More corrections to the PDF

Author: amit112amit

OPS_CPP/DiffOrientRotVec.py

@@ -0,0 +1,67 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Sep 14 12:09:42 2017
+
+@author: amit
+"""
+
+import sympy as sy
+from sympy import sin, cos, sqrt, symbols, Rational, diff, latex
+
+# Convenience function to write our results to file
+def writeListToFile(fileName, listIn, varName):
+    fileStream = open(fileName, 'w')
+    fileStream.write('    u_2 = u0**2 + u1**2 + u2**2\n')    
+    fileStream.write('    u = sqrt(u_2)\n')
+    fileStream.write('    u_3 = u**3\n')    
+    fileStream.write('    u_4 = u**4\n')    
+    fileStream.write('    sin_alpha = sin( 0.5*u )\n')    
+    for i in range(len(listIn)):
+        var = '    ' + varName + '{0}'.format(i) + ' = '
+        fileStream.write(var)
+        #fileStream.write(str(listIn[i]))
+        fileStream.write(str(latex(listIn[i])))
+        fileStream.write('\n\n')
+    fileStream.close()
+
+# Define the symbolic variables to be used
+u0,u1,u2,v0,v1,v2,x0,x1,x2,y0,y1,y2 = \
+    symbols('u0,u1,u2,v0,v1,v2,x0,x1,x2,y0,y1,y2', real=True)
+    
+#Derivatives with respect to x0,x1,x2
+
+u = sqrt( u0**2 + u1**2 + u2**2 )
+alpha = Rational(1,2)*u
+
+p0 = (2*sin(alpha)/u**2)*( u1*u*cos(alpha) + u0*u2*sin(alpha) )
+p1 = (2*sin(alpha)/u**2)*( -u0*u*cos(alpha) + u1*u2*sin(alpha) )
+p2 = cos(alpha)**2 +(sin(alpha)**2/u**2)*( u2**2 -u1**2 - u0**2 )
+
+dp0du0 = diff(p0,u0)
+dp1du0 = diff(p1,u0)
+dp2du0 = diff(p2,u0)
+
+dp0du1 = diff(p0,u1)
+dp1du1 = diff(p1,u1)
+dp2du1 = diff(p2,u1)
+
+dp0du2 = diff(p0,u2)
+dp1du2 = diff(p1,u2)
+dp2du2 = diff(p2,u2)
+
+dpdu = [ dp0du0,dp1du0, dp2du0,\
+        dp0du1,dp1du1, dp2du1,\
+        dp0du2,dp1du2, dp2du2 ]
+
+
+U,A = symbols('U,A')
+
+subsList = [ (sqrt(u0**2 + u1**2 + u2**2)/2, A),\
+            (sqrt(u0**2 + u1**2 + u2**2), U)]
+
+derivatives = []
+for i in range(9):
+    derivatives.append( dpdu[i].subs(subsList) )
+
+writeListToFile( 'Latex.txt',derivatives, 'dpdu' );

OPS_CPP/PythonToCpp2.sh

@@ -0,0 +1,19 @@
+#!/bin/bash
+
+FILE=$1
+
+perl -pi -e 's/U/u/g' $FILE
+perl -pi -e 's/sin\(A\)/sin_alpha/g' $FILE
+perl -pi -e 's/cos\(A\)/cos_alpha/g' $FILE
+perl -pi -e 's/sin_alpha\*\*2/sin_alpha_2/g' $FILE
+perl -pi -e 's/u([0-2])\*\*2/u$1_2/g' $FILE
+perl -pi -e 's/u\*\*([0-9])/u_$1/g' $FILE
+perl -pi -e 's/dpdu0/dp0du0/g' $FILE
+perl -pi -e 's/dpdu1/dp1du0/g' $FILE
+perl -pi -e 's/dpdu2/dp2du0/g' $FILE
+perl -pi -e 's/dpdu3/dp0du1/g' $FILE
+perl -pi -e 's/dpdu4/dp1du1/g' $FILE
+perl -pi -e 's/dpdu5/dp2du1/g' $FILE
+perl -pi -e 's/dpdu6/dp0du2/g' $FILE
+perl -pi -e 's/dpdu7/dp1du2/g' $FILE
+perl -pi -e 's/dpdu8/dp2du2/g' $FILE

OPS_CPP/SimplifyNiNj.py

@@ -0,0 +1,55 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Sep 14 11:48:17 2017
+
+@author: amit
+"""
+import sympy as sy
+from PotentialsSym import conjugation, phi_p, phi_n, phi_c
+
+# Define the symbolic variables to be used
+u0,u1,u2,v0,v1,v2,x0,x1,x2,y0,y1,y2 = \
+    sy.symbols('u0,u1,u2,v0,v1,v2,x0,x1,x2,y0,y1,y2', real=True)
+
+# Convert rotation vector vi to unit quaternion   
+u = sy.sqrt(u0**2 + u1**2 + u2**2)
+p0 = sy.cos( sy.Rational(1,2)*u )
+p1 = sy.sin( sy.Rational(1,2)*u )*(u0/u)
+p2 = sy.sin( sy.Rational(1,2)*u )*(u1/u)
+p3 = sy.sin( sy.Rational(1,2)*u )*(u2/u)
+p = [p0, p1, p2, p3]
+
+# Convert rotation vector vj to unit quaternion    
+v = sy.sqrt(v0**2 + v1**2 + v2**2)
+q0 = sy.cos( sy.Rational(1,2)*v )
+q1 = sy.sin( sy.Rational(1,2)*v )*(v0/v)
+q2 = sy.sin( sy.Rational(1,2)*v )*(v1/v)
+q3 = sy.sin( sy.Rational(1,2)*v )*(v2/v)
+q = [q0, q1, q2, q3]
+
+qz = [0,0,1]
+ni = conjugation( p, qz )
+nj = conjugation( q, qz )
+
+# Make simplifying substitutions
+u,v,u_2,v_2,u_3,v_3,u_4,v_4 = \
+sy.symbols('u,v,u_2,v_2,u_3,v_3,u_4,v_4')
+sin_alpha_i,cos_alpha_i,sin_alpha_j,cos_alpha_j = \
+    sy.symbols('sin_alpha_i,cos_alpha_i,sin_alpha_j,cos_alpha_j')
+
+subsList = [(u0**2 + u1**2 + u2**2, u_2), \
+            (v0**2 + v1**2 + v2**2, v_2), \
+            (sy.sqrt(u_2), u), (sy.sqrt(v_2), v), \
+            (u**2, u_2),(v**2, v_2),\
+            (u**3, u_3),(v**3, v_3), \
+            (u**4, u_4),(v**4, v_4 ), \
+            (sy.sin(u/2), sin_alpha_i),(sy.cos(u/2), cos_alpha_i), \
+            (sy.sin(v/2), sin_alpha_j),(sy.cos(v/2), cos_alpha_j)]
+
+ni_s =[]
+nj_s = []
+for i in range( 3 ):
+    ni_s.append( ni[i].subs(subsList) )
+    nj_s.append( nj[i].subs(subsList) )
+