Author: bugman
Date: Tue Oct 22 12:21:54 2013
New Revision: 21209
URL: http://svn.gna.org/viewcvs/relax?rev=21209&view=rev
Log:
A 20-25% speed increase for the 'NS CPMG 2-site expanded' dispersion model.
Many repetitive mathematical operations have been eliminated and the equations
have been changed to
optimise the calculation speed.
Modified:
branches/relax_disp/lib/dispersion/ns_cpmg_2site_expanded.py
Modified: branches/relax_disp/lib/dispersion/ns_cpmg_2site_expanded.py
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/lib/dispersion/ns_cpmg_2site_expanded.py?rev=21209&r1=21208&r2=21209&view=diff
==============================================================================
--- branches/relax_disp/lib/dispersion/ns_cpmg_2site_expanded.py (original)
+++ branches/relax_disp/lib/dispersion/ns_cpmg_2site_expanded.py Tue Oct 22
12:21:54 2013
@@ -222,7 +222,7 @@
# Python module imports.
from math import log
-from numpy import add, complex, conj, dot, exp, power, real, sqrt
+from numpy import add, conj, dot, exp, power, real, sqrt
# relax module imports.
from lib.float import isNaN
@@ -258,66 +258,84 @@
@type num_cpmg: numpy int16, rank-1 array
"""
+ # Repeditive calculations.
+ half_tcp = 0.5 * tcp
+ k_AB_plus_k_BA = k_AB + k_BA
+ k_BA_minus_k_AB = k_BA - k_AB
+
# The expansion factors (in numpy array form for all dispersion points).
- t3 = complex(0, 1)
+ t3 = 1.j
t4 = t3 * dw
- t5 = k_BA * k_BA
- t8 = 2.0 * t3 * k_BA * dw
+ two_t4 = 2.0 * t4
+ t5 = k_BA**2
+ t8 = two_t4 * k_BA
t10 = 2.0 * k_BA * k_AB
- t11 = dw * dw
- t14 = 2.0 * t3 * k_AB*dw
- t15 = k_AB * k_AB
- t17 = sqrt(t5 - t8 + t10 - t11 + t14 + t15)
- t21 = exp((-k_BA + t4 - k_AB + t17) * tcp/2.0)
+ t11 = dw**2
+ t14 = two_t4 * k_AB
+ t15 = k_AB**2
+ t5_t10_t11_t15 = t5 + t10 - t11 + t15
+ t8_t14 = t8 - t14
+ t17 = sqrt(t5_t10_t11_t15 - t8_t14)
+
+ k_AB_plus_k_BA_minus_t4 = k_AB_plus_k_BA - t4
+ t21 = exp((t17 - k_AB_plus_k_BA_minus_t4) * half_tcp)
t22 = 1.0/t17
- t28 = exp((-k_BA + t4 - k_AB - t17) * tcp/2.0)
- t31 = t21 * t22 * k_AB - t28 * t22 * k_AB
- t33 = sqrt(t5 + t8 + t10 - t11 - t14 + t15)
- t34 = k_BA + t4 - k_AB + t33
- t37 = exp((-k_BA - t4 - k_AB + t33) * tcp)
+ t28 = exp(-(t17 + k_AB_plus_k_BA_minus_t4) * half_tcp)
+ t31 = t22*k_AB * (t21 - t28)
+ t33 = sqrt(t5_t10_t11_t15 + t8_t14)
+
+ k_AB_plus_k_BA_plus_t4 = k_AB_plus_k_BA + t4
+ k_BA_minus_k_AB_plus_t4 = k_BA_minus_k_AB + t4
+ t34 = k_BA_minus_k_AB_plus_t4 + t33
+ t37 = exp((t33 - k_AB_plus_k_BA_plus_t4) * tcp)
t39 = 1.0/t33
- t41 = k_BA + t4 - k_AB - t33
- t44 = exp((-k_BA - t4 - k_AB - t33) * tcp)
