JDFTx  1.2.0
Quadratures for SO(3)/Z2 integration

Files

file  Euler.h
 Various Euler angle related utilities.
 
file  S2quad.h
 Quadratures on S2 used to generate quadratures on SO(3)
 
file  SO3quad.h
 Quadratures for SO(3)
 

Classes

struct  S2quad
 Abstract base class for a S2 quadrature definition (used to generate the SO3 qudarature) More...
 
class  EulerProduct
 Outer-product quadrature on ZYZ euler angles. More...
 
class  Tetrahedron
 Tetrahedron rotation group. More...
 
class  Octahedron
 Octahedron rotation group. More...
 
class  Icosahedron
 Icosahedron rotation group. More...
 
class  S2_7design_24
 Spherical 7-design with 24 nodes. More...
 
class  S2_8design_36
 Spherical 8-design with 36 nodes. More...
 
class  S2_9design_48
 Spherical 9-design with 48 nodes. More...
 
class  S2_10design_60
 Spherical 10-design with 60 nodes. More...
 
class  S2_11design_70
 Spherical 11-design with 70 nodes. More...
 
class  S2_12design_84
 Spherical 12-design with 84 nodes. More...
 
class  S2_13design_94
 Spherical 13-design with 94 nodes. More...
 
class  S2_14design_108
 Spherical 14-design with 108 nodes. More...
 
class  S2_15design_120
 Spherical 15-design with 120 nodes. More...
 
class  S2_16design_144
 Spherical 16-design with 144 nodes. More...
 
class  S2_17design_156
 Spherical 17-design with 156 nodes. More...
 
class  S2_18design_180
 Spherical 18-design with 180 nodes. More...
 
class  S2_19design_204
 Spherical 19-design with 204 nodes. More...
 
class  S2_20design_216
 Spherical 20-design with 216 nodes. More...
 
class  S2_21design_240
 Spherical 21-design with 240 nodes. More...
 
class  SO3quad
 Quadrature for SO(3) More...
 

Enumerations

enum  S2quadType {
  QuadEuler, QuadTetrahedron, QuadOctahedron, QuadIcosahedron,
  Quad7design_24, Quad8design_36, Quad9design_48, Quad10design_60,
  Quad11design_70, Quad12design_84, Quad13design_94, Quad14design_108,
  Quad15design_120, Quad16design_144, Quad17design_156, Quad18design_180,
  Quad19design_204, Quad20design_216, Quad21design_240
}
 List of available quadratures.
 

Functions

vector3 polarUnitVector (double alpha, double beta)
 Get the position of the new Z-axis, given alpha and beta (does not depend on gamma)
 
void getEulerAxis (const vector3<> &newZ, vector3<> &euler)
 Calculates euler[0]=alpha and euler[1]=beta given newZ, the direction of the Z-axis in the rotated frame.
 
matrix3 matrixFromEuler (const vector3<> &euler)
 Calculate rotation matrices from euler angles.
 
vector3 eulerFromMatrix (const matrix3<> &mat)
 Calculate euler angles from rotation matrices.
 
double wigner_d (const int j, const int m1, const int m2, const double beta)
 Wigner d-function d^j_{m1 m2}(beta) for ZYZ Euler angles.
 

Detailed Description