Author: bugman
Date: Wed Nov 19 16:20:53 2014
New Revision: 26624
URL: http://svn.gna.org/viewcvs/relax?rev=26624&view=rev
Log:
Created functions in the relax library for calculating the inter-vector angle
for complex vectors.
This is in the lib.geometry.vectors module. The function
vector_angle_complex_conjugate() has been
created to calculate the angle between two complex vectors. This uses the new
auxiliary function
complex_inner_product() to calculate <v1|v2>.
Modified:
trunk/lib/geometry/vectors.py
Modified: trunk/lib/geometry/vectors.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/lib/geometry/vectors.py?rev=26624&r1=26623&r2=26624&view=diff
==============================================================================
--- trunk/lib/geometry/vectors.py (original)
+++ trunk/lib/geometry/vectors.py Wed Nov 19 16:20:53 2014
@@ -24,9 +24,34 @@
# Python module imports.
from math import acos, atan2, cos, pi, sin
-from numpy import array, cross, dot, float64
+from numpy import array, cross, dot, float64, sqrt
from numpy.linalg import norm
from random import uniform
+
+
+def complex_inner_product(v1=None, v2_conj=None):
+ """Calculate the inner product <v1|v2> for the two complex vectors v1 and
v2.
+
+ This is calculated as::
+ ___
+ \
+ <v1|v2> = > v1i . v2i* ,
+ /__
+ i
+
+ where * is the complex conjugate.
+
+
+ @keyword v1: The first vector.
+ @type v1: numpy rank-1 complex array
+ @keyword v2_conj: The conjugate of the second vector. This is already
in conjugate form to allow for non-standard definitions of the conjugate (for
example Sm* = (-1)^m S-m).
+ @type v2_conj: numpy rank-1 complex array
+ @return: The value of the inner product <v1|v2>.
+ @rtype: float
+ """
+
+ # Return the inner product.
+ return dot(v1, v2_conj)
def random_unit_vector(vector):
@@ -114,6 +139,51 @@
# Calculate and return the angle.
return atan2(norm(cross(vector1, vector2)), dot(vector1, vector2))
+
+
+def vector_angle_complex_conjugate(v1=None, v2=None, v1_conj=None,
v2_conj=None):
+ """Calculate the inter-vector angle between two complex vectors using the
arccos formula.
+
+ The formula is::
+
+ theta = arccos(Re(<v1|v2>) / (|v1|.|v2|)) ,
+
+ where::
+ ___
+ \
+ <v1|v2> = > v1i . v2i* ,
+ /__
+ i
+
+ and::
+
+ |v1| = Re(<v1|v1>) .
+
+
+ @keyword v1: The first vector.
+ @type v1: numpy rank-1 complex array
+ @keyword v2: The second vector.
+ @type v2: numpy rank-1 complex array
+ @keyword v1_conj: The conjugate of the first vector. This is already in
conjugate form to allow for non-standard definitions of the conjugate (for
example Sm* = (-1)^m S-m).
+ @type v1_conj: numpy rank-1 complex array
+ @keyword v2_conj: The conjugate of the second vector. This is already
in conjugate form to allow for non-standard definitions of the conjugate (for
example Sm* = (-1)^m S-m).
+ @type v2_conj: numpy rank-1 complex array
+ @return: The angle between 0 and pi.
+ @rtype: float
+ """
+
+ # The inner products.
+ inner_v1v2 = complex_inner_product(v1=v1, v2_conj=v2_conj)
+ inner_v1v1 = complex_inner_product(v1=v1, v2_conj=v1_conj)
+ inner_v2v2 = complex_inner_product(v1=v2, v2_conj=v2_conj)
+
+ # The normalised inner product, correcting for truncation errors creating
ratios slightly above 1.0.
+ ratio = inner_v1v2.real / (sqrt(inner_v1v1).real * sqrt(inner_v2v2).real)
+ if ratio > 1.0:
+ ratio = 1.0
+
+ # Calculate and return the angle.
+ return acos(ratio)
def vector_angle_normal(vector1, vector2, normal):
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