Index: /trunk/Ohana/src/relastro/doc/parallax.pro
===================================================================
--- /trunk/Ohana/src/relastro/doc/parallax.pro	(revision 6809)
+++ /trunk/Ohana/src/relastro/doc/parallax.pro	(revision 6809)
@@ -0,0 +1,333 @@
+
+macro sample
+  PMsim 15 30 20 10 $ANGLE
+  set dX = zero(X) + 10
+  set dY = zero(Y) + 10
+
+  style -c black
+  plot -x 2 -pt 2 -sz 2.0 X Y -dx dX -dy dY
+
+  # set x = (1000.0/$dS)*cos(t*$TP) + $vX*t
+  # set y = (1000.0/$dS)*sin(t*$TP)*dsin($ANGLE) + $vY*t
+  # plot -c grey60 -x 2 -sz 2.0 -pt 7 x y
+
+  create t 0 1.5 0.01
+  set x = (1000.0/$dS)*cos(t*$TP) + $vX*t
+  set y = (1000.0/$dS)*sin(t*$TP)*dsin($ANGLE) + $vY*t
+  plot -c grey60 -x 0 x y
+
+  # label -x "offset east (milliarcsec)"
+  # label -y "offset north (milliarcsec)"
+end
+
+macro PMsim
+  if ($0 != 6)
+    echo "USAGE: PMsim Do vX vY dP dT"
+    echo "Do : distance in parsec"
+    echo "vX, vY : velocity (milliarcsec/year)"
+    echo "dP : astrometric scatter (arcsec)"
+    echo "dT : ecliptic lattitude (degrees)"
+    break
+  end
+
+  $TP = 2*3.1416
+
+  $dS = $1
+  $vX = $2
+  $vY = $3
+  $dP = $4
+  $dT = $5
+
+  mkbase
+
+  set x = (1000.0/$dS)*cos(t*$TP) + $vX*t
+  set y = (1000.0/$dS)*sin(t*$TP)*dsin($dT) + $vY*t
+
+  gaussdev dx x[] 0.0 $dP
+  gaussdev dy y[] 0.0 $dP 
+
+  set X = x + dx
+  set Y = y + dy
+
+  if ($PLOT)
+    lim -200 200 -200 200; clear; box;
+    style -c black
+    plot -x 2 -pt 2 -sz 2.0 X Y
+    plot -x 0 X Y
+  end
+
+  PMfit X Y t $dT
+
+  if ($PLOT) 
+    label -x "offset east (milliarcsec)"
+    label -y "offset north (milliarcsec)"
+    section a 0 0 1 1
+    lim 0 1 0 1
+    sprintf line "input: D: %5.1f (pc), V: %5.1f, %5.1f (mas/yr), dS: %4.1f" $1 $2 $3 $4
+    textline -fn courier 14 0.15 0.95 "$line"
+    sprintf line "fit:    D: %5.1f (pc), V: %5.1f, %5.1f (mas/yr)" $dS $vX $vY
+    textline -fn courier 14 0.15 0.90 "$line"
+    section default
+  end
+end
+
+macro PMfit
+  if ($0 != 5)
+    echo "USAGE: PMfit X Y t (theta)"
+    echo "X,Y are offsets in milliarcsec"
+    echo "t is time in years"
+    break
+  end
+
+  $TP = 2*3.1416
+  set x = $1
+  set y = $2
+  set t = $3
+  set cs = cos(t*$TP)
+  set snx = sin(t*$TP)*dsin($4)
+
+  mcreate A 3 3
+  create B 0 3
+
+  # define A values:
+  set tmp = cs^2 + snx^2
+  vstat -q tmp
+  zap A 0 0 1 1 -v $TOTAL
+
+  set tmp = t*cs
+  vstat -q tmp
+  zap A 1 0 1 1 -v $TOTAL
+  zap A 0 1 1 1 -v $TOTAL
+
+  set tmp = t*snx
+  vstat -q tmp
+  zap A 2 0 1 1 -v $TOTAL
+  zap A 0 2 1 1 -v $TOTAL
+
+  set tmp = t^2
+  vstat -q tmp
+  zap A 1 1 1 1 -v $TOTAL
+  zap A 2 2 1 1 -v $TOTAL
+
+  zap A 2 1 1 1 -v 0
+  zap A 1 2 1 1 -v 0
+
+  # define B values:
+  set tmp = x*cs + y*snx
+  vstat -q tmp
+  B[0] = $TOTAL
+
+  set tmp = x*t
+  vstat -q tmp
+  B[1] = $TOTAL
+
+  set tmp = y*t
+  vstat -q tmp
+  B[2] = $TOTAL
+
+  gaussj A B
+
+  $dS = 1000/B[0]
+  $vX = B[1]
+  $vY = B[2]
+
+  if ($PLOT)
+    echo "Do: $dS"
+    echo "vX: $vX"
+    echo "vY: $vY"
+
+    set x = (1000.0/$dS)*cos(t*$TP) + $vX*t
+    set y = (1000.0/$dS)*sin(t*$TP)*dsin($4) + $vY*t
+    plot -c red -x 2 -sz 2.0 -pt 7 x y
+  end
+end
+
+macro PMstats
+  
+  if ($0 != 7)
+    echo "USAGE: PMsim Do vX vY dP dT (Niter)"
