Author: bugman
Date: Thu Nov 6 15:48:03 2014
New Revision: 26427
URL: http://svn.gna.org/viewcvs/relax?rev=26427&view=rev
Log:
Simplifications and fixes for the 1st degree frame order matrix calculation for
the pseudo-ellipse.
The compile_1st_matrix_pseudo_ellipse() function of the
lib.frame_order.pseudo_ellipse module has
been significantly simplified by shifting a lot of maths outside of the
quadratic integration.
Modified:
branches/frame_order_cleanup/lib/frame_order/pseudo_ellipse.py
Modified: branches/frame_order_cleanup/lib/frame_order/pseudo_ellipse.py
URL:
http://svn.gna.org/viewcvs/relax/branches/frame_order_cleanup/lib/frame_order/pseudo_ellipse.py?rev=26427&r1=26426&r2=26427&view=diff
==============================================================================
--- branches/frame_order_cleanup/lib/frame_order/pseudo_ellipse.py
(original)
+++ branches/frame_order_cleanup/lib/frame_order/pseudo_ellipse.py Thu Nov
6 15:48:03 2014
@@ -54,7 +54,7 @@
"""
# The surface area normalisation factor.
- fact = 2.0 * sigma_max * pec(theta_x, theta_y)
+ fact = 2.0 * pec(theta_x, theta_y)
# Invert.
if fact == 0.0:
@@ -62,10 +62,13 @@
else:
fact = 1.0 / fact
+ # Sinc value.
+ sinc_smax = sinc(sigma_max/pi)
+
# Numerical integration of phi of each element.
- matrix[0, 0] = fact * quad(part_int_daeg1_pseudo_ellipse_xx, -pi, pi,
args=(theta_x, theta_y, sigma_max), full_output=1)[0]
- matrix[1, 1] = fact * quad(part_int_daeg1_pseudo_ellipse_yy, -pi, pi,
args=(theta_x, theta_y, sigma_max), full_output=1)[0]
- matrix[2, 2] = fact * quad(part_int_daeg1_pseudo_ellipse_zz, -pi, pi,
args=(theta_x, theta_y, sigma_max), full_output=1)[0]
+ matrix[0, 0] = fact * sinc_smax * (2.0*pi +
quad(part_int_daeg1_pseudo_ellipse_xx, -pi, pi, args=(theta_x, theta_y,
sigma_max), full_output=1)[0])
+ matrix[1, 1] = fact * sinc_smax * (2.0*pi +
quad(part_int_daeg1_pseudo_ellipse_yy, -pi, pi, args=(theta_x, theta_y,
sigma_max), full_output=1)[0])
+ matrix[2, 2] = 0.5 * fact * quad(part_int_daeg1_pseudo_ellipse_zz, -pi,
pi, args=(theta_x, theta_y, sigma_max), full_output=1)[0]
# Rotate and return the frame order matrix.
return rotate_daeg(matrix, R_eigen)
@@ -152,7 +155,7 @@
tmax = tmax_pseudo_ellipse(phi, x, y)
# The theta-sigma integral.
- return sin(smax) * (2 * (1 - cos(tmax)) * sin(phi)**2 + cos(phi)**2 *
sin(tmax)**2)
+ return cos(phi)**2 * sin(tmax)**2 - 2.0 * sin(phi)**2 * cos(tmax)
def part_int_daeg1_pseudo_ellipse_yy(phi, x, y, smax):
@@ -174,7 +177,7 @@
tmax = tmax_pseudo_ellipse(phi, x, y)
# The theta-sigma integral.
- return sin(smax) * (2.0 * cos(phi)**2 * (1.0 - cos(tmax)) + sin(phi)**2 *
sin(tmax)**2)
+ return sin(phi)**2 * sin(tmax)**2 - 2.0 * cos(phi)**2 * cos(tmax)
def part_int_daeg1_pseudo_ellipse_zz(phi, x, y, smax):
@@ -196,7 +199,7 @@
tmax = tmax_pseudo_ellipse(phi, x, y)
# The theta-sigma integral.
- return smax * sin(tmax)**2
+ return sin(tmax)**2
def part_int_daeg2_pseudo_ellipse_00(phi, x, y, smax):
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