From 764be9105e36d59a0b9c910503b68818e849a982 Mon Sep 17 00:00:00 2001
From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Thu, 20 Aug 2009 11:15:43 +0200
Subject: [PATCH] more trafo (still sth is wrong!)

---
 vasp_tools/trafoXposcar | 101 +++++++++++++++++++++++++++++++++++++---
 1 file changed, 95 insertions(+), 6 deletions(-)

diff --git a/vasp_tools/trafoXposcar b/vasp_tools/trafoXposcar
index 1aebc4f..1cd5286 100755
--- a/vasp_tools/trafoXposcar
+++ b/vasp_tools/trafoXposcar
@@ -2,10 +2,10 @@
 
 echo "parsing POSCAR file ..."
 
-trg=POSCAR.transformed
-
 theta=$1
 
+trg=POSCAR.Xtrafo$theta
+
 sicnt=`sed -n 6p POSCAR | awk '{ print $1 }'`
 ccnt=`sed -n 6p POSCAR | awk '{ print $2 }'`
 
@@ -35,27 +35,116 @@ echo
 echo "  -----"
 echo "  Trafo: x axis, $theta degree"
 echo "  -----"
+echo
+
+# determine trafo of cartesian coordinates to this one
+normx=`echo $x1 $x2 $x3 | awk '{ print sqrt($1*$1+$2*$2+$3*$3) }'`
+normy=`echo $y1 $y2 $y3 | awk '{ print sqrt($1*$1+$2*$2+$3*$3) }'`
+normz=`echo $z1 $z2 $z3 | awk '{ print sqrt($1*$1+$2*$2+$3*$3) }'`
+echo $normx $normz $normy
+t11=`echo $x1 $normx | awk '{ print $1/$2 }'`
+t12=`echo $x2 $normx | awk '{ print $1/$2 }'`
+t13=`echo $x3 $normx | awk '{ print $1/$2 }'`
+t21=`echo $y1 $normy | awk '{ print $1/$2 }'`
+t22=`echo $y2 $normy | awk '{ print $1/$2 }'`
+t23=`echo $y3 $normy | awk '{ print $1/$2 }'`
+t31=`echo $z1 $normz | awk '{ print $1/$2 }'`
+t32=`echo $z2 $normz | awk '{ print $1/$2 }'`
+t33=`echo $z3 $normz | awk '{ print $1/$2 }'`
+echo "  Matrix from cartesian to used coordinates:"
+echo "  | $t11 $t21 $t31 |"
+echo "  | $t12 $t22 $t32 |"
+echo "  | $t13 $t23 $t33 |"
+echo
+i11=$t11
+i12=$t21
+i13=$t31
+i21=$t12
+i22=$t22
+i23=$t32
+i31=$t13
+i32=$t23
+i33=$t33
+echo "  Inverse matrix (i=t^T):"
+echo "  | $i11 $i21 $i31 |"
+echo "  | $i12 $i22 $i32 |"
+echo "  | $i13 $i23 $i33 |"
+echo
+# i * basis
+X1=`echo $i11 $i21 $i31 $x1 $x2 $x3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+X2=`echo $i12 $i22 $i32 $x1 $x2 $x3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+X3=`echo $i13 $i23 $i33 $x1 $x2 $x3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+
+Y1=`echo $i11 $i21 $i31 $y1 $y2 $y3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+Y2=`echo $i12 $i22 $i32 $y1 $y2 $y3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+Y3=`echo $i13 $i23 $i33 $y1 $y2 $y3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+
+Z1=`echo $i11 $i21 $i31 $z1 $z2 $z3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+Z2=`echo $i12 $i22 $i32 $z1 $z2 $z3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+Z3=`echo $i13 $i23 $i33 $z1 $z2 $z3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+echo "  Basis (in rotation system):"
+echo "      $X1      $Y1      $Z1"
+echo "  x = $X2  y = $Y2  z = $Z2"
+echo "      $X3      $Y3      $Z3"
+echo
 
 costheta=`echo $theta | awk '{ print cos($1*3.1415927/180.0) }'`
 sintheta=`echo $theta | awk '{ print sin($1*3.1415927/180.0) }'`
 
+x1=$X1
+x2=$X2
+x3=$X3
 X1=$x1
 X2=`echo $x2 $x3 $costheta $sintheta | awk '{ print $3*$1-$4*$2 }'`
 X3=`echo $x2 $x3 $costheta $sintheta | awk '{ print $4*$1+$3*$2 }'`
 
+y1=$Y1
+y2=$Y2
+y3=$Y3
 Y1=$y1
 Y2=`echo $y2 $y3 $costheta $sintheta | awk '{ print $3*$1-$4*$2 }'`
 Y3=`echo $y2 $y3 $costheta $sintheta | awk '{ print $4*$1+$3*$2 }'`
 
+z1=$Z1
+z2=$Z2
+z3=$Z3
 Z1=$z1
 Z2=`echo $z2 $z3 $costheta $sintheta | awk '{ print $3*$1-$4*$2 }'`
 Z3=`echo $z2 $z3 $costheta $sintheta | awk '{ print $4*$1+$3*$2 }'`
 
+echo "  Transformed basis (in rotation system):"
+echo "       $X1       $Y1       $Z1"
+echo "  x' = $X2  y' = $Y2  z' = $Z2"
+echo "       $X3       $Y3       $Z3"
 echo
-echo "  Transformed basis:"
-echo "      $X1      $Y1      $Z1"
-echo "  x = $X2  y = $Y2  z = $Z2"
-echo "      $X3      $Y3      $Z3"
+
+# t * basis
+x1=`echo $t11 $t21 $t31 $X1 $X2 $X3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+x2=`echo $t12 $t22 $t32 $X1 $X2 $X3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+x3=`echo $t13 $t23 $t33 $X1 $X2 $X3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+X1=$x1
+X2=$x2
+X3=$x3
+
+y1=`echo $t11 $t21 $t31 $Y1 $Y2 $Y3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+y2=`echo $t12 $t22 $t32 $Y1 $Y2 $Y3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+y3=`echo $t13 $t23 $t33 $Y1 $Y2 $Y3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+Y1=$y1
+Y2=$y2
+Y3=$y3
+
+z1=`echo $t11 $t21 $t31 $Z1 $Z2 $Z3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+z2=`echo $t12 $t22 $t32 $Z1 $Z2 $Z3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+z3=`echo $t13 $t23 $t33 $Z1 $Z2 $Z3 | awk '{ print $1*$4+$2*$5+$3*$6 }'`
+Z1=$z1
+Z2=$z2
+Z3=$z3
+
+
+echo "  Transformed basis (cartesian coordinates):"
+echo "       $X1       $Y1       $Z1"
+echo "  x' = $X2  y' = $Y2  z' = $Z2"
+echo "       $X3       $Y3       $Z3"
 echo
 
 cnt=0
-- 
2.20.1