- t47 = t34 * t37 * t39/2.0 - t41 * t44 * t39/2.0
- t49 = k_BA - t4 - k_AB - t17
+ t41 = k_BA_minus_k_AB_plus_t4 - t33
+ t44 = exp(-(t33 + k_AB_plus_k_BA_plus_t4) * tcp)
+ t47 = 0.5*t39 * (t34*t37 - t41*t44)
+
+ k_BA_minus_k_AB_minus_t4 = k_BA_minus_k_AB - t4
+ t49 = k_BA_minus_k_AB_minus_t4 - t17
t51 = t21 * t49 * t22
- t52 = k_BA - t4 - k_AB + t17
+ t52 = k_BA_minus_k_AB_minus_t4 + t17
t54 = t28 * t52 * t22
t55 = -t51 + t54
- t60 = t37 * t39 * k_AB - t44 * t39 * k_AB
- t62 = t31 * t47 + t55 * t60/2.0
+ t60 = 0.5*t39*k_AB * (t37 - t44)
+ t62 = t31*t47 + t55*t60
t63 = 1.0/k_AB
- t68 = -t52 * t63 * t51/2.0 + t49 * t63 * t54/2.0
- t69 = t62 * t68/2.0
+ t68 = 0.5*t63 * (t49*t54 - t52*t51)
+ t69 = 0.5*t62 * t68
t72 = t37 * t41 * t39
t76 = t44 * t34 * t39
- t78 = -t34 * t63 * t72/2.0 + t41 * t63 * t76/2.0
- t80 = -t72 + t76
- t82 = t31 * t78/2.0 + t55 * t80/4.0
+ t78 = 0.5*t63 * (t41*t76 - t34*t72)
+ t80 = 0.5 * (t76 - t72)
+ t82 = 0.5 * (t31*t78 + t55*t80)
t83 = t82 * t55/2.0
- t88 = t52 * t21 * t22/2.0 - t49 * t28 * t22/2.0
- t91 = t88 * t47 + t68 * t60/2.0
+ t88 = 0.5 * t22 * (t52*t21 - t49*t28)
+ t91 = t88 * t47 + t68*t60
t92 = t91 * t88
- t95 = t88 * t78/2.0 + t68 * t80/4.0
+ t95 = 0.5 * (t88*t78 + t68*t80)
t96 = t95 * t31
t97 = t69 + t83
- t98 = t97 * t97
+ t98 = t97**2
t99 = t92 + t96
- t102 = t99 * t99
+ t102 = t99**2
t108 = t62 * t88 + t82 * t31
- t112 = sqrt(t98 - 2.0 * t99 * t97 + t102 + 4.0 * (t91 * t68/2.0 + t95 *
t55/2.0) * t108)
- t113 = t69 + t83 - t92 - t96 - t112
+ t112 = sqrt(t98 - 2.0 * t99 * t97 + t102 + 2.0 * (t91 * t68 + t95 * t55) *
t108)
+ t97_t99 = t97 + t99
+ t97_nt99 = t97 - t99
+ t113 = t97_nt99 - t112
t115 = num_cpmg
- t116 = power(t69/2.0 + t83/2.0 + t92/2.0 + t96/2.0 + t112/2.0, t115)
+ t116 = power(0.5*(t97_t99 + t112), t115)
t118 = 1.0/t112
- t120 = t69 + t83 - t92 - t96 + t112
- t122 = power(t69/2.0 + t83/2.0 + t92/2.0 + t96/2.0 - t112/2.0, t115)
- t127 = 1.0/t108
- t139 = 1.0/(k_AB + k_BA) * ((-t113 * t116 * t118/2.0 + t120 * t122 *
t118/2.0) * k_BA + (-t113 * t127 * t116 * t120 * t118/2.0 + t120 * t127 * t122
* t113 * t118/2.0) * k_AB/2.0)
+ t120 = t97_nt99 + t112
+ t122 = power(0.5*(t97_t99 - t112), t115)
+ t127 = 0.5/t108
+ t120_t122 = t120*t122
+ t139 = 0.5/(k_AB + k_BA) * ((t120_t122 - t113*t116)*t118*k_BA + (t120_t122
- t116*t120)*t127*t113*t118*k_AB)
# Calculate the initial and final peak intensities.
intensity0 = pA
- intensity = real(t139) * exp(-relax_time * r20)
+ intensity = t139.real * exp(-relax_time * r20)
# The magnetisation vector.
Mx = intensity / intensity0
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