# generic commands for twographbox output size
load "twographbox.in"



set data style lines

set xlabel "{/Times-Italic x} position"
set ylabel "{/Times-Italic P}({/Times-Italic x})"

set nokey

set label "{/Times-Italic P}({/Times-Italic x}_{/*0.8 0})" at -3.4,0.25
set label "{/Times-Italic P}({/Times-Italic x}_{/*0.8 1})" at -5.3,0.1
set label "{/Times-Italic P}({/Times-Italic x}_{/*0.8 1} | {/Times-Italic z}_{/*0.8 1} = 2.5)" at 3.4,0.32
set label "*" at 2.4,0.0
set label "{/Times-Italic z}_{/*0.8 1}" at 2.3,-0.015

n(x,m,s) = (1/(s*sqrt(2*pi)))*exp(-(((x-m)**2)/(2*s**2)))
m0 = 0.0
s0 = 1.5
sx = 2.0
sz = 1.0
m01 = m0
s01 = sqrt(s0**2 + sx**2)
z1 = 2.5
m1 = ((s0**2 + sx**2)*z1 + (sz**2)*m0)/(s0**2 + sx**2 + sz**2)
s1 = sqrt(((s0**2 + sx**2)*(sz**2))/(s0**2 + sx**2 + sz**2))




set output "kalman-one-step.eps"

plot n(x,m0,s0) lw 2, n(x,m01,s01) lw 2, n(x,m1,s1) lw 2