Skip to content

Polylogarithm and assorted functions #30

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
wants to merge 14 commits into
base: master
Choose a base branch
from
Open

Polylogarithm and assorted functions #30

Show file tree
Hide file tree
Changes from 1 commit
Commits
Show all changes
14 commits
Select commit Hold shift + click to select a range
8a2cedb
added harmonic, bernoulli, and polylog functions
mroughan May 31, 2017
a3e193a
added bernoulli, harmonic, and polylog functions/numbers
mroughan Jun 1, 2017
b69a9f6
corrected subscripts in plots of L_n(x)
mroughan Jun 1, 2017
1f63760
edits to bernoulli to (i) optimise speed, (ii) get rid on non-complia…
mroughan Jun 2, 2017
bcad792
improve speed of harmonic by replaceing vectorized code with loops
mroughan Jun 2, 2017
3e75940
corrected throws, and added some tests
mroughan Jun 2, 2017
0ba12ab
corrected throws, and added some tests
mroughan Jun 2, 2017
01f5dc5
minor changes to Li to add in some special cases
mroughan Jun 2, 2017
c236756
replaced dumb loop calculations of power series with something a bit …
mroughan Jun 2, 2017
9122920
removed indent
mroughan Jun 2, 2017
21f6d02
adding tests, and debugging
mroughan Jun 2, 2017
9fd9675
changed Li to polylog
mroughan Jun 2, 2017
384786c
changed Li to polylog
mroughan Jun 2, 2017
a4342dc
added poly_zeta for testing
mroughan Jun 5, 2017
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
20 changes: 19 additions & 1 deletion src/polylog.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -126,6 +126,16 @@ function Dbeta(s::Number)
β = 4.0^(-s) * ( zeta(s,0.25) - zeta(s,0.75) )
end

function polylog_zeta(s::Number, z::Number, accuracy=1.0e-18)
Copy link
Member

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Looks like the accuracy argument isn't being used

# compute using the Hurwitz-zeta function identity
twopi = 2π
x = im * (log(complex(-z)) / twopi)
ss = 1-s
ip = im^ss
return ( gamma(ss)/twopi^(ss) ) * (ip * zeta(ss, 0.5-x) + conj(ip) * zeta(ss, 0.5+x))
end


function polylog_direct(s::Number, z::Number, accuracy=1.0e-18)
# calculate using direct definition
if abs(z) > 1 || ( abs(z) ≈ 1 && real(s) <= 2)
Expand Down Expand Up @@ -201,8 +211,16 @@ function polylog_series_mu(s::Number, z::Number, accuracy=1.0e-18)
else
error("Should not get this case")
end

# should have a case in here for when s is close to a real, positive integer
# seed Wood 9.4
# elseif abs(s - round(real(s))) < 0.01 # not sure where the right cut off is


# could also use Wood 14.1 (square formula) to extend the range over which we sum directly - maybe???

else
# equivalent of Crandalls 1.4 for s non-integer
# equivalent of Crandalls 1.4 for s non-integer, Wood (9.3)
total = gamma(1-s) * (-μ)^(s-1)
# println(" μ=$μ, total = $total")
tmp = 1
Expand Down
6 changes: 4 additions & 2 deletions test/polylog_test2.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,9 @@ for line in eachline(f)
z = parse(Float64, v[3]) + im*parse(Float64, v[4])
L = parse(Float64, v[5]) + im*parse(Float64, v[6])
L2 = SF.polylog(s,z,1.0e-18)
diff = L - L2
L3 = SF.polylog_zeta(s,z)
diff = L - L2
diff3 = L - L3
rel_diff = complex(real(diff)/real(L), imag(diff)/imag(L))

push!(S, s)
Expand All @@ -42,7 +44,7 @@ for line in eachline(f)
push!(rel_errors, rel_diff)

# println(" L = $L, L2 =$L2, diff = $diff, \t\t rel diff = $rel_diff")
println(" s=$s, z=$z, |error|=$(ceil(log10(abs(diff))))")
println(" s=$s, z=$z, |error|=$(ceil(log10(abs(diff)))), |error3|=$(ceil(log10(abs(diff3))))")
end
end

Expand Down