src/numeric/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 <cmath>
#include <cstdlib>
#include <vector>

Namespaces
namespace	numeric
	A 1D histogram based upon a map structure.
Functions
template<typename T >
xyzVector< T >	numeric::operator* (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector
template<typename T >
xyzVector< T >	numeric::product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix * xyzVector product
template<typename T >
xyzVector< T > &	numeric::inplace_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix * xyzVector in-place product
template<typename T >
xyzVector< T >	numeric::transpose_product (xyzMatrix< T > const &m, xyzVector< T > const &v)
	xyzMatrix^T * xyzVector product
template<typename T >
xyzVector< T > &	numeric::inplace_transpose_product (xyzMatrix< T > const &m, xyzVector< T > &v)
	xyzMatrix^T * xyzVector in-place transpose product
template<typename T >
xyzMatrix< T >	numeric::outer_product (xyzVector< T > const &a, xyzVector< T > const &b)
	xyzVector xyzVector outer product
template<typename T >
xyzMatrix< T >	numeric::projection_matrix (xyzVector< T > const &v)
	geometric center
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
template<typename T >
xyzVector< T >	numeric::rotation_axis (xyzMatrix< T > const &R, T &theta)
	Transformation from rotation matrix to helical axis of rotation.
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.
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.
template<typename T >
void	numeric::jacobi_rotation (xyzMatrix< T > const &m, int const i, int const j, xyzMatrix< T > &r)
	Jacobi rotation.
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)

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Detailed Description

xyzVector and xyzMatrix functions

Author:

Frank M. D'Ippolito (Objexx@objexx.com)

Stuart G. Mentzer (Stuart_Mentzer@objexx.com)