lib.frame_order.pseudo_ellipse_free

1 ############################################################################### 2 # # 3 # Copyright (C) 2009-2014 Edward d'Auvergne # 4 # # 5 # This file is part of the program relax (http://www.nmr-relax.com). # 6 # # 7 # This program is free software: you can redistribute it and/or modify # 8 # it under the terms of the GNU General Public License as published by # 9 # the Free Software Foundation, either version 3 of the License, or # 10 # (at your option) any later version. # 11 # # 12 # This program is distributed in the hope that it will be useful, # 13 # but WITHOUT ANY WARRANTY; without even the implied warranty of # 14 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # 15 # GNU General Public License for more details. # 16 # # 17 # You should have received a copy of the GNU General Public License # 18 # along with this program. If not, see <http://www.gnu.org/licenses/>. # 19 # # 20 ############################################################################### 21 22 # Module docstring. 23 """Module for the handling of Frame Order.""" 24 25 # Python module imports. 26 from math import cos, pi, sin 27 try: 28 from scipy.integrate import quad 29 except ImportError: 30 pass 31 32 # relax module imports. 33 from lib.geometry.pec import pec 34 from lib.frame_order.matrix_ops import rotate_daeg 35 from lib.frame_order.pseudo_ellipse import tmax_pseudo_ellipse 36 37

38 -def compile_2nd_matrix_pseudo_ellipse_free_rotor(matrix, Rx2_eigen, theta_x, theta_y):

39 """Generate the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 40 41 @param matrix: The Frame Order matrix, 2nd degree to be populated. 42 @type matrix: numpy 9D, rank-2 array 43 @param Rx2_eigen: The Kronecker product of the eigenframe rotation matrix with itself. 44 @type Rx2_eigen: numpy 9D, rank-2 array 45 @param theta_x: The cone opening angle along x. 46 @type theta_x: float 47 @param theta_y: The cone opening angle along y. 48 @type theta_y: float 49 """ 50 51 # The surface area normalisation factor. 52 fact = 1.0 / (6.0 * pec(theta_x, theta_y)) 53 54 # Diagonal. 55 matrix[0, 0] = fact * (4.0*pi - quad(part_int_daeg2_pseudo_ellipse_free_rotor_00, -pi, pi, args=(theta_x, theta_y), full_output=1)[0]) 56 matrix[1, 1] = matrix[3, 3] = fact * 3.0/2.0 * quad(part_int_daeg2_pseudo_ellipse_free_rotor_11, -pi, pi, args=(theta_x, theta_y), full_output=1)[0] 57 matrix[4, 4] = fact * (4.0*pi - quad(part_int_daeg2_pseudo_ellipse_free_rotor_44, -pi, pi, args=(theta_x, theta_y), full_output=1)[0]) 58 matrix[8, 8] = fact * (4.0*pi - 2.0*quad(part_int_daeg2_pseudo_ellipse_free_rotor_88, -pi, pi, args=(theta_x, theta_y), full_output=1)[0]) 59 60 # Off diagonal set 1. 61 matrix[0, 4] = matrix[0, 0] 62 matrix[4, 0] = matrix[4, 4] 63 matrix[0, 8] = fact * (4.0*pi + quad(part_int_daeg2_pseudo_ellipse_free_rotor_08, -pi, pi, args=(theta_x, theta_y), full_output=1)[0]) 64 matrix[8, 0] = fact * (4.0*pi + quad(part_int_daeg2_pseudo_ellipse_free_rotor_80, -pi, pi, args=(theta_x, theta_y), full_output=1)[0]) 65 matrix[4, 8] = fact * (4.0*pi + quad(part_int_daeg2_pseudo_ellipse_free_rotor_48, -pi, pi, args=(theta_x, theta_y), full_output=1)[0]) 66 matrix[8, 4] = matrix[8, 0] 67 68 # Off diagonal set 2. 69 matrix[1, 3] = matrix[3, 1] = -matrix[1, 1] 70 71 # Rotate and return the frame order matrix. 72 return rotate_daeg(matrix, Rx2_eigen)

73 74

75 -def part_int_daeg2_pseudo_ellipse_free_rotor_00(phi, x, y):

