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#
# Unit test for inverse incomplete gamma integral
#
# z = invigamma( a, p )
# p = igamma( a, z )
#
# Domain restrictions
# 0 < p <= 1
# a > 0
set title "Inverse normalized lower incomplete gamma function"
set xrange [0:1]
set yrange [0:8]
set xlabel "p"
set ylabel "invigamma( a, p )"
set key outside box opaque invert reverse Left
set grid
set tics scale 0
set sample 500
plot invigamma( 0.5, x ) lw 3 title "a = 0.5", \
invigamma( 1.0, x ) lw 3 title "a = 1.0", \
invigamma( 1.5, x ) lw 3 title "a = 1.5", \
invigamma( 2.0, x ) lw 3 title "a = 2.0"
pause -1 "<cr> to continue"
reset
set title "Residual after igamma(invigamma(a,p))"
set xlabel "p"
set ylabel "residual"
set sample 200
residual(a,p) = igamma( a, invigamma(a,p) ) - p
set xrange [0:1]
do for [E=10:-2:-1] {
plot residual( 10**E, x ) title sprintf("a = %g", 10**E)
pause .5
}
pause -1 "<cr> to continue"
E = -3
set title "Residual after igamma(invigamma(a,p))" .\
"\nSuffers from numerical overflow/underflow when a < 0.005"
replot
pause -1 "<cr> to continue"
reset
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