///
/// @brief Sets up matrices for performing CMC in an arbitrary space
///
void mat_polar_rot_matrix()
{
for(int mat=0;mat<mp::num_materials;mat++){
const double phi=cmc::cmc_mat[mat].constraint_phi;
const double theta=cmc::cmc_mat[mat].constraint_theta;
std::vector< std::vector<double> > polar_matrix;
std::vector< std::vector<double> > polar_matrix_tp;
std::vector< std::vector<double> > polar_vector;
double dx,dy,dz; //change in angle in radians
double ddx,ddy,ddz; //change in angle in degrees
double sin_x,sin_y,sin_z,cos_x,cos_y,cos_z;
std::vector<double> reference_vector(3);
double pi=3.14159265358979323846264338327;
//--------------------------------------------------
// Initialise varibales
//--------------------------------------------------
ddx = 0.0;
ddy = phi;
ddz = theta;// assumues x = cos(theta)sin(phi), y = sin(theta)sin(phi)
dx = (ddx/360.0)*2.0*pi;
dy = (ddy/360.0)*2.0*pi;
dz = (ddz/360.0)*2.0*pi;
reference_vector[0] = 0.0;
reference_vector[1] = 0.0;
reference_vector[2] = 1.0;
sin_x = sin(dx);
cos_x = cos(dx);
sin_y = sin(dy);
cos_y = cos(dy);
sin_z = sin(dz);
cos_z = cos(dz);
std::vector< std::vector<double> > x_rotation_matrix,y_rotation_matrix,z_rotation_matrix,ref_vec;
x_rotation_matrix=vmath::set_matrix(3,3);
y_rotation_matrix=vmath::set_matrix(3,3);
z_rotation_matrix=vmath::set_matrix(3,3);
ref_vec=vmath::set_matrix(1,3,reference_vector);
x_rotation_matrix[0][0] = 1.0;
x_rotation_matrix[1][0] = 0.0;
x_rotation_matrix[2][0] = 0.0;
x_rotation_matrix[0][1] = 0.0;
x_rotation_matrix[1][1] = cos_x;
x_rotation_matrix[2][1] = -sin_x;
x_rotation_matrix[0][2] = 0.0;
x_rotation_matrix[1][2] = sin_x;
x_rotation_matrix[2][2] = cos_x;
y_rotation_matrix[0][0] = cos_y;
y_rotation_matrix[1][0] = 0.0;
y_rotation_matrix[2][0] = sin_y;
y_rotation_matrix[0][1] = 0.0;
y_rotation_matrix[1][1] = 1.0;
y_rotation_matrix[2][1] = 0.0;
y_rotation_matrix[0][2] = -sin_y;
y_rotation_matrix[1][2] = 0.0;
y_rotation_matrix[2][2] = cos_y;
z_rotation_matrix[0][0] = cos_z;
z_rotation_matrix[1][0] = -sin_z;
z_rotation_matrix[2][0] = 0.0;
z_rotation_matrix[0][1] = sin_z;
z_rotation_matrix[1][1] = cos_z;
z_rotation_matrix[2][1] = 0.0;
z_rotation_matrix[0][2] = 0.0;
z_rotation_matrix[1][2] = 0.0;
z_rotation_matrix[2][2] = 1.0;
polar_matrix = vmath::matmul(y_rotation_matrix,z_rotation_matrix);
polar_matrix_tp = vmath::transpose(polar_matrix);
polar_vector = vmath::matmul(ref_vec,polar_matrix);
// copy matrices to performance optimised class variables
for (int i=0;i<3;i++){
cmc::cmc_mat[mat].ppolar_vector[i]=polar_vector[0][i];
for (int j=0;j<3;j++){
cmc::cmc_mat[mat].ppolar_matrix[i][j]=polar_matrix[i][j];
cmc::cmc_mat[mat].ppolar_matrix_tp[i][j]=polar_matrix_tp[i][j];
}
}
} // end of loop over materials
} // end of polar rotation initialisation
///
/// @brief Sets up matrices for performing CMC in an arbitrary space
///
/// @param[in] phi Magnetisation azimuthal angle
/// @param[in] theta Magnetisation rotational angle
/// @param[out] polar_matrix Matrix to rotate v to z
/// @param[out] polar_matrix_tp Matrix to rotate z to v
/// @param[out] polar_vector Constraint Vector
/// @return void
///
void polar_rot_matrix(
double phi,
double theta,
std::vector< std::vector<double> > & polar_matrix,
std::vector< std::vector<double> > & polar_matrix_tp,
std::vector< std::vector<double> > & polar_vector)
{
double dx,dy,dz; //change in angle in radians
double ddx,ddy,ddz; //change in angle in degrees
double sin_x,sin_y,sin_z,cos_x,cos_y,cos_z;
std::vector<double> reference_vector(3);
double pi=3.14159265358979323846264338327;
//--------------------------------------------------
// Initialise varibales
//--------------------------------------------------
ddx = 0.0;
ddy = phi;
ddz = theta;// assumues x = cos(theta)sin(phi), y = sin(theta)sin(phi)
dx = (ddx/360.0)*2.0*pi;
dy = (ddy/360.0)*2.0*pi;
dz = (ddz/360.0)*2.0*pi;
reference_vector[0] = 0.0;
reference_vector[1] = 0.0;
reference_vector[2] = 1.0;
sin_x = sin(dx);
cos_x = cos(dx);
sin_y = sin(dy);
cos_y = cos(dy);
sin_z = sin(dz);
cos_z = cos(dz);
std::vector< std::vector<double> > x_rotation_matrix,y_rotation_matrix,z_rotation_matrix,ref_vec;
x_rotation_matrix=vmath::set_matrix(3,3);
y_rotation_matrix=vmath::set_matrix(3,3);
z_rotation_matrix=vmath::set_matrix(3,3);
ref_vec=vmath::set_matrix(1,3,reference_vector);
x_rotation_matrix[0][0] = 1.0;
x_rotation_matrix[1][0] = 0.0;
x_rotation_matrix[2][0] = 0.0;
x_rotation_matrix[0][1] = 0.0;
x_rotation_matrix[1][1] = cos_x;
x_rotation_matrix[2][1] = -sin_x;
x_rotation_matrix[0][2] = 0.0;
x_rotation_matrix[1][2] = sin_x;
x_rotation_matrix[2][2] = cos_x;
y_rotation_matrix[0][0] = cos_y;
y_rotation_matrix[1][0] = 0.0;
y_rotation_matrix[2][0] = sin_y;
y_rotation_matrix[0][1] = 0.0;
y_rotation_matrix[1][1] = 1.0;
y_rotation_matrix[2][1] = 0.0;
y_rotation_matrix[0][2] = -sin_y;
y_rotation_matrix[1][2] = 0.0;
y_rotation_matrix[2][2] = cos_y;
z_rotation_matrix[0][0] = cos_z;
z_rotation_matrix[1][0] = -sin_z;
z_rotation_matrix[2][0] = 0.0;
z_rotation_matrix[0][1] = sin_z;
z_rotation_matrix[1][1] = cos_z;
z_rotation_matrix[2][1] = 0.0;
z_rotation_matrix[0][2] = 0.0;
z_rotation_matrix[1][2] = 0.0;
z_rotation_matrix[2][2] = 1.0;
polar_matrix = vmath::matmul(y_rotation_matrix,z_rotation_matrix);
polar_matrix_tp = vmath::transpose(polar_matrix);
polar_vector = vmath::matmul(ref_vec,polar_matrix);
}