76 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 77 78 @param phi: The azimuthal tilt-torsion angle. 79 @type phi: float 80 @param x: The cone opening angle along x. 81 @type x: float 82 @param y: The cone opening angle along y. 83 @type y: float 84 @return: The theta-sigma partial integral. 85 @rtype: float 86 """ 87 88 # Theta max. 89 tmax = tmax_pseudo_ellipse(phi, x, y) 90 91 # The theta-sigma integral. 92 return cos(phi)**2*cos(tmax)**3 + 3.0*sin(phi)**2*cos(tmax)

93 94

95 -def part_int_daeg2_pseudo_ellipse_free_rotor_08(phi, x, y):

96 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 97 98 @param phi: The azimuthal tilt-torsion angle. 99 @type phi: float 100 @param x: The cone opening angle along x. 101 @type x: float 102 @param y: The cone opening angle along y. 103 @type y: float 104 @return: The theta-sigma partial integral. 105 @rtype: float 106 """ 107 108 # Theta max. 109 tmax = tmax_pseudo_ellipse(phi, x, y) 110 111 # The theta-sigma integral. 112 return cos(phi)**2*(2.0*cos(tmax)**3 - 6.0*cos(tmax))

113 114

115 -def part_int_daeg2_pseudo_ellipse_free_rotor_11(phi, x, y):

116 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 117 118 @param phi: The azimuthal tilt-torsion angle. 119 @type phi: float 120 @param x: The cone opening angle along x. 121 @type x: float 122 @param y: The cone opening angle along y. 123 @type y: float 124 @return: The theta-sigma partial integral. 125 @rtype: float 126 """ 127 128 # Theta max. 129 tmax = tmax_pseudo_ellipse(phi, x, y) 130 131 # The theta-sigma integral. 132 return sin(tmax)**2

133 134

135 -def part_int_daeg2_pseudo_ellipse_free_rotor_44(phi, x, y):

136 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 137 138 @param phi: The azimuthal tilt-torsion angle. 139 @type phi: float 140 @param x: The cone opening angle along x. 141 @type x: float 142 @param y: The cone opening angle along y. 143 @type y: float 144 @return: The theta-sigma partial integral. 145 @rtype: float 146 """ 147 148 # Theta max. 149 tmax = tmax_pseudo_ellipse(phi, x, y) 150 151 # The theta-sigma integral. 152 return sin(phi)**2*cos(tmax)**3 + 3*cos(phi)**2*cos(tmax)

153 154

155 -def part_int_daeg2_pseudo_ellipse_free_rotor_48(phi, x, y):

156 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 157 158 @param phi: The azimuthal tilt-torsion angle. 159 @type phi: float 160 @param x: The cone opening angle along x. 161 @type x: float 162 @param y: The cone opening angle along y. 163 @type y: float 164 @return: The theta-sigma partial integral. 165 @rtype: float 166 """ 167 168 # Theta max. 169 tmax = tmax_pseudo_ellipse(phi, x, y) 170 171 # The theta-sigma integral. 172 return sin(phi)**2*(2.0*cos(tmax)**3 - 6.0*cos(tmax))

173 174

175 -def part_int_daeg2_pseudo_ellipse_free_rotor_80(phi, x, y):

176 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 177 178 @param phi: The azimuthal tilt-torsion angle. 179 @type phi: float 180 @param x: The cone opening angle along x. 181 @type x: float 182 @param y: The cone opening angle along y. 183 @type y: float 184 @return: The theta-sigma partial integral. 185 @rtype: float 186 """ 187 188 # Theta max. 189 tmax = tmax_pseudo_ellipse(phi, x, y) 190 191 # The theta-sigma integral. 192 return cos(tmax)**3 - 3.0*cos(tmax)

193 194

195 -def part_int_daeg2_pseudo_ellipse_free_rotor_88(phi, x, y):

196 """The theta-sigma partial integral of the 2nd degree Frame Order matrix for the free rotor pseudo-ellipse. 197 198 @param phi: The azimuthal tilt-torsion angle. 199 @type phi: float 200 @param x: The cone opening angle along x. 201 @type x: float 202 @param y: The cone opening angle along y. 203 @type y: float 204 @return: The theta-sigma partial integral. 205 @rtype: float 206 """ 207 208 # Theta max. 209 tmax = tmax_pseudo_ellipse(phi, x, y) 210 211 # The theta-sigma integral. 212 return cos(tmax)**3

213

Source Code for Module lib.frame_order.pseudo_ellipse_free_rotor