+    echo "Do : distance in parsec"
+    echo "vX, vY : velocity (milliarcsec/year)"
+    echo "dP : astrometric scatter (arcsec)"
+    echo "dT : ecliptic lattitude (degrees)"
+    break
+  end
+
+  delete -q vx vy ds
+  $PLOT = 0
+
+  for i 0 $6
+    PMsim $1 $2 $3 $4 $5
+    concat $dS ds
+    concat $vX vx
+    concat $vY vy
+  end
+
+  vstat ds
+  vstat vx
+  vstat vy
+
+  set gm = 1000/ds
+  vstat gm
+
+  clear -s -n 1
+  label -fn courier 14
+  # section a 0.0 0.0 0.5 1.0
+  lim {$2-30} {$2+30} {$3-30} {$3+30}; box
+  plot -x 2 -pt 2 -sz 0.5 vx vy
+  label -x "p.m. (east, mas/yr)"
+  label -y "p.m. (east, mas/yr)"
+
+  clear -s -n 2
+  # section b 0.5 0.0 0.5 1.0
+  histogram gm Ng {1000/$1 - 30.0} {1000/$1 + 30.0} 1.0
+  create dg {1000/$1 - 30.0} {1000/$1 + 30.0} 1.0
+  lim dg Ng; box
+  plot -x 1 dg Ng
+
+  label -x "parallax (mas)"
+  label -y "# of tests"
+
+end
+
+macro PMtrend
+
+  PMstats 10 5.0 5.0 10 90 100
+  echo 10
+  PMstats 10 5.0 5.0 {750/2.38/25} 90 100
+  echo {750/2.38/25} 
+  PMstats 10 5.0 5.0 {750/2.38/10} 90 100
+  echo {750/2.38/10} 
+  PMstats 10 5.0 5.0 {750/2.38/5} 90 100
+  echo {750/2.38/5} 
+end
+
+list dist
+  5
+  10
+  15
+  20
+  30
+  40
+  50
+  60
+  70
+  80
+end
+
+macro ParDetect
+
+  local i
+  delete -q xp yp dyp dym
+  
+  $ANGLE = 45
+
+  for i 0 $dist:n
+    PMstats $dist:$i 5.0 5.0 10 $ANGLE 100
+    concat $dist:$i xp
+    concat {1000/$MEAN} yp
+    concat {1000/($MEAN - $SIGMA) - 1000/$MEAN} dyp
+    concat {1000/$MEAN - 1000/($MEAN + $SIGMA)} dym
+  end
+
+  section a 0.0 0.0 0.5 1.0
+
+  lim xp -1.0 101; clear; box; 
+  plot -c black -x 2 xp yp -dy dym +dy dyp
+  
+  delete -q xp yp 
+  concat 0 xp
+  concat 100 xp
+  set yp = xp
+  plot -x 0 -c blue xp yp
+
+  set yp = zero(xp) + 62.5
+  plot -x 0 -c red -lt 1 xp yp
+  style -lt 0  
+  label -x "input dist (pc)" -y "output dist" -fn courier 14
+
+  $PLOT = 0
+  section b 0.5 0.0 0.5 1.0
+  lim -120 120 -120 120; box -labels 1001;
+
+  for i 0 5
+   sample
+  end
+
+  label -x "offset east (milliarcsec)"
+  label +y "offset north"
+  ps -name ParallaxDist.ps
+end
+
+macro fields
+
+  $Dx = 0.25*4800*8/3600
+  $Fo = 1.09
+
+  $dD = 2.65/1.09
+
+  $Nf = 0
+  for i {-30+$dD/2} 90 $dD
+    $Np = int(dcos($i)*1.09*360/2.65) + 1
+    $Nf = $Nf + $Np
+    fprintf "%5.1f %5.1f %4d %4d" $i {dcos($i)*1.09*360/2.65} $Np $Nf 
+  end
+end
+
+macro SNsim
+  $w  = 0.76
+  $m1 = 24.8
+  $mu = 20.4
+
+  lim 13.5 26.5 0.0 4.0; clear; box
+
+  $t = 1
+  SN
+
+  $t = 5
+  SN
+
+  $t = 30
+  SN
+
+  $t = 100
+  SN
+
+  set sn = 5 + zero (m)
+  set lsn = log(sn)
+  plot -lt 2 m lsn
+
+  set sn = 25 + zero (m)
+  set lsn = log(sn)
+  plot -lt 2 m lsn
+
+  set sn = 100 + zero (m)
+  set lsn = log(sn)
+  plot -lt 2 m lsn
+  style -lt 0
+end
+
+macro SN
+  create m 14 26 0.1
+  set sn = ten (-0.2*(2*m - $mu - $m1)) * sqrt($t/$w^2/3.1416)
+  set lsn = log(sn)
+  plot m lsn
+end
+
+# r: 30s @ 5sig = 22.65  (0.6")
+# i: 30s @ 5sig = 22.42  (0.6")
+# i: 30s @ 5sig = 22.27  (for 0.3 mag lower zp)
+
+macro mkbase
+  delete -q t
+  concat 0.0 t
+  concat {10.0/365.0} t
+  concat {20.0/365.0} t
+  concat { 6.0/52.0} t
+
+  concat { 3.0/12.0} t
+  concat { 6.0/12.0} t
+  concat {12.0/12.0} t
+  concat {18.0/12.0} t
+end
+