T >
xyzVector< T >	numeric::center_of_mass (utility::vector1< xyzVector< T > > const &coords)
	calculate center of mass for coordinates More...
template<typename T >
xyzVector< T >	numeric::product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector product More...
template<typename T >
xyzVector< T > &	numeric::inplace_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix * xyzVector in-place product More...
template<typename T >
xyzVector< T >	numeric::transpose_product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix^T * xyzVector product More...
template<typename T >
xyzVector< T > &	numeric::inplace_transpose_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix^T * xyzVector in-place transpose product More...
template<typename T >
xyzMatrix< T >	numeric::outer_product (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector xyzVector outer product More...
template<typename T >
xyzMatrix< T >	numeric::projection_matrix (xyzVector< T > const &v)
	geometric center More...
template<typename T >
xyzMatrix< T >	numeric::inverse (xyzMatrix< T > const &a)
template<typename T >
void	numeric::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	numeric::angle_radians (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3)
	Plane angle in radians: angle value returned. More...
double	numeric::angle_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3)
template<typename T >
T	numeric::angle_degrees (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3)
	Plane angle in degrees: angle value returned. More...
double	numeric::angle_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3)
template<typename T >
T	numeric::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	numeric::angle_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
template<typename T >
T	numeric::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	numeric::angle_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
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)
	Dihedral (torsion) angle in radians: angle value passed. More...
void	numeric::dihedral_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4, double &angle)
template<typename T >
T	numeric::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...
double	numeric::dihedral_radians_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
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)
	Dihedral (torsion) angle in degrees: angle value passed. More...
void	numeric::dihedral_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4, double &angle)
template<typename T >
T	numeric::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...
double	numeric::dihedral_degrees_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
template<typename T >
void	numeric::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...
void	numeric::dihedral_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4, double &angle)
template<typename T >
T	numeric::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...
double	numeric::dihedral_double (xyzVector< double > const &p1, xyzVector< double > const &p2, xyzVector< double > const &p3, xyzVector< double > const &p4)
template<typename T >
xyzMatrix< T >	numeric::rotation_matrix (xyzVector< T > const &axis_angle)
template<typename T >
xyzMatrix< T >	numeric::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 >
xyzMatrix< T >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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 >	numeric::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	numeric::rotation_angle (xyzMatrix< T > const &R)
	Transformation from rotation matrix to magnitude of helical rotation. More...
template<typename T >
xyzVector< T >	numeric::rotation_axis (xyzMatrix< T > const &R, T &theta)
	Transformation from rotation matrix to helical axis of rotation. More...
template<typename T >
xyzVector< T >	numeric::rotation_axis_angle (xyzMatrix< T > const &R)
	Transformation from rotation matrix to compact axis-angle representation. More...
template<typename T >
xyzVector< T >	numeric::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 >	numeric::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	numeric::jacobi_rotation (xyzMatrix< T > const &m, int const i, int const j, xyzMatrix< T > &r)
	Jacobi rotation. More...
template<typename T >
sphericalVector< T >	numeric::xyz_to_spherical (xyzVector< T > const &xyz)
template<typename T >
xyzVector< T >	numeric::spherical_to_xyz (sphericalVector< T > const &spherical)
template<typename T >
xyzVector< T >	numeric::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 >	numeric::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 > >	numeric::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 >	numeric::FArray_to_xyzmatrix (ObjexxFCL::FArray2D< T > const &input)
	convert a 3x3 FArray 2D to an xyzMatrix More...
template<typename T >
ObjexxFCL::FArray2D< T >	numeric::xyzmatrix_to_FArray (numeric::xyzMatrix< T > const &input)
	convert an xyzMatrix to a 3x3 FArray 2D More...

Detailed Description

xyzVector and xyzMatrix functions

Author

Frank M. D'Ippolito (Objex.nosp@m.x@ob.nosp@m.jexx..nosp@m.com)

Stuart G. Mentzer (Stuar.nosp@m.t_Me.nosp@m.ntzer.nosp@m.@obj.nosp@m.exx.c.nosp@m.om)