Index: /branches/eam_branches/ipp-20150112/Ohana/src/opihi/test/ellipse.sh
===================================================================
--- /branches/eam_branches/ipp-20150112/Ohana/src/opihi/test/ellipse.sh	(revision 37856)
+++ /branches/eam_branches/ipp-20150112/Ohana/src/opihi/test/ellipse.sh	(revision 37856)
@@ -0,0 +1,122 @@
+
+macro ShapeToAxes
+  if ($0 != 7)
+    echo "USAGE: ShapeToAxes (sxx) (sxy) (syy) (major) (minor) (theta)"
+    echo " theta is returned in degrees"
+    break
+  end
+
+  # I need the concept of a local vector...
+  # I should be able to test if these are vectors or scalars
+  set _sxx = $1
+  set _sxy = $2
+  set _syy = $3
+
+  set f1 = _syy^-2 + _sxx^-2
+  set f2 = _syy^-2 - _sxx^-2
+  set f3 = sqrt(f2^2 + 4*_sxy^2)
+
+  set _minor = sqrt (2.0 / (f1 + f3))
+
+  # this returns theta in degrees
+  # @ == atan2 -- I should really replace this..
+  set _theta = -0.5 * (+2.0*_sxy @ f2)
+  set aratio2 = (f1 - f3) / (f1 + f3)
+
+  # I can test here if aratio2 is too large/small/nan
+  set _major = sqrt (2.0 / (f1 - f3))
+
+  set $4 = _major
+  set $5 = _minor
+  set $6 = _theta
+end
+
+macro AxesToShapeAlt
+  if ($0 != 7)
+    echo "USAGE: ShapeToAxes (major) (minor) (theta) (sxx) (sxy) (syy)"
+    echo " theta is supplied in degrees"
+    break
+  end
+
+  set _major = $1
+  set _minor = $2
+  set _theta = -1*$3
+
+  set tc2 = dcos(_theta)^2
+  set ts2 = dsin(_theta)^2
+
+  set f1 = tc2*_major^-2 + ts2*_minor^-2
+  set f2 = ts2*_major^-2 + tc2*_minor^-2
+  set f3 = _minor^-2 - _major^-2
+
+  set $4 = +1.0 / sqrt(f1);
+  set $6 = +1.0 / sqrt(f2);
+  set $5 = 0.5*f3*dsin(2*_theta);
+end
+
+macro AxesToShape
+  if ($0 != 7)
+    echo "USAGE: ShapeToAxes (major) (minor) (theta) (sxx) (sxy) (syy)"
+    echo " theta is supplied in degrees"
+    break
+  end
+
+  set _major = $1
+  set _minor = $2
+  set _theta = $3
+
+  set f1 = _minor^-2 + _major^-2
+  set f2 = _minor^-2 - _major^-2
+
+  set sxr = 0.5*f1 - 0.5*f2*dcos(2*_theta);
+  set syr = 0.5*f1 + 0.5*f2*dcos(2*_theta);
+
+  set $4 = +1.0 / sqrt(sxr);
+  set $6 = +1.0 / sqrt(syr);
+  set $5 = -0.5*f2*dsin(2*_theta);
+end
+
+macro test1
+
+  # create a series of ellipses with theta spinning and AR = 2.0
+  $DX = 201
+
+  create theta 0 360 10
+  set major = 20.0 + zero(theta)
+  set minor = 10.0 + zero(theta)
+
+  # AxesToShape major minor theta sxx sxy syy
+  AxesToShape major minor theta sxx sxy syy
+
+  mcreate mosaic {6*($DX + 2)} {6*($DX + 2)} 
+  mcreate base $DX $DX
+  set x = xramp(base) - int(0.5*$DX)
+  set y = yramp(base) - int(0.5*$DX)
+  
+  for i 0 theta[]
+    set r = 0.5*(x/sxx[$i])^2 + 0.5*(y/syy[$i])^2 + sxy[$i]*x*y
+    set object = exp(-r)
+    $ix = $i % 6
+    $iy = int($i / 6)
+    extract object mosaic 0 0 $DX $DX {$ix * ($DX + 1)} {$iy * ($DX + 1)}  {6*($DX + 2)} {6*($DX + 2)} 
+  end    
+
+  tv mosaic -0.01 0.5
+  lim -image
+  clear; box
+
+  for i 0 theta[]
+    $ix = $i % 6
+    $iy = int($i / 6)
+    
+    $dX = $ix * ($DX + 1) + int(0.5*$DX)
+    $dY = $iy * ($DX + 1) + int(0.5*$DX)
+
+    create T 0 360 0.1
+    set Xr = major[$i]*dcos(T)
+    set Yr = minor[$i]*dsin(T)
+    set Xo = Xr*dcos(theta[$i]) - Yr*dsin(theta[$i]) + $dX
+    set Yo = Yr*dcos(theta[$i]) + Xr*dsin(theta[$i]) + $dY
+    plot Xo Yo -x 0 -c red
+  end    
+end